Finite Group Databasebeta

← #17242758

Subgroups — #17242758

Order 4352.

1994 conjugacy classes of subgroups.

The subgroup lattice has 1600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14537101C211yesmaximal, characteristic, complemented
2#14537087C211yesmaximal, characteristic, complemented
3#14536441C211yesmaximal, characteristic, complemented
4#14536441C211yesmaximal, characteristic, complemented
5#14536396C211yesmaximal, characteristic, complemented
6#14536225C211yesmaximal, characteristic, complemented
7#14536210C211yesmaximal, characteristic, complemented
8#14536177C211yesmaximal, characteristic, complemented
9#14536107C211yesmaximal, characteristic, complemented
10#14536008C211yesmaximal, characteristic, complemented
11#14535930C211yesmaximal, characteristic, complemented
12#14535895C211yesmaximal, characteristic, complemented
13#14535827C211yesmaximal, characteristic, complemented
14#14535826C211yesmaximal, characteristic, complemented
15#14535775C211yesmaximal, characteristic, complemented
16#14535408C211yesmaximal, characteristic, complemented
17#14535182C211yesmaximal, characteristic, complemented
18#14535167C211yesmaximal, characteristic, complemented
19#14534570C211yesmaximal, characteristic, complemented
20#14534529C211yesmaximal, characteristic, complemented
21#14533340C211yesmaximal, characteristic, complemented
22#14533116C211yesmaximal, characteristic, complemented
23#14532538C211yesmaximal, characteristic, complemented
24#14532333C211yesmaximal, characteristic, complemented
25#14532174C211yesmaximal, characteristic, complemented
26#14532152C211yesmaximal, characteristic
27#14532112C211yesmaximal, characteristic, complemented
28#14531439C211yesmaximal, characteristic, complemented
29#14531359C211yesmaximal, characteristic, complemented
30C2×#11762697C211yesmaximal, characteristic, complemented
31C17×#2437C211yesmaximal, characteristic, complemented
32C23×C22⋊D17C2211yescharacteristic
33C2×#10587584C2211yescharacteristic, complemented
34C2×#10587633C2211yescharacteristic, complemented
35C2×#10587572C2211yescharacteristic
36C2×#10587572C2211yescharacteristic
37C2×#10587572C2211yescharacteristic, complemented
38C2×#10587616C2211yescharacteristic
39C2×#10587616C2211yescharacteristic
40C2×#10587568C2211yescharacteristic
41C2×#10587639C2211yescharacteristic
42C2×#10587567C2211yescharacteristic, complemented
43C22×#63225C2211yescharacteristic, complemented
44C22×C22⋊Dic17C2211yescharacteristic
45C22×C22⋊Dic17C2211yescharacteristic
46C22×C4×Dic17C2211yescharacteristic, complemented
47C17⋊#401C2211yescharacteristic, complemented
48#11762751C2211yescharacteristic, complemented
49#11762751C2211yescharacteristic, complemented
50#11762751C2211yescharacteristic, complemented
51#11762748C2211yescharacteristic, complemented
52#11762748C2211yescharacteristic, complemented
53#11762748C2211yescharacteristic, complemented
54#11762744C2211yescharacteristic, complemented
55#11762744C2211yescharacteristic, complemented
56#11762742C2211yescharacteristic, complemented
57#11762742C2211yescharacteristic, complemented
58#11762741C2211yescharacteristic, complemented
59#11762741C2211yescharacteristic, complemented
60#11762741C2211yescharacteristic, complemented
61#11762738C2211yescharacteristic, complemented
62#11762738C2211yescharacteristic, complemented
63#11762738C2211yescharacteristic, complemented
64#11762736C2211yescharacteristic, complemented
65#11762736C2211yescharacteristic, complemented
66#11762735C2211yescharacteristic, complemented
67#11762735C2211yescharacteristic, complemented
68#11762735C2211yescharacteristic, complemented
69#11762734C2211yescharacteristic
70#11762734C2211yescharacteristic
71#11762731C2211yescharacteristic, complemented
72#11762731C2211yescharacteristic, complemented
73#11762731C2211yescharacteristic, complemented
74#11762731C2211yescharacteristic, complemented
75#11762731C2211yescharacteristic, complemented
76#11762727C2211yescharacteristic, complemented
77#11762727C2211yescharacteristic, complemented
78#11762726C2211yescharacteristic, complemented
79#11762726C2211yescharacteristic, complemented
80#11762725C2211yescharacteristic
81#11762725C2211yescharacteristic
82#11762725C2211yescharacteristic
83#11762725C2211yescharacteristic
84#11762725C2211yescharacteristic
85#11762725C2211yescharacteristic
86#11762725C2211yescharacteristic
87#11762725C2211yescharacteristic
88#11762720C2211yescharacteristic, complemented
89#11762718C2211yescharacteristic
90#11762718C2211yescharacteristic
91#11762716C2211yescharacteristic, complemented
92#11762716C2211yescharacteristic, complemented
93#11762710C2211yescharacteristic, complemented
94#11762709C2211yescharacteristic
95#11762709C2211yescharacteristic, complemented
96#11762708C2211yescharacteristic, complemented
97#11762703C2211yescharacteristic
98#11762703C2211yescharacteristic, complemented
99#11762701C2211yescharacteristic, complemented
100#11762701C2211yescharacteristic, complemented
101#11762701C2211yescharacteristic, complemented
102#11762699C2211yescharacteristic, complemented
103#11762699C2211yescharacteristic, complemented
104#11762699C2211yescharacteristic, complemented
105#11762699C2211yescharacteristic, complemented
106#11762699C2211yescharacteristic, complemented
107#11762699C2211yescharacteristic, complemented
108#11762699C2211yescharacteristic, complemented
109#11762699C2211yescharacteristic, complemented
110#11762699C2211yescharacteristic, complemented
111#11762698C2211yescharacteristic, complemented
112#11762697C2211yescharacteristic
113#11762697C2211yescharacteristic
114#11762697C2211yescharacteristic
115#11762697C2211yescharacteristic
116#11762697C2211yescharacteristic
117#11762697C2211yescharacteristic, complemented
118#11762697C2211yescharacteristic, complemented
119#11762697C2211yescharacteristic, complemented
120#11762697C2211yescharacteristic, complemented
121#11762697C2211yescharacteristic, complemented
122#11762695C2211yescharacteristic, complemented
123#11762695C2211yescharacteristic, complemented
124#11762695C2211yescharacteristic, complemented
125#11762692C2211yescharacteristic, complemented
126#11762690C2211yescharacteristic, complemented
127#11762688C2211yescharacteristic
128#11762688C2211yescharacteristic
129#11762688C2211yescharacteristic
130#11762688C2211yescharacteristic
131#11762688C2211yescharacteristic
132#11762688C2211yescharacteristic
133#11762688C2211yescharacteristic, complemented
134#11762688C2211yescharacteristic, complemented
135#11762687C2211yescharacteristic, complemented
136#11762687C2211yescharacteristic, complemented
137#11762686C2211yescharacteristic
138#11762686C2211yescharacteristic
139#11762686C2211yescharacteristic
140#11762686C2211yescharacteristic
141#11762686C2211yescharacteristic
142#11762686C2211yescharacteristic
143#11762686C2211yescharacteristic
144#11762686C2211yescharacteristic, complemented
145#11762686C2211yescharacteristic, complemented
146#11762685C2211yescharacteristic
147#11762685C2211yescharacteristic, complemented
148#11762684C2211yescharacteristic
149#11762684C2211yescharacteristic
150#11762684C2211yescharacteristic
151#11762684C2211yescharacteristic, complemented
152#11762681C2211yescharacteristic, complemented
153#11762676C2211yescharacteristic, complemented
154#11762676C2211yescharacteristic, complemented
155#11762674C2211yescharacteristic, complemented
156#11762674C2211yescharacteristic, complemented
157#11762671C2211yescharacteristic, complemented
158#11762670C2211yescharacteristic
159#11762670C2211yescharacteristic
160#11762670C2211yescharacteristic, complemented
161#11762669C2211yescharacteristic, complemented
162#11762669C2211yescharacteristic, complemented
163#11762666C2211yescharacteristic, complemented
164#11762664C2211yescharacteristic
165#11762664C2211yescharacteristic
166#11762664C2211yescharacteristic
167#11762664C2211yescharacteristic
168#11762664C2211yescharacteristic
169C22⋊C4×Dic17C2211yescharacteristic, complemented
170C2×#10587502C2211yescharacteristic, complemented
171C2×#10587502C2211yescharacteristic, complemented
172C2×C17×C22⋊Q8C2211yescharacteristic, complemented
173C2×C17×C22⋊Q8C2211yescharacteristic, complemented
174C22×C22⋊C4×C17C2211yescharacteristic
175C22×C22⋊C4×C17C2211yescharacteristic
176C17×#399C2211yescharacteristic
177C17×#396C2211yescharacteristic
178C17×#396C2211yescharacteristic
179C17×#393C2211yescharacteristic
180C17×#385C2211yescharacteristic, complemented
181C17×#385C2211yescharacteristic, complemented
182C17×#385C2211yescharacteristic, complemented
183C17×#385C2211yescharacteristic, complemented
184C17×#380C2211yescharacteristic, complemented
185C17×#380C2211yescharacteristic, complemented
186C17×#379C2211yescharacteristic
187C25×C17C2311yescharacteristic
188C24×D17C2311yescharacteristic
189C22×Q8×C17C2311yescharacteristic
190C23×C4×C17C2311yescharacteristic
191C23×C4×C17C2311yescharacteristic
192C23×C4×C17C2311yescharacteristic
193C23×C4×C17C2311yescharacteristic
194C22×C22⋊D17—24no—
195C22×C22⋊D17—42no—
196C22×C22⋊D17—42no—
197C22×C22⋊D17C2311yescharacteristic
198C22×C22⋊D17C2311yescharacteristic
199C22×C22⋊D17C2311yescharacteristic
200C22×C22⋊D17C2311yescharacteristic
201C22×C22⋊D17C2311yescharacteristic
202C22×C22⋊D17C2311yescharacteristic
203C22×C22⋊D17C2311yescharacteristic
204C23×Dic17C2311yescharacteristic
205C23×Dic17C2311yescharacteristic
206C23×Dic17C2311yescharacteristic
207C23×Dic17C2311yescharacteristic
208C23×Dic17C2311yescharacteristic
209C22×D68C2311yescharacteristic
210C22×D68C2311yescharacteristic
211C22×C4×D17C2311yescharacteristic
212C17×C22⋊Q8—42no—
213C17×C22⋊Q8—42no—
214C2×C4⋊C4×C17C2311yescharacteristic
215C2×C4⋊C4×C17C2311yescharacteristic
216C2×C4⋊C4×C17C2311yescharacteristic
217C2×C4⋊C4×C17C2311yescharacteristic
218C2×C4⋊C4×C17C2311yescharacteristic
219C2×C4⋊C4×C17C2311yescharacteristic
220C2×C4⋊C4×C17C2311yescharacteristic
221C2×C4⋊C4×C17C2311yescharacteristic
222C2×C4⋊C4×C17C2311yescharacteristic
223C2×C22⋊C4×C17—42no—
224C2×C22⋊C4×C17—42no—
225C2×C22⋊C4×C17C2311yescharacteristic
226C2×C22⋊C4×C17C2311yescharacteristic
227C2×C22⋊C4×C17C2311yescharacteristic
228C2×C22⋊C4×C17C2311yescharacteristic
229C2×C22⋊C4×C17C2311yescharacteristic
230C2×C22⋊C4×C17C2311yescharacteristic
231C2×C22⋊C4×C17C2311yescharacteristic
232C2×C22⋊C4×C17C2311yescharacteristic
233C2×C22⋊C4×C17C2311yescharacteristic
234C2×C22⋊C4×C17C2311yescharacteristic
235C2×C22⋊C4×C17C2311yescharacteristic
236C2×C22⋊C4×C17C2311yescharacteristic
237C2×C22⋊C4×C17C2311yescharacteristic
238C2×C22⋊C4×C17C2311yescharacteristic
239#10587639—24no—
240C2×C22⋊Dic17—24no—
241C2×C22⋊Dic17—42no—
242C2×C22⋊Dic17C2311yescharacteristic
243C2×C22⋊Dic17C2311yescharacteristic
244C2×C22⋊Dic17C2311yescharacteristic
245C2×C22⋊Dic17C2311yescharacteristic
246C2×C22⋊Dic17C2311yescharacteristic
247C2×C22⋊Dic17C2311yescharacteristic
248C2×C22⋊Dic17C2311yescharacteristic
249C2×C22⋊Dic17C2311yescharacteristic
250C2×C22⋊Dic17C2311yescharacteristic
251C2×C22⋊Dic17C2311yescharacteristic
252C2×C22⋊Dic17C2311yescharacteristic
253#10587633—42no—
254#10587616—42no—
255#10587616—42no—
256C2×#63227C2311yescharacteristic
257C2×#63227C2311yescharacteristic
258C2×#63227C2311yescharacteristic
259C2×#63227C2311yescharacteristic
260C2×#63227C2311yescharacteristic
261C2×#63227C2311yescharacteristic
262C2×#63227C2311yescharacteristic
263C2×#63227C2311yescharacteristic
264C2×#63227C2311yescharacteristic
265C2×#63227C2311yescharacteristic
266C2×#63227C2311yescharacteristic
267C2×#63227C2311yescharacteristic
268C2×#63227C2311yescharacteristic
269C2×#63227C2311yescharacteristic
270C2×#63227C2311yescharacteristic
271C2×#63227C2311yescharacteristic
272C2×#63227C2311yescharacteristic
273C2×#63227C2311yescharacteristic
274C2×#63227C2311yescharacteristic
275C2×#63227C2311yescharacteristic
276C2×#63227C2311yescharacteristic
277C2×#63227C2311yescharacteristic
278C2×#63227C2311yescharacteristic
279C2×#63227C2311yescharacteristic
280C2×#63227C2311yescharacteristic
281C2×#63227C2311yescharacteristic
282C2×#63227C2311yescharacteristic
283C2×#63227C2311yescharacteristic
284C2×#63227C2311yescharacteristic
285C2×#63227C2311yescharacteristic
286C2×#63227C2311yescharacteristic
287C2×C4⋊Dic17C2311yescharacteristic
288C2×C4⋊Dic17C2311yescharacteristic
289C2×C4⋊Dic17C2311yescharacteristic
290C2×C4⋊Dic17C2311yescharacteristic
291C2×C4⋊Dic17C2311yescharacteristic
292C2×C4⋊Dic17C2311yescharacteristic
293C2×C4⋊Dic17C2311yescharacteristic
294C2×C4⋊Dic17C2311yescharacteristic
295C2×C4⋊Dic17C2311yescharacteristic
296C2×C4⋊Dic17C2311yescharacteristic
297C2×#63225—42no—
298C2×#63225C2311yescharacteristic
299C2×#63225C2311yescharacteristic
300C2×#63225C2311yescharacteristic
301C2×#63225C2311yescharacteristic
302C2×#63225C2311yescharacteristic
303C2×#63225C2311yescharacteristic
304C2×#63225C2311yescharacteristic
305C2×C4×Dic17—42no—
306C2×C4×Dic17C2311yescharacteristic
307C2×C4×Dic17C2311yescharacteristic
308C2×C4×Dic17C2311yescharacteristic
309C2×C4×Dic17C2311yescharacteristic
310C2×C4×Dic17C2311yescharacteristic
311C2×C4×Dic17C2311yescharacteristic
312C2×C4×Dic17C2311yescharacteristic
313#10587584—42no—
314#10587572—42no—
315#10587572—42no—
316#10587572—42no—
317#10587568—42no—
318#10587567—42no—
319C17×#95C2311yescharacteristic
320C17×#95C2311yescharacteristic
321C17×#95C2311yescharacteristic
322C17×#95C2311yescharacteristic
323C17×#95C2311yescharacteristic
324C17×#95C2311yescharacteristic
325#10587502C2311yescharacteristic
326#10587502C2311yescharacteristic
327#10587502C2311yescharacteristic
328#10587502C2311yescharacteristic
329#10587502C2311yescharacteristic
330#10587502C2311yescharacteristic
331#10587502C2311yescharacteristic
332#10587502C2311yescharacteristic
333#10587502C2311yescharacteristic
334#10587502C2311yescharacteristic
335#10587502C2311yescharacteristic
336#10587502C2311yescharacteristic
337#10587502C2311yescharacteristic
338#10587502C2311yescharacteristic
339#10587502C2311yescharacteristic
340#10587502C2311yescharacteristic
341#10587502C2311yescharacteristic
342#10587502C2311yescharacteristic
343#10587502C2311yescharacteristic
344#10587502C2311yescharacteristic
345#10587502C2311yescharacteristic
346#10587502C2311yescharacteristic
347#10587502C2311yescharacteristic
348#10587502C2311yescharacteristic
349#10587502C2311yescharacteristic
350#10587502C2311yescharacteristic
351#10587502C2311yescharacteristic
352#10587502C2311yescharacteristic
353#10587502C2311yescharacteristic
354#10587502C2311yescharacteristic
355#10587502C2311yescharacteristic
356#10587502C2311yescharacteristic
357#10587502C2311yescharacteristic
358#10587502C2311yescharacteristic
359#10587502C2311yescharacteristic
360#10587502C2311yescharacteristic
361#10587502C2311yescharacteristic
362#10587502C2311yescharacteristic
363C24×C17—22no—
364C24×C17—22no—
365C24×C17—41no—
366C24×C17—41no—
367C24×C17—41no—
368C24×C17—41no—
369C24×C17#4114yes—
370C24×C17C2411yescharacteristic
371C24×C17C2411yescharacteristic
372C24×C17C2411yescharacteristic
373C23×D17—22no—
374C23×D17—41no—
375C23×D17—41no—
376C23×D17—41no—
377C23×D17—41no—
378C23×D17—41no—
379C23×D17—41no—
380C23×D17C2411yescharacteristic
381C23×D17C2411yescharacteristic
382C23×D17C2411yescharacteristic
383C2×Q8×C17—22no—
384C2×Q8×C17—41no—
385C2×Q8×C17—41no—
386C22×C4×C17—22no—
387C22×C4×C17—22no—
388C22×C4×C17—22no—
389C22×C4×C17—41no—
390C22×C4×C17—41no—
391C22×C4×C17—41no—
392C22×C4×C17—41no—
393C22×C4×C17—41no—
394C22×C4×C17—41no—
395C22×C4×C17—41no—
396C22×C4×C17—41no—
397C22×C4×C17—41no—
398C22×C4×C17C2411yescharacteristic
399C22×C4×C17C2411yescharacteristic
400C22×C4×C17C2411yescharacteristic
401C22×C4×C17C2411yescharacteristic
402C22×C4×C17C2411yescharacteristic
403C22×C4×C17C2411yescharacteristic
404C22×C4×C17C2411yescharacteristic
405C22×C4×C17C2411yescharacteristic
406C22×C4×C17C2411yescharacteristic
407C22×C4×C17C2411yescharacteristic
408C22×C4×C17C2411yescharacteristic
409C22×C4×C17C2411yescharacteristic
410C2×C22⋊D17—22no—
411C2×C22⋊D17—22no—
412C2×C22⋊D17—22no—
413C2×C22⋊D17—22no—
414C2×C22⋊D17—22no—
415C2×C22⋊D17—22no—
416C2×C22⋊D17—22no—
417C2×C22⋊D17—22no—
418C2×C22⋊D17—22no—
419C2×C22⋊D17—22no—
420C2×C22⋊D17—22no—
421C2×C22⋊D17—22no—
422C2×C22⋊D17—22no—
423C2×C22⋊D17—41no—
424C2×C22⋊D17—41no—
425C2×C22⋊D17—41no—
426C2×C22⋊D17—41no—
427C2×C22⋊D17—41no—
428C2×C22⋊D17—41no—
429C2×C22⋊D17—41no—
430C2×C22⋊D17—41no—
431C2×C22⋊D17—416no—
432C22×Dic17—22no—
433C22×Dic17—22no—
434C22×Dic17—22no—
435C22×Dic17—22no—
436C22×Dic17—22no—
437C22×Dic17—22no—
438C22×Dic17—22no—
439C22×Dic17—41no—
440C22×Dic17—41no—
441C22×Dic17—41no—
442C22×Dic17—41no—
443C22×Dic17—41no—
444C22×Dic17—41no—
445C22×Dic17—41no—
446C22×Dic17—41no—
447C22×Dic17C2411yescharacteristic
448C22×Dic17C2411yescharacteristic
449C22×Dic17C2411yescharacteristic
450C22×Dic17C2411yescharacteristic
451C22×Dic17C2411yescharacteristic
452C22×Dic17C2411yescharacteristic
453C22×Dic17C2411yescharacteristic
454C22×Dic17C2411yescharacteristic
455C22×Dic17C2411yescharacteristic
456C22×Dic17C2411yescharacteristic
457C22×Dic17C2411yescharacteristic
458C22×Dic17C2411yescharacteristic
459C22×Dic17C2411yescharacteristic
460C2×D68—22no—
461C2×D68—41no—
462C2×D68—41no—
463C2×D68—41no—
464C2×D68—41no—
465C2×D68—41no—
466C2×C4×D17—41no—
467C2×C4×D17—41no—
468C2×C4×D17—41no—
469C4⋊C4×C17—22no—
470C4⋊C4×C17—41no—
471C4⋊C4×C17—41no—
472C4⋊C4×C17—41no—
473C4⋊C4×C17—41no—
474C4⋊C4×C17—41no—
475C4⋊C4×C17—41no—
476C4⋊C4×C17—41no—
477C4⋊C4×C17—41no—
478C22⋊C4×C17—22no—
479C22⋊C4×C17—22no—
480C22⋊C4×C17—22no—
481C22⋊C4×C17—22no—
482C22⋊C4×C17—22no—
483C22⋊C4×C17—22no—
484C22⋊C4×C17—41no—
485C22⋊C4×C17—41no—
486C22⋊C4×C17—41no—
487C22⋊C4×C17—41no—
488C22⋊C4×C17—41no—
489C22⋊C4×C17—41no—
490C22⋊C4×C17—41no—
491C22⋊C4×C17—41no—
492C22⋊Dic17—22no—
493C22⋊Dic17—22no—
494C22⋊Dic17—22no—
495C22⋊Dic17—22no—
496C22⋊Dic17—22no—
497C22⋊Dic17—22no—
498C22⋊Dic17—22no—
499C22⋊Dic17—41no—
500C22⋊Dic17—41no—
501C22⋊Dic17—41no—
502C22⋊Dic17—41no—
503#63227—22no—
504#63227—41no—
505#63227—41no—
506#63227—41no—
507#63227—41no—
508#63227—41no—
509#63227—41no—
510#63227—41no—
511#63227—41no—
512#63227—41no—
513#63227—41no—
514#63227—41no—
515#63227—41no—
516#63227—41no—
517#63227—41no—
518#63227—41no—
519#63227—41no—
520#63227—41no—
521#63227—41no—
522#63227—41no—
523#63227—41no—
524#63227—41no—
525#63227—41no—
526#63227—41no—
527#63227—41no—
528#63227—41no—
529#63227—41no—
530#63227—41no—
531#63227—41no—
532#63227—41no—
533#63227—41no—
534C4⋊Dic17—41no—
535C4⋊Dic17—41no—
536C4⋊Dic17—41no—
537C4⋊Dic17—41no—
538C4⋊Dic17—41no—
539C4⋊Dic17—41no—
540C4⋊Dic17—41no—
541C4⋊Dic17—41no—
542C4⋊Dic17—41no—
543C4⋊Dic17—41no—
544#63225—41no—
545#63225—41no—
546#63225—41no—
547#63225—41no—
548#63225—41no—
549#63225—41no—
550#63225—41no—
551C4×Dic17—22no—
552C4×Dic17—22no—
553C4×Dic17—41no—
554C4×Dic17—41no—
555C4×Dic17—41no—
556C4×Dic17—41no—
557C4×Dic17—41no—
558#36779—171nomaximal, Sylow
559C23×C17—21no—
560C23×C17—21no—
561C23×C17—21no—
562C23×C17—21no—
563C23×C17—21no—
564C23×C17—21no—
565C23×C17—21no—
566C23×C17—21no—
567C23×C17—21no—
568C23×C17—21no—
569C23×C17—21no—
570C23×C17—21no—
571C23×C17—21no—
572C23×C17—21no—
573C23×C17—21no—
574C23×C17—21no—
575C23×C17—28no—
576C23×C17—44no—
577C23×C17—44no—
578C23×C17—82no—
579C23×C17—82no—
580C23×C17—82no—
581C23×C17—82no—
582C23×C17C2×#4112yes—
583C23×C17C2×#4112yes—
584C23×C17C2×#4112yes—
585C23×C17H(5,𝔽2)12yes—
586C23×C17H(5,𝔽2)12yes—
587C23×C17C2511yescharacteristic
588C22×D17—21no—
589C22×D17—21no—
590C22×D17—21no—
591C22×D17—21no—
592C22×D17—21no—
593C22×D17—21no—
594C22×D17—21no—
595C22×D17—21no—
596C22×D17—21no—
597C22×D17—21no—
598C22×D17—21no—
599C22×D17—21no—
600C22×D17—21no—
601C22×D17—21no—
602C22×D17—21no—
603C22×D17—21no—
604C22×D17—21no—
605C22×D17—21no—
606C22×D17—21no—
607C22×D17—21no—
608C22×D17—21no—
609C22×D17—44no—
610C22×D17—82no—
611C22×D17—82no—
612C22×D17—82no—
613C22×D17—82no—
614C22×D17—82no—
615C22×D17—82no—
616Q8×C17—82no—
617C2×C4×C17—21no—
618C2×C4×C17—21no—
619C2×C4×C17—21no—
620C2×C4×C17—21no—
621C2×C4×C17—21no—
622C2×C4×C17—21no—
623C2×C4×C17—21no—
624C2×C4×C17—21no—
625C2×C4×C17—21no—
626C2×C4×C17—21no—
627C2×C4×C17—21no—
628C2×C4×C17—21no—
629C2×C4×C17—21no—
630C2×C4×C17—21no—
631C2×C4×C17—21no—
632C2×C4×C17—21no—
633C2×C4×C17—21no—
634C2×C4×C17—21no—
635C2×C4×C17—21no—
636C2×C4×C17—21no—
637C2×C4×C17—21no—
638C2×C4×C17—21no—
639C2×C4×C17—21no—
640C2×C4×C17—21no—
641C2×C4×C17—21no—
642C2×C4×C17—21no—
643C2×C4×C17—21no—
644C2×C4×C17—21no—
645C2×C4×C17—21no—
646C2×C4×C17—21no—
647C2×C4×C17—21no—
648C2×C4×C17—21no—
649C2×C4×C17—21no—
650C2×C4×C17—21no—
651C2×C4×C17—21no—
652C2×C4×C17—44no—
653C2×C4×C17—82no—
654C2×C4×C17—82no—
655C2×C4×C17—82no—
656C2×C4×C17H(5,𝔽2)12yes—
657C22⋊D17—44no—
658C22⋊D17—44no—
659C22⋊D17—44no—
660C22⋊D17—44no—
661C22⋊D17—44no—
662C22⋊D17—82no—
663C22⋊D17—82no—
664C2×Dic17—21no—
665C2×Dic17—21no—
666C2×Dic17—21no—
667C2×Dic17—21no—
668C2×Dic17—21no—
669C2×Dic17—21no—
670C2×Dic17—21no—
671C2×Dic17—21no—
672C2×Dic17—21no—
673C2×Dic17—21no—
674C2×Dic17—21no—
675C2×Dic17—21no—
676C2×Dic17—21no—
677C2×Dic17—21no—
678C2×Dic17—21no—
679C2×Dic17—21no—
680C2×Dic17—21no—
681C2×Dic17—21no—
682C2×Dic17—21no—
683C2×Dic17—21no—
684C2×Dic17—21no—
685C2×Dic17—21no—
686C2×Dic17—21no—
687C2×Dic17—21no—
688C2×Dic17—21no—
689C2×Dic17—21no—
690C2×Dic17—21no—
691C2×Dic17—21no—
692C2×Dic17—21no—
693C2×Dic17—21no—
694C2×Dic17—21no—
695C2×Dic17—21no—
696C2×Dic17—21no—
697C2×Dic17—21no—
698C2×Dic17—21no—
699C2×Dic17—21no—
700C2×Dic17—21no—
701C2×Dic17—21no—
702C2×Dic17—21no—
703C2×Dic17—44no—
704C2×Dic17—44no—
705C2×Dic17—44no—
706C2×Dic17—44no—
707C2×Dic17—82no—
708D68—82no—
709D68—82no—
710C4×D17—82no—
711#2852—171no—
712#2850—171no—
713#2781—171no—
714#2781—171no—
715#2778—171no—
716#2765—171no—
717#2764—171no—
718#2761—171no—
719#2756—171no—
720#2749—171no—
721#2743—171no—
722#2741—171no—
723#2735—171no—
724#2735—171no—
725#2730—171no—
726#2702—171no—
727#2685—171no—
728#2684—171no—
729#2623—171no—
730#2618—171no—
731#2510—171no—
732#2488—171no—
733#2444—171no—
734#2437D1711yescharacteristic, complemented
735#2425—171no—
736#2412—171no—
737#2410—171no—
738#2405—171no—
739#2321—171no—
740#2308—171no—
741C2×#388—171no—
742C22×C17—22no—
743C22×C17—22no—
744C22×C17—22no—
745C22×C17—22no—
746C22×C17—22no—
747C22×C17—22no—
748C22×C17—22no—
749C22×C17—22no—
750C22×C17—22no—
751C22×C17—22no—
752C22×C17—22no—
753C22×C17—22no—
754C22×C17—41no—
755C22×C17—41no—
756C22×C17—41no—
757C22×C17—41no—
758C22×C17—41no—
759C22×C17—41no—
760C22×C17—41no—
761C22×C17—41no—
762C22×C17—88no—
763C22×C17#53814yes—
764C22×C17C22×#4111yescharacteristic
765C22×C17C2×H(5,𝔽2)11yescharacteristic
766C22×C17C2×H(5,𝔽2)11yescharacteristic
767C22×C17C2×H(5,𝔽2)11yescharacteristic
768C22×C17#58511yescharacteristic
769C22×C17#58511yescharacteristic
770C22×C17#58511yescharacteristic
771C2×D17—41no—
772C2×D17—41no—
773C2×D17—41no—
774C2×D17—41no—
775C2×D17—41no—
776C2×D17—41no—
777C2×D17—41no—
778C2×D17—41no—
779C2×D17—41no—
780C2×D17—41no—
781C2×D17—41no—
782C2×D17—41no—
783C2×D17—41no—
784C2×D17—41no—
785C2×D17—41no—
786C2×D17—41no—
787C2×D17—41no—
788C2×D17—41no—
789C2×D17—41no—
790C2×D17—41no—
791C2×D17—41no—
792C2×D17—88no—
793C4×C17—22no—
794C4×C17—41no—
795C4×C17—41no—
796C4×C17—41no—
797C4×C17—41no—
798C4×C17—41no—
799C4×C17—41no—
800C4×C17—41no—
801C4×C17—41no—
802C4×C17—41no—
803C4×C17—41no—
804C4×C17—41no—
805Dic17—41no—
806Dic17—41no—
807Dic17—41no—
808Dic17—41no—
809Dic17—41no—
810Dic17—41no—
811Dic17—41no—
812Dic17—41no—
813Dic17—41no—
814Dic17—41no—
815Dic17—41no—
816Dic17—41no—
817Dic17—41no—
818C23×D4—171no—
819C2×#126—171no—
820C2×#124—171no—
821C2×#123—171no—
822C2×#123—171no—
823C2×#123—171no—
824C2×C22⋊Q8C2×D1711yescharacteristic, complemented
825C2×C22⋊Q8C2×D1711yescharacteristic, complemented
826C2×#121—171no—
827C2×#121—171no—
828C2×#120—171no—
829C2×#120—171no—
830C2×C4×D4—171no—
831C22×C4⋊C4—171no—
832C22×C22⋊C4—171no—
833C22×C22⋊C4—171no—
834C22×C22⋊C4C2×D1711yescharacteristic
835C22×C22⋊C4C2×D1711yescharacteristic
836C22×C42—171no—
837#401—171no—
838#400—171no—
839#400—171no—
840#400—171no—
841#400—171no—
842#400—171no—
843#400—171no—
844#399—171no—
845#399—171no—
846#399C2×D1711yescharacteristic
847#398—171no—
848#398—171no—
849#398—171no—
850#398—171no—
851#398—171no—
852#397—171no—
853#397—171no—
854#397—171no—
855#397—171no—
856#397—171no—
857#397—171no—
858#397—171no—
859#397—171no—
860#397—171no—
861#397—171no—
862#396—171no—
863#396—171no—
864#396—171no—
865#396—171no—
866#396—171no—
867#396C2×D1711yescharacteristic
868#396C2×D1711yescharacteristic
869#394—171no—
870#394—171no—
871#394—171no—
872#394—171no—
873#394—171no—
874#394—171no—
875#394—171no—
876#394—171no—
877#394—171no—
878#394—171no—
879#394—171no—
880#394—171no—
881#393—171no—
882#393C2×D1711yescharacteristic
883#392—171no—
884#392—171no—
885#391—171no—
886#391—171no—
887#390—171no—
888#390—171no—
889#390—171no—
890#389—171no—
891#388—171no—
892#388—171no—
893#388—171no—
894#388—171no—
895#388—171no—
896#388—171no—
897#388—171no—
898#388—171no—
899#388—171no—
900#388—171no—
901#388—171no—
902#388—171no—
903#388—171no—
904#388—171no—
905#388—171no—
906#388—171no—
907#388—171no—
908#388—171no—
909#388—171no—
910#388—171no—
911#388—171no—
912#388—171no—
913#388—171no—
914#388—171no—
915#388—171no—
916#387—171no—
917#387—171no—
918#387—171no—
919#387—171no—
920#387—171no—
921#386—171no—
922#386—171no—
923#386—171no—
924#386—171no—
925#386—171no—
926#386—171no—
927#386—171no—
928#386—171no—
929#386—171no—
930#386—171no—
931#386—171no—
932#386—171no—
933#386—171no—
934#386—171no—
935#386—171no—
936#386—171no—
937#386—171no—
938#386—171no—
939#386—171no—
940#386—171no—
941#386—171no—
942#385—171no—
943#385—171no—
944#385—171no—
945#385—171no—
946#385—171no—
947#385C2×D1711yescharacteristic, complemented
948#385C2×D1711yescharacteristic, complemented
949#385C2×D1711yescharacteristic, complemented
950#385C2×D1711yescharacteristic, complemented
951#383—171no—
952#383—171no—
953#382—171no—
954#382—171no—
955#381—171no—
956#381—171no—
957#381—171no—
958#381—171no—
959#380—171no—
960#380—171no—
961#380—171no—
962#380C2×D1711yescharacteristic, complemented
963#380C2×D1711yescharacteristic, complemented
964#379—171no—
965#379—171no—
966#379—171no—
967#379—171no—
968#379—171no—
969#379C2×D1711yescharacteristic
970C4×C22⋊C4—171no—
971C2×#95—171no—
972C2×#95—171no—
973C2×C17—24no—
974C2×C17—42no—
975C2×C17—42no—
976C2×C17C2×#53811yescharacteristic
977C2×C17#349111yescharacteristic
978C2×C17#350511yescharacteristic
979C2×C17#353411yescharacteristic
980C2×C17#354211yescharacteristic
981C2×C17#354511yescharacteristic
982C2×C17#356011yescharacteristic
983D17—81no—
984D17—81no—
985D17—81no—
986C25—171no—
987C25C22×D1711yescharacteristic
988C22×Q8C22×D1711yescharacteristic
989C22×D4—171no—
990C22×D4—171no—
991C22×D4—171no—
992C22×D4—171no—
993C22×D4—171no—
994C22×D4—171no—
995C22×D4—171no—
996C22×D4—171no—
997C22×D4—171no—
998C22×D4—344no—
999C22×D4—682no—
1000C22×D4—682no—
1001C23×C4—171no—
1002C23×C4—171no—
1003C23×C4—171no—
1004C23×C4—171no—
1005C23×C4—171no—
1006C23×C4—171no—
1007C23×C4C22×D1711yescharacteristic
1008C23×C4C22×D1711yescharacteristic
1009C23×C4C22×D1711yescharacteristic
1010C23×C4C22×D1711yescharacteristic
1011#126—682no—
1012#124—682no—
1013#123—682no—
1014#123—682no—
1015#123—682no—
1016C22⋊Q8—42no—
1017C22⋊Q8—42no—
1018#121—682no—
1019#121—682no—
1020#120—344no—
1021#120—682no—
1022C4×D4—682no—
1023C2×C4⋊C4—171no—
1024C2×C4⋊C4—171no—
1025C2×C4⋊C4—171no—
1026C2×C4⋊C4—171no—
1027C2×C4⋊C4—171no—
1028C2×C4⋊C4—171no—
1029C2×C4⋊C4—171no—
1030C2×C4⋊C4—171no—
1031C2×C4⋊C4—171no—
1032C2×C4⋊C4—171no—
1033C2×C4⋊C4—171no—
1034C2×C4⋊C4—171no—
1035C2×C4⋊C4—171no—
1036C2×C4⋊C4—171no—
1037C2×C4⋊C4—171no—
1038C2×C4⋊C4—171no—
1039C2×C4⋊C4—171no—
1040C2×C4⋊C4—682no—
1041C2×C4⋊C4C22×D1711yescharacteristic
1042C2×C4⋊C4C22×D1711yescharacteristic
1043C2×C4⋊C4C22×D1711yescharacteristic
1044C2×C4⋊C4C22×D1711yescharacteristic
1045C2×C4⋊C4C22×D1711yescharacteristic
1046C2×C4⋊C4C22×D1711yescharacteristic
1047C2×C4⋊C4C22×D1711yescharacteristic
1048C2×C4⋊C4C22×D1711yescharacteristic
1049C2×C4⋊C4C22×D1711yescharacteristic
1050C2×C22⋊C4—42no—
1051C2×C22⋊C4—42no—
1052C2×C22⋊C4—171no—
1053C2×C22⋊C4—171no—
1054C2×C22⋊C4—171no—
1055C2×C22⋊C4—171no—
1056C2×C22⋊C4—171no—
1057C2×C22⋊C4—171no—
1058C2×C22⋊C4—171no—
1059C2×C22⋊C4—171no—
1060C2×C22⋊C4—171no—
1061C2×C22⋊C4—171no—
1062C2×C22⋊C4—171no—
1063C2×C22⋊C4—171no—
1064C2×C22⋊C4—171no—
1065C2×C22⋊C4—171no—
1066C2×C22⋊C4—171no—
1067C2×C22⋊C4—171no—
1068C2×C22⋊C4—171no—
1069C2×C22⋊C4—171no—
1070C2×C22⋊C4—171no—
1071C2×C22⋊C4—171no—
1072C2×C22⋊C4—171no—
1073C2×C22⋊C4—171no—
1074C2×C22⋊C4—171no—
1075C2×C22⋊C4—171no—
1076C2×C22⋊C4—171no—
1077C2×C22⋊C4—171no—
1078C2×C22⋊C4—171no—
1079C2×C22⋊C4—171no—
1080C2×C22⋊C4—171no—
1081C2×C22⋊C4—171no—
1082C2×C22⋊C4—171no—
1083C2×C22⋊C4—171no—
1084C2×C22⋊C4—171no—
1085C2×C22⋊C4—171no—
1086C2×C22⋊C4—171no—
1087C2×C22⋊C4—171no—
1088C2×C22⋊C4—171no—
1089C2×C22⋊C4—171no—
1090C2×C22⋊C4—171no—
1091C2×C22⋊C4—171no—
1092C2×C22⋊C4—171no—
1093C2×C22⋊C4—171no—
1094C2×C22⋊C4—344no—
1095C2×C22⋊C4—682no—
1096C2×C22⋊C4C22×D1711yescharacteristic
1097C2×C22⋊C4C22×D1711yescharacteristic
1098C2×C22⋊C4C22×D1711yescharacteristic
1099C2×C22⋊C4C22×D1711yescharacteristic
1100C2×C22⋊C4C22×D1711yescharacteristic
1101C2×C22⋊C4C22×D1711yescharacteristic
1102C2×C22⋊C4C22×D1711yescharacteristic
1103C2×C22⋊C4C22×D1711yescharacteristic
1104C2×C22⋊C4C22×D1711yescharacteristic
1105C2×C22⋊C4C22×D1711yescharacteristic
1106C2×C22⋊C4C22×D1711yescharacteristic
1107C2×C22⋊C4C22×D1711yescharacteristic
1108C2×C22⋊C4C22×D1711yescharacteristic
1109C2×C22⋊C4C22×D1711yescharacteristic
1110C2×C42—171no—
1111C2×C42—171no—
1112C2×C42—171no—
1113C2×C42—171no—
1114C2×C42—171no—
1115C2×C42—171no—
1116C2×C42—171no—
1117C2×C42—682no—
1118#95—171no—
1119#95—171no—
1120#95—171no—
1121#95—171no—
1122#95—171no—
1123#95—171no—
1124#95—171no—
1125#95—171no—
1126#95—171no—
1127#95—171no—
1128#95—171no—
1129#95—171no—
1130#95—171no—
1131#95—171no—
1132#95—171no—
1133#95—171no—
1134#95—171no—
1135#95—171no—
1136#95—171no—
1137#95—171no—
1138#95—171no—
1139#95—171no—
1140#95—171no—
1141#95—171no—
1142#95—171no—
1143#95—171no—
1144#95—171no—
1145#95—171no—
1146#95—171no—
1147#95—171no—
1148#95—171no—
1149#95—171no—
1150#95—171no—
1151#95—171no—
1152#95—171no—
1153#95—171no—
1154#95—171no—
1155#95—171no—
1156#95C22×D1711yescharacteristic
1157#95C22×D1711yescharacteristic
1158#95C22×D1711yescharacteristic
1159#95C22×D1711yescharacteristic
1160#95C22×D1711yescharacteristic
1161#95C22×D1711yescharacteristic
1162C17#3677911yescharacteristic, complemented, Sylow
1163C24—22no—
1164C24—22no—
1165C24—41no—
1166C24—41no—
1167C24—41no—
1168C24—41no—
1169C24—171no—
1170C24—171no—
1171C24—171no—
1172C24—342no—
1173C24—681no—
1174C24—681no—
1175C24—681no—
1176C24—681no—
1177C24—681no—
1178C24—681no—
1179C24#6325614yes—
1180C24C23×D1711yescharacteristic
1181C24C23×D1711yescharacteristic
1182C24C23×D1711yescharacteristic
1183C2×Q8—22no—
1184C2×Q8—41no—
1185C2×Q8—41no—
1186C2×D4—342no—
1187C2×D4—342no—
1188C2×D4—342no—
1189C2×D4—342no—
1190C2×D4—342no—
1191C2×D4—342no—
1192C2×D4—342no—
1193C2×D4—342no—
1194C2×D4—342no—
1195C2×D4—342no—
1196C2×D4—342no—
1197C2×D4—342no—
1198C2×D4—342no—
1199C2×D4—342no—
1200C2×D4—681no—
1201C2×D4—681no—
1202C2×D4—681no—
1203C2×D4—681no—
1204C2×D4—681no—
1205C2×D4—681no—
1206C2×D4—681no—
1207C2×D4—681no—
1208C2×D4—681no—
1209C2×D4—681no—
1210C2×D4—681no—
1211C2×D4—681no—
1212C2×D4—681no—
1213C2×D4—6816no—
1214C22×C4—22no—
1215C22×C4—22no—
1216C22×C4—22no—
1217C22×C4—41no—
1218C22×C4—41no—
1219C22×C4—41no—
1220C22×C4—41no—
1221C22×C4—41no—
1222C22×C4—41no—
1223C22×C4—41no—
1224C22×C4—41no—
1225C22×C4—41no—
1226C22×C4—171no—
1227C22×C4—171no—
1228C22×C4—171no—
1229C22×C4—171no—
1230C22×C4—171no—
1231C22×C4—171no—
1232C22×C4—171no—
1233C22×C4—171no—
1234C22×C4—171no—
1235C22×C4—171no—
1236C22×C4—171no—
1237C22×C4—171no—
1238C22×C4—171no—
1239C22×C4—342no—
1240C22×C4—342no—
1241C22×C4—342no—
1242C22×C4—342no—
1243C22×C4—342no—
1244C22×C4—342no—
1245C22×C4—342no—
1246C22×C4—681no—
1247C22×C4—681no—
1248C22×C4—681no—
1249C22×C4—681no—
1250C22×C4—681no—
1251C22×C4—681no—
1252C22×C4—681no—
1253C22×C4—681no—
1254C22×C4—681no—
1255C22×C4—681no—
1256C22×C4—681no—
1257C22×C4C23×D1711yescharacteristic
1258C22×C4C23×D1711yescharacteristic
1259C22×C4C23×D1711yescharacteristic
1260C22×C4C23×D1711yescharacteristic
1261C22×C4C23×D1711yescharacteristic
1262C22×C4C23×D1711yescharacteristic
1263C22×C4C23×D1711yescharacteristic
1264C22×C4C23×D1711yescharacteristic
1265C22×C4C23×D1711yescharacteristic
1266C22×C4C23×D1711yescharacteristic
1267C22×C4C23×D1711yescharacteristic
1268C22×C4C23×D1711yescharacteristic
1269C4⋊C4—22no—
1270C4⋊C4—41no—
1271C4⋊C4—41no—
1272C4⋊C4—41no—
1273C4⋊C4—41no—
1274C4⋊C4—41no—
1275C4⋊C4—41no—
1276C4⋊C4—41no—
1277C4⋊C4—41no—
1278C4⋊C4—681no—
1279C4⋊C4—681no—
1280C4⋊C4—681no—
1281C4⋊C4—681no—
1282C4⋊C4—681no—
1283C4⋊C4—681no—
1284C4⋊C4—681no—
1285C4⋊C4—681no—
1286C4⋊C4—681no—
1287C4⋊C4—681no—
1288C4⋊C4—681no—
1289C4⋊C4—681no—
1290C4⋊C4—681no—
1291C4⋊C4—681no—
1292C4⋊C4—681no—
1293C4⋊C4—681no—
1294C4⋊C4—681no—
1295C22⋊C4—22no—
1296C22⋊C4—22no—
1297C22⋊C4—22no—
1298C22⋊C4—22no—
1299C22⋊C4—22no—
1300C22⋊C4—22no—
1301C22⋊C4—41no—
1302C22⋊C4—41no—
1303C22⋊C4—41no—
1304C22⋊C4—41no—
1305C22⋊C4—41no—
1306C22⋊C4—41no—
1307C22⋊C4—41no—
1308C22⋊C4—41no—
1309C22⋊C4—342no—
1310C22⋊C4—342no—
1311C22⋊C4—342no—
1312C22⋊C4—342no—
1313C22⋊C4—342no—
1314C22⋊C4—342no—
1315C22⋊C4—342no—
1316C22⋊C4—342no—
1317C22⋊C4—681no—
1318C22⋊C4—681no—
1319C22⋊C4—681no—
1320C22⋊C4—681no—
1321C22⋊C4—681no—
1322C22⋊C4—681no—
1323C22⋊C4—681no—
1324C22⋊C4—681no—
1325C22⋊C4—681no—
1326C22⋊C4—681no—
1327C22⋊C4—681no—
1328C22⋊C4—681no—
1329C22⋊C4—681no—
1330C22⋊C4—681no—
1331C22⋊C4—681no—
1332C22⋊C4—681no—
1333C22⋊C4—681no—
1334C22⋊C4—681no—
1335C22⋊C4—681no—
1336C22⋊C4—681no—
1337C22⋊C4—681no—
1338C22⋊C4—681no—
1339C22⋊C4—681no—
1340C22⋊C4—681no—
1341C22⋊C4—681no—
1342C22⋊C4—681no—
1343C22⋊C4—681no—
1344C22⋊C4—681no—
1345C22⋊C4—681no—
1346C22⋊C4—681no—
1347C22⋊C4—681no—
1348C22⋊C4—681no—
1349C22⋊C4—681no—
1350C22⋊C4—681no—
1351C42—342no—
1352C42—342no—
1353C42—681no—
1354C42—681no—
1355C42—681no—
1356C42—681no—
1357C42—681no—
1358C23—21no—
1359C23—21no—
1360C23—21no—
1361C23—21no—
1362C23—21no—
1363C23—21no—
1364C23—21no—
1365C23—21no—
1366C23—21no—
1367C23—21no—
1368C23—21no—
1369C23—21no—
1370C23—21no—
1371C23—21no—
1372C23—21no—
1373C23—21no—
1374C23—28no—
1375C23—44no—
1376C23—44no—
1377C23—82no—
1378C23—82no—
1379C23—82no—
1380C23—82no—
1381C23—341no—
1382C23—341no—
1383C23—341no—
1384C23—341no—
1385C23—341no—
1386C23—341no—
1387C23—341no—
1388C23—341no—
1389C23—341no—
1390C23—341no—
1391C23—341no—
1392C23—341no—
1393C23—341no—
1394C23—341no—
1395C23—341no—
1396C23—341no—
1397C23—341no—
1398C23—341no—
1399C23—341no—
1400C23—341no—
1401C23—341no—
1402C23—684no—
1403C23—1362no—
1404C23—1362no—
1405C23—1362no—
1406C23—1362no—
1407C23—1362no—
1408C23—1362no—
1409C23#1058769112yes—
1410C23C2×#6325612yes—
1411C23C2×#6325612yes—
1412C23C2×#6325612yes—
1413C23#1058769612yes—
1414C23C24×D1711yescharacteristic
1415Q8—82no—
1416D4—684no—
1417D4—684no—
1418D4—684no—
1419D4—684no—
1420D4—684no—
1421D4—1362no—
1422D4—1362no—
1423D4—1362no—
1424D4—1362no—
1425C2×C4—21no—
1426C2×C4—21no—
1427C2×C4—21no—
1428C2×C4—21no—
1429C2×C4—21no—
1430C2×C4—21no—
1431C2×C4—21no—
1432C2×C4—21no—
1433C2×C4—21no—
1434C2×C4—21no—
1435C2×C4—21no—
1436C2×C4—21no—
1437C2×C4—21no—
1438C2×C4—21no—
1439C2×C4—21no—
1440C2×C4—21no—
1441C2×C4—21no—
1442C2×C4—21no—
1443C2×C4—21no—
1444C2×C4—21no—
1445C2×C4—21no—
1446C2×C4—21no—
1447C2×C4—21no—
1448C2×C4—21no—
1449C2×C4—21no—
1450C2×C4—21no—
1451C2×C4—21no—
1452C2×C4—21no—
1453C2×C4—21no—
1454C2×C4—21no—
1455C2×C4—21no—
1456C2×C4—21no—
1457C2×C4—21no—
1458C2×C4—21no—
1459C2×C4—21no—
1460C2×C4—44no—
1461C2×C4—82no—
1462C2×C4—82no—
1463C2×C4—82no—
1464C2×C4—341no—
1465C2×C4—341no—
1466C2×C4—341no—
1467C2×C4—341no—
1468C2×C4—341no—
1469C2×C4—341no—
1470C2×C4—341no—
1471C2×C4—341no—
1472C2×C4—341no—
1473C2×C4—341no—
1474C2×C4—341no—
1475C2×C4—341no—
1476C2×C4—341no—
1477C2×C4—341no—
1478C2×C4—341no—
1479C2×C4—341no—
1480C2×C4—341no—
1481C2×C4—341no—
1482C2×C4—341no—
1483C2×C4—341no—
1484C2×C4—341no—
1485C2×C4—341no—
1486C2×C4—341no—
1487C2×C4—341no—
1488C2×C4—341no—
1489C2×C4—341no—
1490C2×C4—341no—
1491C2×C4—341no—
1492C2×C4—341no—
1493C2×C4—341no—
1494C2×C4—341no—
1495C2×C4—341no—
1496C2×C4—341no—
1497C2×C4—341no—
1498C2×C4—341no—
1499C2×C4—341no—
1500C2×C4—341no—
1501C2×C4—341no—
1502C2×C4—341no—
1503C2×C4—684no—
1504C2×C4—684no—
1505C2×C4—684no—
1506C2×C4—684no—
1507C2×C4—1362no—
1508C2×C4—1362no—
1509C2×C4#1058769112yes—
1510C22—22no—
1511C22—22no—
1512C22—22no—
1513C22—22no—
1514C22—22no—
1515C22—22no—
1516C22—22no—
1517C22—22no—
1518C22—22no—
1519C22—22no—
1520C22—22no—
1521C22—22no—
1522C22—41no—
1523C22—41no—
1524C22—41no—
1525C22—41no—
1526C22—41no—
1527C22—41no—
1528C22—41no—
1529C22—41no—
1530C22—88no—
1531C22—681no—
1532C22—681no—
1533C22—681no—
1534C22—681no—
1535C22—681no—
1536C22—681no—
1537C22—681no—
1538C22—681no—
1539C22—681no—
1540C22—681no—
1541C22—681no—
1542C22—681no—
1543C22—681no—
1544C22—681no—
1545C22—681no—
1546C22—681no—
1547C22—681no—
1548C22—681no—
1549C22—681no—
1550C22—681no—
1551C22—681no—
1552C22—1368no—
1553C22#1176339914yes—
1554C22C22×#6325611yescharacteristic
1555C22C2×#1058769111yescharacteristic
1556C22C2×#1058769111yescharacteristic
1557C22C2×#1058769611yescharacteristic
1558C22#1176364411yescharacteristic
1559C22#1176364411yescharacteristic
1560C22#1176364511yescharacteristic
1561C4—22no—
1562C4—41no—
1563C4—41no—
1564C4—41no—
1565C4—41no—
1566C4—41no—
1567C4—41no—
1568C4—41no—
1569C4—41no—
1570C4—41no—
1571C4—41no—
1572C4—41no—
1573C4—681no—
1574C4—681no—
1575C4—681no—
1576C4—681no—
1577C4—681no—
1578C4—681no—
1579C4—681no—
1580C4—681no—
1581C4—681no—
1582C4—681no—
1583C4—681no—
1584C4—681no—
1585C4—681no—
1586C2—24no—
1587C2—42no—
1588C2—42no—
1589C2—1361no—
1590C2—1361no—
1591C2—1361no—
1592C2C2×#1176339911yescharacteristic
1593C2#1454248311yescharacteristic
1594C2#1454262511yescharacteristic
1595C2#1454296211yescharacteristic
1596C2#1454308611yescharacteristic
1597C2#1454314011yescharacteristic
1598C2#1454332411yescharacteristic
subgroupG/H
center, FrattiniC23C24×D17
commutator, socle, cosocleC23×C17C25
FittingC17×#2437C2
prime radical#14532152C2
hypercenter#2437D17
hypocenterC17#36779
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C23 ◁ #2437

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #14537101C2semidirect
2. #14537087C2semidirect
3. #14536441C2semidirect
4. #14536441C2semidirect
5. #14536396C2semidirect
6. #14536225C2semidirect
7. #14536210C2semidirect
8. #14536177C2semidirect
9. #14536107C2semidirect
10. #14536008C2semidirect
11. #14535930C2semidirect
12. #14535895C2semidirect
13. #14535827C2semidirect
14. #14535826C2semidirect
15. #14535775C2semidirect
16. #14535408C2semidirect
17. #14535182C2semidirect
18. #14535167C2semidirect
19. #14534570C2semidirect
20. #14534529C2semidirect
21. #14533340C2semidirect
22. #14533116C2semidirect
23. #14532538C2semidirect
24. #14532333C2semidirect
25. #14532174C2semidirect
27. #14532112C2semidirect
28. #14531439C2semidirect
29. #14531359C2semidirect
30. C2×#11762697C2semidirect
31. C17×#2437C2semidirect
33. C2×#10587584C22semidirect
34. C2×#10587633C22semidirect
37. C2×#10587572C22semidirect
42. C2×#10587567C22semidirect
43. C22×#63225C22semidirect
46. C22×C4×Dic17C22semidirect
47. C17⋊#401C22semidirect
48. #11762751C22semidirect
49. #11762751C22semidirect
50. #11762751C22semidirect
51. #11762748C22semidirect
52. #11762748C22semidirect
53. #11762748C22semidirect
54. #11762744C22semidirect
55. #11762744C22semidirect
56. #11762742C22semidirect
57. #11762742C22semidirect
58. #11762741C22semidirect
59. #11762741C22semidirect
60. #11762741C22semidirect
61. #11762738C22semidirect
62. #11762738C22semidirect
63. #11762738C22semidirect
64. #11762736C22semidirect
65. #11762736C22semidirect
66. #11762735C22semidirect
67. #11762735C22semidirect
68. #11762735C22semidirect
71. #11762731C22semidirect
72. #11762731C22semidirect
73. #11762731C22semidirect
74. #11762731C22semidirect
75. #11762731C22semidirect
76. #11762727C22semidirect
77. #11762727C22semidirect
78. #11762726C22semidirect
79. #11762726C22semidirect
88. #11762720C22semidirect
91. #11762716C22semidirect
92. #11762716C22semidirect
93. #11762710C22semidirect
95. #11762709C22semidirect
96. #11762708C22semidirect
98. #11762703C22semidirect
99. #11762701C22semidirect
100. #11762701C22semidirect
101. #11762701C22semidirect
102. #11762699C22semidirect
103. #11762699C22semidirect
104. #11762699C22semidirect
105. #11762699C22semidirect
106. #11762699C22semidirect
107. #11762699C22semidirect
108. #11762699C22semidirect
109. #11762699C22semidirect
110. #11762699C22semidirect
111. #11762698C22semidirect
117. #11762697C22semidirect
118. #11762697C22semidirect
119. #11762697C22semidirect
120. #11762697C22semidirect
121. #11762697C22semidirect
122. #11762695C22semidirect
123. #11762695C22semidirect
124. #11762695C22semidirect
125. #11762692C22semidirect
126. #11762690C22semidirect
133. #11762688C22semidirect
134. #11762688C22semidirect
135. #11762687C22semidirect
136. #11762687C22semidirect
144. #11762686C22semidirect
145. #11762686C22semidirect
147. #11762685C22semidirect
151. #11762684C22semidirect
152. #11762681C22semidirect
153. #11762676C22semidirect
154. #11762676C22semidirect
155. #11762674C22semidirect
156. #11762674C22semidirect
157. #11762671C22semidirect
160. #11762670C22semidirect
161. #11762669C22semidirect
162. #11762669C22semidirect
163. #11762666C22semidirect
169. C22⋊C4×Dic17C22semidirect
170. C2×#10587502C22semidirect
171. C2×#10587502C22semidirect
172. C2×C17×C22⋊Q8C22semidirect
173. C2×C17×C22⋊Q8C22semidirect
180. C17×#385C22semidirect
181. C17×#385C22semidirect
182. C17×#385C22semidirect
183. C17×#385C22semidirect
184. C17×#380C22semidirect
185. C17×#380C22semidirect
734. #2437D17semidirect
824. C2×C22⋊Q8C2×D17semidirect
825. C2×C22⋊Q8C2×D17semidirect
947. #385C2×D17semidirect
948. #385C2×D17semidirect
949. #385C2×D17semidirect
950. #385C2×D17semidirect
962. #380C2×D17semidirect
963. #380C2×D17semidirect
1162. C17#36779semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#145371012
#145370872
#145364412
#145363962
#145362252
#145362102
#145361772
#145361072
#145360082
#145359302
#145358952
#145358272
#145358262
#145357752
#145354082
#145351822
#145351672
#145345702
#145345292
#145333402
#145331162
#145325382
#145323332
#145321742
#145321522
#145321122
#145314392
#145313592
C2×#117626972
C17×#24372
#3677917