Finite Group Databasebeta

← #17242679

Subgroups — #17242679

Order 4352.

2078 conjugacy classes of subgroups.

The subgroup lattice has 1622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14537075C211yesmaximal, characteristic, complemented
2#14537065C211yesmaximal, characteristic, complemented
3#14536429C211yesmaximal, characteristic, complemented
4#14536429C211yesmaximal, characteristic, complemented
5#14536268C211yesmaximal, characteristic, complemented
6#14536178C211yesmaximal, characteristic, complemented
7#14536055C211yesmaximal, characteristic, complemented
8#14535993C211yesmaximal, characteristic, complemented
9#14535922C211yesmaximal, characteristic, complemented
10#14535855C211yesmaximal, characteristic, complemented
11#14535543C211yesmaximal, characteristic, complemented
12#14535480C211yesmaximal, characteristic, complemented
13#14535467C211yesmaximal, characteristic, complemented
14#14535402C211yesmaximal, characteristic, complemented
15#14535397C211yesmaximal, characteristic, complemented
16#14535219C211yesmaximal, characteristic, complemented
17#14535021C211yesmaximal, characteristic, complemented
18#14534563C211yesmaximal, characteristic, complemented
19#14534531C211yesmaximal, characteristic, complemented
20#14533709C211yesmaximal, characteristic, complemented
21#14533678C211yesmaximal, characteristic, complemented
22#14532501C211yesmaximal, characteristic, complemented
23#14532338C211yesmaximal, characteristic, complemented
24#14532319C211yesmaximal, characteristic, complemented
25#14532258C211yesmaximal, characteristic, complemented
26#14532241C211yesmaximal, characteristic, complemented
27#14532227C211yesmaximal, characteristic, complemented
28#14531486C211yesmaximal, characteristic, complemented
29#14531415C211yesmaximal, characteristic, complemented
30D17×#385C211yesmaximal, characteristic, complemented
31C17×#2749C211yesmaximal, characteristic, complemented
32C23×C4×D17C2211yescharacteristic
33C2×#10587575C2211yescharacteristic, complemented
34C2×#10587580C2211yescharacteristic
35C2×#10587572C2211yescharacteristic
36C2×#10587569C2211yescharacteristic
37C2×#10587569C2211yescharacteristic
38C2×#10587569C2211yescharacteristic
39C2×#10587569C2211yescharacteristic
40C2×#10587616C2211yescharacteristic
41C2×#10587570C2211yescharacteristic
42C2×#10587570C2211yescharacteristic
43C2×#10587570C2211yescharacteristic
44C2×#10587625C2211yescharacteristic
45C2×#10587624C2211yescharacteristic
46C2×#10587624C2211yescharacteristic, complemented
47C2×#10587568C2211yescharacteristic
48C2×#10587623C2211yescharacteristic
49C2×#10587623C2211yescharacteristic
50C2×C4×D68C2211yescharacteristic
51C2×C4×C22⋊D17C2211yescharacteristic
52C2×#10587567C2211yescharacteristic
53C2×C4⋊C4×D17C2211yescharacteristic
54C2×C4⋊C4×D17C2211yescharacteristic
55C2×C22⋊C4×D17C2211yescharacteristic
56C2×C22⋊C4×D17C2211yescharacteristic
57#11762751C2211yescharacteristic, complemented
58#11762751C2211yescharacteristic, complemented
59#11762751C2211yescharacteristic, complemented
60#11762751C2211yescharacteristic, complemented
61#11762746C2211yescharacteristic
62#11762745C2211yescharacteristic
63#11762745C2211yescharacteristic
64#11762745C2211yescharacteristic, complemented
65#11762745C2211yescharacteristic, complemented
66#11762743C2211yescharacteristic, complemented
67#11762743C2211yescharacteristic, complemented
68#11762743C2211yescharacteristic, complemented
69#11762742C2211yescharacteristic, complemented
70#11762742C2211yescharacteristic, complemented
71#11762741C2211yescharacteristic, complemented
72#11762741C2211yescharacteristic, complemented
73#11762740C2211yescharacteristic, complemented
74#11762738C2211yescharacteristic
75#11762737C2211yescharacteristic, complemented
76#11762734C2211yescharacteristic, complemented
77#11762734C2211yescharacteristic, complemented
78#11762733C2211yescharacteristic, complemented
79#11762732C2211yescharacteristic
80#11762732C2211yescharacteristic
81#11762732C2211yescharacteristic, complemented
82#11762732C2211yescharacteristic, complemented
83#11762732C2211yescharacteristic, complemented
84#11762731C2211yescharacteristic
85#11762731C2211yescharacteristic, complemented
86#11762731C2211yescharacteristic, complemented
87#11762727C2211yescharacteristic
88#11762727C2211yescharacteristic
89#11762725C2211yescharacteristic, complemented
90#11762725C2211yescharacteristic, complemented
91#11762724C2211yescharacteristic
92#11762724C2211yescharacteristic
93#11762724C2211yescharacteristic
94#11762724C2211yescharacteristic, complemented
95#11762724C2211yescharacteristic, complemented
96#11762724C2211yescharacteristic, complemented
97#11762717C2211yescharacteristic
98#11762717C2211yescharacteristic
99#11762712C2211yescharacteristic
100#11762712C2211yescharacteristic
101#11762709C2211yescharacteristic
102#11762709C2211yescharacteristic
103#11762709C2211yescharacteristic
104#11762707C2211yescharacteristic, complemented
105#11762706C2211yescharacteristic, complemented
106#11762706C2211yescharacteristic, complemented
107#11762705C2211yescharacteristic, complemented
108#11762703C2211yescharacteristic, complemented
109#11762702C2211yescharacteristic
110#11762701C2211yescharacteristic, complemented
111#11762701C2211yescharacteristic, complemented
112#11762701C2211yescharacteristic, complemented
113#11762700C2211yescharacteristic
114#11762699C2211yescharacteristic
115#11762698C2211yescharacteristic
116#11762697C2211yescharacteristic, complemented
117#11762696C2211yescharacteristic, complemented
118#11762694C2211yescharacteristic, complemented
119#11762692C2211yescharacteristic, complemented
120#11762692C2211yescharacteristic, complemented
121#11762692C2211yescharacteristic, complemented
122#11762691C2211yescharacteristic, complemented
123#11762689C2211yescharacteristic
124#11762689C2211yescharacteristic
125#11762689C2211yescharacteristic, complemented
126#11762688C2211yescharacteristic
127#11762687C2211yescharacteristic
128#11762687C2211yescharacteristic
129#11762687C2211yescharacteristic
130#11762687C2211yescharacteristic
131#11762686C2211yescharacteristic, complemented
132#11762685C2211yescharacteristic
133#11762685C2211yescharacteristic
134#11762685C2211yescharacteristic
135#11762685C2211yescharacteristic
136#11762685C2211yescharacteristic
137#11762685C2211yescharacteristic
138#11762684C2211yescharacteristic
139#11762684C2211yescharacteristic
140#11762683C2211yescharacteristic
141#11762683C2211yescharacteristic
142#11762683C2211yescharacteristic
143#11762683C2211yescharacteristic
144#11762683C2211yescharacteristic
145#11762683C2211yescharacteristic
146#11762682C2211yescharacteristic
147#11762682C2211yescharacteristic
148#11762682C2211yescharacteristic, complemented
149#11762682C2211yescharacteristic, complemented
150#11762681C2211yescharacteristic
151#11762681C2211yescharacteristic, complemented
152#11762680C2211yescharacteristic
153#11762680C2211yescharacteristic
154#11762675C2211yescharacteristic, complemented
155#11762673C2211yescharacteristic, complemented
156#11762671C2211yescharacteristic
157#11762671C2211yescharacteristic
158#11762671C2211yescharacteristic
159#11762671C2211yescharacteristic, complemented
160#11762668C2211yescharacteristic
161#11762668C2211yescharacteristic
162#11762668C2211yescharacteristic
163#11762668C2211yescharacteristic, complemented
164#11762667C2211yescharacteristic
165#11762667C2211yescharacteristic, complemented
166#11762666C2211yescharacteristic
167#11762666C2211yescharacteristic, complemented
168#11762664C2211yescharacteristic
169#11762656C2211yescharacteristic
170#95×D17C2211yescharacteristic
171#95×D17C2211yescharacteristic
172C17×#400C2211yescharacteristic, complemented
173C17×#397C2211yescharacteristic, complemented
174C17×#397C2211yescharacteristic, complemented
175C17×#396C2211yescharacteristic, complemented
176C17×#394C2211yescharacteristic
177C17×#392C2211yescharacteristic
178C17×#390C2211yescharacteristic, complemented
179C17×#388C2211yescharacteristic
180C17×#386C2211yescharacteristic
181C17×#386C2211yescharacteristic
182C17×#386C2211yescharacteristic
183C17×#386C2211yescharacteristic, complemented
184C17×#385C2211yescharacteristic
185C17×#383C2211yescharacteristic, complemented
186C17×#381C2211yescharacteristic, complemented
187C24×D17C2311yescharacteristic
188C22×D4×C17C2311yescharacteristic
189C22×D4×C17C2311yescharacteristic
190C22×D4×C17C2311yescharacteristic
191C23×C4×C17C2311yescharacteristic
192C23×C4×C17C2311yescharacteristic
193C22×C22⋊D17C2311yescharacteristic
194C22×C22⋊D17C2311yescharacteristic
195C22×C22⋊D17C2311yescharacteristic
196C22×C22⋊D17C2311yescharacteristic
197C22×C22⋊D17C2311yescharacteristic
198C22×C22⋊D17C2311yescharacteristic
199C22×C22⋊D17C2311yescharacteristic
200C23×Dic17C2311yescharacteristic
201C23×Dic17C2311yescharacteristic
202C22×D68C2311yescharacteristic
203C22×D68C2311yescharacteristic
204C22×C4×D17—42no—
205C22×C4×D17—42no—
206C22×C4×D17—42no—
207C22×C4×D17C2311yescharacteristic
208C22×C4×D17C2311yescharacteristic
209C22×C4×D17C2311yescharacteristic
210C22×C4×D17C2311yescharacteristic
211C22×C4×D17C2311yescharacteristic
212C22×C4×D17C2311yescharacteristic
213C22×C4×D17C2311yescharacteristic
214C22×C4×D17C2311yescharacteristic
215C22×C4×D17C2311yescharacteristic
216C2×C4⋊C4×C17C2311yescharacteristic
217C2×C4⋊C4×C17C2311yescharacteristic
218C2×C4⋊C4×C17C2311yescharacteristic
219C2×C4⋊C4×C17C2311yescharacteristic
220C2×C22⋊C4×C17C2311yescharacteristic
221C2×C22⋊C4×C17C2311yescharacteristic
222C2×C22⋊C4×C17C2311yescharacteristic
223C2×C22⋊C4×C17C2311yescharacteristic
224C2×C22⋊C4×C17C2311yescharacteristic
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×C42×C17C2311yescharacteristic
234C2×C22⋊Dic17C2311yescharacteristic
235C2×C22⋊Dic17C2311yescharacteristic
236C2×C22⋊Dic17C2311yescharacteristic
237C2×C22⋊Dic17C2311yescharacteristic
238C2×C22⋊Dic17C2311yescharacteristic
239C2×C22⋊Dic17C2311yescharacteristic
240C2×C22⋊Dic17C2311yescharacteristic
241C2×C22⋊Dic17C2311yescharacteristic
242C2×C22⋊Dic17C2311yescharacteristic
243C2×C22⋊Dic17C2311yescharacteristic
244C2×C22⋊Dic17C2311yescharacteristic
245C2×C22⋊Dic17C2311yescharacteristic
246C2×C22⋊Dic17C2311yescharacteristic
247C2×C22⋊Dic17C2311yescharacteristic
248#10587625—42no—
249#10587624—24no—
250#10587624—42no—
251#10587623—42no—
252#10587623—42no—
253#10587616—42no—
254C4×C22⋊D17—42no—
255C2×#63227C2311yescharacteristic
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×C4⋊Dic17C2311yescharacteristic
279C2×C4⋊Dic17C2311yescharacteristic
280C2×C4⋊Dic17C2311yescharacteristic
281C2×C4⋊Dic17C2311yescharacteristic
282C2×C4⋊Dic17C2311yescharacteristic
283C2×C4⋊Dic17C2311yescharacteristic
284C2×C4⋊Dic17C2311yescharacteristic
285C2×C4⋊Dic17C2311yescharacteristic
286C2×C4⋊Dic17C2311yescharacteristic
287C2×C4⋊Dic17C2311yescharacteristic
288C2×C4⋊Dic17C2311yescharacteristic
289C2×#63225C2311yescharacteristic
290C2×#63225C2311yescharacteristic
291C2×#63225C2311yescharacteristic
292C2×#63225C2311yescharacteristic
293C2×#63225C2311yescharacteristic
294C2×#63225C2311yescharacteristic
295C2×#63225C2311yescharacteristic
296C2×#63225C2311yescharacteristic
297C2×#63225C2311yescharacteristic
298C2×#63225C2311yescharacteristic
299C2×#63225C2311yescharacteristic
300C2×#63225C2311yescharacteristic
301C2×#63225C2311yescharacteristic
302C2×#63225C2311yescharacteristic
303C2×#63225C2311yescharacteristic
304C2×#63225C2311yescharacteristic
305C2×#63225C2311yescharacteristic
306C2×#63225C2311yescharacteristic
307C2×#63225C2311yescharacteristic
308C2×C4×Dic17C2311yescharacteristic
309C2×C4×Dic17C2311yescharacteristic
310C2×C4×Dic17C2311yescharacteristic
311C2×C4×Dic17C2311yescharacteristic
312#10587580—42no—
313C4⋊C4×D17—42no—
314C4⋊C4×D17—42no—
315#10587575—42no—
316#10587572—42no—
317#10587570—42no—
318#10587570—42no—
319#10587570—42no—
320#10587569—42no—
321#10587569—42no—
322#10587569—42no—
323#10587569—42no—
324#10587568—42no—
325#10587567—42no—
326C22⋊C4×D17—24no—
327C22⋊C4×D17—42no—
328C4×D68—24no—
329C17×#95C2311yescharacteristic
330C17×#95C2311yescharacteristic
331C17×#95C2311yescharacteristic
332C17×#95C2311yescharacteristic
333C17×#95C2311yescharacteristic
334C17×#95C2311yescharacteristic
335C17×#95C2311yescharacteristic
336C17×#95C2311yescharacteristic
337C17×#95C2311yescharacteristic
338C17×#95C2311yescharacteristic
339C17×#95C2311yescharacteristic
340C17×#95C2311yescharacteristic
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
363#10587502C2311yescharacteristic
364#10587502C2311yescharacteristic
365#10587502C2311yescharacteristic
366#10587502C2311yescharacteristic
367#10587502C2311yescharacteristic
368#10587502C2311yescharacteristic
369C24×C17C2411yescharacteristic
370C24×C17C2411yescharacteristic
371C24×C17C2411yescharacteristic
372C23×D17—22no—
373C23×D17—22no—
374C23×D17—22no—
375C23×D17—22no—
376C23×D17—22no—
377C23×D17—41no—
378C23×D17—41no—
379C23×D17C2411yescharacteristic
380C23×D17C2411yescharacteristic
381C23×D17C2411yescharacteristic
382C2×D4×C17—22no—
383C2×D4×C17—22no—
384C2×D4×C17—22no—
385C2×D4×C17—41no—
386C2×D4×C17—41no—
387C2×D4×C17—41no—
388C2×D4×C17—41no—
389C2×D4×C17—41no—
390C2×D4×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×C17C2411yescharacteristic
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
409C2×C22⋊D17—22no—
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—41no—
420C2×C22⋊D17—41no—
421C2×C22⋊D17—41no—
422C2×C22⋊D17—41no—
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—
430C22×Dic17—22no—
431C22×Dic17—41no—
432C22×Dic17—41no—
433C22×Dic17—41no—
434C22×Dic17—41no—
435C22×Dic17—41no—
436C22×Dic17C2411yescharacteristic
437C22×Dic17C2411yescharacteristic
438C22×Dic17C2411yescharacteristic
439C22×Dic17C2411yescharacteristic
440C22×Dic17C2411yescharacteristic
441C22×Dic17C2411yescharacteristic
442C22×Dic17C2411yescharacteristic
443C22×Dic17C2411yescharacteristic
444C22×Dic17C2411yescharacteristic
445C22×Dic17C2411yescharacteristic
446C22×Dic17C2411yescharacteristic
447C22×Dic17C2411yescharacteristic
448C22×Dic17C2411yescharacteristic
449C2×D68—22no—
450C2×D68—22no—
451C2×D68—22no—
452C2×D68—22no—
453C2×D68—41no—
454C2×D68—41no—
455C2×C4×D17—22no—
456C2×C4×D17—22no—
457C2×C4×D17—22no—
458C2×C4×D17—22no—
459C2×C4×D17—22no—
460C2×C4×D17—22no—
461C2×C4×D17—22no—
462C2×C4×D17—22no—
463C2×C4×D17—22no—
464C2×C4×D17—22no—
465C2×C4×D17—22no—
466C2×C4×D17—22no—
467C2×C4×D17—41no—
468C2×C4×D17—41no—
469C2×C4×D17—41no—
470C2×C4×D17—41no—
471C2×C4×D17—41no—
472C2×C4×D17—41no—
473C2×C4×D17—41no—
474C2×C4×D17—41no—
475C2×C4×D17—416no—
476C2×C4×D17—41no—
477C2×C4×D17—41no—
478C2×C4×D17—41no—
479C2×C4×D17—41no—
480C2×C4×D17—41no—
481C2×C4×D17—41no—
482C2×C4×D17#4114yes—
483C4⋊C4×C17—41no—
484C4⋊C4×C17—41no—
485C4⋊C4×C17—41no—
486C4⋊C4×C17—41no—
487C22⋊C4×C17—22no—
488C22⋊C4×C17—22no—
489C22⋊C4×C17—41no—
490C22⋊C4×C17—41no—
491C22⋊C4×C17—41no—
492C22⋊C4×C17—41no—
493C22⋊C4×C17—41no—
494C22⋊C4×C17—41no—
495C22⋊C4×C17—41no—
496C22⋊C4×C17—41no—
497C22⋊C4×C17—41no—
498C22⋊C4×C17—41no—
499C22⋊C4×C17—41no—
500C42×C17—22no—
501C22⋊Dic17—22no—
502C22⋊Dic17—22no—
503C22⋊Dic17—22no—
504C22⋊Dic17—22no—
505C22⋊Dic17—41no—
506C22⋊Dic17—41no—
507C22⋊Dic17—41no—
508C22⋊Dic17—41no—
509C22⋊Dic17—41no—
510C22⋊Dic17—41no—
511C22⋊Dic17—41no—
512C22⋊Dic17—41no—
513C22⋊Dic17—41no—
514C22⋊Dic17—41no—
515#63227—22no—
516#63227—22no—
517#63227—22no—
518#63227—22no—
519#63227—22no—
520#63227—22no—
521#63227—22no—
522#63227—22no—
523#63227—22no—
524#63227—22no—
525#63227—22no—
526#63227—41no—
527#63227—41no—
528#63227—41no—
529#63227—41no—
530#63227—41no—
531#63227—41no—
532#63227—41no—
533#63227—41no—
534#63227—41no—
535#63227—41no—
536#63227—41no—
537#63227—41no—
538C4⋊Dic17—22no—
539C4⋊Dic17—22no—
540C4⋊Dic17—22no—
541C4⋊Dic17—22no—
542C4⋊Dic17—41no—
543C4⋊Dic17—41no—
544C4⋊Dic17—41no—
545C4⋊Dic17—41no—
546C4⋊Dic17—41no—
547C4⋊Dic17—41no—
548C4⋊Dic17—41no—
549#63225—22no—
550#63225—22no—
551#63225—41no—
552#63225—41no—
553#63225—41no—
554#63225—41no—
555#63225—41no—
556#63225—41no—
557#63225—41no—
558#63225—41no—
559#63225—41no—
560#63225—41no—
561#63225—41no—
562#63225—41no—
563#63225—41no—
564#63225—41no—
565#63225—41no—
566#63225—41no—
567#63225—41no—
568C4×Dic17—41no—
569C4×Dic17—41no—
570C4×Dic17—41no—
571C4×Dic17—41no—
572#36777—171nomaximal, Sylow
573C23×C17—21no—
574C23×C17—21no—
575C23×C17—21no—
576C23×C17—21no—
577C23×C17—21no—
578C23×C17—21no—
579C23×C17—21no—
580C23×C17—21no—
581C23×C17—21no—
582C23×C17—21no—
583C23×C17—21no—
584C23×C17—21no—
585C23×C17—21no—
586C23×C17—21no—
587C23×C17—21no—
588C23×C17—21no—
589C23×C17—21no—
590C23×C17—21no—
591C23×C17—21no—
592C23×C17—21no—
593C23×C172−1+412yes—
594C23×C17C2511yescharacteristic
595C22×D17—21no—
596C22×D17—21no—
597C22×D17—21no—
598C22×D17—21no—
599C22×D17—28no—
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—21no—
610C22×D17—21no—
611C22×D17—21no—
612C22×D17—21no—
613C22×D17—44no—
614C22×D17—44no—
615C22×D17—44no—
616C22×D17—44no—
617C22×D17—44no—
618C22×D17—44no—
619C22×D17C2×#4112yes—
620C22×D17H(5,𝔽2)12yes—
621C22×D17H(5,𝔽2)12yes—
622C22×D17H(5,𝔽2)12yes—
623D4×C17—82no—
624D4×C17—82no—
625D4×C17—82no—
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—21no—
653C2×C4×C17—21no—
654C2×C4×C17—21no—
655C2×C4×C17—21no—
656C2×C4×C17—21no—
657C2×C4×C17—21no—
658C2×C4×C17—21no—
659C2×C4×C17—21no—
660C2×C4×C17—21no—
661C2×C4×C17—44no—
662C2×C4×C17—82no—
663C2×C4×C17C2×#4112yes—
664C22⋊D17—44no—
665C22⋊D17—44no—
666C22⋊D17—82no—
667C22⋊D17—82no—
668C22⋊D17—82no—
669C22⋊D17—82no—
670C22⋊D17—82no—
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—21no—
704C2×Dic17—21no—
705C2×Dic17—21no—
706C2×Dic17—21no—
707C2×Dic17—21no—
708C2×Dic17—44no—
709C2×Dic17—82no—
710C2×Dic17C2×#4112yes—
711C2×Dic17H(5,𝔽2)12yes—
712D68—44no—
713D68—82no—
714C4×D17—44no—
715C4×D17—44no—
716C4×D17—44no—
717C4×D17—44no—
718C4×D17—44no—
719C4×D17—44no—
720C4×D17—82no—
721C4×D17—82no—
722C4×D17—82no—
723#2849—171no—
724#2847—171no—
725#2780—171no—
726#2780—171no—
727#2768—171no—
728#2761—171no—
729#2753—171no—
730#2749D1711yescharacteristic, complemented
731#2748—171no—
732#2743—171no—
733#2738—171no—
734#2711—171no—
735#2707—171no—
736#2706—171no—
737#2701—171no—
738#2701—171no—
739#2688—171no—
740#2671—171no—
741#2623—171no—
742#2618—171no—
743#2539—171no—
744#2534—171no—
745#2442—171no—
746#2425—171no—
747#2424—171no—
748#2419—171no—
749#2418—171no—
750#2416—171no—
751#2325—171no—
752#2318—171no—
753C2×#385—171no—
754C22×C17—22no—
755C22×C17—22no—
756C22×C17—22no—
757C22×C17—41no—
758C22×C17—41no—
759C22×C17—41no—
760C22×C17—41no—
761C22×C17—41no—
762C22×C17—41no—
763C22×C17—41no—
764C22×C17—41no—
765C22×C17—41no—
766C22×C17—41no—
767C22×C17—41no—
768C22×C17—41no—
769C22×C17—41no—
770C22×C17—41no—
771C22×C17—41no—
772C22×C17—41no—
773C22×C17—41no—
774C22×C17—41no—
775C22×C17C22×#4111yescharacteristic
776C22×C17C2×H(5,𝔽2)11yescharacteristic
777C22×C17C2×H(5,𝔽2)11yescharacteristic
778C22×C17C2×H(5,𝔽2)11yescharacteristic
779C22×C17C2×H(5,𝔽2)11yescharacteristic
780C22×C17C2×2−1+411yescharacteristic
781C22×C17#58511yescharacteristic
782C2×D17—22no—
783C2×D17—22no—
784C2×D17—22no—
785C2×D17—22no—
786C2×D17—22no—
787C2×D17—22no—
788C2×D17—22no—
789C2×D17—22no—
790C2×D17—22no—
791C2×D17—416no—
792C2×D17—41no—
793C2×D17—41no—
794C2×D17—41no—
795C2×D17—41no—
796C2×D17—41no—
797C2×D17—41no—
798C2×D17—41no—
799C2×D17—41no—
800C2×D17—41no—
801C2×D17—41no—
802C2×D17—41no—
803C2×D17#54014yes—
804C4×C17—22no—
805C4×C17—41no—
806C4×C17—41no—
807C4×C17—41no—
808C4×C17—41no—
809C4×C17—41no—
810C4×C17—41no—
811C4×C17—41no—
812C4×C17—41no—
813C4×C17—41no—
814C4×C17—41no—
815C4×C17—41no—
816Dic17—22no—
817Dic17—22no—
818Dic17—41no—
819Dic17—41no—
820Dic17—41no—
821Dic17—41no—
822Dic17—41no—
823Dic17—41no—
824Dic17—41no—
825Dic17—41no—
826Dic17—41no—
827Dic17—41no—
828Dic17—41no—
829C24×C4—171no—
830C2×#125—171no—
831C2×#123—171no—
832C2×#123—171no—
833C2×#123—171no—
834C2×#123—171no—
835C2×#123—171no—
836C2×#123—171no—
837C2×#121—171no—
838C2×#121—171no—
839C2×#121—171no—
840C2×#121—171no—
841C2×#121—171no—
842C2×#121—171no—
843C2×#121—171no—
844C2×#120—171no—
845C2×#120—171no—
846C2×#120—171no—
847C2×C4×D4—171no—
848C2×C4×D4—171no—
849C2×C4×D4—171no—
850C22×C4⋊C4—171no—
851C22×C4⋊C4—171no—
852C22×C22⋊C4—171no—
853C22×C22⋊C4—171no—
854#400—171no—
855#400—171no—
856#400—171no—
857#400—171no—
858#400C2×D1711yescharacteristic, complemented
859#399—171no—
860#399—171no—
861#399—171no—
862#399—171no—
863#399—171no—
864#398—171no—
865#398—171no—
866#398—171no—
867#398—171no—
868#398—171no—
869#398—171no—
870#398—171no—
871#398—171no—
872#397—171no—
873#397—171no—
874#397—171no—
875#397—171no—
876#397C2×D1711yescharacteristic, complemented
877#397C2×D1711yescharacteristic, complemented
878#396—171no—
879#396—171no—
880#396—171no—
881#396—171no—
882#396—171no—
883#396—171no—
884#396—171no—
885#396—171no—
886#396—171no—
887#396C2×D1711yescharacteristic, complemented
888#394—171no—
889#394—171no—
890#394—171no—
891#394—171no—
892#394—171no—
893#394—171no—
894#394—171no—
895#394—171no—
896#394—171no—
897#394—171no—
898#394C2×D1711yescharacteristic
899#392—171no—
900#392—171no—
901#392C2×D1711yescharacteristic
902#390—171no—
903#390—171no—
904#390—171no—
905#390—171no—
906#390—171no—
907#390C2×D1711yescharacteristic, complemented
908#389—171no—
909#389—171no—
910#389—171no—
911#389—171no—
912#388—171no—
913#388—171no—
914#388—171no—
915#388—171no—
916#388—171no—
917#388—171no—
918#388—171no—
919#388—171no—
920#388—171no—
921#388C2×D1711yescharacteristic
922#387—171no—
923#387—171no—
924#387—171no—
925#387—171no—
926#387—171no—
927#387—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#386—171no—
943#386C2×D1711yescharacteristic
944#386C2×D1711yescharacteristic
945#386C2×D1711yescharacteristic
946#386C2×D1711yescharacteristic, complemented
947#385—171no—
948#385—171no—
949#385—171no—
950#385—171no—
951#385—171no—
952#385—171no—
953#385—171no—
954#385—171no—
955#385—171no—
956#385—171no—
957#385—171no—
958#385—171no—
959#385—171no—
960#385—171no—
961#385—171no—
962#385—171no—
963#385C2×D1711yescharacteristic
964#383C2×D1711yescharacteristic, complemented
965#382—171no—
966#382—171no—
967#381—171no—
968#381—171no—
969#381—171no—
970#381—171no—
971#381C2×D1711yescharacteristic, complemented
972#380—171no—
973#380—171no—
974#380—171no—
975#380—171no—
976#380—171no—
977#380—171no—
978#380—171no—
979#380—171no—
980#379—171no—
981C4×C22⋊C4—171no—
982C2×#95—171no—
983C2×#95—171no—
984C2×C17—42no—
985C2×C17—81no—
986C2×C17—81no—
987C2×C17C2×#54011yescharacteristic
988C2×C17#349211yescharacteristic
989C2×C17#350511yescharacteristic
990C2×C17#353211yescharacteristic
991C2×C17#353411yescharacteristic
992C2×C17#353511yescharacteristic
993C2×C17#353611yescharacteristic
994D17—24no—
995D17—42no—
996D17—81no—
997C25—171no—
998C22×D4—171no—
999C22×D4—171no—
1000C22×D4—171no—
1001C22×D4—171no—
1002C22×D4—171no—
1003C22×D4—171no—
1004C22×D4—171no—
1005C22×D4—171no—
1006C22×D4—171no—
1007C22×D4C22×D1711yescharacteristic
1008C22×D4C22×D1711yescharacteristic
1009C22×D4C22×D1711yescharacteristic
1010C23×C4—171no—
1011C23×C4—171no—
1012C23×C4—171no—
1013C23×C4—171no—
1014C23×C4—171no—
1015C23×C4—171no—
1016C23×C4—171no—
1017C23×C4—171no—
1018C23×C4—171no—
1019C23×C4—171no—
1020C23×C4—171no—
1021C23×C4—682no—
1022C23×C4—682no—
1023C23×C4—682no—
1024C23×C4C22×D1711yescharacteristic
1025C23×C4C22×D1711yescharacteristic
1026#125—682no—
1027#123—682no—
1028#123—682no—
1029#123—682no—
1030#123—682no—
1031#123—682no—
1032#123—682no—
1033#121—344no—
1034#121—682no—
1035#121—682no—
1036#121—682no—
1037#121—682no—
1038#121—682no—
1039#121—682no—
1040#120—682no—
1041#120—682no—
1042#120—682no—
1043C4×D4—344no—
1044C4×D4—682no—
1045C4×D4—682no—
1046C2×C4⋊C4—171no—
1047C2×C4⋊C4—171no—
1048C2×C4⋊C4—171no—
1049C2×C4⋊C4—171no—
1050C2×C4⋊C4—171no—
1051C2×C4⋊C4—171no—
1052C2×C4⋊C4—171no—
1053C2×C4⋊C4—171no—
1054C2×C4⋊C4—171no—
1055C2×C4⋊C4—171no—
1056C2×C4⋊C4—171no—
1057C2×C4⋊C4—171no—
1058C2×C4⋊C4—171no—
1059C2×C4⋊C4—171no—
1060C2×C4⋊C4—171no—
1061C2×C4⋊C4—171no—
1062C2×C4⋊C4—171no—
1063C2×C4⋊C4—171no—
1064C2×C4⋊C4—171no—
1065C2×C4⋊C4—171no—
1066C2×C4⋊C4—171no—
1067C2×C4⋊C4—171no—
1068C2×C4⋊C4—171no—
1069C2×C4⋊C4—171no—
1070C2×C4⋊C4—171no—
1071C2×C4⋊C4—171no—
1072C2×C4⋊C4—171no—
1073C2×C4⋊C4—171no—
1074C2×C4⋊C4—171no—
1075C2×C4⋊C4—171no—
1076C2×C4⋊C4—682no—
1077C2×C4⋊C4—682no—
1078C2×C4⋊C4C22×D1711yescharacteristic
1079C2×C4⋊C4C22×D1711yescharacteristic
1080C2×C4⋊C4C22×D1711yescharacteristic
1081C2×C4⋊C4C22×D1711yescharacteristic
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—171no—
1095C2×C22⋊C4—171no—
1096C2×C22⋊C4—171no—
1097C2×C22⋊C4—171no—
1098C2×C22⋊C4—171no—
1099C2×C22⋊C4—171no—
1100C2×C22⋊C4—171no—
1101C2×C22⋊C4—171no—
1102C2×C22⋊C4—171no—
1103C2×C22⋊C4—171no—
1104C2×C22⋊C4—171no—
1105C2×C22⋊C4—171no—
1106C2×C22⋊C4—171no—
1107C2×C22⋊C4—171no—
1108C2×C22⋊C4—171no—
1109C2×C22⋊C4—171no—
1110C2×C22⋊C4—171no—
1111C2×C22⋊C4—171no—
1112C2×C22⋊C4—171no—
1113C2×C22⋊C4—171no—
1114C2×C22⋊C4—171no—
1115C2×C22⋊C4—171no—
1116C2×C22⋊C4—171no—
1117C2×C22⋊C4—171no—
1118C2×C22⋊C4—171no—
1119C2×C22⋊C4—344no—
1120C2×C22⋊C4—682no—
1121C2×C22⋊C4C22×D1711yescharacteristic
1122C2×C22⋊C4C22×D1711yescharacteristic
1123C2×C22⋊C4C22×D1711yescharacteristic
1124C2×C22⋊C4C22×D1711yescharacteristic
1125C2×C22⋊C4C22×D1711yescharacteristic
1126C2×C22⋊C4C22×D1711yescharacteristic
1127C2×C22⋊C4C22×D1711yescharacteristic
1128C2×C22⋊C4C22×D1711yescharacteristic
1129C2×C22⋊C4C22×D1711yescharacteristic
1130C2×C22⋊C4C22×D1711yescharacteristic
1131C2×C22⋊C4C22×D1711yescharacteristic
1132C2×C22⋊C4C22×D1711yescharacteristic
1133C2×C22⋊C4C22×D1711yescharacteristic
1134C2×C42—171no—
1135C2×C42—171no—
1136C2×C42—171no—
1137C2×C42—171no—
1138C2×C42C22×D1711yescharacteristic
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#95—171no—
1157#95—171no—
1158#95—171no—
1159#95—171no—
1160#95—171no—
1161#95—171no—
1162#95—171no—
1163#95—171no—
1164#95—171no—
1165#95—171no—
1166#95—171no—
1167#95C22×D1711yescharacteristic
1168#95C22×D1711yescharacteristic
1169#95C22×D1711yescharacteristic
1170#95C22×D1711yescharacteristic
1171#95C22×D1711yescharacteristic
1172#95C22×D1711yescharacteristic
1173#95C22×D1711yescharacteristic
1174#95C22×D1711yescharacteristic
1175#95C22×D1711yescharacteristic
1176#95C22×D1711yescharacteristic
1177#95C22×D1711yescharacteristic
1178#95C22×D1711yescharacteristic
1179C17#3677711yescharacteristic, complemented, Sylow
1180C24—171no—
1181C24—171no—
1182C24—171no—
1183C24—342no—
1184C24—342no—
1185C24—342no—
1186C24—342no—
1187C24—342no—
1188C24—681no—
1189C24—681no—
1190C24C23×D1711yescharacteristic
1191C24C23×D1711yescharacteristic
1192C24C23×D1711yescharacteristic
1193C2×D4—22no—
1194C2×D4—22no—
1195C2×D4—22no—
1196C2×D4—41no—
1197C2×D4—41no—
1198C2×D4—41no—
1199C2×D4—41no—
1200C2×D4—41no—
1201C2×D4—41no—
1202C2×D4—342no—
1203C2×D4—342no—
1204C2×D4—342no—
1205C2×D4—342no—
1206C2×D4—342no—
1207C2×D4—342no—
1208C2×D4—342no—
1209C2×D4—342no—
1210C2×D4—342no—
1211C2×D4—342no—
1212C2×D4—342no—
1213C2×D4—342no—
1214C2×D4—342no—
1215C2×D4—342no—
1216C2×D4—681no—
1217C2×D4—681no—
1218C2×D4—681no—
1219C2×D4—681no—
1220C2×D4—681no—
1221C2×D4—681no—
1222C2×D4—681no—
1223C2×D4—681no—
1224C2×D4—681no—
1225C2×D4—681no—
1226C2×D4—681no—
1227C2×D4—681no—
1228C2×D4—681no—
1229C22×C4—41no—
1230C22×C4—41no—
1231C22×C4—41no—
1232C22×C4—41no—
1233C22×C4—41no—
1234C22×C4—41no—
1235C22×C4—171no—
1236C22×C4—171no—
1237C22×C4—174no—
1238C22×C4—171no—
1239C22×C4—171no—
1240C22×C4—171no—
1241C22×C4—171no—
1242C22×C4—171no—
1243C22×C4—171no—
1244C22×C4—171no—
1245C22×C4—171no—
1246C22×C4—171no—
1247C22×C4—171no—
1248C22×C4—171no—
1249C22×C4—342no—
1250C22×C4—342no—
1251C22×C4—342no—
1252C22×C4—342no—
1253C22×C4—342no—
1254C22×C4—342no—
1255C22×C4—342no—
1256C22×C4—342no—
1257C22×C4—342no—
1258C22×C4—342no—
1259C22×C4—342no—
1260C22×C4—342no—
1261C22×C4—342no—
1262C22×C4—681no—
1263C22×C4—681no—
1264C22×C4—681no—
1265C22×C4—681no—
1266C22×C4—681no—
1267C22×C4—681no—
1268C22×C4—681no—
1269C22×C4—681no—
1270C22×C4—681no—
1271C22×C4—681no—
1272C22×C4—681no—
1273C22×C4—681no—
1274C22×C4—681no—
1275C22×C4—681no—
1276C22×C4—6816no—
1277C22×C4—681no—
1278C22×C4—681no—
1279C22×C4—681no—
1280C22×C4—681no—
1281C22×C4—681no—
1282C22×C4C23×D1711yescharacteristic
1283C22×C4C23×D1711yescharacteristic
1284C22×C4C23×D1711yescharacteristic
1285C22×C4C23×D1711yescharacteristic
1286C22×C4C23×D1711yescharacteristic
1287C22×C4C23×D1711yescharacteristic
1288C22×C4C23×D1711yescharacteristic
1289C22×C4C23×D1711yescharacteristic
1290C22×C4C23×D1711yescharacteristic
1291C22×C4C23×D1711yescharacteristic
1292C22×C4C23×D1711yescharacteristic
1293C22×C4C23×D1711yescharacteristic
1294C4⋊C4—41no—
1295C4⋊C4—41no—
1296C4⋊C4—41no—
1297C4⋊C4—41no—
1298C4⋊C4—342no—
1299C4⋊C4—342no—
1300C4⋊C4—342no—
1301C4⋊C4—342no—
1302C4⋊C4—342no—
1303C4⋊C4—342no—
1304C4⋊C4—681no—
1305C4⋊C4—681no—
1306C4⋊C4—681no—
1307C4⋊C4—681no—
1308C4⋊C4—681no—
1309C4⋊C4—681no—
1310C4⋊C4—681no—
1311C4⋊C4—681no—
1312C4⋊C4—681no—
1313C4⋊C4—681no—
1314C4⋊C4—681no—
1315C4⋊C4—681no—
1316C4⋊C4—681no—
1317C4⋊C4—681no—
1318C4⋊C4—681no—
1319C4⋊C4—681no—
1320C4⋊C4—681no—
1321C4⋊C4—681no—
1322C4⋊C4—681no—
1323C4⋊C4—681no—
1324C4⋊C4—681no—
1325C4⋊C4—681no—
1326C4⋊C4—681no—
1327C4⋊C4—681no—
1328C22⋊C4—22no—
1329C22⋊C4—22no—
1330C22⋊C4—41no—
1331C22⋊C4—41no—
1332C22⋊C4—41no—
1333C22⋊C4—41no—
1334C22⋊C4—41no—
1335C22⋊C4—41no—
1336C22⋊C4—41no—
1337C22⋊C4—41no—
1338C22⋊C4—41no—
1339C22⋊C4—41no—
1340C22⋊C4—41no—
1341C22⋊C4—342no—
1342C22⋊C4—342no—
1343C22⋊C4—342no—
1344C22⋊C4—342no—
1345C22⋊C4—342no—
1346C22⋊C4—342no—
1347C22⋊C4—342no—
1348C22⋊C4—342no—
1349C22⋊C4—342no—
1350C22⋊C4—342no—
1351C22⋊C4—342no—
1352C22⋊C4—342no—
1353C22⋊C4—342no—
1354C22⋊C4—342no—
1355C22⋊C4—342no—
1356C22⋊C4—681no—
1357C22⋊C4—681no—
1358C22⋊C4—681no—
1359C22⋊C4—681no—
1360C22⋊C4—681no—
1361C22⋊C4—681no—
1362C22⋊C4—681no—
1363C22⋊C4—681no—
1364C22⋊C4—681no—
1365C22⋊C4—681no—
1366C22⋊C4—681no—
1367C22⋊C4—681no—
1368C22⋊C4—681no—
1369C22⋊C4—681no—
1370C22⋊C4—681no—
1371C22⋊C4—681no—
1372C22⋊C4—681no—
1373C22⋊C4—681no—
1374C22⋊C4—681no—
1375C22⋊C4—681no—
1376C22⋊C4—681no—
1377C22⋊C4—681no—
1378C42—22no—
1379C42—681no—
1380C42—681no—
1381C42—681no—
1382C42—681no—
1383C23—21no—
1384C23—21no—
1385C23—21no—
1386C23—21no—
1387C23—21no—
1388C23—21no—
1389C23—21no—
1390C23—21no—
1391C23—21no—
1392C23—21no—
1393C23—21no—
1394C23—21no—
1395C23—21no—
1396C23—21no—
1397C23—21no—
1398C23—21no—
1399C23—21no—
1400C23—21no—
1401C23—21no—
1402C23—21no—
1403C23—172no—
1404C23—172no—
1405C23—172no—
1406C23—172no—
1407C23—348no—
1408C23—341no—
1409C23—341no—
1410C23—341no—
1411C23—341no—
1412C23—341no—
1413C23—341no—
1414C23—341no—
1415C23—341no—
1416C23—341no—
1417C23—341no—
1418C23—341no—
1419C23—341no—
1420C23—341no—
1421C23—341no—
1422C23—341no—
1423C23—341no—
1424C23—341no—
1425C23—684no—
1426C23—684no—
1427C23—684no—
1428C23—684no—
1429C23—684no—
1430C23—684no—
1431C23#1058769712yes—
1432C23C24×D1711yescharacteristic
1433D4—82no—
1434D4—82no—
1435D4—82no—
1436D4—684no—
1437D4—684no—
1438D4—684no—
1439D4—1362no—
1440D4—1362no—
1441D4—1362no—
1442D4—1362no—
1443D4—1362no—
1444D4—1362no—
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—21no—
1461C2×C4—21no—
1462C2×C4—21no—
1463C2×C4—21no—
1464C2×C4—21no—
1465C2×C4—21no—
1466C2×C4—21no—
1467C2×C4—21no—
1468C2×C4—21no—
1469C2×C4—21no—
1470C2×C4—21no—
1471C2×C4—21no—
1472C2×C4—21no—
1473C2×C4—21no—
1474C2×C4—21no—
1475C2×C4—21no—
1476C2×C4—21no—
1477C2×C4—21no—
1478C2×C4—21no—
1479C2×C4—21no—
1480C2×C4—44no—
1481C2×C4—82no—
1482C2×C4—172no—
1483C2×C4—172no—
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—341no—
1504C2×C4—341no—
1505C2×C4—341no—
1506C2×C4—341no—
1507C2×C4—341no—
1508C2×C4—341no—
1509C2×C4—341no—
1510C2×C4—341no—
1511C2×C4—341no—
1512C2×C4—341no—
1513C2×C4—341no—
1514C2×C4—341no—
1515C2×C4—341no—
1516C2×C4—341no—
1517C2×C4—341no—
1518C2×C4—341no—
1519C2×C4—341no—
1520C2×C4—341no—
1521C2×C4—684no—
1522C2×C4—684no—
1523C2×C4—684no—
1524C2×C4—684no—
1525C2×C4—684no—
1526C2×C4—684no—
1527C2×C4—684no—
1528C2×C4—1362no—
1529C2×C4—1362no—
1530C2×C4—1362no—
1531C2×C4—1362no—
1532C2×C4#41×D1712yes—
1533C22—22no—
1534C22—22no—
1535C22—22no—
1536C22—41no—
1537C22—41no—
1538C22—41no—
1539C22—41no—
1540C22—41no—
1541C22—41no—
1542C22—41no—
1543C22—41no—
1544C22—41no—
1545C22—41no—
1546C22—41no—
1547C22—41no—
1548C22—41no—
1549C22—41no—
1550C22—41no—
1551C22—41no—
1552C22—41no—
1553C22—41no—
1554C22—174no—
1555C22—342no—
1556C22—342no—
1557C22—342no—
1558C22—342no—
1559C22—342no—
1560C22—342no—
1561C22—342no—
1562C22—342no—
1563C22—342no—
1564C22—6816no—
1565C22—681no—
1566C22—681no—
1567C22—681no—
1568C22—681no—
1569C22—681no—
1570C22—681no—
1571C22—681no—
1572C22—681no—
1573C22—681no—
1574C22—681no—
1575C22—681no—
1576C22C2×#41×D1711yescharacteristic
1577C22H(5,𝔽2)×D1711yescharacteristic
1578C22H(5,𝔽2)×D1711yescharacteristic
1579C22H(5,𝔽2)×D1711yescharacteristic
1580C22H(5,𝔽2)×D1711yescharacteristic
1581C22C2×#1058769711yescharacteristic
1582C22#1176364511yescharacteristic
1583C4—22no—
1584C4—41no—
1585C4—41no—
1586C4—41no—
1587C4—41no—
1588C4—41no—
1589C4—41no—
1590C4—41no—
1591C4—41no—
1592C4—41no—
1593C4—41no—
1594C4—41no—
1595C4—342no—
1596C4—342no—
1597C4—681no—
1598C4—681no—
1599C4—681no—
1600C4—681no—
1601C4—681no—
1602C4—681no—
1603C4—681no—
1604C4—681no—
1605C4—681no—
1606C4—681no—
1607C4—681no—
1608C2—42no—
1609C2—81no—
1610C2—81no—
1611C2—344no—
1612C2—682no—
1613C2—1361no—
1614C2D17×#54011yescharacteristic
1615C2#1454248811yescharacteristic
1616C2#1454261511yescharacteristic
1617C2#1454293711yescharacteristic
1618C2#1454297311yescharacteristic
1619C2#1454298011yescharacteristic
1620C2#1454300511yescharacteristic
subgroupG/H
center, FrattiniC23C24×D17
commutator, socle, cosocleC23×C17C25
FittingC17×#2749C2
hypercenter#2749D17
hypocenterC17#36777
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C23 ◁ #2749

Complements

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

NH ≅ G/Ntype
1. #14537075C2semidirect
2. #14537065C2semidirect
3. #14536429C2semidirect
4. #14536429C2semidirect
5. #14536268C2semidirect
6. #14536178C2semidirect
7. #14536055C2semidirect
8. #14535993C2semidirect
9. #14535922C2semidirect
10. #14535855C2semidirect
11. #14535543C2semidirect
12. #14535480C2semidirect
13. #14535467C2semidirect
14. #14535402C2semidirect
15. #14535397C2semidirect
16. #14535219C2semidirect
17. #14535021C2semidirect
18. #14534563C2semidirect
19. #14534531C2semidirect
20. #14533709C2semidirect
21. #14533678C2semidirect
22. #14532501C2semidirect
23. #14532338C2semidirect
24. #14532319C2semidirect
25. #14532258C2semidirect
26. #14532241C2semidirect
27. #14532227C2semidirect
28. #14531486C2semidirect
29. #14531415C2semidirect
30. D17×#385C2semidirect
31. C17×#2749C2semidirect
33. C2×#10587575C22semidirect
46. C2×#10587624C22semidirect
57. #11762751C22semidirect
58. #11762751C22semidirect
59. #11762751C22semidirect
60. #11762751C22semidirect
64. #11762745C22semidirect
65. #11762745C22semidirect
66. #11762743C22semidirect
67. #11762743C22semidirect
68. #11762743C22semidirect
69. #11762742C22semidirect
70. #11762742C22semidirect
71. #11762741C22semidirect
72. #11762741C22semidirect
73. #11762740C22semidirect
75. #11762737C22semidirect
76. #11762734C22semidirect
77. #11762734C22semidirect
78. #11762733C22semidirect
81. #11762732C22semidirect
82. #11762732C22semidirect
83. #11762732C22semidirect
85. #11762731C22semidirect
86. #11762731C22semidirect
89. #11762725C22semidirect
90. #11762725C22semidirect
94. #11762724C22semidirect
95. #11762724C22semidirect
96. #11762724C22semidirect
104. #11762707C22semidirect
105. #11762706C22semidirect
106. #11762706C22semidirect
107. #11762705C22semidirect
108. #11762703C22semidirect
110. #11762701C22semidirect
111. #11762701C22semidirect
112. #11762701C22semidirect
116. #11762697C22semidirect
117. #11762696C22semidirect
118. #11762694C22semidirect
119. #11762692C22semidirect
120. #11762692C22semidirect
121. #11762692C22semidirect
122. #11762691C22semidirect
125. #11762689C22semidirect
131. #11762686C22semidirect
148. #11762682C22semidirect
149. #11762682C22semidirect
151. #11762681C22semidirect
154. #11762675C22semidirect
155. #11762673C22semidirect
159. #11762671C22semidirect
163. #11762668C22semidirect
165. #11762667C22semidirect
167. #11762666C22semidirect
172. C17×#400C22semidirect
173. C17×#397C22semidirect
174. C17×#397C22semidirect
175. C17×#396C22semidirect
178. C17×#390C22semidirect
183. C17×#386C22semidirect
185. C17×#383C22semidirect
186. C17×#381C22semidirect
730. #2749D17semidirect
858. #400C2×D17semidirect
876. #397C2×D17semidirect
877. #397C2×D17semidirect
887. #396C2×D17semidirect
907. #390C2×D17semidirect
946. #386C2×D17semidirect
964. #383C2×D17semidirect
971. #381C2×D17semidirect
1179. C17#36777semidirect

Maximal subgroups

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

subgroupindex
#145370752
#145370652
#145364292
#145362682
#145361782
#145360552
#145359932
#145359222
#145358552
#145355432
#145354802
#145354672
#145354022
#145353972
#145352192
#145350212
#145345632
#145345312
#145337092
#145336782
#145325012
#145323382
#145323192
#145322582
#145322412
#145322272
#145314862
#145314152
D17×#3852
C17×#27492
#3677717