Finite Group Databasebeta

← D17×#2827 #17240510

Subgroups — D17×#2827 #17240510

Order 4352.

2218 conjugacy classes of subgroups.

The subgroup lattice has 1590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14536899C211yesmaximal, characteristic, complemented
2#14536898C211yesmaximal, characteristic, complemented
3#14536897C211yesmaximal, characteristic, complemented
4#14536896C211yesmaximal, characteristic, complemented
5#14536895C211yesmaximal, characteristic, complemented
6#14536894C211yesmaximal, characteristic, complemented
7#14536893C211yesmaximal, characteristic, complemented
8#14536892C211yesmaximal, characteristic, complemented
9#14536891C211yesmaximal, characteristic, complemented
10#14536890C211yesmaximal, characteristic, complemented
11#14536889C211yesmaximal, characteristic, complemented
12#14536888C211yesmaximal, characteristic, complemented
13#14536887C211yesmaximal, characteristic, complemented
14#14536886C211yesmaximal, characteristic, complemented
15#14536885C211yesmaximal, characteristic, complemented
16D17×#400C211yesmaximal, characteristic, complemented
17D17×#400C211yesmaximal, characteristic, complemented
18D17×#399C211yesmaximal, characteristic, complemented
19D17×#398C211yesmaximal, characteristic, complemented
20D17×#398C211yesmaximal, characteristic, complemented
21D17×#397C211yesmaximal, characteristic, complemented
22D17×#397C211yesmaximal, characteristic, complemented
23D17×#397C211yesmaximal, characteristic, complemented
24D17×#396C211yesmaximal, characteristic, complemented
25D17×#396C211yesmaximal, characteristic, complemented
26D17×#394C211yesmaximal, characteristic
27D17×#394C211yesmaximal, characteristic
28D17×#386C211yesmaximal, characteristic
29D17×#385C211yesmaximal, characteristic, complemented
30D17×#385C211yesmaximal, characteristic, complemented
31C17×#2827C211yesmaximal, characteristic, complemented
32C22×D4×D17C2211yescharacteristic
33C23×C4×D17C2211yescharacteristic
34C2×C4⋊C4×D17C2211yescharacteristic
35C2×C4⋊C4×D17C2211yescharacteristic
36C2×C4⋊C4×D17C2211yescharacteristic
37C2×C4⋊C4×D17C2211yescharacteristic
38C2×C4⋊C4×D17C2211yescharacteristic
39C2×C4⋊C4×D17C2211yescharacteristic
40C2×C4⋊C4×D17C2211yescharacteristic
41C2×C4⋊C4×D17C2211yescharacteristic
42C2×C4⋊C4×D17C2211yescharacteristic
43C2×C4⋊C4×D17C2211yescharacteristic
44C2×C22⋊C4×D17C2211yescharacteristic
45C2×C22⋊C4×D17C2211yescharacteristic
46C2×C22⋊C4×D17C2211yescharacteristic
47C2×C22⋊C4×D17C2211yescharacteristic
48C2×C22⋊C4×D17C2211yescharacteristic
49C2×C22⋊C4×D17C2211yescharacteristic
50C2×C22⋊C4×D17C2211yescharacteristic
51C2×C22⋊C4×D17C2211yescharacteristic
52C2×C22⋊C4×D17C2211yescharacteristic
53C2×C22⋊C4×D17C2211yescharacteristic
54C2×C22⋊C4×D17C2211yescharacteristic
55#11762751C2211yescharacteristic, complemented
56#11762751C2211yescharacteristic, complemented
57#11762751C2211yescharacteristic, complemented
58#11762751C2211yescharacteristic, complemented
59#11762750C2211yescharacteristic, complemented
60#11762750C2211yescharacteristic, complemented
61#11762750C2211yescharacteristic, complemented
62#11762750C2211yescharacteristic, complemented
63#11762749C2211yescharacteristic, complemented
64#11762749C2211yescharacteristic, complemented
65#11762748C2211yescharacteristic, complemented
66#11762748C2211yescharacteristic, complemented
67#11762747C2211yescharacteristic, complemented
68#11762747C2211yescharacteristic, complemented
69#11762746C2211yescharacteristic, complemented
70#11762745C2211yescharacteristic, complemented
71#11762745C2211yescharacteristic, complemented
72#11762745C2211yescharacteristic, complemented
73#11762744C2211yescharacteristic, complemented
74#11762744C2211yescharacteristic, complemented
75#11762744C2211yescharacteristic, complemented
76#11762743C2211yescharacteristic, complemented
77#11762743C2211yescharacteristic, complemented
78#11762743C2211yescharacteristic, complemented
79#11762743C2211yescharacteristic, complemented
80#11762742C2211yescharacteristic, complemented
81#11762742C2211yescharacteristic, complemented
82#11762742C2211yescharacteristic, complemented
83#11762742C2211yescharacteristic, complemented
84#11762741C2211yescharacteristic, complemented
85#11762741C2211yescharacteristic, complemented
86#11762740C2211yescharacteristic, complemented
87#11762740C2211yescharacteristic, complemented
88#11762739C2211yescharacteristic, complemented
89#11762739C2211yescharacteristic, complemented
90#11762738C2211yescharacteristic, complemented
91#11762738C2211yescharacteristic, complemented
92#11762738C2211yescharacteristic, complemented
93#11762738C2211yescharacteristic, complemented
94#11762738C2211yescharacteristic, complemented
95#11762738C2211yescharacteristic, complemented
96#11762737C2211yescharacteristic, complemented
97#11762737C2211yescharacteristic, complemented
98#11762737C2211yescharacteristic, complemented
99#11762737C2211yescharacteristic, complemented
100#11762737C2211yescharacteristic, complemented
101#11762737C2211yescharacteristic, complemented
102#11762736C2211yescharacteristic, complemented
103#11762736C2211yescharacteristic, complemented
104#11762736C2211yescharacteristic, complemented
105#11762735C2211yescharacteristic, complemented
106#11762735C2211yescharacteristic, complemented
107#11762735C2211yescharacteristic, complemented
108#11762734C2211yescharacteristic, complemented
109#11762734C2211yescharacteristic, complemented
110#11762734C2211yescharacteristic, complemented
111#11762733C2211yescharacteristic, complemented
112#11762733C2211yescharacteristic, complemented
113#11762732C2211yescharacteristic, complemented
114#11762732C2211yescharacteristic, complemented
115#11762732C2211yescharacteristic, complemented
116#11762732C2211yescharacteristic, complemented
117#11762732C2211yescharacteristic, complemented
118#11762732C2211yescharacteristic, complemented
119#11762731C2211yescharacteristic, complemented
120#11762731C2211yescharacteristic, complemented
121#11762731C2211yescharacteristic, complemented
122#11762731C2211yescharacteristic, complemented
123#11762731C2211yescharacteristic, complemented
124#11762731C2211yescharacteristic, complemented
125#11762727C2211yescharacteristic
126#11762727C2211yescharacteristic
127#11762726C2211yescharacteristic
128#11762726C2211yescharacteristic
129#11762725C2211yescharacteristic
130#11762725C2211yescharacteristic
131#11762725C2211yescharacteristic
132#11762725C2211yescharacteristic
133#11762724C2211yescharacteristic
134#11762724C2211yescharacteristic
135#11762724C2211yescharacteristic
136#11762724C2211yescharacteristic
137#11762723C2211yescharacteristic
138#11762723C2211yescharacteristic
139#11762689C2211yescharacteristic
140#11762688C2211yescharacteristic
141#11762687C2211yescharacteristic
142#11762687C2211yescharacteristic
143#11762686C2211yescharacteristic
144#11762685C2211yescharacteristic
145#11762685C2211yescharacteristic
146#11762684C2211yescharacteristic, complemented
147#11762684C2211yescharacteristic, complemented
148#11762683C2211yescharacteristic, complemented
149#11762683C2211yescharacteristic, complemented
150#11762683C2211yescharacteristic, complemented
151#11762683C2211yescharacteristic, complemented
152#11762682C2211yescharacteristic, complemented
153#11762682C2211yescharacteristic, complemented
154#11762681C2211yescharacteristic, complemented
155#11762681C2211yescharacteristic, complemented
156#11762680C2211yescharacteristic, complemented
157#11762680C2211yescharacteristic, complemented
158#11762680C2211yescharacteristic, complemented
159#11762680C2211yescharacteristic, complemented
160#95×D17C2211yescharacteristic
161#95×D17C2211yescharacteristic
162#95×D17C2211yescharacteristic
163#95×D17C2211yescharacteristic
164#95×D17C2211yescharacteristic
165#95×D17C2211yescharacteristic
166#95×D17C2211yescharacteristic
167#95×D17C2211yescharacteristic
168#95×D17C2211yescharacteristic
169#95×D17C2211yescharacteristic
170#95×D17C2211yescharacteristic
171#95×D17C2211yescharacteristic
172C17×#400C2211yescharacteristic, complemented
173C17×#400C2211yescharacteristic, complemented
174C17×#399C2211yescharacteristic, complemented
175C17×#398C2211yescharacteristic, complemented
176C17×#398C2211yescharacteristic, complemented
177C17×#397C2211yescharacteristic, complemented
178C17×#397C2211yescharacteristic, complemented
179C17×#397C2211yescharacteristic, complemented
180C17×#396C2211yescharacteristic, complemented
181C17×#396C2211yescharacteristic, complemented
182C17×#394C2211yescharacteristic
183C17×#394C2211yescharacteristic
184C17×#386C2211yescharacteristic
185C17×#385C2211yescharacteristic, complemented
186C17×#385C2211yescharacteristic, complemented
187C24×D17C2311yescharacteristic
188C24×D17C2311yescharacteristic
189C22×D4×C17C2311yescharacteristic
190C23×C4×C17C2311yescharacteristic
191C22×C22⋊D17C2311yescharacteristic
192C22×C22⋊D17C2311yescharacteristic
193C23×Dic17C2311yescharacteristic
194C2×D4×D17—24no—
195C2×D4×D17—42no—
196C2×D4×D17—42no—
197C22×D68C2311yescharacteristic
198C22×C4×D17—42no—
199C22×C4×D17—42no—
200C22×C4×D17—42no—
201C22×C4×D17C2311yescharacteristic
202C22×C4×D17C2311yescharacteristic
203C22×C4×D17C2311yescharacteristic
204C22×C4×D17C2311yescharacteristic
205C22×C4×D17C2311yescharacteristic
206C22×C4×D17C2311yescharacteristic
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×C4⋊C4×C17C2311yescharacteristic
221C2×C4⋊C4×C17C2311yescharacteristic
222C2×C4⋊C4×C17C2311yescharacteristic
223C2×C4⋊C4×C17C2311yescharacteristic
224C2×C4⋊C4×C17C2311yescharacteristic
225C2×C4⋊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⋊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
248C2×#63227C2311yescharacteristic
249C2×#63227C2311yescharacteristic
250C2×#63227C2311yescharacteristic
251C2×#63227C2311yescharacteristic
252C2×#63227C2311yescharacteristic
253C2×#63227C2311yescharacteristic
254C2×#63227C2311yescharacteristic
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×C4⋊Dic17C2311yescharacteristic
271C2×C4⋊Dic17C2311yescharacteristic
272C2×C4⋊Dic17C2311yescharacteristic
273C2×C4⋊Dic17C2311yescharacteristic
274C2×C4⋊Dic17C2311yescharacteristic
275C2×C4⋊Dic17C2311yescharacteristic
276C2×C4⋊Dic17C2311yescharacteristic
277C2×C4⋊Dic17C2311yescharacteristic
278C2×C4⋊Dic17C2311yescharacteristic
279C2×C4⋊Dic17C2311yescharacteristic
280C2×#63225C2311yescharacteristic
281C2×#63225C2311yescharacteristic
282C2×#63225C2311yescharacteristic
283C2×#63225C2311yescharacteristic
284C2×#63225C2311yescharacteristic
285C2×#63225C2311yescharacteristic
286C2×#63225C2311yescharacteristic
287C2×#63225C2311yescharacteristic
288C2×#63225C2311yescharacteristic
289C2×#63225C2311yescharacteristic
290C2×#63225C2311yescharacteristic
291C2×#63225C2311yescharacteristic
292C2×#63225C2311yescharacteristic
293C2×#63225C2311yescharacteristic
294C2×#63225C2311yescharacteristic
295C2×#63225C2311yescharacteristic
296C2×#63225C2311yescharacteristic
297C2×#63225C2311yescharacteristic
298C2×#63225C2311yescharacteristic
299C2×#63225C2311yescharacteristic
300C4⋊C4×D17—42no—
301C4⋊C4×D17—42no—
302C4⋊C4×D17—42no—
303C4⋊C4×D17—42no—
304C4⋊C4×D17—42no—
305C4⋊C4×D17—42no—
306C4⋊C4×D17—42no—
307C4⋊C4×D17—42no—
308C4⋊C4×D17—42no—
309C4⋊C4×D17—42no—
310C22⋊C4×D17—24no—
311C22⋊C4×D17—24no—
312C22⋊C4×D17—42no—
313C22⋊C4×D17—42no—
314C22⋊C4×D17—42no—
315C22⋊C4×D17—42no—
316C22⋊C4×D17—42no—
317C22⋊C4×D17—42no—
318C22⋊C4×D17—42no—
319C22⋊C4×D17—42no—
320C22⋊C4×D17—42no—
321C17×#95C2311yescharacteristic
322C17×#95C2311yescharacteristic
323C17×#95C2311yescharacteristic
324C17×#95C2311yescharacteristic
325C17×#95C2311yescharacteristic
326C17×#95C2311yescharacteristic
327C17×#95C2311yescharacteristic
328C17×#95C2311yescharacteristic
329C17×#95C2311yescharacteristic
330C17×#95C2311yescharacteristic
331C17×#95C2311yescharacteristic
332C17×#95C2311yescharacteristic
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
363#10587502C2311yescharacteristic
364#10587502C2311yescharacteristic
365#10587502C2311yescharacteristic
366#10587502C2311yescharacteristic
367#10587502C2311yescharacteristic
368#10587502C2311yescharacteristic
369C24×C17C2411yescharacteristic
370C24×C17C2411yescharacteristic
371C23×D17—22no—
372C23×D17—22no—
373C23×D17—22no—
374C23×D17—22no—
375C23×D17—22no—
376C23×D17—22no—
377C23×D17—22no—
378C23×D17—22no—
379C23×D17—22no—
380C23×D17—22no—
381C23×D17—22no—
382C23×D17—22no—
383C23×D17—22no—
384C23×D17#4114yes—
385C23×D17C2411yescharacteristic
386C23×D17C2411yescharacteristic
387C23×D17C2411yescharacteristic
388C2×D4×C17—22no—
389C2×D4×C17—41no—
390C2×D4×C17—41no—
391C22×C4×C17—41no—
392C22×C4×C17—41no—
393C22×C4×C17—41no—
394C22×C4×C17C2411yescharacteristic
395C22×C4×C17C2411yescharacteristic
396C22×C4×C17C2411yescharacteristic
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
407C2×C22⋊D17—22no—
408C2×C22⋊D17—22no—
409C2×C22⋊D17—41no—
410C2×C22⋊D17—41no—
411C2×C22⋊D17—41no—
412C2×C22⋊D17—41no—
413C22×Dic17—41no—
414C22×Dic17—41no—
415C22×Dic17—41no—
416C22×Dic17C2411yescharacteristic
417C22×Dic17C2411yescharacteristic
418C22×Dic17C2411yescharacteristic
419C22×Dic17C2411yescharacteristic
420C22×Dic17C2411yescharacteristic
421C22×Dic17C2411yescharacteristic
422C22×Dic17C2411yescharacteristic
423C22×Dic17C2411yescharacteristic
424C22×Dic17C2411yescharacteristic
425C22×Dic17C2411yescharacteristic
426C22×Dic17C2411yescharacteristic
427C22×Dic17C2411yescharacteristic
428C22×Dic17C2411yescharacteristic
429D4×D17—416no—
430C2×D68—22no—
431C2×D68—41no—
432C2×D68—41no—
433C2×C4×D17—22no—
434C2×C4×D17—22no—
435C2×C4×D17—22no—
436C2×C4×D17—22no—
437C2×C4×D17—22no—
438C2×C4×D17—22no—
439C2×C4×D17—22no—
440C2×C4×D17—22no—
441C2×C4×D17—22no—
442C2×C4×D17—22no—
443C2×C4×D17—22no—
444C2×C4×D17—22no—
445C2×C4×D17—22no—
446C2×C4×D17—22no—
447C2×C4×D17—22no—
448C2×C4×D17—22no—
449C2×C4×D17—22no—
450C2×C4×D17—22no—
451C2×C4×D17—22no—
452C2×C4×D17—22no—
453C2×C4×D17—22no—
454C2×C4×D17—22no—
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—22no—
468C2×C4×D17—22no—
469C2×C4×D17—22no—
470C2×C4×D17—22no—
471C2×C4×D17—22no—
472C2×C4×D17—41no—
473C2×C4×D17—41no—
474C2×C4×D17—41no—
475C2×C4×D17—41no—
476C2×C4×D17—41no—
477C2×C4×D17—41no—
478C2×C4×D17—416no—
479C4⋊C4×C17—41no—
480C4⋊C4×C17—41no—
481C4⋊C4×C17—41no—
482C4⋊C4×C17—41no—
483C4⋊C4×C17—41no—
484C4⋊C4×C17—41no—
485C4⋊C4×C17—41no—
486C4⋊C4×C17—41no—
487C4⋊C4×C17—41no—
488C4⋊C4×C17—41no—
489C22⋊C4×C17—22no—
490C22⋊C4×C17—22no—
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—
500C22⋊Dic17—22no—
501C22⋊Dic17—22no—
502C22⋊Dic17—41no—
503C22⋊Dic17—41no—
504C22⋊Dic17—41no—
505C22⋊Dic17—41no—
506C22⋊Dic17—41no—
507C22⋊Dic17—41no—
508C22⋊Dic17—41no—
509C22⋊Dic17—41no—
510C22⋊Dic17—41no—
511#63227—22no—
512#63227—22no—
513#63227—22no—
514#63227—22no—
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—
533C4⋊Dic17—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—
543#63225—41no—
544#63225—41no—
545#63225—41no—
546#63225—41no—
547#63225—41no—
548#63225—41no—
549#63225—41no—
550#63225—41no—
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—
563C2×#2827—171nomaximal, Sylow
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—21no—
576C23×C17—21no—
577C23×C17C2×#4112yes—
578C23×C17C2511yescharacteristic
579C22×D17—21no—
580C22×D17—21no—
581C22×D17—21no—
582C22×D17—21no—
583C22×D17—21no—
584C22×D17—21no—
585C22×D17—28no—
586C22×D17—28no—
587C22×D17—28no—
588C22×D17—21no—
589C22×D17—21no—
590C22×D17—21no—
591C22×D17—21no—
592C22×D17—21no—
593C22×D17—21no—
594C22×D17—21no—
595C22×D17—44no—
596C22×D17—44no—
597C22×D17—44no—
598C22×D17—44no—
599C22×D17—44no—
600C22×D17—44no—
601C22×D17—44no—
602C22×D17—44no—
603C22×D17—44no—
604C22×D17—44no—
605C22×D17—44no—
606C22×D17C2×#4112yes—
607C22×D17C2×#4112yes—
608C22×D17H(5,𝔽2)12yes—
609C22×D17H(5,𝔽2)12yes—
610C22×D17H(5,𝔽2)12yes—
611C22×D17H(5,𝔽2)12yes—
612C22×D172−1+412yes—
613C22×D172−1+412yes—
614D4×C17—44no—
615C2×C4×C17—21no—
616C2×C4×C17—21no—
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—21no—
653C2×C4×C17—21no—
654C2×C4×C17—44no—
655C22⋊D17—44no—
656C22⋊D17—44no—
657C2×Dic17—21no—
658C2×Dic17—21no—
659C2×Dic17—21no—
660C2×Dic17—21no—
661C2×Dic17—21no—
662C2×Dic17—21no—
663C2×Dic17—21no—
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—44no—
697D68—44no—
698C4×D17—44no—
699C4×D17—44no—
700C4×D17—44no—
701C4×D17—44no—
702C4×D17—44no—
703C4×D17—44no—
704C4×D17—44no—
705C4×D17—44no—
706C4×D17—44no—
707C4×D17—44no—
708C4×D17—44no—
709C4×D17—44no—
710C4×D17—44no—
711C4×D17—44no—
712C4×D17—44no—
713#2827—171no—
714#2827—171no—
715#2827—171no—
716#2827—171no—
717#2827—171no—
718#2827—171no—
719#2827—171no—
720#2827—171no—
721#2827—171no—
722#2827—171no—
723#2827—171no—
724#2827—171no—
725#2827—171no—
726#2827—171no—
727#2827—171no—
728#2827D1711yescharacteristic, direct product factor
729C2×#400—171no—
730C2×#400—171no—
731C2×#399—171no—
732C2×#398—171no—
733C2×#398—171no—
734C2×#397—171no—
735C2×#397—171no—
736C2×#397—171no—
737C2×#396—171no—
738C2×#396—171no—
739C2×#394—171no—
740C2×#394—171no—
741C2×#386—171no—
742C2×#385—171no—
743C2×#385—171no—
744C22×C17—22no—
745C22×C17—22no—
746C22×C17—22no—
747C22×C17—41no—
748C22×C17—41no—
749C22×C17—41no—
750C22×C17—41no—
751C22×C17—41no—
752C22×C17—41no—
753C22×C17—41no—
754C22×C17—41no—
755C22×C17—41no—
756C22×C17—41no—
757C22×C17—41no—
758C22×C17C22×#4111yescharacteristic
759C22×C17C2×H(5,𝔽2)11yescharacteristic
760C22×C17C2×H(5,𝔽2)11yescharacteristic
761C22×C17C2×H(5,𝔽2)11yescharacteristic
762C22×C17C2×H(5,𝔽2)11yescharacteristic
763C22×C17C2×2−1+411yescharacteristic
764C22×C17C2×2−1+411yescharacteristic
765C2×D17—22no—
766C2×D17—22no—
767C2×D17—22no—
768C2×D17—41no—
769C2×D17—41no—
770C2×D17—41no—
771C2×D17—41no—
772C2×D17—416no—
773C2×D17—41no—
774C2×D17—41no—
775C2×D17—41no—
776C2×D17—41no—
777C2×D17—41no—
778C2×D17—41no—
779C2×D17—41no—
780C2×D17—88no—
781C2×D17#53814yes—
782C2×D17#53914yes—
783C2×D17#53914yes—
784C2×D17#56014yes—
785C2×D17#56214yes—
786C2×D17#56214yes—
787C2×D17#56314yes—
788C4×C17—41no—
789C4×C17—41no—
790C4×C17—41no—
791C4×C17—41no—
792C4×C17—41no—
793C4×C17—41no—
794C4×C17—41no—
795C4×C17—41no—
796C4×C17—41no—
797C4×C17—41no—
798C4×C17—41no—
799C4×C17—41no—
800C4×C17—41no—
801Dic17—41no—
802Dic17—41no—
803Dic17—41no—
804Dic17—41no—
805Dic17—41no—
806Dic17—41no—
807Dic17—41no—
808Dic17—41no—
809Dic17—41no—
810Dic17—41no—
811Dic17—41no—
812Dic17—41no—
813Dic17—41no—
814C23×D4—171no—
815C24×C4—171no—
816C22×C4⋊C4—171no—
817C22×C4⋊C4—171no—
818C22×C4⋊C4—171no—
819C22×C4⋊C4—171no—
820C22×C4⋊C4—171no—
821C22×C4⋊C4—171no—
822C22×C4⋊C4—171no—
823C22×C4⋊C4—171no—
824C22×C4⋊C4—171no—
825C22×C4⋊C4—171no—
826C22×C22⋊C4—171no—
827C22×C22⋊C4—171no—
828C22×C22⋊C4—171no—
829C22×C22⋊C4—171no—
830C22×C22⋊C4—171no—
831C22×C22⋊C4—171no—
832C22×C22⋊C4—171no—
833C22×C22⋊C4—171no—
834C22×C22⋊C4—171no—
835C22×C22⋊C4—171no—
836C22×C22⋊C4—171no—
837#400—171no—
838#400—171no—
839#400—171no—
840#400—171no—
841#400—171no—
842#400—171no—
843#400—171no—
844#400—171no—
845#400—171no—
846#400—171no—
847#400—171no—
848#400—171no—
849#400—171no—
850#400—171no—
851#400C2×D1711yescharacteristic, complemented
852#400C2×D1711yescharacteristic, complemented
853#399—171no—
854#399—171no—
855#399—171no—
856#399—171no—
857#399—171no—
858#399—171no—
859#399—171no—
860#399C2×D1711yescharacteristic, complemented
861#398—171no—
862#398—171no—
863#398—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#398—171no—
873#398—171no—
874#398—171no—
875#398C2×D1711yescharacteristic, complemented
876#398C2×D1711yescharacteristic, complemented
877#397—171no—
878#397—171no—
879#397—171no—
880#397—171no—
881#397—171no—
882#397—171no—
883#397—171no—
884#397—171no—
885#397—171no—
886#397—171no—
887#397—171no—
888#397—171no—
889#397—171no—
890#397—171no—
891#397—171no—
892#397—171no—
893#397—171no—
894#397—171no—
895#397—171no—
896#397—171no—
897#397—171no—
898#397C2×D1711yescharacteristic, complemented
899#397C2×D1711yescharacteristic, complemented
900#397C2×D1711yescharacteristic, complemented
901#396—171no—
902#396—171no—
903#396—171no—
904#396—171no—
905#396—171no—
906#396—171no—
907#396—171no—
908#396—171no—
909#396—171no—
910#396—171no—
911#396—171no—
912#396—171no—
913#396—171no—
914#396—171no—
915#396C2×D1711yescharacteristic, complemented
916#396C2×D1711yescharacteristic, complemented
917#394—171no—
918#394—171no—
919#394—171no—
920#394—171no—
921#394—171no—
922#394—171no—
923#394—171no—
924#394—171no—
925#394—171no—
926#394—171no—
927#394—171no—
928#394—171no—
929#394—171no—
930#394—171no—
931#394C2×D1711yescharacteristic
932#394C2×D1711yescharacteristic
933#386—171no—
934#386—171no—
935#386—171no—
936#386—171no—
937#386—171no—
938#386—171no—
939#386—171no—
940#386C2×D1711yescharacteristic
941#385—171no—
942#385—171no—
943#385—171no—
944#385—171no—
945#385—171no—
946#385—171no—
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#385C2×D1711yescharacteristic, complemented
956#385C2×D1711yescharacteristic, complemented
957C2×#95—171no—
958C2×#95—171no—
959C2×#95—171no—
960C2×#95—171no—
961C2×#95—171no—
962C2×#95—171no—
963C2×#95—171no—
964C2×#95—171no—
965C2×#95—171no—
966C2×#95—171no—
967C2×#95—171no—
968C2×#95—171no—
969C2×C17—42no—
970C2×C17—81no—
971C2×C17C2×#53811yescharacteristic
972C2×C17C2×#53911yescharacteristic
973C2×C17C2×#53911yescharacteristic
974C2×C17C2×#56011yescharacteristic
975C2×C17C2×#56211yescharacteristic
976C2×C17C2×#56211yescharacteristic
977C2×C17C2×#56311yescharacteristic
978D17—42no—
979D17—81no—
980D17#282718yesdirect product factor
981C25—171no—
982C25—171no—
983C22×D4—171no—
984C22×D4—171no—
985C22×D4—171no—
986C22×D4—344no—
987C22×D4—682no—
988C22×D4—682no—
989C22×D4C22×D1711yescharacteristic
990C23×C4—171no—
991C23×C4—171no—
992C23×C4—171no—
993C23×C4—171no—
994C23×C4—171no—
995C23×C4—171no—
996C23×C4—171no—
997C23×C4—171no—
998C23×C4—171no—
999C23×C4—171no—
1000C23×C4—171no—
1001C23×C4—171no—
1002C23×C4—171no—
1003C23×C4—171no—
1004C23×C4—171no—
1005C23×C4—171no—
1006C23×C4—682no—
1007C23×C4—682no—
1008C23×C4—682no—
1009C23×C4C22×D1711yescharacteristic
1010C2×C4⋊C4—171no—
1011C2×C4⋊C4—171no—
1012C2×C4⋊C4—171no—
1013C2×C4⋊C4—171no—
1014C2×C4⋊C4—171no—
1015C2×C4⋊C4—171no—
1016C2×C4⋊C4—171no—
1017C2×C4⋊C4—171no—
1018C2×C4⋊C4—171no—
1019C2×C4⋊C4—171no—
1020C2×C4⋊C4—171no—
1021C2×C4⋊C4—171no—
1022C2×C4⋊C4—171no—
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⋊C4—682no—
1042C2×C4⋊C4—682no—
1043C2×C4⋊C4—682no—
1044C2×C4⋊C4—682no—
1045C2×C4⋊C4—682no—
1046C2×C4⋊C4—682no—
1047C2×C4⋊C4—682no—
1048C2×C4⋊C4—682no—
1049C2×C4⋊C4—682no—
1050C2×C4⋊C4C22×D1711yescharacteristic
1051C2×C4⋊C4C22×D1711yescharacteristic
1052C2×C4⋊C4C22×D1711yescharacteristic
1053C2×C4⋊C4C22×D1711yescharacteristic
1054C2×C4⋊C4C22×D1711yescharacteristic
1055C2×C4⋊C4C22×D1711yescharacteristic
1056C2×C4⋊C4C22×D1711yescharacteristic
1057C2×C4⋊C4C22×D1711yescharacteristic
1058C2×C4⋊C4C22×D1711yescharacteristic
1059C2×C4⋊C4C22×D1711yescharacteristic
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—344no—
1094C2×C22⋊C4—344no—
1095C2×C22⋊C4—682no—
1096C2×C22⋊C4—682no—
1097C2×C22⋊C4—682no—
1098C2×C22⋊C4—682no—
1099C2×C22⋊C4—682no—
1100C2×C22⋊C4—682no—
1101C2×C22⋊C4—682no—
1102C2×C22⋊C4—682no—
1103C2×C22⋊C4—682no—
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×C22⋊C4C22×D1711yescharacteristic
1111C2×C22⋊C4C22×D1711yescharacteristic
1112C2×C22⋊C4C22×D1711yescharacteristic
1113C2×C22⋊C4C22×D1711yescharacteristic
1114C2×C22⋊C4C22×D1711yescharacteristic
1115#95—171no—
1116#95—171no—
1117#95—171no—
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#95C22×D1711yescharacteristic
1152#95C22×D1711yescharacteristic
1153#95C22×D1711yescharacteristic
1154#95C22×D1711yescharacteristic
1155#95C22×D1711yescharacteristic
1156#95C22×D1711yescharacteristic
1157#95C22×D1711yescharacteristic
1158#95C22×D1711yescharacteristic
1159#95C22×D1711yescharacteristic
1160#95C22×D1711yescharacteristic
1161#95C22×D1711yescharacteristic
1162#95C22×D1711yescharacteristic
1163C17C2×#282711yescharacteristic, complemented, Sylow
1164C24—171no—
1165C24—174no—
1166C24—171no—
1167C24—171no—
1168C24—342no—
1169C24—342no—
1170C24—342no—
1171C24—342no—
1172C24—342no—
1173C24—342no—
1174C24—342no—
1175C24—342no—
1176C24—342no—
1177C24—342no—
1178C24—342no—
1179C24—342no—
1180C24—342no—
1181C24C23×D1711yescharacteristic
1182C24C23×D1711yescharacteristic
1183C2×D4—22no—
1184C2×D4—41no—
1185C2×D4—41no—
1186C2×D4—342no—
1187C2×D4—342no—
1188C2×D4—342no—
1189C2×D4—681no—
1190C2×D4—681no—
1191C2×D4—681no—
1192C2×D4—681no—
1193C2×D4—681no—
1194C2×D4—681no—
1195C2×D4—6816no—
1196C22×C4—41no—
1197C22×C4—41no—
1198C22×C4—41no—
1199C22×C4—171no—
1200C22×C4—171no—
1201C22×C4—171no—
1202C22×C4—171no—
1203C22×C4—171no—
1204C22×C4—171no—
1205C22×C4—171no—
1206C22×C4—171no—
1207C22×C4—171no—
1208C22×C4—171no—
1209C22×C4—171no—
1210C22×C4—171no—
1211C22×C4—171no—
1212C22×C4—342no—
1213C22×C4—342no—
1214C22×C4—342no—
1215C22×C4—342no—
1216C22×C4—342no—
1217C22×C4—342no—
1218C22×C4—342no—
1219C22×C4—342no—
1220C22×C4—342no—
1221C22×C4—342no—
1222C22×C4—342no—
1223C22×C4—342no—
1224C22×C4—342no—
1225C22×C4—342no—
1226C22×C4—342no—
1227C22×C4—342no—
1228C22×C4—342no—
1229C22×C4—342no—
1230C22×C4—342no—
1231C22×C4—342no—
1232C22×C4—342no—
1233C22×C4—342no—
1234C22×C4—342no—
1235C22×C4—342no—
1236C22×C4—342no—
1237C22×C4—342no—
1238C22×C4—342no—
1239C22×C4—342no—
1240C22×C4—342no—
1241C22×C4—342no—
1242C22×C4—342no—
1243C22×C4—342no—
1244C22×C4—342no—
1245C22×C4—342no—
1246C22×C4—342no—
1247C22×C4—342no—
1248C22×C4—342no—
1249C22×C4—342no—
1250C22×C4—342no—
1251C22×C4—681no—
1252C22×C4—681no—
1253C22×C4—681no—
1254C22×C4—681no—
1255C22×C4—681no—
1256C22×C4—681no—
1257C22×C4—6816no—
1258C22×C4—681no—
1259C22×C4—681no—
1260C22×C4—681no—
1261C22×C4C23×D1711yescharacteristic
1262C22×C4C23×D1711yescharacteristic
1263C22×C4C23×D1711yescharacteristic
1264C22×C4C23×D1711yescharacteristic
1265C22×C4C23×D1711yescharacteristic
1266C22×C4C23×D1711yescharacteristic
1267C22×C4C23×D1711yescharacteristic
1268C22×C4C23×D1711yescharacteristic
1269C22×C4C23×D1711yescharacteristic
1270C22×C4C23×D1711yescharacteristic
1271C22×C4C23×D1711yescharacteristic
1272C22×C4C23×D1711yescharacteristic
1273C22×C4C23×D1711yescharacteristic
1274C4⋊C4—41no—
1275C4⋊C4—41no—
1276C4⋊C4—41no—
1277C4⋊C4—41no—
1278C4⋊C4—41no—
1279C4⋊C4—41no—
1280C4⋊C4—41no—
1281C4⋊C4—41no—
1282C4⋊C4—41no—
1283C4⋊C4—41no—
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—
1295C4⋊C4—681no—
1296C4⋊C4—681no—
1297C4⋊C4—681no—
1298C4⋊C4—681no—
1299C4⋊C4—681no—
1300C4⋊C4—681no—
1301C4⋊C4—681no—
1302C4⋊C4—681no—
1303C4⋊C4—681no—
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—
1314C22⋊C4—22no—
1315C22⋊C4—22no—
1316C22⋊C4—41no—
1317C22⋊C4—41no—
1318C22⋊C4—41no—
1319C22⋊C4—41no—
1320C22⋊C4—41no—
1321C22⋊C4—41no—
1322C22⋊C4—41no—
1323C22⋊C4—41no—
1324C22⋊C4—41no—
1325C22⋊C4—342no—
1326C22⋊C4—342no—
1327C22⋊C4—342no—
1328C22⋊C4—342no—
1329C22⋊C4—342no—
1330C22⋊C4—342no—
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—
1351C22⋊C4—681no—
1352C22⋊C4—681no—
1353C22⋊C4—681no—
1354C22⋊C4—681no—
1355C22⋊C4—681no—
1356C22⋊C4—681no—
1357C22⋊C4—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—172no—
1372C23—172no—
1373C23—172no—
1374C23—172no—
1375C23—172no—
1376C23—172no—
1377C23—172no—
1378C23—172no—
1379C23—348no—
1380C23—348no—
1381C23—348no—
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—684no—
1396C23—684no—
1397C23—684no—
1398C23—684no—
1399C23—684no—
1400C23—684no—
1401C23—684no—
1402C23—684no—
1403C23—684no—
1404C23—684no—
1405C23—684no—
1406C23#41×D1712yes—
1407C23C24×D1711yescharacteristic
1408D4—44no—
1409D4—684no—
1410D4—684no—
1411D4—684no—
1412C2×C4—21no—
1413C2×C4—21no—
1414C2×C4—21no—
1415C2×C4—21no—
1416C2×C4—21no—
1417C2×C4—21no—
1418C2×C4—21no—
1419C2×C4—21no—
1420C2×C4—21no—
1421C2×C4—21no—
1422C2×C4—21no—
1423C2×C4—21no—
1424C2×C4—21no—
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—44no—
1452C2×C4—341no—
1453C2×C4—341no—
1454C2×C4—341no—
1455C2×C4—341no—
1456C2×C4—341no—
1457C2×C4—341no—
1458C2×C4—341no—
1459C2×C4—341no—
1460C2×C4—341no—
1461C2×C4—341no—
1462C2×C4—341no—
1463C2×C4—341no—
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—684no—
1492C2×C4—684no—
1493C2×C4—684no—
1494C2×C4—684no—
1495C2×C4—684no—
1496C2×C4—684no—
1497C2×C4—684no—
1498C2×C4—684no—
1499C2×C4—684no—
1500C2×C4—684no—
1501C2×C4—684no—
1502C2×C4—684no—
1503C2×C4—684no—
1504C2×C4—684no—
1505C2×C4—684no—
1506C2×C4—684no—
1507C22—22no—
1508C22—22no—
1509C22—22no—
1510C22—41no—
1511C22—41no—
1512C22—41no—
1513C22—41no—
1514C22—41no—
1515C22—41no—
1516C22—41no—
1517C22—41no—
1518C22—41no—
1519C22—41no—
1520C22—41no—
1521C22—174no—
1522C22—174no—
1523C22—174no—
1524C22—174no—
1525C22—174no—
1526C22—174no—
1527C22—174no—
1528C22—342no—
1529C22—342no—
1530C22—342no—
1531C22—6816no—
1532C22—681no—
1533C22—681no—
1534C22—681no—
1535C22—681no—
1536C22—681no—
1537C22—681no—
1538C22—681no—
1539C22—681no—
1540C22—681no—
1541C22—681no—
1542C22—681no—
1543C22—1368no—
1544C22C2×#41×D1711yescharacteristic
1545C22H(5,𝔽2)×D1711yescharacteristic
1546C22H(5,𝔽2)×D1711yescharacteristic
1547C22H(5,𝔽2)×D1711yescharacteristic
1548C22H(5,𝔽2)×D1711yescharacteristic
1549C222−1+4×D1711yescharacteristic
1550C222−1+4×D1711yescharacteristic
1551C4—41no—
1552C4—41no—
1553C4—41no—
1554C4—41no—
1555C4—41no—
1556C4—41no—
1557C4—41no—
1558C4—41no—
1559C4—41no—
1560C4—41no—
1561C4—41no—
1562C4—41no—
1563C4—41no—
1564C4—681no—
1565C4—681no—
1566C4—681no—
1567C4—681no—
1568C4—681no—
1569C4—681no—
1570C4—681no—
1571C4—681no—
1572C4—681no—
1573C4—681no—
1574C4—681no—
1575C4—681no—
1576C4—681no—
1577C2—42no—
1578C2—81no—
1579C2—178no—
1580C2—682no—
1581C2—1361no—
1582C2D17×#53811yescharacteristic
1583C2D17×#53911yescharacteristic
1584C2D17×#53911yescharacteristic
1585C2D17×#56011yescharacteristic
1586C2D17×#56211yescharacteristic
1587C2D17×#56211yescharacteristic
1588C2D17×#56311yescharacteristic
subgroupG/H
center, FrattiniC23C24×D17
commutator, socle, cosocleC23×C17C25
FittingC17×#2827C2
prime radicalC22×D4×D17C22
hypercenter#2827D17
hypocenterC17C2×#2827
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C23 ◁ #2827

Complements

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

NH ≅ G/Ntype
1. #14536899C2semidirect
2. #14536898C2semidirect
3. #14536897C2semidirect
4. #14536896C2semidirect
5. #14536895C2semidirect
6. #14536894C2semidirect
7. #14536893C2semidirect
8. #14536892C2semidirect
9. #14536891C2semidirect
10. #14536890C2semidirect
11. #14536889C2semidirect
12. #14536888C2semidirect
13. #14536887C2semidirect
14. #14536886C2semidirect
15. #14536885C2semidirect
16. D17×#400C2semidirect
17. D17×#400C2semidirect
18. D17×#399C2semidirect
19. D17×#398C2semidirect
20. D17×#398C2semidirect
21. D17×#397C2semidirect
22. D17×#397C2semidirect
23. D17×#397C2semidirect
24. D17×#396C2semidirect
25. D17×#396C2semidirect
29. D17×#385C2semidirect
30. D17×#385C2semidirect
31. C17×#2827C2semidirect
55. #11762751C22semidirect
56. #11762751C22semidirect
57. #11762751C22semidirect
58. #11762751C22semidirect
59. #11762750C22semidirect
60. #11762750C22semidirect
61. #11762750C22semidirect
62. #11762750C22semidirect
63. #11762749C22semidirect
64. #11762749C22semidirect
65. #11762748C22semidirect
66. #11762748C22semidirect
67. #11762747C22semidirect
68. #11762747C22semidirect
69. #11762746C22semidirect
70. #11762745C22semidirect
71. #11762745C22semidirect
72. #11762745C22semidirect
73. #11762744C22semidirect
74. #11762744C22semidirect
75. #11762744C22semidirect
76. #11762743C22semidirect
77. #11762743C22semidirect
78. #11762743C22semidirect
79. #11762743C22semidirect
80. #11762742C22semidirect
81. #11762742C22semidirect
82. #11762742C22semidirect
83. #11762742C22semidirect
84. #11762741C22semidirect
85. #11762741C22semidirect
86. #11762740C22semidirect
87. #11762740C22semidirect
88. #11762739C22semidirect
89. #11762739C22semidirect
90. #11762738C22semidirect
91. #11762738C22semidirect
92. #11762738C22semidirect
93. #11762738C22semidirect
94. #11762738C22semidirect
95. #11762738C22semidirect
96. #11762737C22semidirect
97. #11762737C22semidirect
98. #11762737C22semidirect
99. #11762737C22semidirect
100. #11762737C22semidirect
101. #11762737C22semidirect
102. #11762736C22semidirect
103. #11762736C22semidirect
104. #11762736C22semidirect
105. #11762735C22semidirect
106. #11762735C22semidirect
107. #11762735C22semidirect
108. #11762734C22semidirect
109. #11762734C22semidirect
110. #11762734C22semidirect
111. #11762733C22semidirect
112. #11762733C22semidirect
113. #11762732C22semidirect
114. #11762732C22semidirect
115. #11762732C22semidirect
116. #11762732C22semidirect
117. #11762732C22semidirect
118. #11762732C22semidirect
119. #11762731C22semidirect
120. #11762731C22semidirect
121. #11762731C22semidirect
122. #11762731C22semidirect
123. #11762731C22semidirect
124. #11762731C22semidirect
146. #11762684C22semidirect
147. #11762684C22semidirect
148. #11762683C22semidirect
149. #11762683C22semidirect
150. #11762683C22semidirect
151. #11762683C22semidirect
152. #11762682C22semidirect
153. #11762682C22semidirect
154. #11762681C22semidirect
155. #11762681C22semidirect
156. #11762680C22semidirect
157. #11762680C22semidirect
158. #11762680C22semidirect
159. #11762680C22semidirect
172. C17×#400C22semidirect
173. C17×#400C22semidirect
174. C17×#399C22semidirect
175. C17×#398C22semidirect
176. C17×#398C22semidirect
177. C17×#397C22semidirect
178. C17×#397C22semidirect
179. C17×#397C22semidirect
180. C17×#396C22semidirect
181. C17×#396C22semidirect
185. C17×#385C22semidirect
186. C17×#385C22semidirect
728. #2827D17direct (N × H)
851. #400C2×D17semidirect
852. #400C2×D17semidirect
860. #399C2×D17semidirect
875. #398C2×D17semidirect
876. #398C2×D17semidirect
898. #397C2×D17semidirect
899. #397C2×D17semidirect
900. #397C2×D17semidirect
915. #396C2×D17semidirect
916. #396C2×D17semidirect
955. #385C2×D17semidirect
956. #385C2×D17semidirect
980. D17#2827direct (N × H)
1163. C17C2×#2827semidirect

Maximal subgroups

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

subgroupindex
#145368992
#145368982
#145368972
#145368962
#145368952
#145368942
#145368932
#145368922
#145368912
#145368902
#145368892
#145368882
#145368872
#145368862
#145368852
D17×#4002
D17×#3992
D17×#3982
D17×#3972
D17×#3962
D17×#3942
D17×#3862
D17×#3852
C17×#28272
C2×#282717