Finite Group Databasebeta

← #17241854

Subgroups — #17241854

Order 4352.

2184 conjugacy classes of subgroups.

The subgroup lattice has 1636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763392C211yesmaximal, characteristic, complemented
2#14537113C211yesmaximal, characteristic, complemented
3#14537087C211yesmaximal, characteristic, complemented
4#14535697C211yesmaximal, characteristic, complemented
5#14535604C211yesmaximal, characteristic, complemented
6#14535591C211yesmaximal, characteristic, complemented
7#14535550C211yesmaximal, characteristic, complemented
8#14535376C211yesmaximal, characteristic, complemented
9#14535352C211yesmaximal, characteristic, complemented
10#14535328C211yesmaximal, characteristic, complemented
11#14535259C211yesmaximal, characteristic, complemented
12#14535214C211yesmaximal, characteristic, complemented
13#14535184C211yesmaximal, characteristic, complemented
14#14535169C211yesmaximal, characteristic, complemented
15#14535160C211yesmaximal, characteristic, complemented
16#14535080C211yesmaximal, characteristic, complemented
17#14535060C211yesmaximal, characteristic, complemented
18#14535005C211yesmaximal, characteristic, complemented
19#14534987C211yesmaximal, characteristic, complemented
20#14534935C211yesmaximal, characteristic, complemented
21#14534912C211yesmaximal, characteristic, complemented
22#14534471C211yesmaximal, characteristic, complemented
23#14534416C211yesmaximal, characteristic, complemented
24#14534398C211yesmaximal, characteristic, complemented
25#14534381C211yesmaximal, characteristic, complemented
26#14534272C211yesmaximal, characteristic, complemented
27#14533943C211yesmaximal, characteristic, complemented
28#14532214C211yesmaximal, characteristic, complemented
29#14532170C211yesmaximal, characteristic, complemented
30#14531229C211yesmaximal, characteristic, complemented
31C2×C17×#542C211yesmaximal, characteristic, complemented
32#11763392—28no—
33C2×#10587584C2211yescharacteristic
34C2×#10587562C2211yescharacteristic
35C2×#10587633C2211yescharacteristic
36C2×#10587561C2211yescharacteristic
37C2×#10587571C2211yescharacteristic
38C2×#10587580C2211yescharacteristic
39C2×#10587615C2211yescharacteristic
40C2×#10587564C2211yescharacteristic
41C2×#10587632C2211yescharacteristic, complemented
42C2×#10587616C2211yescharacteristic
43C2×#10587570C2211yescharacteristic
44C2×#10587625C2211yescharacteristic
45C2×#10587625C2211yescharacteristic
46C2×#10587568C2211yescharacteristic
47C2×#10587623C2211yescharacteristic
48C2×#10587623C2211yescharacteristic
49C2×C4×C22⋊D17C2211yescharacteristic
50C2×#10587612C2211yescharacteristic
51C22×#63227C2211yescharacteristic
52C22×C4×Dic17C2211yescharacteristic, complemented
53#11762747C2211yescharacteristic, complemented
54#11762747C2211yescharacteristic, complemented
55#11762744C2211yescharacteristic
56#11762744C2211yescharacteristic
57#11762742C2211yescharacteristic, complemented
58#11762739C2211yescharacteristic, complemented
59#11762737C2211yescharacteristic
60#11762737C2211yescharacteristic
61#11762737C2211yescharacteristic
62#11762737C2211yescharacteristic, complemented
63#11762737C2211yescharacteristic, complemented
64#11762735C2211yescharacteristic
65#11762735C2211yescharacteristic
66#11762735C2211yescharacteristic
67#11762735C2211yescharacteristic, complemented
68#11762734C2211yescharacteristic, complemented
69#11762732C2211yescharacteristic, complemented
70#11762731C2211yescharacteristic
71#11762731C2211yescharacteristic
72#11762731C2211yescharacteristic
73#11762729C2211yescharacteristic, complemented
74#11762728C2211yescharacteristic, complemented
75#11762728C2211yescharacteristic, complemented
76#11762726C2211yescharacteristic
77#11762726C2211yescharacteristic
78#11762725C2211yescharacteristic
79#11762725C2211yescharacteristic
80#11762725C2211yescharacteristic
81#11762724C2211yescharacteristic
82#11762724C2211yescharacteristic
83#11762724C2211yescharacteristic
84#11762724C2211yescharacteristic
85#11762724C2211yescharacteristic
86#11762724C2211yescharacteristic
87#11762724C2211yescharacteristic, complemented
88#11762723C2211yescharacteristic
89#11762721C2211yescharacteristic, complemented
90#11762720C2211yescharacteristic
91#11762720C2211yescharacteristic
92#11762720C2211yescharacteristic
93#11762720C2211yescharacteristic
94#11762720C2211yescharacteristic
95#11762720C2211yescharacteristic, complemented
96#11762718C2211yescharacteristic
97#11762718C2211yescharacteristic
98#11762717C2211yescharacteristic
99#11762717C2211yescharacteristic
100#11762717C2211yescharacteristic, complemented
101#11762716C2211yescharacteristic, complemented
102#11762716C2211yescharacteristic, complemented
103#11762715C2211yescharacteristic, complemented
104#11762715C2211yescharacteristic, complemented
105#11762711C2211yescharacteristic
106#11762711C2211yescharacteristic
107#11762710C2211yescharacteristic
108#11762709C2211yescharacteristic
109#11762709C2211yescharacteristic
110#11762709C2211yescharacteristic
111#11762709C2211yescharacteristic, complemented
112#11762705C2211yescharacteristic, complemented
113#11762704C2211yescharacteristic, complemented
114#11762704C2211yescharacteristic, complemented
115#11762704C2211yescharacteristic, complemented
116#11762704C2211yescharacteristic, complemented
117#11762703C2211yescharacteristic, complemented
118#11762703C2211yescharacteristic, complemented
119#11762702C2211yescharacteristic
120#11762702C2211yescharacteristic
121#11762700C2211yescharacteristic
122#11762700C2211yescharacteristic
123#11762700C2211yescharacteristic
124#11762700C2211yescharacteristic
125#11762700C2211yescharacteristic, complemented
126#11762699C2211yescharacteristic
127#11762699C2211yescharacteristic
128#11762699C2211yescharacteristic
129#11762699C2211yescharacteristic
130#11762699C2211yescharacteristic
131#11762699C2211yescharacteristic
132#11762699C2211yescharacteristic
133#11762699C2211yescharacteristic, complemented
134#11762699C2211yescharacteristic, complemented
135#11762699C2211yescharacteristic, complemented
136#11762697C2211yescharacteristic, complemented
137#11762695C2211yescharacteristic, complemented
138#11762695C2211yescharacteristic, complemented
139#11762693C2211yescharacteristic, complemented
140#11762693C2211yescharacteristic, complemented
141#11762693C2211yescharacteristic, complemented
142#11762690C2211yescharacteristic, complemented
143#11762689C2211yescharacteristic
144#11762689C2211yescharacteristic
145#11762689C2211yescharacteristic
146#11762689C2211yescharacteristic, complemented
147#11762688C2211yescharacteristic
148#11762688C2211yescharacteristic
149#11762688C2211yescharacteristic, complemented
150#11762686C2211yescharacteristic
151#11762686C2211yescharacteristic
152#11762686C2211yescharacteristic
153#11762686C2211yescharacteristic, complemented
154#11762686C2211yescharacteristic, complemented
155#11762685C2211yescharacteristic, complemented
156#11762684C2211yescharacteristic, complemented
157#11762684C2211yescharacteristic, complemented
158#11762682C2211yescharacteristic, complemented
159#11762681C2211yescharacteristic
160#11762680C2211yescharacteristic, complemented
161#11762674C2211yescharacteristic, complemented
162#11762670C2211yescharacteristic
163#11762670C2211yescharacteristic
164#11762667C2211yescharacteristic, complemented
165#11762666C2211yescharacteristic, complemented
166#11762664C2211yescharacteristic
167#11762664C2211yescharacteristic
168#11762664C2211yescharacteristic
169C4×C4⋊Dic17C2211yescharacteristic, complemented
170C4×C22⋊Dic17C2211yescharacteristic
171C4×C22⋊Dic17C2211yescharacteristic, complemented
172#11762655C2211yescharacteristic, complemented
173C17×#542—28no—
174C2×C17×C4⋊Q8C2211yescharacteristic, complemented
175C2×C17×#126C2211yescharacteristic
176C2×C17×#126C2211yescharacteristic, complemented
177C2×C17×#124C2211yescharacteristic
178C2×C17×#124C2211yescharacteristic
179C2×C17×#124C2211yescharacteristic, complemented
180C2×C17×#123C2211yescharacteristic
181C2×C17×#123C2211yescharacteristic, complemented
182C2×C17×C22⋊Q8C2211yescharacteristic
183C2×C17×C22⋊Q8C2211yescharacteristic, complemented
184C2×C17×C22⋊Q8C2211yescharacteristic, complemented
185C2×C17×#121C2211yescharacteristic
186C2×C4×Q8×C17C2211yescharacteristic, complemented
187C2×C4×D4×C17C2211yescharacteristic
188C2×C17×#117C2211yescharacteristic, complemented
189C24×D17C2311yescharacteristic
190C22×Q8×C17C2311yescharacteristic
191C22×Q8×C17C2311yescharacteristic
192C22×Q8×C17C2311yescharacteristic
193C22×D4×C17C2311yescharacteristic
194C22×D4×C17C2311yescharacteristic
195C22×D4×C17C2311yescharacteristic
196C23×C4×C17C2311yescharacteristic
197C23×C4×C17C2311yescharacteristic
198C23×C4×C17C2311yescharacteristic
199C22×C22⋊D17C2311yescharacteristic
200C22×C22⋊D17C2311yescharacteristic
201C22×C22⋊D17C2311yescharacteristic
202C22×C22⋊D17C2311yescharacteristic
203C22×C22⋊D17C2311yescharacteristic
204C22×C22⋊D17C2311yescharacteristic
205C22×C22⋊D17C2311yescharacteristic
206C23×Dic17C2311yescharacteristic
207C23×Dic17C2311yescharacteristic
208C23×Dic17C2311yescharacteristic
209C22×D68C2311yescharacteristic
210C22×D68C2311yescharacteristic
211C22×C4×D17C2311yescharacteristic
212C22×Dic34C2311yescharacteristic
213C17×C4⋊Q8—24no—
214C17×#126—24no—
215C17×#126—24no—
216C17×#124—24no—
217C17×#124—24no—
218C17×#124—24no—
219C17×#123—24no—
220C17×#123—24no—
221C17×C22⋊Q8—24no—
222C17×C22⋊Q8—24no—
223C17×C22⋊Q8—24no—
224C17×#121—24no—
225C4×Q8×C17—24no—
226C4×D4×C17D418yescomplemented
227C17×#117—24no—
228C2×C4⋊C4×C17C2311yescharacteristic
229C2×C4⋊C4×C17C2311yescharacteristic
230C2×C4⋊C4×C17C2311yescharacteristic
231C2×C4⋊C4×C17C2311yescharacteristic
232C2×C4⋊C4×C17C2311yescharacteristic
233C2×C4⋊C4×C17C2311yescharacteristic
234C2×C4⋊C4×C17C2311yescharacteristic
235C2×C4⋊C4×C17C2311yescharacteristic
236C2×C4⋊C4×C17C2311yescharacteristic
237C2×C4⋊C4×C17C2311yescharacteristic
238C2×C22⋊C4×C17C2311yescharacteristic
239C2×C22⋊C4×C17C2311yescharacteristic
240C2×C22⋊C4×C17C2311yescharacteristic
241C2×C22⋊C4×C17C2311yescharacteristic
242C2×C22⋊C4×C17C2311yescharacteristic
243C2×C22⋊C4×C17C2311yescharacteristic
244C2×C22⋊C4×C17C2311yescharacteristic
245C2×C22⋊C4×C17C2311yescharacteristic
246C2×C22⋊C4×C17C2311yescharacteristic
247C2×C22⋊C4×C17C2311yescharacteristic
248C2×C22⋊C4×C17C2311yescharacteristic
249C2×C22⋊C4×C17C2311yescharacteristic
250C2×C42×C17C2311yescharacteristic
251C2×C42×C17C2311yescharacteristic
252C2×C42×C17C2311yescharacteristic
253C2×C42×C17C2311yescharacteristic
254C2×C22⋊Dic17C2311yescharacteristic
255C2×C22⋊Dic17C2311yescharacteristic
256C2×C22⋊Dic17C2311yescharacteristic
257C2×C22⋊Dic17C2311yescharacteristic
258C2×C22⋊Dic17C2311yescharacteristic
259C2×C22⋊Dic17C2311yescharacteristic
260C2×C22⋊Dic17C2311yescharacteristic
261C2×C22⋊Dic17C2311yescharacteristic
262C2×C22⋊Dic17C2311yescharacteristic
263C2×C22⋊Dic17C2311yescharacteristic
264C2×C22⋊Dic17C2311yescharacteristic
265C2×C22⋊Dic17C2311yescharacteristic
266C2×C22⋊Dic17C2311yescharacteristic
267#10587633—42no—
268#10587632—42no—
269#10587625—24no—
270#10587625—42no—
271#10587623—24no—
272#10587623—42no—
273#10587616—24no—
274#10587615—24no—
275C4×C22⋊D17—24no—
276C2×#63227—24no—
277C2×#63227C2311yescharacteristic
278C2×#63227C2311yescharacteristic
279C2×#63227C2311yescharacteristic
280C2×#63227C2311yescharacteristic
281C2×#63227C2311yescharacteristic
282C2×#63227C2311yescharacteristic
283C2×#63227C2311yescharacteristic
284C2×#63227C2311yescharacteristic
285C2×#63227C2311yescharacteristic
286C2×#63227C2311yescharacteristic
287C2×#63227C2311yescharacteristic
288C2×#63227C2311yescharacteristic
289C2×#63227C2311yescharacteristic
290C2×#63227C2311yescharacteristic
291C2×#63227C2311yescharacteristic
292C2×#63227C2311yescharacteristic
293C2×#63227C2311yescharacteristic
294C2×#63227C2311yescharacteristic
295C2×#63227C2311yescharacteristic
296C2×#63227C2311yescharacteristic
297C2×#63227C2311yescharacteristic
298C2×#63227C2311yescharacteristic
299C2×#63227C2311yescharacteristic
300C2×#63227C2311yescharacteristic
301C2×#63227C2311yescharacteristic
302C2×#63227C2311yescharacteristic
303C2×#63227C2311yescharacteristic
304C2×#63227C2311yescharacteristic
305C2×#63227C2311yescharacteristic
306C2×#63227C2311yescharacteristic
307C2×#63227C2311yescharacteristic
308#10587612—42no—
309C2×C4⋊Dic17C2311yescharacteristic
310C2×C4⋊Dic17C2311yescharacteristic
311C2×C4⋊Dic17C2311yescharacteristic
312C2×C4⋊Dic17C2311yescharacteristic
313C2×C4⋊Dic17C2311yescharacteristic
314C2×#63225C2311yescharacteristic
315C2×#63225C2311yescharacteristic
316C2×#63225C2311yescharacteristic
317C2×#63225C2311yescharacteristic
318C2×#63225C2311yescharacteristic
319C2×#63225C2311yescharacteristic
320C2×#63225C2311yescharacteristic
321C2×#63225C2311yescharacteristic
322C2×#63225C2311yescharacteristic
323C2×#63225C2311yescharacteristic
324C2×#63225C2311yescharacteristic
325C2×#63225C2311yescharacteristic
326C2×#63225C2311yescharacteristic
327C2×C4×Dic17—42no—
328C2×C4×Dic17C2311yescharacteristic
329C2×C4×Dic17C2311yescharacteristic
330C2×C4×Dic17C2311yescharacteristic
331C2×C4×Dic17C2311yescharacteristic
332C2×C4×Dic17C2311yescharacteristic
333C2×C4×Dic17C2311yescharacteristic
334C2×C4×Dic17C2311yescharacteristic
335#10587584—24no—
336#10587580—24no—
337#10587571—24no—
338#10587570—24no—
339#10587568—24no—
340#10587564—24no—
341#10587562—24no—
342#10587561—24no—
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
369#10587502C2311yescharacteristic
370#10587502C2311yescharacteristic
371#10587502C2311yescharacteristic
372#10587502C2311yescharacteristic
373#10587502C2311yescharacteristic
374#10587502C2311yescharacteristic
375#10587502C2311yescharacteristic
376#10587502C2311yescharacteristic
377#10587502C2311yescharacteristic
378#10587502C2311yescharacteristic
379C24×C17C2411yescharacteristic
380C24×C17C2411yescharacteristic
381C24×C17C2411yescharacteristic
382C23×D17—22no—
383C23×D17—41no—
384C23×D17—41no—
385C23×D17—41no—
386C23×D17—41no—
387C23×D17—41no—
388C23×D17—41no—
389C23×D17C2411yescharacteristic
390C23×D17C2411yescharacteristic
391C23×D17C2411yescharacteristic
392C2×Q8×C17—22no—
393C2×Q8×C17—22no—
394C2×Q8×C17—22no—
395C2×Q8×C17—41no—
396C2×Q8×C17—41no—
397C2×Q8×C17—41no—
398C2×Q8×C17—41no—
399C2×Q8×C17—41no—
400C2×Q8×C17—41no—
401C2×D4×C17—22no—
402C2×D4×C17—22no—
403C2×D4×C17—41no—
404C2×D4×C17—41no—
405C2×D4×C17—41no—
406C2×D4×C17—41no—
407C2×D4×C17—41no—
408C2×D4×C17—41no—
409C2×D4×C17C2×D414yes—
410C22×C4×C17—22no—
411C22×C4×C17—41no—
412C22×C4×C17—41no—
413C22×C4×C17—41no—
414C22×C4×C17—41no—
415C22×C4×C17—41no—
416C22×C4×C17—41no—
417C22×C4×C17C2×D414yes—
418C22×C4×C17C2×D414yes—
419C22×C4×C17C2411yescharacteristic
420C22×C4×C17C2411yescharacteristic
421C22×C4×C17C2411yescharacteristic
422C22×C4×C17C2411yescharacteristic
423C22×C4×C17C2411yescharacteristic
424C22×C4×C17C2411yescharacteristic
425C22×C4×C17C2411yescharacteristic
426C22×C4×C17C2411yescharacteristic
427C22×C4×C17C2411yescharacteristic
428C22×C4×C17C2411yescharacteristic
429C22×C4×C17C2411yescharacteristic
430C22×C4×C17C2411yescharacteristic
431C2×C22⋊D17—22no—
432C2×C22⋊D17—22no—
433C2×C22⋊D17—22no—
434C2×C22⋊D17—22no—
435C2×C22⋊D17—22no—
436C2×C22⋊D17—41no—
437C2×C22⋊D17—41no—
438C2×C22⋊D17—41no—
439C2×C22⋊D17—41no—
440C2×C22⋊D17—41no—
441C2×C22⋊D17—41no—
442C2×C22⋊D17—41no—
443C2×C22⋊D17—41no—
444C2×C22⋊D17—41no—
445C2×C22⋊D17—41no—
446C2×C22⋊D17—41no—
447C2×C22⋊D17—41no—
448C2×C22⋊D17—41no—
449C2×C22⋊D17—41no—
450C2×C22⋊D17—41no—
451C2×C22⋊D17—41no—
452C22×Dic17—22no—
453C22×Dic17—22no—
454C22×Dic17—41no—
455C22×Dic17—41no—
456C22×Dic17—41no—
457C22×Dic17—41no—
458C22×Dic17—41no—
459C22×Dic17—41no—
460C22×Dic17—41no—
461C22×Dic17C2411yescharacteristic
462C22×Dic17C2411yescharacteristic
463C22×Dic17C2411yescharacteristic
464C22×Dic17C2411yescharacteristic
465C22×Dic17C2411yescharacteristic
466C22×Dic17C2411yescharacteristic
467C22×Dic17C2411yescharacteristic
468C22×Dic17C2411yescharacteristic
469C22×Dic17C2411yescharacteristic
470C22×Dic17C2411yescharacteristic
471C22×Dic17C2411yescharacteristic
472C22×Dic17C2411yescharacteristic
473C22×Dic17C2411yescharacteristic
474C2×D68—22no—
475C2×D68—22no—
476C2×D68—41no—
477C2×D68—41no—
478C2×D68—41no—
479C2×D68—41no—
480C2×C4×D17—22no—
481C2×C4×D17—41no—
482C2×C4×D17—41no—
483C2×Dic34—22no—
484C2×Dic34—41no—
485C2×Dic34—41no—
486C4⋊C4×C17—22no—
487C4⋊C4×C17—22no—
488C4⋊C4×C17—22no—
489C4⋊C4×C17—22no—
490C4⋊C4×C17—22no—
491C4⋊C4×C17—22no—
492C4⋊C4×C17—22no—
493C4⋊C4×C17—22no—
494C4⋊C4×C17—22no—
495C4⋊C4×C17C2×D414yes—
496C22⋊C4×C17—22no—
497C22⋊C4×C17—22no—
498C22⋊C4×C17—22no—
499C22⋊C4×C17—22no—
500C22⋊C4×C17—22no—
501C22⋊C4×C17—22no—
502C22⋊C4×C17—22no—
503C22⋊C4×C17—22no—
504C22⋊C4×C17—22no—
505C22⋊C4×C17—22no—
506C22⋊C4×C17C2×D414yes—
507C22⋊C4×C17C2×D414yes—
508C42×C17—22no—
509C42×C17—22no—
510C42×C17—22no—
511C42×C17C2×D414yes—
512C22⋊Dic17—22no—
513C22⋊Dic17—22no—
514C22⋊Dic17—22no—
515C22⋊Dic17—41no—
516C22⋊Dic17—41no—
517C22⋊Dic17—41no—
518C22⋊Dic17—41no—
519C22⋊Dic17—41no—
520C22⋊Dic17—41no—
521C22⋊Dic17—41no—
522C22⋊Dic17—41no—
523C22⋊Dic17—41no—
524C22⋊Dic17—41no—
525#63227—22no—
526#63227—22no—
527#63227—22no—
528#63227—22no—
529#63227—22no—
530#63227—22no—
531#63227—22no—
532#63227—22no—
533#63227—22no—
534#63227—22no—
535#63227—22no—
536#63227—22no—
537#63227—41no—
538#63227—41no—
539#63227—41no—
540#63227—41no—
541#63227—41no—
542#63227—41no—
543#63227—41no—
544#63227—41no—
545#63227—41no—
546#63227—41no—
547#63227—41no—
548#63227—41no—
549#63227—41no—
550#63227—41no—
551#63227—41no—
552#63227—41no—
553#63227—41no—
554#63227—41no—
555#63227—41no—
556C4⋊Dic17—22no—
557C4⋊Dic17—22no—
558C4⋊Dic17—41no—
559C4⋊Dic17—41no—
560C4⋊Dic17—41no—
561#63225—22no—
562#63225—22no—
563#63225—22no—
564#63225—22no—
565#63225—22no—
566#63225—41no—
567#63225—41no—
568#63225—41no—
569#63225—41no—
570#63225—41no—
571#63225—41no—
572#63225—41no—
573#63225—41no—
574C4×Dic17—22no—
575C4×Dic17—22no—
576C4×Dic17—22no—
577C4×Dic17—41no—
578C4×Dic17—41no—
579C4×Dic17—41no—
580C4×Dic17—41no—
581#36745—171nomaximal, Sylow
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×C17—21no—
594C23×C17—21no—
595C23×C17—21no—
596C23×C17—21no—
597C23×C17—21no—
598C23×C17—21no—
599C23×C17—21no—
600C23×C17—21no—
601C23×C17C22×D412yes—
602C23×C17C22×D412yes—
603C23×C17C2511yescharacteristic
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—21no—
614C22×D17—21no—
615C22×D17—21no—
616C22×D17—21no—
617C22×D17—21no—
618C22×D17—21no—
619C22×D17—21no—
620C22×D17—21no—
621C22×D17—21no—
622C22×D17—21no—
623C22×D17—21no—
624C22×D17—21no—
625C22×D17—44no—
626C22×D17—82no—
627C22×D17—82no—
628C22×D17—82no—
629C22×D17—82no—
630C22×D17—82no—
631C22×D17—82no—
632Q8×C17—44no—
633Q8×C17—82no—
634Q8×C17—82no—
635D4×C17—44no—
636D4×C17—82no—
637D4×C17—82no—
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—21no—
662C2×C4×C17—21no—
663C2×C4×C17—21no—
664C2×C4×C17—21no—
665C2×C4×C17—21no—
666C2×C4×C17—21no—
667C2×C4×C17—21no—
668C2×C4×C17—21no—
669C2×C4×C17—44no—
670C2×C4×C17—44no—
671C2×C4×C17—44no—
672C2×C4×C17C22×D412yes—
673C2×C4×C17C22×D412yes—
674C2×C4×C17C22×D412yes—
675C2×C4×C17C22×D412yes—
676C2×C4×C17C22×D412yes—
677C22⋊D17—44no—
678C22⋊D17—82no—
679C22⋊D17—82no—
680C22⋊D17—82no—
681C22⋊D17—82no—
682C22⋊D17—82no—
683C22⋊D17—82no—
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—21no—
709C2×Dic17—21no—
710C2×Dic17—21no—
711C2×Dic17—21no—
712C2×Dic17—21no—
713C2×Dic17—21no—
714C2×Dic17—21no—
715C2×Dic17—21no—
716C2×Dic17—21no—
717C2×Dic17—21no—
718C2×Dic17—21no—
719C2×Dic17—21no—
720C2×Dic17—21no—
721C2×Dic17—21no—
722C2×Dic17—44no—
723C2×Dic17—44no—
724C2×Dic17—82no—
725C2×Dic17H(5,𝔽2)12yes—
726D68—82no—
727D68—82no—
728C4×D17—82no—
729Dic34—82no—
730C2×#542D1711yescharacteristic, complemented
731C2×#538—171no—
732#2854—171no—
733#2850—171no—
734#2723—171no—
735#2716—171no—
736#2715—171no—
737#2712—171no—
738#2700—171no—
739#2698—171no—
740#2696—171no—
741#2691—171no—
742#2688—171no—
743#2686—171no—
744#2685—171no—
745#2684—171no—
746#2676—171no—
747#2674—171no—
748#2670—171no—
749#2668—171no—
750#2663—171no—
751#2661—171no—
752#2610—171no—
753#2604—171no—
754#2602—171no—
755#2601—171no—
756#2592—171no—
757#2561—171no—
758#2415—171no—
759#2411—171no—
760#2290—171no—
761C22×C17—22no—
762C22×C17—22no—
763C22×C17—22no—
764C22×C17—22no—
765C22×C17—22no—
766C22×C17—22no—
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×C17—41no—
776C22×C17—41no—
777C22×C17—41no—
778C22×C17—41no—
779C22×C17—41no—
780C22×C17—41no—
781C22×C17—41no—
782C22×C17C23×D411yescharacteristic
783C22×C17C2×H(5,𝔽2)11yescharacteristic
784C22×C17#58511yescharacteristic
785C22×C17#58511yescharacteristic
786C22×C17#58511yescharacteristic
787C22×C17#58511yescharacteristic
788C22×C17#58511yescharacteristic
789C2×D17—41no—
790C2×D17—41no—
791C2×D17—41no—
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—41no—
804C2×D17—41no—
805C2×D17—41no—
806C2×D17—41no—
807C2×D17—41no—
808C2×D17—41no—
809C2×D17—41no—
810C2×D17—88no—
811C4×C17—22no—
812C4×C17—22no—
813C4×C17—22no—
814C4×C17—22no—
815C4×C17—22no—
816C4×C17—41no—
817C4×C17—41no—
818C4×C17—41no—
819C4×C17—41no—
820C4×C17—41no—
821C4×C17—41no—
822C4×C17—41no—
823Dic17—22no—
824Dic17—41no—
825Dic17—41no—
826Dic17—41no—
827Dic17—41no—
828Dic17—41no—
829Dic17—41no—
830Dic17—41no—
831Dic17—41no—
832Dic17—41no—
833Dic17—41no—
834Dic17—41no—
835Dic17—41no—
836#542—28no—
837#538—348no—
838C2×C4⋊Q8C2×D1711yescharacteristic, complemented
839C2×#126—171no—
840C2×#126—171no—
841C2×#126C2×D1711yescharacteristic
842C2×#126C2×D1711yescharacteristic, complemented
843C2×#124—171no—
844C2×#124—171no—
845C2×#124—171no—
846C2×#124C2×D1711yescharacteristic
847C2×#124C2×D1711yescharacteristic
848C2×#124C2×D1711yescharacteristic, complemented
849C2×#123—171no—
850C2×#123—171no—
851C2×#123C2×D1711yescharacteristic
852C2×#123C2×D1711yescharacteristic, complemented
853C2×C22⋊Q8—171no—
854C2×C22⋊Q8—171no—
855C2×C22⋊Q8C2×D1711yescharacteristic
856C2×C22⋊Q8C2×D1711yescharacteristic, complemented
857C2×C22⋊Q8C2×D1711yescharacteristic, complemented
858C2×#121—171no—
859C2×#121—171no—
860C2×#121—171no—
861C2×#121—171no—
862C2×#121C2×D1711yescharacteristic
863C2×#120—171no—
864C2×#120—171no—
865C2×#120—171no—
866C2×C4×Q8C2×D1711yescharacteristic, complemented
867C2×C4×D4—171no—
868C2×C4×D4C2×D1711yescharacteristic
869C2×#117—171no—
870C2×#117C2×D1711yescharacteristic, complemented
871C22×C22⋊C4—171no—
872C22×C42—171no—
873#400—171no—
874#400—171no—
875#399—171no—
876#399—171no—
877#398—171no—
878#398—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#396—171no—
890#396—171no—
891#396—171no—
892#396—171no—
893#395—171no—
894#395—171no—
895#395—171no—
896#394—171no—
897#394—171no—
898#394—171no—
899#394—171no—
900#394—171no—
901#394—171no—
902#394—171no—
903#394—171no—
904#394—171no—
905#394—171no—
906#394—171no—
907#394—171no—
908#394—171no—
909#393—171no—
910#393—171no—
911#393—171no—
912#393—171no—
913#393—171no—
914#393—171no—
915#393—171no—
916#392—171no—
917#392—171no—
918#392—171no—
919#392—171no—
920#392—171no—
921#391—171no—
922#391—171no—
923#391—171no—
924#391—171no—
925#390—171no—
926#390—171no—
927#390—171no—
928#390—171no—
929#390—171no—
930#390—171no—
931#390—171no—
932#389—171no—
933#389—171no—
934#389—171no—
935#389—171no—
936#389—171no—
937#388—171no—
938#388—171no—
939#388—171no—
940#388—171no—
941#388—171no—
942#388—171no—
943#388—171no—
944#388—171no—
945#388—171no—
946#388—171no—
947#388—171no—
948#388—171no—
949#388—171no—
950#388—171no—
951#388—171no—
952#388—171no—
953#388—171no—
954#388—171no—
955#388—171no—
956#388—171no—
957#387—171no—
958#387—171no—
959#387—171no—
960#387—171no—
961#387—171no—
962#387—171no—
963#386—171no—
964#386—171no—
965#386—171no—
966#386—171no—
967#386—171no—
968#386—171no—
969#386—171no—
970#386—171no—
971#386—171no—
972#386—171no—
973#386—171no—
974#386—171no—
975#386—171no—
976#385—171no—
977#385—171no—
978#385—171no—
979#385—171no—
980#385—171no—
981#382—171no—
982#381—171no—
983#381—171no—
984#380—171no—
985#380—171no—
986#379—171no—
987#379—171no—
988#379—171no—
989C4×C4⋊C4—171no—
990C4×C22⋊C4—171no—
991C4×C22⋊C4—171no—
992#376—171no—
993C2×C17—42no—
994C2×C17—42no—
995C2×C17—81no—
996C2×C17#344911yescharacteristic
997C2×C17#349611yescharacteristic
998C2×C17#350011yescharacteristic
999C2×C17#353311yescharacteristic
1000C2×C17#354011yescharacteristic
1001C2×C17#356611yescharacteristic
1002C2×C17#356811yescharacteristic
1003D17—81no—
1004D17—81no—
1005D17—81no—
1006C25—171no—
1007C22×Q8—171no—
1008C22×Q8C22×D1711yescharacteristic
1009C22×Q8C22×D1711yescharacteristic
1010C22×Q8C22×D1711yescharacteristic
1011C22×D4—171no—
1012C22×D4—171no—
1013C22×D4—171no—
1014C22×D4—171no—
1015C22×D4—171no—
1016C22×D4—171no—
1017C22×D4—171no—
1018C22×D4—171no—
1019C22×D4—171no—
1020C22×D4C22×D1711yescharacteristic
1021C22×D4C22×D1711yescharacteristic
1022C22×D4C22×D1711yescharacteristic
1023C23×C4—171no—
1024C23×C4—171no—
1025C23×C4—171no—
1026C23×C4—171no—
1027C23×C4C22×D1711yescharacteristic
1028C23×C4C22×D1711yescharacteristic
1029C23×C4C22×D1711yescharacteristic
1030C4⋊Q8—24no—
1031#126—24no—
1032#126—24no—
1033#126—344no—
1034#126—344no—
1035#124—24no—
1036#124—24no—
1037#124—24no—
1038#124—344no—
1039#124—344no—
1040#124—682no—
1041#123—24no—
1042#123—24no—
1043#123—344no—
1044#123—344no—
1045C22⋊Q8—24no—
1046C22⋊Q8—24no—
1047C22⋊Q8—24no—
1048C22⋊Q8—344no—
1049C22⋊Q8—682no—
1050#121—24no—
1051#121—344no—
1052#121—344no—
1053#121—344no—
1054#121—682no—
1055#120—344no—
1056#120—344no—
1057#120—682no—
1058C4×Q8—24no—
1059C4×D4—344no—
1060C4×D4C22⋊D1718yescomplemented
1061#117—24no—
1062#117—682no—
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—171no—
1077C2×C4⋊C4—171no—
1078C2×C4⋊C4—171no—
1079C2×C4⋊C4—171no—
1080C2×C4⋊C4—171no—
1081C2×C4⋊C4C22×D1711yescharacteristic
1082C2×C4⋊C4C22×D1711yescharacteristic
1083C2×C4⋊C4C22×D1711yescharacteristic
1084C2×C4⋊C4C22×D1711yescharacteristic
1085C2×C4⋊C4C22×D1711yescharacteristic
1086C2×C4⋊C4C22×D1711yescharacteristic
1087C2×C4⋊C4C22×D1711yescharacteristic
1088C2×C4⋊C4C22×D1711yescharacteristic
1089C2×C4⋊C4C22×D1711yescharacteristic
1090C2×C4⋊C4C22×D1711yescharacteristic
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—171no—
1120C2×C22⋊C4—171no—
1121C2×C22⋊C4—171no—
1122C2×C22⋊C4—171no—
1123C2×C22⋊C4—171no—
1124C2×C22⋊C4—171no—
1125C2×C22⋊C4—171no—
1126C2×C22⋊C4—171no—
1127C2×C22⋊C4—171no—
1128C2×C22⋊C4—171no—
1129C2×C22⋊C4—171no—
1130C2×C22⋊C4—171no—
1131C2×C22⋊C4—171no—
1132C2×C22⋊C4—171no—
1133C2×C22⋊C4—171no—
1134C2×C22⋊C4—171no—
1135C2×C22⋊C4—344no—
1136C2×C22⋊C4C22×D1711yescharacteristic
1137C2×C22⋊C4C22×D1711yescharacteristic
1138C2×C22⋊C4C22×D1711yescharacteristic
1139C2×C22⋊C4C22×D1711yescharacteristic
1140C2×C22⋊C4C22×D1711yescharacteristic
1141C2×C22⋊C4C22×D1711yescharacteristic
1142C2×C22⋊C4C22×D1711yescharacteristic
1143C2×C22⋊C4C22×D1711yescharacteristic
1144C2×C22⋊C4C22×D1711yescharacteristic
1145C2×C22⋊C4C22×D1711yescharacteristic
1146C2×C22⋊C4C22×D1711yescharacteristic
1147C2×C22⋊C4C22×D1711yescharacteristic
1148C2×C42—171no—
1149C2×C42—171no—
1150C2×C42—171no—
1151C2×C42—171no—
1152C2×C42—171no—
1153C2×C42—171no—
1154C2×C42—171no—
1155C2×C42—682no—
1156C2×C42C22×D1711yescharacteristic
1157C2×C42C22×D1711yescharacteristic
1158C2×C42C22×D1711yescharacteristic
1159C2×C42C22×D1711yescharacteristic
1160#95—171no—
1161#95—171no—
1162#95—171no—
1163#95—171no—
1164#95—171no—
1165#95—171no—
1166#95—171no—
1167#95—171no—
1168#95—171no—
1169#95—171no—
1170#95—171no—
1171#95—171no—
1172#95—171no—
1173#95—171no—
1174#95—171no—
1175#95—171no—
1176#95—171no—
1177#95—171no—
1178#95—171no—
1179#95—171no—
1180#95—171no—
1181#95—171no—
1182#95—171no—
1183#95—171no—
1184#95—171no—
1185#95—171no—
1186#95—171no—
1187#95—171no—
1188#95—171no—
1189#95—171no—
1190#95—171no—
1191#95—171no—
1192#95—171no—
1193#95—171no—
1194#95—171no—
1195#95—171no—
1196C17#3674511yescharacteristic, complemented, Sylow
1197C24—171no—
1198C24—171no—
1199C24—171no—
1200C24—342no—
1201C24—681no—
1202C24—681no—
1203C24—681no—
1204C24—681no—
1205C24—681no—
1206C24—681no—
1207C24C23×D1711yescharacteristic
1208C24C23×D1711yescharacteristic
1209C24C23×D1711yescharacteristic
1210C2×Q8—22no—
1211C2×Q8—22no—
1212C2×Q8—22no—
1213C2×Q8—41no—
1214C2×Q8—41no—
1215C2×Q8—41no—
1216C2×Q8—41no—
1217C2×Q8—41no—
1218C2×Q8—41no—
1219C2×Q8—342no—
1220C2×Q8—681no—
1221C2×Q8—681no—
1222C2×D4—22no—
1223C2×D4—22no—
1224C2×D4—41no—
1225C2×D4—41no—
1226C2×D4—41no—
1227C2×D4—41no—
1228C2×D4—41no—
1229C2×D4—41no—
1230C2×D4—342no—
1231C2×D4—342no—
1232C2×D4—342no—
1233C2×D4—342no—
1234C2×D4—342no—
1235C2×D4—342no—
1236C2×D4—342no—
1237C2×D4—681no—
1238C2×D4—681no—
1239C2×D4—681no—
1240C2×D4—681no—
1241C2×D4—681no—
1242C2×D4—681no—
1243C2×D4—681no—
1244C2×D4—681no—
1245C2×D4—681no—
1246C2×D4—681no—
1247C2×D4—681no—
1248C2×D4—681no—
1249C2×D4—681no—
1250C2×D4—681no—
1251C2×D4—681no—
1252C2×D4—681no—
1253C2×D4—681no—
1254C2×D4—681no—
1255C2×D4—681no—
1256C2×D4—681no—
1257C2×D4C2×C22⋊D1714yes—
1258C22×C4—22no—
1259C22×C4—41no—
1260C22×C4—41no—
1261C22×C4—41no—
1262C22×C4—41no—
1263C22×C4—41no—
1264C22×C4—41no—
1265C22×C4—171no—
1266C22×C4—171no—
1267C22×C4—171no—
1268C22×C4—171no—
1269C22×C4—171no—
1270C22×C4—171no—
1271C22×C4—171no—
1272C22×C4—171no—
1273C22×C4—171no—
1274C22×C4—171no—
1275C22×C4—171no—
1276C22×C4—171no—
1277C22×C4—171no—
1278C22×C4—342no—
1279C22×C4—342no—
1280C22×C4—342no—
1281C22×C4—681no—
1282C22×C4—681no—
1283C22×C4—681no—
1284C22×C4—681no—
1285C22×C4—681no—
1286C22×C4—681no—
1287C22×C4—681no—
1288C22×C4—681no—
1289C22×C4—681no—
1290C22×C4C2×C22⋊D1714yes—
1291C22×C4C2×C22⋊D1714yes—
1292C22×C4C23×D1711yescharacteristic
1293C22×C4C23×D1711yescharacteristic
1294C22×C4C23×D1711yescharacteristic
1295C22×C4C23×D1711yescharacteristic
1296C22×C4C23×D1711yescharacteristic
1297C22×C4C23×D1711yescharacteristic
1298C22×C4C23×D1711yescharacteristic
1299C22×C4C23×D1711yescharacteristic
1300C22×C4C23×D1711yescharacteristic
1301C22×C4C23×D1711yescharacteristic
1302C22×C4C23×D1711yescharacteristic
1303C22×C4C23×D1711yescharacteristic
1304C4⋊C4—22no—
1305C4⋊C4—22no—
1306C4⋊C4—22no—
1307C4⋊C4—22no—
1308C4⋊C4—22no—
1309C4⋊C4—22no—
1310C4⋊C4—22no—
1311C4⋊C4—22no—
1312C4⋊C4—22no—
1313C4⋊C4—342no—
1314C4⋊C4—342no—
1315C4⋊C4—342no—
1316C4⋊C4—342no—
1317C4⋊C4—342no—
1318C4⋊C4—342no—
1319C4⋊C4—342no—
1320C4⋊C4—681no—
1321C4⋊C4—681no—
1322C4⋊C4—681no—
1323C4⋊C4—681no—
1324C4⋊C4—681no—
1325C4⋊C4—681no—
1326C4⋊C4—681no—
1327C4⋊C4—681no—
1328C4⋊C4—681no—
1329C4⋊C4—681no—
1330C4⋊C4—681no—
1331C4⋊C4C2×C22⋊D1714yes—
1332C22⋊C4—22no—
1333C22⋊C4—22no—
1334C22⋊C4—22no—
1335C22⋊C4—22no—
1336C22⋊C4—22no—
1337C22⋊C4—22no—
1338C22⋊C4—22no—
1339C22⋊C4—22no—
1340C22⋊C4—22no—
1341C22⋊C4—22no—
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—342no—
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—
1378C22⋊C4—681no—
1379C22⋊C4—681no—
1380C22⋊C4—681no—
1381C22⋊C4—681no—
1382C22⋊C4—681no—
1383C22⋊C4—681no—
1384C22⋊C4—681no—
1385C22⋊C4—681no—
1386C22⋊C4C2×C22⋊D1714yes—
1387C22⋊C4C2×C22⋊D1714yes—
1388C42—22no—
1389C42—22no—
1390C42—22no—
1391C42—342no—
1392C42—342no—
1393C42—342no—
1394C42—681no—
1395C42—681no—
1396C42—681no—
1397C42—681no—
1398C42C2×C22⋊D1714yes—
1399C23—21no—
1400C23—21no—
1401C23—21no—
1402C23—21no—
1403C23—21no—
1404C23—21no—
1405C23—21no—
1406C23—21no—
1407C23—21no—
1408C23—21no—
1409C23—21no—
1410C23—21no—
1411C23—21no—
1412C23—21no—
1413C23—21no—
1414C23—21no—
1415C23—21no—
1416C23—21no—
1417C23—21no—
1418C23—341no—
1419C23—341no—
1420C23—341no—
1421C23—341no—
1422C23—341no—
1423C23—341no—
1424C23—341no—
1425C23—341no—
1426C23—341no—
1427C23—341no—
1428C23—341no—
1429C23—341no—
1430C23—341no—
1431C23—341no—
1432C23—341no—
1433C23—341no—
1434C23—341no—
1435C23—341no—
1436C23—341no—
1437C23—341no—
1438C23—341no—
1439C23—684no—
1440C23—1362no—
1441C23—1362no—
1442C23—1362no—
1443C23—1362no—
1444C23—1362no—
1445C23—1362no—
1446C23C22×C22⋊D1712yes—
1447C23C22×C22⋊D1712yes—
1448C23C24×D1711yescharacteristic
1449Q8—44no—
1450Q8—82no—
1451Q8—82no—
1452Q8—1362no—
1453D4—44no—
1454D4—82no—
1455D4—82no—
1456D4—684no—
1457D4—1362no—
1458D4—1362no—
1459D4—1362no—
1460D4—1362no—
1461D4—1362no—
1462D4—1362no—
1463D4—1362no—
1464D4—1362no—
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—21no—
1481C2×C4—21no—
1482C2×C4—21no—
1483C2×C4—21no—
1484C2×C4—21no—
1485C2×C4—21no—
1486C2×C4—21no—
1487C2×C4—21no—
1488C2×C4—21no—
1489C2×C4—21no—
1490C2×C4—21no—
1491C2×C4—21no—
1492C2×C4—21no—
1493C2×C4—21no—
1494C2×C4—21no—
1495C2×C4—21no—
1496C2×C4—44no—
1497C2×C4—44no—
1498C2×C4—44no—
1499C2×C4—172no—
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—341no—
1522C2×C4—341no—
1523C2×C4—341no—
1524C2×C4—341no—
1525C2×C4—341no—
1526C2×C4—341no—
1527C2×C4—341no—
1528C2×C4—341no—
1529C2×C4—341no—
1530C2×C4—341no—
1531C2×C4—341no—
1532C2×C4—341no—
1533C2×C4—341no—
1534C2×C4—341no—
1535C2×C4—341no—
1536C2×C4—341no—
1537C2×C4—341no—
1538C2×C4—684no—
1539C2×C4—684no—
1540C2×C4—1362no—
1541C2×C4—1362no—
1542C2×C4C22×C22⋊D1712yes—
1543C2×C4C22×C22⋊D1712yes—
1544C2×C4C22×C22⋊D1712yes—
1545C2×C4C22×C22⋊D1712yes—
1546C2×C4C22×C22⋊D1712yes—
1547C22—22no—
1548C22—22no—
1549C22—22no—
1550C22—22no—
1551C22—22no—
1552C22—22no—
1553C22—41no—
1554C22—41no—
1555C22—41no—
1556C22—41no—
1557C22—41no—
1558C22—41no—
1559C22—41no—
1560C22—41no—
1561C22—41no—
1562C22—41no—
1563C22—41no—
1564C22—41no—
1565C22—41no—
1566C22—41no—
1567C22—41no—
1568C22—681no—
1569C22—681no—
1570C22—681no—
1571C22—681no—
1572C22—681no—
1573C22—681no—
1574C22—681no—
1575C22—681no—
1576C22—681no—
1577C22—681no—
1578C22—681no—
1579C22—681no—
1580C22—681no—
1581C22—681no—
1582C22—681no—
1583C22—681no—
1584C22—681no—
1585C22—681no—
1586C22—681no—
1587C22—681no—
1588C22—681no—
1589C22—1368no—
1590C22C23×C22⋊D1711yescharacteristic
1591C22H(5,𝔽2)×D1711yescharacteristic
1592C22#1176364411yescharacteristic
1593C22#1176364511yescharacteristic
1594C22#1176364511yescharacteristic
1595C22#1176364611yescharacteristic
1596C22#1176364611yescharacteristic
1597C4—22no—
1598C4—22no—
1599C4—22no—
1600C4—22no—
1601C4—22no—
1602C4—41no—
1603C4—41no—
1604C4—41no—
1605C4—41no—
1606C4—41no—
1607C4—41no—
1608C4—41no—
1609C4—342no—
1610C4—681no—
1611C4—681no—
1612C4—681no—
1613C4—681no—
1614C4—681no—
1615C4—681no—
1616C4—681no—
1617C4—681no—
1618C4—681no—
1619C4—681no—
1620C4—681no—
1621C4—681no—
1622C2—42no—
1623C2—42no—
1624C2—81no—
1625C2—1361no—
1626C2—1361no—
1627C2—1361no—
1628C2#1454211311yescharacteristic
1629C2#1454254311yescharacteristic
1630C2#1454257811yescharacteristic
1631C2#1454294711yescharacteristic
1632C2#1454304911yescharacteristic
1633C2#1454346411yescharacteristic
1634C2#1454347611yescharacteristic
subgroupG/H
center, FrattiniC23C24×D17
commutator, socle, cosocleC23×C17C25
FittingC2×C17×#542C2
hypercenterC2×#542D17
hypocenterC17#36745
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×#542

Complements

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

NH ≅ G/Ntype
1. C2×#11763392C2semidirect
2. #14537113C2semidirect
3. #14537087C2semidirect
4. #14535697C2semidirect
5. #14535604C2semidirect
6. #14535591C2semidirect
7. #14535550C2semidirect
8. #14535376C2semidirect
9. #14535352C2semidirect
10. #14535328C2semidirect
11. #14535259C2semidirect
12. #14535214C2semidirect
13. #14535184C2semidirect
14. #14535169C2semidirect
15. #14535160C2semidirect
16. #14535080C2semidirect
17. #14535060C2semidirect
18. #14535005C2semidirect
19. #14534987C2semidirect
20. #14534935C2semidirect
21. #14534912C2semidirect
22. #14534471C2semidirect
23. #14534416C2semidirect
24. #14534398C2semidirect
25. #14534381C2semidirect
26. #14534272C2semidirect
27. #14533943C2semidirect
28. #14532214C2semidirect
29. #14532170C2semidirect
30. #14531229C2semidirect
31. C2×C17×#542C2semidirect
41. C2×#10587632C22semidirect
52. C22×C4×Dic17C22semidirect
53. #11762747C22semidirect
54. #11762747C22semidirect
57. #11762742C22semidirect
58. #11762739C22semidirect
62. #11762737C22semidirect
63. #11762737C22semidirect
67. #11762735C22semidirect
68. #11762734C22semidirect
69. #11762732C22semidirect
73. #11762729C22semidirect
74. #11762728C22semidirect
75. #11762728C22semidirect
87. #11762724C22semidirect
89. #11762721C22semidirect
95. #11762720C22semidirect
100. #11762717C22semidirect
101. #11762716C22semidirect
102. #11762716C22semidirect
103. #11762715C22semidirect
104. #11762715C22semidirect
111. #11762709C22semidirect
112. #11762705C22semidirect
113. #11762704C22semidirect
114. #11762704C22semidirect
115. #11762704C22semidirect
116. #11762704C22semidirect
117. #11762703C22semidirect
118. #11762703C22semidirect
125. #11762700C22semidirect
133. #11762699C22semidirect
134. #11762699C22semidirect
135. #11762699C22semidirect
136. #11762697C22semidirect
137. #11762695C22semidirect
138. #11762695C22semidirect
139. #11762693C22semidirect
140. #11762693C22semidirect
141. #11762693C22semidirect
142. #11762690C22semidirect
146. #11762689C22semidirect
149. #11762688C22semidirect
153. #11762686C22semidirect
154. #11762686C22semidirect
155. #11762685C22semidirect
156. #11762684C22semidirect
157. #11762684C22semidirect
158. #11762682C22semidirect
160. #11762680C22semidirect
161. #11762674C22semidirect
164. #11762667C22semidirect
165. #11762666C22semidirect
169. C4×C4⋊Dic17C22semidirect
171. C4×C22⋊Dic17C22semidirect
172. #11762655C22semidirect
174. C2×C17×C4⋊Q8C22semidirect
176. C2×C17×#126C22semidirect
179. C2×C17×#124C22semidirect
181. C2×C17×#123C22semidirect
183. C2×C17×C22⋊Q8C22semidirect
184. C2×C17×C22⋊Q8C22semidirect
186. C2×C4×Q8×C17C22semidirect
188. C2×C17×#117C22semidirect
226. C4×D4×C17D4semidirect
730. C2×#542D17semidirect
838. C2×C4⋊Q8C2×D17semidirect
842. C2×#126C2×D17semidirect
848. C2×#124C2×D17semidirect
852. C2×#123C2×D17semidirect
856. C2×C22⋊Q8C2×D17semidirect
857. C2×C22⋊Q8C2×D17semidirect
866. C2×C4×Q8C2×D17semidirect
870. C2×#117C2×D17semidirect
1060. C4×D4C22⋊D17semidirect
1196. C17#36745semidirect

Maximal subgroups

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

subgroupindex
C2×#117633922
#145371132
#145370872
#145356972
#145356042
#145355912
#145355502
#145353762
#145353522
#145353282
#145352592
#145352142
#145351842
#145351692
#145351602
#145350802
#145350602
#145350052
#145349872
#145349352
#145349122
#145344712
#145344162
#145343982
#145343812
#145342722
#145339432
#145322142
#145321702
#145312292
C2×C17×#5422
#3674517