Finite Group Databasebeta

← C2×#14542607 #17942804

Subgroups — C2×#14542607 #17942804

Order 4352.

6958 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14542607C2132yesmaximal, direct product factor
2C2×#11763536C212yesmaximal, complemented
3C2×#11763534C212yesmaximal, complemented
4C2×#11763520C212yesmaximal, complemented
5C2×#11763517C214yesmaximal, complemented
6C2×#11763515C212yesmaximal, complemented
7C2×#11763513C214yesmaximal, complemented
8C2×#11763439C212yesmaximal, complemented
9C2×#11763437C211yesmaximal, characteristic, complemented
10C2×#11763436C212yesmaximal, complemented
11C2×#11763364C212yesmaximal, complemented
12C2×#11763362C211yesmaximal, characteristic, complemented
13C22×#10587576C211yesmaximal, characteristic, complemented
14C2×#125×D17C212yesmaximal, complemented
15C2×#11763290C211yesmaximal, characteristic
16C2×#11763289C211yesmaximal, characteristic
17C2×#11763277C211yesmaximal, characteristic
18C2×C17×#544C211yesmaximal, characteristic, complemented
19C22×#63252C2211yescharacteristic
20#11763536C22132yescomplemented
21#11763534C22132yescomplemented
22#11763520C22132yescomplemented
23#11763517C22164yescomplemented
24#11763515C22132yescomplemented
25#11763513C22164yescomplemented
26#11763439C22132yescomplemented
27#11763437C22116yescomplemented
28#11763436C22132yescomplemented
29#11763364C22132yescomplemented
30#11763362C22116yescomplemented
31C2×#10587555C2212yes—
32C2×#10587574C2212yes—
33C2×#10587574C2214yes—
34C2×#10587574C2211yescharacteristic
35C2×#10587574C2211yescharacteristic
36C2×#10587630C2214yes—
37C2×#10587556C2212yes—
38C2×#10587576C2212yes—
39C2×#10587576C2212yes—
40C2×#10587576C2212yes—
41C2×#10587576C2212yes—
42C2×#10587576C2211yescharacteristic
43C2×#10587576C2212yes—
44C2×#10587576C2211yescharacteristic
45C2×#10587576C22116yescomplemented
46C2×#10587575C2214yes—
47C2×#10587575C2214yes—
48C2×#10587575C2214yes—
49C2×#10587575C2214yes—
50#125×D17C22132yescomplemented
51C2×#10587583C2214yes—
52C2×#10587583C2214yes—
53C2×#10587582C2214yes—
54C2×#10587582C2214yes—
55C2×#10587564C2214yes—
56C2×#10587564C2212yes—
57C2×#10587564C2212yes—
58C2×#10587632C2214yes—
59C2×#10587632C2214yes—
60#11763290C22116yes—
61#11763289C22116yes—
62#11763277C22116yes—
63C2×Q8×Dic17C2214yes—
64C2×C4×Dic34C2212yes—
65C2×C4×Dic34C2212yes—
66C2×C4×Dic34C2212yes—
67C2×#10587573C2211yescharacteristic
68C2×#10587573C2212yes—
69C2×#10587573C2211yescharacteristic
70C2×#10587573C2214yes—
71C2×C4×D68C2212yes—
72C2×#10587579C2211yescharacteristic
73C2×#10587579C2211yescharacteristic
74C2×#10587579C2212yes—
75C2×C4×C22⋊D17C2214yes—
76C2×#10587567C2212yes—
77C2×#10587567C2212yes—
78C2×#10587567C2214yes—
79C2×#10587612C2211yescharacteristic
80C2×#10587578C2212yes—
81C2×#10587578C2212yes—
82C2×#10587558C2212yes—
83C22×C4⋊Dic17C2211yescharacteristic
84C22×C4⋊Dic17C2212yes—
85C22×#63225C2212yes—
86C2×C4⋊C4×D17C2212yes—
87C2×C4⋊C4×D17C2212yes—
88C2×C4⋊C4×D17C2214yes—
89C2×C4⋊C4×D17C2214yes—
90C22×C4×Dic17C2211yescharacteristic
91C2×C42×D17C2212yes—
92C17×#544C22116yescomplemented
93C2×C17×C4⋊Q8C2212yes—
94C2×C17×C4⋊Q8C2212yes—
95C2×C17×#125C2212yes—
96C2×C17×#125C2212yes—
97C2×C17×C22⋊Q8C2214yes—
98C2×C17×#117C2211yescharacteristic
99C2×C17×#117C2211yescharacteristic
100C22×C4⋊C4×C17C2211yescharacteristic
101C22×Q8×C17C2314yes—
102C23×C4×C17C2312yes—
103C23×C4×C17C2311yescharacteristic
104C22×C22⋊D17C2312yes—
105C23×Dic17C2311yescharacteristic
106C23×Dic17C2311yescharacteristic
107C23×Dic17C2312yes—
108C2×#63252Q8116yescomplemented
109C2×#63252C2318yes—
110C22×D68C2311yescharacteristic
111C22×C4×D17C2312yes—
112C22×C4×D17C2312yes—
113C22×C4×D17C2314yes—
114C22×C4×D17C2314yes—
115C22×C4×D17C2312yes—
116C22×Dic34C2314yes—
117C22×Dic34C2312yes—
118C22×Dic34C2312yes—
119C22×Dic34C2311yescharacteristic
120C17×C4⋊Q8C23116yes—
121C17×C4⋊Q8C23116yes—
122C17×#125C23116yes—
123C17×#125C23116yes—
124C17×C22⋊Q8C23132yes—
125C17×#117C2318yes—
126C17×#117C2318yes—
127C2×C4⋊C4×C17C2312yes—
128C2×C4⋊C4×C17C2312yes—
129C2×C4⋊C4×C17C2318yes—
130C2×C4⋊C4×C17C2311yescharacteristic
131C2×C4⋊C4×C17C2311yescharacteristic
132C2×C4⋊C4×C17C2311yescharacteristic
133C2×C4⋊C4×C17C2311yescharacteristic
134C2×C4⋊C4×C17C2314yes—
135C2×C4⋊C4×C17C2314yes—
136C2×C4⋊C4×C17C2314yes—
137C2×C22⋊C4×C17C2312yes—
138C2×C22⋊C4×C17C2312yes—
139C2×C42×C17C2312yes—
140C2×C42×C17C2312yes—
141C2×C22⋊Dic17C2312yes—
142#10587632C23132yes—
143#10587632C23132yes—
144Q8×Dic17C23132yes—
145#10587630C23132yes—
146C4×C22⋊D17C23132yes—
147C2×#63227C2312yes—
148C2×#63227C2312yes—
149C2×#63227C2314yes—
150C2×#63227C2314yes—
151#10587612C2318yes—
152C2×C4⋊Dic17C2311yescharacteristic
153C2×C4⋊Dic17C2312yes—
154C2×C4⋊Dic17C2312yes—
155C2×C4⋊Dic17C2314yes—
156C2×C4⋊Dic17C23116yes—
157C2×C4⋊Dic17C2312yes—
158C2×C4⋊Dic17C2318yes—
159C2×C4⋊Dic17C2314yes—
160C2×C4⋊Dic17C2311yescharacteristic
161C2×C4⋊Dic17C2312yes—
162C2×C4⋊Dic17C2314yes—
163C2×#63225C23116yes—
164C2×#63225C2312yes—
165C2×#63225C2314yes—
166C2×#63225C2314yes—
167C2×#63225C2314yes—
168C2×#63225C2314yes—
169C2×#63225C2314yes—
170C2×#63225C2314yes—
171C2×#63225C2312yes—
172C2×#63225C2312yes—
173C2×#63225C2312yes—
174C2×#63225C2312yes—
175C2×#63225C2312yes—
176C2×C4×Dic17C2311yescharacteristic
177C2×C4×Dic17C2312yes—
178C2×C4×Dic17C2312yes—
179C2×C4×Dic17C2311yescharacteristic
180C2×C4×Dic17C2311yescharacteristic
181C2×C4×Dic17C2311yescharacteristic
182C2×C4×Dic17C2318yes—
183C2×C4×Dic17C2314yes—
184C2×C4×Dic17C2314yes—
185C2×C4×Dic17C2312yes—
186#10587583C23132yes—
187#10587583C23132yes—
188#10587582C23132yes—
189#10587582C23132yes—
190#10587579C2318yes—
191#10587579C23116yes—
192#10587579C2318yes—
193#10587578C23116yes—
194#10587578C23116yes—
195C4⋊C4×D17C23132yes—
196C4⋊C4×D17C23132yes—
197C4⋊C4×D17C23116yes—
198C4⋊C4×D17C23116yes—
199#10587576C23116yes—
200#10587576C23116yes—
201#10587576C23116yes—
202#10587576C2318yes—
203#10587576C23116yes—
204#10587576C23116yes—
205#10587576C2318yes—
206#10587575C23132yes—
207#10587575C23132yes—
208#10587575C23132yes—
209#10587575C23132yes—
210#10587574C23116yes—
211#10587574C23132yes—
212#10587574C2318yes—
213#10587574C2318yes—
214#10587573C23132yes—
215#10587573C2318yes—
216#10587573C2318yes—
217#10587573C23116yes—
218#10587567C23116yes—
219#10587567C23132yes—
220#10587567C23116yes—
221#10587564C23116yes—
222#10587564C23132yes—
223#10587564C23116yes—
224C4×D68C23116yes—
225#10587558C23116yes—
226C42×D17C23116yes—
227#10587556C23116yes—
228#10587555C23116yes—
229C4×Dic34C23116yes—
230C4×Dic34C23116yes—
231C4×Dic34C23116yes—
232C24×C17C2411yescharacteristic
233C23×D17C2412yes—
234C2×Q8×C17—48no—
235C2×Q8×C17C24116yes—
236C22×C4×C17—44no—
237C22×C4×C17C2×Q818yes—
238C22×C4×C17C2412yes—
239C22×C4×C17C2412yes—
240C22×C4×C17C2412yes—
241C22×C4×C17C2414yes—
242C22×C4×C17C2412yes—
243C22×C4×C17C2418yes—
244C22×C4×C17C2411yescharacteristic
245C22×C4×C17C2411yescharacteristic
246C22×C4×C17C2414yes—
247C2×C22⋊D17C2×Q8116yes—
248C2×C22⋊D17C2418yes—
249C22×Dic17—42no—
250C22×Dic17—42no—
251C22×Dic17—44no—
252C22×Dic17C2412yes—
253C22×Dic17C2411yescharacteristic
254C22×Dic17C2411yescharacteristic
255C22×Dic17C2412yes—
256C22×Dic17C2414yes—
257C22×Dic17C2411yescharacteristic
258C22×Dic17C2411yescharacteristic
259C22×Dic17C2414yes—
260C22×Dic17C2414yes—
261C22×Dic17C2418yes—
262C22×Dic17C2412yes—
263#63252C2×Q8164yescomplemented
264C2×D68C2×Q818yes—
265C2×D68C2414yes—
266C2×C4×D17—48no—
267C2×C4×D17—48no—
268C2×C4×D17—44no—
269C2×C4×D17—44no—
270C2×C4×D17C2×Q8116yes—
271C2×C4×D17C2418yes—
272C2×C4×D17C2418yes—
273C2×C4×D17C24116yes—
274C2×C4×D17C24116yes—
275C2×C4×D17C2418yes—
276C2×Dic34—44no—
277C2×Dic34—48no—
278C2×Dic34—44no—
279C2×Dic34C2×Q818yes—
280C2×Dic34C2418yes—
281C2×Dic34C2418yes—
282C2×Dic34C24116yes—
283C2×Dic34C2414yes—
284C4⋊C4×C17C24116yes—
285C4⋊C4×C17C24116yes—
286C4⋊C4×C17C24116yes—
287C4⋊C4×C17C2414yes—
288C4⋊C4×C17C2414yes—
289C4⋊C4×C17C2418yes—
290C4⋊C4×C17C2418yes—
291C4⋊C4×C17C2414yes—
292C4⋊C4×C17C2414yes—
293C22⋊C4×C17C2418yes—
294C22⋊C4×C17C2418yes—
295C42×C17C2418yes—
296C42×C17C2418yes—
297C22⋊Dic17C2418yes—
298#63227C2418yes—
299#63227C2418yes—
300#63227C24116yes—
301#63227C24116yes—
302C4⋊Dic17C2418yes—
303C4⋊Dic17C2418yes—
304C4⋊Dic17C2418yes—
305C4⋊Dic17C2414yes—
306C4⋊Dic17C2418yes—
307C4⋊Dic17C24116yes—
308C4⋊Dic17C2414yes—
309C4⋊Dic17C24116yes—
310C4⋊Dic17C24116yes—
311#63225C2418yes—
312#63225C2418yes—
313#63225C2418yes—
314#63225C2418yes—
315#63225C24116yes—
316#63225C24116yes—
317#63225C24116yes—
318#63225C2418yes—
319#63225C2418yes—
320#63225C24116yes—
321#63225C24116yes—
322#63225C24116yes—
323C4×Dic17C2418yes—
324C4×Dic17C2414yes—
325C4×Dic17C2414yes—
326C4×Dic17C24116yes—
327C4×Dic17C2414yes—
328C4×Dic17C2418yes—
329C4×Dic17C2418yes—
330C4×Dic17C2414yes—
331C4×Dic17C24116yes—
332C2×#3504—171nomaximal, Sylow
333C23×C17—22no—
334C23×C17—22no—
335C23×C17C22×Q814yes—
336C23×C17C2512yes—
337C23×C17C2511yescharacteristic
338C22×D17—24no—
339C22×D17—24no—
340C22×D17C22×Q818yes—
341C22×D17C2514yes—
342Q8×C17—416no—
343C2×C4×C17—24no—
344C2×C4×C17—24no—
345C2×C4×C17—24no—
346C2×C4×C17—28no—
347C2×C4×C17—24no—
348C2×C4×C17—48no—
349C2×C4×C17C22×Q814yes—
350C2×C4×C17C22×Q814yes—
351C2×C4×C17C22×Q8116yes—
352C2×C4×C17C2514yes—
353C2×C4×C17C2514yes—
354C2×C4×C17C2514yes—
355C2×C4×C17C2514yes—
356C2×C4×C17C2518yes—
357C2×C4×C17C2512yes—
358C2×C4×C17C2512yes—
359C22⋊D17C22×Q8132yes—
360C2×Dic17—24no—
361C2×Dic17—22no—
362C2×Dic17—22no—
363C2×Dic17—24no—
364C2×Dic17—28no—
365C2×Dic17—22no—
366C2×Dic17—22no—
367C2×Dic17—44no—
368C2×Dic17—44no—
369C2×Dic17—48no—
370C2×Dic17C22×Q818yes—
371C2×Dic17C2514yes—
372C2×Dic17C2514yes—
373C2×Dic17C2512yes—
374C2×Dic17C2512yes—
375C2×Dic17C2518yes—
376C2×Dic17C2512yes—
377C2×Dic17C2512yes—
378C2×Dic17C2514yes—
379D68C22×Q8116yes—
380C4×D17—416no—
381C4×D17—416no—
382C4×D17—48no—
383C4×D17—48no—
384C4×D17C22×Q8132yes—
385Dic34—48no—
386Dic34—416no—
387Dic34—48no—
388Dic34C22×Q8116yes—
389#3504—1732no—
390C2×#557—172no—
391C2×#557—172no—
392C2×#554—172no—
393C2×#554—172no—
394C2×#554—174no—
395C2×#554—174no—
396C2×#544—172no—
397C2×#544—172no—
398C2×#544—171no—
399C2×#544D1711yescharacteristic, complemented
400C2×#533—172no—
401C2×#533—171no—
402C22×#125—172no—
403C22×#125—171no—
404C2×#520—171no—
405C2×#520—171no—
406C2×C4×#41—171no—
407C22×C17—22no—
408C22×C17—22no—
409C22×C17—28no—
410C22×C17C23×Q814yes—
411C22×C17C23×Q812yes—
412C22×C17#58512yes—
413C22×C17#58512yes—
414C22×C17C2611yescharacteristic
415C2×D17—24no—
416C2×D17—24no—
417C2×D17—216no—
418C2×D17C23×Q818yes—
419C4×C17—24no—
420C4×C17—24no—
421C4×C17—24no—
422C4×C17—28no—
423C4×C17—24no—
424C4×C17C23×Q814yes—
425C4×C17C23×Q814yes—
426Dic17—24no—
427Dic17—22no—
428Dic17—22no—
429Dic17—24no—
430Dic17—28no—
431Dic17—22no—
432Dic17—22no—
433Dic17C23×Q818yes—
434C22×#41—171no—
435#557—1732no—
436#557—1732no—
437#554—1732no—
438#554—1732no—
439#554—1764no—
440#554—1764no—
441#544—1732no—
442#544—1732no—
443#544—1716no—
444#544C2×D17116yescomplemented
445#533—1732no—
446#533—1716no—
447C2×C4⋊Q8—174no—
448C2×C4⋊Q8—171no—
449C2×C4⋊Q8—171no—
450C2×C4⋊Q8—174no—
451C2×C4⋊Q8—172no—
452C2×C4⋊Q8—172no—
453C2×C4⋊Q8C2×D1712yes—
454C2×C4⋊Q8C2×D1712yes—
455C2×#125—1732no—
456C2×#125—171no—
457C2×#125—172no—
458C2×#125—172no—
459C2×#125—174no—
460C2×#125—174no—
461C2×#125—172no—
462C2×#125—172no—
463C2×#125—1716no—
464C2×#125—171no—
465C2×#125—174no—
466C2×#125—174no—
467C2×#125—172no—
468C2×#125—172no—
469C2×#125C2×D1712yes—
470C2×#125C2×D1712yes—
471C2×C22⋊Q8—174no—
472C2×C22⋊Q8—174no—
473C2×C22⋊Q8—174no—
474C2×C22⋊Q8—174no—
475C2×C22⋊Q8—174no—
476C2×C22⋊Q8—174no—
477C2×C22⋊Q8—172no—
478C2×C22⋊Q8—172no—
479C2×C22⋊Q8—174no—
480C2×C22⋊Q8C2×D1714yes—
481#520—1716no—
482#520—1716no—
483C4×#41—1716no—
484C2×C4×Q8—174no—
485C2×C4×Q8—171no—
486C2×C4×Q8—171no—
487C2×C4×Q8—172no—
488C2×C4×Q8—174no—
489C2×C4×Q8—172no—
490C2×C4×Q8—172no—
491C2×C4×Q8—172no—
492C2×C4×D4—174no—
493C2×C4×D4—171no—
494C2×C4×D4—171no—
495C2×C4×D4—172no—
496C2×C4×D4—172no—
497C2×C4×D4—172no—
498C2×C4×D4—174no—
499C2×C4×D4—172no—
500C2×#117—171no—
501C2×#117—172no—
502C2×#117—172no—
503C2×#117—172no—
504C2×#117C2×D1711yescharacteristic
505C2×#117C2×D1711yescharacteristic
506C22×C4⋊C4—172no—
507C22×C4⋊C4—171no—
508C22×C4⋊C4—172no—
509C22×C4⋊C4—172no—
510C22×C4⋊C4—172no—
511C22×C4⋊C4—174no—
512C22×C4⋊C4—174no—
513C22×C4⋊C4C2×D1711yescharacteristic
514C22×C42—171no—
515C22×C42—172no—
516C2×C17—24no—
517C2×C17#350414yescomplemented
518C2×C17C24×Q811yescharacteristic
519C2×C17C2×#58511yescharacteristic
520C2×C17C2×#58511yescharacteristic
521D17—28no—
522C2×#41—1716no—
523C2×#41—178no—
524C22×Q8—171no—
525C22×Q8—172no—
526C22×Q8—174no—
527C22×Q8—172no—
528C22×Q8C22×D1714yes—
529C22×D4—172no—
530C22×D4—171no—
531C23×C4—172no—
532C23×C4—172no—
533C23×C4—171no—
534C23×C4—171no—
535C23×C4—174no—
536C23×C4—174no—
537C23×C4—172no—
538C23×C4—172no—
539C23×C4C22×D1712yes—
540C23×C4C22×D1711yescharacteristic
541C4⋊Q8—1732no—
542C4⋊Q8—178no—
543C4⋊Q8—178no—
544C4⋊Q8—1732no—
545C4⋊Q8—1716no—
546C4⋊Q8—1716no—
547C4⋊Q8C22×D17116yes—
548C4⋊Q8C22×D17116yes—
549#125—178no—
550#125—1716no—
551#125—1716no—
552#125—1732no—
553#125—1732no—
554#125—1716no—
555#125—1716no—
556#125—178no—
557#125—1732no—
558#125—1732no—
559#125—1716no—
560#125—1716no—
561#125C22×D17116yes—
562#125C22×D17116yes—
563C22⋊Q8—1732no—
564C22⋊Q8—1732no—
565C22⋊Q8—1732no—
566C22⋊Q8—1732no—
567C22⋊Q8—1732no—
568C22⋊Q8—1732no—
569C22⋊Q8—1716no—
570C22⋊Q8—1716no—
571C22⋊Q8—1732no—
572C22⋊Q8C22×D17132yes—
573C4×Q8—1732no—
574C4×Q8—178no—
575C4×Q8—178no—
576C4×Q8—1716no—
577C4×Q8—1732no—
578C4×Q8—1716no—
579C4×Q8—1716no—
580C4×Q8—1716no—
581C4×D4—1732no—
582C4×D4—178no—
583C4×D4—178no—
584C4×D4—1716no—
585C4×D4—1716no—
586C4×D4—1716no—
587C4×D4—1732no—
588C4×D4—1716no—
589#117—178no—
590#117—1716no—
591#117—1716no—
592#117—1716no—
593#117C22×D1718yes—
594#117C22×D1718yes—
595C2×C4⋊C4—172no—
596C2×C4⋊C4—171no—
597C2×C4⋊C4—174no—
598C2×C4⋊C4—172no—
599C2×C4⋊C4—174no—
600C2×C4⋊C4—172no—
601C2×C4⋊C4—174no—
602C2×C4⋊C4—174no—
603C2×C4⋊C4—172no—
604C2×C4⋊C4—178no—
605C2×C4⋊C4—174no—
606C2×C4⋊C4—174no—
607C2×C4⋊C4—174no—
608C2×C4⋊C4—174no—
609C2×C4⋊C4—1716no—
610C2×C4⋊C4—1716no—
611C2×C4⋊C4—171no—
612C2×C4⋊C4—172no—
613C2×C4⋊C4—172no—
614C2×C4⋊C4—172no—
615C2×C4⋊C4—172no—
616C2×C4⋊C4—172no—
617C2×C4⋊C4—172no—
618C2×C4⋊C4—174no—
619C2×C4⋊C4—1716no—
620C2×C4⋊C4—1716no—
621C2×C4⋊C4—1732no—
622C2×C4⋊C4—1732no—
623C2×C4⋊C4C22×D1711yescharacteristic
624C2×C4⋊C4C22×D1712yes—
625C2×C4⋊C4C22×D1714yes—
626C2×C4⋊C4C22×D1714yes—
627C2×C4⋊C4C22×D1712yes—
628C2×C4⋊C4C22×D1718yes—
629C2×C4⋊C4C22×D1711yescharacteristic
630C2×C4⋊C4C22×D1711yescharacteristic
631C2×C4⋊C4C22×D1711yescharacteristic
632C2×C4⋊C4C22×D1714yes—
633C2×C22⋊C4—172no—
634C2×C22⋊C4—174no—
635C2×C22⋊C4—172no—
636C2×C22⋊C4—172no—
637C2×C22⋊C4—174no—
638C2×C22⋊C4C22×D1712yes—
639C2×C22⋊C4C22×D1712yes—
640C2×C42—171no—
641C2×C42—174no—
642C2×C42—174no—
643C2×C42—172no—
644C2×C42—172no—
645C2×C42—172no—
646C2×C42—171no—
647C2×C42—171no—
648C2×C42—178no—
649C2×C42—171no—
650C2×C42—1716no—
651C2×C42C22×D1712yes—
652C2×C42C22×D1712yes—
653C17C2×#350411yescharacteristic, complemented, Sylow
654C24—172no—
655C24C23×D1711yescharacteristic
656#41—1764no—
657C2×Q8—48no—
658C2×Q8—178no—
659C2×Q8—174no—
660C2×Q8—178no—
661C2×Q8—1716no—
662C2×Q8—178no—
663C2×Q8—684no—
664C2×Q8—684no—
665C2×Q8—688no—
666C2×Q8C23×D17116yes—
667C2×D4—1716no—
668C2×D4—178no—
669C2×D4—178no—
670C2×D4—174no—
671C22×C4—44no—
672C22×C4—172no—
673C22×C4—1716no—
674C22×C4—178no—
675C22×C4—171no—
676C22×C4—171no—
677C22×C4—172no—
678C22×C4—171no—
679C22×C4—171no—
680C22×C4—172no—
681C22×C4—174no—
682C22×C4—174no—
683C22×C4—174no—
684C22×C4—178no—
685C22×C4—178no—
686C22×C4—178no—
687C22×C4—1716no—
688C22×C4—1716no—
689C22×C4—688no—
690C22×C4—684no—
691C22×C4—688no—
692C22×C4—684no—
693C22×C4—682no—
694C22×C4—682no—
695C22×C4—684no—
696C22×C4Q8×D1718yes—
697C22×C4C23×D1712yes—
698C22×C4C23×D1712yes—
699C22×C4C23×D1712yes—
700C22×C4C23×D1714yes—
701C22×C4C23×D1712yes—
702C22×C4C23×D1718yes—
703C22×C4C23×D1714yes—
704C22×C4C23×D1711yescharacteristic
705C22×C4C23×D1711yescharacteristic
706C4⋊C4—178no—
707C4⋊C4—174no—
708C4⋊C4—1716no—
709C4⋊C4—178no—
710C4⋊C4—1716no—
711C4⋊C4—178no—
712C4⋊C4—1716no—
713C4⋊C4—1716no—
714C4⋊C4—178no—
715C4⋊C4—1716no—
716C4⋊C4—1716no—
717C4⋊C4—1716no—
718C4⋊C4—1716no—
719C4⋊C4—174no—
720C4⋊C4—178no—
721C4⋊C4—178no—
722C4⋊C4—178no—
723C4⋊C4—178no—
724C4⋊C4—178no—
725C4⋊C4—178no—
726C4⋊C4—1716no—
727C4⋊C4C23×D1714yes—
728C4⋊C4C23×D1718yes—
729C4⋊C4C23×D17116yes—
730C4⋊C4C23×D17116yes—
731C4⋊C4C23×D1718yes—
732C4⋊C4C23×D1714yes—
733C4⋊C4C23×D1714yes—
734C4⋊C4C23×D1714yes—
735C4⋊C4C23×D17116yes—
736C22⋊C4—178no—
737C22⋊C4—1716no—
738C22⋊C4—178no—
739C22⋊C4—178no—
740C22⋊C4—1716no—
741C22⋊C4C23×D1718yes—
742C22⋊C4C23×D1718yes—
743C42—174no—
744C42—174no—
745C42—178no—
746C42—178no—
747C42—174no—
748C42—174no—
749C42—1716no—
750C42—1716no—
751C42—178no—
752C42C23×D1718yes—
753C42C23×D1718yes—
754C23—22no—
755C23—22no—
756C23—178no—
757C23—174no—
758C23—344no—
759C23—344no—
760C23C2×Q8×D1714yes—
761C23C24×D1712yes—
762C23C24×D1711yescharacteristic
763Q8—416no—
764Q8—1716no—
765Q8—688no—
766Q8—688no—
767Q8—6816no—
768D4—1732no—
769D4—1716no—
770C2×C4—28no—
771C2×C4—24no—
772C2×C4—24no—
773C2×C4—24no—
774C2×C4—24no—
775C2×C4—48no—
776C2×C4—178no—
777C2×C4—174no—
778C2×C4—1732no—
779C2×C4—172no—
780C2×C4—172no—
781C2×C4—174no—
782C2×C4—172no—
783C2×C4—172no—
784C2×C4—174no—
785C2×C4—178no—
786C2×C4—342no—
787C2×C4—344no—
788C2×C4—342no—
789C2×C4—342no—
790C2×C4—348no—
791C2×C4—342no—
792C2×C4—344no—
793C2×C4—6816no—
794C2×C4—688no—
795C2×C4—6816no—
796C2×C4—688no—
797C2×C4—684no—
798C2×C4—684no—
799C2×C4—688no—
800C2×C4C2×Q8×D1714yes—
801C2×C4C2×Q8×D1714yes—
802C2×C4C2×Q8×D17116yes—
803C2×C4C24×D1714yes—
804C2×C4C24×D1714yes—
805C2×C4C24×D1714yes—
806C2×C4C24×D1718yes—
807C2×C4C24×D1714yes—
808C2×C4C24×D1712yes—
809C2×C4C24×D1712yes—
810C22—28no—
811C22—22no—
812C22—22no—
813C22—178no—
814C22—3416no—
815C22—344no—
816C22—344no—
817C22C22×Q8×D1714yes—
818C22C22×Q8×D1712yes—
819C22#1176364412yes—
820C22#1176364612yes—
821C22C25×D1711yescharacteristic
822C4—28no—
823C4—24no—
824C4—24no—
825C4—24no—
826C4—24no—
827C4—178no—
828C4—342no—
829C4—344no—
830C4—342no—
831C4—342no—
832C4—348no—
833C4—342no—
834C4—344no—
835C4C22×Q8×D1714yes—
836C4C22×Q8×D1714yes—
837C2—24no—
838C2—348no—
839C2#1454260714yesdirect product factor
840C2C23×Q8×D1711yescharacteristic
841C2C2×#1176364411yescharacteristic
842C2C2×#1176364611yescharacteristic
subgroupG/H
centerC23C24×D17
commutator, cosocleC22×C17C26
FrattiniC22C25×D17
FittingC2×C17×#544C2
socleC23×C17C25
prime radicalC22×#63252C22
hypercenterC2×#544D17
hypocenterC17C2×#3504
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×#544

Complements

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

NH ≅ G/Ntype
1. #14542607C2direct (N × H)
2. C2×#11763536C2semidirect
3. C2×#11763534C2semidirect
4. C2×#11763520C2semidirect
5. C2×#11763517C2semidirect
6. C2×#11763515C2semidirect
7. C2×#11763513C2semidirect
8. C2×#11763439C2semidirect
9. C2×#11763437C2semidirect
10. C2×#11763436C2semidirect
11. C2×#11763364C2semidirect
12. C2×#11763362C2semidirect
13. C22×#10587576C2semidirect
14. C2×#125×D17C2semidirect
18. C2×C17×#544C2semidirect
20. #11763536C22semidirect
21. #11763534C22semidirect
22. #11763520C22semidirect
23. #11763517C22semidirect
24. #11763515C22semidirect
25. #11763513C22semidirect
26. #11763439C22semidirect
27. #11763437C22semidirect
28. #11763436C22semidirect
29. #11763364C22semidirect
30. #11763362C22semidirect
45. C2×#10587576C22semidirect
50. #125×D17C22semidirect
92. C17×#544C22semidirect
108. C2×#63252Q8semidirect
263. #63252C2×Q8semidirect
399. C2×#544D17semidirect
444. #544C2×D17semidirect
517. C2×C17#3504semidirect
653. C17C2×#3504semidirect
839. C2#14542607direct (N × H)

Maximal subgroups

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

subgroupindex
#145426072
C2×#117635362
C2×#117635342
C2×#117635202
C2×#117635172
C2×#117635152
C2×#117635132
C2×#117634392
C2×#117634372
C2×#117634362
C2×#117633642
C2×#117633622
C22×#105875762
C2×#125×D172
C2×#117632902
C2×#117632892
C2×#117632772
C2×C17×#5442
C2×#350417