Finite Group Databasebeta

← C2×#22622752 #33965743

Subgroups — C2×#22622752 #33965743

Order 18688.

1886 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989297C211yesmaximal, characteristic, complemented
2#22622752C2116yesmaximal, direct product factor
3C2×#17988955C211yesmaximal, characteristic, complemented
4C2×#17988946C211yesmaximal, characteristic, complemented
5C2×#17988941C211yesmaximal, characteristic, complemented
6C2×#17988894C211yesmaximal, characteristic, complemented
7C2×#17988872C211yesmaximal, characteristic, complemented
8C2×#17988887C211yesmaximal, characteristic, complemented
9C2×#17988799C211yesmaximal, characteristic
10C2×#17988799C211yesmaximal, characteristic
11C2×#17988789C211yesmaximal, characteristic, complemented
12C2×#17988718C211yesmaximal, characteristic, complemented
13C2×#17988697C211yesmaximal, characteristic
14C2×#17988685C211yesmaximal, characteristic, complemented
15C2×C4×#11924015C211yesmaximal, characteristic, complemented
16C2×#556×C73C211yesmaximal, characteristic, complemented
17C22×#11924015C2211yescharacteristic
18C22×#11924015C2211yescharacteristic
19C22×#11924013C2211yescharacteristic
20#17989297—24no—
21#17989297C2218yescomplemented
22C2×#14556591C2211yescharacteristic
23C2×#14556583C2211yescharacteristic
24C2×#14556583C2211yescharacteristic
25C2×#14556569—21no—
26C2×#14556569—21no—
27C2×#14556567—21no—
28C2×C4×D292C2211yescharacteristic
29C2×C4×D292C2211yescharacteristic
30C2×C4×D292C2211yescharacteristic
31C2×C4⋊C4×D73—21no—
32#17988955C2218yescomplemented
33#17988946C2218yescomplemented
34#17988941C2218yescomplemented
35#17988894C2218yescomplemented
36#17988887C2218yescomplemented
37#17988872C2218yescomplemented
38#17988799C2218yes—
39#17988799C2218yes—
40#17988789C2218yescomplemented
41#17988718C2218yescomplemented
42#17988697C2218yes—
43#17988685C2218yescomplemented
44C4×#11924015C2218yescomplemented
45C2×#14556524C2211yescharacteristic
46C2×#14556522C2211yescharacteristic
47C2×#14556522C2211yescharacteristic
48C2×C4⋊#10596831C2211yescharacteristic
49C2×C4⋊#10596831C2211yescharacteristic
50C2×C4⋊#10596831C2211yescharacteristic
51C2×#14556515C2211yescharacteristic
52C2×#14556515C2211yescharacteristic
53C2×#14556515C2211yescharacteristic
54C2×#14556515C2211yescharacteristic
55C2×#14556515C2211yescharacteristic
56C2×#14556515C2211yescharacteristic
57C2×#14556512C2211yescharacteristic
58C2×#14556512C2211yescharacteristic
59C2×#14556512C2211yescharacteristic
60C2×#14556511C2211yescharacteristic
61C2×#14556502C2211yescharacteristic
62C2×#14556502C2211yescharacteristic
63C2×C4×#10596831C2211yescharacteristic
64#556×C73—24no—
65#556×C73C2218yescomplemented
66C2×C4⋊Q8×C73C2211yescharacteristic
67C2×#126×C73—21no—
68C2×#126×C73—21no—
69C2×#124×C73C2211yescharacteristic
70C2×#124×C73C2211yescharacteristic
71C2×C22⋊Q8×C73—21no—
72C2×C4×Q8×C73C2211yescharacteristic
73C2×C4×Q8×C73C2211yescharacteristic
74C2×C4×Q8×C73C2211yescharacteristic
75C2×C4×D4×C73C2211yescharacteristic
76C2×#117×C73—21no—
77C22×Dic146—21no—
78C22×D292C2311yescharacteristic
79C22×C4×D73—21no—
80C22×C4×D73—21no—
81C22×C4×D73—21no—
82C2×#11924015—24no—
83C2×#11924015—24no—
84C2×#11924015C2314yes—
85C2×#11924015C2314yes—
86C2×#11924013—24no—
87C2×#11924013C2314yes—
88C22×#10596831C2311yescharacteristic
89C22×#10596831C2311yescharacteristic
90C22×#10596831C2311yescharacteristic
91C22×#10596831C2311yescharacteristic
92#14556591—22no—
93#14556591C2314yes—
94#14556583—22no—
95#14556583—22no—
96#14556583C2314yes—
97#14556583C2314yes—
98#14556569—28no—
99#14556569—28no—
100#14556567—28no—
101C4×D292—22no—
102C4×D292—22no—
103C4×D292—22no—
104C4×D292C2314yes—
105C4×D292C2314yes—
106C4×D292C2314yes—
107C2×C4⋊Dic73—21no—
108C2×C4⋊Dic73C2311yescharacteristic
109C2×C4⋊Dic73C2311yescharacteristic
110C2×C4⋊Dic73C2311yescharacteristic
111C2×#11924007—21no—
112C2×#11924007—21no—
113C2×#11924007—21no—
114C2×#11924007—21no—
115C4⋊C4×D73—28no—
116C2×#11924005—21no—
117C2×#11924005—21no—
118C2×#11924005—21no—
119#14556524C2314yes—
120#14556522C2314yes—
121#14556522C2314yes—
122C4⋊#10596831C2314yes—
123C4⋊#10596831C2314yes—
124C4⋊#10596831C2314yes—
125#14556515C2314yes—
126#14556515C2314yes—
127#14556515C2314yes—
128#14556515C2314yes—
129#14556515C2314yes—
130#14556515C2314yes—
131#14556512C2314yes—
132#14556512C2314yes—
133#14556512C2314yes—
134#14556511C2314yes—
135#14556502C2314yes—
136#14556502C2314yes—
137C4×#10596831C2314yes—
138C22×Q8×C73D411yescharacteristic
139C22×Q8×C73C2311yescharacteristic
140C22×Q8×C73C2311yescharacteristic
141C22×D4×C73C2311yescharacteristic
142C23×C4×C73—21no—
143C4⋊Q8×C73—22no—
144C4⋊Q8×C73C2314yes—
145#126×C73—28no—
146#126×C73—28no—
147#124×C73—22no—
148#124×C73—22no—
149#124×C73C2314yes—
150#124×C73C2314yes—
151C22⋊Q8×C73—28no—
152C4×Q8×C73—22no—
153C4×Q8×C73—22no—
154C4×Q8×C73D414yes—
155C4×Q8×C73C2314yes—
156C4×Q8×C73C2314yes—
157C4×Q8×C73C2314yes—
158C4×D4×C73—22no—
159C4×D4×C73C2314yes—
160#117×C73—28no—
161C2×C4⋊C4×C73—21no—
162C2×C4⋊C4×C73—21no—
163C2×C4⋊C4×C73—21no—
164C2×C4⋊C4×C73—21no—
165C2×C4⋊C4×C73D411yescharacteristic
166C2×C4⋊C4×C73D411yescharacteristic
167C2×C4⋊C4×C73D411yescharacteristic
168C2×C4⋊C4×C73C2311yescharacteristic
169C2×C22⋊C4×C73—21no—
170C2×C22⋊C4×C73—21no—
171C2×C22⋊C4×C73—21no—
172C2×C22⋊C4×C73—21no—
173C2×C22⋊C4×C73—21no—
174C2×C42×C73—21no—
175C2×C42×C73—21no—
176C2×C42×C73C2311yescharacteristic
177C2×C42×C73C2311yescharacteristic
178C2×C42×C73C2311yescharacteristic
179C23×D73—21no—
180C2×Dic146—24no—
181C2×Dic146—82no—
182C2×D292—21no—
183C2×D292—22no—
184C2×D292#4114yes—
185C2×D292C2412yes—
186C22×Dic73—21no—
187C22×Dic73—21no—
188C22×Dic73—21no—
189C2×C4×D73—24no—
190C2×C4×D73—24no—
191C2×C4×D73—24no—
192C2×C4×D73—44no—
193C2×C4×D73—82no—
194C2×C4×D73—82no—
195#11924015—28no—
196#11924015—28no—
197#11924013—28no—
198C2×#10596831—22no—
199C2×#10596831—22no—
200C2×#10596831—22no—
201C2×#10596831—22no—
202C2×#10596831C2412yes—
203C2×#10596831C2412yes—
204C2×#10596831C2412yes—
205C2×#10596831C2412yes—
206C4⋊Dic73—24no—
207C4⋊Dic73—21no—
208C4⋊Dic73—21no—
209C4⋊Dic73—21no—
210C4⋊Dic73C2412yes—
211C4⋊Dic73C2412yes—
212C4⋊Dic73C2412yes—
213#11924007—24no—
214#11924007—24no—
215#11924007—24no—
216#11924007—24no—
217#11924005—24no—
218#11924005—24no—
219#11924005—24no—
220C24×C73—21no—
221C2×Q8×C73—21no—
222C2×Q8×C73—21no—
223C2×Q8×C73—22no—
224C2×Q8×C73—22no—
225C2×Q8×C73—22no—
226C2×Q8×C73—22no—
227C2×Q8×C73—42no—
228C2×Q8×C73C2×D414yes—
229C2×Q8×C73C2412yes—
230C2×Q8×C73C2412yes—
231C2×D4×C73—21no—
232C2×D4×C73—22no—
233C2×D4×C73—22no—
234C2×D4×C73C2412yes—
235C22×C4×C73—21no—
236C22×C4×C73—21no—
237C22×C4×C73—21no—
238C22×C4×C73—24no—
239C22×C4×C73—44no—
240C22×C4×C73C2×D411yescharacteristic
241C22×C4×C73C2×D411yescharacteristic
242C22×C4×C73C2×D411yescharacteristic
243C22×C4×C73C2×D411yescharacteristic
244C22×C4×C73C2×D411yescharacteristic
245C22×C4×C73C2×D411yescharacteristic
246C22×C4×C73C2411yescharacteristic
247C4⋊C4×C73—24no—
248C4⋊C4×C73—24no—
249C4⋊C4×C73—24no—
250C4⋊C4×C73—24no—
251C4⋊C4×C73—21no—
252C4⋊C4×C73C2×D414yes—
253C4⋊C4×C73C2×D414yes—
254C4⋊C4×C73C2×D414yes—
255C4⋊C4×C73C2412yes—
256C22⋊C4×C73—24no—
257C22⋊C4×C73—24no—
258C22⋊C4×C73—24no—
259C22⋊C4×C73—24no—
260C22⋊C4×C73—24no—
261C42×C73—24no—
262C42×C73—24no—
263C42×C73C2×D412yes—
264C42×C73C2×D412yes—
265C42×C73C2×D412yes—
266C42×C73C2412yes—
267C42×C73C2412yes—
268C42×C73C2412yes—
269C23×C73—22no—
270C23×C73—42no—
271C23×C73—42no—
272C23×C73—42no—
273C23×C73C22×D411yescharacteristic
274C22×D73—24no—
275C22×D73—22no—
276C22×D73—42no—
277C22×D73—42no—
278Q8×C73—22no—
279Q8×C73—22no—
280Q8×C73—22no—
281Q8×C73—22no—
282Q8×C73—44no—
283Q8×C73—42no—
284Q8×C73—42no—
285D4×C73—22no—
286D4×C73—22no—
287D4×C73—42no—
288C2×C4×C73—22no—
289C2×C4×C73—22no—
290C2×C4×C73—22no—
291C2×C4×C73—22no—
292C2×C4×C73—22no—
293C2×C4×C73—22no—
294C2×C4×C73—22no—
295C2×C4×C73—22no—
296C2×C4×C73—22no—
297C2×C4×C73—48no—
298C2×C4×C73—42no—
299C2×C4×C73—42no—
300C2×C4×C73—42no—
301C2×C4×C73C22×D412yes—
302C2×C4×C73C22×D412yes—
303C2×C4×C73C22×D412yes—
304C2×C4×C73C22×D412yes—
305C2×C4×C73C22×D412yes—
306C2×C4×C73C22×D412yes—
307C2×C4×C73C22×D411yescharacteristic
308C2×C4×C73C2×#4112yes—
309C2×C4×C732−1+412yes—
310C2×C4×C73C2511yescharacteristic
311C2×Dic73—22no—
312C2×Dic73—22no—
313C2×Dic73—22no—
314C2×Dic73—42no—
315C2×Dic73—42no—
316C2×Dic73—42no—
317D292—24no—
318D292—22no—
319D292C2×#4114yes—
320C4×D73—48no—
321C4×D73—84no—
322C4×D73—84no—
323Dic146—84no—
324#10596831—22no—
325#10596831—22no—
326#10596831—22no—
327#10596831—22no—
328C22×C73—42no—
329C22×C73—42no—
330C22×C73—42no—
331C22×C73—84no—
332C22×C73#54812yes—
333C22×C73#57512yes—
334C22×C73#57712yes—
335C22×C73C23×D411yescharacteristic
336C2×D73—24no—
337C2×D73—48no—
338C2×D73—42no—
339C2×D73—42no—
340C4×C73—22no—
341C4×C73—22no—
342C4×C73—22no—
343C4×C73—22no—
344C4×C73—22no—
345C4×C73—22no—
346C4×C73—42no—
347C4×C73—42no—
348C4×C73—42no—
349C4×C73#54812yes—
350C4×C73C22×#4111yescharacteristic
351C4×C73C2×2−1+411yescharacteristic
352Dic73—42no—
353Dic73—42no—
354Dic73—42no—
355C2×#3376—731nomaximal, Sylow
356C2×C73—82no—
357C2×C73#337614yescomplemented
358C2×C73C2×#54811yescharacteristic
359C2×C73C2×#57511yescharacteristic
360C2×C73C2×#57711yescharacteristic
361D73—44no—
362C2×#556D7311yescharacteristic, complemented
363C2×#554—731no—
364#3376—7316no—
365C2×#491—731no—
366C2×#489—731no—
367C2×#488—731no—
368C2×#479—731no—
369C2×#475—731no—
370C2×#478—731no—
371C2×#463—731no—
372C2×#463—731no—
373C2×#461—731no—
374C2×#446—731no—
375C2×#442—731no—
376C2×#440—731no—
377C2×C4×SD16—731no—
378C73C2×#337611yescharacteristic, complemented, Sylow
379C22×SD16—731no—
380C22×SD16—731no—
381C22×D8—731no—
382#556—24no—
383#556C2×D7318yescomplemented
384#554—738no—
385#554—1464no—
386C2×C4⋊Q8—731no—
387C2×C4⋊Q8C2×D7311yescharacteristic
388C2×#126—21no—
389C2×#126—21no—
390C2×#125—731no—
391C2×#125—731no—
392C2×#124C2×D7311yescharacteristic
393C2×#124C2×D7311yescharacteristic
394C2×C22⋊Q8—21no—
395C2×C22⋊Q8—1461no—
396C2×C22⋊Q8—1461no—
397C2×C22⋊Q8—1461no—
398C2×C4×Q8C2×D7311yescharacteristic
399C2×C4×Q8C2×D7311yescharacteristic
400C2×C4×Q8C2×D7311yescharacteristic
401C2×C4×D4—731no—
402C2×C4×D4—731no—
403C2×C4×D4—731no—
404C2×C4×D4C2×D7311yescharacteristic
405C2×#117—21no—
406C22×C4⋊C4—1461no—
407#491—738no—
408#489—738no—
409#488—738no—
410#479—738no—
411#478—738no—
412#475—738no—
413#463—738no—
414#463—738no—
415#461—738no—
416#446—738no—
417#442—738no—
418#440—738no—
419C4×SD16—738no—
420C2×#107—731no—
421C2×#106—731no—
422C2×#106—731no—
423C2×C4⋊C8—731no—
424C2×C4⋊C8—731no—
425C2×C4⋊C8—731no—
426C2×#103—731no—
427C2×#103—731no—
428C2×#103—731no—
429C2×#103—731no—
430C2×#103—731no—
431C2×#103—731no—
432C2×#102—731no—
433C2×#102—731no—
434C2×#102—731no—
435C2×#102—731no—
436C2×#97—731no—
437C2×#97—731no—
438C2×C4×C8—731no—
439C22×Q8—1461no—
440C22×Q8C22⋊D7311yescharacteristic
441C22×Q8C22×D7311yescharacteristic
442C22×Q8C22×D7311yescharacteristic
443C22×D4—731no—
444C22×D4C22×D7311yescharacteristic
445C23×C4—21no—
446C23×C4—1461no—
447C23×C4—1461no—
448C23×C4—1461no—
449C2×SD16—734no—
450C2×SD16—734no—
451C2×SD16—1464no—
452C2×SD16—1464no—
453C2×D8—734no—
454C2×D8—1464no—
455C22×C8—731no—
456C22×C8—731no—
457C22×C8—731no—
458C22×C8—731no—
459C4⋊Q8—22no—
460C4⋊Q8—734no—
461C4⋊Q8—1462no—
462C4⋊Q8C22×D7314yes—
463#126—28no—
464#126—28no—
465#125—734no—
466#125—734no—
467#125—1462no—
468#125—1462no—
469#124—22no—
470#124—22no—
471#124C22×D7314yes—
472#124C22×D7314yes—
473C22⋊Q8—28no—
474C22⋊Q8—1468no—
475C22⋊Q8—1468no—
476C22⋊Q8—1468no—
477C4×Q8—22no—
478C4×Q8—22no—
479C4×Q8C22⋊D7314yes—
480C4×Q8C22×D7314yes—
481C4×Q8C22×D7314yes—
482C4×Q8C22×D7314yes—
483C4×D4—22no—
484C4×D4—734no—
485C4×D4—734no—
486C4×D4—734no—
487C4×D4—1462no—
488C4×D4—1462no—
489C4×D4—1462no—
490C4×D4C22×D7314yes—
491#117—28no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—21no—
495C2×C4⋊C4—21no—
496C2×C4⋊C4—731no—
497C2×C4⋊C4—731no—
498C2×C4⋊C4—731no—
499C2×C4⋊C4—1461no—
500C2×C4⋊C4—1461no—
501C2×C4⋊C4—1461no—
502C2×C4⋊C4—1461no—
503C2×C4⋊C4—1461no—
504C2×C4⋊C4—1468no—
505C2×C4⋊C4C22⋊D7311yescharacteristic
506C2×C4⋊C4C22⋊D7311yescharacteristic
507C2×C4⋊C4C22⋊D7311yescharacteristic
508C2×C4⋊C4C22×D7311yescharacteristic
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4—1461no—
515C2×C22⋊C4—1461no—
516C2×C22⋊C4—1461no—
517C2×C42—21no—
518C2×C42—21no—
519C2×C42C22×D7311yescharacteristic
520C2×C42C22×D7311yescharacteristic
521C2×C42C22×D7311yescharacteristic
522#107—734no—
523#106—734no—
524#106—734no—
525C4⋊C8—734no—
526C4⋊C8—734no—
527C4⋊C8—734no—
528#103—734no—
529#103—734no—
530#103—734no—
531#103—734no—
532#103—734no—
533#103—734no—
534#102—734no—
535#102—734no—
536#102—734no—
537#102—734no—
538#97—734no—
539#97—734no—
540C4×C8—734no—
541C24—21no—
542C24—1461no—
543C2×Q8—21no—
544C2×Q8—21no—
545C2×Q8—22no—
546C2×Q8—22no—
547C2×Q8—22no—
548C2×Q8—22no—
549C2×Q8—42no—
550C2×Q8—5842no—
551C2×Q8—1464no—
552C2×Q8C2×C22⋊D7314yes—
553C2×Q8C23×D7312yes—
554C2×Q8C23×D7312yes—
555C2×D4—21no—
556C2×D4—22no—
557C2×D4—22no—
558C2×D4—734no—
559C2×D4—732no—
560C2×D4—1461no—
561C2×D4—1462no—
562C2×D4C23×D7312yes—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—24no—
567C22×C4—44no—
568C22×C4—2924no—
569C22×C4—5842no—
570C22×C4—5842no—
571C22×C4—1461no—
572C22×C4—1461no—
573C22×C4—1461no—
574C22×C4—1464no—
575C22×C4—1464no—
576C22×C4—1464no—
577C22×C4C2×C22⋊D7311yescharacteristic
578C22×C4C2×C22⋊D7311yescharacteristic
579C22×C4C2×C22⋊D7311yescharacteristic
580C22×C4C2×C22⋊D7311yescharacteristic
581C22×C4C2×C22⋊D7311yescharacteristic
582C22×C4C2×C22⋊D7311yescharacteristic
583C22×C4C23×D7311yescharacteristic
584SD16—1468no—
585SD16—1468no—
586D8—1468no—
587C2×C8—732no—
588C2×C8—732no—
589C2×C8—732no—
590C2×C8—732no—
591C2×C8—1462no—
592C2×C8—1462no—
593C2×C8—1462no—
594C2×C8—1462no—
595C4⋊C4—24no—
596C4⋊C4—24no—
597C4⋊C4—24no—
598C4⋊C4—24no—
599C4⋊C4—21no—
600C4⋊C4—732no—
601C4⋊C4—732no—
602C4⋊C4—732no—
603C4⋊C4—1464no—
604C4⋊C4—1464no—
605C4⋊C4—1464no—
606C4⋊C4—1464no—
607C4⋊C4—1461no—
608C4⋊C4—1461no—
609C4⋊C4—1461no—
610C4⋊C4—1464no—
611C4⋊C4C2×C22⋊D7314yes—
612C4⋊C4C2×C22⋊D7314yes—
613C4⋊C4C2×C22⋊D7314yes—
614C4⋊C4C23×D7312yes—
615C22⋊C4—24no—
616C22⋊C4—24no—
617C22⋊C4—24no—
618C22⋊C4—24no—
619C22⋊C4—24no—
620C22⋊C4—1464no—
621C22⋊C4—1464no—
622C22⋊C4—1464no—
623C42—24no—
624C42—24no—
625C42C2×C22⋊D7312yes—
626C42C2×C22⋊D7312yes—
627C42C2×C22⋊D7312yes—
628C42C23×D7312yes—
629C42C23×D7312yes—
630C42C23×D7312yes—
631C23—22no—
632C23—42no—
633C23—42no—
634C23—42no—
635C23—2922no—
636C23—2922no—
637C23—1462no—
638C23—1464no—
639C23C22×C22⋊D7311yescharacteristic
640Q8—22no—
641Q8—22no—
642Q8—22no—
643Q8—22no—
644Q8—44no—
645Q8—42no—
646Q8—42no—
647Q8—5844no—
648D4—22no—
649D4—22no—
650D4—42no—
651D4—734no—
652D4—1462no—
653D4—1464no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—48no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—2928no—
668C2×C4—2922no—
669C2×C4—2922no—
670C2×C4—2922no—
671C2×C4—5844no—
672C2×C4—5844no—
673C2×C4—1462no—
674C2×C4—1462no—
675C2×C4—1462no—
676C2×C4C22×C22⋊D7312yes—
677C2×C4C22×C22⋊D7312yes—
678C2×C4C22×C22⋊D7312yes—
679C2×C4C22×C22⋊D7312yes—
680C2×C4C22×C22⋊D7312yes—
681C2×C4C22×C22⋊D7312yes—
682C2×C4C22×C22⋊D7311yescharacteristic
683C2×C4#41×D7312yes—
684C2×C4#1455663812yes—
685C2×C4C24×D7311yescharacteristic
686C8—1462no—
687C8—1462no—
688C8—1462no—
689C8—1462no—
690C22—42no—
691C22—42no—
692C22—42no—
693C22—84no—
694C22—2928no—
695C22—2922no—
696C22—2922no—
697C22—1464no—
698C22#1798924412yes—
699C22#1798938512yes—
700C22#1798939512yes—
701C22C23×C22⋊D7311yescharacteristic
702C4—22no—
703C4—22no—
704C4—22no—
705C4—22no—
706C4—22no—
707C4—22no—
708C4—42no—
709C4—42no—
710C4—42no—
711C4—2922no—
712C4—2922no—
713C4—2922no—
714C4#1798924412yes—
715C4C2×#41×D7311yescharacteristic
716C4C2×#1455663811yescharacteristic
717C2—82no—
718C2—2924no—
719C2#2262275214yesdirect product factor
720C2C2×#1798924411yescharacteristic
721C2C2×#1798938511yescharacteristic
722C2C2×#1798939511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×#556×C73C2
socleC23×C73C22×D4
prime radicalC22×#11924013C22
hypercenterC2×#556D73
hypocenterC73C2×#3376
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#556

Complements

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

NH ≅ G/Ntype
1. C2×#17989297C2semidirect
2. #22622752C2direct (N × H)
3. C2×#17988955C2semidirect
4. C2×#17988946C2semidirect
5. C2×#17988941C2semidirect
6. C2×#17988894C2semidirect
7. C2×#17988872C2semidirect
8. C2×#17988887C2semidirect
11. C2×#17988789C2semidirect
12. C2×#17988718C2semidirect
14. C2×#17988685C2semidirect
15. C2×C4×#11924015C2semidirect
16. C2×#556×C73C2semidirect
21. #17989297C22semidirect
32. #17988955C22semidirect
33. #17988946C22semidirect
34. #17988941C22semidirect
35. #17988894C22semidirect
36. #17988887C22semidirect
37. #17988872C22semidirect
40. #17988789C22semidirect
41. #17988718C22semidirect
43. #17988685C22semidirect
44. C4×#11924015C22semidirect
65. #556×C73C22semidirect
357. C2×C73#3376semidirect
362. C2×#556D73semidirect
378. C73C2×#3376semidirect
383. #556C2×D73semidirect
719. C2#22622752direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179892972
#226227522
C2×#179889552
C2×#179889462
C2×#179889412
C2×#179888942
C2×#179888722
C2×#179888872
C2×#179887992
C2×#179887892
C2×#179887182
C2×#179886972
C2×#179886852
C2×C4×#119240152
C2×#556×C732
C2×#337673