Finite Group Databasebeta

← C2×#22620208 #33954315

Subgroups — C2×#22620208 #33954315

Order 18688.

2134 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989208C211yesmaximal, characteristic, complemented
2#22620208C2116yesmaximal, direct product factor
3C2×#17988905C211yesmaximal, characteristic, complemented
4C2×#17988917C211yesmaximal, characteristic, complemented
5C2×#17988872C211yesmaximal, characteristic, complemented
6C2×#17988877C211yesmaximal, characteristic, complemented
7C2×#17988809C211yesmaximal, characteristic, complemented
8C2×#17988802C211yesmaximal, characteristic, complemented
9C2×#17988749C211yesmaximal, characteristic, complemented
10C2×#17988732C211yesmaximal, characteristic
11C2×#17988697C211yesmaximal, characteristic, complemented
12C2×#17988692C211yesmaximal, characteristic, complemented
13C2×C4×#11924015C211yesmaximal, characteristic, complemented
14C2×C4×#11924016C211yesmaximal, characteristic, complemented
15C2×#17988648C211yesmaximal, characteristic, complemented
16C2×#520×C73C211yesmaximal, characteristic, complemented
17C22×#11924018C2211yescharacteristic
18C22×#11924016C2211yescharacteristic
19C22×#11924015C2211yescharacteristic
20C22×#11924013C2211yescharacteristic
21#17989208—24no—
22#17989208C2218yescomplemented
23C2×#14556591C2211yescharacteristic
24C2×#14556586—21no—
25C2×#14556579C2211yescharacteristic
26C2×#14556577—21no—
27C2×#14556573—21no—
28C2×#14556570C2211yescharacteristic
29C2×#14556569—21no—
30C2×#14556565C2211yescharacteristic
31C2×C4×Dic146C2211yescharacteristic
32C2×C4×D292C2211yescharacteristic
33#17988917C2218yescomplemented
34#17988905C2218yescomplemented
35#17988877C2218yescomplemented
36#17988872C2218yescomplemented
37#17988809C2218yescomplemented
38#17988802C2218yescomplemented
39#17988749C2218yescomplemented
40#17988732C2218yes—
41#17988697C2218yescomplemented
42#17988692C2218yescomplemented
43C4×#11924015C2218yescomplemented
44C4×#11924016C2218yescomplemented
45#17988648C2218yescomplemented
46C2×#14556522C2211yescharacteristic
47C2×#14556522C2211yescharacteristic
48C2×#14556522C2211yescharacteristic
49C2×#14556522C2211yescharacteristic
50C2×C4⋊#10596831C2211yescharacteristic
51C2×C4⋊#10596831C2211yescharacteristic
52C2×#14556515C2211yescharacteristic
53C2×#14556515C2211yescharacteristic
54C2×#14556514C2211yescharacteristic
55C2×#14556514C2211yescharacteristic
56C2×#14556512C2211yescharacteristic
57C2×#14556512C2211yescharacteristic
58C2×#14556511C2211yescharacteristic
59C2×#14556511C2211yescharacteristic
60C2×C22⋊#10596831C2211yescharacteristic
61C2×C22⋊#10596831C2211yescharacteristic
62C2×#14556502C2211yescharacteristic
63C2×C4×#10596831C2211yescharacteristic
64C22×#41×C73C2211yescharacteristic
65#520×C73—24no—
66#520×C73C2218yescomplemented
67C2×C4×Q8×C73C2211yescharacteristic
68C2×C4×Q8×C73C2211yescharacteristic
69C2×C4×D4×C73—21no—
70C2×C4×D4×C73—21no—
71C2×C4×D4×C73C2211yescharacteristic
72C2×C4×D4×C73C2211yescharacteristic
73C2×#117×C73—21no—
74C2×#117×C73C2211yescharacteristic
75C22×C4⋊C4×C73—21no—
76C22×C4⋊C4×C73C2211yescharacteristic
77C22×Dic146—21no—
78C22×Dic146C2311yescharacteristic
79C22×D292C2311yescharacteristic
80C22×C22⋊D73—21no—
81C22×C4×D73—21no—
82C2×#11924018—24no—
83C2×#11924018C2314yes—
84C2×#11924016—24no—
85C2×#11924016C2314yes—
86C2×#11924015—24no—
87C2×#11924015C2314yes—
88C2×#11924013—24no—
89C2×#11924013C2314yes—
90C22×#10596831C2311yescharacteristic
91C22×#10596831C2311yescharacteristic
92C22×#10596831C2311yescharacteristic
93C22×#10596831C2311yescharacteristic
94#14556591—22no—
95#14556591C2314yes—
96#14556586—28no—
97#14556579—22no—
98#14556579C2314yes—
99#14556577—28no—
100#14556573—28no—
101#14556570—22no—
102#14556570C2314yes—
103#14556569—28no—
104#14556565—22no—
105#14556565C2314yes—
106C4×Dic146—22no—
107C4×Dic146C2314yes—
108C4×D292—22no—
109C4×D292C2314yes—
110C2×C4⋊Dic73—21no—
111C2×C4⋊Dic73C2311yescharacteristic
112C2×C4⋊Dic73C2311yescharacteristic
113C2×#11924007—21no—
114C2×#11924007—21no—
115C2×C22⋊Dic73—21no—
116C2×#11924005—21no—
117C2×#11924005—21no—
118C2×#11924005—21no—
119C2×#11924005—21no—
120C2×C4×Dic73—21no—
121#14556522C2314yes—
122#14556522C2314yes—
123#14556522C2314yes—
124#14556522C2314yes—
125C4⋊#10596831C2314yes—
126C4⋊#10596831C2314yes—
127#14556515C2314yes—
128#14556515C2314yes—
129#14556514C2314yes—
130#14556514C2314yes—
131#14556512C2314yes—
132#14556512C2314yes—
133#14556511C2314yes—
134#14556511C2314yes—
135C22⋊#10596831C2314yes—
136C22⋊#10596831C2314yes—
137#14556502C2314yes—
138C4×#10596831C2314yes—
139C2×#41×C73—24no—
140C2×#41×C73—24no—
141C2×#41×C73—22no—
142C2×#41×C73C2314yes—
143C22×Q8×C73C2311yescharacteristic
144C22×D4×C73—21no—
145C22×D4×C73C2311yescharacteristic
146C23×C4×C73—21no—
147C23×C4×C73—21no—
148C23×C4×C73—21no—
149C23×C4×C73—21no—
150C23×C4×C73C2311yescharacteristic
151C4×Q8×C73—22no—
152C4×Q8×C73—22no—
153C4×Q8×C73C2314yes—
154C4×Q8×C73C2314yes—
155C4×D4×C73—28no—
156C4×D4×C73—28no—
157C4×D4×C73—22no—
158C4×D4×C73—22no—
159C4×D4×C73C2314yes—
160C4×D4×C73C2314yes—
161#117×C73—28no—
162#117×C73D414yes—
163#117×C73C2314yes—
164C2×C4⋊C4×C73—21no—
165C2×C4⋊C4×C73—21no—
166C2×C4⋊C4×C73—21no—
167C2×C4⋊C4×C73—22no—
168C2×C4⋊C4×C73—28no—
169C2×C4⋊C4×C73D411yescharacteristic
170C2×C4⋊C4×C73D411yescharacteristic
171C2×C4⋊C4×C73C2311yescharacteristic
172C2×C4⋊C4×C73C2311yescharacteristic
173C2×C4⋊C4×C73C2314yes—
174C2×C22⋊C4×C73—21no—
175C2×C22⋊C4×C73—21no—
176C2×C22⋊C4×C73D411yescharacteristic
177C2×C22⋊C4×C73D411yescharacteristic
178C2×C42×C73—21no—
179C2×C42×C73—21no—
180C2×C42×C73C2311yescharacteristic
181C2×C42×C73C2311yescharacteristic
182C23×D73—21no—
183C2×Dic146—22no—
184C2×Dic146—22no—
185C2×Dic146—21no—
186C2×Dic146—24no—
187C2×Dic146—82no—
188C2×Dic146C2412yes—
189C2×D292—22no—
190C2×D292—22no—
191C2×D292—21no—
192C2×D292C2412yes—
193C2×C22⋊D73—24no—
194C2×C22⋊D73—82no—
195C22×Dic73—21no—
196C22×Dic73—21no—
197C22×Dic73—21no—
198C2×C4×D73—24no—
199C2×C4×D73—82no—
200#11924018—28no—
201#11924016—28no—
202#11924015—28no—
203#11924013—28no—
204C2×#10596831—22no—
205C2×#10596831—22no—
206C2×#10596831—22no—
207C2×#10596831—22no—
208C2×#10596831C2412yes—
209C2×#10596831C2412yes—
210C2×#10596831C2412yes—
211C2×#10596831C2412yes—
212C4⋊Dic73—24no—
213C4⋊Dic73—21no—
214C4⋊Dic73—21no—
215C4⋊Dic73C2412yes—
216C4⋊Dic73C2412yes—
217#11924007—24no—
218#11924007—24no—
219C22⋊Dic73—24no—
220#11924005—24no—
221#11924005—24no—
222#11924005—24no—
223#11924005—24no—
224C4×Dic73—24no—
225C24×C73—21no—
226C24×C73C2×D411yescharacteristic
227#41×C73—216no—
228#41×C73—28no—
229#41×C73—28no—
230C2×Q8×C73—21no—
231C2×Q8×C73—22no—
232C2×Q8×C73#4114yes—
233C2×Q8×C73C2412yes—
234C2×D4×C73—28no—
235C2×D4×C73—24no—
236C2×D4×C73—21no—
237C2×D4×C73—22no—
238C2×D4×C73#4114yes—
239C2×D4×C73C2412yes—
240C22×C4×C73—28no—
241C22×C4×C73—21no—
242C22×C4×C73—24no—
243C22×C4×C73—22no—
244C22×C4×C73—22no—
245C22×C4×C73—21no—
246C22×C4×C73—21no—
247C22×C4×C73—24no—
248C22×C4×C73—24no—
249C22×C4×C73—24no—
250C22×C4×C73—82no—
251C22×C4×C73—82no—
252C22×C4×C73—82no—
253C22×C4×C73C2×D411yescharacteristic
254C22×C4×C73C2×D411yescharacteristic
255C22×C4×C73C2×D411yescharacteristic
256C22×C4×C73C2×D411yescharacteristic
257C22×C4×C73C2×D411yescharacteristic
258C22×C4×C73C2×D412yes—
259C22×C4×C73C2412yes—
260C22×C4×C73C2411yescharacteristic
261C4⋊C4×C73—24no—
262C4⋊C4×C73—24no—
263C4⋊C4×C73—24no—
264C4⋊C4×C73—21no—
265C4⋊C4×C73—21no—
266C4⋊C4×C73C2×D414yes—
267C4⋊C4×C73C2×D414yes—
268C4⋊C4×C73C2412yes—
269C4⋊C4×C73C2412yes—
270C22⋊C4×C73—24no—
271C22⋊C4×C73—24no—
272C22⋊C4×C73C2×D414yes—
273C22⋊C4×C73C2×D414yes—
274C42×C73—24no—
275C42×C73—24no—
276C42×C73C2×D412yes—
277C42×C73C2×D412yes—
278C42×C73C2412yes—
279C42×C73C2412yes—
280C23×C73—22no—
281C23×C73—24no—
282C23×C73—22no—
283C23×C73—22no—
284C23×C73—22no—
285C23×C73—42no—
286C23×C73—42no—
287C23×C73C22×D412yes—
288C23×C73C22×D411yescharacteristic
289C22×D73—22no—
290C22×D73—42no—
291C22×D73—42no—
292C22×D73—42no—
293Q8×C73—24no—
294Q8×C73—22no—
295Q8×C73C2×#4114yes—
296D4×C73—216no—
297D4×C73—24no—
298D4×C73—22no—
299D4×C73C2×#4114yes—
300C2×C4×C73—216no—
301C2×C4×C73—22no—
302C2×C4×C73—24no—
303C2×C4×C73—22no—
304C2×C4×C73—22no—
305C2×C4×C73—22no—
306C2×C4×C73—22no—
307C2×C4×C73—22no—
308C2×C4×C73—24no—
309C2×C4×C73—22no—
310C2×C4×C73—22no—
311C2×C4×C73—22no—
312C2×C4×C73—22no—
313C2×C4×C73—42no—
314C2×C4×C73—42no—
315C2×C4×C73—84no—
316C2×C4×C73—84no—
317C2×C4×C73—84no—
318C2×C4×C73C22×D412yes—
319C2×C4×C73C22×D412yes—
320C2×C4×C73C22×D412yes—
321C2×C4×C73C22×D412yes—
322C2×C4×C73C22×D412yes—
323C2×C4×C73C22×D411yescharacteristic
324C2×C4×C73C2×#4112yes—
325C2×C4×C73C2×#4112yes—
326C2×C4×C73C2511yescharacteristic
327C22⋊D73—84no—
328C2×Dic73—22no—
329C2×Dic73—22no—
330C2×Dic73—22no—
331C2×Dic73—42no—
332C2×Dic73—42no—
333C2×Dic73—42no—
334D292—22no—
335D292—22no—
336D292—42no—
337C4×D73—84no—
338Dic146—22no—
339Dic146—22no—
340Dic146—42no—
341Dic146—84no—
342#10596831—22no—
343#10596831—22no—
344#10596831—22no—
345#10596831—22no—
346C22×C73—22no—
347C22×C73—24no—
348C22×C73—22no—
349C22×C73—22no—
350C22×C73—44no—
351C22×C73—48no—
352C22×C73—42no—
353C22×C73—42no—
354C22×C73#52512yes—
355C22×C73#57712yes—
356C22×C73#57712yes—
357C22×C73C23×D411yescharacteristic
358C2×D73—42no—
359C2×D73—42no—
360C2×D73—42no—
361C2×D73—84no—
362C4×C73—22no—
363C4×C73—24no—
364C4×C73—22no—
365C4×C73—22no—
366C4×C73—22no—
367C4×C73—22no—
368C4×C73—42no—
369C4×C73—42no—
370C4×C73#52512yes—
371C4×C73C22×#4111yescharacteristic
372C4×C73C22×#4111yescharacteristic
373Dic73—42no—
374Dic73—42no—
375Dic73—42no—
376C2×#3125—731nomaximal, Sylow
377C2×C73—42no—
378C2×C73—44no—
379C2×C73#312514yescomplemented
380C2×C73C2×#52511yescharacteristic
381C2×C73C2×#57711yescharacteristic
382C2×C73C2×#57711yescharacteristic
383D73—82no—
384C2×#542—731no—
385C2×#520D7311yescharacteristic, complemented
386#3125—7316no—
387C2×#481—731no—
388C2×#483—731no—
389C2×#475—731no—
390C2×#476—731no—
391C2×#464—731no—
392C2×#463—731no—
393C2×#452—731no—
394C2×#449—731no—
395C2×#442—731no—
396C2×#441—731no—
397C2×C4×SD16—731no—
398C2×C4×SD16—731no—
399C2×#433—731no—
400C73C2×#312511yescharacteristic, complemented, Sylow
401C22×#41C2×D7311yescharacteristic
402C22×Q16—731no—
403C22×SD16—731no—
404C22×SD16—731no—
405C22×D8—731no—
406#542—738no—
407#542—1464no—
408C2×C4⋊Q8—731no—
409C2×#126—1461no—
410C2×#124—731no—
411C2×#124—1461no—
412C2×#123—1461no—
413C2×C22⋊Q8—731no—
414C2×C22⋊Q8—1461no—
415C2×#121—731no—
416#520—24no—
417#520C2×D7318yescomplemented
418C2×C4×Q8—731no—
419C2×C4×Q8C2×D7311yescharacteristic
420C2×C4×Q8C2×D7311yescharacteristic
421C2×C4×D4—21no—
422C2×C4×D4—21no—
423C2×C4×D4—731no—
424C2×C4×D4C2×D7311yescharacteristic
425C2×C4×D4C2×D7311yescharacteristic
426C2×#117—21no—
427C2×#117C2×D7311yescharacteristic
428C22×C4⋊C4—21no—
429C22×C4⋊C4C2×D7311yescharacteristic
430#483—738no—
431#481—738no—
432#476—738no—
433#475—738no—
434#464—738no—
435#463—738no—
436#452—738no—
437#449—738no—
438#442—738no—
439#441—738no—
440C4×SD16—738no—
441C4×SD16—738no—
442#433—738no—
443C2×#106—731no—
444C2×#106—731no—
445C2×#106—731no—
446C2×#106—731no—
447C2×C4⋊C8—731no—
448C2×C4⋊C8—731no—
449C2×#103—731no—
450C2×#103—731no—
451C2×#103—731no—
452C2×#103—731no—
453C2×#102—731no—
454C2×#102—731no—
455C2×#102—731no—
456C2×#102—731no—
457C2×C22⋊C8—731no—
458C2×C22⋊C8—731no—
459C2×#97—731no—
460C2×C4×C8—731no—
461C2×#41—24no—
462C2×#41—24no—
463C2×#41—22no—
464C2×#41C22×D7314yes—
465C22×Q8—731no—
466C22×Q8—1461no—
467C22×Q8C22×D7311yescharacteristic
468C22×D4—21no—
469C22×D4—731no—
470C22×D4—1461no—
471C22×D4C22×D7311yescharacteristic
472C23×C4—21no—
473C23×C4—21no—
474C23×C4—21no—
475C23×C4—21no—
476C23×C4—1461no—
477C23×C4C22×D7311yescharacteristic
478C2×Q16—734no—
479C2×Q16—1464no—
480C2×SD16—734no—
481C2×SD16—734no—
482C2×SD16—1464no—
483C2×SD16—1464no—
484C2×D8—734no—
485C2×D8—1464no—
486C22×C8—731no—
487C22×C8—731no—
488C22×C8—731no—
489C22×C8—731no—
490C4⋊Q8—734no—
491C4⋊Q8—1462no—
492#126—1468no—
493#124—734no—
494#124—1468no—
495#124—1462no—
496#123—1468no—
497C22⋊Q8—734no—
498C22⋊Q8—1462no—
499C22⋊Q8—1468no—
500#121—734no—
501#121—1462no—
502C4×Q8—22no—
503C4×Q8—22no—
504C4×Q8—734no—
505C4×Q8—1462no—
506C4×Q8C22×D7314yes—
507C4×Q8C22×D7314yes—
508C4×D4—28no—
509C4×D4—28no—
510C4×D4—22no—
511C4×D4—22no—
512C4×D4—734no—
513C4×D4—1462no—
514C4×D4C22×D7314yes—
515C4×D4C22×D7314yes—
516#117—28no—
517#117C22⋊D7314yes—
518#117C22×D7314yes—
519C2×C4⋊C4—21no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—21no—
522C2×C4⋊C4—22no—
523C2×C4⋊C4—28no—
524C2×C4⋊C4—731no—
525C2×C4⋊C4—731no—
526C2×C4⋊C4—1461no—
527C2×C4⋊C4—1461no—
528C2×C4⋊C4—1461no—
529C2×C4⋊C4C22⋊D7311yescharacteristic
530C2×C4⋊C4C22⋊D7311yescharacteristic
531C2×C4⋊C4C22×D7311yescharacteristic
532C2×C4⋊C4C22×D7311yescharacteristic
533C2×C4⋊C4C22×D7314yes—
534C2×C22⋊C4—21no—
535C2×C22⋊C4—21no—
536C2×C22⋊C4—1461no—
537C2×C22⋊C4—1461no—
538C2×C22⋊C4—1461no—
539C2×C22⋊C4—1461no—
540C2×C22⋊C4—1461no—
541C2×C22⋊C4C22⋊D7311yescharacteristic
542C2×C22⋊C4C22⋊D7311yescharacteristic
543C2×C42—21no—
544C2×C42—21no—
545C2×C42—1461no—
546C2×C42C22×D7311yescharacteristic
547C2×C42C22×D7311yescharacteristic
548#106—734no—
549#106—734no—
550#106—734no—
551#106—734no—
552C4⋊C8—734no—
553C4⋊C8—734no—
554#103—734no—
555#103—734no—
556#103—734no—
557#103—734no—
558#102—734no—
559#102—734no—
560#102—734no—
561#102—734no—
562C22⋊C8—734no—
563C22⋊C8—734no—
564#97—734no—
565C4×C8—734no—
566C24—21no—
567C24—1461no—
568C24C2×C22⋊D7311yescharacteristic
569#41—216no—
570#41—28no—
571#41—28no—
572C2×Q8—21no—
573C2×Q8—22no—
574C2×Q8—5842no—
575C2×Q8—732no—
576C2×Q8—1462no—
577C2×Q8—1462no—
578C2×Q8—1461no—
579C2×Q8—1464no—
580C2×Q8#1192402814yes—
581C2×Q8C23×D7312yes—
582C2×D4—28no—
583C2×D4—24no—
584C2×D4—21no—
585C2×D4—22no—
586C2×D4—5842no—
587C2×D4—732no—
588C2×D4—1464no—
589C2×D4—1461no—
590C2×D4—1462no—
591C2×D4—1462no—
592C2×D4#1192402814yes—
593C2×D4C23×D7312yes—
594C22×C4—28no—
595C22×C4—21no—
596C22×C4—24no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—24no—
602C22×C4—24no—
603C22×C4—24no—
604C22×C4—82no—
605C22×C4—82no—
606C22×C4—82no—
607C22×C4—5842no—
608C22×C4—1461no—
609C22×C4—1461no—
610C22×C4—1461no—
611C22×C4—1464no—
612C22×C4C2×C22⋊D7312yes—
613C22×C4C2×C22⋊D7311yescharacteristic
614C22×C4C2×C22⋊D7311yescharacteristic
615C22×C4C2×C22⋊D7311yescharacteristic
616C22×C4C2×C22⋊D7311yescharacteristic
617C22×C4C2×C22⋊D7311yescharacteristic
618C22×C4C23×D7312yes—
619C22×C4C23×D7311yescharacteristic
620Q16—1468no—
621SD16—1468no—
622SD16—1468no—
623D8—1468no—
624C2×C8—732no—
625C2×C8—732no—
626C2×C8—732no—
627C2×C8—732no—
628C2×C8—1462no—
629C2×C8—1462no—
630C2×C8—1462no—
631C2×C8—1462no—
632C4⋊C4—24no—
633C4⋊C4—24no—
634C4⋊C4—24no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—732no—
638C4⋊C4—732no—
639C4⋊C4—1464no—
640C4⋊C4—1464no—
641C4⋊C4—1461no—
642C4⋊C4—1461no—
643C4⋊C4—1464no—
644C4⋊C4C2×C22⋊D7314yes—
645C4⋊C4C2×C22⋊D7314yes—
646C4⋊C4C23×D7312yes—
647C4⋊C4C23×D7312yes—
648C22⋊C4—24no—
649C22⋊C4—24no—
650C22⋊C4—1464no—
651C22⋊C4—1464no—
652C22⋊C4—1464no—
653C22⋊C4—1464no—
654C22⋊C4—1464no—
655C22⋊C4C2×C22⋊D7314yes—
656C22⋊C4C2×C22⋊D7314yes—
657C42—24no—
658C42—24no—
659C42—1464no—
660C42C2×C22⋊D7312yes—
661C42C2×C22⋊D7312yes—
662C42C23×D7312yes—
663C42C23×D7312yes—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—24no—
669C23—42no—
670C23—42no—
671C23—2922no—
672C23—2922no—
673C23—2922no—
674C23—1462no—
675C23C22×C22⋊D7312yes—
676C23C22×C22⋊D7311yescharacteristic
677Q8—22no—
678Q8—24no—
679Q8—2922no—
680Q8—5844no—
681Q8—1462no—
682Q8—1462no—
683Q8C2×#1192402814yes—
684D4—216no—
685D4—22no—
686D4—24no—
687D4—2922no—
688D4—5844no—
689D4—1462no—
690D4—1462no—
691D4C2×#1192402814yes—
692C2×C4—216no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—24no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—24no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—84no—
708C2×C4—84no—
709C2×C4—84no—
710C2×C4—2922no—
711C2×C4—2922no—
712C2×C4—2922no—
713C2×C4—5844no—
714C2×C4—1462no—
715C2×C4—1462no—
716C2×C4—1462no—
717C2×C4C22×C22⋊D7312yes—
718C2×C4C22×C22⋊D7312yes—
719C2×C4C22×C22⋊D7312yes—
720C2×C4C22×C22⋊D7312yes—
721C2×C4C22×C22⋊D7312yes—
722C2×C4C22×C22⋊D7311yescharacteristic
723C2×C4C2×#1192402812yes—
724C2×C4C2×#1192402812yes—
725C2×C4C24×D7311yescharacteristic
726C8—1462no—
727C8—1462no—
728C8—1462no—
729C8—1462no—
730C22—22no—
731C22—22no—
732C22—22no—
733C22—24no—
734C22—44no—
735C22—48no—
736C22—42no—
737C22—42no—
738C22—2922no—
739C22—2922no—
740C22—2922no—
741C22—5844no—
742C22#1798909812yes—
743C22#1798939512yes—
744C22#1798939812yes—
745C22C23×C22⋊D7311yescharacteristic
746C4—22no—
747C4—22no—
748C4—22no—
749C4—22no—
750C4—22no—
751C4—24no—
752C4—42no—
753C4—42no—
754C4—2922no—
755C4—2922no—
756C4—2922no—
757C4#1798909812yes—
758C4C22×#1192402811yescharacteristic
759C4C22×#1192402811yescharacteristic
760C2—42no—
761C2—44no—
762C2—5842no—
763C2#2262020814yesdirect product factor
764C2C2×#1798909811yescharacteristic
765C2C2×#1798939511yescharacteristic
766C2C2×#1798939811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×#520×C73C2
socleC23×C73C22×D4
prime radicalC2×#17988732C2
hypercenterC2×#520D73
hypocenterC73C2×#3125
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#520

Complements

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

NH ≅ G/Ntype
1. C2×#17989208C2semidirect
2. #22620208C2direct (N × H)
3. C2×#17988905C2semidirect
4. C2×#17988917C2semidirect
5. C2×#17988872C2semidirect
6. C2×#17988877C2semidirect
7. C2×#17988809C2semidirect
8. C2×#17988802C2semidirect
9. C2×#17988749C2semidirect
11. C2×#17988697C2semidirect
12. C2×#17988692C2semidirect
13. C2×C4×#11924015C2semidirect
14. C2×C4×#11924016C2semidirect
15. C2×#17988648C2semidirect
16. C2×#520×C73C2semidirect
22. #17989208C22semidirect
33. #17988917C22semidirect
34. #17988905C22semidirect
35. #17988877C22semidirect
36. #17988872C22semidirect
37. #17988809C22semidirect
38. #17988802C22semidirect
39. #17988749C22semidirect
41. #17988697C22semidirect
42. #17988692C22semidirect
43. C4×#11924015C22semidirect
44. C4×#11924016C22semidirect
45. #17988648C22semidirect
66. #520×C73C22semidirect
379. C2×C73#3125semidirect
385. C2×#520D73semidirect
400. C73C2×#3125semidirect
417. #520C2×D73semidirect
763. C2#22620208direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179892082
#226202082
C2×#179889052
C2×#179889172
C2×#179888722
C2×#179888772
C2×#179888092
C2×#179888022
C2×#179887492
C2×#179887322
C2×#179886972
C2×#179886922
C2×C4×#119240152
C2×C4×#119240162
C2×#179886482
C2×#520×C732
C2×#312573