Finite Group Databasebeta

← C2×#22621991 #33962712

Subgroups — C2×#22621991 #33962712

Order 18688.

2114 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989246C211yesmaximal, characteristic
2#22621991C2116yesmaximal, direct product factor
3C2×#17988949C211yesmaximal, characteristic, complemented
4C2×#17988928C211yesmaximal, characteristic, complemented
5C2×#17988911C211yesmaximal, characteristic, complemented
6C2×#17988879C211yesmaximal, characteristic, complemented
7C2×#17988835C211yesmaximal, characteristic, complemented
8C2×#17988826C211yesmaximal, characteristic, complemented
9C2×#17988809C211yesmaximal, characteristic, complemented
10C2×#17988747C211yesmaximal, characteristic, complemented
11C2×#17988742C211yesmaximal, characteristic, complemented
12C2×#17988692C211yesmaximal, characteristic, complemented
13C2×#17988659C211yesmaximal, characteristic, complemented
14C2×#17988595C211yesmaximal, characteristic, complemented
15C2×#17988581C211yesmaximal, characteristic, complemented
16C2×#556×C73C211yesmaximal, characteristic, complemented
17C22×#11924028C2211yescharacteristic
18C23×Dic146C2211yescharacteristic
19C22×#11924018C2211yescharacteristic
20C22×#11924018C2211yescharacteristic
21C22×#11924015C2211yescharacteristic
22C22×#11924012C2211yescharacteristic
23C23×#10596831C2211yescharacteristic
24#17989246—24no—
25#17989246C2218yes—
26C2×#14556579C2211yescharacteristic
27C2×#14556577—21no—
28C2×#14556570C2211yescharacteristic
29C2×#14556569—21no—
30C2×#14556565C2211yescharacteristic
31C2×#14556563—21no—
32C2×C4×Dic146C2211yescharacteristic
33C2×#14556551—21no—
34#17988949C2218yescomplemented
35#17988928C2218yescomplemented
36#17988911C2218yescomplemented
37#17988879C2218yescomplemented
38#17988835C2218yescomplemented
39#17988826C2218yescomplemented
40#17988809C2218yescomplemented
41#17988747C2218yescomplemented
42#17988742C2218yescomplemented
43#17988692C2218yescomplemented
44#17988659C2218yescomplemented
45C2×#14556524C2211yescharacteristic
46C2×#14556524C2211yescharacteristic
47C2×#14556522C2211yescharacteristic
48C2×C4⋊#10596831C2211yescharacteristic
49#17988595C2218yescomplemented
50#17988581C2218yescomplemented
51C2×#14556515C2211yescharacteristic
52C2×#14556514C2211yescharacteristic
53C2×#14556514C2211yescharacteristic
54C2×#14556514C2211yescharacteristic
55C2×#14556514C2211yescharacteristic
56C2×#14556514C2211yescharacteristic
57C2×#14556514C2211yescharacteristic
58C2×#14556511C2211yescharacteristic
59C2×#14556511C2211yescharacteristic
60C2×#14556511C2211yescharacteristic
61C2×C22⋊#10596831C2211yescharacteristic
62C2×C22⋊#10596831C2211yescharacteristic
63C2×#14556502C2211yescharacteristic
64#556×C73—24no—
65#556×C73C2218yescomplemented
66C2×C4⋊Q8×C73C2211yescharacteristic
67C2×#126×C73—21no—
68C2×#126×C73—21no—
69C2×#124×C73—21no—
70C2×C22⋊Q8×C73C2211yescharacteristic
71C2×C22⋊Q8×C73C2211yescharacteristic
72C2×C4×Q8×C73—21no—
73C2×C4×Q8×C73C2211yescharacteristic
74C2×C4×D4×C73C2211yescharacteristic
75C2×#117×C73C2211yescharacteristic
76C2×#117×C73C2211yescharacteristic
77C2×#11924028—24no—
78C2×#11924028—22no—
79C2×#11924028—42no—
80C2×#11924028C2314yes—
81C22×Dic146—24no—
82C22×Dic146—22no—
83C22×Dic146—21no—
84C22×Dic146—42no—
85C22×Dic146C2311yescharacteristic
86C22×Dic146C2314yes—
87C22×Dic146C2311yescharacteristic
88C22×D292C2311yescharacteristic
89C22×C22⋊D73—21no—
90C22×C22⋊D73—21no—
91C23×Dic73—21no—
92C22×C4×D73—21no—
93C2×#11924018—24no—
94C2×#11924018—42no—
95C2×#11924018C2314yes—
96C2×#11924018C2314yes—
97C2×#11924015—42no—
98C2×#11924015C2314yes—
99C2×#11924012—42no—
100C2×#11924012C2314yes—
101C22×#10596831—42no—
102C22×#10596831C2311yescharacteristic
103C22×#10596831C2311yescharacteristic
104C22×#10596831C2311yescharacteristic
105C22×#10596831C2311yescharacteristic
106C22×#10596831C2314yes—
107#14556579—22no—
108#14556579C2314yes—
109#14556577—28no—
110#14556570—22no—
111#14556570C2314yes—
112#14556569—28no—
113#14556565—22no—
114#14556565C2314yes—
115#14556563—28no—
116C4×Dic146—22no—
117C4×Dic146C2314yes—
118#14556551—28no—
119C2×C4⋊Dic73C2311yescharacteristic
120C2×#11924007—21no—
121C2×#11924007—21no—
122C2×C22⋊Dic73—21no—
123C2×#11924005—21no—
124C2×#11924005—21no—
125C2×#11924005—21no—
126C2×C4×Dic73—21no—
127#14556524C2314yes—
128#14556524C2314yes—
129#14556522C2314yes—
130C4⋊#10596831C2314yes—
131#14556515C2314yes—
132#14556514C2314yes—
133#14556514C2314yes—
134#14556514C2314yes—
135#14556514C2314yes—
136#14556514C2314yes—
137#14556514C2314yes—
138#14556511C2314yes—
139#14556511C2314yes—
140#14556511C2314yes—
141C22⋊#10596831C2314yes—
142C22⋊#10596831C2314yes—
143#14556502C2314yes—
144C22×Q8×C73—21no—
145C22×Q8×C73C2311yescharacteristic
146C22×D4×C73D411yescharacteristic
147C23×C4×C73C2311yescharacteristic
148C23×C4×C73C2311yescharacteristic
149C4⋊Q8×C73—22no—
150C4⋊Q8×C73C2314yes—
151#126×C73—28no—
152#126×C73—28no—
153#124×C73—28no—
154C22⋊Q8×C73—22no—
155C22⋊Q8×C73—22no—
156C22⋊Q8×C73C2314yes—
157C22⋊Q8×C73C2314yes—
158C4×Q8×C73—28no—
159C4×Q8×C73—22no—
160C4×Q8×C73C2314yes—
161C4×D4×C73D414yes—
162C4×D4×C73C2314yes—
163#117×C73—22no—
164#117×C73—22no—
165#117×C73C2314yes—
166#117×C73C2314yes—
167C2×C4⋊C4×C73—21no—
168C2×C4⋊C4×C73—21no—
169C2×C4⋊C4×C73—21no—
170C2×C4⋊C4×C73—21no—
171C2×C4⋊C4×C73D411yescharacteristic
172C2×C4⋊C4×C73C2311yescharacteristic
173C2×C4⋊C4×C73C2311yescharacteristic
174C2×C4⋊C4×C73C2311yescharacteristic
175C2×C22⋊C4×C73—21no—
176C2×C22⋊C4×C73—21no—
177C2×C22⋊C4×C73—21no—
178C2×C22⋊C4×C73—21no—
179C2×C22⋊C4×C73D411yescharacteristic
180C2×C22⋊C4×C73D411yescharacteristic
181C2×C42×C73—21no—
182C2×C42×C73—21no—
183C2×C42×C73—21no—
184C2×C42×C73C2311yescharacteristic
185C23×D73—21no—
186#11924028—28no—
187#11924028—44no—
188#11924028—48no—
189C2×Dic146—21no—
190C2×Dic146—22no—
191C2×Dic146—22no—
192C2×Dic146—22no—
193C2×Dic146—28no—
194C2×Dic146—24no—
195C2×Dic146—21no—
196C2×Dic146—44no—
197C2×Dic146—48no—
198C2×Dic146—44no—
199C2×Dic146#4114yes—
200C2×Dic146C2412yes—
201C2×Dic146C2412yes—
202C2×D292—22no—
203C2×D292—22no—
204C2×D292—21no—
205C2×D292C2412yes—
206C2×C22⋊D73—24no—
207C2×C22⋊D73—24no—
208C2×C22⋊D73—44no—
209C2×C22⋊D73—44no—
210C22×Dic73—21no—
211C22×Dic73—21no—
212C22×Dic73—21no—
213C22×Dic73—24no—
214C22×Dic73—44no—
215C2×C4×D73—24no—
216C2×C4×D73—44no—
217#11924018—28no—
218#11924018—44no—
219#11924015—44no—
220#11924012—44no—
221C2×#10596831—22no—
222C2×#10596831—22no—
223C2×#10596831—22no—
224C2×#10596831—22no—
225C2×#10596831—44no—
226C2×#10596831C2412yes—
227C2×#10596831C2412yes—
228C2×#10596831C2412yes—
229C2×#10596831C2412yes—
230C4⋊Dic73—21no—
231C4⋊Dic73C2412yes—
232#11924007—24no—
233#11924007—24no—
234C22⋊Dic73—24no—
235#11924005—24no—
236#11924005—24no—
237#11924005—24no—
238C4×Dic73—24no—
239C24×C73C2×D411yescharacteristic
240C24×C73C2×D411yescharacteristic
241C2×Q8×C73—21no—
242C2×Q8×C73—24no—
243C2×Q8×C73—22no—
244C2×Q8×C73—22no—
245C2×Q8×C73—44no—
246C2×Q8×C73C2412yes—
247C2×D4×C73—42no—
248C2×D4×C73C2×D414yes—
249C22×C4×C73—22no—
250C22×C4×C73—22no—
251C22×C4×C73—22no—
252C22×C4×C73—22no—
253C22×C4×C73—21no—
254C22×C4×C73—21no—
255C22×C4×C73—21no—
256C22×C4×C73—21no—
257C22×C4×C73C2×D411yescharacteristic
258C22×C4×C73C2×D411yescharacteristic
259C22×C4×C73C2×D411yescharacteristic
260C22×C4×C73C2×D411yescharacteristic
261C22×C4×C73C2×D412yes—
262C22×C4×C73C2×D412yes—
263C22×C4×C73C2412yes—
264C22×C4×C73C2412yes—
265C22×C4×C73C2411yescharacteristic
266C4⋊C4×C73—24no—
267C4⋊C4×C73—24no—
268C4⋊C4×C73—24no—
269C4⋊C4×C73—24no—
270C4⋊C4×C73—21no—
271C4⋊C4×C73—21no—
272C4⋊C4×C73—21no—
273C4⋊C4×C73C2×D414yes—
274C4⋊C4×C73C2412yes—
275C4⋊C4×C73C2412yes—
276C4⋊C4×C73C2412yes—
277C22⋊C4×C73—24no—
278C22⋊C4×C73—24no—
279C22⋊C4×C73—24no—
280C22⋊C4×C73—24no—
281C22⋊C4×C73C2×D414yes—
282C22⋊C4×C73C2×D414yes—
283C42×C73—24no—
284C42×C73—24no—
285C42×C73—24no—
286C42×C73C2×D412yes—
287C42×C73C2412yes—
288C23×C73—22no—
289C23×C73—22no—
290C23×C73—22no—
291C23×C73—22no—
292C23×C73—22no—
293C23×C73—22no—
294C23×C73C22×D412yes—
295C23×C73C22×D412yes—
296C23×C73C22×D411yescharacteristic
297C22×D73—22no—
298C22×D73—42no—
299C22×D73—42no—
300C22×D73—42no—
301Q8×C73—22no—
302Q8×C73—22no—
303Q8×C73—48no—
304Q8×C73—42no—
305D4×C73—44no—
306C2×C4×C73—22no—
307C2×C4×C73—22no—
308C2×C4×C73—22no—
309C2×C4×C73—22no—
310C2×C4×C73—24no—
311C2×C4×C73—24no—
312C2×C4×C73—22no—
313C2×C4×C73—22no—
314C2×C4×C73—22no—
315C2×C4×C73—22no—
316C2×C4×C73—22no—
317C2×C4×C73—22no—
318C2×C4×C73—22no—
319C2×C4×C73—22no—
320C2×C4×C73—42no—
321C2×C4×C73—42no—
322C2×C4×C73—42no—
323C2×C4×C73—42no—
324C2×C4×C73C22×D412yes—
325C2×C4×C73C22×D412yes—
326C2×C4×C73C22×D412yes—
327C2×C4×C73C22×D412yes—
328C2×C4×C73C22×D411yescharacteristic
329C2×C4×C73C2×#4112yes—
330C2×C4×C73H(5,𝔽2)12yes—
331C2×C4×C73C2511yescharacteristic
332C22⋊D73—48no—
333C22⋊D73—48no—
334C2×Dic73—24no—
335C2×Dic73—22no—
336C2×Dic73—22no—
337C2×Dic73—22no—
338C2×Dic73—48no—
339C2×Dic73—42no—
340C2×Dic73—42no—
341D292—22no—
342D292—22no—
343D292—42no—
344C4×D73—48no—
345Dic146—24no—
346Dic146—22no—
347Dic146—22no—
348Dic146—22no—
349Dic146—48no—
350Dic146—42no—
351Dic146C2×#4114yes—
352#10596831—22no—
353#10596831—22no—
354#10596831—22no—
355#10596831—22no—
356C22×C73—22no—
357C22×C73—22no—
358C22×C73—22no—
359C22×C73—22no—
360C22×C73—22no—
361C22×C73—22no—
362C22×C73—44no—
363C22×C73—44no—
364C22×C73#54612yes—
365C22×C73#57512yes—
366C22×C73#57812yes—
367C22×C73C23×D411yescharacteristic
368C2×D73—42no—
369C2×D73—42no—
370C2×D73—42no—
371C2×D73—84no—
372C4×C73—22no—
373C4×C73—22no—
374C4×C73—22no—
375C4×C73—22no—
376C4×C73—42no—
377C4×C73—42no—
378C4×C73—42no—
379C4×C73—42no—
380C4×C73#54612yes—
381C4×C73C22×#4111yescharacteristic
382C4×C73C2×H(5,𝔽2)11yescharacteristic
383Dic73—24no—
384Dic73—42no—
385Dic73—42no—
386C2×#3313—731nomaximal, Sylow
387C2×C73—42no—
388C2×C73—42no—
389C2×C73#331314yescomplemented
390C2×C73C2×#54611yescharacteristic
391C2×C73C2×#57511yescharacteristic
392C2×C73C2×#57811yescharacteristic
393D73—82no—
394C2×#556D7311yescharacteristic, complemented
395C2×#548—731no—
396#3313—7316no—
397C2×#489—731no—
398C2×#485—731no—
399C2×#482—731no—
400C2×#477—731no—
401C2×#468—731no—
402C2×#467—731no—
403C2×#464—731no—
404C2×#452—731no—
405C2×#451—731no—
406C2×#441—731no—
407C2×#435—731no—
408C2×#419—731no—
409C2×#416—731no—
410C73C2×#331311yescharacteristic, complemented, Sylow
411C22×#41—731no—
412C23×Q8—731no—
413C22×Q16—731no—
414C22×Q16—731no—
415C22×SD16—731no—
416C22×M16—731no—
417C23×C8—731no—
418#556—24no—
419#556C2×D7318yescomplemented
420#548—738no—
421#548—1464no—
422C2×C4⋊Q8C2×D7311yescharacteristic
423C2×#126—21no—
424C2×#126—21no—
425C2×#124—21no—
426C2×#124—731no—
427C2×#124—1461no—
428C2×C22⋊Q8—731no—
429C2×C22⋊Q8—1461no—
430C2×C22⋊Q8C2×D7311yescharacteristic
431C2×C22⋊Q8C2×D7311yescharacteristic
432C2×#121—731no—
433C2×#121—1461no—
434C2×C4×Q8—21no—
435C2×C4×Q8—731no—
436C2×C4×Q8C2×D7311yescharacteristic
437C2×C4×D4—1461no—
438C2×C4×D4C2×D7311yescharacteristic
439C2×#117C2×D7311yescharacteristic
440C2×#117C2×D7311yescharacteristic
441#489—738no—
442#485—738no—
443#482—738no—
444#477—738no—
445#468—738no—
446#467—738no—
447#464—738no—
448#452—738no—
449#451—738no—
450#441—738no—
451#435—738no—
452C2×#107—731no—
453C2×#107—731no—
454C2×#106—731no—
455C2×C4⋊C8—731no—
456#419—738no—
457#416—738no—
458C2×#103—731no—
459C2×#103—731no—
460C2×#103—731no—
461C2×#103—731no—
462C2×#103—731no—
463C2×#103—731no—
464C2×#103—731no—
465C2×#102—731no—
466C2×#102—731no—
467C2×#102—731no—
468C2×C22⋊C8—731no—
469C2×C22⋊C8—731no—
470C2×#97—731no—
471C2×#41—2922no—
472C2×#41—734no—
473C2×#41—1464no—
474C2×#41—1462no—
475C22×Q8—21no—
476C22×Q8—2922no—
477C22×Q8—734no—
478C22×Q8—731no—
479C22×Q8—731no—
480C22×Q8—1464no—
481C22×Q8—1461no—
482C22×Q8—1462no—
483C22×Q8C22×D7311yescharacteristic
484C22×D4—731no—
485C22×D4—1461no—
486C22×D4—1461no—
487C22×D4C22⋊D7311yescharacteristic
488C23×C4—1461no—
489C23×C4—1461no—
490C23×C4C22×D7311yescharacteristic
491C23×C4C22×D7311yescharacteristic
492C2×Q16—2922no—
493C2×Q16—734no—
494C2×Q16—734no—
495C2×Q16—1464no—
496C2×SD16—2922no—
497C2×SD16—734no—
498C2×M16—2922no—
499C2×M16—734no—
500C22×C8—2922no—
501C22×C8—734no—
502C22×C8—731no—
503C22×C8—731no—
504C22×C8—731no—
505C22×C8—731no—
506C4⋊Q8—22no—
507C4⋊Q8C22×D7314yes—
508#126—28no—
509#126—28no—
510#124—28no—
511#124—734no—
512#124—1468no—
513#124—1462no—
514C22⋊Q8—22no—
515C22⋊Q8—22no—
516C22⋊Q8—734no—
517C22⋊Q8—1462no—
518C22⋊Q8—1468no—
519C22⋊Q8C22×D7314yes—
520C22⋊Q8C22×D7314yes—
521#121—734no—
522#121—1468no—
523#121—1462no—
524C4×Q8—28no—
525C4×Q8—22no—
526C4×Q8—734no—
527C4×Q8—1462no—
528C4×Q8C22×D7314yes—
529C4×D4—1468no—
530C4×D4C22⋊D7314yes—
531C4×D4C22×D7314yes—
532#117—22no—
533#117—22no—
534#117C22×D7314yes—
535#117C22×D7314yes—
536C2×C4⋊C4—21no—
537C2×C4⋊C4—21no—
538C2×C4⋊C4—21no—
539C2×C4⋊C4—21no—
540C2×C4⋊C4—731no—
541C2×C4⋊C4—1461no—
542C2×C4⋊C4—1461no—
543C2×C4⋊C4C22⋊D7311yescharacteristic
544C2×C4⋊C4C22×D7311yescharacteristic
545C2×C4⋊C4C22×D7311yescharacteristic
546C2×C4⋊C4C22×D7311yescharacteristic
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—1461no—
552C2×C22⋊C4—1461no—
553C2×C22⋊C4—1461no—
554C2×C22⋊C4—1461no—
555C2×C22⋊C4C22⋊D7311yescharacteristic
556C2×C22⋊C4C22⋊D7311yescharacteristic
557C2×C42—21no—
558C2×C42—21no—
559C2×C42—21no—
560C2×C42—1461no—
561C2×C42C22×D7311yescharacteristic
562#107—734no—
563#107—734no—
564#106—734no—
565C4⋊C8—734no—
566#103—734no—
567#103—734no—
568#103—734no—
569#103—734no—
570#103—734no—
571#103—734no—
572#103—734no—
573#102—734no—
574#102—734no—
575#102—734no—
576C22⋊C8—734no—
577C22⋊C8—734no—
578#97—734no—
579C24—1461no—
580C24C2×C22⋊D7311yescharacteristic
581C24C2×C22⋊D7311yescharacteristic
582#41—2928no—
583#41—2924no—
584#41—1468no—
585C2×Q8—21no—
586C2×Q8—24no—
587C2×Q8—22no—
588C2×Q8—22no—
589C2×Q8—44no—
590C2×Q8—2928no—
591C2×Q8—2924no—
592C2×Q8—2924no—
593C2×Q8—734no—
594C2×Q8—732no—
595C2×Q8—732no—
596C2×Q8—1468no—
597C2×Q8—1462no—
598C2×Q8—1462no—
599C2×Q8—1461no—
600C2×Q8—1464no—
601C2×Q8—1461no—
602C2×Q8—1462no—
603C2×Q8C23×D7312yes—
604C2×D4—42no—
605C2×D4—2924no—
606C2×D4—2924no—
607C2×D4—732no—
608C2×D4—1464no—
609C2×D4—1464no—
610C2×D4—1461no—
611C2×D4—1462no—
612C2×D4—1462no—
613C2×D4C2×C22⋊D7314yes—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—2924no—
623C22×C4—2924no—
624C22×C4—1464no—
625C22×C4—1461no—
626C22×C4—1461no—
627C22×C4—1464no—
628C22×C4—1461no—
629C22×C4C2×C22⋊D7312yes—
630C22×C4C2×C22⋊D7312yes—
631C22×C4C2×C22⋊D7311yescharacteristic
632C22×C4C2×C22⋊D7311yescharacteristic
633C22×C4C2×C22⋊D7311yescharacteristic
634C22×C4C2×C22⋊D7311yescharacteristic
635C22×C4C23×D7312yes—
636C22×C4C23×D7312yes—
637C22×C4C23×D7311yescharacteristic
638Q16—2924no—
639Q16—1468no—
640SD16—2924no—
641M16—2924no—
642C2×C8—2924no—
643C2×C8—732no—
644C2×C8—732no—
645C2×C8—732no—
646C2×C8—732no—
647C2×C8—1462no—
648C2×C8—1462no—
649C2×C8—1462no—
650C2×C8—1462no—
651C4⋊C4—24no—
652C4⋊C4—24no—
653C4⋊C4—24no—
654C4⋊C4—24no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—732no—
659C4⋊C4—1464no—
660C4⋊C4—1464no—
661C4⋊C4—1461no—
662C4⋊C4C2×C22⋊D7314yes—
663C4⋊C4C23×D7312yes—
664C4⋊C4C23×D7312yes—
665C4⋊C4C23×D7312yes—
666C22⋊C4—24no—
667C22⋊C4—24no—
668C22⋊C4—24no—
669C22⋊C4—24no—
670C22⋊C4—1464no—
671C22⋊C4—1464no—
672C22⋊C4—1464no—
673C22⋊C4—1464no—
674C22⋊C4C2×C22⋊D7314yes—
675C22⋊C4C2×C22⋊D7314yes—
676C42—24no—
677C42—24no—
678C42—24no—
679C42—1464no—
680C42C2×C22⋊D7312yes—
681C42C23×D7312yes—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—22no—
688C23—2922no—
689C23—2922no—
690C23—2922no—
691C23—1462no—
692C23C22×C22⋊D7312yes—
693C23C22×C22⋊D7312yes—
694C23C22×C22⋊D7311yescharacteristic
695Q8—22no—
696Q8—22no—
697Q8—48no—
698Q8—42no—
699Q8—2928no—
700Q8—2922no—
701Q8—734no—
702Q8—1462no—
703Q8—1462no—
704Q8—1462no—
705Q8—1464no—
706D4—44no—
707D4—2928no—
708D4—2928no—
709D4—2922no—
710D4—1462no—
711D4—1462no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—24no—
721C2×C4—24no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—2928no—
731C2×C4—2922no—
732C2×C4—2922no—
733C2×C4—2928no—
734C2×C4—1462no—
735C2×C4—1462no—
736C2×C4—1462no—
737C2×C4—1464no—
738C2×C4C22×C22⋊D7312yes—
739C2×C4C22×C22⋊D7312yes—
740C2×C4C22×C22⋊D7312yes—
741C2×C4C22×C22⋊D7312yes—
742C2×C4C22×C22⋊D7311yescharacteristic
743C2×C4#41×D7312yes—
744C2×C4#1455663712yes—
745C2×C4C24×D7311yescharacteristic
746C8—1462no—
747C8—1462no—
748C8—1462no—
749C8—1462no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—22no—
754C22—22no—
755C22—22no—
756C22—44no—
757C22—44no—
758C22—2922no—
759C22—2922no—
760C22—2922no—
761C22—5844no—
762C22#1798922512yes—
763C22#1798938512yes—
764C22#1798940212yes—
765C22C23×C22⋊D7311yescharacteristic
766C4—22no—
767C4—22no—
768C4—22no—
769C4—22no—
770C4—42no—
771C4—42no—
772C4—42no—
773C4—42no—
774C4—2922no—
775C4—2922no—
776C4—1464no—
777C4#1798922512yes—
778C4C2×#41×D7311yescharacteristic
779C4C2×#1455663711yescharacteristic
780C2—42no—
781C2—42no—
782C2—5842no—
783C2#2262199114yesdirect product factor
784C2C2×#1798922511yescharacteristic
785C2C2×#1798938511yescharacteristic
786C2C2×#1798940211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×#556×C73C2
socleC23×C73C22×D4
prime radicalC2×#17989246C2
hypercenterC2×#556D73
hypocenterC73C2×#3313
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#556

Complements

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

NH ≅ G/Ntype
2. #22621991C2direct (N × H)
3. C2×#17988949C2semidirect
4. C2×#17988928C2semidirect
5. C2×#17988911C2semidirect
6. C2×#17988879C2semidirect
7. C2×#17988835C2semidirect
8. C2×#17988826C2semidirect
9. C2×#17988809C2semidirect
10. C2×#17988747C2semidirect
11. C2×#17988742C2semidirect
12. C2×#17988692C2semidirect
13. C2×#17988659C2semidirect
14. C2×#17988595C2semidirect
15. C2×#17988581C2semidirect
16. C2×#556×C73C2semidirect
34. #17988949C22semidirect
35. #17988928C22semidirect
36. #17988911C22semidirect
37. #17988879C22semidirect
38. #17988835C22semidirect
39. #17988826C22semidirect
40. #17988809C22semidirect
41. #17988747C22semidirect
42. #17988742C22semidirect
43. #17988692C22semidirect
44. #17988659C22semidirect
49. #17988595C22semidirect
50. #17988581C22semidirect
65. #556×C73C22semidirect
389. C2×C73#3313semidirect
394. C2×#556D73semidirect
410. C73C2×#3313semidirect
419. #556C2×D73semidirect
783. C2#22621991direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179892462
#226219912
C2×#179889492
C2×#179889282
C2×#179889112
C2×#179888792
C2×#179888352
C2×#179888262
C2×#179888092
C2×#179887472
C2×#179887422
C2×#179886922
C2×#179886592
C2×#179885952
C2×#179885812
C2×#556×C732
C2×#331373