Finite Group Databasebeta

← C2×#22621985 #33962593

Subgroups — C2×#22621985 #33962593

Order 18688.

2094 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989276C211yesmaximal, characteristic
2C2×#17989250C211yesmaximal, characteristic
3#22621985C2116yesmaximal, direct product factor
4C2×#17988954C211yesmaximal, characteristic, complemented
5C2×#17988919C211yesmaximal, characteristic, complemented
6C2×#17988893C211yesmaximal, characteristic, complemented
7C2×#17988843C211yesmaximal, characteristic, complemented
8C2×#17988829C211yesmaximal, characteristic, complemented
9C2×#17988796C211yesmaximal, characteristic, complemented
10C2×#17988745C211yesmaximal, characteristic, complemented
11C2×#17988744C211yesmaximal, characteristic, complemented
12C2×#17988693C211yesmaximal, characteristic, complemented
13C2×#17988661C211yesmaximal, characteristic
14C2×#17988595C211yesmaximal, characteristic, complemented
15C2×#103×D73C211yesmaximal, characteristic, complemented
16C2×#485×C73C211yesmaximal, characteristic, complemented
17C23×Dic146C2211yescharacteristic
18C22×Q8×D73C2211yescharacteristic
19C22×Dic292C2211yescharacteristic
20C22×Dic292C2211yescharacteristic
21C22×#11924018C2211yescharacteristic
22C22×#11924012C2211yescharacteristic
23C22×C8×D73C2211yescharacteristic
24#17989276—24no—
25#17989276C2218yes—
26#17989250—24no—
27#17989250C2218yes—
28C2×#14556590—21no—
29C2×#14556589C2211yescharacteristic
30C2×#14556584—21no—
31C2×#14556583—21no—
32C2×#14556582C2211yescharacteristic
33C2×#14556573—21no—
34C2×#14556571C2211yescharacteristic
35C2×#14556571C2211yescharacteristic
36C2×#14556570C2211yescharacteristic
37C2×#14556569—21no—
38C2×#14556568—21no—
39C2×#14556556C2211yescharacteristic
40C2×#14556556C2211yescharacteristic
41C2×C4×C22⋊D73C2211yescharacteristic
42C2×#14556551—21no—
43C2×#14556548—21no—
44C2×C4⋊C4×D73C2211yescharacteristic
45#17988954C2218yescomplemented
46#17988919C2218yescomplemented
47#17988893C2218yescomplemented
48#17988843C2218yescomplemented
49#17988829C2218yescomplemented
50#17988796C2218yescomplemented
51#17988745C2218yescomplemented
52#17988744C2218yescomplemented
53#17988693C2218yescomplemented
54#17988661C2218yes—
55C2×#14556522C2211yescharacteristic
56C2×#14556520C2211yescharacteristic
57#17988595C2218yescomplemented
58C2×#14556516C2211yescharacteristic
59C2×#14556516C2211yescharacteristic
60C2×#14556515C2211yescharacteristic
61C2×#14556514C2211yescharacteristic
62C2×#14556514C2211yescharacteristic
63C2×#14556514C2211yescharacteristic
64C2×#14556514C2211yescharacteristic
65C2×#14556514C2211yescharacteristic
66#103×D73C2218yescomplemented
67C2×#14556503C2211yescharacteristic
68C2×#14556501C2211yescharacteristic
69C2×C22⋊Q8×C73C2211yescharacteristic
70C2×#117×C73C2211yescharacteristic
71#485×C73C2218yescomplemented
72C2×#107×C73C2211yescharacteristic
73C2×#106×C73C2211yescharacteristic
74C2×#103×C73C2211yescharacteristic
75C2×#103×C73C2211yescharacteristic
76C2×C22⋊C8×C73C2211yescharacteristic
77C22×Dic146—21no—
78C22×Dic146—24no—
79C22×Dic146—21no—
80C22×Dic146—22no—
81C22×Dic146—42no—
82C22×Dic146C2311yescharacteristic
83C22×Dic146C2311yescharacteristic
84C22×Dic146C2314yes—
85C22×Dic146C2311yescharacteristic
86C2×Q8×D73—22no—
87C2×Q8×D73—24no—
88C2×Q8×D73—42no—
89C2×Q8×D73C2314yes—
90C22×C22⋊D73D411yescharacteristic
91C23×Dic73—21no—
92C22×C4×D73—21no—
93C22×C4×D73—21no—
94C22×C4×D73C2311yescharacteristic
95C2×Dic292—24no—
96C2×Dic292—42no—
97C2×Dic292C2314yes—
98C2×Dic292C2314yes—
99C2×#11924018—42no—
100C2×#11924018C2314yes—
101C2×#11924012—42no—
102C2×#11924012C2314yes—
103C22×#10596831C2311yescharacteristic
104C22×#10596831C2311yescharacteristic
105C2×C8×D73—42no—
106C2×C8×D73C2314yes—
107#14556590—28no—
108#14556589—22no—
109#14556589C2314yes—
110#14556584—28no—
111#14556583—28no—
112#14556582—22no—
113#14556582C2314yes—
114#14556573—28no—
115#14556571—22no—
116#14556571—22no—
117#14556571C2314yes—
118#14556571C2314yes—
119#14556570—22no—
120#14556570C2314yes—
121#14556569—28no—
122#14556568—28no—
123#14556556—22no—
124#14556556—22no—
125#14556556C2314yes—
126#14556556C2314yes—
127C4×C22⋊D73D414yes—
128C4×C22⋊D73C2314yes—
129#14556551—28no—
130#14556548—28no—
131C2×C4⋊Dic73—21no—
132C2×C4⋊Dic73—21no—
133C2×C4⋊Dic73—21no—
134C2×C4⋊Dic73C2311yescharacteristic
135C2×#11924007—21no—
136C2×#11924007—21no—
137C2×#11924007—21no—
138C2×#11924007—21no—
139C2×#11924007—21no—
140C2×#11924007—21no—
141C2×#11924007—21no—
142C2×#11924007D411yescharacteristic
143C4⋊C4×D73—22no—
144C4⋊C4×D73C2314yes—
145C2×C22⋊Dic73—21no—
146C2×C22⋊Dic73D411yescharacteristic
147C2×#11924005—21no—
148C2×#11924005—21no—
149C2×#11924005D411yescharacteristic
150C2×C4×Dic73—21no—
151C2×C4×Dic73—21no—
152C2×C4×Dic73C2311yescharacteristic
153#14556522C2314yes—
154#14556520C2314yes—
155#14556516C2314yes—
156#14556516C2314yes—
157#14556515C2314yes—
158#14556514C2314yes—
159#14556514C2314yes—
160#14556514C2314yes—
161#14556514C2314yes—
162#14556514C2314yes—
163#14556503C2314yes—
164#14556501C2314yes—
165C22×Q8×C73C2311yescharacteristic
166C23×C4×C73C2311yescharacteristic
167C22×C8×C73C2311yescharacteristic
168C22×C8×C73C2311yescharacteristic
169C22⋊Q8×C73—22no—
170C22⋊Q8×C73C2314yes—
171#117×C73—22no—
172#117×C73C2314yes—
173C2×C4⋊C4×C73—21no—
174C2×C4⋊C4×C73C2311yescharacteristic
175C2×C4⋊C4×C73C2311yescharacteristic
176C2×C4⋊C4×C73C2311yescharacteristic
177C2×C22⋊C4×C73—21no—
178C2×C22⋊C4×C73—21no—
179C2×C42×C73—21no—
180#107×C73C2314yes—
181#106×C73C2314yes—
182#103×C73C2314yes—
183#103×C73C2314yes—
184C22⋊C8×C73C2314yes—
185C23×D73C2×D411yescharacteristic
186C2×Dic146—21no—
187C2×Dic146—22no—
188C2×Dic146—22no—
189C2×Dic146—22no—
190C2×Dic146—22no—
191C2×Dic146—22no—
192C2×Dic146—28no—
193C2×Dic146—21no—
194C2×Dic146—24no—
195C2×Dic146—21no—
196C2×Dic146—24no—
197C2×Dic146—44no—
198C2×Dic146—48no—
199C2×Dic146—44no—
200C2×Dic146—44no—
201C2×Dic146#4114yes—
202C2×Dic146C2412yes—
203C2×Dic146C2412yes—
204C2×Dic146C2412yes—
205Q8×D73—28no—
206Q8×D73—44no—
207Q8×D73—48no—
208C2×C22⋊D73—24no—
209C2×C22⋊D73C2×D414yes—
210C22×Dic73—21no—
211C22×Dic73—21no—
212C22×Dic73—21no—
213C22×Dic73—21no—
214C22×Dic73—24no—
215C22×Dic73—44no—
216C22×Dic73C2×D411yescharacteristic
217C22×Dic73C2×D411yescharacteristic
218C22×Dic73C2×D411yescharacteristic
219C2×C4×D73—22no—
220C2×C4×D73—22no—
221C2×C4×D73—24no—
222C2×C4×D73—24no—
223C2×C4×D73—44no—
224C2×C4×D73—44no—
225C2×C4×D73C2×D412yes—
226C2×C4×D73C2412yes—
227Dic292—28no—
228Dic292—44no—
229#11924018—44no—
230#11924012—44no—
231C2×#10596831—22no—
232C2×#10596831—22no—
233C2×#10596831C2412yes—
234C2×#10596831C2412yes—
235C8×D73—44no—
236C4⋊Dic73—21no—
237C4⋊Dic73—24no—
238C4⋊Dic73—24no—
239C4⋊Dic73—24no—
240C4⋊Dic73C2412yes—
241#11924007—24no—
242#11924007—24no—
243#11924007—24no—
244#11924007—24no—
245#11924007—24no—
246#11924007—24no—
247#11924007—24no—
248#11924007C2×D414yes—
249C22⋊Dic73—24no—
250C22⋊Dic73C2×D414yes—
251#11924005—24no—
252#11924005—24no—
253#11924005C2×D414yes—
254C4×Dic73—24no—
255C4×Dic73—24no—
256C4×Dic73C2×D412yes—
257C4×Dic73C2412yes—
258C24×C73C2×D411yescharacteristic
259C2×Q8×C73—21no—
260C2×Q8×C73—22no—
261C2×Q8×C73—22no—
262C2×Q8×C73C2412yes—
263C22×C4×C73—22no—
264C22×C4×C73—22no—
265C22×C4×C73—21no—
266C22×C4×C73—21no—
267C22×C4×C73—21no—
268C22×C4×C73—21no—
269C22×C4×C73C2×D411yescharacteristic
270C22×C4×C73C2×D412yes—
271C22×C4×C73C2412yes—
272C22×C4×C73C2411yescharacteristic
273C2×C8×C73—22no—
274C2×C8×C73—22no—
275C2×C8×C73C2412yes—
276C2×C8×C73C2412yes—
277C4⋊C4×C73—24no—
278C4⋊C4×C73—21no—
279C4⋊C4×C73—21no—
280C4⋊C4×C73—21no—
281C4⋊C4×C73C2412yes—
282C4⋊C4×C73C2412yes—
283C4⋊C4×C73C2412yes—
284C22⋊C4×C73—24no—
285C22⋊C4×C73—24no—
286C42×C73—24no—
287C23×C73—22no—
288C23×C73—22no—
289C23×C73—22no—
290C23×C73C22×D412yes—
291C23×C73C22×D411yescharacteristic
292C22×D73—22no—
293C22×D73—22no—
294C22×D73#13714yes—
295C22×D73C22×D412yes—
296Q8×C73—22no—
297Q8×C73—22no—
298Q8×C73—42no—
299C2×C4×C73—22no—
300C2×C4×C73—24no—
301C2×C4×C73—22no—
302C2×C4×C73—22no—
303C2×C4×C73—22no—
304C2×C4×C73—22no—
305C2×C4×C73—22no—
306C2×C4×C73—22no—
307C2×C4×C73—42no—
308C2×C4×C73—42no—
309C2×C4×C73—42no—
310C2×C4×C73—42no—
311C2×C4×C73C22×D412yes—
312C2×C4×C73C22×D411yescharacteristic
313C2×C4×C73C2×#4112yes—
314C2×C4×C73H(5,𝔽2)12yes—
315C2×C4×C73C2511yescharacteristic
316C22⋊D73—28no—
317C2×Dic73—22no—
318C2×Dic73—24no—
319C2×Dic73—22no—
320C2×Dic73—22no—
321C2×Dic73—22no—
322C2×Dic73—22no—
323C2×Dic73—22no—
324C2×Dic73—22no—
325C2×Dic73—48no—
326C2×Dic73—42no—
327C2×Dic73—42no—
328C2×Dic73—42no—
329C2×Dic73C22×D412yes—
330C2×Dic73C22×D412yes—
331C2×Dic73C22×D412yes—
332C4×D73—24no—
333C4×D73—22no—
334C4×D73—22no—
335C4×D73—48no—
336C4×D73—48no—
337Dic146—24no—
338Dic146—22no—
339Dic146—22no—
340Dic146—22no—
341Dic146—22no—
342Dic146—22no—
343Dic146—48no—
344Dic146—48no—
345Dic146—42no—
346Dic146—42no—
347Dic146C2×#4114yes—
348C8×C73—22no—
349C8×C73—22no—
350#10596831—22no—
351#10596831—22no—
352C22×C73—22no—
353C22×C73—22no—
354C22×C73—22no—
355C22×C73—44no—
356C22×C73#54612yes—
357C22×C73C2×#13712yes—
358C22×C73#57812yes—
359C22×C73C23×D411yescharacteristic
360C2×D73—22no—
361C2×D73—28no—
362C2×D73—22no—
363C2×D73C2×#13714yes—
364C4×C73—22no—
365C4×C73—42no—
366C4×C73—42no—
367C4×C73—42no—
368C4×C73—42no—
369C4×C73#54612yes—
370C4×C73C22×#4111yescharacteristic
371C4×C73C2×H(5,𝔽2)11yescharacteristic
372Dic73—24no—
373Dic73—22no—
374Dic73—22no—
375Dic73—22no—
376Dic73—42no—
377Dic73—42no—
378Dic73—42no—
379C2×#3312—731nomaximal, Sylow
380C2×C73—42no—
381C2×C73#331214yescomplemented
382C2×C73C2×#54611yescharacteristic
383C2×C73C22×#13711yescharacteristic
384C2×C73C2×#57811yescharacteristic
385D73—24no—
386C2×#552—731no—
387C2×D4×Q8—731no—
388#3312—7316no—
389C2×#491—731no—
390C2×#485D7311yescharacteristic, complemented
391C2×#483—731no—
392C2×#479—731no—
393C2×#470—731no—
394C2×#467—731no—
395C2×#462—731no—
396C2×#451—731no—
397C2×#451—731no—
398C2×#441—731no—
399C2×#435—731no—
400C2×#419—731no—
401C22×#103—731no—
402C73C2×#331211yescharacteristic, complemented, Sylow
403C23×Q8—731no—
404C23×Q8—731no—
405C22×Q16—731no—
406C22×Q16—731no—
407C22×Q16—731no—
408C22×M16—731no—
409C23×C8—731no—
410#552—738no—
411#552—1464no—
412D4×Q8—738no—
413D4×Q8—1464no—
414C2×C4⋊Q8—731no—
415C2×C4⋊Q8—1461no—
416C2×#126—1461no—
417C2×#125—731no—
418C2×#125—1461no—
419C2×#123—1461no—
420C2×C22⋊Q8—731no—
421C2×C22⋊Q8—731no—
422C2×C22⋊Q8—731no—
423C2×C22⋊Q8—1461no—
424C2×C22⋊Q8—1461no—
425C2×C22⋊Q8C2×D7311yescharacteristic
426C2×C4×Q8—731no—
427C2×C4×Q8—731no—
428C2×C4×D4—731no—
429C2×C4×D4—1461no—
430C2×#117—1461no—
431C2×#117C2×D7311yescharacteristic
432C22×C4⋊C4—731no—
433#491—738no—
434#485C2×D7318yescomplemented
435#483—738no—
436#479—738no—
437#470—738no—
438#467—738no—
439#462—738no—
440#451—738no—
441#451—738no—
442#441—738no—
443#435—738no—
444C2×#107C2×D7311yescharacteristic
445C2×#106—731no—
446C2×#106C2×D7311yescharacteristic
447C2×C4⋊C8—731no—
448#419—738no—
449C2×#103—731no—
450C2×#103—731no—
451C2×#103—731no—
452C2×#103—731no—
453C2×#103—731no—
454C2×#103—731no—
455C2×#103—731no—
456C2×#103—731no—
457C2×#103—738no—
458C2×#103C2×D7311yescharacteristic
459C2×#103C2×D7311yescharacteristic
460C2×C22⋊C8—731no—
461C2×C22⋊C8C2×D7311yescharacteristic
462C2×#97—731no—
463C22×Q8—2922no—
464C22×Q8—2922no—
465C22×Q8—734no—
466C22×Q8—734no—
467C22×Q8—731no—
468C22×Q8—731no—
469C22×Q8—731no—
470C22×Q8—1464no—
471C22×Q8—1461no—
472C22×Q8—1464no—
473C22×Q8—1462no—
474C22×Q8—1461no—
475C22×Q8—1462no—
476C22×Q8C22×D7311yescharacteristic
477C22×D4—731no—
478C23×C4—731no—
479C23×C4—1461no—
480C23×C4—1461no—
481C23×C4—1461no—
482C23×C4C22×D7311yescharacteristic
483C2×Q16—2922no—
484C2×Q16—2922no—
485C2×Q16—734no—
486C2×Q16—734no—
487C2×Q16—734no—
488C2×Q16—1464no—
489C2×M16—2922no—
490C2×M16—734no—
491C22×C8—2922no—
492C22×C8—734no—
493C22×C8—731no—
494C22×C8—731no—
495C22×C8C22×D7311yescharacteristic
496C22×C8C22×D7311yescharacteristic
497C4⋊Q8—734no—
498C4⋊Q8—1462no—
499C4⋊Q8—1468no—
500#126—1468no—
501#125—734no—
502#125—1468no—
503#125—1462no—
504#123—1468no—
505C22⋊Q8—22no—
506C22⋊Q8—734no—
507C22⋊Q8—734no—
508C22⋊Q8—734no—
509C22⋊Q8—1468no—
510C22⋊Q8—1468no—
511C22⋊Q8—1462no—
512C22⋊Q8—1462no—
513C22⋊Q8—1462no—
514C22⋊Q8C22×D7314yes—
515C4×Q8—734no—
516C4×Q8—734no—
517C4×Q8—1462no—
518C4×Q8—1462no—
519C4×D4—734no—
520C4×D4—734no—
521C4×D4—1468no—
522#117—22no—
523#117—1468no—
524#117C22×D7314yes—
525C2×C4⋊C4—21no—
526C2×C4⋊C4—731no—
527C2×C4⋊C4—731no—
528C2×C4⋊C4—734no—
529C2×C4⋊C4—1462no—
530C2×C4⋊C4—1461no—
531C2×C4⋊C4—1461no—
532C2×C4⋊C4—1461no—
533C2×C4⋊C4—1461no—
534C2×C4⋊C4—1461no—
535C2×C4⋊C4—1461no—
536C2×C4⋊C4—1461no—
537C2×C4⋊C4—1461no—
538C2×C4⋊C4—1461no—
539C2×C4⋊C4—1461no—
540C2×C4⋊C4C22×D7311yescharacteristic
541C2×C4⋊C4C22×D7311yescharacteristic
542C2×C4⋊C4C22×D7311yescharacteristic
543C2×C22⋊C4—21no—
544C2×C22⋊C4—21no—
545C2×C22⋊C4—731no—
546C2×C22⋊C4—731no—
547C2×C22⋊C4—1461no—
548C2×C22⋊C4—1461no—
549C2×C22⋊C4—1461no—
550C2×C42—21no—
551C2×C42—731no—
552C2×C42—1461no—
553C2×C42—1461no—
554#107C22×D7314yes—
555#106—734no—
556#106C22×D7314yes—
557C4⋊C8—734no—
558#103—734no—
559#103—734no—
560#103—734no—
561#103—734no—
562#103—734no—
563#103—734no—
564#103—734no—
565#103—734no—
566#103C22×D7314yes—
567#103C22×D7314yes—
568C22⋊C8—734no—
569C22⋊C8C22×D7314yes—
570#97—734no—
571C24—731no—
572C24D4×D7311yescharacteristic
573C2×Q8—21no—
574C2×Q8—22no—
575C2×Q8—22no—
576C2×Q8—2928no—
577C2×Q8—2924no—
578C2×Q8—2924no—
579C2×Q8—2924no—
580C2×Q8—2924no—
581C2×Q8—2928no—
582C2×Q8—734no—
583C2×Q8—732no—
584C2×Q8—732no—
585C2×Q8—732no—
586C2×Q8—1468no—
587C2×Q8—1464no—
588C2×Q8—1468no—
589C2×Q8—1462no—
590C2×Q8—1462no—
591C2×Q8—1462no—
592C2×Q8—1462no—
593C2×Q8—1461no—
594C2×Q8—1461no—
595C2×Q8—1464no—
596C2×Q8—1461no—
597C2×Q8—1462no—
598C2×Q8C23×D7312yes—
599C2×D4—734no—
600C2×D4—1464no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—2924no—
608C22×C4—2924no—
609C22×C4—2924no—
610C22×C4—731no—
611C22×C4—731no—
612C22×C4—731no—
613C22×C4—732no—
614C22×C4—732no—
615C22×C4—1464no—
616C22×C4—1464no—
617C22×C4—1464no—
618C22×C4—1461no—
619C22×C4—1461no—
620C22×C4—1461no—
621C22×C4—1461no—
622C22×C4—1462no—
623C22×C4—1462no—
624C22×C4D4×D7312yes—
625C22×C4D4×D7311yescharacteristic
626C22×C4C23×D7312yes—
627C22×C4C23×D7311yescharacteristic
628Q16—2924no—
629Q16—2924no—
630Q16—1468no—
631M16—2924no—
632C2×C8—22no—
633C2×C8—22no—
634C2×C8—2924no—
635C2×C8—732no—
636C2×C8—732no—
637C2×C8—1462no—
638C2×C8—1462no—
639C2×C8C23×D7312yes—
640C2×C8C23×D7312yes—
641C4⋊C4—24no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—734no—
646C4⋊C4—732no—
647C4⋊C4—1464no—
648C4⋊C4—1464no—
649C4⋊C4—1464no—
650C4⋊C4—1464no—
651C4⋊C4—1464no—
652C4⋊C4—1464no—
653C4⋊C4—1464no—
654C4⋊C4—1464no—
655C4⋊C4—1464no—
656C4⋊C4—1464no—
657C4⋊C4—1461no—
658C4⋊C4C23×D7312yes—
659C4⋊C4C23×D7312yes—
660C4⋊C4C23×D7312yes—
661C22⋊C4—24no—
662C22⋊C4—24no—
663C22⋊C4—734no—
664C22⋊C4—734no—
665C22⋊C4—1464no—
666C22⋊C4—1464no—
667C22⋊C4—1464no—
668C42—24no—
669C42—732no—
670C42—732no—
671C42—1464no—
672C42—1464no—
673C23—22no—
674C23—22no—
675C23—22no—
676C23—734no—
677C23—732no—
678C23—1462no—
679C23—1462no—
680C23C2×D4×D7312yes—
681C23C2×D4×D7311yescharacteristic
682Q8—22no—
683Q8—22no—
684Q8—42no—
685Q8—2928no—
686Q8—2928no—
687Q8—2922no—
688Q8—2922no—
689Q8—734no—
690Q8—1462no—
691Q8—1462no—
692Q8—1462no—
693Q8—1462no—
694Q8—1462no—
695Q8—1464no—
696D4—1468no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—24no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—2928no—
710C2×C4—2928no—
711C2×C4—2922no—
712C2×C4—2922no—
713C2×C4—2922no—
714C2×C4—2928no—
715C2×C4—732no—
716C2×C4—732no—
717C2×C4—732no—
718C2×C4—1462no—
719C2×C4—1462no—
720C2×C4—1462no—
721C2×C4—1462no—
722C2×C4—1462no—
723C2×C4—1462no—
724C2×C4—1464no—
725C2×C4—1462no—
726C2×C4—1462no—
727C2×C4—1462no—
728C2×C4—1464no—
729C2×C4C2×D4×D7312yes—
730C2×C4C2×D4×D7311yescharacteristic
731C2×C4#41×D7312yes—
732C2×C4#1455663712yes—
733C2×C4C24×D7311yescharacteristic
734C8—22no—
735C8—22no—
736C8—1462no—
737C8—1462no—
738C22—22no—
739C22—22no—
740C22—22no—
741C22—44no—
742C22—734no—
743C22—1468no—
744C22—1462no—
745C22—1462no—
746C22#1798922912yes—
747C22#137×D7312yes—
748C22#1798940112yes—
749C22C22×D4×D7311yescharacteristic
750C4—22no—
751C4—42no—
752C4—42no—
753C4—42no—
754C4—42no—
755C4—2922no—
756C4—2922no—
757C4—2922no—
758C4—1464no—
759C4—1462no—
760C4—1462no—
761C4—1462no—
762C4#1798922912yes—
763C4C2×#41×D7311yescharacteristic
764C4C2×#1455663711yescharacteristic
765C2—42no—
766C2—1464no—
767C2#2262198514yesdirect product factor
768C2C2×#1798922911yescharacteristic
769C2C2×#137×D7311yescharacteristic
770C2C2×#1798940111yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×#485×C73C2
socleC23×C73C22×D4
prime radicalC22×C22⋊D73D4
hypercenterC2×#485D73
hypocenterC73C2×#3312
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#485

Complements

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

NH ≅ G/Ntype
3. #22621985C2direct (N × H)
4. C2×#17988954C2semidirect
5. C2×#17988919C2semidirect
6. C2×#17988893C2semidirect
7. C2×#17988843C2semidirect
8. C2×#17988829C2semidirect
9. C2×#17988796C2semidirect
10. C2×#17988745C2semidirect
11. C2×#17988744C2semidirect
12. C2×#17988693C2semidirect
14. C2×#17988595C2semidirect
15. C2×#103×D73C2semidirect
16. C2×#485×C73C2semidirect
45. #17988954C22semidirect
46. #17988919C22semidirect
47. #17988893C22semidirect
48. #17988843C22semidirect
49. #17988829C22semidirect
50. #17988796C22semidirect
51. #17988745C22semidirect
52. #17988744C22semidirect
53. #17988693C22semidirect
57. #17988595C22semidirect
66. #103×D73C22semidirect
71. #485×C73C22semidirect
381. C2×C73#3312semidirect
390. C2×#485D73semidirect
402. C73C2×#3312semidirect
434. #485C2×D73semidirect
767. C2#22621985direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179892762
C2×#179892502
#226219852
C2×#179889542
C2×#179889192
C2×#179888932
C2×#179888432
C2×#179888292
C2×#179887962
C2×#179887452
C2×#179887442
C2×#179886932
C2×#179886612
C2×#179885952
C2×#103×D732
C2×#485×C732
C2×#331273