Finite Group Databasebeta

← C2×#22621984 #33962592

Subgroups — C2×#22621984 #33962592

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×#17989277C211yesmaximal, characteristic
2C2×D4×Dic146C211yesmaximal, characteristic
3#22621984C2116yesmaximal, direct product factor
4C2×#17988956C211yesmaximal, characteristic, complemented
5C2×#17988929C211yesmaximal, characteristic, complemented
6C2×#17988918C211yesmaximal, characteristic, complemented
7C2×#17988895C211yesmaximal, characteristic, complemented
8C2×#17988845C211yesmaximal, characteristic, complemented
9C2×#17988828C211yesmaximal, characteristic, complemented
10C2×#17988798C211yesmaximal, characteristic, complemented
11C2×#17988745C211yesmaximal, characteristic, complemented
12C2×#17988745C211yesmaximal, characteristic, complemented
13C2×#17988695C211yesmaximal, characteristic, complemented
14C2×#17988597C211yesmaximal, characteristic, complemented
15C22×#14556516C211yesmaximal, characteristic, complemented
16C2×#435×C73C211yesmaximal, characteristic
17C23×Dic146C2211yescharacteristic
18C23×Dic146C2211yescharacteristic
19C22×Dic292C2211yescharacteristic
20C22×Dic292C2211yescharacteristic
21C22×Dic292C2211yescharacteristic
22#17989277—24no—
23#17989277C2218yes—
24D4×Dic146—24no—
25D4×Dic146C2218yes—
26C2×#14556591C2211yescharacteristic
27C2×#14556590—21no—
28C2×#14556584—21no—
29C2×#14556583C2211yescharacteristic
30C2×#14556581—21no—
31C2×#14556572—21no—
32C2×#14556570C2211yescharacteristic
33C2×#14556570C2211yescharacteristic
34C2×#14556570C2211yescharacteristic
35C2×#14556570C2211yescharacteristic
36C2×#14556568—21no—
37C2×#14556568—21no—
38C2×C4×Dic146C2211yescharacteristic
39C2×C4×Dic146C2211yescharacteristic
40C2×D4×Dic73—21no—
41C2×#14556550C2211yescharacteristic
42C2×#14556547—21no—
43C22×C4⋊Dic73C2211yescharacteristic
44#17988956C2218yescomplemented
45#17988929C2218yescomplemented
46#17988918C2218yescomplemented
47#17988895C2218yescomplemented
48#17988845C2218yescomplemented
49#17988828C2218yescomplemented
50#17988798C2218yescomplemented
51#17988745C2218yescomplemented
52#17988745C2218yescomplemented
53#17988695C2218yescomplemented
54C2×#14556525C2211yescharacteristic
55C2×#14556523C2211yescharacteristic
56C2×#14556523C2211yescharacteristic
57#17988597C2218yescomplemented
58C2×#14556516C2211yescharacteristic
59C2×#14556516C2211yescharacteristic
60C2×#14556516C2211yescharacteristic
61C2×#14556516C2211yescharacteristic
62C2×#14556516C2211yescharacteristic
63C2×#14556516C2211yescharacteristic
64C2×#14556516C2211yescharacteristic
65C2×#14556516C2211yescharacteristic
66C2×#14556516C2211yescharacteristic
67C2×#14556516C2211yescharacteristic
68C2×#14556516C2218yescomplemented
69C22×M16×C73C2211yescharacteristic
70C23×C8×C73C2211yescharacteristic
71C2×C4×D4×C73C2211yescharacteristic
72#435×C73C2218yes—
73C2×C4⋊C8×C73C2211yescharacteristic
74C2×C22⋊C8×C73C2211yescharacteristic
75C2×C22⋊C8×C73C2211yescharacteristic
76C2×#97×C73C2211yescharacteristic
77C22×Dic146—24no—
78C22×Dic146—24no—
79C22×Dic146—21no—
80C22×Dic146—21no—
81C22×Dic146—22no—
82C22×Dic146—22no—
83C22×Dic146—42no—
84C22×Dic146—42no—
85C22×Dic146C2311yescharacteristic
86C22×Dic146C2311yescharacteristic
87C22×Dic146C2311yescharacteristic
88C22×Dic146C2314yes—
89C22×Dic146C2314yes—
90C22×Dic146C2311yescharacteristic
91C23×Dic73—21no—
92C23×Dic73—21no—
93C23×Dic73—21no—
94C2×Dic292—24no—
95C2×Dic292—42no—
96C2×Dic292—42no—
97C2×Dic292C2314yes—
98C2×Dic292C2314yes—
99C2×Dic292C2314yes—
100#14556591—22no—
101#14556591C2314yes—
102#14556590—28no—
103#14556584—28no—
104#14556583—22no—
105#14556583C2314yes—
106#14556581—28no—
107#14556572—28no—
108#14556570—22no—
109#14556570—22no—
110#14556570—22no—
111#14556570—22no—
112#14556570C2314yes—
113#14556570C2314yes—
114#14556570C2314yes—
115#14556570C2314yes—
116#14556568—28no—
117#14556568—28no—
118C4×Dic146—22no—
119C4×Dic146—22no—
120C4×Dic146C2314yes—
121C4×Dic146C2314yes—
122D4×Dic73—28no—
123#14556550—22no—
124#14556550C2314yes—
125#14556547—28no—
126C2×C4⋊Dic73—21no—
127C2×C4⋊Dic73—21no—
128C2×C4⋊Dic73—22no—
129C2×C4⋊Dic73—21no—
130C2×C4⋊Dic73C2311yescharacteristic
131C2×C4⋊Dic73C2311yescharacteristic
132C2×C4⋊Dic73C2311yescharacteristic
133C2×C4⋊Dic73C2311yescharacteristic
134C2×C4⋊Dic73C2314yes—
135C2×#11924007—21no—
136C2×#11924007—21no—
137C2×#11924007—21no—
138C2×#11924007—21no—
139C2×#11924007—21no—
140C2×#11924007—21no—
141C2×#11924007—21no—
142C2×#11924007—21no—
143C2×C22⋊Dic73—21no—
144C2×C22⋊Dic73—21no—
145C2×C22⋊Dic73—21no—
146C2×C22⋊Dic73—21no—
147C2×C22⋊Dic73—21no—
148C2×C4×Dic73—21no—
149C2×C4×Dic73—21no—
150C2×C4×Dic73—21no—
151#14556525C2314yes—
152#14556523C2314yes—
153#14556523C2314yes—
154#14556516C2314yes—
155#14556516C2314yes—
156#14556516C2314yes—
157#14556516C2314yes—
158#14556516C2314yes—
159#14556516C2314yes—
160#14556516C2314yes—
161#14556516C2314yes—
162#14556516C2314yes—
163#14556516C2314yes—
164C22×D4×C73D411yescharacteristic
165C23×C4×C73C2311yescharacteristic
166C23×C4×C73C2311yescharacteristic
167C2×M16×C73—42no—
168C2×M16×C73C2314yes—
169C22×C8×C73—42no—
170C22×C8×C73C2311yescharacteristic
171C22×C8×C73C2311yescharacteristic
172C22×C8×C73C2311yescharacteristic
173C22×C8×C73C2311yescharacteristic
174C22×C8×C73C2314yes—
175C4×D4×C73D414yes—
176C4×D4×C73C2314yes—
177C2×C4⋊C4×C73D411yescharacteristic
178C2×C22⋊C4×C73D411yescharacteristic
179C2×C22⋊C4×C73D411yescharacteristic
180C2×C42×C73C2311yescharacteristic
181C4⋊C8×C73C2314yes—
182C22⋊C8×C73C2314yes—
183C22⋊C8×C73C2314yes—
184#97×C73C2314yes—
185C2×Dic146—21no—
186C2×Dic146—22no—
187C2×Dic146—22no—
188C2×Dic146—22no—
189C2×Dic146—22no—
190C2×Dic146—22no—
191C2×Dic146—22no—
192C2×Dic146—22no—
193C2×Dic146—28no—
194C2×Dic146—28no—
195C2×Dic146—21no—
196C2×Dic146—24no—
197C2×Dic146—24no—
198C2×Dic146—21no—
199C2×Dic146—21no—
200C2×Dic146—44no—
201C2×Dic146—44no—
202C2×Dic146—48no—
203C2×Dic146—48no—
204C2×Dic146—44no—
205C2×Dic146—44no—
206C2×Dic146#4114yes—
207C2×Dic146C2412yes—
208C2×Dic146C2412yes—
209C2×Dic146C2412yes—
210C2×Dic146C2412yes—
211C22×Dic73—21no—
212C22×Dic73—21no—
213C22×Dic73—21no—
214C22×Dic73—21no—
215C22×Dic73—21no—
216C22×Dic73—21no—
217C22×Dic73—21no—
218C22×Dic73—21no—
219C22×Dic73—24no—
220C22×Dic73—24no—
221C22×Dic73—24no—
222C22×Dic73—44no—
223C22×Dic73—44no—
224C22×Dic73—44no—
225Dic292—28no—
226Dic292—44no—
227Dic292—44no—
228C4⋊Dic73—21no—
229C4⋊Dic73—21no—
230C4⋊Dic73—24no—
231C4⋊Dic73—24no—
232C4⋊Dic73—24no—
233C4⋊Dic73—21no—
234C4⋊Dic73—21no—
235C4⋊Dic73C2412yes—
236C4⋊Dic73C2412yes—
237C4⋊Dic73C2412yes—
238C4⋊Dic73C2412yes—
239#11924007—24no—
240#11924007—24no—
241#11924007—24no—
242#11924007—24no—
243#11924007—24no—
244#11924007—24no—
245#11924007—24no—
246#11924007—24no—
247C22⋊Dic73—24no—
248C22⋊Dic73—24no—
249C22⋊Dic73—24no—
250C22⋊Dic73—24no—
251C22⋊Dic73—24no—
252C4×Dic73—24no—
253C4×Dic73—24no—
254C4×Dic73—24no—
255C24×C73C2×D411yescharacteristic
256C24×C73C2×D411yescharacteristic
257C2×D4×C73—24no—
258C2×D4×C73C2×D414yes—
259C22×C4×C73—22no—
260C22×C4×C73—22no—
261C22×C4×C73—22no—
262C22×C4×C73—22no—
263C22×C4×C73C2×D411yescharacteristic
264C22×C4×C73C2×D411yescharacteristic
265C22×C4×C73C2×D411yescharacteristic
266C22×C4×C73C2×D411yescharacteristic
267C22×C4×C73C2×D412yes—
268C22×C4×C73C2×D412yes—
269C22×C4×C73C2412yes—
270C22×C4×C73C2412yes—
271C22×C4×C73C2411yescharacteristic
272M16×C73—44no—
273C2×C8×C73—22no—
274C2×C8×C73—22no—
275C2×C8×C73—22no—
276C2×C8×C73—22no—
277C2×C8×C73—44no—
278C2×C8×C73C2412yes—
279C2×C8×C73C2412yes—
280C2×C8×C73C2412yes—
281C2×C8×C73C2412yes—
282C4⋊C4×C73C2×D414yes—
283C22⋊C4×C73C2×D414yes—
284C22⋊C4×C73C2×D414yes—
285C42×C73C2×D412yes—
286C42×C73C2412yes—
287C23×C73—22no—
288C23×C73—22no—
289C23×C73—22no—
290C23×C73—22no—
291C23×C73—22no—
292C23×C73#13714yes—
293C23×C73C22×D412yes—
294C23×C73C22×D412yes—
295C23×C73C22×D411yescharacteristic
296D4×C73—28no—
297C2×C4×C73—22no—
298C2×C4×C73—22no—
299C2×C4×C73—22no—
300C2×C4×C73—22no—
301C2×C4×C73—24no—
302C2×C4×C73—24no—
303C2×C4×C73—22no—
304C2×C4×C73—22no—
305C2×C4×C73—22no—
306C2×C4×C73—22no—
307C2×C4×C73C22×D412yes—
308C2×C4×C73C22×D412yes—
309C2×C4×C73C22×D412yes—
310C2×C4×C73C22×D412yes—
311C2×C4×C73C22×D411yescharacteristic
312C2×C4×C73C2×#4112yes—
313C2×C4×C73H(5,𝔽2)12yes—
314C2×C4×C73C2511yescharacteristic
315C2×Dic73—24no—
316C2×Dic73—22no—
317C2×Dic73—22no—
318C2×Dic73—22no—
319C2×Dic73—22no—
320C2×Dic73—22no—
321C2×Dic73—22no—
322C2×Dic73—22no—
323C2×Dic73—22no—
324C2×Dic73—48no—
325C2×Dic73—48no—
326C2×Dic73—42no—
327C2×Dic73—42no—
328C2×Dic73—42no—
329C2×Dic73—48no—
330C2×Dic73—42no—
331C2×Dic73—42no—
332C2×Dic73—42no—
333C2×Dic73—42no—
334Dic146—24no—
335Dic146—22no—
336Dic146—22no—
337Dic146—22no—
338Dic146—22no—
339Dic146—22no—
340Dic146—22no—
341Dic146—22no—
342Dic146—48no—
343Dic146—48no—
344Dic146—42no—
345Dic146—42no—
346Dic146—42no—
347Dic146C2×#4114yes—
348C8×C73—22no—
349C8×C73—22no—
350C8×C73—22no—
351C8×C73—22no—
352C22×C73—22no—
353C22×C73—28no—
354C22×C73—22no—
355C22×C73—22no—
356C22×C73—22no—
357C22×C73—22no—
358C22×C73—44no—
359C22×C73#54612yes—
360C22×C73C2×#13714yes—
361C22×C73C2×#13712yes—
362C22×C73#57812yes—
363C22×C73C23×D411yescharacteristic
364C4×C73—22no—
365C4×C73—22no—
366C4×C73—22no—
367C4×C73—22no—
368C4×C73#54612yes—
369C4×C73C22×#4111yescharacteristic
370C4×C73C2×H(5,𝔽2)11yescharacteristic
371Dic73—24no—
372Dic73—42no—
373Dic73—42no—
374Dic73—42no—
375Dic73—42no—
376Dic73—42no—
377Dic73—42no—
378Dic73—42no—
379C2×#3312—731nomaximal, Sylow
380C2×C73—24no—
381C2×C73—42no—
382C2×C73#331214yescomplemented
383C2×C73C2×#54611yescharacteristic
384C2×C73C22×#13711yescharacteristic
385C2×C73C2×#57811yescharacteristic
386C2×#552—731no—
387C2×D4×Q8—731no—
388#3312—7316no—
389C2×#491—731no—
390C2×#485—731no—
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×#435D7311yescharacteristic
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×M16C2×D7311yescharacteristic
409C23×C8C2×D7311yescharacteristic
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—731no—
424C2×C22⋊Q8—1461no—
425C2×C22⋊Q8—1461no—
426C2×C4×Q8—731no—
427C2×C4×Q8—731no—
428C2×C4×D4—1461no—
429C2×C4×D4C2×D7311yescharacteristic
430C2×#117—731no—
431C2×#117—1461no—
432C22×C4⋊C4—731no—
433#491—738no—
434#485—738no—
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#435C2×D7318yes—
444C2×#107—731no—
445C2×#106—731no—
446C2×#106—731no—
447C2×C4⋊C8C2×D7311yescharacteristic
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—731no—
458C2×#103—738no—
459C2×#103—731no—
460C2×C22⋊C8C2×D7311yescharacteristic
461C2×C22⋊C8C2×D7311yescharacteristic
462C2×#97C2×D7311yescharacteristic
463C22×Q8—2922no—
464C22×Q8—2922no—
465C22×Q8—734no—
466C22×Q8—734no—
467C22×Q8—731no—
468C22×Q8—731no—
469C22×Q8—731no—
470C22×Q8—731no—
471C22×Q8—1464no—
472C22×Q8—1464no—
473C22×Q8—1461no—
474C22×Q8—1461no—
475C22×Q8—1462no—
476C22×Q8—1462no—
477C22×D4D29211yescharacteristic
478C23×C4—1461no—
479C23×C4—1461no—
480C23×C4—1461no—
481C23×C4C22×D7311yescharacteristic
482C23×C4C22×D7311yescharacteristic
483C2×Q16—2922no—
484C2×Q16—2922no—
485C2×Q16—734no—
486C2×Q16—734no—
487C2×Q16—734no—
488C2×Q16—1464no—
489C2×M16—42no—
490C2×M16C22×D7314yes—
491C22×C8—42no—
492C22×C8C22×D7311yescharacteristic
493C22×C8C22×D7311yescharacteristic
494C22×C8C22×D7311yescharacteristic
495C22×C8C22×D7311yescharacteristic
496C22×C8C22×D7314yes—
497C4⋊Q8—734no—
498C4⋊Q8—1468no—
499C4⋊Q8—1462no—
500#126—1468no—
501#125—734no—
502#125—1468no—
503#125—1462no—
504#123—1468no—
505C22⋊Q8—734no—
506C22⋊Q8—734no—
507C22⋊Q8—734no—
508C22⋊Q8—734no—
509C22⋊Q8—1462no—
510C22⋊Q8—1462no—
511C22⋊Q8—1462no—
512C22⋊Q8—1462no—
513C22⋊Q8—1468no—
514C22⋊Q8—1468no—
515C4×Q8—734no—
516C4×Q8—734no—
517C4×Q8—1462no—
518C4×Q8—1462no—
519C4×D4—1468no—
520C4×D4D29214yes—
521C4×D4C22×D7314yes—
522#117—734no—
523#117—1462no—
524#117—1468no—
525C2×C4⋊C4—731no—
526C2×C4⋊C4—731no—
527C2×C4⋊C4—734no—
528C2×C4⋊C4—731no—
529C2×C4⋊C4—731no—
530C2×C4⋊C4—1461no—
531C2×C4⋊C4—1462no—
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⋊C4—1461no—
541C2×C4⋊C4—1461no—
542C2×C4⋊C4D29211yescharacteristic
543C2×C22⋊C4—1461no—
544C2×C22⋊C4—1461no—
545C2×C22⋊C4—1461no—
546C2×C22⋊C4—1461no—
547C2×C22⋊C4—1461no—
548C2×C22⋊C4D29211yescharacteristic
549C2×C22⋊C4D29211yescharacteristic
550C2×C42—1461no—
551C2×C42—1461no—
552C2×C42—1461no—
553C2×C42C22×D7311yescharacteristic
554#107—734no—
555#106—734no—
556#106—734no—
557C4⋊C8C22×D7314yes—
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#103—734no—
567#103—734no—
568C22⋊C8C22×D7314yes—
569C22⋊C8C22×D7314yes—
570#97C22×D7314yes—
571C24C2×D29211yescharacteristic
572C24C2×D29211yescharacteristic
573C2×Q8—2928no—
574C2×Q8—2928no—
575C2×Q8—2924no—
576C2×Q8—2924no—
577C2×Q8—2924no—
578C2×Q8—2924no—
579C2×Q8—734no—
580C2×Q8—732no—
581C2×Q8—732no—
582C2×Q8—732no—
583C2×Q8—732no—
584C2×Q8—1468no—
585C2×Q8—1468no—
586C2×Q8—1462no—
587C2×Q8—1462no—
588C2×Q8—1462no—
589C2×Q8—1462no—
590C2×Q8—1462no—
591C2×Q8—1462no—
592C2×Q8—1461no—
593C2×Q8—1461no—
594C2×Q8—1461no—
595C2×Q8—1464no—
596C2×Q8—1464no—
597C2×Q8—1461no—
598C2×Q8—1462no—
599C2×D4—24no—
600C2×D4C2×D29214yes—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—2924no—
606C22×C4—2924no—
607C22×C4—2924no—
608C22×C4—1464no—
609C22×C4—1464no—
610C22×C4—1464no—
611C22×C4—1461no—
612C22×C4—1461no—
613C22×C4—1461no—
614C22×C4—1461no—
615C22×C4—1461no—
616C22×C4—1461no—
617C22×C4—1461no—
618C22×C4—1461no—
619C22×C4C2×D29212yes—
620C22×C4C2×D29212yes—
621C22×C4C2×D29211yescharacteristic
622C22×C4C2×D29211yescharacteristic
623C22×C4C2×D29211yescharacteristic
624C22×C4C2×D29211yescharacteristic
625C22×C4C23×D7312yes—
626C22×C4C23×D7312yes—
627C22×C4C23×D7311yescharacteristic
628Q16—2924no—
629Q16—2924no—
630Q16—1468no—
631M16—44no—
632C2×C8—22no—
633C2×C8—22no—
634C2×C8—22no—
635C2×C8—22no—
636C2×C8—44no—
637C2×C8C23×D7312yes—
638C2×C8C23×D7312yes—
639C2×C8C23×D7312yes—
640C2×C8C23×D7312yes—
641C4⋊C4—732no—
642C4⋊C4—732no—
643C4⋊C4—732no—
644C4⋊C4—732no—
645C4⋊C4—1464no—
646C4⋊C4—1464no—
647C4⋊C4—1464no—
648C4⋊C4—1464no—
649C4⋊C4—1464no—
650C4⋊C4—1464no—
651C4⋊C4—1464no—
652C4⋊C4—1464no—
653C4⋊C4—1461no—
654C4⋊C4—1461no—
655C4⋊C4—1464no—
656C4⋊C4—1461no—
657C4⋊C4—1461no—
658C4⋊C4—1464no—
659C4⋊C4—1464no—
660C4⋊C4C2×D29214yes—
661C22⋊C4—1464no—
662C22⋊C4—1464no—
663C22⋊C4—1464no—
664C22⋊C4—1464no—
665C22⋊C4—1464no—
666C22⋊C4C2×D29214yes—
667C22⋊C4C2×D29214yes—
668C42—1464no—
669C42—1464no—
670C42—1464no—
671C42C2×D29212yes—
672C42C23×D7312yes—
673C23—22no—
674C23—22no—
675C23—22no—
676C23—22no—
677C23—22no—
678C23#1455662414yes—
679C23C22×D29212yes—
680C23C22×D29212yes—
681C23C22×D29211yescharacteristic
682Q8—2928no—
683Q8—2928no—
684Q8—2922no—
685Q8—2922no—
686Q8—2922no—
687Q8—734no—
688Q8—1462no—
689Q8—1462no—
690Q8—1462no—
691Q8—1462no—
692Q8—1462no—
693Q8—1462no—
694Q8—1462no—
695Q8—1464no—
696D4—28no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—2928no—
708C2×C4—2922no—
709C2×C4—2922no—
710C2×C4—2922no—
711C2×C4—2922no—
712C2×C4—2922no—
713C2×C4—2922no—
714C2×C4—2922no—
715C2×C4—2928no—
716C2×C4—2928no—
717C2×C4—1462no—
718C2×C4—1462no—
719C2×C4—1462no—
720C2×C4—1462no—
721C2×C4—1462no—
722C2×C4—1462no—
723C2×C4—1462no—
724C2×C4—1462no—
725C2×C4—1464no—
726C2×C4C22×D29212yes—
727C2×C4C22×D29212yes—
728C2×C4C22×D29212yes—
729C2×C4C22×D29212yes—
730C2×C4C22×D29211yescharacteristic
731C2×C4#41×D7312yes—
732C2×C4#1455663612yes—
733C2×C4C24×D7311yescharacteristic
734C8—22no—
735C8—22no—
736C8—22no—
737C8—22no—
738C22—28no—
739C22—22no—
740C22—22no—
741C22—22no—
742C22—22no—
743C22—22no—
744C22—44no—
745C22#1798923212yes—
746C22C2×#1455662414yes—
747C22C2×#1455662412yes—
748C22#1798940412yes—
749C22C23×D29211yescharacteristic
750C4—22no—
751C4—22no—
752C4—22no—
753C4—22no—
754C4—2922no—
755C4—2922no—
756C4—2922no—
757C4—2922no—
758C4—2922no—
759C4—2922no—
760C4—2922no—
761C4—1464no—
762C4#1798923212yes—
763C4C2×#41×D7311yescharacteristic
764C4C2×#1455663611yescharacteristic
765C2—24no—
766C2—42no—
767C2#2262198414yesdirect product factor
768C2C2×#1798923211yescharacteristic
769C2C22×#1455662411yescharacteristic
770C2C2×#1798940411yescharacteristic
subgroupG/H
centerC23C22×D292
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×#435×C73C2
socleC23×C73C22×D4
prime radicalC22×D4×C73D4
hypercenterC2×#435D73
hypocenterC73C2×#3312
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
3. #22621984C2direct (N × H)
4. C2×#17988956C2semidirect
5. C2×#17988929C2semidirect
6. C2×#17988918C2semidirect
7. C2×#17988895C2semidirect
8. C2×#17988845C2semidirect
9. C2×#17988828C2semidirect
10. C2×#17988798C2semidirect
11. C2×#17988745C2semidirect
12. C2×#17988745C2semidirect
13. C2×#17988695C2semidirect
14. C2×#17988597C2semidirect
15. C22×#14556516C2semidirect
44. #17988956C22semidirect
45. #17988929C22semidirect
46. #17988918C22semidirect
47. #17988895C22semidirect
48. #17988845C22semidirect
49. #17988828C22semidirect
50. #17988798C22semidirect
51. #17988745C22semidirect
52. #17988745C22semidirect
53. #17988695C22semidirect
57. #17988597C22semidirect
68. C2×#14556516C22semidirect
382. C2×C73#3312semidirect
402. C73C2×#3312semidirect
767. C2#22621984direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179892772
C2×D4×Dic1462
#226219842
C2×#179889562
C2×#179889292
C2×#179889182
C2×#179888952
C2×#179888452
C2×#179888282
C2×#179887982
C2×#179887452
C2×#179886952
C2×#179885972
C22×#145565162
C2×#435×C732
C2×#331273