Finite Group Databasebeta

← C2×#21457872 #30556621

Subgroups — C2×#21457872 #30556621

Order 15616.

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×#16840452C211yesmaximal, characteristic
2C2×D4×Dic122C211yesmaximal, characteristic
3#21457872C2116yesmaximal, direct product factor
4C2×#16840131C211yesmaximal, characteristic, complemented
5C2×#16840104C211yesmaximal, characteristic, complemented
6C2×#16840093C211yesmaximal, characteristic, complemented
7C2×#16840070C211yesmaximal, characteristic, complemented
8C2×#16840020C211yesmaximal, characteristic, complemented
9C2×#16840003C211yesmaximal, characteristic, complemented
10C2×#16839973C211yesmaximal, characteristic, complemented
11C2×#16839920C211yesmaximal, characteristic, complemented
12C2×#16839920C211yesmaximal, characteristic, complemented
13C2×#16839870C211yesmaximal, characteristic, complemented
14C2×#16839772C211yesmaximal, characteristic, complemented
15C22×#14519702C211yesmaximal, characteristic, complemented
16C2×C61×#435C211yesmaximal, characteristic
17C23×Dic122C2211yescharacteristic
18C23×Dic122C2211yescharacteristic
19C22×Dic244C2211yescharacteristic
20C22×Dic244C2211yescharacteristic
21C22×Dic244C2211yescharacteristic
22#16840452—24no—
23#16840452C2218yes—
24D4×Dic122—24no—
25D4×Dic122C2218yes—
26C2×#14519777C2211yescharacteristic
27C2×#14519776—21no—
28C2×#14519770—21no—
29C2×#14519769C2211yescharacteristic
30C2×#14519767—21no—
31C2×#14519758—21no—
32C2×#14519756C2211yescharacteristic
33C2×#14519756C2211yescharacteristic
34C2×#14519756C2211yescharacteristic
35C2×#14519756C2211yescharacteristic
36C2×#14519754—21no—
37C2×#14519754—21no—
38C2×C4×Dic122C2211yescharacteristic
39C2×C4×Dic122C2211yescharacteristic
40C2×D4×Dic61—21no—
41C2×#14519736C2211yescharacteristic
42C2×#14519733—21no—
43C22×C4⋊Dic61C2211yescharacteristic
44#16840131C2218yescomplemented
45#16840104C2218yescomplemented
46#16840093C2218yescomplemented
47#16840070C2218yescomplemented
48#16840020C2218yescomplemented
49#16840003C2218yescomplemented
50#16839973C2218yescomplemented
51#16839920C2218yescomplemented
52#16839920C2218yescomplemented
53#16839870C2218yescomplemented
54C2×#14519711C2211yescharacteristic
55C2×#14519709C2211yescharacteristic
56C2×#14519709C2211yescharacteristic
57#16839772C2218yescomplemented
58C2×#14519702C2211yescharacteristic
59C2×#14519702C2211yescharacteristic
60C2×#14519702C2211yescharacteristic
61C2×#14519702C2211yescharacteristic
62C2×#14519702C2211yescharacteristic
63C2×#14519702C2211yescharacteristic
64C2×#14519702C2211yescharacteristic
65C2×#14519702C2211yescharacteristic
66C2×#14519702C2211yescharacteristic
67C2×#14519702C2211yescharacteristic
68C2×#14519702C2218yescomplemented
69C22×M16×C61C2211yescharacteristic
70C23×C8×C61C2211yescharacteristic
71C2×C4×D4×C61C2211yescharacteristic
72C61×#435C2218yes—
73C2×C4⋊C8×C61C2211yescharacteristic
74C2×C22⋊C8×C61C2211yescharacteristic
75C2×C22⋊C8×C61C2211yescharacteristic
76C2×#97×C61C2211yescharacteristic
77C22×Dic122—24no—
78C22×Dic122—24no—
79C22×Dic122—21no—
80C22×Dic122—21no—
81C22×Dic122—22no—
82C22×Dic122—22no—
83C22×Dic122—42no—
84C22×Dic122—42no—
85C22×Dic122C2311yescharacteristic
86C22×Dic122C2311yescharacteristic
87C22×Dic122C2311yescharacteristic
88C22×Dic122C2314yes—
89C22×Dic122C2314yes—
90C22×Dic122C2311yescharacteristic
91C23×Dic61—21no—
92C23×Dic61—21no—
93C23×Dic61—21no—
94C2×Dic244—24no—
95C2×Dic244—42no—
96C2×Dic244—42no—
97C2×Dic244C2314yes—
98C2×Dic244C2314yes—
99C2×Dic244C2314yes—
100#14519777—22no—
101#14519777C2314yes—
102#14519776—28no—
103#14519770—28no—
104#14519769—22no—
105#14519769C2314yes—
106#14519767—28no—
107#14519758—28no—
108#14519756—22no—
109#14519756—22no—
110#14519756—22no—
111#14519756—22no—
112#14519756C2314yes—
113#14519756C2314yes—
114#14519756C2314yes—
115#14519756C2314yes—
116#14519754—28no—
117#14519754—28no—
118C4×Dic122—22no—
119C4×Dic122—22no—
120C4×Dic122C2314yes—
121C4×Dic122C2314yes—
122D4×Dic61—28no—
123#14519736—22no—
124#14519736C2314yes—
125#14519733—28no—
126C2×C4⋊Dic61—22no—
127C2×C4⋊Dic61—21no—
128C2×C4⋊Dic61—21no—
129C2×C4⋊Dic61—21no—
130C2×C4⋊Dic61C2314yes—
131C2×C4⋊Dic61C2311yescharacteristic
132C2×C4⋊Dic61C2311yescharacteristic
133C2×C4⋊Dic61C2311yescharacteristic
134C2×C4⋊Dic61C2311yescharacteristic
135C2×#11758196—21no—
136C2×#11758196—21no—
137C2×#11758196—21no—
138C2×#11758196—21no—
139C2×#11758196—21no—
140C2×#11758196—21no—
141C2×#11758196—21no—
142C2×#11758196—21no—
143C2×C22⋊Dic61—21no—
144C2×C22⋊Dic61—21no—
145C2×C22⋊Dic61—21no—
146C2×C22⋊Dic61—21no—
147C2×C22⋊Dic61—21no—
148C2×C4×Dic61—21no—
149C2×C4×Dic61—21no—
150C2×C4×Dic61—21no—
151#14519711C2314yes—
152#14519709C2314yes—
153#14519709C2314yes—
154#14519702C2314yes—
155#14519702C2314yes—
156#14519702C2314yes—
157#14519702C2314yes—
158#14519702C2314yes—
159#14519702C2314yes—
160#14519702C2314yes—
161#14519702C2314yes—
162#14519702C2314yes—
163#14519702C2314yes—
164C22×D4×C61D411yescharacteristic
165C23×C4×C61C2311yescharacteristic
166C23×C4×C61C2311yescharacteristic
167C2×M16×C61—42no—
168C2×M16×C61C2314yes—
169C22×C8×C61—42no—
170C22×C8×C61C2311yescharacteristic
171C22×C8×C61C2311yescharacteristic
172C22×C8×C61C2311yescharacteristic
173C22×C8×C61C2311yescharacteristic
174C22×C8×C61C2314yes—
175C4×D4×C61D414yes—
176C4×D4×C61C2314yes—
177C2×C4⋊C4×C61D411yescharacteristic
178C2×C22⋊C4×C61D411yescharacteristic
179C2×C22⋊C4×C61D411yescharacteristic
180C2×C42×C61C2311yescharacteristic
181C4⋊C8×C61C2314yes—
182C22⋊C8×C61C2314yes—
183C22⋊C8×C61C2314yes—
184#97×C61C2314yes—
185C24×C61C2×D411yescharacteristic
186C24×C61C2×D411yescharacteristic
187C2×D4×C61—24no—
188C2×D4×C61C2×D414yes—
189C22×C4×C61—22no—
190C22×C4×C61—22no—
191C22×C4×C61—22no—
192C22×C4×C61—22no—
193C22×C4×C61C2×D411yescharacteristic
194C22×C4×C61C2×D411yescharacteristic
195C22×C4×C61C2×D412yes—
196C22×C4×C61C2×D412yes—
197C22×C4×C61C2×D411yescharacteristic
198C22×C4×C61C2×D411yescharacteristic
199C22×C4×C61C2412yes—
200C22×C4×C61C2412yes—
201C22×C4×C61C2411yescharacteristic
202C22×Dic61—21no—
203C22×Dic61—21no—
204C22×Dic61—21no—
205C22×Dic61—24no—
206C22×Dic61—24no—
207C22×Dic61—21no—
208C22×Dic61—21no—
209C22×Dic61—24no—
210C22×Dic61—21no—
211C22×Dic61—21no—
212C22×Dic61—21no—
213C22×Dic61—44no—
214C22×Dic61—44no—
215C22×Dic61—44no—
216C2×Dic122—21no—
217C2×Dic122—22no—
218C2×Dic122—22no—
219C2×Dic122—22no—
220C2×Dic122—22no—
221C2×Dic122—22no—
222C2×Dic122—22no—
223C2×Dic122—22no—
224C2×Dic122—28no—
225C2×Dic122—28no—
226C2×Dic122—24no—
227C2×Dic122—24no—
228C2×Dic122—21no—
229C2×Dic122—21no—
230C2×Dic122—21no—
231C2×Dic122—44no—
232C2×Dic122—44no—
233C2×Dic122—48no—
234C2×Dic122—48no—
235C2×Dic122—44no—
236C2×Dic122—44no—
237C2×Dic122#4114yes—
238C2×Dic122C2412yes—
239C2×Dic122C2412yes—
240C2×Dic122C2412yes—
241C2×Dic122C2412yes—
242M16×C61—44no—
243C2×C8×C61—22no—
244C2×C8×C61—22no—
245C2×C8×C61—22no—
246C2×C8×C61—22no—
247C2×C8×C61—44no—
248C2×C8×C61C2412yes—
249C2×C8×C61C2412yes—
250C2×C8×C61C2412yes—
251C2×C8×C61C2412yes—
252C4⋊C4×C61C2×D414yes—
253C22⋊C4×C61C2×D414yes—
254C22⋊C4×C61C2×D414yes—
255C42×C61C2×D412yes—
256C42×C61C2412yes—
257C22⋊Dic61—24no—
258C22⋊Dic61—24no—
259C22⋊Dic61—24no—
260C22⋊Dic61—24no—
261C22⋊Dic61—24no—
262C4⋊Dic61—21no—
263C4⋊Dic61—21no—
264C4⋊Dic61—24no—
265C4⋊Dic61—24no—
266C4⋊Dic61—24no—
267C4⋊Dic61—21no—
268C4⋊Dic61—21no—
269C4⋊Dic61C2412yes—
270C4⋊Dic61C2412yes—
271C4⋊Dic61C2412yes—
272C4⋊Dic61C2412yes—
273#11758196—24no—
274#11758196—24no—
275#11758196—24no—
276#11758196—24no—
277#11758196—24no—
278#11758196—24no—
279#11758196—24no—
280#11758196—24no—
281C4×Dic61—24no—
282C4×Dic61—24no—
283C4×Dic61—24no—
284Dic244—28no—
285Dic244—44no—
286Dic244—44no—
287C23×C61—22no—
288C23×C61—22no—
289C23×C61—22no—
290C23×C61—22no—
291C23×C61—22no—
292C23×C61#13714yes—
293C23×C61C22×D412yes—
294C23×C61C22×D412yes—
295C23×C61C22×D411yescharacteristic
296D4×C61—28no—
297C2×C4×C61—22no—
298C2×C4×C61—22no—
299C2×C4×C61—22no—
300C2×C4×C61—22no—
301C2×C4×C61—24no—
302C2×C4×C61—24no—
303C2×C4×C61—22no—
304C2×C4×C61—22no—
305C2×C4×C61—22no—
306C2×C4×C61—22no—
307C2×C4×C61C22×D412yes—
308C2×C4×C61C22×D412yes—
309C2×C4×C61C22×D412yes—
310C2×C4×C61C22×D412yes—
311C2×C4×C61C22×D411yescharacteristic
312C2×C4×C61C2×#4112yes—
313C2×C4×C61H(5,𝔽2)12yes—
314C2×C4×C61C2511yescharacteristic
315C2×Dic61—24no—
316C2×Dic61—22no—
317C2×Dic61—22no—
318C2×Dic61—22no—
319C2×Dic61—22no—
320C2×Dic61—22no—
321C2×Dic61—22no—
322C2×Dic61—22no—
323C2×Dic61—22no—
324C2×Dic61—48no—
325C2×Dic61—48no—
326C2×Dic61—42no—
327C2×Dic61—42no—
328C2×Dic61—42no—
329C2×Dic61—48no—
330C2×Dic61—42no—
331C2×Dic61—42no—
332C2×Dic61—42no—
333C2×Dic61—42no—
334Dic122—24no—
335Dic122—22no—
336Dic122—22no—
337Dic122—22no—
338Dic122—22no—
339Dic122—22no—
340Dic122—22no—
341Dic122—22no—
342Dic122—48no—
343Dic122—48no—
344Dic122—42no—
345Dic122—42no—
346Dic122—42no—
347Dic122C2×#4114yes—
348C8×C61—22no—
349C8×C61—22no—
350C8×C61—22no—
351C8×C61—22no—
352C2×#3312—611nomaximal, Sylow
353C22×C61—22no—
354C22×C61—28no—
355C22×C61—22no—
356C22×C61—22no—
357C22×C61—22no—
358C22×C61—22no—
359C22×C61—44no—
360C22×C61#54612yes—
361C22×C61C2×#13714yes—
362C22×C61C2×#13712yes—
363C22×C61#57812yes—
364C22×C61C23×D411yescharacteristic
365C4×C61—22no—
366C4×C61—22no—
367C4×C61—22no—
368C4×C61—22no—
369C4×C61#54612yes—
370C4×C61C22×#4111yescharacteristic
371C4×C61C2×H(5,𝔽2)11yescharacteristic
372Dic61—24no—
373Dic61—42no—
374Dic61—42no—
375Dic61—42no—
376Dic61—42no—
377Dic61—42no—
378Dic61—42no—
379Dic61—42no—
380C2×#552—611no—
381C2×D4×Q8—611no—
382#3312—6116no—
383C2×#491—611no—
384C2×#485—611no—
385C2×#483—611no—
386C2×#479—611no—
387C2×#470—611no—
388C2×#467—611no—
389C2×#462—611no—
390C2×#451—611no—
391C2×#451—611no—
392C2×#441—611no—
393C2×#435D6111yescharacteristic
394C2×#419—611no—
395C22×#103—611no—
396C2×C61—24no—
397C2×C61—42no—
398C2×C61#331214yescomplemented
399C2×C61C2×#54611yescharacteristic
400C2×C61C22×#13711yescharacteristic
401C2×C61C2×#57811yescharacteristic
402C23×Q8—611no—
403C23×Q8—611no—
404C22×Q16—611no—
405C22×Q16—611no—
406C22×Q16—611no—
407C22×M16C2×D6111yescharacteristic
408C23×C8C2×D6111yescharacteristic
409#552—618no—
410#552—1224no—
411D4×Q8—618no—
412D4×Q8—1224no—
413C2×C4⋊Q8—611no—
414C2×C4⋊Q8—1221no—
415C2×#126—1221no—
416C2×#125—611no—
417C2×#125—1221no—
418C2×#123—1221no—
419C2×C22⋊Q8—611no—
420C2×C22⋊Q8—611no—
421C2×C22⋊Q8—611no—
422C2×C22⋊Q8—611no—
423C2×C22⋊Q8—1221no—
424C2×C22⋊Q8—1221no—
425C2×C4×Q8—611no—
426C2×C4×Q8—611no—
427C2×C4×D4—1221no—
428C2×C4×D4C2×D6111yescharacteristic
429C2×#117—611no—
430C2×#117—1221no—
431C22×C4⋊C4—611no—
432#491—618no—
433#485—618no—
434#483—618no—
435#479—618no—
436#470—618no—
437#467—618no—
438#462—618no—
439#451—618no—
440#451—618no—
441#441—618no—
442#435C2×D6118yes—
443C2×#107—611no—
444C2×#106—611no—
445C2×#106—611no—
446C2×C4⋊C8C2×D6111yescharacteristic
447#419—618no—
448C2×#103—611no—
449C2×#103—611no—
450C2×#103—611no—
451C2×#103—611no—
452C2×#103—611no—
453C2×#103—611no—
454C2×#103—611no—
455C2×#103—611no—
456C2×#103—611no—
457C2×#103—611no—
458C2×#103—618no—
459C2×C22⋊C8C2×D6111yescharacteristic
460C2×C22⋊C8C2×D6111yescharacteristic
461C2×#97C2×D6111yescharacteristic
462C61C2×#331211yescharacteristic, complemented, Sylow
463C22×Q8—611no—
464C22×Q8—611no—
465C22×Q8—611no—
466C22×Q8—611no—
467C22×Q8—614no—
468C22×Q8—614no—
469C22×Q8—1224no—
470C22×Q8—1224no—
471C22×Q8—1221no—
472C22×Q8—1221no—
473C22×Q8—1222no—
474C22×Q8—1222no—
475C22×Q8—2442no—
476C22×Q8—2442no—
477C22×D4D24411yescharacteristic
478C23×C4—1221no—
479C23×C4—1221no—
480C23×C4—1221no—
481C23×C4C22×D6111yescharacteristic
482C23×C4C22×D6111yescharacteristic
483C2×Q16—614no—
484C2×Q16—614no—
485C2×Q16—614no—
486C2×Q16—1224no—
487C2×Q16—2442no—
488C2×Q16—2442no—
489C2×M16—42no—
490C2×M16C22×D6114yes—
491C22×C8—42no—
492C22×C8C22×D6111yescharacteristic
493C22×C8C22×D6111yescharacteristic
494C22×C8C22×D6111yescharacteristic
495C22×C8C22×D6111yescharacteristic
496C22×C8C22×D6114yes—
497C4⋊Q8—614no—
498C4⋊Q8—1228no—
499C4⋊Q8—1222no—
500#126—1228no—
501#125—614no—
502#125—1228no—
503#125—1222no—
504#123—1228no—
505C22⋊Q8—614no—
506C22⋊Q8—614no—
507C22⋊Q8—614no—
508C22⋊Q8—614no—
509C22⋊Q8—1222no—
510C22⋊Q8—1222no—
511C22⋊Q8—1222no—
512C22⋊Q8—1222no—
513C22⋊Q8—1228no—
514C22⋊Q8—1228no—
515C4×Q8—614no—
516C4×Q8—614no—
517C4×Q8—1222no—
518C4×Q8—1222no—
519C4×D4—1228no—
520C4×D4D24414yes—
521C4×D4C22×D6114yes—
522#117—614no—
523#117—1222no—
524#117—1228no—
525C2×C4⋊C4—611no—
526C2×C4⋊C4—611no—
527C2×C4⋊C4—614no—
528C2×C4⋊C4—611no—
529C2×C4⋊C4—611no—
530C2×C4⋊C4—1221no—
531C2×C4⋊C4—1222no—
532C2×C4⋊C4—1221no—
533C2×C4⋊C4—1221no—
534C2×C4⋊C4—1221no—
535C2×C4⋊C4—1221no—
536C2×C4⋊C4—1221no—
537C2×C4⋊C4—1221no—
538C2×C4⋊C4—1221no—
539C2×C4⋊C4—1221no—
540C2×C4⋊C4—1221no—
541C2×C4⋊C4—1221no—
542C2×C4⋊C4D24411yescharacteristic
543C2×C22⋊C4—1221no—
544C2×C22⋊C4—1221no—
545C2×C22⋊C4—1221no—
546C2×C22⋊C4—1221no—
547C2×C22⋊C4—1221no—
548C2×C22⋊C4D24411yescharacteristic
549C2×C22⋊C4D24411yescharacteristic
550C2×C42—1221no—
551C2×C42—1221no—
552C2×C42—1221no—
553C2×C42C22×D6111yescharacteristic
554#107—614no—
555#106—614no—
556#106—614no—
557C4⋊C8C22×D6114yes—
558#103—614no—
559#103—614no—
560#103—614no—
561#103—614no—
562#103—614no—
563#103—614no—
564#103—614no—
565#103—614no—
566#103—614no—
567#103—614no—
568C22⋊C8C22×D6114yes—
569C22⋊C8C22×D6114yes—
570#97C22×D6114yes—
571C24C2×D24411yescharacteristic
572C24C2×D24411yescharacteristic
573C2×Q8—614no—
574C2×Q8—612no—
575C2×Q8—612no—
576C2×Q8—612no—
577C2×Q8—612no—
578C2×Q8—1228no—
579C2×Q8—1228no—
580C2×Q8—1221no—
581C2×Q8—1221no—
582C2×Q8—1224no—
583C2×Q8—1224no—
584C2×Q8—1221no—
585C2×Q8—1221no—
586C2×Q8—1222no—
587C2×Q8—1222no—
588C2×Q8—1222no—
589C2×Q8—1222no—
590C2×Q8—1222no—
591C2×Q8—1222no—
592C2×Q8—1222no—
593C2×Q8—2444no—
594C2×Q8—2444no—
595C2×Q8—2444no—
596C2×Q8—2444no—
597C2×Q8—2448no—
598C2×Q8—2448no—
599C2×D4—24no—
600C2×D4C2×D24414yes—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—1221no—
606C22×C4—1224no—
607C22×C4—1224no—
608C22×C4—1224no—
609C22×C4—1221no—
610C22×C4—1221no—
611C22×C4—1221no—
612C22×C4—1221no—
613C22×C4—1221no—
614C22×C4—1221no—
615C22×C4—1221no—
616C22×C4—2444no—
617C22×C4—2444no—
618C22×C4—2444no—
619C22×C4C2×D24412yes—
620C22×C4C2×D24412yes—
621C22×C4C2×D24411yescharacteristic
622C22×C4C2×D24411yescharacteristic
623C22×C4C2×D24411yescharacteristic
624C22×C4C2×D24411yescharacteristic
625C22×C4C23×D6112yes—
626C22×C4C23×D6112yes—
627C22×C4C23×D6111yescharacteristic
628Q16—1228no—
629Q16—2444no—
630Q16—2444no—
631M16—44no—
632C2×C8—22no—
633C2×C8—22no—
634C2×C8—22no—
635C2×C8—22no—
636C2×C8—44no—
637C2×C8C23×D6112yes—
638C2×C8C23×D6112yes—
639C2×C8C23×D6112yes—
640C2×C8C23×D6112yes—
641C4⋊C4—612no—
642C4⋊C4—612no—
643C4⋊C4—612no—
644C4⋊C4—612no—
645C4⋊C4—1221no—
646C4⋊C4—1221no—
647C4⋊C4—1224no—
648C4⋊C4—1221no—
649C4⋊C4—1221no—
650C4⋊C4—1224no—
651C4⋊C4—1224no—
652C4⋊C4—1224no—
653C4⋊C4—1224no—
654C4⋊C4—1224no—
655C4⋊C4—1224no—
656C4⋊C4—1224no—
657C4⋊C4—1224no—
658C4⋊C4—1224no—
659C4⋊C4—1224no—
660C4⋊C4C2×D24414yes—
661C22⋊C4—1224no—
662C22⋊C4—1224no—
663C22⋊C4—1224no—
664C22⋊C4—1224no—
665C22⋊C4—1224no—
666C22⋊C4C2×D24414yes—
667C22⋊C4C2×D24414yes—
668C42—1224no—
669C42—1224no—
670C42—1224no—
671C42C2×D24412yes—
672C42C23×D6112yes—
673C23—22no—
674C23—22no—
675C23—22no—
676C23—22no—
677C23—22no—
678C23#1451981014yes—
679C23C22×D24412yes—
680C23C22×D24412yes—
681C23C22×D24411yescharacteristic
682Q8—614no—
683Q8—1222no—
684Q8—1224no—
685Q8—1222no—
686Q8—1222no—
687Q8—1222no—
688Q8—1222no—
689Q8—1222no—
690Q8—1222no—
691Q8—2448no—
692Q8—2448no—
693Q8—2442no—
694Q8—2442no—
695Q8—2442no—
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—1222no—
708C2×C4—1224no—
709C2×C4—1222no—
710C2×C4—1222no—
711C2×C4—1222no—
712C2×C4—1222no—
713C2×C4—1222no—
714C2×C4—1222no—
715C2×C4—1222no—
716C2×C4—2448no—
717C2×C4—2448no—
718C2×C4—2448no—
719C2×C4—2442no—
720C2×C4—2442no—
721C2×C4—2442no—
722C2×C4—2442no—
723C2×C4—2442no—
724C2×C4—2442no—
725C2×C4—2442no—
726C2×C4C22×D24412yes—
727C2×C4C22×D24412yes—
728C2×C4C22×D24412yes—
729C2×C4C22×D24412yes—
730C2×C4C22×D24411yescharacteristic
731C2×C4#41×D6112yes—
732C2×C4#1451982212yes—
733C2×C4C24×D6111yescharacteristic
734C8—22no—
735C8—22no—
736C8—22no—
737C8—22no—
738C22—22no—
739C22—22no—
740C22—28no—
741C22—22no—
742C22—22no—
743C22—22no—
744C22—44no—
745C22#1684040712yes—
746C22C2×#1451981014yes—
747C22C2×#1451981012yes—
748C22#1684057912yes—
749C22C23×D24411yescharacteristic
750C4—22no—
751C4—22no—
752C4—22no—
753C4—22no—
754C4—1224no—
755C4—2442no—
756C4—2442no—
757C4—2442no—
758C4—2442no—
759C4—2442no—
760C4—2442no—
761C4—2442no—
762C4#1684040712yes—
763C4C2×#41×D6111yescharacteristic
764C4C2×#1451982211yescharacteristic
765C2—24no—
766C2—42no—
767C2#2145787214yesdirect product factor
768C2C2×#1684040711yescharacteristic
769C2C22×#1451981011yescharacteristic
770C2C2×#1684057911yescharacteristic
subgroupG/H
centerC23C22×D244
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#435C2
socleC23×C61C22×D4
prime radicalC22×D4×C61D4
hypercenterC2×#435D61
hypocenterC61C2×#3312
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
3. #21457872C2direct (N × H)
4. C2×#16840131C2semidirect
5. C2×#16840104C2semidirect
6. C2×#16840093C2semidirect
7. C2×#16840070C2semidirect
8. C2×#16840020C2semidirect
9. C2×#16840003C2semidirect
10. C2×#16839973C2semidirect
11. C2×#16839920C2semidirect
12. C2×#16839920C2semidirect
13. C2×#16839870C2semidirect
14. C2×#16839772C2semidirect
15. C22×#14519702C2semidirect
44. #16840131C22semidirect
45. #16840104C22semidirect
46. #16840093C22semidirect
47. #16840070C22semidirect
48. #16840020C22semidirect
49. #16840003C22semidirect
50. #16839973C22semidirect
51. #16839920C22semidirect
52. #16839920C22semidirect
53. #16839870C22semidirect
57. #16839772C22semidirect
68. C2×#14519702C22semidirect
398. C2×C61#3312semidirect
462. C61C2×#3312semidirect
767. C2#21457872direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404522
C2×D4×Dic1222
#214578722
C2×#168401312
C2×#168401042
C2×#168400932
C2×#168400702
C2×#168400202
C2×#168400032
C2×#168399732
C2×#168399202
C2×#168398702
C2×#168397722
C22×#145197022
C2×C61×#4352
C2×#331261