Finite Group Databasebeta

← C2×#21458100 #30556896

Subgroups — C2×#21458100 #30556896

Order 15616.

2082 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×#16840480C211yesmaximal, characteristic
2C2×#16840425C211yesmaximal, characteristic
3#21458100C2116yesmaximal, direct product factor
4C2×#16840111C211yesmaximal, characteristic, complemented
5C2×#16840105C211yesmaximal, characteristic, complemented
6C2×#16840046C211yesmaximal, characteristic, complemented
7C2×#16840021C211yesmaximal, characteristic, complemented
8C2×#16840018C211yesmaximal, characteristic, complemented
9C2×#16839971C211yesmaximal, characteristic, complemented
10C2×#16839920C211yesmaximal, characteristic, complemented
11C2×#16839919C211yesmaximal, characteristic, complemented
12C2×#16839856C211yesmaximal, characteristic, complemented
13C2×#16839837C211yesmaximal, characteristic
14C2×#16839770C211yesmaximal, characteristic, complemented
15C2×#16839769C211yesmaximal, characteristic, complemented
16C2×C61×#485C211yesmaximal, characteristic, complemented
17C23×Dic122C2211yescharacteristic
18C22×Q8×D61C2211yescharacteristic
19C22×Dic244C2211yescharacteristic
20C22×Dic244C2211yescharacteristic
21C22×#11758202C2211yescharacteristic
22C22×#11758194C2211yescharacteristic
23C22×#11758189C2211yescharacteristic
24#16840480—24no—
25#16840480C2218yes—
26#16840425—24no—
27#16840425C2218yes—
28C2×#14519776—21no—
29C2×#14519776C2211yescharacteristic
30C2×#14519775C2211yescharacteristic
31C2×#14519771—21no—
32C2×#14519770—21no—
33C2×#14519763—21no—
34C2×#14519757C2211yescharacteristic
35C2×#14519757C2211yescharacteristic
36C2×#14519756C2211yescharacteristic
37C2×#14519755—21no—
38C2×#14519754—21no—
39C2×C4×Dic122—21no—
40C2×#14519742C2211yescharacteristic
41C2×#14519742C2211yescharacteristic
42C2×C4×C22⋊D61C2211yescharacteristic
43C2×#14519737—21no—
44C2×#14519735C2211yescharacteristic
45#16840111C2218yescomplemented
46#16840105C2218yescomplemented
47#16840046C2218yescomplemented
48#16840021C2218yescomplemented
49#16840018C2218yescomplemented
50#16839971C2218yescomplemented
51#16839920C2218yescomplemented
52#16839919C2218yescomplemented
53#16839856C2218yescomplemented
54#16839837C2218yes—
55C2×#14519708C2211yescharacteristic
56C2×#14519706C2211yescharacteristic
57#16839770C2218yescomplemented
58#16839769C2218yescomplemented
59C2×#14519702C2211yescharacteristic
60C2×#14519702C2211yescharacteristic
61C2×#14519701C2211yescharacteristic
62C2×#14519700C2211yescharacteristic
63C2×#14519700C2211yescharacteristic
64C2×#14519700C2211yescharacteristic
65C2×#14519700C2211yescharacteristic
66C2×#14519700C2211yescharacteristic
67C2×#14519689C2211yescharacteristic
68C2×C8×Dic61C2211yescharacteristic
69C2×C22⋊Q8×C61C2211yescharacteristic
70C2×#117×C61C2211yescharacteristic
71C61×#485C2218yescomplemented
72C2×#107×C61C2211yescharacteristic
73C2×#106×C61C2211yescharacteristic
74C2×#103×C61C2211yescharacteristic
75C2×#103×C61C2211yescharacteristic
76C2×C22⋊C8×C61C2211yescharacteristic
77C22×Dic122—24no—
78C22×Dic122—21no—
79C22×Dic122—22no—
80C22×Dic122—21no—
81C22×Dic122—21no—
82C22×Dic122—42no—
83C22×Dic122C2311yescharacteristic
84C22×Dic122C2311yescharacteristic
85C22×Dic122C2314yes—
86C22×Dic122C2311yescharacteristic
87C2×Q8×D61—22no—
88C2×Q8×D61—24no—
89C2×Q8×D61—42no—
90C2×Q8×D61C2314yes—
91C22×C22⋊D61D411yescharacteristic
92C23×Dic61—21no—
93C22×C4×D61—21no—
94C22×C4×D61C2311yescharacteristic
95C2×Dic244—24no—
96C2×Dic244—42no—
97C2×Dic244C2314yes—
98C2×Dic244C2314yes—
99C2×#11758202—42no—
100C2×#11758202C2314yes—
101C2×#11758194—42no—
102C2×#11758194C2314yes—
103C2×#11758189—42no—
104C2×#11758189C2314yes—
105C22×#92418C2311yescharacteristic
106C22×#92418C2311yescharacteristic
107#14519776—28no—
108#14519776—22no—
109#14519776C2314yes—
110#14519775—22no—
111#14519775C2314yes—
112#14519771—28no—
113#14519770—28no—
114#14519763—28no—
115#14519757—22no—
116#14519757—22no—
117#14519757C2314yes—
118#14519757C2314yes—
119#14519756—22no—
120#14519756C2314yes—
121#14519755—28no—
122#14519754—28no—
123C4×Dic122—28no—
124#14519742—22no—
125#14519742—22no—
126#14519742C2314yes—
127#14519742C2314yes—
128C4×C22⋊D61D414yes—
129C4×C22⋊D61C2314yes—
130#14519737—28no—
131#14519735—22no—
132#14519735C2314yes—
133C2×C4⋊Dic61—21no—
134C2×C4⋊Dic61—21no—
135C2×C4⋊Dic61C2311yescharacteristic
136C2×#11758196—21no—
137C2×#11758196—21no—
138C2×#11758196—21no—
139C2×#11758196—21no—
140C2×#11758196—21no—
141C2×#11758196—21no—
142C2×#11758196D411yescharacteristic
143C2×C22⋊Dic61—21no—
144C2×C22⋊Dic61D411yescharacteristic
145C2×#11758198—21no—
146C2×#11758198—21no—
147C2×#11758198—21no—
148C2×#11758198D411yescharacteristic
149C2×C4×Dic61—21no—
150C2×C4×Dic61—21no—
151C2×C4×Dic61—21no—
152C2×C4×Dic61C2311yescharacteristic
153#14519708C2314yes—
154#14519706C2314yes—
155#14519702C2314yes—
156#14519702C2314yes—
157#14519701C2314yes—
158#14519700C2314yes—
159#14519700C2314yes—
160#14519700C2314yes—
161#14519700C2314yes—
162#14519700C2314yes—
163#14519689C2314yes—
164C8×Dic61C2314yes—
165C22×Q8×C61C2311yescharacteristic
166C23×C4×C61C2311yescharacteristic
167C22×C8×C61C2311yescharacteristic
168C22×C8×C61C2311yescharacteristic
169C22⋊Q8×C61—22no—
170C22⋊Q8×C61C2314yes—
171#117×C61—22no—
172#117×C61C2314yes—
173C2×C4⋊C4×C61—21no—
174C2×C4⋊C4×C61C2311yescharacteristic
175C2×C4⋊C4×C61C2311yescharacteristic
176C2×C4⋊C4×C61C2311yescharacteristic
177C2×C22⋊C4×C61—21no—
178C2×C22⋊C4×C61—21no—
179C2×C42×C61—21no—
180#107×C61C2314yes—
181#106×C61C2314yes—
182#103×C61C2314yes—
183#103×C61C2314yes—
184C22⋊C8×C61C2314yes—
185C24×C61C2×D411yescharacteristic
186C23×D61C2×D411yescharacteristic
187C2×Q8×C61—21no—
188C2×Q8×C61—22no—
189C2×Q8×C61—22no—
190C2×Q8×C61C2412yes—
191C22×C4×C61—22no—
192C22×C4×C61—22no—
193C22×C4×C61—21no—
194C22×C4×C61—21no—
195C22×C4×C61—21no—
196C22×C4×C61—21no—
197C22×C4×C61C2×D411yescharacteristic
198C22×C4×C61C2×D412yes—
199C22×C4×C61C2412yes—
200C22×C4×C61C2411yescharacteristic
201C2×C22⋊D61—24no—
202C2×C22⋊D61C2×D414yes—
203C22×Dic61—21no—
204C22×Dic61—21no—
205C22×Dic61—24no—
206C22×Dic61—21no—
207C22×Dic61—21no—
208C22×Dic61—44no—
209C22×Dic61C2×D411yescharacteristic
210C22×Dic61C2×D411yescharacteristic
211C22×Dic61C2×D411yescharacteristic
212Q8×D61—28no—
213Q8×D61—44no—
214Q8×D61—48no—
215C2×C4×D61—22no—
216C2×C4×D61—22no—
217C2×C4×D61—24no—
218C2×C4×D61—44no—
219C2×C4×D61C2×D412yes—
220C2×C4×D61C2412yes—
221C2×Dic122—21no—
222C2×Dic122—22no—
223C2×Dic122—22no—
224C2×Dic122—22no—
225C2×Dic122—22no—
226C2×Dic122—22no—
227C2×Dic122—28no—
228C2×Dic122—24no—
229C2×Dic122—21no—
230C2×Dic122—21no—
231C2×Dic122—24no—
232C2×Dic122—24no—
233C2×Dic122—44no—
234C2×Dic122—48no—
235C2×Dic122—44no—
236C2×Dic122—44no—
237C2×Dic122—44no—
238C2×Dic122#4114yes—
239C2×Dic122C2412yes—
240C2×Dic122C2412yes—
241C2×Dic122C2412yes—
242C2×C8×C61—22no—
243C2×C8×C61—22no—
244C2×C8×C61C2412yes—
245C2×C8×C61C2412yes—
246C4⋊C4×C61—24no—
247C4⋊C4×C61—21no—
248C4⋊C4×C61—21no—
249C4⋊C4×C61—21no—
250C4⋊C4×C61C2412yes—
251C4⋊C4×C61C2412yes—
252C4⋊C4×C61C2412yes—
253C22⋊C4×C61—24no—
254C22⋊C4×C61—24no—
255C42×C61—24no—
256C22⋊Dic61—24no—
257C22⋊Dic61C2×D414yes—
258#11758202—44no—
259#11758198—24no—
260#11758198—24no—
261#11758198—24no—
262#11758198C2×D414yes—
263C4⋊Dic61—21no—
264C4⋊Dic61—24no—
265C4⋊Dic61—24no—
266C4⋊Dic61C2412yes—
267#11758196—24no—
268#11758196—24no—
269#11758196—24no—
270#11758196—24no—
271#11758196—24no—
272#11758196—24no—
273#11758196C2×D414yes—
274C4×Dic61—24no—
275C4×Dic61—24no—
276C4×Dic61—24no—
277C4×Dic61C2×D412yes—
278C4×Dic61C2412yes—
279#11758194—44no—
280C2×#92418—22no—
281C2×#92418—22no—
282C2×#92418C2412yes—
283C2×#92418C2412yes—
284Dic244—28no—
285Dic244—44no—
286#11758189—44no—
287C23×C61—22no—
288C23×C61—22no—
289C23×C61—22no—
290C23×C61C22×D412yes—
291C23×C61C22×D411yescharacteristic
292C22×D61—22no—
293C22×D61—22no—
294C22×D61—22no—
295C22×D61C22×D412yes—
296Q8×C61—22no—
297Q8×C61—22no—
298Q8×C61—42no—
299C2×C4×C61—22no—
300C2×C4×C61—24no—
301C2×C4×C61—22no—
302C2×C4×C61—22no—
303C2×C4×C61—22no—
304C2×C4×C61—22no—
305C2×C4×C61—22no—
306C2×C4×C61—22no—
307C2×C4×C61—42no—
308C2×C4×C61—42no—
309C2×C4×C61—42no—
310C2×C4×C61—42no—
311C2×C4×C61C22×D412yes—
312C2×C4×C61C22×D411yescharacteristic
313C2×C4×C61C2×#4112yes—
314C2×C4×C61H(5,𝔽2)12yes—
315C2×C4×C61C2511yescharacteristic
316C22⋊D61—28no—
317C2×Dic61—24no—
318C2×Dic61—22no—
319C2×Dic61—22no—
320C2×Dic61—22no—
321C2×Dic61—22no—
322C2×Dic61—22no—
323C2×Dic61—22no—
324C2×Dic61—48no—
325C2×Dic61—42no—
326C2×Dic61—42no—
327C2×Dic61—42no—
328C2×Dic61#13714yes—
329C2×Dic61C22×D412yes—
330C2×Dic61C22×D412yes—
331C2×Dic61C22×D412yes—
332C4×D61—24no—
333C4×D61—22no—
334C4×D61—22no—
335C4×D61—48no—
336Dic122—24no—
337Dic122—22no—
338Dic122—22no—
339Dic122—22no—
340Dic122—22no—
341Dic122—22no—
342Dic122—48no—
343Dic122—48no—
344Dic122—42no—
345Dic122—42no—
346Dic122—48no—
347Dic122C2×#4114yes—
348C8×C61—22no—
349C8×C61—22no—
350#92418—22no—
351#92418—22no—
352C2×#3328—611nomaximal, Sylow
353C22×C61—22no—
354C22×C61—22no—
355C22×C61—22no—
356C22×C61—44no—
357C22×C61#54612yes—
358C22×C61C2×#13712yes—
359C22×C61#57812yes—
360C22×C61C23×D411yescharacteristic
361C2×D61—22no—
362C2×D61—22no—
363C2×D61—22no—
364C2×D61—44no—
365C4×C61—22no—
366C4×C61—42no—
367C4×C61—42no—
368C4×C61—42no—
369C4×C61—42no—
370C4×C61#54612yes—
371C4×C61C22×#4111yescharacteristic
372C4×C61C2×H(5,𝔽2)11yescharacteristic
373Dic61—24no—
374Dic61—22no—
375Dic61—22no—
376Dic61—42no—
377Dic61—42no—
378Dic61—42no—
379Dic61C2×#13714yes—
380C2×#556—611no—
381C2×D4×Q8—611no—
382#3328—6116no—
383C2×#487—611no—
384C2×#485—611no—
385C2×#485D6111yescharacteristic, complemented
386C2×#475—611no—
387C2×#470—611no—
388C2×#470—611no—
389C2×#462—611no—
390C2×#451—611no—
391C2×#451—611no—
392C2×C4×Q16—611no—
393C2×#436—611no—
394C2×#419—611no—
395C2×#419—611no—
396C2×C61—42no—
397C2×C61#332814yescomplemented
398C2×C61C2×#54611yescharacteristic
399C2×C61C22×#13711yescharacteristic
400C2×C61C2×#57811yescharacteristic
401D61—42no—
402C23×Q8—611no—
403C23×Q8—611no—
404C22×Q16—611no—
405C22×Q16—611no—
406C22×Q16—611no—
407C22×M16—611no—
408C22×M16—611no—
409#556—618no—
410#556—1224no—
411D4×Q8—618no—
412D4×Q8—1224no—
413C2×C4⋊Q8—611no—
414C2×C4⋊Q8—611no—
415C2×C4⋊Q8—1221no—
416C2×#126—1221no—
417C2×#126—1221no—
418C2×#124—1221no—
419C2×C22⋊Q8—611no—
420C2×C22⋊Q8—611no—
421C2×C22⋊Q8—611no—
422C2×C22⋊Q8—1221no—
423C2×C22⋊Q8—1221no—
424C2×C22⋊Q8C2×D6111yescharacteristic
425C2×C4×Q8—611no—
426C2×C4×Q8—611no—
427C2×C4×Q8—1221no—
428C2×C4×D4—611no—
429C2×C4×D4—1221no—
430C2×#117—611no—
431C2×#117C2×D6111yescharacteristic
432#487—618no—
433#485—618no—
434#485C2×D6118yescomplemented
435#475—618no—
436#470—618no—
437#470—618no—
438#462—618no—
439#451—618no—
440#451—618no—
441C4×Q16—618no—
442#436—618no—
443C2×#107C2×D6111yescharacteristic
444C2×#106—611no—
445C2×#106C2×D6111yescharacteristic
446C2×C4⋊C8—611no—
447#419—618no—
448#419—618no—
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×#103C2×D6111yescharacteristic
458C2×#103C2×D6111yescharacteristic
459C2×C22⋊C8—611no—
460C2×C22⋊C8C2×D6111yescharacteristic
461C2×C4×C8—611no—
462C61C2×#332811yescharacteristic, complemented, Sylow
463C22×Q8—614no—
464C22×Q8—611no—
465C22×Q8—611no—
466C22×Q8—611no—
467C22×Q8—614no—
468C22×Q8—1221no—
469C22×Q8—1221no—
470C22×Q8—1224no—
471C22×Q8—1222no—
472C22×Q8—1221no—
473C22×Q8—1222no—
474C22×Q8—1224no—
475C22×Q8—2442no—
476C22×Q8—2442no—
477C22×Q8C22×D6111yescharacteristic
478C22×D4—611no—
479C23×C4—611no—
480C23×C4—1221no—
481C23×C4—1221no—
482C23×C4C22×D6111yescharacteristic
483C2×Q16—614no—
484C2×Q16—614no—
485C2×Q16—614no—
486C2×Q16—1224no—
487C2×Q16—2442no—
488C2×Q16—2442no—
489C2×M16—614no—
490C2×M16—614no—
491C2×M16—2442no—
492C2×M16—2442no—
493C22×C8—611no—
494C22×C8—611no—
495C22×C8C22×D6111yescharacteristic
496C22×C8C22×D6111yescharacteristic
497C4⋊Q8—614no—
498C4⋊Q8—614no—
499C4⋊Q8—1222no—
500C4⋊Q8—1222no—
501C4⋊Q8—1228no—
502#126—1228no—
503#126—1228no—
504#124—1228no—
505C22⋊Q8—22no—
506C22⋊Q8—614no—
507C22⋊Q8—614no—
508C22⋊Q8—614no—
509C22⋊Q8—1228no—
510C22⋊Q8—1228no—
511C22⋊Q8—1222no—
512C22⋊Q8—1222no—
513C22⋊Q8—1222no—
514C22⋊Q8C22×D6114yes—
515C4×Q8—614no—
516C4×Q8—614no—
517C4×Q8—1228no—
518C4×Q8—1222no—
519C4×Q8—1222no—
520C4×D4—614no—
521C4×D4—614no—
522C4×D4—1228no—
523#117—22no—
524#117—614no—
525#117—1222no—
526#117C22×D6114yes—
527C2×C4⋊C4—21no—
528C2×C4⋊C4—611no—
529C2×C4⋊C4—611no—
530C2×C4⋊C4—1221no—
531C2×C4⋊C4—1221no—
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⋊C4C22×D6111yescharacteristic
539C2×C4⋊C4C22×D6111yescharacteristic
540C2×C4⋊C4C22×D6111yescharacteristic
541C2×C22⋊C4—21no—
542C2×C22⋊C4—21no—
543C2×C22⋊C4—611no—
544C2×C22⋊C4—611no—
545C2×C22⋊C4—1221no—
546C2×C22⋊C4—1221no—
547C2×C22⋊C4—1221no—
548C2×C22⋊C4—1221no—
549C2×C42—21no—
550C2×C42—611no—
551C2×C42—1221no—
552C2×C42—1221no—
553C2×C42—1221no—
554#107C22×D6114yes—
555#106—614no—
556#106C22×D6114yes—
557C4⋊C8—614no—
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#103C22×D6114yes—
567#103C22×D6114yes—
568C22⋊C8—614no—
569C22⋊C8C22×D6114yes—
570C4×C8—614no—
571C24—611no—
572C24D4×D6111yescharacteristic
573C2×Q8—21no—
574C2×Q8—22no—
575C2×Q8—22no—
576C2×Q8—614no—
577C2×Q8—612no—
578C2×Q8—612no—
579C2×Q8—612no—
580C2×Q8—1224no—
581C2×Q8—1224no—
582C2×Q8—1228no—
583C2×Q8—1221no—
584C2×Q8—1221no—
585C2×Q8—1224no—
586C2×Q8—1221no—
587C2×Q8—1222no—
588C2×Q8—1228no—
589C2×Q8—1222no—
590C2×Q8—1222no—
591C2×Q8—1222no—
592C2×Q8—1222no—
593C2×Q8—2444no—
594C2×Q8—2444no—
595C2×Q8—2448no—
596C2×Q8—2444no—
597C2×Q8—2444no—
598C2×Q8—2444no—
599C2×Q8—2448no—
600C2×Q8C23×D6112yes—
601C2×D4—614no—
602C2×D4—1224no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—611no—
610C22×C4—611no—
611C22×C4—611no—
612C22×C4—612no—
613C22×C4—612no—
614C22×C4—1224no—
615C22×C4—1221no—
616C22×C4—1222no—
617C22×C4—1222no—
618C22×C4—1224no—
619C22×C4—1221no—
620C22×C4—1221no—
621C22×C4—1221no—
622C22×C4—2444no—
623C22×C4—2444no—
624C22×C4D4×D6112yes—
625C22×C4D4×D6111yescharacteristic
626C22×C4C23×D6112yes—
627C22×C4C23×D6111yescharacteristic
628Q16—1228no—
629Q16—2444no—
630Q16—2444no—
631M16—2444no—
632M16—2444no—
633C2×C8—22no—
634C2×C8—22no—
635C2×C8—612no—
636C2×C8—612no—
637C2×C8—1222no—
638C2×C8—1222no—
639C2×C8C23×D6112yes—
640C2×C8C23×D6112yes—
641C4⋊C4—24no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—614no—
646C4⋊C4—612no—
647C4⋊C4—1224no—
648C4⋊C4—1224no—
649C4⋊C4—1224no—
650C4⋊C4—1224no—
651C4⋊C4—1224no—
652C4⋊C4—1224no—
653C4⋊C4—1224no—
654C4⋊C4—1221no—
655C4⋊C4—1224no—
656C4⋊C4C23×D6112yes—
657C4⋊C4C23×D6112yes—
658C4⋊C4C23×D6112yes—
659C22⋊C4—24no—
660C22⋊C4—24no—
661C22⋊C4—614no—
662C22⋊C4—614no—
663C22⋊C4—1224no—
664C22⋊C4—1224no—
665C22⋊C4—1224no—
666C22⋊C4—1224no—
667C42—24no—
668C42—612no—
669C42—612no—
670C42—1224no—
671C42—1224no—
672C42—1224no—
673C23—22no—
674C23—22no—
675C23—22no—
676C23—612no—
677C23—1222no—
678C23—1222no—
679C23—1222no—
680C23C2×D4×D6112yes—
681C23C2×D4×D6111yescharacteristic
682Q8—22no—
683Q8—22no—
684Q8—42no—
685Q8—614no—
686Q8—1222no—
687Q8—1224no—
688Q8—1222no—
689Q8—1222no—
690Q8—1222no—
691Q8—1222no—
692Q8—2448no—
693Q8—2448no—
694Q8—2448no—
695Q8—2442no—
696Q8—2442no—
697D4—1228no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—24no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—614no—
711C2×C4—612no—
712C2×C4—612no—
713C2×C4—612no—
714C2×C4—1222no—
715C2×C4—1222no—
716C2×C4—1222no—
717C2×C4—1224no—
718C2×C4—1222no—
719C2×C4—1222no—
720C2×C4—1224no—
721C2×C4—1222no—
722C2×C4—1222no—
723C2×C4—1222no—
724C2×C4—2448no—
725C2×C4—2448no—
726C2×C4—2442no—
727C2×C4—2442no—
728C2×C4—2442no—
729C2×C4C2×D4×D6112yes—
730C2×C4C2×D4×D6111yescharacteristic
731C2×C4#41×D6112yes—
732C2×C4#1451982312yes—
733C2×C4C24×D6111yescharacteristic
734C8—22no—
735C8—22no—
736C8—1222no—
737C8—1222no—
738C22—22no—
739C22—22no—
740C22—22no—
741C22—44no—
742C22—1222no—
743C22—1222no—
744C22—1222no—
745C22—2444no—
746C22#1684040412yes—
747C22#137×D6112yes—
748C22#1684057612yes—
749C22C22×D4×D6111yescharacteristic
750C4—22no—
751C4—42no—
752C4—42no—
753C4—42no—
754C4—42no—
755C4—614no—
756C4—1222no—
757C4—1224no—
758C4—1222no—
759C4—2442no—
760C4—2442no—
761C4—2442no—
762C4#1684040412yes—
763C4C2×#41×D6111yescharacteristic
764C4C2×#1451982311yescharacteristic
765C2—42no—
766C2—2442no—
767C2#2145810014yesdirect product factor
768C2C2×#1684040411yescharacteristic
769C2C2×#137×D6111yescharacteristic
770C2C2×#1684057611yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#485C2
socleC23×C61C22×D4
prime radicalC22×C22⋊D61D4
hypercenterC2×#485D61
hypocenterC61C2×#3328
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#485

Complements

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

NH ≅ G/Ntype
3. #21458100C2direct (N × H)
4. C2×#16840111C2semidirect
5. C2×#16840105C2semidirect
6. C2×#16840046C2semidirect
7. C2×#16840021C2semidirect
8. C2×#16840018C2semidirect
9. C2×#16839971C2semidirect
10. C2×#16839920C2semidirect
11. C2×#16839919C2semidirect
12. C2×#16839856C2semidirect
14. C2×#16839770C2semidirect
15. C2×#16839769C2semidirect
16. C2×C61×#485C2semidirect
45. #16840111C22semidirect
46. #16840105C22semidirect
47. #16840046C22semidirect
48. #16840021C22semidirect
49. #16840018C22semidirect
50. #16839971C22semidirect
51. #16839920C22semidirect
52. #16839919C22semidirect
53. #16839856C22semidirect
57. #16839770C22semidirect
58. #16839769C22semidirect
71. C61×#485C22semidirect
385. C2×#485D61semidirect
397. C2×C61#3328semidirect
434. #485C2×D61semidirect
462. C61C2×#3328semidirect
767. C2#21458100direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404802
C2×#168404252
#214581002
C2×#168401112
C2×#168401052
C2×#168400462
C2×#168400212
C2×#168400182
C2×#168399712
C2×#168399202
C2×#168399192
C2×#168398562
C2×#168398372
C2×#168397702
C2×#168397692
C2×C61×#4852
C2×#332861