Finite Group Databasebeta

← C2×#21457732 #30556448

Subgroups — C2×#21457732 #30556448

Order 15616.

2146 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×#16840480C211yesmaximal, characteristic, complemented
2C2×#16840411C211yesmaximal, characteristic
3#21457732C2116yesmaximal, direct product factor
4C2×#16840111C211yesmaximal, characteristic, complemented
5C2×#16840103C211yesmaximal, characteristic, complemented
6C2×#16840102C211yesmaximal, characteristic, complemented
7C2×#16840040C211yesmaximal, characteristic, complemented
8C2×#16840003C211yesmaximal, characteristic, complemented
9C2×#16840002C211yesmaximal, characteristic, complemented
10C2×#16839971C211yesmaximal, characteristic, complemented
11C2×#16839925C211yesmaximal, characteristic, complemented
12C2×#16839924C211yesmaximal, characteristic, complemented
13C2×#16839853C211yesmaximal, characteristic, complemented
14C2×C8×C22⋊D61C211yesmaximal, characteristic, complemented
15C2×#16839755C211yesmaximal, characteristic, complemented
16C2×C61×#416C211yesmaximal, characteristic, complemented
17C22×#11758224C2211yescharacteristic
18C22×Dic244C2211yescharacteristic
19C22×#11758202C2211yescharacteristic
20C22×#11758200C2211yescharacteristic
21C22×C8×D61C2211yescharacteristic
22#16840480—24no—
23#16840480C2218yescomplemented
24#16840411—24no—
25#16840411C2218yes—
26C2×#14519776C2211yescharacteristic
27C2×#14519775C2211yescharacteristic
28C2×#14519771—21no—
29C2×#14519770—21no—
30C2×#14519763—21no—
31C2×#14519760—21no—
32C2×#14519758—21no—
33C2×#14519757C2211yescharacteristic
34C2×#14519756C2211yescharacteristic
35C2×#14519756C2211yescharacteristic
36C2×#14519753C2211yescharacteristic
37C2×#14519749—21no—
38C2×C4×Dic122—21no—
39C2×#14519742C2211yescharacteristic
40C2×D4×Dic61C2211yescharacteristic
41C2×C4×C22⋊D61C2211yescharacteristic
42C2×#14519735C2211yescharacteristic
43C22×#11758196—21no—
44#16840111C2218yescomplemented
45#16840103C2218yescomplemented
46#16840102C2218yescomplemented
47#16840040C2218yescomplemented
48#16840003C2218yescomplemented
49#16840002C2218yescomplemented
50#16839971C2218yescomplemented
51#16839925C2218yescomplemented
52#16839924C2218yescomplemented
53#16839853C2218yescomplemented
54C8×C22⋊D61C2218yescomplemented
55C2×#14519711C2211yescharacteristic
56C2×#14519710C2211yescharacteristic
57C2×#14519708C2211yescharacteristic
58C2×#14519706C2211yescharacteristic
59#16839755C2218yescomplemented
60C2×#14519702C2211yescharacteristic
61C2×#14519702C2211yescharacteristic
62C2×#14519701C2211yescharacteristic
63C2×#14519700C2211yescharacteristic
64C2×#14519700C2211yescharacteristic
65C2×#14519698C2211yescharacteristic
66C2×C22⋊#92418C2211yescharacteristic
67C2×#14519689C2211yescharacteristic
68C2×C8×Dic61C2211yescharacteristic
69C22×#41×C61C2211yescharacteristic
70C23×C8×C61C2211yescharacteristic
71C2×#117×C61C2211yescharacteristic
72C61×#416C2218yescomplemented
73C2×#103×C61C2211yescharacteristic
74C2×#103×C61C2211yescharacteristic
75C2×#102×C61C2211yescharacteristic
76C2×#102×C61C2211yescharacteristic
77C2×#11758224—24no—
78C2×#11758224—22no—
79C2×#11758224—42no—
80C2×#11758224C2314yes—
81C22×Dic122—21no—
82C22×Dic122C2311yescharacteristic
83C22×Dic122C2311yescharacteristic
84C22×C22⋊D61—21no—
85C22×C22⋊D61D411yescharacteristic
86C23×Dic61—21no—
87C23×Dic61—21no—
88C22×C4×D61C2311yescharacteristic
89C2×Dic244—42no—
90C2×Dic244C2314yes—
91C2×#11758202—42no—
92C2×#11758202C2314yes—
93C2×#11758200—24no—
94C2×#11758200C2314yes—
95C22×#92418C2311yescharacteristic
96C22×#92418C2311yescharacteristic
97C2×C8×D61—42no—
98C2×C8×D61C2314yes—
99#14519776—22no—
100#14519776C2314yes—
101#14519775—22no—
102#14519775C2314yes—
103#14519771—28no—
104#14519770—28no—
105#14519763—28no—
106#14519760—28no—
107#14519758—28no—
108#14519757—22no—
109#14519757C2314yes—
110#14519756—22no—
111#14519756—22no—
112#14519756C2314yes—
113#14519756C2314yes—
114#14519753—22no—
115#14519753C2314yes—
116#14519749—28no—
117C4×Dic122—28no—
118#14519742—22no—
119#14519742C2314yes—
120D4×Dic61—22no—
121D4×Dic61C2314yes—
122C4×C22⋊D61D414yes—
123C4×C22⋊D61C2314yes—
124#14519735—22no—
125#14519735C2314yes—
126C2×C4⋊Dic61—21no—
127C2×C4⋊Dic61C2311yescharacteristic
128C2×C4⋊Dic61C2311yescharacteristic
129C2×#11758196—21no—
130C2×#11758196—21no—
131C2×#11758196—21no—
132C2×#11758196—21no—
133C2×#11758196—21no—
134C2×#11758196—21no—
135C2×#11758196—21no—
136C2×#11758196—28no—
137C2×#11758196D411yescharacteristic
138C2×C22⋊Dic61—21no—
139C2×C22⋊Dic61—21no—
140C2×C22⋊Dic61—21no—
141C2×C22⋊Dic61D411yescharacteristic
142C2×#11758198—21no—
143C2×#11758198—21no—
144C2×#11758198—21no—
145C2×#11758198D411yescharacteristic
146C2×C4×Dic61—21no—
147C2×C4×Dic61—21no—
148C2×C4×Dic61C2311yescharacteristic
149#14519711C2314yes—
150#14519710C2314yes—
151#14519708C2314yes—
152#14519706C2314yes—
153#14519702C2314yes—
154#14519702C2314yes—
155#14519701C2314yes—
156#14519700C2314yes—
157#14519700C2314yes—
158#14519698C2314yes—
159C22⋊#92418C2314yes—
160#14519689C2314yes—
161C8×Dic61C2314yes—
162C2×#41×C61—22no—
163C2×#41×C61—24no—
164C2×#41×C61—42no—
165C2×#41×C61C2314yes—
166C22×Q8×C61C2311yescharacteristic
167C22×D4×C61—21no—
168C22×D4×C61C2311yescharacteristic
169C23×C4×C61—21no—
170C23×C4×C61C2311yescharacteristic
171C22×C8×C61—42no—
172C22×C8×C61C2311yescharacteristic
173C22×C8×C61C2311yescharacteristic
174C22×C8×C61C2314yes—
175#117×C61—22no—
176#117×C61C2314yes—
177C2×C4⋊C4×C61C2311yescharacteristic
178C2×C4⋊C4×C61C2311yescharacteristic
179C2×C22⋊C4×C61—21no—
180C2×C42×C61—21no—
181#103×C61C2314yes—
182#103×C61C2314yes—
183#102×C61C2314yes—
184#102×C61C2314yes—
185C24×C61—21no—
186C24×C61C2×D411yescharacteristic
187C23×D61C2×D411yescharacteristic
188#41×C61—28no—
189#41×C61—44no—
190#41×C61—48no—
191C2×Q8×C61—21no—
192C2×Q8×C61—22no—
193C2×Q8×C61—22no—
194C2×Q8×C61C2412yes—
195C2×D4×C61—24no—
196C2×D4×C61—21no—
197C2×D4×C61—22no—
198C2×D4×C61—44no—
199C2×D4×C61#4114yes—
200C2×D4×C61C2412yes—
201C22×C4×C61—22no—
202C22×C4×C61—22no—
203C22×C4×C61—21no—
204C22×C4×C61—21no—
205C22×C4×C61—21no—
206C22×C4×C61—24no—
207C22×C4×C61—44no—
208C22×C4×C61C2×D411yescharacteristic
209C22×C4×C61C2×D412yes—
210C22×C4×C61C2412yes—
211C22×C4×C61C2411yescharacteristic
212C2×C22⋊D61—24no—
213C2×C22⋊D61—24no—
214C2×C22⋊D61—44no—
215C2×C22⋊D61C2×D414yes—
216C22×Dic61—21no—
217C22×Dic61—21no—
218C22×Dic61—21no—
219C22×Dic61—21no—
220C22×Dic61—24no—
221C22×Dic61—24no—
222C22×Dic61—44no—
223C22×Dic61—44no—
224C22×Dic61C2×D411yescharacteristic
225C22×Dic61C2×D411yescharacteristic
226C22×Dic61C2×D411yescharacteristic
227#11758224—28no—
228#11758224—44no—
229#11758224—48no—
230C2×C4×D61—22no—
231C2×C4×D61—22no—
232C2×C4×D61C2×D412yes—
233C2×C4×D61C2412yes—
234C2×Dic122—22no—
235C2×Dic122—22no—
236C2×Dic122—22no—
237C2×Dic122—22no—
238C2×Dic122—21no—
239C2×Dic122—21no—
240C2×Dic122—24no—
241C2×Dic122—44no—
242C2×Dic122C2412yes—
243C2×Dic122C2412yes—
244C2×C8×C61—22no—
245C2×C8×C61—22no—
246C2×C8×C61—44no—
247C2×C8×C61C2412yes—
248C2×C8×C61C2412yes—
249C4⋊C4×C61—21no—
250C4⋊C4×C61—21no—
251C4⋊C4×C61C2412yes—
252C4⋊C4×C61C2412yes—
253C22⋊C4×C61—24no—
254C42×C61—24no—
255C22⋊Dic61—24no—
256C22⋊Dic61—24no—
257C22⋊Dic61—24no—
258C22⋊Dic61C2×D414yes—
259#11758202—44no—
260#11758200—28no—
261#11758198—24no—
262#11758198—24no—
263#11758198—24no—
264#11758198C2×D414yes—
265C4⋊Dic61—21no—
266C4⋊Dic61—21no—
267C4⋊Dic61—24no—
268C4⋊Dic61C2412yes—
269C4⋊Dic61C2412yes—
270#11758196—24no—
271#11758196—24no—
272#11758196—24no—
273#11758196—24no—
274#11758196—24no—
275#11758196—24no—
276#11758196—24no—
277#11758196C2×D414yes—
278C4×Dic61—24no—
279C4×Dic61—24no—
280C4×Dic61C2×D412yes—
281C4×Dic61C2412yes—
282C2×#92418—22no—
283C2×#92418—22no—
284C2×#92418C2412yes—
285C2×#92418C2412yes—
286Dic244—44no—
287C8×D61—44no—
288C23×C61—24no—
289C23×C61—22no—
290C23×C61—22no—
291C23×C61—22no—
292C23×C61—22no—
293C23×C61—42no—
294C23×C61—42no—
295C23×C61C22×D412yes—
296C23×C61C22×D411yescharacteristic
297C22×D61—22no—
298C22×D61—22no—
299C22×D61—22no—
300C22×D61C22×D412yes—
301Q8×C61—22no—
302Q8×C61—22no—
303Q8×C61—42no—
304D4×C61—24no—
305D4×C61—22no—
306D4×C61—48no—
307D4×C61C2×#4114yes—
308C2×C4×C61—22no—
309C2×C4×C61—24no—
310C2×C4×C61—22no—
311C2×C4×C61—22no—
312C2×C4×C61—22no—
313C2×C4×C61—22no—
314C2×C4×C61—22no—
315C2×C4×C61—48no—
316C2×C4×C61—42no—
317C2×C4×C61—42no—
318C2×C4×C61—42no—
319C2×C4×C61C22×D412yes—
320C2×C4×C61C22×D411yescharacteristic
321C2×C4×C61C2×#4112yes—
322C2×C4×C61H(5,𝔽2)12yes—
323C2×C4×C61C2511yescharacteristic
324C22⋊D61—28no—
325C22⋊D61—48no—
326C2×Dic61—22no—
327C2×Dic61—22no—
328C2×Dic61—22no—
329C2×Dic61—22no—
330C2×Dic61—22no—
331C2×Dic61—22no—
332C2×Dic61—48no—
333C2×Dic61—42no—
334C2×Dic61—42no—
335C2×Dic61—42no—
336C2×Dic61—42no—
337C2×Dic61—48no—
338C2×Dic61#13514yes—
339C2×Dic61C22×D412yes—
340C2×Dic61C22×D412yes—
341C2×Dic61C22×D412yes—
342C4×D61—24no—
343C4×D61—22no—
344C4×D61—22no—
345Dic122—22no—
346Dic122—22no—
347Dic122—22no—
348Dic122—22no—
349Dic122—42no—
350Dic122—42no—
351Dic122—48no—
352C8×C61—22no—
353C8×C61—22no—
354#92418—22no—
355#92418—22no—
356C2×#3302—611nomaximal, Sylow
357C22×C61—24no—
358C22×C61—22no—
359C22×C61—22no—
360C22×C61—22no—
361C22×C61—44no—
362C22×C61—48no—
363C22×C61—42no—
364C22×C61—42no—
365C22×C61#54612yes—
366C22×C61C2×#13512yes—
367C22×C61#57812yes—
368C22×C61C23×D411yescharacteristic
369C2×D61—22no—
370C2×D61—22no—
371C2×D61—22no—
372C2×D61—44no—
373C4×C61—22no—
374C4×C61—42no—
375C4×C61—42no—
376C4×C61—42no—
377C4×C61#54612yes—
378C4×C61C22×#4111yescharacteristic
379C4×C61C2×H(5,𝔽2)11yescharacteristic
380Dic61—22no—
381Dic61—22no—
382Dic61—42no—
383Dic61—42no—
384Dic61—42no—
385Dic61—42no—
386Dic61C2×#13514yes—
387C2×#556—611no—
388C2×#547—611no—
389#3302—6116no—
390C2×#487—611no—
391C2×#485—611no—
392C2×#485—611no—
393C2×#474—611no—
394C2×#467—611no—
395C2×#467—611no—
396C2×#462—611no—
397C2×#452—611no—
398C2×#452—611no—
399C2×C4×SD16—611no—
400C2×C8×D4—611no—
401C2×#416—611no—
402C2×#416D6111yescharacteristic, complemented
403C2×C61—42no—
404C2×C61—44no—
405C2×C61#330214yescomplemented
406C2×C61C2×#54611yescharacteristic
407C2×C61C22×#13511yescharacteristic
408C2×C61C2×#57811yescharacteristic
409D61—42no—
410C22×#41—611no—
411C22×#41C2×D6111yescharacteristic
412C22×Q16—611no—
413C22×Q16—611no—
414C22×SD16—611no—
415C23×C8—611no—
416C23×C8C2×D6111yescharacteristic
417#556—618no—
418#556—1224no—
419#547—618no—
420#547—1224no—
421C2×C4⋊Q8—611no—
422C2×C4⋊Q8—611no—
423C2×#126—1221no—
424C2×#126—1221no—
425C2×#124—1221no—
426C2×#123—1221no—
427C2×#123—1221no—
428C2×C22⋊Q8—611no—
429C2×C22⋊Q8—611no—
430C2×C22⋊Q8—611no—
431C2×C22⋊Q8—611no—
432C2×#121—1221no—
433C2×C4×Q8—611no—
434C2×C4×Q8—1221no—
435C2×C4×D4—611no—
436C2×C4×D4—611no—
437C2×#117—611no—
438C2×#117C2×D6111yescharacteristic
439C22×C4⋊C4—1221no—
440#487—618no—
441#485—618no—
442#485—618no—
443#474—618no—
444#467—618no—
445#467—618no—
446#462—618no—
447#452—618no—
448#452—618no—
449C4×SD16—618no—
450C8×D4—618no—
451C2×#107—611no—
452C2×#107—611no—
453C2×#106—611no—
454C2×C4⋊C8—611no—
455#416—618no—
456#416C2×D6118yescomplemented
457C2×#103—611no—
458C2×#103—611no—
459C2×#103—611no—
460C2×#103—611no—
461C2×#103—611no—
462C2×#103C2×D6111yescharacteristic
463C2×#103C2×D6111yescharacteristic
464C2×#102—611no—
465C2×#102C2×D6111yescharacteristic
466C2×#102C2×D6111yescharacteristic
467C2×C22⋊C8—611no—
468C2×C22⋊C8—611no—
469C2×C4×C8—611no—
470C61C2×#330211yescharacteristic, complemented, Sylow
471C2×#41—22no—
472C2×#41—24no—
473C2×#41—42no—
474C2×#41—614no—
475C2×#41—1222no—
476C2×#41—1224no—
477C2×#41—2442no—
478C2×#41C22×D6114yes—
479C22×Q8—611no—
480C22×Q8—611no—
481C22×Q8—1221no—
482C22×Q8C22×D6111yescharacteristic
483C22×D4—21no—
484C22×D4—611no—
485C22×D4—1221no—
486C22×D4C22×D6111yescharacteristic
487C23×C4—21no—
488C23×C4—611no—
489C23×C4—1221no—
490C23×C4—1221no—
491C23×C4C22×D6111yescharacteristic
492C2×Q16—614no—
493C2×Q16—614no—
494C2×Q16—2442no—
495C2×Q16—2442no—
496C2×SD16—614no—
497C2×SD16—1224no—
498C22×C8—42no—
499C22×C8—611no—
500C22×C8—611no—
501C22×C8—614no—
502C22×C8—2442no—
503C22×C8C22×D6111yescharacteristic
504C22×C8C22×D6111yescharacteristic
505C22×C8C22×D6114yes—
506C4⋊Q8—614no—
507C4⋊Q8—614no—
508C4⋊Q8—1222no—
509C4⋊Q8—1222no—
510#126—1228no—
511#126—1228no—
512#124—1228no—
513#123—1228no—
514#123—1228no—
515C22⋊Q8—614no—
516C22⋊Q8—614no—
517C22⋊Q8—614no—
518C22⋊Q8—614no—
519C22⋊Q8—1222no—
520C22⋊Q8—1222no—
521C22⋊Q8—1222no—
522C22⋊Q8—1222no—
523#121—1228no—
524C4×Q8—614no—
525C4×Q8—1228no—
526C4×Q8—1222no—
527C4×D4—614no—
528C4×D4—614no—
529C4×D4—614no—
530C4×D4—1222no—
531#117—22no—
532#117—614no—
533#117—1222no—
534#117C22×D6114yes—
535C2×C4⋊C4—611no—
536C2×C4⋊C4—611no—
537C2×C4⋊C4—611no—
538C2×C4⋊C4—1228no—
539C2×C4⋊C4—1221no—
540C2×C4⋊C4—1221no—
541C2×C4⋊C4—1221no—
542C2×C4⋊C4—1221no—
543C2×C4⋊C4—1221no—
544C2×C4⋊C4—1221no—
545C2×C4⋊C4—1221no—
546C2×C4⋊C4—1221no—
547C2×C4⋊C4C22×D6111yescharacteristic
548C2×C4⋊C4C22×D6111yescharacteristic
549C2×C22⋊C4—21no—
550C2×C22⋊C4—611no—
551C2×C22⋊C4—611no—
552C2×C22⋊C4—1221no—
553C2×C22⋊C4—1221no—
554C2×C22⋊C4—1221no—
555C2×C22⋊C4—1221no—
556C2×C22⋊C4—1221no—
557C2×C22⋊C4—1221no—
558C2×C42—21no—
559C2×C42—611no—
560C2×C42—1221no—
561C2×C42—1221no—
562#107—614no—
563#107—614no—
564#106—614no—
565C4⋊C8—614no—
566#103—614no—
567#103—614no—
568#103—614no—
569#103—614no—
570#103—614no—
571#103C22×D6114yes—
572#103C22×D6114yes—
573#102—614no—
574#102C22×D6114yes—
575#102C22×D6114yes—
576C22⋊C8—614no—
577C22⋊C8—614no—
578C4×C8—614no—
579C24—21no—
580C24—611no—
581C24D4×D6111yescharacteristic
582#41—28no—
583#41—44no—
584#41—48no—
585#41—1228no—
586#41—2444no—
587#41—2448no—
588C2×Q8—21no—
589C2×Q8—22no—
590C2×Q8—22no—
591C2×Q8—612no—
592C2×Q8—612no—
593C2×Q8—1224no—
594C2×Q8—1221no—
595C2×Q8—1221no—
596C2×Q8—1222no—
597C2×Q8—1222no—
598C2×Q8—1222no—
599C2×Q8—1222no—
600C2×Q8—2444no—
601C2×Q8C23×D6112yes—
602C2×D4—24no—
603C2×D4—21no—
604C2×D4—22no—
605C2×D4—44no—
606C2×D4—614no—
607C2×D4—1224no—
608C2×D4—1224no—
609C2×D4—2444no—
610C2×D4#1175822214yes—
611C2×D4C23×D6112yes—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—24no—
618C22×C4—44no—
619C22×C4—611no—
620C22×C4—611no—
621C22×C4—611no—
622C22×C4—612no—
623C22×C4—612no—
624C22×C4—1224no—
625C22×C4—1224no—
626C22×C4—1222no—
627C22×C4—1222no—
628C22×C4—1221no—
629C22×C4—1221no—
630C22×C4—1221no—
631C22×C4—1221no—
632C22×C4—2444no—
633C22×C4—2444no—
634C22×C4D4×D6112yes—
635C22×C4D4×D6111yescharacteristic
636C22×C4C23×D6112yes—
637C22×C4C23×D6111yescharacteristic
638Q16—2444no—
639Q16—2444no—
640SD16—1228no—
641C2×C8—22no—
642C2×C8—22no—
643C2×C8—44no—
644C2×C8—612no—
645C2×C8—612no—
646C2×C8—1222no—
647C2×C8—1222no—
648C2×C8—2444no—
649C2×C8C23×D6112yes—
650C2×C8C23×D6112yes—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—614no—
654C4⋊C4—612no—
655C4⋊C4—612no—
656C4⋊C4—1224no—
657C4⋊C4—1224no—
658C4⋊C4—1224no—
659C4⋊C4—1224no—
660C4⋊C4—1224no—
661C4⋊C4—1224no—
662C4⋊C4—1221no—
663C4⋊C4—1221no—
664C4⋊C4—1224no—
665C4⋊C4—1224no—
666C4⋊C4C23×D6112yes—
667C4⋊C4C23×D6112yes—
668C22⋊C4—24no—
669C22⋊C4—614no—
670C22⋊C4—614no—
671C22⋊C4—1224no—
672C22⋊C4—1224no—
673C22⋊C4—1224no—
674C22⋊C4—1224no—
675C22⋊C4—1224no—
676C22⋊C4—1224no—
677C42—24no—
678C42—612no—
679C42—612no—
680C42—1224no—
681C42—1224no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—24no—
687C23—42no—
688C23—42no—
689C23—612no—
690C23—1222no—
691C23—1222no—
692C23—1222no—
693C23C2×D4×D6112yes—
694C23C2×D4×D6111yescharacteristic
695Q8—22no—
696Q8—22no—
697Q8—42no—
698Q8—1222no—
699Q8—1222no—
700Q8—1222no—
701Q8—1222no—
702Q8—2448no—
703Q8—2442no—
704Q8—2442no—
705D4—22no—
706D4—24no—
707D4—48no—
708D4—1228no—
709D4—2448no—
710D4C2×#1175822214yes—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—24no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—48no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—614no—
723C2×C4—612no—
724C2×C4—612no—
725C2×C4—612no—
726C2×C4—1222no—
727C2×C4—1222no—
728C2×C4—1222no—
729C2×C4—1222no—
730C2×C4—1224no—
731C2×C4—1222no—
732C2×C4—1222no—
733C2×C4—1222no—
734C2×C4—1222no—
735C2×C4—2448no—
736C2×C4—2448no—
737C2×C4—2442no—
738C2×C4—2442no—
739C2×C4—2442no—
740C2×C4—2442no—
741C2×C4C2×D4×D6112yes—
742C2×C4C2×D4×D6111yescharacteristic
743C2×C4C2×#1175822212yes—
744C2×C4#1451982212yes—
745C2×C4C24×D6111yescharacteristic
746C8—22no—
747C8—22no—
748C8—1222no—
749C8—1222no—
750C22—22no—
751C22—22no—
752C22—24no—
753C22—22no—
754C22—42no—
755C22—44no—
756C22—48no—
757C22—42no—
758C22—1222no—
759C22—1222no—
760C22—1222no—
761C22—2444no—
762C22#1684040212yes—
763C22#135×D6112yes—
764C22#1684057612yes—
765C22C22×D4×D6111yescharacteristic
766C4—22no—
767C4—42no—
768C4—42no—
769C4—42no—
770C4—614no—
771C4—1222no—
772C4—1222no—
773C4—2442no—
774C4—2442no—
775C4—2442no—
776C4—2442no—
777C4#1684040212yes—
778C4C22×#1175822211yescharacteristic
779C4C2×#1451982211yescharacteristic
780C2—42no—
781C2—44no—
782C2—2442no—
783C2#2145773214yesdirect product factor
784C2C2×#1684040211yescharacteristic
785C2C2×#135×D6111yescharacteristic
786C2C2×#1684057611yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#416C2
socleC23×C61C22×D4
prime radicalC2×#16840411C2
hypercenterC2×#416D61
hypocenterC61C2×#3302
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#416

Complements

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

NH ≅ G/Ntype
1. C2×#16840480C2semidirect
3. #21457732C2direct (N × H)
4. C2×#16840111C2semidirect
5. C2×#16840103C2semidirect
6. C2×#16840102C2semidirect
7. C2×#16840040C2semidirect
8. C2×#16840003C2semidirect
9. C2×#16840002C2semidirect
10. C2×#16839971C2semidirect
11. C2×#16839925C2semidirect
12. C2×#16839924C2semidirect
13. C2×#16839853C2semidirect
14. C2×C8×C22⋊D61C2semidirect
15. C2×#16839755C2semidirect
16. C2×C61×#416C2semidirect
23. #16840480C22semidirect
44. #16840111C22semidirect
45. #16840103C22semidirect
46. #16840102C22semidirect
47. #16840040C22semidirect
48. #16840003C22semidirect
49. #16840002C22semidirect
50. #16839971C22semidirect
51. #16839925C22semidirect
52. #16839924C22semidirect
53. #16839853C22semidirect
54. C8×C22⋊D61C22semidirect
59. #16839755C22semidirect
72. C61×#416C22semidirect
402. C2×#416D61semidirect
405. C2×C61#3302semidirect
456. #416C2×D61semidirect
470. C61C2×#3302semidirect
783. C2#21457732direct (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×#168404112
#214577322
C2×#168401112
C2×#168401032
C2×#168401022
C2×#168400402
C2×#168400032
C2×#168400022
C2×#168399712
C2×#168399252
C2×#168399242
C2×#168398532
C2×C8×C22⋊D612
C2×#168397552
C2×C61×#4162
C2×#330261