Finite Group Databasebeta

← C2×#21457892 #30556754

Subgroups — C2×#21457892 #30556754

Order 15616.

2114 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×#16840485C211yesmaximal, characteristic, complemented
2C2×#16840420C211yesmaximal, characteristic
3#21457892C2116yesmaximal, direct product factor
4C2×#16840121C211yesmaximal, characteristic, complemented
5C2×#16840102C211yesmaximal, characteristic, complemented
6C2×#16840084C211yesmaximal, characteristic, complemented
7C2×#16840058C211yesmaximal, characteristic, complemented
8C2×#16840005C211yesmaximal, characteristic, complemented
9C2×#16840000C211yesmaximal, characteristic, complemented
10C2×#16839921C211yesmaximal, characteristic, complemented
11C2×#16839916C211yesmaximal, characteristic, complemented
12C2×#16839867C211yesmaximal, characteristic, complemented
13C2×#16839832C211yesmaximal, characteristic, complemented
14C2×#16839769C211yesmaximal, characteristic, complemented
15C2×#16839755C211yesmaximal, characteristic, complemented
16C2×C61×#464C211yesmaximal, characteristic, complemented
17C22×#11758224C2211yescharacteristic
18C22×Q8×D61C2211yescharacteristic
19C22×#11758202C2211yescharacteristic
20C22×#11758189C2211yescharacteristic
21C22×C8×D61C2211yescharacteristic
22#16840485—24no—
23#16840485C2218yescomplemented
24#16840420—24no—
25#16840420C2218yes—
26C2×#14519777C2211yescharacteristic
27C2×#14519772—21no—
28C2×#14519772—21no—
29C2×#14519765—21no—
30C2×#14519763—21no—
31C2×#14519754—21no—
32C2×#14519753C2211yescharacteristic
33C2×#14519753C2211yescharacteristic
34C2×#14519753C2211yescharacteristic
35C2×#14519750—21no—
36C2×#14519748C2211yescharacteristic
37C2×C4×Dic122—21no—
38C2×C4×Dic122C2211yescharacteristic
39C2×C4×D244C2211yescharacteristic
40C2×#14519737—21no—
41C2×#14519735C2211yescharacteristic
42C2×#14519735C2211yescharacteristic
43#16840121C2218yescomplemented
44#16840102C2218yescomplemented
45#16840084C2218yescomplemented
46#16840058C2218yescomplemented
47#16840005C2218yescomplemented
48#16840000C2218yescomplemented
49#16839921C2218yescomplemented
50#16839916C2218yescomplemented
51#16839867C2218yescomplemented
52#16839832C2218yescomplemented
53C2×#14519711C2211yescharacteristic
54C2×#14519711C2211yescharacteristic
55C2×#14519708C2211yescharacteristic
56#16839769C2218yescomplemented
57#16839755C2218yescomplemented
58C2×#14519702C2211yescharacteristic
59C2×#14519702C2211yescharacteristic
60C2×#14519701C2211yescharacteristic
61C2×#14519701C2211yescharacteristic
62C2×#14519701C2211yescharacteristic
63C2×#14519700C2211yescharacteristic
64C2×#14519698C2211yescharacteristic
65C2×#14519698C2211yescharacteristic
66C2×#14519689C2211yescharacteristic
67C2×#14519689C2211yescharacteristic
68C2×#14519688C2211yescharacteristic
69C22×Q16×C61C2211yescharacteristic
70C22×SD16×C61C2211yescharacteristic
71C2×#124×C61C2211yescharacteristic
72C2×C4×Q8×C61C2211yescharacteristic
73C61×#464C2218yescomplemented
74C2×C4⋊C8×C61C2211yescharacteristic
75C2×#103×C61C2211yescharacteristic
76C2×#102×C61C2211yescharacteristic
77C2×#11758224—22no—
78C2×#11758224—24no—
79C2×#11758224—42no—
80C2×#11758224C2314yes—
81C22×Dic122—21no—
82C22×Dic122—21no—
83C22×Dic122C2311yescharacteristic
84C2×Q8×D61—22no—
85C2×Q8×D61—24no—
86C2×Q8×D61—42no—
87C2×Q8×D61C2314yes—
88C22×D244D411yescharacteristic
89C22×C22⋊D61—21no—
90C22×C22⋊D61—21no—
91C23×Dic61—21no—
92C22×C4×D61—21no—
93C22×C4×D61C2311yescharacteristic
94C22×C4×D61C2311yescharacteristic
95C2×#11758202—24no—
96C2×#11758202C2314yes—
97C2×#11758189—42no—
98C2×#11758189C2314yes—
99C22×#92418C2311yescharacteristic
100C22×#92418C2311yescharacteristic
101C2×C8×D61—42no—
102C2×C8×D61C2314yes—
103#14519777—22no—
104#14519777C2314yes—
105#14519772—28no—
106#14519772—28no—
107#14519765—28no—
108#14519763—28no—
109#14519754—28no—
110#14519753—22no—
111#14519753—22no—
112#14519753—22no—
113#14519753C2314yes—
114#14519753C2314yes—
115#14519753C2314yes—
116#14519750—28no—
117#14519748—22no—
118#14519748C2314yes—
119C4×Dic122—22no—
120C4×Dic122—28no—
121C4×Dic122C2314yes—
122C4×D244D414yes—
123C4×D244C2314yes—
124#14519737—28no—
125#14519735—22no—
126#14519735—22no—
127#14519735C2314yes—
128#14519735C2314yes—
129C2×C4⋊Dic61—21no—
130C2×C4⋊Dic61D411yescharacteristic
131C2×C4⋊Dic61C2311yescharacteristic
132C2×C4⋊Dic61C2311yescharacteristic
133C2×C4⋊Dic61C2311yescharacteristic
134C2×#11758196—21no—
135C2×#11758196—21no—
136C2×#11758196—21no—
137C2×#11758196—21no—
138C2×C22⋊Dic61—21no—
139C2×#11758198—21no—
140C2×#11758198—21no—
141C2×#11758198—21no—
142C2×#11758198—21no—
143C2×#11758198—21no—
144C2×#11758198D411yescharacteristic
145C2×#11758198D411yescharacteristic
146C2×C4×Dic61—21no—
147C2×C4×Dic61—21no—
148C2×C4×Dic61—21no—
149#14519711C2314yes—
150#14519711C2314yes—
151#14519708C2314yes—
152#14519702C2314yes—
153#14519702C2314yes—
154#14519701C2314yes—
155#14519701C2314yes—
156#14519701C2314yes—
157#14519700C2314yes—
158#14519698C2314yes—
159#14519698C2314yes—
160#14519689C2314yes—
161#14519689C2314yes—
162#14519688C2314yes—
163C22×Q8×C61C2311yescharacteristic
164C22×Q8×C61C2311yescharacteristic
165C22×D4×C61C2311yescharacteristic
166C2×Q16×C61—42no—
167C2×Q16×C61C2314yes—
168C2×SD16×C61—42no—
169C2×SD16×C61C2314yes—
170C22×C8×C61C2311yescharacteristic
171C22×C8×C61C2311yescharacteristic
172#124×C61—22no—
173#124×C61C2314yes—
174C4×Q8×C61—22no—
175C4×Q8×C61C2314yes—
176C2×C4⋊C4×C61—21no—
177C2×C4⋊C4×C61C2311yescharacteristic
178C2×C22⋊C4×C61—21no—
179C2×C22⋊C4×C61—21no—
180C2×C42×C61—21no—
181C2×C42×C61C2311yescharacteristic
182C4⋊C8×C61C2314yes—
183#103×C61C2314yes—
184#102×C61C2314yes—
185C24×C61—21no—
186C23×D61C2×D411yescharacteristic
187C23×D61C2×D411yescharacteristic
188C2×Q8×C61—21no—
189C2×Q8×C61—21no—
190C2×Q8×C61—22no—
191C2×Q8×C61—22no—
192C2×Q8×C61—22no—
193C2×Q8×C61—22no—
194C2×Q8×C61C2412yes—
195C2×Q8×C61C2412yes—
196C2×D4×C61—21no—
197C2×D4×C61—22no—
198C2×D4×C61—22no—
199C2×D4×C61C2412yes—
200C22×C4×C61—21no—
201C22×C4×C61—21no—
202C22×C4×C61—21no—
203C22×C4×C61C2×D411yescharacteristic
204C22×C4×C61C2×D411yescharacteristic
205C22×C4×C61C2411yescharacteristic
206C2×C22⋊D61—24no—
207C2×C22⋊D61—24no—
208C2×C22⋊D61—44no—
209C2×C22⋊D61—44no—
210C22×Dic61—21no—
211C22×Dic61—21no—
212C22×Dic61—21no—
213C22×Dic61—21no—
214C22×Dic61—24no—
215C22×Dic61—44no—
216C22×Dic61C2×D411yescharacteristic
217C22×Dic61C2×D411yescharacteristic
218Q8×D61—28no—
219Q8×D61—44no—
220Q8×D61—48no—
221#11758224—28no—
222#11758224—44no—
223#11758224—48no—
224C2×D244—42no—
225C2×D244C2×D414yes—
226C2×C4×D61—22no—
227C2×C4×D61—22no—
228C2×C4×D61—22no—
229C2×C4×D61—22no—
230C2×C4×D61—24no—
231C2×C4×D61—44no—
232C2×C4×D61C2×D412yes—
233C2×C4×D61C2×D412yes—
234C2×C4×D61C2412yes—
235C2×C4×D61C2412yes—
236C2×Dic122—21no—
237C2×Dic122—22no—
238C2×Dic122—24no—
239C2×Dic122—24no—
240C2×Dic122—44no—
241C2×Dic122—44no—
242C2×Dic122#4114yes—
243C2×Dic122C2412yes—
244Q16×C61—44no—
245SD16×C61—44no—
246C2×C8×C61—22no—
247C2×C8×C61—22no—
248C2×C8×C61C2412yes—
249C2×C8×C61C2412yes—
250C4⋊C4×C61—24no—
251C4⋊C4×C61—21no—
252C4⋊C4×C61C2412yes—
253C22⋊C4×C61—24no—
254C22⋊C4×C61—24no—
255C42×C61—24no—
256C42×C61C2×D412yes—
257C42×C61C2412yes—
258C22⋊Dic61—24no—
259#11758202—28no—
260#11758198—24no—
261#11758198—24no—
262#11758198—24no—
263#11758198—24no—
264#11758198—24no—
265#11758198C2×D414yes—
266#11758198C2×D414yes—
267C4⋊Dic61—24no—
268C4⋊Dic61—21no—
269C4⋊Dic61—21no—
270C4⋊Dic61—21no—
271C4⋊Dic61C2×D414yes—
272C4⋊Dic61C2412yes—
273C4⋊Dic61C2412yes—
274C4⋊Dic61C2412yes—
275#11758196—24no—
276#11758196—24no—
277#11758196—24no—
278#11758196—24no—
279C4×Dic61—24no—
280C4×Dic61—24no—
281C4×Dic61—24no—
282C2×#92418—22no—
283C2×#92418—22no—
284C2×#92418C2412yes—
285C2×#92418C2412yes—
286#11758189—44no—
287C8×D61—44no—
288C23×C61—22no—
289C23×C61—42no—
290C23×C61—42no—
291C23×C61—42no—
292C23×C61C22×D411yescharacteristic
293C22×D61—22no—
294C22×D61—22no—
295C22×D61—22no—
296C22×D61—22no—
297C22×D61—22no—
298C22×D61—22no—
299C22×D61C22×D412yes—
300C22×D61C22×D412yes—
301Q8×C61—22no—
302Q8×C61—22no—
303Q8×C61—22no—
304Q8×C61—22no—
305Q8×C61—42no—
306Q8×C61—42no—
307D4×C61—22no—
308D4×C61—22no—
309D4×C61—42no—
310C2×C4×C61—22no—
311C2×C4×C61—22no—
312C2×C4×C61—22no—
313C2×C4×C61—22no—
314C2×C4×C61—22no—
315C2×C4×C61—42no—
316C2×C4×C61—42no—
317C2×C4×C61—42no—
318C2×C4×C61C22×D412yes—
319C2×C4×C61C22×D412yes—
320C2×C4×C61C22×D411yescharacteristic
321C2×C4×C61C2×#4112yes—
322C2×C4×C61H(5,𝔽2)12yes—
323C2×C4×C61C2511yescharacteristic
324C22⋊D61—48no—
325C22⋊D61—48no—
326C2×Dic61—24no—
327C2×Dic61—22no—
328C2×Dic61—22no—
329C2×Dic61—22no—
330C2×Dic61—22no—
331C2×Dic61—22no—
332C2×Dic61—22no—
333C2×Dic61—48no—
334C2×Dic61—42no—
335C2×Dic61—42no—
336C2×Dic61—42no—
337C2×Dic61C22×D412yes—
338C2×Dic61C22×D412yes—
339D244—44no—
340C4×D61—24no—
341C4×D61—24no—
342C4×D61—22no—
343C4×D61—22no—
344C4×D61—22no—
345C4×D61—22no—
346C4×D61—48no—
347Dic122—24no—
348Dic122—22no—
349Dic122—48no—
350Dic122—48no—
351Dic122C2×#4114yes—
352C8×C61—22no—
353C8×C61—22no—
354#92418—22no—
355#92418—22no—
356C2×#3313—611nomaximal, Sylow
357C22×C61—42no—
358C22×C61—42no—
359C22×C61—42no—
360C22×C61—84no—
361C22×C61#54612yes—
362C22×C61#57512yes—
363C22×C61#57812yes—
364C22×C61C23×D411yescharacteristic
365C2×D61—22no—
366C2×D61—22no—
367C2×D61—22no—
368C2×D61—22no—
369C2×D61—22no—
370C2×D61—22no—
371C2×D61—44no—
372C2×D61—44no—
373C4×C61—22no—
374C4×C61—22no—
375C4×C61—42no—
376C4×C61—42no—
377C4×C61—42no—
378C4×C61#54612yes—
379C4×C61C22×#4111yescharacteristic
380C4×C61C2×H(5,𝔽2)11yescharacteristic
381Dic61—24no—
382Dic61—22no—
383Dic61—22no—
384Dic61—42no—
385Dic61—42no—
386Dic61—42no—
387C2×#556—611no—
388C2×#548—611no—
389#3313—6116no—
390C2×#489—611no—
391C2×#485—611no—
392C2×#482—611no—
393C2×#477—611no—
394C2×#468—611no—
395C2×#467—611no—
396C2×#464D6111yescharacteristic, complemented
397C2×#452—611no—
398C2×#451—611no—
399C2×#441—611no—
400C2×#435—611no—
401C2×#419—611no—
402C2×#416—611no—
403C2×C61—82no—
404C2×C61#331314yescomplemented
405C2×C61C2×#54611yescharacteristic
406C2×C61C2×#57511yescharacteristic
407C2×C61C2×#57811yescharacteristic
408D61—42no—
409D61—42no—
410C22×#41—611no—
411C23×Q8—611no—
412C22×Q16—611no—
413C22×Q16C2×D6111yescharacteristic
414C22×SD16C2×D6111yescharacteristic
415C22×M16—611no—
416C23×C8—611no—
417#556—618no—
418#556—1224no—
419#548—618no—
420#548—1224no—
421C2×C4⋊Q8—611no—
422C2×#126—1221no—
423C2×#126—1221no—
424C2×#124—1221no—
425C2×#124—1221no—
426C2×#124C2×D6111yescharacteristic
427C2×C22⋊Q8—611no—
428C2×C22⋊Q8—611no—
429C2×C22⋊Q8—611no—
430C2×C22⋊Q8—1221no—
431C2×#121—611no—
432C2×#121—1221no—
433C2×C4×Q8—611no—
434C2×C4×Q8—1221no—
435C2×C4×Q8C2×D6111yescharacteristic
436C2×C4×D4—611no—
437C2×C4×D4—1221no—
438C2×#117—611no—
439C2×#117—611no—
440#489—618no—
441#485—618no—
442#482—618no—
443#477—618no—
444#468—618no—
445#467—618no—
446#464C2×D6118yescomplemented
447#452—618no—
448#451—618no—
449#441—618no—
450#435—618no—
451C2×#107—611no—
452C2×#107—611no—
453C2×#106—611no—
454C2×C4⋊C8C2×D6111yescharacteristic
455#419—618no—
456#416—618no—
457C2×#103—611no—
458C2×#103—611no—
459C2×#103—611no—
460C2×#103—611no—
461C2×#103—611no—
462C2×#103—611no—
463C2×#103C2×D6111yescharacteristic
464C2×#102—611no—
465C2×#102—611no—
466C2×#102C2×D6111yescharacteristic
467C2×C22⋊C8—611no—
468C2×C22⋊C8—611no—
469C2×#97—611no—
470C61C2×#331311yescharacteristic, complemented, Sylow
471C2×#41—614no—
472C2×#41—1222no—
473C2×#41—1224no—
474C2×#41—2442no—
475C22×Q8—614no—
476C22×Q8—611no—
477C22×Q8—1221no—
478C22×Q8—1222no—
479C22×Q8—1221no—
480C22×Q8—1224no—
481C22×Q8—2442no—
482C22×Q8C22×D6111yescharacteristic
483C22×Q8C22×D6111yescharacteristic
484C22×D4—611no—
485C22×D4—1221no—
486C22×D4—1221no—
487C22×D4C22×D6111yescharacteristic
488C23×C4—611no—
489C23×C4—611no—
490C23×C4—1221no—
491C23×C4—1221no—
492C2×Q16—42no—
493C2×Q16—614no—
494C2×Q16—1224no—
495C2×Q16C22×D6114yes—
496C2×SD16—42no—
497C2×SD16C22×D6114yes—
498C2×M16—614no—
499C2×M16—2442no—
500C22×C8—611no—
501C22×C8—611no—
502C22×C8—614no—
503C22×C8—2442no—
504C22×C8C22×D6111yescharacteristic
505C22×C8C22×D6111yescharacteristic
506C4⋊Q8—614no—
507C4⋊Q8—1222no—
508#126—1228no—
509#126—1228no—
510#124—22no—
511#124—1228no—
512#124—1228no—
513#124C22×D6114yes—
514C22⋊Q8—614no—
515C22⋊Q8—614no—
516C22⋊Q8—614no—
517C22⋊Q8—1228no—
518C22⋊Q8—1222no—
519C22⋊Q8—1222no—
520C22⋊Q8—1222no—
521#121—614no—
522#121—1228no—
523#121—1222no—
524C4×Q8—22no—
525C4×Q8—614no—
526C4×Q8—1228no—
527C4×Q8—1222no—
528C4×Q8C22×D6114yes—
529C4×D4—614no—
530C4×D4—614no—
531C4×D4—1228no—
532#117—614no—
533#117—614no—
534#117—1222no—
535#117—1222no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4—611no—
538C2×C4⋊C4—611no—
539C2×C4⋊C4—611no—
540C2×C4⋊C4—611no—
541C2×C4⋊C4—1221no—
542C2×C4⋊C4—1221no—
543C2×C4⋊C4—1221no—
544C2×C4⋊C4—1221no—
545C2×C4⋊C4—1221no—
546C2×C4⋊C4C22×D6111yescharacteristic
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—611no—
550C2×C22⋊C4—611no—
551C2×C22⋊C4—1221no—
552C2×C22⋊C4—1221no—
553C2×C22⋊C4—1221no—
554C2×C22⋊C4—1221no—
555C2×C22⋊C4—1221no—
556C2×C22⋊C4—1221no—
557C2×C42—21no—
558C2×C42—1221no—
559C2×C42—1221no—
560C2×C42—1221no—
561C2×C42C22×D6111yescharacteristic
562#107—614no—
563#107—614no—
564#106—614no—
565C4⋊C8C22×D6114yes—
566#103—614no—
567#103—614no—
568#103—614no—
569#103—614no—
570#103—614no—
571#103—614no—
572#103C22×D6114yes—
573#102—614no—
574#102—614no—
575#102C22×D6114yes—
576C22⋊C8—614no—
577C22⋊C8—614no—
578#97—614no—
579C24—21no—
580C24—611no—
581C24—611no—
582#41—1228no—
583#41—2444no—
584#41—2448no—
585C2×Q8—21no—
586C2×Q8—21no—
587C2×Q8—22no—
588C2×Q8—22no—
589C2×Q8—22no—
590C2×Q8—22no—
591C2×Q8—614no—
592C2×Q8—612no—
593C2×Q8—1224no—
594C2×Q8—1221no—
595C2×Q8—1224no—
596C2×Q8—1222no—
597C2×Q8—1228no—
598C2×Q8—2444no—
599C2×Q8—2444no—
600C2×Q8—2444no—
601C2×Q8—2448no—
602C2×Q8C23×D6112yes—
603C2×Q8C23×D6112yes—
604C2×D4—21no—
605C2×D4—22no—
606C2×D4—22no—
607C2×D4—614no—
608C2×D4—1224no—
609C2×D4—1224no—
610C2×D4—2442no—
611C2×D4—2444no—
612C2×D4—2444no—
613C2×D4C23×D6112yes—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—611no—
618C22×C4—611no—
619C22×C4—612no—
620C22×C4—612no—
621C22×C4—612no—
622C22×C4—612no—
623C22×C4—1224no—
624C22×C4—1224no—
625C22×C4—1221no—
626C22×C4—1222no—
627C22×C4—1222no—
628C22×C4—1222no—
629C22×C4—1222no—
630C22×C4—1221no—
631C22×C4—1221no—
632C22×C4—1221no—
633C22×C4—2444no—
634C22×C4—2444no—
635C22×C4D4×D6111yescharacteristic
636C22×C4D4×D6111yescharacteristic
637C22×C4C23×D6111yescharacteristic
638Q16—44no—
639Q16—1228no—
640SD16—44no—
641M16—2444no—
642C2×C8—22no—
643C2×C8—22no—
644C2×C8—612no—
645C2×C8—612no—
646C2×C8—1222no—
647C2×C8—1222no—
648C2×C8—2444no—
649C2×C8C23×D6112yes—
650C2×C8C23×D6112yes—
651C4⋊C4—24no—
652C4⋊C4—21no—
653C4⋊C4—614no—
654C4⋊C4—612no—
655C4⋊C4—612no—
656C4⋊C4—612no—
657C4⋊C4—1224no—
658C4⋊C4—1224no—
659C4⋊C4—1224no—
660C4⋊C4—1221no—
661C4⋊C4—1221no—
662C4⋊C4—1221no—
663C4⋊C4—1224no—
664C4⋊C4—1224no—
665C4⋊C4C23×D6112yes—
666C22⋊C4—24no—
667C22⋊C4—24no—
668C22⋊C4—614no—
669C22⋊C4—614no—
670C22⋊C4—1224no—
671C22⋊C4—1224no—
672C22⋊C4—1224no—
673C22⋊C4—1224no—
674C22⋊C4—1224no—
675C22⋊C4—1224no—
676C42—24no—
677C42—1224no—
678C42—1224no—
679C42—1224no—
680C42D4×D6112yes—
681C42C23×D6112yes—
682C23—22no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—612no—
687C23—612no—
688C23—1222no—
689C23—1222no—
690C23—1222no—
691C23—1222no—
692C23—1222no—
693C23—1222no—
694C23C2×D4×D6111yescharacteristic
695Q8—22no—
696Q8—22no—
697Q8—22no—
698Q8—22no—
699Q8—42no—
700Q8—42no—
701Q8—614no—
702Q8—1222no—
703Q8—1224no—
704Q8—2448no—
705Q8—2448no—
706D4—22no—
707D4—22no—
708D4—42no—
709D4—2444no—
710D4—2448no—
711D4—2448no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—612no—
721C2×C4—612no—
722C2×C4—1222no—
723C2×C4—1222no—
724C2×C4—1222no—
725C2×C4—1224no—
726C2×C4—1222no—
727C2×C4—1222no—
728C2×C4—1222no—
729C2×C4—1222no—
730C2×C4—1224no—
731C2×C4—1224no—
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×C4C2×D4×D6112yes—
741C2×C4C2×D4×D6112yes—
742C2×C4C2×D4×D6111yescharacteristic
743C2×C4#41×D6112yes—
744C2×C4#1451982212yes—
745C2×C4C24×D6111yescharacteristic
746C8—22no—
747C8—22no—
748C8—1222no—
749C8—1222no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—84no—
754C22—1222no—
755C22—1222no—
756C22—1222no—
757C22—1222no—
758C22—1222no—
759C22—1222no—
760C22—2444no—
761C22—2444no—
762C22#1684040912yes—
763C22#1684056112yes—
764C22#1684057612yes—
765C22C22×D4×D6111yescharacteristic
766C4—22no—
767C4—22no—
768C4—42no—
769C4—42no—
770C4—42no—
771C4—1222no—
772C4—1222no—
773C4—1224no—
774C4—2442no—
775C4—2442no—
776C4—2442no—
777C4#1684040912yes—
778C4C2×#41×D6111yescharacteristic
779C4C2×#1451982211yescharacteristic
780C2—82no—
781C2—2442no—
782C2—2442no—
783C2#2145789214yesdirect product factor
784C2C2×#1684040911yescharacteristic
785C2C2×#1684056111yescharacteristic
786C2C2×#1684057611yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#464C2
socleC23×C61C22×D4
prime radicalC2×#16840420C2
hypercenterC2×#464D61
hypocenterC61C2×#3313
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#464

Complements

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

NH ≅ G/Ntype
1. C2×#16840485C2semidirect
3. #21457892C2direct (N × H)
4. C2×#16840121C2semidirect
5. C2×#16840102C2semidirect
6. C2×#16840084C2semidirect
7. C2×#16840058C2semidirect
8. C2×#16840005C2semidirect
9. C2×#16840000C2semidirect
10. C2×#16839921C2semidirect
11. C2×#16839916C2semidirect
12. C2×#16839867C2semidirect
13. C2×#16839832C2semidirect
14. C2×#16839769C2semidirect
15. C2×#16839755C2semidirect
16. C2×C61×#464C2semidirect
23. #16840485C22semidirect
43. #16840121C22semidirect
44. #16840102C22semidirect
45. #16840084C22semidirect
46. #16840058C22semidirect
47. #16840005C22semidirect
48. #16840000C22semidirect
49. #16839921C22semidirect
50. #16839916C22semidirect
51. #16839867C22semidirect
52. #16839832C22semidirect
56. #16839769C22semidirect
57. #16839755C22semidirect
73. C61×#464C22semidirect
396. C2×#464D61semidirect
404. C2×C61#3313semidirect
446. #464C2×D61semidirect
470. C61C2×#3313semidirect
783. C2#21457892direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404852
C2×#168404202
#214578922
C2×#168401212
C2×#168401022
C2×#168400842
C2×#168400582
C2×#168400052
C2×#168400002
C2×#168399212
C2×#168399162
C2×#168398672
C2×#168398322
C2×#168397692
C2×#168397552
C2×C61×#4642
C2×#331361