Finite Group Databasebeta

← C2×#21457930 #30556603

Subgroups — C2×#21457930 #30556603

Order 15616.

2158 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840469C211yesmaximal, characteristic, complemented
2#21457930C2116yesmaximal, direct product factor
3C2×#16840121C211yesmaximal, characteristic, complemented
4C2×#16840078C211yesmaximal, characteristic, complemented
5C2×#16840090C211yesmaximal, characteristic, complemented
6C2×#16840047C211yesmaximal, characteristic, complemented
7C2×#16840018C211yesmaximal, characteristic, complemented
8C2×#16839989C211yesmaximal, characteristic, complemented
9C2×#16839981C211yesmaximal, characteristic, complemented
10C2×#16839924C211yesmaximal, characteristic, complemented
11C2×#16839918C211yesmaximal, characteristic, complemented
12C2×#16839867C211yesmaximal, characteristic, complemented
13C2×#16839834C211yesmaximal, characteristic, complemented
14C2×#16839763C211yesmaximal, characteristic, complemented
15C22×#14519701C211yesmaximal, characteristic, complemented
16C2×C61×#548C211yesmaximal, characteristic
17C22×#11758202C2211yescharacteristic
18C22×#11758202C2211yescharacteristic
19C22×#11758200C2211yescharacteristic
20C22×#11758194C2211yescharacteristic
21C23×#92418C2211yescharacteristic
22#16840469—24no—
23#16840469C2218yescomplemented
24C2×#14519777C2211yescharacteristic
25C2×#14519768—21no—
26C2×#14519756C2211yescharacteristic
27C2×#14519756C2211yescharacteristic
28C2×#14519754—21no—
29C2×#14519754—21no—
30C2×C4×Dic122C2211yescharacteristic
31C2×D4×Dic61—21no—
32C22×C4⋊Dic61C2211yescharacteristic
33C22×C4⋊Dic61C2211yescharacteristic
34#16840121C2218yescomplemented
35#16840090C2218yescomplemented
36#16840078C2218yescomplemented
37#16840047C2218yescomplemented
38#16840018C2218yescomplemented
39#16839989C2218yescomplemented
40#16839981C2218yescomplemented
41#16839924C2218yescomplemented
42#16839918C2218yescomplemented
43#16839867C2218yescomplemented
44#16839834C2218yescomplemented
45C2×#14519708C2211yescharacteristic
46C2×#14519708C2211yescharacteristic
47C2×#14519708C2211yescharacteristic
48C2×C4⋊#92418C2211yescharacteristic
49#16839763C2218yescomplemented
50C2×#14519701C2211yescharacteristic
51C2×#14519701C2211yescharacteristic
52C2×#14519701C2211yescharacteristic
53C2×#14519701C2211yescharacteristic
54C2×#14519701C2211yescharacteristic
55C2×#14519701C2211yescharacteristic
56C2×#14519701C2218yescomplemented
57C2×#14519700C2211yescharacteristic
58C2×#14519698C2211yescharacteristic
59C2×#14519698C2211yescharacteristic
60C2×#14519698C2211yescharacteristic
61C2×C22⋊#92418C2211yescharacteristic
62C2×C22⋊#92418C2211yescharacteristic
63C2×#14519688C2211yescharacteristic
64C22×#41×C61C2211yescharacteristic
65C23×Q8×C61C2211yescharacteristic
66C61×#548—24no—
67C61×#548C2218yes—
68C2×#124×C61—21no—
69C2×#124×C61C2211yescharacteristic
70C2×C22⋊Q8×C61—21no—
71C2×C22⋊Q8×C61C2211yescharacteristic
72C2×#121×C61—21no—
73C2×#121×C61C2211yescharacteristic
74C2×C4×Q8×C61C2211yescharacteristic
75C2×C4×D4×C61—21no—
76C2×C4×D4×C61C2211yescharacteristic
77C22×Dic122—21no—
78C22×Dic122C2311yescharacteristic
79C23×Dic61—21no—
80C23×Dic61—21no—
81C2×#11758202—24no—
82C2×#11758202—42no—
83C2×#11758202C2314yes—
84C2×#11758202C2314yes—
85C2×#11758200—42no—
86C2×#11758200C2314yes—
87C2×#11758194—42no—
88C2×#11758194C2314yes—
89C22×#92418—42no—
90C22×#92418C2311yescharacteristic
91C22×#92418C2311yescharacteristic
92C22×#92418C2311yescharacteristic
93C22×#92418C2311yescharacteristic
94C22×#92418C2314yes—
95#14519777—22no—
96#14519777C2314yes—
97#14519768—28no—
98#14519756—22no—
99#14519756—22no—
100#14519756C2314yes—
101#14519756C2314yes—
102#14519754—28no—
103#14519754—28no—
104C4×Dic122—22no—
105C4×Dic122C2314yes—
106D4×Dic61—28no—
107C2×C4⋊Dic61—22no—
108C2×C4⋊Dic61—22no—
109C2×C4⋊Dic61—21no—
110C2×C4⋊Dic61—21no—
111C2×C4⋊Dic61—21no—
112C2×C4⋊Dic61C2311yescharacteristic
113C2×C4⋊Dic61C2314yes—
114C2×C4⋊Dic61C2314yes—
115C2×C4⋊Dic61C2311yescharacteristic
116C2×C4⋊Dic61C2311yescharacteristic
117C2×#11758196—21no—
118C2×#11758196—21no—
119C2×#11758196—21no—
120C2×C22⋊Dic61—21no—
121C2×C22⋊Dic61—21no—
122C2×C4×Dic61—21no—
123#14519708C2314yes—
124#14519708C2314yes—
125#14519708C2314yes—
126C4⋊#92418C2314yes—
127#14519701C2314yes—
128#14519701C2314yes—
129#14519701C2314yes—
130#14519701C2314yes—
131#14519701C2314yes—
132#14519701C2314yes—
133#14519700C2314yes—
134#14519698C2314yes—
135#14519698C2314yes—
136#14519698C2314yes—
137C22⋊#92418C2314yes—
138C22⋊#92418C2314yes—
139#14519688C2314yes—
140C2×#41×C61—22no—
141C2×#41×C61—24no—
142C2×#41×C61—42no—
143C2×#41×C61C2314yes—
144C22×Q8×C61—22no—
145C22×Q8×C61—21no—
146C22×Q8×C61—24no—
147C22×Q8×C61—42no—
148C22×Q8×C61C2311yescharacteristic
149C22×Q8×C61C2314yes—
150C22×Q8×C61C2311yescharacteristic
151C22×D4×C61—21no—
152C22×D4×C61—21no—
153C22×D4×C61D411yescharacteristic
154C22×D4×C61C2311yescharacteristic
155C23×C4×C61—21no—
156C23×C4×C61—21no—
157C23×C4×C61C2311yescharacteristic
158C23×C4×C61C2311yescharacteristic
159#124×C61—28no—
160#124×C61—22no—
161#124×C61C2314yes—
162C22⋊Q8×C61—22no—
163C22⋊Q8×C61—28no—
164C22⋊Q8×C61C2314yes—
165#121×C61—28no—
166#121×C61—22no—
167#121×C61C2314yes—
168C4×Q8×C61—22no—
169C4×Q8×C61C2314yes—
170C4×D4×C61—28no—
171C4×D4×C61D414yes—
172C4×D4×C61C2314yes—
173C2×C4⋊C4×C61—21no—
174C2×C4⋊C4×C61—21no—
175C2×C4⋊C4×C61D411yescharacteristic
176C2×C4⋊C4×C61C2311yescharacteristic
177C2×C22⋊C4×C61—21no—
178C2×C22⋊C4×C61—21no—
179C2×C22⋊C4×C61—21no—
180C2×C22⋊C4×C61—21no—
181C2×C22⋊C4×C61D411yescharacteristic
182C2×C22⋊C4×C61D411yescharacteristic
183C2×C42×C61—21no—
184C2×C42×C61C2311yescharacteristic
185C24×C61—21no—
186C24×C61C2×D411yescharacteristic
187C24×C61C2×D411yescharacteristic
188#41×C61—28no—
189#41×C61—44no—
190#41×C61—48no—
191C2×Q8×C61—21no—
192C2×Q8×C61—24no—
193C2×Q8×C61—21no—
194C2×Q8×C61—22no—
195C2×Q8×C61—28no—
196C2×Q8×C61—22no—
197C2×Q8×C61—22no—
198C2×Q8×C61—44no—
199C2×Q8×C61—44no—
200C2×Q8×C61—48no—
201C2×Q8×C61#4114yes—
202C2×Q8×C61C2412yes—
203C2×Q8×C61C2412yes—
204C2×D4×C61—24no—
205C2×D4×C61—24no—
206C2×D4×C61—24no—
207C2×D4×C61—21no—
208C2×D4×C61—22no—
209C2×D4×C61—22no—
210C2×D4×C61—44no—
211C2×D4×C61—44no—
212C2×D4×C61C2×D414yes—
213C2×D4×C61C2412yes—
214C22×C4×C61—21no—
215C22×C4×C61—22no—
216C22×C4×C61—22no—
217C22×C4×C61—22no—
218C22×C4×C61—22no—
219C22×C4×C61—21no—
220C22×C4×C61—21no—
221C22×C4×C61—24no—
222C22×C4×C61—24no—
223C22×C4×C61—44no—
224C22×C4×C61—44no—
225C22×C4×C61C2×D411yescharacteristic
226C22×C4×C61C2×D411yescharacteristic
227C22×C4×C61C2×D411yescharacteristic
228C22×C4×C61C2×D411yescharacteristic
229C22×C4×C61C2×D412yes—
230C22×C4×C61C2×D412yes—
231C22×C4×C61C2412yes—
232C22×C4×C61C2412yes—
233C22×C4×C61C2411yescharacteristic
234C22×Dic61—21no—
235C22×Dic61—21no—
236C22×Dic61—21no—
237C22×Dic61—21no—
238C22×Dic61—24no—
239C22×Dic61—24no—
240C22×Dic61—82no—
241C22×Dic61—82no—
242C2×Dic122—22no—
243C2×Dic122—22no—
244C2×Dic122—21no—
245C2×Dic122—24no—
246C2×Dic122—82no—
247C2×Dic122C2412yes—
248C4⋊C4×C61—24no—
249C4⋊C4×C61—24no—
250C4⋊C4×C61—21no—
251C4⋊C4×C61C2×D414yes—
252C4⋊C4×C61C2412yes—
253C22⋊C4×C61—24no—
254C22⋊C4×C61—24no—
255C22⋊C4×C61—24no—
256C22⋊C4×C61—24no—
257C22⋊C4×C61C2×D414yes—
258C22⋊C4×C61C2×D414yes—
259C42×C61—24no—
260C42×C61C2×D412yes—
261C42×C61C2412yes—
262C22⋊Dic61—24no—
263C22⋊Dic61—24no—
264#11758202—28no—
265#11758202—44no—
266#11758200—44no—
267C4⋊Dic61—21no—
268C4⋊Dic61—24no—
269C4⋊Dic61—24no—
270C4⋊Dic61—21no—
271C4⋊Dic61—21no—
272C4⋊Dic61—24no—
273C4⋊Dic61C2412yes—
274C4⋊Dic61C2412yes—
275C4⋊Dic61C2412yes—
276#11758196—24no—
277#11758196—24no—
278#11758196—24no—
279C4×Dic61—24no—
280#11758194—44no—
281C2×#92418—22no—
282C2×#92418—22no—
283C2×#92418—22no—
284C2×#92418—22no—
285C2×#92418—44no—
286C2×#92418C2412yes—
287C2×#92418C2412yes—
288C2×#92418C2412yes—
289C2×#92418C2412yes—
290C23×C61—22no—
291C23×C61—22no—
292C23×C61—22no—
293C23×C61—22no—
294C23×C61—22no—
295C23×C61—22no—
296C23×C61—42no—
297C23×C61—42no—
298C23×C61—42no—
299C23×C61#13714yes—
300C23×C61C22×D412yes—
301C23×C61C22×D412yes—
302C23×C61C22×D411yescharacteristic
303Q8×C61—24no—
304Q8×C61—22no—
305Q8×C61—22no—
306Q8×C61—22no—
307Q8×C61—48no—
308Q8×C61—42no—
309Q8×C61C2×#4114yes—
310D4×C61—28no—
311D4×C61—22no—
312D4×C61—22no—
313D4×C61—48no—
314D4×C61—48no—
315D4×C61—42no—
316C2×C4×C61—22no—
317C2×C4×C61—22no—
318C2×C4×C61—24no—
319C2×C4×C61—22no—
320C2×C4×C61—22no—
321C2×C4×C61—22no—
322C2×C4×C61—24no—
323C2×C4×C61—24no—
324C2×C4×C61—22no—
325C2×C4×C61—22no—
326C2×C4×C61—22no—
327C2×C4×C61—22no—
328C2×C4×C61—22no—
329C2×C4×C61—22no—
330C2×C4×C61—48no—
331C2×C4×C61—48no—
332C2×C4×C61—42no—
333C2×C4×C61—42no—
334C2×C4×C61C22×D412yes—
335C2×C4×C61C22×D412yes—
336C2×C4×C61C22×D412yes—
337C2×C4×C61C22×D412yes—
338C2×C4×C61C22×D411yescharacteristic
339C2×C4×C61C2×#4112yes—
340C2×C4×C61H(5,𝔽2)12yes—
341C2×C4×C61C2511yescharacteristic
342C2×Dic61—22no—
343C2×Dic61—22no—
344C2×Dic61—22no—
345C2×Dic61—22no—
346C2×Dic61—42no—
347C2×Dic61—42no—
348C2×Dic61—42no—
349C2×Dic61—42no—
350C2×Dic61—84no—
351C2×Dic61—84no—
352Dic122—22no—
353Dic122—22no—
354Dic122—42no—
355Dic122—84no—
356#92418—22no—
357#92418—22no—
358#92418—22no—
359#92418—22no—
360C2×#3316—611nomaximal, Sylow
361C22×C61—22no—
362C22×C61—28no—
363C22×C61—22no—
364C22×C61—22no—
365C22×C61—22no—
366C22×C61—22no—
367C22×C61—44no—
368C22×C61—42no—
369C22×C61—42no—
370C22×C61—42no—
371C22×C61—84no—
372C22×C61#54612yes—
373C22×C61C2×#13714yes—
374C22×C61C2×#13712yes—
375C22×C61#57712yes—
376C22×C61C23×D411yescharacteristic
377C4×C61—22no—
378C4×C61—22no—
379C4×C61—24no—
380C4×C61—22no—
381C4×C61—22no—
382C4×C61—42no—
383C4×C61—42no—
384C4×C61#54612yes—
385C4×C61C22×#4111yescharacteristic
386C4×C61C2×H(5,𝔽2)11yescharacteristic
387Dic61—42no—
388Dic61—42no—
389Dic61—42no—
390Dic61—42no—
391C2×#554—611no—
392C2×#548D6111yescharacteristic
393#3316—6116no—
394C2×#489—611no—
395C2×#481—611no—
396C2×#483—611no—
397C2×#475—611no—
398C2×#470—611no—
399C2×#465—611no—
400C2×#464—611no—
401C2×#452—611no—
402C2×#451—611no—
403C2×#441—611no—
404C2×#435—611no—
405C2×#417—611no—
406C22×#103—611no—
407C2×C61—24no—
408C2×C61—42no—
409C2×C61—82no—
410C2×C61#331614yescomplemented
411C2×C61C2×#54611yescharacteristic
412C2×C61C22×#13711yescharacteristic
413C2×C61C2×#57711yescharacteristic
414C22×#41C2×D6111yescharacteristic
415C23×Q8C2×D6111yescharacteristic
416C22×Q16—611no—
417C22×Q16—611no—
418C22×SD16—611no—
419C22×M16—611no—
420C23×C8—611no—
421#554—618no—
422#554—1224no—
423#548—24no—
424#548C2×D6118yes—
425C2×C4⋊Q8—611no—
426C2×#125—1221no—
427C2×#124—21no—
428C2×#124C2×D6111yescharacteristic
429C2×C22⋊Q8—21no—
430C2×C22⋊Q8—611no—
431C2×C22⋊Q8—611no—
432C2×C22⋊Q8—1221no—
433C2×C22⋊Q8—1221no—
434C2×C22⋊Q8C2×D6111yescharacteristic
435C2×#121—21no—
436C2×#121C2×D6111yescharacteristic
437C2×C4×Q8—611no—
438C2×C4×Q8C2×D6111yescharacteristic
439C2×C4×D4—21no—
440C2×C4×D4—1221no—
441C2×C4×D4C2×D6111yescharacteristic
442C22×C4⋊C4—611no—
443C22×C4⋊C4—611no—
444#489—618no—
445#483—618no—
446#481—618no—
447#475—618no—
448#470—618no—
449#465—618no—
450#464—618no—
451#452—618no—
452#451—618no—
453#441—618no—
454#435—618no—
455C2×#106—611no—
456C2×#106—611no—
457C2×#106—611no—
458C2×C4⋊C8—611no—
459#417—618no—
460C2×#103—611no—
461C2×#103—611no—
462C2×#103—611no—
463C2×#103—611no—
464C2×#103—611no—
465C2×#103—611no—
466C2×#103—618no—
467C2×#103—611no—
468C2×#102—611no—
469C2×#102—611no—
470C2×#102—611no—
471C2×C22⋊C8—611no—
472C2×C22⋊C8—611no—
473C2×#97—611no—
474C61C2×#331611yescharacteristic, complemented, Sylow
475C2×#41—22no—
476C2×#41—24no—
477C2×#41—42no—
478C2×#41C22×D6114yes—
479C22×Q8—21no—
480C22×Q8—22no—
481C22×Q8—24no—
482C22×Q8—42no—
483C22×Q8—611no—
484C22×Q8—1221no—
485C22×Q8C22×D6111yescharacteristic
486C22×Q8C22×D6114yes—
487C22×Q8C22×D6111yescharacteristic
488C22×D4—21no—
489C22×D4—21no—
490C22×D4C22⋊D6111yescharacteristic
491C22×D4C22×D6111yescharacteristic
492C23×C4—21no—
493C23×C4—21no—
494C23×C4—1221no—
495C23×C4—1221no—
496C23×C4C22×D6111yescharacteristic
497C23×C4C22×D6111yescharacteristic
498C2×Q16—614no—
499C2×Q16—614no—
500C2×Q16—1224no—
501C2×Q16—2442no—
502C2×SD16—614no—
503C2×SD16—2442no—
504C2×M16—614no—
505C2×M16—2442no—
506C22×C8—611no—
507C22×C8—611no—
508C22×C8—611no—
509C22×C8—611no—
510C22×C8—614no—
511C22×C8—2442no—
512C4⋊Q8—614no—
513C4⋊Q8—1222no—
514#125—1228no—
515#124—28no—
516#124—22no—
517#124C22×D6114yes—
518C22⋊Q8—22no—
519C22⋊Q8—28no—
520C22⋊Q8—614no—
521C22⋊Q8—614no—
522C22⋊Q8—1222no—
523C22⋊Q8—1222no—
524C22⋊Q8—1228no—
525C22⋊Q8—1228no—
526C22⋊Q8C22×D6114yes—
527#121—28no—
528#121—22no—
529#121C22×D6114yes—
530C4×Q8—22no—
531C4×Q8—614no—
532C4×Q8—1222no—
533C4×Q8C22×D6114yes—
534C4×D4—28no—
535C4×D4—1228no—
536C4×D4C22⋊D6114yes—
537C4×D4C22×D6114yes—
538C2×C4⋊C4—21no—
539C2×C4⋊C4—21no—
540C2×C4⋊C4—611no—
541C2×C4⋊C4—611no—
542C2×C4⋊C4—611no—
543C2×C4⋊C4—614no—
544C2×C4⋊C4—614no—
545C2×C4⋊C4—1221no—
546C2×C4⋊C4—1221no—
547C2×C4⋊C4—1222no—
548C2×C4⋊C4—1222no—
549C2×C4⋊C4—1221no—
550C2×C4⋊C4—1221no—
551C2×C4⋊C4—1221no—
552C2×C4⋊C4—1221no—
553C2×C4⋊C4C22⋊D6111yescharacteristic
554C2×C4⋊C4C22×D6111yescharacteristic
555C2×C22⋊C4—21no—
556C2×C22⋊C4—21no—
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4—1221no—
560C2×C22⋊C4—1221no—
561C2×C22⋊C4C22⋊D6111yescharacteristic
562C2×C22⋊C4C22⋊D6111yescharacteristic
563C2×C42—21no—
564C2×C42—1221no—
565C2×C42C22×D6111yescharacteristic
566#106—614no—
567#106—614no—
568#106—614no—
569C4⋊C8—614no—
570#103—614no—
571#103—614no—
572#103—614no—
573#103—614no—
574#103—614no—
575#103—614no—
576#103—614no—
577#102—614no—
578#102—614no—
579#102—614no—
580C22⋊C8—614no—
581C22⋊C8—614no—
582#97—614no—
583C24—21no—
584C24C2×C22⋊D6111yescharacteristic
585C24C2×C22⋊D6111yescharacteristic
586#41—28no—
587#41—44no—
588#41—48no—
589C2×Q8—21no—
590C2×Q8—24no—
591C2×Q8—21no—
592C2×Q8—22no—
593C2×Q8—28no—
594C2×Q8—22no—
595C2×Q8—22no—
596C2×Q8—44no—
597C2×Q8—44no—
598C2×Q8—48no—
599C2×Q8—612no—
600C2×Q8—1224no—
601C2×Q8—1221no—
602C2×Q8—1222no—
603C2×Q8—1222no—
604C2×Q8—4882no—
605C2×Q8#1175822414yes—
606C2×Q8C23×D6112yes—
607C2×Q8C23×D6112yes—
608C2×D4—24no—
609C2×D4—24no—
610C2×D4—24no—
611C2×D4—21no—
612C2×D4—22no—
613C2×D4—22no—
614C2×D4—44no—
615C2×D4—44no—
616C2×D4C2×C22⋊D6114yes—
617C2×D4C23×D6112yes—
618C22×C4—21no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—24no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—24no—
627C22×C4—44no—
628C22×C4—44no—
629C22×C4—1224no—
630C22×C4—1224no—
631C22×C4—1221no—
632C22×C4—1221no—
633C22×C4—1221no—
634C22×C4—1221no—
635C22×C4—4882no—
636C22×C4—4882no—
637C22×C4C2×C22⋊D6112yes—
638C22×C4C2×C22⋊D6112yes—
639C22×C4C2×C22⋊D6111yescharacteristic
640C22×C4C2×C22⋊D6111yescharacteristic
641C22×C4C2×C22⋊D6111yescharacteristic
642C22×C4C2×C22⋊D6111yescharacteristic
643C22×C4C23×D6112yes—
644C22×C4C23×D6112yes—
645C22×C4C23×D6111yescharacteristic
646Q16—1228no—
647Q16—2444no—
648SD16—2444no—
649M16—2444no—
650C2×C8—612no—
651C2×C8—612no—
652C2×C8—612no—
653C2×C8—612no—
654C2×C8—1222no—
655C2×C8—1222no—
656C2×C8—1222no—
657C2×C8—1222no—
658C2×C8—2444no—
659C4⋊C4—24no—
660C4⋊C4—24no—
661C4⋊C4—21no—
662C4⋊C4—612no—
663C4⋊C4—612no—
664C4⋊C4—612no—
665C4⋊C4—1221no—
666C4⋊C4—1224no—
667C4⋊C4—1224no—
668C4⋊C4—1221no—
669C4⋊C4—1221no—
670C4⋊C4—1224no—
671C4⋊C4—1224no—
672C4⋊C4—1224no—
673C4⋊C4—1224no—
674C4⋊C4C2×C22⋊D6114yes—
675C4⋊C4C23×D6112yes—
676C22⋊C4—24no—
677C22⋊C4—24no—
678C22⋊C4—24no—
679C22⋊C4—24no—
680C22⋊C4—1224no—
681C22⋊C4—1224no—
682C22⋊C4C2×C22⋊D6114yes—
683C22⋊C4C2×C22⋊D6114yes—
684C42—24no—
685C42—1224no—
686C42C2×C22⋊D6112yes—
687C42C23×D6112yes—
688C23—22no—
689C23—22no—
690C23—22no—
691C23—22no—
692C23—22no—
693C23—22no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23#1451980714yes—
698C23C22×C22⋊D6112yes—
699C23C22×C22⋊D6112yes—
700C23C22×C22⋊D6111yescharacteristic
701Q8—22no—
702Q8—24no—
703Q8—22no—
704Q8—22no—
705Q8—48no—
706Q8—42no—
707Q8—1222no—
708Q8—1222no—
709Q8—4884no—
710Q8—2442no—
711Q8C2×#1175822414yes—
712D4—28no—
713D4—22no—
714D4—22no—
715D4—48no—
716D4—48no—
717D4—42no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—24no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—24no—
729C2×C4—24no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—48no—
733C2×C4—48no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—1222no—
737C2×C4—1222no—
738C2×C4—1222no—
739C2×C4—1222no—
740C2×C4—4884no—
741C2×C4—4884no—
742C2×C4—2442no—
743C2×C4—2442no—
744C2×C4—2442no—
745C2×C4—2442no—
746C2×C4C22×C22⋊D6112yes—
747C2×C4C22×C22⋊D6112yes—
748C2×C4C22×C22⋊D6112yes—
749C2×C4C22×C22⋊D6112yes—
750C2×C4C22×C22⋊D6111yescharacteristic
751C2×C4C2×#1175822412yes—
752C2×C4#1451982212yes—
753C2×C4C24×D6111yescharacteristic
754C8—1222no—
755C8—1222no—
756C8—1222no—
757C8—1222no—
758C22—28no—
759C22—22no—
760C22—22no—
761C22—22no—
762C22—22no—
763C22—22no—
764C22—44no—
765C22—42no—
766C22—42no—
767C22—42no—
768C22—84no—
769C22#1684040612yes—
770C22C2×#1451980714yes—
771C22C2×#1451980712yes—
772C22#1684057012yes—
773C22C23×C22⋊D6111yescharacteristic
774C4—22no—
775C4—22no—
776C4—24no—
777C4—22no—
778C4—22no—
779C4—42no—
780C4—42no—
781C4—2442no—
782C4—2442no—
783C4—2442no—
784C4—2442no—
785C4#1684040612yes—
786C4C22×#1175822411yescharacteristic
787C4C2×#1451982211yescharacteristic
788C2—24no—
789C2—42no—
790C2—82no—
791C2#2145793014yesdirect product factor
792C2C2×#1684040611yescharacteristic
793C2C22×#1451980711yescharacteristic
794C2C2×#1684057011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
Fitting, prime radicalC2×C61×#548C2
socleC23×C61C22×D4
hypercenterC2×#548D61
hypocenterC61C2×#3316
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. C2×#16840469C2semidirect
2. #21457930C2direct (N × H)
3. C2×#16840121C2semidirect
4. C2×#16840078C2semidirect
5. C2×#16840090C2semidirect
6. C2×#16840047C2semidirect
7. C2×#16840018C2semidirect
8. C2×#16839989C2semidirect
9. C2×#16839981C2semidirect
10. C2×#16839924C2semidirect
11. C2×#16839918C2semidirect
12. C2×#16839867C2semidirect
13. C2×#16839834C2semidirect
14. C2×#16839763C2semidirect
15. C22×#14519701C2semidirect
23. #16840469C22semidirect
34. #16840121C22semidirect
35. #16840090C22semidirect
36. #16840078C22semidirect
37. #16840047C22semidirect
38. #16840018C22semidirect
39. #16839989C22semidirect
40. #16839981C22semidirect
41. #16839924C22semidirect
42. #16839918C22semidirect
43. #16839867C22semidirect
44. #16839834C22semidirect
49. #16839763C22semidirect
56. C2×#14519701C22semidirect
410. C2×C61#3316semidirect
474. C61C2×#3316semidirect
791. C2#21457930direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404692
#214579302
C2×#168401212
C2×#168400782
C2×#168400902
C2×#168400472
C2×#168400182
C2×#168399892
C2×#168399812
C2×#168399242
C2×#168399182
C2×#168398672
C2×#168398342
C2×#168397632
C22×#145197012
C2×C61×#5482
C2×#331661