Finite Group Databasebeta

← #29718024

Subgroups — #29718024

Order 15616.

1528 conjugacy classes of subgroups.

The subgroup lattice has 918 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840010C211yesmaximal, characteristic, complemented
2C2×#16839907C211yesmaximal, characteristic, complemented
3C2×#16839907C211yesmaximal, characteristic, complemented
4C2×#16839763C211yesmaximal, characteristic, complemented
5#21449259C211yesmaximal, characteristic, complemented
6#21447062C211yesmaximal, characteristic, complemented
7#21447019C211yesmaximal, characteristic, complemented
8#21446902C211yesmaximal, characteristic, complemented
9#21446820C211yesmaximal, characteristic, complemented
10#21446167C211yesmaximal, characteristic, complemented
11#21446127C211yesmaximal, characteristic, complemented
12#21446117C211yesmaximal, characteristic, complemented
13#21446066C211yesmaximal, characteristic, complemented
14#21445759C211yesmaximal, characteristic, complemented
15C2×C61×#547C211yesmaximal, characteristic, complemented
16C22×#11758201C2211yescharacteristic
17C22×#11758201C2211yescharacteristic
18C22×#11758199C2211yescharacteristic
19C22×#11758194C2211yescharacteristic
20C2×#14519751C2211yescharacteristic
21C2×#14519751C2211yescharacteristic
22C2×#14519749—21no—
23C22×C4⋊Dic61C2211yescharacteristic
24#16840010—24no—
25#16839907—24no—
26#16839907—24no—
27C2×#14519710C2211yescharacteristic
28#16839763—24no—
29C2×#14519701C2211yescharacteristic
30C2×#14519701C2211yescharacteristic
31C2×#14519701C2211yescharacteristic
32C2×#14519701C2211yescharacteristic
33C2×#14519701C2211yescharacteristic
34C2×#14519701C2211yescharacteristic
35C2×#14519698C2211yescharacteristic
36C2×#14519698C2211yescharacteristic
37C2×#14519698C2211yescharacteristic
38C2×#14519697C2211yescharacteristic
39C2×C22⋊#92418C2211yescharacteristic
40C2×C22⋊#92418C2211yescharacteristic
41C2×C22⋊#92418C2211yescharacteristic
42#16839684—21no—
43#16839678—21no—
44#16839664C2211yescharacteristic
45#16839660C2211yescharacteristic
46#16839639—21no—
47#16839622C2211yescharacteristic
48#16839524C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839517C2211yescharacteristic
51#16839517C2211yescharacteristic
52C22×#41×C61C2211yescharacteristic
53C22×#41×C61C2211yescharacteristic
54C61×#547—24no—
55C61×#547—24no—
56C2×C4⋊Q8×C61C2211yescharacteristic
57C2×#123×C61—21no—
58C2×#123×C61—21no—
59C2×C22⋊Q8×C61C2211yescharacteristic
60C2×C22⋊Q8×C61C2211yescharacteristic
61C2×#121×C61—21no—
62C2×C4×D4×C61C2211yescharacteristic
63C2×C4×D4×C61C2211yescharacteristic
64C22×C4⋊C4×C61—21no—
65C22×D244C2311yescharacteristic
66C22×C22⋊D61—21no—
67C22×C22⋊D61—21no—
68C23×Dic61—21no—
69C2×#11758201—22no—
70C2×#11758201—22no—
71C2×#11758201—22no—
72C2×#11758201—41no—
73C2×#11758201—41no—
74C2×#11758201—41no—
75C2×#11758199—22no—
76C2×#11758199—22no—
77C2×#11758199—22no—
78C2×#11758194—22no—
79C2×#11758194—22no—
80C2×#11758194—41no—
81C22×#92418C2311yescharacteristic
82C22×#92418C2311yescharacteristic
83C22×#92418C2311yescharacteristic
84C22×#92418C2311yescharacteristic
85#14519751—22no—
86#14519751—22no—
87#14519751—22no—
88#14519751—41no—
89#14519749—44no—
90C2×C4⋊Dic61—22no—
91C2×C4⋊Dic61—21no—
92C2×C4⋊Dic61—41no—
93C2×C4⋊Dic61C2311yescharacteristic
94C2×C4⋊Dic61C2311yescharacteristic
95C2×C4⋊Dic61C2311yescharacteristic
96C2×#11758196—21no—
97C2×C22⋊Dic61—21no—
98C2×#11758198—21no—
99C2×#11758198—21no—
100C2×#11758198—21no—
101C2×#11758198—21no—
102#14519710—22no—
103#14519701—22no—
104#14519701—22no—
105#14519701—22no—
106#14519701—22no—
107#14519701—22no—
108#14519701—41no—
109#14519698—22no—
110#14519698—22no—
111#14519698D414yescomplemented
112#14519697—22no—
113C22⋊#92418—22no—
114C22⋊#92418—22no—
115C22⋊#92418—41no—
116#14519684—21no—
117#14519684—21no—
118C2×#41×C61—22no—
119C2×#41×C61—22no—
120C2×#41×C61—22no—
121C2×#41×C61—22no—
122C2×#41×C61—22no—
123C2×#41×C61—22no—
124C2×#41×C61—22no—
125C2×#41×C61—41no—
126C2×#41×C61—41no—
127C2×#41×C61—41no—
128C2×#41×C61—41no—
129C2×#41×C61D414yescomplemented
130C22×Q8×C61C2311yescharacteristic
131C22×Q8×C61C2311yescharacteristic
132C22×D4×C61—21no—
133C22×D4×C61—21no—
134C22×D4×C61D411yescharacteristic
135C22×D4×C61C2311yescharacteristic
136C23×C4×C61—21no—
137C23×C4×C61—21no—
138C23×C4×C61—21no—
139C23×C4×C61C2311yescharacteristic
140C23×C4×C61C2311yescharacteristic
141C4⋊Q8×C61—22no—
142C4⋊Q8×C61—22no—
143#123×C61—28no—
144#123×C61—28no—
145C22⋊Q8×C61—22no—
146C22⋊Q8×C61—22no—
147C22⋊Q8×C61—22no—
148C22⋊Q8×C61D414yescomplemented
149#121×C61—28no—
150C4×D4×C61—22no—
151C4×D4×C61—22no—
152C4×D4×C61—22no—
153C4×D4×C61—22no—
154C2×C4⋊C4×C61—28no—
155C2×C4⋊C4×C61—21no—
156C2×C4⋊C4×C61—21no—
157C2×C4⋊C4×C61—21no—
158C2×C4⋊C4×C61—21no—
159C2×C4⋊C4×C61D411yescharacteristic
160C2×C4⋊C4×C61C2311yescharacteristic
161C2×C22⋊C4×C61—21no—
162C2×C22⋊C4×C61—21no—
163C2×C22⋊C4×C61—21no—
164C2×C22⋊C4×C61D411yescharacteristic
165C2×C22⋊C4×C61D411yescharacteristic
166C2×C42×C61C2311yescharacteristic
167C24×C61—21no—
168C24×C61C2×D411yescharacteristic
169C24×C61C2×D411yescharacteristic
170C23×D61—21no—
171#41×C61—28no—
172#41×C61—44no—
173#41×C61—44no—
174#41×C61—44no—
175#41×C61—44no—
176#41×C61—44no—
177#41×C61—44no—
178#41×C61—44no—
179C2×Q8×C61—21no—
180C2×Q8×C61—21no—
181C2×Q8×C61—21no—
182C2×Q8×C61—21no—
183C2×Q8×C61—21no—
184C2×Q8×C61—21no—
185C2×Q8×C61—21no—
186C2×Q8×C61—21no—
187C2×Q8×C61—21no—
188C2×Q8×C61—21no—
189C2×Q8×C61C2×D412yes—
190C2×Q8×C61C2×D412yes—
191C2×D4×C61—24no—
192C2×D4×C61—22no—
193C2×D4×C61—24no—
194C2×D4×C61—22no—
195C2×D4×C61—21no—
196C2×D4×C61—21no—
197C2×D4×C61—21no—
198C2×D4×C61—41no—
199C2×D4×C61—42no—
200C2×D4×C61—42no—
201C2×D4×C61—42no—
202C2×D4×C61—42no—
203C2×D4×C61C2×D412yes—
204C2×D4×C61C2×D412yes—
205C2×D4×C61#4112yes—
206C22×C4×C61—21no—
207C22×C4×C61—21no—
208C22×C4×C61—21no—
209C22×C4×C61—21no—
210C22×C4×C61—24no—
211C22×C4×C61—24no—
212C22×C4×C61—21no—
213C22×C4×C61—21no—
214C22×C4×C61—21no—
215C22×C4×C61—24no—
216C22×C4×C61—21no—
217C22×C4×C61—21no—
218C22×C4×C61—21no—
219C22×C4×C61—21no—
220C22×C4×C61—21no—
221C22×C4×C61—21no—
222C22×C4×C61—42no—
223C22×C4×C61—42no—
224C22×C4×C61—42no—
225C22×C4×C61—42no—
226C22×C4×C61—42no—
227C22×C4×C61—42no—
228C22×C4×C61C2×D411yescharacteristic
229C22×C4×C61C2×D411yescharacteristic
230C22×C4×C61C2×D411yescharacteristic
231C22×C4×C61C2×D412yes—
232C22×C4×C61C2×D412yes—
233C22×C4×C61C2×D411yescharacteristic
234C22×C4×C61C2411yescharacteristic
235C2×C22⋊D61—42no—
236C2×C22⋊D61—42no—
237C2×C22⋊D61—42no—
238C2×C22⋊D61—42no—
239C2×C22⋊D61—42no—
240C2×C22⋊D61—81no—
241C22×Dic61—21no—
242C22×Dic61—21no—
243C22×Dic61—21no—
244C22×Dic61—42no—
245C22×Dic61—42no—
246C22×Dic61—81no—
247C2×D244—21no—
248C2×D244—21no—
249C2×D244—21no—
250C2×D244—21no—
251C2×D244—21no—
252C2×D244—21no—
253C4⋊C4×C61—24no—
254C4⋊C4×C61—24no—
255C4⋊C4×C61—24no—
256C4⋊C4×C61—22no—
257C4⋊C4×C61—24no—
258C4⋊C4×C61—21no—
259C4⋊C4×C61C2×D412yes—
260C22⋊C4×C61—24no—
261C22⋊C4×C61—24no—
262C22⋊C4×C61—24no—
263C22⋊C4×C61—22no—
264C22⋊C4×C61—22no—
265C42×C61—21no—
266C42×C61—21no—
267C22⋊Dic61—42no—
268#11758201—44no—
269#11758201—44no—
270#11758199—44no—
271#11758198—42no—
272#11758198—42no—
273#11758198—42no—
274#11758198—81no—
275C4⋊Dic61—21no—
276C4⋊Dic61—21no—
277C4⋊Dic61—21no—
278C4⋊Dic61—21no—
279C4⋊Dic61—21no—
280C4⋊Dic61—42no—
281C4⋊Dic61C2×D412yes—
282#11758196—42no—
283#11758194—44no—
284C2×#92418—21no—
285C2×#92418—21no—
286C2×#92418—21no—
287C2×#92418—21no—
288C2×#92418—21no—
289C2×#92418—21no—
290C2×#92418—21no—
291C2×#92418—21no—
292C2×#92418—21no—
293C2×#92418—21no—
294C2×#92418—21no—
295C2×#92418C2×D412yes—
296C23×C61—22no—
297C23×C61—21no—
298C23×C61—22no—
299C23×C61—21no—
300C23×C61—22no—
301C23×C61—21no—
302C23×C61—21no—
303C23×C61—21no—
304C23×C61—21no—
305C23×C61—21no—
306C23×C61—21no—
307C23×C61—21no—
308C23×C61—21no—
309C23×C61—21no—
310C23×C61—21no—
311C23×C61—21no—
312C23×C61—41no—
313C23×C61—41no—
314C23×C61—41no—
315C23×C61—41no—
316C23×C61#12012yes—
317C23×C61C22×D411yescharacteristic
318C22×D61—41no—
319C22×D61—41no—
320C22×D61—41no—
321C22×D61—41no—
322C22×D61—41no—
323C22×D61—41no—
324C22×D61—41no—
325Q8×C61—22no—
326Q8×C61—22no—
327Q8×C61—22no—
328Q8×C61—22no—
329Q8×C61—41no—
330Q8×C61—41no—
331Q8×C61—41no—
332Q8×C61—41no—
333D4×C61—22no—
334D4×C61—22no—
335D4×C61—22no—
336D4×C61—44no—
337D4×C61—48no—
338D4×C61—48no—
339D4×C61#12114yescomplemented
340C2×C4×C61—21no—
341C2×C4×C61—21no—
342C2×C4×C61—21no—
343C2×C4×C61—21no—
344C2×C4×C61—22no—
345C2×C4×C61—22no—
346C2×C4×C61—22no—
347C2×C4×C61—22no—
348C2×C4×C61—21no—
349C2×C4×C61—22no—
350C2×C4×C61—21no—
351C2×C4×C61—22no—
352C2×C4×C61—22no—
353C2×C4×C61—21no—
354C2×C4×C61—21no—
355C2×C4×C61—21no—
356C2×C4×C61—21no—
357C2×C4×C61—48no—
358C2×C4×C61—48no—
359C2×C4×C61—48no—
360C2×C4×C61—41no—
361C2×C4×C61—41no—
362C2×C4×C61—41no—
363C2×C4×C61—41no—
364C2×C4×C61—41no—
365C2×C4×C61—41no—
366C2×C4×C61—41no—
367C2×C4×C61—41no—
368C2×C4×C61—41no—
369C2×C4×C61—41no—
370C2×C4×C61#12012yes—
371C2×C4×C61AGL(1,ℤ/8)12yes—
372C2×C4×C61C22×D411yescharacteristic
373C2×C4×C61C22×D411yescharacteristic
374C2×C4×C61C22×D411yescharacteristic
375C2×C4×C61C2×#4111yescharacteristic
376C2×C4×C61H(5,𝔽2)11yescharacteristic
377C2×C4×C61H(5,𝔽2)11yescharacteristic
378C22⋊D61—84no—
379C22⋊D61—84no—
380C2×Dic61—22no—
381C2×Dic61—41no—
382C2×Dic61—41no—
383C2×Dic61—41no—
384C2×Dic61—41no—
385C2×Dic61—41no—
386C2×Dic61—41no—
387C2×Dic61—41no—
388C2×Dic61—41no—
389C2×Dic61—84no—
390D244—41no—
391D244—41no—
392D244—41no—
393D244—41no—
394#92418—22no—
395#92418—41no—
396#92418—41no—
397#92418—41no—
398#24454—611nomaximal, Sylow
399C22×C61—22no—
400C22×C61—24no—
401C22×C61—22no—
402C22×C61—22no—
403C22×C61—41no—
404C22×C61—42no—
405C22×C61—42no—
406C22×C61—42no—
407C22×C61—41no—
408C22×C61—42no—
409C22×C61—41no—
410C22×C61—42no—
411C22×C61—41no—
412C22×C61—42no—
413C22×C61—41no—
414C22×C61—41no—
415C22×C61—41no—
416C22×C61—41no—
417C22×C61—41no—
418C22×C61—41no—
419C22×C61—41no—
420C22×C61C2×#12011yescharacteristic
421C22×C61D4211yescharacteristic
422C22×C61#54611yescharacteristic
423C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
424C22×C61#57511yescharacteristic
425C22×C61#57711yescharacteristic
426C22×C61#57811yescharacteristic
427C2×D61—81no—
428C2×D61—81no—
429C2×D61—81no—
430C2×D61—81no—
431C2×D61—81no—
432C2×D61—81no—
433C2×D61—81no—
434C4×C61—22no—
435C4×C61—22no—
436C4×C61—41no—
437C4×C61—42no—
438C4×C61—42no—
439C4×C61—42no—
440C4×C61—41no—
441C4×C61C2×#12111yescharacteristic
442C4×C61#53411yescharacteristic
443C4×C61D4211yescharacteristic
444C4×C61#54611yescharacteristic
445Dic61—42no—
446Dic61—81no—
447Dic61—81no—
448C2×#547D6111yescharacteristic, complemented
449C2×#468—611no—
450C2×#449—611no—
451C2×#449—611no—
452C2×#417—611no—
453#2416—611no—
454#2043—611no—
455#2036—611no—
456#2013—611no—
457#2000—611no—
458#1879—611no—
459#1872—611no—
460#1870—611no—
461#1862—611no—
462#1788—611no—
463C2×C61—42no—
464C2×C61—44no—
465C2×C61—81no—
466C2×C61#241011yescharacteristic
467C2×C61#300611yescharacteristic
468C2×C61#301311yescharacteristic
469C2×C61#326911yescharacteristic
470C2×C61#327211yescharacteristic
471C2×C61#330711yescharacteristic
472C2×C61#333011yescharacteristic
473D61—161no—
474C22×#41C2×D6111yescharacteristic
475C22×#41C2×D6111yescharacteristic
476C22×SD16—611no—
477C22×SD16—611no—
478C22×D8—611no—
479C22×M16—611no—
480#547—24no—
481#547—24no—
482C2×C4⋊Q8C2×D6111yescharacteristic
483C2×#123—21no—
484C2×#123—21no—
485C2×C22⋊Q8C2×D6111yescharacteristic
486C2×C22⋊Q8C2×D6111yescharacteristic
487C2×#121—21no—
488C2×#121—611no—
489C2×#121—611no—
490C2×#121—1221no—
491C2×C4×D4C2×D6111yescharacteristic
492C2×C4×D4C2×D6111yescharacteristic
493C22×C4⋊C4—21no—
494C22×C4⋊C4—611no—
495#468—1224no—
496#449—1224no—
497#449—1224no—
498C2×#107—611no—
499#417—1224no—
500C2×#103—611no—
501C2×#103—611no—
502C2×#103—611no—
503C2×#103—611no—
504C2×#103—611no—
505C2×#103—611no—
506C2×#102—611no—
507C2×#102—611no—
508C2×#102—611no—
509C2×#102—611no—
510C2×C22⋊C8—611no—
511C2×C22⋊C8—611no—
512C2×C22⋊C8—611no—
513#396—1221no—
514#394—1221no—
515#390—611no—
516#389—611no—
517#386—1221no—
518#380—611no—
519#340—611no—
520#340—611no—
521#336—611no—
522#336—611no—
523C61#2445411yescharacteristic, complemented, Sylow
524C2×#41—22no—
525C2×#41—22no—
526C2×#41—22no—
527C2×#41—22no—
528C2×#41—22no—
529C2×#41—22no—
530C2×#41—22no—
531C2×#41—41no—
532C2×#41—41no—
533C2×#41—41no—
534C2×#41—41no—
535C2×#41C22⋊D6114yescomplemented
536C22×Q8C22×D6111yescharacteristic
537C22×Q8C22×D6111yescharacteristic
538C22×D4—21no—
539C22×D4—21no—
540C22×D4—611no—
541C22×D4—1221no—
542C22×D4—1221no—
543C22×D4C22⋊D6111yescharacteristic
544C22×D4C22×D6111yescharacteristic
545C23×C4—21no—
546C23×C4—21no—
547C23×C4—21no—
548C23×C4—1221no—
549C23×C4C22×D6111yescharacteristic
550C23×C4C22×D6111yescharacteristic
551C2×SD16—1222no—
552C2×SD16—1222no—
553C2×SD16—1222no—
554C2×SD16—2441no—
555C2×SD16—2441no—
556C2×SD16—2441no—
557C2×D8—1222no—
558C2×D8—1222no—
559C2×D8—1222no—
560C2×M16—1222no—
561C2×M16—1222no—
562C2×M16—2441no—
563C22×C8—611no—
564C22×C8—611no—
565C22×C8—611no—
566C22×C8—611no—
567C4⋊Q8—22no—
568C4⋊Q8—22no—
569#123—28no—
570#123—28no—
571C22⋊Q8—22no—
572C22⋊Q8—22no—
573C22⋊Q8—22no—
574C22⋊Q8C22⋊D6114yescomplemented
575#121—28no—
576#121—1222no—
577#121—1222no—
578#121—1222no—
579#121—2441no—
580#121—2444no—
581C4×D4—22no—
582C4×D4—22no—
583C4×D4—22no—
584C4×D4—22no—
585C2×C4⋊C4—28no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4—611no—
591C2×C4⋊C4—611no—
592C2×C4⋊C4—611no—
593C2×C4⋊C4—1222no—
594C2×C4⋊C4—1221no—
595C2×C4⋊C4—1221no—
596C2×C4⋊C4—2441no—
597C2×C4⋊C4C22⋊D6111yescharacteristic
598C2×C4⋊C4C22×D6111yescharacteristic
599C2×C22⋊C4—21no—
600C2×C22⋊C4—21no—
601C2×C22⋊C4—21no—
602C2×C22⋊C4—1221no—
603C2×C22⋊C4—1221no—
604C2×C22⋊C4—1221no—
605C2×C22⋊C4—1221no—
606C2×C22⋊C4—1221no—
607C2×C22⋊C4C22⋊D6111yescharacteristic
608C2×C22⋊C4C22⋊D6111yescharacteristic
609C2×C42C22×D6111yescharacteristic
610#107—1222no—
611#103—1222no—
612#103—1222no—
613#103—1222no—
614#103—1222no—
615#103—1222no—
616#103—2441no—
617#102—614no—
618#102—1222no—
619#102—1222no—
620#102—1222no—
621C22⋊C8—1222no—
622C22⋊C8—1222no—
623C22⋊C8—2441no—
624#95—1221no—
625#95—1221no—
626C24—21no—
627C24—1221no—
628C24C2×C22⋊D6111yescharacteristic
629C24C2×C22⋊D6111yescharacteristic
630#41—28no—
631#41—44no—
632#41—44no—
633#41—44no—
634#41—44no—
635#41—44no—
636#41—44no—
637#41—44no—
638C2×Q8—21no—
639C2×Q8—21no—
640C2×Q8—21no—
641C2×Q8—21no—
642C2×Q8—21no—
643C2×Q8—21no—
644C2×Q8—21no—
645C2×Q8—21no—
646C2×Q8—21no—
647C2×Q8—21no—
648C2×Q8C2×C22⋊D6112yes—
649C2×Q8C2×C22⋊D6112yes—
650C2×D4—24no—
651C2×D4—22no—
652C2×D4—24no—
653C2×D4—21no—
654C2×D4—21no—
655C2×D4—21no—
656C2×D4—22no—
657C2×D4—41no—
658C2×D4—42no—
659C2×D4—42no—
660C2×D4—42no—
661C2×D4—42no—
662C2×D4—1221no—
663C2×D4—1221no—
664C2×D4—1221no—
665C2×D4—1221no—
666C2×D4—1221no—
667C2×D4—1221no—
668C2×D4—4881no—
669C2×D4—2442no—
670C2×D4—2442no—
671C2×D4—2442no—
672C2×D4—2442no—
673C2×D4—2442no—
674C2×D4D4×D6112yes—
675C2×D4#1175822412yes—
676C2×D4C2×C22⋊D6112yes—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—24no—
682C22×C4—24no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—24no—
693C22×C4—42no—
694C22×C4—42no—
695C22×C4—42no—
696C22×C4—42no—
697C22×C4—42no—
698C22×C4—42no—
699C22×C4—1221no—
700C22×C4—1221no—
701C22×C4—1221no—
702C22×C4—4881no—
703C22×C4—2442no—
704C22×C4—2442no—
705C22×C4C2×C22⋊D6111yescharacteristic
706C22×C4C2×C22⋊D6111yescharacteristic
707C22×C4C2×C22⋊D6112yes—
708C22×C4C2×C22⋊D6112yes—
709C22×C4C2×C22⋊D6111yescharacteristic
710C22×C4C2×C22⋊D6111yescharacteristic
711C22×C4C23×D6111yescharacteristic
712SD16—2444no—
713SD16—2444no—
714D8—2444no—
715M16—2444no—
716C2×C8—612no—
717C2×C8—1221no—
718C2×C8—1221no—
719C2×C8—1221no—
720C2×C8—1221no—
721C2×C8—1221no—
722C2×C8—1221no—
723C2×C8—1221no—
724C2×C8—1221no—
725C2×C8—1221no—
726C2×C8—1221no—
727C2×C8—1221no—
728C4⋊C4—24no—
729C4⋊C4—24no—
730C4⋊C4—24no—
731C4⋊C4—21no—
732C4⋊C4—22no—
733C4⋊C4—24no—
734C4⋊C4—612no—
735C4⋊C4—1221no—
736C4⋊C4—1221no—
737C4⋊C4—1221no—
738C4⋊C4—1221no—
739C4⋊C4—1221no—
740C4⋊C4—2442no—
741C4⋊C4—2442no—
742C4⋊C4C2×C22⋊D6112yes—
743C22⋊C4—24no—
744C22⋊C4—24no—
745C22⋊C4—24no—
746C22⋊C4—22no—
747C22⋊C4—22no—
748C22⋊C4—4881no—
749C22⋊C4—2442no—
750C22⋊C4—2442no—
751C22⋊C4—2442no—
752C22⋊C4—2442no—
753C42—21no—
754C42—21no—
755C23—22no—
756C23—21no—
757C23—21no—
758C23—21no—
759C23—21no—
760C23—21no—
761C23—22no—
762C23—21no—
763C23—22no—
764C23—21no—
765C23—21no—
766C23—21no—
767C23—21no—
768C23—21no—
769C23—21no—
770C23—21no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—2441no—
776C23—2441no—
777C23—2441no—
778C23—2441no—
779C23—2441no—
780C23—2441no—
781C23—2441no—
782C23#1451974612yes—
783C23C22×C22⋊D6111yescharacteristic
784Q8—22no—
785Q8—22no—
786Q8—22no—
787Q8—22no—
788Q8—41no—
789Q8—41no—
790Q8—41no—
791Q8—41no—
792D4—22no—
793D4—22no—
794D4—22no—
795D4—44no—
796D4—48no—
797D4—48no—
798D4—4884no—
799D4—4884no—
800D4—2441no—
801D4—2441no—
802D4—2441no—
803D4—2441no—
804D4#1451974914yescomplemented
805C2×C4—21no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—21no—
814C2×C4—22no—
815C2×C4—21no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—21no—
819C2×C4—21no—
820C2×C4—21no—
821C2×C4—21no—
822C2×C4—48no—
823C2×C4—48no—
824C2×C4—48no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—1222no—
836C2×C4—4884no—
837C2×C4—2441no—
838C2×C4—2441no—
839C2×C4—2441no—
840C2×C4—2441no—
841C2×C4—2441no—
842C2×C4—2441no—
843C2×C4—2441no—
844C2×C4—2441no—
845C2×C4#1451974612yes—
846C2×C4#1451980212yes—
847C2×C4C2×D4×D6111yescharacteristic
848C2×C4C22×C22⋊D6111yescharacteristic
849C2×C4C22×C22⋊D6111yescharacteristic
850C2×C4C2×#1175822411yescharacteristic
851C2×C4#1451982211yescharacteristic
852C2×C4#1451982211yescharacteristic
853C8—1222no—
854C8—2441no—
855C8—2441no—
856C8—2441no—
857C22—22no—
858C22—22no—
859C22—22no—
860C22—24no—
861C22—41no—
862C22—42no—
863C22—42no—
864C22—41no—
865C22—42no—
866C22—41no—
867C22—42no—
868C22—41no—
869C22—42no—
870C22—42no—
871C22—41no—
872C22—41no—
873C22—41no—
874C22—41no—
875C22—41no—
876C22—41no—
877C22—41no—
878C22—4881no—
879C22—4881no—
880C22—4881no—
881C22—4881no—
882C22—4881no—
883C22—4881no—
884C22—4881no—
885C22C2×#1451974611yescharacteristic
886C22D4×C22⋊D6111yescharacteristic
887C22#1684040611yescharacteristic
888C22C2×#1451980211yescharacteristic
889C22#1684056011yescharacteristic
890C22#1684057011yescharacteristic
891C22#1684057711yescharacteristic
892C4—22no—
893C4—22no—
894C4—41no—
895C4—42no—
896C4—41no—
897C4—42no—
898C4—42no—
899C4—4881no—
900C4—4881no—
901C4—2442no—
902C4C2×#1451974911yescharacteristic
903C4#1684032111yescharacteristic
904C4D4×C22⋊D6111yescharacteristic
905C4#1684040611yescharacteristic
906C2—42no—
907C2—44no—
908C2—81no—
909C2—9761no—
910C2#2144919311yescharacteristic
911C2#2145507111yescharacteristic
912C2#2145513411yescharacteristic
913C2#2145737011yescharacteristic
914C2#2145741911yescharacteristic
915C2#2145779511yescharacteristic
916C2#2145812411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#547C2
socleC23×C61C22×D4
hypercenterC2×#547D61
hypocenterC61#24454
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#547

Complements

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

NH ≅ G/Ntype
1. C2×#16840010C2semidirect
2. C2×#16839907C2semidirect
3. C2×#16839907C2semidirect
4. C2×#16839763C2semidirect
5. #21449259C2semidirect
6. #21447062C2semidirect
7. #21447019C2semidirect
8. #21446902C2semidirect
9. #21446820C2semidirect
10. #21446167C2semidirect
11. #21446127C2semidirect
12. #21446117C2semidirect
13. #21446066C2semidirect
14. #21445759C2semidirect
15. C2×C61×#547C2semidirect
111. #14519698D4semidirect
129. C2×#41×C61D4semidirect
148. C22⋊Q8×C61D4semidirect
339. D4×C61#121semidirect
448. C2×#547D61semidirect
523. C61#24454semidirect
535. C2×#41C22⋊D61semidirect
574. C22⋊Q8C22⋊D61semidirect
804. D4#14519749semidirect

Maximal subgroups

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

subgroupindex
C2×#168400102
C2×#168399072
C2×#168397632
#214492592
#214470622
#214470192
#214469022
#214468202
#214461672
#214461272
#214461172
#214460662
#214457592
C2×C61×#5472
#2445461