Finite Group Databasebeta

← #29717799

Subgroups — #29717799

Order 15616.

1534 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×#16839996C211yesmaximal, characteristic, complemented
2C2×#16839907C211yesmaximal, characteristic, complemented
3C2×#16839901C211yesmaximal, characteristic, complemented
4C22×#14519701C211yesmaximal, characteristic, complemented
5#21449259C211yesmaximal, characteristic, complemented
6#21447055C211yesmaximal, characteristic, complemented
7#21447019C211yesmaximal, characteristic, complemented
8#21446896C211yesmaximal, characteristic, complemented
9#21446820C211yesmaximal, characteristic, complemented
10#21446174C211yesmaximal, characteristic, complemented
11#21446137C211yesmaximal, characteristic, complemented
12#21446112C211yesmaximal, characteristic, complemented
13#21446073C211yesmaximal, characteristic, complemented
14#21445759C211yesmaximal, characteristic, complemented
15C2×C61×#548C211yesmaximal, characteristic, complemented
16C22×#11758201C2211yescharacteristic
17C22×#11758201C2211yescharacteristic
18C22×#11758199C2211yescharacteristic
19C23×#92418C2211yescharacteristic
20C2×#14519751C2211yescharacteristic
21C2×#14519751C2211yescharacteristic
22C2×#14519749—21no—
23C22×C4⋊Dic61C2211yescharacteristic
24#16839996—24no—
25#16839907—24no—
26#16839901—24no—
27C2×#14519710C2211yescharacteristic
28C2×#14519701—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
53C23×Q8×C61C2211yescharacteristic
54C61×#548—24no—
55C61×#548—24no—
56C2×#124×C61—21no—
57C2×#124×C61C2211yescharacteristic
58C2×C22⋊Q8×C61—21no—
59C2×C22⋊Q8×C61C2211yescharacteristic
60C2×#121×C61—21no—
61C2×#121×C61C2211yescharacteristic
62C2×C4×Q8×C61C2211yescharacteristic
63C2×C4×D4×C61—21no—
64C2×C4×D4×C61C2211yescharacteristic
65C22×D244C2311yescharacteristic
66C22×C22⋊D61—21no—
67C22×C22⋊D61—21no—
68C23×Dic61—21no—
69C2×#11758201—22no—
70C2×#11758201—22no—
71C2×#11758201—22no—
72C2×#11758201—22no—
73C2×#11758201—41no—
74C2×#11758201—41no—
75C2×#11758199—22no—
76C2×#11758199—22no—
77C2×#11758199—41no—
78C22×#92418—22no—
79C22×#92418—22no—
80C22×#92418—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#14519701D414yescomplemented
109#14519698—22no—
110#14519698—22no—
111#14519698—41no—
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—41no—
123C2×#41×C61—41no—
124C22×Q8×C61—22no—
125C22×Q8×C61—21no—
126C22×Q8×C61—22no—
127C22×Q8×C61—22no—
128C22×Q8×C61—41no—
129C22×Q8×C61—41no—
130C22×Q8×C61D414yescomplemented
131C22×Q8×C61C2311yescharacteristic
132C22×Q8×C61C2311yescharacteristic
133C22×D4×C61—21no—
134C22×D4×C61—21no—
135C22×D4×C61D411yescharacteristic
136C22×D4×C61C2311yescharacteristic
137C23×C4×C61—21no—
138C23×C4×C61—21no—
139C23×C4×C61C2311yescharacteristic
140C23×C4×C61C2311yescharacteristic
141#124×C61—28no—
142#124×C61—22no—
143#124×C61—22no—
144C22⋊Q8×C61—28no—
145C22⋊Q8×C61—22no—
146C22⋊Q8×C61—22no—
147#121×C61—28no—
148#121×C61—22no—
149#121×C61D414yescomplemented
150C4×Q8×C61—22no—
151C4×Q8×C61—22no—
152C4×D4×C61—28no—
153C4×D4×C61—22no—
154C4×D4×C61—22no—
155C2×C4⋊C4×C61—21no—
156C2×C4⋊C4×C61—21no—
157C2×C4⋊C4×C61D411yescharacteristic
158C2×C4⋊C4×C61C2311yescharacteristic
159C2×C22⋊C4×C61—21no—
160C2×C22⋊C4×C61—21no—
161C2×C22⋊C4×C61—21no—
162C2×C22⋊C4×C61—21no—
163C2×C22⋊C4×C61D411yescharacteristic
164C2×C22⋊C4×C61D411yescharacteristic
165C2×C42×C61—21no—
166C2×C42×C61C2311yescharacteristic
167C24×C61—21no—
168C24×C61C2×D411yescharacteristic
169C24×C61C2×D411yescharacteristic
170C23×D61—21no—
171#41×C61—44no—
172#41×C61—44no—
173#41×C61—44no—
174#41×C61—44no—
175C2×Q8×C61—24no—
176C2×Q8×C61—21no—
177C2×Q8×C61—21no—
178C2×Q8×C61—21no—
179C2×Q8×C61—21no—
180C2×Q8×C61—28no—
181C2×Q8×C61—21no—
182C2×Q8×C61—21no—
183C2×Q8×C61—21no—
184C2×Q8×C61—21no—
185C2×Q8×C61—42no—
186C2×Q8×C61—42no—
187C2×Q8×C61—44no—
188C2×Q8×C61—44no—
189C2×Q8×C61—44no—
190C2×Q8×C61C2×D412yes—
191C2×Q8×C61C2×D412yes—
192C2×Q8×C61C2×D412yes—
193C2×Q8×C61#4112yes—
194C2×D4×C61—24no—
195C2×D4×C61—22no—
196C2×D4×C61—24no—
197C2×D4×C61—22no—
198C2×D4×C61—22no—
199C2×D4×C61—21no—
200C2×D4×C61—21no—
201C2×D4×C61—21no—
202C2×D4×C61—21no—
203C2×D4×C61—21no—
204C2×D4×C61—42no—
205C2×D4×C61—42no—
206C2×D4×C61—42no—
207C2×D4×C61—42no—
208C2×D4×C61C2×D412yes—
209C22×C4×C61—21no—
210C22×C4×C61—21no—
211C22×C4×C61—21no—
212C22×C4×C61—21no—
213C22×C4×C61—21no—
214C22×C4×C61—24no—
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—21no—
223C22×C4×C61—21no—
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×D411yescharacteristic
232C22×C4×C61C2×D412yes—
233C22×C4×C61C2×D412yes—
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—22no—
256C4⋊C4×C61—21no—
257C4⋊C4×C61C2×D412yes—
258C22⋊C4×C61—24no—
259C22⋊C4×C61—24no—
260C22⋊C4×C61—24no—
261C22⋊C4×C61—22no—
262C22⋊C4×C61—24no—
263C22⋊C4×C61—22no—
264C42×C61—24no—
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—
283C2×#92418—21no—
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—44no—
295C2×#92418C2×D412yes—
296C23×C61—21no—
297C23×C61—21no—
298C23×C61—21no—
299C23×C61—21no—
300C23×C61—21no—
301C23×C61—22no—
302C23×C61—21no—
303C23×C61—21no—
304C23×C61—21no—
305C23×C61—21no—
306C23×C61—21no—
307C23×C61—21no—
308C23×C61—41no—
309C23×C61—41no—
310C23×C61—41no—
311C23×C61—41no—
312C23×C61—41no—
313C23×C61—41no—
314C23×C61#12012yes—
315C23×C61#13512yes—
316C23×C61AGL(1,ℤ/8)12yes—
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—22no—
330Q8×C61—48no—
331Q8×C61—41no—
332Q8×C61—41no—
333Q8×C61#12114yescomplemented
334D4×C61—22no—
335D4×C61—22no—
336D4×C61—48no—
337D4×C61—44no—
338D4×C61—48no—
339D4×C61—41no—
340D4×C61—41no—
341C2×C4×C61—22no—
342C2×C4×C61—21no—
343C2×C4×C61—22no—
344C2×C4×C61—21no—
345C2×C4×C61—22no—
346C2×C4×C61—22no—
347C2×C4×C61—22no—
348C2×C4×C61—22no—
349C2×C4×C61—22no—
350C2×C4×C61—21no—
351C2×C4×C61—21no—
352C2×C4×C61—22no—
353C2×C4×C61—22no—
354C2×C4×C61—21no—
355C2×C4×C61—21no—
356C2×C4×C61—21no—
357C2×C4×C61—21no—
358C2×C4×C61—21no—
359C2×C4×C61—21no—
360C2×C4×C61—21no—
361C2×C4×C61—48no—
362C2×C4×C61—48no—
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—41no—
371C2×C4×C61#12012yes—
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#24439—611nomaximal, Sylow
399C22×C61—22no—
400C22×C61—22no—
401C22×C61—22no—
402C22×C61—22no—
403C22×C61—22no—
404C22×C61—22no—
405C22×C61—42no—
406C22×C61—41no—
407C22×C61—41no—
408C22×C61—42no—
409C22×C61—41no—
410C22×C61—41no—
411C22×C61—42no—
412C22×C61—41no—
413C22×C61—41no—
414C22×C61—41no—
415C22×C61—81no—
416C22×C61—81no—
417C22×C61—81no—
418C22×C61—81no—
419C22×C61#44914yescomplemented
420C22×C61C2×#12011yescharacteristic
421C22×C61D4211yescharacteristic
422C22×C61#54611yescharacteristic
423C22×C61C2×#13511yescharacteristic
424C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
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—24no—
436C4×C61—41no—
437C4×C61—42no—
438C4×C61—41no—
439C4×C61—42no—
440C4×C61—41no—
441C4×C61C2×#12111yescharacteristic
442C4×C61#53411yescharacteristic
443C4×C61D4211yescharacteristic
444C4×C61#54611yescharacteristic
445Dic61—42no—
446Dic61—81no—
447Dic61—81no—
448C2×#548D6111yescharacteristic, complemented
449C2×#466—611no—
450C2×#449—611no—
451C2×#448—611no—
452C22×#103—611no—
453#2416—611no—
454#2042—611no—
455#2036—611no—
456#2012—611no—
457#2000—611no—
458#1880—611no—
459#1874—611no—
460#1869—611no—
461#1863—611no—
462#1788—611no—
463C2×C61—24no—
464C2×C61—81no—
465C2×C61—82no—
466C2×C61#241011yescharacteristic
467C2×C61C2×#44911yescharacteristic
468C2×C61#301311yescharacteristic
469C2×C61#326511yescharacteristic
470C2×C61#328511yescharacteristic
471C2×C61#330111yescharacteristic
472C2×C61#330811yescharacteristic
473D61—161no—
474C22×#41C2×D6111yescharacteristic
475C23×Q8C2×D6111yescharacteristic
476C22×SD16—611no—
477C22×SD16—611no—
478C22×D8—611no—
479C23×C8—611no—
480#548—24no—
481#548—24no—
482C2×#124—21no—
483C2×#124C2×D6111yescharacteristic
484C2×C22⋊Q8—21no—
485C2×C22⋊Q8C2×D6111yescharacteristic
486C2×#121—21no—
487C2×#121—611no—
488C2×#121—611no—
489C2×#121—1221no—
490C2×#121C2×D6111yescharacteristic
491C2×C4×Q8C2×D6111yescharacteristic
492C2×C4×D4—21no—
493C2×C4×D4C2×D6111yescharacteristic
494C22×C4⋊C4—611no—
495#466—1224no—
496#449—1224no—
497#448—1224no—
498C2×#107—611no—
499C2×#103—611no—
500C2×#103—611no—
501C2×#103—611no—
502C2×#103—611no—
503C2×#103—611no—
504C2×#103—611no—
505C2×#103—1224no—
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#2443911yescharacteristic, complemented, Sylow
524C2×#41—22no—
525C2×#41—22no—
526C2×#41—22no—
527C2×#41—22no—
528C2×#41—41no—
529C2×#41—41no—
530C22×Q8—21no—
531C22×Q8—22no—
532C22×Q8—22no—
533C22×Q8—22no—
534C22×Q8—41no—
535C22×Q8—41no—
536C22×Q8C22⋊D6114yescomplemented
537C22×Q8C22×D6111yescharacteristic
538C22×Q8C22×D6111yescharacteristic
539C22×D4—21no—
540C22×D4—21no—
541C22×D4—611no—
542C22×D4—1221no—
543C22×D4—1221no—
544C22×D4C22⋊D6111yescharacteristic
545C22×D4C22×D6111yescharacteristic
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—1222no—
555C2×SD16—2441no—
556C2×SD16—2441no—
557C2×D8—1222no—
558C2×D8—1222no—
559C2×D8—2441no—
560C22×C8—611no—
561C22×C8—611no—
562C22×C8—611no—
563C22×C8—611no—
564C22×C8—1222no—
565C22×C8—1222no—
566C22×C8—2441no—
567#124—28no—
568#124—22no—
569#124—22no—
570C22⋊Q8—28no—
571C22⋊Q8—22no—
572C22⋊Q8—22no—
573#121—28no—
574#121—22no—
575#121—1222no—
576#121—1222no—
577#121—1222no—
578#121—2441no—
579#121—2444no—
580#121C22⋊D6114yescomplemented
581C4×Q8—22no—
582C4×Q8—22no—
583C4×D4—28no—
584C4×D4—22no—
585C4×D4—22no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4—611no—
589C2×C4⋊C4—611no—
590C2×C4⋊C4—611no—
591C2×C4⋊C4—1222no—
592C2×C4⋊C4—1221no—
593C2×C4⋊C4—1221no—
594C2×C4⋊C4—2441no—
595C2×C4⋊C4C22⋊D6111yescharacteristic
596C2×C4⋊C4C22×D6111yescharacteristic
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—21no—
600C2×C22⋊C4—21no—
601C2×C22⋊C4—1221no—
602C2×C22⋊C4—1221no—
603C2×C22⋊C4—1221no—
604C2×C22⋊C4—1221no—
605C2×C22⋊C4—1221no—
606C2×C22⋊C4C22⋊D6111yescharacteristic
607C2×C22⋊C4C22⋊D6111yescharacteristic
608C2×C42—21no—
609C2×C42C22×D6111yescharacteristic
610#107—1222no—
611#103—614no—
612#103—1222no—
613#103—1222no—
614#103—1222no—
615#103—1222no—
616#103—1222no—
617#102—1222no—
618#102—1222no—
619#102—1222no—
620#102—2441no—
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—44no—
631#41—44no—
632#41—44no—
633#41—44no—
634C2×Q8—21no—
635C2×Q8—21no—
636C2×Q8—21no—
637C2×Q8—21no—
638C2×Q8—24no—
639C2×Q8—28no—
640C2×Q8—21no—
641C2×Q8—21no—
642C2×Q8—21no—
643C2×Q8—21no—
644C2×Q8—42no—
645C2×Q8—42no—
646C2×Q8—44no—
647C2×Q8—44no—
648C2×Q8—44no—
649C2×Q8D4×D6112yes—
650C2×Q8#1175822412yes—
651C2×Q8C2×C22⋊D6112yes—
652C2×Q8C2×C22⋊D6112yes—
653C2×D4—24no—
654C2×D4—22no—
655C2×D4—24no—
656C2×D4—22no—
657C2×D4—22no—
658C2×D4—21no—
659C2×D4—21no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—42no—
664C2×D4—42no—
665C2×D4—42no—
666C2×D4—42no—
667C2×D4—1221no—
668C2×D4—1221no—
669C2×D4—1221no—
670C2×D4—1221no—
671C2×D4—1221no—
672C2×D4—1221no—
673C2×D4—4881no—
674C2×D4—2442no—
675C2×D4—2442no—
676C2×D4—2442no—
677C2×D4—2442no—
678C2×D4—2442no—
679C2×D4C2×C22⋊D6112yes—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—24no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—24no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
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⋊D6111yescharacteristic
708C22×C4C2×C22⋊D6112yes—
709C22×C4C2×C22⋊D6112yes—
710C22×C4C2×C22⋊D6111yescharacteristic
711C22×C4C23×D6111yescharacteristic
712SD16—2444no—
713SD16—2444no—
714D8—2444no—
715C2×C8—612no—
716C2×C8—1221no—
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—2444no—
728C4⋊C4—24no—
729C4⋊C4—24no—
730C4⋊C4—21no—
731C4⋊C4—22no—
732C4⋊C4—612no—
733C4⋊C4—1221no—
734C4⋊C4—1221no—
735C4⋊C4—1221no—
736C4⋊C4—1221no—
737C4⋊C4—1221no—
738C4⋊C4—2442no—
739C4⋊C4—2442no—
740C4⋊C4C2×C22⋊D6112yes—
741C22⋊C4—24no—
742C22⋊C4—24no—
743C22⋊C4—24no—
744C22⋊C4—22no—
745C22⋊C4—24no—
746C22⋊C4—22no—
747C22⋊C4—4881no—
748C22⋊C4—2442no—
749C22⋊C4—2442no—
750C22⋊C4—2442no—
751C22⋊C4—2442no—
752C42—24no—
753C42—21no—
754C42—21no—
755C23—21no—
756C23—21no—
757C23—21no—
758C23—21no—
759C23—21no—
760C23—22no—
761C23—21no—
762C23—21no—
763C23—21no—
764C23—21no—
765C23—21no—
766C23—21no—
767C23—41no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—2441no—
774C23—2441no—
775C23—2441no—
776C23—2441no—
777C23—2441no—
778C23—2441no—
779C23—2441no—
780C23#1451974612yes—
781C23#1451979712yes—
782C23#1451980212yes—
783C23C22×C22⋊D6111yescharacteristic
784Q8—22no—
785Q8—22no—
786Q8—22no—
787Q8—22no—
788Q8—22no—
789Q8—48no—
790Q8—41no—
791Q8—41no—
792Q8#1451974914yescomplemented
793D4—22no—
794D4—22no—
795D4—48no—
796D4—44no—
797D4—48no—
798D4—41no—
799D4—41no—
800D4—4884no—
801D4—4884no—
802D4—2441no—
803D4—2441no—
804D4—2441no—
805D4—2441no—
806C2×C4—22no—
807C2×C4—21no—
808C2×C4—22no—
809C2×C4—21no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—21no—
820C2×C4—21no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—21no—
825C2×C4—21no—
826C2×C4—48no—
827C2×C4—48no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—1222no—
837C2×C4—4884no—
838C2×C4—2441no—
839C2×C4—2441no—
840C2×C4—2441no—
841C2×C4—2441no—
842C2×C4—2441no—
843C2×C4—2441no—
844C2×C4—2441no—
845C2×C4—2441no—
846C2×C4#1451974612yes—
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—22no—
861C22—22no—
862C22—22no—
863C22—41no—
864C22—42no—
865C22—41no—
866C22—41no—
867C22—41no—
868C22—41no—
869C22—41no—
870C22—42no—
871C22—42no—
872C22—41no—
873C22—81no—
874C22—81no—
875C22—81no—
876C22—81no—
877C22—4881no—
878C22—4881no—
879C22—4881no—
880C22—4881no—
881C22—4881no—
882C22—4881no—
883C22—4881no—
884C22#1683990714yescomplemented
885C22C2×#1451974611yescharacteristic
886C22D4×C22⋊D6111yescharacteristic
887C22#1684040611yescharacteristic
888C22C2×#1451979711yescharacteristic
889C22C2×#1451980211yescharacteristic
890C22#1684057011yescharacteristic
891C22#1684057711yescharacteristic
892C4—22no—
893C4—24no—
894C4—41no—
895C4—41no—
896C4—42no—
897C4—41no—
898C4—42no—
899C4—4881no—
900C4—4881no—
901C4—2442no—
902C4C2×#1451974911yescharacteristic
903C4#1684032111yescharacteristic
904C4D4×C22⋊D6111yescharacteristic
905C4#1684040611yescharacteristic
906C2—24no—
907C2—81no—
908C2—82no—
909C2—9761no—
910C2#2144919311yescharacteristic
911C2C2×#1683990711yescharacteristic
912C2#2145513411yescharacteristic
913C2#2145731511yescharacteristic
914C2#2145755611yescharacteristic
915C2#2145772111yescharacteristic
916C2#2145781011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#548C2
socleC23×C61C22×D4
hypercenterC2×#548D61
hypocenterC61#24439
LCSG ▷ C22×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×#16839996C2semidirect
2. C2×#16839907C2semidirect
3. C2×#16839901C2semidirect
4. C22×#14519701C2semidirect
5. #21449259C2semidirect
6. #21447055C2semidirect
7. #21447019C2semidirect
8. #21446896C2semidirect
9. #21446820C2semidirect
10. #21446174C2semidirect
11. #21446137C2semidirect
12. #21446112C2semidirect
13. #21446073C2semidirect
14. #21445759C2semidirect
15. C2×C61×#548C2semidirect
108. #14519701D4semidirect
130. C22×Q8×C61D4semidirect
149. #121×C61D4semidirect
333. Q8×C61#121semidirect
419. C22×C61#449semidirect
448. C2×#548D61semidirect
523. C61#24439semidirect
536. C22×Q8C22⋊D61semidirect
580. #121C22⋊D61semidirect
792. Q8#14519749semidirect
884. C22#16839907semidirect

Maximal subgroups

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

subgroupindex
C2×#168399962
C2×#168399072
C2×#168399012
C22×#145197012
#214492592
#214470552
#214470192
#214468962
#214468202
#214461742
#214461372
#214461122
#214460732
#214457592
C2×C61×#5482
#2443961