Finite Group Databasebeta

← #29715639

Subgroups — #29715639

Order 15616.

1566 conjugacy classes of subgroups.

The subgroup lattice has 924 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840408C211yesmaximal, characteristic
2C2×#16839984C211yesmaximal, characteristic, complemented
3C2×#16839922C211yesmaximal, characteristic, complemented
4C2×#16839912C211yesmaximal, characteristic, complemented
5C2×#16839860C211yesmaximal, characteristic, complemented
6#21447022C211yesmaximal, characteristic, complemented
7#21447001C211yesmaximal, characteristic, complemented
8#21446827C211yesmaximal, characteristic, complemented
9#21446820C211yesmaximal, characteristic, complemented
10#21446633C211yesmaximal, characteristic, complemented
11#21446618C211yesmaximal, characteristic, complemented
12#21445816C211yesmaximal, characteristic, complemented
13#21445757C211yesmaximal, characteristic, complemented
14#21445749C211yesmaximal, characteristic, complemented
15C61×#2538C211yesmaximal, characteristic, complemented
16C22×#11758222C2211yescharacteristic
17C23×D244C2211yescharacteristic
18C22×#11758202C2211yescharacteristic, complemented
19C22×#11758201C2211yescharacteristic
20C22×#11758201C2211yescharacteristic
21#16840408—24no—
22#16840408—24no—
23C2×#14519765C2211yescharacteristic
24C2×#14519762—21no—
25C2×#14519756C2211yescharacteristic
26C2×#14519751C2211yescharacteristic
27C2×#14519750—21no—
28C2×#14519745—21no—
29C2×C4×D244C2211yescharacteristic
30C2×C22⋊C4×D61—21no—
31#16839984—24no—
32#16839922—24no—
33#16839912—24no—
34#16839860—24no—
35C2×#14519710C2211yescharacteristic, complemented
36C2×C4⋊#92418C2211yescharacteristic, complemented
37C2×#14519701C2211yescharacteristic, complemented
38C2×#14519700C2211yescharacteristic, complemented
39C2×#14519700C2211yescharacteristic, complemented
40C2×#14519700C2211yescharacteristic, complemented
41C2×#14519697C2211yescharacteristic
42C2×#14519697C2211yescharacteristic
43C2×#14519697C2211yescharacteristic
44C2×#14519697C2211yescharacteristic
45C2×#14519697C2211yescharacteristic
46C2×#14519697C2211yescharacteristic
47C2×C22⋊#92418C2211yescharacteristic
48C2×C22⋊#92418C2211yescharacteristic
49C2×C22⋊#92418C2211yescharacteristic, complemented
50C2×C22⋊#92418C2211yescharacteristic, complemented
51C2×#14519688C2211yescharacteristic, complemented
52#16839524C2211yescharacteristic, complemented
53#16839524C2211yescharacteristic, complemented
54C2×C22⋊Q8×C61C2211yescharacteristic
55C2×C22⋊Q8×C61C2211yescharacteristic, complemented
56C2×C4×Q8×C61C2211yescharacteristic, complemented
57C2×C4×D4×C61C2211yescharacteristic
58C61×#396—21no—
59C61×#396—21no—
60C61×#390—21no—
61C61×#389—21no—
62C61×#384C2211yescharacteristic, complemented
63C61×#380C2211yescharacteristic
64C61×#380C2211yescharacteristic, complemented
65C24×D61—21no—
66C2×#11758222—22no—
67C2×#11758222—22no—
68C2×#11758222—22no—
69C2×#11758222—22no—
70C2×#11758222—41no—
71C2×#11758222—41no—
72C22×Dic122C2311yescharacteristic
73C22×D244—21no—
74C22×D244—22no—
75C22×D244—22no—
76C22×D244—22no—
77C22×D244—22no—
78C22×D244—41no—
79C22×D244—41no—
80C22×D244C2311yescharacteristic
81C22×D244C2311yescharacteristic
82C22×C22⋊D61—21no—
83C22×C22⋊D61—21no—
84C22×C4×D61—21no—
85C22×C4×D61—21no—
86C2×#11758202—22no—
87C2×#11758202—22no—
88C2×#11758202—41no—
89C2×#11758201—22no—
90C2×#11758201—22no—
91C2×#11758201—22no—
92C2×#11758201—22no—
93C2×#11758201—41no—
94C2×#11758201D414yescomplemented
95C22×#92418C2311yescharacteristic
96C22×#92418C2311yescharacteristic
97C22×#92418C2311yescharacteristic
98C22×#92418C2311yescharacteristic
99#14519765—22no—
100#14519765D414yes—
101#14519762—28no—
102#14519756—22no—
103#14519756—22no—
104#14519751—22no—
105#14519751—22no—
106#14519750—28no—
107#14519745—28no—
108C4×D244—22no—
109C4×D244D414yes—
110C2×C4⋊Dic61C2311yescharacteristic
111C2×#11758196—21no—
112C2×C22⋊Dic61—21no—
113C2×#11758198—21no—
114C2×#11758198—21no—
115C2×#11758198—21no—
116C2×#11758198—21no—
117C22⋊C4×D61—28no—
118#14519710—22no—
119C4⋊#92418—22no—
120#14519701—22no—
121#14519700—22no—
122#14519700—22no—
123#14519700—41no—
124#14519697—22no—
125#14519697—22no—
126#14519697—22no—
127#14519697—22no—
128#14519697—22no—
129#14519697—41no—
130C22⋊#92418—22no—
131C22⋊#92418—22no—
132C22⋊#92418—41no—
133C22⋊#92418—41no—
134#14519688—22no—
135C22×Q8×C61C2311yescharacteristic
136C22×D4×C61D411yescharacteristic
137C23×C4×C61C2311yescharacteristic
138C23×C4×C61C2311yescharacteristic
139C22⋊Q8×C61—22no—
140C22⋊Q8×C61—22no—
141C22⋊Q8×C61—41no—
142C22⋊Q8×C61—41no—
143C4×Q8×C61—22no—
144C4×Q8×C61—22no—
145C4×D4×C61—22no—
146C4×D4×C61—22no—
147C2×C4⋊C4×C61—21no—
148C2×C4⋊C4×C61—21no—
149C2×C4⋊C4×C61—21no—
150C2×C4⋊C4×C61—21no—
151C2×C4⋊C4×C61—21no—
152C2×C4⋊C4×C61D411yescharacteristic
153C2×C4⋊C4×C61C2311yescharacteristic
154C2×C4⋊C4×C61C2311yescharacteristic
155C2×C4⋊C4×C61C2311yescharacteristic
156C2×C22⋊C4×C61—21no—
157C2×C22⋊C4×C61—21no—
158C2×C22⋊C4×C61—21no—
159C2×C22⋊C4×C61—21no—
160C2×C22⋊C4×C61D411yescharacteristic
161C2×C22⋊C4×C61D411yescharacteristic
162C2×C42×C61—21no—
163C2×C42×C61C2311yescharacteristic
164#95×C61—21no—
165#95×C61—21no—
166C24×C61C2×D411yescharacteristic
167C24×C61C2×D411yescharacteristic
168C23×D61—21no—
169C23×D61—21no—
170C23×D61—24no—
171C23×D61—42no—
172C23×D61—42no—
173C23×D61—42no—
174C23×D61—42no—
175C23×D61—81no—
176C23×D61—81no—
177C2×Q8×C61—21no—
178C2×Q8×C61—21no—
179C2×Q8×C61—21no—
180C2×Q8×C61—21no—
181C2×Q8×C61—21no—
182C2×Q8×C61C2×D412yes—
183C2×D4×C61—22no—
184C2×D4×C61—22no—
185C2×D4×C61—41no—
186C22×C4×C61—21no—
187C22×C4×C61—21no—
188C22×C4×C61—21no—
189C22×C4×C61—21no—
190C22×C4×C61—21no—
191C22×C4×C61—21no—
192C22×C4×C61—21no—
193C22×C4×C61—21no—
194C22×C4×C61—21no—
195C22×C4×C61—21no—
196C22×C4×C61—21no—
197C22×C4×C61—21no—
198C22×C4×C61—21no—
199C22×C4×C61—21no—
200C22×C4×C61—21no—
201C22×C4×C61—21no—
202C22×C4×C61C2×D411yescharacteristic
203C22×C4×C61C2×D411yescharacteristic
204C22×C4×C61C2×D411yescharacteristic
205C22×C4×C61C2×D411yescharacteristic
206C22×C4×C61C2411yescharacteristic
207C2×C22⋊D61—24no—
208C2×C22⋊D61—24no—
209C2×C22⋊D61—42no—
210C2×C22⋊D61—42no—
211C2×C22⋊D61—81no—
212C2×C22⋊D61—81no—
213C22×Dic61—21no—
214C22×Dic61—21no—
215#11758222—44no—
216#11758222—44no—
217#11758222—44no—
218#11758222—44no—
219C2×D244—21no—
220C2×D244—21no—
221C2×D244—21no—
222C2×D244—21no—
223C2×D244—21no—
224C2×D244—21no—
225C2×D244—21no—
226C2×D244—24no—
227C2×D244—21no—
228C2×D244—44no—
229C2×D244—44no—
230C2×D244—44no—
231C2×D244—42no—
232C2×D244—42no—
233C2×D244—44no—
234C2×D244C2×D412yes—
235C2×D244C2×D412yes—
236C2×D244C2×D412yes—
237C2×D244#4112yes—
238C2×C4×D61—24no—
239C2×C4×D61—24no—
240C2×C4×D61—42no—
241C2×C4×D61—42no—
242C2×C4×D61—81no—
243C2×C4×D61—81no—
244C2×Dic122—21no—
245C2×Dic122—21no—
246C2×Dic122—21no—
247C2×Dic122—21no—
248C2×Dic122—21no—
249C2×Dic122C2×D412yes—
250C4⋊C4×C61—22no—
251C4⋊C4×C61—21no—
252C4⋊C4×C61—21no—
253C4⋊C4×C61—21no—
254C4⋊C4×C61—21no—
255C4⋊C4×C61—21no—
256C4⋊C4×C61—21no—
257C4⋊C4×C61—42no—
258C4⋊C4×C61—42no—
259C4⋊C4×C61—42no—
260C4⋊C4×C61—42no—
261C4⋊C4×C61—81no—
262C22⋊C4×C61—22no—
263C22⋊C4×C61—22no—
264C22⋊C4×C61—42no—
265C22⋊C4×C61—42no—
266C22⋊C4×C61—81no—
267C22⋊C4×C61—81no—
268C42×C61—42no—
269C42×C61C2×D412yes—
270C42×C61C2×D412yes—
271C22⋊Dic61—24no—
272#11758202—44no—
273#11758201—28no—
274#11758201—44no—
275#11758198—24no—
276#11758198—24no—
277#11758198—24no—
278#11758198—24no—
279C4⋊Dic61—21no—
280C4⋊Dic61C2×D412yes—
281#11758196—24no—
282C2×#92418—21no—
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×#92418C2×D412yes—
294C23×C61—21no—
295C23×C61—21no—
296C23×C61—21no—
297C23×C61—21no—
298C23×C61—21no—
299C23×C61—21no—
300C23×C61—21no—
301C23×C61—21no—
302C23×C61—21no—
303C23×C61—21no—
304C23×C61—21no—
305C23×C61—21no—
306C23×C61—21no—
307C23×C61#13712yes—
308C23×C61C22×D411yescharacteristic
309C22×D61—22no—
310C22×D61—22no—
311C22×D61—22no—
312C22×D61—22no—
313C22×D61—48no—
314C22×D61—41no—
315C22×D61—41no—
316C22×D61—41no—
317C22×D61—41no—
318C22×D61—48no—
319C22×D61—41no—
320C22×D61—41no—
321C22×D61—41no—
322C22×D61—41no—
323C22×D61—41no—
324C22×D61—41no—
325C22×D61—84no—
326C22×D61—84no—
327C22×D61—84no—
328C22×D61—84no—
329C22×D61—84no—
330Q8×C61—22no—
331Q8×C61—22no—
332Q8×C61—41no—
333Q8×C61—41no—
334D4×C61—44no—
335C2×C4×C61—21no—
336C2×C4×C61—21no—
337C2×C4×C61—21no—
338C2×C4×C61—21no—
339C2×C4×C61—21no—
340C2×C4×C61—21no—
341C2×C4×C61—22no—
342C2×C4×C61—21no—
343C2×C4×C61—21no—
344C2×C4×C61—21no—
345C2×C4×C61—21no—
346C2×C4×C61—41no—
347C2×C4×C61—41no—
348C2×C4×C61—41no—
349C2×C4×C61—41no—
350C2×C4×C61—41no—
351C2×C4×C61—41no—
352C2×C4×C61—41no—
353C2×C4×C61—41no—
354C2×C4×C61—41no—
355C2×C4×C61—41no—
356C2×C4×C61—41no—
357C2×C4×C61—41no—
358C2×C4×C61—41no—
359C2×C4×C61—41no—
360C2×C4×C61—41no—
361C2×C4×C61—41no—
362C2×C4×C61—41no—
363C2×C4×C61—41no—
364C2×C4×C61—41no—
365C2×C4×C61#12012yes—
366C2×C4×C61#12012yes—
367C2×C4×C61C22×D411yescharacteristic
368C2×C4×C61C22×D411yescharacteristic
369C2×C4×C61C22×D411yescharacteristic
370C2×C4×C61C2×#4111yescharacteristic
371C2×C4×C61H(5,𝔽2)11yescharacteristic
372C2×C4×C61H(5,𝔽2)11yescharacteristic
373C22⋊D61—48no—
374C22⋊D61—84no—
375C2×Dic61—22no—
376C2×Dic61—22no—
377C2×Dic61—41no—
378C2×Dic61—41no—
379C2×Dic61—41no—
380C2×Dic61—41no—
381D244—22no—
382D244—22no—
383D244—22no—
384D244—22no—
385D244—22no—
386D244—48no—
387D244—41no—
388D244—41no—
389D244#12114yes—
390C4×D61—48no—
391C4×D61—84no—
392Dic122—22no—
393Dic122—22no—
394Dic122—41no—
395Dic122—41no—
396#92418—22no—
397#92418—41no—
398#92418—41no—
399#92418—41no—
400#24259—611nomaximal, Sylow
401C22×C61—22no—
402C22×C61—22no—
403C22×C61—22no—
404C22×C61—41no—
405C22×C61—41no—
406C22×C61—41no—
407C22×C61—41no—
408C22×C61—41no—
409C22×C61—41no—
410C22×C61—41no—
411C22×C61—41no—
412C22×C61—41no—
413C22×C61—41no—
414C22×C61—41no—
415C22×C61C2×#12011yescharacteristic
416C22×C61D4211yescharacteristic
417C22×C61#54611yescharacteristic
418C22×C61C2×#13711yescharacteristic
419C22×C61#57511yescharacteristic
420C22×C61#57611yescharacteristic
421C22×C61#57711yescharacteristic
422C2×D61—24no—
423C2×D61—42no—
424C2×D61—42no—
425C2×D61—42no—
426C2×D61—42no—
427C2×D61—42no—
428C2×D61—42no—
429C2×D61—42no—
430C2×D61—42no—
431C2×D61—42no—
432C2×D61—816no—
433C2×D61—81no—
434C2×D61—81no—
435C2×D61—81no—
436C2×D61—81no—
437C4×C61—22no—
438C4×C61—22no—
439C4×C61—41no—
440C4×C61—41no—
441C4×C61—42no—
442C4×C61—81no—
443C4×C61—81no—
444C4×C61—81no—
445C4×C61C2×#12111yescharacteristic
446C4×C61#53511yescharacteristic
447C4×C61D4211yescharacteristic
448C4×C61#54611yescharacteristic
449Dic61—42no—
450Dic61—42no—
451C2×#546—611no—
452C2×#464—611no—
453C2×#452—611no—
454C2×#450—611no—
455C2×#440—611no—
456#2538D6111yescharacteristic, complemented
457#2036—611no—
458#2033—611no—
459#2001—611no—
460#2000—611no—
461#1959—611no—
462#1955—611no—
463#1802—611no—
464#1788—611no—
465#1786—611no—
466C2×C61—42no—
467C2×C61—81no—
468C2×C61#240811yescharacteristic
469C2×C61#300711yescharacteristic
470C2×C61#301211yescharacteristic
471C2×C61#326611yescharacteristic
472C2×C61#326811yescharacteristic
473C2×C61#331111yescharacteristic
474C2×C61#331411yescharacteristic
475D61—44no—
476D61—82no—
477C22×#41—611no—
478C23×D4—611no—
479C22×Q16—611no—
480C22×SD16—611no—
481C22×SD16—611no—
482#546—1224no—
483#546—1224no—
484C2×#124—611no—
485C2×#123—1221no—
486C2×C22⋊Q8—611no—
487C2×C22⋊Q8C2×D6111yescharacteristic
488C2×C22⋊Q8C2×D6111yescharacteristic, complemented
489C2×#121—611no—
490C2×#121—1221no—
491C2×#120—1221no—
492C2×C4×Q8C2×D6111yescharacteristic, complemented
493C2×C4×D4—611no—
494C2×C4×D4C2×D6111yescharacteristic
495C22×C22⋊C4—1221no—
496#464—1224no—
497#452—1224no—
498#450—1224no—
499#440—1224no—
500C2×#107—611no—
501C2×C4⋊C8—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×#102—611no—
511C2×#102—611no—
512C2×C22⋊C8—611no—
513C2×C22⋊C8—611no—
514C2×C22⋊C8—611no—
515C2×C22⋊C8—611no—
516C2×#97—611no—
517#396—21no—
518#396—21no—
519#390—21no—
520#389—21no—
521#384C2×D6111yescharacteristic, complemented
522#380C2×D6111yescharacteristic
523#380C2×D6111yescharacteristic, complemented
524#340—611no—
525#340—611no—
526C61#2425911yescharacteristic, complemented, Sylow
527C25—1221no—
528C2×#41—1222no—
529C2×#41—1222no—
530C2×#41—1222no—
531C2×#41—1222no—
532C2×#41—2441no—
533C2×#41—2441no—
534C22×Q8—611no—
535C22×Q8C22×D6111yescharacteristic
536C22×D4—611no—
537C22×D4—611no—
538C22×D4—1222no—
539C22×D4—1222no—
540C22×D4—1222no—
541C22×D4—1222no—
542C22×D4—1221no—
543C22×D4—1221no—
544C22×D4—1221no—
545C22×D4—2441no—
546C22×D4—2441no—
547C22×D4C22⋊D6111yescharacteristic
548C23×C4—1221no—
549C23×C4—1221no—
550C23×C4C22×D6111yescharacteristic
551C23×C4C22×D6111yescharacteristic
552C2×Q16—1222no—
553C2×Q16—1222no—
554C2×Q16—2441no—
555C2×SD16—614no—
556C2×SD16—1222no—
557C2×SD16—1222no—
558C2×SD16—1222no—
559C2×SD16—1222no—
560C2×SD16—2441no—
561C22×C8—611no—
562C22×C8—611no—
563C22×C8—611no—
564C22×C8—611no—
565#124—614no—
566#124—1222no—
567#123—1228no—
568C22⋊Q8—22no—
569C22⋊Q8—22no—
570C22⋊Q8—41no—
571C22⋊Q8—41no—
572C22⋊Q8—1222no—
573C22⋊Q8—1222no—
574#121—1228no—
575#121—1222no—
576#121—1222no—
577#120—1228no—
578C4×Q8—22no—
579C4×Q8—22no—
580C4×D4—22no—
581C4×D4—22no—
582C4×D4—614no—
583C4×D4—1222no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—611no—
590C2×C4⋊C4—1221no—
591C2×C4⋊C4C22⋊D6111yescharacteristic
592C2×C4⋊C4C22×D6111yescharacteristic
593C2×C4⋊C4C22×D6111yescharacteristic
594C2×C4⋊C4C22×D6111yescharacteristic
595C2×C22⋊C4—21no—
596C2×C22⋊C4—21no—
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—1228no—
600C2×C22⋊C4—1221no—
601C2×C22⋊C4—1221no—
602C2×C22⋊C4—1221no—
603C2×C22⋊C4—1221no—
604C2×C22⋊C4—1221no—
605C2×C22⋊C4C22⋊D6111yescharacteristic
606C2×C22⋊C4C22⋊D6111yescharacteristic
607C2×C42—21no—
608C2×C42C22×D6111yescharacteristic
609#107—1222no—
610C4⋊C8—1222no—
611#103—1222no—
612#103—1222no—
613#103—1222no—
614#103—2441no—
615#102—1222no—
616#102—1222no—
617#102—1222no—
618#102—1222no—
619#102—1222no—
620#102—2441no—
621C22⋊C8—1222no—
622C22⋊C8—1222no—
623C22⋊C8—2441no—
624C22⋊C8—2441no—
625#97—1222no—
626#95—21no—
627#95—21no—
628C24—1224no—
629C24—1221no—
630C24—1221no—
631C24—4881no—
632C24—4881no—
633C24—2442no—
634C24—2442no—
635C24—2442no—
636C24—2442no—
637C24C2×C22⋊D6111yescharacteristic
638C24C2×C22⋊D6111yescharacteristic
639#41—2444no—
640#41—2444no—
641#41—2444no—
642#41—2444no—
643C2×Q8—21no—
644C2×Q8—21no—
645C2×Q8—21no—
646C2×Q8—21no—
647C2×Q8—21no—
648C2×Q8—612no—
649C2×Q8—1221no—
650C2×Q8—1221no—
651C2×Q8—1221no—
652C2×Q8—1221no—
653C2×Q8—1221no—
654C2×Q8D4×D6112yes—
655C2×D4—22no—
656C2×D4—22no—
657C2×D4—41no—
658C2×D4—612no—
659C2×D4—612no—
660C2×D4—612no—
661C2×D4—612no—
662C2×D4—1224no—
663C2×D4—1224no—
664C2×D4—1224no—
665C2×D4—1221no—
666C2×D4—1221no—
667C2×D4—1221no—
668C2×D4—1221no—
669C2×D4—1221no—
670C2×D4—1221no—
671C2×D4—1221no—
672C2×D4—1221no—
673C2×D4—4881no—
674C2×D4—4881no—
675C2×D4—2442no—
676C2×D4—2442no—
677C2×D4—2444no—
678C2×D4—2444no—
679C2×D4—2444no—
680C2×D4—2444no—
681C2×D4—2442no—
682C2×D4—2442no—
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—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—1224no—
700C22×C4—1221no—
701C22×C4—1221no—
702C22×C4—1224no—
703C22×C4—4881no—
704C22×C4—4881no—
705C22×C4—2442no—
706C22×C4—2442no—
707C22×C4C2×C22⋊D6111yescharacteristic
708C22×C4C2×C22⋊D6111yescharacteristic
709C22×C4C2×C22⋊D6111yescharacteristic
710C22×C4C2×C22⋊D6111yescharacteristic
711C22×C4C23×D6111yescharacteristic
712Q16—2444no—
713SD16—1228no—
714SD16—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—
727C4⋊C4—22no—
728C4⋊C4—21no—
729C4⋊C4—21no—
730C4⋊C4—21no—
731C4⋊C4—21no—
732C4⋊C4—21no—
733C4⋊C4—21no—
734C4⋊C4—42no—
735C4⋊C4—42no—
736C4⋊C4—42no—
737C4⋊C4—42no—
738C4⋊C4—81no—
739C4⋊C4—612no—
740C4⋊C4—1224no—
741C4⋊C4—1221no—
742C22⋊C4—22no—
743C22⋊C4—22no—
744C22⋊C4—42no—
745C22⋊C4—42no—
746C22⋊C4—81no—
747C22⋊C4—81no—
748C22⋊C4—1224no—
749C22⋊C4—1224no—
750C22⋊C4—1224no—
751C22⋊C4—1224no—
752C22⋊C4—1224no—
753C42—42no—
754C42D4×D6112yes—
755C42D4×D6112yes—
756C23—21no—
757C23—21no—
758C23—21no—
759C23—21no—
760C23—21no—
761C23—21no—
762C23—21no—
763C23—21no—
764C23—21no—
765C23—21no—
766C23—21no—
767C23—21no—
768C23—21no—
769C23—1222no—
770C23—1222no—
771C23—1222no—
772C23—1222no—
773C23—4884no—
774C23—4884no—
775C23—4884no—
776C23—4884no—
777C23—4884no—
778C23—2448no—
779C23—2448no—
780C23—2441no—
781C23—2441no—
782C23—2441no—
783C23—2441no—
784C23—2441no—
785C23—2441no—
786C23—2441no—
787C23—2441no—
788C23—2441no—
789C23—2441no—
790C23#1451980812yes—
791C23C22×C22⋊D6111yescharacteristic
792Q8—22no—
793Q8—22no—
794Q8—41no—
795Q8—41no—
796Q8—1222no—
797Q8—1222no—
798Q8—2441no—
799Q8—2441no—
800D4—44no—
801D4—614no—
802D4—1222no—
803D4—1222no—
804D4—1222no—
805D4—1222no—
806D4—1222no—
807D4—4884no—
808D4—2448no—
809D4—2448no—
810D4—2441no—
811D4—2441no—
812C2×C4—21no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—22no—
819C2×C4—21no—
820C2×C4—21no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—41no—
824C2×C4—41no—
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—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—1222no—
843C2×C4—1222no—
844C2×C4—4884no—
845C2×C4—2448no—
846C2×C4—2441no—
847C2×C4—2441no—
848C2×C4—2441no—
849C2×C4—2441no—
850C2×C4#1451974512yes—
851C2×C4#1451974512yes—
852C2×C4C2×D4×D6111yescharacteristic
853C2×C4C2×D4×D6111yescharacteristic
854C2×C4C2×D4×D6111yescharacteristic
855C2×C4#41×D6111yescharacteristic
856C2×C4#1451982211yescharacteristic
857C2×C4#1451982311yescharacteristic
858C8—1222no—
859C8—2441no—
860C8—2441no—
861C8—2441no—
862C22—22no—
863C22—22no—
864C22—22no—
865C22—41no—
866C22—41no—
867C22—41no—
868C22—41no—
869C22—41no—
870C22—41no—
871C22—41no—
872C22—41no—
873C22—41no—
874C22—41no—
875C22—41no—
876C22—1224no—
877C22—48816no—
878C22—4881no—
879C22—4881no—
880C22—4881no—
881C22—4881no—
882C22—2442no—
883C22—2442no—
884C22—2442no—
885C22—2442no—
886C22—2442no—
887C22—2442no—
888C22—2442no—
889C22—2442no—
890C22—2442no—
891C22C2×#1451974511yescharacteristic
892C22D4×C22⋊D6111yescharacteristic
893C22#1684040011yescharacteristic
894C22C2×#1451980811yescharacteristic
895C22#1684056011yescharacteristic
896C22#1684056511yescharacteristic
897C22#1684057011yescharacteristic
898C4—22no—
899C4—22no—
900C4—41no—
901C4—41no—
902C4—42no—
903C4—81no—
904C4—81no—
905C4—81no—
906C4—2442no—
907C4—2442no—
908C4#121×D6111yescharacteristic
909C4#1684032811yescharacteristic
910C4#1684039611yescharacteristic
911C4#1684040911yescharacteristic
912C2—42no—
913C2—81no—
914C2—4882no—
915C2—2444no—
916C2#2144917111yescharacteristic
917C2#2145507711yescharacteristic
918C2#2145512011yescharacteristic
919C2#2145733011yescharacteristic
920C2#2145736011yescharacteristic
921C2#2145784911yescharacteristic
922C2#2145789411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2538C2
socleC23×C61C22×D4
prime radicalC2×#16840408C2
hypercenter#2538D61
hypocenterC61#24259
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2538

Complements

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

NH ≅ G/Ntype
2. C2×#16839984C2semidirect
3. C2×#16839922C2semidirect
4. C2×#16839912C2semidirect
5. C2×#16839860C2semidirect
6. #21447022C2semidirect
7. #21447001C2semidirect
8. #21446827C2semidirect
9. #21446820C2semidirect
10. #21446633C2semidirect
11. #21446618C2semidirect
12. #21445816C2semidirect
13. #21445757C2semidirect
14. #21445749C2semidirect
15. C61×#2538C2semidirect
18. C22×#11758202C22semidirect
35. C2×#14519710C22semidirect
36. C2×C4⋊#92418C22semidirect
37. C2×#14519701C22semidirect
38. C2×#14519700C22semidirect
39. C2×#14519700C22semidirect
40. C2×#14519700C22semidirect
49. C2×C22⋊#92418C22semidirect
50. C2×C22⋊#92418C22semidirect
51. C2×#14519688C22semidirect
52. #16839524C22semidirect
53. #16839524C22semidirect
55. C2×C22⋊Q8×C61C22semidirect
56. C2×C4×Q8×C61C22semidirect
62. C61×#384C22semidirect
64. C61×#380C22semidirect
94. C2×#11758201D4semidirect
456. #2538D61semidirect
488. C2×C22⋊Q8C2×D61semidirect
492. C2×C4×Q8C2×D61semidirect
521. #384C2×D61semidirect
523. #380C2×D61semidirect
526. C61#24259semidirect

Maximal subgroups

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

subgroupindex
C2×#168404082
C2×#168399842
C2×#168399222
C2×#168399122
C2×#168398602
#214470222
#214470012
#214468272
#214468202
#214466332
#214466182
#214458162
#214457572
#214457492
C61×#25382
#2425961