Finite Group Databasebeta

← #29717784

Subgroups — #29717784

Order 15616.

1498 conjugacy classes of subgroups.

The subgroup lattice has 910 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839993C211yesmaximal, characteristic, complemented
2C2×#16839907C211yesmaximal, characteristic, complemented
3C2×#16839907C211yesmaximal, characteristic, complemented
4C2×#16839758C211yesmaximal, characteristic, complemented
5#21449237C211yesmaximal, characteristic, complemented
6#21447062C211yesmaximal, characteristic, complemented
7#21447012C211yesmaximal, characteristic, complemented
8#21446902C211yesmaximal, characteristic, complemented
9#21446820C211yesmaximal, characteristic, complemented
10#21446167C211yesmaximal, characteristic, complemented
11#21446132C211yesmaximal, characteristic, complemented
12#21446112C211yesmaximal, characteristic, complemented
13#21446080C211yesmaximal, characteristic, complemented
14#21445759C211yesmaximal, characteristic, complemented
15C2×C61×#547C211yesmaximal, characteristic, complemented
16C22×#11758201C2211yescharacteristic
17C22×#11758201C2211yescharacteristic
18C22×#11758199C2211yescharacteristic
19C23×#92418C2211yescharacteristic
20C2×#14519751C2211yescharacteristic
21C2×#14519751C2211yescharacteristic
22C2×#14519736C2211yescharacteristic
23#16839993—24no—
24#16839907—24no—
25#16839907—24no—
26C2×#14519708C2211yescharacteristic
27#16839758—24no—
28C2×#14519701C2211yescharacteristic
29C2×#14519701C2211yescharacteristic
30C2×#14519701C2211yescharacteristic
31C2×#14519701C2211yescharacteristic
32C2×#14519701C2211yescharacteristic
33C2×#14519701C2211yescharacteristic
34C2×#14519698C2211yescharacteristic
35C2×#14519698C2211yescharacteristic
36C2×#14519698C2211yescharacteristic
37C2×#14519697C2211yescharacteristic
38C2×C22⋊#92418C2211yescharacteristic
39C2×C22⋊#92418C2211yescharacteristic
40C2×C22⋊#92418C2211yescharacteristic
41#16839677—21no—
42#16839670—21no—
43#16839664C2211yescharacteristic
44#16839662—21no—
45#16839660C2211yescharacteristic
46#16839652—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—
68C2×#11758201—22no—
69C2×#11758201—22no—
70C2×#11758201—22no—
71C2×#11758201—41no—
72C2×#11758201—41no—
73C2×#11758201—41no—
74C2×#11758199—22no—
75C2×#11758199—22no—
76C2×#11758199—22no—
77C22×#92418—22no—
78C22×#92418—22no—
79C22×#92418—41no—
80C22×#92418C2311yescharacteristic
81C22×#92418C2311yescharacteristic
82C22×#92418C2311yescharacteristic
83C22×#92418C2311yescharacteristic
84#14519751—22no—
85#14519751—22no—
86#14519751—22no—
87#14519751—41no—
88#14519736—22no—
89#14519736—41no—
90C2×C4⋊Dic61C2311yescharacteristic
91C2×C4⋊Dic61C2311yescharacteristic
92C2×C4⋊Dic61C2311yescharacteristic
93C2×#11758196—21no—
94C2×C22⋊Dic61—21no—
95C2×C22⋊Dic61—21no—
96C2×#11758198—21no—
97C2×#11758198—21no—
98C2×#11758198—21no—
99C2×#11758198—21no—
100C2×C4×Dic61—21no—
101#14519708—22no—
102#14519701—22no—
103#14519701—22no—
104#14519701—22no—
105#14519701—22no—
106#14519701—22no—
107#14519701—41no—
108#14519698—22no—
109#14519698—22no—
110#14519698D414yescomplemented
111#14519697—22no—
112C22⋊#92418—22no—
113C22⋊#92418—22no—
114C22⋊#92418—41no—
115#14519684—21no—
116#14519684—21no—
117C2×#41×C61—22no—
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—41no—
125C2×#41×C61—41no—
126C2×#41×C61—41no—
127C2×#41×C61—41no—
128C2×#41×C61D414yescomplemented
129C22×Q8×C61C2311yescharacteristic
130C22×Q8×C61C2311yescharacteristic
131C22×D4×C61—21no—
132C22×D4×C61—21no—
133C22×D4×C61D411yescharacteristic
134C22×D4×C61C2311yescharacteristic
135C23×C4×C61—21no—
136C23×C4×C61—21no—
137C23×C4×C61—21no—
138C23×C4×C61C2311yescharacteristic
139C23×C4×C61C2311yescharacteristic
140C4⋊Q8×C61—22no—
141C4⋊Q8×C61—22no—
142#123×C61—28no—
143#123×C61—28no—
144C22⋊Q8×C61—22no—
145C22⋊Q8×C61—22no—
146C22⋊Q8×C61—22no—
147C22⋊Q8×C61D414yescomplemented
148#121×C61—28no—
149C4×D4×C61—22no—
150C4×D4×C61—22no—
151C4×D4×C61—22no—
152C4×D4×C61—22no—
153C2×C4⋊C4×C61—28no—
154C2×C4⋊C4×C61—21no—
155C2×C4⋊C4×C61—21no—
156C2×C4⋊C4×C61—21no—
157C2×C4⋊C4×C61—21no—
158C2×C4⋊C4×C61D411yescharacteristic
159C2×C4⋊C4×C61C2311yescharacteristic
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×C61C2311yescharacteristic
166C24×C61—21no—
167C24×C61C2×D411yescharacteristic
168C24×C61C2×D411yescharacteristic
169C23×D61—21no—
170#41×C61—28no—
171#41×C61—44no—
172#41×C61—44no—
173#41×C61—44no—
174#41×C61—44no—
175#41×C61—44no—
176#41×C61—44no—
177#41×C61—44no—
178C2×Q8×C61—21no—
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×C61C2×D412yes—
189C2×Q8×C61C2×D412yes—
190C2×D4×C61—24no—
191C2×D4×C61—22no—
192C2×D4×C61—24no—
193C2×D4×C61—22no—
194C2×D4×C61—21no—
195C2×D4×C61—21no—
196C2×D4×C61—21no—
197C2×D4×C61—41no—
198C2×D4×C61—42no—
199C2×D4×C61—42no—
200C2×D4×C61—42no—
201C2×D4×C61—42no—
202C2×D4×C61C2×D412yes—
203C2×D4×C61C2×D412yes—
204C2×D4×C61#4112yes—
205C22×C4×C61—21no—
206C22×C4×C61—21no—
207C22×C4×C61—21no—
208C22×C4×C61—21no—
209C22×C4×C61—24no—
210C22×C4×C61—24no—
211C22×C4×C61—21no—
212C22×C4×C61—21no—
213C22×C4×C61—21no—
214C22×C4×C61—24no—
215C22×C4×C61—21no—
216C22×C4×C61—21no—
217C22×C4×C61—21no—
218C22×C4×C61—21no—
219C22×C4×C61—21no—
220C22×C4×C61—21no—
221C22×C4×C61—42no—
222C22×C4×C61—42no—
223C22×C4×C61—42no—
224C22×C4×C61—42no—
225C22×C4×C61—42no—
226C22×C4×C61—42no—
227C22×C4×C61C2×D411yescharacteristic
228C22×C4×C61C2×D411yescharacteristic
229C22×C4×C61C2×D411yescharacteristic
230C22×C4×C61C2×D412yes—
231C22×C4×C61C2×D412yes—
232C22×C4×C61C2×D411yescharacteristic
233C22×C4×C61C2411yescharacteristic
234C2×C22⋊D61—42no—
235C2×C22⋊D61—42no—
236C2×C22⋊D61—42no—
237C2×C22⋊D61—81no—
238C2×C22⋊D61—81no—
239C2×C22⋊D61—81no—
240C22×Dic61—21no—
241C22×Dic61—21no—
242C22×Dic61—21no—
243C2×D244—21no—
244C2×D244—21no—
245C2×D244—21no—
246C2×D244—21no—
247C2×D244—21no—
248C2×D244—21no—
249C4⋊C4×C61—24no—
250C4⋊C4×C61—24no—
251C4⋊C4×C61—24no—
252C4⋊C4×C61—22no—
253C4⋊C4×C61—24no—
254C4⋊C4×C61—21no—
255C4⋊C4×C61C2×D412yes—
256C22⋊C4×C61—24no—
257C22⋊C4×C61—24no—
258C22⋊C4×C61—24no—
259C22⋊C4×C61—22no—
260C22⋊C4×C61—22no—
261C42×C61—21no—
262C42×C61—21no—
263C22⋊Dic61—42no—
264C22⋊Dic61—81no—
265#11758201—44no—
266#11758201—44no—
267#11758199—44no—
268#11758198—42no—
269#11758198—42no—
270#11758198—42no—
271#11758198—81no—
272C4⋊Dic61—21no—
273C4⋊Dic61—21no—
274C4⋊Dic61—21no—
275C4⋊Dic61—21no—
276C4⋊Dic61—21no—
277C4⋊Dic61C2×D412yes—
278#11758196—81no—
279C4×Dic61—42no—
280C2×#92418—21no—
281C2×#92418—21no—
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—44no—
292C2×#92418C2×D412yes—
293C23×C61—22no—
294C23×C61—21no—
295C23×C61—22no—
296C23×C61—21no—
297C23×C61—22no—
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—21no—
308C23×C61—21no—
309C23×C61—41no—
310C23×C61—41no—
311C23×C61—41no—
312C23×C61—41no—
313C23×C61#12012yes—
314C23×C61C22×D411yescharacteristic
315C22×D61—41no—
316C22×D61—41no—
317C22×D61—41no—
318C22×D61—41no—
319C22×D61—41no—
320C22×D61—41no—
321C22×D61—41no—
322Q8×C61—22no—
323Q8×C61—22no—
324Q8×C61—22no—
325Q8×C61—22no—
326Q8×C61—41no—
327Q8×C61—41no—
328Q8×C61—41no—
329Q8×C61—41no—
330D4×C61—22no—
331D4×C61—22no—
332D4×C61—22no—
333D4×C61—44no—
334D4×C61—48no—
335D4×C61—48no—
336D4×C61#12114yes—
337C2×C4×C61—21no—
338C2×C4×C61—21no—
339C2×C4×C61—21no—
340C2×C4×C61—21no—
341C2×C4×C61—22no—
342C2×C4×C61—22no—
343C2×C4×C61—22no—
344C2×C4×C61—22no—
345C2×C4×C61—21no—
346C2×C4×C61—22no—
347C2×C4×C61—21no—
348C2×C4×C61—22no—
349C2×C4×C61—22no—
350C2×C4×C61—21no—
351C2×C4×C61—21no—
352C2×C4×C61—21no—
353C2×C4×C61—21no—
354C2×C4×C61—48no—
355C2×C4×C61—48no—
356C2×C4×C61—48no—
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—41no—
366C2×C4×C61—41no—
367C2×C4×C61#12012yes—
368C2×C4×C61#13512yes—
369C2×C4×C61C22×D411yescharacteristic
370C2×C4×C61C22×D411yescharacteristic
371C2×C4×C61C22×D411yescharacteristic
372C2×C4×C61C2×#4111yescharacteristic
373C2×C4×C61H(5,𝔽2)11yescharacteristic
374C2×C4×C61H(5,𝔽2)11yescharacteristic
375C22⋊D61—84no—
376C22⋊D61—84no—
377C2×Dic61—22no—
378C2×Dic61—41no—
379C2×Dic61—41no—
380C2×Dic61—41no—
381C2×Dic61—41no—
382C2×Dic61—41no—
383C2×Dic61—41no—
384C2×Dic61—41no—
385C2×Dic61—41no—
386D244—41no—
387D244—41no—
388D244—41no—
389D244—41no—
390#92418—22no—
391#92418—41no—
392#92418—41no—
393#92418—41no—
394#24438—611nomaximal, Sylow
395C22×C61—22no—
396C22×C61—24no—
397C22×C61—22no—
398C22×C61—22no—
399C22×C61—42no—
400C22×C61—42no—
401C22×C61—41no—
402C22×C61—42no—
403C22×C61—41no—
404C22×C61—42no—
405C22×C61—41no—
406C22×C61—42no—
407C22×C61—41no—
408C22×C61—42no—
409C22×C61—41no—
410C22×C61—41no—
411C22×C61—41no—
412C22×C61—41no—
413C22×C61—41no—
414C22×C61—41no—
415C22×C61—41no—
416C22×C61C2×#12011yescharacteristic
417C22×C61D4211yescharacteristic
418C22×C61#54611yescharacteristic
419C22×C61C2×#13511yescharacteristic
420C22×C61#57511yescharacteristic
421C22×C61#57711yescharacteristic
422C22×C61#57711yescharacteristic
423C2×D61—81no—
424C2×D61—81no—
425C2×D61—81no—
426C2×D61—81no—
427C2×D61—81no—
428C2×D61—81no—
429C2×D61—81no—
430C4×C61—22no—
431C4×C61—22no—
432C4×C61—41no—
433C4×C61—42no—
434C4×C61—42no—
435C4×C61—42no—
436C4×C61—41no—
437C4×C61C2×#12111yescharacteristic
438C4×C61#53411yescharacteristic
439C4×C61D4211yescharacteristic
440C4×C61#54611yescharacteristic
441Dic61—42no—
442Dic61—81no—
443Dic61—81no—
444C2×#547D6111yescharacteristic, complemented
445C2×#465—611no—
446C2×#449—611no—
447C2×#449—611no—
448C2×#416—611no—
449#2414—611no—
450#2043—611no—
451#2035—611no—
452#2013—611no—
453#2000—611no—
454#1879—611no—
455#1873—611no—
456#1869—611no—
457#1864—611no—
458#1788—611no—
459C2×C61—42no—
460C2×C61—44no—
461C2×C61—81no—
462C2×C61#241011yescharacteristic
463C2×C61#300211yescharacteristic
464C2×C61#301011yescharacteristic
465C2×C61#326711yescharacteristic
466C2×C61#328411yescharacteristic
467C2×C61#330311yescharacteristic
468C2×C61#330711yescharacteristic
469D61—161no—
470C22×#41C2×D6111yescharacteristic
471C22×#41C2×D6111yescharacteristic
472C22×SD16—611no—
473C22×SD16—611no—
474C22×D8—611no—
475C23×C8—611no—
476#547—24no—
477#547—24no—
478C2×C4⋊Q8C2×D6111yescharacteristic
479C2×#123—21no—
480C2×#123—21no—
481C2×C22⋊Q8C2×D6111yescharacteristic
482C2×C22⋊Q8C2×D6111yescharacteristic
483C2×#121—21no—
484C2×#121—611no—
485C2×#121—611no—
486C2×C4×D4C2×D6111yescharacteristic
487C2×C4×D4C2×D6111yescharacteristic
488C2×#117—611no—
489C22×C4⋊C4—21no—
490#465—1224no—
491#449—1224no—
492#449—1224no—
493C2×#106—611no—
494#416—1224no—
495C2×#103—611no—
496C2×#103—611no—
497C2×#103—611no—
498C2×#103—611no—
499C2×#103—611no—
500C2×#103—611no—
501C2×#102—611no—
502C2×#102—611no—
503C2×#102—611no—
504C2×#102—611no—
505C2×C22⋊C8—611no—
506C2×C22⋊C8—611no—
507C2×C22⋊C8—611no—
508#394—1221no—
509#392—1221no—
510#390—611no—
511#390—1221no—
512#389—611no—
513#388—1221no—
514#380—611no—
515#340—611no—
516#340—611no—
517#336—611no—
518#336—611no—
519C61#2443811yescharacteristic, complemented, Sylow
520C2×#41—22no—
521C2×#41—22no—
522C2×#41—22no—
523C2×#41—22no—
524C2×#41—22no—
525C2×#41—22no—
526C2×#41—22no—
527C2×#41—41no—
528C2×#41—41no—
529C2×#41—41no—
530C2×#41—41no—
531C2×#41C22⋊D6114yescomplemented
532C22×Q8C22×D6111yescharacteristic
533C22×Q8C22×D6111yescharacteristic
534C22×D4—21no—
535C22×D4—21no—
536C22×D4—611no—
537C22×D4—1221no—
538C22×D4—1221no—
539C22×D4C22⋊D6111yescharacteristic
540C22×D4C22×D6111yescharacteristic
541C23×C4—21no—
542C23×C4—21no—
543C23×C4—21no—
544C23×C4C22×D6111yescharacteristic
545C23×C4C22×D6111yescharacteristic
546C2×SD16—1222no—
547C2×SD16—1222no—
548C2×SD16—1222no—
549C2×SD16—2441no—
550C2×SD16—2441no—
551C2×SD16—2441no—
552C2×D8—1222no—
553C2×D8—1222no—
554C2×D8—1222no—
555C22×C8—611no—
556C22×C8—611no—
557C22×C8—611no—
558C22×C8—611no—
559C22×C8—1222no—
560C22×C8—1222no—
561C22×C8—2441no—
562C4⋊Q8—22no—
563C4⋊Q8—22no—
564#123—28no—
565#123—28no—
566C22⋊Q8—22no—
567C22⋊Q8—22no—
568C22⋊Q8—22no—
569C22⋊Q8C22⋊D6114yescomplemented
570#121—28no—
571#121—1222no—
572#121—1222no—
573#121—1222no—
574#121—2441no—
575C4×D4—22no—
576C4×D4—22no—
577C4×D4—22no—
578C4×D4—22no—
579#117—1222no—
580#117—2441no—
581C2×C4⋊C4—28no—
582C2×C4⋊C4—21no—
583C2×C4⋊C4—21no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—611no—
587C2×C4⋊C4—611no—
588C2×C4⋊C4—611no—
589C2×C4⋊C4—1221no—
590C2×C4⋊C4C22⋊D6111yescharacteristic
591C2×C4⋊C4C22×D6111yescharacteristic
592C2×C22⋊C4—21no—
593C2×C22⋊C4—21no—
594C2×C22⋊C4—21no—
595C2×C22⋊C4—1221no—
596C2×C22⋊C4—1221no—
597C2×C22⋊C4—1221no—
598C2×C22⋊C4—1221no—
599C2×C22⋊C4—1221no—
600C2×C22⋊C4—1221no—
601C2×C22⋊C4C22⋊D6111yescharacteristic
602C2×C22⋊C4C22⋊D6111yescharacteristic
603C2×C42—1221no—
604C2×C42C22×D6111yescharacteristic
605#106—1222no—
606#103—1222no—
607#103—1222no—
608#103—1222no—
609#103—1222no—
610#103—1222no—
611#103—2441no—
612#102—614no—
613#102—1222no—
614#102—1222no—
615#102—1222no—
616C22⋊C8—1222no—
617C22⋊C8—1222no—
618C22⋊C8—2441no—
619#95—1221no—
620#95—1221no—
621C24—21no—
622C24—1221no—
623C24C2×C22⋊D6111yescharacteristic
624C24C2×C22⋊D6111yescharacteristic
625#41—28no—
626#41—44no—
627#41—44no—
628#41—44no—
629#41—44no—
630#41—44no—
631#41—44no—
632#41—44no—
633C2×Q8—21no—
634C2×Q8—21no—
635C2×Q8—21no—
636C2×Q8—21no—
637C2×Q8—21no—
638C2×Q8—21no—
639C2×Q8—21no—
640C2×Q8—21no—
641C2×Q8—21no—
642C2×Q8—21no—
643C2×Q8C2×C22⋊D6112yes—
644C2×Q8C2×C22⋊D6112yes—
645C2×D4—24no—
646C2×D4—22no—
647C2×D4—24no—
648C2×D4—21no—
649C2×D4—21no—
650C2×D4—21no—
651C2×D4—22no—
652C2×D4—41no—
653C2×D4—42no—
654C2×D4—42no—
655C2×D4—42no—
656C2×D4—42no—
657C2×D4—1221no—
658C2×D4—1221no—
659C2×D4—1221no—
660C2×D4—1221no—
661C2×D4—1221no—
662C2×D4—1221no—
663C2×D4—4881no—
664C2×D4—4881no—
665C2×D4—4881no—
666C2×D4—2442no—
667C2×D4—2442no—
668C2×D4—2442no—
669C2×D4D4×D6112yes—
670C2×D4#1175822412yes—
671C2×D4C2×C22⋊D6112yes—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—24no—
677C22×C4—24no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—24no—
688C22×C4—42no—
689C22×C4—42no—
690C22×C4—42no—
691C22×C4—42no—
692C22×C4—42no—
693C22×C4—42no—
694C22×C4—1221no—
695C22×C4—1221no—
696C22×C4—1221no—
697C22×C4C2×C22⋊D6111yescharacteristic
698C22×C4C2×C22⋊D6111yescharacteristic
699C22×C4C2×C22⋊D6112yes—
700C22×C4C2×C22⋊D6112yes—
701C22×C4C2×C22⋊D6111yescharacteristic
702C22×C4C2×C22⋊D6111yescharacteristic
703C22×C4C23×D6111yescharacteristic
704SD16—2444no—
705SD16—2444no—
706D8—2444no—
707C2×C8—612no—
708C2×C8—1221no—
709C2×C8—1221no—
710C2×C8—1221no—
711C2×C8—1221no—
712C2×C8—1221no—
713C2×C8—1221no—
714C2×C8—1221no—
715C2×C8—1221no—
716C2×C8—1221no—
717C2×C8—1221no—
718C2×C8—1221no—
719C2×C8—2444no—
720C4⋊C4—24no—
721C4⋊C4—24no—
722C4⋊C4—24no—
723C4⋊C4—21no—
724C4⋊C4—22no—
725C4⋊C4—24no—
726C4⋊C4—612no—
727C4⋊C4—1221no—
728C4⋊C4—1221no—
729C4⋊C4—1221no—
730C4⋊C4—1221no—
731C4⋊C4—1221no—
732C4⋊C4—4881no—
733C4⋊C4C2×C22⋊D6112yes—
734C22⋊C4—24no—
735C22⋊C4—24no—
736C22⋊C4—24no—
737C22⋊C4—22no—
738C22⋊C4—22no—
739C22⋊C4—4881no—
740C22⋊C4—4881no—
741C22⋊C4—2442no—
742C22⋊C4—2442no—
743C22⋊C4—2442no—
744C22⋊C4—2442no—
745C42—21no—
746C42—21no—
747C42—2442no—
748C23—22no—
749C23—21no—
750C23—21no—
751C23—21no—
752C23—21no—
753C23—21no—
754C23—22no—
755C23—21no—
756C23—22no—
757C23—21no—
758C23—21no—
759C23—21no—
760C23—21no—
761C23—21no—
762C23—21no—
763C23—21no—
764C23—41no—
765C23—41no—
766C23—41no—
767C23—41no—
768C23—2441no—
769C23—2441no—
770C23—2441no—
771C23—2441no—
772C23—2441no—
773C23—2441no—
774C23—2441no—
775C23#1451974612yes—
776C23C22×C22⋊D6111yescharacteristic
777Q8—22no—
778Q8—22no—
779Q8—22no—
780Q8—22no—
781Q8—41no—
782Q8—41no—
783Q8—41no—
784Q8—41no—
785D4—22no—
786D4—22no—
787D4—22no—
788D4—44no—
789D4—48no—
790D4—48no—
791D4—4884no—
792D4—4884no—
793D4—2441no—
794D4—2441no—
795D4—2441no—
796D4—2441no—
797D4#1451974914yes—
798C2×C4—21no—
799C2×C4—21no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—21no—
807C2×C4—22no—
808C2×C4—21no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—21no—
812C2×C4—21no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—48no—
816C2×C4—48no—
817C2×C4—48no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—1222no—
829C2×C4—2441no—
830C2×C4—2441no—
831C2×C4—2441no—
832C2×C4—2441no—
833C2×C4—2441no—
834C2×C4—2441no—
835C2×C4—2441no—
836C2×C4—2441no—
837C2×C4#1451974612yes—
838C2×C4#1451979712yes—
839C2×C4C2×D4×D6111yescharacteristic
840C2×C4C22×C22⋊D6111yescharacteristic
841C2×C4C22×C22⋊D6111yescharacteristic
842C2×C4C2×#1175822411yescharacteristic
843C2×C4#1451982211yescharacteristic
844C2×C4#1451982211yescharacteristic
845C8—1222no—
846C8—2441no—
847C8—2441no—
848C8—2441no—
849C22—22no—
850C22—22no—
851C22—22no—
852C22—24no—
853C22—42no—
854C22—41no—
855C22—42no—
856C22—41no—
857C22—42no—
858C22—41no—
859C22—42no—
860C22—42no—
861C22—41no—
862C22—42no—
863C22—41no—
864C22—41no—
865C22—41no—
866C22—41no—
867C22—41no—
868C22—41no—
869C22—41no—
870C22—4881no—
871C22—4881no—
872C22—4881no—
873C22—4881no—
874C22—4881no—
875C22—4881no—
876C22—4881no—
877C22C2×#1451974611yescharacteristic
878C22D4×C22⋊D6111yescharacteristic
879C22#1684040611yescharacteristic
880C22C2×#1451979711yescharacteristic
881C22#1684056011yescharacteristic
882C22#1684057011yescharacteristic
883C22#1684057011yescharacteristic
884C4—22no—
885C4—22no—
886C4—41no—
887C4—42no—
888C4—41no—
889C4—42no—
890C4—42no—
891C4—4881no—
892C4—4881no—
893C4—2442no—
894C4C2×#1451974911yescharacteristic
895C4#1684032111yescharacteristic
896C4D4×C22⋊D6111yescharacteristic
897C4#1684040611yescharacteristic
898C2—42no—
899C2—44no—
900C2—81no—
901C2—9761no—
902C2#2144919311yescharacteristic
903C2#2145503711yescharacteristic
904C2#2145510511yescharacteristic
905C2#2145734511yescharacteristic
906C2#2145754511yescharacteristic
907C2#2145774711yescharacteristic
908C2#2145779511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#547C2
socleC23×C61C22×D4
hypercenterC2×#547D61
hypocenterC61#24438
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×#16839993C2semidirect
2. C2×#16839907C2semidirect
3. C2×#16839907C2semidirect
4. C2×#16839758C2semidirect
5. #21449237C2semidirect
6. #21447062C2semidirect
7. #21447012C2semidirect
8. #21446902C2semidirect
9. #21446820C2semidirect
10. #21446167C2semidirect
11. #21446132C2semidirect
12. #21446112C2semidirect
13. #21446080C2semidirect
14. #21445759C2semidirect
15. C2×C61×#547C2semidirect
110. #14519698D4semidirect
128. C2×#41×C61D4semidirect
147. C22⋊Q8×C61D4semidirect
444. C2×#547D61semidirect
519. C61#24438semidirect
531. C2×#41C22⋊D61semidirect
569. C22⋊Q8C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168399932
C2×#168399072
C2×#168397582
#214492372
#214470622
#214470122
#214469022
#214468202
#214461672
#214461322
#214461122
#214460802
#214457592
C2×C61×#5472
#2443861