Finite Group Databasebeta

← #29695568

Subgroups — #29695568

Order 15616.

1598 conjugacy classes of subgroups.

The subgroup lattice has 890 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839834C211yesmaximal, characteristic, complemented
2C2×#16839767C211yesmaximal, characteristic, complemented
3C2×#16839758C211yesmaximal, characteristic, complemented
4#21448768C211yesmaximal, characteristic, complemented
5#21446752C211yesmaximal, characteristic, complemented
6#21446636C211yesmaximal, characteristic, complemented
7#21446253C211yesmaximal, characteristic, complemented
8#21446248C211yesmaximal, characteristic, complemented
9#21446142C211yesmaximal, characteristic, complemented
10#21446132C211yesmaximal, characteristic, complemented
11#21445819C211yesmaximal, characteristic, complemented
12#21445759C211yesmaximal, characteristic, complemented
13#21445750C211yesmaximal, characteristic, complemented
14#21445644C211yesmaximal, characteristic, complemented
15C2×C61×#546C211yesmaximal, characteristic
16C22×#11758194C2211yescharacteristic
17C23×#92418C2211yescharacteristic, complemented
18C2×#14519736C2211yescharacteristic
19C2×#14519736C2211yescharacteristic, complemented
20#16839834—24no—
21C2×C4⋊#92418C2211yescharacteristic, complemented
22#16839767—24no—
23#16839758—24no—
24C2×#14519701C2211yescharacteristic, complemented
25C2×#14519701C2211yescharacteristic, complemented
26C2×#14519701C2211yescharacteristic, complemented
27C2×#14519701C2211yescharacteristic, complemented
28C2×#14519698C2211yescharacteristic
29C2×#14519698C2211yescharacteristic
30C2×#14519698C2211yescharacteristic
31C2×#14519698C2211yescharacteristic
32C2×#14519698C2211yescharacteristic
33C2×#14519698C2211yescharacteristic
34C2×#14519698C2211yescharacteristic
35C2×#14519698C2211yescharacteristic
36C2×C22⋊#92418C2211yescharacteristic
37C2×C22⋊#92418C2211yescharacteristic, complemented
38C2×#14519688C2211yescharacteristic, complemented
39#16839665—21no—
40#16839655—21no—
41#16839655—21no—
42#16839632C2211yescharacteristic, complemented
43#16839622C2211yescharacteristic
44#16839622C2211yescharacteristic, complemented
45C4⋊C4×Dic61—21no—
46C4×C4⋊Dic61C2211yescharacteristic, complemented
47#16839524C2211yescharacteristic, complemented
48#16839524C2211yescharacteristic, complemented
49#16839524C2211yescharacteristic, complemented
50#16839524C2211yescharacteristic, complemented
51C22×#41×C61C2211yescharacteristic
52C23×D4×C61C2211yescharacteristic
53C61×#546—24no—
54C61×#546C418yescomplemented
55C2×#124×C61C2211yescharacteristic
56C2×#123×C61—21no—
57C2×C22⋊Q8×C61C2211yescharacteristic
58C2×#121×C61—21no—
59C2×#121×C61C2211yescharacteristic
60C2×#120×C61—21no—
61C2×C4×D4×C61C2211yescharacteristic
62C2×C4×D4×C61C2211yescharacteristic
63C22×C22⋊C4×C61—21no—
64C2×#11758194—22no—
65C2×#11758194—22no—
66C2×#11758194—41no—
67C22×#92418—22no—
68C22×#92418—22no—
69C22×#92418—41no—
70C22×#92418C2311yescharacteristic
71C22×#92418C2311yescharacteristic
72C22×#92418C2311yescharacteristic
73C22×#92418C2311yescharacteristic
74#14519736—22no—
75#14519736—22no—
76#14519736—41no—
77#14519736—41no—
78C2×C4⋊Dic61—21no—
79C2×C4⋊Dic61—21no—
80C2×C4⋊Dic61C2311yescharacteristic
81C2×C4⋊Dic61C2311yescharacteristic
82C2×C4⋊Dic61C2311yescharacteristic
83C2×C4⋊Dic61C2311yescharacteristic
84C2×C22⋊Dic61—21no—
85C2×C22⋊Dic61—21no—
86C2×C22⋊Dic61—21no—
87C2×C22⋊Dic61—21no—
88C2×C4×Dic61—21no—
89C2×C4×Dic61—21no—
90C2×C4×Dic61—21no—
91C4⋊#92418—22no—
92#14519701—22no—
93#14519701—22no—
94#14519701—41no—
95#14519701—41no—
96#14519698—22no—
97#14519698—22no—
98#14519698—22no—
99#14519698—22no—
100#14519698—22no—
101#14519698—41no—
102#14519698—41no—
103#14519698D414yescomplemented
104C22⋊#92418—22no—
105C22⋊#92418—22no—
106#14519688—22no—
107#14519684—21no—
108#14519684—21no—
109#14519684—21no—
110C25×C61—21no—
111C2×#41×C61—22no—
112C2×#41×C61—22no—
113C2×#41×C61—22no—
114C2×#41×C61—41no—
115C2×#41×C61—41no—
116C2×#41×C61C2×C414yes—
117C22×Q8×C61C2311yescharacteristic
118C22×D4×C61—22no—
119C22×D4×C61—22no—
120C22×D4×C61—21no—
121C22×D4×C61—21no—
122C22×D4×C61—22no—
123C22×D4×C61—21no—
124C22×D4×C61—41no—
125C22×D4×C61—41no—
126C22×D4×C61C2×C414yes—
127C22×D4×C61D411yescharacteristic
128C22×D4×C61C2311yescharacteristic
129C22×D4×C61C2311yescharacteristic
130C23×C4×C61—21no—
131C23×C4×C61—21no—
132C23×C4×C61C2311yescharacteristic
133C23×C4×C61C2311yescharacteristic
134#124×C61—22no—
135#124×C61C2×C414yes—
136#123×C61—28no—
137C22⋊Q8×C61—22no—
138C22⋊Q8×C61C2×C414yes—
139#121×C61—22no—
140#121×C61—28no—
141#121×C61C2×C414yes—
142#120×C61—28no—
143C4×D4×C61—22no—
144C4×D4×C61C2×C414yes—
145C4×D4×C61C2×C414yes—
146C4×D4×C61D414yes—
147C2×C4⋊C4×C61—21no—
148C2×C4⋊C4×C61D411yescharacteristic
149C2×C4⋊C4×C61C2311yescharacteristic
150C2×C22⋊C4×C61—21no—
151C2×C22⋊C4×C61—21no—
152C2×C22⋊C4×C61—21no—
153C2×C22⋊C4×C61—21no—
154C2×C22⋊C4×C61—21no—
155C2×C22⋊C4×C61—28no—
156C2×C22⋊C4×C61D411yescharacteristic
157C2×C22⋊C4×C61D411yescharacteristic
158C2×C42×C61C2311yescharacteristic
159C24×C61—21no—
160C24×C61—21no—
161C24×C61—24no—
162C24×C61—42no—
163C24×C61—42no—
164C24×C61—42no—
165C24×C61—42no—
166C24×C61—81no—
167C24×C61—81no—
168C24×C61C2×D411yescharacteristic
169C24×C61C2×D411yescharacteristic
170#41×C61—28no—
171#41×C61—44no—
172#41×C61—44no—
173#41×C61—44no—
174C2×Q8×C61—21no—
175C2×Q8×C61—21no—
176C2×Q8×C61—21no—
177C2×Q8×C61—21no—
178C2×Q8×C61—21no—
179C2×Q8×C61C22×C412yes—
180C2×D4×C61—28no—
181C2×D4×C61—24no—
182C2×D4×C61—24no—
183C2×D4×C61—24no—
184C2×D4×C61—21no—
185C2×D4×C61—21no—
186C2×D4×C61—21no—
187C2×D4×C61—21no—
188C2×D4×C61—21no—
189C2×D4×C61—21no—
190C2×D4×C61—21no—
191C2×D4×C61—21no—
192C2×D4×C61—44no—
193C2×D4×C61—44no—
194C2×D4×C61—44no—
195C2×D4×C61—41no—
196C2×D4×C61—41no—
197C2×D4×C61—42no—
198C2×D4×C61—42no—
199C2×D4×C61—42no—
200C2×D4×C61—42no—
201C2×D4×C61—81no—
202C2×D4×C61—81no—
203C2×D4×C61C22⋊C414yes—
204C2×D4×C61C22×C412yes—
205C2×D4×C61C22×C412yes—
206C2×D4×C61C2×D412yes—
207C2×D4×C61#4112yes—
208C22×C4×C61—21no—
209C22×C4×C61—21no—
210C22×C4×C61—21no—
211C22×C4×C61—21no—
212C22×C4×C61—21no—
213C22×C4×C61—21no—
214C22×C4×C61—21no—
215C22×C4×C61—21no—
216C22×C4×C61—21no—
217C22×C4×C61—21no—
218C22×C4×C61—24no—
219C22×C4×C61—24no—
220C22×C4×C61—42no—
221C22×C4×C61—42no—
222C22×C4×C61—81no—
223C22×C4×C61—81no—
224C22×C4×C61C22×C412yes—
225C22×C4×C61C22×C412yes—
226C22×C4×C61C2×D411yescharacteristic
227C22×C4×C61C2×D411yescharacteristic
228C22×C4×C61C2×D411yescharacteristic
229C22×C4×C61C2×D411yescharacteristic
230C22×C4×C61C2×D412yes—
231C22×C4×C61C2×D412yes—
232C22×C4×C61C2411yescharacteristic
233C22×Dic61—21no—
234C22×Dic61—21no—
235C22×Dic61—21no—
236C22×Dic61—21no—
237C4⋊C4×C61—24no—
238C4⋊C4×C61—21no—
239C4⋊C4×C61C22⋊C414yes—
240C4⋊C4×C61C22×C412yes—
241C22⋊C4×C61—24no—
242C22⋊C4×C61—24no—
243C22⋊C4×C61—24no—
244C22⋊C4×C61—24no—
245C22⋊C4×C61—24no—
246C22⋊C4×C61C22⋊C414yes—
247C22⋊C4×C61C22⋊C414yes—
248C42×C61C22×C412yes—
249C42×C61C2×D412yes—
250C22⋊Dic61—42no—
251C22⋊Dic61—42no—
252C22⋊Dic61—81no—
253C22⋊Dic61—81no—
254C4⋊Dic61—21no—
255C4⋊Dic61—21no—
256C4⋊Dic61—21no—
257C4⋊Dic61—21no—
258C4⋊Dic61—21no—
259C4⋊Dic61—21no—
260C4⋊Dic61—21no—
261C4⋊Dic61—42no—
262C4⋊Dic61—81no—
263C4⋊Dic61C2×D412yes—
264C4×Dic61—42no—
265C4×Dic61—42no—
266C4×Dic61—42no—
267#11758194—44no—
268C2×#92418—21no—
269C2×#92418—21no—
270C2×#92418—21no—
271C2×#92418—21no—
272C2×#92418—21no—
273C2×#92418—21no—
274C2×#92418—21no—
275C2×#92418—21no—
276C2×#92418—21no—
277C2×#92418—21no—
278C2×#92418—21no—
279C2×#92418—44no—
280C2×#92418C2×D412yes—
281C23×C61—22no—
282C23×C61—21no—
283C23×C61—21no—
284C23×C61—22no—
285C23×C61—21no—
286C23×C61—21no—
287C23×C61—22no—
288C23×C61—21no—
289C23×C61—21no—
290C23×C61—21no—
291C23×C61—21no—
292C23×C61—21no—
293C23×C61—21no—
294C23×C61—21no—
295C23×C61—21no—
296C23×C61—22no—
297C23×C61—48no—
298C23×C61—48no—
299C23×C61—41no—
300C23×C61—41no—
301C23×C61—41no—
302C23×C61—41no—
303C23×C61—41no—
304C23×C61—41no—
305C23×C61—41no—
306C23×C61—41no—
307C23×C61—41no—
308C23×C61—41no—
309C23×C61—84no—
310C23×C61—84no—
311C23×C61—84no—
312C23×C61—84no—
313C23×C61—84no—
314C23×C61C2×C22⋊C412yes—
315C23×C61C2×C22⋊C412yes—
316C23×C61C22×D411yescharacteristic
317Q8×C61—22no—
318Q8×C61—22no—
319Q8×C61—41no—
320Q8×C61—41no—
321D4×C61—22no—
322D4×C61—22no—
323D4×C61—22no—
324D4×C61—22no—
325D4×C61—22no—
326D4×C61—44no—
327D4×C61—48no—
328D4×C61—48no—
329D4×C61—41no—
330D4×C61—41no—
331D4×C61—84no—
332D4×C61C4×D414yes—
333C2×C4×C61—21no—
334C2×C4×C61—21no—
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—22no—
343C2×C4×C61—22no—
344C2×C4×C61—22no—
345C2×C4×C61—22no—
346C2×C4×C61—22no—
347C2×C4×C61—22no—
348C2×C4×C61—22no—
349C2×C4×C61—22no—
350C2×C4×C61—22no—
351C2×C4×C61—48no—
352C2×C4×C61—41no—
353C2×C4×C61—41no—
354C2×C4×C61—41no—
355C2×C4×C61—41no—
356C2×C4×C61—84no—
357C2×C4×C61C2×C22⋊C412yes—
358C2×C4×C61C2×C22⋊C412yes—
359C2×C4×C61C2×C22⋊C412yes—
360C2×C4×C61C2×C22⋊C412yes—
361C2×C4×C61C23×C411yescharacteristic
362C2×C4×C61C22×D411yescharacteristic
363C2×C4×C61C22×D411yescharacteristic
364C2×C4×C61C2×#4111yescharacteristic
365C2×C4×C61H(5,𝔽2)11yescharacteristic
366C2×C4×C61H(5,𝔽2)11yescharacteristic
367C2×Dic61—22no—
368C2×Dic61—41no—
369C2×Dic61—41no—
370C2×Dic61—41no—
371C2×Dic61—41no—
372C2×Dic61—41no—
373C2×Dic61—41no—
374C2×Dic61—41no—
375C2×Dic61—41no—
376C2×Dic61—41no—
377C2×Dic61—41no—
378C2×Dic61—41no—
379#92418—22no—
380#92418—41no—
381#92418—41no—
382#92418—41no—
383#22424—611nomaximal, Sylow
384C22×C61—22no—
385C22×C61—22no—
386C22×C61—24no—
387C22×C61—22no—
388C22×C61—22no—
389C22×C61—22no—
390C22×C61—22no—
391C22×C61—42no—
392C22×C61—42no—
393C22×C61—41no—
394C22×C61—41no—
395C22×C61—42no—
396C22×C61—41no—
397C22×C61—41no—
398C22×C61—42no—
399C22×C61—41no—
400C22×C61—41no—
401C22×C61—42no—
402C22×C61—41no—
403C22×C61—41no—
404C22×C61—42no—
405C22×C61—42no—
406C22×C61—42no—
407C22×C61—42no—
408C22×C61—816no—
409C22×C61—81no—
410C22×C61—81no—
411C22×C61—81no—
412C22×C61—81no—
413C22×C61C22×C22⋊C411yescharacteristic
414C22×C61D4211yescharacteristic
415C22×C61#54611yescharacteristic
416C22×C61#57511yescharacteristic
417C22×C61#57511yescharacteristic
418C22×C61#57611yescharacteristic
419C22×C61#57711yescharacteristic
420C4×C61—22no—
421C4×C61—22no—
422C4×C61—22no—
423C4×C61—22no—
424C4×C61—42no—
425C4×C61—42no—
426C4×C61C2×C4×D411yescharacteristic
427C4×C61#51811yescharacteristic
428C4×C61D4211yescharacteristic
429C4×C61#54611yescharacteristic
430Dic61—42no—
431Dic61—81no—
432Dic61—81no—
433Dic61—81no—
434C2×#546D6111yescharacteristic
435C2×#435—611no—
436C2×#418—611no—
437C2×#416—611no—
438#2354—611no—
439#1983—611no—
440#1959—611no—
441#1894—611no—
442#1893—611no—
443#1875—611no—
444#1873—611no—
445#1802—611no—
446#1788—611no—
447#1786—611no—
448#1762—611no—
449C2×C61—42no—
450C2×C61—42no—
451C2×C61—44no—
452C2×C61—82no—
453C2×C61D4×C22⋊C411yescharacteristic
454C2×C61#289611yescharacteristic
455C2×C61#289711yescharacteristic
456C2×C61#326711yescharacteristic
457C2×C61#326811yescharacteristic
458C2×C61#331111yescharacteristic
459C2×C61#331911yescharacteristic
460C22×#41C2×D6111yescharacteristic
461C23×D4C2×D6111yescharacteristic
462C22×M16—611no—
463C23×C8—611no—
464#546—24no—
465#546Dic6118yescomplemented
466C2×#124C2×D6111yescharacteristic
467C2×#123—21no—
468C2×C22⋊Q8C2×D6111yescharacteristic
469C2×#121—21no—
470C2×#121C2×D6111yescharacteristic
471C2×#120—21no—
472C2×C4×D4C2×D6111yescharacteristic
473C2×C4×D4C2×D6111yescharacteristic
474C2×#117—611no—
475C2×#117—611no—
476C22×C22⋊C4—21no—
477#435—1224no—
478C2×C4⋊C8—611no—
479#418—1224no—
480#416—1224no—
481C2×#103—611no—
482C2×#103—611no—
483C2×#103—611no—
484C2×#103—611no—
485C2×#102—611no—
486C2×#102—611no—
487C2×#102—611no—
488C2×#102—611no—
489C2×#102—611no—
490C2×#102—611no—
491C2×#102—611no—
492C2×#102—611no—
493C2×C22⋊C8—611no—
494C2×C22⋊C8—611no—
495C2×#97—611no—
496#390—1221no—
497#388—1221no—
498#388—1221no—
499#384—611no—
500#380—611no—
501#380—611no—
502C4×C4⋊C4—611no—
503C4×C4⋊C4—1221no—
504#340—611no—
505#340—611no—
506#340—611no—
507#340—611no—
508C61#2242411yescharacteristic, complemented, Sylow
509C25—21no—
510C2×#41—22no—
511C2×#41—22no—
512C2×#41—22no—
513C2×#41—41no—
514C2×#41—41no—
515C2×#41C2×Dic6114yes—
516C22×Q8C22×D6111yescharacteristic
517C22×D4—22no—
518C22×D4—22no—
519C22×D4—21no—
520C22×D4—21no—
521C22×D4—21no—
522C22×D4—22no—
523C22×D4—41no—
524C22×D4—41no—
525C22×D4C2×Dic6114yes—
526C22×D4C22⋊D6111yescharacteristic
527C22×D4C22×D6111yescharacteristic
528C22×D4C22×D6111yescharacteristic
529C23×C4—21no—
530C23×C4—21no—
531C23×C4C22×D6111yescharacteristic
532C23×C4C22×D6111yescharacteristic
533C2×M16—1222no—
534C2×M16—1222no—
535C2×M16—2441no—
536C22×C8—611no—
537C22×C8—611no—
538C22×C8—611no—
539C22×C8—611no—
540C22×C8—1222no—
541C22×C8—1222no—
542C22×C8—2441no—
543#124—22no—
544#124C2×Dic6114yes—
545#123—28no—
546C22⋊Q8—22no—
547C22⋊Q8C2×Dic6114yes—
548#121—22no—
549#121—28no—
550#121C2×Dic6114yes—
551#120—28no—
552C4×D4—22no—
553C4×D4C2×Dic6114yes—
554C4×D4C2×Dic6114yes—
555C4×D4C22⋊D6114yes—
556#117—1222no—
557#117—1222no—
558#117—2441no—
559#117—2441no—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—611no—
562C2×C4⋊C4—611no—
563C2×C4⋊C4—611no—
564C2×C4⋊C4—611no—
565C2×C4⋊C4—1221no—
566C2×C4⋊C4—1221no—
567C2×C4⋊C4C22⋊D6111yescharacteristic
568C2×C4⋊C4C22×D6111yescharacteristic
569C2×C22⋊C4—21no—
570C2×C22⋊C4—21no—
571C2×C22⋊C4—21no—
572C2×C22⋊C4—21no—
573C2×C22⋊C4—21no—
574C2×C22⋊C4—28no—
575C2×C22⋊C4—1221no—
576C2×C22⋊C4—1221no—
577C2×C22⋊C4—1221no—
578C2×C22⋊C4—1221no—
579C2×C22⋊C4C22⋊D6111yescharacteristic
580C2×C22⋊C4C22⋊D6111yescharacteristic
581C2×C42—1221no—
582C2×C42—1221no—
583C2×C42—1221no—
584C2×C42C22×D6111yescharacteristic
585C4⋊C8—1222no—
586#103—1222no—
587#103—1222no—
588#103—2441no—
589#103—2441no—
590#102—614no—
591#102—1222no—
592#102—1222no—
593#102—1222no—
594#102—1222no—
595#102—1222no—
596#102—2441no—
597#102—2441no—
598C22⋊C8—1222no—
599C22⋊C8—1222no—
600#97—1222no—
601#95—1221no—
602#95—1221no—
603#95—1221no—
604C24—21no—
605C24—21no—
606C24—24no—
607C24—42no—
608C24—42no—
609C24—42no—
610C24—42no—
611C24—81no—
612C24—81no—
613C24C2×C22⋊D6111yescharacteristic
614C24C2×C22⋊D6111yescharacteristic
615#41—28no—
616#41—44no—
617#41—44no—
618#41—44no—
619C2×Q8—21no—
620C2×Q8—21no—
621C2×Q8—21no—
622C2×Q8—21no—
623C2×Q8—21no—
624C2×Q8C22×Dic6112yes—
625C2×D4—28no—
626C2×D4—24no—
627C2×D4—24no—
628C2×D4—21no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4—21no—
634C2×D4—21no—
635C2×D4—21no—
636C2×D4—24no—
637C2×D4—44no—
638C2×D4—44no—
639C2×D4—44no—
640C2×D4—41no—
641C2×D4—41no—
642C2×D4—42no—
643C2×D4—42no—
644C2×D4—42no—
645C2×D4—42no—
646C2×D4—81no—
647C2×D4—81no—
648C2×D4C22⋊Dic6114yes—
649C2×D4D4×D6112yes—
650C2×D4#1175822412yes—
651C2×D4C22×Dic6112yes—
652C2×D4C22×Dic6112yes—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—24no—
664C22×C4—24no—
665C22×C4—42no—
666C22×C4—42no—
667C22×C4—81no—
668C22×C4—81no—
669C22×C4—1221no—
670C22×C4—1221no—
671C22×C4—1221no—
672C22×C4—1221no—
673C22×C4C22×Dic6112yes—
674C22×C4C22×Dic6112yes—
675C22×C4C2×C22⋊D6112yes—
676C22×C4C2×C22⋊D6112yes—
677C22×C4C2×C22⋊D6111yescharacteristic
678C22×C4C2×C22⋊D6111yescharacteristic
679C22×C4C2×C22⋊D6111yescharacteristic
680C22×C4C2×C22⋊D6111yescharacteristic
681C22×C4C23×D6111yescharacteristic
682M16—2444no—
683C2×C8—612no—
684C2×C8—1221no—
685C2×C8—1221no—
686C2×C8—1221no—
687C2×C8—1221no—
688C2×C8—1221no—
689C2×C8—1221no—
690C2×C8—1221no—
691C2×C8—1221no—
692C2×C8—1221no—
693C2×C8—1221no—
694C2×C8—1221no—
695C2×C8—2444no—
696C4⋊C4—21no—
697C4⋊C4—24no—
698C4⋊C4—612no—
699C4⋊C4—1221no—
700C4⋊C4—1221no—
701C4⋊C4—1221no—
702C4⋊C4—1221no—
703C4⋊C4—1221no—
704C4⋊C4—1221no—
705C4⋊C4—1221no—
706C4⋊C4—4881no—
707C4⋊C4—2442no—
708C4⋊C4C22⋊Dic6114yes—
709C4⋊C4C22×Dic6112yes—
710C22⋊C4—24no—
711C22⋊C4—24no—
712C22⋊C4—24no—
713C22⋊C4—24no—
714C22⋊C4—24no—
715C22⋊C4—4881no—
716C22⋊C4—4881no—
717C22⋊C4—2442no—
718C22⋊C4—2442no—
719C22⋊C4C22⋊Dic6114yes—
720C22⋊C4C22⋊Dic6114yes—
721C42—2442no—
722C42—2442no—
723C42—2442no—
724C42C22×Dic6112yes—
725C42C2×C22⋊D6112yes—
726C23—22no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—21no—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—22no—
738C23—21no—
739C23—21no—
740C23—22no—
741C23—22no—
742C23—48no—
743C23—48no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23—41no—
754C23—84no—
755C23—84no—
756C23—84no—
757C23—84no—
758C23—84no—
759C23C2×C22⋊Dic6112yes—
760C23C2×C22⋊Dic6112yes—
761C23C22×C22⋊D6111yescharacteristic
762Q8—22no—
763Q8—22no—
764Q8—41no—
765Q8—41no—
766D4—22no—
767D4—22no—
768D4—22no—
769D4—22no—
770D4—22no—
771D4—44no—
772D4—48no—
773D4—48no—
774D4—41no—
775D4—41no—
776D4—84no—
777D4D4×Dic6114yes—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—48no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—84no—
802C2×C4—1222no—
803C2×C4—2441no—
804C2×C4—2441no—
805C2×C4—2441no—
806C2×C4—2441no—
807C2×C4—2441no—
808C2×C4—2441no—
809C2×C4—2441no—
810C2×C4—2441no—
811C2×C4—2441no—
812C2×C4—2441no—
813C2×C4—2441no—
814C2×C4C2×C22⋊Dic6112yes—
815C2×C4C2×C22⋊Dic6112yes—
816C2×C4C2×C22⋊Dic6112yes—
817C2×C4C2×C22⋊Dic6112yes—
818C2×C4C23×Dic6111yescharacteristic
819C2×C4C2×D4×D6111yescharacteristic
820C2×C4C22×C22⋊D6111yescharacteristic
821C2×C4C2×#1175822411yescharacteristic
822C2×C4#1451982211yescharacteristic
823C2×C4#1451982211yescharacteristic
824C8—1222no—
825C8—2441no—
826C8—2441no—
827C8—2441no—
828C22—22no—
829C22—22no—
830C22—22no—
831C22—22no—
832C22—22no—
833C22—22no—
834C22—24no—
835C22—42no—
836C22—42no—
837C22—41no—
838C22—41no—
839C22—42no—
840C22—41no—
841C22—41no—
842C22—42no—
843C22—41no—
844C22—41no—
845C22—42no—
846C22—41no—
847C22—41no—
848C22—42no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—816no—
853C22—81no—
854C22—81no—
855C22—81no—
856C22—81no—
857C22C22×C22⋊Dic6111yescharacteristic
858C22D4×C22⋊D6111yescharacteristic
859C22#1684040611yescharacteristic
860C22#1684056011yescharacteristic
861C22#1684056011yescharacteristic
862C22#1684056511yescharacteristic
863C22#1684057311yescharacteristic
864C4—22no—
865C4—22no—
866C4—22no—
867C4—22no—
868C4—42no—
869C4—42no—
870C4—4881no—
871C4—4881no—
872C4—4881no—
873C4—2442no—
874C4C2×D4×Dic6111yescharacteristic
875C4#1684023711yescharacteristic
876C4D4×C22⋊D6111yescharacteristic
877C4#1684040611yescharacteristic
878C2—42no—
879C2—42no—
880C2—44no—
881C2—82no—
882C2D4×C22⋊Dic6111yescharacteristic
883C2#2145433811yescharacteristic
884C2#2145434511yescharacteristic
885C2#2145734011yescharacteristic
886C2#2145735511yescharacteristic
887C2#2145785511yescharacteristic
888C2#2145797511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
Fitting, prime radicalC2×C61×#546C2
socleC23×C61C22×D4
cosocleC22×C4×C61C24
hypercenterC2×#546D61
hypocenterC61#22424
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#546

Complements

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

NH ≅ G/Ntype
1. C2×#16839834C2semidirect
2. C2×#16839767C2semidirect
3. C2×#16839758C2semidirect
4. #21448768C2semidirect
5. #21446752C2semidirect
6. #21446636C2semidirect
7. #21446253C2semidirect
8. #21446248C2semidirect
9. #21446142C2semidirect
10. #21446132C2semidirect
11. #21445819C2semidirect
12. #21445759C2semidirect
13. #21445750C2semidirect
14. #21445644C2semidirect
17. C23×#92418C22semidirect
19. C2×#14519736C22semidirect
21. C2×C4⋊#92418C22semidirect
24. C2×#14519701C22semidirect
25. C2×#14519701C22semidirect
26. C2×#14519701C22semidirect
27. C2×#14519701C22semidirect
37. C2×C22⋊#92418C22semidirect
38. C2×#14519688C22semidirect
42. #16839632C22semidirect
44. #16839622C22semidirect
46. C4×C4⋊Dic61C22semidirect
47. #16839524C22semidirect
48. #16839524C22semidirect
49. #16839524C22semidirect
50. #16839524C22semidirect
54. C61×#546C4semidirect
103. #14519698D4semidirect
465. #546Dic61semidirect
508. C61#22424semidirect

Maximal subgroups

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

subgroupindex
C2×#168398342
C2×#168397672
C2×#168397582
#214487682
#214467522
#214466362
#214462532
#214462482
#214461422
#214461322
#214458192
#214457592
#214457502
#214456442
C2×C61×#5462
#2242461