Finite Group Databasebeta

← #29695538

Subgroups — #29695538

Order 15616.

1530 conjugacy classes of subgroups.

The subgroup lattice has 882 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839834C211yesmaximal, characteristic, complemented
2C2×#16839763C211yesmaximal, characteristic, complemented
3C2×#16839758C211yesmaximal, characteristic, complemented
4#21448748C211yesmaximal, characteristic, complemented
5#21446747C211yesmaximal, characteristic, complemented
6#21446644C211yesmaximal, characteristic, complemented
7#21446258C211yesmaximal, characteristic, complemented
8#21446248C211yesmaximal, characteristic, complemented
9#21446142C211yesmaximal, characteristic, complemented
10#21446137C211yesmaximal, characteristic, complemented
11#21445834C211yesmaximal, characteristic, complemented
12#21445759C211yesmaximal, characteristic, complemented
13#21445759C211yesmaximal, characteristic, complemented
14#21445649C211yesmaximal, characteristic, complemented
15C2×C61×#550C211yesmaximal, characteristic
16C22×#11758194C2211yescharacteristic
17C23×#92418C2211yescharacteristic
18C2×#14519736C2211yescharacteristic
19C22×C4⋊Dic61C2211yescharacteristic
20#16839834—24no—
21C2×C4⋊#92418C2211yescharacteristic
22#16839763—24no—
23#16839758—24no—
24C2×#14519701C2211yescharacteristic
25C2×#14519701C2211yescharacteristic
26C2×#14519701C2211yescharacteristic
27C2×#14519701C2211yescharacteristic
28C2×#14519698C2211yescharacteristic
29C2×#14519698C2211yescharacteristic
30C2×#14519698C2211yescharacteristic
31C2×#14519698C2211yescharacteristic
32C2×#14519698C2211yescharacteristic
33C2×#14519698C2211yescharacteristic
34C2×#14519698C2211yescharacteristic
35C2×#14519698C2211yescharacteristic
36C2×C22⋊#92418C2211yescharacteristic
37C2×C22⋊#92418C2211yescharacteristic
38C2×#14519688C2211yescharacteristic
39#16839655—21no—
40#16839648—21no—
41#16839642—21no—
42#16839628C2211yescharacteristic
43#16839622C2211yescharacteristic
44#16839622C2211yescharacteristic
45C4×C4⋊Dic61C2211yescharacteristic
46C22⋊C4×Dic61—21no—
47#16839524C2211yescharacteristic
48#16839524C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839524C2211yescharacteristic
51C22×#41×C61C2211yescharacteristic
52C22×#41×C61C2211yescharacteristic
53C61×#550—24no—
54C61×#550C418yescomplemented
55C2×#127×C61—21no—
56C2×#127×C61C2211yescharacteristic
57C2×#121×C61—21no—
58C2×#121×C61—21no—
59C2×#121×C61C2211yescharacteristic
60C2×#121×C61C2211yescharacteristic
61C2×C4×Q8×C61C2211yescharacteristic
62C2×C4×D4×C61—21no—
63C2×C4×D4×C61C2211yescharacteristic
64C23×Dic61—21no—
65C2×#11758194—22no—
66C2×#11758194—22no—
67C2×#11758194—41no—
68C22×#92418—22no—
69C22×#92418—22no—
70C22×#92418—41no—
71C22×#92418C2311yescharacteristic
72C22×#92418C2311yescharacteristic
73C22×#92418C2311yescharacteristic
74C22×#92418C2311yescharacteristic
75#14519736—22no—
76#14519736—41no—
77C2×C4⋊Dic61—22no—
78C2×C4⋊Dic61—21no—
79C2×C4⋊Dic61—41no—
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×C4×Dic61—21no—
88C2×C4×Dic61—21no—
89C4⋊#92418—22no—
90#14519701—22no—
91#14519701—22no—
92#14519701—22no—
93#14519701D414yescomplemented
94#14519698—22no—
95#14519698—22no—
96#14519698—22no—
97#14519698—22no—
98#14519698—41no—
99#14519698—41no—
100#14519698—41no—
101#14519698—41no—
102C22⋊#92418—22no—
103C22⋊#92418—22no—
104#14519688—22no—
105#14519684—21no—
106#14519684—21no—
107#14519684—21no—
108#14519684—21no—
109#14519684—21no—
110C2×#41×C61—22no—
111C2×#41×C61—22no—
112C2×#41×C61—22no—
113C2×#41×C61—22no—
114C2×#41×C61—22no—
115C2×#41×C61—22no—
116C2×#41×C61—41no—
117C2×#41×C61—41no—
118C2×#41×C61—41no—
119C2×#41×C61—41no—
120C2×#41×C61C2×C414yes—
121C2×#41×C61C2×C414yescomplemented
122C22×Q8×C61C2311yescharacteristic
123C22×D4×C61—21no—
124C22×D4×C61—21no—
125C22×D4×C61—21no—
126C22×D4×C61—21no—
127C22×D4×C61—21no—
128C22×D4×C61—21no—
129C22×D4×C61D411yescharacteristic
130C22×D4×C61C2311yescharacteristic
131C22×D4×C61C2311yescharacteristic
132C23×C4×C61—21no—
133C23×C4×C61—21no—
134C23×C4×C61C2311yescharacteristic
135C23×C4×C61C2311yescharacteristic
136#127×C61—28no—
137#127×C61—22no—
138#127×C61C2×C414yescomplemented
139#121×C61—22no—
140#121×C61—22no—
141#121×C61—28no—
142#121×C61—28no—
143#121×C61C2×C414yes—
144#121×C61C2×C414yescomplemented
145C4×Q8×C61—22no—
146C4×Q8×C61C2×C414yescomplemented
147C4×D4×C61—28no—
148C4×D4×C61C2×C414yes—
149C4×D4×C61D414yes—
150C2×C4⋊C4×C61—21no—
151C2×C4⋊C4×C61D411yescharacteristic
152C2×C4⋊C4×C61C2311yescharacteristic
153C2×C22⋊C4×C61—21no—
154C2×C22⋊C4×C61—21no—
155C2×C22⋊C4×C61D411yescharacteristic
156C2×C22⋊C4×C61D411yescharacteristic
157C2×C42×C61—21no—
158C2×C42×C61C2311yescharacteristic
159C24×C61—21no—
160C24×C61—21no—
161C24×C61C2×D411yescharacteristic
162C24×C61C2×D411yescharacteristic
163#41×C61—28no—
164#41×C61—28no—
165#41×C61—44no—
166#41×C61—44no—
167#41×C61—44no—
168#41×C61—44no—
169#41×C61—44no—
170#41×C61—44no—
171C2×Q8×C61—21no—
172C2×Q8×C61—21no—
173C2×Q8×C61—21no—
174C2×Q8×C61C22×C412yes—
175C2×Q8×C61C2×D412yes—
176C2×Q8×C61#4112yes—
177C2×D4×C61—24no—
178C2×D4×C61—24no—
179C2×D4×C61—24no—
180C2×D4×C61—24no—
181C2×D4×C61—24no—
182C2×D4×C61—24no—
183C2×D4×C61—21no—
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—21no—
193C2×D4×C61—41no—
194C2×D4×C61—41no—
195C2×D4×C61—42no—
196C2×D4×C61—42no—
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×C61—81no—
204C2×D4×C61—81no—
205C2×D4×C61—81no—
206C2×D4×C61—81no—
207C2×D4×C61C22⋊C414yes—
208C2×D4×C61C22×C412yes—
209C2×D4×C61C22×C412yes—
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—21no—
219C22×C4×C61—21no—
220C22×C4×C61—24no—
221C22×C4×C61—24no—
222C22×C4×C61—42no—
223C22×C4×C61—42no—
224C22×C4×C61—42no—
225C22×C4×C61—42no—
226C22×C4×C61C22×C412yes—
227C22×C4×C61C22×C412yes—
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
235C22×Dic61—21no—
236C22×Dic61—21no—
237C22×Dic61—21no—
238C22×Dic61—21no—
239C22×Dic61—42no—
240C22×Dic61—42no—
241C22×Dic61—81no—
242C4⋊C4×C61—24no—
243C4⋊C4×C61—21no—
244C4⋊C4×C61C22⋊C414yes—
245C4⋊C4×C61C22×C412yes—
246C22⋊C4×C61—24no—
247C22⋊C4×C61—24no—
248C22⋊C4×C61C22⋊C414yes—
249C22⋊C4×C61C22⋊C414yes—
250C42×C61—24no—
251C42×C61C22×C412yes—
252C42×C61C2×D412yes—
253C22⋊Dic61—42no—
254C22⋊Dic61—42no—
255C22⋊Dic61—81no—
256C4⋊Dic61—21no—
257C4⋊Dic61—21no—
258C4⋊Dic61—21no—
259C4⋊Dic61—21no—
260C4⋊Dic61—21no—
261C4⋊Dic61—21no—
262C4⋊Dic61—21no—
263C4⋊Dic61—42no—
264C4⋊Dic61C2×D412yes—
265C4×Dic61—42no—
266C4×Dic61—81no—
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—21no—
282C23×C61—21no—
283C23×C61—21no—
284C23×C61—21no—
285C23×C61—21no—
286C23×C61—21no—
287C23×C61—21no—
288C23×C61—21no—
289C23×C61—21no—
290C23×C61—21no—
291C23×C61—21no—
292C23×C61—21no—
293C23×C61—22no—
294C23×C61—22no—
295C23×C61—41no—
296C23×C61—41no—
297C23×C61—41no—
298C23×C61—41no—
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×C61C2×C22⋊C412yes—
308C23×C61C2×C22⋊C412yes—
309C23×C61C22×D411yescharacteristic
310Q8×C61—22no—
311Q8×C61—22no—
312Q8×C61—22no—
313Q8×C61C4×D414yes—
314D4×C61—22no—
315D4×C61—22no—
316D4×C61—22no—
317D4×C61—22no—
318D4×C61—44no—
319D4×C61—48no—
320D4×C61—48no—
321D4×C61—48no—
322D4×C61—41no—
323D4×C61—41no—
324D4×C61—41no—
325D4×C61—41no—
326D4×C61—84no—
327D4×C61—84no—
328D4×C61—84no—
329C2×C4×C61—22no—
330C2×C4×C61—21no—
331C2×C4×C61—21no—
332C2×C4×C61—22no—
333C2×C4×C61—21no—
334C2×C4×C61—21no—
335C2×C4×C61—22no—
336C2×C4×C61—21no—
337C2×C4×C61—21no—
338C2×C4×C61—21no—
339C2×C4×C61—21no—
340C2×C4×C61—22no—
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—48no—
350C2×C4×C61—48no—
351C2×C4×C61—41no—
352C2×C4×C61—41no—
353C2×C4×C61C2×C22⋊C412yes—
354C2×C4×C61C2×C22⋊C412yes—
355C2×C4×C61C2×C22⋊C412yes—
356C2×C4×C61C2×C22⋊C412yes—
357C2×C4×C61C23×C411yescharacteristic
358C2×C4×C61C22×D411yescharacteristic
359C2×C4×C61C22×D411yescharacteristic
360C2×C4×C61C2×#4111yescharacteristic
361C2×C4×C61H(5,𝔽2)11yescharacteristic
362C2×C4×C61H(5,𝔽2)11yescharacteristic
363C2×Dic61—22no—
364C2×Dic61—41no—
365C2×Dic61—41no—
366C2×Dic61—41no—
367C2×Dic61—41no—
368C2×Dic61—41no—
369C2×Dic61—41no—
370C2×Dic61—41no—
371C2×Dic61—41no—
372C2×Dic61—41no—
373C2×Dic61—41no—
374C2×Dic61—41no—
375C2×Dic61—84no—
376#92418—22no—
377#92418—41no—
378#92418—41no—
379#92418—41no—
380#22422—611nomaximal, Sylow
381C22×C61—22no—
382C22×C61—22no—
383C22×C61—22no—
384C22×C61—22no—
385C22×C61—22no—
386C22×C61—22no—
387C22×C61—41no—
388C22×C61—41no—
389C22×C61—41no—
390C22×C61—41no—
391C22×C61—41no—
392C22×C61—41no—
393C22×C61—41no—
394C22×C61—41no—
395C22×C61—42no—
396C22×C61—42no—
397C22×C61—42no—
398C22×C61—42no—
399C22×C61—42no—
400C22×C61—42no—
401C22×C61—81no—
402C22×C61—81no—
403C22×C61—81no—
404C22×C61—81no—
405C22×C61—81no—
406C22×C61—81no—
407C22×C61—81no—
408C22×C61—81no—
409C22×C61C22×C22⋊C411yescharacteristic
410C22×C61D4211yescharacteristic
411C22×C61#54611yescharacteristic
412C22×C61#57511yescharacteristic
413C22×C61#57511yescharacteristic
414C22×C61#57611yescharacteristic
415C22×C61#57711yescharacteristic
416C4×C61—22no—
417C4×C61—22no—
418C4×C61—24no—
419C4×C61—22no—
420C4×C61—22no—
421C4×C61—42no—
422C4×C61C2×C4×D411yescharacteristic
423C4×C61#51811yescharacteristic
424C4×C61D4211yescharacteristic
425C4×C61#54611yescharacteristic
426Dic61—42no—
427Dic61—81no—
428Dic61—81no—
429Dic61—81no—
430C2×#550D6111yescharacteristic
431C2×#435—611no—
432C2×#417—611no—
433C2×#416—611no—
434#2352—611no—
435#1982—611no—
436#1961—611no—
437#1895—611no—
438#1893—611no—
439#1875—611no—
440#1874—611no—
441#1805—611no—
442#1788—611no—
443#1788—611no—
444#1763—611no—
445C2×C61—42no—
446C2×C61—42no—
447C2×C61—82no—
448C2×C61—82no—
449C2×C61D4×C22⋊C411yescharacteristic
450C2×C61#289611yescharacteristic
451C2×C61#289711yescharacteristic
452C2×C61#326811yescharacteristic
453C2×C61#327111yescharacteristic
454C2×C61#330911yescharacteristic
455C2×C61#331711yescharacteristic
456C22×#41C2×D6111yescharacteristic
457C22×#41C2×D6111yescharacteristic
458C22×M16—611no—
459C23×C8—611no—
460#550—24no—
461#550Dic6118yescomplemented
462C2×#127—21no—
463C2×#127C2×D6111yescharacteristic
464C2×#121—21no—
465C2×#121—21no—
466C2×#121C2×D6111yescharacteristic
467C2×#121C2×D6111yescharacteristic
468C2×C4×Q8C2×D6111yescharacteristic
469C2×C4×D4—21no—
470C2×C4×D4C2×D6111yescharacteristic
471C2×#117—611no—
472C22×C4⋊C4—611no—
473#435—1224no—
474C2×C4⋊C8—611no—
475#417—1224no—
476#416—1224no—
477C2×#103—611no—
478C2×#103—611no—
479C2×#103—611no—
480C2×#103—611no—
481C2×#102—611no—
482C2×#102—611no—
483C2×#102—611no—
484C2×#102—611no—
485C2×#102—611no—
486C2×#102—611no—
487C2×#102—611no—
488C2×#102—611no—
489C2×C22⋊C8—611no—
490C2×C22⋊C8—611no—
491C2×#97—611no—
492#388—1221no—
493#387—1221no—
494#386—1221no—
495#382—611no—
496#380—611no—
497#380—611no—
498C4×C4⋊C4—611no—
499C4×C22⋊C4—1221no—
500#340—611no—
501#340—611no—
502#340—611no—
503#340—611no—
504C61#2242211yescharacteristic, complemented, Sylow
505C2×#41—22no—
506C2×#41—22no—
507C2×#41—22no—
508C2×#41—22no—
509C2×#41—22no—
510C2×#41—22no—
511C2×#41—41no—
512C2×#41—41no—
513C2×#41—41no—
514C2×#41—41no—
515C2×#41C2×Dic6114yes—
516C2×#41C2×Dic6114yescomplemented
517C22×Q8C22×D6111yescharacteristic
518C22×D4—21no—
519C22×D4—21no—
520C22×D4—21no—
521C22×D4—21no—
522C22×D4—21no—
523C22×D4—21no—
524C22×D4C22⋊D6111yescharacteristic
525C22×D4C22×D6111yescharacteristic
526C22×D4C22×D6111yescharacteristic
527C23×C4—21no—
528C23×C4—21no—
529C23×C4—1221no—
530C23×C4C22×D6111yescharacteristic
531C23×C4C22×D6111yescharacteristic
532C2×M16—1222no—
533C2×M16—1222no—
534C2×M16—2441no—
535C22×C8—611no—
536C22×C8—611no—
537C22×C8—611no—
538C22×C8—611no—
539C22×C8—1222no—
540C22×C8—1222no—
541C22×C8—2441no—
542#127—28no—
543#127—22no—
544#127C2×Dic6114yescomplemented
545#121—22no—
546#121—22no—
547#121—28no—
548#121—28no—
549#121C2×Dic6114yes—
550#121C2×Dic6114yescomplemented
551C4×Q8—22no—
552C4×Q8C2×Dic6114yescomplemented
553C4×D4—28no—
554C4×D4C2×Dic6114yes—
555C4×D4C22⋊D6114yes—
556#117—1222no—
557#117—2441no—
558C2×C4⋊C4—21no—
559C2×C4⋊C4—611no—
560C2×C4⋊C4—611no—
561C2×C4⋊C4—611no—
562C2×C4⋊C4—611no—
563C2×C4⋊C4—1222no—
564C2×C4⋊C4—1221no—
565C2×C4⋊C4—2441no—
566C2×C4⋊C4C22⋊D6111yescharacteristic
567C2×C4⋊C4C22×D6111yescharacteristic
568C2×C22⋊C4—21no—
569C2×C22⋊C4—21no—
570C2×C22⋊C4—1221no—
571C2×C22⋊C4—1221no—
572C2×C22⋊C4—1221no—
573C2×C22⋊C4C22⋊D6111yescharacteristic
574C2×C22⋊C4C22⋊D6111yescharacteristic
575C2×C42—21no—
576C2×C42—1221no—
577C2×C42—1221no—
578C2×C42C22×D6111yescharacteristic
579C4⋊C8—1222no—
580#103—614no—
581#103—1222no—
582#103—1222no—
583#103—1222no—
584#102—1222no—
585#102—1222no—
586#102—1222no—
587#102—1222no—
588#102—2441no—
589#102—2441no—
590#102—2441no—
591#102—2441no—
592C22⋊C8—1222no—
593C22⋊C8—1222no—
594#97—1222no—
595#95—1221no—
596#95—1221no—
597#95—1221no—
598#95—1221no—
599#95—1221no—
600C24—21no—
601C24—21no—
602C24C2×C22⋊D6111yescharacteristic
603C24C2×C22⋊D6111yescharacteristic
604#41—28no—
605#41—28no—
606#41—44no—
607#41—44no—
608#41—44no—
609#41—44no—
610#41—44no—
611#41—44no—
612C2×Q8—21no—
613C2×Q8—21no—
614C2×Q8—21no—
615C2×Q8D4×D6112yes—
616C2×Q8#1175822412yes—
617C2×Q8C22×Dic6112yes—
618C2×D4—24no—
619C2×D4—24no—
620C2×D4—24no—
621C2×D4—24no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—21no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—24no—
633C2×D4—24no—
634C2×D4—41no—
635C2×D4—41no—
636C2×D4—42no—
637C2×D4—42no—
638C2×D4—42no—
639C2×D4—42no—
640C2×D4—42no—
641C2×D4—42no—
642C2×D4—81no—
643C2×D4—81no—
644C2×D4—81no—
645C2×D4—81no—
646C2×D4—81no—
647C2×D4—81no—
648C2×D4C22⋊Dic6114yes—
649C2×D4C22×Dic6112yes—
650C2×D4C22×Dic6112yes—
651C22×C4—21no—
652C22×C4—21no—
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—24no—
662C22×C4—24no—
663C22×C4—42no—
664C22×C4—42no—
665C22×C4—42no—
666C22×C4—42no—
667C22×C4—1221no—
668C22×C4—1221no—
669C22×C4—1221no—
670C22×C4—1221no—
671C22×C4—4881no—
672C22×C4—2442no—
673C22×C4—2442no—
674C22×C4C22×Dic6112yes—
675C22×C4C22×Dic6112yes—
676C22×C4C2×C22⋊D6112yes—
677C22×C4C2×C22⋊D6112yes—
678C22×C4C2×C22⋊D6111yescharacteristic
679C22×C4C2×C22⋊D6111yescharacteristic
680C22×C4C2×C22⋊D6111yescharacteristic
681C22×C4C2×C22⋊D6111yescharacteristic
682C22×C4C23×D6111yescharacteristic
683M16—2444no—
684C2×C8—612no—
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—1221no—
696C2×C8—2444no—
697C4⋊C4—21no—
698C4⋊C4—24no—
699C4⋊C4—612no—
700C4⋊C4—1221no—
701C4⋊C4—1221no—
702C4⋊C4—1221no—
703C4⋊C4—1221no—
704C4⋊C4—1221no—
705C4⋊C4—1221no—
706C4⋊C4—1221no—
707C4⋊C4—2442no—
708C4⋊C4C22⋊Dic6114yes—
709C4⋊C4C22×Dic6112yes—
710C22⋊C4—24no—
711C22⋊C4—24no—
712C22⋊C4—4881no—
713C22⋊C4—2442no—
714C22⋊C4—2442no—
715C22⋊C4C22⋊Dic6114yes—
716C22⋊C4C22⋊Dic6114yes—
717C42—24no—
718C42—4881no—
719C42—2442no—
720C42C22×Dic6112yes—
721C42C2×C22⋊D6112yes—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—21no—
734C23—22no—
735C23—22no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23C2×C22⋊Dic6112yes—
749C23C2×C22⋊Dic6112yes—
750C23C22×C22⋊D6111yescharacteristic
751Q8—22no—
752Q8—22no—
753Q8—22no—
754Q8D4×Dic6114yes—
755D4—22no—
756D4—22no—
757D4—22no—
758D4—22no—
759D4—44no—
760D4—48no—
761D4—48no—
762D4—48no—
763D4—41no—
764D4—41no—
765D4—41no—
766D4—41no—
767D4—84no—
768D4—84no—
769D4—84no—
770C2×C4—22no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—22no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—48no—
791C2×C4—48no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—1222no—
795C2×C4—4884no—
796C2×C4—2441no—
797C2×C4—2441no—
798C2×C4—2441no—
799C2×C4—2441no—
800C2×C4—2441no—
801C2×C4—2441no—
802C2×C4—2441no—
803C2×C4—2441no—
804C2×C4—2441no—
805C2×C4—2441no—
806C2×C4—2441no—
807C2×C4C2×C22⋊Dic6112yes—
808C2×C4C2×C22⋊Dic6112yes—
809C2×C4C2×C22⋊Dic6112yes—
810C2×C4C2×C22⋊Dic6112yes—
811C2×C4C23×Dic6111yescharacteristic
812C2×C4C2×D4×D6111yescharacteristic
813C2×C4C22×C22⋊D6111yescharacteristic
814C2×C4C2×#1175822411yescharacteristic
815C2×C4#1451982211yescharacteristic
816C2×C4#1451982211yescharacteristic
817C8—1222no—
818C8—2441no—
819C8—2441no—
820C8—2441no—
821C22—22no—
822C22—22no—
823C22—22no—
824C22—22no—
825C22—22no—
826C22—22no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—41no—
834C22—41no—
835C22—42no—
836C22—42no—
837C22—42no—
838C22—42no—
839C22—42no—
840C22—42no—
841C22—81no—
842C22—81no—
843C22—81no—
844C22—81no—
845C22—81no—
846C22—81no—
847C22—81no—
848C22—81no—
849C22C22×C22⋊Dic6111yescharacteristic
850C22D4×C22⋊D6111yescharacteristic
851C22#1684040611yescharacteristic
852C22#1684056011yescharacteristic
853C22#1684056011yescharacteristic
854C22#1684056511yescharacteristic
855C22#1684057311yescharacteristic
856C4—22no—
857C4—22no—
858C4—22no—
859C4—22no—
860C4—24no—
861C4—42no—
862C4—4881no—
863C4—4881no—
864C4—4881no—
865C4—2442no—
866C4C2×D4×Dic6111yescharacteristic
867C4#1684023711yescharacteristic
868C4D4×C22⋊D6111yescharacteristic
869C4#1684040611yescharacteristic
870C2—42no—
871C2—42no—
872C2—82no—
873C2—82no—
874C2D4×C22⋊Dic6111yescharacteristic
875C2#2145433811yescharacteristic
876C2#2145434511yescharacteristic
877C2#2145736011yescharacteristic
878C2#2145740011yescharacteristic
879C2#2145782511yescharacteristic
880C2#2145794511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
Fitting, prime radicalC2×C61×#550C2
socleC23×C61C22×D4
cosocleC22×C4×C61C24
hypercenterC2×#550D61
hypocenterC61#22422
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#550

Complements

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

NH ≅ G/Ntype
1. C2×#16839834C2semidirect
2. C2×#16839763C2semidirect
3. C2×#16839758C2semidirect
4. #21448748C2semidirect
5. #21446747C2semidirect
6. #21446644C2semidirect
7. #21446258C2semidirect
8. #21446248C2semidirect
9. #21446142C2semidirect
10. #21446137C2semidirect
11. #21445834C2semidirect
12. #21445759C2semidirect
13. #21445759C2semidirect
14. #21445649C2semidirect
54. C61×#550C4semidirect
93. #14519701D4semidirect
121. C2×#41×C61C2×C4semidirect
138. #127×C61C2×C4semidirect
144. #121×C61C2×C4semidirect
146. C4×Q8×C61C2×C4semidirect
461. #550Dic61semidirect
504. C61#22422semidirect
516. C2×#41C2×Dic61semidirect
544. #127C2×Dic61semidirect
550. #121C2×Dic61semidirect
552. C4×Q8C2×Dic61semidirect

Maximal subgroups

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

subgroupindex
C2×#168398342
C2×#168397632
C2×#168397582
#214487482
#214467472
#214466442
#214462582
#214462482
#214461422
#214461372
#214458342
#214457592
#214456492
C2×C61×#5502
#2242261