Finite Group Databasebeta

← #29695613

Subgroups — #29695613

Order 15616.

1606 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839840C211yesmaximal, characteristic, complemented
2C2×#16839763C211yesmaximal, characteristic, complemented
3C2×#16839767C211yesmaximal, characteristic, complemented
4#21448748C211yesmaximal, characteristic, complemented
5#21446752C211yesmaximal, characteristic, complemented
6#21446631C211yesmaximal, characteristic, complemented
7#21446258C211yesmaximal, characteristic, complemented
8#21446253C211yesmaximal, characteristic, complemented
9#21446137C211yesmaximal, characteristic, complemented
10#21446132C211yesmaximal, characteristic, complemented
11#21445829C211yesmaximal, characteristic, complemented
12#21445759C211yesmaximal, characteristic, complemented
13#21445750C211yesmaximal, characteristic, complemented
14C4×#14519698C211yesmaximal, characteristic, complemented
15C2×C61×#546C211yesmaximal, characteristic
16C22×#11758194C2211yescharacteristic
17C22×#11758194C2211yescharacteristic, complemented
18C2×#14519736C2211yescharacteristic
19C22×C4⋊Dic61C2211yescharacteristic, complemented
20#16839840—24no—
21C2×C4⋊#92418C2211yescharacteristic, complemented
22#16839767—24no—
23#16839763—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×C4×#92418C2211yescharacteristic, complemented
39#16839655—21no—
40#16839648—21no—
41#16839642—21no—
42#16839628C2211yescharacteristic, complemented
43#16839622C2211yescharacteristic
44#16839622C2211yescharacteristic, complemented
45C4×C4⋊Dic61C2211yescharacteristic, complemented
46C22⋊C4×Dic61—21no—
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—
64C23×Dic61—21no—
65C2×#11758194—22no—
66C2×#11758194—22no—
67C2×#11758194—22no—
68C2×#11758194—22no—
69C2×#11758194—41no—
70C2×#11758194—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—41no—
93#14519701—41no—
94#14519698—22no—
95#14519698—22no—
96#14519698—22no—
97#14519698—22no—
98#14519698—22no—
99#14519698—41no—
100#14519698—41no—
101#14519698D414yescomplemented
102C22⋊#92418—22no—
103C22⋊#92418—22no—
104C4×#92418—22no—
105#14519684—21no—
106#14519684—21no—
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×C414yescomplemented
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×C414yescomplemented
136#123×C61—28no—
137C22⋊Q8×C61—22no—
138C22⋊Q8×C61C2×C414yescomplemented
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×C414yescomplemented
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—
237C22×Dic61—42no—
238C22×Dic61—42no—
239C22×Dic61—81no—
240C4⋊C4×C61—24no—
241C4⋊C4×C61—21no—
242C4⋊C4×C61C22⋊C414yes—
243C4⋊C4×C61C22×C412yes—
244C22⋊C4×C61—24no—
245C22⋊C4×C61—24no—
246C22⋊C4×C61—24no—
247C22⋊C4×C61—24no—
248C22⋊C4×C61—24no—
249C22⋊C4×C61C22⋊C414yes—
250C22⋊C4×C61C22⋊C414yes—
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—
268#11758194—44no—
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—21no—
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—
379C2×Dic61—84no—
380#92418—22no—
381#92418—41no—
382#92418—41no—
383#92418—41no—
384#22427—611nomaximal, Sylow
385C22×C61—22no—
386C22×C61—22no—
387C22×C61—24no—
388C22×C61—22no—
389C22×C61—22no—
390C22×C61—22no—
391C22×C61—22no—
392C22×C61—42no—
393C22×C61—42no—
394C22×C61—41no—
395C22×C61—41no—
396C22×C61—42no—
397C22×C61—41no—
398C22×C61—41no—
399C22×C61—42no—
400C22×C61—41no—
401C22×C61—41no—
402C22×C61—42no—
403C22×C61—41no—
404C22×C61—41no—
405C22×C61—42no—
406C22×C61—42no—
407C22×C61—42no—
408C22×C61—42no—
409C22×C61—816no—
410C22×C61—81no—
411C22×C61—81no—
412C22×C61—81no—
413C22×C61—81no—
414C22×C61C22×C22⋊C411yescharacteristic
415C22×C61D4211yescharacteristic
416C22×C61#54611yescharacteristic
417C22×C61#57511yescharacteristic
418C22×C61#57511yescharacteristic
419C22×C61#57611yescharacteristic
420C22×C61#57711yescharacteristic
421C4×C61—22no—
422C4×C61—22no—
423C4×C61—22no—
424C4×C61—22no—
425C4×C61—42no—
426C4×C61—42no—
427C4×C61C2×C4×D411yescharacteristic
428C4×C61#51811yescharacteristic
429C4×C61D4211yescharacteristic
430C4×C61#54611yescharacteristic
431Dic61—42no—
432Dic61—81no—
433Dic61—81no—
434Dic61—81no—
435C2×#546D6111yescharacteristic
436C2×#436—611no—
437C2×#417—611no—
438C2×#418—611no—
439#2352—611no—
440#1983—611no—
441#1958—611no—
442#1895—611no—
443#1894—611no—
444#1874—611no—
445#1873—611no—
446#1804—611no—
447#1788—611no—
448#1786—611no—
449C4×#102—611no—
450C2×C61—42no—
451C2×C61—42no—
452C2×C61—44no—
453C2×C61—82no—
454C2×C61D4×C22⋊C411yescharacteristic
455C2×C61#289611yescharacteristic
456C2×C61#289711yescharacteristic
457C2×C61#327311yescharacteristic
458C2×C61#327511yescharacteristic
459C2×C61#332211yescharacteristic
460C2×C61#332311yescharacteristic
461C22×#41C2×D6111yescharacteristic
462C23×D4C2×D6111yescharacteristic
463C22×M16—611no—
464C22×M16—611no—
465#546—24no—
466#546Dic6118yescomplemented
467C2×#124C2×D6111yescharacteristic
468C2×#123—21no—
469C2×C22⋊Q8C2×D6111yescharacteristic
470C2×#121—21no—
471C2×#121C2×D6111yescharacteristic
472C2×#120—21no—
473C2×C4×D4C2×D6111yescharacteristic
474C2×C4×D4C2×D6111yescharacteristic
475C2×#117—611no—
476C22×C4⋊C4—611no—
477C22×C22⋊C4—21no—
478#436—1224no—
479C2×C4⋊C8—611no—
480#418—1224no—
481#417—1224no—
482C2×#103—611no—
483C2×#103—611no—
484C2×#103—611no—
485C2×#103—611no—
486C2×#102—611no—
487C2×#102—611no—
488C2×#102—611no—
489C2×#102—611no—
490C2×#102—611no—
491C2×#102—611no—
492C2×#102—611no—
493C2×#102—611no—
494C2×C22⋊C8—611no—
495C2×C22⋊C8—611no—
496C2×C4×C8—611no—
497#388—1221no—
498#387—1221no—
499#386—1221no—
500#382—611no—
501#380—611no—
502#380—611no—
503C4×C4⋊C4—611no—
504C4×C22⋊C4—1221no—
505#340—611no—
506#340—611no—
507#340—611no—
508#340—611no—
509C61#2242711yescharacteristic, complemented, Sylow
510C25—21no—
511C2×#41—22no—
512C2×#41—22no—
513C2×#41—22no—
514C2×#41—41no—
515C2×#41—41no—
516C2×#41C2×Dic6114yes—
517C22×Q8C22×D6111yescharacteristic
518C22×D4—22no—
519C22×D4—22no—
520C22×D4—21no—
521C22×D4—21no—
522C22×D4—21no—
523C22×D4—22no—
524C22×D4—41no—
525C22×D4—41no—
526C22×D4C2×Dic6114yescomplemented
527C22×D4C22⋊D6111yescharacteristic
528C22×D4C22×D6111yescharacteristic
529C22×D4C22×D6111yescharacteristic
530C23×C4—21no—
531C23×C4—21no—
532C23×C4—1221no—
533C23×C4C22×D6111yescharacteristic
534C23×C4C22×D6111yescharacteristic
535C2×M16—1222no—
536C2×M16—1222no—
537C2×M16—1222no—
538C2×M16—1222no—
539C2×M16—2441no—
540C2×M16—2441no—
541C22×C8—611no—
542C22×C8—611no—
543C22×C8—611no—
544C22×C8—611no—
545#124—22no—
546#124C2×Dic6114yescomplemented
547#123—28no—
548C22⋊Q8—22no—
549C22⋊Q8C2×Dic6114yescomplemented
550#121—22no—
551#121—28no—
552#121C2×Dic6114yes—
553#120—28no—
554C4×D4—22no—
555C4×D4C2×Dic6114yes—
556C4×D4C2×Dic6114yescomplemented
557C4×D4C22⋊D6114yes—
558#117—1222no—
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—1222no—
566C2×C4⋊C4—1221no—
567C2×C4⋊C4—2441no—
568C2×C4⋊C4C22⋊D6111yescharacteristic
569C2×C4⋊C4C22×D6111yescharacteristic
570C2×C22⋊C4—21no—
571C2×C22⋊C4—21no—
572C2×C22⋊C4—21no—
573C2×C22⋊C4—21no—
574C2×C22⋊C4—21no—
575C2×C22⋊C4—28no—
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×C42C22×D6111yescharacteristic
584C4⋊C8—1222no—
585#103—1222no—
586#103—1222no—
587#103—2441no—
588#103—2441no—
589#102—614no—
590#102—1222no—
591#102—1222no—
592#102—1222no—
593#102—1222no—
594#102—1222no—
595#102—2441no—
596#102—2441no—
597C22⋊C8—1222no—
598C22⋊C8—1222no—
599C4×C8—1222no—
600#95—1221no—
601#95—1221no—
602#95—1221no—
603#95—1221no—
604#95—1221no—
605C24—21no—
606C24—21no—
607C24—24no—
608C24—42no—
609C24—42no—
610C24—42no—
611C24—42no—
612C24—81no—
613C24—81no—
614C24C2×C22⋊D6111yescharacteristic
615C24C2×C22⋊D6111yescharacteristic
616#41—28no—
617#41—44no—
618#41—44no—
619#41—44no—
620C2×Q8—21no—
621C2×Q8—21no—
622C2×Q8—21no—
623C2×Q8—21no—
624C2×Q8—21no—
625C2×Q8C22×Dic6112yes—
626C2×D4—28no—
627C2×D4—24no—
628C2×D4—24no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4—21no—
634C2×D4—21no—
635C2×D4—21no—
636C2×D4—21no—
637C2×D4—24no—
638C2×D4—44no—
639C2×D4—44no—
640C2×D4—44no—
641C2×D4—41no—
642C2×D4—41no—
643C2×D4—42no—
644C2×D4—42no—
645C2×D4—42no—
646C2×D4—42no—
647C2×D4—81no—
648C2×D4—81no—
649C2×D4C22⋊Dic6114yes—
650C2×D4D4×D6112yes—
651C2×D4#1175822412yes—
652C2×D4C22×Dic6112yes—
653C2×D4C22×Dic6112yes—
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—21no—
664C22×C4—24no—
665C22×C4—24no—
666C22×C4—42no—
667C22×C4—42no—
668C22×C4—81no—
669C22×C4—81no—
670C22×C4—1221no—
671C22×C4—1221no—
672C22×C4—1221no—
673C22×C4—1221no—
674C22×C4—4881no—
675C22×C4—2442no—
676C22×C4—2442no—
677C22×C4C22×Dic6112yes—
678C22×C4C22×Dic6112yes—
679C22×C4C2×C22⋊D6112yes—
680C22×C4C2×C22⋊D6112yes—
681C22×C4C2×C22⋊D6111yescharacteristic
682C22×C4C2×C22⋊D6111yescharacteristic
683C22×C4C2×C22⋊D6111yescharacteristic
684C22×C4C2×C22⋊D6111yescharacteristic
685C22×C4C23×D6111yescharacteristic
686M16—2444no—
687M16—2444no—
688C2×C8—612no—
689C2×C8—1221no—
690C2×C8—1221no—
691C2×C8—1221no—
692C2×C8—1221no—
693C2×C8—1221no—
694C2×C8—1221no—
695C2×C8—1221no—
696C2×C8—1221no—
697C2×C8—1221no—
698C2×C8—1221no—
699C2×C8—1221no—
700C4⋊C4—21no—
701C4⋊C4—24no—
702C4⋊C4—612no—
703C4⋊C4—1221no—
704C4⋊C4—1221no—
705C4⋊C4—1221no—
706C4⋊C4—1221no—
707C4⋊C4—1221no—
708C4⋊C4—1221no—
709C4⋊C4—1221no—
710C4⋊C4—2442no—
711C4⋊C4C22⋊Dic6114yes—
712C4⋊C4C22×Dic6112yes—
713C22⋊C4—24no—
714C22⋊C4—24no—
715C22⋊C4—24no—
716C22⋊C4—24no—
717C22⋊C4—24no—
718C22⋊C4—4881no—
719C22⋊C4—2442no—
720C22⋊C4—2442no—
721C22⋊C4C22⋊Dic6114yes—
722C22⋊C4C22⋊Dic6114yes—
723C42—4881no—
724C42—2442no—
725C42C22×Dic6112yes—
726C42C2×C22⋊D6112yes—
727C23—22no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—21no—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—21no—
738C23—22no—
739C23—21no—
740C23—21no—
741C23—22no—
742C23—22no—
743C23—48no—
744C23—48no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23—41no—
754C23—41no—
755C23—84no—
756C23—84no—
757C23—84no—
758C23—84no—
759C23—84no—
760C23C2×C22⋊Dic6112yes—
761C23C2×C22⋊Dic6112yes—
762C23C22×C22⋊D6111yescharacteristic
763Q8—22no—
764Q8—22no—
765Q8—41no—
766Q8—41no—
767D4—22no—
768D4—22no—
769D4—22no—
770D4—22no—
771D4—22no—
772D4—44no—
773D4—48no—
774D4—48no—
775D4—41no—
776D4—41no—
777D4—84no—
778D4D4×Dic6114yes—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
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—22no—
797C2×C4—48no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—84no—
803C2×C4—1222no—
804C2×C4—4884no—
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×C4—2441no—
815C2×C4—2441no—
816C2×C4C2×C22⋊Dic6112yes—
817C2×C4C2×C22⋊Dic6112yes—
818C2×C4C2×C22⋊Dic6112yes—
819C2×C4C2×C22⋊Dic6112yes—
820C2×C4C23×Dic6111yescharacteristic
821C2×C4C2×D4×D6111yescharacteristic
822C2×C4C22×C22⋊D6111yescharacteristic
823C2×C4C2×#1175822411yescharacteristic
824C2×C4#1451982211yescharacteristic
825C2×C4#1451982211yescharacteristic
826C8—1222no—
827C8—2441no—
828C8—2441no—
829C8—2441no—
830C22—22no—
831C22—22no—
832C22—22no—
833C22—22no—
834C22—22no—
835C22—22no—
836C22—24no—
837C22—42no—
838C22—42no—
839C22—41no—
840C22—41no—
841C22—42no—
842C22—41no—
843C22—41no—
844C22—42no—
845C22—41no—
846C22—41no—
847C22—42no—
848C22—41no—
849C22—41no—
850C22—42no—
851C22—42no—
852C22—42no—
853C22—42no—
854C22—816no—
855C22—81no—
856C22—81no—
857C22—81no—
858C22—81no—
859C22C22×C22⋊Dic6111yescharacteristic
860C22D4×C22⋊D6111yescharacteristic
861C22#1684040611yescharacteristic
862C22#1684056011yescharacteristic
863C22#1684056011yescharacteristic
864C22#1684056511yescharacteristic
865C22#1684057311yescharacteristic
866C4—22no—
867C4—22no—
868C4—22no—
869C4—22no—
870C4—42no—
871C4—42no—
872C4—4881no—
873C4—4881no—
874C4—4881no—
875C4—2442no—
876C4C2×D4×Dic6111yescharacteristic
877C4#1684023711yescharacteristic
878C4D4×C22⋊D6111yescharacteristic
879C4#1684040611yescharacteristic
880C2—42no—
881C2—42no—
882C2—44no—
883C2—82no—
884C2D4×C22⋊Dic6111yescharacteristic
885C2#2145433811yescharacteristic
886C2#2145434511yescharacteristic
887C2#2145742611yescharacteristic
888C2#2145744611yescharacteristic
889C2#2145802011yescharacteristic
890C2#2145803511yescharacteristic
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#22427
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×#16839840C2semidirect
2. C2×#16839763C2semidirect
3. C2×#16839767C2semidirect
4. #21448748C2semidirect
5. #21446752C2semidirect
6. #21446631C2semidirect
7. #21446258C2semidirect
8. #21446253C2semidirect
9. #21446137C2semidirect
10. #21446132C2semidirect
11. #21445829C2semidirect
12. #21445759C2semidirect
13. #21445750C2semidirect
14. C4×#14519698C2semidirect
17. C22×#11758194C22semidirect
19. C22×C4⋊Dic61C22semidirect
21. C2×C4⋊#92418C22semidirect
24. C2×#14519701C22semidirect
25. C2×#14519701C22semidirect
26. C2×#14519701C22semidirect
27. C2×#14519701C22semidirect
37. C2×C22⋊#92418C22semidirect
38. C2×C4×#92418C22semidirect
42. #16839628C22semidirect
44. #16839622C22semidirect
45. C4×C4⋊Dic61C22semidirect
47. #16839524C22semidirect
48. #16839524C22semidirect
49. #16839524C22semidirect
50. #16839524C22semidirect
54. C61×#546C4semidirect
101. #14519698D4semidirect
126. C22×D4×C61C2×C4semidirect
135. #124×C61C2×C4semidirect
138. C22⋊Q8×C61C2×C4semidirect
145. C4×D4×C61C2×C4semidirect
466. #546Dic61semidirect
509. C61#22427semidirect
526. C22×D4C2×Dic61semidirect
546. #124C2×Dic61semidirect
549. C22⋊Q8C2×Dic61semidirect
556. C4×D4C2×Dic61semidirect

Maximal subgroups

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

subgroupindex
C2×#168398402
C2×#168397632
C2×#168397672
#214487482
#214467522
#214466312
#214462582
#214462532
#214461372
#214461322
#214458292
#214457592
#214457502
C4×#145196982
C2×C61×#5462
#2242761