Finite Group Databasebeta

← #29695493

Subgroups — #29695493

Order 15616.

1670 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839834C211yesmaximal, characteristic, complemented
2C2×#16839763C211yesmaximal, characteristic, complemented
3C22×#14519698C211yesmaximal, characteristic, complemented
4D4×C4⋊Dic61C211yesmaximal, characteristic, complemented
5#21446752C211yesmaximal, characteristic, complemented
6#21446636C211yesmaximal, characteristic, complemented
7#21446258C211yesmaximal, characteristic, complemented
8#21446243C211yesmaximal, characteristic, complemented
9#21446137C211yesmaximal, characteristic, complemented
10#21446127C211yesmaximal, characteristic, complemented
11#21445819C211yesmaximal, characteristic, complemented
12#21445759C211yesmaximal, characteristic, complemented
13#21445750C211yesmaximal, characteristic, complemented
14#21445644C211yesmaximal, characteristic, complemented
15C2×C61×#546C211yesmaximal, characteristic
16C22×#11758194C2211yescharacteristic, complemented
17C23×#92418C2211yescharacteristic
18C2×D4×Dic61—21no—
19C22×C4⋊Dic61C2211yescharacteristic
20C22×C4⋊Dic61C2211yescharacteristic, complemented
21#16839834—24no—
22C2×C4⋊#92418C2211yescharacteristic, complemented
23#16839763—24no—
24C2×#14519701C2211yescharacteristic, complemented
25C2×#14519701C2211yescharacteristic, complemented
26C2×#14519701C2211yescharacteristic, complemented
27C2×#14519701C2211yescharacteristic, complemented
28C2×#14519698—24no—
29C2×#14519698C2211yescharacteristic
30C2×#14519698C2211yescharacteristic
31C2×#14519698C2211yescharacteristic
32C2×#14519698C2211yescharacteristic
33C2×#14519698C2211yescharacteristic
34C2×#14519698C2211yescharacteristic
35C2×#14519698C2211yescharacteristic
36C2×#14519698C2211yescharacteristic
37C2×C22⋊#92418C2211yescharacteristic
38C2×C22⋊#92418C2211yescharacteristic, complemented
39C2×#14519688C2211yescharacteristic, complemented
40#16839661—21no—
41#16839637—21no—
42#16839637—21no—
43#16839632C2211yescharacteristic, complemented
44#16839622C2211yescharacteristic
45#16839622C2211yescharacteristic, complemented
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—
64C23×Dic61—21no—
65C23×Dic61—21no—
66C2×#11758194—22no—
67C2×#11758194—22no—
68C2×#11758194—41no—
69C22×#92418—22no—
70C22×#92418—22no—
71C22×#92418—41no—
72C22×#92418C2311yescharacteristic
73C22×#92418C2311yescharacteristic
74C22×#92418C2311yescharacteristic
75C22×#92418C2311yescharacteristic
76D4×Dic61—44no—
77C2×C4⋊Dic61—22no—
78C2×C4⋊Dic61—22no—
79C2×C4⋊Dic61—21no—
80C2×C4⋊Dic61—21no—
81C2×C4⋊Dic61—21no—
82C2×C4⋊Dic61—21no—
83C2×C4⋊Dic61—41no—
84C2×C4⋊Dic61—41no—
85C2×C4⋊Dic61C2311yescharacteristic
86C2×C4⋊Dic61C2311yescharacteristic
87C2×C4⋊Dic61C2311yescharacteristic
88C2×C4⋊Dic61C2311yescharacteristic
89C2×C22⋊Dic61—21no—
90C2×C22⋊Dic61—21no—
91C2×C4×Dic61—21no—
92C4⋊#92418—22no—
93#14519701—22no—
94#14519701—22no—
95#14519701—41no—
96#14519701—41no—
97#14519698—22no—
98#14519698—22no—
99#14519698—22no—
100#14519698—22no—
101#14519698—22no—
102#14519698—41no—
103#14519698—41no—
104#14519698D414yescomplemented
105C22⋊#92418—22no—
106C22⋊#92418—22no—
107#14519688—22no—
108#14519684—21no—
109#14519684—21no—
110#14519684—21no—
111C25×C61—21no—
112C2×#41×C61—22no—
113C2×#41×C61—22no—
114C2×#41×C61—22no—
115C2×#41×C61—41no—
116C2×#41×C61—41no—
117C2×#41×C61C2×C414yescomplemented
118C22×Q8×C61C2311yescharacteristic
119C22×D4×C61—22no—
120C22×D4×C61—22no—
121C22×D4×C61—21no—
122C22×D4×C61—21no—
123C22×D4×C61—22no—
124C22×D4×C61—21no—
125C22×D4×C61—41no—
126C22×D4×C61—41no—
127C22×D4×C61C2×C414yescomplemented
128C22×D4×C61D411yescharacteristic
129C22×D4×C61C2311yescharacteristic
130C22×D4×C61C2311yescharacteristic
131C23×C4×C61—21no—
132C23×C4×C61—21no—
133C23×C4×C61C2311yescharacteristic
134C23×C4×C61C2311yescharacteristic
135#124×C61—22no—
136#124×C61C2×C414yescomplemented
137#123×C61—28no—
138C22⋊Q8×C61—22no—
139C22⋊Q8×C61C2×C414yescomplemented
140#121×C61—22no—
141#121×C61—28no—
142#121×C61C2×C414yescomplemented
143#120×C61—28no—
144C4×D4×C61—22no—
145C4×D4×C61C2×C414yes—
146C4×D4×C61C2×C414yescomplemented
147C4×D4×C61D414yes—
148C2×C4⋊C4×C61—21no—
149C2×C4⋊C4×C61D411yescharacteristic
150C2×C4⋊C4×C61C2311yescharacteristic
151C2×C22⋊C4×C61—21no—
152C2×C22⋊C4×C61—21no—
153C2×C22⋊C4×C61—21no—
154C2×C22⋊C4×C61—21no—
155C2×C22⋊C4×C61—21no—
156C2×C22⋊C4×C61—28no—
157C2×C22⋊C4×C61D411yescharacteristic
158C2×C22⋊C4×C61D411yescharacteristic
159C2×C42×C61C2311yescharacteristic
160C24×C61—21no—
161C24×C61—21no—
162C24×C61—24no—
163C24×C61—42no—
164C24×C61—42no—
165C24×C61—42no—
166C24×C61—42no—
167C24×C61—81no—
168C24×C61—81no—
169C24×C61C2×D411yescharacteristic
170C24×C61C2×D411yescharacteristic
171#41×C61—28no—
172#41×C61—44no—
173#41×C61—44no—
174#41×C61—44no—
175C2×Q8×C61—21no—
176C2×Q8×C61—21no—
177C2×Q8×C61—21no—
178C2×Q8×C61—21no—
179C2×Q8×C61—21no—
180C2×Q8×C61C22×C412yes—
181C2×D4×C61—22no—
182C2×D4×C61—22no—
183C2×D4×C61—28no—
184C2×D4×C61—24no—
185C2×D4×C61—24no—
186C2×D4×C61—24no—
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—21no—
194C2×D4×C61—21no—
195C2×D4×C61—44no—
196C2×D4×C61—44no—
197C2×D4×C61—44no—
198C2×D4×C61—42no—
199C2×D4×C61—42no—
200C2×D4×C61—42no—
201C2×D4×C61—42no—
202C2×D4×C61—81no—
203C2×D4×C61—81no—
204C2×D4×C61C22⋊C414yes—
205C2×D4×C61C22×C412yes—
206C2×D4×C61C22×C412yes—
207C2×D4×C61C2×D412yes—
208C2×D4×C61#4112yes—
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—21no—
219C22×C4×C61—24no—
220C22×C4×C61—24no—
221C22×C4×C61—42no—
222C22×C4×C61—42no—
223C22×C4×C61—81no—
224C22×C4×C61—81no—
225C22×C4×C61C22×C412yes—
226C22×C4×C61C22×C412yes—
227C22×C4×C61C2×D411yescharacteristic
228C22×C4×C61C2×D411yescharacteristic
229C22×C4×C61C2×D411yescharacteristic
230C22×C4×C61C2×D411yescharacteristic
231C22×C4×C61C2×D412yes—
232C22×C4×C61C2×D412yes—
233C22×C4×C61C2411yescharacteristic
234C22×Dic61—21no—
235C22×Dic61—21no—
236C22×Dic61—21no—
237C22×Dic61—21no—
238C22×Dic61—42no—
239C22×Dic61—42no—
240C22×Dic61—42no—
241C22×Dic61—42no—
242C22×Dic61—81no—
243C22×Dic61—81no—
244C4⋊C4×C61—24no—
245C4⋊C4×C61—21no—
246C4⋊C4×C61C22⋊C414yes—
247C4⋊C4×C61C22×C412yes—
248C22⋊C4×C61—24no—
249C22⋊C4×C61—24no—
250C22⋊C4×C61—24no—
251C22⋊C4×C61—24no—
252C22⋊C4×C61—24no—
253C22⋊C4×C61C22⋊C414yes—
254C22⋊C4×C61C22⋊C414yes—
255C42×C61C22×C412yes—
256C42×C61C2×D412yes—
257C22⋊Dic61—42no—
258C22⋊Dic61—42no—
259C4⋊Dic61—21no—
260C4⋊Dic61—21no—
261C4⋊Dic61—21no—
262C4⋊Dic61—21no—
263C4⋊Dic61—21no—
264C4⋊Dic61—21no—
265C4⋊Dic61—21no—
266C4⋊Dic61—42no—
267C4⋊Dic61—42no—
268C4⋊Dic61—42no—
269C4⋊Dic61—81no—
270C4⋊Dic61C2×D412yes—
271C4×Dic61—42no—
272#11758194—44no—
273C2×#92418—21no—
274C2×#92418—21no—
275C2×#92418—21no—
276C2×#92418—21no—
277C2×#92418—21no—
278C2×#92418—21no—
279C2×#92418—21no—
280C2×#92418—21no—
281C2×#92418—21no—
282C2×#92418—21no—
283C2×#92418—21no—
284C2×#92418—44no—
285C2×#92418C2×D412yes—
286C23×C61—21no—
287C23×C61—21no—
288C23×C61—21no—
289C23×C61—21no—
290C23×C61—22no—
291C23×C61—21no—
292C23×C61—22no—
293C23×C61—21no—
294C23×C61—22no—
295C23×C61—21no—
296C23×C61—21no—
297C23×C61—21no—
298C23×C61—21no—
299C23×C61—22no—
300C23×C61—48no—
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—41no—
310C23×C61—41no—
311C23×C61—48no—
312C23×C61—84no—
313C23×C61—84no—
314C23×C61—84no—
315C23×C61—84no—
316C23×C61—84no—
317C23×C61C2×C22⋊C412yes—
318C23×C61C2×C22⋊C412yes—
319C23×C61AGL(1,ℤ/8)12yes—
320C23×C61#13712yes—
321C23×C61C22×D411yescharacteristic
322Q8×C61—22no—
323Q8×C61—22no—
324Q8×C61—41no—
325Q8×C61—41no—
326D4×C61—28no—
327D4×C61—22no—
328D4×C61—22no—
329D4×C61—22no—
330D4×C61—22no—
331D4×C61—22no—
332D4×C61—48no—
333D4×C61—48no—
334D4×C61—41no—
335D4×C61—41no—
336D4×C61—84no—
337D4×C61C4×D414yescomplemented
338C2×C4×C61—21no—
339C2×C4×C61—21no—
340C2×C4×C61—21no—
341C2×C4×C61—21no—
342C2×C4×C61—21no—
343C2×C4×C61—21no—
344C2×C4×C61—21no—
345C2×C4×C61—21no—
346C2×C4×C61—22no—
347C2×C4×C61—22no—
348C2×C4×C61—22no—
349C2×C4×C61—22no—
350C2×C4×C61—22no—
351C2×C4×C61—22no—
352C2×C4×C61—22no—
353C2×C4×C61—22no—
354C2×C4×C61—22no—
355C2×C4×C61—22no—
356C2×C4×C61—48no—
357C2×C4×C61—41no—
358C2×C4×C61—41no—
359C2×C4×C61—41no—
360C2×C4×C61—41no—
361C2×C4×C61—84no—
362C2×C4×C61C2×C22⋊C412yes—
363C2×C4×C61C2×C22⋊C412yes—
364C2×C4×C61C2×C22⋊C412yes—
365C2×C4×C61C2×C22⋊C412yes—
366C2×C4×C61C23×C411yescharacteristic
367C2×C4×C61C22×D411yescharacteristic
368C2×C4×C61C22×D411yescharacteristic
369C2×C4×C61C2×#4111yescharacteristic
370C2×C4×C61H(5,𝔽2)11yescharacteristic
371C2×C4×C61H(5,𝔽2)11yescharacteristic
372C2×Dic61—22no—
373C2×Dic61—41no—
374C2×Dic61—41no—
375C2×Dic61—41no—
376C2×Dic61—41no—
377C2×Dic61—41no—
378C2×Dic61—41no—
379C2×Dic61—41no—
380C2×Dic61—41no—
381C2×Dic61—41no—
382C2×Dic61—41no—
383C2×Dic61—41no—
384C2×Dic61—84no—
385C2×Dic61—84no—
386#92418—22no—
387#92418—41no—
388#92418—41no—
389#92418—41no—
390#22419—611nomaximal, Sylow
391C22×C61—22no—
392C22×C61—22no—
393C22×C61—22no—
394C22×C61—22no—
395C22×C61—22no—
396C22×C61—22no—
397C22×C61—22no—
398C22×C61—24no—
399C22×C61—22no—
400C22×C61—22no—
401C22×C61—42no—
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—42no—
411C22×C61—42no—
412C22×C61—42no—
413C22×C61—42no—
414C22×C61—816no—
415C22×C61—81no—
416C22×C61—81no—
417C22×C61—81no—
418C22×C61—81no—
419C22×C61#41714yescomplemented
420C22×C61C22×C22⋊C411yescharacteristic
421C22×C61D4211yescharacteristic
422C22×C61#54611yescharacteristic
423C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
424C22×C61C2×#13711yescharacteristic
425C22×C61#57611yescharacteristic
426C22×C61#57711yescharacteristic
427C4×C61—22no—
428C4×C61—22no—
429C4×C61—22no—
430C4×C61—22no—
431C4×C61—42no—
432C4×C61—42no—
433C4×C61C2×C4×D411yescharacteristic
434C4×C61#51811yescharacteristic
435C4×C61D4211yescharacteristic
436C4×C61#54611yescharacteristic
437Dic61—42no—
438Dic61—81no—
439Dic61—81no—
440Dic61—81no—
441C2×#546D6111yescharacteristic
442C2×#435—611no—
443C2×#417—611no—
444C22×#102—611no—
445D4×C4⋊C4—611no—
446#1983—611no—
447#1959—611no—
448#1895—611no—
449#1892—611no—
450#1874—611no—
451#1872—611no—
452#1802—611no—
453#1788—611no—
454#1786—611no—
455#1762—611no—
456C2×C61—24no—
457C2×C61—42no—
458C2×C61—44no—
459C2×C61—82no—
460C2×C61D4×C22⋊C411yescharacteristic
461C2×C61C2×#41711yescharacteristic
462C2×C61#289711yescharacteristic
463C2×C61#326411yescharacteristic
464C2×C61#326611yescharacteristic
465C2×C61#330611yescharacteristic
466C2×C61#331411yescharacteristic
467C22×#41C2×D6111yescharacteristic
468C23×D4C2×D6111yescharacteristic
469C22×M16—611no—
470C23×C8—611no—
471#546—24no—
472#546Dic6118yescomplemented
473C2×#124C2×D6111yescharacteristic
474C2×#123—21no—
475C2×C22⋊Q8C2×D6111yescharacteristic
476C2×#121—21no—
477C2×#121C2×D6111yescharacteristic
478C2×#120—21no—
479C2×C4×D4—1221no—
480C2×C4×D4C2×D6111yescharacteristic
481C2×C4×D4C2×D6111yescharacteristic
482C22×C4⋊C4—611no—
483C22×C4⋊C4—611no—
484C22×C22⋊C4—21no—
485#435—1224no—
486C2×C4⋊C8—611no—
487#417—1224no—
488C2×#103—611no—
489C2×#103—611no—
490C2×#103—611no—
491C2×#103—611no—
492C2×#102—611no—
493C2×#102—611no—
494C2×#102—611no—
495C2×#102—611no—
496C2×#102—611no—
497C2×#102—611no—
498C2×#102—611no—
499C2×#102—611no—
500C2×#102—1224no—
501C2×C22⋊C8—611no—
502C2×C22⋊C8—611no—
503C2×#97—611no—
504#389—1221no—
505#385—1221no—
506#385—1221no—
507#384—611no—
508#380—611no—
509#380—611no—
510C4×C4⋊C4—611no—
511#340—611no—
512#340—611no—
513#340—611no—
514#340—611no—
515C61#2241911yescharacteristic, complemented, Sylow
516C25—21no—
517C2×#41—22no—
518C2×#41—22no—
519C2×#41—22no—
520C2×#41—41no—
521C2×#41—41no—
522C2×#41C2×Dic6114yescomplemented
523C22×Q8C22×D6111yescharacteristic
524C22×D4—22no—
525C22×D4—22no—
526C22×D4—21no—
527C22×D4—21no—
528C22×D4—21no—
529C22×D4—22no—
530C22×D4—41no—
531C22×D4—41no—
532C22×D4C2×Dic6114yescomplemented
533C22×D4C22⋊D6111yescharacteristic
534C22×D4C22×D6111yescharacteristic
535C22×D4C22×D6111yescharacteristic
536C23×C4—21no—
537C23×C4—21no—
538C23×C4—1221no—
539C23×C4—1221no—
540C23×C4C22×D6111yescharacteristic
541C23×C4C22×D6111yescharacteristic
542C2×M16—1222no—
543C2×M16—1222no—
544C2×M16—2441no—
545C22×C8—611no—
546C22×C8—611no—
547C22×C8—611no—
548C22×C8—611no—
549C22×C8—1222no—
550C22×C8—1222no—
551C22×C8—2441no—
552#124—22no—
553#124C2×Dic6114yescomplemented
554#123—28no—
555C22⋊Q8—22no—
556C22⋊Q8C2×Dic6114yescomplemented
557#121—22no—
558#121—28no—
559#121C2×Dic6114yescomplemented
560#120—28no—
561C4×D4—22no—
562C4×D4—2444no—
563C4×D4C2×Dic6114yes—
564C4×D4C2×Dic6114yescomplemented
565C4×D4C22⋊D6114yes—
566C2×C4⋊C4—21no—
567C2×C4⋊C4—611no—
568C2×C4⋊C4—611no—
569C2×C4⋊C4—611no—
570C2×C4⋊C4—611no—
571C2×C4⋊C4—1222no—
572C2×C4⋊C4—1222no—
573C2×C4⋊C4—1221no—
574C2×C4⋊C4—1221no—
575C2×C4⋊C4—1221no—
576C2×C4⋊C4—1221no—
577C2×C4⋊C4—2441no—
578C2×C4⋊C4—2441no—
579C2×C4⋊C4C22⋊D6111yescharacteristic
580C2×C4⋊C4C22×D6111yescharacteristic
581C2×C22⋊C4—21no—
582C2×C22⋊C4—21no—
583C2×C22⋊C4—21no—
584C2×C22⋊C4—21no—
585C2×C22⋊C4—21no—
586C2×C22⋊C4—28no—
587C2×C22⋊C4—1221no—
588C2×C22⋊C4—1221no—
589C2×C22⋊C4C22⋊D6111yescharacteristic
590C2×C22⋊C4C22⋊D6111yescharacteristic
591C2×C42—1221no—
592C2×C42C22×D6111yescharacteristic
593C4⋊C8—1222no—
594#103—1222no—
595#103—1222no—
596#103—2441no—
597#103—2441no—
598#102—614no—
599#102—1222no—
600#102—1222no—
601#102—1222no—
602#102—1222no—
603#102—1222no—
604#102—2441no—
605#102—2441no—
606C22⋊C8—1222no—
607C22⋊C8—1222no—
608#97—1222no—
609#95—1221no—
610#95—1221no—
611#95—1221no—
612C24—21no—
613C24—21no—
614C24—24no—
615C24—42no—
616C24—42no—
617C24—42no—
618C24—42no—
619C24—81no—
620C24—81no—
621C24C2×C22⋊D6111yescharacteristic
622C24C2×C22⋊D6111yescharacteristic
623#41—28no—
624#41—44no—
625#41—44no—
626#41—44no—
627C2×Q8—21no—
628C2×Q8—21no—
629C2×Q8—21no—
630C2×Q8—21no—
631C2×Q8—21no—
632C2×Q8C22×Dic6112yes—
633C2×D4—22no—
634C2×D4—22no—
635C2×D4—28no—
636C2×D4—24no—
637C2×D4—24no—
638C2×D4—21no—
639C2×D4—21no—
640C2×D4—21no—
641C2×D4—21no—
642C2×D4—21no—
643C2×D4—21no—
644C2×D4—21no—
645C2×D4—21no—
646C2×D4—24no—
647C2×D4—44no—
648C2×D4—44no—
649C2×D4—44no—
650C2×D4—42no—
651C2×D4—42no—
652C2×D4—42no—
653C2×D4—42no—
654C2×D4—81no—
655C2×D4—81no—
656C2×D4C22⋊Dic6114yes—
657C2×D4D4×D6112yes—
658C2×D4#1175822412yes—
659C2×D4C22×Dic6112yes—
660C2×D4C22×Dic6112yes—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—24no—
672C22×C4—24no—
673C22×C4—42no—
674C22×C4—42no—
675C22×C4—81no—
676C22×C4—81no—
677C22×C4—1221no—
678C22×C4—1221no—
679C22×C4—1221no—
680C22×C4—1221no—
681C22×C4—4881no—
682C22×C4—4881no—
683C22×C4—2442no—
684C22×C4—2442no—
685C22×C4—2442no—
686C22×C4—2442no—
687C22×C4C22×Dic6112yes—
688C22×C4C22×Dic6112yes—
689C22×C4C2×C22⋊D6112yes—
690C22×C4C2×C22⋊D6112yes—
691C22×C4C2×C22⋊D6111yescharacteristic
692C22×C4C2×C22⋊D6111yescharacteristic
693C22×C4C2×C22⋊D6111yescharacteristic
694C22×C4C2×C22⋊D6111yescharacteristic
695C22×C4C23×D6111yescharacteristic
696M16—2444no—
697C2×C8—612no—
698C2×C8—1221no—
699C2×C8—1221no—
700C2×C8—1221no—
701C2×C8—1221no—
702C2×C8—1221no—
703C2×C8—1221no—
704C2×C8—1221no—
705C2×C8—1221no—
706C2×C8—1221no—
707C2×C8—1221no—
708C2×C8—1221no—
709C2×C8—2444no—
710C4⋊C4—21no—
711C4⋊C4—24no—
712C4⋊C4—612no—
713C4⋊C4—1221no—
714C4⋊C4—1221no—
715C4⋊C4—1221no—
716C4⋊C4—1221no—
717C4⋊C4—1221no—
718C4⋊C4—1221no—
719C4⋊C4—1221no—
720C4⋊C4—4881no—
721C4⋊C4—2442no—
722C4⋊C4—2442no—
723C4⋊C4—2442no—
724C4⋊C4C22⋊Dic6114yes—
725C4⋊C4C22×Dic6112yes—
726C22⋊C4—24no—
727C22⋊C4—24no—
728C22⋊C4—24no—
729C22⋊C4—24no—
730C22⋊C4—24no—
731C22⋊C4—2442no—
732C22⋊C4—2442no—
733C22⋊C4C22⋊Dic6114yes—
734C22⋊C4C22⋊Dic6114yes—
735C42—2442no—
736C42C22×Dic6112yes—
737C42C2×C22⋊D6112yes—
738C23—21no—
739C23—21no—
740C23—21no—
741C23—21no—
742C23—22no—
743C23—21no—
744C23—21no—
745C23—21no—
746C23—21no—
747C23—21no—
748C23—22no—
749C23—21no—
750C23—22no—
751C23—22no—
752C23—48no—
753C23—41no—
754C23—41no—
755C23—41no—
756C23—41no—
757C23—48no—
758C23—41no—
759C23—41no—
760C23—41no—
761C23—41no—
762C23—41no—
763C23—41no—
764C23—84no—
765C23—84no—
766C23—84no—
767C23—84no—
768C23—84no—
769C23C2×C22⋊Dic6112yes—
770C23C2×C22⋊Dic6112yes—
771C23#1451980212yes—
772C23#1451980712yes—
773C23C22×C22⋊D6111yescharacteristic
774Q8—22no—
775Q8—22no—
776Q8—41no—
777Q8—41no—
778D4—28no—
779D4—22no—
780D4—22no—
781D4—22no—
782D4—22no—
783D4—22no—
784D4—48no—
785D4—48no—
786D4—41no—
787D4—41no—
788D4—84no—
789D4D4×Dic6114yescomplemented
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—48no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—84no—
814C2×C4—1222no—
815C2×C4—4884no—
816C2×C4—4884no—
817C2×C4—2441no—
818C2×C4—2441no—
819C2×C4—2441no—
820C2×C4—2441no—
821C2×C4—2441no—
822C2×C4—2441no—
823C2×C4—2441no—
824C2×C4—2441no—
825C2×C4—2441no—
826C2×C4—2441no—
827C2×C4—2441no—
828C2×C4C2×C22⋊Dic6112yes—
829C2×C4C2×C22⋊Dic6112yes—
830C2×C4C2×C22⋊Dic6112yes—
831C2×C4C2×C22⋊Dic6112yes—
832C2×C4C23×Dic6111yescharacteristic
833C2×C4C2×D4×D6111yescharacteristic
834C2×C4C22×C22⋊D6111yescharacteristic
835C2×C4C2×#1175822411yescharacteristic
836C2×C4#1451982211yescharacteristic
837C2×C4#1451982211yescharacteristic
838C8—1222no—
839C8—2441no—
840C8—2441no—
841C8—2441no—
842C22—22no—
843C22—22no—
844C22—22no—
845C22—22no—
846C22—22no—
847C22—22no—
848C22—22no—
849C22—22no—
850C22—24no—
851C22—22no—
852C22—42no—
853C22—41no—
854C22—42no—
855C22—41no—
856C22—42no—
857C22—41no—
858C22—42no—
859C22—41no—
860C22—42no—
861C22—42no—
862C22—42no—
863C22—42no—
864C22—42no—
865C22—816no—
866C22—81no—
867C22—81no—
868C22—81no—
869C22—81no—
870C22#1683976314yescomplemented
871C22C22×C22⋊Dic6111yescharacteristic
872C22D4×C22⋊D6111yescharacteristic
873C22#1684040611yescharacteristic
874C22C2×#1451980211yescharacteristic
875C22C2×#1451980711yescharacteristic
876C22#1684056511yescharacteristic
877C22#1684057311yescharacteristic
878C4—22no—
879C4—22no—
880C4—22no—
881C4—22no—
882C4—42no—
883C4—42no—
884C4—4881no—
885C4—4881no—
886C4—4881no—
887C4—2442no—
888C4C2×D4×Dic6111yescharacteristic
889C4#1684023711yescharacteristic
890C4D4×C22⋊D6111yescharacteristic
891C4#1684040611yescharacteristic
892C2—24no—
893C2—42no—
894C2—44no—
895C2—82no—
896C2D4×C22⋊Dic6111yescharacteristic
897C2C2×#1683976311yescharacteristic
898C2#2145434511yescharacteristic
899C2#2145730011yescharacteristic
900C2#2145732511yescharacteristic
901C2#2145778011yescharacteristic
902C2#2145790011yescharacteristic
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#22419
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×#16839763C2semidirect
3. C22×#14519698C2semidirect
4. D4×C4⋊Dic61C2semidirect
5. #21446752C2semidirect
6. #21446636C2semidirect
7. #21446258C2semidirect
8. #21446243C2semidirect
9. #21446137C2semidirect
10. #21446127C2semidirect
11. #21445819C2semidirect
12. #21445759C2semidirect
13. #21445750C2semidirect
14. #21445644C2semidirect
16. C22×#11758194C22semidirect
20. C22×C4⋊Dic61C22semidirect
22. C2×C4⋊#92418C22semidirect
24. C2×#14519701C22semidirect
25. C2×#14519701C22semidirect
26. C2×#14519701C22semidirect
27. C2×#14519701C22semidirect
38. C2×C22⋊#92418C22semidirect
39. C2×#14519688C22semidirect
43. #16839632C22semidirect
45. #16839622C22semidirect
46. C4×C4⋊Dic61C22semidirect
47. #16839524C22semidirect
48. #16839524C22semidirect
49. #16839524C22semidirect
50. #16839524C22semidirect
54. C61×#546C4semidirect
104. #14519698D4semidirect
117. C2×#41×C61C2×C4semidirect
127. C22×D4×C61C2×C4semidirect
136. #124×C61C2×C4semidirect
139. C22⋊Q8×C61C2×C4semidirect
142. #121×C61C2×C4semidirect
146. C4×D4×C61C2×C4semidirect
337. D4×C61C4×D4semidirect
419. C22×C61#417semidirect
472. #546Dic61semidirect
515. C61#22419semidirect
522. C2×#41C2×Dic61semidirect
532. C22×D4C2×Dic61semidirect
553. #124C2×Dic61semidirect
556. C22⋊Q8C2×Dic61semidirect
559. #121C2×Dic61semidirect
564. C4×D4C2×Dic61semidirect
789. D4D4×Dic61semidirect
870. C22#16839763semidirect

Maximal subgroups

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

subgroupindex
C2×#168398342
C2×#168397632
C22×#145196982
D4×C4⋊Dic612
#214467522
#214466362
#214462582
#214462432
#214461372
#214461272
#214458192
#214457592
#214457502
#214456442
C2×C61×#5462
#2241961