Finite Group Databasebeta

← #29689130

Subgroups — #29689130

Order 15616.

1390 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839729C211yesmaximal, characteristic, complemented
2#21448411C211yesmaximal, characteristic, complemented
3#21446258C211yesmaximal, characteristic, complemented
4#21446253C211yesmaximal, characteristic, complemented
5#21446248C211yesmaximal, characteristic, complemented
6#21446243C211yesmaximal, characteristic, complemented
7#21446142C211yesmaximal, characteristic, complemented
8#21446137C211yesmaximal, characteristic, complemented
9#21446132C211yesmaximal, characteristic, complemented
10#21446127C211yesmaximal, characteristic, complemented
11#21445909C211yesmaximal, characteristic, complemented
12#21445905C211yesmaximal, characteristic, complemented
13#21445759C211yesmaximal, characteristic, complemented
14#21445759C211yesmaximal, characteristic, complemented
15C2×C61×#537C211yesmaximal, characteristic
16C22×#11758194C2211yescharacteristic
17C23×#92418C2211yescharacteristic
18C2×#14519736C2211yescharacteristic
19C22×C4⋊Dic61C2211yescharacteristic
20C2×#14519701C2211yescharacteristic
21C2×#14519701C2211yescharacteristic
22C2×#14519701C2211yescharacteristic
23C2×#14519701C2211yescharacteristic
24C2×#14519698C2211yescharacteristic
25C2×#14519698C2211yescharacteristic
26C2×#14519698C2211yescharacteristic
27C2×#14519698C2211yescharacteristic
28#16839729—24no—
29C2×C22⋊#92418C2211yescharacteristic
30C2×C22⋊#92418C2211yescharacteristic
31C2×C22⋊#92418C2211yescharacteristic
32C2×C22⋊#92418C2211yescharacteristic
33#16839669—21no—
34#16839665—21no—
35#16839642—21no—
36#16839642—21no—
37#16839622C2211yescharacteristic
38#16839622C2211yescharacteristic
39#16839622C2211yescharacteristic
40#16839622C2211yescharacteristic
41#16839524C2211yescharacteristic
42#16839524C2211yescharacteristic
43#16839524C2211yescharacteristic
44#16839524C2211yescharacteristic
45#16839524C2211yescharacteristic
46#16839524C2211yescharacteristic
47#16839524C2211yescharacteristic
48#16839524C2211yescharacteristic
49C22×#41×C61C2211yescharacteristic
50C22×#41×C61C2211yescharacteristic
51C61×#537—24no—
52C61×#537C418yescomplemented
53C2×C22⋊Q8×C61—21no—
54C2×C22⋊Q8×C61C2211yescharacteristic
55C2×C22⋊Q8×C61C2211yescharacteristic
56C2×#121×C61—21no—
57C2×#121×C61—21no—
58C2×#121×C61—21no—
59C2×#121×C61C2211yescharacteristic
60C2×#121×C61C2211yescharacteristic
61C22×C4⋊C4×C61C2211yescharacteristic
62C23×Dic61—21no—
63C2×#11758194—22no—
64C2×#11758194—41no—
65C2×#11758194—41no—
66C22×#92418—22no—
67C22×#92418—41no—
68C22×#92418—41no—
69C22×#92418C2311yescharacteristic
70C22×#92418C2311yescharacteristic
71C22×#92418C2311yescharacteristic
72C22×#92418C2311yescharacteristic
73#14519736—41no—
74#14519736—41no—
75C2×C4⋊Dic61—21no—
76C2×C4⋊Dic61—41no—
77C2×C4⋊Dic61—41no—
78C2×C4⋊Dic61C2311yescharacteristic
79C2×C4⋊Dic61C2311yescharacteristic
80C2×C4⋊Dic61C2311yescharacteristic
81C2×C4⋊Dic61C2311yescharacteristic
82C2×C22⋊Dic61—21no—
83C2×C22⋊Dic61—21no—
84C2×C22⋊Dic61—21no—
85C2×C22⋊Dic61—21no—
86C2×C22⋊Dic61—21no—
87C2×C4×Dic61—21no—
88#14519701—41no—
89#14519701—41no—
90#14519701—41no—
91#14519701—41no—
92#14519698—41no—
93#14519698—41no—
94#14519698—41no—
95#14519698—41no—
96C22⋊#92418—22no—
97C22⋊#92418—22no—
98C22⋊#92418—22no—
99C22⋊#92418—22no—
100#14519684—21no—
101#14519684—21no—
102#14519684—21no—
103#14519684—21no—
104C2×#41×C61—22no—
105C2×#41×C61—41no—
106C2×#41×C61—41no—
107C2×#41×C61—41no—
108C2×#41×C61—41no—
109C2×#41×C61—41no—
110C2×#41×C61—41no—
111C2×#41×C61—41no—
112C2×#41×C61—41no—
113C2×#41×C61C2×C414yes—
114C2×#41×C61C2×C414yescomplemented
115C2×#41×C61D414yes—
116C22×Q8×C61D411yescharacteristic
117C22×Q8×C61C2311yescharacteristic
118C22×D4×C61—21no—
119C22×D4×C61—21no—
120C22×D4×C61—21no—
121C22×D4×C61D411yescharacteristic
122C22×D4×C61D411yescharacteristic
123C22×D4×C61D411yescharacteristic
124C22×D4×C61C2311yescharacteristic
125C23×C4×C61—21no—
126C23×C4×C61—21no—
127C23×C4×C61C2311yescharacteristic
128C23×C4×C61C2311yescharacteristic
129C23×C4×C61C2311yescharacteristic
130C22⋊Q8×C61—28no—
131C22⋊Q8×C61—22no—
132C22⋊Q8×C61—22no—
133C22⋊Q8×C61C2×C414yes—
134C22⋊Q8×C61C2×C414yescomplemented
135#121×C61—28no—
136#121×C61—28no—
137#121×C61—28no—
138#121×C61—22no—
139#121×C61—22no—
140#121×C61C2×C414yes—
141#121×C61C2×C414yescomplemented
142C2×C4⋊C4×C61—22no—
143C2×C4⋊C4×C61—21no—
144C2×C4⋊C4×C61—21no—
145C2×C4⋊C4×C61—21no—
146C2×C4⋊C4×C61C2×C414yescomplemented
147C2×C4⋊C4×C61C2311yescharacteristic
148C2×C4⋊C4×C61C2311yescharacteristic
149C2×C22⋊C4×C61—21no—
150C2×C22⋊C4×C61—21no—
151C2×C22⋊C4×C61—21no—
152C2×C22⋊C4×C61—21no—
153C24×C61—21no—
154C24×C61C2×D411yescharacteristic
155C24×C61C2×D411yescharacteristic
156C24×C61C2×D411yescharacteristic
157#41×C61—44no—
158#41×C61—44no—
159#41×C61—44no—
160#41×C61—44no—
161#41×C61—44no—
162#41×C61—44no—
163#41×C61—44no—
164#41×C61—44no—
165C2×Q8×C61—21no—
166C2×Q8×C61—21no—
167C2×Q8×C61—21no—
168C2×Q8×C61—21no—
169C2×Q8×C61—21no—
170C2×Q8×C61—41no—
171C2×Q8×C61—41no—
172C2×Q8×C61C22⋊C414yes—
173C2×Q8×C61C22×C412yes—
174C2×D4×C61—24no—
175C2×D4×C61—24no—
176C2×D4×C61—24no—
177C2×D4×C61—21no—
178C2×D4×C61—21no—
179C2×D4×C61—21no—
180C2×D4×C61—21no—
181C2×D4×C61—21no—
182C2×D4×C61—41no—
183C2×D4×C61—41no—
184C2×D4×C61—41no—
185C2×D4×C61—41no—
186C2×D4×C61—41no—
187C2×D4×C61—41no—
188C2×D4×C61—42no—
189C2×D4×C61—42no—
190C2×D4×C61—81no—
191C2×D4×C61—81no—
192C2×D4×C61—81no—
193C2×D4×C61—81no—
194C2×D4×C61C22⋊C414yes—
195C2×D4×C61C22⋊C414yes—
196C2×D4×C61C22⋊C414yes—
197C2×D4×C61C22×C412yes—
198C22×C4×C61—21no—
199C22×C4×C61—21no—
200C22×C4×C61—21no—
201C22×C4×C61—21no—
202C22×C4×C61—21no—
203C22×C4×C61—21no—
204C22×C4×C61—21no—
205C22×C4×C61—21no—
206C22×C4×C61—21no—
207C22×C4×C61—21no—
208C22×C4×C61—21no—
209C22×C4×C61—21no—
210C22×C4×C61—21no—
211C22×C4×C61—21no—
212C22×C4×C61—21no—
213C22×C4×C61—24no—
214C22×C4×C61—24no—
215C22×C4×C61—42no—
216C22×C4×C61—42no—
217C22×C4×C61—81no—
218C22×C4×C61—81no—
219C22×C4×C61C22×C412yes—
220C22×C4×C61C22×C412yes—
221C22×C4×C61C22×C412yes—
222C22×C4×C61C2×D411yescharacteristic
223C22×C4×C61C2×D411yescharacteristic
224C22×C4×C61C2×D411yescharacteristic
225C22×C4×C61C2×D412yes—
226C22×C4×C61C2×D412yes—
227C22×C4×C61C2×D412yes—
228C22×C4×C61C2411yescharacteristic
229C22×Dic61—21no—
230C22×Dic61—21no—
231C22×Dic61—21no—
232C22×Dic61—21no—
233C22×Dic61—42no—
234C22×Dic61—81no—
235C22×Dic61—81no—
236C4⋊C4×C61—24no—
237C4⋊C4×C61—24no—
238C4⋊C4×C61—24no—
239C4⋊C4×C61—21no—
240C4⋊C4×C61—21no—
241C4⋊C4×C61C22×C412yes—
242C4⋊C4×C61C22×C412yes—
243C22⋊C4×C61—24no—
244C22⋊C4×C61—24no—
245C22⋊C4×C61—24no—
246C22⋊C4×C61—24no—
247C22⋊Dic61—42no—
248C22⋊Dic61—81no—
249C22⋊Dic61—81no—
250C22⋊Dic61—81no—
251C22⋊Dic61—81no—
252C4⋊Dic61—21no—
253C4⋊Dic61—21no—
254C4⋊Dic61—21no—
255C4⋊Dic61—21no—
256C4⋊Dic61—21no—
257C4⋊Dic61—21no—
258C4⋊Dic61—21no—
259C4⋊Dic61—21no—
260C4⋊Dic61—42no—
261C4×Dic61—42no—
262#11758194—44no—
263C2×#92418—21no—
264C2×#92418—21no—
265C2×#92418—21no—
266C2×#92418—21no—
267C2×#92418—21no—
268C2×#92418—21no—
269C2×#92418—21no—
270C2×#92418—21no—
271C2×#92418—21no—
272C2×#92418—21no—
273C2×#92418—21no—
274C2×#92418—21no—
275C2×#92418—44no—
276C23×C61—21no—
277C23×C61—21no—
278C23×C61—21no—
279C23×C61—21no—
280C23×C61—21no—
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—21no—
294C23×C61—22no—
295C23×C61—41no—
296C23×C61—41no—
297C23×C61—41no—
298C23×C61—41no—
299C23×C61—41no—
300C23×C61—41no—
301C23×C61C2×C22⋊C412yes—
302C23×C61C2×C22⋊C412yes—
303C23×C61C2×C22⋊C412yes—
304C23×C61C22×D411yescharacteristic
305Q8×C61—22no—
306Q8×C61—22no—
307Q8×C61—44no—
308Q8×C61—41no—
309Q8×C61—41no—
310D4×C61—22no—
311D4×C61—22no—
312D4×C61—44no—
313D4×C61—44no—
314D4×C61—44no—
315D4×C61—48no—
316D4×C61—41no—
317D4×C61—41no—
318D4×C61—84no—
319D4×C61—84no—
320C2×C4×C61—21no—
321C2×C4×C61—21no—
322C2×C4×C61—21no—
323C2×C4×C61—21no—
324C2×C4×C61—21no—
325C2×C4×C61—21no—
326C2×C4×C61—22no—
327C2×C4×C61—22no—
328C2×C4×C61—22no—
329C2×C4×C61—22no—
330C2×C4×C61—22no—
331C2×C4×C61—22no—
332C2×C4×C61—22no—
333C2×C4×C61—22no—
334C2×C4×C61—22no—
335C2×C4×C61—22no—
336C2×C4×C61—22no—
337C2×C4×C61—22no—
338C2×C4×C61—22no—
339C2×C4×C61—22no—
340C2×C4×C61—22no—
341C2×C4×C61—48no—
342C2×C4×C61—41no—
343C2×C4×C61—41no—
344C2×C4×C61—41no—
345C2×C4×C61—41no—
346C2×C4×C61—41no—
347C2×C4×C61—41no—
348C2×C4×C61—84no—
349C2×C4×C61C2×C22⋊C412yes—
350C2×C4×C61C2×C22⋊C412yes—
351C2×C4×C61C2×C22⋊C412yes—
352C2×C4×C61C23×C411yescharacteristic
353C2×C4×C61C22×D411yescharacteristic
354C2×C4×C61H(5,𝔽2)11yescharacteristic
355C2×C4×C61H(5,𝔽2)11yescharacteristic
356C2×C4×C61H(5,𝔽2)11yescharacteristic
357C2×C4×C61H(5,𝔽2)11yescharacteristic
358C2×Dic61—41no—
359C2×Dic61—41no—
360C2×Dic61—41no—
361C2×Dic61—41no—
362C2×Dic61—41no—
363C2×Dic61—41no—
364C2×Dic61—41no—
365C2×Dic61—41no—
366C2×Dic61—41no—
367C2×Dic61—41no—
368C2×Dic61—41no—
369C2×Dic61—41no—
370C2×Dic61—84no—
371#92418—41no—
372#92418—41no—
373#92418—41no—
374#92418—41no—
375#21772—611nomaximal, Sylow
376C22×C61—22no—
377C22×C61—22no—
378C22×C61—22no—
379C22×C61—22no—
380C22×C61—22no—
381C22×C61—22no—
382C22×C61—22no—
383C22×C61—22no—
384C22×C61—22no—
385C22×C61—41no—
386C22×C61—41no—
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—41no—
396C22×C61—41no—
397C22×C61—42no—
398C22×C61—42no—
399C22×C61—42no—
400C22×C61—81no—
401C22×C61—81no—
402C22×C61—81no—
403C22×C61—81no—
404C22×C61C22×C22⋊C411yescharacteristic
405C22×C61#53411yescharacteristic
406C22×C61#53411yescharacteristic
407C22×C61#57611yescharacteristic
408C22×C61#57711yescharacteristic
409C22×C61#57711yescharacteristic
410C22×C61#57811yescharacteristic
411C4×C61—22no—
412C4×C61—22no—
413C4×C61—22no—
414C4×C61—42no—
415C4×C61—42no—
416C4×C61—42no—
417C4×C61#51811yescharacteristic
418C4×C61#51811yescharacteristic
419C4×C61#53411yescharacteristic
420C4×C61#53411yescharacteristic
421Dic61—81no—
422Dic61—81no—
423Dic61—81no—
424Dic61—81no—
425C2×#537D6111yescharacteristic
426C2×#408—611no—
427#2311—611no—
428#1895—611no—
429#1894—611no—
430#1893—611no—
431#1892—611no—
432#1875—611no—
433#1874—611no—
434#1873—611no—
435#1872—611no—
436#1824—611no—
437#1823—611no—
438#1788—611no—
439#1788—611no—
440C2×C61—42no—
441C2×C61—42no—
442C2×C61—42no—
443C2×C61—82no—
444C2×C61#230811yescharacteristic
445C2×C61#289711yescharacteristic
446C2×C61#289811yescharacteristic
447C2×C61#319811yescharacteristic
448C2×C61#320111yescharacteristic
449C2×C61#320311yescharacteristic
450C2×C61#320411yescharacteristic
451C22×#41C2×D6111yescharacteristic
452C22×#41C2×D6111yescharacteristic
453C22×M16—611no—
454C23×C8—611no—
455#537—24no—
456#537Dic6118yescomplemented
457C2×C22⋊Q8—21no—
458C2×C22⋊Q8C2×D6111yescharacteristic
459C2×C22⋊Q8C2×D6111yescharacteristic
460C2×#121—21no—
461C2×#121—21no—
462C2×#121—21no—
463C2×#121C2×D6111yescharacteristic
464C2×#121C2×D6111yescharacteristic
465C2×#117—611no—
466C22×C4⋊C4—611no—
467C22×C4⋊C4C2×D6111yescharacteristic
468C2×#103—611no—
469C2×#103—611no—
470C2×#103—611no—
471C2×#103—611no—
472C2×#102—611no—
473C2×#102—611no—
474C2×#102—611no—
475C2×#102—611no—
476#408—1224no—
477C2×C22⋊C8—611no—
478C2×C22⋊C8—611no—
479C2×C22⋊C8—611no—
480C2×C22⋊C8—611no—
481#391—1221no—
482#390—1221no—
483#386—1221no—
484#386—1221no—
485#380—611no—
486#380—611no—
487#380—611no—
488#380—611no—
489#340—611no—
490#340—611no—
491#340—611no—
492#340—611no—
493#340—611no—
494#340—611no—
495#340—611no—
496#340—611no—
497C61#2177211yescharacteristic, complemented, Sylow
498C2×#41—22no—
499C2×#41—41no—
500C2×#41—41no—
501C2×#41—41no—
502C2×#41—41no—
503C2×#41—41no—
504C2×#41—41no—
505C2×#41—41no—
506C2×#41—41no—
507C2×#41C2×Dic6114yes—
508C2×#41C2×Dic6114yescomplemented
509C2×#41C22⋊D6114yes—
510C22×Q8C22⋊D6111yescharacteristic
511C22×Q8C22×D6111yescharacteristic
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4C22⋊D6111yescharacteristic
516C22×D4C22⋊D6111yescharacteristic
517C22×D4C22⋊D6111yescharacteristic
518C22×D4C22×D6111yescharacteristic
519C23×C4—21no—
520C23×C4—21no—
521C23×C4—1221no—
522C23×C4C22×D6111yescharacteristic
523C23×C4C22×D6111yescharacteristic
524C23×C4C22×D6111yescharacteristic
525C2×M16—1222no—
526C2×M16—2441no—
527C2×M16—2441no—
528C22×C8—611no—
529C22×C8—611no—
530C22×C8—611no—
531C22×C8—611no—
532C22×C8—1222no—
533C22×C8—2441no—
534C22×C8—2441no—
535C22⋊Q8—28no—
536C22⋊Q8—22no—
537C22⋊Q8—22no—
538C22⋊Q8C2×Dic6114yes—
539C22⋊Q8C2×Dic6114yescomplemented
540#121—28no—
541#121—28no—
542#121—28no—
543#121—22no—
544#121—22no—
545#121C2×Dic6114yes—
546#121C2×Dic6114yescomplemented
547#117—2441no—
548#117—2441no—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—22no—
551C2×C4⋊C4—21no—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—611no—
554C2×C4⋊C4—611no—
555C2×C4⋊C4—611no—
556C2×C4⋊C4—611no—
557C2×C4⋊C4—1221no—
558C2×C4⋊C4—2441no—
559C2×C4⋊C4—2441no—
560C2×C4⋊C4C2×Dic6114yescomplemented
561C2×C4⋊C4C22×D6111yescharacteristic
562C2×C4⋊C4C22×D6111yescharacteristic
563C2×C22⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C22⋊C4—21no—
566C2×C22⋊C4—21no—
567C2×C22⋊C4—1221no—
568C2×C22⋊C4—1221no—
569C2×C22⋊C4—1221no—
570C2×C22⋊C4—1221no—
571C2×C22⋊C4—1221no—
572C2×C42—1221no—
573#103—2441no—
574#103—2441no—
575#103—2441no—
576#103—2441no—
577#102—2441no—
578#102—2441no—
579#102—2441no—
580#102—2441no—
581C22⋊C8—1222no—
582C22⋊C8—1222no—
583C22⋊C8—1222no—
584C22⋊C8—1222no—
585#95—1221no—
586#95—1221no—
587#95—1221no—
588#95—1221no—
589C24—21no—
590C24C2×C22⋊D6111yescharacteristic
591C24C2×C22⋊D6111yescharacteristic
592C24C2×C22⋊D6111yescharacteristic
593#41—44no—
594#41—44no—
595#41—44no—
596#41—44no—
597#41—44no—
598#41—44no—
599#41—44no—
600#41—44no—
601C2×Q8—21no—
602C2×Q8—21no—
603C2×Q8—21no—
604C2×Q8—21no—
605C2×Q8—21no—
606C2×Q8—41no—
607C2×Q8—41no—
608C2×Q8C22⋊Dic6114yes—
609C2×Q8C22×Dic6112yes—
610C2×D4—24no—
611C2×D4—24no—
612C2×D4—24no—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—21no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4—41no—
619C2×D4—41no—
620C2×D4—41no—
621C2×D4—41no—
622C2×D4—41no—
623C2×D4—41no—
624C2×D4—42no—
625C2×D4—42no—
626C2×D4—81no—
627C2×D4—81no—
628C2×D4—81no—
629C2×D4—81no—
630C2×D4C22⋊Dic6114yes—
631C2×D4C22⋊Dic6114yes—
632C2×D4C22⋊Dic6114yes—
633C2×D4C22×Dic6112yes—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—24no—
650C22×C4—24no—
651C22×C4—42no—
652C22×C4—42no—
653C22×C4—81no—
654C22×C4—81no—
655C22×C4—1221no—
656C22×C4—1221no—
657C22×C4—1221no—
658C22×C4—1221no—
659C22×C4—4881no—
660C22×C4—4881no—
661C22×C4—2442no—
662C22×C4C22×Dic6112yes—
663C22×C4C22×Dic6112yes—
664C22×C4C22×Dic6112yes—
665C22×C4C2×C22⋊D6112yes—
666C22×C4C2×C22⋊D6112yes—
667C22×C4C2×C22⋊D6112yes—
668C22×C4C2×C22⋊D6111yescharacteristic
669C22×C4C2×C22⋊D6111yescharacteristic
670C22×C4C2×C22⋊D6111yescharacteristic
671C22×C4C23×D6111yescharacteristic
672M16—2444no—
673C2×C8—1221no—
674C2×C8—1221no—
675C2×C8—1221no—
676C2×C8—1221no—
677C2×C8—1221no—
678C2×C8—1221no—
679C2×C8—1221no—
680C2×C8—1221no—
681C2×C8—1221no—
682C2×C8—1221no—
683C2×C8—1221no—
684C2×C8—1221no—
685C2×C8—2444no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—24no—
689C4⋊C4—24no—
690C4⋊C4—24no—
691C4⋊C4—1221no—
692C4⋊C4—1221no—
693C4⋊C4—1221no—
694C4⋊C4—1221no—
695C4⋊C4—1221no—
696C4⋊C4—1221no—
697C4⋊C4—1221no—
698C4⋊C4—1221no—
699C4⋊C4—2442no—
700C4⋊C4C22×Dic6112yes—
701C4⋊C4C22×Dic6112yes—
702C22⋊C4—24no—
703C22⋊C4—24no—
704C22⋊C4—24no—
705C22⋊C4—24no—
706C22⋊C4—4881no—
707C22⋊C4—4881no—
708C22⋊C4—4881no—
709C22⋊C4—4881no—
710C22⋊C4—2442no—
711C42—2442no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—22no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23C2×C22⋊Dic6112yes—
738C23C2×C22⋊Dic6112yes—
739C23C2×C22⋊Dic6112yes—
740C23C22×C22⋊D6111yescharacteristic
741Q8—22no—
742Q8—22no—
743Q8—44no—
744Q8—41no—
745Q8—41no—
746D4—22no—
747D4—22no—
748D4—44no—
749D4—44no—
750D4—44no—
751D4—48no—
752D4—41no—
753D4—41no—
754D4—84no—
755D4—84no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—48no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—84no—
785C2×C4—4884no—
786C2×C4—2441no—
787C2×C4—2441no—
788C2×C4—2441no—
789C2×C4—2441no—
790C2×C4—2441no—
791C2×C4—2441no—
792C2×C4—2441no—
793C2×C4—2441no—
794C2×C4—2441no—
795C2×C4—2441no—
796C2×C4—2441no—
797C2×C4—2441no—
798C2×C4C2×C22⋊Dic6112yes—
799C2×C4C2×C22⋊Dic6112yes—
800C2×C4C2×C22⋊Dic6112yes—
801C2×C4C23×Dic6111yescharacteristic
802C2×C4C22×C22⋊D6111yescharacteristic
803C2×C4#1451982211yescharacteristic
804C2×C4#1451982211yescharacteristic
805C2×C4#1451982211yescharacteristic
806C2×C4#1451982211yescharacteristic
807C8—2441no—
808C8—2441no—
809C8—2441no—
810C8—2441no—
811C22—22no—
812C22—22no—
813C22—22no—
814C22—22no—
815C22—22no—
816C22—22no—
817C22—22no—
818C22—22no—
819C22—22no—
820C22—41no—
821C22—41no—
822C22—41no—
823C22—41no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—42no—
833C22—42no—
834C22—42no—
835C22—81no—
836C22—81no—
837C22—81no—
838C22—81no—
839C22C22×C22⋊Dic6111yescharacteristic
840C22#1684032111yescharacteristic
841C22#1684032111yescharacteristic
842C22#1684056511yescharacteristic
843C22#1684057011yescharacteristic
844C22#1684057311yescharacteristic
845C22#1684057711yescharacteristic
846C4—22no—
847C4—22no—
848C4—22no—
849C4—42no—
850C4—42no—
851C4—42no—
852C4—4881no—
853C4—4881no—
854C4—4881no—
855C4—4881no—
856C4#1684023711yescharacteristic
857C4#1684023711yescharacteristic
858C4#1684032111yescharacteristic
859C4#1684032111yescharacteristic
860C2—42no—
861C2—42no—
862C2—42no—
863C2—82no—
864C2#2144839711yescharacteristic
865C2#2145434511yescharacteristic
866C2#2145435211yescharacteristic
867C2#2145666511yescharacteristic
868C2#2145669511yescharacteristic
869C2#2145671611yescharacteristic
870C2#2145672511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
Fitting, prime radicalC2×C61×#537C2
socleC23×C61C22×D4
cosocleC22×C4×C61C24
hypercenterC2×#537D61
hypocenterC61#21772
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×#41 ◁ C2×#537

Complements

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

NH ≅ G/Ntype
1. C2×#16839729C2semidirect
2. #21448411C2semidirect
3. #21446258C2semidirect
4. #21446253C2semidirect
5. #21446248C2semidirect
6. #21446243C2semidirect
7. #21446142C2semidirect
8. #21446137C2semidirect
9. #21446132C2semidirect
10. #21446127C2semidirect
11. #21445909C2semidirect
12. #21445905C2semidirect
13. #21445759C2semidirect
14. #21445759C2semidirect
52. C61×#537C4semidirect
114. C2×#41×C61C2×C4semidirect
134. C22⋊Q8×C61C2×C4semidirect
141. #121×C61C2×C4semidirect
146. C2×C4⋊C4×C61C2×C4semidirect
456. #537Dic61semidirect
497. C61#21772semidirect
508. C2×#41C2×Dic61semidirect
539. C22⋊Q8C2×Dic61semidirect
546. #121C2×Dic61semidirect
560. C2×C4⋊C4C2×Dic61semidirect

Maximal subgroups

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

subgroupindex
C2×#168397292
#214484112
#214462582
#214462532
#214462482
#214462432
#214461422
#214461372
#214461322
#214461272
#214459092
#214459052
#214457592
C2×C61×#5372
#2177261