Finite Group Databasebeta

← #29695669

Subgroups — #29695669

Order 15616.

1582 conjugacy classes of subgroups.

The subgroup lattice has 894 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840431C211yesmaximal, characteristic
2C2×#16839837C211yesmaximal, characteristic, complemented
3C2×#16839763C211yesmaximal, characteristic, complemented
4C2×#16839762C211yesmaximal, characteristic, complemented
5#21448715C211yesmaximal, characteristic, complemented
6#21446744C211yesmaximal, characteristic, complemented
7#21446623C211yesmaximal, characteristic, complemented
8#21446255C211yesmaximal, characteristic, complemented
9#21446254C211yesmaximal, characteristic, complemented
10#21446134C211yesmaximal, characteristic, complemented
11#21446133C211yesmaximal, characteristic, complemented
12#21445822C211yesmaximal, characteristic, complemented
13#21445758C211yesmaximal, characteristic, complemented
14#103×Dic61C211yesmaximal, characteristic, complemented
15C61×#1788C211yesmaximal, characteristic, complemented
16C22×#11758226C2211yescharacteristic
17C22×#11758194C2211yescharacteristic
18C22×#11758189C2211yescharacteristic
19#16840431—24no—
20#16840431C418yescomplemented
21C2×#14519773—21no—
22C2×#14519773C2211yescharacteristic
23C2×#14519751—21no—
24C2×#14519751C2211yescharacteristic
25C2×#14519748—21no—
26C2×#14519748C2211yescharacteristic
27C2×Q8×Dic61C2211yescharacteristic
28C2×C4×C22⋊D61—21no—
29C2×C4×C22⋊D61C2211yescharacteristic
30C2×#14519737—21no—
31C22×C4⋊Dic61C2211yescharacteristic
32C2×C4⋊C4×D61C2211yescharacteristic
33#16839837—24no—
34C2×#14519706C2211yescharacteristic
35#16839763—24no—
36#16839762—24no—
37C2×#14519701C2211yescharacteristic
38C2×#14519701C2211yescharacteristic
39C2×#14519699C2211yescharacteristic
40C2×#14519699C2211yescharacteristic
41C2×#14519698C2211yescharacteristic
42C2×#14519698C2211yescharacteristic
43C2×#14519697C2211yescharacteristic
44C2×#14519697C2211yescharacteristic
45C2×#14519689C2211yescharacteristic
46C2×C8×Dic61C2211yescharacteristic
47#16839659—21no—
48#16839636—21no—
49#16839634—21no—
50#16839631C2211yescharacteristic
51#16839619C2211yescharacteristic
52C4⋊C4×Dic61C2211yescharacteristic
53#16839525C2211yescharacteristic
54#16839525C2211yescharacteristic
55#16839524C2211yescharacteristic
56#16839524C2211yescharacteristic
57C22×#41×C61C2211yescharacteristic
58C2×#103×C61C2211yescharacteristic
59C2×#103×C61C2211yescharacteristic
60C2×#102×C61C2211yescharacteristic
61C2×#102×C61C2211yescharacteristic
62C2×C22⋊C8×C61C2211yescharacteristic
63C61×#380C2211yescharacteristic
64C2×#11758226—22no—
65C2×#11758226—22no—
66C2×#11758226—22no—
67C2×#11758226—41no—
68C2×#11758226—41no—
69C2×#11758226C2×C414yescomplemented
70C22×D244—21no—
71C22×D244C2311yescharacteristic
72C22×C22⋊D61—21no—
73C22×C22⋊D61—21no—
74C22×C22⋊D61—21no—
75C22×C22⋊D61—21no—
76C22×C22⋊D61D411yescharacteristic
77C23×Dic61—21no—
78C22×C4×D61—21no—
79C22×C4×D61—21no—
80C22×C4×D61C2311yescharacteristic
81C2×#11758194—22no—
82C2×#11758194—22no—
83C2×#11758194—41no—
84C2×#11758189—22no—
85C2×#11758189—22no—
86C2×#11758189—41no—
87C22×#92418C2311yescharacteristic
88C22×#92418C2311yescharacteristic
89#14519773—28no—
90#14519773—22no—
91#14519773C2×C414yescomplemented
92#14519751—22no—
93#14519751—28no—
94#14519751C2×C414yescomplemented
95#14519748—22no—
96#14519748—28no—
97#14519748C2×C414yescomplemented
98Q8×Dic61—22no—
99Q8×Dic61C2×C414yescomplemented
100C4×C22⋊D61—28no—
101C4×C22⋊D61C2×C414yes—
102C4×C22⋊D61D414yes—
103#14519737—44no—
104C2×C4⋊Dic61—21no—
105C2×C4⋊Dic61—22no—
106C2×C4⋊Dic61—21no—
107C2×C4⋊Dic61—41no—
108C2×C4⋊Dic61C2311yescharacteristic
109C2×C4⋊Dic61C2311yescharacteristic
110C2×C4⋊Dic61C2311yescharacteristic
111C2×#11758196—21no—
112C2×#11758196—21no—
113C2×#11758196—21no—
114C2×#11758196D411yescharacteristic
115C4⋊C4×D61—22no—
116C4⋊C4×D61—41no—
117C2×C22⋊Dic61—21no—
118C2×C22⋊Dic61D411yescharacteristic
119C2×#11758198—21no—
120C2×#11758198—21no—
121C2×#11758198D411yescharacteristic
122C2×C4×Dic61—21no—
123C2×C4×Dic61—21no—
124C2×C4×Dic61C2311yescharacteristic
125#14519706—22no—
126#14519701—22no—
127#14519701D414yescomplemented
128#14519699—22no—
129#14519699—41no—
130#14519698—22no—
131#14519698—22no—
132#14519697—22no—
133#14519697—41no—
134#14519689—22no—
135C8×Dic61—22no—
136#14519684—21no—
137#14519684—21no—
138C2×#41×C61—22no—
139C2×#41×C61—22no—
140C2×#41×C61—22no—
141C2×#41×C61—41no—
142C2×#41×C61—41no—
143C2×#41×C61C2×C414yescomplemented
144C22×Q8×C61C2311yescharacteristic
145C22×D4×C61—21no—
146C22×D4×C61C2311yescharacteristic
147C23×C4×C61—21no—
148C23×C4×C61C2311yescharacteristic
149C22×C8×C61C2311yescharacteristic
150C22×C8×C61C2311yescharacteristic
151C2×C4⋊C4×C61C2311yescharacteristic
152C2×C4⋊C4×C61C2311yescharacteristic
153C2×C22⋊C4×C61—21no—
154#103×C61—22no—
155#103×C61—22no—
156#102×C61—41no—
157#102×C61—41no—
158C22⋊C8×C61—22no—
159#95×C61—21no—
160C24×C61—21no—
161C24×C61C2×D411yescharacteristic
162C23×D61—21no—
163C23×D61C2×D411yescharacteristic
164#41×C61—28no—
165#41×C61—44no—
166#41×C61—44no—
167#41×C61—44no—
168C2×Q8×C61—21no—
169C2×Q8×C61—21no—
170C2×Q8×C61—21no—
171C2×Q8×C61C22×C412yes—
172C2×Q8×C61C2×D412yes—
173C2×Q8×C61#4112yes—
174C2×D4×C61—24no—
175C2×D4×C61—21no—
176C2×D4×C61—21no—
177C2×D4×C61—21no—
178C2×D4×C61—21no—
179C2×D4×C61—21no—
180C2×D4×C61—42no—
181C2×D4×C61—42no—
182C2×D4×C61C22×C412yes—
183C22×C4×C61—21no—
184C22×C4×C61—21no—
185C22×C4×C61—21no—
186C22×C4×C61—21no—
187C22×C4×C61—21no—
188C22×C4×C61—24no—
189C22×C4×C61—21no—
190C22×C4×C61—21no—
191C22×C4×C61—42no—
192C22×C4×C61—42no—
193C22×C4×C61C22×C412yes—
194C22×C4×C61C2×D411yescharacteristic
195C22×C4×C61C2×D412yes—
196C22×C4×C61C2411yescharacteristic
197C2×C22⋊D61—24no—
198C2×C22⋊D61—24no—
199C2×C22⋊D61—24no—
200C2×C22⋊D61—24no—
201C2×C22⋊D61—22no—
202C2×C22⋊D61—22no—
203C2×C22⋊D61—42no—
204C2×C22⋊D61—42no—
205C2×C22⋊D61—81no—
206C2×C22⋊D61—81no—
207C2×C22⋊D61—81no—
208C2×C22⋊D61—81no—
209C2×C22⋊D61—81no—
210C2×C22⋊D61—81no—
211C2×C22⋊D61C22⋊C414yes—
212C22×Dic61—21no—
213C22×Dic61—21no—
214C22×Dic61—21no—
215C22×Dic61—42no—
216C22×Dic61—42no—
217C22×Dic61—81no—
218C22×Dic61C2×D411yescharacteristic
219C22×Dic61C2×D411yescharacteristic
220C22×Dic61C2×D411yescharacteristic
221#11758226—28no—
222#11758226—44no—
223#11758226—44no—
224#11758226—44no—
225C2×D244—21no—
226C2×D244—21no—
227C2×D244—21no—
228C2×D244—21no—
229C2×D244—24no—
230C2×D244—21no—
231C2×D244—42no—
232C2×D244—42no—
233C2×D244C22×C412yes—
234C2×C4×D61—21no—
235C2×C4×D61—21no—
236C2×C4×D61—21no—
237C2×C4×D61—21no—
238C2×C4×D61—24no—
239C2×C4×D61—42no—
240C2×C4×D61—42no—
241C2×C4×D61—42no—
242C2×C4×D61—42no—
243C2×C4×D61—81no—
244C2×C4×D61C22×C412yes—
245C2×C4×D61C2×D412yes—
246C2×C8×C61—21no—
247C2×C8×C61—21no—
248C2×C8×C61—21no—
249C2×C8×C61—21no—
250C2×C8×C61—21no—
251C2×C8×C61—21no—
252C4⋊C4×C61—21no—
253C4⋊C4×C61—21no—
254C4⋊C4×C61—21no—
255C4⋊C4×C61—21no—
256C22⋊C4×C61—42no—
257C22⋊Dic61—24no—
258C22⋊Dic61C22⋊C414yes—
259#11758198—24no—
260#11758198—42no—
261#11758198C22⋊C414yes—
262C4⋊Dic61—21no—
263C4⋊Dic61—21no—
264C4⋊Dic61—24no—
265C4⋊Dic61—21no—
266C4⋊Dic61—21no—
267C4⋊Dic61—42no—
268C4⋊Dic61C22×C412yes—
269C4⋊Dic61C2×D412yes—
270#11758196—42no—
271#11758196—42no—
272#11758196—81no—
273#11758196C22⋊C414yes—
274C4×Dic61—24no—
275C4×Dic61—42no—
276C4×Dic61C22×C412yes—
277C4×Dic61C2×D412yes—
278#11758194—44no—
279C2×#92418—21no—
280C2×#92418—21no—
281C2×#92418—21no—
282C2×#92418—21no—
283C2×#92418—21no—
284C2×#92418C2×D412yes—
285#11758189—44no—
286C23×C61—21no—
287C23×C61—21no—
288C23×C61—21no—
289C23×C61—21no—
290C23×C61—21no—
291C23×C61—21no—
292C23×C61—22no—
293C23×C61—41no—
294C23×C61—41no—
295C23×C61—41no—
296C23×C61—41no—
297C23×C61—41no—
298C23×C61—41no—
299C23×C61C2×C22⋊C412yes—
300C23×C61C22×D411yescharacteristic
301C22×D61—21no—
302C22×D61—21no—
303C22×D61—21no—
304C22×D61—21no—
305C22×D61—21no—
306C22×D61—21no—
307C22×D61—22no—
308C22×D61—41no—
309C22×D61—41no—
310C22×D61—41no—
311C22×D61—41no—
312C22×D61—41no—
313C22×D61—41no—
314C22×D61C2×C22⋊C412yes—
315Q8×C61—22no—
316Q8×C61—22no—
317Q8×C61—22no—
318Q8×C61C4×D414yescomplemented
319D4×C61—22no—
320D4×C61—22no—
321D4×C61—48no—
322D4×C61—41no—
323D4×C61—41no—
324C2×C4×C61—22no—
325C2×C4×C61—21no—
326C2×C4×C61—22no—
327C2×C4×C61—22no—
328C2×C4×C61—21no—
329C2×C4×C61—22no—
330C2×C4×C61—22no—
331C2×C4×C61—22no—
332C2×C4×C61—22no—
333C2×C4×C61—48no—
334C2×C4×C61—41no—
335C2×C4×C61—41no—
336C2×C4×C61—41no—
337C2×C4×C61—41no—
338C2×C4×C61—41no—
339C2×C4×C61—41no—
340C2×C4×C61C2×C22⋊C412yes—
341C2×C4×C61C23×C411yescharacteristic
342C2×C4×C61C22×D411yescharacteristic
343C2×C4×C61C22×D411yescharacteristic
344C2×C4×C61C2×#4111yescharacteristic
345C2×C4×C61H(5,𝔽2)11yescharacteristic
346C2×C4×C61H(5,𝔽2)11yescharacteristic
347C22⋊D61—28no—
348C22⋊D61—48no—
349C22⋊D61—84no—
350C22⋊D61—84no—
351C22⋊D61—84no—
352C2×Dic61—21no—
353C2×Dic61—21no—
354C2×Dic61—21no—
355C2×Dic61—21no—
356C2×Dic61—22no—
357C2×Dic61—22no—
358C2×Dic61—41no—
359C2×Dic61—41no—
360C2×Dic61—41no—
361C2×Dic61—41no—
362C2×Dic61—41no—
363C2×Dic61—41no—
364C2×Dic61—41no—
365C2×Dic61—84no—
366C2×Dic61C2×C22⋊C412yes—
367C2×Dic61C2×C22⋊C412yes—
368C2×Dic61C2×C22⋊C412yes—
369C2×Dic61AGL(1,ℤ/8)12yes—
370C2×Dic61#13712yes—
371D244—22no—
372D244—22no—
373D244—48no—
374D244—41no—
375D244—41no—
376C4×D61—22no—
377C4×D61—22no—
378C4×D61—22no—
379C4×D61—22no—
380C4×D61—48no—
381C4×D61—84no—
382C8×C61—41no—
383C8×C61—41no—
384#92418—22no—
385#92418—41no—
386#22432—611nomaximal, Sylow
387C22×C61—22no—
388C22×C61—22no—
389C22×C61—22no—
390C22×C61—41no—
391C22×C61—41no—
392C22×C61—41no—
393C22×C61—41no—
394C22×C61—42no—
395C22×C61—42no—
396C22×C61—42no—
397C22×C61—81no—
398C22×C61—81no—
399C22×C61—81no—
400C22×C61—81no—
401C22×C61C22×C22⋊C411yescharacteristic
402C22×C61D4211yescharacteristic
403C22×C61#54611yescharacteristic
404C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
405C22×C61C2×#13711yescharacteristic
406C22×C61#57611yescharacteristic
407C22×C61#57711yescharacteristic
408C2×D61—22no—
409C2×D61—22no—
410C2×D61—22no—
411C2×D61—41no—
412C2×D61—41no—
413C2×D61—41no—
414C2×D61—41no—
415C2×D61—42no—
416C2×D61—42no—
417C2×D61—42no—
418C2×D61—81no—
419C2×D61—81no—
420C2×D61—81no—
421C2×D61—81no—
422C4×C61—24no—
423C4×C61—22no—
424C4×C61—81no—
425C4×C61—81no—
426C4×C61C2×C4×D411yescharacteristic
427C4×C61#51811yescharacteristic
428C4×C61D4211yescharacteristic
429C4×C61#54611yescharacteristic
430Dic61—22no—
431Dic61—22no—
432Dic61—42no—
433Dic61—42no—
434Dic61—81no—
435Dic61#41714yescomplemented
436C2×#550—611no—
437C2×#436—611no—
438C2×#417—611no—
439C2×#417—611no—
440D4×C4⋊C4—611no—
441#1982—611no—
442#1957—611no—
443#1895—611no—
444#1895—611no—
445#1874—611no—
446#1874—611no—
447#1803—611no—
448#1788—611no—
449#1788D6111yescharacteristic, complemented
450C4×#103—611no—
451C2×C61—42no—
452C2×C61—82no—
453C2×C61D4×C22⋊C411yescharacteristic
454C2×C61C2×#41711yescharacteristic
455C2×C61#289711yescharacteristic
456C2×C61#327411yescharacteristic
457C2×C61#327811yescharacteristic
458C2×C61#333211yescharacteristic
459C2×C61#333311yescharacteristic
460D61—42no—
461D61—82no—
462C22×#41—611no—
463C22×#41C2×D6111yescharacteristic
464C22×M16—611no—
465C22×M16—611no—
466#550—618no—
467#550—1224no—
468C2×#127—611no—
469C2×#127—1221no—
470C2×#121—611no—
471C2×#121—611no—
472C2×#121—1221no—
473C2×#121—1221no—
474C2×C4×Q8—611no—
475C2×C4×D4—611no—
476C2×C4×D4—1221no—
477C2×C4×D4—1221no—
478C22×C4⋊C4—611no—
479C22×C4⋊C4—611no—
480#436—1224no—
481C2×C4⋊C8—611no—
482#417—1224no—
483#417—1224no—
484C2×#103—611no—
485C2×#103—611no—
486C2×#103C2×D6111yescharacteristic
487C2×#103C2×D6111yescharacteristic
488C2×#102—611no—
489C2×#102—611no—
490C2×#102—611no—
491C2×#102—611no—
492C2×#102—611no—
493C2×#102—611no—
494C2×#102C2×D6111yescharacteristic
495C2×#102C2×D6111yescharacteristic
496C2×C22⋊C8—611no—
497C2×C22⋊C8C2×D6111yescharacteristic
498C2×C4×C8—611no—
499#389—1221no—
500#385—1221no—
501#385—1221no—
502#384—611no—
503#380—611no—
504#380C2×D6111yescharacteristic
505C4×C4⋊C4—611no—
506#340—611no—
507#340—611no—
508#340—611no—
509#340—611no—
510C61#2243211yescharacteristic, complemented, Sylow
511C2×#41—22no—
512C2×#41—22no—
513C2×#41—22no—
514C2×#41—41no—
515C2×#41—41no—
516C2×#41—614no—
517C2×#41—1222no—
518C2×#41—1222no—
519C2×#41—1222no—
520C2×#41—2441no—
521C2×#41—2441no—
522C2×#41C4×D6114yescomplemented
523C22×Q8C22×D6111yescharacteristic
524C22×D4—21no—
525C22×D4—611no—
526C22×D4—611no—
527C22×D4—1221no—
528C22×D4—1221no—
529C22×D4—1221no—
530C22×D4—1221no—
531C22×D4—1221no—
532C22×D4C22×D6111yescharacteristic
533C23×C4—21no—
534C23×C4—611no—
535C23×C4—1221no—
536C23×C4—1221no—
537C23×C4—1221no—
538C23×C4C22×D6111yescharacteristic
539C2×M16—1222no—
540C2×M16—1222no—
541C2×M16—1222no—
542C2×M16—1222no—
543C2×M16—2441no—
544C2×M16—2441no—
545C22×C8—611no—
546C22×C8—611no—
547C22×C8C22×D6111yescharacteristic
548C22×C8C22×D6111yescharacteristic
549#127—614no—
550#127—1222no—
551#127—1228no—
552#121—614no—
553#121—614no—
554#121—1228no—
555#121—1228no—
556#121—1222no—
557#121—1222no—
558C4×Q8—614no—
559C4×Q8—1222no—
560C4×D4—614no—
561C4×D4—614no—
562C4×D4—1228no—
563C4×D4—2444no—
564C2×C4⋊C4—611no—
565C2×C4⋊C4—611no—
566C2×C4⋊C4—611no—
567C2×C4⋊C4—611no—
568C2×C4⋊C4—1222no—
569C2×C4⋊C4—1222no—
570C2×C4⋊C4—1221no—
571C2×C4⋊C4—1221no—
572C2×C4⋊C4—1221no—
573C2×C4⋊C4—1221no—
574C2×C4⋊C4—1221no—
575C2×C4⋊C4—2441no—
576C2×C4⋊C4—2441no—
577C2×C4⋊C4C22×D6111yescharacteristic
578C2×C4⋊C4C22×D6111yescharacteristic
579C2×C22⋊C4—21no—
580C2×C22⋊C4—611no—
581C2×C22⋊C4—611no—
582C2×C22⋊C4—1221no—
583C2×C22⋊C4—1221no—
584C2×C22⋊C4—1221no—
585C2×C42—611no—
586C2×C42—1221no—
587C2×C42—1221no—
588C4⋊C8—1222no—
589#103—22no—
590#103—22no—
591#103—614no—
592#103—1222no—
593#102—41no—
594#102—41no—
595#102—1222no—
596#102—1222no—
597#102—1222no—
598#102—1222no—
599#102—2441no—
600#102—2441no—
601C22⋊C8—22no—
602C22⋊C8—1222no—
603C4×C8—1222no—
604#95—21no—
605#95—1221no—
606#95—1221no—
607C24—21no—
608C24—611no—
609C24—1221no—
610C24D4×D6111yescharacteristic
611#41—28no—
612#41—44no—
613#41—44no—
614#41—44no—
615#41—1228no—
616#41—2444no—
617#41—2444no—
618#41—2444no—
619C2×Q8—21no—
620C2×Q8—21no—
621C2×Q8—21no—
622C2×Q8C2×C4×D6112yes—
623C2×Q8D4×D6112yes—
624C2×Q8#1175822412yes—
625C2×D4—24no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—21no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—42no—
632C2×D4—42no—
633C2×D4—614no—
634C2×D4—612no—
635C2×D4—1224no—
636C2×D4—1222no—
637C2×D4—1222no—
638C2×D4—1224no—
639C2×D4—1224no—
640C2×D4—1224no—
641C2×D4—1224no—
642C2×D4—1221no—
643C2×D4—1221no—
644C2×D4—1221no—
645C2×D4—1221no—
646C2×D4—1221no—
647C2×D4—4881no—
648C2×D4—4881no—
649C2×D4—4881no—
650C2×D4—4881no—
651C2×D4—4881no—
652C2×D4—4881no—
653C2×D4—2442no—
654C2×D4—2442no—
655C2×D4—2442no—
656C2×D4—2442no—
657C2×D4C2×C4×D6112yes—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—24no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—42no—
667C22×C4—42no—
668C22×C4—611no—
669C22×C4—611no—
670C22×C4—611no—
671C22×C4—612no—
672C22×C4—612no—
673C22×C4—1224no—
674C22×C4—1221no—
675C22×C4—1221no—
676C22×C4—1221no—
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×C4—2442no—
688C22×C4—2442no—
689C22×C4C2×C4×D6112yes—
690C22×C4D4×D6112yes—
691C22×C4D4×D6111yescharacteristic
692C22×C4C23×D6111yescharacteristic
693M16—2444no—
694M16—2444no—
695C2×C8—21no—
696C2×C8—21no—
697C2×C8—21no—
698C2×C8—21no—
699C2×C8—21no—
700C2×C8—21no—
701C2×C8—612no—
702C2×C8—1221no—
703C2×C8—1221no—
704C2×C8—1221no—
705C2×C8—1221no—
706C2×C8—1221no—
707C4⋊C4—21no—
708C4⋊C4—21no—
709C4⋊C4—21no—
710C4⋊C4—21no—
711C4⋊C4—614no—
712C4⋊C4—612no—
713C4⋊C4—612no—
714C4⋊C4—1224no—
715C4⋊C4—1221no—
716C4⋊C4—1221no—
717C4⋊C4—1221no—
718C4⋊C4—1221no—
719C4⋊C4—4881no—
720C4⋊C4—2442no—
721C4⋊C4—2442no—
722C4⋊C4—2442no—
723C22⋊C4—42no—
724C22⋊C4—614no—
725C22⋊C4—614no—
726C22⋊C4—1224no—
727C22⋊C4—1224no—
728C22⋊C4—2442no—
729C42—612no—
730C42—612no—
731C42—1224no—
732C42—2442no—
733C23—21no—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—21no—
738C23—21no—
739C23—22no—
740C23—41no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—612no—
747C23—1221no—
748C23—1221no—
749C23—1221no—
750C23—1221no—
751C23—1221no—
752C23—1221no—
753C23—1222no—
754C23—2441no—
755C23—2441no—
756C23—2441no—
757C23—2441no—
758C23—2441no—
759C23—2441no—
760C23C22⋊C4×D6112yes—
761C23C2×D4×D6111yescharacteristic
762Q8—22no—
763Q8—22no—
764Q8—22no—
765Q8#1451973714yescomplemented
766D4—22no—
767D4—22no—
768D4—48no—
769D4—41no—
770D4—41no—
771D4—1228no—
772D4—1222no—
773D4—1222no—
774D4—4884no—
775D4—4884no—
776D4—4884no—
777D4—2448no—
778D4—2448no—
779D4—2441no—
780D4—2441no—
781C2×C4—22no—
782C2×C4—21no—
783C2×C4—22no—
784C2×C4—21no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—48no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—612no—
798C2×C4—612no—
799C2×C4—612no—
800C2×C4—612no—
801C2×C4—612no—
802C2×C4—1221no—
803C2×C4—1221no—
804C2×C4—1221no—
805C2×C4—1221no—
806C2×C4—1222no—
807C2×C4—1222no—
808C2×C4—1222no—
809C2×C4—1222no—
810C2×C4—1222no—
811C2×C4—1222no—
812C2×C4—4884no—
813C2×C4—4884no—
814C2×C4—2448no—
815C2×C4—2441no—
816C2×C4—2441no—
817C2×C4—2441no—
818C2×C4—2441no—
819C2×C4—2441no—
820C2×C4—2441no—
821C2×C4—2441no—
822C2×C4C22⋊C4×D6112yes—
823C2×C4C22×C4×D6111yescharacteristic
824C2×C4C2×D4×D6111yescharacteristic
825C2×C4C2×D4×D6111yescharacteristic
826C2×C4C2×#1175822411yescharacteristic
827C2×C4#1451982211yescharacteristic
828C2×C4#1451982211yescharacteristic
829C8—41no—
830C8—41no—
831C8—1222no—
832C8—2441no—
833C22—22no—
834C22—22no—
835C22—22no—
836C22—41no—
837C22—41no—
838C22—41no—
839C22—41no—
840C22—42no—
841C22—42no—
842C22—42no—
843C22—81no—
844C22—81no—
845C22—81no—
846C22—81no—
847C22—1222no—
848C22—1222no—
849C22—1222no—
850C22—4881no—
851C22—4881no—
852C22—4881no—
853C22—4881no—
854C22—2442no—
855C22—2442no—
856C22—2442no—
857C22—2441no—
858C22—2441no—
859C22—2441no—
860C22—2441no—
861C22C2×C22⋊C4×D6111yescharacteristic
862C22#1684039411yescharacteristic
863C22#1684039911yescharacteristic
864C22AGL(1,ℤ/8)×D6111yescharacteristic
865C22#137×D6111yescharacteristic
866C22#1684056411yescharacteristic
867C22#1684056911yescharacteristic
868C4—22no—
869C4—24no—
870C4—81no—
871C4—81no—
872C4—614no—
873C4—1222no—
874C4—1222no—
875C4—4881no—
876C4—2442no—
877C4—2442no—
878C4C2×#1451973711yescharacteristic
879C4#1684023511yescharacteristic
880C4#1684039411yescharacteristic
881C4#1684039911yescharacteristic
882C2—42no—
883C2—82no—
884C2—4882no—
885C2—2442no—
886C2#2144863511yescharacteristic
887C2#417×D6111yescharacteristic
888C2#2145434111yescharacteristic
889C2#2145743211yescharacteristic
890C2#2145747811yescharacteristic
891C2#2145813911yescharacteristic
892C2#2145815011yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1788C2
socleC23×C61C22×D4
prime radicalC2×#16840431C2
cosocleC22×C4×C61C24
hypercenter#1788D61
hypocenterC61#22432
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1788

Complements

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

NH ≅ G/Ntype
2. C2×#16839837C2semidirect
3. C2×#16839763C2semidirect
4. C2×#16839762C2semidirect
5. #21448715C2semidirect
6. #21446744C2semidirect
7. #21446623C2semidirect
8. #21446255C2semidirect
9. #21446254C2semidirect
10. #21446134C2semidirect
11. #21446133C2semidirect
12. #21445822C2semidirect
13. #21445758C2semidirect
14. #103×Dic61C2semidirect
15. C61×#1788C2semidirect
20. #16840431C4semidirect
69. C2×#11758226C2×C4semidirect
91. #14519773C2×C4semidirect
94. #14519751C2×C4semidirect
97. #14519748C2×C4semidirect
99. Q8×Dic61C2×C4semidirect
127. #14519701D4semidirect
143. C2×#41×C61C2×C4semidirect
318. Q8×C61C4×D4semidirect
435. Dic61#417semidirect
449. #1788D61semidirect
510. C61#22432semidirect
522. C2×#41C4×D61semidirect
765. Q8#14519737semidirect

Maximal subgroups

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

subgroupindex
C2×#168404312
C2×#168398372
C2×#168397632
C2×#168397622
#214487152
#214467442
#214466232
#214462552
#214462542
#214461342
#214461332
#214458222
#214457582
#103×Dic612
C61×#17882
#2243261