Finite Group Databasebeta

← #29695606

Subgroups — #29695606

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×#16840400C211yesmaximal, characteristic
2C2×#16839837C211yesmaximal, characteristic, complemented
3C2×#16839763C211yesmaximal, characteristic, complemented
4C2×#16839765C211yesmaximal, characteristic, complemented
5#21448750C211yesmaximal, characteristic, complemented
6#21446748C211yesmaximal, characteristic, complemented
7#21446627C211yesmaximal, characteristic, complemented
8#21446255C211yesmaximal, characteristic, complemented
9#21446249C211yesmaximal, characteristic, complemented
10#21446134C211yesmaximal, characteristic, complemented
11#21446128C211yesmaximal, characteristic, complemented
12#21445827C211yesmaximal, characteristic, complemented
13#21445748C211yesmaximal, characteristic, complemented
14#102×Dic61C211yesmaximal, characteristic, complemented
15C61×#1788C211yesmaximal, characteristic, complemented
16C22×D4×D61C2211yescharacteristic
17C22×#11758194C2211yescharacteristic, complemented
18C22×#11758189C2211yescharacteristic
19#16840400—24no—
20#16840400C418yescomplemented
21C2×#14519766C2211yescharacteristic
22C2×#14519760—21no—
23C2×#14519753C2211yescharacteristic
24C2×#14519751C2211yescharacteristic
25C2×#14519749—21no—
26C2×#14519745—21no—
27C2×D4×Dic61C2211yescharacteristic
28C2×C4×C22⋊D61C2211yescharacteristic
29C2×#14519735C2211yescharacteristic
30C22×C4⋊Dic61C2211yescharacteristic, complemented
31C22×#11758198—21no—
32#16839837—24no—
33C2×#14519706C2211yescharacteristic, complemented
34#16839765—24no—
35#16839763—24no—
36C2×#14519701C2211yescharacteristic, complemented
37C2×#14519701C2211yescharacteristic, complemented
38C2×#14519699C2211yescharacteristic
39C2×#14519699C2211yescharacteristic
40C2×#14519698C2211yescharacteristic
41C2×#14519698C2211yescharacteristic
42C2×#14519697C2211yescharacteristic
43C2×#14519697C2211yescharacteristic
44C2×#14519689C2211yescharacteristic
45C2×C8×Dic61C2211yescharacteristic, complemented
46#16839654—21no—
47#16839649—21no—
48#16839639—21no—
49#16839627C2211yescharacteristic, complemented
50#16839619C2211yescharacteristic
51C4⋊C4×Dic61C2211yescharacteristic, complemented
52C22⋊C4×Dic61—21no—
53#16839525C2211yescharacteristic, complemented
54#16839525C2211yescharacteristic, complemented
55#16839524C2211yescharacteristic, complemented
56#16839524C2211yescharacteristic, complemented
57C22×#41×C61C2211yescharacteristic
58C2×#103×C61C2211yescharacteristic, complemented
59C2×#103×C61C2211yescharacteristic, complemented
60C2×#102×C61C2211yescharacteristic
61C2×#102×C61C2211yescharacteristic
62C2×C22⋊C8×C61C2211yescharacteristic, complemented
63C61×#380C2211yescharacteristic, complemented
64C24×D61—21no—
65C22×D244C2311yescharacteristic
66C22×C22⋊D61—21no—
67C22×C22⋊D61—21no—
68C22×C22⋊D61D411yescharacteristic
69C2×D4×D61—22no—
70C2×D4×D61—22no—
71C2×D4×D61—22no—
72C2×D4×D61—41no—
73C2×D4×D61—41no—
74C2×D4×D61C2×C414yescomplemented
75C23×Dic61—21no—
76C23×Dic61—21no—
77C22×C4×D61C2311yescharacteristic
78C2×#11758194—22no—
79C2×#11758194—22no—
80C2×#11758194—41no—
81C2×#11758189—22no—
82C2×#11758189—22no—
83C2×#11758189—41no—
84C22×#92418C2311yescharacteristic
85C22×#92418C2311yescharacteristic
86#14519766—22no—
87#14519766C2×C414yescomplemented
88#14519760—28no—
89#14519753—22no—
90#14519753C2×C414yescomplemented
91#14519751—22no—
92#14519751C2×C414yes—
93#14519749—28no—
94#14519745—28no—
95D4×Dic61—22no—
96D4×Dic61C2×C414yescomplemented
97C4×C22⋊D61C2×C414yes—
98C4×C22⋊D61D414yes—
99#14519735—22no—
100#14519735—41no—
101C2×C4⋊Dic61—22no—
102C2×C4⋊Dic61—21no—
103C2×C4⋊Dic61—41no—
104C2×C4⋊Dic61C2311yescharacteristic
105C2×C4⋊Dic61C2311yescharacteristic
106C2×C4⋊Dic61C2311yescharacteristic
107C2×#11758196—21no—
108C2×#11758196D411yescharacteristic
109C2×C22⋊Dic61—21no—
110C2×C22⋊Dic61D411yescharacteristic
111C2×#11758198—21no—
112C2×#11758198—21no—
113C2×#11758198—21no—
114C2×#11758198—21no—
115C2×#11758198—28no—
116C2×#11758198—21no—
117C2×#11758198—21no—
118C2×#11758198D411yescharacteristic
119C2×C4×Dic61—21no—
120C2×C4×Dic61—21no—
121C2×C4×Dic61C2311yescharacteristic
122#14519706—22no—
123#14519701—22no—
124#14519701—22no—
125#14519699—22no—
126#14519699—41no—
127#14519698—22no—
128#14519698D414yescomplemented
129#14519697—22no—
130#14519697—41no—
131#14519689—22no—
132C8×Dic61—22no—
133#14519684—21no—
134#14519684—21no—
135#14519684—21no—
136#14519684—21no—
137C2×#41×C61—22no—
138C2×#41×C61—22no—
139C2×#41×C61—22no—
140C2×#41×C61—41no—
141C2×#41×C61—41no—
142C2×#41×C61C2×C414yes—
143C22×Q8×C61C2311yescharacteristic
144C22×D4×C61—21no—
145C22×D4×C61C2311yescharacteristic
146C23×C4×C61—21no—
147C23×C4×C61C2311yescharacteristic
148C22×C8×C61C2311yescharacteristic
149C22×C8×C61C2311yescharacteristic
150C2×C4⋊C4×C61C2311yescharacteristic
151C2×C4⋊C4×C61C2311yescharacteristic
152C2×C22⋊C4×C61—21no—
153#103×C61—41no—
154#103×C61—41no—
155#102×C61—22no—
156#102×C61—22no—
157C22⋊C8×C61—22no—
158#95×C61—21no—
159C24×C61—21no—
160C24×C61C2×D411yescharacteristic
161C23×D61—21no—
162C23×D61—24no—
163C23×D61—42no—
164C23×D61—42no—
165C23×D61—42no—
166C23×D61—42no—
167C23×D61—81no—
168C23×D61—81no—
169C23×D61C2×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—24no—
181C2×D4×C61—21no—
182C2×D4×C61—21no—
183C2×D4×C61—21no—
184C2×D4×C61—42no—
185C2×D4×C61—42no—
186C2×D4×C61C22×C412yes—
187C2×D4×C61C2×D412yes—
188C2×D4×C61#4112yes—
189C22×C4×C61—21no—
190C22×C4×C61—21no—
191C22×C4×C61—21no—
192C22×C4×C61—21no—
193C22×C4×C61—21no—
194C22×C4×C61—24no—
195C22×C4×C61—21no—
196C22×C4×C61—21no—
197C22×C4×C61—42no—
198C22×C4×C61—42no—
199C22×C4×C61C22×C412yes—
200C22×C4×C61C2×D411yescharacteristic
201C22×C4×C61C2×D412yes—
202C22×C4×C61C2411yescharacteristic
203C2×C22⋊D61—24no—
204C2×C22⋊D61—24no—
205C2×C22⋊D61—41no—
206C2×C22⋊D61—41no—
207C2×C22⋊D61—42no—
208C2×C22⋊D61—42no—
209C2×C22⋊D61—81no—
210C2×C22⋊D61—81no—
211C2×C22⋊D61C22⋊C414yes—
212C22×Dic61—21no—
213C22×Dic61—21no—
214C22×Dic61—24no—
215C22×Dic61—21no—
216C22×Dic61—42no—
217C22×Dic61—42no—
218C22×Dic61—81no—
219C22×Dic61—81no—
220C22×Dic61—81no—
221C22×Dic61C2×D411yescharacteristic
222C22×Dic61C2×D411yescharacteristic
223C22×Dic61C2×D411yescharacteristic
224D4×D61—28no—
225D4×D61—44no—
226D4×D61—44no—
227D4×D61—44no—
228C2×D244—21no—
229C2×D244—21no—
230C2×D244—21no—
231C2×D244—21no—
232C2×D244—21no—
233C2×D244C22×C412yes—
234C2×C4×D61—21no—
235C2×C4×D61—21no—
236C2×C4×D61—21no—
237C2×C4×D61—21no—
238C2×C4×D61C22×C412yes—
239C2×C4×D61C2×D412yes—
240C2×C8×C61—21no—
241C2×C8×C61—21no—
242C2×C8×C61—21no—
243C2×C8×C61—21no—
244C2×C8×C61—21no—
245C2×C8×C61—21no—
246C4⋊C4×C61—21no—
247C4⋊C4×C61—21no—
248C4⋊C4×C61—21no—
249C4⋊C4×C61—21no—
250C22⋊C4×C61—42no—
251C22⋊Dic61—24no—
252C22⋊Dic61C22⋊C414yes—
253#11758198—24no—
254#11758198—24no—
255#11758198—24no—
256#11758198—24no—
257#11758198—42no—
258#11758198—81no—
259#11758198C22⋊C414yes—
260C4⋊Dic61—21no—
261C4⋊Dic61—21no—
262C4⋊Dic61—21no—
263C4⋊Dic61—21no—
264C4⋊Dic61—42no—
265C4⋊Dic61C22×C412yes—
266C4⋊Dic61C2×D412yes—
267#11758196—24no—
268#11758196C22⋊C414yes—
269C4×Dic61—42no—
270C4×Dic61—81no—
271C4×Dic61C22×C412yes—
272C4×Dic61C2×D412yes—
273#11758194—44no—
274C2×#92418—21no—
275C2×#92418—21no—
276C2×#92418—21no—
277C2×#92418—21no—
278C2×#92418—21no—
279C2×#92418C2×D412yes—
280#11758189—44no—
281C23×C61—22no—
282C23×C61—21no—
283C23×C61—22no—
284C23×C61—22no—
285C23×C61—21no—
286C23×C61—21no—
287C23×C61—21no—
288C23×C61—21no—
289C23×C61—21no—
290C23×C61—41no—
291C23×C61—41no—
292C23×C61—41no—
293C23×C61—41no—
294C23×C61C2×C22⋊C412yes—
295C23×C61C22×D411yescharacteristic
296C22×D61—21no—
297C22×D61—21no—
298C22×D61—21no—
299C22×D61—21no—
300C22×D61—21no—
301C22×D61—21no—
302C22×D61—22no—
303C22×D61—48no—
304C22×D61—48no—
305C22×D61—41no—
306C22×D61—41no—
307C22×D61—41no—
308C22×D61—41no—
309C22×D61—41no—
310C22×D61—41no—
311C22×D61—84no—
312C22×D61—84no—
313C22×D61—84no—
314C22×D61—84no—
315C22×D61—84no—
316C22×D61C2×C22⋊C412yes—
317Q8×C61—22no—
318Q8×C61—22no—
319Q8×C61—41no—
320Q8×C61—41no—
321D4×C61—22no—
322D4×C61—22no—
323D4×C61—22no—
324D4×C61—48no—
325D4×C61C4×D414yes—
326C2×C4×C61—21no—
327C2×C4×C61—21no—
328C2×C4×C61—22no—
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×C61—41no—
341C2×C4×C61—41no—
342C2×C4×C61C2×C22⋊C412yes—
343C2×C4×C61C23×C411yescharacteristic
344C2×C4×C61C22×D411yescharacteristic
345C2×C4×C61C22×D411yescharacteristic
346C2×C4×C61C2×#4111yescharacteristic
347C2×C4×C61H(5,𝔽2)11yescharacteristic
348C2×C4×C61H(5,𝔽2)11yescharacteristic
349C22⋊D61—44no—
350C22⋊D61—48no—
351C22⋊D61—84no—
352C2×Dic61—21no—
353C2×Dic61—21no—
354C2×Dic61—21no—
355C2×Dic61—21no—
356C2×Dic61—21no—
357C2×Dic61—21no—
358C2×Dic61—22no—
359C2×Dic61—22no—
360C2×Dic61—41no—
361C2×Dic61—41no—
362C2×Dic61—41no—
363C2×Dic61—41no—
364C2×Dic61—41no—
365C2×Dic61—41no—
366C2×Dic61—41no—
367C2×Dic61—84no—
368C2×Dic61—84no—
369C2×Dic61C2×C22⋊C412yes—
370C2×Dic61C2×C22⋊C412yes—
371C2×Dic61C2×C22⋊C412yes—
372D244—22no—
373D244—22no—
374D244—41no—
375D244—41no—
376C4×D61—22no—
377C4×D61—22no—
378C4×D61—22no—
379C4×D61—22no—
380C8×C61—41no—
381C8×C61—41no—
382#92418—22no—
383#92418—41no—
384#22427—611nomaximal, Sylow
385C22×C61—24no—
386C22×C61—22no—
387C22×C61—22no—
388C22×C61—22no—
389C22×C61—42no—
390C22×C61—42no—
391C22×C61—41no—
392C22×C61—42no—
393C22×C61—42no—
394C22×C61—41no—
395C22×C61—42no—
396C22×C61—41no—
397C22×C61—42no—
398C22×C61—41no—
399C22×C61C22×C22⋊C411yescharacteristic
400C22×C61D4211yescharacteristic
401C22×C61#54611yescharacteristic
402C22×C61#57511yescharacteristic
403C22×C61#57511yescharacteristic
404C22×C61#57611yescharacteristic
405C22×C61#57711yescharacteristic
406C2×D61—22no—
407C2×D61—22no—
408C2×D61—22no—
409C2×D61—41no—
410C2×D61—41no—
411C2×D61—41no—
412C2×D61—41no—
413C2×D61—42no—
414C2×D61—42no—
415C2×D61—42no—
416C2×D61—816no—
417C2×D61—81no—
418C2×D61—81no—
419C2×D61—81no—
420C2×D61—81no—
421C4×C61—22no—
422C4×C61—42no—
423C4×C61—81no—
424C4×C61—81no—
425C4×C61C2×C4×D411yescharacteristic
426C4×C61#51811yescharacteristic
427C4×C61D4211yescharacteristic
428C4×C61#54611yescharacteristic
429Dic61—22no—
430Dic61—22no—
431Dic61—22no—
432Dic61—42no—
433Dic61—42no—
434Dic61—81no—
435C2×#546—611no—
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#1788D6111yescharacteristic, complemented
448#1786—611no—
449C4×#102—611no—
450C2×C61—44no—
451C2×C61—42no—
452C2×C61D4×C22⋊C411yescharacteristic
453C2×C61#289611yescharacteristic
454C2×C61#289711yescharacteristic
455C2×C61#327311yescharacteristic
456C2×C61#327511yescharacteristic
457C2×C61#332211yescharacteristic
458C2×C61#332311yescharacteristic
459D61—42no—
460D61—82no—
461C22×#41C2×D6111yescharacteristic
462C23×D4—611no—
463C22×M16—611no—
464C22×M16—611no—
465#546—618no—
466#546—1224no—
467C2×#124—611no—
468C2×#123—1221no—
469C2×C22⋊Q8—611no—
470C2×#121—611no—
471C2×#121—1221no—
472C2×#120—1221no—
473C2×C4×D4—611no—
474C2×C4×D4—611no—
475C2×#117—611no—
476C22×C4⋊C4—611no—
477C22×C22⋊C4—1221no—
478#436—1224no—
479C2×C4⋊C8—611no—
480#418—1224no—
481#417—1224no—
482C2×#103—611no—
483C2×#103—611no—
484C2×#103C2×D6111yescharacteristic, complemented
485C2×#103C2×D6111yescharacteristic, complemented
486C2×#102—611no—
487C2×#102—611no—
488C2×#102—611no—
489C2×#102—611no—
490C2×#102—611no—
491C2×#102—611no—
492C2×#102C2×D6111yescharacteristic
493C2×#102C2×D6111yescharacteristic
494C2×C22⋊C8—611no—
495C2×C22⋊C8C2×D6111yescharacteristic, complemented
496C2×C4×C8—611no—
497#388—1221no—
498#387—1221no—
499#386—1221no—
500#382—611no—
501#380—611no—
502#380C2×D6111yescharacteristic, complemented
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—1221no—
511C2×#41—22no—
512C2×#41—22no—
513C2×#41—22no—
514C2×#41—41no—
515C2×#41—41no—
516C2×#41C4×D6114yes—
517C22×Q8C22×D6111yescharacteristic
518C22×D4—21no—
519C22×D4—611no—
520C22×D4—614no—
521C22×D4—611no—
522C22×D4—1222no—
523C22×D4—1221no—
524C22×D4—1222no—
525C22×D4—1222no—
526C22×D4—1221no—
527C22×D4—2441no—
528C22×D4—2441no—
529C22×D4C22×D6111yescharacteristic
530C23×C4—21no—
531C23×C4—611no—
532C23×C4—1221no—
533C23×C4—1221no—
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×C8C22×D6111yescharacteristic
544C22×C8C22×D6111yescharacteristic
545#124—614no—
546#124—1222no—
547#123—1228no—
548C22⋊Q8—614no—
549C22⋊Q8—1222no—
550#121—614no—
551#121—1228no—
552#121—1222no—
553#120—1228no—
554C4×D4—614no—
555C4×D4—614no—
556C4×D4—614no—
557C4×D4—1222no—
558#117—1222no—
559#117—2441no—
560C2×C4⋊C4—611no—
561C2×C4⋊C4—611no—
562C2×C4⋊C4—611no—
563C2×C4⋊C4—611no—
564C2×C4⋊C4—1222no—
565C2×C4⋊C4—1221no—
566C2×C4⋊C4—1221no—
567C2×C4⋊C4—2441no—
568C2×C4⋊C4C22×D6111yescharacteristic
569C2×C4⋊C4C22×D6111yescharacteristic
570C2×C22⋊C4—21no—
571C2×C22⋊C4—611no—
572C2×C22⋊C4—611no—
573C2×C22⋊C4—1228no—
574C2×C22⋊C4—1221no—
575C2×C22⋊C4—1221no—
576C2×C22⋊C4—1221no—
577C2×C22⋊C4—1221no—
578C2×C22⋊C4—1221no—
579C2×C22⋊C4—1221no—
580C2×C22⋊C4—1221no—
581C2×C42—611no—
582C2×C42—1221no—
583C2×C42—1221no—
584C4⋊C8—1222no—
585#103—41no—
586#103—41no—
587#103—1222no—
588#103—1222no—
589#102—22no—
590#102—22no—
591#102—614no—
592#102—1222no—
593#102—1222no—
594#102—1222no—
595#102—2441no—
596#102—2441no—
597C22⋊C8—22no—
598C22⋊C8—1222no—
599C4×C8—1222no—
600#95—21no—
601#95—1221no—
602#95—1221no—
603#95—1221no—
604#95—1221no—
605C24—21no—
606C24—611no—
607C24—1224no—
608C24—1221no—
609C24—4881no—
610C24—4881no—
611C24—2442no—
612C24—2442no—
613C24—2442no—
614C24—2442no—
615C24D4×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×Q8C2×C4×D6112yes—
626C2×D4—24no—
627C2×D4—21no—
628C2×D4—21no—
629C2×D4—21no—
630C2×D4—42no—
631C2×D4—42no—
632C2×D4—614no—
633C2×D4—612no—
634C2×D4—1224no—
635C2×D4—1228no—
636C2×D4—1224no—
637C2×D4—1221no—
638C2×D4—1221no—
639C2×D4—1221no—
640C2×D4—1221no—
641C2×D4—1221no—
642C2×D4—4881no—
643C2×D4—4881no—
644C2×D4—2444no—
645C2×D4—2444no—
646C2×D4—2444no—
647C2×D4—2441no—
648C2×D4—2441no—
649C2×D4—2442no—
650C2×D4—2442no—
651C2×D4C2×C4×D6112yes—
652C2×D4D4×D6112yes—
653C2×D4#1175822412yes—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—24no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—42no—
663C22×C4—42no—
664C22×C4—611no—
665C22×C4—611no—
666C22×C4—611no—
667C22×C4—612no—
668C22×C4—612no—
669C22×C4—1224no—
670C22×C4—1221no—
671C22×C4—1221no—
672C22×C4—1221no—
673C22×C4—1221no—
674C22×C4—1221no—
675C22×C4—1221no—
676C22×C4—1221no—
677C22×C4—4881no—
678C22×C4—4881no—
679C22×C4—4881no—
680C22×C4—2442no—
681C22×C4—2442no—
682C22×C4C2×C4×D6112yes—
683C22×C4D4×D6112yes—
684C22×C4D4×D6111yescharacteristic
685C22×C4C23×D6111yescharacteristic
686M16—2444no—
687M16—2444no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—21no—
694C2×C8—612no—
695C2×C8—1221no—
696C2×C8—1221no—
697C2×C8—1221no—
698C2×C8—1221no—
699C2×C8—1221no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—614no—
705C4⋊C4—612no—
706C4⋊C4—612no—
707C4⋊C4—1224no—
708C4⋊C4—1221no—
709C4⋊C4—1221no—
710C4⋊C4—1221no—
711C4⋊C4—1221no—
712C4⋊C4—2442no—
713C22⋊C4—42no—
714C22⋊C4—614no—
715C22⋊C4—614no—
716C22⋊C4—1224no—
717C22⋊C4—1224no—
718C22⋊C4—1224no—
719C22⋊C4—1224no—
720C22⋊C4—1224no—
721C22⋊C4—4881no—
722C22⋊C4—2442no—
723C42—612no—
724C42—612no—
725C42—4881no—
726C42—2442no—
727C23—22no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—22no—
734C23—21no—
735C23—22no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23—41no—
740C23—612no—
741C23—1221no—
742C23—1221no—
743C23—1221no—
744C23—1221no—
745C23—1221no—
746C23—1221no—
747C23—1222no—
748C23—4884no—
749C23—4884no—
750C23—4884no—
751C23—4884no—
752C23—4884no—
753C23—2448no—
754C23—2448no—
755C23—2441no—
756C23—2441no—
757C23—2441no—
758C23—2441no—
759C23—2441no—
760C23—2441no—
761C23C22⋊C4×D6112yes—
762C23C2×D4×D6111yescharacteristic
763Q8—22no—
764Q8—22no—
765Q8—41no—
766Q8—41no—
767D4—22no—
768D4—22no—
769D4—22no—
770D4—48no—
771D4—1222no—
772D4—1222no—
773D4—4884no—
774D4—2444no—
775D4—2448no—
776D4—2441no—
777D4—2441no—
778D4#1451973714yes—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—48no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—612no—
796C2×C4—612no—
797C2×C4—612no—
798C2×C4—1221no—
799C2×C4—1221no—
800C2×C4—1221no—
801C2×C4—1221no—
802C2×C4—1221no—
803C2×C4—1221no—
804C2×C4—1222no—
805C2×C4—1222no—
806C2×C4—1222no—
807C2×C4—1222no—
808C2×C4—1222no—
809C2×C4—1222no—
810C2×C4—4884no—
811C2×C4—4884no—
812C2×C4—2441no—
813C2×C4—2441no—
814C2×C4—2441no—
815C2×C4—2441no—
816C2×C4—2441no—
817C2×C4—2441no—
818C2×C4—2441no—
819C2×C4C22⋊C4×D6112yes—
820C2×C4C22×C4×D6111yescharacteristic
821C2×C4C2×D4×D6111yescharacteristic
822C2×C4C2×D4×D6111yescharacteristic
823C2×C4C2×#1175822411yescharacteristic
824C2×C4#1451982211yescharacteristic
825C2×C4#1451982211yescharacteristic
826C8—41no—
827C8—41no—
828C8—1222no—
829C8—2441no—
830C22—22no—
831C22—22no—
832C22—24no—
833C22—22no—
834C22—42no—
835C22—41no—
836C22—42no—
837C22—41no—
838C22—42no—
839C22—41no—
840C22—42no—
841C22—41no—
842C22—42no—
843C22—42no—
844C22—1222no—
845C22—1222no—
846C22—1222no—
847C22—48816no—
848C22—4881no—
849C22—4881no—
850C22—4881no—
851C22—4881no—
852C22—2442no—
853C22—2442no—
854C22—2442no—
855C22—2441no—
856C22—2441no—
857C22—2441no—
858C22—2441no—
859C22C2×C22⋊C4×D6111yescharacteristic
860C22#1684039411yescharacteristic
861C22#1684039911yescharacteristic
862C22#1684055811yescharacteristic
863C22#1684056111yescharacteristic
864C22#1684056411yescharacteristic
865C22#1684056911yescharacteristic
866C4—22no—
867C4—42no—
868C4—81no—
869C4—81no—
870C4—1222no—
871C4—1222no—
872C4—1222no—
873C4—4881no—
874C4—2442no—
875C4—2442no—
876C4C2×#1451973711yescharacteristic
877C4#1684023511yescharacteristic
878C4#1684039411yescharacteristic
879C4#1684039911yescharacteristic
880C2—42no—
881C2—44no—
882C2—4882no—
883C2—2442no—
884C2#2144863511yescharacteristic
885C2#2145433511yescharacteristic
886C2#2145434111yescharacteristic
887C2#2145742311yescharacteristic
888C2#2145744811yescharacteristic
889C2#2145801311yescharacteristic
890C2#2145802811yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1788C2
socleC23×C61C22×D4
prime radicalC2×#16840400C2
cosocleC22×C4×C61C24
hypercenter#1788D61
hypocenterC61#22427
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×#16839765C2semidirect
5. #21448750C2semidirect
6. #21446748C2semidirect
7. #21446627C2semidirect
8. #21446255C2semidirect
9. #21446249C2semidirect
10. #21446134C2semidirect
11. #21446128C2semidirect
12. #21445827C2semidirect
13. #21445748C2semidirect
14. #102×Dic61C2semidirect
15. C61×#1788C2semidirect
17. C22×#11758194C22semidirect
20. #16840400C4semidirect
30. C22×C4⋊Dic61C22semidirect
33. C2×#14519706C22semidirect
36. C2×#14519701C22semidirect
37. C2×#14519701C22semidirect
45. C2×C8×Dic61C22semidirect
49. #16839627C22semidirect
51. C4⋊C4×Dic61C22semidirect
53. #16839525C22semidirect
54. #16839525C22semidirect
55. #16839524C22semidirect
56. #16839524C22semidirect
58. C2×#103×C61C22semidirect
59. C2×#103×C61C22semidirect
62. C2×C22⋊C8×C61C22semidirect
63. C61×#380C22semidirect
74. C2×D4×D61C2×C4semidirect
87. #14519766C2×C4semidirect
90. #14519753C2×C4semidirect
96. D4×Dic61C2×C4semidirect
128. #14519698D4semidirect
447. #1788D61semidirect
484. C2×#103C2×D61semidirect
485. C2×#103C2×D61semidirect
495. C2×C22⋊C8C2×D61semidirect
502. #380C2×D61semidirect
509. C61#22427semidirect

Maximal subgroups

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

subgroupindex
C2×#168404002
C2×#168398372
C2×#168397632
C2×#168397652
#214487502
#214467482
#214466272
#214462552
#214462492
#214461342
#214461282
#214458272
#214457482
#102×Dic612
C61×#17882
#2242761