Finite Group Databasebeta

← #29695609

Subgroups — #29695609

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×#16840406C211yesmaximal, characteristic
2C2×#16839838C211yesmaximal, characteristic, complemented
3C2×#16839760C211yesmaximal, characteristic, complemented
4#21448749C211yesmaximal, characteristic, complemented
5#21446750C211yesmaximal, characteristic, complemented
6#21446629C211yesmaximal, characteristic, complemented
7#21446254C211yesmaximal, characteristic, complemented
8#21446252C211yesmaximal, characteristic, complemented
9#21446133C211yesmaximal, characteristic, complemented
10#21446131C211yesmaximal, characteristic, complemented
11#21445827C211yesmaximal, characteristic, complemented
12#21445756C211yesmaximal, characteristic, complemented
13#21445750C211yesmaximal, characteristic, complemented
14#102×Dic61C211yesmaximal, characteristic, complemented
15C2×C61×#418C211yesmaximal, characteristic, complemented
16C22×#11758224C2211yescharacteristic
17C22×#11758189C2211yescharacteristic, complemented
18#16840406—24no—
19#16840406C418yescomplemented
20C2×#14519764C2211yescharacteristic
21C2×#14519758—21no—
22C2×#14519756C2211yescharacteristic
23C2×#14519749—21no—
24C2×#14519748C2211yescharacteristic
25C2×#14519746—21no—
26C2×D4×Dic61C2211yescharacteristic
27C2×C4×C22⋊D61C2211yescharacteristic
28C2×C4⋊C4×D61C2211yescharacteristic, complemented
29C22×C22⋊Dic61—21no—
30#16839838—24no—
31C2×#14519706C2211yescharacteristic, complemented
32#16839760—24no—
33C2×#14519702C2211yescharacteristic, complemented
34C2×#14519702C2211yescharacteristic, complemented
35C2×#14519700C2211yescharacteristic, complemented
36C2×#14519700C2211yescharacteristic, complemented
37C2×#14519698C2211yescharacteristic
38C2×#14519698C2211yescharacteristic
39C2×#14519698C2211yescharacteristic
40C2×#14519698C2211yescharacteristic
41C2×C22⋊#92418C2211yescharacteristic
42C2×#14519689C2211yescharacteristic, complemented
43C2×C8×Dic61C2211yescharacteristic, complemented
44#16839656—21no—
45#16839646—21no—
46#16839638—21no—
47#16839627C2211yescharacteristic, complemented
48#16839622C2211yescharacteristic
49#16839619C2211yescharacteristic, complemented
50C4⋊C4×Dic61C2211yescharacteristic, complemented
51C4×#11758198—21no—
52#16839525C2211yescharacteristic, complemented
53#16839525C2211yescharacteristic, complemented
54#16839524C2211yescharacteristic, complemented
55#16839524C2211yescharacteristic, complemented
56C23×D4×C61C2211yescharacteristic
57C22×M16×C61C2211yescharacteristic
58C2×#117×C61C2211yescharacteristic
59C61×#418—24no—
60C2×#102×C61C2211yescharacteristic
61C2×#102×C61C2211yescharacteristic
62C2×#102×C61C2211yescharacteristic
63C2×#102×C61C2211yescharacteristic
64C2×#11758224—22no—
65C2×#11758224—22no—
66C2×#11758224—22no—
67C2×#11758224—41no—
68C2×#11758224—41no—
69C2×#11758224C2×C414yes—
70C22×Dic122C2311yescharacteristic
71C22×C22⋊D61—21no—
72C22×C22⋊D61—21no—
73C22×C22⋊D61D411yescharacteristic
74C23×Dic61—21no—
75C23×Dic61—21no—
76C22×C4×D61—21no—
77C22×C4×D61C2311yescharacteristic
78C2×#11758189—22no—
79C2×#11758189—22no—
80C2×#11758189—41no—
81C22×#92418C2311yescharacteristic
82C22×#92418C2311yescharacteristic
83#14519764—22no—
84#14519764C2×C414yescomplemented
85#14519758—28no—
86#14519756—22no—
87#14519756C2×C414yescomplemented
88#14519749—28no—
89#14519748—22no—
90#14519748C2×C414yes—
91#14519746—28no—
92D4×Dic61—22no—
93D4×Dic61C2×C414yescomplemented
94C4×C22⋊D61C2×C414yes—
95C4×C22⋊D61D414yes—
96C2×C4⋊Dic61C2311yescharacteristic
97C2×C4⋊Dic61C2311yescharacteristic
98C2×C4⋊Dic61C2311yescharacteristic
99C2×#11758196—21no—
100C2×#11758196—21no—
101C2×#11758196D411yescharacteristic
102C4⋊C4×D61—22no—
103C4⋊C4×D61—41no—
104C2×C22⋊Dic61—21no—
105C2×C22⋊Dic61—21no—
106C2×C22⋊Dic61—21no—
107C2×C22⋊Dic61—21no—
108C2×C22⋊Dic61—21no—
109C2×C22⋊Dic61—28no—
110C2×C22⋊Dic61—21no—
111C2×C22⋊Dic61D411yescharacteristic
112C2×#11758198—21no—
113C2×#11758198D411yescharacteristic
114C2×C4×Dic61—21no—
115C2×C4×Dic61C2311yescharacteristic
116#14519706—22no—
117#14519702—22no—
118#14519702—41no—
119#14519700—22no—
120#14519700—41no—
121#14519698—22no—
122#14519698—22no—
123#14519698—41no—
124#14519698—41no—
125C22⋊#92418—22no—
126#14519689—22no—
127C8×Dic61—22no—
128#14519684—21no—
129#14519684—21no—
130#14519684—21no—
131#14519684—21no—
132#14519684—21no—
133C25×C61—21no—
134C22×D4×C61—22no—
135C22×D4×C61—22no—
136C22×D4×C61—21no—
137C22×D4×C61—22no—
138C22×D4×C61—41no—
139C22×D4×C61—41no—
140C22×D4×C61C2×C414yescomplemented
141C22×D4×C61C2311yescharacteristic
142C22×D4×C61C2311yescharacteristic
143C23×C4×C61C2311yescharacteristic
144C2×M16×C61—22no—
145C2×M16×C61—22no—
146C2×M16×C61—41no—
147C22×C8×C61C2311yescharacteristic
148C22×C8×C61C2311yescharacteristic
149#117×C61—22no—
150#117×C61—41no—
151C2×C4⋊C4×C61C2311yescharacteristic
152C2×C4⋊C4×C61C2311yescharacteristic
153C2×C22⋊C4×C61—21no—
154C2×C42×C61—21no—
155#102×C61—22no—
156#102×C61—22no—
157#102×C61—22no—
158#102×C61D414yescomplemented
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
169C23×D61C2×D411yescharacteristic
170C2×D4×C61—28no—
171C2×D4×C61—24no—
172C2×D4×C61—21no—
173C2×D4×C61—21no—
174C2×D4×C61—21no—
175C2×D4×C61—21no—
176C2×D4×C61—21no—
177C2×D4×C61—21no—
178C2×D4×C61—21no—
179C2×D4×C61—21no—
180C2×D4×C61—44no—
181C2×D4×C61—44no—
182C2×D4×C61—44no—
183C2×D4×C61—42no—
184C2×D4×C61—42no—
185C2×D4×C61C22×C412yes—
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—21no—
195C22×C4×C61C22×C412yes—
196C22×C4×C61C2×D411yescharacteristic
197C22×C4×C61C2×D412yes—
198C22×C4×C61C2411yescharacteristic
199C2×C22⋊D61—24no—
200C2×C22⋊D61—24no—
201C2×C22⋊D61—41no—
202C2×C22⋊D61—41no—
203C2×C22⋊D61—42no—
204C2×C22⋊D61—42no—
205C2×C22⋊D61—81no—
206C2×C22⋊D61—81no—
207C2×C22⋊D61C22⋊C414yes—
208C22×Dic61—21no—
209C22×Dic61—21no—
210C22×Dic61—24no—
211C22×Dic61—24no—
212C22×Dic61—21no—
213C22×Dic61—21no—
214C22×Dic61—42no—
215C22×Dic61—42no—
216C22×Dic61—81no—
217C22×Dic61—81no—
218C22×Dic61C2×D411yescharacteristic
219C22×Dic61C2×D411yescharacteristic
220C22×Dic61C2×D411yescharacteristic
221#11758224—28no—
222#11758224—44no—
223#11758224—44no—
224#11758224—44no—
225C2×C4×D61—21no—
226C2×C4×D61—21no—
227C2×C4×D61—21no—
228C2×C4×D61—21no—
229C2×C4×D61—42no—
230C2×C4×D61—42no—
231C2×C4×D61—81no—
232C2×C4×D61C22×C412yes—
233C2×C4×D61C2×D412yes—
234C2×Dic122—21no—
235C2×Dic122—21no—
236C2×Dic122—21no—
237C2×Dic122—21no—
238C2×Dic122—21no—
239C2×Dic122C22×C412yes—
240M16×C61—44no—
241C2×C8×C61—21no—
242C2×C8×C61—21no—
243C2×C8×C61—21no—
244C2×C8×C61—21no—
245C2×C8×C61—21no—
246C2×C8×C61C2×D412yes—
247C4⋊C4×C61—21no—
248C4⋊C4×C61—21no—
249C4⋊C4×C61—21no—
250C4⋊C4×C61C2×D412yes—
251C22⋊C4×C61—42no—
252C42×C61—42no—
253C22⋊Dic61—24no—
254C22⋊Dic61—24no—
255C22⋊Dic61—24no—
256C22⋊Dic61—24no—
257C22⋊Dic61—24no—
258C22⋊Dic61—81no—
259C22⋊Dic61C22⋊C414yes—
260#11758198—42no—
261#11758198C22⋊C414yes—
262C4⋊Dic61—21no—
263C4⋊Dic61—21no—
264C4⋊Dic61—21no—
265C4⋊Dic61—21no—
266C4⋊Dic61—21no—
267C4⋊Dic61C22×C412yes—
268#11758196—24no—
269#11758196—42no—
270#11758196C22⋊C414yes—
271C4×Dic61—81no—
272C4×Dic61C22×C412yes—
273C4×Dic61C2×D412yes—
274C2×#92418—21no—
275C2×#92418—21no—
276C2×#92418—21no—
277C2×#92418—21no—
278C2×#92418—21no—
279C2×#92418—21no—
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—22no—
291C23×C61—48no—
292C23×C61—48no—
293C23×C61—41no—
294C23×C61—41no—
295C23×C61—41no—
296C23×C61—41no—
297C23×C61—41no—
298C23×C61—41no—
299C23×C61—41no—
300C23×C61—41no—
301C23×C61—41no—
302C23×C61—41no—
303C23×C61—84no—
304C23×C61—84no—
305C23×C61—84no—
306C23×C61—84no—
307C23×C61—84no—
308C23×C61C2×C22⋊C412yes—
309C23×C61C22×D411yescharacteristic
310C22×D61—21no—
311C22×D61—21no—
312C22×D61—21no—
313C22×D61—21no—
314C22×D61—21no—
315C22×D61—21no—
316C22×D61C2×C22⋊C412yes—
317D4×C61—22no—
318D4×C61—22no—
319D4×C61—22no—
320D4×C61—22no—
321D4×C61—22no—
322D4×C61—48no—
323D4×C61—41no—
324D4×C61—41no—
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—41no—
334C2×C4×C61—41no—
335C2×C4×C61—41no—
336C2×C4×C61—41no—
337C2×C4×C61—41no—
338C2×C4×C61C2×C22⋊C412yes—
339C2×C4×C61C23×C411yescharacteristic
340C2×C4×C61C22×D411yescharacteristic
341C2×C4×C61C22×D411yescharacteristic
342C2×C4×C61C2×#4111yescharacteristic
343C2×C4×C61H(5,𝔽2)11yescharacteristic
344C2×C4×C61H(5,𝔽2)11yescharacteristic
345C22⋊D61—44no—
346C22⋊D61—48no—
347C22⋊D61—84no—
348C2×Dic61—21no—
349C2×Dic61—21no—
350C2×Dic61—21no—
351C2×Dic61—21no—
352C2×Dic61—21no—
353C2×Dic61—21no—
354C2×Dic61—22no—
355C2×Dic61—22no—
356C2×Dic61—48no—
357C2×Dic61—41no—
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—84no—
368C2×Dic61C2×C22⋊C412yes—
369C2×Dic61C2×C22⋊C412yes—
370C2×Dic61C2×C22⋊C412yes—
371C4×D61—22no—
372C4×D61—22no—
373C4×D61—22no—
374C4×D61—22no—
375C4×D61—84no—
376Dic122—22no—
377Dic122—22no—
378Dic122—41no—
379Dic122—41no—
380C8×C61—22no—
381C8×C61—41no—
382#92418—41no—
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—41no—
394C22×C61—42no—
395C22×C61—41no—
396C22×C61—42no—
397C22×C61—41no—
398C22×C61—42no—
399C22×C61—42no—
400C22×C61—42no—
401C22×C61—42no—
402C22×C61—816no—
403C22×C61—81no—
404C22×C61—81no—
405C22×C61—81no—
406C22×C61—81no—
407C22×C61C22×C22⋊C411yescharacteristic
408C22×C61D4211yescharacteristic
409C22×C61#54611yescharacteristic
410C22×C61#57511yescharacteristic
411C22×C61#57511yescharacteristic
412C22×C61#57611yescharacteristic
413C22×C61#57711yescharacteristic
414C2×D61—22no—
415C2×D61—22no—
416C2×D61—22no—
417C2×D61—41no—
418C2×D61—41no—
419C2×D61—41no—
420C2×D61—41no—
421C4×C61—22no—
422C4×C61—42no—
423C4×C61—81no—
424C4×C61C2×C4×D411yescharacteristic
425C4×C61#51811yescharacteristic
426C4×C61D4211yescharacteristic
427C4×C61#54611yescharacteristic
428Dic61—22no—
429Dic61—22no—
430Dic61—22no—
431Dic61—42no—
432Dic61—42no—
433Dic61—81no—
434Dic61—81no—
435C2×#546—611no—
436C2×#436—611no—
437C2×#417—611no—
438C2×#418D6111yescharacteristic, complemented
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—44no—
452C2×C61—82no—
453C2×C61D4×C22⋊C411yescharacteristic
454C2×C61#289611yescharacteristic
455C2×C61#289711yescharacteristic
456C2×C61#327311yescharacteristic
457C2×C61#327511yescharacteristic
458C2×C61#332211yescharacteristic
459C2×C61#332311yescharacteristic
460D61—42no—
461C22×#41—611no—
462C23×D4C2×D6111yescharacteristic
463C22×M16—611no—
464C22×M16C2×D6111yescharacteristic
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×#117C2×D6111yescharacteristic
476C22×C4⋊C4—611no—
477C22×C22⋊C4—1221no—
478#436—1224no—
479C2×C4⋊C8—611no—
480#418—24no—
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×#102C2×D6111yescharacteristic
491C2×#102C2×D6111yescharacteristic
492C2×#102C2×D6111yescharacteristic
493C2×#102C2×D6111yescharacteristic
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—614no—
512C2×#41—1222no—
513C2×#41—1222no—
514C2×#41—1222no—
515C2×#41—2441no—
516C2×#41—2441no—
517C22×Q8—611no—
518C22×D4—22no—
519C22×D4—22no—
520C22×D4—21no—
521C22×D4—22no—
522C22×D4—41no—
523C22×D4—41no—
524C22×D4—611no—
525C22×D4—1221no—
526C22×D4—1221no—
527C22×D4C4×D6114yescomplemented
528C22×D4C22×D6111yescharacteristic
529C22×D4C22×D6111yescharacteristic
530C23×C4—611no—
531C23×C4—1221no—
532C23×C4—1221no—
533C23×C4—1221no—
534C23×C4C22×D6111yescharacteristic
535C2×M16—22no—
536C2×M16—22no—
537C2×M16—41no—
538C2×M16—1222no—
539C2×M16—1222no—
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—22no—
559#117—41no—
560C2×C4⋊C4—611no—
561C2×C4⋊C4—611no—
562C2×C4⋊C4—611no—
563C2×C4⋊C4—611no—
564C2×C4⋊C4—1221no—
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—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—21no—
582C2×C42—611no—
583C2×C42—1221no—
584C4⋊C8—1222no—
585#103—1222no—
586#103—1222no—
587#103—2441no—
588#103—2441no—
589#102—22no—
590#102—22no—
591#102—22no—
592#102—1222no—
593#102—1222no—
594#102—2441no—
595#102—2441no—
596#102C22⋊D6114yescomplemented
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—
614C24—611no—
615C24D4×D6111yescharacteristic
616#41—1228no—
617#41—2444no—
618#41—2444no—
619#41—2444no—
620C2×Q8—612no—
621C2×Q8—1221no—
622C2×Q8—1221no—
623C2×Q8—1221no—
624C2×Q8—1221no—
625C2×Q8—1221no—
626C2×D4—28no—
627C2×D4—21no—
628C2×D4—21no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4—21no—
634C2×D4—21no—
635C2×D4—24no—
636C2×D4—44no—
637C2×D4—44no—
638C2×D4—44no—
639C2×D4—42no—
640C2×D4—42no—
641C2×D4—614no—
642C2×D4—1224no—
643C2×D4—1224no—
644C2×D4—4881no—
645C2×D4—4881no—
646C2×D4—2441no—
647C2×D4—2441no—
648C2×D4—2442no—
649C2×D4—2442no—
650C2×D4C2×C4×D6112yes—
651C2×D4C2×C4×D6112yes—
652C2×D4#1175822212yes—
653C2×D4C2×C22⋊D6112yes—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—611no—
661C22×C4—611no—
662C22×C4—611no—
663C22×C4—612no—
664C22×C4—612no—
665C22×C4—1224no—
666C22×C4—1224no—
667C22×C4—1221no—
668C22×C4—1221no—
669C22×C4—1221no—
670C22×C4—1221no—
671C22×C4—1221no—
672C22×C4—1221no—
673C22×C4—1221no—
674C22×C4—1221no—
675C22×C4—4881no—
676C22×C4—4881no—
677C22×C4—4881no—
678C22×C4—2442no—
679C22×C4—2442no—
680C22×C4—2442no—
681C22×C4—2442no—
682C22×C4C2×C4×D6112yes—
683C22×C4D4×D6112yes—
684C22×C4D4×D6111yescharacteristic
685C22×C4C23×D6111yescharacteristic
686M16—44no—
687M16—2444no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—1221no—
694C2×C8—1221no—
695C2×C8—1221no—
696C2×C8—1221no—
697C2×C8—1221no—
698C2×C8—1221no—
699C2×C8C2×C22⋊D6112yes—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—614no—
704C4⋊C4—612no—
705C4⋊C4—1221no—
706C4⋊C4—1224no—
707C4⋊C4—1221no—
708C4⋊C4—1221no—
709C4⋊C4—1221no—
710C4⋊C4—1221no—
711C4⋊C4—2442no—
712C4⋊C4C2×C22⋊D6112yes—
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—42no—
724C42—612no—
725C42—612no—
726C42—4881no—
727C23—22no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—22no—
734C23—21no—
735C23—22no—
736C23—22no—
737C23—48no—
738C23—48no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—84no—
750C23—84no—
751C23—84no—
752C23—84no—
753C23—84no—
754C23—612no—
755C23—1221no—
756C23—1221no—
757C23—1221no—
758C23—1221no—
759C23—1221no—
760C23—1221no—
761C23C22⋊C4×D6112yes—
762C23C2×D4×D6111yescharacteristic
763Q8—1222no—
764Q8—1222no—
765Q8—2441no—
766Q8—2441no—
767D4—22no—
768D4—22no—
769D4—22no—
770D4—22no—
771D4—22no—
772D4—48no—
773D4—41no—
774D4—41no—
775D4—4884no—
776D4—2444no—
777D4—2448no—
778D4C4×C22⋊D6114yes—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—612no—
792C2×C4—612no—
793C2×C4—612no—
794C2×C4—1221no—
795C2×C4—1221no—
796C2×C4—1221no—
797C2×C4—1221no—
798C2×C4—1221no—
799C2×C4—1221no—
800C2×C4—1222no—
801C2×C4—1222no—
802C2×C4—1222no—
803C2×C4—1222no—
804C2×C4—1222no—
805C2×C4—1222no—
806C2×C4—4884no—
807C2×C4—4884no—
808C2×C4—2448no—
809C2×C4—2441no—
810C2×C4—2441no—
811C2×C4—2441no—
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×C4C22×C22⋊D6111yescharacteristic
823C2×C4C2×#1175822211yescharacteristic
824C2×C4#1451982211yescharacteristic
825C2×C4#1451982211yescharacteristic
826C8—22no—
827C8—41no—
828C8—2441no—
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—42no—
845C22—42no—
846C22—42no—
847C22—816no—
848C22—81no—
849C22—81no—
850C22—81no—
851C22—81no—
852C22—1222no—
853C22—1222no—
854C22—1222no—
855C22—2441no—
856C22—2441no—
857C22—2441no—
858C22—2441no—
859C22C2×C22⋊C4×D6111yescharacteristic
860C22D4×C22⋊D6111yescharacteristic
861C22#1684040211yescharacteristic
862C22#1684055811yescharacteristic
863C22#1684055811yescharacteristic
864C22#1684056611yescharacteristic
865C22#1684057211yescharacteristic
866C4—22no—
867C4—42no—
868C4—81no—
869C4—1222no—
870C4—1222no—
871C4—1222no—
872C4—4881no—
873C4—4881no—
874C4—2442no—
875C4—2442no—
876C4C2×C4×C22⋊D6111yescharacteristic
877C4#1684023511yescharacteristic
878C4D4×C22⋊D6111yescharacteristic
879C4#1684040211yescharacteristic
880C2—42no—
881C2—44no—
882C2—82no—
883C2—2442no—
884C2C22⋊C4×C22⋊D6111yescharacteristic
885C2#2145433311yescharacteristic
886C2#2145434411yescharacteristic
887C2#2145742411yescharacteristic
888C2#2145745011yescharacteristic
889C2#2145801611yescharacteristic
890C2#2145803111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#418C2
socleC23×C61C22×D4
prime radicalC2×#16840406C2
cosocleC22×C4×C61C24
hypercenterC2×#418D61
hypocenterC61#22427
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#418

Complements

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

NH ≅ G/Ntype
2. C2×#16839838C2semidirect
3. C2×#16839760C2semidirect
4. #21448749C2semidirect
5. #21446750C2semidirect
6. #21446629C2semidirect
7. #21446254C2semidirect
8. #21446252C2semidirect
9. #21446133C2semidirect
10. #21446131C2semidirect
11. #21445827C2semidirect
12. #21445756C2semidirect
13. #21445750C2semidirect
14. #102×Dic61C2semidirect
15. C2×C61×#418C2semidirect
17. C22×#11758189C22semidirect
19. #16840406C4semidirect
28. C2×C4⋊C4×D61C22semidirect
31. C2×#14519706C22semidirect
33. C2×#14519702C22semidirect
34. C2×#14519702C22semidirect
35. C2×#14519700C22semidirect
36. C2×#14519700C22semidirect
42. C2×#14519689C22semidirect
43. C2×C8×Dic61C22semidirect
47. #16839627C22semidirect
49. #16839619C22semidirect
50. C4⋊C4×Dic61C22semidirect
52. #16839525C22semidirect
53. #16839525C22semidirect
54. #16839524C22semidirect
55. #16839524C22semidirect
84. #14519764C2×C4semidirect
87. #14519756C2×C4semidirect
93. D4×Dic61C2×C4semidirect
140. C22×D4×C61C2×C4semidirect
158. #102×C61D4semidirect
438. C2×#418D61semidirect
509. C61#22427semidirect
527. C22×D4C4×D61semidirect
596. #102C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168404062
C2×#168398382
C2×#168397602
#214487492
#214467502
#214466292
#214462542
#214462522
#214461332
#214461312
#214458272
#214457562
#214457502
#102×Dic612
C2×C61×#4182
#2242761