Finite Group Databasebeta

← #29695564

Subgroups — #29695564

Order 15616.

1598 conjugacy classes of subgroups.

The subgroup lattice has 890 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840400C211yesmaximal, characteristic
2C2×#16839833C211yesmaximal, characteristic, complemented
3C2×#16839765C211yesmaximal, characteristic, complemented
4#21448769C211yesmaximal, characteristic, complemented
5#21446748C211yesmaximal, characteristic, complemented
6#21446632C211yesmaximal, characteristic, complemented
7#21446249C211yesmaximal, characteristic, complemented
8#21446247C211yesmaximal, characteristic, complemented
9#21446141C211yesmaximal, characteristic, complemented
10#21446128C211yesmaximal, characteristic, complemented
11#21445817C211yesmaximal, characteristic, complemented
12#21445759C211yesmaximal, characteristic, complemented
13#21445748C211yesmaximal, characteristic, complemented
14#21445646C211yesmaximal, characteristic, complemented
15C2×C61×#416C211yesmaximal, characteristic, complemented
16C22×D4×D61C2211yescharacteristic
17C22×#11758189C2211yescharacteristic
18#16840400—24no—
19#16840400C418yescomplemented
20C2×#14519766C2211yescharacteristic
21C2×#14519760—21no—
22C2×#14519753C2211yescharacteristic
23C2×#14519751C2211yescharacteristic
24C2×#14519749—21no—
25C2×#14519745—21no—
26C2×D4×Dic61C2211yescharacteristic
27C2×C4×C22⋊D61C2211yescharacteristic
28C2×#14519735C2211yescharacteristic
29C22×#11758198—21no—
30#16839833—24no—
31C2×#14519706C2211yescharacteristic, complemented
32#16839765—24no—
33C2×#14519701C2211yescharacteristic, complemented
34C2×#14519701C2211yescharacteristic, complemented
35C2×#14519699C2211yescharacteristic
36C2×#14519699C2211yescharacteristic
37C2×#14519698C2211yescharacteristic
38C2×#14519698C2211yescharacteristic
39C2×#14519697C2211yescharacteristic
40C2×#14519697C2211yescharacteristic
41C2×C22⋊#92418C2211yescharacteristic, complemented
42C2×#14519689C2211yescharacteristic
43C2×#14519687C2211yescharacteristic, complemented
44#16839662—21no—
45#16839653—21no—
46#16839650—21no—
47#16839631C2211yescharacteristic, complemented
48#16839622C2211yescharacteristic, complemented
49#16839619C2211yescharacteristic
50C4⋊C4×Dic61C2211yescharacteristic, complemented
51C4×#11758196—21no—
52#16839525C2211yescharacteristic, complemented
53#16839525C2211yescharacteristic, complemented
54#16839524C2211yescharacteristic, complemented
55#16839524C2211yescharacteristic, complemented
56C22×#41×C61C2211yescharacteristic
57C23×C8×C61C2211yescharacteristic, complemented
58C2×#117×C61C2211yescharacteristic, complemented
59C61×#416—24no—
60C2×#103×C61C2211yescharacteristic, complemented
61C2×#103×C61C2211yescharacteristic, complemented
62C2×#102×C61C2211yescharacteristic
63C2×#102×C61C2211yescharacteristic
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×C414yes—
75C23×Dic61—21no—
76C22×C4×D61C2311yescharacteristic
77C2×#11758189—22no—
78C2×#11758189—22no—
79C2×#11758189—41no—
80C22×#92418C2311yescharacteristic
81C22×#92418C2311yescharacteristic
82#14519766—22no—
83#14519766C2×C414yes—
84#14519760—28no—
85#14519753—22no—
86#14519753C2×C414yes—
87#14519751—22no—
88#14519751C2×C414yes—
89#14519749—28no—
90#14519745—28no—
91D4×Dic61—22no—
92D4×Dic61C2×C414yes—
93C4×C22⋊D61C2×C414yes—
94C4×C22⋊D61D414yes—
95#14519735—22no—
96#14519735—41no—
97C2×C4⋊Dic61C2311yescharacteristic
98C2×C4⋊Dic61C2311yescharacteristic
99C2×C4⋊Dic61C2311yescharacteristic
100C2×#11758196—21no—
101C2×#11758196—21no—
102C2×#11758196—21no—
103C2×#11758196D411yescharacteristic
104C2×C22⋊Dic61—21no—
105C2×C22⋊Dic61—21no—
106C2×C22⋊Dic61D411yescharacteristic
107C2×#11758198—21no—
108C2×#11758198—21no—
109C2×#11758198—21no—
110C2×#11758198—21no—
111C2×#11758198—28no—
112C2×#11758198—21no—
113C2×#11758198—21no—
114C2×#11758198D411yescharacteristic
115C2×C4×Dic61—21no—
116C2×C4×Dic61—21no—
117C2×C4×Dic61C2311yescharacteristic
118#14519706—22no—
119#14519701—41no—
120#14519701—41no—
121#14519699—22no—
122#14519699—41no—
123#14519698—22no—
124#14519698—22no—
125#14519697—22no—
126#14519697—41no—
127C22⋊#92418—22no—
128#14519689—22no—
129#14519687—22no—
130#14519684—21no—
131#14519684—21no—
132#14519684—21no—
133C2×#41×C61—22no—
134C2×#41×C61—22no—
135C2×#41×C61—22no—
136C2×#41×C61—41no—
137C2×#41×C61—41no—
138C2×#41×C61C2×C414yes—
139C22×Q8×C61C2311yescharacteristic
140C22×D4×C61—21no—
141C22×D4×C61C2311yescharacteristic
142C23×C4×C61—21no—
143C23×C4×C61C2311yescharacteristic
144C22×C8×C61—22no—
145C22×C8×C61—22no—
146C22×C8×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#103×C61—22no—
156#103×C61—22no—
157#102×C61—22no—
158#102×C61D414yescomplemented
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—21no—
195C22×C4×C61—24no—
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—24no—
214C22×Dic61—21no—
215C22×Dic61—21no—
216C22×Dic61—81no—
217C22×Dic61—81no—
218C22×Dic61C2×D411yescharacteristic
219C22×Dic61C2×D411yescharacteristic
220C22×Dic61C2×D411yescharacteristic
221D4×D61—28no—
222D4×D61—44no—
223D4×D61—44no—
224D4×D61—44no—
225C2×D244—21no—
226C2×D244—21no—
227C2×D244—21no—
228C2×D244—21no—
229C2×D244—21no—
230C2×D244C22×C412yes—
231C2×C4×D61—21no—
232C2×C4×D61—21no—
233C2×C4×D61—21no—
234C2×C4×D61—21no—
235C2×C4×D61C22×C412yes—
236C2×C4×D61C2×D412yes—
237C2×C8×C61—21no—
238C2×C8×C61—21no—
239C2×C8×C61—21no—
240C2×C8×C61—21no—
241C2×C8×C61—21no—
242C2×C8×C61—44no—
243C2×C8×C61C2×D412yes—
244C4⋊C4×C61—21no—
245C4⋊C4×C61—21no—
246C4⋊C4×C61—21no—
247C4⋊C4×C61C2×D412yes—
248C22⋊C4×C61—42no—
249C42×C61—42no—
250C22⋊Dic61—24no—
251C22⋊Dic61—81no—
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—21no—
265C4⋊Dic61C22×C412yes—
266#11758196—24no—
267#11758196—42no—
268#11758196—81no—
269#11758196C22⋊C414yes—
270C4×Dic61—42no—
271C4×Dic61—42no—
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—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—22no—
334C2×C4×C61—48no—
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—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—
371D244—22no—
372D244—22no—
373D244—41no—
374D244—41no—
375C4×D61—22no—
376C4×D61—22no—
377C4×D61—22no—
378C4×D61—22no—
379C8×C61—22no—
380C8×C61—41no—
381#92418—41no—
382#92418—41no—
383#22424—611nomaximal, Sylow
384C22×C61—24no—
385C22×C61—22no—
386C22×C61—22no—
387C22×C61—22no—
388C22×C61—42no—
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×C61C22×C22⋊C411yescharacteristic
399C22×C61D4211yescharacteristic
400C22×C61#54611yescharacteristic
401C22×C61#57511yescharacteristic
402C22×C61#57511yescharacteristic
403C22×C61#57611yescharacteristic
404C22×C61#57711yescharacteristic
405C2×D61—22no—
406C2×D61—22no—
407C2×D61—22no—
408C2×D61—41no—
409C2×D61—41no—
410C2×D61—41no—
411C2×D61—41no—
412C2×D61—42no—
413C2×D61—42no—
414C2×D61—42no—
415C2×D61—816no—
416C2×D61—81no—
417C2×D61—81no—
418C2×D61—81no—
419C2×D61—81no—
420C4×C61—22no—
421C4×C61—42no—
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—81no—
433Dic61—81no—
434C2×#546—611no—
435C2×#435—611no—
436C2×#418—611no—
437C2×#416D6111yescharacteristic, complemented
438#2354—611no—
439#1983—611no—
440#1959—611no—
441#1894—611no—
442#1893—611no—
443#1875—611no—
444#1873—611no—
445#1802—611no—
446#1788—611no—
447#1786—611no—
448#1762—611no—
449C2×C61—44no—
450C2×C61—42no—
451C2×C61D4×C22⋊C411yescharacteristic
452C2×C61#289611yescharacteristic
453C2×C61#289711yescharacteristic
454C2×C61#326711yescharacteristic
455C2×C61#326811yescharacteristic
456C2×C61#331111yescharacteristic
457C2×C61#331911yescharacteristic
458D61—42no—
459D61—82no—
460C22×#41C2×D6111yescharacteristic
461C23×D4—611no—
462C22×M16—611no—
463C23×C8C2×D6111yescharacteristic, complemented
464#546—618no—
465#546—1224no—
466C2×#124—611no—
467C2×#123—1221no—
468C2×C22⋊Q8—611no—
469C2×#121—611no—
470C2×#121—1221no—
471C2×#120—1221no—
472C2×C4×D4—611no—
473C2×C4×D4—611no—
474C2×#117—611no—
475C2×#117C2×D6111yescharacteristic, complemented
476C22×C22⋊C4—1221no—
477#435—1224no—
478C2×C4⋊C8—611no—
479#418—1224no—
480#416—24no—
481C2×#103—611no—
482C2×#103—611no—
483C2×#103C2×D6111yescharacteristic, complemented
484C2×#103C2×D6111yescharacteristic, complemented
485C2×#102—611no—
486C2×#102—611no—
487C2×#102—611no—
488C2×#102—611no—
489C2×#102—611no—
490C2×#102—611no—
491C2×#102C2×D6111yescharacteristic
492C2×#102C2×D6111yescharacteristic
493C2×C22⋊C8—611no—
494C2×C22⋊C8—611no—
495C2×#97—611no—
496#390—1221no—
497#388—1221no—
498#388—1221no—
499#384—611no—
500#380—611no—
501#380—611no—
502C4×C4⋊C4—611no—
503C4×C4⋊C4—1221no—
504#340—611no—
505#340—611no—
506#340—611no—
507#340—611no—
508C61#2242411yescharacteristic, complemented, Sylow
509C25—1221no—
510C2×#41—22no—
511C2×#41—22no—
512C2×#41—22no—
513C2×#41—41no—
514C2×#41—41no—
515C2×#41C4×D6114yes—
516C22×Q8C22×D6111yescharacteristic
517C22×D4—21no—
518C22×D4—611no—
519C22×D4—614no—
520C22×D4—611no—
521C22×D4—1222no—
522C22×D4—1221no—
523C22×D4—1222no—
524C22×D4—1222no—
525C22×D4—1221no—
526C22×D4—2441no—
527C22×D4—2441no—
528C22×D4C22×D6111yescharacteristic
529C23×C4—21no—
530C23×C4—611no—
531C23×C4—1221no—
532C23×C4C22×D6111yescharacteristic
533C2×M16—1222no—
534C2×M16—1222no—
535C2×M16—2441no—
536C22×C8—22no—
537C22×C8—22no—
538C22×C8—41no—
539C22×C8—611no—
540C22×C8—611no—
541C22×C8C22×D6111yescharacteristic
542C22×C8C22×D6111yescharacteristic
543#124—614no—
544#124—1222no—
545#123—1228no—
546C22⋊Q8—614no—
547C22⋊Q8—1222no—
548#121—614no—
549#121—1228no—
550#121—1222no—
551#120—1228no—
552C4×D4—614no—
553C4×D4—614no—
554C4×D4—614no—
555C4×D4—1222no—
556#117—22no—
557#117—41no—
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—1221no—
565C2×C4⋊C4—1221no—
566C2×C4⋊C4—1221no—
567C2×C4⋊C4C22×D6111yescharacteristic
568C2×C4⋊C4C22×D6111yescharacteristic
569C2×C22⋊C4—21no—
570C2×C22⋊C4—611no—
571C2×C22⋊C4—611no—
572C2×C22⋊C4—1228no—
573C2×C22⋊C4—1221no—
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—
584C2×C42—1221no—
585C4⋊C8—1222no—
586#103—22no—
587#103—22no—
588#103—2441no—
589#103—2441no—
590#102—22no—
591#102—1222no—
592#102—1222no—
593#102—1222no—
594#102—1222no—
595#102—2441no—
596#102—2441no—
597#102C22⋊D6114yescomplemented
598C22⋊C8—1222no—
599C22⋊C8—1222no—
600#97—1222no—
601#95—1221no—
602#95—1221no—
603#95—1221no—
604C24—21no—
605C24—611no—
606C24—1224no—
607C24—1221no—
608C24—4881no—
609C24—4881no—
610C24—2442no—
611C24—2442no—
612C24—2442no—
613C24—2442no—
614C24D4×D6111yescharacteristic
615#41—28no—
616#41—44no—
617#41—44no—
618#41—44no—
619C2×Q8—21no—
620C2×Q8—21no—
621C2×Q8—21no—
622C2×Q8—21no—
623C2×Q8—21no—
624C2×Q8C2×C4×D6112yes—
625C2×D4—24no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—21no—
629C2×D4—42no—
630C2×D4—42no—
631C2×D4—614no—
632C2×D4—612no—
633C2×D4—1224no—
634C2×D4—1228no—
635C2×D4—1224no—
636C2×D4—1221no—
637C2×D4—1221no—
638C2×D4—1221no—
639C2×D4—1221no—
640C2×D4—1221no—
641C2×D4—4881no—
642C2×D4—4881no—
643C2×D4—2444no—
644C2×D4—2444no—
645C2×D4—2444no—
646C2×D4—2441no—
647C2×D4—2441no—
648C2×D4—2442no—
649C2×D4—2442no—
650C2×D4C2×C4×D6112yes—
651C2×D4#1175822212yes—
652C2×D4C2×C22⋊D6112yes—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—24no—
660C22×C4—21no—
661C22×C4—42no—
662C22×C4—42no—
663C22×C4—611no—
664C22×C4—611no—
665C22×C4—611no—
666C22×C4—612no—
667C22×C4—612no—
668C22×C4—1224no—
669C22×C4—1221no—
670C22×C4—1221no—
671C22×C4—1221no—
672C22×C4—1221no—
673C22×C4—1221no—
674C22×C4—1221no—
675C22×C4—1221no—
676C22×C4—4881no—
677C22×C4—4881no—
678C22×C4C2×C4×D6112yes—
679C22×C4D4×D6112yes—
680C22×C4D4×D6111yescharacteristic
681C22×C4C23×D6111yescharacteristic
682M16—2444no—
683C2×C8—21no—
684C2×C8—21no—
685C2×C8—21no—
686C2×C8—21no—
687C2×C8—21no—
688C2×C8—44no—
689C2×C8—1221no—
690C2×C8—1221no—
691C2×C8—1221no—
692C2×C8—1221no—
693C2×C8—1221no—
694C2×C8—1221no—
695C2×C8C2×C22⋊D6112yes—
696C4⋊C4—21no—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4—614no—
700C4⋊C4—612no—
701C4⋊C4—1224no—
702C4⋊C4—1221no—
703C4⋊C4—1221no—
704C4⋊C4—1221no—
705C4⋊C4—1221no—
706C4⋊C4—1221no—
707C4⋊C4—4881no—
708C4⋊C4—2442no—
709C4⋊C4C2×C22⋊D6112yes—
710C22⋊C4—42no—
711C22⋊C4—614no—
712C22⋊C4—614no—
713C22⋊C4—1224no—
714C22⋊C4—1224no—
715C22⋊C4—1224no—
716C22⋊C4—1224no—
717C22⋊C4—1224no—
718C22⋊C4—4881no—
719C22⋊C4—4881no—
720C22⋊C4—2442no—
721C42—42no—
722C42—612no—
723C42—612no—
724C42—2442no—
725C42—2442no—
726C23—22no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—22no—
733C23—21no—
734C23—22no—
735C23—41no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23—612no—
740C23—1221no—
741C23—1221no—
742C23—1221no—
743C23—1221no—
744C23—1221no—
745C23—1221no—
746C23—1222no—
747C23—4884no—
748C23—4884no—
749C23—4884no—
750C23—4884no—
751C23—4884no—
752C23—2448no—
753C23—2448no—
754C23—2441no—
755C23—2441no—
756C23—2441no—
757C23—2441no—
758C23—2441no—
759C23—2441no—
760C23C22⋊C4×D6112yes—
761C23C2×D4×D6111yescharacteristic
762Q8—22no—
763Q8—22no—
764Q8—41no—
765Q8—41no—
766D4—22no—
767D4—22no—
768D4—22no—
769D4—48no—
770D4—1222no—
771D4—1222no—
772D4—4884no—
773D4—2444no—
774D4—2448no—
775D4—2441no—
776D4—2441no—
777D4C4×C22⋊D6114yes—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—22no—
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—612no—
795C2×C4—612no—
796C2×C4—612no—
797C2×C4—1221no—
798C2×C4—1221no—
799C2×C4—1221no—
800C2×C4—1221no—
801C2×C4—1221no—
802C2×C4—1221no—
803C2×C4—1222no—
804C2×C4—1222no—
805C2×C4—1222no—
806C2×C4—1222no—
807C2×C4—1222no—
808C2×C4—4884no—
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×C4C22⋊C4×D6112yes—
818C2×C4C22×C4×D6111yescharacteristic
819C2×C4C2×D4×D6111yescharacteristic
820C2×C4C22×C22⋊D6111yescharacteristic
821C2×C4C2×#1175822211yescharacteristic
822C2×C4#1451982211yescharacteristic
823C2×C4#1451982211yescharacteristic
824C8—22no—
825C8—41no—
826C8—2441no—
827C8—2441no—
828C22—22no—
829C22—22no—
830C22—24no—
831C22—22no—
832C22—42no—
833C22—41no—
834C22—42no—
835C22—41no—
836C22—42no—
837C22—41no—
838C22—42no—
839C22—41no—
840C22—42no—
841C22—42no—
842C22—1222no—
843C22—1222no—
844C22—1222no—
845C22—48816no—
846C22—4881no—
847C22—4881no—
848C22—4881no—
849C22—4881no—
850C22—2442no—
851C22—2442no—
852C22—2442no—
853C22—2441no—
854C22—2441no—
855C22—2441no—
856C22—2441no—
857C22C2×C22⋊C4×D6111yescharacteristic
858C22D4×C22⋊D6111yescharacteristic
859C22#1684040211yescharacteristic
860C22#1684055911yescharacteristic
861C22#1684055911yescharacteristic
862C22#1684056411yescharacteristic
863C22#1684056911yescharacteristic
864C4—22no—
865C4—42no—
866C4—42no—
867C4—81no—
868C4—1222no—
869C4—1222no—
870C4—1222no—
871C4—4881no—
872C4—4881no—
873C4—2442no—
874C4C2×C4×C22⋊D6111yescharacteristic
875C4#1684023511yescharacteristic
876C4D4×C22⋊D6111yescharacteristic
877C4#1684040211yescharacteristic
878C2—42no—
879C2—44no—
880C2—4882no—
881C2—2442no—
882C2C22⋊C4×C22⋊D6111yescharacteristic
883C2#2145433411yescharacteristic
884C2#2145434111yescharacteristic
885C2#2145734411yescharacteristic
886C2#2145735911yescharacteristic
887C2#2145785111yescharacteristic
888C2#2145797111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#416C2
socleC23×C61C22×D4
prime radicalC2×#16840400C2
cosocleC22×C4×C61C24
hypercenterC2×#416D61
hypocenterC61#22424
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#416

Complements

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

NH ≅ G/Ntype
2. C2×#16839833C2semidirect
3. C2×#16839765C2semidirect
4. #21448769C2semidirect
5. #21446748C2semidirect
6. #21446632C2semidirect
7. #21446249C2semidirect
8. #21446247C2semidirect
9. #21446141C2semidirect
10. #21446128C2semidirect
11. #21445817C2semidirect
12. #21445759C2semidirect
13. #21445748C2semidirect
14. #21445646C2semidirect
15. C2×C61×#416C2semidirect
19. #16840400C4semidirect
31. C2×#14519706C22semidirect
33. C2×#14519701C22semidirect
34. C2×#14519701C22semidirect
41. C2×C22⋊#92418C22semidirect
43. C2×#14519687C22semidirect
47. #16839631C22semidirect
48. #16839622C22semidirect
50. C4⋊C4×Dic61C22semidirect
52. #16839525C22semidirect
53. #16839525C22semidirect
54. #16839524C22semidirect
55. #16839524C22semidirect
57. C23×C8×C61C22semidirect
58. C2×#117×C61C22semidirect
60. C2×#103×C61C22semidirect
61. C2×#103×C61C22semidirect
158. #102×C61D4semidirect
437. C2×#416D61semidirect
463. C23×C8C2×D61semidirect
475. C2×#117C2×D61semidirect
483. C2×#103C2×D61semidirect
484. C2×#103C2×D61semidirect
508. C61#22424semidirect
597. #102C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168404002
C2×#168398332
C2×#168397652
#214487692
#214467482
#214466322
#214462492
#214462472
#214461412
#214461282
#214458172
#214457592
#214457482
#214456462
C2×C61×#4162
#2242461