Finite Group Databasebeta

← #29695562

Subgroups — #29695562

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×#16840408C211yesmaximal, characteristic
2C2×#16839834C211yesmaximal, characteristic, complemented
3C2×#16839766C211yesmaximal, characteristic, complemented
4C2×#16839756C211yesmaximal, characteristic, complemented
5#21446751C211yesmaximal, characteristic, complemented
6#21446633C211yesmaximal, characteristic, complemented
7#21446250C211yesmaximal, characteristic, complemented
8#21446245C211yesmaximal, characteristic, complemented
9#21446141C211yesmaximal, characteristic, complemented
10#21446131C211yesmaximal, characteristic, complemented
11#21445816C211yesmaximal, characteristic, complemented
12#21445757C211yesmaximal, characteristic, complemented
13#21445749C211yesmaximal, characteristic, complemented
14#21445647C211yesmaximal, characteristic, complemented
15C61×#2354C211yesmaximal, characteristic, complemented
16C22×#11758222C2211yescharacteristic
17C23×D244C2211yescharacteristic
18C22×#11758194C2211yescharacteristic
19C23×#92418C2211yescharacteristic, complemented
20#16840408—24no—
21#16840408C418yescomplemented
22C2×#14519765C2211yescharacteristic
23C2×#14519762—21no—
24C2×#14519756C2211yescharacteristic
25C2×#14519751C2211yescharacteristic
26C2×#14519750—21no—
27C2×#14519745—21no—
28C2×C4×D244C2211yescharacteristic
29C2×C22⋊C4×D61—21no—
30#16839834—24no—
31C2×C4⋊#92418C2211yescharacteristic, complemented
32#16839766—24no—
33#16839756—24no—
34C2×#14519700C2211yescharacteristic, complemented
35C2×#14519700C2211yescharacteristic, complemented
36C2×#14519700C2211yescharacteristic, complemented
37C2×#14519700C2211yescharacteristic, complemented
38C2×#14519697C2211yescharacteristic
39C2×#14519697C2211yescharacteristic
40C2×#14519697C2211yescharacteristic
41C2×#14519697C2211yescharacteristic
42C2×#14519697C2211yescharacteristic
43C2×#14519697C2211yescharacteristic
44C2×#14519697C2211yescharacteristic
45C2×#14519697C2211yescharacteristic
46C2×C22⋊#92418C2211yescharacteristic
47C2×C22⋊#92418C2211yescharacteristic, complemented
48C2×#14519688C2211yescharacteristic, complemented
49#16839524C2211yescharacteristic, complemented
50#16839524C2211yescharacteristic, complemented
51#16839524C2211yescharacteristic, complemented
52#16839524C2211yescharacteristic, complemented
53C2×C4×D4×C61C2211yescharacteristic
54C2×#117×C61C2211yescharacteristic
55C2×#117×C61C2211yescharacteristic, complemented
56C61×#390—21no—
57C61×#388—21no—
58C61×#388—21no—
59C61×#384C2211yescharacteristic, complemented
60C61×#380C2211yescharacteristic
61C61×#380C2211yescharacteristic, complemented
62C4×C4⋊C4×C61—21no—
63C4×C4⋊C4×C61C2211yescharacteristic, complemented
64C24×D61—21no—
65C2×#11758222—22no—
66C2×#11758222—22no—
67C2×#11758222—22no—
68C2×#11758222—41no—
69C2×#11758222—41no—
70C2×#11758222C2×C414yes—
71C22×Dic122C2311yescharacteristic
72C22×D244—22no—
73C22×D244—22no—
74C22×D244—21no—
75C22×D244—22no—
76C22×D244—41no—
77C22×D244—41no—
78C22×D244C2×C414yes—
79C22×D244C2311yescharacteristic
80C22×D244C2311yescharacteristic
81C22×C22⋊D61—21no—
82C22×C22⋊D61—21no—
83C22×C4×D61—21no—
84C22×C4×D61—21no—
85C2×#11758194—22no—
86C2×#11758194—22no—
87C2×#11758194—41no—
88C22×#92418—22no—
89C22×#92418—22no—
90C22×#92418—41no—
91C22×#92418C2311yescharacteristic
92C22×#92418C2311yescharacteristic
93C22×#92418C2311yescharacteristic
94C22×#92418C2311yescharacteristic
95#14519765—22no—
96#14519765C2×C414yes—
97#14519762—28no—
98#14519756—22no—
99#14519756C2×C414yes—
100#14519751—22no—
101#14519751C2×C414yes—
102#14519750—28no—
103#14519745—28no—
104C4×D244—22no—
105C4×D244C2×C414yes—
106C2×C4⋊Dic61C2311yescharacteristic
107C2×#11758196—21no—
108C2×C22⋊Dic61—21no—
109C2×#11758198—21no—
110C2×#11758198—21no—
111C2×#11758198—21no—
112C2×#11758198—21no—
113C22⋊C4×D61—28no—
114C4⋊#92418—22no—
115#14519700—22no—
116#14519700—22no—
117#14519700—41no—
118#14519700—41no—
119#14519697—22no—
120#14519697—22no—
121#14519697—22no—
122#14519697—22no—
123#14519697—22no—
124#14519697—41no—
125#14519697—41no—
126#14519697D414yescomplemented
127C22⋊#92418—22no—
128C22⋊#92418—22no—
129#14519688—22no—
130C22×D4×C61D411yescharacteristic
131C23×C4×C61C2311yescharacteristic
132C23×C4×C61C2311yescharacteristic
133C4×D4×C61C2×C414yes—
134C4×D4×C61D414yes—
135#117×C61—22no—
136#117×C61—22no—
137#117×C61—41no—
138#117×C61—41no—
139C2×C4⋊C4×C61—21no—
140C2×C4⋊C4×C61—21no—
141C2×C4⋊C4×C61D411yescharacteristic
142C2×C4⋊C4×C61C2311yescharacteristic
143C2×C4⋊C4×C61C2311yescharacteristic
144C2×C4⋊C4×C61C2311yescharacteristic
145C2×C4⋊C4×C61C2311yescharacteristic
146C2×C22⋊C4×C61—21no—
147C2×C22⋊C4×C61—21no—
148C2×C22⋊C4×C61—21no—
149C2×C22⋊C4×C61—21no—
150C2×C22⋊C4×C61D411yescharacteristic
151C2×C22⋊C4×C61D411yescharacteristic
152C2×C42×C61—21no—
153C2×C42×C61—21no—
154C2×C42×C61—21no—
155C2×C42×C61C2311yescharacteristic
156#95×C61—21no—
157#95×C61—21no—
158#95×C61—21no—
159C24×C61C2×D411yescharacteristic
160C24×C61C2×D411yescharacteristic
161C23×D61—21no—
162C23×D61—21no—
163C23×D61—24no—
164C23×D61—42no—
165C23×D61—42no—
166C23×D61—42no—
167C23×D61—42no—
168C23×D61—81no—
169C23×D61—81no—
170C2×D4×C61—41no—
171C2×D4×C61—41no—
172C2×D4×C61C22⋊C414yes—
173C22×C4×C61—21no—
174C22×C4×C61—21no—
175C22×C4×C61—21no—
176C22×C4×C61—21no—
177C22×C4×C61—21no—
178C22×C4×C61—21no—
179C22×C4×C61—21no—
180C22×C4×C61—21no—
181C22×C4×C61—21no—
182C22×C4×C61—21no—
183C22×C4×C61—21no—
184C22×C4×C61—21no—
185C22×C4×C61C22×C412yes—
186C22×C4×C61C22×C412yes—
187C22×C4×C61C2×D411yescharacteristic
188C22×C4×C61C2×D411yescharacteristic
189C22×C4×C61C2×D411yescharacteristic
190C22×C4×C61C2×D411yescharacteristic
191C22×C4×C61C2×D412yes—
192C22×C4×C61C2×D412yes—
193C22×C4×C61C2411yescharacteristic
194C2×C22⋊D61—24no—
195C2×C22⋊D61—24no—
196C2×C22⋊D61—42no—
197C2×C22⋊D61—42no—
198C2×C22⋊D61—81no—
199C2×C22⋊D61—81no—
200C22×Dic61—21no—
201C22×Dic61—21no—
202#11758222—28no—
203#11758222—44no—
204#11758222—44no—
205#11758222—44no—
206C2×D244—21no—
207C2×D244—21no—
208C2×D244—21no—
209C2×D244—21no—
210C2×D244—21no—
211C2×D244—21no—
212C2×D244—21no—
213C2×D244—28no—
214C2×D244—24no—
215C2×D244—21no—
216C2×D244—44no—
217C2×D244—44no—
218C2×D244—44no—
219C2×D244—42no—
220C2×D244—42no—
221C2×D244C22×C412yes—
222C2×D244C22×C412yes—
223C2×D244C2×D412yes—
224C2×D244#4112yes—
225C2×C4×D61—24no—
226C2×C4×D61—24no—
227C2×C4×D61—42no—
228C2×C4×D61—42no—
229C2×C4×D61—81no—
230C2×C4×D61—81no—
231C2×Dic122—21no—
232C2×Dic122—21no—
233C2×Dic122—21no—
234C2×Dic122—21no—
235C2×Dic122—21no—
236C2×Dic122C22×C412yes—
237C4⋊C4×C61—21no—
238C4⋊C4×C61—21no—
239C4⋊C4×C61—21no—
240C4⋊C4×C61—21no—
241C4⋊C4×C61—21no—
242C4⋊C4×C61—21no—
243C4⋊C4×C61—21no—
244C4⋊C4×C61—42no—
245C4⋊C4×C61—81no—
246C4⋊C4×C61C22⋊C414yes—
247C4⋊C4×C61C2×D412yes—
248C22⋊C4×C61—42no—
249C22⋊C4×C61—42no—
250C22⋊C4×C61—81no—
251C22⋊C4×C61—81no—
252C22⋊C4×C61C22⋊C414yes—
253C22⋊C4×C61C22⋊C414yes—
254C42×C61—42no—
255C42×C61—42no—
256C42×C61—42no—
257C42×C61C22×C412yes—
258C42×C61C2×D412yes—
259C22⋊Dic61—24no—
260#11758198—24no—
261#11758198—24no—
262#11758198—24no—
263#11758198—24no—
264C4⋊Dic61—21no—
265C4⋊Dic61C22×C412yes—
266#11758196—24no—
267#11758194—44no—
268C2×#92418—21no—
269C2×#92418—21no—
270C2×#92418—21no—
271C2×#92418—21no—
272C2×#92418—21no—
273C2×#92418—21no—
274C2×#92418—21no—
275C2×#92418—21no—
276C2×#92418—21no—
277C2×#92418—21no—
278C2×#92418—21no—
279C2×#92418—44no—
280C2×#92418C2×D412yes—
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×C61C2×C22⋊C412yes—
294C23×C61C2×C22⋊C412yes—
295C23×C61C22×D411yescharacteristic
296C22×D61—22no—
297C22×D61—22no—
298C22×D61—22no—
299C22×D61—22no—
300C22×D61—48no—
301C22×D61—41no—
302C22×D61—41no—
303C22×D61—41no—
304C22×D61—41no—
305C22×D61—48no—
306C22×D61—41no—
307C22×D61—41no—
308C22×D61—41no—
309C22×D61—41no—
310C22×D61—41no—
311C22×D61—41no—
312C22×D61—84no—
313C22×D61—84no—
314C22×D61—84no—
315C22×D61—84no—
316C22×D61—84no—
317D4×C61—44no—
318C2×C4×C61—21no—
319C2×C4×C61—21no—
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—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×C61—41no—
343C2×C4×C61—41no—
344C2×C4×C61—41no—
345C2×C4×C61—41no—
346C2×C4×C61C2×C22⋊C412yes—
347C2×C4×C61C2×C22⋊C412yes—
348C2×C4×C61C2×C22⋊C412yes—
349C2×C4×C61C2×C22⋊C412yes—
350C2×C4×C61C23×C411yescharacteristic
351C2×C4×C61C22×D411yescharacteristic
352C2×C4×C61C22×D411yescharacteristic
353C2×C4×C61C2×#4111yescharacteristic
354C2×C4×C61H(5,𝔽2)11yescharacteristic
355C2×C4×C61H(5,𝔽2)11yescharacteristic
356C22⋊D61—48no—
357C22⋊D61—84no—
358C2×Dic61—22no—
359C2×Dic61—22no—
360C2×Dic61—41no—
361C2×Dic61—41no—
362C2×Dic61—41no—
363C2×Dic61—41no—
364D244—22no—
365D244—22no—
366D244—22no—
367D244—22no—
368D244—22no—
369D244—48no—
370D244—41no—
371D244—41no—
372D244C4×D414yes—
373C4×D61—48no—
374C4×D61—84no—
375Dic122—22no—
376Dic122—22no—
377Dic122—41no—
378Dic122—41no—
379#92418—22no—
380#92418—41no—
381#92418—41no—
382#92418—41no—
383#22424—611nomaximal, Sylow
384C22×C61—22no—
385C22×C61—22no—
386C22×C61—22no—
387C22×C61—22no—
388C22×C61—22no—
389C22×C61—22no—
390C22×C61—41no—
391C22×C61—41no—
392C22×C61—41no—
393C22×C61—41no—
394C22×C61—41no—
395C22×C61—41no—
396C22×C61—41no—
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—24no—
406C2×D61—42no—
407C2×D61—42no—
408C2×D61—42no—
409C2×D61—42no—
410C2×D61—42no—
411C2×D61—42no—
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—22no—
422C4×C61—22no—
423C4×C61—22no—
424C4×C61—42no—
425C4×C61—81no—
426C4×C61—81no—
427C4×C61—81no—
428C4×C61C2×C4×D411yescharacteristic
429C4×C61#51811yescharacteristic
430C4×C61D4211yescharacteristic
431C4×C61#54611yescharacteristic
432Dic61—42no—
433Dic61—42no—
434C2×#546—611no—
435C2×#435—611no—
436C2×#418—611no—
437C2×#416—611no—
438#2354D6111yescharacteristic, complemented
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—42no—
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—44no—
459D61—82no—
460C22×#41—611no—
461C23×D4—611no—
462C22×M16—611no—
463C23×C8—611no—
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×D4C2×D6111yescharacteristic
474C2×#117C2×D6111yescharacteristic
475C2×#117C2×D6111yescharacteristic, complemented
476C22×C22⋊C4—1221no—
477#435—1224no—
478C2×C4⋊C8—611no—
479#418—1224no—
480#416—1224no—
481C2×#103—611no—
482C2×#103—611no—
483C2×#103—611no—
484C2×#103—611no—
485C2×#102—611no—
486C2×#102—611no—
487C2×#102—611no—
488C2×#102—611no—
489C2×#102—611no—
490C2×#102—611no—
491C2×#102—611no—
492C2×#102—611no—
493C2×C22⋊C8—611no—
494C2×C22⋊C8—611no—
495C2×#97—611no—
496#390—21no—
497#388—21no—
498#388—21no—
499#384C2×D6111yescharacteristic, complemented
500#380C2×D6111yescharacteristic
501#380C2×D6111yescharacteristic, complemented
502C4×C4⋊C4—21no—
503C4×C4⋊C4C2×D6111yescharacteristic, complemented
504#340—611no—
505#340—611no—
506#340—611no—
507#340—611no—
508C61#2242411yescharacteristic, complemented, Sylow
509C25—1221no—
510C2×#41—614no—
511C2×#41—1222no—
512C2×#41—1222no—
513C2×#41—1222no—
514C2×#41—2441no—
515C2×#41—2441no—
516C22×Q8—611no—
517C22×D4—614no—
518C22×D4—611no—
519C22×D4—611no—
520C22×D4—1222no—
521C22×D4—1222no—
522C22×D4—1221no—
523C22×D4—1221no—
524C22×D4—1222no—
525C22×D4—1221no—
526C22×D4—2441no—
527C22×D4—2441no—
528C22×D4C22⋊D6111yescharacteristic
529C23×C4—1221no—
530C23×C4—1221no—
531C23×C4C22×D6111yescharacteristic
532C23×C4C22×D6111yescharacteristic
533C2×M16—1222no—
534C2×M16—1222no—
535C2×M16—2441no—
536C22×C8—611no—
537C22×C8—611no—
538C22×C8—611no—
539C22×C8—611no—
540C22×C8—1222no—
541C22×C8—1222no—
542C22×C8—2441no—
543#124—614no—
544#124—1222no—
545#123—1228no—
546C22⋊Q8—614no—
547C22⋊Q8—1222no—
548#121—614no—
549#121—1222no—
550#121—1228no—
551#120—1228no—
552C4×D4—614no—
553C4×D4—1222no—
554C4×D4C4×D6114yes—
555C4×D4D24414yes—
556#117—22no—
557#117—22no—
558#117—41no—
559#117—41no—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—21no—
562C2×C4⋊C4—611no—
563C2×C4⋊C4—1221no—
564C2×C4⋊C4C22⋊D6111yescharacteristic
565C2×C4⋊C4C22×D6111yescharacteristic
566C2×C4⋊C4C22×D6111yescharacteristic
567C2×C4⋊C4C22×D6111yescharacteristic
568C2×C4⋊C4C22×D6111yescharacteristic
569C2×C22⋊C4—21no—
570C2×C22⋊C4—21no—
571C2×C22⋊C4—21no—
572C2×C22⋊C4—21no—
573C2×C22⋊C4—1221no—
574C2×C22⋊C4—1221no—
575C2×C22⋊C4—1221no—
576C2×C22⋊C4—1221no—
577C2×C22⋊C4—1221no—
578C2×C22⋊C4—1228no—
579C2×C22⋊C4C22⋊D6111yescharacteristic
580C2×C22⋊C4C22⋊D6111yescharacteristic
581C2×C42—21no—
582C2×C42—21no—
583C2×C42—21no—
584C2×C42C22×D6111yescharacteristic
585C4⋊C8—1222no—
586#103—1222no—
587#103—1222no—
588#103—2441no—
589#103—2441no—
590#102—614no—
591#102—1222no—
592#102—1222no—
593#102—1222no—
594#102—1222no—
595#102—1222no—
596#102—2441no—
597#102—2441no—
598C22⋊C8—1222no—
599C22⋊C8—1222no—
600#97—1222no—
601#95—21no—
602#95—21no—
603#95—21no—
604C24—1221no—
605C24—1224no—
606C24—1221no—
607C24—4881no—
608C24—4881no—
609C24—2442no—
610C24—2442no—
611C24—2442no—
612C24—2442no—
613C24C2×C22⋊D6111yescharacteristic
614C24C2×C22⋊D6111yescharacteristic
615#41—1228no—
616#41—2444no—
617#41—2444no—
618#41—2444no—
619C2×Q8—612no—
620C2×Q8—1221no—
621C2×Q8—1221no—
622C2×Q8—1221no—
623C2×Q8—1221no—
624C2×Q8—1221no—
625C2×D4—41no—
626C2×D4—41no—
627C2×D4—612no—
628C2×D4—612no—
629C2×D4—612no—
630C2×D4—612no—
631C2×D4—1228no—
632C2×D4—1224no—
633C2×D4—1224no—
634C2×D4—1221no—
635C2×D4—1221no—
636C2×D4—1221no—
637C2×D4—1221no—
638C2×D4—1221no—
639C2×D4—1221no—
640C2×D4—1221no—
641C2×D4—1221no—
642C2×D4—1224no—
643C2×D4—4881no—
644C2×D4—4881no—
645C2×D4—2444no—
646C2×D4—2444no—
647C2×D4—2444no—
648C2×D4—2442no—
649C2×D4—2442no—
650C2×D4—2442no—
651C2×D4—2442no—
652C2×D4#1175819814yes—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—1221no—
666C22×C4—1221no—
667C22×C4—1224no—
668C22×C4—1224no—
669C22×C4—4881no—
670C22×C4—4881no—
671C22×C4—2442no—
672C22×C4—2442no—
673C22×C4C2×C4×D6112yes—
674C22×C4C2×C4×D6112yes—
675C22×C4C2×D24412yes—
676C22×C4C2×D24412yes—
677C22×C4C2×C22⋊D6111yescharacteristic
678C22×C4C2×C22⋊D6111yescharacteristic
679C22×C4C2×C22⋊D6111yescharacteristic
680C22×C4C2×C22⋊D6111yescharacteristic
681C22×C4C23×D6111yescharacteristic
682M16—2444no—
683C2×C8—612no—
684C2×C8—1221no—
685C2×C8—1221no—
686C2×C8—1221no—
687C2×C8—1221no—
688C2×C8—1221no—
689C2×C8—1221no—
690C2×C8—1221no—
691C2×C8—1221no—
692C2×C8—1221no—
693C2×C8—1221no—
694C2×C8—1221no—
695C2×C8—2444no—
696C4⋊C4—21no—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—42no—
704C4⋊C4—81no—
705C4⋊C4—612no—
706C4⋊C4—1221no—
707C4⋊C4—1224no—
708C4⋊C4#1175819814yes—
709C4⋊C4D4×D6112yes—
710C22⋊C4—42no—
711C22⋊C4—42no—
712C22⋊C4—81no—
713C22⋊C4—81no—
714C22⋊C4—1224no—
715C22⋊C4—1224no—
716C22⋊C4—1224no—
717C22⋊C4—1224no—
718C22⋊C4—1224no—
719C22⋊C4#1175819814yes—
720C22⋊C4#1175819814yes—
721C42—42no—
722C42—42no—
723C42—42no—
724C42C2×C4×D6112yes—
725C42C2×D24412yes—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—21no—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—21no—
738C23—1222no—
739C23—1222no—
740C23—1222no—
741C23—1222no—
742C23—4884no—
743C23—4884no—
744C23—4884no—
745C23—4884no—
746C23—4884no—
747C23—2448no—
748C23—2448no—
749C23—2441no—
750C23—2441no—
751C23—2441no—
752C23—2441no—
753C23—2441no—
754C23—2441no—
755C23—2441no—
756C23—2441no—
757C23—2441no—
758C23—2441no—
759C23C2×#1175819812yes—
760C23C2×#1175819812yes—
761C23C22×C22⋊D6111yescharacteristic
762Q8—1222no—
763Q8—1222no—
764Q8—2441no—
765Q8—2441no—
766D4—44no—
767D4—614no—
768D4—1222no—
769D4—1222no—
770D4—1222no—
771D4—1222no—
772D4—1222no—
773D4—4884no—
774D4—2448no—
775D4—2448no—
776D4—2441no—
777D4—2441no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—1222no—
807C2×C4—1222no—
808C2×C4—4884no—
809C2×C4—2448no—
810C2×C4—2441no—
811C2×C4—2441no—
812C2×C4—2441no—
813C2×C4—2441no—
814C2×C4C2×#1175819812yes—
815C2×C4C2×#1175819812yes—
816C2×C4C2×#1175819812yes—
817C2×C4C2×#1175819812yes—
818C2×C4C22×C4×D6111yescharacteristic
819C2×C4C2×D4×D6111yescharacteristic
820C2×C4C22×D24411yescharacteristic
821C2×C4#41×D6111yescharacteristic
822C2×C4#1451982211yescharacteristic
823C2×C4#1451982311yescharacteristic
824C8—1222no—
825C8—2441no—
826C8—2441no—
827C8—2441no—
828C22—22no—
829C22—22no—
830C22—22no—
831C22—22no—
832C22—22no—
833C22—22no—
834C22—41no—
835C22—41no—
836C22—41no—
837C22—41no—
838C22—41no—
839C22—41no—
840C22—41no—
841C22—41no—
842C22—1224no—
843C22—48816no—
844C22—4881no—
845C22—4881no—
846C22—4881no—
847C22—4881no—
848C22—2442no—
849C22—2442no—
850C22—2442no—
851C22—2442no—
852C22—2442no—
853C22—2442no—
854C22—2442no—
855C22—2442no—
856C22—2442no—
857C22C22×#1175819811yescharacteristic
858C22D4×C22⋊D6111yescharacteristic
859C22#1684040011yescharacteristic
860C22#1684056011yescharacteristic
861C22#1684056011yescharacteristic
862C22#1684056511yescharacteristic
863C22#1684057011yescharacteristic
864C4—22no—
865C4—22no—
866C4—22no—
867C4—22no—
868C4—42no—
869C4—81no—
870C4—81no—
871C4—81no—
872C4—2442no—
873C4—2442no—
874C4C4×D4×D6111yescharacteristic
875C4#1684023411yescharacteristic
876C4D4×D24411yescharacteristic
877C4#1684040711yescharacteristic
878C2—42no—
879C2—42no—
880C2—4882no—
881C2—2444no—
882C2D4×#1175819811yescharacteristic
883C2#2145433611yescharacteristic
884C2#2145434211yescharacteristic
885C2#2145734511yescharacteristic
886C2#2145736011yescharacteristic
887C2#2145784911yescharacteristic
888C2#2145796911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#2354C2
socleC23×C61C22×D4
prime radicalC2×#16840408C2
cosocleC22×C4×C61C24
hypercenter#2354D61
hypocenterC61#22424
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2354

Complements

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

NH ≅ G/Ntype
2. C2×#16839834C2semidirect
3. C2×#16839766C2semidirect
4. C2×#16839756C2semidirect
5. #21446751C2semidirect
6. #21446633C2semidirect
7. #21446250C2semidirect
8. #21446245C2semidirect
9. #21446141C2semidirect
10. #21446131C2semidirect
11. #21445816C2semidirect
12. #21445757C2semidirect
13. #21445749C2semidirect
14. #21445647C2semidirect
15. C61×#2354C2semidirect
19. C23×#92418C22semidirect
21. #16840408C4semidirect
31. C2×C4⋊#92418C22semidirect
34. C2×#14519700C22semidirect
35. C2×#14519700C22semidirect
36. C2×#14519700C22semidirect
37. C2×#14519700C22semidirect
47. C2×C22⋊#92418C22semidirect
48. C2×#14519688C22semidirect
49. #16839524C22semidirect
50. #16839524C22semidirect
51. #16839524C22semidirect
52. #16839524C22semidirect
55. C2×#117×C61C22semidirect
59. C61×#384C22semidirect
61. C61×#380C22semidirect
63. C4×C4⋊C4×C61C22semidirect
126. #14519697D4semidirect
438. #2354D61semidirect
475. C2×#117C2×D61semidirect
499. #384C2×D61semidirect
501. #380C2×D61semidirect
503. C4×C4⋊C4C2×D61semidirect
508. C61#22424semidirect

Maximal subgroups

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

subgroupindex
C2×#168404082
C2×#168398342
C2×#168397662
C2×#168397562
#214467512
#214466332
#214462502
#214462452
#214461412
#214461312
#214458162
#214457572
#214457492
#214456472
C61×#23542
#2242461