Finite Group Databasebeta

← #29722305

Subgroups — #29722305

Order 15616.

990 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840010C211yesmaximal, characteristic, complemented
2C2×#16839993C211yesmaximal, characteristic, complemented
3C2×#16839834C211yesmaximal, characteristic, complemented
4C2×#16839798C211yesmaximal, characteristic, complemented
5#21449237C211yesmaximal, characteristic
6#21447200C211yesmaximal, characteristic, complemented
7#21447190C211yesmaximal, characteristic, complemented
8#21447012C211yesmaximal, characteristic, complemented
9#21447008C211yesmaximal, characteristic, complemented
10#21446703C211yesmaximal, characteristic, complemented
11#21446554C211yesmaximal, characteristic, complemented
12#21446141C211yesmaximal, characteristic, complemented
13#21446132C211yesmaximal, characteristic, complemented
14#21445850C211yesmaximal, characteristic, complemented
15C61×#2415C211yesmaximal, characteristic, complemented
16C22×#11758201C2211yescharacteristic
17C22×#11758194C2211yescharacteristic
18C23×#92418C2211yescharacteristic
19C2×#14519751C2211yescharacteristic
20C2×#14519751C2211yescharacteristic
21C2×#14519736C2211yescharacteristic
22#16840010—24no—
23#16839993—24no—
24#16839834—24no—
25#16839798—24no—
26C2×#14519710C2211yescharacteristic
27C2×#14519710C2211yescharacteristic
28C2×#14519708C2211yescharacteristic
29C2×#14519708C2211yescharacteristic
30C2×#14519708C2211yescharacteristic
31C2×C4⋊#92418C2211yescharacteristic
32C2×#14519701C2211yescharacteristic
33C2×#14519701C2211yescharacteristic
34C2×#14519701C2211yescharacteristic
35C2×#14519697C2211yescharacteristic
36C2×#14519697C2211yescharacteristic
37C2×#14519697C2211yescharacteristic
38C2×C22⋊#92418C2211yescharacteristic
39C2×C22⋊#92418C2211yescharacteristic
40C2×#14519688C2211yescharacteristic
41#16839677—21no—
42#16839670—21no—
43#16839664C2211yescharacteristic
44#16839662—21no—
45#16839660C2211yescharacteristic
46#16839652—21no—
47#16839622C2211yescharacteristic
48#16839524C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839524C2211yescharacteristic
52C2×C22⋊Q8×C61C2211yescharacteristic
53C2×C22⋊Q8×C61C2211yescharacteristic
54C2×C4×D4×C61C2211yescharacteristic
55C2×#117×C61C2211yescharacteristic
56C61×#397—21no—
57C61×#394—21no—
58C61×#391C2211yescharacteristic
59C61×#389—21no—
60C61×#389C2211yescharacteristic
61C61×#388—21no—
62C61×#380C2211yescharacteristic
63C22×D244C2311yescharacteristic
64C22×C22⋊D61—21no—
65C22×C22⋊D61—21no—
66C2×#11758201—22no—
67C2×#11758201—22no—
68C2×#11758201—22no—
69C2×#11758194—22no—
70C2×#11758194—22no—
71C2×#11758194—22no—
72C22×#92418—22no—
73C22×#92418—22no—
74C22×#92418D414yescomplemented
75C22×#92418C2311yescharacteristic
76C22×#92418C2311yescharacteristic
77C22×#92418C2311yescharacteristic
78C22×#92418C2311yescharacteristic
79#14519751—22no—
80#14519751—22no—
81#14519751—22no—
82#14519751—41no—
83#14519736—22no—
84#14519736—41no—
85C2×C4⋊Dic61C2311yescharacteristic
86C2×C4⋊Dic61C2311yescharacteristic
87C2×C4⋊Dic61C2311yescharacteristic
88C2×#11758196—21no—
89C2×C22⋊Dic61—21no—
90C2×C22⋊Dic61—21no—
91C2×#11758198—21no—
92C2×#11758198—21no—
93C2×#11758198—21no—
94C2×#11758198—21no—
95C2×C4×Dic61—21no—
96#14519710—22no—
97#14519710D414yescomplemented
98#14519708—22no—
99#14519708—22no—
100#14519708—22no—
101C4⋊#92418—22no—
102#14519701—22no—
103#14519701—22no—
104#14519701—41no—
105#14519697—22no—
106#14519697—22no—
107#14519697—41no—
108C22⋊#92418—22no—
109C22⋊#92418—22no—
110#14519688—22no—
111#14519684—21no—
112#14519684—21no—
113C22×Q8×C61C2311yescharacteristic
114C22×D4×C61D411yescharacteristic
115C23×C4×C61C2311yescharacteristic
116C23×C4×C61C2311yescharacteristic
117C22⋊Q8×C61—22no—
118C22⋊Q8×C61—22no—
119C22⋊Q8×C61—22no—
120C22⋊Q8×C61—41no—
121C4×D4×C61—22no—
122C4×D4×C61—22no—
123#117×C61—22no—
124#117×C61—41no—
125C2×C4⋊C4×C61—21no—
126C2×C4⋊C4×C61—21no—
127C2×C4⋊C4×C61—21no—
128C2×C4⋊C4×C61D411yescharacteristic
129C2×C4⋊C4×C61C2311yescharacteristic
130C2×C4⋊C4×C61C2311yescharacteristic
131C2×C4⋊C4×C61C2311yescharacteristic
132C2×C22⋊C4×C61—21no—
133C2×C22⋊C4×C61—21no—
134C2×C22⋊C4×C61—21no—
135C2×C22⋊C4×C61—21no—
136C2×C22⋊C4×C61D411yescharacteristic
137C2×C22⋊C4×C61D411yescharacteristic
138C2×C42×C61—21no—
139C2×C42×C61C2311yescharacteristic
140#95×C61—21no—
141#95×C61—21no—
142#95×C61—21no—
143#95×C61—21no—
144C24×C61C2×D411yescharacteristic
145C24×C61C2×D411yescharacteristic
146C23×D61—21no—
147C2×Q8×C61—21no—
148C2×Q8×C61—21no—
149C2×Q8×C61—21no—
150C2×Q8×C61—21no—
151C2×Q8×C61—21no—
152C2×Q8×C61—21no—
153C2×D4×C61—22no—
154C2×D4×C61—41no—
155C2×D4×C61—41no—
156C22×C4×C61—21no—
157C22×C4×C61—21no—
158C22×C4×C61—21no—
159C22×C4×C61—21no—
160C22×C4×C61—21no—
161C22×C4×C61—21no—
162C22×C4×C61—21no—
163C22×C4×C61—21no—
164C22×C4×C61—21no—
165C22×C4×C61—21no—
166C22×C4×C61—21no—
167C22×C4×C61—21no—
168C22×C4×C61—21no—
169C22×C4×C61—21no—
170C22×C4×C61C2×D411yescharacteristic
171C22×C4×C61C2×D411yescharacteristic
172C22×C4×C61C2×D411yescharacteristic
173C22×C4×C61C2×D411yescharacteristic
174C22×C4×C61C2×D412yes—
175C22×C4×C61#4112yes—
176C22×C4×C61C2411yescharacteristic
177C2×C22⋊D61—42no—
178C2×C22⋊D61—42no—
179C2×C22⋊D61—42no—
180C2×C22⋊D61—81no—
181C2×C22⋊D61—81no—
182C2×C22⋊D61—81no—
183C22×Dic61—21no—
184C22×Dic61—21no—
185C22×Dic61—21no—
186C2×D244—21no—
187C2×D244—21no—
188C2×D244—21no—
189C2×D244—21no—
190C2×D244—21no—
191C2×D244—21no—
192C4⋊C4×C61—22no—
193C4⋊C4×C61—21no—
194C4⋊C4×C61—21no—
195C4⋊C4×C61—21no—
196C4⋊C4×C61—21no—
197C4⋊C4×C61—21no—
198C4⋊C4×C61—42no—
199C4⋊C4×C61—42no—
200C4⋊C4×C61—42no—
201C4⋊C4×C61C2×D412yes—
202C22⋊C4×C61—22no—
203C22⋊C4×C61—22no—
204C22⋊C4×C61—42no—
205C22⋊C4×C61—42no—
206C22⋊C4×C61—42no—
207C22⋊C4×C61—42no—
208C42×C61—21no—
209C42×C61—21no—
210C42×C61—42no—
211C22⋊Dic61—42no—
212C22⋊Dic61—81no—
213#11758201—44no—
214#11758198—42no—
215#11758198—42no—
216#11758198—42no—
217#11758198—81no—
218C4⋊Dic61—21no—
219C4⋊Dic61—21no—
220C4⋊Dic61—21no—
221C4⋊Dic61—21no—
222C4⋊Dic61—21no—
223C4⋊Dic61C2×D412yes—
224#11758196—81no—
225C4×Dic61—42no—
226#11758194—44no—
227C2×#92418—21no—
228C2×#92418—21no—
229C2×#92418—28no—
230C2×#92418—21no—
231C2×#92418—21no—
232C2×#92418—21no—
233C2×#92418—21no—
234C2×#92418—21no—
235C2×#92418—21no—
236C2×#92418C2×D412yes—
237C2×#92418C2×D412yes—
238C2×#92418C2×D412yes—
239C2×#92418#4112yes—
240C23×C61—21no—
241C23×C61—21no—
242C23×C61—21no—
243C23×C61—21no—
244C23×C61—21no—
245C23×C61—21no—
246C23×C61—21no—
247C23×C61—21no—
248C23×C61—21no—
249C23×C61—21no—
250C23×C61—21no—
251C23×C61—21no—
252C23×C61—21no—
253C23×C61#12112yes—
254C23×C61C22×D411yescharacteristic
255C22×D61—41no—
256C22×D61—41no—
257C22×D61—41no—
258C22×D61—41no—
259C22×D61—41no—
260C22×D61—41no—
261C22×D61—41no—
262Q8×C61—41no—
263Q8×C61—41no—
264Q8×C61—41no—
265Q8×C61—41no—
266D4×C61—44no—
267C2×C4×C61—21no—
268C2×C4×C61—21no—
269C2×C4×C61—22no—
270C2×C4×C61—22no—
271C2×C4×C61—22no—
272C2×C4×C61—22no—
273C2×C4×C61—21no—
274C2×C4×C61—21no—
275C2×C4×C61—21no—
276C2×C4×C61—21no—
277C2×C4×C61—22no—
278C2×C4×C61—21no—
279C2×C4×C61—21no—
280C2×C4×C61—21no—
281C2×C4×C61—21no—
282C2×C4×C61—21no—
283C2×C4×C61—41no—
284C2×C4×C61—41no—
285C2×C4×C61—41no—
286C2×C4×C61—41no—
287C2×C4×C61—41no—
288C2×C4×C61—41no—
289C2×C4×C61—41no—
290C2×C4×C61—41no—
291C2×C4×C61—41no—
292C2×C4×C61—41no—
293C2×C4×C61—41no—
294C2×C4×C61—41no—
295C2×C4×C61—41no—
296C2×C4×C61—41no—
297C2×C4×C61—41no—
298C2×C4×C61#12112yes—
299C2×C4×C61C22×D411yescharacteristic
300C2×C4×C61C22×D411yescharacteristic
301C2×C4×C61C2×#4111yescharacteristic
302C2×C4×C61C2×#4111yescharacteristic
303C2×C4×C61H(5,𝔽2)11yescharacteristic
304C2×C4×C612−1+411yescharacteristic
305C22⋊D61—84no—
306C22⋊D61—84no—
307C2×Dic61—22no—
308C2×Dic61—41no—
309C2×Dic61—41no—
310C2×Dic61—41no—
311C2×Dic61—41no—
312C2×Dic61—41no—
313C2×Dic61—41no—
314C2×Dic61—41no—
315C2×Dic61—41no—
316D244—41no—
317D244—41no—
318D244—41no—
319D244—41no—
320#92418—22no—
321#92418—41no—
322#92418—41no—
323#92418#12114yes—
324#24786—611nomaximal, Sylow
325C22×C61—22no—
326C22×C61—22no—
327C22×C61—22no—
328C22×C61—41no—
329C22×C61—41no—
330C22×C61—41no—
331C22×C61—41no—
332C22×C61—41no—
333C22×C61—41no—
334C22×C61—41no—
335C22×C61—41no—
336C22×C61—41no—
337C22×C61—41no—
338C22×C61—41no—
339C22×C61C2×#12111yescharacteristic
340C22×C61D4211yescharacteristic
341C22×C61#54711yescharacteristic
342C22×C61#57511yescharacteristic
343C22×C61#57511yescharacteristic
344C22×C61#57711yescharacteristic
345C22×C61#57711yescharacteristic
346C2×D61—81no—
347C2×D61—81no—
348C2×D61—81no—
349C2×D61—81no—
350C2×D61—81no—
351C2×D61—81no—
352C2×D61—81no—
353C4×C61—22no—
354C4×C61—41no—
355C4×C61—42no—
356C4×C61—41no—
357C4×C61—41no—
358C4×C61—81no—
359C4×C61—81no—
360C4×C61—81no—
361C4×C61C2×#12111yescharacteristic
362C4×C61#53711yescharacteristic
363C4×C61#54811yescharacteristic
364C4×C61#55311yescharacteristic
365Dic61—42no—
366Dic61—81no—
367Dic61—81no—
368C2×#468—611no—
369C2×#465—611no—
370C2×#435—611no—
371C2×#427—611no—
372#2415D6111yescharacteristic, complemented
373#2414—611no—
374#2066—611no—
375#2065—611no—
376#2035—611no—
377#2034—611no—
378#1973—611no—
379#1943—611no—
380#1875—611no—
381#1873—611no—
382#1809—611no—
383C2×C61—42no—
384C2×C61—81no—
385C2×C61#241611yescharacteristic
386C2×C61#305411yescharacteristic
387C2×C61#305711yescharacteristic
388C2×C61#326711yescharacteristic
389C2×C61#327111yescharacteristic
390C2×C61#334811yescharacteristic
391C2×C61#335011yescharacteristic
392D61—161no—
393C22×SD16—611no—
394C22×M16—611no—
395C23×C8—611no—
396C2×C22⋊Q8C2×D6111yescharacteristic
397C2×C22⋊Q8C2×D6111yescharacteristic
398C2×#121—611no—
399C2×#121—611no—
400C2×C4×D4C2×D6111yescharacteristic
401C2×#117—611no—
402C2×#117C2×D6111yescharacteristic
403#468—1224no—
404#465—1224no—
405#435—1224no—
406#427—1224no—
407C2×#107—611no—
408C2×#107—611no—
409C2×#106—611no—
410C2×#106—611no—
411C2×#106—611no—
412C2×C4⋊C8—611no—
413C2×#103—611no—
414C2×#103—611no—
415C2×#103—611no—
416C2×#102—611no—
417C2×#102—611no—
418C2×#102—611no—
419C2×C22⋊C8—611no—
420C2×C22⋊C8—611no—
421C2×#97—611no—
422#397—21no—
423#394—21no—
424#394—1221no—
425#392—1221no—
426#391C2×D6111yescharacteristic
427#390—611no—
428#390—1221no—
429#389—21no—
430#389—611no—
431#389C2×D6111yescharacteristic
432#388—21no—
433#388—1221no—
434#380—611no—
435#380C2×D6111yescharacteristic
436#340—611no—
437#340—611no—
438#340—611no—
439#340—611no—
440C61#2478611yescharacteristic, complemented, Sylow
441C22×Q8C22×D6111yescharacteristic
442C22×D4—611no—
443C22×D4—1221no—
444C22×D4—1221no—
445C22×D4C22⋊D6111yescharacteristic
446C23×C4C22×D6111yescharacteristic
447C23×C4C22×D6111yescharacteristic
448C2×SD16—1222no—
449C2×SD16—1222no—
450C2×SD16—1222no—
451C2×M16—1222no—
452C2×M16—1222no—
453C2×M16—1222no—
454C22×C8—611no—
455C22×C8—614no—
456C22×C8—611no—
457C22×C8—611no—
458C22×C8—611no—
459C22×C8—1222no—
460C22×C8—1222no—
461C22⋊Q8—22no—
462C22⋊Q8—22no—
463C22⋊Q8—22no—
464C22⋊Q8—41no—
465#121—1222no—
466#121—1222no—
467#121—1222no—
468#121—2441no—
469C4×D4—22no—
470C4×D4—22no—
471#117—22no—
472#117—41no—
473#117—1222no—
474#117—2441no—
475C2×C4⋊C4—21no—
476C2×C4⋊C4—21no—
477C2×C4⋊C4—21no—
478C2×C4⋊C4—611no—
479C2×C4⋊C4—611no—
480C2×C4⋊C4—611no—
481C2×C4⋊C4—1221no—
482C2×C4⋊C4C22⋊D6111yescharacteristic
483C2×C4⋊C4C22×D6111yescharacteristic
484C2×C4⋊C4C22×D6111yescharacteristic
485C2×C4⋊C4C22×D6111yescharacteristic
486C2×C22⋊C4—21no—
487C2×C22⋊C4—21no—
488C2×C22⋊C4—21no—
489C2×C22⋊C4—21no—
490C2×C22⋊C4—1221no—
491C2×C22⋊C4—1221no—
492C2×C22⋊C4—1221no—
493C2×C22⋊C4—1221no—
494C2×C22⋊C4—1221no—
495C2×C22⋊C4—1221no—
496C2×C22⋊C4C22⋊D6111yescharacteristic
497C2×C22⋊C4C22⋊D6111yescharacteristic
498C2×C42—21no—
499C2×C42—1221no—
500C2×C42C22×D6111yescharacteristic
501#107—614no—
502#107—1222no—
503#106—1222no—
504#106—1222no—
505#106—1222no—
506C4⋊C8—1222no—
507#103—1222no—
508#103—1222no—
509#103—2441no—
510#102—1222no—
511#102—1222no—
512#102—2441no—
513C22⋊C8—1222no—
514C22⋊C8—1222no—
515#97—1222no—
516#95—21no—
517#95—21no—
518#95—21no—
519#95—21no—
520#95—1221no—
521#95—1221no—
522C24—1221no—
523C24C2×C22⋊D6111yescharacteristic
524C24C2×C22⋊D6111yescharacteristic
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8—21no—
529C2×Q8—21no—
530C2×Q8—21no—
531C2×D4—22no—
532C2×D4—41no—
533C2×D4—41no—
534C2×D4—1221no—
535C2×D4—1221no—
536C2×D4—1221no—
537C2×D4—1221no—
538C2×D4—1221no—
539C2×D4—1221no—
540C2×D4—4881no—
541C2×D4—4881no—
542C2×D4—4881no—
543C2×D4—2442no—
544C2×D4—2442no—
545C2×D4—2442no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—1221no—
561C22×C4—1221no—
562C22×C4—1221no—
563C22×C4D4×D6112yes—
564C22×C4#1175822412yes—
565C22×C4C2×C22⋊D6111yescharacteristic
566C22×C4C2×C22⋊D6111yescharacteristic
567C22×C4C2×C22⋊D6111yescharacteristic
568C22×C4C2×C22⋊D6111yescharacteristic
569C22×C4C23×D6111yescharacteristic
570SD16—2444no—
571M16—2444no—
572C2×C8—612no—
573C2×C8—612no—
574C2×C8—612no—
575C2×C8—612no—
576C2×C8—1228no—
577C2×C8—1221no—
578C2×C8—1221no—
579C2×C8—1221no—
580C2×C8—1221no—
581C2×C8—1221no—
582C2×C8—1221no—
583C2×C8—1221no—
584C2×C8—1221no—
585C4⋊C4—21no—
586C4⋊C4—22no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—42no—
592C4⋊C4—42no—
593C4⋊C4—42no—
594C4⋊C4—612no—
595C4⋊C4—1221no—
596C4⋊C4—1221no—
597C4⋊C4—1221no—
598C4⋊C4—1221no—
599C4⋊C4—1221no—
600C4⋊C4—4881no—
601C4⋊C4D4×D6112yes—
602C22⋊C4—22no—
603C22⋊C4—22no—
604C22⋊C4—42no—
605C22⋊C4—42no—
606C22⋊C4—42no—
607C22⋊C4—42no—
608C22⋊C4—4881no—
609C22⋊C4—4881no—
610C22⋊C4—2442no—
611C22⋊C4—2442no—
612C22⋊C4—2442no—
613C22⋊C4—2442no—
614C42—21no—
615C42—21no—
616C42—42no—
617C42—2442no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—2441no—
632C23—2441no—
633C23—2441no—
634C23—2441no—
635C23—2441no—
636C23—2441no—
637C23—2441no—
638C23#1451974912yes—
639C23C22×C22⋊D6111yescharacteristic
640Q8—41no—
641Q8—41no—
642Q8—41no—
643Q8—41no—
644D4—44no—
645D4—4884no—
646D4—4884no—
647D4—2441no—
648D4—2441no—
649D4—2441no—
650D4—2441no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—22no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—1222no—
683C2×C4—2441no—
684C2×C4—2441no—
685C2×C4—2441no—
686C2×C4—2441no—
687C2×C4—2441no—
688C2×C4—2441no—
689C2×C4—2441no—
690C2×C4—2441no—
691C2×C4#1451974912yes—
692C2×C4C2×D4×D6111yescharacteristic
693C2×C4C2×D4×D6111yescharacteristic
694C2×C4#41×D6111yescharacteristic
695C2×C4C2×#1175822411yescharacteristic
696C2×C4#1451982211yescharacteristic
697C2×C4#1451982411yescharacteristic
698C8—614no—
699C8—1222no—
700C8—2441no—
701C8—2441no—
702C22—22no—
703C22—22no—
704C22—22no—
705C22—41no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22—41no—
712C22—41no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—4881no—
717C22—4881no—
718C22—4881no—
719C22—4881no—
720C22—4881no—
721C22—4881no—
722C22—4881no—
723C22C2×#1451974911yescharacteristic
724C22D4×C22⋊D6111yescharacteristic
725C22#1684041111yescharacteristic
726C22#1684056011yescharacteristic
727C22#1684056011yescharacteristic
728C22#1684057011yescharacteristic
729C22#1684057011yescharacteristic
730C4—22no—
731C4—41no—
732C4—41no—
733C4—41no—
734C4—42no—
735C4—81no—
736C4—81no—
737C4—81no—
738C4—4881no—
739C4—4881no—
740C4—2442no—
741C4#121×D6111yescharacteristic
742C4#1684033911yescharacteristic
743C4#1684041811yescharacteristic
744C4#1684045511yescharacteristic
745C2—42no—
746C2—81no—
747C2—9761no—
748C2#2144925611yescharacteristic
749C2#2145542511yescharacteristic
750C2#2145546011yescharacteristic
751C2#2145734511yescharacteristic
752C2#2145740511yescharacteristic
753C2#2145832811yescharacteristic
754C2#2145836411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2415C2
socleC23×C61C22×D4
prime radical#21449237C2
hypercenter#2415D61
hypocenterC61#24786
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2415

Complements

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

NH ≅ G/Ntype
1. C2×#16840010C2semidirect
2. C2×#16839993C2semidirect
3. C2×#16839834C2semidirect
4. C2×#16839798C2semidirect
6. #21447200C2semidirect
7. #21447190C2semidirect
8. #21447012C2semidirect
9. #21447008C2semidirect
10. #21446703C2semidirect
11. #21446554C2semidirect
12. #21446141C2semidirect
13. #21446132C2semidirect
14. #21445850C2semidirect
15. C61×#2415C2semidirect
74. C22×#92418D4semidirect
97. #14519710D4semidirect
372. #2415D61semidirect
440. C61#24786semidirect

Maximal subgroups

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

subgroupindex
C2×#168400102
C2×#168399932
C2×#168398342
C2×#168397982
#214492372
#214472002
#214471902
#214470122
#214470082
#214467032
#214465542
#214461412
#214461322
#214458502
C61×#24152
#2478661