Finite Group Databasebeta

← #29723843

Subgroups — #29723843

Order 15616.

1070 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839907C211yesmaximal, characteristic
2C2×C4×#11758199C211yesmaximal, characteristic, complemented
3#21449333C211yesmaximal, characteristic, complemented
4#21447357C211yesmaximal, characteristic, complemented
5#21447250C211yesmaximal, characteristic, complemented
6#21447134C211yesmaximal, characteristic, complemented
7#21447001C211yesmaximal, characteristic, complemented
8#21446498C211yesmaximal, characteristic, complemented
9#21446427C211yesmaximal, characteristic, complemented
10#21446167C211yesmaximal, characteristic, complemented
11#21446156C211yesmaximal, characteristic, complemented
12#21446066C211yesmaximal, characteristic, complemented
13#21445819C211yesmaximal, characteristic, complemented
14#21445759C211yesmaximal, characteristic, complemented
15C61×#2339C211yesmaximal, characteristic, complemented
16C22×#11758201C2211yescharacteristic
17C22×#11758199C2211yescharacteristic
18C2×#14519759—21no—
19C2×#14519751C2211yescharacteristic
20C2×C4×D244C2211yescharacteristic
21#16839907—24no—
22C4×#11758199—24no—
23C2×#14519710C2211yescharacteristic
24C2×#14519710C2211yescharacteristic
25C2×C4⋊#92418C2211yescharacteristic
26C2×#14519701C2211yescharacteristic
27C2×#14519701C2211yescharacteristic
28C2×#14519701C2211yescharacteristic
29C2×#14519698C2211yescharacteristic
30C2×#14519698C2211yescharacteristic
31C2×#14519698C2211yescharacteristic
32C2×#14519697C2211yescharacteristic
33C2×#14519697C2211yescharacteristic
34C2×C22⋊#92418C2211yescharacteristic
35C2×C22⋊#92418C2211yescharacteristic
36C2×C4×#92418C2211yescharacteristic
37#16839689—21no—
38#16839678—21no—
39#16839664C2211yescharacteristic
40#16839660C2211yescharacteristic
41#16839636—21no—
42#16839632C2211yescharacteristic
43#16839622C2211yescharacteristic
44#16839524C2211yescharacteristic
45#16839524C2211yescharacteristic
46#16839524C2211yescharacteristic
47#16839524C2211yescharacteristic
48#16839517C2211yescharacteristic
49#16839517C2211yescharacteristic
50C22×#41×C61C2211yescharacteristic
51C2×C4×D4×C61C2211yescharacteristic
52C2×C4×D4×C61C2211yescharacteristic
53C61×#391C2211yescharacteristic
54C61×#391C2211yescharacteristic
55C61×#386—21no—
56C61×#386—21no—
57C61×#381—21no—
58C61×#380C2211yescharacteristic
59C4×C22⋊C4×C61C2211yescharacteristic
60C2×#95×C61—21no—
61C22×D244C2311yescharacteristic
62C22×C22⋊D61—21no—
63C22×C4×D61—21no—
64C2×#11758201—22no—
65C2×#11758201—22no—
66C2×#11758201—41no—
67C2×#11758199—22no—
68C2×#11758199—22no—
69C2×#11758199D414yes—
70C22×#92418C2311yescharacteristic
71C22×#92418C2311yescharacteristic
72C22×#92418C2311yescharacteristic
73C22×#92418C2311yescharacteristic
74#14519759—44no—
75#14519751—22no—
76#14519751—41no—
77C4×D244—22no—
78C4×D244—41no—
79C2×C4⋊Dic61—21no—
80C2×C4⋊Dic61—21no—
81C2×C4⋊Dic61C2311yescharacteristic
82C2×C4⋊Dic61C2311yescharacteristic
83C2×C4⋊Dic61C2311yescharacteristic
84C2×#11758196—21no—
85C2×C22⋊Dic61—21no—
86C2×#11758198—21no—
87C2×#11758198—21no—
88C2×#11758198—21no—
89C2×#11758198—21no—
90#14519710—22no—
91#14519710—41no—
92C4⋊#92418—41no—
93#14519701—22no—
94#14519701—22no—
95#14519701—41no—
96#14519698—22no—
97#14519698—22no—
98#14519698—22no—
99#14519697—22no—
100#14519697—41no—
101C22⋊#92418—22no—
102C22⋊#92418—41no—
103C4×#92418—22no—
104#14519684—21no—
105#14519684—21no—
106C2×#41×C61—22no—
107C2×#41×C61—22no—
108C2×#41×C61—22no—
109C2×#41×C61—22no—
110C2×#41×C61—41no—
111C2×#41×C61—41no—
112C22×Q8×C61C2311yescharacteristic
113C22×D4×C61—21no—
114C22×D4×C61C2311yescharacteristic
115C23×C4×C61—21no—
116C23×C4×C61—21no—
117C23×C4×C61—21no—
118C23×C4×C61C2311yescharacteristic
119C4×D4×C61—22no—
120C4×D4×C61—22no—
121C4×D4×C61—41no—
122C4×D4×C61—41no—
123C2×C4⋊C4×C61C2311yescharacteristic
124C2×C4⋊C4×C61C2311yescharacteristic
125C2×C22⋊C4×C61—21no—
126C2×C22⋊C4×C61—21no—
127C2×C22⋊C4×C61—21no—
128C2×C22⋊C4×C61D411yescharacteristic
129C2×C22⋊C4×C61D411yescharacteristic
130C2×C42×C61C2311yescharacteristic
131C2×C42×C61C2311yescharacteristic
132#95×C61—21no—
133#95×C61—21no—
134#95×C61—21no—
135#95×C61—21no—
136#95×C61—21no—
137#95×C61D411yescharacteristic
138#95×C61D411yescharacteristic
139C24×C61—21no—
140C24×C61C2×D411yescharacteristic
141C23×D61—21no—
142#41×C61—44no—
143#41×C61—44no—
144#41×C61—44no—
145#41×C61—44no—
146C2×Q8×C61—21no—
147C2×Q8×C61—21no—
148C2×Q8×C61—21no—
149C2×Q8×C61—21no—
150C2×Q8×C61—21no—
151C2×Q8×C61#4112yes—
152C2×D4×C61—24no—
153C2×D4×C61—21no—
154C2×D4×C61—21no—
155C2×D4×C61—21no—
156C2×D4×C61—42no—
157C2×D4×C61—42no—
158C2×D4×C61C2×D412yes—
159C2×D4×C61#4112yes—
160C2×D4×C61#4112yes—
161C22×C4×C61—24no—
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×C61—21no—
171C22×C4×C61—42no—
172C22×C4×C61—42no—
173C22×C4×C61—42no—
174C22×C4×C61—42no—
175C22×C4×C61—42no—
176C22×C4×C61—42no—
177C22×C4×C61—81no—
178C22×C4×C61—81no—
179C22×C4×C61C2×D411yescharacteristic
180C22×C4×C61C2×D411yescharacteristic
181C22×C4×C61C2×D411yescharacteristic
182C22×C4×C61C2×D411yescharacteristic
183C22×C4×C61C2×D411yescharacteristic
184C22×C4×C61C2411yescharacteristic
185C2×C22⋊D61—42no—
186C2×C22⋊D61—42no—
187C2×C22⋊D61—81no—
188C22×Dic61—21no—
189C22×Dic61—21no—
190C22×Dic61—21no—
191C2×D244—21no—
192C2×D244—21no—
193C2×D244—21no—
194C2×D244—21no—
195C2×D244—21no—
196C2×D244C2×D412yes—
197C2×C4×D61—42no—
198C2×C4×D61—42no—
199C2×C4×D61—81no—
200C4⋊C4×C61—21no—
201C4⋊C4×C61—21no—
202C4⋊C4×C61—21no—
203C4⋊C4×C61—21no—
204C22⋊C4×C61—22no—
205C22⋊C4×C61—22no—
206C22⋊C4×C61—42no—
207C22⋊C4×C61—42no—
208C22⋊C4×C61—81no—
209C42×C61—21no—
210C42×C61—21no—
211C42×C61—21no—
212C42×C61—21no—
213C22⋊Dic61—42no—
214#11758201—44no—
215#11758199—28no—
216#11758198—42no—
217#11758198—42no—
218#11758198—42no—
219#11758198—42no—
220C4⋊Dic61—21no—
221C4⋊Dic61—21no—
222C4⋊Dic61—21no—
223C4⋊Dic61—21no—
224C4⋊Dic61—21no—
225C4⋊Dic61—21no—
226C4⋊Dic61—42no—
227C4⋊Dic61—81no—
228#11758196—42no—
229C2×#92418—21no—
230C2×#92418—21no—
231C2×#92418—21no—
232C2×#92418—21no—
233C2×#92418—21no—
234C2×#92418—21no—
235C2×#92418—21no—
236C2×#92418—21no—
237C2×#92418—21no—
238C2×#92418—21no—
239C2×#92418—21no—
240C2×#92418C2×D412yes—
241C23×C61—22no—
242C23×C61—22no—
243C23×C61—22no—
244C23×C61—21no—
245C23×C61—21no—
246C23×C61—21no—
247C23×C61—21no—
248C23×C61—21no—
249C23×C61—21no—
250C23×C61—21no—
251C23×C61—41no—
252C23×C61—41no—
253C23×C61—41no—
254C23×C61—41no—
255C23×C61C22×D411yescharacteristic
256C22×D61—22no—
257C22×D61—41no—
258C22×D61—41no—
259C22×D61—41no—
260C22×D61—41no—
261C22×D61—41no—
262C22×D61—41no—
263Q8×C61—22no—
264Q8×C61—22no—
265Q8×C61—41no—
266Q8×C61—41no—
267D4×C61—22no—
268D4×C61—22no—
269D4×C61—22no—
270D4×C61—48no—
271D4×C61#12314yescomplemented
272C2×C4×C61—21no—
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—21no—
284C2×C4×C61—21no—
285C2×C4×C61—21no—
286C2×C4×C61—48no—
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—41no—
299C2×C4×C61—84no—
300C2×C4×C61—84no—
301C2×C4×C61#13512yes—
302C2×C4×C61AGL(1,ℤ/8)12yes—
303C2×C4×C61C22×D411yescharacteristic
304C2×C4×C61C2×#4111yescharacteristic
305C2×C4×C61C2×#4111yescharacteristic
306C2×C4×C61C2×#4111yescharacteristic
307C2×C4×C61H(5,𝔽2)11yescharacteristic
308C2×C4×C61H(5,𝔽2)11yescharacteristic
309C22⋊D61—84no—
310C2×Dic61—41no—
311C2×Dic61—41no—
312C2×Dic61—41no—
313C2×Dic61—41no—
314C2×Dic61—41no—
315C2×Dic61—41no—
316C2×Dic61—41no—
317C2×Dic61—41no—
318C2×Dic61—41no—
319D244—22no—
320D244—22no—
321D244—41no—
322D244—41no—
323C4×D61—84no—
324#92418—22no—
325#92418—41no—
326#92418—41no—
327#92418—41no—
328#24899—611nomaximal, Sylow
329C22×C61—24no—
330C22×C61—42no—
331C22×C61—42no—
332C22×C61—42no—
333C22×C61—42no—
334C22×C61—42no—
335C22×C61—42no—
336C22×C61—41no—
337C22×C61—41no—
338C22×C61—41no—
339C22×C61—41no—
340C22×C61—41no—
341C22×C61—41no—
342C22×C61—41no—
343C22×C61#52511yescharacteristic
344C22×C61D4211yescharacteristic
345C22×C61#54611yescharacteristic
346C22×C61C2×#13511yescharacteristic
347C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
348C22×C61#57611yescharacteristic
349C22×C61#57811yescharacteristic
350C2×D61—42no—
351C2×D61—42no—
352C2×D61—42no—
353C2×D61—81no—
354C2×D61—81no—
355C2×D61—81no—
356C2×D61—81no—
357C4×C61—22no—
358C4×C61—22no—
359C4×C61—41no—
360C4×C61—41no—
361C4×C61—42no—
362C4×C61—41no—
363C4×C61—81no—
364C4×C61—81no—
365C4×C61C2×#12311yescharacteristic
366C4×C61#53811yescharacteristic
367C4×C61#54611yescharacteristic
368C4×C61#55111yescharacteristic
369Dic61—81no—
370Dic61—81no—
371Dic61—81no—
372C2×#449—611no—
373C2×C4×D8—611no—
374#2422—611no—
375#2339D6111yescharacteristic, complemented
376#2095—611no—
377#2076—611no—
378#2055—611no—
379#2033—611no—
380#1933—611no—
381#1923—611no—
382#1879—611no—
383#1877—611no—
384#1862—611no—
385#1802—611no—
386#1788—611no—
387C2×C61—44no—
388C2×C61—81no—
389C2×C61#241811yescharacteristic
390C2×C61#310611yescharacteristic
391C2×C61#312411yescharacteristic
392C2×C61#326411yescharacteristic
393C2×C61#328311yescharacteristic
394C2×C61#329711yescharacteristic
395C2×C61#333011yescharacteristic
396D61—82no—
397C22×#41C2×D6111yescharacteristic
398C22×SD16—611no—
399C22×D8—611no—
400C2×#123—1221no—
401C2×#121—611no—
402C2×C4×D4—611no—
403C2×C4×D4C2×D6111yescharacteristic
404C2×C4×D4C2×D6111yescharacteristic
405#449—1224no—
406C4×D8—1224no—
407C2×#107—611no—
408C2×#107—611no—
409C2×C4⋊C8—611no—
410C2×#103—611no—
411C2×#103—611no—
412C2×#103—611no—
413C2×#102—611no—
414C2×#102—611no—
415C2×#102—611no—
416C2×#102—611no—
417C2×#102—611no—
418C2×C22⋊C8—611no—
419C2×C22⋊C8—611no—
420C2×C4×C8—611no—
421#397—1221no—
422#394—1221no—
423#391C2×D6111yescharacteristic
424#391C2×D6111yescharacteristic
425#390—611no—
426#389—611no—
427#386—21no—
428#386—21no—
429#385—1221no—
430#384—611no—
431#381—21no—
432#380—611no—
433#380C2×D6111yescharacteristic
434C4×C22⋊C4C2×D6111yescharacteristic
435C2×#95—21no—
436#340—611no—
437#340—611no—
438#340—611no—
439#340—611no—
440#336—611no—
441#336—611no—
442C61#2489911yescharacteristic, complemented, Sylow
443C2×#41—22no—
444C2×#41—22no—
445C2×#41—22no—
446C2×#41—22no—
447C2×#41—41no—
448C2×#41—41no—
449C22×Q8C22×D6111yescharacteristic
450C22×D4—21no—
451C22×D4—611no—
452C22×D4—1221no—
453C22×D4C22×D6111yescharacteristic
454C23×C4—21no—
455C23×C4—21no—
456C23×C4—21no—
457C23×C4—1221no—
458C23×C4C22×D6111yescharacteristic
459C2×SD16—1222no—
460C2×SD16—1222no—
461C2×SD16—2441no—
462C2×D8—614no—
463C2×D8—1222no—
464C2×D8—1222no—
465C22×C8—611no—
466C22×C8—611no—
467C22×C8—611no—
468C22×C8—611no—
469#123—2444no—
470#121—1222no—
471#121—2441no—
472C4×D4—22no—
473C4×D4—22no—
474C4×D4—41no—
475C4×D4—41no—
476C4×D4—1222no—
477C4×D4—2441no—
478C2×C4⋊C4—611no—
479C2×C4⋊C4—611no—
480C2×C4⋊C4—611no—
481C2×C4⋊C4—1221no—
482C2×C4⋊C4—1221no—
483C2×C4⋊C4—1221no—
484C2×C4⋊C4C22×D6111yescharacteristic
485C2×C4⋊C4C22×D6111yescharacteristic
486C2×C22⋊C4—21no—
487C2×C22⋊C4—21no—
488C2×C22⋊C4—21no—
489C2×C22⋊C4—1221no—
490C2×C22⋊C4—1221no—
491C2×C22⋊C4—1221no—
492C2×C22⋊C4—1221no—
493C2×C22⋊C4—1221no—
494C2×C22⋊C4C22⋊D6111yescharacteristic
495C2×C22⋊C4C22⋊D6111yescharacteristic
496C2×C42C22×D6111yescharacteristic
497C2×C42C22×D6111yescharacteristic
498#107—1222no—
499#107—2441no—
500C4⋊C8—2441no—
501#103—1222no—
502#103—1222no—
503#103—2441no—
504#102—1222no—
505#102—1222no—
506#102—1222no—
507#102—1222no—
508#102—2441no—
509C22⋊C8—1222no—
510C22⋊C8—2441no—
511C4×C8—1222no—
512#95—21no—
513#95—21no—
514#95—21no—
515#95—21no—
516#95—21no—
517#95—1221no—
518#95—1221no—
519#95C22⋊D6111yescharacteristic
520#95C22⋊D6111yescharacteristic
521C24—21no—
522C24—1221no—
523C24C2×C22⋊D6111yescharacteristic
524#41—44no—
525#41—44no—
526#41—44no—
527#41—44no—
528C2×Q8—21no—
529C2×Q8—21no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—21no—
533C2×Q8#1175822212yes—
534C2×D4—24no—
535C2×D4—21no—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—42no—
539C2×D4—42no—
540C2×D4—612no—
541C2×D4—1221no—
542C2×D4—1221no—
543C2×D4—1221no—
544C2×D4—1221no—
545C2×D4—1221no—
546C2×D4—4881no—
547C2×D4—2442no—
548C2×D4—2442no—
549C2×D4#1175822212yes—
550C2×D4D4×D6112yes—
551C2×D4#1175822412yes—
552C22×C4—24no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—42no—
563C22×C4—42no—
564C22×C4—42no—
565C22×C4—42no—
566C22×C4—42no—
567C22×C4—42no—
568C22×C4—81no—
569C22×C4—81no—
570C22×C4—1221no—
571C22×C4—1221no—
572C22×C4—1221no—
573C22×C4—4881no—
574C22×C4—2442no—
575C22×C4—2442no—
576C22×C4C2×C22⋊D6111yescharacteristic
577C22×C4C2×C22⋊D6111yescharacteristic
578C22×C4C2×C22⋊D6111yescharacteristic
579C22×C4C2×C22⋊D6111yescharacteristic
580C22×C4C2×C22⋊D6111yescharacteristic
581C22×C4C23×D6111yescharacteristic
582SD16—2444no—
583D8—1228no—
584C2×C8—612no—
585C2×C8—1221no—
586C2×C8—1221no—
587C2×C8—1221no—
588C2×C8—1221no—
589C2×C8—1221no—
590C2×C8—1221no—
591C2×C8—1221no—
592C2×C8—1221no—
593C2×C8—1221no—
594C2×C8—1221no—
595C2×C8—1221no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—1221no—
601C4⋊C4—1221no—
602C4⋊C4—1221no—
603C4⋊C4—1221no—
604C4⋊C4—1221no—
605C4⋊C4—1221no—
606C4⋊C4—4881no—
607C4⋊C4—2442no—
608C4⋊C4—2442no—
609C22⋊C4—22no—
610C22⋊C4—22no—
611C22⋊C4—42no—
612C22⋊C4—42no—
613C22⋊C4—81no—
614C22⋊C4—2442no—
615C22⋊C4—2442no—
616C22⋊C4—2442no—
617C22⋊C4—2442no—
618C22⋊C4—2442no—
619C42—21no—
620C42—21no—
621C42—21no—
622C42—21no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—1222no—
638C23—2441no—
639C23—2441no—
640C23—2441no—
641C23—2441no—
642C23—2441no—
643C23—2441no—
644C23C22×C22⋊D6111yescharacteristic
645Q8—22no—
646Q8—22no—
647Q8—41no—
648Q8—41no—
649D4—22no—
650D4—22no—
651D4—22no—
652D4—48no—
653D4—1222no—
654D4—1222no—
655D4—4884no—
656D4—2441no—
657D4—2441no—
658D4#1451975914yescomplemented
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—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—48no—
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—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—84no—
687C2×C4—84no—
688C2×C4—4884no—
689C2×C4—2441no—
690C2×C4—2441no—
691C2×C4—2441no—
692C2×C4—2441no—
693C2×C4—2441no—
694C2×C4—2441no—
695C2×C4—2441no—
696C2×C4—2441no—
697C2×C4—2441no—
698C2×C4#1451979712yes—
699C2×C4#1451980212yes—
700C2×C4C2×D4×D6111yescharacteristic
701C2×C4C2×#1175822411yescharacteristic
702C2×C4C2×#1175822211yescharacteristic
703C2×C4C2×#1175822211yescharacteristic
704C2×C4#1451982211yescharacteristic
705C2×C4#1451982211yescharacteristic
706C8—1222no—
707C8—2441no—
708C8—2441no—
709C8—2441no—
710C22—24no—
711C22—42no—
712C22—42no—
713C22—42no—
714C22—42no—
715C22—42no—
716C22—42no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22—41no—
721C22—41no—
722C22—41no—
723C22—41no—
724C22—4881no—
725C22—4881no—
726C22—4881no—
727C22—4881no—
728C22—2442no—
729C22—2442no—
730C22—2442no—
731C22#1684027311yescharacteristic
732C22D4×C22⋊D6111yescharacteristic
733C22#1684040611yescharacteristic
734C22C2×#1451979711yescharacteristic
735C22C2×#1451980211yescharacteristic
736C22#1684056511yescharacteristic
737C22#1684057711yescharacteristic
738C4—22no—
739C4—22no—
740C4—41no—
741C4—42no—
742C4—41no—
743C4—41no—
744C4—81no—
745C4—81no—
746C4—4881no—
747C4—4881no—
748C4—4881no—
749C4C2×#1451975911yescharacteristic
750C4#1684035011yescharacteristic
751C4#1684040211yescharacteristic
752C4#1684043811yescharacteristic
753C2—44no—
754C2—81no—
755C2—4882no—
756C2#2144928111yescharacteristic
757C2#2145587911yescharacteristic
758C2#2145608111yescharacteristic
759C2#2145730011yescharacteristic
760C2#2145753711yescharacteristic
761C2#2145766911yescharacteristic
762C2#2145812411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2339C2
socleC23×C61C22×D4
prime radicalC2×#16839907C2
hypercenter#2339D61
hypocenterC61#24899
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2339

Complements

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

NH ≅ G/Ntype
2. C2×C4×#11758199C2semidirect
3. #21449333C2semidirect
4. #21447357C2semidirect
5. #21447250C2semidirect
6. #21447134C2semidirect
7. #21447001C2semidirect
8. #21446498C2semidirect
9. #21446427C2semidirect
10. #21446167C2semidirect
11. #21446156C2semidirect
12. #21446066C2semidirect
13. #21445819C2semidirect
14. #21445759C2semidirect
15. C61×#2339C2semidirect
271. D4×C61#123semidirect
375. #2339D61semidirect
442. C61#24899semidirect
658. D4#14519759semidirect

Maximal subgroups

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

subgroupindex
C2×#168399072
C2×C4×#117581992
#214493332
#214473572
#214472502
#214471342
#214470012
#214464982
#214464272
#214461672
#214461562
#214460662
#214458192
#214457592
C61×#23392
#2489961