Finite Group Databasebeta

← #29723798

Subgroups — #29723798

Order 15616.

1042 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839907C211yesmaximal, characteristic
2C2×C4×#11758201C211yesmaximal, characteristic, complemented
3#21449333C211yesmaximal, characteristic, complemented
4#21447352C211yesmaximal, characteristic, complemented
5#21447255C211yesmaximal, characteristic, complemented
6#21447129C211yesmaximal, characteristic, complemented
7#21447008C211yesmaximal, characteristic, complemented
8#21446505C211yesmaximal, characteristic, complemented
9#21446427C211yesmaximal, characteristic, complemented
10#21446174C211yesmaximal, characteristic, complemented
11#21446170C211yesmaximal, characteristic, complemented
12#21446087C211yesmaximal, characteristic, complemented
13#21445824C211yesmaximal, characteristic, complemented
14#21445759C211yesmaximal, characteristic, complemented
15C61×#2341C211yesmaximal, characteristic, complemented
16C22×#11758201C2211yescharacteristic
17C22×#11758199C2211yescharacteristic
18C2×#14519759—21no—
19C2×#14519751C2211yescharacteristic
20C2×C4×D244C2211yescharacteristic
21#16839907—24no—
22C4×#11758201—24no—
23C2×#14519708C2211yescharacteristic
24C2×#14519708C2211yescharacteristic
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×Q8×C61C2211yescharacteristic
52C2×C4×Q8×C61C2211yescharacteristic
53C61×#390—21no—
54C61×#390—21no—
55C61×#390C2211yescharacteristic
56C61×#390C2211yescharacteristic
57C61×#380—21no—
58C61×#380C2211yescharacteristic
59C4×C22⋊C4×C61—21no—
60C4×C22⋊C4×C61C2211yescharacteristic
61C22×D244C2311yescharacteristic
62C22×C22⋊D61—21no—
63C22×C4×D61—21no—
64C2×#11758201—22no—
65C2×#11758201—22no—
66C2×#11758201D414yes—
67C2×#11758199—22no—
68C2×#11758199—22no—
69C2×#11758199—41no—
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#14519708—22no—
91#14519708—41no—
92C4⋊#92418—41no—
93#14519701—22no—
94#14519701—22no—
95#14519701—22no—
96#14519698—22no—
97#14519698—22no—
98#14519698—41no—
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×C61C2311yescharacteristic
117C4×Q8×C61—22no—
118C4×Q8×C61—22no—
119C4×Q8×C61—41no—
120C4×Q8×C61—41no—
121C2×C4⋊C4×C61—21no—
122C2×C4⋊C4×C61—21no—
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×C61—21no—
129C2×C22⋊C4×C61—21no—
130C2×C22⋊C4×C61D411yescharacteristic
131C2×C22⋊C4×C61D411yescharacteristic
132C2×C42×C61—21no—
133C2×C42×C61—21no—
134C2×C42×C61C2311yescharacteristic
135C2×C42×C61C2311yescharacteristic
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×C61C2×D412yes—
150C2×Q8×C61#4112yes—
151C2×Q8×C61#4112yes—
152C2×D4×C61—24no—
153C2×D4×C61—21no—
154C2×D4×C61—21no—
155C2×D4×C61—21no—
156C2×D4×C61—21no—
157C2×D4×C61—21no—
158C2×D4×C61—42no—
159C2×D4×C61—42no—
160C2×D4×C61#4112yes—
161C22×C4×C61—21no—
162C22×C4×C61—24no—
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×C61C2×D411yescharacteristic
174C22×C4×C61C2×D411yescharacteristic
175C22×C4×C61C2×D411yescharacteristic
176C22×C4×C61C2×D411yescharacteristic
177C22×C4×C61C2×D411yescharacteristic
178C22×C4×C61C2411yescharacteristic
179C2×C22⋊D61—42no—
180C2×C22⋊D61—42no—
181C2×C22⋊D61—81no—
182C22×Dic61—21no—
183C22×Dic61—21no—
184C22×Dic61—21no—
185C2×D244—21no—
186C2×D244—21no—
187C2×D244—21no—
188C2×D244—21no—
189C2×D244—21no—
190C2×D244C2×D412yes—
191C2×C4×D61—42no—
192C2×C4×D61—42no—
193C2×C4×D61—81no—
194C4⋊C4×C61—21no—
195C4⋊C4×C61—21no—
196C4⋊C4×C61—21no—
197C4⋊C4×C61—21no—
198C4⋊C4×C61—42no—
199C4⋊C4×C61—42no—
200C22⋊C4×C61—22no—
201C22⋊C4×C61—22no—
202C22⋊C4×C61—42no—
203C22⋊C4×C61—42no—
204C22⋊C4×C61—81no—
205C22⋊C4×C61—81no—
206C22⋊C4×C61—81no—
207C42×C61—21no—
208C42×C61—21no—
209C42×C61—21no—
210C42×C61—21no—
211C42×C61—42no—
212C42×C61—42no—
213C22⋊Dic61—42no—
214#11758201—28no—
215#11758199—44no—
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—21no—
242C23×C61—22no—
243C23×C61—21no—
244C23×C61—21no—
245C23×C61—21no—
246C23×C61—21no—
247C23×C61—21no—
248C23×C61—21no—
249C23×C61—41no—
250C23×C61—41no—
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—22no—
266Q8×C61#12314yescomplemented
267D4×C61—22no—
268D4×C61—22no—
269D4×C61—48no—
270D4×C61—41no—
271D4×C61—41no—
272C2×C4×C61—22no—
273C2×C4×C61—21no—
274C2×C4×C61—22no—
275C2×C4×C61—21no—
276C2×C4×C61—22no—
277C2×C4×C61—21no—
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—21no—
287C2×C4×C61—21no—
288C2×C4×C61—48no—
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#13512yes—
300C2×C4×C61AGL(1,ℤ/8)12yes—
301C2×C4×C61C22×D411yescharacteristic
302C2×C4×C61C2×#4111yescharacteristic
303C2×C4×C61C2×#4111yescharacteristic
304C2×C4×C61C2×#4111yescharacteristic
305C2×C4×C61H(5,𝔽2)11yescharacteristic
306C2×C4×C61H(5,𝔽2)11yescharacteristic
307C22⋊D61—84no—
308C2×Dic61—41no—
309C2×Dic61—41no—
310C2×Dic61—41no—
311C2×Dic61—41no—
312C2×Dic61—41no—
313C2×Dic61—41no—
314C2×Dic61—41no—
315C2×Dic61—41no—
316C2×Dic61—41no—
317D244—22no—
318D244—22no—
319D244—41no—
320D244—41no—
321C4×D61—84no—
322#92418—22no—
323#92418—41no—
324#92418—41no—
325#92418—41no—
326#24896—611nomaximal, Sylow
327C22×C61—41no—
328C22×C61—41no—
329C22×C61—42no—
330C22×C61—41no—
331C22×C61—42no—
332C22×C61—42no—
333C22×C61—41no—
334C22×C61—41no—
335C22×C61—41no—
336C22×C61—41no—
337C22×C61—81no—
338C22×C61—81no—
339C22×C61—81no—
340C22×C61—81no—
341C22×C61#52511yescharacteristic
342C22×C61D4211yescharacteristic
343C22×C61#54611yescharacteristic
344C22×C61C2×#13511yescharacteristic
345C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
346C22×C61#57711yescharacteristic
347C22×C61#57711yescharacteristic
348C2×D61—42no—
349C2×D61—42no—
350C2×D61—42no—
351C2×D61—81no—
352C2×D61—81no—
353C2×D61—81no—
354C2×D61—81no—
355C4×C61—24no—
356C4×C61—22no—
357C4×C61—22no—
358C4×C61—41no—
359C4×C61—41no—
360C4×C61—41no—
361C4×C61—81no—
362C4×C61—81no—
363C4×C61C2×#12311yescharacteristic
364C4×C61#53811yescharacteristic
365C4×C61#54611yescharacteristic
366C4×C61#55111yescharacteristic
367Dic61—81no—
368Dic61—81no—
369Dic61—81no—
370C2×#449—611no—
371C2×C4×SD16—611no—
372#2422—611no—
373#2341D6111yescharacteristic, complemented
374#2094—611no—
375#2077—611no—
376#2054—611no—
377#2034—611no—
378#1934—611no—
379#1923—611no—
380#1880—611no—
381#1879—611no—
382#1865—611no—
383#1803—611no—
384#1788—611no—
385C2×C61—81no—
386C2×C61—82no—
387C2×C61#241811yescharacteristic
388C2×C61#310611yescharacteristic
389C2×C61#312511yescharacteristic
390C2×C61#326511yescharacteristic
391C2×C61#328411yescharacteristic
392C2×C61#330111yescharacteristic
393C2×C61#333211yescharacteristic
394D61—82no—
395C22×#41C2×D6111yescharacteristic
396C22×SD16—611no—
397C22×D8—611no—
398C2×#123—1221no—
399C2×#121—611no—
400C2×C4×Q8C2×D6111yescharacteristic
401C2×C4×Q8C2×D6111yescharacteristic
402C2×C4×D4—611no—
403#449—1224no—
404C4×SD16—1224no—
405C2×#106—611no—
406C2×#106—611no—
407C2×C4⋊C8—611no—
408C2×#103—611no—
409C2×#103—611no—
410C2×#103—611no—
411C2×#102—611no—
412C2×#102—611no—
413C2×#102—611no—
414C2×#102—611no—
415C2×#102—611no—
416C2×C22⋊C8—611no—
417C2×C22⋊C8—611no—
418C2×C4×C8—611no—
419#397—1221no—
420#394—1221no—
421#390—21no—
422#390—21no—
423#390—611no—
424#390C2×D6111yescharacteristic
425#390C2×D6111yescharacteristic
426#389—611no—
427#385—1221no—
428#384—611no—
429#380—21no—
430#380—611no—
431#380C2×D6111yescharacteristic
432C4×C22⋊C4—21no—
433C4×C22⋊C4C2×D6111yescharacteristic
434#340—611no—
435#340—611no—
436#340—611no—
437#340—611no—
438#336—611no—
439#336—611no—
440C61#2489611yescharacteristic, complemented, Sylow
441C2×#41—22no—
442C2×#41—22no—
443C2×#41—22no—
444C2×#41—22no—
445C2×#41—41no—
446C2×#41—41no—
447C22×Q8C22×D6111yescharacteristic
448C22×D4—21no—
449C22×D4—611no—
450C22×D4—1221no—
451C22×D4C22×D6111yescharacteristic
452C23×C4—21no—
453C23×C4—1221no—
454C23×C4C22×D6111yescharacteristic
455C2×SD16—614no—
456C2×SD16—1222no—
457C2×SD16—1222no—
458C2×D8—1222no—
459C2×D8—1222no—
460C2×D8—2441no—
461C22×C8—611no—
462C22×C8—611no—
463C22×C8—611no—
464C22×C8—611no—
465#123—2444no—
466#121—1222no—
467#121—2441no—
468C4×Q8—22no—
469C4×Q8—22no—
470C4×Q8—41no—
471C4×Q8—41no—
472C4×D4—1222no—
473C4×D4—2441no—
474C2×C4⋊C4—21no—
475C2×C4⋊C4—21no—
476C2×C4⋊C4—611no—
477C2×C4⋊C4—611no—
478C2×C4⋊C4—611no—
479C2×C4⋊C4—1221no—
480C2×C4⋊C4—1221no—
481C2×C4⋊C4—1221no—
482C2×C4⋊C4C22×D6111yescharacteristic
483C2×C4⋊C4C22×D6111yescharacteristic
484C2×C22⋊C4—21no—
485C2×C22⋊C4—21no—
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×C42—21no—
497C2×C42—21no—
498C2×C42C22×D6111yescharacteristic
499C2×C42C22×D6111yescharacteristic
500#106—1222no—
501#106—2441no—
502C4⋊C8—2441no—
503#103—1222no—
504#103—1222no—
505#103—1222no—
506#102—1222no—
507#102—1222no—
508#102—1222no—
509#102—2441no—
510#102—2441no—
511C22⋊C8—1222no—
512C22⋊C8—2441no—
513C4×C8—1222no—
514#95—21no—
515#95—1221no—
516#95—1221no—
517#95C22⋊D6111yescharacteristic
518#95C22⋊D6111yescharacteristic
519C24—21no—
520C24—1221no—
521C24C2×C22⋊D6111yescharacteristic
522#41—44no—
523#41—44no—
524#41—44no—
525#41—44no—
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8—21no—
529C2×Q8#1175822212yes—
530C2×Q8D4×D6112yes—
531C2×Q8#1175822412yes—
532C2×D4—24no—
533C2×D4—21no—
534C2×D4—21no—
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—
550C22×C4—21no—
551C22×C4—24no—
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—42no—
561C22×C4—42no—
562C22×C4—1221no—
563C22×C4—1221no—
564C22×C4—1221no—
565C22×C4—4881no—
566C22×C4—2442no—
567C22×C4—2442no—
568C22×C4C2×C22⋊D6111yescharacteristic
569C22×C4C2×C22⋊D6111yescharacteristic
570C22×C4C2×C22⋊D6111yescharacteristic
571C22×C4C2×C22⋊D6111yescharacteristic
572C22×C4C2×C22⋊D6111yescharacteristic
573C22×C4C23×D6111yescharacteristic
574SD16—1228no—
575D8—2444no—
576C2×C8—612no—
577C2×C8—1221no—
578C2×C8—1221no—
579C2×C8—1221no—
580C2×C8—1221no—
581C2×C8—1221no—
582C2×C8—1221no—
583C2×C8—1221no—
584C2×C8—1221no—
585C2×C8—1221no—
586C2×C8—1221no—
587C2×C8—1221no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—42no—
593C4⋊C4—42no—
594C4⋊C4—1221no—
595C4⋊C4—1221no—
596C4⋊C4—1221no—
597C4⋊C4—1221no—
598C4⋊C4—1221no—
599C4⋊C4—1221no—
600C4⋊C4—4881no—
601C4⋊C4—2442no—
602C4⋊C4—2442no—
603C22⋊C4—22no—
604C22⋊C4—22no—
605C22⋊C4—42no—
606C22⋊C4—42no—
607C22⋊C4—81no—
608C22⋊C4—81no—
609C22⋊C4—81no—
610C22⋊C4—2442no—
611C22⋊C4—2442no—
612C22⋊C4—2442no—
613C22⋊C4—2442no—
614C22⋊C4—2442no—
615C42—21no—
616C42—21no—
617C42—21no—
618C42—21no—
619C42—42no—
620C42—42no—
621C23—21no—
622C23—22no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—1222no—
636C23—2441no—
637C23—2441no—
638C23—2441no—
639C23—2441no—
640C23—2441no—
641C23—2441no—
642C23C22×C22⋊D6111yescharacteristic
643Q8—22no—
644Q8—22no—
645Q8—22no—
646Q8#1451975914yescomplemented
647D4—22no—
648D4—22no—
649D4—48no—
650D4—41no—
651D4—41no—
652D4—1222no—
653D4—1222no—
654D4—4884no—
655D4—2441no—
656D4—2441no—
657C2×C4—22no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—22no—
662C2×C4—21no—
663C2×C4—22no—
664C2×C4—21no—
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—4884no—
685C2×C4—2441no—
686C2×C4—2441no—
687C2×C4—2441no—
688C2×C4—2441no—
689C2×C4—2441no—
690C2×C4—2441no—
691C2×C4—2441no—
692C2×C4—2441no—
693C2×C4—2441no—
694C2×C4#1451979712yes—
695C2×C4#1451980212yes—
696C2×C4C2×D4×D6111yescharacteristic
697C2×C4C2×#1175822411yescharacteristic
698C2×C4C2×#1175822211yescharacteristic
699C2×C4C2×#1175822211yescharacteristic
700C2×C4#1451982211yescharacteristic
701C2×C4#1451982211yescharacteristic
702C8—1222no—
703C8—2441no—
704C8—2441no—
705C8—2441no—
706C22—41no—
707C22—42no—
708C22—41no—
709C22—42no—
710C22—41no—
711C22—41no—
712C22—41no—
713C22—41no—
714C22—42no—
715C22—41no—
716C22—81no—
717C22—81no—
718C22—81no—
719C22—81no—
720C22—4881no—
721C22—4881no—
722C22—4881no—
723C22—4881no—
724C22—2442no—
725C22—2442no—
726C22—2442no—
727C22#1684027311yescharacteristic
728C22D4×C22⋊D6111yescharacteristic
729C22#1684040611yescharacteristic
730C22C2×#1451979711yescharacteristic
731C22C2×#1451980211yescharacteristic
732C22#1684057011yescharacteristic
733C22#1684057311yescharacteristic
734C4—22no—
735C4—24no—
736C4—22no—
737C4—41no—
738C4—41no—
739C4—41no—
740C4—81no—
741C4—81no—
742C4—4881no—
743C4—4881no—
744C4—4881no—
745C4C2×#1451975911yescharacteristic
746C4#1684035011yescharacteristic
747C4#1684040211yescharacteristic
748C4#1684043811yescharacteristic
749C2—81no—
750C2—82no—
751C2—4882no—
752C2#2144928111yescharacteristic
753C2#2145587911yescharacteristic
754C2#2145609611yescharacteristic
755C2#2145731511yescharacteristic
756C2#2145754911yescharacteristic
757C2#2145772111yescharacteristic
758C2#2145814611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2341C2
socleC23×C61C22×D4
prime radicalC2×#16839907C2
hypercenter#2341D61
hypocenterC61#24896
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2341

Complements

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

NH ≅ G/Ntype
2. C2×C4×#11758201C2semidirect
3. #21449333C2semidirect
4. #21447352C2semidirect
5. #21447255C2semidirect
6. #21447129C2semidirect
7. #21447008C2semidirect
8. #21446505C2semidirect
9. #21446427C2semidirect
10. #21446174C2semidirect
11. #21446170C2semidirect
12. #21446087C2semidirect
13. #21445824C2semidirect
14. #21445759C2semidirect
15. C61×#2341C2semidirect
266. Q8×C61#123semidirect
373. #2341D61semidirect
440. C61#24896semidirect
646. Q8#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×#117582012
#214493332
#214473522
#214472552
#214471292
#214470082
#214465052
#214464272
#214461742
#214461702
#214460872
#214458242
#214457592
C61×#23412
#2489661