Finite Group Databasebeta

← #29696970

Subgroups — #29696970

Order 15616.

1018 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×#16839813C211yesmaximal, characteristic, complemented
2C2×#16839728C211yesmaximal, characteristic
3#21448305C211yesmaximal, characteristic
4#21446430C211yesmaximal, characteristic, complemented
5#21446425C211yesmaximal, characteristic, complemented
6#21446425C211yesmaximal, characteristic, complemented
7#21446423C211yesmaximal, characteristic, complemented
8#21446001C211yesmaximal, characteristic, complemented
9#21445997C211yesmaximal, characteristic, complemented
10#21445886C211yesmaximal, characteristic, complemented
11#21445802C211yesmaximal, characteristic, complemented
12#21445730C211yesmaximal, characteristic
13#21445603C211yesmaximal, characteristic, complemented
14#21445586C211yesmaximal, characteristic, complemented
15C8×C22⋊C4×C61C211yesmaximal, characteristic, complemented
16C22×#11758222C2211yescharacteristic
17C22×#11758194C2211yescharacteristic
18C2×#14519734C2211yescharacteristic
19C2×C42×D61C2211yescharacteristic
20#16839813—24no—
21C2×#14519706C2211yescharacteristic
22C2×#14519706C2211yescharacteristic
23C2×#14519706C2211yescharacteristic
24C2×#14519706C2211yescharacteristic
25#16839728—24no—
26C2×C22⋊#92418C2211yescharacteristic
27C2×#14519689C2211yescharacteristic
28C2×#14519689C2211yescharacteristic
29C2×#14519689C2211yescharacteristic
30C2×#14519689C2211yescharacteristic
31C2×#14519689C2211yescharacteristic
32C2×#14519689C2211yescharacteristic
33C2×#14519689C2211yescharacteristic
34C2×#14519689C2211yescharacteristic
35C2×#14519688C2211yescharacteristic
36C2×C4×#92418C2211yescharacteristic
37#16839666C411yescharacteristic
38#16839666C411yescharacteristic
39#16839662C411yescharacteristic
40#16839662C411yescharacteristic
41#16839640C411yescharacteristic
42#16839640C411yescharacteristic
43#16839638C411yescharacteristic
44#16839638C411yescharacteristic
45C4×#11758198C2211yescharacteristic
46C4×#11758198C2211yescharacteristic
47C4×C22⋊Dic61C2211yescharacteristic
48#16839517C2211yescharacteristic
49#16839517C2211yescharacteristic
50#16839516C2211yescharacteristic
51#16839516C2211yescharacteristic
52#16839516C2211yescharacteristic
53#16839516C2211yescharacteristic
54C23×C8×C61C2211yescharacteristic
55C2×C22⋊C8×C61C2211yescharacteristic
56C2×C4×C8×C61C2211yescharacteristic
57C2×C4×C8×C61C2211yescharacteristic
58C4×C22⋊C4×C61C2211yescharacteristic
59C61×#336C2211yescharacteristic
60C61×#336C2211yescharacteristic
61C2×#11758222—22no—
62C2×#11758222—22no—
63C2×#11758222—22no—
64C2×#11758222—22no—
65C2×#11758222—41no—
66C2×#11758222—41no—
67C22×Dic122C2×C411yescharacteristic
68C22×D244C2×C411yescharacteristic
69C22×C22⋊D61C2×C411yescharacteristic
70C22×C22⋊D61C2×C411yescharacteristic
71C22×C4×D61C2×C411yescharacteristic
72C22×C4×D61C2×C411yescharacteristic
73C22×C4×D61C2311yescharacteristic
74C22×C4×D61C2311yescharacteristic
75C2×#11758194—22no—
76C2×#11758194—22no—
77C2×#11758194—41no—
78C22×#92418C2311yescharacteristic
79C22×#92418C2311yescharacteristic
80C22×#92418C2311yescharacteristic
81C22×#92418C2311yescharacteristic
82#14519734—41no—
83#14519734—41no—
84C2×#11758196C2×C411yescharacteristic
85C2×#11758196C2×C411yescharacteristic
86C2×C22⋊Dic61C2×C411yescharacteristic
87C2×C22⋊Dic61C2×C411yescharacteristic
88C2×#11758198C2×C411yescharacteristic
89C2×#11758198C2×C411yescharacteristic
90C2×#11758198C2×C411yescharacteristic
91C2×#11758198C2×C411yescharacteristic
92C2×#11758198C2×C411yescharacteristic
93C2×#11758198C2×C411yescharacteristic
94C2×C4×Dic61C2×C411yescharacteristic
95C2×C4×Dic61C2×C411yescharacteristic
96C2×C4×Dic61C2311yescharacteristic
97C2×C4×Dic61C2311yescharacteristic
98C42×D61—22no—
99C42×D61—22no—
100#14519706—22no—
101#14519706—22no—
102#14519706—41no—
103#14519706—41no—
104C22⋊#92418—22no—
105#14519689—22no—
106#14519689—22no—
107#14519689—22no—
108#14519689—22no—
109#14519689—22no—
110#14519689—41no—
111#14519689—41no—
112#14519689D414yes—
113#14519688—41no—
114C4×#92418—22no—
115#14519684C2×C411yescharacteristic
116#14519684C2×C411yescharacteristic
117#14519684C2×C411yescharacteristic
118#14519684C2×C411yescharacteristic
119#14519684C2×C411yescharacteristic
120#14519684C2×C411yescharacteristic
121C23×C4×C61C2311yescharacteristic
122C22×C8×C61—22no—
123C22×C8×C61—22no—
124C22×C8×C61—41no—
125C22×C8×C61C2311yescharacteristic
126C22×C8×C61C2311yescharacteristic
127C22×C8×C61C2311yescharacteristic
128C22×C8×C61C2311yescharacteristic
129C2×C22⋊C4×C61C2×C411yescharacteristic
130C2×C22⋊C4×C61C2×C411yescharacteristic
131C2×C42×C61C2311yescharacteristic
132C2×C42×C61C2311yescharacteristic
133C22⋊C8×C61—22no—
134C4×C8×C61—22no—
135C4×C8×C61—41no—
136#95×C61C2×C411yescharacteristic
137#95×C61C2×C411yescharacteristic
138C24×C61C22×C411yescharacteristic
139C23×D61C22×C411yescharacteristic
140C23×D61C22×C411yescharacteristic
141C22×C4×C61—21no—
142C22×C4×C61—21no—
143C22×C4×C61—21no—
144C22×C4×C61—21no—
145C22×C4×C61C22×C411yescharacteristic
146C22×C4×C61C22×C411yescharacteristic
147C22×C4×C61C22×C411yescharacteristic
148C22×C4×C61C22×C411yescharacteristic
149C22×C4×C61C22×C411yescharacteristic
150C22×C4×C61#4112yes—
151C22×C4×C61#4112yes—
152C22×C4×C61C2411yescharacteristic
153C2×C22⋊D61—22no—
154C2×C22⋊D61—22no—
155C2×C22⋊D61—22no—
156C2×C22⋊D61—22no—
157C2×C22⋊D61—41no—
158C2×C22⋊D61—41no—
159C22×Dic61C22×C411yescharacteristic
160C22×Dic61C22×C411yescharacteristic
161C22×Dic61C22×C411yescharacteristic
162C22×Dic61C22×C411yescharacteristic
163C22×Dic61C22×C411yescharacteristic
164C22×Dic61C22×C411yescharacteristic
165#11758222—44no—
166#11758222—44no—
167#11758222—44no—
168#11758222—44no—
169C2×D244—22no—
170C2×D244—22no—
171C2×D244—41no—
172C2×C4×D61—22no—
173C2×C4×D61—22no—
174C2×C4×D61—21no—
175C2×C4×D61—21no—
176C2×C4×D61—21no—
177C2×C4×D61—21no—
178C2×C4×D61—22no—
179C2×C4×D61—22no—
180C2×C4×D61—22no—
181C2×C4×D61—21no—
182C2×C4×D61—21no—
183C2×C4×D61—21no—
184C2×C4×D61—21no—
185C2×C4×D61—21no—
186C2×C4×D61—21no—
187C2×C4×D61—41no—
188C2×C4×D61C2×D412yes—
189C2×C4×D61#4112yes—
190C2×Dic122—22no—
191C2×Dic122—22no—
192C2×Dic122—41no—
193C2×C8×C61—21no—
194C2×C8×C61—21no—
195C2×C8×C61—21no—
196C2×C8×C61—21no—
197C2×C8×C61—21no—
198C2×C8×C61—21no—
199C2×C8×C61—21no—
200C2×C8×C61—21no—
201C2×C8×C61—21no—
202C2×C8×C61—21no—
203C2×C8×C61—21no—
204C2×C8×C61—44no—
205C2×C8×C61C2×D412yes—
206C22⋊C4×C61—22no—
207C22⋊C4×C61—22no—
208C42×C61—21no—
209C42×C61—21no—
210C42×C61—21no—
211C42×C61—21no—
212C22⋊Dic61—22no—
213C22⋊Dic61—41no—
214#11758198—22no—
215#11758198—22no—
216#11758198—22no—
217#11758198—41no—
218#11758198—41no—
219#11758198—41no—
220#11758196—41no—
221#11758196—41no—
222C4×Dic61—21no—
223C4×Dic61—21no—
224C4×Dic61—21no—
225C4×Dic61—21no—
226C4×Dic61—22no—
227C4×Dic61—22no—
228#11758194—44no—
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—21no—
243C23×C61—21no—
244C23×C61—21no—
245C23×C61—21no—
246C23×C61—21no—
247C23×C61#11712yes—
248C23×C61C23×C411yescharacteristic
249C22×D61—21no—
250C22×D61—21no—
251C22×D61—21no—
252C22×D61—21no—
253C22×D61—21no—
254C22×D61—21no—
255C22×D61—21no—
256C22×D61—21no—
257C22×D61—21no—
258C22×D61—21no—
259C22×D61—21no—
260C22×D61—21no—
261C22×D61—21no—
262C22×D61C4×D412yes—
263C2×C4×C61—21no—
264C2×C4×C61—21no—
265C2×C4×C61—21no—
266C2×C4×C61—21no—
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—21no—
278C2×C4×C61—21no—
279C2×C4×C61#11712yes—
280C2×C4×C61#13112yes—
281C2×C4×C61#13112yes—
282C2×C4×C61C22×D411yescharacteristic
283C2×C4×C61C2×#4111yescharacteristic
284C2×C4×C61C2×#4111yescharacteristic
285C2×C4×C61C2×#4111yescharacteristic
286C2×C4×C61H(5,𝔽2)11yescharacteristic
287C2×C4×C61H(5,𝔽2)11yescharacteristic
288C22⋊D61—44no—
289C22⋊D61—44no—
290C2×Dic61—21no—
291C2×Dic61—21no—
292C2×Dic61—21no—
293C2×Dic61—21no—
294C2×Dic61—21no—
295C2×Dic61—21no—
296C2×Dic61—21no—
297C2×Dic61—21no—
298C2×Dic61—21no—
299C2×Dic61—21no—
300C2×Dic61—21no—
301C2×Dic61—21no—
302C2×Dic61—21no—
303C2×Dic61—21no—
304C2×Dic61—21no—
305C2×Dic61—21no—
306C2×Dic61C4×D412yes—
307C2×Dic61#13112yes—
308D244—44no—
309C4×D61—28no—
310C4×D61—22no—
311C4×D61—22no—
312C4×D61—22no—
313C4×D61—22no—
314C4×D61—44no—
315C4×D61—41no—
316C4×D61—41no—
317C4×D61—41no—
318C4×D61—41no—
319Dic122—44no—
320C8×C61—22no—
321C8×C61—41no—
322C8×C61—41no—
323C8×C61—41no—
324#92418—22no—
325#92418—41no—
326#92418—41no—
327#92418—41no—
328#22556—611nomaximal, Sylow
329C22×C61—22no—
330C22×C61—22no—
331C22×C61—22no—
332C22×C61—41no—
333C22×C61—41no—
334C22×C61—41no—
335C22×C61—41no—
336C22×C61C2×#11711yescharacteristic
337C22×C61C2×C4×D411yescharacteristic
338C22×C61#51811yescharacteristic
339C22×C61C2×#13111yescharacteristic
340C22×C61C2×#13111yescharacteristic
341C22×C61C2×#13111yescharacteristic
342C22×C61#56811yescharacteristic
343C2×D61—22no—
344C2×D61—22no—
345C2×D61—22no—
346C2×D61—41no—
347C2×D61—41no—
348C2×D61—41no—
349C2×D61—41no—
350C2×D61—41no—
351C2×D61—41no—
352C2×D61—41no—
353C2×D61—41no—
354C2×D61—41no—
355C2×D61—41no—
356C2×D61—41no—
357C4×C61—22no—
358C4×C61—22no—
359C4×C61—22no—
360C4×C61—41no—
361C4×C61—41no—
362C4×C61#54611yescharacteristic
363C4×C61#54611yescharacteristic
364C4×C61#55111yescharacteristic
365C4×C61#55111yescharacteristic
366Dic61—22no—
367Dic61—22no—
368Dic61—41no—
369Dic61—41no—
370Dic61—41no—
371Dic61—41no—
372C2×#431—611no—
373C2×#408—611no—
374#2297—611no—
375#1924—611no—
376#1923—611no—
377#1923—611no—
378#1923—611no—
379#1851—611no—
380#1850—611no—
381#1817—611no—
382#1798—611no—
383#1780—611no—
384#1753—611no—
385C8×C22⋊C4D6111yescharacteristic, complemented
386#1750—611no—
387C2×C61—42no—
388C2×C61#234211yescharacteristic
389C2×C61#292211yescharacteristic
390C2×C61#292511yescharacteristic
391C2×C61#292911yescharacteristic
392C2×C61#293311yescharacteristic
393C2×C61#297911yescharacteristic
394C2×C61#298111yescharacteristic
395D61—42no—
396D61—81no—
397C22×#41—611no—
398C22×M16—611no—
399C23×C8C2×D6111yescharacteristic
400C2×#117—611no—
401C22×C42—611no—
402#431—1224no—
403C2×C4⋊C8—611no—
404C2×C4⋊C8—611no—
405C2×C4⋊C8—611no—
406C2×C4⋊C8—611no—
407#408—1224no—
408C2×C22⋊C8—611no—
409C2×C22⋊C8—611no—
410C2×C22⋊C8—611no—
411C2×C22⋊C8—611no—
412C2×C22⋊C8—611no—
413C2×C22⋊C8—611no—
414C2×C22⋊C8—611no—
415C2×C22⋊C8—611no—
416C2×C22⋊C8—611no—
417C2×C22⋊C8C2×D6111yescharacteristic
418C2×#97—611no—
419C2×C4×C8—611no—
420C2×C4×C8C2×D6111yescharacteristic
421C2×C4×C8C2×D6111yescharacteristic
422#391—611no—
423#391—611no—
424#390—611no—
425#390—611no—
426#386—611no—
427#386—611no—
428#386—611no—
429#386—611no—
430C4×C22⋊C4—611no—
431C4×C22⋊C4—611no—
432C4×C22⋊C4—611no—
433C4×C22⋊C4C2×D6111yescharacteristic
434#336—611no—
435#336—611no—
436#336—611no—
437#336—611no—
438#336—611no—
439#336—611no—
440#336C2×D6111yescharacteristic
441#336C2×D6111yescharacteristic
442C61#2255611yescharacteristic, complemented, Sylow
443C2×#41—1222no—
444C2×#41—1222no—
445C2×#41—1222no—
446C2×#41—1222no—
447C2×#41—2441no—
448C2×#41—2441no—
449C22×Q8—611no—
450C22×D4—611no—
451C22×D4—611no—
452C22×D4—611no—
453C23×C4—611no—
454C23×C4—611no—
455C23×C4—611no—
456C23×C4—611no—
457C23×C4C22×D6111yescharacteristic
458C2×M16—1222no—
459C2×M16—1222no—
460C2×M16—2441no—
461C22×C8—22no—
462C22×C8—22no—
463C22×C8—41no—
464C22×C8—611no—
465C22×C8—611no—
466C22×C8—611no—
467C22×C8—611no—
468C22×C8C22×D6111yescharacteristic
469C22×C8C22×D6111yescharacteristic
470C22×C8C22×D6111yescharacteristic
471C22×C8C22×D6111yescharacteristic
472#117—2441no—
473#117—2441no—
474C2×C4⋊C4—611no—
475C2×C4⋊C4—611no—
476C2×C22⋊C4—611no—
477C2×C22⋊C4—611no—
478C2×C22⋊C4—611no—
479C2×C22⋊C4—611no—
480C2×C22⋊C4—611no—
481C2×C22⋊C4—611no—
482C2×C22⋊C4—611no—
483C2×C22⋊C4—611no—
484C2×C22⋊C4C4×D6111yescharacteristic
485C2×C22⋊C4C4×D6111yescharacteristic
486C2×C42—611no—
487C2×C42—611no—
488C2×C42—611no—
489C2×C42—611no—
490C2×C42—1222no—
491C2×C42—1222no—
492C2×C42C22×D6111yescharacteristic
493C2×C42C22×D6111yescharacteristic
494C4⋊C8—1222no—
495C4⋊C8—1222no—
496C4⋊C8—2441no—
497C4⋊C8—2441no—
498C22⋊C8—22no—
499C22⋊C8—614no—
500C22⋊C8—1222no—
501C22⋊C8—1222no—
502C22⋊C8—1222no—
503C22⋊C8—1222no—
504C22⋊C8—1222no—
505C22⋊C8—1222no—
506C22⋊C8—2441no—
507C22⋊C8—2441no—
508#97—2441no—
509C4×C8—22no—
510C4×C8—41no—
511C4×C8—1222no—
512#95—611no—
513#95—611no—
514#95—611no—
515#95—611no—
516#95—611no—
517#95—611no—
518#95C4×D6111yescharacteristic
519#95C4×D6111yescharacteristic
520C24—611no—
521C24—611no—
522C24C2×C4×D6111yescharacteristic
523#41—2444no—
524#41—2444no—
525#41—2444no—
526#41—2444no—
527C2×Q8—1222no—
528C2×Q8—1222no—
529C2×Q8—2441no—
530C2×D4—1222no—
531C2×D4—1222no—
532C2×D4—1222no—
533C2×D4—1222no—
534C2×D4—1222no—
535C2×D4—1222no—
536C2×D4—2441no—
537C2×D4—2441no—
538C2×D4—2441no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—611no—
544C22×C4—611no—
545C22×C4—612no—
546C22×C4—612no—
547C22×C4—611no—
548C22×C4—611no—
549C22×C4—611no—
550C22×C4—611no—
551C22×C4—1222no—
552C22×C4—1222no—
553C22×C4—1222no—
554C22×C4—1221no—
555C22×C4—1221no—
556C22×C4—1221no—
557C22×C4—1221no—
558C22×C4—1222no—
559C22×C4—1221no—
560C22×C4—1221no—
561C22×C4—1221no—
562C22×C4—1221no—
563C22×C4—1221no—
564C22×C4—1221no—
565C22×C4—1222no—
566C22×C4—2441no—
567C22×C4C2×C4×D6111yescharacteristic
568C22×C4C2×C4×D6111yescharacteristic
569C22×C4C2×C4×D6111yescharacteristic
570C22×C4C2×C4×D6111yescharacteristic
571C22×C4C2×C4×D6111yescharacteristic
572C22×C4#1175822212yes—
573C22×C4#1175822212yes—
574C22×C4C23×D6111yescharacteristic
575M16—2444no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—44no—
588C2×C8—612no—
589C2×C8—1221no—
590C2×C8—1221no—
591C2×C8—1221no—
592C2×C8—1221no—
593C2×C8—1221no—
594C2×C8—1221no—
595C2×C8—1221no—
596C2×C8—1221no—
597C2×C8—1221no—
598C2×C8—1221no—
599C2×C8—1221no—
600C2×C8D4×D6112yes—
601C4⋊C4—2441no—
602C4⋊C4—2441no—
603C22⋊C4—22no—
604C22⋊C4—22no—
605C22⋊C4—1222no—
606C22⋊C4—1222no—
607C22⋊C4—1222no—
608C22⋊C4—1222no—
609C22⋊C4—2441no—
610C22⋊C4—2441no—
611C22⋊C4—2441no—
612C22⋊C4—2441no—
613C42—21no—
614C42—21no—
615C42—21no—
616C42—21no—
617C42—1222no—
618C42—1222no—
619C42—1221no—
620C42—1221no—
621C42—1221no—
622C42—1221no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—612no—
630C23—1221no—
631C23—1221no—
632C23—1221no—
633C23—1221no—
634C23—1221no—
635C23—1221no—
636C23—1221no—
637C23—1221no—
638C23—1221no—
639C23—1221no—
640C23—1221no—
641C23—1221no—
642C23—1221no—
643C23#1451973412yes—
644C23C22×C4×D6111yescharacteristic
645Q8—2444no—
646D4—2444no—
647D4—2444no—
648D4—2444no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—612no—
666C2×C4—612no—
667C2×C4—1228no—
668C2×C4—1221no—
669C2×C4—1221no—
670C2×C4—1221no—
671C2×C4—1221no—
672C2×C4—1222no—
673C2×C4—1222no—
674C2×C4—1222no—
675C2×C4—1222no—
676C2×C4—1221no—
677C2×C4—1221no—
678C2×C4—1221no—
679C2×C4—1221no—
680C2×C4—1221no—
681C2×C4—1221no—
682C2×C4—1221no—
683C2×C4—1221no—
684C2×C4—1221no—
685C2×C4—1221no—
686C2×C4—1221no—
687C2×C4—1221no—
688C2×C4—2444no—
689C2×C4—2441no—
690C2×C4—2441no—
691C2×C4—2441no—
692C2×C4—2441no—
693C2×C4#1451973412yes—
694C2×C4#1451978312yes—
695C2×C4#1451978312yes—
696C2×C4C2×D4×D6111yescharacteristic
697C2×C4#41×D6111yescharacteristic
698C2×C4C2×#1175822211yescharacteristic
699C2×C4C2×#1175822211yescharacteristic
700C2×C4#1451982211yescharacteristic
701C2×C4#1451982311yescharacteristic
702C8—22no—
703C8—41no—
704C8—41no—
705C8—41no—
706C8—1222no—
707C8—2441no—
708C8—2441no—
709C8—2441no—
710C22—22no—
711C22—22no—
712C22—22no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—1222no—
718C22—1222no—
719C22—1222no—
720C22—2441no—
721C22—2441no—
722C22—2441no—
723C22—2441no—
724C22—2441no—
725C22—2441no—
726C22—2441no—
727C22—2441no—
728C22—2441no—
729C22—2441no—
730C22—2441no—
731C22C2×#1451973411yescharacteristic
732C22C4×D4×D6111yescharacteristic
733C22#1684023411yescharacteristic
734C22#131×D6111yescharacteristic
735C22C2×#1451978311yescharacteristic
736C22C2×#1451978311yescharacteristic
737C22#1684052711yescharacteristic
738C4—22no—
739C4—22no—
740C4—22no—
741C4—41no—
742C4—41no—
743C4—1222no—
744C4—1222no—
745C4—2441no—
746C4—2441no—
747C4—2441no—
748C4—2441no—
749C4#1684040211yescharacteristic
750C4#1684040811yescharacteristic
751C4#1684043611yescharacteristic
752C4#1684044111yescharacteristic
753C2—42no—
754C2—4881no—
755C2—2442no—
756C2#2144866211yescharacteristic
757C2#2145446111yescharacteristic
758C2#2145448311yescharacteristic
759C2#2145450811yescharacteristic
760C2#2145453911yescharacteristic
761C2#2145488211yescharacteristic
762C2#2145489311yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D61
commutator, socleC23×C61C23×C4
FittingC8×C22⋊C4×C61C2
prime radicalC22×#11758222C22
cosocleC22×C4×C61C24
hypercenterC8×C22⋊C4D61
hypocenterC61#22556
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C8×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#16839813C2semidirect
4. #21446430C2semidirect
5. #21446425C2semidirect
6. #21446425C2semidirect
7. #21446423C2semidirect
8. #21446001C2semidirect
9. #21445997C2semidirect
10. #21445886C2semidirect
11. #21445802C2semidirect
13. #21445603C2semidirect
14. #21445586C2semidirect
15. C8×C22⋊C4×C61C2semidirect
385. C8×C22⋊C4D61semidirect
442. C61#22556semidirect

Maximal subgroups

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

subgroupindex
C2×#168398132
C2×#168397282
#214483052
#214464302
#214464252
#214464232
#214460012
#214459972
#214458862
#214458022
#214457302
#214456032
#214455862
C8×C22⋊C4×C612
#2255661