Finite Group Databasebeta

← #29696973

Subgroups — #29696973

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×#16839812C211yesmaximal, characteristic, complemented
2C2×#16839727C211yesmaximal, characteristic
3#21448307C211yesmaximal, characteristic
4#21446430C211yesmaximal, characteristic, complemented
5#21446424C211yesmaximal, characteristic, complemented
6#21446424C211yesmaximal, characteristic, complemented
7#21446423C211yesmaximal, characteristic, complemented
8#21446000C211yesmaximal, characteristic, complemented
9#21445995C211yesmaximal, characteristic, complemented
10#21445885C211yesmaximal, characteristic, complemented
11#21445730C211yesmaximal, characteristic
12#21445601C211yesmaximal, characteristic, complemented
13#21445589C211yesmaximal, characteristic, complemented
14#21445585C211yesmaximal, characteristic, complemented
15C61×#1798C211yesmaximal, characteristic, complemented
16C22×#11758222C2211yescharacteristic
17C22×#11758189C2211yescharacteristic
18C22×C8×D61C2211yescharacteristic
19C22×C4×Dic61C2211yescharacteristic
20#16839812—24no—
21C2×#14519706C2211yescharacteristic
22C2×#14519706C2211yescharacteristic
23#16839727—24no—
24C2×C22⋊#92418C2211yescharacteristic
25C2×C22⋊#92418C2211yescharacteristic
26C2×#14519689C2211yescharacteristic
27C2×#14519689C2211yescharacteristic
28C2×#14519689C2211yescharacteristic
29C2×#14519689C2211yescharacteristic
30C2×#14519689C2211yescharacteristic
31C2×#14519689C2211yescharacteristic
32C2×#14519688C2211yescharacteristic
33C2×C4×#92418C2211yescharacteristic
34C2×C8×Dic61C2211yescharacteristic
35C2×C8×Dic61C2211yescharacteristic
36#16839667C411yescharacteristic
37#16839667C411yescharacteristic
38#16839663C411yescharacteristic
39#16839663C411yescharacteristic
40#16839639C411yescharacteristic
41#16839639C411yescharacteristic
42#16839639C411yescharacteristic
43#16839639C411yescharacteristic
44C4×#11758198C2211yescharacteristic
45C4×#11758198C2211yescharacteristic
46C4×#11758198C2211yescharacteristic
47C4×#11758198C2211yescharacteristic
48#16839517C2211yescharacteristic
49#16839517C2211yescharacteristic
50#16839516C2211yescharacteristic
51#16839516C2211yescharacteristic
52#16839516C2211yescharacteristic
53#16839516C2211yescharacteristic
54C2×#117×C61C2211yescharacteristic
55C2×C4⋊C8×C61C2211yescharacteristic
56C2×C4⋊C8×C61C2211yescharacteristic
57C2×C22⋊C8×C61C2211yescharacteristic
58C2×C22⋊C8×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
71C23×Dic61C2×C411yescharacteristic
72C23×Dic61C2×C411yescharacteristic
73C22×C4×D61C2311yescharacteristic
74C22×C4×D61C2311yescharacteristic
75C2×#11758189—22no—
76C2×#11758189—22no—
77C2×#11758189—41no—
78C22×#92418C2311yescharacteristic
79C22×#92418C2311yescharacteristic
80C22×#92418C2311yescharacteristic
81C22×#92418C2311yescharacteristic
82C2×C8×D61—22no—
83C2×C8×D61—22no—
84C2×C8×D61—41no—
85C2×#11758198C2×C411yescharacteristic
86C2×#11758198C2×C411yescharacteristic
87C2×#11758198C2×C411yescharacteristic
88C2×#11758198C2×C411yescharacteristic
89C2×#11758198C2×C411yescharacteristic
90C2×#11758198C2×C411yescharacteristic
91C2×#11758198C2×C411yescharacteristic
92C2×#11758198C2×C411yescharacteristic
93C2×C4×Dic61—22no—
94C2×C4×Dic61—22no—
95C2×C4×Dic61C2×C411yescharacteristic
96C2×C4×Dic61C2×C411yescharacteristic
97C2×C4×Dic61C2311yescharacteristic
98C2×C4×Dic61C2311yescharacteristic
99#14519706—22no—
100#14519706—22no—
101C22⋊#92418—22no—
102C22⋊#92418D414yes—
103#14519689—22no—
104#14519689—22no—
105#14519689—22no—
106#14519689—22no—
107#14519689—41no—
108#14519689—41no—
109#14519688—41no—
110C4×#92418—41no—
111C8×Dic61—22no—
112C8×Dic61—22no—
113#14519684C2×C411yescharacteristic
114#14519684C2×C411yescharacteristic
115#14519684C2×C411yescharacteristic
116#14519684C2×C411yescharacteristic
117#14519684C2×C411yescharacteristic
118#14519684C2×C411yescharacteristic
119#14519684C2×C411yescharacteristic
120#14519684C2×C411yescharacteristic
121C23×C4×C61C2311yescharacteristic
122C22×C8×C61C2311yescharacteristic
123C22×C8×C61C2311yescharacteristic
124C22×C8×C61C2311yescharacteristic
125C22×C8×C61C2311yescharacteristic
126#117×C61—41no—
127#117×C61—41no—
128C2×C4⋊C4×C61C2×C411yescharacteristic
129C2×C4⋊C4×C61C2×C411yescharacteristic
130C2×C22⋊C4×C61C2×C411yescharacteristic
131C2×C22⋊C4×C61C2×C411yescharacteristic
132C2×C42×C61C2311yescharacteristic
133C2×C42×C61C2311yescharacteristic
134C4⋊C8×C61—41no—
135C4⋊C8×C61—41no—
136C22⋊C8×C61—22no—
137C22⋊C8×C61—22no—
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×C61C2×D412yes—
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×Dic61—22no—
160C22×Dic61—22no—
161C22×Dic61—22no—
162C22×Dic61—22no—
163C22×Dic61—22no—
164C22×Dic61—41no—
165C22×Dic61C22×C411yescharacteristic
166C22×Dic61C22×C411yescharacteristic
167C22×Dic61C22×C411yescharacteristic
168C22×Dic61C22×C411yescharacteristic
169C22×Dic61C22×C411yescharacteristic
170C22×Dic61C22×C411yescharacteristic
171#11758222—44no—
172#11758222—44no—
173#11758222—44no—
174#11758222—44no—
175C2×D244—22no—
176C2×D244—22no—
177C2×D244—41no—
178C2×C4×D61—21no—
179C2×C4×D61—21no—
180C2×C4×D61—21no—
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—21no—
188C2×C4×D61#4112yes—
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—21no—
205C4⋊C4×C61—41no—
206C4⋊C4×C61—41no—
207C22⋊C4×C61—41no—
208C22⋊C4×C61—41no—
209C42×C61—21no—
210C42×C61—21no—
211C42×C61—21no—
212C42×C61—21no—
213#11758198—22no—
214#11758198—22no—
215#11758198—22no—
216#11758198—22no—
217#11758198—22no—
218#11758198—22no—
219#11758198—41no—
220#11758198—41no—
221C4×Dic61—22no—
222C4×Dic61—22no—
223C4×Dic61—21no—
224C4×Dic61—21no—
225C4×Dic61—21no—
226C4×Dic61—21no—
227C2×#92418—21no—
228C2×#92418—21no—
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×#92418C2×D412yes—
238C2×#92418C2×D412yes—
239#11758189—44no—
240C8×D61—44no—
241C23×C61—21no—
242C23×C61—21no—
243C23×C61—21no—
244C23×C61—21no—
245C23×C61—21no—
246C23×C61—21no—
247C23×C61C4×D412yes—
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×D61#11712yes—
263C2×C4×C61—21no—
264C2×C4×C61—21no—
265C2×C4×C61—22no—
266C2×C4×C61—22no—
267C2×C4×C61—22no—
268C2×C4×C61—22no—
269C2×C4×C61—21no—
270C2×C4×C61—21no—
271C2×C4×C61—21no—
272C2×C4×C61—21no—
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—21no—
280C2×C4×C61—21no—
281C2×C4×C61C4×D412yes—
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—28no—
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—44no—
306C2×Dic61#11712yes—
307C2×Dic61#13112yes—
308C2×Dic61#13112yes—
309C2×Dic61#13112yes—
310D244—44no—
311C4×D61—22no—
312C4×D61—22no—
313C4×D61—22no—
314C4×D61—22no—
315C4×D61—41no—
316C4×D61—41no—
317C4×D61—41no—
318C4×D61—41no—
319Dic122—44no—
320C8×C61—41no—
321C8×C61—41no—
322C8×C61—41no—
323C8×C61—41no—
324#92418—22no—
325#92418—22no—
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—41no—
359C4×C61—41no—
360C4×C61—41no—
361C4×C61—41no—
362C4×C61#54611yescharacteristic
363C4×C61#54611yescharacteristic
364C4×C61#55111yescharacteristic
365C4×C61#55111yescharacteristic
366Dic61—22no—
367Dic61—22no—
368Dic61—22no—
369Dic61—22no—
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#1798D6111yescharacteristic, complemented
383#1780—611no—
384#1753—611no—
385C8×C22⋊C4—611no—
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×C8—611no—
400C2×#117C2×D6111yescharacteristic
401C22×C42—611no—
402#431—1224no—
403C2×C4⋊C8—611no—
404C2×C4⋊C8—611no—
405C2×C4⋊C8C2×D6111yescharacteristic
406C2×C4⋊C8C2×D6111yescharacteristic
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⋊C8C2×D6111yescharacteristic
417C2×C22⋊C8C2×D6111yescharacteristic
418C2×#97—611no—
419C2×C4×C8—611no—
420C2×C4×C8—611no—
421C2×C4×C8—611no—
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⋊C4—611no—
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—611no—
462C22×C8—611no—
463C22×C8—611no—
464C22×C8—611no—
465C22×C8—1222no—
466C22×C8—1222no—
467C22×C8—2441no—
468C22×C8C22×D6111yescharacteristic
469C22×C8C22×D6111yescharacteristic
470C22×C8C22×D6111yescharacteristic
471C22×C8C22×D6111yescharacteristic
472#117—41no—
473#117—41no—
474C2×C4⋊C4C4×D6111yescharacteristic
475C2×C4⋊C4C4×D6111yescharacteristic
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—41no—
495C4⋊C8—41no—
496C4⋊C8—1222no—
497C4⋊C8—1222no—
498C22⋊C8—22no—
499C22⋊C8—22no—
500C22⋊C8—614no—
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—1222no—
510C4×C8—1222no—
511C4×C8—2441no—
512#95—611no—
513#95—611no—
514#95—611no—
515#95—611no—
516#95—611no—
517#95—611no—
518#95—611no—
519#95—611no—
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—611no—
546C22×C4—611no—
547C22×C4—612no—
548C22×C4—612no—
549C22×C4—611no—
550C22×C4—611no—
551C22×C4—1222no—
552C22×C4—1222no—
553C22×C4—1222no—
554C22×C4—1222no—
555C22×C4—1221no—
556C22×C4—1221no—
557C22×C4—1221no—
558C22×C4—1221no—
559C22×C4—1222no—
560C22×C4—1221no—
561C22×C4—1221no—
562C22×C4—1221no—
563C22×C4—1221no—
564C22×C4—1221no—
565C22×C4—1221no—
566C22×C4—2441no—
567C22×C4C2×C4×D6111yescharacteristic
568C22×C4C2×C4×D6111yescharacteristic
569C22×C4C2×C4×D6111yescharacteristic
570C22×C4C2×C4×D6111yescharacteristic
571C22×C4C2×C4×D6111yescharacteristic
572C22×C4D4×D6112yes—
573C22×C4#1175822612yes—
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—21no—
588C2×C8—612no—
589C2×C8—612no—
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×C8—2444no—
601C4⋊C4—41no—
602C4⋊C4—41no—
603C22⋊C4—41no—
604C22⋊C4—41no—
605C22⋊C4—1222no—
606C22⋊C4—1222no—
607C22⋊C4—1222no—
608C22⋊C4—1222no—
609C22⋊C4—1222no—
610C22⋊C4—1222no—
611C22⋊C4—2441no—
612C22⋊C4—2441no—
613C42—21no—
614C42—21no—
615C42—21no—
616C42—21no—
617C42—1221no—
618C42—1221no—
619C42—1221no—
620C42—1221no—
621C42—1222no—
622C42—1222no—
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#1451973912yes—
644C23C22×C4×D6111yescharacteristic
645Q8—2444no—
646D4—2444no—
647D4—2444no—
648D4—2444no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—612no—
668C2×C4—612no—
669C2×C4—612no—
670C2×C4—612no—
671C2×C4—1228no—
672C2×C4—1221no—
673C2×C4—1221no—
674C2×C4—1221no—
675C2×C4—1221no—
676C2×C4—1221no—
677C2×C4—1221no—
678C2×C4—1221no—
679C2×C4—1221no—
680C2×C4—1222no—
681C2×C4—1222no—
682C2×C4—1222no—
683C2×C4—1222no—
684C2×C4—1221no—
685C2×C4—1221no—
686C2×C4—1221no—
687C2×C4—1221no—
688C2×C4—1221no—
689C2×C4—1221no—
690C2×C4—2444no—
691C2×C4—2441no—
692C2×C4—2441no—
693C2×C4—2441no—
694C2×C4—2441no—
695C2×C4#1451973912yes—
696C2×C4C2×D4×D6111yescharacteristic
697C2×C4#41×D6111yescharacteristic
698C2×C4#41×D6111yescharacteristic
699C2×C4C2×#1175822611yescharacteristic
700C2×C4#1451982211yescharacteristic
701C2×C4#1451982211yescharacteristic
702C8—41no—
703C8—41no—
704C8—41no—
705C8—41no—
706C8—1222no—
707C8—1222no—
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—
731C22#117×D6111yescharacteristic
732C22C2×#1451973911yescharacteristic
733C22#1684023511yescharacteristic
734C22#131×D6111yescharacteristic
735C22#131×D6111yescharacteristic
736C22#131×D6111yescharacteristic
737C22#1684052711yescharacteristic
738C4—22no—
739C4—41no—
740C4—41no—
741C4—41no—
742C4—41no—
743C4—1222no—
744C4—1222no—
745C4—1222no—
746C4—1222no—
747C4—2441no—
748C4—2441no—
749C4#1684040111yescharacteristic
750C4#1684040111yescharacteristic
751C4#1684043911yescharacteristic
752C4#1684043911yescharacteristic
753C2—42no—
754C2—4881no—
755C2—2442no—
756C2#2144866511yescharacteristic
757C2#2145446011yescharacteristic
758C2#2145448211yescharacteristic
759C2#2145451211yescharacteristic
760C2#2145454311yescharacteristic
761C2#2145488311yescharacteristic
762C2#2145489211yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D61
commutator, socleC23×C61C23×C4
FittingC61×#1798C2
prime radicalC22×#11758222C22
cosocleC22×C4×C61C24
hypercenter#1798D61
hypocenterC61#22556
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ #1798

Complements

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

NH ≅ G/Ntype
1. C2×#16839812C2semidirect
4. #21446430C2semidirect
5. #21446424C2semidirect
6. #21446424C2semidirect
7. #21446423C2semidirect
8. #21446000C2semidirect
9. #21445995C2semidirect
10. #21445885C2semidirect
12. #21445601C2semidirect
13. #21445589C2semidirect
14. #21445585C2semidirect
15. C61×#1798C2semidirect
382. #1798D61semidirect
442. C61#22556semidirect

Maximal subgroups

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

subgroupindex
C2×#168398122
C2×#168397272
#214483072
#214464302
#214464242
#214464232
#214460002
#214459952
#214458852
#214457302
#214456012
#214455892
#214455852
C61×#17982
#2255661