Finite Group Databasebeta

← #29706577

Subgroups — #29706577

Order 15616.

882 conjugacy classes of subgroups.

The subgroup lattice has 806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21449098C211yesmaximal, characteristic
2#21446117C211yesmaximal, characteristic, complemented
3#21446116C211yesmaximal, characteristic, complemented
4#21446116C211yesmaximal, characteristic, complemented
5#21446115C211yesmaximal, characteristic, complemented
6#21446114C211yesmaximal, characteristic, complemented
7#21446114C211yesmaximal, characteristic, complemented
8#21446113C211yesmaximal, characteristic, complemented
9#21446113C211yesmaximal, characteristic, complemented
10#21446110C211yesmaximal, characteristic, complemented
11#21446108C211yesmaximal, characteristic, complemented
12#21446108C211yesmaximal, characteristic, complemented
13#21445963C211yesmaximal, characteristic, complemented
14#21445963C211yesmaximal, characteristic, complemented
15C61×#1870C211yesmaximal, characteristic, complemented
16C22×#11758194C2211yescharacteristic
17C22×#11758189C2211yescharacteristic
18C22×C8×D61C2211yescharacteristic
19C2×C4×D244C2211yescharacteristic
20C2×C4×C22⋊D61C2211yescharacteristic
21C2×C4×C22⋊D61C2211yescharacteristic
22C2×C4×C22⋊D61C2211yescharacteristic
23C2×C4×C22⋊D61C2211yescharacteristic
24C2×C22⋊#92418C2211yescharacteristic
25C2×C22⋊#92418C2211yescharacteristic
26C2×C22⋊#92418C2211yescharacteristic
27C2×#14519689C2211yescharacteristic
28C2×#14519689C2211yescharacteristic
29C2×#14519689C2211yescharacteristic
30C2×#14519689C2211yescharacteristic
31C2×#14519689C2211yescharacteristic
32C2×#14519689C2211yescharacteristic
33#16839698C411yescharacteristic
34#16839698C411yescharacteristic
35#16839697C411yescharacteristic
36#16839697C411yescharacteristic
37#16839671C411yescharacteristic
38#16839671C411yescharacteristic
39#16839670C411yescharacteristic
40#16839670C411yescharacteristic
41#16839608C2211yescharacteristic
42#16839517C2211yescharacteristic
43#16839517C2211yescharacteristic
44#16839516C2211yescharacteristic
45#16839516C2211yescharacteristic
46#16839516C2211yescharacteristic
47#16839516C2211yescharacteristic
48#16839516C2211yescharacteristic
49#16839516C2211yescharacteristic
50#16839516C2211yescharacteristic
51#16839516C2211yescharacteristic
52C22×M16×C61C2211yescharacteristic
53C2×C4×D4×C61C2211yescharacteristic
54C2×C22⋊C8×C61C2211yescharacteristic
55C2×C22⋊C8×C61C2211yescharacteristic
56C2×C22⋊C8×C61C2211yescharacteristic
57C61×#336C2211yescharacteristic
58C61×#336C2211yescharacteristic
59C22×D244C2×C411yescharacteristic
60C22×C22⋊D61C2×C411yescharacteristic
61C22×C22⋊D61C2×C411yescharacteristic
62C22×C22⋊D61C2×C411yescharacteristic
63C22×C22⋊D61C2×C411yescharacteristic
64C22×C4×D61C2311yescharacteristic
65C22×C4×D61C2311yescharacteristic
66C2×#11758194—41no—
67C2×#11758194—41no—
68C2×#11758194—41no—
69C2×#11758189—41no—
70C2×#11758189—41no—
71C2×#11758189—41no—
72C22×#92418C2311yescharacteristic
73C22×#92418C2311yescharacteristic
74C22×#92418C2311yescharacteristic
75C22×#92418C2311yescharacteristic
76C2×C8×D61—41no—
77C2×C8×D61—41no—
78C2×C8×D61—41no—
79C4×D244—41no—
80C4×D244—41no—
81C4×C22⋊D61—41no—
82C4×C22⋊D61—41no—
83C4×C22⋊D61—41no—
84C4×C22⋊D61—41no—
85C4×C22⋊D61—41no—
86C4×C22⋊D61—41no—
87C4×C22⋊D61—41no—
88C4×C22⋊D61—41no—
89C2×C4⋊Dic61C2×C411yescharacteristic
90C2×#11758196C2×C411yescharacteristic
91C2×#11758196C2×C411yescharacteristic
92C2×#11758196C2×C411yescharacteristic
93C2×#11758196C2×C411yescharacteristic
94C2×C22⋊Dic61C2×C411yescharacteristic
95C2×C22⋊Dic61C2×C411yescharacteristic
96C2×C22⋊Dic61C2×C411yescharacteristic
97C2×C22⋊Dic61C2×C411yescharacteristic
98C2×#11758198C2×C411yescharacteristic
99C2×#11758198C2×C411yescharacteristic
100C2×#11758198C2×C411yescharacteristic
101C2×#11758198C2×C411yescharacteristic
102C2×#11758198C2×C411yescharacteristic
103C2×#11758198C2×C411yescharacteristic
104C2×C4×Dic61C2311yescharacteristic
105C2×C4×Dic61C2311yescharacteristic
106C22⋊#92418—41no—
107C22⋊#92418—41no—
108C22⋊#92418—41no—
109#14519689—41no—
110#14519689—41no—
111#14519689—41no—
112#14519689—41no—
113#14519689—41no—
114#14519689—41no—
115#14519684C2×C411yescharacteristic
116#14519684C2×C411yescharacteristic
117#14519684C2×C411yescharacteristic
118#14519684C2×C411yescharacteristic
119C22×D4×C61C2×C411yescharacteristic
120C23×C4×C61C2311yescharacteristic
121C23×C4×C61C2311yescharacteristic
122C2×M16×C61—41no—
123C2×M16×C61—41no—
124C2×M16×C61—41no—
125C22×C8×C61C2311yescharacteristic
126C22×C8×C61C2311yescharacteristic
127C22×C8×C61C2311yescharacteristic
128C22×C8×C61C2311yescharacteristic
129C4×D4×C61—41no—
130C4×D4×C61—41no—
131C2×C4⋊C4×C61C2×C411yescharacteristic
132C2×C22⋊C4×C61C2×C411yescharacteristic
133C2×C22⋊C4×C61C2×C411yescharacteristic
134C2×C42×C61C2311yescharacteristic
135C22⋊C8×C61—41no—
136C22⋊C8×C61—41no—
137C22⋊C8×C61—41no—
138C24×C61C22×C411yescharacteristic
139C24×C61C22×C411yescharacteristic
140C23×D61C22×C411yescharacteristic
141C23×D61C22×C411yescharacteristic
142C2×D4×C61—41no—
143C2×D4×C61—41no—
144C2×D4×C61—41no—
145C22×C4×C61—21no—
146C22×C4×C61—21no—
147C22×C4×C61—21no—
148C22×C4×C61—21no—
149C22×C4×C61—21no—
150C22×C4×C61—21no—
151C22×C4×C61—21no—
152C22×C4×C61—21no—
153C22×C4×C61—21no—
154C22×C4×C61—21no—
155C22×C4×C61—21no—
156C22×C4×C61—21no—
157C22×C4×C61C22×C411yescharacteristic
158C22×C4×C61C22×C411yescharacteristic
159C22×C4×C61C22×C411yescharacteristic
160C22×C4×C61C22×C411yescharacteristic
161C22×C4×C61C2411yescharacteristic
162C2×C22⋊D61—22no—
163C2×C22⋊D61—22no—
164C2×C22⋊D61—41no—
165C2×C22⋊D61—41no—
166C2×C22⋊D61—41no—
167C2×C22⋊D61—41no—
168C2×C22⋊D61—41no—
169C2×C22⋊D61—41no—
170C2×C22⋊D61—41no—
171C2×C22⋊D61—41no—
172C2×C22⋊D61—41no—
173C2×C22⋊D61—41no—
174C22×Dic61C22×C411yescharacteristic
175C22×Dic61C22×C411yescharacteristic
176C22×Dic61C22×C411yescharacteristic
177C22×Dic61C22×C411yescharacteristic
178C22×Dic61C22×C411yescharacteristic
179C22×Dic61C22×C411yescharacteristic
180C2×D244—22no—
181C2×D244—41no—
182C2×D244—41no—
183C2×C4×D61—21no—
184C2×C4×D61—21no—
185C2×C4×D61—21no—
186C2×C4×D61—21no—
187C2×C4×D61—21no—
188C2×C4×D61—21no—
189C2×C4×D61—21no—
190C2×C4×D61—21no—
191C2×C4×D61—21no—
192C2×C4×D61—21no—
193C2×C4×D61—21no—
194C2×C4×D61—21no—
195M16×C61—44no—
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—
205C2×C8×C61—21no—
206C2×C8×C61—21no—
207C2×C8×C61—21no—
208C4⋊C4×C61—41no—
209C22⋊C4×C61—41no—
210C22⋊C4×C61—41no—
211C42×C61—21no—
212C42×C61—21no—
213C22⋊Dic61—41no—
214C22⋊Dic61—41no—
215C22⋊Dic61—41no—
216C22⋊Dic61—41no—
217#11758198—41no—
218#11758198—41no—
219#11758198—41no—
220#11758198—41no—
221#11758198—41no—
222#11758198—41no—
223C4⋊Dic61—41no—
224#11758196—41no—
225#11758196—41no—
226#11758196—41no—
227#11758196—41no—
228C4×Dic61—21no—
229C4×Dic61—21no—
230C4×Dic61—21no—
231C4×Dic61—21no—
232#11758194—44no—
233C2×#92418—21no—
234C2×#92418—21no—
235C2×#92418—21no—
236C2×#92418—21no—
237C2×#92418—21no—
238C2×#92418—21no—
239C2×#92418—21no—
240C2×#92418—21no—
241C2×#92418—21no—
242C2×#92418—21no—
243C2×#92418—21no—
244C2×#92418—21no—
245#11758189—44no—
246C8×D61—44no—
247C23×C61—21no—
248C23×C61—21no—
249C23×C61—21no—
250C23×C61—21no—
251C23×C61—21no—
252C23×C61—21no—
253C23×C61—21no—
254C23×C61—21no—
255C23×C61—21no—
256C23×C61—21no—
257C23×C61—21no—
258C23×C61—21no—
259C23×C61—21no—
260C23×C61—21no—
261C23×C61C23×C411yescharacteristic
262C22×D61—21no—
263C22×D61—21no—
264C22×D61—21no—
265C22×D61—21no—
266C22×D61—21no—
267C22×D61—21no—
268C22×D61—21no—
269C22×D61—21no—
270C22×D61—21no—
271C22×D61—21no—
272C22×D61—21no—
273C22×D61—21no—
274C22×D61—21no—
275C22×D61#13112yes—
276D4×C61—44no—
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—21no—
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×C61H(5,𝔽2)11yescharacteristic
298C2×C4×C61H(5,𝔽2)11yescharacteristic
299C2×C4×C61H(5,𝔽2)11yescharacteristic
300C2×C4×C61H(5,𝔽2)11yescharacteristic
301C2×C4×C61H(5,𝔽2)11yescharacteristic
302C2×C4×C61H(5,𝔽2)11yescharacteristic
303C22⋊D61—44no—
304C22⋊D61—44no—
305C22⋊D61—44no—
306C22⋊D61—44no—
307C2×Dic61—21no—
308C2×Dic61—21no—
309C2×Dic61—21no—
310C2×Dic61—21no—
311C2×Dic61—21no—
312C2×Dic61—21no—
313C2×Dic61—21no—
314C2×Dic61—21no—
315C2×Dic61—21no—
316C2×Dic61—21no—
317C2×Dic61—21no—
318C2×Dic61—21no—
319C2×Dic61—21no—
320C2×Dic61—21no—
321C2×Dic61—21no—
322C2×Dic61—21no—
323C2×Dic61—21no—
324C2×Dic61—21no—
325D244—44no—
326C4×D61—41no—
327C4×D61—41no—
328C4×D61—41no—
329C4×D61—41no—
330C4×D61—41no—
331C4×D61—41no—
332C4×D61—41no—
333C4×D61—41no—
334C8×C61—41no—
335C8×C61—41no—
336C8×C61—41no—
337C8×C61—41no—
338#92418—41no—
339#92418—41no—
340#92418—41no—
341#92418—41no—
342#23359—611nomaximal, Sylow
343C22×C61—41no—
344C22×C61—41no—
345C22×C61—41no—
346C22×C61—41no—
347C22×C61—41no—
348C22×C61—41no—
349C22×C61—41no—
350C22×C61—41no—
351C22×C61—41no—
352C22×C61—41no—
353C22×C61—41no—
354C22×C61—41no—
355C22×C61—41no—
356C22×C61—41no—
357C22×C61#51811yescharacteristic
358C22×C61#51811yescharacteristic
359C22×C61#51811yescharacteristic
360C22×C61C2×#13111yescharacteristic
361C22×C61#56811yescharacteristic
362C22×C61#56811yescharacteristic
363C22×C61#56811yescharacteristic
364C2×D61—22no—
365C2×D61—22no—
366C2×D61—22no—
367C2×D61—41no—
368C2×D61—41no—
369C2×D61—41no—
370C2×D61—41no—
371C2×D61—41no—
372C2×D61—41no—
373C2×D61—41no—
374C2×D61—41no—
375C2×D61—41no—
376C2×D61—41no—
377C2×D61—41no—
378C4×C61—41no—
379C4×C61—41no—
380C4×C61—41no—
381C4×C61—41no—
382C4×C61#56011yescharacteristic
383C4×C61#56011yescharacteristic
384C4×C61#56011yescharacteristic
385C4×C61#56011yescharacteristic
386Dic61—41no—
387Dic61—41no—
388Dic61—41no—
389Dic61—41no—
390Dic61—41no—
391Dic61—41no—
392#2397—611no—
393#1870—611no—
394#1870—611no—
395#1870—611no—
396#1870—611no—
397#1870—611no—
398#1870—611no—
399#1870—611no—
400#1870—611no—
401#1870D6111yescharacteristic, complemented
402#1869—611no—
403#1869—611no—
404#1869—611no—
405#1840—611no—
406#1840—611no—
407C2×C61—81no—
408C2×C61—81no—
409C2×C61#238011yescharacteristic
410C2×C61#297611yescharacteristic
411C2×C61#297611yescharacteristic
412C2×C61#297611yescharacteristic
413C2×C61#297811yescharacteristic
414C2×C61#297811yescharacteristic
415C2×C61#297811yescharacteristic
416D61—42no—
417D61—81no—
418C22×M16—611no—
419C22×M16—611no—
420C22×M16C2×D6111yescharacteristic
421C23×C8—611no—
422C2×C4×D4—611no—
423C2×C4×D4—611no—
424C2×C4×D4—611no—
425C2×C4×D4—611no—
426C2×C4×D4—611no—
427C2×C4×D4C2×D6111yescharacteristic
428C2×C22⋊C8—611no—
429C2×C22⋊C8—611no—
430C2×C22⋊C8—611no—
431C2×C22⋊C8—611no—
432C2×C22⋊C8—611no—
433C2×C22⋊C8—611no—
434C2×C22⋊C8—611no—
435C2×C22⋊C8—611no—
436C2×C22⋊C8—611no—
437C2×C22⋊C8C2×D6111yescharacteristic
438C2×C22⋊C8C2×D6111yescharacteristic
439C2×C22⋊C8C2×D6111yescharacteristic
440#399—611no—
441#399—611no—
442#399—611no—
443#399—611no—
444#392—611no—
445#392—611no—
446#392—611no—
447#392—611no—
448#376—611no—
449#336—611no—
450#336—611no—
451#336—611no—
452#336—611no—
453#336—611no—
454#336—611no—
455#336—611no—
456#336—611no—
457#336—611no—
458#336—611no—
459#336C2×D6111yescharacteristic
460#336C2×D6111yescharacteristic
461C61#2335911yescharacteristic, complemented, Sylow
462C22×D4—611no—
463C22×D4—611no—
464C22×D4—611no—
465C22×D4—611no—
466C22×D4—611no—
467C22×D4C4×D6111yescharacteristic
468C23×C4—611no—
469C23×C4—611no—
470C23×C4C22×D6111yescharacteristic
471C23×C4C22×D6111yescharacteristic
472C2×M16—41no—
473C2×M16—41no—
474C2×M16—41no—
475C2×M16—2441no—
476C2×M16—2441no—
477C2×M16—2441no—
478C2×M16—2441no—
479C2×M16—2441no—
480C2×M16—2441no—
481C22×C8—611no—
482C22×C8—611no—
483C22×C8—611no—
484C22×C8—611no—
485C22×C8—2441no—
486C22×C8—2441no—
487C22×C8—2441no—
488C22×C8C22×D6111yescharacteristic
489C22×C8C22×D6111yescharacteristic
490C22×C8C22×D6111yescharacteristic
491C22×C8C22×D6111yescharacteristic
492C4×D4—41no—
493C4×D4—41no—
494C4×D4—2441no—
495C4×D4—2441no—
496C4×D4—2441no—
497C4×D4—2441no—
498C4×D4—2441no—
499C4×D4—2441no—
500C4×D4—2441no—
501C4×D4—2441no—
502C4×D4—2441no—
503C4×D4—2441no—
504C2×C4⋊C4—611no—
505C2×C4⋊C4—611no—
506C2×C4⋊C4—611no—
507C2×C4⋊C4—611no—
508C2×C4⋊C4—611no—
509C2×C4⋊C4C4×D6111yescharacteristic
510C2×C22⋊C4—611no—
511C2×C22⋊C4—611no—
512C2×C22⋊C4—611no—
513C2×C22⋊C4—611no—
514C2×C22⋊C4—611no—
515C2×C22⋊C4—611no—
516C2×C22⋊C4—611no—
517C2×C22⋊C4—611no—
518C2×C22⋊C4—611no—
519C2×C22⋊C4—611no—
520C2×C22⋊C4C4×D6111yescharacteristic
521C2×C22⋊C4C4×D6111yescharacteristic
522C2×C42—611no—
523C2×C42—611no—
524C2×C42C22×D6111yescharacteristic
525C22⋊C8—41no—
526C22⋊C8—41no—
527C22⋊C8—41no—
528C22⋊C8—2441no—
529C22⋊C8—2441no—
530C22⋊C8—2441no—
531C22⋊C8—2441no—
532C22⋊C8—2441no—
533C22⋊C8—2441no—
534C22⋊C8—2441no—
535C22⋊C8—2441no—
536C22⋊C8—2441no—
537#95—611no—
538#95—611no—
539#95—611no—
540#95—611no—
541C24—611no—
542C24—611no—
543C24C2×C4×D6111yescharacteristic
544C24C2×C4×D6111yescharacteristic
545C2×D4—41no—
546C2×D4—41no—
547C2×D4—41no—
548C2×D4—1222no—
549C2×D4—1222no—
550C2×D4—1222no—
551C2×D4—2441no—
552C2×D4—2441no—
553C2×D4—2441no—
554C2×D4—2441no—
555C2×D4—2441no—
556C2×D4—2441no—
557C2×D4—2441no—
558C2×D4—2441no—
559C2×D4—2441no—
560C2×D4—2441no—
561C2×D4—2441no—
562C2×D4—2441no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—611no—
576C22×C4—611no—
577C22×C4—611no—
578C22×C4—611no—
579C22×C4—611no—
580C22×C4—611no—
581C22×C4—1221no—
582C22×C4—1221no—
583C22×C4—1221no—
584C22×C4—1221no—
585C22×C4—1221no—
586C22×C4—1221no—
587C22×C4—1221no—
588C22×C4—1221no—
589C22×C4—1221no—
590C22×C4—1221no—
591C22×C4—1221no—
592C22×C4—1221no—
593C22×C4C2×C4×D6111yescharacteristic
594C22×C4C2×C4×D6111yescharacteristic
595C22×C4C2×C4×D6111yescharacteristic
596C22×C4C2×C4×D6111yescharacteristic
597C22×C4C23×D6111yescharacteristic
598M16—44no—
599M16—2444no—
600M16—2444no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—1221no—
614C2×C8—1221no—
615C2×C8—1221no—
616C2×C8—1221no—
617C2×C8—1221no—
618C2×C8—1221no—
619C2×C8—1221no—
620C2×C8—1221no—
621C2×C8—1221no—
622C2×C8—1221no—
623C2×C8—1221no—
624C2×C8—1221no—
625C2×C8—2444no—
626C4⋊C4—41no—
627C4⋊C4—2441no—
628C4⋊C4—2441no—
629C4⋊C4—2441no—
630C4⋊C4—2441no—
631C4⋊C4—2441no—
632C22⋊C4—41no—
633C22⋊C4—41no—
634C22⋊C4—2441no—
635C22⋊C4—2441no—
636C22⋊C4—2441no—
637C22⋊C4—2441no—
638C22⋊C4—2441no—
639C22⋊C4—2441no—
640C22⋊C4—2441no—
641C22⋊C4—2441no—
642C22⋊C4—2441no—
643C22⋊C4—2441no—
644C42—21no—
645C42—21no—
646C42—1221no—
647C42—1221no—
648C42—1221no—
649C42—1221no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—612no—
665C23—1221no—
666C23—1221no—
667C23—1221no—
668C23—1221no—
669C23—1221no—
670C23—1221no—
671C23—1221no—
672C23—1221no—
673C23—1221no—
674C23—1221no—
675C23—1221no—
676C23—1221no—
677C23—1221no—
678C23C22×C4×D6111yescharacteristic
679D4—44no—
680D4—2444no—
681D4—2444no—
682D4—2444no—
683D4—2444no—
684D4—2444no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—1221no—
706C2×C4—1221no—
707C2×C4—1221no—
708C2×C4—1221no—
709C2×C4—1221no—
710C2×C4—1221no—
711C2×C4—1221no—
712C2×C4—1221no—
713C2×C4—1221no—
714C2×C4—1221no—
715C2×C4—1221no—
716C2×C4—1221no—
717C2×C4—1221no—
718C2×C4—1221no—
719C2×C4—1221no—
720C2×C4—1221no—
721C2×C4—1221no—
722C2×C4—1221no—
723C2×C4—2441no—
724C2×C4—2441no—
725C2×C4—2441no—
726C2×C4—2441no—
727C2×C4—2441no—
728C2×C4—2441no—
729C2×C4—2441no—
730C2×C4—2441no—
731C2×C4#1451982211yescharacteristic
732C2×C4#1451982211yescharacteristic
733C2×C4#1451982211yescharacteristic
734C2×C4#1451982211yescharacteristic
735C2×C4#1451982311yescharacteristic
736C2×C4#1451982311yescharacteristic
737C8—41no—
738C8—41no—
739C8—41no—
740C8—41no—
741C8—2441no—
742C8—2441no—
743C8—2441no—
744C8—2441no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—1222no—
760C22—1222no—
761C22—1222no—
762C22—2441no—
763C22—2441no—
764C22—2441no—
765C22—2441no—
766C22—2441no—
767C22—2441no—
768C22—2441no—
769C22—2441no—
770C22—2441no—
771C22—2441no—
772C22—2441no—
773C22#1684023411yescharacteristic
774C22#1684023411yescharacteristic
775C22#1684023511yescharacteristic
776C22#131×D6111yescharacteristic
777C22#1684052711yescharacteristic
778C22#1684052811yescharacteristic
779C22#1684052811yescharacteristic
780C4—41no—
781C4—41no—
782C4—41no—
783C4—41no—
784C4—2441no—
785C4—2441no—
786C4—2441no—
787C4—2441no—
788C4—2441no—
789C4—2441no—
790C4#1684050011yescharacteristic
791C4#1684050011yescharacteristic
792C4#1684050111yescharacteristic
793C4#1684050211yescharacteristic
794C2—81no—
795C2—81no—
796C2—4881no—
797C2—2442no—
798C2#2144899411yescharacteristic
799C2#2145486211yescharacteristic
800C2#2145486311yescharacteristic
801C2#2145486611yescharacteristic
802C2#2145487611yescharacteristic
803C2#2145487811yescharacteristic
804C2#2145487911yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D61
commutator, socleC23×C61C23×C4
FittingC61×#1870C2
prime radical#21449098C2
cosocleC22×C4×C61C24
hypercenter#1870D61
hypocenterC61#23359
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ #1870

Complements

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

NH ≅ G/Ntype
2. #21446117C2semidirect
3. #21446116C2semidirect
4. #21446116C2semidirect
5. #21446115C2semidirect
6. #21446114C2semidirect
7. #21446114C2semidirect
8. #21446113C2semidirect
9. #21446113C2semidirect
10. #21446110C2semidirect
11. #21446108C2semidirect
12. #21446108C2semidirect
13. #21445963C2semidirect
14. #21445963C2semidirect
15. C61×#1870C2semidirect
401. #1870D61semidirect
461. C61#23359semidirect

Maximal subgroups

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

subgroupindex
#214490982
#214461172
#214461162
#214461152
#214461142
#214461132
#214461102
#214461082
#214459632
C61×#18702
#2335961