Finite Group Databasebeta

← #29730991

Subgroups — #29730991

Order 15616.

1034 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840018C211yesmaximal, characteristic, complemented
2C2×#16839993C211yesmaximal, characteristic, complemented
3C2×#16839984C211yesmaximal, characteristic, complemented
4C2×#16839834C211yesmaximal, characteristic, complemented
5#21450758C211yesmaximal, characteristic
6#21447015C211yesmaximal, characteristic, complemented
7#21447008C211yesmaximal, characteristic, complemented
8#21446827C211yesmaximal, characteristic, complemented
9#21446820C211yesmaximal, characteristic, complemented
10#21446633C211yesmaximal, characteristic, complemented
11#21446580C211yesmaximal, characteristic, complemented
12#21446255C211yesmaximal, characteristic, complemented
13#21446240C211yesmaximal, characteristic, complemented
14#21445649C211yesmaximal, characteristic, complemented
15C61×#2538C211yesmaximal, characteristic, complemented
16C22×#11758202C2211yescharacteristic
17C22×#11758201C2211yescharacteristic
18C22×#11758194C2211yescharacteristic
19C23×#92418C2211yescharacteristic
20C2×#14519765C2211yescharacteristic
21C2×#14519756C2211yescharacteristic
22C2×#14519756C2211yescharacteristic
23C2×#14519751C2211yescharacteristic
24C2×#14519751C2211yescharacteristic
25#16840018—24no—
26#16839993—24no—
27#16839984—24no—
28#16839834—24no—
29C2×#14519708C2211yescharacteristic
30C2×#14519708C2211yescharacteristic
31C2×C4⋊#92418C2211yescharacteristic
32C2×#14519701C2211yescharacteristic
33C2×#14519701C2211yescharacteristic
34C2×#14519700C2211yescharacteristic
35C2×#14519700C2211yescharacteristic
36C2×#14519700C2211yescharacteristic
37C2×#14519697C2211yescharacteristic
38C2×#14519697C2211yescharacteristic
39C2×#14519697C2211yescharacteristic
40C2×C22⋊#92418C2211yescharacteristic
41C2×C22⋊#92418C2211yescharacteristic
42C2×#14519688C2211yescharacteristic
43#16839697—21no—
44#16839670—21no—
45#16839662—21no—
46#16839662—21no—
47C4×C4⋊Dic61C2211yescharacteristic
48#16839524C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839524C2211yescharacteristic
52C2×C22⋊Q8×C61C2211yescharacteristic
53C2×C22⋊Q8×C61C2211yescharacteristic
54C2×C4×Q8×C61C2211yescharacteristic
55C2×C4×D4×C61C2211yescharacteristic
56C61×#396—21no—
57C61×#396—21no—
58C61×#390—21no—
59C61×#389—21no—
60C61×#384C2211yescharacteristic
61C61×#380C2211yescharacteristic
62C61×#380C2211yescharacteristic
63C22×Dic122C2311yescharacteristic
64C22×D244C2311yescharacteristic
65C22×C22⋊D61—21no—
66C22×C22⋊D61—21no—
67C2×#11758202—22no—
68C2×#11758202—22no—
69C2×#11758202—41no—
70C2×#11758201—22no—
71C2×#11758201—22no—
72C2×#11758201—41no—
73C2×#11758194—22no—
74C2×#11758194—22no—
75C2×#11758194—41no—
76C22×#92418—22no—
77C22×#92418—22no—
78C22×#92418—41no—
79C22×#92418C2311yescharacteristic
80C22×#92418C2311yescharacteristic
81C22×#92418C2311yescharacteristic
82C22×#92418C2311yescharacteristic
83#14519765—22no—
84#14519765—22no—
85#14519756—22no—
86#14519756—22no—
87#14519756—41no—
88#14519756—41no—
89#14519751—22no—
90#14519751—22no—
91#14519751—41no—
92#14519751—41no—
93C2×C4⋊Dic61C2311yescharacteristic
94C2×C4⋊Dic61C2311yescharacteristic
95C2×#11758196—21no—
96C2×#11758196—21no—
97C2×C22⋊Dic61—21no—
98C2×C22⋊Dic61—21no—
99C2×#11758198—21no—
100C2×#11758198—21no—
101C2×#11758198—21no—
102C2×#11758198—21no—
103C2×C4×Dic61—21no—
104#14519708—22no—
105#14519708—22no—
106C4⋊#92418D414yescomplemented
107#14519701—22no—
108#14519701D414yescomplemented
109#14519700—22no—
110#14519700—22no—
111#14519700—41no—
112#14519697—22no—
113#14519697—22no—
114#14519697—41no—
115C22⋊#92418—22no—
116C22⋊#92418—22no—
117#14519688—22no—
118#14519684—21no—
119C22×Q8×C61C2311yescharacteristic
120C22×D4×C61D411yescharacteristic
121C23×C4×C61C2311yescharacteristic
122C23×C4×C61C2311yescharacteristic
123C22⋊Q8×C61—22no—
124C22⋊Q8×C61—22no—
125C22⋊Q8×C61—41no—
126C22⋊Q8×C61—41no—
127C4×Q8×C61—22no—
128C4×Q8×C61—22no—
129C4×D4×C61—22no—
130C4×D4×C61—22no—
131C2×C4⋊C4×C61—21no—
132C2×C4⋊C4×C61—21no—
133C2×C4⋊C4×C61—21no—
134C2×C4⋊C4×C61—21no—
135C2×C4⋊C4×C61—21no—
136C2×C4⋊C4×C61D411yescharacteristic
137C2×C4⋊C4×C61C2311yescharacteristic
138C2×C4⋊C4×C61C2311yescharacteristic
139C2×C4⋊C4×C61C2311yescharacteristic
140C2×C22⋊C4×C61—21no—
141C2×C22⋊C4×C61—21no—
142C2×C22⋊C4×C61—21no—
143C2×C22⋊C4×C61—21no—
144C2×C22⋊C4×C61D411yescharacteristic
145C2×C22⋊C4×C61D411yescharacteristic
146C2×C42×C61—21no—
147C2×C42×C61C2311yescharacteristic
148#95×C61—21no—
149#95×C61—21no—
150C24×C61C2×D411yescharacteristic
151C24×C61C2×D411yescharacteristic
152C23×D61—21no—
153C2×Q8×C61—21no—
154C2×Q8×C61—21no—
155C2×Q8×C61—21no—
156C2×Q8×C61—21no—
157C2×Q8×C61—21no—
158C2×Q8×C61C2×D412yes—
159C2×D4×C61—22no—
160C2×D4×C61—22no—
161C2×D4×C61—41no—
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—21no—
172C22×C4×C61—21no—
173C22×C4×C61—21no—
174C22×C4×C61—21no—
175C22×C4×C61—21no—
176C22×C4×C61—21no—
177C22×C4×C61—21no—
178C22×C4×C61C2×D411yescharacteristic
179C22×C4×C61C2×D411yescharacteristic
180C22×C4×C61C2×D411yescharacteristic
181C22×C4×C61C2×D411yescharacteristic
182C22×C4×C61C2411yescharacteristic
183C2×C22⋊D61—42no—
184C2×C22⋊D61—42no—
185C2×C22⋊D61—42no—
186C2×C22⋊D61—42no—
187C2×C22⋊D61—81no—
188C2×C22⋊D61—81no—
189C22×Dic61—21no—
190C22×Dic61—21no—
191C22×Dic61—21no—
192C2×D244—21no—
193C2×D244—21no—
194C2×D244—21no—
195C2×D244—21no—
196C2×D244—21no—
197C2×D244—21no—
198C2×Dic122—21no—
199C2×Dic122—21no—
200C2×Dic122—21no—
201C2×Dic122—21no—
202C2×Dic122—21no—
203C2×Dic122—21no—
204C4⋊C4×C61—22no—
205C4⋊C4×C61—21no—
206C4⋊C4×C61—21no—
207C4⋊C4×C61—21no—
208C4⋊C4×C61—21no—
209C4⋊C4×C61—21no—
210C4⋊C4×C61—21no—
211C4⋊C4×C61—42no—
212C4⋊C4×C61—42no—
213C4⋊C4×C61—42no—
214C4⋊C4×C61—42no—
215C4⋊C4×C61—81no—
216C22⋊C4×C61—22no—
217C22⋊C4×C61—22no—
218C22⋊C4×C61—42no—
219C22⋊C4×C61—42no—
220C22⋊C4×C61—81no—
221C22⋊C4×C61—81no—
222C42×C61—42no—
223C42×C61C2×D412yes—
224C42×C61#4112yes—
225C22⋊Dic61—42no—
226C22⋊Dic61—42no—
227#11758202—44no—
228#11758201—44no—
229#11758198—42no—
230#11758198—42no—
231#11758198—42no—
232#11758198—42no—
233C4⋊Dic61—21no—
234C4⋊Dic61—21no—
235C4⋊Dic61C2×D412yes—
236C4⋊Dic61#4112yes—
237#11758196—42no—
238#11758196—42no—
239C4×Dic61—81no—
240#11758194—44no—
241C2×#92418—21no—
242C2×#92418—21no—
243C2×#92418—21no—
244C2×#92418—21no—
245C2×#92418—21no—
246C2×#92418—21no—
247C2×#92418—21no—
248C2×#92418—21no—
249C2×#92418—21no—
250C2×#92418—44no—
251C2×#92418C2×D412yes—
252C2×#92418C2×D412yes—
253C2×#92418C2×D412yes—
254C23×C61—21no—
255C23×C61—21no—
256C23×C61—21no—
257C23×C61—21no—
258C23×C61—21no—
259C23×C61—21no—
260C23×C61—21no—
261C23×C61—21no—
262C23×C61—21no—
263C23×C61—21no—
264C23×C61—21no—
265C23×C61—21no—
266C23×C61—21no—
267C23×C61#13712yes—
268C23×C61C22×D411yescharacteristic
269C22×D61—41no—
270C22×D61—41no—
271C22×D61—41no—
272C22×D61—41no—
273C22×D61—41no—
274C22×D61—41no—
275C22×D61—41no—
276Q8×C61—22no—
277Q8×C61—22no—
278Q8×C61—41no—
279Q8×C61—41no—
280D4×C61—44no—
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—22no—
290C2×C4×C61—21no—
291C2×C4×C61—21no—
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—41no—
300C2×C4×C61—41no—
301C2×C4×C61—41no—
302C2×C4×C61—41no—
303C2×C4×C61—41no—
304C2×C4×C61—41no—
305C2×C4×C61—41no—
306C2×C4×C61—41no—
307C2×C4×C61—41no—
308C2×C4×C61—41no—
309C2×C4×C61—41no—
310C2×C4×C61—41no—
311C2×C4×C61#12112yes—
312C2×C4×C61#12112yes—
313C2×C4×C61C22×D411yescharacteristic
314C2×C4×C61C22×D411yescharacteristic
315C2×C4×C61C2×#4111yescharacteristic
316C2×C4×C61C2×#4111yescharacteristic
317C2×C4×C61H(5,𝔽2)11yescharacteristic
318C2×C4×C61H(5,𝔽2)11yescharacteristic
319C22⋊D61—84no—
320C22⋊D61—84no—
321C2×Dic61—22no—
322C2×Dic61—22no—
323C2×Dic61—41no—
324C2×Dic61—41no—
325C2×Dic61—41no—
326C2×Dic61—41no—
327C2×Dic61—41no—
328C2×Dic61—41no—
329C2×Dic61—41no—
330D244—41no—
331D244—41no—
332D244—41no—
333D244—41no—
334Dic122—41no—
335Dic122—41no—
336Dic122—41no—
337Dic122—41no—
338#92418—22no—
339#92418—22no—
340#92418—22no—
341#92418—41no—
342#25403—611nomaximal, Sylow
343C22×C61—22no—
344C22×C61—22no—
345C22×C61—22no—
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×C61C2×#12111yescharacteristic
358C22×C61D4211yescharacteristic
359C22×C61#54611yescharacteristic
360C22×C61C2×#13711yescharacteristic
361C22×C61#57511yescharacteristic
362C22×C61#57711yescharacteristic
363C22×C61#57711yescharacteristic
364C2×D61—81no—
365C2×D61—81no—
366C2×D61—81no—
367C2×D61—81no—
368C2×D61—81no—
369C2×D61—81no—
370C2×D61—81no—
371C4×C61—22no—
372C4×C61—22no—
373C4×C61—41no—
374C4×C61—41no—
375C4×C61—42no—
376C4×C61—81no—
377C4×C61—81no—
378C4×C61—81no—
379C4×C61#53211yescharacteristic
380C4×C61#54011yescharacteristic
381C4×C61D4211yescharacteristic
382C4×C61#55011yescharacteristic
383Dic61—42no—
384Dic61—42no—
385Dic61—81no—
386C2×#470—611no—
387C2×#465—611no—
388C2×#464—611no—
389C2×#435—611no—
390#2540—611no—
391#2538D6111yescharacteristic, complemented
392#2035—611no—
393#2034—611no—
394#2001—611no—
395#2000—611no—
396#1959—611no—
397#1948—611no—
398#1895—611no—
399#1892—611no—
400#1763—611no—
401C2×C61—42no—
402C2×C61—81no—
403C2×C61#242811yescharacteristic
404C2×C61#305611yescharacteristic
405C2×C61#306011yescharacteristic
406C2×C61#326611yescharacteristic
407C2×C61#327111yescharacteristic
408C2×C61#331111yescharacteristic
409C2×C61#331611yescharacteristic
410D61—161no—
411C22×Q16—611no—
412C22×SD16—611no—
413C22×M16—611no—
414C23×C8—611no—
415C2×#124—611no—
416C2×C22⋊Q8—611no—
417C2×C22⋊Q8—611no—
418C2×C22⋊Q8C2×D6111yescharacteristic
419C2×C22⋊Q8C2×D6111yescharacteristic
420C2×#121—611no—
421C2×#121—611no—
422C2×C4×Q8C2×D6111yescharacteristic
423C2×C4×D4C2×D6111yescharacteristic
424#470—1224no—
425#465—1224no—
426#464—1224no—
427#435—1224no—
428C2×#106—611no—
429C2×#106—611no—
430C2×C4⋊C8—611no—
431C2×#103—611no—
432C2×#103—611no—
433C2×#103—611no—
434C2×#103—611no—
435C2×#103—611no—
436C2×#102—611no—
437C2×#102—611no—
438C2×#102—611no—
439C2×C22⋊C8—611no—
440C2×C22⋊C8—611no—
441C2×#97—611no—
442#399—1221no—
443#396—21no—
444#396—21no—
445#392—1221no—
446#390—21no—
447#390—1221no—
448#390—1221no—
449#389—21no—
450#384C2×D6111yescharacteristic
451#380C2×D6111yescharacteristic
452#380C2×D6111yescharacteristic
453C4×C4⋊C4—611no—
454#340—611no—
455#340—611no—
456#340—611no—
457#340—611no—
458C61#2540311yescharacteristic, complemented, Sylow
459C22×Q8—611no—
460C22×Q8C22×D6111yescharacteristic
461C22×D4—611no—
462C22×D4—1221no—
463C22×D4—1221no—
464C22×D4C22⋊D6111yescharacteristic
465C23×C4C22×D6111yescharacteristic
466C23×C4C22×D6111yescharacteristic
467C2×Q16—1222no—
468C2×Q16—1222no—
469C2×Q16—2441no—
470C2×SD16—1222no—
471C2×SD16—1222no—
472C2×SD16—2441no—
473C2×M16—1222no—
474C2×M16—1222no—
475C2×M16—2441no—
476C22×C8—611no—
477C22×C8—611no—
478C22×C8—611no—
479C22×C8—611no—
480C22×C8—1222no—
481C22×C8—1222no—
482C22×C8—2441no—
483#124—1222no—
484#124—1222no—
485C22⋊Q8—22no—
486C22⋊Q8—22no—
487C22⋊Q8—41no—
488C22⋊Q8—41no—
489C22⋊Q8—1222no—
490C22⋊Q8—1222no—
491C22⋊Q8—2441no—
492C22⋊Q8—2441no—
493#121—1222no—
494#121—1222no—
495#121—2441no—
496#121—2441no—
497C4×Q8—22no—
498C4×Q8—22no—
499C4×D4—22no—
500C4×D4—22no—
501C2×C4⋊C4—21no—
502C2×C4⋊C4—21no—
503C2×C4⋊C4—21no—
504C2×C4⋊C4—21no—
505C2×C4⋊C4—21no—
506C2×C4⋊C4—611no—
507C2×C4⋊C4—611no—
508C2×C4⋊C4—1221no—
509C2×C4⋊C4—1221no—
510C2×C4⋊C4C22⋊D6111yescharacteristic
511C2×C4⋊C4C22×D6111yescharacteristic
512C2×C4⋊C4C22×D6111yescharacteristic
513C2×C4⋊C4C22×D6111yescharacteristic
514C2×C22⋊C4—21no—
515C2×C22⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C22⋊C4—1221no—
519C2×C22⋊C4—1221no—
520C2×C22⋊C4—1221no—
521C2×C22⋊C4—1221no—
522C2×C22⋊C4—1221no—
523C2×C22⋊C4—1221no—
524C2×C22⋊C4C22⋊D6111yescharacteristic
525C2×C22⋊C4C22⋊D6111yescharacteristic
526C2×C42—21no—
527C2×C42—1221no—
528C2×C42C22×D6111yescharacteristic
529#106—1222no—
530#106—1222no—
531C4⋊C8—614no—
532#103—614no—
533#103—1222no—
534#103—1222no—
535#103—1222no—
536#103—2441no—
537#102—1222no—
538#102—1222no—
539#102—2441no—
540C22⋊C8—1222no—
541C22⋊C8—1222no—
542#97—1222no—
543#95—21no—
544#95—21no—
545#95—1221no—
546C24—1221no—
547C24C2×C22⋊D6111yescharacteristic
548C24C2×C22⋊D6111yescharacteristic
549C2×Q8—21no—
550C2×Q8—21no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8—21no—
554C2×Q8—1221no—
555C2×Q8—1221no—
556C2×Q8—1221no—
557C2×Q8—1221no—
558C2×Q8—1221no—
559C2×Q8—1221no—
560C2×Q8D4×D6112yes—
561C2×D4—22no—
562C2×D4—22no—
563C2×D4—41no—
564C2×D4—1221no—
565C2×D4—1221no—
566C2×D4—1221no—
567C2×D4—1221no—
568C2×D4—1221no—
569C2×D4—1221no—
570C2×D4—4881no—
571C2×D4—4881no—
572C2×D4—2442no—
573C2×D4—2442no—
574C2×D4—2442no—
575C2×D4—2442no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—1221no—
593C22×C4—1221no—
594C22×C4—1221no—
595C22×C4C2×C22⋊D6111yescharacteristic
596C22×C4C2×C22⋊D6111yescharacteristic
597C22×C4C2×C22⋊D6111yescharacteristic
598C22×C4C2×C22⋊D6111yescharacteristic
599C22×C4C23×D6111yescharacteristic
600Q16—2444no—
601SD16—2444no—
602M16—2444no—
603C2×C8—612no—
604C2×C8—612no—
605C2×C8—612no—
606C2×C8—1221no—
607C2×C8—1221no—
608C2×C8—1221no—
609C2×C8—1221no—
610C2×C8—1221no—
611C2×C8—1221no—
612C2×C8—1221no—
613C2×C8—1221no—
614C2×C8—1221no—
615C2×C8—2444no—
616C4⋊C4—22no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—42no—
624C4⋊C4—42no—
625C4⋊C4—42no—
626C4⋊C4—42no—
627C4⋊C4—81no—
628C4⋊C4—612no—
629C4⋊C4—612no—
630C4⋊C4—1221no—
631C4⋊C4—1221no—
632C4⋊C4—2442no—
633C4⋊C4—2442no—
634C22⋊C4—22no—
635C22⋊C4—22no—
636C22⋊C4—42no—
637C22⋊C4—42no—
638C22⋊C4—81no—
639C22⋊C4—81no—
640C22⋊C4—2442no—
641C22⋊C4—2442no—
642C22⋊C4—2442no—
643C22⋊C4—2442no—
644C22⋊C4—2442no—
645C22⋊C4—2442no—
646C42—42no—
647C42—4881no—
648C42D4×D6112yes—
649C42#1175822412yes—
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—2441no—
664C23—2441no—
665C23—2441no—
666C23—2441no—
667C23—2441no—
668C23—2441no—
669C23—2441no—
670C23#1451980812yes—
671C23C22×C22⋊D6111yescharacteristic
672Q8—22no—
673Q8—22no—
674Q8—41no—
675Q8—41no—
676Q8—2441no—
677Q8—2441no—
678Q8—2441no—
679Q8—2441no—
680D4—44no—
681D4—4884no—
682D4—4884no—
683D4—2441no—
684D4—2441no—
685D4—2441no—
686D4—2441no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—22no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—1222no—
718C2×C4—1222no—
719C2×C4—2441no—
720C2×C4—2441no—
721C2×C4—2441no—
722C2×C4—2441no—
723C2×C4—2441no—
724C2×C4—2441no—
725C2×C4—2441no—
726C2×C4#1451974912yes—
727C2×C4#1451974912yes—
728C2×C4C2×D4×D6111yescharacteristic
729C2×C4C2×D4×D6111yescharacteristic
730C2×C4#41×D6111yescharacteristic
731C2×C4C2×#1175822411yescharacteristic
732C2×C4#1451982211yescharacteristic
733C2×C4#1451982311yescharacteristic
734C8—1222no—
735C8—1222no—
736C8—1222no—
737C8—2441no—
738C22—22no—
739C22—22no—
740C22—22no—
741C22—41no—
742C22—41no—
743C22—41no—
744C22—41no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—4881no—
753C22—4881no—
754C22—4881no—
755C22—4881no—
756C22—4881no—
757C22—4881no—
758C22—4881no—
759C22C2×#1451974911yescharacteristic
760C22D4×C22⋊D6111yescharacteristic
761C22#1684040011yescharacteristic
762C22C2×#1451980811yescharacteristic
763C22#1684056011yescharacteristic
764C22#1684057011yescharacteristic
765C22#1684057311yescharacteristic
766C4—22no—
767C4—22no—
768C4—41no—
769C4—41no—
770C4—42no—
771C4—81no—
772C4—81no—
773C4—81no—
774C4—4881no—
775C4—2442no—
776C4—2442no—
777C4#1684030711yescharacteristic
778C4#1684036511yescharacteristic
779C4#1684039611yescharacteristic
780C4#1684043011yescharacteristic
781C2—42no—
782C2—81no—
783C2—9761no—
784C2#2144940911yescharacteristic
785C2#2145544511yescharacteristic
786C2#2145547811yescharacteristic
787C2#2145733011yescharacteristic
788C2#2145740011yescharacteristic
789C2#2145784911yescharacteristic
790C2#2145792411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2538C2
socleC23×C61C22×D4
prime radical#21450758C2
hypercenter#2538D61
hypocenterC61#25403
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2538

Complements

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

NH ≅ G/Ntype
1. C2×#16840018C2semidirect
2. C2×#16839993C2semidirect
3. C2×#16839984C2semidirect
4. C2×#16839834C2semidirect
6. #21447015C2semidirect
7. #21447008C2semidirect
8. #21446827C2semidirect
9. #21446820C2semidirect
10. #21446633C2semidirect
11. #21446580C2semidirect
12. #21446255C2semidirect
13. #21446240C2semidirect
14. #21445649C2semidirect
15. C61×#2538C2semidirect
106. C4⋊#92418D4semidirect
108. #14519701D4semidirect
391. #2538D61semidirect
458. C61#25403semidirect

Maximal subgroups

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

subgroupindex
C2×#168400182
C2×#168399932
C2×#168399842
C2×#168398342
#214507582
#214470152
#214470082
#214468272
#214468202
#214466332
#214465802
#214462552
#214462402
#214456492
C61×#25382
#2540361