Finite Group Databasebeta

← #29730946

Subgroups — #29730946

Order 15616.

1048 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840006C211yesmaximal, characteristic, complemented
2C2×#16839989C211yesmaximal, characteristic, complemented
3C2×#16839967C211yesmaximal, characteristic, complemented
4C2×#16839834C211yesmaximal, characteristic, complemented
5#21450772C211yesmaximal, characteristic, complemented
6#21447022C211yesmaximal, characteristic, complemented
7#21447015C211yesmaximal, characteristic, complemented
8#21446822C211yesmaximal, characteristic, complemented
9#21446822C211yesmaximal, characteristic, complemented
10#21446638C211yesmaximal, characteristic, complemented
11#21446585C211yesmaximal, characteristic, complemented
12#21446250C211yesmaximal, characteristic, complemented
13#21446240C211yesmaximal, characteristic, complemented
14#21445644C211yesmaximal, characteristic, complemented
15C61×#2535C211yesmaximal, characteristic
16C22×#11758200C2211yescharacteristic
17C22×#11758200C2211yescharacteristic
18C22×#11758194C2211yescharacteristic
19C23×#92418C2211yescharacteristic
20C2×#14519777C2211yescharacteristic
21C2×#14519756C2211yescharacteristic
22C2×#14519756C2211yescharacteristic
23C2×#14519756C2211yescharacteristic
24C2×#14519756C2211yescharacteristic
25#16840006—24no—
26#16839989—24no—
27#16839967—24no—
28#16839834—24no—
29C2×#14519710C2211yescharacteristic
30C2×#14519708C2211yescharacteristic
31C2×C4⋊#92418C2211yescharacteristic
32C2×#14519700C2211yescharacteristic
33C2×#14519700C2211yescharacteristic
34C2×#14519700C2211yescharacteristic
35C2×#14519700C2211yescharacteristic
36C2×#14519700C2211yescharacteristic
37C2×#14519700C2211yescharacteristic
38C2×#14519698C2211yescharacteristic
39C2×#14519698C2211yescharacteristic
40C2×C22⋊#92418C2211yescharacteristic
41C2×C22⋊#92418C2211yescharacteristic
42C2×#14519688C2211yescharacteristic
43#16839698—21no—
44#16839698—21no—
45#16839665—21no—
46#16839631—21no—
47C4×C4⋊Dic61C2211yescharacteristic
48#16839524C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839524C2211yescharacteristic
52C2×#121×C61C2211yescharacteristic
53C2×#121×C61C2211yescharacteristic
54C2×C4×D4×C61C2211yescharacteristic
55C2×C4×D4×C61C2211yescharacteristic
56C61×#397—21no—
57C61×#392—21no—
58C61×#386—21no—
59C61×#386—21no—
60C61×#382C2211yescharacteristic
61C61×#380C2211yescharacteristic
62C61×#380C2211yescharacteristic
63C22×Dic122C2311yescharacteristic
64C22×Dic122C2311yescharacteristic
65C2×#11758200—22no—
66C2×#11758200—22no—
67C2×#11758200—22no—
68C2×#11758200—22no—
69C2×#11758200—41no—
70C2×#11758200—41no—
71C2×#11758194—22no—
72C2×#11758194—22no—
73C2×#11758194—41no—
74C22×#92418—22no—
75C22×#92418—22no—
76C22×#92418—41no—
77C22×#92418C2311yescharacteristic
78C22×#92418C2311yescharacteristic
79C22×#92418C2311yescharacteristic
80C22×#92418C2311yescharacteristic
81#14519777—22no—
82#14519777—22no—
83#14519756—22no—
84#14519756—22no—
85#14519756—22no—
86#14519756—22no—
87#14519756—41no—
88#14519756—41no—
89#14519756—41no—
90#14519756—41no—
91C2×C4⋊Dic61—21no—
92C2×C4⋊Dic61—21no—
93C2×C4⋊Dic61C2311yescharacteristic
94C2×C4⋊Dic61C2311yescharacteristic
95C2×#11758196—21no—
96C2×#11758196—21no—
97C2×#11758196—21no—
98C2×#11758196—21no—
99C2×C22⋊Dic61—21no—
100C2×C22⋊Dic61—21no—
101C2×C22⋊Dic61—21no—
102C2×C22⋊Dic61—21no—
103C2×C4×Dic61—21no—
104#14519710—22no—
105#14519708—22no—
106C4⋊#92418D414yescomplemented
107#14519700—22no—
108#14519700—22no—
109#14519700—22no—
110#14519700—22no—
111#14519700—41no—
112#14519700—41no—
113#14519698—22no—
114#14519698D414yescomplemented
115C22⋊#92418—22no—
116C22⋊#92418—22no—
117#14519688—22no—
118#14519684—21no—
119C22×D4×C61—21no—
120C22×D4×C61—21no—
121C22×D4×C61D411yescharacteristic
122C22×D4×C61C2311yescharacteristic
123C23×C4×C61—21no—
124C23×C4×C61C2311yescharacteristic
125C23×C4×C61C2311yescharacteristic
126#121×C61—22no—
127#121×C61—22no—
128#121×C61—41no—
129#121×C61—41no—
130C4×D4×C61—22no—
131C4×D4×C61—22no—
132C4×D4×C61—22no—
133C4×D4×C61—22no—
134C2×C4⋊C4×C61D411yescharacteristic
135C2×C4⋊C4×C61C2311yescharacteristic
136C2×C4⋊C4×C61C2311yescharacteristic
137C2×C4⋊C4×C61C2311yescharacteristic
138C2×C22⋊C4×C61—21no—
139C2×C22⋊C4×C61—21no—
140C2×C22⋊C4×C61—21no—
141C2×C22⋊C4×C61—21no—
142C2×C22⋊C4×C61—21no—
143C2×C22⋊C4×C61D411yescharacteristic
144C2×C22⋊C4×C61D411yescharacteristic
145C2×C42×C61C2311yescharacteristic
146#95×C61—21no—
147#95×C61—21no—
148#95×C61—21no—
149#95×C61—21no—
150C24×C61—21no—
151C24×C61C2×D411yescharacteristic
152C24×C61C2×D411yescharacteristic
153C2×D4×C61—22no—
154C2×D4×C61—22no—
155C2×D4×C61—21no—
156C2×D4×C61—21no—
157C2×D4×C61—21no—
158C2×D4×C61—21no—
159C2×D4×C61—21no—
160C2×D4×C61—41no—
161C2×D4×C61—42no—
162C2×D4×C61—42no—
163C2×D4×C61—42no—
164C2×D4×C61—42no—
165C2×D4×C61—81no—
166C2×D4×C61—81no—
167C2×D4×C61C2×D412yes—
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×C61—21no—
179C22×C4×C61—21no—
180C22×C4×C61—21no—
181C22×C4×C61—21no—
182C22×C4×C61—21no—
183C22×C4×C61—42no—
184C22×C4×C61—81no—
185C22×C4×C61—81no—
186C22×C4×C61C2×D411yescharacteristic
187C22×C4×C61C2×D411yescharacteristic
188C22×C4×C61C2×D411yescharacteristic
189C22×C4×C61C2×D411yescharacteristic
190C22×C4×C61C2411yescharacteristic
191C22×Dic61—21no—
192C22×Dic61—21no—
193C22×Dic61—21no—
194C22×Dic61—21no—
195C2×Dic122—21no—
196C2×Dic122—21no—
197C2×Dic122—21no—
198C2×Dic122—21no—
199C2×Dic122—21no—
200C2×Dic122—21no—
201C2×Dic122—21no—
202C2×Dic122—21no—
203C2×Dic122—21no—
204C2×Dic122—21no—
205C2×Dic122—21no—
206C2×Dic122—21no—
207C4⋊C4×C61—22no—
208C4⋊C4×C61—21no—
209C4⋊C4×C61—21no—
210C4⋊C4×C61—21no—
211C4⋊C4×C61—21no—
212C4⋊C4×C61—21no—
213C4⋊C4×C61—21no—
214C22⋊C4×C61—22no—
215C22⋊C4×C61—22no—
216C22⋊C4×C61—42no—
217C22⋊C4×C61—42no—
218C22⋊C4×C61—42no—
219C22⋊C4×C61—81no—
220C22⋊C4×C61—81no—
221C42×C61C2×D412yes—
222C42×C61#4112yes—
223C22⋊Dic61—42no—
224C22⋊Dic61—42no—
225C22⋊Dic61—42no—
226C22⋊Dic61—42no—
227#11758200—44no—
228#11758200—44no—
229C4⋊Dic61—21no—
230C4⋊Dic61—21no—
231C4⋊Dic61—42no—
232C4⋊Dic61—42no—
233C4⋊Dic61C2×D412yes—
234C4⋊Dic61#4112yes—
235#11758196—42no—
236#11758196—42no—
237#11758196—42no—
238#11758196—42no—
239C4×Dic61—42no—
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—22no—
263C23×C61—21no—
264C23×C61—21no—
265C23×C61—21no—
266C23×C61—21no—
267C23×C61—21no—
268C23×C61—41no—
269C23×C61—41no—
270C23×C61—41no—
271C23×C61—41no—
272C23×C61—41no—
273C23×C61—41no—
274C23×C61#13712yes—
275C23×C61C22×D411yescharacteristic
276D4×C61—22no—
277D4×C61—22no—
278D4×C61—44no—
279D4×C61—41no—
280D4×C61—41no—
281D4×C61—84no—
282D4×C61—84no—
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—21no—
290C2×C4×C61—21no—
291C2×C4×C61—21no—
292C2×C4×C61—21no—
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—84no—
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
319C2×Dic61—22no—
320C2×Dic61—22no—
321C2×Dic61—41no—
322C2×Dic61—41no—
323C2×Dic61—41no—
324C2×Dic61—41no—
325C2×Dic61—41no—
326C2×Dic61—41no—
327C2×Dic61—41no—
328C2×Dic61—41no—
329C2×Dic61—41no—
330C2×Dic61—41no—
331Dic122—41no—
332Dic122—41no—
333Dic122—41no—
334Dic122—41no—
335Dic122—41no—
336Dic122—41no—
337Dic122—41no—
338Dic122—41no—
339#92418—22no—
340#92418—22no—
341#92418—22no—
342#92418—41no—
343#25400—611nomaximal, Sylow
344C22×C61—22no—
345C22×C61—22no—
346C22×C61—22no—
347C22×C61—41no—
348C22×C61—41no—
349C22×C61—41no—
350C22×C61—41no—
351C22×C61—41no—
352C22×C61—42no—
353C22×C61—42no—
354C22×C61—41no—
355C22×C61—41no—
356C22×C61—42no—
357C22×C61—41no—
358C22×C61—41no—
359C22×C61—41no—
360C22×C61—41no—
361C22×C61—81no—
362C22×C61—81no—
363C22×C61—81no—
364C22×C61—81no—
365C22×C61C2×#12111yescharacteristic
366C22×C61D4211yescharacteristic
367C22×C61#54611yescharacteristic
368C22×C61C2×#13711yescharacteristic
369C22×C61#57511yescharacteristic
370C22×C61#57711yescharacteristic
371C22×C61#57711yescharacteristic
372C4×C61—22no—
373C4×C61—22no—
374C4×C61—41no—
375C4×C61—41no—
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—
386Dic61—81no—
387C2×#468—611no—
388C2×#465—611no—
389C2×#461—611no—
390C2×#435—611no—
391#2542—611no—
392#2535D6111yescharacteristic
393#2036—611no—
394#2035—611no—
395#2000—611no—
396#2000—611no—
397#1960—611no—
398#1949—611no—
399#1894—611no—
400#1892—611no—
401#1762—611no—
402C2×C61—42no—
403C2×C61—81no—
404C2×C61—82no—
405C2×C61#242811yescharacteristic
406C2×C61#305611yescharacteristic
407C2×C61#305711yescharacteristic
408C2×C61#326611yescharacteristic
409C2×C61#326711yescharacteristic
410C2×C61#330711yescharacteristic
411C2×C61#332011yescharacteristic
412C22×SD16—611no—
413C22×SD16—611no—
414C22×M16—611no—
415C23×C8—611no—
416C2×C4⋊Q8—611no—
417C2×C22⋊Q8—611no—
418C2×C22⋊Q8—611no—
419C2×C22⋊Q8—611no—
420C2×C22⋊Q8—611no—
421C2×#121C2×D6111yescharacteristic
422C2×#121C2×D6111yescharacteristic
423C2×C4×D4C2×D6111yescharacteristic
424C2×C4×D4C2×D6111yescharacteristic
425#468—1224no—
426#465—1224no—
427#461—1224no—
428#435—1224no—
429C2×#107—611no—
430C2×#106—611no—
431C2×C4⋊C8—611no—
432C2×#103—611no—
433C2×#103—611no—
434C2×#103—611no—
435C2×#103—611no—
436C2×#103—611no—
437C2×#103—611no—
438C2×#102—611no—
439C2×#102—611no—
440C2×C22⋊C8—611no—
441C2×C22⋊C8—611no—
442C2×#97—611no—
443#399—1221no—
444#399—1221no—
445#397—21no—
446#392—21no—
447#390—1221no—
448#386—21no—
449#386—21no—
450#384—1221no—
451#382C2×D6111yescharacteristic
452#380C2×D6111yescharacteristic
453#380C2×D6111yescharacteristic
454C4×C4⋊C4—611no—
455#340—611no—
456#340—611no—
457#340—611no—
458#340—611no—
459C61#2540011yescharacteristic, complemented, Sylow
460C22×Q8—611no—
461C22×Q8—611no—
462C22×D4—21no—
463C22×D4—21no—
464C22×D4C22⋊D6111yescharacteristic
465C22×D4C22×D6111yescharacteristic
466C23×C4—21no—
467C23×C4C22×D6111yescharacteristic
468C23×C4C22×D6111yescharacteristic
469C2×SD16—1222no—
470C2×SD16—1222no—
471C2×SD16—1222no—
472C2×SD16—1222no—
473C2×SD16—2441no—
474C2×SD16—2441no—
475C2×M16—1222no—
476C2×M16—1222no—
477C2×M16—2441no—
478C22×C8—611no—
479C22×C8—611no—
480C22×C8—611no—
481C22×C8—611no—
482C22×C8—1222no—
483C22×C8—1222no—
484C22×C8—2441no—
485C4⋊Q8—1222no—
486C4⋊Q8—1222no—
487C22⋊Q8—1222no—
488C22⋊Q8—1222no—
489C22⋊Q8—1222no—
490C22⋊Q8—1222no—
491C22⋊Q8—2441no—
492C22⋊Q8—2441no—
493C22⋊Q8—2441no—
494C22⋊Q8—2441no—
495#121—22no—
496#121—22no—
497#121—41no—
498#121—41no—
499C4×D4—22no—
500C4×D4—22no—
501C4×D4—22no—
502C4×D4—22no—
503C2×C4⋊C4—611no—
504C2×C4⋊C4—611no—
505C2×C4⋊C4—1221no—
506C2×C4⋊C4—1221no—
507C2×C4⋊C4—1221no—
508C2×C4⋊C4—1221no—
509C2×C4⋊C4—1221no—
510C2×C4⋊C4—1221no—
511C2×C4⋊C4C22⋊D6111yescharacteristic
512C2×C4⋊C4C22×D6111yescharacteristic
513C2×C4⋊C4C22×D6111yescharacteristic
514C2×C4⋊C4C22×D6111yescharacteristic
515C2×C22⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C22⋊C4—21no—
519C2×C22⋊C4—21no—
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—1221no—
527C2×C42C22×D6111yescharacteristic
528#107—1222no—
529#106—1222no—
530C4⋊C8—614no—
531#103—1222no—
532#103—1222no—
533#103—1222no—
534#103—1222no—
535#103—2441no—
536#103—2441no—
537#102—614no—
538#102—1222no—
539C22⋊C8—1222no—
540C22⋊C8—1222no—
541#97—1222no—
542#95—21no—
543#95—21no—
544#95—21no—
545#95—21no—
546#95—1221no—
547C24—21no—
548C24C2×C22⋊D6111yescharacteristic
549C24C2×C22⋊D6111yescharacteristic
550C2×Q8—1221no—
551C2×Q8—1221no—
552C2×Q8—1221no—
553C2×Q8—1221no—
554C2×Q8—1221no—
555C2×Q8—1221no—
556C2×Q8—1221no—
557C2×Q8—1221no—
558C2×Q8—1221no—
559C2×Q8—1221no—
560C2×Q8—1221no—
561C2×Q8—1221no—
562C2×D4—22no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—22no—
569C2×D4—41no—
570C2×D4—42no—
571C2×D4—42no—
572C2×D4—42no—
573C2×D4—42no—
574C2×D4—81no—
575C2×D4—81no—
576C2×D4D4×D6112yes—
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—42no—
593C22×C4—81no—
594C22×C4—81no—
595C22×C4—1221no—
596C22×C4—1221no—
597C22×C4—1221no—
598C22×C4—1221no—
599C22×C4C2×C22⋊D6111yescharacteristic
600C22×C4C2×C22⋊D6111yescharacteristic
601C22×C4C2×C22⋊D6111yescharacteristic
602C22×C4C2×C22⋊D6111yescharacteristic
603C22×C4C23×D6111yescharacteristic
604SD16—2444no—
605SD16—2444no—
606M16—2444no—
607C2×C8—612no—
608C2×C8—612no—
609C2×C8—612no—
610C2×C8—1221no—
611C2×C8—1221no—
612C2×C8—1221no—
613C2×C8—1221no—
614C2×C8—1221no—
615C2×C8—1221no—
616C2×C8—1221no—
617C2×C8—1221no—
618C2×C8—1221no—
619C2×C8—2444no—
620C4⋊C4—22no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—612no—
628C4⋊C4—612no—
629C4⋊C4—1221no—
630C4⋊C4—1221no—
631C4⋊C4—2442no—
632C4⋊C4—2442no—
633C4⋊C4—2442no—
634C4⋊C4—2442no—
635C4⋊C4—2442no—
636C4⋊C4—2442no—
637C22⋊C4—22no—
638C22⋊C4—22no—
639C22⋊C4—42no—
640C22⋊C4—42no—
641C22⋊C4—42no—
642C22⋊C4—81no—
643C22⋊C4—81no—
644C22⋊C4—2442no—
645C22⋊C4—2442no—
646C22⋊C4—2442no—
647C22⋊C4—2442no—
648C42—2442no—
649C42D4×D6112yes—
650C42#1175822412yes—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—22no—
663C23—21no—
664C23—21no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23#1451980712yes—
672C23C22×C22⋊D6111yescharacteristic
673Q8—2441no—
674Q8—2441no—
675Q8—2441no—
676Q8—2441no—
677Q8—2441no—
678Q8—2441no—
679Q8—2441no—
680Q8—2441no—
681D4—22no—
682D4—22no—
683D4—44no—
684D4—41no—
685D4—41no—
686D4—84no—
687D4—84no—
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—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—84no—
716C2×C4—1222no—
717C2×C4—1222no—
718C2×C4—2441no—
719C2×C4—2441no—
720C2×C4—2441no—
721C2×C4—2441no—
722C2×C4—2441no—
723C2×C4—2441no—
724C2×C4—2441no—
725C2×C4—2441no—
726C2×C4—2441no—
727C2×C4—2441no—
728C2×C4#1451974912yes—
729C2×C4#1451974912yes—
730C2×C4C2×D4×D6111yescharacteristic
731C2×C4C2×D4×D6111yescharacteristic
732C2×C4#41×D6111yescharacteristic
733C2×C4C2×#1175822411yescharacteristic
734C2×C4#1451982211yescharacteristic
735C2×C4#1451982311yescharacteristic
736C8—1222no—
737C8—1222no—
738C8—1222no—
739C8—2441no—
740C22—22no—
741C22—22no—
742C22—22no—
743C22—41no—
744C22—41no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—41no—
750C22—41no—
751C22—42no—
752C22—41no—
753C22—41no—
754C22—42no—
755C22—41no—
756C22—42no—
757C22—81no—
758C22—81no—
759C22—81no—
760C22—81no—
761C22C2×#1451974911yescharacteristic
762C22D4×C22⋊D6111yescharacteristic
763C22#1684040011yescharacteristic
764C22C2×#1451980711yescharacteristic
765C22#1684056011yescharacteristic
766C22#1684057311yescharacteristic
767C22#1684057311yescharacteristic
768C4—22no—
769C4—22no—
770C4—41no—
771C4—41no—
772C4—81no—
773C4—81no—
774C4—81no—
775C4—4881no—
776C4—4881no—
777C4—2442no—
778C4—2442no—
779C4#1684030711yescharacteristic
780C4#1684036511yescharacteristic
781C4#1684039611yescharacteristic
782C4#1684043011yescharacteristic
783C2—42no—
784C2—81no—
785C2—82no—
786C2#2144940911yescharacteristic
787C2#2145545111yescharacteristic
788C2#2145545511yescharacteristic
789C2#2145732511yescharacteristic
790C2#2145734011yescharacteristic
791C2#2145778911yescharacteristic
792C2#2145798411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
Fitting, prime radicalC61×#2535C2
socleC23×C61C22×D4
hypercenter#2535D61
hypocenterC61#25400
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2535

Complements

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

NH ≅ G/Ntype
1. C2×#16840006C2semidirect
2. C2×#16839989C2semidirect
3. C2×#16839967C2semidirect
4. C2×#16839834C2semidirect
5. #21450772C2semidirect
6. #21447022C2semidirect
7. #21447015C2semidirect
8. #21446822C2semidirect
9. #21446822C2semidirect
10. #21446638C2semidirect
11. #21446585C2semidirect
12. #21446250C2semidirect
13. #21446240C2semidirect
14. #21445644C2semidirect
106. C4⋊#92418D4semidirect
114. #14519698D4semidirect
459. C61#25400semidirect

Maximal subgroups

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

subgroupindex
C2×#168400062
C2×#168399892
C2×#168399672
C2×#168398342
#214507722
#214470222
#214470152
#214468222
#214466382
#214465852
#214462502
#214462402
#214456442
C61×#25352
#2540061