Finite Group Databasebeta

← #29707343

Subgroups — #29707343

Order 15616.

1362 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840392C211yesmaximal, characteristic, complemented
2C2×#16839765C211yesmaximal, characteristic
3C2×#102×D61C211yesmaximal, characteristic
4#21448398C211yesmaximal, characteristic
5#21446964C211yesmaximal, characteristic, complemented
6#21446963C211yesmaximal, characteristic, complemented
7#21446962C211yesmaximal, characteristic, complemented
8#21446956C211yesmaximal, characteristic, complemented
9#21446955C211yesmaximal, characteristic, complemented
10#21446954C211yesmaximal, characteristic, complemented
11#21446953C211yesmaximal, characteristic, complemented
12#21445537C211yesmaximal, characteristic, complemented
13#21445534C211yesmaximal, characteristic, complemented
14#21445514C211yesmaximal, characteristic, complemented
15C61×#2025C211yesmaximal, characteristic, complemented
16C22×D4×D61C2211yescharacteristic
17C22×#11758189C2211yescharacteristic
18C22×C8×D61C2211yescharacteristic
19#16840392—24no—
20#16840392—24no—
21C2×#14519777C2211yescharacteristic, complemented
22C2×#14519776—21no—
23C2×#14519776C2211yescharacteristic, complemented
24C2×#14519768C2211yescharacteristic, complemented
25C2×#14519767—21no—
26C2×#14519757—21no—
27C2×#14519755—21no—
28C2×#14519735C2211yescharacteristic
29C2×#14519735C2211yescharacteristic
30C2×#14519734C2211yescharacteristic
31C2×C4⋊C4×D61C2211yescharacteristic
32#16839765—24no—
33C2×#14519699C2211yescharacteristic
34C2×#14519699C2211yescharacteristic
35C2×#14519698C2211yescharacteristic
36C2×#14519698C2211yescharacteristic
37C2×#14519697C2211yescharacteristic
38C2×#14519697C2211yescharacteristic
39#102×D61—24no—
40#16839665C2211yescharacteristic
41#16839664C2211yescharacteristic
42#16839663C2211yescharacteristic
43#16839662—21no—
44#16839662—21no—
45#16839617—21no—
46#16839617—21no—
47#16839525C2211yescharacteristic, complemented
48#16839525C2211yescharacteristic, complemented
49#16839524C2211yescharacteristic, complemented
50#16839524C2211yescharacteristic, complemented
51#16839524C2211yescharacteristic, complemented
52#16839524C2211yescharacteristic, complemented
53#16839517C2211yescharacteristic, complemented
54#16839516C2211yescharacteristic, complemented
55#16839516C2211yescharacteristic, complemented
56C2×#125×C61C2211yescharacteristic, complemented
57C2×#102×C61C2211yescharacteristic
58C2×#102×C61C2211yescharacteristic
59C61×#390C2211yescharacteristic
60C61×#340C2211yescharacteristic, complemented
61C61×#340C2211yescharacteristic, complemented
62C61×#336C2211yescharacteristic, complemented
63C24×D61—21no—
64C22×Dic122—21no—
65C22×Dic122—21no—
66C22×D244C2311yescharacteristic
67C22×C22⋊D61—21no—
68C2×D4×D61—22no—
69C2×D4×D61—22no—
70C2×D4×D61—22no—
71C2×D4×D61—22no—
72C2×D4×D61—22no—
73C2×D4×D61Q814yescomplemented
74C22×C4×D61—21no—
75C22×C4×D61C2311yescharacteristic
76C2×#11758189—22no—
77C2×#11758189—22no—
78C2×#11758189—22no—
79C22×#92418C2311yescharacteristic
80C22×#92418C2311yescharacteristic
81C2×C8×D61—22no—
82C2×C8×D61—22no—
83C2×C8×D61—22no—
84#14519777—22no—
85#14519777—22no—
86#14519776—28no—
87#14519776—22no—
88#14519776—22no—
89#14519768—22no—
90#14519768—22no—
91#14519767—28no—
92#14519757—28no—
93#14519755—28no—
94#14519735—22no—
95#14519735—22no—
96#14519735—22no—
97#14519735D414yes—
98#14519734—22no—
99#14519734—22no—
100C2×C4⋊Dic61—21no—
101C2×C4⋊Dic61—21no—
102C2×C4⋊Dic61C2311yescharacteristic
103C2×C4⋊Dic61C2311yescharacteristic
104C2×C4⋊Dic61C2311yescharacteristic
105C2×#11758196—21no—
106C2×#11758196—21no—
107C2×#11758196—21no—
108C2×#11758196D411yescharacteristic
109C2×#11758196D411yescharacteristic
110C4⋊C4×D61—22no—
111C4⋊C4×D61D414yes—
112C2×C22⋊Dic61—21no—
113C2×C22⋊Dic61—21no—
114C2×#11758198—21no—
115C2×#11758198—21no—
116C2×#11758198—21no—
117C2×#11758198—21no—
118C2×#11758198—21no—
119C2×#11758198—21no—
120C2×#11758198D411yescharacteristic
121C2×#11758198D411yescharacteristic
122C2×C4×Dic61—21no—
123C2×C4×Dic61—21no—
124C2×C4×Dic61C2311yescharacteristic
125#14519699—22no—
126#14519699—22no—
127#14519698—22no—
128#14519698—22no—
129#14519697—22no—
130#14519697—22no—
131C22×D4×C61C2311yescharacteristic
132C22×C8×C61C2311yescharacteristic
133C22×C8×C61C2311yescharacteristic
134#125×C61—22no—
135#125×C61—22no—
136C2×C4⋊C4×C61—21no—
137C2×C4⋊C4×C61—21no—
138C2×C4⋊C4×C61C2311yescharacteristic
139C2×C4⋊C4×C61C2311yescharacteristic
140C2×C4⋊C4×C61C2311yescharacteristic
141C2×C22⋊C4×C61—21no—
142C2×C22⋊C4×C61—21no—
143C2×C42×C61C2311yescharacteristic
144#102×C61—22no—
145#102×C61—22no—
146C24×C61—21no—
147C23×D61—21no—
148C23×D61—24no—
149C23×D61—42no—
150C23×D61—42no—
151C23×D61—81no—
152C23×D61—81no—
153C23×D61—81no—
154C23×D61—81no—
155C23×D61C2×D411yescharacteristic
156C2×D4×C61—21no—
157C2×D4×C61—21no—
158C2×D4×C61—21no—
159C2×D4×C61—21no—
160C2×D4×C61—21no—
161C2×D4×C61C2×Q812yes—
162C22×C4×C61—21no—
163C22×C4×C61—21no—
164C22×C4×C61—21no—
165C22×C4×C61C2×D411yescharacteristic
166C22×C4×C61C2×D411yescharacteristic
167C22×C4×C61C2411yescharacteristic
168C2×C22⋊D61—24no—
169C2×C22⋊D61—42no—
170C2×C22⋊D61—42no—
171C22×Dic61—21no—
172C22×Dic61—21no—
173C22×Dic61—21no—
174C22×Dic61C2×D411yescharacteristic
175C22×Dic61C2×D411yescharacteristic
176C22×Dic61C2×D411yescharacteristic
177D4×D61—28no—
178D4×D61—28no—
179D4×D61—44no—
180D4×D61—44no—
181C2×D244—21no—
182C2×D244—21no—
183C2×D244—21no—
184C2×D244—21no—
185C2×D244—21no—
186C2×D244C2×Q812yes—
187C2×C4×D61—24no—
188C2×C4×D61—81no—
189C2×C4×D61—81no—
190C2×C4×D61C2×D412yes—
191C2×C4×D61C2×D412yes—
192C2×C4×D61C2×Q812yes—
193C2×C4×D61#4112yes—
194C2×C4×D61#4112yes—
195C2×C4×D61#4112yes—
196C2×Dic122—24no—
197C2×Dic122—24no—
198C2×Dic122—81no—
199C2×Dic122—81no—
200C2×Dic122—81no—
201C2×Dic122—81no—
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—24no—
209C4⋊C4×C61—24no—
210C4⋊C4×C61—21no—
211C4⋊C4×C61—21no—
212C4⋊C4×C61—21no—
213C4⋊C4×C61—21no—
214C4⋊C4×C61C2×D412yes—
215C4⋊C4×C61C2×D412yes—
216C22⋊C4×C61—81no—
217C22⋊C4×C61—81no—
218C42×C61—21no—
219C42×C61—21no—
220C22⋊Dic61—81no—
221C22⋊Dic61—81no—
222#11758198—24no—
223#11758198—22no—
224#11758198—22no—
225#11758198—42no—
226#11758198—81no—
227#11758198—81no—
228#11758198—81no—
229#11758198—81no—
230C4⋊Dic61—24no—
231C4⋊Dic61—24no—
232C4⋊Dic61—21no—
233C4⋊Dic61—21no—
234C4⋊Dic61—21no—
235C4⋊Dic61—21no—
236C4⋊Dic61C2×D412yes—
237C4⋊Dic61C2×D412yes—
238#11758196—24no—
239#11758196—24no—
240#11758196—24no—
241#11758196—22no—
242#11758196—22no—
243C4×Dic61—21no—
244C4×Dic61—21no—
245C4×Dic61—24no—
246C4×Dic61—42no—
247C2×#92418—21no—
248C2×#92418—21no—
249C2×#92418—21no—
250C2×#92418—21no—
251C2×#92418—21no—
252C2×#92418—21no—
253#11758189—44no—
254C8×D61—44no—
255C23×C61—22no—
256C23×C61—41no—
257C23×C61—41no—
258C23×C61—41no—
259C23×C61—41no—
260C23×C61—41no—
261C23×C61—41no—
262C23×C61C22×D411yescharacteristic
263C22×D61—21no—
264C22×D61—21no—
265C22×D61—21no—
266C22×D61—21no—
267C22×D61—22no—
268C22×D61—41no—
269C22×D61—41no—
270C22×D61—41no—
271C22×D61—41no—
272C22×D61—41no—
273C22×D61—41no—
274C22×D61—48no—
275C22×D61—84no—
276C22×D61—84no—
277C22×D61—84no—
278C22×D61—84no—
279C22×D61—84no—
280C22×D61—84no—
281C22×D61#12012yes—
282C22×D61C22⋊Q812yes—
283C22×D61#12412yes—
284D4×C61—22no—
285D4×C61—22no—
286D4×C61—41no—
287D4×C61—41no—
288C2×C4×C61—22no—
289C2×C4×C61—22no—
290C2×C4×C61—21no—
291C2×C4×C61—21no—
292C2×C4×C61—21no—
293C2×C4×C61—21no—
294C2×C4×C61—21no—
295C2×C4×C61—21no—
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×C61C22×D411yescharacteristic
304C2×C4×C61C22×D411yescharacteristic
305C2×C4×C61C22×Q811yescharacteristic
306C2×C4×C61C2×#4111yescharacteristic
307C2×C4×C61C2×#4111yescharacteristic
308C2×C4×C61C2×#4111yescharacteristic
309C22⋊D61—48no—
310C2×Dic61—21no—
311C2×Dic61—21no—
312C2×Dic61—22no—
313C2×Dic61—22no—
314C2×Dic61—21no—
315C2×Dic61—21no—
316C2×Dic61—21no—
317C2×Dic61—21no—
318C2×Dic61—41no—
319C2×Dic61—41no—
320C2×Dic61—41no—
321C2×Dic61—41no—
322C2×Dic61—41no—
323C2×Dic61—41no—
324C2×Dic61—41no—
325C2×Dic61#12012yes—
326C2×Dic61C22⋊Q812yes—
327C2×Dic61#12412yes—
328D244—22no—
329D244—22no—
330D244—41no—
331D244—41no—
332C4×D61—84no—
333C4×D61C22⋊Q814yes—
334C4×D61C22⋊Q814yes—
335C4×D61#12414yes—
336C4×D61#12414yes—
337Dic122—84no—
338Dic122—84no—
339C8×C61—41no—
340C8×C61—41no—
341#92418—41no—
342#92418—41no—
343#23456—611nomaximal, Sylow
344C22×C61—42no—
345C22×C61—42no—
346C22×C61—42no—
347C22×C61—81no—
348C22×C61—81no—
349C22×C61—81no—
350C22×C61—81no—
351C22×C61C2×#12011yescharacteristic
352C22×C61C2×C22⋊Q811yescharacteristic
353C22×C61C2×#12411yescharacteristic
354C22×C61#57611yescharacteristic
355C22×C61#57611yescharacteristic
356C22×C61#57711yescharacteristic
357C22×C61#57711yescharacteristic
358C2×D61—22no—
359C2×D61—22no—
360C2×D61—22no—
361C2×D61—22no—
362C2×D61—22no—
363C2×D61—22no—
364C2×D61—42no—
365C2×D61—42no—
366C2×D61—42no—
367C2×D61—816no—
368C2×D61—81no—
369C2×D61—81no—
370C2×D61—81no—
371C2×D61—81no—
372C2×D61#39314yes—
373C4×C61—41no—
374C4×C61—42no—
375C4×C61—41no—
376C4×C61—42no—
377C4×C61—81no—
378C4×C61C2×C22⋊Q811yescharacteristic
379C4×C61C2×C22⋊Q811yescharacteristic
380C4×C61C2×#12411yescharacteristic
381C4×C61C2×#12411yescharacteristic
382Dic61—41no—
383Dic61—42no—
384Dic61—42no—
385Dic61—41no—
386Dic61—81no—
387Dic61#39314yes—
388C2×#544—611no—
389C2×#418—611no—
390C22×#102—611no—
391#2309—611no—
392#2025—611no—
393#2025—611no—
394#2025—611no—
395#2025D6111yescharacteristic, complemented
396#2023—611no—
397#2023—611no—
398#2023—611no—
399#2023—611no—
400#1736—611no—
401#1735—611no—
402#1729—611no—
403C2×C61—82no—
404C2×C61C2×#39311yescharacteristic
405C2×C61#300811yescharacteristic
406C2×C61#301011yescharacteristic
407C2×C61#308111yescharacteristic
408C2×C61#308111yescharacteristic
409C2×C61#313611yescharacteristic
410C2×C61#313611yescharacteristic
411D61—24no—
412D61—82no—
413C23×D4—611no—
414C22×M16—611no—
415C23×C8—611no—
416#544—1224no—
417#544—1224no—
418C2×C4⋊Q8—611no—
419C2×C4⋊Q8—611no—
420C2×C4⋊Q8—1221no—
421C2×#125—611no—
422C2×#125—1221no—
423C2×#125C2×D6111yescharacteristic, complemented
424C2×C22⋊Q8—1221no—
425C2×C22⋊Q8—1221no—
426C2×#117—611no—
427C2×#117—611no—
428C2×#117—611no—
429C22×C4⋊C4—611no—
430#418—1224no—
431C2×#102—611no—
432C2×#102—611no—
433C2×#102—611no—
434C2×#102—611no—
435C2×#102—611no—
436C2×#102—611no—
437C2×#102—1224no—
438C2×#102C2×D6111yescharacteristic
439C2×#102C2×D6111yescharacteristic
440#390—611no—
441#390—611no—
442#390—611no—
443#390—1221no—
444#390—1221no—
445#390C2×D6111yescharacteristic
446#379—1221no—
447#379—1221no—
448#340—611no—
449#340—611no—
450#340—611no—
451#340—611no—
452#340—611no—
453#340—611no—
454#340C2×D6111yescharacteristic, complemented
455#340C2×D6111yescharacteristic, complemented
456#336—611no—
457#336—611no—
458#336—611no—
459#336C2×D6111yescharacteristic, complemented
460C61#2345611yescharacteristic, complemented, Sylow
461C25—1221no—
462C22×Q8—1221no—
463C22×Q8—1221no—
464C22×D4—614no—
465C22×D4—611no—
466C22×D4—1222no—
467C22×D4—1222no—
468C22×D4—1222no—
469C22×D4—1222no—
470C22×D4—1222no—
471C22×D4—1221no—
472C22×D4C22×D6111yescharacteristic
473C23×C4—611no—
474C23×C4—1221no—
475C2×M16—1222no—
476C2×M16—1222no—
477C2×M16—1222no—
478C22×C8—611no—
479C22×C8—611no—
480C22×C8—1222no—
481C22×C8—1222no—
482C22×C8—1222no—
483C22×C8C22×D6111yescharacteristic
484C22×C8C22×D6111yescharacteristic
485C4⋊Q8—1222no—
486C4⋊Q8—1222no—
487C4⋊Q8—1222no—
488C4⋊Q8—1228no—
489C4⋊Q8—1222no—
490#125—22no—
491#125—22no—
492#125—1222no—
493#125—1228no—
494#125—1222no—
495C22⋊Q8—1228no—
496C22⋊Q8—1228no—
497#117—614no—
498#117—1222no—
499#117—1222no—
500#117—1222no—
501#117—1222no—
502#117—1222no—
503C2×C4⋊C4—21no—
504C2×C4⋊C4—21no—
505C2×C4⋊C4—611no—
506C2×C4⋊C4—611no—
507C2×C4⋊C4—614no—
508C2×C4⋊C4—611no—
509C2×C4⋊C4—611no—
510C2×C4⋊C4—611no—
511C2×C4⋊C4—1222no—
512C2×C4⋊C4—1221no—
513C2×C4⋊C4—1221no—
514C2×C4⋊C4—1221no—
515C2×C4⋊C4—1221no—
516C2×C4⋊C4—1221no—
517C2×C4⋊C4C22×D6111yescharacteristic
518C2×C4⋊C4C22×D6111yescharacteristic
519C2×C4⋊C4C22×D6111yescharacteristic
520C2×C22⋊C4—21no—
521C2×C22⋊C4—21no—
522C2×C22⋊C4—611no—
523C2×C22⋊C4—611no—
524C2×C22⋊C4—1221no—
525C2×C22⋊C4—1221no—
526C2×C22⋊C4—1221no—
527C2×C22⋊C4—1221no—
528C2×C22⋊C4—1221no—
529C2×C22⋊C4—1221no—
530C2×C22⋊C4—1221no—
531C2×C22⋊C4—1221no—
532C2×C42—611no—
533C2×C42—1221no—
534C2×C42—1221no—
535C2×C42C22×D6111yescharacteristic
536#102—22no—
537#102—22no—
538#102—1222no—
539#102—1222no—
540#102—1222no—
541#102—1222no—
542#102—1222no—
543#102—1222no—
544C24—21no—
545C24—611no—
546C24—1224no—
547C24—1221no—
548C24—4881no—
549C24—4881no—
550C24—4881no—
551C24—4881no—
552C24—2442no—
553C24—2442no—
554C2×Q8—1224no—
555C2×Q8—1224no—
556C2×Q8—4881no—
557C2×Q8—4881no—
558C2×Q8—4881no—
559C2×Q8—4881no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—612no—
566C2×D4—1228no—
567C2×D4—1228no—
568C2×D4—1224no—
569C2×D4—1221no—
570C2×D4—1221no—
571C2×D4—1221no—
572C2×D4—1221no—
573C2×D4—1221no—
574C2×D4—2444no—
575C2×D4—2444no—
576C2×D4—2442no—
577C2×D4—2442no—
578C2×D4Q8×D6112yes—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—611no—
583C22×C4—612no—
584C22×C4—612no—
585C22×C4—612no—
586C22×C4—612no—
587C22×C4—612no—
588C22×C4—612no—
589C22×C4—611no—
590C22×C4—611no—
591C22×C4—1224no—
592C22×C4—1221no—
593C22×C4—1221no—
594C22×C4—1221no—
595C22×C4—4881no—
596C22×C4—4881no—
597C22×C4D4×D6111yescharacteristic
598C22×C4D4×D6111yescharacteristic
599C22×C4C23×D6111yescharacteristic
600M16—2444no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—1221no—
608C2×C8—1221no—
609C2×C8—1221no—
610C2×C8—1221no—
611C2×C8—1221no—
612C2×C8—1221no—
613C2×C8—2444no—
614C4⋊C4—24no—
615C4⋊C4—24no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—612no—
621C4⋊C4—612no—
622C4⋊C4—1224no—
623C4⋊C4—1222no—
624C4⋊C4—1222no—
625C4⋊C4—1224no—
626C4⋊C4—1224no—
627C4⋊C4—1224no—
628C4⋊C4—1224no—
629C4⋊C4—1221no—
630C4⋊C4—1221no—
631C4⋊C4—1221no—
632C4⋊C4—1221no—
633C4⋊C4D4×D6112yes—
634C4⋊C4D4×D6112yes—
635C22⋊C4—81no—
636C22⋊C4—81no—
637C22⋊C4—1222no—
638C22⋊C4—1222no—
639C22⋊C4—1224no—
640C22⋊C4—4881no—
641C22⋊C4—4881no—
642C22⋊C4—4881no—
643C22⋊C4—4881no—
644C22⋊C4—4881no—
645C22⋊C4—4881no—
646C22⋊C4—2442no—
647C42—21no—
648C42—21no—
649C42—1224no—
650C42—1221no—
651C42—1221no—
652C42—2442no—
653C23—22no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—612no—
661C23—612no—
662C23—612no—
663C23—1221no—
664C23—1221no—
665C23—1221no—
666C23—1221no—
667C23—1222no—
668C23—4884no—
669C23—4884no—
670C23—4884no—
671C23—4884no—
672C23—4884no—
673C23—4884no—
674C23—2448no—
675C23—2441no—
676C23—2441no—
677C23—2441no—
678C23—2441no—
679C23—2441no—
680C23—2441no—
681C23C2×D4×D6111yescharacteristic
682Q8—4884no—
683Q8—4884no—
684D4—22no—
685D4—22no—
686D4—41no—
687D4—41no—
688D4—1222no—
689D4—1222no—
690D4—2448no—
691D4—2441no—
692D4—2441no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—612no—
709C2×C4—612no—
710C2×C4—612no—
711C2×C4—614no—
712C2×C4—614no—
713C2×C4—614no—
714C2×C4—614no—
715C2×C4—1222no—
716C2×C4—1221no—
717C2×C4—1221no—
718C2×C4—1222no—
719C2×C4—1221no—
720C2×C4—1221no—
721C2×C4—1221no—
722C2×C4—1221no—
723C2×C4—4884no—
724C2×C4—2441no—
725C2×C4—2441no—
726C2×C4—2441no—
727C2×C4—2441no—
728C2×C4—2441no—
729C2×C4—2441no—
730C2×C4—2441no—
731C2×C4C2×D4×D6111yescharacteristic
732C2×C4C2×D4×D6111yescharacteristic
733C2×C4C2×Q8×D6111yescharacteristic
734C2×C4#41×D6111yescharacteristic
735C2×C4#41×D6111yescharacteristic
736C2×C4#41×D6111yescharacteristic
737C8—41no—
738C8—41no—
739C8—2441no—
740C8—2441no—
741C22—42no—
742C22—42no—
743C22—42no—
744C22—81no—
745C22—81no—
746C22—81no—
747C22—81no—
748C22—614no—
749C22—1222no—
750C22—1222no—
751C22—1222no—
752C22—1222no—
753C22—1222no—
754C22—1222no—
755C22—48816no—
756C22—4881no—
757C22—4881no—
758C22—4881no—
759C22—4881no—
760C22—2442no—
761C22—2442no—
762C22—2442no—
763C22#120×D6111yescharacteristic
764C22C22⋊Q8×D6111yescharacteristic
765C22#124×D6111yescharacteristic
766C22#1684056411yescharacteristic
767C22#1684056611yescharacteristic
768C22#1684056911yescharacteristic
769C22#1684057211yescharacteristic
770C4—41no—
771C4—42no—
772C4—41no—
773C4—42no—
774C4—81no—
775C4—614no—
776C4—4881no—
777C4—2441no—
778C4—2442no—
779C4—2442no—
780C4—2441no—
781C4C22⋊Q8×D6111yescharacteristic
782C4C22⋊Q8×D6111yescharacteristic
783C4#124×D6111yescharacteristic
784C4#124×D6111yescharacteristic
785C2—82no—
786C2—1224no—
787C2—4882no—
788C2#393×D6111yescharacteristic
789C2#2145508411yescharacteristic
790C2#2145510211yescharacteristic
791C2#2145564711yescharacteristic
792C2#2145564911yescharacteristic
793C2#2145617211yescharacteristic
794C2#2145617411yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2025C2
socleC23×C61C22×D4
prime radicalC22×D4×D61C22
hypercenter#2025D61
hypocenterC61#23456
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2025

Complements

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

NH ≅ G/Ntype
1. C2×#16840392C2semidirect
5. #21446964C2semidirect
6. #21446963C2semidirect
7. #21446962C2semidirect
8. #21446956C2semidirect
9. #21446955C2semidirect
10. #21446954C2semidirect
11. #21446953C2semidirect
12. #21445537C2semidirect
13. #21445534C2semidirect
14. #21445514C2semidirect
15. C61×#2025C2semidirect
21. C2×#14519777C22semidirect
23. C2×#14519776C22semidirect
24. C2×#14519768C22semidirect
47. #16839525C22semidirect
48. #16839525C22semidirect
49. #16839524C22semidirect
50. #16839524C22semidirect
51. #16839524C22semidirect
52. #16839524C22semidirect
53. #16839517C22semidirect
54. #16839516C22semidirect
55. #16839516C22semidirect
56. C2×#125×C61C22semidirect
60. C61×#340C22semidirect
61. C61×#340C22semidirect
62. C61×#336C22semidirect
73. C2×D4×D61Q8semidirect
395. #2025D61semidirect
423. C2×#125C2×D61semidirect
454. #340C2×D61semidirect
455. #340C2×D61semidirect
459. #336C2×D61semidirect
460. C61#23456semidirect

Maximal subgroups

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

subgroupindex
C2×#168403922
C2×#168397652
C2×#102×D612
#214483982
#214469642
#214469632
#214469622
#214469562
#214469552
#214469542
#214469532
#214455372
#214455342
#214455142
C61×#20252
#2345661