Finite Group Databasebeta

← #29707364

Subgroups — #29707364

Order 15616.

1250 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840392C211yesmaximal, characteristic, complemented
2C2×#16839760C211yesmaximal, characteristic
3C2×#16839755C211yesmaximal, characteristic
4#21448409C211yesmaximal, characteristic
5#21446969C211yesmaximal, characteristic, complemented
6#21446967C211yesmaximal, characteristic, complemented
7#21446963C211yesmaximal, characteristic, complemented
8#21446961C211yesmaximal, characteristic, complemented
9#21446959C211yesmaximal, characteristic, complemented
10#21446955C211yesmaximal, characteristic, complemented
11#21446953C211yesmaximal, characteristic, complemented
12#21445537C211yesmaximal, characteristic, complemented
13#340×D61C211yesmaximal, characteristic, complemented
14#21445514C211yesmaximal, characteristic, complemented
15C61×#2025C211yesmaximal, characteristic, complemented
16C22×#11758224C2211yescharacteristic
17C22×#11758189C2211yescharacteristic
18C22×C8×D61C2211yescharacteristic
19#16840392—24no—
20#16840392—24no—
21C2×#14519777C2211yescharacteristic
22C2×#14519776—21no—
23C2×#14519776C2211yescharacteristic
24C2×#14519768C2211yescharacteristic
25C2×#14519767—21no—
26C2×#14519757—21no—
27C2×#14519755—21no—
28C2×#14519735C2211yescharacteristic
29C2×#14519734C2211yescharacteristic
30C2×C4⋊C4×D61C2211yescharacteristic
31C2×C4⋊C4×D61C2211yescharacteristic
32#16839760—24no—
33#16839755—24no—
34C2×#14519702C2211yescharacteristic
35C2×#14519702C2211yescharacteristic
36C2×#14519700C2211yescharacteristic
37C2×#14519700C2211yescharacteristic
38C2×#14519698C2211yescharacteristic
39C2×#14519698C2211yescharacteristic
40#16839668C2211yescharacteristic
41#16839667C2211yescharacteristic
42#16839665C2211yescharacteristic
43#16839638—21no—
44#16839638—21no—
45#16839620—21no—
46#16839620—21no—
47#16839525C2211yescharacteristic
48#16839525C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839524C2211yescharacteristic
52#16839524C2211yescharacteristic
53#16839517C2211yescharacteristic
54#16839516C2211yescharacteristic
55#16839516C2211yescharacteristic
56C2×#125×C61C2211yescharacteristic
57C2×#102×C61C2211yescharacteristic
58C2×#102×C61C2211yescharacteristic
59C61×#390C2211yescharacteristic
60C61×#340C2211yescharacteristic
61C61×#340C2211yescharacteristic
62C61×#336C2211yescharacteristic
63C2×#11758224—22no—
64C2×#11758224—22no—
65C2×#11758224—22no—
66C2×#11758224—22no—
67C2×#11758224—22no—
68C2×#11758224Q814yescomplemented
69C22×Dic122—21no—
70C22×Dic122—21no—
71C22×Dic122C2311yescharacteristic
72C22×C22⋊D61—21no—
73C23×Dic61—21no—
74C22×C4×D61—21no—
75C22×C4×D61—21no—
76C22×C4×D61C2311yescharacteristic
77C2×#11758189—22no—
78C2×#11758189—22no—
79C2×#11758189—22no—
80C22×#92418C2311yescharacteristic
81C22×#92418C2311yescharacteristic
82C2×C8×D61—22no—
83C2×C8×D61—22no—
84C2×C8×D61—22no—
85#14519777—22no—
86#14519777—22no—
87#14519776—28no—
88#14519776—22no—
89#14519776—22no—
90#14519768—22no—
91#14519768—22no—
92#14519767—28no—
93#14519757—28no—
94#14519755—28no—
95#14519735—22no—
96#14519735D414yes—
97#14519734—22no—
98#14519734—22no—
99C2×C4⋊Dic61—21no—
100C2×C4⋊Dic61—21no—
101C2×C4⋊Dic61C2311yescharacteristic
102C2×C4⋊Dic61C2311yescharacteristic
103C2×C4⋊Dic61C2311yescharacteristic
104C2×#11758196—21no—
105C2×#11758196—21no—
106C2×#11758196—21no—
107C2×#11758196—21no—
108C2×#11758196D411yescharacteristic
109C2×#11758196D411yescharacteristic
110C4⋊C4×D61—22no—
111C4⋊C4×D61—22no—
112C4⋊C4×D61—22no—
113C4⋊C4×D61D414yes—
114C2×C22⋊Dic61—21no—
115C2×C22⋊Dic61—21no—
116C2×#11758198—21no—
117C2×#11758198D411yescharacteristic
118C2×#11758198D411yescharacteristic
119C2×C4×Dic61—21no—
120C2×C4×Dic61C2311yescharacteristic
121#14519702—22no—
122#14519702—22no—
123#14519700—22no—
124#14519700—22no—
125#14519698—22no—
126#14519698—22no—
127#14519684—21no—
128#14519684—21no—
129#14519684—21no—
130#14519684—21no—
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×D61C2×D411yescharacteristic
148C2×D4×C61—21no—
149C2×D4×C61—21no—
150C2×D4×C61—21no—
151C2×D4×C61—21no—
152C2×D4×C61—21no—
153C2×D4×C61C2×Q812yes—
154C22×C4×C61—21no—
155C22×C4×C61—21no—
156C22×C4×C61—21no—
157C22×C4×C61C2×D411yescharacteristic
158C22×C4×C61C2×D411yescharacteristic
159C22×C4×C61C2411yescharacteristic
160C2×C22⋊D61—24no—
161C2×C22⋊D61—42no—
162C2×C22⋊D61—42no—
163C22×Dic61—21no—
164C22×Dic61—21no—
165C22×Dic61—21no—
166C22×Dic61—24no—
167C22×Dic61—21no—
168C22×Dic61—42no—
169C22×Dic61—42no—
170C22×Dic61C2×D411yescharacteristic
171C22×Dic61C2×D411yescharacteristic
172C22×Dic61C2×D411yescharacteristic
173#11758224—28no—
174#11758224—28no—
175#11758224—44no—
176#11758224—44no—
177C2×C4×D61—24no—
178C2×C4×D61—42no—
179C2×C4×D61—81no—
180C2×C4×D61—81no—
181C2×C4×D61—81no—
182C2×C4×D61—81no—
183C2×C4×D61C2×D412yes—
184C2×C4×D61C2×D412yes—
185C2×C4×D61C2×Q812yes—
186C2×C4×D61#4112yes—
187C2×C4×D61#4112yes—
188C2×C4×D61#4112yes—
189C2×Dic122—21no—
190C2×Dic122—21no—
191C2×Dic122—21no—
192C2×Dic122—21no—
193C2×Dic122—21no—
194C2×Dic122—24no—
195C2×Dic122—24no—
196C2×Dic122—81no—
197C2×Dic122—81no—
198C2×Dic122—81no—
199C2×Dic122—81no—
200C2×Dic122C2×Q812yes—
201C2×C8×C61—21no—
202C2×C8×C61—21no—
203C2×C8×C61—21no—
204C2×C8×C61—21no—
205C2×C8×C61—21no—
206C2×C8×C61—21no—
207C4⋊C4×C61—24no—
208C4⋊C4×C61—24no—
209C4⋊C4×C61—21no—
210C4⋊C4×C61—21no—
211C4⋊C4×C61—21no—
212C4⋊C4×C61—21no—
213C4⋊C4×C61C2×D412yes—
214C4⋊C4×C61C2×D412yes—
215C22⋊C4×C61—81no—
216C22⋊C4×C61—81no—
217C42×C61—21no—
218C42×C61—21no—
219C22⋊Dic61—81no—
220C22⋊Dic61—81no—
221#11758198—24no—
222#11758198—22no—
223#11758198—22no—
224C4⋊Dic61—24no—
225C4⋊Dic61—24no—
226C4⋊Dic61—21no—
227C4⋊Dic61—21no—
228C4⋊Dic61—21no—
229C4⋊Dic61—21no—
230C4⋊Dic61C2×D412yes—
231C4⋊Dic61C2×D412yes—
232#11758196—24no—
233#11758196—24no—
234#11758196—24no—
235#11758196—22no—
236#11758196—22no—
237#11758196—42no—
238C4×Dic61—21no—
239C4×Dic61—21no—
240C4×Dic61—24no—
241C2×#92418—21no—
242C2×#92418—21no—
243C2×#92418—21no—
244C2×#92418—21no—
245C2×#92418—21no—
246C2×#92418—21no—
247#11758189—44no—
248C8×D61—44no—
249C23×C61—22no—
250C23×C61—41no—
251C23×C61—41no—
252C23×C61—41no—
253C23×C61—41no—
254C23×C61—41no—
255C23×C61—41no—
256C23×C61C22×D411yescharacteristic
257C22×D61—21no—
258C22×D61—21no—
259C22×D61—21no—
260C22×D61—21no—
261C22×D61#12012yes—
262C22×D61C22⋊Q812yes—
263C22×D61#12412yes—
264D4×C61—22no—
265D4×C61—22no—
266D4×C61—41no—
267D4×C61—41no—
268C2×C4×C61—22no—
269C2×C4×C61—22no—
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—41no—
277C2×C4×C61—41no—
278C2×C4×C61—41no—
279C2×C4×C61—41no—
280C2×C4×C61—41no—
281C2×C4×C61—41no—
282C2×C4×C61—41no—
283C2×C4×C61C22×D411yescharacteristic
284C2×C4×C61C22×D411yescharacteristic
285C2×C4×C61C22×Q811yescharacteristic
286C2×C4×C61C2×#4111yescharacteristic
287C2×C4×C61C2×#4111yescharacteristic
288C2×C4×C61C2×#4111yescharacteristic
289C22⋊D61—48no—
290C2×Dic61—21no—
291C2×Dic61—21no—
292C2×Dic61—22no—
293C2×Dic61—22no—
294C2×Dic61—22no—
295C2×Dic61—21no—
296C2×Dic61—21no—
297C2×Dic61—21no—
298C2×Dic61—21no—
299C2×Dic61—41no—
300C2×Dic61—41no—
301C2×Dic61—41no—
302C2×Dic61—41no—
303C2×Dic61—41no—
304C2×Dic61—41no—
305C2×Dic61—48no—
306C2×Dic61—41no—
307C2×Dic61—41no—
308C2×Dic61—41no—
309C2×Dic61#12012yes—
310C2×Dic61C22⋊Q812yes—
311C2×Dic61#12412yes—
312C4×D61—84no—
313C4×D61—84no—
314C4×D61C22⋊Q814yes—
315C4×D61C22⋊Q814yes—
316C4×D61#12414yes—
317C4×D61#12414yes—
318Dic122—22no—
319Dic122—22no—
320Dic122—41no—
321Dic122—41no—
322Dic122—84no—
323Dic122—84no—
324C8×C61—41no—
325C8×C61—41no—
326#92418—41no—
327#92418—41no—
328#23458—611nomaximal, Sylow
329C22×C61—42no—
330C22×C61—42no—
331C22×C61—42no—
332C22×C61—81no—
333C22×C61—81no—
334C22×C61—81no—
335C22×C61—81no—
336C22×C61C2×#12011yescharacteristic
337C22×C61C2×C22⋊Q811yescharacteristic
338C22×C61C2×#12411yescharacteristic
339C22×C61#57611yescharacteristic
340C22×C61#57711yescharacteristic
341C22×C61#57711yescharacteristic
342C22×C61#57811yescharacteristic
343C2×D61—22no—
344C2×D61—22no—
345C2×D61—22no—
346C2×D61—22no—
347C2×D61—22no—
348C2×D61—22no—
349C2×D61#39314yes—
350C4×C61—41no—
351C4×C61—42no—
352C4×C61—41no—
353C4×C61—42no—
354C4×C61—81no—
355C4×C61C2×C22⋊Q811yescharacteristic
356C4×C61C2×C22⋊Q811yescharacteristic
357C4×C61C2×#12411yescharacteristic
358C4×C61C2×#12411yescharacteristic
359Dic61—42no—
360Dic61—41no—
361Dic61—42no—
362Dic61—42no—
363Dic61—41no—
364Dic61—81no—
365Dic61#39314yes—
366C2×#544—611no—
367C2×#417—611no—
368C2×#416—611no—
369#2311—611no—
370#2026—611no—
371#2026—611no—
372#2025—611no—
373#2025D6111yescharacteristic, complemented
374#2024—611no—
375#2024—611no—
376#2023—611no—
377#2023—611no—
378#1736—611no—
379C2×#340—611no—
380#1729—611no—
381C2×C61—82no—
382C2×C61C2×#39311yescharacteristic
383C2×C61#301211yescharacteristic
384C2×C61#301311yescharacteristic
385C2×C61#308311yescharacteristic
386C2×C61#308411yescharacteristic
387C2×C61#313611yescharacteristic
388C2×C61#313711yescharacteristic
389D61—24no—
390C22×#41—611no—
391C22×M16—611no—
392C23×C8—611no—
393#544—1224no—
394#544—1224no—
395C2×C4⋊Q8—611no—
396C2×C4⋊Q8—611no—
397C2×C4⋊Q8—1221no—
398C2×#125—611no—
399C2×#125—1221no—
400C2×#125C2×D6111yescharacteristic
401C2×C22⋊Q8—1221no—
402C2×C22⋊Q8—1221no—
403C2×#117—611no—
404C2×#117—611no—
405C22×C4⋊C4—611no—
406C22×C4⋊C4—611no—
407#417—1224no—
408#416—1224no—
409C2×#103—611no—
410C2×#103—611no—
411C2×#103—611no—
412C2×#103—611no—
413C2×#102—611no—
414C2×#102—611no—
415C2×#102C2×D6111yescharacteristic
416C2×#102C2×D6111yescharacteristic
417#391—611no—
418#391—611no—
419#390—611no—
420#390C2×D6111yescharacteristic
421#386—1221no—
422#386—1221no—
423#380—1221no—
424#380—1221no—
425#340—611no—
426#340—611no—
427#340—611no—
428#340—611no—
429#340—611no—
430#340—611no—
431#340C2×D6111yescharacteristic
432#340C2×D6111yescharacteristic
433#336—611no—
434#336—611no—
435#336—611no—
436#336C2×D6111yescharacteristic
437C61#2345811yescharacteristic, complemented, Sylow
438C2×#41—614no—
439C2×#41—1222no—
440C2×#41—1222no—
441C2×#41—1222no—
442C2×#41—1222no—
443C2×#41—1222no—
444C22×Q8—611no—
445C22×Q8—1221no—
446C22×Q8—1221no—
447C22×D4—1221no—
448C22×D4C22×D6111yescharacteristic
449C23×C4—611no—
450C23×C4—1221no—
451C23×C4—1221no—
452C23×C4—1221no—
453C2×M16—1222no—
454C2×M16—1222no—
455C2×M16—1222no—
456C22×C8—611no—
457C22×C8—611no—
458C22×C8—1222no—
459C22×C8—1222no—
460C22×C8—1222no—
461C22×C8C22×D6111yescharacteristic
462C22×C8C22×D6111yescharacteristic
463C4⋊Q8—1222no—
464C4⋊Q8—1222no—
465C4⋊Q8—1222no—
466C4⋊Q8—1228no—
467C4⋊Q8—1222no—
468#125—22no—
469#125—22no—
470#125—1222no—
471#125—1228no—
472#125—1222no—
473C22⋊Q8—1228no—
474C22⋊Q8—1228no—
475#117—614no—
476#117—1222no—
477#117—1222no—
478#117—1222no—
479C2×C4⋊C4—21no—
480C2×C4⋊C4—21no—
481C2×C4⋊C4—611no—
482C2×C4⋊C4—611no—
483C2×C4⋊C4—614no—
484C2×C4⋊C4—611no—
485C2×C4⋊C4—611no—
486C2×C4⋊C4—611no—
487C2×C4⋊C4—1222no—
488C2×C4⋊C4—1222no—
489C2×C4⋊C4—1222no—
490C2×C4⋊C4—1221no—
491C2×C4⋊C4—1221no—
492C2×C4⋊C4—1221no—
493C2×C4⋊C4—1221no—
494C2×C4⋊C4—1221no—
495C2×C4⋊C4—1221no—
496C2×C4⋊C4C22×D6111yescharacteristic
497C2×C4⋊C4C22×D6111yescharacteristic
498C2×C4⋊C4C22×D6111yescharacteristic
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—611no—
502C2×C22⋊C4—611no—
503C2×C22⋊C4—1221no—
504C2×C22⋊C4—1221no—
505C2×C22⋊C4—1221no—
506C2×C42—611no—
507C2×C42—1221no—
508C2×C42C22×D6111yescharacteristic
509#103—1222no—
510#103—1222no—
511#103—1222no—
512#103—1222no—
513#102—22no—
514#102—22no—
515#102—1222no—
516#102—1222no—
517#95—1221no—
518#95—1221no—
519#95—1221no—
520#95—1221no—
521C24—21no—
522C24—611no—
523#41—1228no—
524#41—1228no—
525#41—2444no—
526#41—2444no—
527C2×Q8—612no—
528C2×Q8—1224no—
529C2×Q8—1224no—
530C2×Q8—1221no—
531C2×Q8—1221no—
532C2×Q8—1221no—
533C2×Q8—1221no—
534C2×Q8—1221no—
535C2×Q8—4881no—
536C2×Q8—4881no—
537C2×Q8—4881no—
538C2×Q8—4881no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—1224no—
545C2×D4—2442no—
546C2×D4—2442no—
547C2×D4Q8×D6112yes—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—611no—
552C22×C4—612no—
553C22×C4—612no—
554C22×C4—612no—
555C22×C4—612no—
556C22×C4—612no—
557C22×C4—612no—
558C22×C4—611no—
559C22×C4—611no—
560C22×C4—1224no—
561C22×C4—1224no—
562C22×C4—1221no—
563C22×C4—1221no—
564C22×C4—1221no—
565C22×C4—1221no—
566C22×C4—4881no—
567C22×C4—4881no—
568C22×C4—4881no—
569C22×C4—4881no—
570C22×C4—2442no—
571C22×C4—2442no—
572C22×C4—2442no—
573C22×C4D4×D6111yescharacteristic
574C22×C4D4×D6111yescharacteristic
575C22×C4C23×D6111yescharacteristic
576M16—2444no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—1221no—
584C2×C8—1221no—
585C2×C8—1221no—
586C2×C8—1221no—
587C2×C8—1221no—
588C2×C8—1221no—
589C2×C8—2444no—
590C4⋊C4—24no—
591C4⋊C4—24no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—612no—
597C4⋊C4—612no—
598C4⋊C4—1224no—
599C4⋊C4—1222no—
600C4⋊C4—1222no—
601C4⋊C4—1224no—
602C4⋊C4—1224no—
603C4⋊C4—1224no—
604C4⋊C4—1224no—
605C4⋊C4—1221no—
606C4⋊C4—1221no—
607C4⋊C4—1221no—
608C4⋊C4—1221no—
609C4⋊C4—2442no—
610C4⋊C4D4×D6112yes—
611C4⋊C4D4×D6112yes—
612C22⋊C4—81no—
613C22⋊C4—81no—
614C22⋊C4—1222no—
615C22⋊C4—1222no—
616C22⋊C4—1224no—
617C22⋊C4—4881no—
618C22⋊C4—4881no—
619C42—21no—
620C42—21no—
621C42—1224no—
622C42—1221no—
623C42—1221no—
624C23—22no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—612no—
632C23—612no—
633C23—612no—
634C23—1221no—
635C23—1221no—
636C23—1221no—
637C23—1221no—
638C23C2×D4×D6111yescharacteristic
639Q8—1222no—
640Q8—1222no—
641Q8—4884no—
642Q8—4884no—
643Q8—2441no—
644Q8—2441no—
645D4—22no—
646D4—22no—
647D4—41no—
648D4—41no—
649D4—2448no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—612no—
666C2×C4—612no—
667C2×C4—612no—
668C2×C4—614no—
669C2×C4—614no—
670C2×C4—614no—
671C2×C4—614no—
672C2×C4—1222no—
673C2×C4—1221no—
674C2×C4—1221no—
675C2×C4—1222no—
676C2×C4—1222no—
677C2×C4—1221no—
678C2×C4—1221no—
679C2×C4—1221no—
680C2×C4—1221no—
681C2×C4—4884no—
682C2×C4—4884no—
683C2×C4—2448no—
684C2×C4—2441no—
685C2×C4—2441no—
686C2×C4—2441no—
687C2×C4—2441no—
688C2×C4—2441no—
689C2×C4—2441no—
690C2×C4—2441no—
691C2×C4—2441no—
692C2×C4—2441no—
693C2×C4C2×D4×D6111yescharacteristic
694C2×C4C2×D4×D6111yescharacteristic
695C2×C4C2×Q8×D6111yescharacteristic
696C2×C4#41×D6111yescharacteristic
697C2×C4#41×D6111yescharacteristic
698C2×C4#41×D6111yescharacteristic
699C8—41no—
700C8—41no—
701C8—2441no—
702C8—2441no—
703C22—42no—
704C22—42no—
705C22—42no—
706C22—81no—
707C22—81no—
708C22—81no—
709C22—81no—
710C22—614no—
711C22—1222no—
712C22—1222no—
713C22—1222no—
714C22—1222no—
715C22—1222no—
716C22—1222no—
717C22#120×D6111yescharacteristic
718C22C22⋊Q8×D6111yescharacteristic
719C22#124×D6111yescharacteristic
720C22#1684056611yescharacteristic
721C22#1684056911yescharacteristic
722C22#1684057211yescharacteristic
723C22#1684057611yescharacteristic
724C4—41no—
725C4—42no—
726C4—41no—
727C4—42no—
728C4—81no—
729C4—614no—
730C4—4881no—
731C4—2441no—
732C4—2442no—
733C4—2442no—
734C4—2441no—
735C4—2442no—
736C4C22⋊Q8×D6111yescharacteristic
737C4C22⋊Q8×D6111yescharacteristic
738C4#124×D6111yescharacteristic
739C4#124×D6111yescharacteristic
740C2—82no—
741C2—1224no—
742C2#393×D6111yescharacteristic
743C2#2145512111yescharacteristic
744C2#2145513211yescharacteristic
745C2#2145567111yescharacteristic
746C2#2145568211yescharacteristic
747C2#2145617411yescharacteristic
748C2#2145618311yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2025C2
socleC23×C61C22×D4
prime radicalC22×#11758224C22
hypercenter#2025D61
hypocenterC61#23458
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. #21446969C2semidirect
6. #21446967C2semidirect
7. #21446963C2semidirect
8. #21446961C2semidirect
9. #21446959C2semidirect
10. #21446955C2semidirect
11. #21446953C2semidirect
12. #21445537C2semidirect
13. #340×D61C2semidirect
14. #21445514C2semidirect
15. C61×#2025C2semidirect
68. C2×#11758224Q8semidirect
373. #2025D61semidirect
437. C61#23458semidirect

Maximal subgroups

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

subgroupindex
C2×#168403922
C2×#168397602
C2×#168397552
#214484092
#214469692
#214469672
#214469632
#214469612
#214469592
#214469552
#214469532
#214455372
#340×D612
#214455142
C61×#20252
#2345861