Finite Group Databasebeta

← #29730961

Subgroups — #29730961

Order 15616.

1118 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840013C211yesmaximal, characteristic, complemented
2C2×#16839989C211yesmaximal, characteristic, complemented
3C2×#16839977C211yesmaximal, characteristic, complemented
4C2×#16839834C211yesmaximal, characteristic, complemented
5#21450758C211yesmaximal, characteristic, complemented
6#21447015C211yesmaximal, characteristic, complemented
7#21447008C211yesmaximal, characteristic, complemented
8#21446822C211yesmaximal, characteristic, complemented
9#21446815C211yesmaximal, characteristic, complemented
10#21446633C211yesmaximal, characteristic, complemented
11#21446580C211yesmaximal, characteristic, complemented
12#21446250C211yesmaximal, characteristic, complemented
13#21446245C211yesmaximal, characteristic, complemented
14#21445644C211yesmaximal, characteristic, complemented
15C61×#2537C211yesmaximal, characteristic, complemented
16C22×#11758200C2211yescharacteristic
17C22×#11758199C2211yescharacteristic
18C22×#11758194C2211yescharacteristic
19C23×#92418C2211yescharacteristic
20C2×#14519765C2211yescharacteristic
21C2×#14519756C2211yescharacteristic
22C2×#14519756C2211yescharacteristic
23C2×#14519751C2211yescharacteristic
24C2×#14519751C2211yescharacteristic
25#16840013—24no—
26#16839989—24no—
27#16839977—24no—
28#16839834—24no—
29C2×#14519708C2211yescharacteristic
30C2×#14519708C2211yescharacteristic
31C2×C4⋊#92418C2211yescharacteristic
32C2×#14519700C2211yescharacteristic
33C2×#14519700C2211yescharacteristic
34C2×#14519700C2211yescharacteristic
35C2×#14519698C2211yescharacteristic
36C2×#14519698C2211yescharacteristic
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×#121×C61—21no—
53C2×#121×C61C2211yescharacteristic
54C2×#121×C61C2211yescharacteristic
55C2×C4×D4×C61C2211yescharacteristic
56C2×C4×D4×C61C2211yescharacteristic
57C61×#394—21no—
58C61×#394—21no—
59C61×#384C2211yescharacteristic
60C61×#380—21no—
61C61×#380C2211yescharacteristic
62C61×#380C2211yescharacteristic
63C22×Dic122C2311yescharacteristic
64C22×D244C2311yescharacteristic
65C22×C22⋊D61—21no—
66C22×C22⋊D61—21no—
67C2×#11758200—22no—
68C2×#11758200—22no—
69C2×#11758200—41no—
70C2×#11758199—22no—
71C2×#11758199—22no—
72C2×#11758199—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#14519700—22no—
108#14519700—22no—
109#14519700—41no—
110#14519698—22no—
111#14519698D414yescomplemented
112#14519697—22no—
113#14519697—22no—
114#14519697—41no—
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—
130#121×C61—44no—
131C4×D4×C61—22no—
132C4×D4×C61—22no—
133C4×D4×C61—22no—
134C4×D4×C61—22no—
135C2×C4⋊C4×C61—21no—
136C2×C4⋊C4×C61—21no—
137C2×C4⋊C4×C61D411yescharacteristic
138C2×C4⋊C4×C61C2311yescharacteristic
139C2×C4⋊C4×C61C2311yescharacteristic
140C2×C4⋊C4×C61C2311yescharacteristic
141C2×C22⋊C4×C61—21no—
142C2×C22⋊C4×C61—21no—
143C2×C22⋊C4×C61—21no—
144C2×C22⋊C4×C61—21no—
145C2×C22⋊C4×C61—21no—
146C2×C22⋊C4×C61D411yescharacteristic
147C2×C22⋊C4×C61D411yescharacteristic
148C2×C42×C61C2311yescharacteristic
149#95×C61—21no—
150#95×C61—21no—
151C24×C61—21no—
152C24×C61C2×D411yescharacteristic
153C24×C61C2×D411yescharacteristic
154C23×D61—21no—
155C2×D4×C61—22no—
156C2×D4×C61—22no—
157C2×D4×C61—21no—
158C2×D4×C61—21no—
159C2×D4×C61—21no—
160C2×D4×C61—21no—
161C2×D4×C61—21no—
162C2×D4×C61—41no—
163C2×D4×C61—42no—
164C2×D4×C61—42no—
165C2×D4×C61—42no—
166C2×D4×C61—42no—
167C2×D4×C61—81no—
168C2×D4×C61—81no—
169C2×D4×C61C2×D412yes—
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—21no—
184C22×C4×C61—21no—
185C22×C4×C61—42no—
186C22×C4×C61—42no—
187C22×C4×C61—42no—
188C22×C4×C61C2×D411yescharacteristic
189C22×C4×C61C2×D411yescharacteristic
190C22×C4×C61C2×D411yescharacteristic
191C22×C4×C61C2×D411yescharacteristic
192C22×C4×C61C2411yescharacteristic
193C2×C22⋊D61—42no—
194C2×C22⋊D61—42no—
195C2×C22⋊D61—42no—
196C2×C22⋊D61—42no—
197C2×C22⋊D61—81no—
198C2×C22⋊D61—81no—
199C22×Dic61—21no—
200C22×Dic61—21no—
201C22×Dic61—21no—
202C2×D244—21no—
203C2×D244—21no—
204C2×D244—21no—
205C2×D244—21no—
206C2×D244—21no—
207C2×D244—21no—
208C2×Dic122—21no—
209C2×Dic122—21no—
210C2×Dic122—21no—
211C2×Dic122—21no—
212C2×Dic122—21no—
213C2×Dic122—21no—
214C4⋊C4×C61—22no—
215C4⋊C4×C61—21no—
216C4⋊C4×C61—21no—
217C4⋊C4×C61—21no—
218C4⋊C4×C61—21no—
219C4⋊C4×C61—21no—
220C4⋊C4×C61—21no—
221C4⋊C4×C61—42no—
222C4⋊C4×C61—81no—
223C22⋊C4×C61—22no—
224C22⋊C4×C61—22no—
225C22⋊C4×C61—42no—
226C22⋊C4×C61—42no—
227C22⋊C4×C61—42no—
228C22⋊C4×C61—42no—
229C22⋊C4×C61—42no—
230C42×C61C2×D412yes—
231C42×C61#4112yes—
232C22⋊Dic61—42no—
233C22⋊Dic61—42no—
234#11758200—44no—
235#11758199—44no—
236#11758198—42no—
237#11758198—42no—
238#11758198—42no—
239#11758198—42no—
240C4⋊Dic61—21no—
241C4⋊Dic61—21no—
242C4⋊Dic61C2×D412yes—
243C4⋊Dic61#4112yes—
244#11758196—42no—
245#11758196—42no—
246C4×Dic61—81no—
247#11758194—44no—
248C2×#92418—21no—
249C2×#92418—21no—
250C2×#92418—21no—
251C2×#92418—21no—
252C2×#92418—21no—
253C2×#92418—21no—
254C2×#92418—21no—
255C2×#92418—21no—
256C2×#92418—21no—
257C2×#92418—44no—
258C2×#92418C2×D412yes—
259C2×#92418C2×D412yes—
260C2×#92418C2×D412yes—
261C23×C61—21no—
262C23×C61—21no—
263C23×C61—21no—
264C23×C61—21no—
265C23×C61—21no—
266C23×C61—21no—
267C23×C61—21no—
268C23×C61—22no—
269C23×C61—21no—
270C23×C61—21no—
271C23×C61—21no—
272C23×C61—21no—
273C23×C61—21no—
274C23×C61—21no—
275C23×C61—41no—
276C23×C61—41no—
277C23×C61—41no—
278C23×C61—41no—
279C23×C61—41no—
280C23×C61—41no—
281C23×C61AGL(1,ℤ/8)12yes—
282C23×C61C22×D411yescharacteristic
283C22×D61—41no—
284C22×D61—41no—
285C22×D61—41no—
286C22×D61—41no—
287C22×D61—41no—
288C22×D61—41no—
289C22×D61—41no—
290D4×C61—22no—
291D4×C61—22no—
292D4×C61—44no—
293D4×C61—41no—
294D4×C61—41no—
295D4×C61—84no—
296D4×C61—84no—
297C2×C4×C61—21no—
298C2×C4×C61—21no—
299C2×C4×C61—21no—
300C2×C4×C61—21no—
301C2×C4×C61—21no—
302C2×C4×C61—21no—
303C2×C4×C61—21no—
304C2×C4×C61—21no—
305C2×C4×C61—21no—
306C2×C4×C61—21no—
307C2×C4×C61—41no—
308C2×C4×C61—41no—
309C2×C4×C61—41no—
310C2×C4×C61—41no—
311C2×C4×C61—41no—
312C2×C4×C61—41no—
313C2×C4×C61—41no—
314C2×C4×C61—41no—
315C2×C4×C61—41no—
316C2×C4×C61—41no—
317C2×C4×C61—41no—
318C2×C4×C61—41no—
319C2×C4×C61—41no—
320C2×C4×C61—41no—
321C2×C4×C61—41no—
322C2×C4×C61—41no—
323C2×C4×C61—41no—
324C2×C4×C61—84no—
325C2×C4×C61#12112yes—
326C2×C4×C61#12112yes—
327C2×C4×C61C22×D411yescharacteristic
328C2×C4×C61C22×D411yescharacteristic
329C2×C4×C61C2×#4111yescharacteristic
330C2×C4×C61C2×#4111yescharacteristic
331C2×C4×C61H(5,𝔽2)11yescharacteristic
332C2×C4×C61H(5,𝔽2)11yescharacteristic
333C22⋊D61—84no—
334C22⋊D61—84no—
335C2×Dic61—22no—
336C2×Dic61—22no—
337C2×Dic61—41no—
338C2×Dic61—41no—
339C2×Dic61—41no—
340C2×Dic61—41no—
341C2×Dic61—41no—
342C2×Dic61—41no—
343C2×Dic61—41no—
344D244—41no—
345D244—41no—
346D244—41no—
347D244—41no—
348Dic122—41no—
349Dic122—41no—
350Dic122—41no—
351Dic122—41no—
352#92418—22no—
353#92418—22no—
354#92418—22no—
355#92418—41no—
356#25401—611nomaximal, Sylow
357C22×C61—22no—
358C22×C61—22no—
359C22×C61—22no—
360C22×C61—41no—
361C22×C61—41no—
362C22×C61—41no—
363C22×C61—41no—
364C22×C61—41no—
365C22×C61—42no—
366C22×C61—41no—
367C22×C61—42no—
368C22×C61—41no—
369C22×C61—42no—
370C22×C61—41no—
371C22×C61—41no—
372C22×C61—41no—
373C22×C61—41no—
374C22×C61—81no—
375C22×C61—81no—
376C22×C61—81no—
377C22×C61—81no—
378C22×C61C2×#12111yescharacteristic
379C22×C61D4211yescharacteristic
380C22×C61#54611yescharacteristic
381C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
382C22×C61#57511yescharacteristic
383C22×C61#57711yescharacteristic
384C22×C61#57711yescharacteristic
385C2×D61—81no—
386C2×D61—81no—
387C2×D61—81no—
388C2×D61—81no—
389C2×D61—81no—
390C2×D61—81no—
391C2×D61—81no—
392C4×C61—22no—
393C4×C61—22no—
394C4×C61—41no—
395C4×C61—41no—
396C4×C61—81no—
397C4×C61—81no—
398C4×C61—81no—
399C4×C61#53211yescharacteristic
400C4×C61#54011yescharacteristic
401C4×C61D4211yescharacteristic
402C4×C61#55011yescharacteristic
403Dic61—42no—
404Dic61—42no—
405Dic61—81no—
406C2×#469—611no—
407C2×#465—611no—
408C2×#463—611no—
409C2×#435—611no—
410#2540—611no—
411#2537D6111yescharacteristic, complemented
412#2035—611no—
413#2034—611no—
414#2000—611no—
415#1999—611no—
416#1959—611no—
417#1948—611no—
418#1894—611no—
419#1893—611no—
420#1762—611no—
421C2×C61—42no—
422C2×C61—81no—
423C2×C61—82no—
424C2×C61#242811yescharacteristic
425C2×C61#305511yescharacteristic
426C2×C61#306011yescharacteristic
427C2×C61#326511yescharacteristic
428C2×C61#326711yescharacteristic
429C2×C61#330611yescharacteristic
430C2×C61#332111yescharacteristic
431D61—161no—
432C22×SD16—611no—
433C22×D8—611no—
434C22×M16—611no—
435C23×C8—611no—
436C2×#124—611no—
437C2×C22⋊Q8—611no—
438C2×C22⋊Q8—611no—
439C2×#121—21no—
440C2×#121—611no—
441C2×#121—611no—
442C2×#121C2×D6111yescharacteristic
443C2×#121C2×D6111yescharacteristic
444C2×C4×D4C2×D6111yescharacteristic
445C2×C4×D4C2×D6111yescharacteristic
446#469—1224no—
447#465—1224no—
448#463—1224no—
449#435—1224no—
450C2×#106—611no—
451C2×#106—611no—
452C2×C4⋊C8—611no—
453C2×#103—611no—
454C2×#103—611no—
455C2×#103—611no—
456C2×#102—611no—
457C2×#102—611no—
458C2×#102—611no—
459C2×#102—611no—
460C2×#102—611no—
461C2×C22⋊C8—611no—
462C2×C22⋊C8—611no—
463C2×#97—611no—
464#399—1221no—
465#394—21no—
466#394—21no—
467#392—1221no—
468#390—1221no—
469#390—1221no—
470#384C2×D6111yescharacteristic
471#380—21no—
472#380C2×D6111yescharacteristic
473#380C2×D6111yescharacteristic
474C4×C4⋊C4—611no—
475#340—611no—
476#340—611no—
477#340—611no—
478#340—611no—
479C61#2540111yescharacteristic, complemented, Sylow
480C22×Q8—611no—
481C22×D4—21no—
482C22×D4—21no—
483C22×D4—611no—
484C22×D4—1221no—
485C22×D4—1221no—
486C22×D4C22⋊D6111yescharacteristic
487C22×D4C22×D6111yescharacteristic
488C23×C4—21no—
489C23×C4C22×D6111yescharacteristic
490C23×C4C22×D6111yescharacteristic
491C2×SD16—1222no—
492C2×SD16—1222no—
493C2×SD16—2441no—
494C2×D8—1222no—
495C2×D8—1222no—
496C2×D8—2441no—
497C2×M16—1222no—
498C2×M16—1222no—
499C2×M16—2441no—
500C22×C8—611no—
501C22×C8—611no—
502C22×C8—611no—
503C22×C8—611no—
504C22×C8—1222no—
505C22×C8—1222no—
506C22×C8—2441no—
507#124—1222no—
508#124—1222no—
509C22⋊Q8—1222no—
510C22⋊Q8—1222no—
511C22⋊Q8—2441no—
512C22⋊Q8—2441no—
513#121—22no—
514#121—22no—
515#121—41no—
516#121—41no—
517#121—44no—
518#121—1222no—
519#121—1222no—
520#121—2441no—
521#121—2441no—
522C4×D4—22no—
523C4×D4—22no—
524C4×D4—22no—
525C4×D4—22no—
526C2×C4⋊C4—21no—
527C2×C4⋊C4—21no—
528C2×C4⋊C4—611no—
529C2×C4⋊C4—611no—
530C2×C4⋊C4—1221no—
531C2×C4⋊C4—1221no—
532C2×C4⋊C4C22⋊D6111yescharacteristic
533C2×C4⋊C4C22×D6111yescharacteristic
534C2×C4⋊C4C22×D6111yescharacteristic
535C2×C4⋊C4C22×D6111yescharacteristic
536C2×C22⋊C4—21no—
537C2×C22⋊C4—21no—
538C2×C22⋊C4—21no—
539C2×C22⋊C4—21no—
540C2×C22⋊C4—21no—
541C2×C22⋊C4—1221no—
542C2×C22⋊C4—1221no—
543C2×C22⋊C4—1221no—
544C2×C22⋊C4—1221no—
545C2×C22⋊C4—1221no—
546C2×C22⋊C4—1221no—
547C2×C22⋊C4C22⋊D6111yescharacteristic
548C2×C22⋊C4C22⋊D6111yescharacteristic
549C2×C42—1221no—
550C2×C42C22×D6111yescharacteristic
551#106—1222no—
552#106—1222no—
553C4⋊C8—614no—
554#103—1222no—
555#103—1222no—
556#103—2441no—
557#102—614no—
558#102—1222no—
559#102—1222no—
560#102—1222no—
561#102—2441no—
562C22⋊C8—1222no—
563C22⋊C8—1222no—
564#97—1222no—
565#95—21no—
566#95—21no—
567#95—1221no—
568C24—21no—
569C24—1221no—
570C24C2×C22⋊D6111yescharacteristic
571C24C2×C22⋊D6111yescharacteristic
572C2×Q8—1221no—
573C2×Q8—1221no—
574C2×Q8—1221no—
575C2×Q8—1221no—
576C2×Q8—1221no—
577C2×Q8—1221no—
578C2×D4—22no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—22no—
585C2×D4—41no—
586C2×D4—42no—
587C2×D4—42no—
588C2×D4—42no—
589C2×D4—42no—
590C2×D4—81no—
591C2×D4—81no—
592C2×D4—1221no—
593C2×D4—1221no—
594C2×D4—1221no—
595C2×D4—1221no—
596C2×D4—1221no—
597C2×D4—1221no—
598C2×D4—4881no—
599C2×D4—4881no—
600C2×D4—2442no—
601C2×D4—2442no—
602C2×D4—2442no—
603C2×D4—2442no—
604C2×D4D4×D6112yes—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—42no—
621C22×C4—42no—
622C22×C4—42no—
623C22×C4—1221no—
624C22×C4—1221no—
625C22×C4—1221no—
626C22×C4C2×C22⋊D6111yescharacteristic
627C22×C4C2×C22⋊D6111yescharacteristic
628C22×C4C2×C22⋊D6111yescharacteristic
629C22×C4C2×C22⋊D6111yescharacteristic
630C22×C4C23×D6111yescharacteristic
631SD16—2444no—
632D8—2444no—
633M16—2444no—
634C2×C8—612no—
635C2×C8—612no—
636C2×C8—612no—
637C2×C8—1221no—
638C2×C8—1221no—
639C2×C8—1221no—
640C2×C8—1221no—
641C2×C8—1221no—
642C2×C8—1221no—
643C2×C8—1221no—
644C2×C8—1221no—
645C2×C8—1221no—
646C2×C8—2444no—
647C4⋊C4—22no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—42no—
655C4⋊C4—81no—
656C4⋊C4—612no—
657C4⋊C4—612no—
658C4⋊C4—1221no—
659C4⋊C4—1221no—
660C4⋊C4—2442no—
661C4⋊C4—2442no—
662C22⋊C4—22no—
663C22⋊C4—22no—
664C22⋊C4—42no—
665C22⋊C4—42no—
666C22⋊C4—42no—
667C22⋊C4—42no—
668C22⋊C4—42no—
669C22⋊C4—2442no—
670C22⋊C4—2442no—
671C22⋊C4—2442no—
672C22⋊C4—2442no—
673C22⋊C4—2442no—
674C22⋊C4—2442no—
675C42—4881no—
676C42D4×D6112yes—
677C42#1175822412yes—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—22no—
690C23—21no—
691C23—21no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—41no—
696C23—41no—
697C23—41no—
698C23—2441no—
699C23—2441no—
700C23—2441no—
701C23—2441no—
702C23—2441no—
703C23—2441no—
704C23—2441no—
705C23#1451980312yes—
706C23C22×C22⋊D6111yescharacteristic
707Q8—2441no—
708Q8—2441no—
709Q8—2441no—
710Q8—2441no—
711D4—22no—
712D4—22no—
713D4—44no—
714D4—41no—
715D4—41no—
716D4—84no—
717D4—84no—
718D4—4884no—
719D4—4884no—
720D4—2441no—
721D4—2441no—
722D4—2441no—
723D4—2441no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—84no—
752C2×C4—1222no—
753C2×C4—1222no—
754C2×C4—2441no—
755C2×C4—2441no—
756C2×C4—2441no—
757C2×C4—2441no—
758C2×C4—2441no—
759C2×C4—2441no—
760C2×C4—2441no—
761C2×C4#1451974912yes—
762C2×C4#1451974912yes—
763C2×C4C2×D4×D6111yescharacteristic
764C2×C4C2×D4×D6111yescharacteristic
765C2×C4#41×D6111yescharacteristic
766C2×C4C2×#1175822411yescharacteristic
767C2×C4#1451982211yescharacteristic
768C2×C4#1451982311yescharacteristic
769C8—1222no—
770C8—1222no—
771C8—1222no—
772C8—2441no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—41no—
780C22—41no—
781C22—41no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—42no—
786C22—41no—
787C22—42no—
788C22—41no—
789C22—42no—
790C22—81no—
791C22—81no—
792C22—81no—
793C22—81no—
794C22—4881no—
795C22—4881no—
796C22—4881no—
797C22—4881no—
798C22—4881no—
799C22—4881no—
800C22—4881no—
801C22C2×#1451974911yescharacteristic
802C22D4×C22⋊D6111yescharacteristic
803C22#1684040011yescharacteristic
804C22C2×#1451980311yescharacteristic
805C22#1684056011yescharacteristic
806C22#1684057011yescharacteristic
807C22#1684057311yescharacteristic
808C4—22no—
809C4—22no—
810C4—41no—
811C4—41no—
812C4—81no—
813C4—81no—
814C4—81no—
815C4—4881no—
816C4—2442no—
817C4—2442no—
818C4#1684030711yescharacteristic
819C4#1684036511yescharacteristic
820C4#1684039611yescharacteristic
821C4#1684043011yescharacteristic
822C2—42no—
823C2—81no—
824C2—82no—
825C2—9761no—
826C2#2144940911yescharacteristic
827C2#2145543411yescharacteristic
828C2#2145547811yescharacteristic
829C2#2145731011yescharacteristic
830C2#2145734511yescharacteristic
831C2#2145777411yescharacteristic
832C2#2145799911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2537C2
socleC23×C61C22×D4
hypercenter#2537D61
hypocenterC61#25401
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2537

Complements

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

NH ≅ G/Ntype
1. C2×#16840013C2semidirect
2. C2×#16839989C2semidirect
3. C2×#16839977C2semidirect
4. C2×#16839834C2semidirect
5. #21450758C2semidirect
6. #21447015C2semidirect
7. #21447008C2semidirect
8. #21446822C2semidirect
9. #21446815C2semidirect
10. #21446633C2semidirect
11. #21446580C2semidirect
12. #21446250C2semidirect
13. #21446245C2semidirect
14. #21445644C2semidirect
15. C61×#2537C2semidirect
106. C4⋊#92418D4semidirect
111. #14519698D4semidirect
411. #2537D61semidirect
479. C61#25401semidirect

Maximal subgroups

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

subgroupindex
C2×#168400132
C2×#168399892
C2×#168399772
C2×#168398342
#214507582
#214470152
#214470082
#214468222
#214468152
#214466332
#214465802
#214462502
#214462452
#214456442
C61×#25372
#2540161