Finite Group Databasebeta

← #29737096

Subgroups — #29737096

Order 15616.

1162 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#102×D61C211yesmaximal, characteristic
2#21449539C211yesmaximal, characteristic, complemented
3D4×#11758198C211yesmaximal, characteristic
4#21447337C211yesmaximal, characteristic, complemented
5#21447206C211yesmaximal, characteristic, complemented
6#21447188C211yesmaximal, characteristic, complemented
7#21446962C211yesmaximal, characteristic, complemented
8#21446080C211yesmaximal, characteristic, complemented
9#21446068C211yesmaximal, characteristic, complemented
10#21446010C211yesmaximal, characteristic, complemented
11#21445995C211yesmaximal, characteristic, complemented
12#21445845C211yesmaximal, characteristic, complemented
13#21445827C211yesmaximal, characteristic, complemented
14#21445748C211yesmaximal, characteristic
15C2×C61×#478C211yesmaximal, characteristic, complemented
16C22×D4×D61C2211yescharacteristic
17C22×C8×D61C2211yescharacteristic
18C2×D4×Dic61C2211yescharacteristic
19C2×C4⋊C4×D61C2211yescharacteristic
20C22×#11758198—21no—
21C2×#14519711C2211yescharacteristic, complemented
22C2×#14519708C2211yescharacteristic, complemented
23C2×#14519706C2211yescharacteristic, complemented
24C2×#14519699C2211yescharacteristic
25C2×#14519699C2211yescharacteristic
26C2×#14519698C2211yescharacteristic
27C2×#14519698C2211yescharacteristic
28C2×#14519697C2211yescharacteristic
29C2×#14519697C2211yescharacteristic
30#102×D61—24no—
31C2×#14519689C2211yescharacteristic
32#16839700—21no—
33#16839695—21no—
34#16839664C2211yescharacteristic
35#16839663C2211yescharacteristic
36#16839661C2211yescharacteristic, complemented
37#16839660C2211yescharacteristic, complemented
38#16839641—21no—
39#16839639—21no—
40#16839633—21no—
41#16839627C2211yescharacteristic, complemented
42#16839619—21no—
43#16839619C2211yescharacteristic
44#16839619C2211yescharacteristic
45#16839617—21no—
46C4×#11758198C2211yescharacteristic
47#16839525C2211yescharacteristic, complemented
48#16839524C2211yescharacteristic, complemented
49#16839524C2211yescharacteristic, complemented
50#16839524C2211yescharacteristic, complemented
51#16839517C2211yescharacteristic, complemented
52#16839516C2211yescharacteristic, complemented
53C2×#125×C61C2211yescharacteristic, complemented
54C2×C4×D4×C61C2211yescharacteristic
55C61×#478—24no—
56C2×#107×C61C2211yescharacteristic, complemented
57C2×#106×C61C2211yescharacteristic, complemented
58C2×C4⋊C8×C61C2211yescharacteristic, complemented
59C2×#102×C61C2211yescharacteristic
60C2×#102×C61C2211yescharacteristic
61C24×D61—21no—
62C22×D244C2311yescharacteristic
63C22×C22⋊D61—21no—
64C2×D4×D61—22no—
65C2×D4×D61—22no—
66C2×D4×D61—22no—
67C2×D4×D61—41no—
68C2×D4×D61—41no—
69C2×D4×D61Q814yes—
70C23×Dic61—21no—
71C22×C4×D61—21no—
72C22×C4×D61C2311yescharacteristic
73C22×#92418C2311yescharacteristic
74C22×#92418C2311yescharacteristic
75C2×C8×D61—22no—
76C2×C8×D61—22no—
77C2×C8×D61—41no—
78D4×Dic61—22no—
79D4×Dic61—41no—
80C2×C4⋊Dic61—21no—
81C2×C4⋊Dic61C2311yescharacteristic
82C2×C4⋊Dic61C2311yescharacteristic
83C2×C4⋊Dic61C2311yescharacteristic
84C2×#11758196—21no—
85C2×#11758196—21no—
86C4⋊C4×D61—22no—
87C4⋊C4×D61—41no—
88C2×C22⋊Dic61—21no—
89C2×#11758198—21no—
90C2×#11758198—21no—
91C2×#11758198—21no—
92C2×#11758198—21no—
93C2×#11758198—21no—
94C2×#11758198—21no—
95C2×#11758198—44no—
96C2×#11758198D411yescharacteristic
97C2×#11758198D411yescharacteristic
98C2×C4×Dic61C2311yescharacteristic
99#14519711—41no—
100#14519708—41no—
101#14519706—41no—
102#14519699—22no—
103#14519699—41no—
104#14519698—22no—
105#14519698—22no—
106#14519697—22no—
107#14519697—41no—
108#14519689—22no—
109#14519684—21no—
110#14519684—21no—
111#14519684—21no—
112#14519684—21no—
113#14519684—21no—
114#14519684—21no—
115#14519684D411yescharacteristic
116#14519684D411yescharacteristic
117C22×D4×C61C2311yescharacteristic
118C23×C4×C61—21no—
119C22×C8×C61C2311yescharacteristic
120C22×C8×C61C2311yescharacteristic
121#125×C61—22no—
122#125×C61—41no—
123C4×D4×C61—22no—
124C4×D4×C61—41no—
125C2×C4⋊C4×C61—21no—
126C2×C4⋊C4×C61—21no—
127C2×C4⋊C4×C61C2311yescharacteristic
128C2×C4⋊C4×C61C2311yescharacteristic
129C2×C4⋊C4×C61C2311yescharacteristic
130C2×C22⋊C4×C61—21no—
131C2×C42×C61C2311yescharacteristic
132#107×C61—22no—
133#106×C61—22no—
134C4⋊C8×C61—22no—
135#102×C61—22no—
136#102×C61D414yes—
137C24×C61—21no—
138C23×D61—21no—
139C23×D61—24no—
140C23×D61—42no—
141C23×D61—42no—
142C23×D61—42no—
143C23×D61—42no—
144C23×D61—81no—
145C23×D61—81no—
146C23×D61C2×D411yescharacteristic
147C2×D4×C61—21no—
148C2×D4×C61—21no—
149C2×D4×C61—21no—
150C2×D4×C61C2×D412yes—
151C2×D4×C61C2×Q812yes—
152C2×D4×C61#4112yes—
153C22×C4×C61—21no—
154C22×C4×C61—21no—
155C22×C4×C61—21no—
156C22×C4×C61—42no—
157C22×C4×C61—42no—
158C22×C4×C61—81no—
159C22×C4×C61C2×D411yescharacteristic
160C22×C4×C61C2×D411yescharacteristic
161C22×C4×C61C2411yescharacteristic
162C2×C22⋊D61—24no—
163C2×C22⋊D61—42no—
164C2×C22⋊D61—42no—
165C22×Dic61—21no—
166C22×Dic61—21no—
167C22×Dic61—21no—
168C22×Dic61—42no—
169C22×Dic61—42no—
170C22×Dic61—81no—
171C22×Dic61C2×D411yescharacteristic
172C22×Dic61C2×D411yescharacteristic
173C22×Dic61C2×D411yescharacteristic
174D4×D61—28no—
175D4×D61—44no—
176D4×D61—44no—
177D4×D61—44no—
178C2×D244—21no—
179C2×D244—21no—
180C2×D244—21no—
181C2×D244—21no—
182C2×D244—21no—
183C2×D244C2×Q812yes—
184C2×C4×D61—21no—
185C2×C4×D61—21no—
186C2×C4×D61—21no—
187C2×C4×D61—21no—
188C2×C4×D61—42no—
189C2×C4×D61—42no—
190C2×C4×D61—81no—
191C2×C4×D61C2×Q812yes—
192C2×C4×D61#4112yes—
193C2×C8×C61—21no—
194C2×C8×C61—21no—
195C2×C8×C61—21no—
196C2×C8×C61—21no—
197C2×C8×C61—21no—
198C2×C8×C61C2×D412yes—
199C4⋊C4×C61—21no—
200C4⋊C4×C61—21no—
201C4⋊C4×C61—21no—
202C4⋊C4×C61—21no—
203C4⋊C4×C61—21no—
204C4⋊C4×C61—42no—
205C4⋊C4×C61—42no—
206C4⋊C4×C61C2×D412yes—
207C22⋊C4×C61—42no—
208C42×C61—21no—
209C42×C61—21no—
210C22⋊Dic61—42no—
211#11758198—22no—
212#11758198—22no—
213#11758198—42no—
214#11758198—42no—
215#11758198—42no—
216#11758198—42no—
217#11758198—81no—
218#11758198—81no—
219C4⋊Dic61—21no—
220C4⋊Dic61—21no—
221C4⋊Dic61—21no—
222C4⋊Dic61—21no—
223C4⋊Dic61—21no—
224C4⋊Dic61—21no—
225C4⋊Dic61—81no—
226#11758196—42no—
227#11758196—81no—
228C4×Dic61—21no—
229C4×Dic61—21no—
230C2×#92418—21no—
231C2×#92418—21no—
232C2×#92418—21no—
233C2×#92418—21no—
234C2×#92418—21no—
235C2×#92418—21no—
236C8×D61—44no—
237C23×C61—22no—
238C23×C61—22no—
239C23×C61—22no—
240C23×C61—41no—
241C23×C61—41no—
242C23×C61—41no—
243C23×C61—41no—
244C23×C61C22×D411yescharacteristic
245C22×D61—21no—
246C22×D61—21no—
247C22×D61—21no—
248C22×D61—21no—
249C22×D61—22no—
250C22×D61—48no—
251C22×D61—41no—
252C22×D61—41no—
253C22×D61—41no—
254C22×D61—41no—
255C22×D61—41no—
256C22×D61—41no—
257C22×D61—48no—
258C22×D61—84no—
259C22×D61—84no—
260C22×D61—84no—
261C22×D61—84no—
262C22×D61—84no—
263C22×D61C22⋊Q812yes—
264C22×D61#13512yes—
265C22×D61AGL(1,ℤ/8)12yes—
266D4×C61—22no—
267D4×C61—22no—
268D4×C61—22no—
269D4×C61C22⋊Q814yes—
270C2×C4×C61—22no—
271C2×C4×C61—21no—
272C2×C4×C61—21no—
273C2×C4×C61—21no—
274C2×C4×C61—21no—
275C2×C4×C61—21no—
276C2×C4×C61—21no—
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×C61—41no—
284C2×C4×C61—41no—
285C2×C4×C61—84no—
286C2×C4×C61C22×D411yescharacteristic
287C2×C4×C61C22×Q811yescharacteristic
288C2×C4×C61C2×#4111yescharacteristic
289C2×C4×C61C2×#4111yescharacteristic
290C2×C4×C61H(5,𝔽2)11yescharacteristic
291C2×C4×C61H(5,𝔽2)11yescharacteristic
292C22⋊D61—48no—
293C2×Dic61—21no—
294C2×Dic61—21no—
295C2×Dic61—21no—
296C2×Dic61—21no—
297C2×Dic61—21no—
298C2×Dic61—21no—
299C2×Dic61—21no—
300C2×Dic61—21no—
301C2×Dic61—41no—
302C2×Dic61—41no—
303C2×Dic61—41no—
304C2×Dic61—41no—
305C2×Dic61—41no—
306C2×Dic61—41no—
307C2×Dic61—41no—
308C2×Dic61—41no—
309C2×Dic61—41no—
310C2×Dic61—84no—
311C2×Dic61C22⋊Q812yes—
312D244—22no—
313D244—22no—
314D244—41no—
315D244—41no—
316C4×D61—22no—
317C4×D61—22no—
318C4×D61—22no—
319C4×D61—22no—
320C4×D61—84no—
321C8×C61—22no—
322C8×C61—41no—
323#92418—41no—
324#92418—41no—
325#25952—611nomaximal, Sylow
326C22×C61—24no—
327C22×C61—42no—
328C22×C61—42no—
329C22×C61—42no—
330C22×C61—42no—
331C22×C61—42no—
332C22×C61—42no—
333C22×C61C2×C22⋊Q811yescharacteristic
334C22×C61D4211yescharacteristic
335C22×C61#54611yescharacteristic
336C22×C61C2×#13511yescharacteristic
337C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
338C22×C61#57611yescharacteristic
339C22×C61#57711yescharacteristic
340C2×D61—22no—
341C2×D61—22no—
342C2×D61—22no—
343C2×D61—22no—
344C2×D61—22no—
345C2×D61—22no—
346C2×D61—42no—
347C2×D61—42no—
348C2×D61—42no—
349C2×D61—816no—
350C2×D61—81no—
351C2×D61—81no—
352C2×D61—81no—
353C2×D61—81no—
354C2×D61#47814yescomplemented
355C4×C61—41no—
356C4×C61—42no—
357C4×C61—41no—
358C4×C61—81no—
359C4×C61—81no—
360C4×C61C2×C22⋊Q811yescharacteristic
361C4×C61#54311yescharacteristic
362C4×C61#54611yescharacteristic
363C4×C61#55111yescharacteristic
364Dic61—22no—
365Dic61—41no—
366Dic61—41no—
367Dic61—81no—
368Dic61—81no—
369Dic61—81no—
370C2×#478D6111yescharacteristic, complemented
371C22×#102—611no—
372#2442—611no—
373D4×C22⋊C4—611no—
374#2092—611no—
375#2067—611no—
376#2065—611no—
377#2025—611no—
378#1864—611no—
379#1862—611no—
380#1853—611no—
381#1850—611no—
382#1808—611no—
383#1804—611no—
384#1786—611no—
385C2×C61—44no—
386C2×C61#243711yescharacteristic
387C2×C61C2×#47811yescharacteristic
388C2×C61#308111yescharacteristic
389C2×C61#326511yescharacteristic
390C2×C61#328011yescharacteristic
391C2×C61#329611yescharacteristic
392C2×C61#331811yescharacteristic
393D61—24no—
394D61—82no—
395C23×D4—611no—
396C23×C8—611no—
397C2×#125C2×D6111yescharacteristic, complemented
398C2×C4×D4—611no—
399C2×C4×D4C2×D6111yescharacteristic
400C22×C4⋊C4—611no—
401C22×C22⋊C4—1221no—
402#478—24no—
403C2×#107—611no—
404C2×#107C2×D6111yescharacteristic, complemented
405C2×#106—611no—
406C2×#106C2×D6111yescharacteristic, complemented
407C2×C4⋊C8—611no—
408C2×C4⋊C8C2×D6111yescharacteristic, complemented
409C2×#102—611no—
410C2×#102—611no—
411C2×#102—611no—
412C2×#102—611no—
413C2×#102—611no—
414C2×#102—611no—
415C2×#102—1224no—
416C2×#102C2×D6111yescharacteristic
417C2×#102C2×D6111yescharacteristic
418C2×C22⋊C8—611no—
419#400—1221no—
420#398—1221no—
421#390—611no—
422#390—611no—
423#389—611no—
424#389—611no—
425#386—1221no—
426#386—1221no—
427#385—1221no—
428#382—611no—
429#380—611no—
430#380—611no—
431#380—1221no—
432#379—1221no—
433C4×C22⋊C4—611no—
434#340—611no—
435#340—611no—
436#340—611no—
437#340—611no—
438#336—611no—
439#336—611no—
440C61#2595211yescharacteristic, complemented, Sylow
441C25—1221no—
442C22×D4—614no—
443C22×D4—611no—
444C22×D4—1222no—
445C22×D4—1221no—
446C22×D4—1222no—
447C22×D4—1222no—
448C22×D4—2441no—
449C22×D4—2441no—
450C22×D4C22×D6111yescharacteristic
451C23×C4—21no—
452C23×C4—611no—
453C23×C4—1221no—
454C23×C4—1221no—
455C22×C8—611no—
456C22×C8—611no—
457C22×C8—1222no—
458C22×C8—1222no—
459C22×C8—2441no—
460C22×C8C22×D6111yescharacteristic
461C22×C8C22×D6111yescharacteristic
462#125—22no—
463#125—41no—
464C4×D4—22no—
465C4×D4—41no—
466C4×D4—1222no—
467C4×D4—2441no—
468C2×C4⋊C4—21no—
469C2×C4⋊C4—21no—
470C2×C4⋊C4—611no—
471C2×C4⋊C4—611no—
472C2×C4⋊C4—611no—
473C2×C4⋊C4—1222no—
474C2×C4⋊C4—1221no—
475C2×C4⋊C4—1221no—
476C2×C4⋊C4—1221no—
477C2×C4⋊C4—2441no—
478C2×C4⋊C4C22×D6111yescharacteristic
479C2×C4⋊C4C22×D6111yescharacteristic
480C2×C4⋊C4C22×D6111yescharacteristic
481C2×C22⋊C4—21no—
482C2×C22⋊C4—611no—
483C2×C22⋊C4—611no—
484C2×C22⋊C4—1221no—
485C2×C22⋊C4—1221no—
486C2×C22⋊C4—1221no—
487C2×C22⋊C4—1221no—
488C2×C22⋊C4—1221no—
489C2×C22⋊C4—1221no—
490C2×C22⋊C4—1221no—
491C2×C22⋊C4—2444no—
492C2×C42—611no—
493C2×C42C22×D6111yescharacteristic
494#107—22no—
495#107—2441no—
496#106—22no—
497#106—2441no—
498C4⋊C8—22no—
499C4⋊C8—2441no—
500#102—22no—
501#102—1222no—
502#102—1222no—
503#102—1222no—
504#102—1222no—
505#102—2441no—
506#102—2441no—
507#102C22⋊D6114yes—
508C22⋊C8—1222no—
509#95—611no—
510#95—611no—
511#95—1221no—
512#95—1221no—
513#95—1221no—
514#95—1221no—
515#95—1221no—
516#95—1221no—
517C24—21no—
518C24—611no—
519C24—1224no—
520C24—1221no—
521C24—4881no—
522C24—4881no—
523C24—2442no—
524C24—2442no—
525C24—2442no—
526C24—2442no—
527C2×D4—21no—
528C2×D4—21no—
529C2×D4—21no—
530C2×D4—612no—
531C2×D4—1224no—
532C2×D4—1228no—
533C2×D4—1221no—
534C2×D4—1221no—
535C2×D4—1221no—
536C2×D4—1221no—
537C2×D4—1221no—
538C2×D4—2444no—
539C2×D4—2444no—
540C2×D4—2444no—
541C2×D4—2442no—
542C2×D4—2442no—
543C2×D4Q8×D6112yes—
544C2×D4#1175822612yes—
545C2×D4C2×C22⋊D6112yes—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—42no—
550C22×C4—42no—
551C22×C4—81no—
552C22×C4—611no—
553C22×C4—612no—
554C22×C4—612no—
555C22×C4—611no—
556C22×C4—611no—
557C22×C4—1221no—
558C22×C4—1221no—
559C22×C4—1221no—
560C22×C4—1221no—
561C22×C4—1221no—
562C22×C4—1221no—
563C22×C4—1221no—
564C22×C4—4881no—
565C22×C4—4881no—
566C22×C4—2442no—
567C22×C4—2442no—
568C22×C4—2442no—
569C22×C4—2442no—
570C22×C4D4×D6111yescharacteristic
571C22×C4D4×D6111yescharacteristic
572C22×C4C23×D6111yescharacteristic
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—1221no—
579C2×C8—1221no—
580C2×C8—1221no—
581C2×C8—1221no—
582C2×C8—1221no—
583C2×C8—1221no—
584C2×C8—2444no—
585C2×C8C2×C22⋊D6112yes—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—42no—
592C4⋊C4—42no—
593C4⋊C4—1221no—
594C4⋊C4—1221no—
595C4⋊C4—1221no—
596C4⋊C4—1221no—
597C4⋊C4—1221no—
598C4⋊C4—1221no—
599C4⋊C4—4881no—
600C4⋊C4—4881no—
601C4⋊C4—2442no—
602C4⋊C4C2×C22⋊D6112yes—
603C22⋊C4—42no—
604C22⋊C4—1222no—
605C22⋊C4—1222no—
606C22⋊C4—4881no—
607C22⋊C4—4881no—
608C22⋊C4—2442no—
609C22⋊C4—2442no—
610C22⋊C4—2442no—
611C22⋊C4—2442no—
612C22⋊C4—2442no—
613C42—21no—
614C42—21no—
615C42—1221no—
616C42—1221no—
617C23—22no—
618C23—22no—
619C23—22no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—612no—
625C23—612no—
626C23—612no—
627C23—1221no—
628C23—1221no—
629C23—1221no—
630C23—1221no—
631C23—1222no—
632C23—4884no—
633C23—4884no—
634C23—4884no—
635C23—4884no—
636C23—4884no—
637C23—2448no—
638C23—2448no—
639C23—2441no—
640C23—2441no—
641C23—2441no—
642C23—2441no—
643C23—2441no—
644C23—2441no—
645C23C2×D4×D6111yescharacteristic
646D4—22no—
647D4—22no—
648D4—22no—
649D4—1222no—
650D4—1222no—
651D4—2448no—
652D4—2441no—
653D4—2441no—
654D4#1451975314yes—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—22no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—84no—
671C2×C4—612no—
672C2×C4—1221no—
673C2×C4—1221no—
674C2×C4—1222no—
675C2×C4—1222no—
676C2×C4—1222no—
677C2×C4—1222no—
678C2×C4—1221no—
679C2×C4—1221no—
680C2×C4—1221no—
681C2×C4—1221no—
682C2×C4—1221no—
683C2×C4—1221no—
684C2×C4—4884no—
685C2×C4—4884no—
686C2×C4—2441no—
687C2×C4—2441no—
688C2×C4—2441no—
689C2×C4—2441no—
690C2×C4—2441no—
691C2×C4—2441no—
692C2×C4—2441no—
693C2×C4—2441no—
694C2×C4—2441no—
695C2×C4C22×C22⋊D6111yescharacteristic
696C2×C4C2×Q8×D6111yescharacteristic
697C2×C4#41×D6111yescharacteristic
698C2×C4C2×#1175822611yescharacteristic
699C2×C4#1451982211yescharacteristic
700C2×C4#1451982311yescharacteristic
701C8—22no—
702C8—41no—
703C8—2441no—
704C8—2441no—
705C22—24no—
706C22—42no—
707C22—42no—
708C22—42no—
709C22—42no—
710C22—42no—
711C22—42no—
712C22—614no—
713C22—1222no—
714C22—1222no—
715C22—1222no—
716C22—1222no—
717C22—1222no—
718C22—1222no—
719C22—48816no—
720C22—4881no—
721C22—4881no—
722C22—4881no—
723C22—4881no—
724C22—2442no—
725C22—2442no—
726C22—2442no—
727C22C22⋊Q8×D6111yescharacteristic
728C22D4×C22⋊D6111yescharacteristic
729C22#1684040311yescharacteristic
730C22#135×D6111yescharacteristic
731C22AGL(1,ℤ/8)×D6111yescharacteristic
732C22#1684056411yescharacteristic
733C22#1684057211yescharacteristic
734C4—41no—
735C4—42no—
736C4—41no—
737C4—81no—
738C4—81no—
739C4—1222no—
740C4—4881no—
741C4—4881no—
742C4—4881no—
743C4—2441no—
744C4—2441no—
745C4C2×#1451975311yescharacteristic
746C4#1684038711yescharacteristic
747C4#1684040011yescharacteristic
748C4#1684043911yescharacteristic
749C2—44no—
750C2—1224no—
751C2—4882no—
752C2#2144948211yescharacteristic
753C2#478×D6111yescharacteristic
754C2#2145564711yescharacteristic
755C2#2145730811yescharacteristic
756C2#2145749811yescharacteristic
757C2#2145765111yescharacteristic
758C2#2145795711yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#478C2
socleC23×C61C22×D4
prime radicalC22×D4×D61C22
hypercenterC2×#478D61
hypocenterC61#25952
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#478

Complements

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

NH ≅ G/Ntype
2. #21449539C2semidirect
4. #21447337C2semidirect
5. #21447206C2semidirect
6. #21447188C2semidirect
7. #21446962C2semidirect
8. #21446080C2semidirect
9. #21446068C2semidirect
10. #21446010C2semidirect
11. #21445995C2semidirect
12. #21445845C2semidirect
13. #21445827C2semidirect
15. C2×C61×#478C2semidirect
21. C2×#14519711C22semidirect
22. C2×#14519708C22semidirect
23. C2×#14519706C22semidirect
36. #16839661C22semidirect
37. #16839660C22semidirect
41. #16839627C22semidirect
47. #16839525C22semidirect
48. #16839524C22semidirect
49. #16839524C22semidirect
50. #16839524C22semidirect
51. #16839517C22semidirect
52. #16839516C22semidirect
53. C2×#125×C61C22semidirect
56. C2×#107×C61C22semidirect
57. C2×#106×C61C22semidirect
58. C2×C4⋊C8×C61C22semidirect
354. C2×D61#478semidirect
370. C2×#478D61semidirect
397. C2×#125C2×D61semidirect
404. C2×#107C2×D61semidirect
406. C2×#106C2×D61semidirect
408. C2×C4⋊C8C2×D61semidirect
440. C61#25952semidirect

Maximal subgroups

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

subgroupindex
C2×#102×D612
#214495392
D4×#117581982
#214473372
#214472062
#214471882
#214469622
#214460802
#214460682
#214460102
#214459952
#214458452
#214458272
#214457482
C2×C61×#4782
#2595261