Finite Group Databasebeta

← #29723870

Subgroups — #29723870

Order 15616.

1156 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839912C211yesmaximal, characteristic
2C2×C4×#11758201C211yesmaximal, characteristic, complemented
3C22⋊C4×D244C211yesmaximal, characteristic
4#21447353C211yesmaximal, characteristic, complemented
5#21447256C211yesmaximal, characteristic, complemented
6#21447134C211yesmaximal, characteristic, complemented
7#21447012C211yesmaximal, characteristic, complemented
8#21446501C211yesmaximal, characteristic, complemented
9#21446427C211yesmaximal, characteristic, complemented
10#21446174C211yesmaximal, characteristic, complemented
11#21446156C211yesmaximal, characteristic, complemented
12#21446079C211yesmaximal, characteristic, complemented
13#21445816C211yesmaximal, characteristic, complemented
14#21445749C211yesmaximal, characteristic
15C61×#2423C211yesmaximal, characteristic, complemented
16C23×D244C2211yescharacteristic
17C22×#11758201C2211yescharacteristic
18C22×#11758201C2211yescharacteristic
19C2×C4×D244C2211yescharacteristic
20C2×C4×D244C2211yescharacteristic
21C2×C22⋊C4×D61—21no—
22#16839912—24no—
23C4×#11758201—24no—
24C2×#14519708C2211yescharacteristic, complemented
25C2×#14519708C2211yescharacteristic, complemented
26C2×C4⋊#92418C2211yescharacteristic, complemented
27C2×#14519701C2211yescharacteristic, complemented
28C2×#14519701C2211yescharacteristic, complemented
29C2×#14519697C2211yescharacteristic
30C2×#14519697C2211yescharacteristic
31C2×#14519697C2211yescharacteristic
32C2×#14519697C2211yescharacteristic
33C2×#14519697C2211yescharacteristic
34C2×#14519697C2211yescharacteristic
35C2×C22⋊#92418C2211yescharacteristic
36C2×C22⋊#92418C2211yescharacteristic
37C2×C4×#92418C2211yescharacteristic, complemented
38#16839664C2211yescharacteristic
39#16839664C2211yescharacteristic
40#16839640—21no—
41#16839640—21no—
42#16839622C2211yescharacteristic
43#16839617—21no—
44#16839524C2211yescharacteristic, complemented
45#16839524C2211yescharacteristic, complemented
46#16839524C2211yescharacteristic, complemented
47#16839524C2211yescharacteristic, complemented
48#16839517C2211yescharacteristic, complemented
49#16839517C2211yescharacteristic, complemented
50C2×C22⋊Q8×C61C2211yescharacteristic
51C2×C4×Q8×C61C2211yescharacteristic, complemented
52C61×#399—21no—
53C61×#398—21no—
54C61×#391C2211yescharacteristic, complemented
55C61×#389C2211yescharacteristic, complemented
56C61×#388—21no—
57C61×#387—21no—
58C61×#384C2211yescharacteristic, complemented
59C61×#380C2211yescharacteristic
60C4×C22⋊C4×C61C2211yescharacteristic
61C24×D61—21no—
62C22×D244—21no—
63C22×D244—22no—
64C22×D244—22no—
65C22×D244—22no—
66C22×D244—22no—
67C22×D244—41no—
68C22×D244—41no—
69C22×D244C2311yescharacteristic
70C22×D244C2311yescharacteristic
71C22×C4×D61—21no—
72C22×C4×D61—21no—
73C2×#11758201—22no—
74C2×#11758201—22no—
75C2×#11758201—22no—
76C2×#11758201—22no—
77C2×#11758201—41no—
78C2×#11758201D414yes—
79C22×#92418C2311yescharacteristic
80C22×#92418C2311yescharacteristic
81C22×#92418C2311yescharacteristic
82C22×#92418C2311yescharacteristic
83C4×D244—22no—
84C4×D244—22no—
85C4×D244—41no—
86C4×D244—41no—
87C2×C4⋊Dic61C2311yescharacteristic
88C2×C4⋊Dic61C2311yescharacteristic
89C2×C22⋊Dic61—21no—
90C2×#11758198—21no—
91C2×#11758198—21no—
92C2×#11758198—21no—
93C2×#11758198—21no—
94C2×#11758198—21no—
95C2×#11758198—21no—
96C22⋊C4×D61—44no—
97#14519708—22no—
98#14519708—41no—
99C4⋊#92418—41no—
100#14519701—22no—
101#14519701—41no—
102#14519697—22no—
103#14519697—22no—
104#14519697—22no—
105#14519697—22no—
106#14519697—22no—
107#14519697—41no—
108C22⋊#92418—22no—
109C22⋊#92418—41no—
110C4×#92418—22no—
111#14519684—21no—
112C22×Q8×C61C2311yescharacteristic
113C23×C4×C61C2311yescharacteristic
114C22⋊Q8×C61—22no—
115C22⋊Q8×C61—41no—
116C4×Q8×C61—22no—
117C4×Q8×C61—41no—
118C2×C4⋊C4×C61—21no—
119C2×C4⋊C4×C61—21no—
120C2×C4⋊C4×C61—21no—
121C2×C4⋊C4×C61—21no—
122C2×C4⋊C4×C61—21no—
123C2×C4⋊C4×C61C2311yescharacteristic
124C2×C4⋊C4×C61C2311yescharacteristic
125C2×C4⋊C4×C61C2311yescharacteristic
126C2×C22⋊C4×C61—21no—
127C2×C22⋊C4×C61—21no—
128C2×C22⋊C4×C61D411yescharacteristic
129C2×C22⋊C4×C61D411yescharacteristic
130C2×C42×C61—21no—
131C2×C42×C61C2311yescharacteristic
132C2×C42×C61C2311yescharacteristic
133#95×C61—21no—
134#95×C61—21no—
135#95×C61—21no—
136#95×C61—21no—
137#95×C61D411yescharacteristic
138#95×C61D411yescharacteristic
139C24×C61C2×D411yescharacteristic
140C23×D61—21no—
141C23×D61—21no—
142C23×D61—24no—
143C23×D61—42no—
144C23×D61—42no—
145C23×D61—42no—
146C23×D61—42no—
147C23×D61—81no—
148C23×D61—81no—
149C2×Q8×C61—21no—
150C2×Q8×C61—21no—
151C2×Q8×C61—21no—
152C2×Q8×C61—21no—
153C2×Q8×C61—21no—
154C2×Q8×C61C2×D412yes—
155C22×C4×C61—21no—
156C22×C4×C61—21no—
157C22×C4×C61—21no—
158C22×C4×C61—21no—
159C22×C4×C61—21no—
160C22×C4×C61—21no—
161C22×C4×C61—21no—
162C22×C4×C61—21no—
163C22×C4×C61—21no—
164C22×C4×C61—21no—
165C22×C4×C61C2×D411yescharacteristic
166C22×C4×C61C2×D411yescharacteristic
167C22×C4×C61C2×D411yescharacteristic
168C22×C4×C61C2×D411yescharacteristic
169C22×C4×C61C2×D411yescharacteristic
170C22×C4×C61C2411yescharacteristic
171C22×Dic61—21no—
172C22×Dic61—21no—
173C2×D244—21no—
174C2×D244—21no—
175C2×D244—21no—
176C2×D244—21no—
177C2×D244—21no—
178C2×D244—21no—
179C2×D244—21no—
180C2×D244—24no—
181C2×D244—21no—
182C2×D244—44no—
183C2×D244—44no—
184C2×D244—44no—
185C2×D244—42no—
186C2×D244—42no—
187C2×D244—44no—
188C2×D244C2×D412yes—
189C2×D244#4112yes—
190C2×D244#4112yes—
191C2×D244#4112yes—
192C2×C4×D61—42no—
193C2×C4×D61—42no—
194C2×C4×D61—42no—
195C2×C4×D61—42no—
196C2×C4×D61—81no—
197C2×C4×D61—81no—
198C4⋊C4×C61—21no—
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×C61—42no—
207C4⋊C4×C61—81no—
208C4⋊C4×C61—81no—
209C22⋊C4×C61—41no—
210C22⋊C4×C61—42no—
211C22⋊C4×C61—81no—
212C22⋊C4×C61SD1614yescomplemented
213C42×C61—21no—
214C42×C61—21no—
215C42×C61—21no—
216C42×C61—21no—
217C42×C61—42no—
218C22⋊Dic61—42no—
219#11758201—28no—
220#11758201—44no—
221#11758198—42no—
222#11758198—42no—
223#11758198—42no—
224#11758198—42no—
225#11758198—81no—
226#11758198—81no—
227C4⋊Dic61—21no—
228C4⋊Dic61—21no—
229C4⋊Dic61—21no—
230C4⋊Dic61—21no—
231C2×#92418—21no—
232C2×#92418—21no—
233C2×#92418—21no—
234C2×#92418—21no—
235C2×#92418—21no—
236C2×#92418—21no—
237C2×#92418—21no—
238C2×#92418—21no—
239C2×#92418—21no—
240C2×#92418—21no—
241C2×#92418—21no—
242C2×#92418C2×D412yes—
243C23×C61—21no—
244C23×C61—21no—
245C23×C61—21no—
246C23×C61—21no—
247C23×C61—21no—
248C23×C61—21no—
249C23×C61C2×SD1612yes—
250C23×C61C22×D411yescharacteristic
251C22×D61—22no—
252C22×D61—22no—
253C22×D61—22no—
254C22×D61—22no—
255C22×D61—48no—
256C22×D61—41no—
257C22×D61—41no—
258C22×D61—41no—
259C22×D61—41no—
260C22×D61—48no—
261C22×D61—41no—
262C22×D61—41no—
263C22×D61—41no—
264C22×D61—41no—
265C22×D61—41no—
266C22×D61—41no—
267C22×D61—84no—
268C22×D61—84no—
269C22×D61—84no—
270C22×D61—84no—
271C22×D61—84no—
272Q8×C61—22no—
273Q8×C61—22no—
274Q8×C61—41no—
275Q8×C61—41no—
276C2×C4×C61—21no—
277C2×C4×C61—21no—
278C2×C4×C61—21no—
279C2×C4×C61—21no—
280C2×C4×C61—21no—
281C2×C4×C61—21no—
282C2×C4×C61—22no—
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—41no—
291C2×C4×C61—41no—
292C2×C4×C61—41no—
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×C61C2×SD1612yes—
306C2×C4×C61C2×SD1612yes—
307C2×C4×C61C22×D411yescharacteristic
308C2×C4×C61C2×#4111yescharacteristic
309C2×C4×C61C2×#4111yescharacteristic
310C2×C4×C61C2×#4111yescharacteristic
311C2×C4×C61H(5,𝔽2)11yescharacteristic
312C2×C4×C61H(5,𝔽2)11yescharacteristic
313C2×Dic61—41no—
314C2×Dic61—41no—
315C2×Dic61—41no—
316C2×Dic61—41no—
317C2×Dic61—41no—
318C2×Dic61—41no—
319D244—22no—
320D244—22no—
321D244—22no—
322D244—22no—
323D244—22no—
324D244—48no—
325D244—41no—
326D244—41no—
327D244#12314yes—
328C4×D61—84no—
329C4×D61—84no—
330#92418—22no—
331#92418—41no—
332#92418—41no—
333#92418—41no—
334#24901—611nomaximal, Sylow
335C22×C61—22no—
336C22×C61—22no—
337C22×C61—22no—
338C22×C61—41no—
339C22×C61—41no—
340C22×C61—41no—
341C22×C61—41no—
342C22×C61#52511yescharacteristic
343C22×C61D4211yescharacteristic
344C22×C61#54611yescharacteristic
345C22×C61C22×SD1611yescharacteristic
346C22×C61#57511yescharacteristic
347C22×C61#57611yescharacteristic
348C22×C61#57711yescharacteristic
349C2×D61—24no—
350C2×D61—42no—
351C2×D61—42no—
352C2×D61—42no—
353C2×D61—42no—
354C2×D61—42no—
355C2×D61—42no—
356C2×D61—42no—
357C2×D61—42no—
358C2×D61—42no—
359C2×D61—816no—
360C2×D61—81no—
361C2×D61—81no—
362C2×D61—81no—
363C2×D61—81no—
364C4×C61—22no—
365C4×C61—22no—
366C4×C61—41no—
367C4×C61—42no—
368C4×C61—41no—
369C4×C61—41no—
370C4×C61—81no—
371C4×C61—81no—
372C4×C61—81no—
373C4×C61C2×#12311yescharacteristic
374C4×C61#53811yescharacteristic
375C4×C61#54611yescharacteristic
376C4×C61#55111yescharacteristic
377Dic61—81no—
378Dic61—81no—
379C2×#450—611no—
380C2×C4×SD16—611no—
381#2423D6111yescharacteristic, complemented
382D4×C22⋊C4—611no—
383#2094—611no—
384#2077—611no—
385#2055—611no—
386#2035—611no—
387#1934—611no—
388#1923—611no—
389#1880—611no—
390#1877—611no—
391#1864—611no—
392#1802—611no—
393#1786—611no—
394C2×C61—42no—
395C2×C61#241811yescharacteristic
396C2×C61#310111yescharacteristic
397C2×C61#311811yescharacteristic
398C2×C61#326811yescharacteristic
399C2×C61D4×SD1611yescharacteristic
400C2×C61#329511yescharacteristic
401C2×C61#332311yescharacteristic
402D61—44no—
403D61—82no—
404C23×D4—611no—
405C22×SD16—611no—
406C22×SD16—611no—
407C2×C22⋊Q8C2×D6111yescharacteristic
408C2×C4×Q8C2×D6111yescharacteristic, complemented
409C2×C4×D4—611no—
410C2×C4×D4—611no—
411C22×C22⋊C4—1221no—
412#450—1224no—
413C4×SD16—1224no—
414C2×#106—611no—
415C2×#106—611no—
416C2×C4⋊C8—611no—
417C2×#103—611no—
418C2×#103—611no—
419C2×#102—611no—
420C2×#102—611no—
421C2×#102—611no—
422C2×#102—611no—
423C2×#102—611no—
424C2×#102—611no—
425C2×C22⋊C8—611no—
426C2×C22⋊C8—611no—
427C2×C4×C8—611no—
428#399—21no—
429#398—21no—
430#391C2×D6111yescharacteristic, complemented
431#390—611no—
432#390—611no—
433#389C2×D6111yescharacteristic, complemented
434#388—21no—
435#387—21no—
436#386—1221no—
437#386—1221no—
438#384C2×D6111yescharacteristic, complemented
439#380—611no—
440#380C2×D6111yescharacteristic
441#379—1221no—
442C4×C22⋊C4C2×D6111yescharacteristic
443#340—611no—
444#340—611no—
445#340—611no—
446#340—611no—
447#336—611no—
448#336—611no—
449C61#2490111yescharacteristic, complemented, Sylow
450C25—1221no—
451C22×Q8C22×D6111yescharacteristic
452C22×D4—611no—
453C22×D4—611no—
454C22×D4—1222no—
455C22×D4—1222no—
456C22×D4—1222no—
457C22×D4—1222no—
458C22×D4—1221no—
459C22×D4—2441no—
460C22×D4—2441no—
461C23×C4—1221no—
462C23×C4—1221no—
463C23×C4C22×D6111yescharacteristic
464C2×SD16—614no—
465C2×SD16—1222no—
466C2×SD16—1222no—
467C2×SD16—1222no—
468C2×SD16—1222no—
469C2×SD16—2441no—
470C22×C8—611no—
471C22×C8—611no—
472C22×C8—611no—
473C22×C8—611no—
474C22⋊Q8—22no—
475C22⋊Q8—41no—
476C4×Q8—22no—
477C4×Q8—41no—
478C4×D4—1222no—
479C4×D4—1222no—
480C4×D4—2441no—
481C4×D4—2441no—
482C2×C4⋊C4—21no—
483C2×C4⋊C4—21no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—21no—
486C2×C4⋊C4—21no—
487C2×C4⋊C4—611no—
488C2×C4⋊C4—611no—
489C2×C4⋊C4C22×D6111yescharacteristic
490C2×C4⋊C4C22×D6111yescharacteristic
491C2×C4⋊C4C22×D6111yescharacteristic
492C2×C22⋊C4—21no—
493C2×C22⋊C4—21no—
494C2×C22⋊C4—1221no—
495C2×C22⋊C4—1221no—
496C2×C22⋊C4—1221no—
497C2×C22⋊C4—1221no—
498C2×C22⋊C4—1221no—
499C2×C22⋊C4—1221no—
500C2×C22⋊C4—1221no—
501C2×C22⋊C4—2444no—
502C2×C22⋊C4C22⋊D6111yescharacteristic
503C2×C22⋊C4C22⋊D6111yescharacteristic
504C2×C42—21no—
505C2×C42C22×D6111yescharacteristic
506C2×C42C22×D6111yescharacteristic
507#106—1222no—
508#106—2441no—
509C4⋊C8—2441no—
510#103—1222no—
511#103—2441no—
512#102—1222no—
513#102—1222no—
514#102—1222no—
515#102—1222no—
516#102—1222no—
517#102—2441no—
518C22⋊C8—1222no—
519C22⋊C8—2441no—
520C4×C8—1222no—
521#95—21no—
522#95—21no—
523#95—21no—
524#95—21no—
525#95—1221no—
526#95C22⋊D6111yescharacteristic
527#95C22⋊D6111yescharacteristic
528C24—1224no—
529C24—1221no—
530C24—1221no—
531C24—4881no—
532C24—4881no—
533C24—2442no—
534C24—2442no—
535C24—2442no—
536C24—2442no—
537C24C2×C22⋊D6111yescharacteristic
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8—21no—
542C2×Q8—21no—
543C2×Q8D4×D6112yes—
544C2×D4—612no—
545C2×D4—612no—
546C2×D4—612no—
547C2×D4—612no—
548C2×D4—1224no—
549C2×D4—1221no—
550C2×D4—1221no—
551C2×D4—1221no—
552C2×D4—1221no—
553C2×D4—1221no—
554C2×D4—1221no—
555C2×D4—1221no—
556C2×D4—1221no—
557C2×D4—2442no—
558C2×D4—2442no—
559C2×D4—2444no—
560C2×D4—2444no—
561C2×D4—2444no—
562C2×D4—2444no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—1221no—
574C22×C4—1221no—
575C22×C4—4881no—
576C22×C4—4881no—
577C22×C4—2442no—
578C22×C4—2442no—
579C22×C4—2442no—
580C22×C4—2442no—
581C22×C4C2×C22⋊D6111yescharacteristic
582C22×C4C2×C22⋊D6111yescharacteristic
583C22×C4C2×C22⋊D6111yescharacteristic
584C22×C4C2×C22⋊D6111yescharacteristic
585C22×C4C2×C22⋊D6111yescharacteristic
586C22×C4C23×D6111yescharacteristic
587SD16—1228no—
588SD16—2444no—
589C2×C8—612no—
590C2×C8—1221no—
591C2×C8—1221no—
592C2×C8—1221no—
593C2×C8—1221no—
594C2×C8—1221no—
595C2×C8—1221no—
596C2×C8—1221no—
597C2×C8—1221no—
598C2×C8—1221no—
599C2×C8—1221no—
600C2×C8—1221no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—42no—
608C4⋊C4—42no—
609C4⋊C4—42no—
610C4⋊C4—81no—
611C4⋊C4—81no—
612C4⋊C4—1221no—
613C4⋊C4—1221no—
614C4⋊C4—1221no—
615C4⋊C4—1221no—
616C22⋊C4—41no—
617C22⋊C4—42no—
618C22⋊C4—81no—
619C22⋊C4—4881no—
620C22⋊C4—4881no—
621C22⋊C4—2442no—
622C22⋊C4—2442no—
623C22⋊C4—2442no—
624C22⋊C4—2442no—
625C22⋊C4—2442no—
626C22⋊C4#1175820114yescomplemented
627C42—21no—
628C42—21no—
629C42—21no—
630C42—21no—
631C42—42no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—1222no—
639C23—1222no—
640C23—1222no—
641C23—1222no—
642C23—4884no—
643C23—4884no—
644C23—4884no—
645C23—4884no—
646C23—4884no—
647C23—2448no—
648C23—2448no—
649C23—2441no—
650C23—2441no—
651C23—2441no—
652C23—2441no—
653C23—2441no—
654C23—2441no—
655C23—2441no—
656C23—2441no—
657C23—2441no—
658C23—2441no—
659C23C2×#1175820112yes—
660C23C22×C22⋊D6111yescharacteristic
661Q8—22no—
662Q8—22no—
663Q8—41no—
664Q8—41no—
665D4—614no—
666D4—1222no—
667D4—1222no—
668D4—1222no—
669D4—1222no—
670D4—1222no—
671D4—2448no—
672D4—2441no—
673D4—2441no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—22no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—4884no—
704C2×C4—4884no—
705C2×C4—2441no—
706C2×C4—2441no—
707C2×C4—2441no—
708C2×C4—2441no—
709C2×C4—2441no—
710C2×C4—2441no—
711C2×C4C2×#1175820112yes—
712C2×C4C2×#1175820112yes—
713C2×C4C2×D4×D6111yescharacteristic
714C2×C4#41×D6111yescharacteristic
715C2×C4#41×D6111yescharacteristic
716C2×C4#41×D6111yescharacteristic
717C2×C4#1451982211yescharacteristic
718C2×C4#1451982311yescharacteristic
719C8—1222no—
720C8—2441no—
721C8—2441no—
722C8—2441no—
723C22—22no—
724C22—22no—
725C22—22no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—41no—
730C22—1224no—
731C22—48816no—
732C22—4881no—
733C22—4881no—
734C22—4881no—
735C22—4881no—
736C22—2442no—
737C22—2442no—
738C22—2442no—
739C22—2442no—
740C22—2442no—
741C22—2442no—
742C22—2442no—
743C22—2442no—
744C22—2442no—
745C22#1684026911yescharacteristic
746C22D4×C22⋊D6111yescharacteristic
747C22#1684040011yescharacteristic
748C22C22×#1175820111yescharacteristic
749C22#1684056011yescharacteristic
750C22#1684056511yescharacteristic
751C22#1684057011yescharacteristic
752C4—22no—
753C4—22no—
754C4—41no—
755C4—42no—
756C4—41no—
757C4—41no—
758C4—81no—
759C4—81no—
760C4—81no—
761C4—4881no—
762C4—4881no—
763C4#123×D6111yescharacteristic
764C4#1684034811yescharacteristic
765C4#1684040411yescharacteristic
766C4#1684044011yescharacteristic
767C2—42no—
768C2—4882no—
769C2—2444no—
770C2#2144927811yescharacteristic
771C2#2145582311yescharacteristic
772C2#2145599711yescharacteristic
773C2#2145736011yescharacteristic
774C2D4×#1175820111yescharacteristic
775C2#2145763711yescharacteristic
776C2#2145802911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2423C2
socleC23×C61C22×D4
prime radicalC23×D244C22
hypercenter#2423D61
hypocenterC61#24901
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2423

Complements

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

NH ≅ G/Ntype
2. C2×C4×#11758201C2semidirect
4. #21447353C2semidirect
5. #21447256C2semidirect
6. #21447134C2semidirect
7. #21447012C2semidirect
8. #21446501C2semidirect
9. #21446427C2semidirect
10. #21446174C2semidirect
11. #21446156C2semidirect
12. #21446079C2semidirect
13. #21445816C2semidirect
15. C61×#2423C2semidirect
24. C2×#14519708C22semidirect
25. C2×#14519708C22semidirect
26. C2×C4⋊#92418C22semidirect
27. C2×#14519701C22semidirect
28. C2×#14519701C22semidirect
37. C2×C4×#92418C22semidirect
44. #16839524C22semidirect
45. #16839524C22semidirect
46. #16839524C22semidirect
47. #16839524C22semidirect
48. #16839517C22semidirect
49. #16839517C22semidirect
51. C2×C4×Q8×C61C22semidirect
54. C61×#391C22semidirect
55. C61×#389C22semidirect
58. C61×#384C22semidirect
212. C22⋊C4×C61SD16semidirect
381. #2423D61semidirect
408. C2×C4×Q8C2×D61semidirect
430. #391C2×D61semidirect
433. #389C2×D61semidirect
438. #384C2×D61semidirect
449. C61#24901semidirect
626. C22⋊C4#11758201semidirect

Maximal subgroups

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

subgroupindex
C2×#168399122
C2×C4×#117582012
C22⋊C4×D2442
#214473532
#214472562
#214471342
#214470122
#214465012
#214464272
#214461742
#214461562
#214460792
#214458162
#214457492
C61×#24232
#2490161