Finite Group Databasebeta

← #29723930

Subgroups — #29723930

Order 15616.

1148 conjugacy classes of subgroups.

The subgroup lattice has 774 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#21447343C211yesmaximal, characteristic, complemented
5#21447255C211yesmaximal, characteristic, complemented
6#21447134C211yesmaximal, characteristic, complemented
7#21447019C211yesmaximal, characteristic, complemented
8#21446501C211yesmaximal, characteristic, complemented
9#21446427C211yesmaximal, characteristic, complemented
10#21446174C211yesmaximal, characteristic, complemented
11#21446156C211yesmaximal, characteristic, complemented
12#21446065C211yesmaximal, characteristic, complemented
13#21445826C211yesmaximal, characteristic, complemented
14#21445749C211yesmaximal, characteristic
15C61×#2421C211yesmaximal, 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×#14519710C2211yescharacteristic, 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×#400—21no—
53C61×#397—21no—
54C61×#391C2211yescharacteristic, complemented
55C61×#389C2211yescharacteristic, complemented
56C61×#388—21no—
57C61×#387—21no—
58C61×#382C2211yescharacteristic, 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#14519710—41no—
98#14519708—22no—
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×C61C2311yescharacteristic
122C2×C4⋊C4×C61C2311yescharacteristic
123C2×C4⋊C4×C61C2311yescharacteristic
124C2×C22⋊C4×C61—21no—
125C2×C22⋊C4×C61—21no—
126C2×C22⋊C4×C61D411yescharacteristic
127C2×C22⋊C4×C61D411yescharacteristic
128C2×C42×C61—21no—
129C2×C42×C61C2311yescharacteristic
130C2×C42×C61C2311yescharacteristic
131#95×C61—21no—
132#95×C61—21no—
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—
207C22⋊C4×C61—22no—
208C22⋊C4×C61—22no—
209C22⋊C4×C61—42no—
210C22⋊C4×C61—42no—
211C42×C61—21no—
212C42×C61—21no—
213C42×C61—21no—
214C42×C61—21no—
215C42×C61—42no—
216C22⋊Dic61—42no—
217#11758201—28no—
218#11758201—44no—
219#11758198—42no—
220#11758198—42no—
221#11758198—42no—
222#11758198—42no—
223#11758198—81no—
224#11758198—81no—
225C4⋊Dic61—21no—
226C4⋊Dic61—21no—
227C4⋊Dic61—21no—
228C4⋊Dic61—21no—
229C2×#92418—21no—
230C2×#92418—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×#92418C2×D412yes—
241C23×C61—21no—
242C23×C61—21no—
243C23×C61—21no—
244C23×C61—21no—
245C23×C61—21no—
246C23×C61—21no—
247C23×C61#13512yes—
248C23×C61C22×D411yescharacteristic
249C22×D61—22no—
250C22×D61—22no—
251C22×D61—22no—
252C22×D61—22no—
253C22×D61—48no—
254C22×D61—41no—
255C22×D61—41no—
256C22×D61—41no—
257C22×D61—41no—
258C22×D61—48no—
259C22×D61—41no—
260C22×D61—41no—
261C22×D61—41no—
262C22×D61—41no—
263C22×D61—41no—
264C22×D61—41no—
265C22×D61—84no—
266C22×D61—84no—
267C22×D61—84no—
268C22×D61—84no—
269C22×D61—84no—
270Q8×C61—22no—
271Q8×C61—22no—
272Q8×C61—41no—
273Q8×C61—41no—
274C2×C4×C61—21no—
275C2×C4×C61—21no—
276C2×C4×C61—21no—
277C2×C4×C61—21no—
278C2×C4×C61—22no—
279C2×C4×C61—21no—
280C2×C4×C61—21no—
281C2×C4×C61—21no—
282C2×C4×C61—21no—
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—41no—
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×C61AGL(1,ℤ/8)12yes—
305C2×C4×C61C22×D411yescharacteristic
306C2×C4×C61C2×#4111yescharacteristic
307C2×C4×C61C2×#4111yescharacteristic
308C2×C4×C61C2×#4111yescharacteristic
309C2×C4×C61H(5,𝔽2)11yescharacteristic
310C2×C4×C61H(5,𝔽2)11yescharacteristic
311C2×Dic61—41no—
312C2×Dic61—41no—
313C2×Dic61—41no—
314C2×Dic61—41no—
315C2×Dic61—41no—
316C2×Dic61—41no—
317D244—22no—
318D244—22no—
319D244—22no—
320D244—22no—
321D244—22no—
322D244—48no—
323D244—41no—
324D244—41no—
325D244#12314yes—
326C4×D61—84no—
327C4×D61—84no—
328#92418—22no—
329#92418—41no—
330#92418—41no—
331#92418—41no—
332#24905—611nomaximal, Sylow
333C22×C61—22no—
334C22×C61—22no—
335C22×C61—22no—
336C22×C61—41no—
337C22×C61—41no—
338C22×C61—41no—
339C22×C61—41no—
340C22×C61#52511yescharacteristic
341C22×C61D4211yescharacteristic
342C22×C61#54611yescharacteristic
343C22×C61C2×#13511yescharacteristic
344C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
345C22×C61#57711yescharacteristic
346C22×C61#57711yescharacteristic
347C2×D61—24no—
348C2×D61—42no—
349C2×D61—42no—
350C2×D61—42no—
351C2×D61—42no—
352C2×D61—42no—
353C2×D61—42no—
354C2×D61—42no—
355C2×D61—42no—
356C2×D61—42no—
357C2×D61—816no—
358C2×D61—81no—
359C2×D61—81no—
360C2×D61—81no—
361C2×D61—81no—
362C4×C61—22no—
363C4×C61—41no—
364C4×C61—42no—
365C4×C61—41no—
366C4×C61—41no—
367C4×C61—41no—
368C4×C61—81no—
369C4×C61—81no—
370C4×C61—81no—
371C4×C61C2×#12311yescharacteristic
372C4×C61#53811yescharacteristic
373C4×C61#54611yescharacteristic
374C4×C61#55111yescharacteristic
375Dic61—81no—
376Dic61—81no—
377C2×#450—611no—
378C2×C4×SD16—611no—
379#2421D6111yescharacteristic, complemented
380D4×C22⋊C4—611no—
381#2092—611no—
382#2077—611no—
383#2055—611no—
384#2036—611no—
385#1934—611no—
386#1923—611no—
387#1880—611no—
388#1877—611no—
389#1862—611no—
390#1804—611no—
391#1786—611no—
392C2×C61—42no—
393C2×C61#241811yescharacteristic
394C2×C61#310511yescharacteristic
395C2×C61#312311yescharacteristic
396C2×C61#326511yescharacteristic
397C2×C61#328211yescharacteristic
398C2×C61#329611yescharacteristic
399C2×C61#332411yescharacteristic
400D61—44no—
401D61—82no—
402C23×D4—611no—
403C22×SD16—611no—
404C22×SD16—611no—
405C2×C22⋊Q8C2×D6111yescharacteristic
406C2×C4×Q8C2×D6111yescharacteristic, complemented
407C2×C4×D4—611no—
408C2×C4×D4—611no—
409C22×C22⋊C4—1221no—
410#450—1224no—
411C4×SD16—1224no—
412C2×#107—611no—
413C2×#106—611no—
414C2×C4⋊C8—611no—
415C2×#103—611no—
416C2×#103—611no—
417C2×#102—611no—
418C2×#102—611no—
419C2×#102—611no—
420C2×#102—611no—
421C2×#102—611no—
422C2×#102—611no—
423C2×C22⋊C8—611no—
424C2×C22⋊C8—611no—
425C2×C4×C8—611no—
426#400—21no—
427#397—21no—
428#391C2×D6111yescharacteristic, complemented
429#390—611no—
430#390—611no—
431#389C2×D6111yescharacteristic, complemented
432#388—21no—
433#387—21no—
434#386—1221no—
435#386—1221no—
436#382C2×D6111yescharacteristic, complemented
437#380—611no—
438#380C2×D6111yescharacteristic
439#379—1221no—
440C4×C22⋊C4C2×D6111yescharacteristic
441#340—611no—
442#340—611no—
443#340—611no—
444#340—611no—
445#336—611no—
446#336—611no—
447C61#2490511yescharacteristic, complemented, Sylow
448C25—1221no—
449C22×Q8C22×D6111yescharacteristic
450C22×D4—611no—
451C22×D4—611no—
452C22×D4—1222no—
453C22×D4—1222no—
454C22×D4—1222no—
455C22×D4—1222no—
456C22×D4—1221no—
457C22×D4—2441no—
458C22×D4—2441no—
459C23×C4—1221no—
460C23×C4—1221no—
461C23×C4C22×D6111yescharacteristic
462C2×SD16—614no—
463C2×SD16—1222no—
464C2×SD16—1222no—
465C2×SD16—1222no—
466C2×SD16—1222no—
467C2×SD16—2441no—
468C22×C8—611no—
469C22×C8—611no—
470C22×C8—611no—
471C22×C8—611no—
472C22⋊Q8—22no—
473C22⋊Q8—41no—
474C4×Q8—22no—
475C4×Q8—41no—
476C4×D4—1222no—
477C4×D4—1222no—
478C4×D4—2441no—
479C4×D4—2441no—
480C2×C4⋊C4—21no—
481C2×C4⋊C4—21no—
482C2×C4⋊C4—21no—
483C2×C4⋊C4—611no—
484C2×C4⋊C4—611no—
485C2×C4⋊C4C22×D6111yescharacteristic
486C2×C4⋊C4C22×D6111yescharacteristic
487C2×C4⋊C4C22×D6111yescharacteristic
488C2×C22⋊C4—21no—
489C2×C22⋊C4—21no—
490C2×C22⋊C4—1221no—
491C2×C22⋊C4—1221no—
492C2×C22⋊C4—1221no—
493C2×C22⋊C4—1221no—
494C2×C22⋊C4—1221no—
495C2×C22⋊C4—1221no—
496C2×C22⋊C4—1221no—
497C2×C22⋊C4—2444no—
498C2×C22⋊C4C22⋊D6111yescharacteristic
499C2×C22⋊C4C22⋊D6111yescharacteristic
500C2×C42—21no—
501C2×C42C22×D6111yescharacteristic
502C2×C42C22×D6111yescharacteristic
503#107—2441no—
504#106—1222no—
505C4⋊C8—2441no—
506#103—1222no—
507#103—2441no—
508#102—1222no—
509#102—1222no—
510#102—1222no—
511#102—1222no—
512#102—1222no—
513#102—2441no—
514C22⋊C8—1222no—
515C22⋊C8—2441no—
516C4×C8—1222no—
517#95—21no—
518#95—21no—
519#95—21no—
520#95—21no—
521#95—21no—
522#95—21no—
523#95—1221no—
524#95C22⋊D6111yescharacteristic
525#95C22⋊D6111yescharacteristic
526C24—1224no—
527C24—1221no—
528C24—1221no—
529C24—4881no—
530C24—4881no—
531C24—2442no—
532C24—2442no—
533C24—2442no—
534C24—2442no—
535C24C2×C22⋊D6111yescharacteristic
536C2×Q8—21no—
537C2×Q8—21no—
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8D4×D6112yes—
542C2×D4—612no—
543C2×D4—612no—
544C2×D4—612no—
545C2×D4—612no—
546C2×D4—1224no—
547C2×D4—1221no—
548C2×D4—1221no—
549C2×D4—1221no—
550C2×D4—1221no—
551C2×D4—1221no—
552C2×D4—1221no—
553C2×D4—1221no—
554C2×D4—1221no—
555C2×D4—2442no—
556C2×D4—2442no—
557C2×D4—2444no—
558C2×D4—2444no—
559C2×D4—2444no—
560C2×D4—2444no—
561C22×C4—21no—
562C22×C4—21no—
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—1221no—
572C22×C4—1221no—
573C22×C4—4881no—
574C22×C4—4881no—
575C22×C4—2442no—
576C22×C4—2442no—
577C22×C4—2442no—
578C22×C4—2442no—
579C22×C4C2×C22⋊D6111yescharacteristic
580C22×C4C2×C22⋊D6111yescharacteristic
581C22×C4C2×C22⋊D6111yescharacteristic
582C22×C4C2×C22⋊D6111yescharacteristic
583C22×C4C2×C22⋊D6111yescharacteristic
584C22×C4C23×D6111yescharacteristic
585SD16—1228no—
586SD16—2444no—
587C2×C8—612no—
588C2×C8—1221no—
589C2×C8—1221no—
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—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—42no—
606C4⋊C4—42no—
607C4⋊C4—42no—
608C4⋊C4—1221no—
609C4⋊C4—1221no—
610C4⋊C4—1221no—
611C4⋊C4—1221no—
612C22⋊C4—22no—
613C22⋊C4—22no—
614C22⋊C4—42no—
615C22⋊C4—42no—
616C22⋊C4—4881no—
617C22⋊C4—4881no—
618C22⋊C4—2442no—
619C22⋊C4—2442no—
620C22⋊C4—2442no—
621C22⋊C4—2442no—
622C22⋊C4—2442no—
623C42—21no—
624C42—21no—
625C42—21no—
626C42—21no—
627C42—42no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—1222no—
635C23—1222no—
636C23—1222no—
637C23—1222no—
638C23—4884no—
639C23—4884no—
640C23—4884no—
641C23—4884no—
642C23—4884no—
643C23—2448no—
644C23—2448no—
645C23—2441no—
646C23—2441no—
647C23—2441no—
648C23—2441no—
649C23—2441no—
650C23—2441no—
651C23—2441no—
652C23—2441no—
653C23—2441no—
654C23—2441no—
655C23#1451979712yes—
656C23C22×C22⋊D6111yescharacteristic
657Q8—22no—
658Q8—22no—
659Q8—41no—
660Q8—41no—
661D4—614no—
662D4—1222no—
663D4—1222no—
664D4—1222no—
665D4—1222no—
666D4—1222no—
667D4—2448no—
668D4—2441no—
669D4—2441no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—22no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
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—4884no—
701C2×C4—4884no—
702C2×C4—2441no—
703C2×C4—2441no—
704C2×C4—2441no—
705C2×C4—2441no—
706C2×C4—2441no—
707C2×C4—2441no—
708C2×C4#1451980212yes—
709C2×C4C2×D4×D6111yescharacteristic
710C2×C4#41×D6111yescharacteristic
711C2×C4#41×D6111yescharacteristic
712C2×C4#41×D6111yescharacteristic
713C2×C4#1451982211yescharacteristic
714C2×C4#1451982311yescharacteristic
715C8—1222no—
716C8—2441no—
717C8—2441no—
718C8—2441no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—41no—
723C22—41no—
724C22—41no—
725C22—41no—
726C22—1224no—
727C22—48816no—
728C22—4881no—
729C22—4881no—
730C22—4881no—
731C22—4881no—
732C22—2442no—
733C22—2442no—
734C22—2442no—
735C22—2442no—
736C22—2442no—
737C22—2442no—
738C22—2442no—
739C22—2442no—
740C22—2442no—
741C22#1684026911yescharacteristic
742C22D4×C22⋊D6111yescharacteristic
743C22#1684040011yescharacteristic
744C22C2×#1451979711yescharacteristic
745C22C2×#1451980211yescharacteristic
746C22#1684057011yescharacteristic
747C22#1684057011yescharacteristic
748C4—22no—
749C4—41no—
750C4—42no—
751C4—41no—
752C4—41no—
753C4—41no—
754C4—81no—
755C4—81no—
756C4—81no—
757C4—4881no—
758C4—4881no—
759C4#123×D6111yescharacteristic
760C4#1684034811yescharacteristic
761C4#1684040411yescharacteristic
762C4#1684044011yescharacteristic
763C2—42no—
764C2—4882no—
765C2—2444no—
766C2#2144927811yescharacteristic
767C2#2145586211yescharacteristic
768C2#2145606611yescharacteristic
769C2#2145731511yescharacteristic
770C2#2145752711yescharacteristic
771C2#2145764811yescharacteristic
772C2#2145804411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2421C2
socleC23×C61C22×D4
prime radicalC23×D244C22
hypercenter#2421D61
hypocenterC61#24905
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2421

Complements

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

NH ≅ G/Ntype
2. C2×C4×#11758201C2semidirect
4. #21447343C2semidirect
5. #21447255C2semidirect
6. #21447134C2semidirect
7. #21447019C2semidirect
8. #21446501C2semidirect
9. #21446427C2semidirect
10. #21446174C2semidirect
11. #21446156C2semidirect
12. #21446065C2semidirect
13. #21445826C2semidirect
15. C61×#2421C2semidirect
24. C2×#14519710C22semidirect
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×#382C22semidirect
379. #2421D61semidirect
406. C2×C4×Q8C2×D61semidirect
428. #391C2×D61semidirect
431. #389C2×D61semidirect
436. #382C2×D61semidirect
447. C61#24905semidirect

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
#214473432
#214472552
#214471342
#214470192
#214465012
#214464272
#214461742
#214461562
#214460652
#214458262
#214457492
C61×#24212
#2490561