Finite Group Databasebeta

← #29723878

Subgroups — #29723878

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×#16839915C211yesmaximal, characteristic
2C2×C4×#11758190C211yesmaximal, characteristic, complemented
3#21449344C211yesmaximal, characteristic, complemented
4C22⋊C4×D244C211yesmaximal, characteristic
5#21447351C211yesmaximal, characteristic, complemented
6#21447252C211yesmaximal, characteristic, complemented
7#21447137C211yesmaximal, characteristic, complemented
8#21447016C211yesmaximal, characteristic, complemented
9#21446502C211yesmaximal, characteristic, complemented
10#21446173C211yesmaximal, characteristic, complemented
11#21446152C211yesmaximal, characteristic, complemented
12#21446083C211yesmaximal, characteristic, complemented
13#21445820C211yesmaximal, characteristic, complemented
14#21445751C211yesmaximal, characteristic
15C61×#1923C211yesmaximal, characteristic, complemented
16C23×D244C2211yescharacteristic
17C22×#11758190C2211yescharacteristic
18C22×#11758190C2211yescharacteristic
19C2×#14519756C2211yescharacteristic
20C2×C4×Dic122C2211yescharacteristic, complemented
21C2×C4×D244C2211yescharacteristic
22C2×C4×D244C2211yescharacteristic
23C2×C22⋊C4×D61—21no—
24#16839915—24no—
25C4×#11758190—24no—
26C2×#14519709C2211yescharacteristic, complemented
27C2×#14519709C2211yescharacteristic, complemented
28C2×#14519702C2211yescharacteristic, complemented
29C2×#14519702C2211yescharacteristic, complemented
30C2×#14519699C2211yescharacteristic
31C2×#14519699C2211yescharacteristic
32C2×#14519699C2211yescharacteristic
33C2×#14519699C2211yescharacteristic
34C2×#14519699C2211yescharacteristic
35C2×#14519699C2211yescharacteristic
36#16839698—21no—
37#16839696—21no—
38#16839668C2211yescharacteristic, complemented
39#16839664C2211yescharacteristic
40#16839664C2211yescharacteristic
41#16839660C2211yescharacteristic, complemented
42#16839655—21no—
43#16839645—21no—
44#16839640—21no—
45#16839640—21no—
46#16839632C2211yescharacteristic, complemented
47#16839622C2211yescharacteristic
48#16839622C2211yescharacteristic
49#16839617—21no—
50#16839525C2211yescharacteristic, complemented
51#16839525C2211yescharacteristic, complemented
52#16839525C2211yescharacteristic, complemented
53#16839525C2211yescharacteristic, complemented
54C2×C4⋊C8×C61C2211yescharacteristic, complemented
55C2×C22⋊C8×C61C2211yescharacteristic
56C2×C22⋊C8×C61C2211yescharacteristic
57C2×C4×C8×C61C2211yescharacteristic, complemented
58C4×C22⋊C4×C61C2211yescharacteristic
59C61×#336C2211yescharacteristic, complemented
60C61×#336C2211yescharacteristic, complemented
61C24×D61—21no—
62C22×Dic122C2311yescharacteristic
63C22×D244—21no—
64C22×D244—22no—
65C22×D244—22no—
66C22×D244—22no—
67C22×D244—22no—
68C22×D244—41no—
69C22×D244—41no—
70C22×D244C2311yescharacteristic
71C22×D244C2311yescharacteristic
72C22×C4×D61—21no—
73C22×C4×D61—21no—
74C2×#11758190—22no—
75C2×#11758190—22no—
76C2×#11758190—22no—
77C2×#11758190—22no—
78C2×#11758190—41no—
79C2×#11758190D414yes—
80#14519756—22no—
81#14519756—41no—
82C4×Dic122—22no—
83C4×Dic122—41no—
84C4×D244—22no—
85C4×D244—22no—
86C4×D244—41no—
87C4×D244—41no—
88C2×C4⋊Dic61—21no—
89C2×C4⋊Dic61—21no—
90C2×C4⋊Dic61C2311yescharacteristic
91C2×C4⋊Dic61C2311yescharacteristic
92C2×C4⋊Dic61C2311yescharacteristic
93C2×C4⋊Dic61C2311yescharacteristic
94C2×C4⋊Dic61C2311yescharacteristic
95C2×#11758196—21no—
96C2×#11758196—21no—
97C2×#11758196—21no—
98C2×C22⋊Dic61—21no—
99C2×C22⋊Dic61—21no—
100C2×C22⋊Dic61—21no—
101C2×#11758198—21no—
102C2×#11758198—21no—
103C2×#11758198—21no—
104C2×#11758198—21no—
105C2×#11758198—21no—
106C2×#11758198—21no—
107C22⋊C4×D61—44no—
108C2×C4×Dic61—21no—
109#14519709—22no—
110#14519709—41no—
111#14519702—22no—
112#14519702—41no—
113#14519699—22no—
114#14519699—22no—
115#14519699—22no—
116#14519699—22no—
117#14519699—22no—
118#14519699—41no—
119#14519684—21no—
120#14519684—21no—
121#14519684—21no—
122#14519684—21no—
123#14519684—21no—
124C23×C4×C61C2311yescharacteristic
125C22×C8×C61C2311yescharacteristic
126C22×C8×C61C2311yescharacteristic
127C22×C8×C61C2311yescharacteristic
128C22×C8×C61C2311yescharacteristic
129C2×C22⋊C4×C61D411yescharacteristic
130C2×C22⋊C4×C61D411yescharacteristic
131C2×C42×C61C2311yescharacteristic
132C2×C42×C61C2311yescharacteristic
133C4⋊C8×C61—41no—
134C22⋊C8×C61—22no—
135C22⋊C8×C61—41no—
136C4×C8×C61—22no—
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—
149C22×C4×C61—21no—
150C22×C4×C61—21no—
151C22×C4×C61—21no—
152C22×C4×C61—21no—
153C22×C4×C61—21no—
154C22×C4×C61—21no—
155C22×C4×C61C2×D411yescharacteristic
156C22×C4×C61C2×D411yescharacteristic
157C22×C4×C61C2×D411yescharacteristic
158C22×C4×C61C2×D411yescharacteristic
159C22×C4×C61C2×D411yescharacteristic
160C22×C4×C61C2411yescharacteristic
161C22×Dic61—21no—
162C22×Dic61—21no—
163C22×Dic61—21no—
164C22×Dic61—21no—
165C22×Dic61—21no—
166C22×Dic61—21no—
167C2×D244—21no—
168C2×D244—21no—
169C2×D244—21no—
170C2×D244—21no—
171C2×D244—21no—
172C2×D244—21no—
173C2×D244—21no—
174C2×D244—24no—
175C2×D244—21no—
176C2×D244—44no—
177C2×D244—44no—
178C2×D244—44no—
179C2×D244—42no—
180C2×D244—42no—
181C2×D244—44no—
182C2×D244C2×D412yes—
183C2×D244#4112yes—
184C2×D244#4112yes—
185C2×D244#4112yes—
186C2×C4×D61—42no—
187C2×C4×D61—42no—
188C2×C4×D61—42no—
189C2×C4×D61—42no—
190C2×C4×D61—81no—
191C2×C4×D61—81no—
192C2×Dic122—21no—
193C2×Dic122—21no—
194C2×Dic122—21no—
195C2×Dic122—21no—
196C2×Dic122—21no—
197C2×Dic122C2×D412yes—
198C2×C8×C61—21no—
199C2×C8×C61—21no—
200C2×C8×C61—21no—
201C2×C8×C61—21no—
202C2×C8×C61—21no—
203C2×C8×C61—21no—
204C2×C8×C61—21no—
205C2×C8×C61—21no—
206C2×C8×C61—21no—
207C2×C8×C61—21no—
208C2×C8×C61—21no—
209C2×C8×C61C2×D412yes—
210C22⋊C4×C61—41no—
211C22⋊C4×C61SD1614yescomplemented
212C42×C61—21no—
213C42×C61—21no—
214C42×C61—21no—
215C42×C61—21no—
216C22⋊Dic61—42no—
217C22⋊Dic61—42no—
218C22⋊Dic61—81no—
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—
229C4⋊Dic61—21no—
230C4⋊Dic61—21no—
231C4⋊Dic61—21no—
232C4⋊Dic61—21no—
233C4⋊Dic61—21no—
234C4⋊Dic61—21no—
235C4⋊Dic61—42no—
236C4⋊Dic61—81no—
237#11758196—42no—
238#11758196—42no—
239#11758196—81no—
240C4×Dic61—42no—
241#11758190—28no—
242#11758190—44no—
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—
272C2×C4×C61—21no—
273C2×C4×C61—21no—
274C2×C4×C61—21no—
275C2×C4×C61—21no—
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—21no—
283C2×C4×C61—21no—
284C2×C4×C61—21no—
285C2×C4×C61—41no—
286C2×C4×C61—41no—
287C2×C4×C61—41no—
288C2×C4×C61—41no—
289C2×C4×C61C2×SD1612yes—
290C2×C4×C61C2×SD1612yes—
291C2×C4×C61C22×D411yescharacteristic
292C2×C4×C61C2×#4111yescharacteristic
293C2×C4×C61C2×#4111yescharacteristic
294C2×C4×C61C2×#4111yescharacteristic
295C2×C4×C61H(5,𝔽2)11yescharacteristic
296C2×C4×C61H(5,𝔽2)11yescharacteristic
297C2×Dic61—22no—
298C2×Dic61—41no—
299C2×Dic61—41no—
300C2×Dic61—41no—
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—41no—
311C2×Dic61—41no—
312C2×Dic61—41no—
313C2×Dic61—41no—
314C2×Dic61—41no—
315D244—22no—
316D244—22no—
317D244—22no—
318D244—22no—
319D244—22no—
320D244—48no—
321D244—41no—
322D244—41no—
323D244#12314yes—
324C4×D61—84no—
325C4×D61—84no—
326Dic122—22no—
327Dic122—22no—
328Dic122—41no—
329Dic122—41no—
330C8×C61—22no—
331C8×C61—41no—
332C8×C61—41no—
333C8×C61—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—41no—
368C4×C61—41no—
369C4×C61C2×#12311yescharacteristic
370C4×C61#53811yescharacteristic
371C4×C61#54611yescharacteristic
372C4×C61#55111yescharacteristic
373Dic61—42no—
374Dic61—81no—
375Dic61—81no—
376Dic61—81no—
377Dic61—81no—
378Dic61—81no—
379C2×#450—611no—
380C2×C4×SD16—611no—
381#2423—611no—
382D4×C22⋊C4—611no—
383#2094—611no—
384#2077—611no—
385#2055—611no—
386#2035—611no—
387#1934—611no—
388#1923D6111yescharacteristic, complemented
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⋊Q8—611no—
408C2×C4×Q8—611no—
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⋊C8C2×D6111yescharacteristic, complemented
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⋊C8C2×D6111yescharacteristic
426C2×C22⋊C8C2×D6111yescharacteristic
427C2×C4×C8C2×D6111yescharacteristic, complemented
428#399—1221no—
429#398—1221no—
430#391—611no—
431#390—611no—
432#390—611no—
433#389—611no—
434#388—1221no—
435#387—1221no—
436#386—1221no—
437#386—1221no—
438#384—611no—
439#380—611no—
440#380—611no—
441#379—1221no—
442C4×C22⋊C4C2×D6111yescharacteristic
443#340—611no—
444#340—611no—
445#340—611no—
446#340—611no—
447#336C2×D6111yescharacteristic, complemented
448#336C2×D6111yescharacteristic, complemented
449C61#2490111yescharacteristic, complemented, Sylow
450C25—1221no—
451C22×Q8—611no—
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×C8C22×D6111yescharacteristic
471C22×C8C22×D6111yescharacteristic
472C22×C8C22×D6111yescharacteristic
473C22×C8C22×D6111yescharacteristic
474C22⋊Q8—1222no—
475C22⋊Q8—2441no—
476C4×Q8—1222no—
477C4×Q8—2441no—
478C4×D4—1222no—
479C4×D4—1222no—
480C4×D4—2441no—
481C4×D4—2441no—
482C2×C4⋊C4—611no—
483C2×C4⋊C4—611no—
484C2×C4⋊C4—611no—
485C2×C4⋊C4—611no—
486C2×C4⋊C4—611no—
487C2×C4⋊C4—1221no—
488C2×C4⋊C4—1221no—
489C2×C4⋊C4—1221no—
490C2×C4⋊C4—1221no—
491C2×C4⋊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—1221no—
498C2×C22⋊C4—1221no—
499C2×C22⋊C4—1221no—
500C2×C22⋊C4—1221no—
501C2×C22⋊C4—2444no—
502C2×C22⋊C4D24411yescharacteristic
503C2×C22⋊C4D24411yescharacteristic
504C2×C42—1221no—
505C2×C42C22×D6111yescharacteristic
506C2×C42C22×D6111yescharacteristic
507#106—1222no—
508#106—2441no—
509C4⋊C8—41no—
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—22no—
519C22⋊C8—41no—
520C4×C8—22no—
521#95—1221no—
522#95—1221no—
523#95—1221no—
524#95—1221no—
525#95—1221no—
526#95D24411yescharacteristic
527#95D24411yescharacteristic
528C24—1224no—
529C24—1221no—
530C24—1221no—
531C24—4881no—
532C24—4881no—
533C24—2442no—
534C24—2442no—
535C24—2442no—
536C24—2442no—
537C24C2×D24411yescharacteristic
538C2×Q8—612no—
539C2×Q8—1221no—
540C2×Q8—1221no—
541C2×Q8—1221no—
542C2×Q8—1221no—
543C2×Q8—1221no—
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—1221no—
570C22×C4—1221no—
571C22×C4—1221no—
572C22×C4—1221no—
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×D24411yescharacteristic
582C22×C4C2×D24411yescharacteristic
583C22×C4C2×D24411yescharacteristic
584C22×C4C2×D24411yescharacteristic
585C22×C4C2×D24411yescharacteristic
586C22×C4C23×D6111yescharacteristic
587SD16—1228no—
588SD16—2444no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8D4×D6112yes—
601C4⋊C4—1221no—
602C4⋊C4—1221no—
603C4⋊C4—1221no—
604C4⋊C4—1221no—
605C4⋊C4—1221no—
606C4⋊C4—1221no—
607C4⋊C4—1221no—
608C4⋊C4—1221no—
609C4⋊C4—1221no—
610C4⋊C4—1221no—
611C4⋊C4—4881no—
612C4⋊C4—4881no—
613C4⋊C4—2442no—
614C4⋊C4—2442no—
615C4⋊C4—2442no—
616C22⋊C4—41no—
617C22⋊C4—4881no—
618C22⋊C4—4881no—
619C22⋊C4—4881no—
620C22⋊C4—2442no—
621C22⋊C4—2442no—
622C22⋊C4—2442no—
623C22⋊C4—2442no—
624C22⋊C4—2442no—
625C22⋊C4—2442no—
626C22⋊C4#1175819014yescomplemented
627C42—21no—
628C42—21no—
629C42—21no—
630C42—21no—
631C42—2442no—
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×#1175819012yes—
660C23C22×D24411yescharacteristic
661Q8—1222no—
662Q8—1222no—
663Q8—2441no—
664Q8—2441no—
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—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—1222no—
692C2×C4—4884no—
693C2×C4—4884no—
694C2×C4—2441no—
695C2×C4—2441no—
696C2×C4—2441no—
697C2×C4—2441no—
698C2×C4—2441no—
699C2×C4—2441no—
700C2×C4—2441no—
701C2×C4—2441no—
702C2×C4—2441no—
703C2×C4—2441no—
704C2×C4—2441no—
705C2×C4—2441no—
706C2×C4—2441no—
707C2×C4—2441no—
708C2×C4—2441no—
709C2×C4—2441no—
710C2×C4—2441no—
711C2×C4C2×#1175819012yes—
712C2×C4C2×#1175819012yes—
713C2×C4C2×D4×D6111yescharacteristic
714C2×C4#41×D6111yescharacteristic
715C2×C4#41×D6111yescharacteristic
716C2×C4#41×D6111yescharacteristic
717C2×C4#1451982211yescharacteristic
718C2×C4#1451982311yescharacteristic
719C8—22no—
720C8—41no—
721C8—41no—
722C8—41no—
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#1684027411yescharacteristic
746C22D4×D24411yescharacteristic
747C22#1684040711yescharacteristic
748C22C22×#1175819011yescharacteristic
749C22#1684056211yescharacteristic
750C22#1684056711yescharacteristic
751C22#1684057411yescharacteristic
752C4—22no—
753C4—22no—
754C4—41no—
755C4—41no—
756C4—41no—
757C4—4881no—
758C4—4881no—
759C4—4881no—
760C4—4881no—
761C4—4881no—
762C4—2442no—
763C4#123×D6111yescharacteristic
764C4#1684034611yescharacteristic
765C4#1684040911yescharacteristic
766C4#1684043711yescharacteristic
767C2—42no—
768C2—4882no—
769C2—2444no—
770C2#2144928611yescharacteristic
771C2#2145582811yescharacteristic
772C2#2145600511yescharacteristic
773C2#2145736411yescharacteristic
774C2D4×#1175819011yescharacteristic
775C2#2145764411yescharacteristic
776C2#2145803711yescharacteristic
subgroupG/H
centerC23C22×D244
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#1923C2
socleC23×C61C22×D4
prime radicalC23×D244C22
hypercenter#1923D61
hypocenterC61#24901
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #1923

Complements

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

NH ≅ G/Ntype
2. C2×C4×#11758190C2semidirect
3. #21449344C2semidirect
5. #21447351C2semidirect
6. #21447252C2semidirect
7. #21447137C2semidirect
8. #21447016C2semidirect
9. #21446502C2semidirect
10. #21446173C2semidirect
11. #21446152C2semidirect
12. #21446083C2semidirect
13. #21445820C2semidirect
15. C61×#1923C2semidirect
20. C2×C4×Dic122C22semidirect
26. C2×#14519709C22semidirect
27. C2×#14519709C22semidirect
28. C2×#14519702C22semidirect
29. C2×#14519702C22semidirect
38. #16839668C22semidirect
41. #16839660C22semidirect
46. #16839632C22semidirect
50. #16839525C22semidirect
51. #16839525C22semidirect
52. #16839525C22semidirect
53. #16839525C22semidirect
54. C2×C4⋊C8×C61C22semidirect
57. C2×C4×C8×C61C22semidirect
59. C61×#336C22semidirect
60. C61×#336C22semidirect
211. C22⋊C4×C61SD16semidirect
388. #1923D61semidirect
416. C2×C4⋊C8C2×D61semidirect
427. C2×C4×C8C2×D61semidirect
447. #336C2×D61semidirect
448. #336C2×D61semidirect
449. C61#24901semidirect
626. C22⋊C4#11758190semidirect

Maximal subgroups

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

subgroupindex
C2×#168399152
C2×C4×#117581902
#214493442
C22⋊C4×D2442
#214473512
#214472522
#214471372
#214470162
#214465022
#214461732
#214461522
#214460832
#214458202
#214457512
C61×#19232
#2490161