Finite Group Databasebeta

← #29730296

Subgroups — #29730296

Order 15616.

860 conjugacy classes of subgroups.

The subgroup lattice has 682 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840058C211yesmaximal, characteristic, complemented
2#21450811C211yesmaximal, characteristic
3#21450728C211yesmaximal, characteristic
4#21447247C211yesmaximal, characteristic, complemented
5#21447242C211yesmaximal, characteristic, complemented
6#21447023C211yesmaximal, characteristic, complemented
7#21447016C211yesmaximal, characteristic, complemented
8#21446792C211yesmaximal, characteristic, complemented
9#21446589C211yesmaximal, characteristic, complemented
10#21446252C211yesmaximal, characteristic, complemented
11#21446242C211yesmaximal, characteristic, complemented
12#21445852C211yesmaximal, characteristic, complemented
13#21445848C211yesmaximal, characteristic, complemented
14#21445650C211yesmaximal, characteristic, complemented
15C2×C61×#435C211yesmaximal, characteristic
16C2×#14519777C2211yescharacteristic
17C2×#14519764—21no—
18C2×#14519756C2211yescharacteristic
19C2×#14519756C2211yescharacteristic
20C2×C4×Dic122C2211yescharacteristic
21#16840058—24no—
22C2×#14519711C2211yescharacteristic
23C2×#14519711C2211yescharacteristic
24C2×#14519711C2211yescharacteristic
25C2×#14519709C2211yescharacteristic
26C2×#14519702C2211yescharacteristic
27C2×#14519702C2211yescharacteristic
28C2×#14519702C2211yescharacteristic
29C2×#14519702C2211yescharacteristic
30#16839693—21no—
31#16839687—21no—
32#16839687—21no—
33#16839676—21no—
34#16839667—21no—
35#16839650—21no—
36#16839650—21no—
37#16839628C2211yescharacteristic
38#16839622C2211yescharacteristic
39#16839622C2211yescharacteristic
40#16839622C2211yescharacteristic
41#16839622C2211yescharacteristic
42#16839622C2211yescharacteristic
43#16839622C2211yescharacteristic
44C4×C4⋊Dic61C2211yescharacteristic
45#16839525C2211yescharacteristic
46#16839525C2211yescharacteristic
47#16839525C2211yescharacteristic
48#16839525C2211yescharacteristic
49#16839525C2211yescharacteristic
50#16839525C2211yescharacteristic
51#16839525C2211yescharacteristic
52#16839525C2211yescharacteristic
53C22×M16×C61C2211yescharacteristic
54C23×C8×C61C2211yescharacteristic
55C2×C4×D4×C61C2211yescharacteristic
56C61×#435—24no—
57C2×C4⋊C8×C61C2211yescharacteristic
58C2×C22⋊C8×C61C2211yescharacteristic
59C2×C22⋊C8×C61C2211yescharacteristic
60C2×#97×C61C2211yescharacteristic
61C22×Dic122—21no—
62C22×Dic122C2311yescharacteristic
63#14519777—22no—
64#14519777—22no—
65#14519764—44no—
66#14519756—22no—
67#14519756—22no—
68#14519756—41no—
69#14519756—41no—
70C4×Dic122—22no—
71C4×Dic122—22no—
72C2×C4⋊Dic61—21no—
73C2×C4⋊Dic61C2311yescharacteristic
74C2×C4⋊Dic61C2311yescharacteristic
75C2×C4⋊Dic61C2311yescharacteristic
76C2×C4⋊Dic61C2311yescharacteristic
77C2×C4⋊Dic61C2311yescharacteristic
78C2×C4⋊Dic61C2311yescharacteristic
79C2×C4⋊Dic61C2311yescharacteristic
80C2×#11758196—21no—
81C2×#11758196—21no—
82C2×#11758196—21no—
83C2×C22⋊Dic61—21no—
84C2×C22⋊Dic61—21no—
85C2×C22⋊Dic61—21no—
86C2×C22⋊Dic61—21no—
87C2×C22⋊Dic61—21no—
88C2×C22⋊Dic61—21no—
89C2×C22⋊Dic61—21no—
90C2×C22⋊Dic61—21no—
91C2×C4×Dic61—21no—
92C2×C4×Dic61—21no—
93#14519711—22no—
94#14519711—22no—
95#14519711—41no—
96#14519709—41no—
97#14519702—22no—
98#14519702—22no—
99#14519702—22no—
100#14519702—22no—
101#14519684—21no—
102#14519684—21no—
103#14519684—21no—
104#14519684—21no—
105#14519684—21no—
106#14519684—21no—
107#14519684—21no—
108#14519684—21no—
109#14519684—21no—
110C22×D4×C61D411yescharacteristic
111C23×C4×C61C2311yescharacteristic
112C23×C4×C61C2311yescharacteristic
113C2×M16×C61—22no—
114C2×M16×C61—22no—
115C2×M16×C61—41no—
116C22×C8×C61—22no—
117C22×C8×C61—22no—
118C22×C8×C61—41no—
119C22×C8×C61C2311yescharacteristic
120C22×C8×C61C2311yescharacteristic
121C22×C8×C61C2311yescharacteristic
122C22×C8×C61C2311yescharacteristic
123C4×D4×C61—22no—
124C4×D4×C61—22no—
125C2×C4⋊C4×C61D411yescharacteristic
126C2×C22⋊C4×C61D411yescharacteristic
127C2×C22⋊C4×C61D411yescharacteristic
128C2×C42×C61C2311yescharacteristic
129C4⋊C8×C61D414yes—
130C22⋊C8×C61—22no—
131C22⋊C8×C61—22no—
132#97×C61—22no—
133C24×C61C2×D411yescharacteristic
134C24×C61C2×D411yescharacteristic
135C2×D4×C61—22no—
136C2×D4×C61—22no—
137C2×D4×C61—41no—
138C22×C4×C61—21no—
139C22×C4×C61—21no—
140C22×C4×C61—21no—
141C22×C4×C61—21no—
142C22×C4×C61—21no—
143C22×C4×C61—21no—
144C22×C4×C61—21no—
145C22×C4×C61—21no—
146C22×C4×C61—21no—
147C22×C4×C61—21no—
148C22×C4×C61—21no—
149C22×C4×C61—21no—
150C22×C4×C61C2×D411yescharacteristic
151C22×C4×C61C2×D411yescharacteristic
152C22×C4×C61C2×D411yescharacteristic
153C22×C4×C61C2×D411yescharacteristic
154C22×C4×C61C2411yescharacteristic
155C22×Dic61—21no—
156C22×Dic61—21no—
157C22×Dic61—21no—
158C22×Dic61—21no—
159C22×Dic61—21no—
160C22×Dic61—21no—
161C22×Dic61—21no—
162C22×Dic61—21no—
163C2×Dic122—21no—
164C2×Dic122—21no—
165C2×Dic122—21no—
166C2×Dic122—21no—
167C2×Dic122—21no—
168C2×Dic122—42no—
169C2×Dic122—42no—
170C2×Dic122—42no—
171C2×Dic122#4112yes—
172M16×C61—44no—
173C2×C8×C61—21no—
174C2×C8×C61—21no—
175C2×C8×C61—21no—
176C2×C8×C61—21no—
177C2×C8×C61—21no—
178C2×C8×C61—21no—
179C2×C8×C61—21no—
180C2×C8×C61—21no—
181C2×C8×C61—21no—
182C2×C8×C61—44no—
183C2×C8×C61C2×D412yes—
184C2×C8×C61C2×D412yes—
185C2×C8×C61#4112yes—
186C4⋊C4×C61—22no—
187C22⋊C4×C61—22no—
188C22⋊C4×C61—22no—
189C42×C61C2×D412yes—
190C42×C61#4112yes—
191C22⋊Dic61—42no—
192C22⋊Dic61—42no—
193C22⋊Dic61—42no—
194C22⋊Dic61—42no—
195C22⋊Dic61—42no—
196C22⋊Dic61—42no—
197C22⋊Dic61—42no—
198C22⋊Dic61—42no—
199C4⋊Dic61—21no—
200C4⋊Dic61—21no—
201C4⋊Dic61—21no—
202C4⋊Dic61—21no—
203C4⋊Dic61—21no—
204C4⋊Dic61—21no—
205C4⋊Dic61—21no—
206C4⋊Dic61—21no—
207C4⋊Dic61—21no—
208C4⋊Dic61—21no—
209C4⋊Dic61—21no—
210C4⋊Dic61—21no—
211C4⋊Dic61—21no—
212C4⋊Dic61—21no—
213C4⋊Dic61—42no—
214#11758196—42no—
215#11758196—42no—
216#11758196—42no—
217C4×Dic61—42no—
218C4×Dic61—42no—
219C23×C61—21no—
220C23×C61—21no—
221C23×C61—21no—
222C23×C61—21no—
223C23×C61—21no—
224C23×C61—21no—
225C23×C61—21no—
226C23×C61—21no—
227C23×C61—21no—
228C23×C61—21no—
229C23×C61—21no—
230C23×C61—21no—
231C23×C61—21no—
232C23×C61AGL(1,ℤ/8)12yes—
233C23×C61C22×D411yescharacteristic
234D4×C61—44no—
235C2×C4×C61—21no—
236C2×C4×C61—21no—
237C2×C4×C61—21no—
238C2×C4×C61—21no—
239C2×C4×C61—21no—
240C2×C4×C61—21no—
241C2×C4×C61—21no—
242C2×C4×C61—21no—
243C2×C4×C61—21no—
244C2×C4×C61—21no—
245C2×C4×C61—41no—
246C2×C4×C61—41no—
247C2×C4×C61—41no—
248C2×C4×C61—41no—
249C2×C4×C61—41no—
250C2×C4×C61—41no—
251C2×C4×C61—41no—
252C2×C4×C61—41no—
253C2×C4×C61#12112yes—
254C2×C4×C61#12112yes—
255C2×C4×C61C22×D411yescharacteristic
256C2×C4×C61C2×#4111yescharacteristic
257C2×C4×C61C2×#4111yescharacteristic
258C2×C4×C61C2×#4111yescharacteristic
259C2×C4×C61H(5,𝔽2)11yescharacteristic
260C2×C4×C612−1+411yescharacteristic
261C2×Dic61—22no—
262C2×Dic61—41no—
263C2×Dic61—41no—
264C2×Dic61—41no—
265C2×Dic61—41no—
266C2×Dic61—41no—
267C2×Dic61—41no—
268C2×Dic61—41no—
269C2×Dic61—41no—
270C2×Dic61—41no—
271C2×Dic61—41no—
272C2×Dic61—41no—
273C2×Dic61—41no—
274C2×Dic61—41no—
275C2×Dic61—41no—
276C2×Dic61—41no—
277C2×Dic61—41no—
278C2×Dic61—41no—
279C2×Dic61—41no—
280C2×Dic61—41no—
281C2×Dic61—41no—
282C2×Dic61—41no—
283C2×Dic61—41no—
284C2×Dic61—41no—
285Dic122—22no—
286Dic122—22no—
287Dic122—41no—
288Dic122—41no—
289Dic122—84no—
290C8×C61—22no—
291C8×C61—22no—
292C8×C61—22no—
293C8×C61—41no—
294#25352—611nomaximal, Sylow
295C22×C61—22no—
296C22×C61—22no—
297C22×C61—22no—
298C22×C61—41no—
299C22×C61—41no—
300C22×C61—41no—
301C22×C61—41no—
302C22×C61—41no—
303C22×C61—41no—
304C22×C61—41no—
305C22×C61—41no—
306C22×C61—41no—
307C22×C61—41no—
308C22×C61—41no—
309C22×C61C2×#12111yescharacteristic
310C22×C61#54611yescharacteristic
311C22×C61#54711yescharacteristic
312C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
313C22×C61#57511yescharacteristic
314C22×C61#57811yescharacteristic
315C22×C61#57811yescharacteristic
316C4×C61—22no—
317C4×C61—22no—
318C4×C61—41no—
319C4×C61—41no—
320C4×C61#52911yescharacteristic
321C4×C61#54211yescharacteristic
322C4×C61#54611yescharacteristic
323C4×C61#54811yescharacteristic
324Dic61—42no—
325Dic61—81no—
326Dic61—81no—
327Dic61—81no—
328Dic61—81no—
329Dic61—81no—
330Dic61—81no—
331Dic61—81no—
332C2×#477—611no—
333C2×#435D6111yescharacteristic
334#2547—611no—
335#2536—611no—
336#2076—611no—
337#2075—611no—
338#2036—611no—
339#2035—611no—
340#1993—611no—
341#1949—611no—
342#1894—611no—
343#1892—611no—
344#1809—611no—
345#1808—611no—
346#1763—611no—
347C2×C61—42no—
348C2×C61—81no—
349C2×C61#242711yescharacteristic
350C2×C61#305511yescharacteristic
351C2×C61#305911yescharacteristic
352C2×C61#330811yescharacteristic
353C2×C61#331311yescharacteristic
354C2×C61#334311yescharacteristic
355C2×C61#334911yescharacteristic
356C22×M16C2×D6111yescharacteristic
357C23×C8C2×D6111yescharacteristic
358C2×C4⋊Q8—611no—
359C2×#124—1221no—
360C2×C22⋊Q8—611no—
361C2×C22⋊Q8—611no—
362C2×C4×Q8—611no—
363C2×C4×D4C2×D6111yescharacteristic
364#477—1224no—
365#435—24no—
366C2×#107—611no—
367C2×#107—611no—
368C2×#107—611no—
369C2×#106—611no—
370C2×C4⋊C8C2×D6111yescharacteristic
371C2×#103—611no—
372C2×#103—611no—
373C2×#103—611no—
374C2×#103—611no—
375C2×C22⋊C8C2×D6111yescharacteristic
376C2×C22⋊C8C2×D6111yescharacteristic
377C2×#97C2×D6111yescharacteristic
378#398—1221no—
379#397—1221no—
380#397—1221no—
381#394—1221no—
382#391—1221no—
383#388—1221no—
384#388—1221no—
385#382—611no—
386#380—611no—
387#380—611no—
388#380—611no—
389#380—611no—
390#380—611no—
391#380—611no—
392C4×C4⋊C4—611no—
393#340—611no—
394#340—611no—
395#340—611no—
396#340—611no—
397#340—611no—
398#340—611no—
399#340—611no—
400#340—611no—
401C61#2535211yescharacteristic, complemented, Sylow
402C22×Q8—611no—
403C22×Q8—1221no—
404C22×D4D24411yescharacteristic
405C23×C4C22×D6111yescharacteristic
406C23×C4C22×D6111yescharacteristic
407C2×M16—22no—
408C2×M16—22no—
409C2×M16—41no—
410C22×C8—22no—
411C22×C8—22no—
412C22×C8—41no—
413C22×C8C22×D6111yescharacteristic
414C22×C8C22×D6111yescharacteristic
415C22×C8C22×D6111yescharacteristic
416C22×C8C22×D6111yescharacteristic
417C4⋊Q8—1222no—
418C4⋊Q8—1222no—
419#124—2444no—
420C22⋊Q8—1222no—
421C22⋊Q8—1222no—
422C22⋊Q8—2441no—
423C22⋊Q8—2441no—
424C4×Q8—1222no—
425C4×Q8—1222no—
426C4×D4—22no—
427C4×D4—22no—
428C2×C4⋊C4—611no—
429C2×C4⋊C4—611no—
430C2×C4⋊C4—611no—
431C2×C4⋊C4—611no—
432C2×C4⋊C4—611no—
433C2×C4⋊C4—611no—
434C2×C4⋊C4—611no—
435C2×C4⋊C4—1221no—
436C2×C4⋊C4—1221no—
437C2×C4⋊C4—1221no—
438C2×C4⋊C4—1221no—
439C2×C4⋊C4D24411yescharacteristic
440C2×C22⋊C4—1221no—
441C2×C22⋊C4—1221no—
442C2×C22⋊C4—1221no—
443C2×C22⋊C4—1221no—
444C2×C22⋊C4—1221no—
445C2×C22⋊C4—1221no—
446C2×C22⋊C4—1221no—
447C2×C22⋊C4—1221no—
448C2×C22⋊C4D24411yescharacteristic
449C2×C22⋊C4D24411yescharacteristic
450C2×C42—1221no—
451C2×C42—1221no—
452C2×C42C22×D6111yescharacteristic
453#107—1222no—
454#107—1222no—
455#107—2441no—
456#106—2441no—
457C4⋊C8C22⋊D6114yes—
458#103—1222no—
459#103—1222no—
460#103—1222no—
461#103—1222no—
462C22⋊C8—22no—
463C22⋊C8—22no—
464#97—22no—
465#95—1221no—
466#95—1221no—
467#95—1221no—
468#95—1221no—
469#95—1221no—
470#95—1221no—
471#95—1221no—
472#95—1221no—
473#95—1221no—
474C24C2×D24411yescharacteristic
475C24C2×D24411yescharacteristic
476C2×Q8—612no—
477C2×Q8—1221no—
478C2×Q8—1221no—
479C2×Q8—1221no—
480C2×Q8—1221no—
481C2×Q8—1221no—
482C2×Q8—2442no—
483C2×Q8—2442no—
484C2×Q8—2442no—
485C2×D4—22no—
486C2×D4—22no—
487C2×D4—41no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—1221no—
501C22×C4—1221no—
502C22×C4—1221no—
503C22×C4—1221no—
504C22×C4—1221no—
505C22×C4—1221no—
506C22×C4—1221no—
507C22×C4—1221no—
508C22×C4C2×D24411yescharacteristic
509C22×C4C2×D24411yescharacteristic
510C22×C4C2×D24411yescharacteristic
511C22×C4C2×D24411yescharacteristic
512C22×C4C23×D6111yescharacteristic
513M16—44no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—44no—
524C2×C8#1175822412yes—
525C2×C8C2×C22⋊D6112yes—
526C2×C8C2×C22⋊D6112yes—
527C4⋊C4—22no—
528C4⋊C4—1221no—
529C4⋊C4—1221no—
530C4⋊C4—1221no—
531C4⋊C4—1221no—
532C4⋊C4—1221no—
533C4⋊C4—1221no—
534C4⋊C4—1221no—
535C4⋊C4—1221no—
536C4⋊C4—1221no—
537C4⋊C4—1221no—
538C4⋊C4—1221no—
539C4⋊C4—1221no—
540C4⋊C4—1221no—
541C4⋊C4—1221no—
542C4⋊C4—2442no—
543C4⋊C4—2442no—
544C4⋊C4—2442no—
545C4⋊C4—2442no—
546C22⋊C4—22no—
547C22⋊C4—22no—
548C22⋊C4—2442no—
549C22⋊C4—2442no—
550C22⋊C4—2442no—
551C22⋊C4—2442no—
552C22⋊C4—2442no—
553C22⋊C4—2442no—
554C22⋊C4—2442no—
555C22⋊C4—2442no—
556C42—2442no—
557C42—2442no—
558C42#1175822212yes—
559C42C2×C22⋊D6112yes—
560C23—21no—
561C23—21no—
562C23—21no—
563C23—21no—
564C23—21no—
565C23—21no—
566C23—21no—
567C23—21no—
568C23—21no—
569C23—21no—
570C23—21no—
571C23—21no—
572C23—21no—
573C23#1451980512yes—
574C23C22×D24411yescharacteristic
575Q8—1222no—
576Q8—1222no—
577Q8—4884no—
578Q8—2441no—
579Q8—2441no—
580D4—44no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—1222no—
600C2×C4—2441no—
601C2×C4—2441no—
602C2×C4—2441no—
603C2×C4—2441no—
604C2×C4—2441no—
605C2×C4—2441no—
606C2×C4—2441no—
607C2×C4—2441no—
608C2×C4—2441no—
609C2×C4—2441no—
610C2×C4—2441no—
611C2×C4—2441no—
612C2×C4—2441no—
613C2×C4—2441no—
614C2×C4—2441no—
615C2×C4—2441no—
616C2×C4—2441no—
617C2×C4—2441no—
618C2×C4—2441no—
619C2×C4—2441no—
620C2×C4—2441no—
621C2×C4—2441no—
622C2×C4—2441no—
623C2×C4#1451975112yes—
624C2×C4#1451975112yes—
625C2×C4C22×C22⋊D6111yescharacteristic
626C2×C4#41×D6111yescharacteristic
627C2×C4C2×#1175822411yescharacteristic
628C2×C4C2×#1175822211yescharacteristic
629C2×C4#1451982211yescharacteristic
630C2×C4#1451982411yescharacteristic
631C8—22no—
632C8—22no—
633C8—22no—
634C8—41no—
635C22—22no—
636C22—22no—
637C22—22no—
638C22—41no—
639C22—41no—
640C22—41no—
641C22—41no—
642C22—41no—
643C22—41no—
644C22—41no—
645C22—41no—
646C22—41no—
647C22—41no—
648C22—41no—
649C22C2×#1451975111yescharacteristic
650C22#1684040711yescharacteristic
651C22#1684041611yescharacteristic
652C22C2×#1451980511yescharacteristic
653C22#1684056211yescharacteristic
654C22#1684057911yescharacteristic
655C22#1684057911yescharacteristic
656C4—22no—
657C4—22no—
658C4—41no—
659C4—41no—
660C4—4881no—
661C4—4881no—
662C4—4881no—
663C4—4881no—
664C4—4881no—
665C4—4881no—
666C4—4881no—
667C4—2442no—
668C4#1684029411yescharacteristic
669C4#1684037711yescharacteristic
670C4#1684040611yescharacteristic
671C4#1684041911yescharacteristic
672C2—42no—
673C2—81no—
674C2#2144939011yescharacteristic
675C2#2145543811yescharacteristic
676C2#2145547411yescharacteristic
677C2#2145781211yescharacteristic
678C2#2145788711yescharacteristic
679C2#2145826111yescharacteristic
680C2#2145835111yescharacteristic
subgroupG/H
centerC23C22×D244
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#435C2
socleC23×C61C22×D4
prime radicalC22×D4×C61D4
hypercenterC2×#435D61
hypocenterC61#25352
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
1. C2×#16840058C2semidirect
4. #21447247C2semidirect
5. #21447242C2semidirect
6. #21447023C2semidirect
7. #21447016C2semidirect
8. #21446792C2semidirect
9. #21446589C2semidirect
10. #21446252C2semidirect
11. #21446242C2semidirect
12. #21445852C2semidirect
13. #21445848C2semidirect
14. #21445650C2semidirect
401. C61#25352semidirect

Maximal subgroups

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

subgroupindex
C2×#168400582
#214508112
#214507282
#214472472
#214472422
#214470232
#214470162
#214467922
#214465892
#214462522
#214462422
#214458522
#214458482
#214456502
C2×C61×#4352
#2535261