Finite Group Databasebeta

← #29730189

Subgroups — #29730189

Order 15616.

850 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840066C211yesmaximal, characteristic, complemented
2C2×D4×#92418C211yesmaximal, characteristic
3#21450728C211yesmaximal, characteristic
4#21447256C211yesmaximal, characteristic, complemented
5#21447245C211yesmaximal, characteristic, complemented
6#21447022C211yesmaximal, characteristic, complemented
7#21447015C211yesmaximal, characteristic, complemented
8#21446785C211yesmaximal, characteristic, complemented
9#21446587C211yesmaximal, characteristic, complemented
10#21446240C211yesmaximal, characteristic, complemented
11#21446240C211yesmaximal, characteristic, complemented
12#21445846C211yesmaximal, characteristic, complemented
13#21445842C211yesmaximal, characteristic, complemented
14C4×#14519700C211yesmaximal, characteristic, complemented
15C61×#2562C211yesmaximal, characteristic
16C23×#92418C2211yescharacteristic
17C23×#92418C2211yescharacteristic
18C2×#14519756C2211yescharacteristic
19C2×#14519756C2211yescharacteristic
20C2×C4×Dic122C2211yescharacteristic
21#16840066—24no—
22D4×#92418—24no—
23C2×#14519710C2211yescharacteristic
24C2×#14519710C2211yescharacteristic
25C2×#14519708C2211yescharacteristic
26C2×#14519708C2211yescharacteristic
27C2×C4⋊#92418C2211yescharacteristic
28C2×#14519700C2211yescharacteristic
29C2×#14519700C2211yescharacteristic
30C2×#14519700C2211yescharacteristic
31C2×#14519700C2211yescharacteristic
32C2×C22⋊#92418C2211yescharacteristic
33C2×C22⋊#92418C2211yescharacteristic
34C2×C4×#92418C2211yescharacteristic
35#16839693—21no—
36#16839676—21no—
37#16839650—21no—
38#16839650—21no—
39#16839628C2211yescharacteristic
40#16839622C2211yescharacteristic
41#16839622C2211yescharacteristic
42#16839524C2211yescharacteristic
43#16839524C2211yescharacteristic
44#16839524C2211yescharacteristic
45#16839524C2211yescharacteristic
46#16839524C2211yescharacteristic
47#16839524C2211yescharacteristic
48#16839524C2211yescharacteristic
49#16839524C2211yescharacteristic
50C2×#125×C61C2211yescharacteristic
51C2×C4×D4×C61C2211yescharacteristic
52C61×#400—21no—
53C61×#394—21no—
54C61×#388—21no—
55C61×#388—21no—
56C61×#380C2211yescharacteristic
57C61×#380C2211yescharacteristic
58C61×#380C2211yescharacteristic
59C61×#380C2211yescharacteristic
60C4×C4⋊C4×C61C2211yescharacteristic
61C22×Dic122C2311yescharacteristic
62C22×#92418—22no—
63C22×#92418—22no—
64C22×#92418—22no—
65C22×#92418—22no—
66C22×#92418—41no—
67C22×#92418—41no—
68C22×#92418C2311yescharacteristic
69C22×#92418C2311yescharacteristic
70C22×#92418C2311yescharacteristic
71C22×#92418C2311yescharacteristic
72#14519756—22no—
73#14519756—22no—
74#14519756—41no—
75#14519756—41no—
76C4×Dic122—22no—
77C4×Dic122—22no—
78C2×C4⋊Dic61C2311yescharacteristic
79C2×C4⋊Dic61C2311yescharacteristic
80C2×C4⋊Dic61C2311yescharacteristic
81C2×#11758196—21no—
82C2×#11758196—21no—
83C2×#11758196—21no—
84C2×C22⋊Dic61—21no—
85C2×C22⋊Dic61—21no—
86C2×C22⋊Dic61—21no—
87C2×C22⋊Dic61—21no—
88C2×C4×Dic61—21no—
89#14519710—22no—
90#14519710—41no—
91#14519708—22no—
92#14519708—41no—
93C4⋊#92418D414yes—
94#14519700—22no—
95#14519700—22no—
96#14519700—22no—
97#14519700—22no—
98C22⋊#92418—22no—
99C22⋊#92418—22no—
100C4×#92418—22no—
101#14519684—21no—
102#14519684—21no—
103#14519684—21no—
104#14519684—21no—
105C22×D4×C61D411yescharacteristic
106C23×C4×C61C2311yescharacteristic
107C23×C4×C61C2311yescharacteristic
108#125×C61—22no—
109#125×C61—22no—
110C4×D4×C61—22no—
111C4×D4×C61—22no—
112C2×C4⋊C4×C61—21no—
113C2×C4⋊C4×C61—21no—
114C2×C4⋊C4×C61D411yescharacteristic
115C2×C4⋊C4×C61C2311yescharacteristic
116C2×C4⋊C4×C61C2311yescharacteristic
117C2×C4⋊C4×C61C2311yescharacteristic
118C2×C4⋊C4×C61C2311yescharacteristic
119C2×C22⋊C4×C61—21no—
120C2×C22⋊C4×C61—21no—
121C2×C22⋊C4×C61—21no—
122C2×C22⋊C4×C61—21no—
123C2×C22⋊C4×C61D411yescharacteristic
124C2×C22⋊C4×C61D411yescharacteristic
125C2×C42×C61—21no—
126C2×C42×C61C2311yescharacteristic
127#95×C61—21no—
128#95×C61—21no—
129#95×C61—21no—
130#95×C61—21no—
131#95×C61—21no—
132C24×C61C2×D411yescharacteristic
133C24×C61C2×D411yescharacteristic
134C2×D4×C61—22no—
135C2×D4×C61—22no—
136C2×D4×C61—22no—
137C22×C4×C61—21no—
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×C61—21no—
151C22×C4×C61—21no—
152C22×C4×C61—21no—
153C22×C4×C61C2×D411yescharacteristic
154C22×C4×C61C2×D411yescharacteristic
155C22×C4×C61C2×D411yescharacteristic
156C22×C4×C61C2×D411yescharacteristic
157C22×C4×C61C2411yescharacteristic
158C22×Dic61—21no—
159C22×Dic61—21no—
160C22×Dic61—21no—
161C22×Dic61—21no—
162C2×Dic122—21no—
163C2×Dic122—21no—
164C2×Dic122—21no—
165C2×Dic122—21no—
166C2×Dic122—21no—
167C2×Dic122#4112yes—
168C4⋊C4×C61—22no—
169C4⋊C4×C61—21no—
170C4⋊C4×C61—21no—
171C4⋊C4×C61—21no—
172C4⋊C4×C61—21no—
173C4⋊C4×C61—21no—
174C4⋊C4×C61—21no—
175C4⋊C4×C61—21no—
176C4⋊C4×C61—21no—
177C4⋊C4×C61—42no—
178C4⋊C4×C61—42no—
179C22⋊C4×C61—22no—
180C22⋊C4×C61—22no—
181C22⋊C4×C61—42no—
182C22⋊C4×C61—42no—
183C22⋊C4×C61—81no—
184C22⋊C4×C61—81no—
185C42×C61—81no—
186C42×C61C2×D412yes—
187C42×C61#4112yes—
188C22⋊Dic61—42no—
189C22⋊Dic61—42no—
190C22⋊Dic61—42no—
191C22⋊Dic61—42no—
192C4⋊Dic61—21no—
193C4⋊Dic61—21no—
194C4⋊Dic61—21no—
195C4⋊Dic61—21no—
196C4⋊Dic61—21no—
197C4⋊Dic61—21no—
198#11758196—42no—
199#11758196—42no—
200#11758196—42no—
201C4×Dic61—42no—
202C2×#92418—21no—
203C2×#92418—21no—
204C2×#92418—21no—
205C2×#92418—21no—
206C2×#92418—21no—
207C2×#92418—21no—
208C2×#92418—21no—
209C2×#92418—21no—
210C2×#92418—21no—
211C2×#92418—44no—
212C2×#92418—44no—
213C2×#92418C2×D412yes—
214C2×#92418C2×D412yes—
215C2×#92418#4112yes—
216C23×C61—21no—
217C23×C61—21no—
218C23×C61—21no—
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#13512yes—
229C23×C61#13512yes—
230C23×C61C22×D411yescharacteristic
231D4×C61—28no—
232C2×C4×C61—21no—
233C2×C4×C61—21no—
234C2×C4×C61—21no—
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—41no—
243C2×C4×C61—41no—
244C2×C4×C61—41no—
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—41no—
254C2×C4×C61—41no—
255C2×C4×C61—41no—
256C2×C4×C61—41no—
257C2×C4×C61—41no—
258C2×C4×C61—41no—
259C2×C4×C61—41no—
260C2×C4×C61—41no—
261C2×C4×C61—41no—
262C2×C4×C61#12112yes—
263C2×C4×C61#12112yes—
264C2×C4×C61C22×D411yescharacteristic
265C2×C4×C61C2×#4111yescharacteristic
266C2×C4×C61C2×#4111yescharacteristic
267C2×C4×C61C2×#4111yescharacteristic
268C2×C4×C61H(5,𝔽2)11yescharacteristic
269C2×C4×C612−1+411yescharacteristic
270C2×Dic61—22no—
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—
282Dic122—22no—
283Dic122—22no—
284Dic122—41no—
285Dic122—41no—
286#92418—22no—
287#92418—22no—
288#92418—22no—
289#92418—41no—
290#25343—611nomaximal, Sylow
291C22×C61—22no—
292C22×C61—22no—
293C22×C61—22no—
294C22×C61—22no—
295C22×C61—22no—
296C22×C61—22no—
297C22×C61—41no—
298C22×C61—41no—
299C22×C61—41no—
300C22×C61—41no—
301C22×C61—41no—
302C22×C61—41no—
303C22×C61—41no—
304C22×C61—41no—
305C22×C61C2×#12111yescharacteristic
306C22×C61#54611yescharacteristic
307C22×C61#54711yescharacteristic
308C22×C61C2×#13511yescharacteristic
309C22×C61C2×#13511yescharacteristic
310C22×C61#57711yescharacteristic
311C22×C61#57811yescharacteristic
312C4×C61—22no—
313C4×C61—22no—
314C4×C61—41no—
315C4×C61—41no—
316C4×C61—81no—
317C4×C61—81no—
318C4×C61—81no—
319C4×C61—81no—
320C4×C61#52911yescharacteristic
321C4×C61#54211yescharacteristic
322C4×C61#54611yescharacteristic
323C4×C61#54811yescharacteristic
324Dic61—42no—
325Dic61—81no—
326Dic61—81no—
327Dic61—81no—
328C2×#479—611no—
329C2×C8×D4—611no—
330#2562D6111yescharacteristic
331#2536—611no—
332#2077—611no—
333#2075—611no—
334#2036—611no—
335#2035—611no—
336#1991—611no—
337#1949—611no—
338#1892—611no—
339#1892—611no—
340#1808—611no—
341#1807—611no—
342C4×#103—611no—
343C2×C61—42no—
344C2×C61—42no—
345C2×C61#242711yescharacteristic
346C2×C61#305011yescharacteristic
347C2×C61#306311yescharacteristic
348C2×C61#330011yescharacteristic
349C2×C61#330111yescharacteristic
350C2×C61#333611yescharacteristic
351C2×C61#333711yescharacteristic
352C23×C8—611no—
353C23×C8—611no—
354C2×#125C2×D6111yescharacteristic
355C2×C22⋊Q8—611no—
356C2×C22⋊Q8—611no—
357C2×C4×Q8—611no—
358C2×C4×D4C2×D6111yescharacteristic
359#479—1224no—
360C8×D4—1224no—
361C2×#107—611no—
362C2×#107—611no—
363C2×#106—611no—
364C2×#106—611no—
365C2×C4⋊C8—611no—
366C2×#103—611no—
367C2×#103—611no—
368C2×#103—611no—
369C2×#103—611no—
370C2×C22⋊C8—611no—
371C2×C22⋊C8—611no—
372C2×C4×C8—611no—
373#400—21no—
374#398—1221no—
375#394—21no—
376#394—1221no—
377#388—21no—
378#388—21no—
379#388—1221no—
380#388—1221no—
381#382—611no—
382#380—611no—
383#380—611no—
384#380C2×D6111yescharacteristic
385#380C2×D6111yescharacteristic
386#380C2×D6111yescharacteristic
387#380C2×D6111yescharacteristic
388C4×C4⋊C4C2×D6111yescharacteristic
389#340—611no—
390#340—611no—
391#340—611no—
392#340—611no—
393#340—611no—
394#340—611no—
395#340—611no—
396#340—611no—
397C61#2534311yescharacteristic, complemented, Sylow
398C22×Q8—611no—
399C22×D4C22⋊D6111yescharacteristic
400C23×C4C22×D6111yescharacteristic
401C23×C4C22×D6111yescharacteristic
402C22×C8—611no—
403C22×C8—611no—
404C22×C8—611no—
405C22×C8—611no—
406C22×C8—1222no—
407C22×C8—1222no—
408C22×C8—1222no—
409C22×C8—1222no—
410C22×C8—2441no—
411C22×C8—2441no—
412#125—22no—
413#125—22no—
414C22⋊Q8—1222no—
415C22⋊Q8—1222no—
416C22⋊Q8—2441no—
417C22⋊Q8—2441no—
418C4×Q8—1222no—
419C4×Q8—1222no—
420C4×D4—22no—
421C4×D4—22no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—611no—
425C2×C4⋊C4—611no—
426C2×C4⋊C4—611no—
427C2×C4⋊C4—1221no—
428C2×C4⋊C4—1221no—
429C2×C4⋊C4—1221no—
430C2×C4⋊C4C22⋊D6111yescharacteristic
431C2×C4⋊C4C22×D6111yescharacteristic
432C2×C4⋊C4C22×D6111yescharacteristic
433C2×C4⋊C4C22×D6111yescharacteristic
434C2×C4⋊C4C22×D6111yescharacteristic
435C2×C22⋊C4—21no—
436C2×C22⋊C4—21no—
437C2×C22⋊C4—21no—
438C2×C22⋊C4—21no—
439C2×C22⋊C4—1221no—
440C2×C22⋊C4—1221no—
441C2×C22⋊C4—1221no—
442C2×C22⋊C4—1221no—
443C2×C22⋊C4C22⋊D6111yescharacteristic
444C2×C22⋊C4C22⋊D6111yescharacteristic
445C2×C42—21no—
446C2×C42—1221no—
447C2×C42C22×D6111yescharacteristic
448#107—1222no—
449#107—2441no—
450#106—1222no—
451#106—2441no—
452C4⋊C8—614no—
453#103—1222no—
454#103—1222no—
455#103—1222no—
456#103—1222no—
457C22⋊C8—1222no—
458C22⋊C8—1222no—
459C4×C8—1222no—
460#95—21no—
461#95—21no—
462#95—21no—
463#95—21no—
464#95—21no—
465#95—1221no—
466#95—1221no—
467#95—1221no—
468#95—1221no—
469C24C2×C22⋊D6111yescharacteristic
470C24C2×C22⋊D6111yescharacteristic
471C2×Q8—612no—
472C2×Q8—1221no—
473C2×Q8—1221no—
474C2×Q8—1221no—
475C2×Q8—1221no—
476C2×Q8—1221no—
477C2×D4—22no—
478C2×D4—22no—
479C2×D4—22no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
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—1221no—
497C22×C4—1221no—
498C22×C4—1221no—
499C22×C4—1221no—
500C22×C4C2×C22⋊D6111yescharacteristic
501C22×C4C2×C22⋊D6111yescharacteristic
502C22×C4C2×C22⋊D6111yescharacteristic
503C22×C4C2×C22⋊D6111yescharacteristic
504C22×C4C23×D6111yescharacteristic
505C2×C8—612no—
506C2×C8—612no—
507C2×C8—612no—
508C2×C8—1221no—
509C2×C8—1221no—
510C2×C8—1221no—
511C2×C8—1221no—
512C2×C8—1221no—
513C2×C8—1221no—
514C2×C8—1221no—
515C2×C8—1221no—
516C2×C8—1221no—
517C2×C8—2444no—
518C2×C8—2444no—
519C4⋊C4—22no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—42no—
529C4⋊C4—42no—
530C4⋊C4—1221no—
531C4⋊C4—1221no—
532C4⋊C4—1221no—
533C4⋊C4—1221no—
534C4⋊C4—1221no—
535C4⋊C4—1221no—
536C4⋊C4—2442no—
537C4⋊C4—2442no—
538C4⋊C4—2442no—
539C22⋊C4—22no—
540C22⋊C4—22no—
541C22⋊C4—42no—
542C22⋊C4—42no—
543C22⋊C4—81no—
544C22⋊C4—81no—
545C22⋊C4—2442no—
546C22⋊C4—2442no—
547C22⋊C4—2442no—
548C22⋊C4—2442no—
549C42—81no—
550C42—2442no—
551C42D4×D6112yes—
552C42#1175822412yes—
553C23—21no—
554C23—21no—
555C23—21no—
556C23—21no—
557C23—21no—
558C23—21no—
559C23—21no—
560C23—21no—
561C23—21no—
562C23—21no—
563C23—21no—
564C23—21no—
565C23#1451979712yes—
566C23#1451979712yes—
567C23C22×C22⋊D6111yescharacteristic
568Q8—1222no—
569Q8—1222no—
570Q8—2441no—
571Q8—2441no—
572D4—28no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
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—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—1222no—
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#1451974912yes—
616C2×C4#1451974912yes—
617C2×C4C2×D4×D6111yescharacteristic
618C2×C4#41×D6111yescharacteristic
619C2×C4#41×D6111yescharacteristic
620C2×C4C2×#1175822411yescharacteristic
621C2×C4#1451982311yescharacteristic
622C2×C4#1451982411yescharacteristic
623C8—1222no—
624C8—1222no—
625C8—1222no—
626C8—2441no—
627C22—22no—
628C22—22no—
629C22—22no—
630C22—22no—
631C22—22no—
632C22—22no—
633C22—41no—
634C22—41no—
635C22—41no—
636C22—41no—
637C22—41no—
638C22—41no—
639C22—41no—
640C22—41no—
641C22C2×#1451974911yescharacteristic
642C22#1684040011yescharacteristic
643C22#1684041111yescharacteristic
644C22C2×#1451979711yescharacteristic
645C22C2×#1451979711yescharacteristic
646C22#1684057311yescharacteristic
647C22#1684057711yescharacteristic
648C4—22no—
649C4—22no—
650C4—41no—
651C4—41no—
652C4—81no—
653C4—81no—
654C4—81no—
655C4—81no—
656C4—4881no—
657C4—4881no—
658C4—4881no—
659C4—2442no—
660C4#1684029111yescharacteristic
661C4#1684038111yescharacteristic
662C4#1684040511yescharacteristic
663C4#1684042011yescharacteristic
664C2—42no—
665C2—42no—
666C2#2144939911yescharacteristic
667C2#2145539711yescharacteristic
668C2#2145551211yescharacteristic
669C2#2145770011yescharacteristic
670C2#2145771511yescharacteristic
671C2#2145818111yescharacteristic
672C2#2145819211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2562C2
socleC23×C61C22×D4
prime radicalC22×D4×C61D4
hypercenter#2562D61
hypocenterC61#25343
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2562

Complements

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

NH ≅ G/Ntype
1. C2×#16840066C2semidirect
4. #21447256C2semidirect
5. #21447245C2semidirect
6. #21447022C2semidirect
7. #21447015C2semidirect
8. #21446785C2semidirect
9. #21446587C2semidirect
10. #21446240C2semidirect
11. #21446240C2semidirect
12. #21445846C2semidirect
13. #21445842C2semidirect
14. C4×#14519700C2semidirect
397. C61#25343semidirect

Maximal subgroups

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

subgroupindex
C2×#168400662
C2×D4×#924182
#214507282
#214472562
#214472452
#214470222
#214470152
#214467852
#214465872
#214462402
#214458462
#214458422
C4×#145197002
C61×#25622
#2534361