Finite Group Databasebeta

← #29690618

Subgroups — #29690618

Order 15616.

762 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839823C211yesmaximal, characteristic
2#21448442C211yesmaximal, characteristic
3#21446587C211yesmaximal, characteristic, complemented
4#21446587C211yesmaximal, characteristic, complemented
5#21446582C211yesmaximal, characteristic, complemented
6#21446577C211yesmaximal, characteristic, complemented
7#21446016C211yesmaximal, characteristic
8#21446016C211yesmaximal, characteristic
9#21446011C211yesmaximal, characteristic
10#21446006C211yesmaximal, characteristic
11#21445988C211yesmaximal, characteristic, complemented
12#21445981C211yesmaximal, characteristic, complemented
13#21445954C211yesmaximal, characteristic, complemented
14#21445946C211yesmaximal, characteristic, complemented
15C61×#2314C211yesmaximal, characteristic
16C2×#14519736C2211yescharacteristic
17C22×C4⋊Dic61C2211yescharacteristic
18#16839823C418yescomplemented
19C2×#14519710C2211yescharacteristic
20C2×#14519710C2211yescharacteristic
21C2×#14519710C2211yescharacteristic
22C2×#14519710C2211yescharacteristic
23C2×#14519708C2211yescharacteristic
24C2×#14519708C2211yescharacteristic
25C2×#14519708C2211yescharacteristic
26C2×#14519708C2211yescharacteristic
27C2×C4⋊#92418C2211yescharacteristic
28C2×C4⋊#92418C2211yescharacteristic
29C2×C22⋊#92418C2211yescharacteristic
30C2×C22⋊#92418C2211yescharacteristic
31C2×#14519688C2211yescharacteristic
32C2×C4×#92418C2211yescharacteristic
33#16839661—21no—
34#16839661—21no—
35#16839637—21no—
36#16839637—21no—
37#16839632C2211yescharacteristic
38#16839632C2211yescharacteristic
39#16839628C2211yescharacteristic
40#16839628C2211yescharacteristic
41#16839524C2211yescharacteristic
42#16839524C2211yescharacteristic
43#16839524C2211yescharacteristic
44#16839524C2211yescharacteristic
45#16839524C2211yescharacteristic
46#16839524C2211yescharacteristic
47#16839524C2211yescharacteristic
48#16839524C2211yescharacteristic
49C2×#117×C61C2211yescharacteristic
50C61×#388—21no—
51C61×#388—21no—
52C61×#387—21no—
53C61×#387—21no—
54C61×#384C2211yescharacteristic
55C61×#382C2211yescharacteristic
56C61×#380C2211yescharacteristic
57C61×#380C2211yescharacteristic
58C4×C4⋊C4×C61C2211yescharacteristic
59C4×C4⋊C4×C61C2211yescharacteristic
60C23×Dic61—21no—
61C22×#92418C2311yescharacteristic
62C22×#92418C2311yescharacteristic
63C22×#92418C2311yescharacteristic
64C22×#92418C2311yescharacteristic
65#14519736—41no—
66#14519736—41no—
67C2×C4⋊Dic61—21no—
68C2×C4⋊Dic61—21no—
69C2×C4⋊Dic61—21no—
70C2×C4⋊Dic61—21no—
71C2×C4⋊Dic61—21no—
72C2×C4⋊Dic61—41no—
73C2×C4⋊Dic61—41no—
74C2×C4⋊Dic61C2311yescharacteristic
75C2×C4⋊Dic61C2311yescharacteristic
76C2×C4⋊Dic61C2311yescharacteristic
77C2×C4⋊Dic61C2311yescharacteristic
78C2×C22⋊Dic61—21no—
79C2×C4×Dic61—21no—
80#14519710—41no—
81#14519710—41no—
82#14519710—41no—
83#14519710—41no—
84#14519708—41no—
85#14519708—41no—
86#14519708—41no—
87#14519708—41no—
88C4⋊#92418C2×C414yescomplemented
89C4⋊#92418C2×C414yescomplemented
90C22⋊#92418C2×C414yes—
91C22⋊#92418C2×C414yes—
92#14519688C2×C414yescomplemented
93C4×#92418C2×C414yescomplemented
94#14519684—21no—
95#14519684—21no—
96#14519684—21no—
97#14519684—21no—
98C23×C4×C61C2311yescharacteristic
99#117×C61C2×C414yes—
100#117×C61Q814yes—
101C2×C4⋊C4×C61—21no—
102C2×C4⋊C4×C61—21no—
103C2×C4⋊C4×C61D411yescharacteristic
104C2×C4⋊C4×C61D411yescharacteristic
105C2×C4⋊C4×C61C2311yescharacteristic
106C2×C4⋊C4×C61C2311yescharacteristic
107C2×C4⋊C4×C61C2311yescharacteristic
108C2×C4⋊C4×C61C2311yescharacteristic
109C2×C22⋊C4×C61—21no—
110C2×C22⋊C4×C61—21no—
111C2×C22⋊C4×C61D411yescharacteristic
112C2×C22⋊C4×C61D411yescharacteristic
113C2×C42×C61—21no—
114C2×C42×C61—21no—
115C2×C42×C61C2311yescharacteristic
116C2×C42×C61C2311yescharacteristic
117#95×C61—21no—
118#95×C61—21no—
119#95×C61—21no—
120#95×C61—21no—
121#95×C61—21no—
122#95×C61—21no—
123C24×C61C2×D411yescharacteristic
124C22×C4×C61—21no—
125C22×C4×C61—21no—
126C22×C4×C61—21no—
127C22×C4×C61—21no—
128C22×C4×C61—21no—
129C22×C4×C61—21no—
130C22×C4×C61—21no—
131C22×C4×C61—21no—
132C22×C4×C61C22×C412yes—
133C22×C4×C61C2×D411yescharacteristic
134C22×C4×C61C2×D411yescharacteristic
135C22×C4×C61C2×D411yescharacteristic
136C22×C4×C61C2×D411yescharacteristic
137C22×C4×C61C2×D411yescharacteristic
138C22×C4×C61C2×Q812yes—
139C22×C4×C61C2411yescharacteristic
140C22×Dic61—21no—
141C22×Dic61—21no—
142C22×Dic61—21no—
143C22×Dic61—21no—
144C22×Dic61—42no—
145C22×Dic61—81no—
146C22×Dic61—81no—
147C4⋊C4×C61—21no—
148C4⋊C4×C61—21no—
149C4⋊C4×C61—21no—
150C4⋊C4×C61—21no—
151C4⋊C4×C61—21no—
152C4⋊C4×C61—21no—
153C4⋊C4×C61—21no—
154C4⋊C4×C61—21no—
155C4⋊C4×C61—81no—
156C4⋊C4×C61—81no—
157C4⋊C4×C61C4⋊C414yes—
158C4⋊C4×C61C4⋊C414yes—
159C22⋊C4×C61—81no—
160C22⋊C4×C61—81no—
161C22⋊C4×C61C4⋊C414yes—
162C22⋊C4×C61C4⋊C414yes—
163C42×C61—81no—
164C42×C61—81no—
165C42×C61C22×C412yes—
166C42×C61C22×C412yes—
167C42×C61C2×Q812yes—
168C42×C61C2×Q812yes—
169C22⋊Dic61—42no—
170C4⋊Dic61—21no—
171C4⋊Dic61—21no—
172C4⋊Dic61—21no—
173C4⋊Dic61—21no—
174C4⋊Dic61—21no—
175C4⋊Dic61—21no—
176C4⋊Dic61—21no—
177C4⋊Dic61—21no—
178C4⋊Dic61—42no—
179C4⋊Dic61—81no—
180C4⋊Dic61—81no—
181C4⋊Dic61—81no—
182C4⋊Dic61—81no—
183C4×Dic61—42no—
184C2×#92418—21no—
185C2×#92418—21no—
186C2×#92418—21no—
187C2×#92418—21no—
188C2×#92418—21no—
189C2×#92418—21no—
190C2×#92418—21no—
191C2×#92418—21no—
192C2×#92418C22×C412yes—
193C2×#92418C22×C412yes—
194C2×#92418C22×C412yes—
195C2×#92418C22×C412yes—
196C23×C61—21no—
197C23×C61—21no—
198C23×C61—21no—
199C23×C61—21no—
200C23×C61—21no—
201C23×C61—21no—
202C23×C61C2×C4⋊C412yes—
203C23×C61C22×D411yescharacteristic
204C2×C4×C61—21no—
205C2×C4×C61—21no—
206C2×C4×C61—21no—
207C2×C4×C61—21no—
208C2×C4×C61—21no—
209C2×C4×C61—21no—
210C2×C4×C61—21no—
211C2×C4×C61—21no—
212C2×C4×C61—21no—
213C2×C4×C61—21no—
214C2×C4×C61—22no—
215C2×C4×C61—22no—
216C2×C4×C61—22no—
217C2×C4×C61—22no—
218C2×C4×C61—41no—
219C2×C4×C61—41no—
220C2×C4×C61—41no—
221C2×C4×C61—41no—
222C2×C4×C61—41no—
223C2×C4×C61—41no—
224C2×C4×C61—41no—
225C2×C4×C61—41no—
226C2×C4×C61—41no—
227C2×C4×C61—41no—
228C2×C4×C61—41no—
229C2×C4×C61—41no—
230C2×C4×C61C2×C4⋊C412yes—
231C2×C4×C61C2×C4⋊C412yes—
232C2×C4×C61C2×C4⋊C412yes—
233C2×C4×C61C2×C4⋊C412yes—
234C2×C4×C61C2×C4⋊C412yes—
235C2×C4×C61C23×C411yescharacteristic
236C2×C4×C61C22×Q811yescharacteristic
237C2×C4×C61H(5,𝔽2)11yescharacteristic
238C2×C4×C61H(5,𝔽2)11yescharacteristic
239C2×C4×C612−1+411yescharacteristic
240C2×C4×C612−1+411yescharacteristic
241C2×Dic61—41no—
242C2×Dic61—41no—
243C2×Dic61—41no—
244C2×Dic61—41no—
245C2×Dic61—41no—
246C2×Dic61—41no—
247C2×Dic61—41no—
248C2×Dic61—41no—
249C2×Dic61—41no—
250C2×Dic61—41no—
251C2×Dic61—41no—
252C2×Dic61—41no—
253C2×Dic61—84no—
254#92418—22no—
255#92418—22no—
256#92418—22no—
257#92418—22no—
258#21992—611nomaximal, Sylow
259C22×C61—22no—
260C22×C61—22no—
261C22×C61—22no—
262C22×C61—41no—
263C22×C61—41no—
264C22×C61—41no—
265C22×C61—41no—
266C22×C61C22×C4⋊C411yescharacteristic
267C22×C61#53511yescharacteristic
268C22×C61#53611yescharacteristic
269C22×C61#57611yescharacteristic
270C22×C61#57711yescharacteristic
271C22×C61#57711yescharacteristic
272C22×C61#57811yescharacteristic
273C4×C61—22no—
274C4×C61—22no—
275C4×C61—22no—
276C4×C61—22no—
277C4×C61—22no—
278C4×C61—81no—
279C4×C61—81no—
280C4×C61—81no—
281C4×C61—81no—
282C4×C61#52011yescharacteristic
283C4×C61#52011yescharacteristic
284C4×C61#54411yescharacteristic
285C4×C61#54411yescharacteristic
286Dic61—81no—
287Dic61—81no—
288Dic61—81no—
289Dic61—81no—
290C2×#433—611no—
291#2317—611no—
292#2314D6111yescharacteristic
293#1949—611no—
294#1949—611no—
295#1948—611no—
296#1947—611no—
297#1854—611no—
298#1854—611no—
299#1853—611no—
300#1852—611no—
301#1847—611no—
302#1846—611no—
303#1836—611no—
304#1834—611no—
305C2×C61—42no—
306C2×C61#231711yescharacteristic
307C2×C61#291211yescharacteristic
308C2×C61#291311yescharacteristic
309C2×C61#322411yescharacteristic
310C2×C61#322511yescharacteristic
311C2×C61#324111yescharacteristic
312C2×C61#324211yescharacteristic
313C2×#117—611no—
314C2×#117C2×D6111yescharacteristic
315C22×C4⋊C4—611no—
316#433—618no—
317C2×#107—611no—
318C2×#107—611no—
319C2×#107—611no—
320C2×#107—611no—
321C2×#106—611no—
322C2×#106—611no—
323C2×#106—611no—
324C2×#106—611no—
325C2×C4⋊C8—611no—
326C2×C4⋊C8—611no—
327C2×C22⋊C8—611no—
328C2×C22⋊C8—611no—
329C2×#97—611no—
330C2×C4×C8—611no—
331#389—1221no—
332#389—1221no—
333#388—21no—
334#388—21no—
335#387—21no—
336#387—21no—
337#385—1221no—
338#385—1221no—
339#384—611no—
340#384—611no—
341#384C2×D6111yescharacteristic
342#382—611no—
343#382—611no—
344#382C2×D6111yescharacteristic
345#380C2×D6111yescharacteristic
346#380C2×D6111yescharacteristic
347C4×C4⋊C4C2×D6111yescharacteristic
348C4×C4⋊C4C2×D6111yescharacteristic
349#340—611no—
350#340—611no—
351#340—611no—
352#340—611no—
353#340—611no—
354#340—611no—
355#340—611no—
356#340—611no—
357C61#2199211yescharacteristic, complemented, Sylow
358C23×C4—1221no—
359C23×C4C22×D6111yescharacteristic
360C22×C8—611no—
361C22×C8—611no—
362C22×C8—611no—
363C22×C8—611no—
364#117—2441no—
365#117—2441no—
366#117Dic12214yes—
367#117C4×D6114yes—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—611no—
371C2×C4⋊C4—611no—
372C2×C4⋊C4—611no—
373C2×C4⋊C4—611no—
374C2×C4⋊C4—1221no—
375C2×C4⋊C4—1221no—
376C2×C4⋊C4—1221no—
377C2×C4⋊C4—1221no—
378C2×C4⋊C4—1221no—
379C2×C4⋊C4—2441no—
380C2×C4⋊C4—2441no—
381C2×C4⋊C4C22⋊D6111yescharacteristic
382C2×C4⋊C4C22⋊D6111yescharacteristic
383C2×C4⋊C4C22×D6111yescharacteristic
384C2×C4⋊C4C22×D6111yescharacteristic
385C2×C4⋊C4C22×D6111yescharacteristic
386C2×C4⋊C4C22×D6111yescharacteristic
387C2×C22⋊C4—21no—
388C2×C22⋊C4—21no—
389C2×C22⋊C4—1221no—
390C2×C22⋊C4C22⋊D6111yescharacteristic
391C2×C22⋊C4C22⋊D6111yescharacteristic
392C2×C42—21no—
393C2×C42—21no—
394C2×C42—1221no—
395C2×C42C22×D6111yescharacteristic
396C2×C42C22×D6111yescharacteristic
397#107—2441no—
398#107—2441no—
399#107—2441no—
400#107—2441no—
401#106—2441no—
402#106—2441no—
403#106—2441no—
404#106—2441no—
405C4⋊C8—614no—
406C4⋊C8—614no—
407C22⋊C8—614no—
408C22⋊C8—614no—
409#97—614no—
410C4×C8—614no—
411#95—21no—
412#95—21no—
413#95—21no—
414#95—21no—
415#95—21no—
416#95—21no—
417#95—1221no—
418#95—1221no—
419#95—1221no—
420#95—1221no—
421C24C2×C22⋊D6111yescharacteristic
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—1221no—
431C22×C4—1221no—
432C22×C4—1221no—
433C22×C4—1221no—
434C22×C4—4881no—
435C22×C4—4881no—
436C22×C4—2442no—
437C22×C4C2×Dic12212yes—
438C22×C4C2×C4×D6112yes—
439C22×C4C2×C22⋊D6111yescharacteristic
440C22×C4C2×C22⋊D6111yescharacteristic
441C22×C4C2×C22⋊D6111yescharacteristic
442C22×C4C2×C22⋊D6111yescharacteristic
443C22×C4C2×C22⋊D6111yescharacteristic
444C22×C4C23×D6111yescharacteristic
445C2×C8—612no—
446C2×C8—612no—
447C2×C8—612no—
448C2×C8—612no—
449C2×C8—1221no—
450C2×C8—1221no—
451C2×C8—1221no—
452C2×C8—1221no—
453C2×C8—1221no—
454C2×C8—1221no—
455C2×C8—1221no—
456C2×C8—1221no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—81no—
466C4⋊C4—81no—
467C4⋊C4—1221no—
468C4⋊C4—1221no—
469C4⋊C4—1221no—
470C4⋊C4—1221no—
471C4⋊C4—1221no—
472C4⋊C4—1221no—
473C4⋊C4—1221no—
474C4⋊C4—1221no—
475C4⋊C4—4881no—
476C4⋊C4—4881no—
477C4⋊C4—4881no—
478C4⋊C4—4881no—
479C4⋊C4—2442no—
480C4⋊C4#1175819614yes—
481C4⋊C4#1175819614yes—
482C22⋊C4—81no—
483C22⋊C4—81no—
484C22⋊C4—2442no—
485C22⋊C4#1175819614yes—
486C22⋊C4#1175819614yes—
487C42—81no—
488C42—81no—
489C42—2442no—
490C42C2×Dic12212yes—
491C42C2×Dic12212yes—
492C42C2×C4×D6112yes—
493C42C2×C4×D6112yes—
494C23—21no—
495C23—21no—
496C23—21no—
497C23—21no—
498C23—21no—
499C23—21no—
500C23C2×#1175819612yes—
501C23C22×C22⋊D6111yescharacteristic
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—4884no—
529C2×C4—2441no—
530C2×C4—2441no—
531C2×C4—2441no—
532C2×C4—2441no—
533C2×C4—2441no—
534C2×C4—2441no—
535C2×C4—2441no—
536C2×C4—2441no—
537C2×C4—2441no—
538C2×C4—2441no—
539C2×C4—2441no—
540C2×C4—2441no—
541C2×C4C2×#1175819612yes—
542C2×C4C2×#1175819612yes—
543C2×C4C2×#1175819612yes—
544C2×C4C2×#1175819612yes—
545C2×C4C2×#1175819612yes—
546C2×C4C22×C4×D6111yescharacteristic
547C2×C4C22×Dic12211yescharacteristic
548C2×C4#1451982311yescharacteristic
549C2×C4#1451982311yescharacteristic
550C2×C4#1451982411yescharacteristic
551C2×C4#1451982411yescharacteristic
552C8—1222no—
553C8—1222no—
554C8—1222no—
555C8—1222no—
556C22—22no—
557C22—22no—
558C22—22no—
559C22—41no—
560C22—41no—
561C22—41no—
562C22—41no—
563C22C22×#1175819611yescharacteristic
564C22#1684032611yescharacteristic
565C22#1684033311yescharacteristic
566C22#1684056511yescharacteristic
567C22#1684057011yescharacteristic
568C22#1684057311yescharacteristic
569C22#1684057711yescharacteristic
570C4—22no—
571C4—22no—
572C4—22no—
573C4—22no—
574C4—22no—
575C4—81no—
576C4—81no—
577C4—81no—
578C4—81no—
579C4—4881no—
580C4—4881no—
581C4—4881no—
582C4—4881no—
583C4#1684024211yescharacteristic
584C4#1684024211yescharacteristic
585C4#1684039011yescharacteristic
586C4#1684039011yescharacteristic
587C2—42no—
588C2#2144843911yescharacteristic
589C2#2145441211yescharacteristic
590C2#2145441711yescharacteristic
591C2#2145690711yescharacteristic
592C2#2145692211yescharacteristic
593C2#2145706611yescharacteristic
594C2#2145708111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#2314C2
socleC23×C61C22×D4
prime radicalC24×C61C2×D4
cosocleC22×C4×C61C24
hypercenter#2314D61
hypocenterC61#21992
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2314

Complements

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

NH ≅ G/Ntype
3. #21446587C2semidirect
4. #21446587C2semidirect
5. #21446582C2semidirect
6. #21446577C2semidirect
11. #21445988C2semidirect
12. #21445981C2semidirect
13. #21445954C2semidirect
14. #21445946C2semidirect
18. #16839823C4semidirect
88. C4⋊#92418C2×C4semidirect
89. C4⋊#92418C2×C4semidirect
92. #14519688C2×C4semidirect
93. C4×#92418C2×C4semidirect
357. C61#21992semidirect

Maximal subgroups

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

subgroupindex
C2×#168398232
#214484422
#214465872
#214465822
#214465772
#214460162
#214460112
#214460062
#214459882
#214459812
#214459542
#214459462
C61×#23142
#2199261