Finite Group Databasebeta

← #29575978

Subgroups — #29575978

Order 15616.

530 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 530 conjugacy classes of subgroups — too many to draw. Only its 91 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454858C211yesmaximal, characteristic
2#21451737C211yesmaximal, characteristic
3C4×#14519691C211yesmaximal, characteristic
4#21444339C211yesmaximal, characteristic, complemented
5#21443673C211yesmaximal, characteristic, complemented
6#21443672C211yesmaximal, characteristic, complemented
7C61×#1508C211yesmaximal, characteristic, complemented
8C2×C4×C22⋊D61C2211yescharacteristic
9#16839838—22no—
10#16839837—22no—
11#16839812—21no—
12C2×#14519691—21no—
13#16839726C2211yescharacteristic
14#16839724—21no—
15#16839693C411yescharacteristic, complemented
16#16839690—21no—
17#16839688C411yescharacteristic, complemented
18#16839681C411yescharacteristic, complemented
19#16839677—21no—
20#16839673C411yescharacteristic, complemented
21#16839643—21no—
22#16839633—21no—
23#16839625C2211yescharacteristic
24C4×C22⋊Dic61C2211yescharacteristic
25#16839528—21no—
26#16839499—22no—
27C2×C22⋊Q8×C61C2211yescharacteristic
28C61×#407C2211yescharacteristic
29C4×C22⋊C4×C61C2211yescharacteristic
30C61×#328—22no—
31C22×C22⋊D61D411yescharacteristic
32C22×C4×D61D411yescharacteristic
33C2×#11758194—21no—
34C2×#11758189—22no—
35C4×C22⋊D61—21no—
36C4×C22⋊D61—21no—
37C4×C22⋊D61—21no—
38C4×C22⋊D61—21no—
39C2×#11758196—21no—
40C2×#11758196—21no—
41C2×#11758196C2×C411yescharacteristic
42C2×C22⋊Dic61—21no—
43C2×C22⋊Dic61—21no—
44C2×C22⋊Dic61D411yescharacteristic
45C2×#11758198—21no—
46C2×#11758198—21no—
47C2×#11758198C2×C411yescharacteristic
48C2×C4×Dic61—21no—
49C2×C4×Dic61D411yescharacteristic
50#14519706—22no—
51#14519691—24no—
52C22⋊#92418—21no—
53C22⋊#92418D412yes—
54#14519689—22no—
55C8×Dic61—22no—
56#14519684—21no—
57#14519684—21no—
58#14519684—21no—
59#14519684—21no—
60#14519684—21no—
61#14519684—21no—
62#14519684C2×C411yescharacteristic
63#14519684C2×C411yescharacteristic
64C22×Q8×C61C2×C411yescharacteristic
65C23×C4×C61C2311yescharacteristic
66C2×M16×C61—21no—
67C22⋊Q8×C61—21no—
68C22⋊Q8×C61—21no—
69C22⋊Q8×C61—21no—
70C22⋊Q8×C61—21no—
71C2×C4⋊C4×C61—21no—
72C2×C4⋊C4×C61C2×C411yescharacteristic
73C2×C22⋊C4×C61—21no—
74C2×C22⋊C4×C61—21no—
75C2×C42×C61—21no—
76C22⋊C8×C61—21no—
77C22⋊C8×C61D412yes—
78#95×C61—21no—
79C24×C61C2×D411yescharacteristic
80C23×D61C22⋊C411yescharacteristic
81C2×Q8×C61—21no—
82C2×Q8×C61—21no—
83C2×Q8×C61—81no—
84C22×C4×C61—21no—
85C22×C4×C61—21no—
86C22×C4×C61—41no—
87C22×C4×C61—81no—
88C22×C4×C61C22×C411yescharacteristic
89C22×C4×C61C2×D411yescharacteristic
90C22×C4×C61C2×D411yescharacteristic
91C22×C4×C61C2×D411yescharacteristic
92C22×C4×C61#4111yescharacteristic
93C22×C4×C61#4111yescharacteristic
94C2×C22⋊D61—21no—
95C2×C22⋊D61—21no—
96C2×C22⋊D61—22no—
97C2×C22⋊D61—41no—
98C22×Dic61—21no—
99C22×Dic61—21no—
100C22×Dic61—41no—
101C22×Dic61C22⋊C411yescharacteristic
102C22×Dic61C22⋊C411yescharacteristic
103C22×Dic61C22⋊C411yescharacteristic
104C2×C4×D61—21no—
105C2×C4×D61—21no—
106C2×C4×D61—81no—
107M16×C61—81no—
108C2×C8×C61—22no—
109C4⋊C4×C61—21no—
110C4⋊C4×C61—21no—
111C4⋊C4×C61—41no—
112C4⋊C4×C61—41no—
113C22⋊C4×C61—22no—
114C22⋊C4×C61—41no—
115C22⋊C4×C61—41no—
116C22⋊C4×C61—41no—
117C42×C61—81no—
118C22⋊Dic61—21no—
119C22⋊Dic61—21no—
120C22⋊Dic61—22no—
121C22⋊Dic61—41no—
122C22⋊Dic61—81no—
123#11758198—21no—
124#11758198—21no—
125#11758198—42no—
126#11758198—81no—
127#11758196—21no—
128#11758196—21no—
129#11758196—42no—
130#11758196—81no—
131C4×Dic61—21no—
132C4×Dic61—21no—
133C4×Dic61—81no—
134#11758194—81no—
135C2×#92418—22no—
136#11758189—82no—
137C23×C61—21no—
138C23×C61—21no—
139C23×C61—41no—
140C23×C61—41no—
141C23×C61C2×C22⋊C411yescharacteristic
142C23×C61#12111yescharacteristic
143C23×C61#12111yescharacteristic
144C22×D61—21no—
145C22×D61—21no—
146C22×D61—21no—
147C22×D61—41no—
148C22×D61—41no—
149Q8×C61—81no—
150Q8×C61—81no—
151C2×C4×C61—41no—
152C2×C4×C61—41no—
153C2×C4×C61—41no—
154C2×C4×C61—41no—
155C2×C4×C61—41no—
156C2×C4×C61—41no—
157C2×C4×C61—41no—
158C2×C4×C61—41no—
159C2×C4×C61—42no—
160C2×C4×C61—41no—
161C2×C4×C61—41no—
162C2×C4×C61—41no—
163C2×C4×C61—41no—
164C2×C4×C61—81no—
165C2×C4×C61—81no—
166C2×C4×C61C4×D411yescharacteristic
167C2×C4×C61C4×D411yescharacteristic
168C2×C4×C61#12011yescharacteristic
169C2×C4×C61#12311yescharacteristic
170C22⋊D61—42no—
171C22⋊D61—42no—
172C2×Dic61—21no—
173C2×Dic61—21no—
174C2×Dic61—21no—
175C2×Dic61—21no—
176C2×Dic61—41no—
177C2×Dic61—41no—
178C2×Dic61—41no—
179C2×Dic61—41no—
180C2×Dic61—42no—
181C2×Dic61—41no—
182C2×Dic61—41no—
183C2×Dic61—41no—
184C2×Dic61—41no—
185C2×Dic61—81no—
186C2×Dic61—81no—
187C2×Dic61#10412yes—
188C4×D61—42no—
189C4×D61—81no—
190C8×C61—42no—
191#92418—42no—
192#9184—611nomaximal, Sylow
193C22×C61—21no—
194C22×C61—21no—
195C22×C61—21no—
196C22×C61—21no—
197C22×C61—21no—
198C22×C61—21no—
199C22×C61—21no—
200C22×C61—21no—
201C22×C61—81no—
202C22×C61—81no—
203C22×C61#38611yescharacteristic
204C22×C61C2×#10411yescharacteristic
205C22×C61#42111yescharacteristic
206C2×D61—42no—
207C2×D61—41no—
208C2×D61—41no—
209C2×D61—41no—
210C2×D61—81no—
211C4×C61—21no—
212C4×C61—21no—
213C4×C61—21no—
214C4×C61—21no—
215C4×C61—82no—
216C4×C61—81no—
217C4×C61—81no—
218Dic61—22no—
219Dic61—41no—
220Dic61—41no—
221Dic61—81no—
222Dic61—81no—
223Dic61—82no—
224#2975—611no—
225#2638—611no—
226C4×#99—611no—
227#1508—611no—
228#1508D6111yescharacteristic, complemented
229#1284—611no—
230#1284—611no—
231C2×C61—21no—
232C2×C61—21no—
233C2×C61—41no—
234C2×C61—41no—
235C2×C61#187111yescharacteristic
236C2×C61#190911yescharacteristic
237C2×C61#191311yescharacteristic
238D61—81no—
239C2×C22⋊Q8C2×D6111yescharacteristic
240C2×C4×D4—611no—
241#436—1222no—
242#436—1222no—
243#431—1221no—
244C2×#99—1221no—
245#407—611no—
246#407—1221no—
247#407C2×D6111yescharacteristic
248#398—611no—
249#397—611no—
250#397—1221no—
251#395—611no—
252#394—1221no—
253#393—611no—
254#387—1221no—
255#385—1221no—
256#381—611no—
257C4×C22⋊C4—611no—
258C4×C22⋊C4C2×D6111yescharacteristic
259#342—1221no—
260#328—22no—
261#328—1222no—
262C61#918411yescharacteristic, complemented, Sylow
263C22×Q8C4×D6111yescharacteristic
264C22×D4—611no—
265C23×C4—611no—
266C23×C4C22×D6111yescharacteristic
267C2×M16—21no—
268C2×M16—1222no—
269C2×M16—1221no—
270C22⋊Q8—21no—
271C22⋊Q8—21no—
272C22⋊Q8—21no—
273C22⋊Q8—21no—
274C4×D4—1221no—
275C4×D4—1221no—
276C4×D4—1221no—
277C4×D4—1221no—
278C2×C4⋊C4—21no—
279C2×C4⋊C4—611no—
280C2×C4⋊C4—1221no—
281C2×C4⋊C4—1221no—
282C2×C4⋊C4C4×D6111yescharacteristic
283C2×C22⋊C4—21no—
284C2×C22⋊C4—21no—
285C2×C22⋊C4—611no—
286C2×C22⋊C4—611no—
287C2×C22⋊C4—1221no—
288C2×C22⋊C4—1221no—
289C2×C22⋊C4—1221no—
290C2×C22⋊C4—1221no—
291C2×C42—21no—
292C2×C42—611no—
293C2×C42—1221no—
294C4⋊C8—1222no—
295#99—1224no—
296C22⋊C8—21no—
297C22⋊C8—612no—
298C22⋊C8—1222no—
299C22⋊C8—1221no—
300C22⋊C8C22⋊D6112yes—
301C4×C8—1222no—
302#95—21no—
303#95—611no—
304#95—611no—
305#95—1221no—
306#95—1221no—
307#95—1221no—
308#95—1221no—
309#95—1221no—
310#95—1221no—
311C24—611no—
312C24D4×D6111yescharacteristic
313C2×Q8—21no—
314C2×Q8—21no—
315C2×Q8—81no—
316C2×D4—1222no—
317C2×D4—1221no—
318C2×D4—1221no—
319C2×D4—2441no—
320C22×C4—21no—
321C22×C4—21no—
322C22×C4—41no—
323C22×C4—81no—
324C22×C4—611no—
325C22×C4—611no—
326C22×C4—611no—
327C22×C4—1221no—
328C22×C4—1221no—
329C22×C4—1221no—
330C22×C4—1221no—
331C22×C4—4881no—
332C22×C4—2441no—
333C22×C4C2×C4×D6111yescharacteristic
334C22×C4#1175822211yescharacteristic
335C22×C4D4×D6111yescharacteristic
336C22×C4D4×D6111yescharacteristic
337C22×C4#1175822411yescharacteristic
338C22×C4C2×C22⋊D6111yescharacteristic
339M16—81no—
340M16—4882no—
341M16—4881no—
342C2×C8—22no—
343C2×C8—1222no—
344C4⋊C4—21no—
345C4⋊C4—21no—
346C4⋊C4—41no—
347C4⋊C4—41no—
348C4⋊C4—1221no—
349C4⋊C4—1221no—
350C4⋊C4—4881no—
351C4⋊C4—2442no—
352C22⋊C4—22no—
353C22⋊C4—41no—
354C22⋊C4—41no—
355C22⋊C4—41no—
356C22⋊C4—1221no—
357C22⋊C4—1221no—
358C22⋊C4—1221no—
359C22⋊C4—1221no—
360C22⋊C4—1222no—
361C22⋊C4—4881no—
362C22⋊C4—4881no—
363C22⋊C4—2442no—
364C22⋊C4—2441no—
365C42—81no—
366C42—1221no—
367C42—1221no—
368C42—4881no—
369C23—21no—
370C23—21no—
371C23—41no—
372C23—41no—
373C23—1221no—
374C23—1221no—
375C23—1221no—
376C23—2441no—
377C23—2441no—
378C23C22⋊C4×D6111yescharacteristic
379C23#1451974811yescharacteristic
380C23#1451975011yescharacteristic
381Q8—81no—
382Q8—81no—
383D4—2442no—
384D4—2442no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—42no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—81no—
399C2×C4—81no—
400C2×C4—612no—
401C2×C4—1221no—
402C2×C4—1221no—
403C2×C4—1221no—
404C2×C4—1221no—
405C2×C4—4881no—
406C2×C4—4881no—
407C2×C4—4881no—
408C2×C4—2442no—
409C2×C4—2442no—
410C2×C4—2441no—
411C2×C4—2441no—
412C2×C4—2441no—
413C2×C4—2441no—
414C2×C4—2441no—
415C2×C4—2441no—
416C2×C4—2441no—
417C2×C4—2441no—
418C2×C4#1451973711yescharacteristic
419C2×C4C4×C22⋊D6111yescharacteristic
420C2×C4#1451974511yescharacteristic
421C2×C4#1451975911yescharacteristic
422C8—42no—
423C8—2442no—
424C22—21no—
425C22—21no—
426C22—21no—
427C22—21no—
428C22—21no—
429C22—21no—
430C22—21no—
431C22—21no—
432C22—81no—
433C22—81no—
434C22—4881no—
435C22—2442no—
436C22—2441no—
437C22—2441no—
438C22—2441no—
439C22#1683963811yescharacteristic
440C22#104×D6111yescharacteristic
441C22#1683977711yescharacteristic
442C4—21no—
443C4—21no—
444C4—21no—
445C4—21no—
446C4—82no—
447C4—81no—
448C4—81no—
449C4—1222no—
450C4—4881no—
451C4—4881no—
452C4—4882no—
453C4—2441no—
454C4—2441no—
455C2—21no—
456C2—21no—
457C2—41no—
458C2—41no—
459C2—4881no—
460C2#2144611811yescharacteristic
461C2#2144633811yescharacteristic
462C2#2144635811yescharacteristic
subgroupG/H
centerC22#16839638
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#1508C2
socleC22×C61#386
prime radicalC22×C22⋊D61D4
cosocleC23×C4×C61C23
hypercenter#1508D61
hypocenterC61#9184
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1508

Complements

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

NH ≅ G/Ntype
4. #21444339C2semidirect
5. #21443673C2semidirect
6. #21443672C2semidirect
7. C61×#1508C2semidirect
15. #16839693C4semidirect
17. #16839688C4semidirect
18. #16839681C4semidirect
20. #16839673C4semidirect
228. #1508D61semidirect
262. C61#9184semidirect

Maximal subgroups

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

subgroupindex
#214548582
#214517372
C4×#145196912
#214443392
#214436732
#214436722
C61×#15082
#918461