Finite Group Databasebeta

← #30601825

Subgroups — #30601825

Order 15616.

468 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 96 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#21461994C211yesmaximal, characteristic, complemented
2#21461982C211yesmaximal, characteristic
3C4×#14519845C211yesmaximal, characteristic, complemented
4#21461203C211yesmaximal, characteristic, complemented
5#21461200C211yesmaximal, characteristic
6C8×#11758213C211yesmaximal, characteristic, complemented
7#21456380C211yesmaximal, characteristic
8#16840781C2211yescharacteristic
9C2×#14519845—21no—
10C2×#14519842—22no—
11C4×#11758213C2211yescharacteristic
12C4×C4⋊#6923C2211yescharacteristic
13C4×C4⋊#6923C2211yescharacteristic
14#16840636—21no—
15#16840632—22no—
16#16840616—22no—
17#16840614—22no—
18#92420⋊C8—21no—
19C8×#92420—21no—
20#16840317C2211yescharacteristic
21#16840313C2211yescharacteristic
22#16840135C411yescharacteristic, complemented
23#16840114C411yescharacteristic, complemented
24#16840110C411yescharacteristic, complemented
25#16839992—21no—
26#16839992—21no—
27#16839849—21no—
28#16839849—21no—
29C4×C8×D61C2211yescharacteristic
30C61×#498C411yescharacteristic, complemented
31C2×#11758213D412yes—
32C2×C4⋊#6923—21no—
33C2×C4⋊#6923—21no—
34C2×C4×#6923—21no—
35C2×C4×#6923—21no—
36#14519845—24no—
37C4⋊#92420—21no—
38#14519842—44no—
39#14519834D412yes—
40#14519832—21no—
41C4×#92420—21no—
42C4×#92420—21no—
43(C2×#6923)⋊C4—21no—
44(C2×#6923)⋊C4—21no—
45C2×#11758226—21no—
46C2×#11758190—21no—
47C2×#11758190—21no—
48C2×C8×D61D411yescharacteristic
49C2×C8×D61D411yescharacteristic
50#14519777C2×C411yescharacteristic
51#14519774C2×C411yescharacteristic
52#14519768—21no—
53#14519766—21no—
54#14519757—21no—
55#14519753—21no—
56#14519752—21no—
57#14519752—21no—
58Q8×Dic61—21no—
59#14519742—21no—
60#14519739—21no—
61#14519739—21no—
62#14519735—21no—
63C42×D61C2311yescharacteristic
64#14519700—21no—
65#14519700—21no—
66#14519697—21no—
67#14519697—21no—
68C4×#92418C2×C411yescharacteristic
69C8×Dic61D411yescharacteristic
70C8×Dic61D411yescharacteristic
71C4⋊Q8×C61C2×C411yescharacteristic
72C4⋊Q8×C61C2×C411yescharacteristic
73#106×C61—21no—
74#106×C61—21no—
75C4×C8×C61C2×C411yescharacteristic
76C22×#6923—41no—
77C22×#6923—41no—
78C2×Q8×C61—21no—
79C2×Q8×C61—21no—
80#11758226—42no—
81#11758226—42no—
82C2×D244—21no—
83C2×D244—21no—
84C2×D244—21no—
85C2×D244—41no—
86C2×C4×D61—41no—
87C2×C4×D61C2×D411yescharacteristic
88C2×C4×D61C2×D411yescharacteristic
89C2×C4×D61C2×D411yescharacteristic
90C2×Dic122—21no—
91C2×#92420—22no—
92C2×#92420—22no—
93C4⋊#6923—22no—
94C4⋊#6923—22no—
95C4⋊#6923—41no—
96C4⋊#6923—41no—
97C4×#6923—42no—
98C4×#6923—42no—
99#11758213—22no—
100#11758213SD1614yescomplemented
101C2×C8×C61C22⋊C411yescharacteristic
102C2×C8×C61C22⋊C411yescharacteristic
103C4⋊C4×C61—21no—
104C4⋊C4×C61—21no—
105C4⋊C4×C61—21no—
106C4⋊C4×C61—21no—
107C42×C61C22×C411yescharacteristic
108#11758198—41no—
109#11758198—41no—
110#11758198—41no—
111C4⋊Dic61—21no—
112C4⋊Dic61—21no—
113C4⋊Dic61—41no—
114#11758196—41no—
115C4×Dic61—41no—
116C4×Dic61C2×D411yescharacteristic
117C4×Dic61#4111yescharacteristic
118C4×Dic61#4111yescharacteristic
119C2×#92418C22⋊C411yescharacteristic
120C2×#92418C22⋊C411yescharacteristic
121#11758190—42no—
122#11758190—42no—
123C8×D61—22no—
124C8×D61—41no—
125C22×D61—41no—
126C22×D61#12711yescharacteristic
127C2×#6923—42no—
128C2×#6923—42no—
129C2×#6923—81no—
130C2×#6923—81no—
131C2×#6923—81no—
132C2×#6923—81no—
133Q8×C61—42no—
134Q8×C61—81no—
135C2×C4×C61—41no—
136C2×C4×C61—41no—
137C2×C4×C61C2×C22⋊C411yescharacteristic
138C2×C4×C61C4×D411yescharacteristic
139C2×C4×C61C4×D411yescharacteristic
140C2×Dic61—41no—
141C2×Dic61#12111yescharacteristic
142C2×Dic61#12111yescharacteristic
143C2×Dic61#12411yescharacteristic
144D244—41no—
145D244—41no—
146D244—42no—
147D244—81no—
148D244—81no—
149D244—81no—
150C4×D61—21no—
151C4×D61—21no—
152C4×D61—41no—
153C4×D61—82no—
154C4×D61C2×SD1612yes—
155C4×D61#13512yes—
156Dic122—41no—
157Dic122—41no—
158#92420—24no—
159#92420—42no—
160C8×C61—21no—
161C8×C61#10412yescomplemented
162#92418—21no—
163#92418—21no—
164#9717—611nomaximal, Sylow
165C22×C61#39011yescharacteristic
166C2×D61—21no—
167C2×D61—21no—
168C2×D61—81no—
169C2×D61—81no—
170C2×D61—81no—
171C2×D61#49211yescharacteristic
172C2×D61#49511yescharacteristic
173#6923—82no—
174#6923—82no—
175C4×C61—21no—
176C4×C61—81no—
177C4×C61—81no—
178C4×C61C2×#10411yescharacteristic
179C4×C61#42111yescharacteristic
180C4×C61C4×SD1612yes—
181Dic61—21no—
182Dic61—21no—
183Dic61—81no—
184Dic61#46512yes—
185#3167—611no—
186#1986—611no—
187#1980—611no—
188C4×#106—611no—
189#1503—611no—
190#1502—611no—
191C8×M16—611no—
192C2×C61#196811yescharacteristic
193C2×C61#197611yescharacteristic
194C2×C61#198011yescharacteristic
195D61—21no—
196D61—21no—
197D61—161no—
198#533—611no—
199#532—611no—
200#498#692311yescharacteristic, complemented
201#492—611no—
202#487—611no—
203#486—611no—
204#465—1221no—
205#465—1221no—
206C4×SD16—1221no—
207C4×SD16—1221no—
208#431—611no—
209C2×#106—1221no—
210C2×#104—1222no—
211C4×M16—611no—
212C2×C4×C8—611no—
213C4×C4⋊C4—611no—
214C4×C4⋊C4—611no—
215#340—1221no—
216#339—1222no—
217#328—1222no—
218#327—1222no—
219#322—1221no—
220C82—1221no—
221C61#971711yescharacteristic, complemented, Sylow
222C2×#41—1221no—
223C2×SD16—1221no—
224C2×SD16—1221no—
225C2×M16—612no—
226C22×C8—611no—
227C22×C8—611no—
228C4⋊Q8—611no—
229C4⋊Q8C2×#692311yescharacteristic
230C4⋊Q8C2×#692311yescharacteristic
231#127—611no—
232#125—1221no—
233#124—1221no—
234C22⋊Q8—1221no—
235C22⋊Q8—1221no—
236#121—1221no—
237#121—1221no—
238C4×Q8—1221no—
239C4×Q8—1221no—
240C4×D4—1221no—
241C4×D4—1221no—
242#117—1221no—
243C2×C4⋊C4—1221no—
244C2×C4⋊C4—1221no—
245C2×C42—611no—
246C2×C42—1221no—
247C2×C42—1221no—
248#106—21no—
249#106—21no—
250#106—1224no—
251C4⋊C8—1221no—
252#104—2444no—
253#103—1221no—
254#103—1221no—
255#102—1221no—
256#102—1221no—
257C22⋊C8—612no—
258#97—1221no—
259C4×C8—611no—
260C4×C8—611no—
261C4×C8—611no—
262C4×C8—1221no—
263C4×C8—1221no—
264C4×C8C2×#692311yescharacteristic
265#95—1221no—
266#95—1221no—
267#41—2442no—
268#41—2442no—
269C2×Q8—21no—
270C2×Q8—21no—
271C2×Q8—1221no—
272C2×D4—1221no—
273C2×D4—1221no—
274C2×D4—1221no—
275C2×D4—2441no—
276C22×C4—611no—
277C22×C4—611no—
278C22×C4—611no—
279C22×C4—2441no—
280C22×C4—2441no—
281C22×C4—2441no—
282SD16—2442no—
283SD16—2442no—
284M16—614no—
285M16—1222no—
286C2×C8—611no—
287C2×C8—611no—
288C2×C8—1222no—
289C2×C8—1222no—
290C2×C8—1222no—
291C2×C8—2441no—
292C2×C8C22⋊#692311yescharacteristic
293C2×C8C22⋊#692311yescharacteristic
294C4⋊C4—21no—
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—21no—
298C4⋊C4—1222no—
299C4⋊C4—1222no—
300C4⋊C4—1221no—
301C4⋊C4—1221no—
302C4⋊C4—2441no—
303C4⋊C4—2441no—
304C4⋊C4—2441no—
305C4⋊C4—2441no—
306C22⋊C4—2441no—
307C22⋊C4—2441no—
308C22⋊C4—2441no—
309C42—611no—
310C42—611no—
311C42—611no—
312C42—2441no—
313C42—2442no—
314C42—2442no—
315C42C22×#692311yescharacteristic
316C23—611no—
317C23—2441no—
318Q8—42no—
319Q8—81no—
320Q8—2441no—
321Q8—2441no—
322D4—4881no—
323D4—4881no—
324D4—4881no—
325D4—2441no—
326D4—2441no—
327D4—2442no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—611no—
331C2×C4—612no—
332C2×C4—612no—
333C2×C4—611no—
334C2×C4—611no—
335C2×C4—1221no—
336C2×C4—1221no—
337C2×C4—4882no—
338C2×C4—4881no—
339C2×C4—4881no—
340C2×C4—4881no—
341C2×C4—4881no—
342C2×C4—2441no—
343C2×C4—2442no—
344C2×C4—2442no—
345C2×C4—2441no—
346C2×C4C2×C22⋊#692311yescharacteristic
347C2×C4D4×#692311yescharacteristic
348C2×C4D4×#692311yescharacteristic
349C8—21no—
350C8—1224no—
351C8—1221no—
352C8—1221no—
353C8—2442no—
354C8#1451984212yescomplemented
355C22—611no—
356C22—611no—
357C22—1221no—
358C22—1221no—
359C22—4881no—
360C22—4881no—
361C22—4881no—
362C22#1684071411yescharacteristic
363C4—21no—
364C4—81no—
365C4—81no—
366C4—612no—
367C4—1221no—
368C4—1221no—
369C4—4882no—
370C4—4882no—
371C4—4881no—
372C4C2×#1451984211yescharacteristic
373C4#1684076111yescharacteristic
374C4SD16×#692312yes—
375C2—1221no—
376C2—1221no—
377C2—9761no—
378C2#2146196411yescharacteristic
379C2#2146197711yescharacteristic
380C2#2146198211yescharacteristic
subgroupG/H
centerC22#16840714
commutatorC42×C61C22×C4
FrattiniC42C22×#6923
FittingC61×#498C4
socleC22×C61#390
prime radical#16840313C22
cosocleC42×D61C23
hypercenter#498#6923
hypocenterC61#9717
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #498

Complements

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

NH ≅ G/Ntype
1. #21461994C2semidirect
3. C4×#14519845C2semidirect
4. #21461203C2semidirect
6. C8×#11758213C2semidirect
22. #16840135C4semidirect
23. #16840114C4semidirect
24. #16840110C4semidirect
30. C61×#498C4semidirect
100. #11758213SD16semidirect
161. C8×C61#104semidirect
200. #498#6923semidirect
221. C61#9717semidirect
354. C8#14519842semidirect

Maximal subgroups

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

subgroupindex
#214619942
#214619822
C4×#145198452
#214612032
#214612002
C8×#117582132
#214563802
#971761