Finite Group Databasebeta

← #30595133

Subgroups — #30595133

Order 15616.

262 conjugacy classes of subgroups; only the 42 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 42 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#21461825C211yesmaximal, characteristic
2#21461353C211yesmaximal, characteristic
3#356×D61C211yesmaximal, characteristic
4#16840830C411yescharacteristic
5#16840785—21no—
6#16840755—21no—
7D61⋊#101C411yescharacteristic
8#16840633—21no—
9#16840622—21no—
10#16840622C412yescomplemented
11C4⋊Q8×D61C2211yescharacteristic
12#101×D61—21no—
13#16839561C411yescharacteristic, complemented
14#16839560—21no—
15C61×#356C411yescharacteristic, complemented
16D61⋊M16—21no—
17Q8×#6923—42no—
18#14519856—21no—
19#14519856—41no—
20#14519844—22no—
21#14519840—42no—
22#14519838—41no—
23#14519834—41no—
24#14519832—41no—
25C2×Q8×D61C2×C411yescharacteristic
26C2×Q8×D61D411yescharacteristic
27M16×D61—41no—
28#14519777Q811yescharacteristic
29#14519776—41no—
30#14519775C2×C411yescharacteristic
31#14519775D411yescharacteristic
32C4⋊C4×D61—41no—
33C42×D61D411yescharacteristic
34#14519696—21no—
35#14519695—41no—
36C4⋊Q8×C61C2×C411yescharacteristic
37#101×C61—21no—
38C2×Q8×C61C4211yescharacteristic
39C2×Q8×C61C22⋊C411yescharacteristic
40Q8×D61—41no—
41Q8×D61—41no—
42Q8×D61—41no—
43Q8×D61—41no—
44C2×C4×D61—21no—
45C2×C4×D61—21no—
46C2×C4×D61—21no—
47C2×C4×D61C22⋊C411yescharacteristic
48C2×Dic122—21no—
49C2×Dic122—21no—
50C2×Dic122C4⋊C411yescharacteristic
51C2×Dic122C4⋊C411yescharacteristic
52C22⋊#6923—41no—
53#11758217—41no—
54C2×#92420—42no—
55C4⋊#6923—22no—
56C4⋊#6923—42no—
57C4×#6923—41no—
58C4×#6923—42no—
59#11758213—41no—
60D61⋊C8—41no—
61M16×C61—41no—
62C4⋊C4×C61—41no—
63C42×C61C4⋊C411yescharacteristic
64C4⋊Dic61—41no—
65#11758196—41no—
66#11758196—41no—
67C4×Dic61—21no—
68C4×Dic61C22⋊C411yescharacteristic
69#11758194—41no—
70#11758189—81no—
71C8×D61—81no—
72C22×D61#9911yescharacteristic
73C2×#6923—42no—
74Q8×C61—41no—
75Q8×C61—41no—
76C2×C4×C61—21no—
77C2×C4×C61—21no—
78C2×C4×C61—21no—
79C2×C4×C61#9511yescharacteristic
80C2×Dic61—21no—
81C2×Dic61—21no—
82C2×Dic61—21no—
83C2×Dic61#9911yescharacteristic
84C4×D61—21no—
85C4×D61—21no—
86C4×D61—42no—
87C4×D61—41no—
88C4×D61—41no—
89C4×D61—41no—
90C4×D61—41no—
91Dic122—42no—
92Dic122—41no—
93Dic122—41no—
94Dic122—81no—
95#92420—81no—
96#92420—82no—
97C8×C61—81no—
98#92418—81no—
99#7483—611nomaximal, Sylow
100C22×C61#34211yescharacteristic
101C2×D61—41no—
102C2×D61AΣL(1,𝔽16)11yescharacteristic
103C2×D61#35211yescharacteristic
104#6923—82no—
105C4×C61—21no—
106C4×C61—41no—
107C4×C61—41no—
108C4×C61—41no—
109Dic61—22no—
110Dic61—21no—
111Dic61—41no—
112Dic61—41no—
113C2×#356—611no—
114#1886—611no—
115#1558—611no—
116C2×C61—21no—
117C2×C61#139011yescharacteristic
118D61—21no—
119D61—21no—
120C2×C4⋊Q8—611no—
121#519—611no—
122#432—1221no—
123#419—1221no—
124C2×#101—611no—
125C2×#101—1221no—
126#356—611no—
127#356—1221no—
128#356#692311yescharacteristic, complemented
129#339—1221no—
130#333—612no—
131#333—1221no—
132C61#748311yescharacteristic, complemented, Sylow
133C22×Q8—611no—
134C22×Q8—611no—
135C2×M16—1221no—
136C2×M16—2441no—
137C4⋊Q8—611no—
138C4⋊Q8—611no—
139C4⋊Q8—611no—
140C4⋊Q8—2441no—
141C4⋊Q8C2×#692311yescharacteristic
142C4×Q8—2442no—
143#117—1221no—
144#117—2441no—
145C2×C4⋊C4—2441no—
146C2×C42—611no—
147C4⋊C8—1222no—
148#103—2442no—
149#101—21no—
150#101—1221no—
151#101—2441no—
152#101—2441no—
153C22⋊C8—2441no—
154#97—2441no—
155C2×Q8—611no—
156C2×Q8—611no—
157C2×Q8—1221no—
158C2×Q8—1221no—
159C2×Q8—2441no—
160C2×Q8—2441no—
161C2×Q8—2441no—
162C2×Q8—2441no—
163C2×Q8C4×#692311yescharacteristic
164C2×Q8C22⋊#692311yescharacteristic
165C22×C4—611no—
166C22×C4—1221no—
167C22×C4—1221no—
168C22×C4—1221no—
169M16—41no—
170M16—4881no—
171M16—2441no—
172M16—2441no—
173M16—2441no—
174C2×C8—4881no—
175C2×C8—2442no—
176C2×C8—2441no—
177C4⋊C4—41no—
178C4⋊C4—1222no—
179C4⋊C4—2441no—
180C4⋊C4—2441no—
181C4⋊C4—2441no—
182C4⋊C4—2442no—
183C22⋊C4—2441no—
184C42—611no—
185C42—1221no—
186C42—2441no—
187C42—2442no—
188C42C4⋊#692311yescharacteristic
189C23—611no—
190Q8—41no—
191Q8—41no—
192Q8—4881no—
193Q8—2441no—
194Q8—2441no—
195Q8—2442no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—611no—
200C2×C4—1221no—
201C2×C4—1221no—
202C2×C4—1221no—
203C2×C4—1221no—
204C2×C4—1221no—
205C2×C4—2442no—
206C2×C4—2441no—
207C2×C4—2441no—
208C2×C4—2441no—
209C2×C4—2441no—
210C2×C4—2442no—
211C2×C4(C2×#6923)⋊C411yescharacteristic
212C8—81no—
213C8—4881no—
214C8—4882no—
215C8—4881no—
216C22—611no—
217C22—611no—
218C22—2441no—
219C22#1684063911yescharacteristic
220C4—21no—
221C4—41no—
222C4—41no—
223C4—41no—
224C4—1222no—
225C4—1221no—
226C4—4882no—
227C4—2441no—
228C4—2441no—
229C2—21no—
230C2—1221no—
231C2—1221no—
232C2#2146090211yescharacteristic
subgroupG/H
centerC2#21460902
commutatorC2×Q8×C61C42
FrattiniC4⋊Q8C2×#6923
FittingC61×#356C4
socleC2×C61#1390
prime radicalC22×D61#99
cosocleC4⋊Q8×D61C22
hypercenter#356#6923
hypocenterC61#7483
LCSG ▷ C2×Q8×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C4⋊Q8 ◁ #356

Complements

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

NH ≅ G/Ntype
10. #16840622C4semidirect
13. #16839561C4semidirect
15. C61×#356C4semidirect
128. #356#6923semidirect
132. C61#7483semidirect

Maximal subgroups

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

subgroupindex
#214618252
#214613532
#356×D612
#748361