Finite Group Databasebeta

← #30595165

Subgroups — #30595165

Order 15616.

276 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 276 conjugacy classes of subgroups — too many to draw. Only its 44 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
2D61⋊#333C211yesmaximal, characteristic
3#356×D61C211yesmaximal, characteristic
4#16840830C411yescharacteristic
5D61⋊(C4⋊C8)—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—
17C2×D61⋊C8—41no—
18Q8×#6923—42no—
19#14519856—21no—
20#14519856—41no—
21#14519844—22no—
22C4⋊#92420—41no—
23#14519840—42no—
24#14519838—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—
61D61⋊C8—82no—
62M16×C61—41no—
63C4⋊C4×C61—41no—
64C42×C61C4⋊C411yescharacteristic
65C4⋊Dic61—41no—
66#11758196—41no—
67#11758196—41no—
68C4×Dic61—21no—
69C4×Dic61C22⋊C411yescharacteristic
70#11758194—41no—
71#11758189—81no—
72C8×D61—81no—
73C22×D61#9911yescharacteristic
74C2×#6923—42no—
75Q8×C61—41no—
76Q8×C61—41no—
77C2×C4×C61—21no—
78C2×C4×C61—21no—
79C2×C4×C61—21no—
80C2×C4×C61#9511yescharacteristic
81C2×Dic61—21no—
82C2×Dic61—21no—
83C2×Dic61—21no—
84C2×Dic61#9911yescharacteristic
85C4×D61—22no—
86C4×D61—22no—
87C4×D61—21no—
88C4×D61—21no—
89C4×D61—41no—
90C4×D61—41no—
91C4×D61—41no—
92C4×D61—41no—
93Dic122—42no—
94Dic122—41no—
95Dic122—41no—
96Dic122—81no—
97#92420—81no—
98#92420—82no—
99C8×C61—81no—
100#92418—81no—
101#7491—611nomaximal, Sylow
102C22×C61#34211yescharacteristic
103C2×D61—22no—
104C2×D61AΣL(1,𝔽16)11yescharacteristic
105C2×D61#35211yescharacteristic
106#6923—82no—
107C4×C61—22no—
108C4×C61—21no—
109C4×C61—41no—
110C4×C61—41no—
111Dic61—21no—
112Dic61—21no—
113Dic61—21no—
114Dic61—41no—
115Dic61—41no—
116C2×#356—611no—
117#1886—611no—
118C2×#333—611no—
119C2×C61—21no—
120C2×C61#139011yescharacteristic
121D61—21no—
122D61#140512yes—
123C2×C4⋊Q8—611no—
124#519—611no—
125C2×C4⋊C8—1221no—
126#419—1221no—
127C2×#101—611no—
128C2×#101—1221no—
129#356—611no—
130#356—1221no—
131#356#692311yescharacteristic, complemented
132#339—1221no—
133#333—612no—
134#333—1221no—
135C61#749111yescharacteristic, complemented, Sylow
136C22×Q8—611no—
137C22×Q8—611no—
138C2×M16—1221no—
139C2×M16—2441no—
140C22×C8—2441no—
141C4⋊Q8—611no—
142C4⋊Q8—611no—
143C4⋊Q8—611no—
144C4⋊Q8—2441no—
145C4⋊Q8C2×#692311yescharacteristic
146C4×Q8—2442no—
147#117—1221no—
148#117—2441no—
149C2×C4⋊C4—2441no—
150C2×C42—611no—
151C4⋊C8—1222no—
152C4⋊C8—2441no—
153#103—2442no—
154#101—21no—
155#101—1221no—
156#101—2441no—
157#101—2441no—
158C2×Q8—611no—
159C2×Q8—611no—
160C2×Q8—1221no—
161C2×Q8—1221no—
162C2×Q8—2441no—
163C2×Q8—2441no—
164C2×Q8—2441no—
165C2×Q8—2441no—
166C2×Q8C4×#692311yescharacteristic
167C2×Q8C22⋊#692311yescharacteristic
168C22×C4—611no—
169C22×C4—1221no—
170C22×C4—1221no—
171C22×C4—1221no—
172M16—41no—
173M16—4881no—
174M16—2441no—
175M16—2441no—
176M16—2441no—
177C2×C8—4881no—
178C2×C8—4882no—
179C2×C8—2441no—
180C2×C8—2442no—
181C4⋊C4—41no—
182C4⋊C4—1222no—
183C4⋊C4—2441no—
184C4⋊C4—2441no—
185C4⋊C4—2441no—
186C4⋊C4—2442no—
187C22⋊C4—2441no—
188C42—611no—
189C42—1221no—
190C42—2441no—
191C42—2442no—
192C42C4⋊#692311yescharacteristic
193C23—611no—
194Q8—41no—
195Q8—41no—
196Q8—4881no—
197Q8—2441no—
198Q8—2441no—
199Q8—2442no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—611no—
204C2×C4—1221no—
205C2×C4—1221no—
206C2×C4—1222no—
207C2×C4—1222no—
208C2×C4—1221no—
209C2×C4—1221no—
210C2×C4—1221no—
211C2×C4—2441no—
212C2×C4—2441no—
213C2×C4—2441no—
214C2×C4—2441no—
215C2×C4—2442no—
216C2×C4(C2×#6923)⋊C411yescharacteristic
217C8—81no—
218C8—4881no—
219C8—4882no—
220C8—4881no—
221C22—611no—
222C22—611no—
223C22—1222no—
224C22#1684063911yescharacteristic
225C4—22no—
226C4—21no—
227C4—41no—
228C4—41no—
229C4—1221no—
230C4—1221no—
231C4—1221no—
232C4—4882no—
233C4—2441no—
234C4—2441no—
235C2—21no—
236C2—612no—
237C2—1221no—
238C2#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#7491
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
131. #356#6923semidirect
135. C61#7491semidirect

Maximal subgroups

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

subgroupindex
#214618252
D61⋊#3332
#356×D612
#749161