Finite Group Databasebeta

← #30594436

Subgroups — #30594436

Order 15616.

290 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 52 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#21461716C211yesmaximal, characteristic
2#21461072C211yesmaximal, characteristic
3#21445588C211yesmaximal, characteristic
4#16840782—21no—
5#16840705—21no—
6#16840640—21no—
7#16840640C412yes—
8#16840608C412yescomplemented
9#16840606—21no—
10C2×#14519734C2211yescharacteristic
11C2×#14519689—21no—
12C2×C4×#92418C411yescharacteristic, complemented
13#16839516—21no—
14C2×#97×C61C411yescharacteristic, complemented
15C2×C22⋊#6923—22no—
16#14519844—41no—
17C22⋊#92420—22no—
18#14519832—41no—
19(C2×#6923)⋊C4—41no—
20(C2×#6923)⋊C4—41no—
21C22×C4×D61D411yescharacteristic
22C22×#92418—21no—
23#14519734—41no—
24#14519734—41no—
25C2×#11758196C2×C411yescharacteristic
26C2×#11758196Q811yescharacteristic
27C2×#11758198C2×C411yescharacteristic
28C2×#11758198D411yescharacteristic
29C2×C4×Dic61D411yescharacteristic
30#14519689—24no—
31C4×#92418—41no—
32C22×C8×C61—21no—
33C2×C42×C61C2×C411yescharacteristic
34#97×C61—41no—
35C23×D61C22⋊C411yescharacteristic
36C22×#6923—42no—
37C22×C4×C61C4211yescharacteristic
38C22×C4×C61C22⋊C411yescharacteristic
39C22×C4×C61C4⋊C411yescharacteristic
40C22×Dic61C22⋊C411yescharacteristic
41C22×Dic61C4⋊C411yescharacteristic
42C22×Dic61C4⋊C411yescharacteristic
43C2×C4×D61—22no—
44C2×C4×D61—21no—
45C2×C4×D61—21no—
46C2×C4×D61—41no—
47C22⋊#6923—42no—
48C22⋊#6923—42no—
49C2×#92420—42no—
50C2×C8×C61—22no—
51C2×C8×C61—41no—
52C2×C8×C61—41no—
53C42×C61—21no—
54C42×C61—21no—
55#11758198—41no—
56#11758198—41no—
57#11758196—41no—
58#11758196—41no—
59C4×Dic61—21no—
60C4×Dic61—21no—
61C2×#92418—22no—
62C2×#92418—41no—
63C2×#92418—41no—
64C23×C61#9511yescharacteristic
65C22×D61—21no—
66C22×D61—21no—
67C22×D61—41no—
68C22×D61—41no—
69C22×D61#10412yes—
70C2×#6923—82no—
71C2×#6923—82no—
72C2×#6923—82no—
73C2×C4×C61—21no—
74C2×C4×C61—21no—
75C2×C4×C61—21no—
76C2×C4×C61—21no—
77C2×C4×C61—41no—
78C2×C4×C61—41no—
79C2×C4×C61#9911yescharacteristic
80C2×C4×C61#9911yescharacteristic
81C2×Dic61—21no—
82C2×Dic61—21no—
83C2×Dic61—21no—
84C2×Dic61—21no—
85C2×Dic61—21no—
86C2×Dic61—41no—
87C2×Dic61—41no—
88C4×D61—42no—
89C4×D61—42no—
90#92420—82no—
91C8×C61—42no—
92#92418—42no—
93#7214—611nomaximal, Sylow
94C22×C61—21no—
95C22×C61—21no—
96C22×C61H(3,ℤ/4)11yescharacteristic
97C22×C61#33911yescharacteristic
98C22×C61#34211yescharacteristic
99C2×D61—22no—
100C2×D61—41no—
101C2×D61—41no—
102C2×D61—42no—
103C2×D61—81no—
104#6923—162no—
105C4×C61—21no—
106C4×C61—21no—
107C4×C61—41no—
108C4×C61—41no—
109Dic61—41no—
110Dic61—41no—
111Dic61—41no—
112#1820—611no—
113#1750—611no—
114#1464—611no—
115C2×C61—21no—
116C2×C61—21no—
117C2×C61#128411yescharacteristic
118C2×C61#139111yescharacteristic
119C2×C61#139511yescharacteristic
120D61—42no—
121C2×#117—611no—
122#432—1221no—
123C2×C22⋊C8—1221no—
124C2×#97#692311yescharacteristic, complemented
125C2×C4×C8—611no—
126#381—1221no—
127#342—612no—
128#342—1221no—
129#336—1221no—
130#324—612no—
131#323—1221no—
132C61#721411yescharacteristic, complemented, Sylow
133C23×C4—611no—
134C22×C8—21no—
135C22×C8—1221no—
136#117—2441no—
137#117—2441no—
138C2×C4⋊C4—611no—
139C2×C4⋊C4—611no—
140C2×C22⋊C4—611no—
141C2×C22⋊C4—611no—
142C2×C22⋊C4—1222no—
143C2×C42—611no—
144C2×C42C2×#692311yescharacteristic
145C4⋊C8—2441no—
146C22⋊C8—1224no—
147C22⋊C8—1222no—
148#97—41no—
149#97—2441no—
150C4×C8—2441no—
151#95—2441no—
152#95—2441no—
153C24—611no—
154C22×C4—611no—
155C22×C4—611no—
156C22×C4—611no—
157C22×C4—1222no—
158C22×C4—1221no—
159C22×C4—1221no—
160C22×C4—2441no—
161C22×C4—2442no—
162C22×C4C4×#692311yescharacteristic
163C22×C4C4⋊#692311yescharacteristic
164C22×C4C22⋊#692311yescharacteristic
165C2×C8—22no—
166C2×C8—41no—
167C2×C8—41no—
168C2×C8—1222no—
169C2×C8—2442no—
170C2×C8—2441no—
171C2×C8—2441no—
172C4⋊C4—2441no—
173C4⋊C4—2441no—
174C22⋊C4—2441no—
175C22⋊C4—2441no—
176C22⋊C4—2442no—
177C22⋊C4—2442no—
178C42—21no—
179C42—21no—
180C42—1221no—
181C42—1221no—
182C23—612no—
183C23—1221no—
184C23—1221no—
185C23—2441no—
186C23—2441no—
187C23(C2×#6923)⋊C411yescharacteristic
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—21no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—1221no—
195C2×C4—1221no—
196C2×C4—1221no—
197C2×C4—1221no—
198C2×C4—1221no—
199C2×C4—4882no—
200C2×C4—4882no—
201C2×C4—4882no—
202C2×C4—2442no—
203C2×C4—2442no—
204C2×C4—2441no—
205C2×C4—2441no—
206C2×C4#1451983511yescharacteristic
207C2×C4#1451983611yescharacteristic
208C8—42no—
209C8—4882no—
210C8—2442no—
211C22—21no—
212C22—21no—
213C22—1222no—
214C22—4881no—
215C22—2442no—
216C22—2441no—
217C22—2441no—
218C22#1684062911yescharacteristic
219C22#1684063311yescharacteristic
220C22#1684064011yescharacteristic
221C4—21no—
222C4—21no—
223C4—41no—
224C4—41no—
225C4—9762no—
226C4—2441no—
227C4—2441no—
228C4—2441no—
229C2—21no—
230C2—21no—
231C2—2442no—
232C2#2146066711yescharacteristic
233C2#2146090811yescharacteristic
234C2#2146092011yescharacteristic
subgroupG/H
centerC22#16840640
commutatorC22×C4×C61C42
FrattiniC2×C42C2×#6923
FittingC2×#97×C61C4
socleC22×C61#342
prime radicalC23×D61C22⋊C4
cosocleC2×#14519734C22
hypercenterC2×#97#6923
hypocenterC61#7214
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42 ◁ C2×#97

Complements

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

NH ≅ G/Ntype
8. #16840608C4semidirect
12. C2×C4×#92418C4semidirect
14. C2×#97×C61C4semidirect
124. C2×#97#6923semidirect
132. C61#7214semidirect

Maximal subgroups

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

subgroupindex
#214617162
#214610722
#214455882
#721461