Finite Group Databasebeta

← #30602164

Subgroups — #30602164

Order 15616.

518 conjugacy classes of subgroups; only the 132 normal subgroups are shown.

normal subgroups only

This group has 518 conjugacy classes of subgroups — too many to draw. Only its 132 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#21461736C211yesmaximal, characteristic
2C4×#14519832C211yesmaximal, characteristic
3#21460655C214yesmaximal
4C4⋊Q8×Dic61C211yesmaximal, characteristic
5C2×C4⋊#92420C2212yes—
6C2×#14519832—21no—
7C2×#14519832—21no—
8C2×C4×#92420C2212yes—
9#16840628—21no—
10#16840628—21no—
11C2×Q8×Dic61—21no—
12#16839669—21no—
13#16839661—21no—
14#16839661C412yes—
15#16839632C411yescharacteristic
16C4⋊C4×Dic61—21no—
17C4⋊C4×Dic61C2212yes—
18C42×Dic61C2211yescharacteristic
19C2×C4⋊Q8×C61C411yescharacteristic
20C22×#92420—22no—
21C22×#92420—22no—
22C4⋊#92420—24no—
23#14519832—24no—
24#14519832—24no—
25C4×#92420—22no—
26C4×#92420Q814yescomplemented
27Q8×Dic61—44no—
28C2×C4⋊Dic61—21no—
29C2×C4⋊Dic61—21no—
30C2×C4⋊Dic61—22no—
31C2×C4⋊Dic61C2×C412yes—
32C2×C4×Dic61—22no—
33C2×C4×Dic61C2×C411yescharacteristic
34C2×C4×Dic61D411yescharacteristic
35C2×C4×Dic61D411yescharacteristic
36C2×C4×Dic61D411yescharacteristic
37C2×C4×Dic61D411yescharacteristic
38C2×C4×Dic61C2311yescharacteristic
39#14519684—22no—
40#14519684—22no—
41C22×Q8×C61—21no—
42C4⋊Q8×C61—24no—
43C2×C4⋊C4×C61—21no—
44C2×C4⋊C4×C61C2×C412yes—
45C2×C42×C61C2×C411yescharacteristic
46C2×Q8×C61—24no—
47C2×Q8×C61—42no—
48C2×Q8×C61—42no—
49C22×C4×C61—22no—
50C22×C4×C61C22⋊C411yescharacteristic
51C22×C4×C61C22⋊C411yescharacteristic
52C22×C4×C61C22×C411yescharacteristic
53C22×Dic61—22no—
54C22×Dic61C22⋊C411yescharacteristic
55C22×Dic61C22⋊C411yescharacteristic
56C22×Dic61C2×D411yescharacteristic
57C22×Dic61C2×D411yescharacteristic
58C2×#92420—24no—
59C2×#92420—24no—
60C2×#92420—24no—
61C2×#92420—42no—
62C2×#92420—42no—
63C2×#92420—42no—
64C4⋊C4×C61—24no—
65C4⋊C4×C61—22no—
66C4⋊C4×C61M1614yes—
67C42×C61—22no—
68C4⋊Dic61—24no—
69C4⋊Dic61—44no—
70C4⋊Dic61—42no—
71C4⋊Dic61—42no—
72C4×Dic61—22no—
73C4×Dic61—22no—
74C4×Dic61—22no—
75C4×Dic61—22no—
76C4×Dic61—22no—
77C4×Dic61—44no—
78C4×Dic61C2×Q812yes—
79C4×Dic61#4112yes—
80C23×C61C2×C22⋊C411yescharacteristic
81Q8×C61—48no—
82C2×C4×C61—21no—
83C2×C4×C61—21no—
84C2×C4×C61—21no—
85C2×C4×C61—21no—
86C2×C4×C61—24no—
87C2×C4×C61—42no—
88C2×C4×C61—42no—
89C2×C4×C61#10412yes—
90C2×C4×C61#10412yes—
91C2×C4×C61C4×Q812yes—
92C2×C4×C61C2×M1612yes—
93C2×C4×C61#13112yes—
94C2×Dic61—21no—
95C2×Dic61—21no—
96C2×Dic61—21no—
97C2×Dic61—21no—
98C2×Dic61—21no—
99C2×Dic61—21no—
100C2×Dic61—21no—
101C2×Dic61—21no—
102C2×Dic61—42no—
103C2×Dic61—42no—
104C2×Dic61—42no—
105C2×Dic61C22⋊Q812yes—
106C2×Dic61#12411yescharacteristic
107C2×Dic61C4⋊Q811yescharacteristic
108C2×Dic61AGL(1,ℤ/8)12yes—
109C2×Dic61#13712yes—
110#92420—28no—
111#92420—82no—
112#9877—611nomaximal, Sylow
113C22×C61#39111yescharacteristic
114C22×C61#40711yescharacteristic
115C22×C61#40811yescharacteristic
116C22×C61#41811yescharacteristic
117C22×C61#41911yescharacteristic
118C22×C61C2×#10411yescharacteristic
119C22×C61C2×#10411yescharacteristic
120C4×C61—22no—
121C4×C61—22no—
122C4×C61—44no—
123C4×C61#44614yes—
124Dic61—22no—
125Dic61—41no—
126Dic61—41no—
127Dic61—82no—
128Dic61#48912yes—
129Dic61#50112yes—
130C4×C4⋊Q8—611no—
131#1831—611no—
132C4×#97—611no—
133#1279—614no—
134C2×C61#148411yescharacteristic
135C2×C61#148511yescharacteristic
136C2×C61#149011yescharacteristic
137C2×C61#149111yescharacteristic
138C2×C61#198511yescharacteristic
139C2×C61#199311yescharacteristic
140C2×C61#199411yescharacteristic
141C2×C4⋊Q8#692311yescharacteristic
142C2×C4×Q8—1221no—
143C2×C4⋊C8—612no—
144C2×#97—1221no—
145C2×#97—1221no—
146C2×C4×C8—612no—
147#391—1221no—
148#389—612no—
149#389—1221no—
150#384—611no—
151C4×C4⋊C4—612no—
152C4×C4⋊C4—1221no—
153C43—611no—
154#336—1221no—
155#336—1221no—
156C61#987711yescharacteristic, complemented, Sylow
157C22×Q8—21no—
158C22×C8—1222no—
159C22×C8—1222no—
160C4⋊Q8—24no—
161C4×Q8—2444no—
162C2×C4⋊C4—21no—
163C2×C4⋊C4—612no—
164C2×C4⋊C4—1222no—
165C2×C4⋊C4—1221no—
166C2×C4⋊C4—1221no—
167C2×C4⋊C4C2×#692312yes—
168C2×C42—611no—
169C2×C42—611no—
170C2×C42—611no—
171C2×C42—611no—
172C2×C42—611no—
173C2×C42—611no—
174C2×C42—1222no—
175C2×C42C2×#692311yescharacteristic
176C4⋊C8—1224no—
177#97—1224no—
178#97—1224no—
179C4×C8—614no—
180C4×C8—1222no—
181#95—1222no—
182#95—1222no—
183C2×Q8—24no—
184C2×Q8—42no—
185C2×Q8—42no—
186C22×C4—22no—
187C22×C4—611no—
188C22×C4—611no—
189C22×C4—611no—
190C22×C4—611no—
191C22×C4—1222no—
192C22×C4C22⋊#692311yescharacteristic
193C22×C4C22⋊#692311yescharacteristic
194C22×C4C22×#692311yescharacteristic
195C2×C8—1224no—
196C2×C8—1224no—
197C2×C8—1224no—
198C2×C8—2442no—
199C2×C8—2442no—
200C2×C8—2442no—
201C4⋊C4—24no—
202C4⋊C4—22no—
203C4⋊C4—1224no—
204C4⋊C4—2442no—
205C4⋊C4—2444no—
206C4⋊C4—2442no—
207C4⋊C4#1175821714yes—
208C42—22no—
209C42—612no—
210C42—612no—
211C42—1222no—
212C42—1222no—
213C42—1222no—
214C42—1222no—
215C42—1222no—
216C42—2444no—
217C23C2×C22⋊#692311yescharacteristic
218Q8—48no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—24no—
224C2×C4—42no—
225C2×C4—42no—
226C2×C4—611no—
227C2×C4—611no—
228C2×C4—612no—
229C2×C4—612no—
230C2×C4—612no—
231C2×C4—1221no—
232C2×C4—1221no—
233C2×C4—1221no—
234C2×C4—1221no—
235C2×C4—1221no—
236C2×C4—1221no—
237C2×C4—1221no—
238C2×C4—1221no—
239C2×C4—2442no—
240C2×C4—2442no—
241C2×C4—2442no—
242C2×C4#1451984112yes—
243C2×C4#1451984212yes—
244C2×C4Q8×#692312yes—
245C2×C4C2×#1175821712yes—
246C2×C4#1451986512yes—
247C8—1228no—
248C8—4882no—
249C22(C2×#6923)⋊Q811yescharacteristic
250C22#1684073211yescharacteristic
251C22#1684073711yescharacteristic
252C22#1684075411yescharacteristic
253C22#1684075511yescharacteristic
254C22C2×#1451984111yescharacteristic
255C22C2×#1451984211yescharacteristic
256C4—22no—
257C4—22no—
258C4—44no—
259C4—612no—
260C4—612no—
261C4—1222no—
262C4—4882no—
263C4—2441no—
264C4—2441no—
265C4#1684081314yes—
266C2#2146114011yescharacteristic
267C2#2146114311yescharacteristic
268C2#2146115811yescharacteristic
269C2#2146116111yescharacteristic
270C2#2146199311yescharacteristic
271C2#2146200311yescharacteristic
272C2#2146200411yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC2×C4⋊Q8×C61C4
socle, prime radicalC23×C61C2×C22⋊C4
cosocleC2×C4×Dic61C23
hypercenterC2×C4⋊Q8#6923
hypocenterC61#9877
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
26. C4×#92420Q8semidirect
156. C61#9877semidirect

Maximal subgroups

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

subgroupindex
#214617362
C4×#145198322
#214606552
C4⋊Q8×Dic612
#987761