Finite Group Databasebeta

← #30601739

Subgroups — #30601739

Order 15616.

552 conjugacy classes of subgroups; only the 138 normal subgroups are shown.

normal subgroups only

This group has 552 conjugacy classes of subgroups — too many to draw. Only its 138 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#21461605C211yesmaximal, characteristic
2C4×#14519844C211yesmaximal, characteristic
3C2×Q8⋊#92420C214yesmaximal
4C4⋊Q8×Dic61C211yesmaximal, characteristic
5C2×#14519844—21no—
6C2×C4⋊#92420C2212yes—
7C2×#14519832—21no—
8C2×C4×#92420C2212yes—
9#16840628—21no—
10#16840628—21no—
11Q8⋊#92420—28no—
12C2×Q8×Dic61C2212yes—
13#16839669C412yes—
14#16839661—21no—
15#16839661—21no—
16#16839632C411yescharacteristic
17C4⋊C4×Dic61—21no—
18C4⋊C4×Dic61—21no—
19C42×Dic61C2211yescharacteristic
20C2×C4⋊Q8×C61C411yescharacteristic
21C22×#92420—22no—
22C22×#92420—22no—
23#14519844—24no—
24C4⋊#92420—22no—
25C4⋊#92420D414yes—
26#14519832—42no—
27C4×#92420—24no—
28Q8×Dic61—24no—
29Q8×Dic61—24no—
30C2×C4⋊Dic61—21no—
31C2×C4⋊Dic61—21no—
32C2×C4⋊Dic61—22no—
33C2×C4⋊Dic61C2×C412yes—
34C2×C4×Dic61—22no—
35C2×C4×Dic61C2×C411yescharacteristic
36C2×C4×Dic61D411yescharacteristic
37C2×C4×Dic61D411yescharacteristic
38C2×C4×Dic61D411yescharacteristic
39C2×C4×Dic61D411yescharacteristic
40C2×C4×Dic61C2311yescharacteristic
41#14519684—22no—
42#14519684—22no—
43C22×Q8×C61C2×C412yes—
44C4⋊Q8×C61—24no—
45C2×C4⋊C4×C61—21no—
46C2×C4⋊C4×C61—21no—
47C2×C42×C61C2×C411yescharacteristic
48C2×Q8×C61—22no—
49C2×Q8×C61—24no—
50C2×Q8×C61—24no—
51C2×Q8×C61M1614yes—
52C22×C4×C61—22no—
53C22×C4×C61C22⋊C411yescharacteristic
54C22×C4×C61C22⋊C411yescharacteristic
55C22×C4×C61C22×C411yescharacteristic
56C22×Dic61—22no—
57C22×Dic61C22⋊C411yescharacteristic
58C22×Dic61C22⋊C411yescharacteristic
59C22×Dic61C2×D411yescharacteristic
60C22×Dic61C2×D411yescharacteristic
61C2×#92420—24no—
62C2×#92420—24no—
63C2×#92420—42no—
64C2×#92420—42no—
65C2×#92420—42no—
66C2×#92420—42no—
67C4⋊C4×C61—24no—
68C4⋊C4×C61—24no—
69C42×C61—22no—
70C4⋊Dic61—24no—
71C4⋊Dic61—42no—
72C4⋊Dic61—42no—
73C4⋊Dic61—42no—
74C4⋊Dic61—42no—
75C4×Dic61—22no—
76C4×Dic61—22no—
77C4×Dic61—22no—
78C4×Dic61—41no—
79C4×Dic61—44no—
80C4×Dic61SD1612yes—
81C4×Dic61Q1612yes—
82C4×Dic61C2×D412yes—
83C4×Dic61#4112yes—
84C23×C61C2×C22⋊C411yescharacteristic
85Q8×C61—28no—
86Q8×C61—44no—
87C2×C4×C61—21no—
88C2×C4×C61—21no—
89C2×C4×C61—21no—
90C2×C4×C61—21no—
91C2×C4×C61—24no—
92C2×C4×C61—42no—
93C2×C4×C61—42no—
94C2×C4×C61#10312yes—
95C2×C4×C61#10412yes—
96C2×C4×C61C4×D412yes—
97C2×C4×C61C2×M1612yes—
98C2×C4×C61#13112yes—
99C2×Dic61—21no—
100C2×Dic61—21no—
101C2×Dic61—21no—
102C2×Dic61—21no—
103C2×Dic61—21no—
104C2×Dic61—21no—
105C2×Dic61—21no—
106C2×Dic61—42no—
107C2×Dic61—42no—
108C2×Dic61—42no—
109C2×Dic61#10312yes—
110C2×Dic61#12112yes—
111C2×Dic61#12411yescharacteristic
112C2×Dic61#12711yescharacteristic
113C2×Dic61C2×SD1611yescharacteristic
114C2×Dic61C2×Q1611yescharacteristic
115C2×Dic61#13712yes—
116#92420—44no—
117#92420—44no—
118#9677—611nomaximal, Sylow
119C22×C61#39011yescharacteristic
120C22×C61#40711yescharacteristic
121C22×C61#40811yescharacteristic
122C22×C61C2×#10311yescharacteristic
123C22×C61#41911yescharacteristic
124C22×C61C2×#10411yescharacteristic
125C22×C61#42111yescharacteristic
126C4×C61—22no—
127C4×C61—22no—
128C4×C61—44no—
129C4×C61#43514yes—
130Dic61—21no—
131Dic61—21no—
132Dic61—22no—
133Dic61—41no—
134Dic61—82no—
135Dic61#46112yes—
136Dic61#46212yes—
137C4×C4⋊Q8—611no—
138#1767—611no—
139C4×C4⋊C8—611no—
140C2×Q8⋊C8—614no—
141C2×C61#148711yescharacteristic
142C2×C61#149111yescharacteristic
143C2×C61#149311yescharacteristic
144C2×C61#149711yescharacteristic
145C2×C61#195511yescharacteristic
146C2×C61#198011yescharacteristic
147C2×C61#198111yescharacteristic
148C2×C4⋊Q8#692311yescharacteristic
149C2×C4×Q8—612no—
150C2×C4⋊C8—612no—
151C2×C4⋊C8—1221no—
152C2×#97—1221no—
153C2×C4×C8—612no—
154#391—612no—
155#389—1221no—
156#389—1221no—
157#384—611no—
158C4×C4⋊C4—1221no—
159C4×C4⋊C4—1221no—
160C43—611no—
161#336—1221no—
162#336—1221no—
163Q8⋊C8—1228no—
164C61#967711yescharacteristic, complemented, Sylow
165C22×Q8C2×#692312yes—
166C22×C8—1222no—
167C22×C8—1222no—
168C4⋊Q8—24no—
169C4×Q8—1224no—
170C4×Q8—1224no—
171C2×C4⋊C4—21no—
172C2×C4⋊C4—21no—
173C2×C4⋊C4—612no—
174C2×C4⋊C4—1222no—
175C2×C4⋊C4—1221no—
176C2×C4⋊C4—1221no—
177C2×C42—611no—
178C2×C42—611no—
179C2×C42—611no—
180C2×C42—611no—
181C2×C42—611no—
182C2×C42—611no—
183C2×C42—1222no—
184C2×C42C2×#692311yescharacteristic
185C4⋊C8—614no—
186C4⋊C8—1222no—
187C4⋊C8—1224no—
188#97—2442no—
189C4×C8—1224no—
190#95—1222no—
191#95—1222no—
192C2×Q8—22no—
193C2×Q8—24no—
194C2×Q8—24no—
195C2×Q8#1175821714yes—
196C22×C4—22no—
197C22×C4—611no—
198C22×C4—611no—
199C22×C4—611no—
200C22×C4—611no—
201C22×C4—1222no—
202C22×C4C22⋊#692311yescharacteristic
203C22×C4C22⋊#692311yescharacteristic
204C22×C4C22×#692311yescharacteristic
205C2×C8—1224no—
206C2×C8—1224no—
207C2×C8—2442no—
208C2×C8—2442no—
209C2×C8—2442no—
210C2×C8—2442no—
211C4⋊C4—24no—
212C4⋊C4—24no—
213C4⋊C4—1224no—
214C4⋊C4—2442no—
215C4⋊C4—2442no—
216C4⋊C4—2442no—
217C4⋊C4—2442no—
218C42—22no—
219C42—612no—
220C42—612no—
221C42—612no—
222C42—612no—
223C42—1222no—
224C42—1222no—
225C42—1222no—
226C42—2441no—
227C42—2444no—
228C23C2×C22⋊#692311yescharacteristic
229Q8—28no—
230Q8—44no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—24no—
236C2×C4—42no—
237C2×C4—42no—
238C2×C4—612no—
239C2×C4—611no—
240C2×C4—611no—
241C2×C4—612no—
242C2×C4—611no—
243C2×C4—611no—
244C2×C4—612no—
245C2×C4—1221no—
246C2×C4—1221no—
247C2×C4—1221no—
248C2×C4—1221no—
249C2×C4—1221no—
250C2×C4—1221no—
251C2×C4—1221no—
252C2×C4—2442no—
253C2×C4—2442no—
254C2×C4—2442no—
255C2×C4#1451984012yes—
256C2×C4#1451984212yes—
257C2×C4D4×#692312yes—
258C2×C4C2×#1175821712yes—
259C2×C4#1451986412yes—
260C8—2444no—
261C8—2444no—
262C22#1684071411yescharacteristic
263C22#1684073211yescharacteristic
264C22#1684073611yescharacteristic
265C22C2×#1451984011yescharacteristic
266C22#1684075511yescharacteristic
267C22C2×#1451984211yescharacteristic
268C22#1684076111yescharacteristic
269C4—22no—
270C4—22no—
271C4—44no—
272C4—612no—
273C4—612no—
274C4—1222no—
275C4—1221no—
276C4—1221no—
277C4—4882no—
278C4—2441no—
279C4#1684079314yes—
280C2#2146114711yescharacteristic
281C2#2146116111yescharacteristic
282C2#2146116811yescharacteristic
283C2#2146118211yescharacteristic
284C2#2146194311yescharacteristic
285C2#2146198211yescharacteristic
286C2#2146198511yescharacteristic
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#9677
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
164. C61#9677semidirect

Maximal subgroups

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

subgroupindex
#214616052
C4×#145198442
C2×Q8⋊#924202
C4⋊Q8×Dic612
#967761