Finite Group Databasebeta

← #30595563

Subgroups — #30595563

Order 15616.

462 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 108 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#21461747C211yesmaximal, characteristic
2#21461604C211yesmaximal, characteristic
3#21460637C214yesmaximal
4C4⋊Q8×Dic61C211yesmaximal, characteristic
5C2×#14519844—21no—
6C2×#14519832—21no—
7#16840628—21no—
8#16840628—21no—
9#16840628C2212yes—
10#16840628C2212yes—
11C2×Q8×Dic61—21no—
12#16839669—21no—
13#16839661—21no—
14#16839661C2212yes—
15#16839632C411yescharacteristic
16C4⋊C4×Dic61—21no—
17C4⋊C4×Dic61C412yes—
18C42×Dic61C2211yescharacteristic
19C2×C4⋊Q8×C61C411yescharacteristic
20C22×#92420—22no—
21C22×#92420—22no—
22#14519844—24no—
23#14519832—42no—
24Q8×Dic61—42no—
25Q8×Dic61—42no—
26C2×C4⋊Dic61—21no—
27C2×C4⋊Dic61—21no—
28C2×C4⋊Dic61—22no—
29C2×C4⋊Dic61C2×C412yes—
30C2×C4×Dic61—22no—
31C2×C4×Dic61C2×C411yescharacteristic
32C2×C4×Dic61D411yescharacteristic
33C2×C4×Dic61D411yescharacteristic
34C2×C4×Dic61D411yescharacteristic
35C2×C4×Dic61D411yescharacteristic
36C2×C4×Dic61C2311yescharacteristic
37#14519684—22no—
38#14519684—22no—
39C22×Q8×C61—21no—
40C4⋊Q8×C61—24no—
41C2×C4⋊C4×C61—21no—
42C2×C4⋊C4×C61C2×C412yes—
43C2×C42×C61C2×C411yescharacteristic
44C2×Q8×C61—24no—
45C2×Q8×C61—42no—
46C2×Q8×C61—42no—
47C22×C4×C61—22no—
48C22×C4×C61C22⋊C411yescharacteristic
49C22×C4×C61C22⋊C411yescharacteristic
50C22×C4×C61C22×C411yescharacteristic
51C22×Dic61—22no—
52C22×Dic61C22⋊C411yescharacteristic
53C22×Dic61C22⋊C411yescharacteristic
54C22×Dic61C2×D411yescharacteristic
55C22×Dic61C2×D411yescharacteristic
56C2×#92420—24no—
57C2×#92420—42no—
58C2×#92420—42no—
59C2×#92420—42no—
60C2×#92420—42no—
61C2×#92420—42no—
62C4⋊C4×C61—24no—
63C4⋊C4×C61—22no—
64C4⋊C4×C61M1614yes—
65C42×C61—22no—
66C4⋊Dic61—42no—
67C4⋊Dic61—42no—
68C4⋊Dic61—42no—
69C4⋊Dic61—42no—
70C4⋊Dic61—42no—
71C4×Dic61—22no—
72C4×Dic61—22no—
73C4×Dic61—22no—
74C4×Dic61—41no—
75C4×Dic61—41no—
76C4×Dic61—44no—
77C4×Dic61D812yes—
78C4×Dic61SD1612yes—
79C23×C61C2×C22⋊C411yescharacteristic
80Q8×C61—48no—
81C2×C4×C61—21no—
82C2×C4×C61—21no—
83C2×C4×C61—21no—
84C2×C4×C61—21no—
85C2×C4×C61—21no—
86C2×C4×C61—21no—
87C2×C4×C61—24no—
88C2×C4×C61—42no—
89C2×C4×C61—42no—
90C2×C4×C61#10212yes—
91C2×C4×C61#10412yes—
92C2×C4×C61C2×M1612yes—
93C2×Dic61—21no—
94C2×Dic61—21no—
95C2×Dic61—21no—
96C2×Dic61—21no—
97C2×Dic61—21no—
98C2×Dic61—21no—
99C2×Dic61—21no—
100C2×Dic61—21no—
101C2×Dic61—42no—
102C2×Dic61—42no—
103C2×Dic61—42no—
104C2×Dic61#10112yes—
105C2×Dic61#10212yes—
106C2×Dic61C2×D811yescharacteristic
107C2×Dic61C2×SD1611yescharacteristic
108C2×Dic61#13712yes—
109#92420—44no—
110#92420—82no—
111#7625—611nomaximal, Sylow
112C22×C61#40711yescharacteristic
113C22×C61#41011yescharacteristic
114C22×C61C2×#10111yescharacteristic
115C22×C61C2×#10211yescharacteristic
116C22×C61#41911yescharacteristic
117C22×C61C2×#10411yescharacteristic
118C22×C61#42111yescharacteristic
119C4×C61—22no—
120C4×C61—22no—
121C4×C61—22no—
122C4×C61—44no—
123Dic61—22no—
124Dic61—21no—
125Dic61—21no—
126Dic61—22no—
127Dic61—22no—
128Dic61—82no—
129C4×C4⋊Q8—611no—
130#1839—611no—
131#1767—611no—
132#1271—614no—
133C2×C61#146711yescharacteristic
134C2×C61#148611yescharacteristic
135C2×C61#149111yescharacteristic
136C2×C61#150211yescharacteristic
137C2×C61#151511yescharacteristic
138C2×C61#153111yescharacteristic
139C2×C61#154611yescharacteristic
140C2×C4⋊Q8#692311yescharacteristic
141C2×C4×Q8—1221no—
142C2×C4⋊C8—1221no—
143C2×#97—1221no—
144#391—1221no—
145#389—612no—
146#389—1221no—
147#384—611no—
148C4×C4⋊C4—612no—
149C4×C4⋊C4—1221no—
150C43—611no—
151#336—612no—
152#336—612no—
153#336—1221no—
154#336—1221no—
155C61#762511yescharacteristic, complemented, Sylow
156C22×Q8—21no—
157C22×C8—1222no—
158C22×C8—1222no—
159C4⋊Q8—24no—
160C4×Q8—2442no—
161C4×Q8—2442no—
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—2442no—
178#95—1222no—
179#95—1222no—
180C2×Q8—24no—
181C2×Q8—42no—
182C2×Q8—42no—
183C22×C4—22no—
184C22×C4—611no—
185C22×C4—611no—
186C22×C4—611no—
187C22×C4—611no—
188C22×C4—1222no—
189C22×C4C22⋊#692311yescharacteristic
190C22×C4C22⋊#692311yescharacteristic
191C22×C4C22×#692311yescharacteristic
192C2×C8—1224no—
193C2×C8—2442no—
194C2×C8—2442no—
195C2×C8—2442no—
196C2×C8—2442no—
197C2×C8—2442no—
198C4⋊C4—24no—
199C4⋊C4—22no—
200C4⋊C4—2442no—
201C4⋊C4—2442no—
202C4⋊C4—2442no—
203C4⋊C4—2442no—
204C4⋊C4—2442no—
205C4⋊C4#1175821714yes—
206C42—22no—
207C42—612no—
208C42—612no—
209C42—1222no—
210C42—1222no—
211C42—1222no—
212C42—2441no—
213C42—2441no—
214C42—2444no—
215C23C2×C22⋊#692311yescharacteristic
216Q8—48no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—24no—
224C2×C4—42no—
225C2×C4—42no—
226C2×C4—612no—
227C2×C4—612no—
228C2×C4—611no—
229C2×C4—611no—
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#1451983912yes—
243C2×C4#1451984212yes—
244C2×C4C2×#1175821712yes—
245C8—4882no—
246C8—2444no—
247C22#1684073211yescharacteristic
248C22#1684074311yescharacteristic
249C22D61⋊#10111yescharacteristic
250C22C2×#1451983911yescharacteristic
251C22#1684075511yescharacteristic
252C22C2×#1451984211yescharacteristic
253C22#1684076011yescharacteristic
254C4—22no—
255C4—22no—
256C4—22no—
257C4—44no—
258C4—1222no—
259C4—1222no—
260C4—1221no—
261C4—1221no—
262C4—1222no—
263C4—4882no—
264C2#2146108211yescharacteristic
265C2#2146114411yescharacteristic
266C2#2146116111yescharacteristic
267C2#2146120011yescharacteristic
268C2#2146124211yescharacteristic
269C2#2146129311yescharacteristic
270C2#2146132911yescharacteristic
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#7625
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
155. C61#7625semidirect

Maximal subgroups

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

subgroupindex
#214617472
#214616042
#214606372
C4⋊Q8×Dic612
#762561