Finite Group Databasebeta

← #30604205

Subgroups — #30604205

Order 15616.

376 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 74 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#21461082C212yesmaximal
2#21460759C212yesmaximal
3#21460749C212yesmaximal
4#21448539C211yesmaximal, characteristic
5#16840782—22no—
6#16840607—22no—
7#16840607C2214yes—
8C2×Q8×Dic61C411yescharacteristic
9C2×Q8×Dic61C2211yescharacteristic
10#16839669C411yescharacteristic
11#16839669C2211yescharacteristic
12#16839648—22no—
13#16839648—22no—
14#16839628C2211yescharacteristic
15#16839608C411yescharacteristic
16C2×C4⋊Q8×C61C411yescharacteristic
17#14519844—42no—
18C22⋊#92420—24no—
19#14519832—42no—
20Q8×Dic61—42no—
21Q8×Dic61—42no—
22C2×C4⋊Dic61—21no—
23C2×C4⋊Dic61C2×C411yescharacteristic
24C2×C4⋊Dic61D412yes—
25C2×C4⋊Dic61C2311yescharacteristic
26C2×C4×Dic61—21no—
27C2×C4×Dic61C2×C411yescharacteristic
28C2×C4×Dic61C2×C411yescharacteristic
29C2×C4×Dic61D412yes—
30#14519684—22no—
31#14519684—21no—
32#14519684—21no—
33#14519684—22no—
34#14519684—22no—
35C22×Q8×C61C2×C411yescharacteristic
36C22×Q8×C61C2×C411yescharacteristic
37C4⋊Q8×C61—22no—
38C4⋊Q8×C61—22no—
39C2×C4⋊C4×C61—22no—
40C2×C42×C61C2×C411yescharacteristic
41C2×Q8×C61—21no—
42C2×Q8×C61—21no—
43C2×Q8×C61—21no—
44C2×Q8×C61—41no—
45C2×Q8×C61—41no—
46C2×Q8×C61—41no—
47C2×Q8×C61—41no—
48C2×Q8×C61M1612yes—
49C22×C4×C61—21no—
50C22×C4×C61—21no—
51C22×C4×C61C22⋊C412yes—
52C22×C4×C61C22×C411yescharacteristic
53C22×Dic61—21no—
54C22×Dic61—21no—
55C22×Dic61C22⋊C411yescharacteristic
56C22×Dic61C22⋊C411yescharacteristic
57C22×Dic61C2×D412yes—
58C2×#92420—44no—
59C4⋊C4×C61—28no—
60C42×C61—21no—
61C42×C61M1612yes—
62C4⋊Dic61—42no—
63C4⋊Dic61—41no—
64C4⋊Dic61—42no—
65C4⋊Dic61—41no—
66C4×Dic61—22no—
67C4×Dic61—22no—
68C4×Dic61—22no—
69C4×Dic61—42no—
70C4×Dic61—41no—
71C23×C61C2×C22⋊C411yescharacteristic
72Q8×C61—42no—
73Q8×C61—42no—
74Q8×C61—42no—
75Q8×C61—42no—
76C2×C4×C61—21no—
77C2×C4×C61—21no—
78C2×C4×C61—22no—
79C2×C4×C61—22no—
80C2×C4×C61—22no—
81C2×C4×C61—22no—
82C2×C4×C61—22no—
83C2×C4×C61—41no—
84C2×C4×C61—41no—
85C2×C4×C61—41no—
86C2×C4×C61—41no—
87C2×C4×C61C2×M1611yescharacteristic
88C2×C4×C61C2×M1611yescharacteristic
89C2×Dic61—21no—
90C2×Dic61—22no—
91C2×Dic61—41no—
92C2×Dic61—41no—
93C2×Dic61—42no—
94C2×Dic61—41no—
95C2×Dic61—41no—
96C2×Dic61—42no—
97C2×Dic61—41no—
98C2×Dic61—41no—
99C2×Dic61#9912yes—
100#92420—84no—
101#11536—611nomaximal, Sylow
102C22×C61—21no—
103C22×C61—21no—
104C22×C61#40711yescharacteristic
105C22×C61C2×#9911yescharacteristic
106C22×C61#41311yescharacteristic
107C4×C61—21no—
108C4×C61—21no—
109C4×C61—42no—
110C4×C61—42no—
111C4×C61—42no—
112Dic61—22no—
113Dic61—42no—
114Dic61—41no—
115Dic61—81no—
116Dic61—81no—
117#2327—611no—
118#1467—612no—
119#1324—612no—
120#1319—612no—
121C2×C61—21no—
122C2×C61—21no—
123C2×C61#146511yescharacteristic
124C2×C61#212911yescharacteristic
125C2×C61#213311yescharacteristic
126C2×C4⋊Q8#692311yescharacteristic
127C2×C4×Q8—611no—
128C2×C4×Q8—611no—
129#432—1222no—
130#391—611no—
131#391—611no—
132#387—1222no—
133#387—1222no—
134#382—611no—
135#376—611no—
136#324—614no—
137#324—1222no—
138C61#1153611yescharacteristic, complemented, Sylow
139C22×Q8C2×#692311yescharacteristic
140C22×Q8C2×#692311yescharacteristic
141C4⋊Q8—22no—
142C4⋊Q8—22no—
143C4×Q8—2442no—
144C4×Q8—2442no—
145C2×C4⋊C4—22no—
146C2×C4⋊C4—612no—
147C2×C4⋊C4—611no—
148C2×C4⋊C4—611no—
149C2×C4⋊C4—1221no—
150C2×C42—612no—
151C2×C42—611no—
152C2×C42—611no—
153C2×C42—1221no—
154C2×C42C2×#692311yescharacteristic
155C4⋊C8—2442no—
156C22⋊C8—1224no—
157#97—2442no—
158#95—1221no—
159#95—1221no—
160#95—1222no—
161#95—1222no—
162#95—1222no—
163C2×Q8—21no—
164C2×Q8—21no—
165C2×Q8—21no—
166C2×Q8—41no—
167C2×Q8—41no—
168C2×Q8—41no—
169C2×Q8—41no—
170C2×Q8#1175821712yes—
171C22×C4—21no—
172C22×C4—21no—
173C22×C4—611no—
174C22×C4—612no—
175C22×C4—611no—
176C22×C4—1221no—
177C22×C4—1221no—
178C22×C4C22⋊#692312yes—
179C22×C4C22×#692311yescharacteristic
180C2×C8—2444no—
181C4⋊C4—28no—
182C4⋊C4—2441no—
183C4⋊C4—2442no—
184C4⋊C4—2441no—
185C4⋊C4—2442no—
186C42—21no—
187C42—1222no—
188C42—1222no—
189C42—1222no—
190C42—2441no—
191C42—2442no—
192C42#1175821712yes—
193C23C2×C22⋊#692311yescharacteristic
194Q8—42no—
195Q8—42no—
196Q8—42no—
197Q8—42no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—41no—
206C2×C4—41no—
207C2×C4—41no—
208C2×C4—41no—
209C2×C4—612no—
210C2×C4—1221no—
211C2×C4—1222no—
212C2×C4—2441no—
213C2×C4—2441no—
214C2×C4—2441no—
215C2×C4—2442no—
216C2×C4—2441no—
217C2×C4—2441no—
218C2×C4—2442no—
219C2×C4—2441no—
220C2×C4C2×#1175821711yescharacteristic
221C2×C4C2×#1175821711yescharacteristic
222C8—4884no—
223C22—21no—
224C22—21no—
225C22#1684073211yescharacteristic
226C22D61⋊#9911yescharacteristic
227C22#1684074911yescharacteristic
228C4—21no—
229C4—21no—
230C4—42no—
231C4—42no—
232C4—42no—
233C4—1222no—
234C4—4881no—
235C4—4881no—
236C4—2442no—
237C4—2441no—
238C2—21no—
239C2—21no—
240C2#2146107511yescharacteristic
241C2#2146210211yescharacteristic
242C2#2146211711yescharacteristic
subgroupG/H
centerC22D61⋊#99
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC2×C4⋊Q8×C61C4
socleC22×C61C2×#99
prime radicalC23×C61C2×C22⋊C4
cosocleC2×C4⋊Dic61C23
hypercenterC2×C4⋊Q8#6923
hypocenterC61#11536
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
138. C61#11536semidirect

Maximal subgroups

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

subgroupindex
#214610822
#214607592
#214607492
#214485392
#1153661