Finite Group Databasebeta

← #30605501

Subgroups — #30605501

Order 15616.

388 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 80 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#21461685C211yesmaximal, characteristic
2#21461061C211yesmaximal, characteristic
3#21460820C214yesmaximal
4#21451028C211yesmaximal, characteristic
5#16840779—21no—
6#16840765—21no—
7C2×#14519838—21no—
8#16840642C2212yes—
9#16840608C2212yes—
10#16840607—21no—
11C2×C4×Dic122C2211yescharacteristic
12#16839681C412yes—
13#16839681C2212yes—
14#16839667—21no—
15#16839658—21no—
16#16839658—21no—
17#16839631—21no—
18C4×C4⋊Dic61C411yescharacteristic
19C2×C4⋊Q8×C61C411yescharacteristic
20C2×#11758217—22no—
21#14519844—41no—
22#14519844—41no—
23C4⋊#92420—41no—
24#14519838—42no—
25C22⋊#92420—22no—
26C4×#92420—41no—
27C22×Dic122D411yescharacteristic
28C4×Dic122—41no—
29C4×Dic122—41no—
30C2×C4⋊Dic61—21no—
31C2×C4⋊Dic61D411yescharacteristic
32C2×#11758196—22no—
33C2×#11758196—22no—
34C2×#11758196C2×C411yescharacteristic
35C2×#11758196C2311yescharacteristic
36C2×C4×Dic61—21no—
37C2×C4×Dic61D411yescharacteristic
38C2×C4×Dic61D411yescharacteristic
39#14519684—22no—
40#14519684—22no—
41#14519684C2×C412yes—
42C22×Q8×C61C2×C412yes—
43C4⋊Q8×C61—41no—
44C4⋊Q8×C61—41no—
45C2×C4⋊C4×C61—21no—
46C2×C4⋊C4×C61—21no—
47C2×C42×C61C2×C411yescharacteristic
48C2×Q8×C61—42no—
49C2×Q8×C61—82no—
50C22×C4×C61—22no—
51C22×C4×C61C22⋊C411yescharacteristic
52C22×C4×C61C22⋊C411yescharacteristic
53C22×C4×C61C22×C411yescharacteristic
54C22×Dic61—22no—
55C22×Dic61C22⋊C411yescharacteristic
56C22×Dic61C22⋊C411yescharacteristic
57C22×Dic61C2×D411yescharacteristic
58C22×Dic61C2×D411yescharacteristic
59C2×Dic122—41no—
60C2×Dic122—41no—
61C2×Dic122SD1612yes—
62C2×Dic122Q1612yes—
63#11758217—42no—
64#11758217—42no—
65C2×#92420—42no—
66C2×#92420—42no—
67C4⋊C4×C61—42no—
68C4⋊C4×C61—41no—
69C4⋊C4×C61—41no—
70C42×C61—21no—
71C42×C61—21no—
72C4⋊Dic61—24no—
73C4⋊Dic61—41no—
74#11758196—41no—
75#11758196—41no—
76#11758196—82no—
77#11758196—82no—
78C4×Dic61—21no—
79C4×Dic61—21no—
80C4×Dic61—21no—
81C4×Dic61—21no—
82C4×Dic61—42no—
83C23×C61C2×C22⋊C411yescharacteristic
84Q8×C61—84no—
85C2×C4×C61—21no—
86C2×C4×C61—21no—
87C2×C4×C61—22no—
88C2×C4×C61—21no—
89C2×C4×C61—41no—
90C2×C4×C61—42no—
91C2×C4×C61—42no—
92C2×C4×C61—42no—
93C2×C4×C61#9911yescharacteristic
94C2×C4×C61#9911yescharacteristic
95C2×C4×C61#10312yes—
96C2×Dic61—21no—
97C2×Dic61—21no—
98C2×Dic61—21no—
99C2×Dic61—21no—
100C2×Dic61—24no—
101C2×Dic61—21no—
102C2×Dic61—21no—
103C2×Dic61—42no—
104C2×Dic61—42no—
105C2×Dic61—41no—
106C2×Dic61—41no—
107C2×Dic61#10312yes—
108C2×Dic61C2×SD1611yescharacteristic
109C2×Dic61C2×Q1611yescharacteristic
110Dic122—42no—
111Dic122—42no—
112#92420—82no—
113#92420—82no—
114#11908—611nomaximal, Sylow
115C22×C61—21no—
116C22×C61—21no—
117C22×C61C2×#9911yescharacteristic
118C22×C61C2×#10311yescharacteristic
119C22×C61#42111yescharacteristic
120C4×C61—21no—
121C4×C61—22no—
122C4×C61—41no—
123C4×C61—82no—
124C4×C61#35612yes—
125Dic61—21no—
126Dic61—22no—
127Dic61—21no—
128Dic61—44no—
129Dic61—41no—
130Dic61—41no—
131#2567—611no—
132#1801—611no—
133#1461—611no—
134#1354—614no—
135C2×C61—21no—
136C2×C61—21no—
137C2×C61#152011yescharacteristic
138C2×C61#212211yescharacteristic
139C2×C61C2×#35611yescharacteristic
140C2×C4⋊Q8#692311yescharacteristic
141C2×C4×Q8—611no—
142#431—1221no—
143#423—1221no—
144C2×#101—1221no—
145#395—612no—
146#395—612no—
147#391—1221no—
148#389—1221no—
149#389—1221no—
150#384—1221no—
151C4×C4⋊C4—611no—
152#343—612no—
153#324—612no—
154#324—1221no—
155C61#1190811yescharacteristic, complemented, Sylow
156C22×Q8—611no—
157C22×Q8C2×#692312yes—
158C2×M16—1222no—
159C4⋊Q8—41no—
160C4⋊Q8—41no—
161C4×Q8—2441no—
162C4×Q8—2441no—
163C2×C4⋊C4—21no—
164C2×C4⋊C4—21no—
165C2×C4⋊C4—611no—
166C2×C4⋊C4—611no—
167C2×C4⋊C4—611no—
168C2×C4⋊C4—1221no—
169C2×C4⋊C4—1222no—
170C2×C4⋊C4—1222no—
171C2×C42—611no—
172C2×C42—611no—
173C2×C42—1221no—
174C2×C42C2×#692311yescharacteristic
175C4⋊C8—2441no—
176C4⋊C8—2441no—
177C4⋊C8—2441no—
178#101—2442no—
179C22⋊C8—1222no—
180C4×C8—2441no—
181#95—612no—
182#95—1222no—
183#95—1222no—
184C2×Q8—42no—
185C2×Q8—82no—
186C2×Q8—612no—
187C2×Q8—612no—
188C2×Q8—2441no—
189C2×Q8—2441no—
190C22×C4—22no—
191C22×C4—611no—
192C22×C4—611no—
193C22×C4—611no—
194C22×C4—611no—
195C22×C4—1222no—
196C22×C4C22⋊#692311yescharacteristic
197C22×C4C22⋊#692311yescharacteristic
198C22×C4C22×#692311yescharacteristic
199M16—2442no—
200M16—2442no—
201C2×C8—2442no—
202C2×C8—2442no—
203C4⋊C4—42no—
204C4⋊C4—41no—
205C4⋊C4—41no—
206C4⋊C4—1224no—
207C4⋊C4—4882no—
208C4⋊C4—4882no—
209C4⋊C4—2441no—
210C4⋊C4—2441no—
211C4⋊C4—2441no—
212C42—21no—
213C42—21no—
214C42—1221no—
215C42—1221no—
216C42—1221no—
217C42—1221no—
218C42—2442no—
219C23C2×C22⋊#692311yescharacteristic
220Q8—84no—
221Q8—2442no—
222Q8—2442no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—22no—
226C2×C4—21no—
227C2×C4—41no—
228C2×C4—42no—
229C2×C4—42no—
230C2×C4—42no—
231C2×C4—612no—
232C2×C4—611no—
233C2×C4—611no—
234C2×C4—1221no—
235C2×C4—1221no—
236C2×C4—1221no—
237C2×C4—1221no—
238C2×C4—1224no—
239C2×C4—1221no—
240C2×C4—1221no—
241C2×C4—2442no—
242C2×C4—2442no—
243C2×C4—2441no—
244C2×C4—2441no—
245C2×C4#1451983511yescharacteristic
246C2×C4#1451983511yescharacteristic
247C2×C4#1451984012yes—
248C8—4882no—
249C8—4882no—
250C22—21no—
251C22—21no—
252C22C2×#1451983511yescharacteristic
253C22C2×#1451984011yescharacteristic
254C22#1684076111yescharacteristic
255C4—22no—
256C4—21no—
257C4—41no—
258C4—82no—
259C4—1221no—
260C4—1222no—
261C4—1221no—
262C4—2444no—
263C4—2441no—
264C4—2441no—
265C4#1684067212yes—
266C2—21no—
267C2—21no—
268C2#2146125911yescharacteristic
269C2#2146207811yescharacteristic
270C2C2×#1684067211yescharacteristic
subgroupG/H
centerC22C2×#14519835
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC2×C4⋊Q8×C61C4
socleC22×C61C2×#99
prime radicalC23×C61C2×C22⋊C4
cosocleC2×#11758196C23
hypercenterC2×C4⋊Q8#6923
hypocenterC61#11908
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
155. C61#11908semidirect

Maximal subgroups

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

subgroupindex
#214616852
#214610612
#214608202
#214510282
#1190861