Finite Group Databasebeta

← #30605183

Subgroups — #30605183

Order 15616.

368 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 66 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#21461720C211yesmaximal, characteristic
2#21461072C211yesmaximal, characteristic
3#21460820C214yesmaximal, complemented
4#21451641C211yesmaximal, characteristic
5#16840782—21no—
6#16840734—21no—
7#16840642—21no—
8#16840642C2212yes—
9#16840608C2212yes—
10#16840606—21no—
11C2×#14519734C2211yescharacteristic
12#16839700—21no—
13#16839697—21no—
14#16839681C2212yes—
15#16839673C412yes—
16#16839658—21no—
17#16839628C411yescharacteristic
18#16839619—21no—
19C2×C4⋊Q8×C61C411yescharacteristic
20C2×#11758217—22no—
21#14519844—41no—
22#14519834—41no—
23#14519834—41no—
24C22⋊#92420—22no—
25#14519832—41no—
26C22×C4×D61D411yescharacteristic
27#14519734—41no—
28#14519734—41no—
29C2×C4⋊Dic61—21no—
30C2×#11758196—22no—
31C2×#11758196D411yescharacteristic
32C2×#11758196C2311yescharacteristic
33C2×#11758198—22no—
34C2×#11758198C2×C411yescharacteristic
35C2×#11758198D411yescharacteristic
36C2×C4×Dic61D411yescharacteristic
37#14519684—21no—
38#14519684—22no—
39#14519684—22no—
40#14519684C2×C412yes—
41C22×Q8×C61C2×C412yes—
42C4⋊Q8×C61—41no—
43C4⋊Q8×C61—41no—
44C2×C4⋊C4×C61—21no—
45C2×C4⋊C4×C61—21no—
46C2×C42×C61C2×C411yescharacteristic
47C23×D61C22⋊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×Dic61C2×D411yescharacteristic
57C22×Dic61C2×D411yescharacteristic
58C2×C4×D61—21no—
59C2×C4×D61—21no—
60C2×C4×D61—22no—
61C2×C4×D61—41no—
62#11758217—42no—
63#11758217—42no—
64C2×#92420—42no—
65C2×#92420—42no—
66C4⋊C4×C61—42no—
67C4⋊C4×C61—41no—
68C4⋊C4×C61—41no—
69C42×C61—21no—
70C42×C61—21no—
71#11758198—41no—
72#11758198—41no—
73#11758198—82no—
74C4⋊Dic61—42no—
75#11758196—41no—
76#11758196—41no—
77#11758196—82no—
78C4×Dic61—21no—
79C4×Dic61—21no—
80C23×C61C2×C22⋊C411yescharacteristic
81C22×D61—21no—
82C22×D61—21no—
83C22×D61—21no—
84C22×D61—41no—
85C22×D61—41no—
86Q8×C61—84no—
87C2×C4×C61—21no—
88C2×C4×C61—21no—
89C2×C4×C61—21no—
90C2×C4×C61—21no—
91C2×C4×C61—41no—
92C2×C4×C61—41no—
93C2×C4×C61—42no—
94C2×C4×C61—42no—
95C2×C4×C61—42no—
96C2×C4×C61#9911yescharacteristic
97C2×C4×C61#9911yescharacteristic
98C2×Dic61—21no—
99C2×Dic61—21no—
100C2×Dic61—21no—
101C2×Dic61—21no—
102C2×Dic61—41no—
103C2×Dic61—41no—
104C2×Dic61—42no—
105C2×Dic61—42no—
106C2×Dic61—42no—
107C2×Dic61#13712yes—
108C4×D61—42no—
109C4×D61—42no—
110#92420—82no—
111#92420—82no—
112#11819—611nomaximal, Sylow
113C22×C61—21no—
114C22×C61—21no—
115C22×C61C2×#9911yescharacteristic
116C22×C61#41911yescharacteristic
117C22×C61#42111yescharacteristic
118C2×D61—42no—
119C2×D61—41no—
120C2×D61—41no—
121C2×D61—41no—
122C2×D61—81no—
123C4×C61—21no—
124C4×C61—21no—
125C4×C61—41no—
126C4×C61—41no—
127C4×C61—82no—
128Dic61—22no—
129Dic61—41no—
130Dic61—41no—
131Dic61—82no—
132#2628—611no—
133#1822—611no—
134#1464—611no—
135#1354—614no—
136C2×C61—21no—
137C2×C61—21no—
138C2×C61#151111yescharacteristic
139C2×C61#212211yescharacteristic
140C2×C61#213511yescharacteristic
141D61—81no—
142C2×C4⋊Q8#692311yescharacteristic
143C2×#117—611no—
144#432—1221no—
145#407—1221no—
146#400—1221no—
147#399—1221no—
148#395—612no—
149#393—612no—
150#389—1221no—
151#382—611no—
152#380—1221no—
153#343—612no—
154#343—1221no—
155#324—612no—
156#323—1221no—
157C61#1181911yescharacteristic, complemented, Sylow
158C22×Q8C2×#692312yes—
159C23×C4—611no—
160C2×M16—1222no—
161C4⋊Q8—41no—
162C4⋊Q8—41no—
163#117—2441no—
164#117—2441no—
165C2×C4⋊C4—21no—
166C2×C4⋊C4—21no—
167C2×C4⋊C4—611no—
168C2×C4⋊C4—611no—
169C2×C4⋊C4—1222no—
170C2×C4⋊C4—1221no—
171C2×C22⋊C4—611no—
172C2×C22⋊C4—611no—
173C2×C22⋊C4—1222no—
174C2×C42—611no—
175C2×C42C2×#692311yescharacteristic
176C4⋊C8—2441no—
177C22⋊C8—1222no—
178C22⋊C8—2441no—
179C22⋊C8—2441no—
180#97—2441no—
181#95—612no—
182#95—1222no—
183#95—1222no—
184#95—1221no—
185C24—611no—
186C2×Q8—42no—
187C2×Q8—82no—
188C22×C4—22no—
189C22×C4—611no—
190C22×C4—611no—
191C22×C4—611no—
192C22×C4—1222no—
193C22×C4—1221no—
194C22×C4—1221no—
195C22×C4—1222no—
196C22×C4—2441no—
197C22×C4C22⋊#692311yescharacteristic
198C22×C4C22⋊#692311yescharacteristic
199C22×C4C22×#692311yescharacteristic
200M16—2442no—
201M16—2442no—
202C2×C8—2442no—
203C2×C8—2442no—
204C4⋊C4—42no—
205C4⋊C4—41no—
206C4⋊C4—41no—
207C4⋊C4—4882no—
208C4⋊C4—2441no—
209C4⋊C4—2441no—
210C4⋊C4—2442no—
211C22⋊C4—4882no—
212C22⋊C4—2441no—
213C22⋊C4—2441no—
214C42—21no—
215C42—21no—
216C42—1221no—
217C42—1221no—
218C23—1221no—
219C23—1221no—
220C23—1221no—
221C23—2441no—
222C23—2441no—
223C23C2×C22⋊#692311yescharacteristic
224Q8—84no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—41no—
230C2×C4—41no—
231C2×C4—42no—
232C2×C4—42no—
233C2×C4—42no—
234C2×C4—612no—
235C2×C4—1221no—
236C2×C4—1221no—
237C2×C4—1221no—
238C2×C4—1221no—
239C2×C4—2442no—
240C2×C4—2442no—
241C2×C4—2442no—
242C2×C4—2442no—
243C2×C4—2442no—
244C2×C4—2441no—
245C2×C4—2441no—
246C2×C4#1451983511yescharacteristic
247C2×C4#1451983511yescharacteristic
248C8—4882no—
249C8—4882no—
250C22—21no—
251C22—21no—
252C22—4881no—
253C22—2442no—
254C22—2441no—
255C22—2441no—
256C22—2441no—
257C22C2×#1451983511yescharacteristic
258C22#1684075511yescharacteristic
259C22#1684076111yescharacteristic
260C4—21no—
261C4—21no—
262C4—41no—
263C4—41no—
264C4—82no—
265C4—1222no—
266C4—4882no—
267C4—2441no—
268C4—2441no—
269C2—21no—
270C2—21no—
271C2—4881no—
272C2#2146122911yescharacteristic
273C2#2146207811yescharacteristic
274C2#2146212111yescharacteristic
subgroupG/H
centerC22C2×#14519835
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC2×C4⋊Q8×C61C4
socleC22×C61C2×#99
prime radicalC23×D61C22⋊C4
cosocleC2×#11758196C23
hypercenterC2×C4⋊Q8#6923
hypocenterC61#11819
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
3. #21460820C2semidirect
157. C61#11819semidirect

Maximal subgroups

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

subgroupindex
#214617202
#214610722
#214608202
#214516412
#1181961