Finite Group Databasebeta

← #30607264

Subgroups — #30607264

Order 15616.

566 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 566 conjugacy classes of subgroups — too many to draw. Only its 76 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#21461654C212yesmaximal
2#21460917C212yesmaximal, complemented
3#21460916C212yesmaximal, complemented
4#21448402C211yesmaximal, characteristic
5C2×#14519838—22no—
6C2×#14519838C2214yes—
7#16840734—22no—
8C22×Q8×D61C2211yescharacteristic
9C2×#14519735C411yescharacteristic
10C2×#14519734C411yescharacteristic
11#16839669C411yescharacteristic
12#16839668C2211yescharacteristic
13#16839667C2211yescharacteristic
14#16839666—22no—
15#16839624—22no—
16C61×#391C411yescharacteristic
17C2×#11758217—24no—
18#14519838—28no—
19#14519838—44no—
20#14519834—44no—
21C22×Dic122D412yes—
22C22×Dic122C2311yescharacteristic
23C2×Q8×D61—24no—
24C2×Q8×D61—42no—
25C2×Q8×D61—42no—
26C22×C4×D61C2×C411yescharacteristic
27C22×C4×D61D412yes—
28#14519735—42no—
29#14519734—42no—
30C2×C4⋊Dic61C2×C411yescharacteristic
31C2×#11758196—21no—
32C2×#11758198—21no—
33C2×#11758198—21no—
34C2×C4×Dic61—21no—
35C2×C4×Dic61C2×C411yescharacteristic
36#14519684—22no—
37#14519684—22no—
38#14519684—22no—
39C22×Q8×C61C2×C411yescharacteristic
40C2×C4⋊C4×C61C2×C411yescharacteristic
41C2×C42×C61C2×C411yescharacteristic
42#95×C61—22no—
43C23×D61C22⋊C411yescharacteristic
44C2×Q8×C61—22no—
45C2×Q8×C61—41no—
46C2×Q8×C61—41no—
47C22×C4×C61—21no—
48C22×C4×C61—21no—
49C22×C4×C61C22⋊C412yes—
50C22×C4×C61C22×C411yescharacteristic
51C22×Dic61—21no—
52C22×Dic61—21no—
53C22×Dic61C22⋊C411yescharacteristic
54C22×Dic61C2×D412yes—
55Q8×D61—416no—
56C2×C4×D61—22no—
57C2×C4×D61—22no—
58C2×C4×D61—22no—
59C2×C4×D61—24no—
60C2×C4×D61—24no—
61C2×C4×D61—42no—
62C2×Dic122—24no—
63C2×Dic122—24no—
64C2×Dic122—42no—
65C2×Dic122—41no—
66C2×Dic122—41no—
67C2×Dic122#4114yes—
68#11758217—44no—
69#11758217—44no—
70C2×#92420—44no—
71C4⋊C4×C61—41no—
72C42×C61—41no—
73#11758198—42no—
74#11758198—42no—
75C4⋊Dic61—41no—
76#11758196—42no—
77C4×Dic61—42no—
78C4×Dic61—41no—
79C23×C61C2×C22⋊C411yescharacteristic
80C22×D61—21no—
81C22×D61—21no—
82C22×D61—41no—
83C22×D61—41no—
84C22×D61#9912yes—
85Q8×C61—44no—
86C2×C4×C61—21no—
87C2×C4×C61—21no—
88C2×C4×C61—22no—
89C2×C4×C61—22no—
90C2×C4×C61—22no—
91C2×C4×C61—41no—
92C2×C4×C61—41no—
93C2×C4×C61—42no—
94C2×C4×C61—41no—
95C2×C4×C61—41no—
96C2×C4×C61#11712yes—
97C2×Dic61—21no—
98C2×Dic61—21no—
99C2×Dic61—22no—
100C2×Dic61—22no—
101C2×Dic61—41no—
102C2×Dic61—41no—
103C2×Dic61—42no—
104C2×Dic61—41no—
105C2×Dic61—41no—
106C2×Dic61#9912yes—
107C2×Dic61#12314yes—
108C4×D61—28no—
109C4×D61—48no—
110Dic122—44no—
111Dic122—48no—
112#92420—84no—
113#12862—611nomaximal, Sylow
114C22×C61—21no—
115C22×C61—21no—
116C22×C61#38111yescharacteristic
117C22×C61C2×#9911yescharacteristic
118C22×C61C2×#9911yescharacteristic
119C2×D61—22no—
120C2×D61—22no—
121C2×D61—22no—
122C2×D61—42no—
123C2×D61—42no—
124C4×C61—22no—
125C4×C61—42no—
126C4×C61—81no—
127C4×C61—81no—
128Dic61—24no—
129Dic61—22no—
130Dic61—81no—
131Dic61—81no—
132#2310—611no—
133#1784—612no—
134#1394—612no—
135#1394—612no—
136C2×C61—21no—
137C2×C61—21no—
138C2×C61#181911yescharacteristic
139C2×C61#213311yescharacteristic
140C2×C61#213311yescharacteristic
141D61—42no—
142C23×Q8—611no—
143C2×#117—611no—
144C2×#117—611no—
145C2×#101—614no—
146C2×#101—1222no—
147#407—1222no—
148#391—611no—
149#391—611no—
150#391—611no—
151#391—1222no—
152#391#692311yescharacteristic
153#381—1222no—
154C61#1286211yescharacteristic, complemented, Sylow
155C22×Q8—612no—
156C22×Q8—611no—
157C22×Q8—1224no—
158C22×Q8—2442no—
159C22×Q8—2442no—
160C22×Q8C2×#692311yescharacteristic
161C23×C4—611no—
162C23×C4—612no—
163C2×M16—1224no—
164#117—2442no—
165#117—2442no—
166C2×C4⋊C4—611no—
167C2×C4⋊C4—1221no—
168C2×C4⋊C4C2×#692311yescharacteristic
169C2×C22⋊C4—1221no—
170C2×C22⋊C4—1221no—
171C2×C42—611no—
172C2×C42—1221no—
173C2×C42C2×#692311yescharacteristic
174#101—1228no—
175#101—2444no—
176C22⋊C8—2444no—
177#95—22no—
178#95—1222no—
179#95—1222no—
180#95—1222no—
181C24—611no—
182C2×Q8—22no—
183C2×Q8—41no—
184C2×Q8—41no—
185C2×Q8—614no—
186C2×Q8—1224no—
187C2×Q8—1224no—
188C2×Q8—2441no—
189C2×Q8—2441no—
190C2×Q8—2442no—
191C2×Q8—24416no—
192C22×C4—21no—
193C22×C4—21no—
194C22×C4—612no—
195C22×C4—611no—
196C22×C4—1222no—
197C22×C4—1224no—
198C22×C4—1222no—
199C22×C4—1224no—
200C22×C4—1222no—
201C22×C4—1221no—
202C22×C4—1221no—
203C22×C4—2442no—
204C22×C4C22⋊#692312yes—
205C22×C4C22×#692311yescharacteristic
206M16—2444no—
207M16—2444no—
208C2×C8—2444no—
209C4⋊C4—41no—
210C4⋊C4—2441no—
211C4⋊C4—2442no—
212C22⋊C4—2442no—
213C22⋊C4—2442no—
214C42—41no—
215C42—2441no—
216C42—2442no—
217C23—612no—
218C23—1221no—
219C23—1221no—
220C23—2441no—
221C23—2441no—
222C23C2×C22⋊#692311yescharacteristic
223Q8—44no—
224Q8—2444no—
225Q8—2448no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—22no—
229C2×C4—22no—
230C2×C4—22no—
231C2×C4—41no—
232C2×C4—41no—
233C2×C4—42no—
234C2×C4—41no—
235C2×C4—41no—
236C2×C4—614no—
237C2×C4—612no—
238C2×C4—1228no—
239C2×C4—1221no—
240C2×C4—1222no—
241C2×C4—1221no—
242C2×C4—1222no—
243C2×C4—2448no—
244C2×C4—2441no—
245C2×C4—2441no—
246C2×C4—2442no—
247C2×C4—2441no—
248C2×C4—2441no—
249C2×C4#1451985612yes—
250C8—4884no—
251C22—21no—
252C22—21no—
253C22—1222no—
254C22—1222no—
255C22—1222no—
256C22—2442no—
257C22—2442no—
258C22#1684070511yescharacteristic
259C22D61⋊#9911yescharacteristic
260C22D61⋊#9911yescharacteristic
261C4—22no—
262C4—42no—
263C4—81no—
264C4—81no—
265C4—1224no—
266C4—1222no—
267C4—4881no—
268C4—4881no—
269C2—21no—
270C2—21no—
271C2—2442no—
272C2#2146171511yescharacteristic
273C2#2146211511yescharacteristic
274C2#2146211711yescharacteristic
subgroupG/H
centerC22D61⋊#99
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#391C4
socleC22×C61C2×#99
prime radicalC23×D61C22⋊C4
cosocleC22×Dic122C23
hypercenter#391#6923
hypocenterC61#12862
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ #391

Complements

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

NH ≅ G/Ntype
2. #21460917C2semidirect
3. #21460916C2semidirect
154. C61#12862semidirect

Maximal subgroups

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

subgroupindex
#214616542
#214609172
#214609162
#214484022
#1286261