Finite Group Databasebeta

← #30601621

Subgroups — #30601621

Order 15616.

530 conjugacy classes of subgroups; only the 134 normal subgroups are shown.

normal subgroups only

This group has 530 conjugacy classes of subgroups — too many to draw. Only its 134 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#21461736C211yesmaximal, characteristic
2#21461533C211yesmaximal, characteristic
3C2×#16840612C212yesmaximal
4C2×Q8⋊#92420C212yesmaximal
5#21448388C211yesmaximal, characteristic
6C2×C4⋊#92420C2212yes—
7C2×C4×#92420C2212yes—
8#16840628—22no—
9#16840628—22no—
10#16840612—24no—
11Q8⋊#92420—24no—
12C2×#14519775C411yescharacteristic
13C2×Q8×Dic61C2211yescharacteristic
14C2×#14519742C2211yescharacteristic
15#16839668C411yescharacteristic
16#16839659—22no—
17#16839631C411yescharacteristic
18#16839613—22no—
19C42×Dic61C2211yescharacteristic
20C61×#391C411yescharacteristic
21C22×#92420—22no—
22C22×#92420—22no—
23C4⋊#92420—22no—
24C4⋊#92420—22no—
25C4×#92420—22no—
26C4×#92420D414yes—
27C22×Dic122C2×C411yescharacteristic
28#14519775—22no—
29#14519775C814yescomplemented
30Q8×Dic61—22no—
31Q8×Dic61—22no—
32#14519742—22no—
33#14519742—22no—
34C2×C4⋊Dic61—21no—
35C2×C4⋊Dic61C2×C411yescharacteristic
36C2×#11758196—22no—
37C2×#11758196—22no—
38C2×#11758196—21no—
39C2×C4×Dic61—21no—
40C2×C4×Dic61—21no—
41C2×C4×Dic61C2×C411yescharacteristic
42C2×C4×Dic61D412yes—
43C2×C4×Dic61D412yes—
44C2×C4×Dic61C2311yescharacteristic
45#14519684—22no—
46C22×Q8×C61C2×C411yescharacteristic
47C2×C4⋊C4×C61C2×C411yescharacteristic
48C2×C42×C61C2×C411yescharacteristic
49#95×C61—22no—
50C2×Q8×C61—21no—
51C2×Q8×C61—22no—
52C2×Q8×C61—22no—
53C2×Q8×C61C2×C812yes—
54C22×C4×C61—21no—
55C22×C4×C61—21no—
56C22×C4×C61C22⋊C412yes—
57C22×C4×C61C22×C411yescharacteristic
58C22×Dic61—21no—
59C22×Dic61—21no—
60C22×Dic61C22⋊C412yes—
61C22×Dic61C2×D411yescharacteristic
62C22×Dic61C2×D411yescharacteristic
63C2×Dic122—22no—
64C2×Dic122—22no—
65C2×Dic122—21no—
66C2×Dic122C2×C812yes—
67C2×#92420—24no—
68C2×#92420—44no—
69C2×#92420—42no—
70C2×#92420—44no—
71C4⋊C4×C61—22no—
72C42×C61—22no—
73C4⋊Dic61—22no—
74C4⋊Dic61—42no—
75#11758196—28no—
76#11758196—44no—
77#11758196—42no—
78C4×Dic61—24no—
79C4×Dic61—42no—
80C4×Dic61—41no—
81C4×Dic61—41no—
82C4×Dic61—41no—
83C4×Dic61—41no—
84C4×Dic61C2×C812yes—
85C4×Dic61M1612yes—
86C4×Dic61C2×D412yes—
87C4×Dic61#4112yes—
88C23×C61C2×C22⋊C411yescharacteristic
89Q8×C61—24no—
90Q8×C61—42no—
91C2×C4×C61—22no—
92C2×C4×C61—22no—
93C2×C4×C61—22no—
94C2×C4×C61—22no—
95C2×C4×C61—41no—
96C2×C4×C61—41no—
97C2×C4×C61—41no—
98C2×C4×C61—42no—
99C2×C4×C61C4×D412yes—
100C2×C4×C61C22×C811yescharacteristic
101C2×C4×C61C2×M1611yescharacteristic
102C2×C4×C61#13112yes—
103C2×Dic61—22no—
104C2×Dic61—22no—
105C2×Dic61—22no—
106C2×Dic61—22no—
107C2×Dic61—41no—
108C2×Dic61—41no—
109C2×Dic61—41no—
110C2×Dic61—42no—
111C2×Dic61C22⋊C814yes—
112C2×Dic61#12112yes—
113C2×Dic61#12411yescharacteristic
114C2×Dic61#12711yescharacteristic
115C2×Dic61#13714yes—
116Dic122—24no—
117Dic122—42no—
118#92420—44no—
119#92420—82no—
120#9641—611nomaximal, Sylow
121C22×C61#39011yescharacteristic
122C22×C61C2×C22⋊C811yescharacteristic
123C22×C61#40811yescharacteristic
124C22×C61#41912yes—
125C22×C61#42112yes—
126C4×C61—42no—
127C4×C61—42no—
128C4×C61—81no—
129C4×C61C8×D412yes—
130C4×C61#43612yes—
131Dic61—22no—
132Dic61—24no—
133Dic61—42no—
134Dic61—81no—
135Dic61#49112yes—
136Dic61#49712yes—
137C4×C4⋊Q8—611no—
138#1831—611no—
139#1744—611no—
140C2×Q8⋊C8—612no—
141C2×Q8⋊C8—612no—
142C2×C61#147912yes—
143C2×C61#149712yes—
144C2×C61#195411yescharacteristic
145C2×C61#196011yescharacteristic
146C2×C61#196311yescharacteristic
147C2×C4⋊Q8—611no—
148C2×C4×Q8—611no—
149C2×C4×Q8—611no—
150C2×C4⋊C8—612no—
151C2×C4×C8—612no—
152#391—611no—
153#391#692311yescharacteristic
154#389—1222no—
155#384—611no—
156C4×C4⋊C4—1222no—
157C43—611no—
158#336—1222no—
159#336—1222no—
160Q8⋊C8—1224no—
161Q8⋊C8—1224no—
162C61#964111yescharacteristic, complemented, Sylow
163C22×Q8—611no—
164C22×Q8C2×#692311yescharacteristic
165C22×C8—1222no—
166C22×C8—1222no—
167C4⋊Q8—614no—
168C4⋊Q8—1222no—
169C4×Q8—1222no—
170C4×Q8—1222no—
171C4×Q8—1222no—
172C4×Q8—1222no—
173C2×C4⋊C4—611no—
174C2×C4⋊C4—1222no—
175C2×C4⋊C4—1221no—
176C2×C4⋊C4—1221no—
177C2×C4⋊C4—1222no—
178C2×C4⋊C4C2×#692311yescharacteristic
179C2×C42—611no—
180C2×C42—611no—
181C2×C42—612no—
182C2×C42—612no—
183C2×C42—1221no—
184C2×C42—1221no—
185C2×C42C2×#692311yescharacteristic
186C4⋊C8—1222no—
187C4⋊C8—1222no—
188C4×C8—614no—
189C4×C8—1222no—
190#95—22no—
191#95—1222no—
192C2×Q8—21no—
193C2×Q8—22no—
194C2×Q8—22no—
195C2×Q8—612no—
196C2×Q8—1221no—
197C2×Q8—1222no—
198C2×Q8—1222no—
199C2×Q8D61⋊C812yes—
200C22×C4—21no—
201C22×C4—21no—
202C22×C4—611no—
203C22×C4—611no—
204C22×C4—612no—
205C22×C4—1221no—
206C22×C4—1221no—
207C22×C4C22⋊#692312yes—
208C22×C4C22×#692311yescharacteristic
209C2×C8—1224no—
210C2×C8—2442no—
211C2×C8—2444no—
212C2×C8—2444no—
213C4⋊C4—22no—
214C4⋊C4—1228no—
215C4⋊C4—1222no—
216C4⋊C4—2442no—
217C4⋊C4—2442no—
218C4⋊C4—2444no—
219C42—22no—
220C42—612no—
221C42—612no—
222C42—612no—
223C42—612no—
224C42—1224no—
225C42—2442no—
226C42—2441no—
227C42—2441no—
228C42—2441no—
229C42—2441no—
230C23C2×C22⋊#692311yescharacteristic
231Q8—24no—
232Q8—42no—
233Q8—1224no—
234Q8—2442no—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—41no—
240C2×C4—41no—
241C2×C4—41no—
242C2×C4—42no—
243C2×C4—611no—
244C2×C4—611no—
245C2×C4—614no—
246C2×C4—612no—
247C2×C4—614no—
248C2×C4—1222no—
249C2×C4—1222no—
250C2×C4—1222no—
251C2×C4—1222no—
252C2×C4—2441no—
253C2×C4—2442no—
254C2×C4—2441no—
255C2×C4—2441no—
256C2×C4D4×#692312yes—
257C2×C4C2×D61⋊C811yescharacteristic
258C2×C4D61⋊M1611yescharacteristic
259C2×C4#1451986412yes—
260C8—4882no—
261C8—2444no—
262C22#1684071411yescharacteristic
263C22D61⋊(C22⋊C8)11yescharacteristic
264C22#1684073511yescharacteristic
265C22#1684075512yes—
266C22#1684075912yes—
267C4—42no—
268C4—42no—
269C4—81no—
270C4—612no—
271C4—612no—
272C4—1224no—
273C4—1222no—
274C4—4881no—
275C4—2442no—
276C4#1684078912yes—
277C4#1684079512yes—
278C2#2146112212yes—
279C2#2146118112yes—
280C2#2146194211yescharacteristic
281C2#2146195011yescharacteristic
282C2#2146195611yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC2×C4×C61C22×C8
FrattiniC22×C4C22×#6923
FittingC61×#391C4
socle, prime radicalC23×C61C2×C22⋊C4
cosocleC2×C4×Dic61C23
hypercenter#391#6923
hypocenterC61#9641
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #391

Complements

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

NH ≅ G/Ntype
29. #14519775C8semidirect
162. C61#9641semidirect

Maximal subgroups

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

subgroupindex
#214617362
#214615332
C2×#168406122
C2×Q8⋊#924202
#214483882
#964161