Finite Group Databasebeta

← #30601640

Subgroups — #30601640

Order 15616.

558 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 558 conjugacy classes of subgroups — too many to draw. Only its 126 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#21461734C211yesmaximal, characteristic
2C4×#14519832C211yesmaximal, characteristic
3C2×#16840612C212yesmaximal
4C2×Q8⋊#92420C212yesmaximal
5#21448388C211yesmaximal, characteristic
6C2×C4⋊#92420C2212yes—
7C2×#14519832—22no—
8C2×C4×#92420C2212yes—
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—
25#14519832—28no—
26C4×#92420—22no—
27C4×#92420D414yes—
28C22×Dic122C2×C411yescharacteristic
29#14519775—22no—
30#14519775—22no—
31Q8×Dic61—22no—
32Q8×Dic61—22no—
33#14519742—22no—
34#14519742—22no—
35C2×C4⋊Dic61—21no—
36C2×C4⋊Dic61C2×C411yescharacteristic
37C2×#11758196—22no—
38C2×#11758196—22no—
39C2×#11758196—21no—
40C2×C4×Dic61—21no—
41C2×C4×Dic61—21no—
42C2×C4×Dic61C2×C411yescharacteristic
43C2×C4×Dic61D412yes—
44C2×C4×Dic61D412yes—
45C2×C4×Dic61C2311yescharacteristic
46#14519684—22no—
47C22×Q8×C61C2×C411yescharacteristic
48C2×C4⋊C4×C61C2×C411yescharacteristic
49C2×C42×C61C2×C411yescharacteristic
50#95×C61—22no—
51C2×Q8×C61—21no—
52C2×Q8×C61—22no—
53C2×Q8×C61—22no—
54C2×Q8×C61M1612yes—
55C22×C4×C61—21no—
56C22×C4×C61—21no—
57C22×C4×C61C22⋊C412yes—
58C22×C4×C61C22×C411yescharacteristic
59C22×Dic61—21no—
60C22×Dic61—21no—
61C22×Dic61C22⋊C412yes—
62C22×Dic61C2×D411yescharacteristic
63C22×Dic61C2×D411yescharacteristic
64C2×Dic122—22no—
65C2×Dic122—22no—
66C2×Dic122—21no—
67C2×Dic122M1612yes—
68C2×#92420—28no—
69C2×#92420—24no—
70C2×#92420—42no—
71C2×#92420—44no—
72C4⋊C4×C61—22no—
73C42×C61—22no—
74C4⋊Dic61—22no—
75C4⋊Dic61—42no—
76#11758196—28no—
77#11758196—44no—
78#11758196—42no—
79C4×Dic61—21no—
80C4×Dic61—21no—
81C4×Dic61—24no—
82C4×Dic61—24no—
83C4×Dic61—41no—
84C4×Dic61—41no—
85C4×Dic61—41no—
86C4×Dic61—41no—
87C4×Dic61C2×D412yes—
88C4×Dic61#4112yes—
89C23×C61C2×C22⋊C411yescharacteristic
90Q8×C61—24no—
91Q8×C61—42no—
92C2×C4×C61—22no—
93C2×C4×C61—22no—
94C2×C4×C61—22no—
95C2×C4×C61—22no—
96C2×C4×C61—41no—
97C2×C4×C61—41no—
98C2×C4×C61—41no—
99C2×C4×C61—42no—
100C2×C4×C61C4×D412yes—
101C2×C4×C61C2×M1611yescharacteristic
102C2×C4×C61C2×M1611yescharacteristic
103C2×C4×C61#13112yes—
104C2×Dic61—22no—
105C2×Dic61—22no—
106C2×Dic61—22no—
107C2×Dic61—22no—
108C2×Dic61—41no—
109C2×Dic61—41no—
110C2×Dic61—41no—
111C2×Dic61—42no—
112C2×Dic61#10414yes—
113C2×Dic61#12112yes—
114C2×Dic61#12411yescharacteristic
115C2×Dic61#12711yescharacteristic
116C2×Dic61#13714yes—
117Dic122—24no—
118Dic122—42no—
119#92420—28no—
120#92420—82no—
121#9647—611nomaximal, Sylow
122C22×C61#39011yescharacteristic
123C22×C61#40711yescharacteristic
124C22×C61#40811yescharacteristic
125C22×C61#41912yes—
126C22×C61C2×#10412yes—
127C4×C61—42no—
128C4×C61—42no—
129C4×C61—81no—
130C4×C61#43512yes—
131C4×C61#43512yes—
132Dic61—22no—
133Dic61—24no—
134Dic61—42no—
135Dic61—81no—
136Dic61#49112yes—
137Dic61#49712yes—
138C4×C4⋊Q8—611no—
139#1831—611no—
140C4×#97—611no—
141C2×Q8⋊C8—612no—
142C2×Q8⋊C8—612no—
143C2×C61#148512yes—
144C2×C61#149112yes—
145C2×C61#195511yescharacteristic
146C2×C61#196011yescharacteristic
147C2×C61#196211yescharacteristic
148C2×C4⋊Q8—611no—
149C2×C4×Q8—611no—
150C2×C4×Q8—611no—
151C2×C4⋊C8—612no—
152C2×#97—1222no—
153C2×C4×C8—612no—
154#391—611no—
155#391#692311yescharacteristic
156#389—1222no—
157#384—611no—
158C4×C4⋊C4—1222no—
159C43—611no—
160#336—1222no—
161Q8⋊C8—1224no—
162Q8⋊C8—1224no—
163C61#964711yescharacteristic, complemented, Sylow
164C22×Q8—611no—
165C22×Q8C2×#692311yescharacteristic
166C22×C8—1222no—
167C22×C8—1222no—
168C4⋊Q8—1222no—
169C4⋊Q8—1222no—
170C4×Q8—1222no—
171C4×Q8—1222no—
172C4×Q8—1222no—
173C4×Q8—1222no—
174C2×C4⋊C4—611no—
175C2×C4⋊C4—1222no—
176C2×C4⋊C4—1221no—
177C2×C4⋊C4—1221no—
178C2×C4⋊C4—1222no—
179C2×C4⋊C4C2×#692311yescharacteristic
180C2×C42—611no—
181C2×C42—612no—
182C2×C42—612no—
183C2×C42—611no—
184C2×C42—1221no—
185C2×C42—1221no—
186C2×C42C2×#692311yescharacteristic
187C4⋊C8—1222no—
188C4⋊C8—1222no—
189#97—1228no—
190C4×C8—614no—
191C4×C8—1222no—
192#95—22no—
193#95—1222no—
194C2×Q8—21no—
195C2×Q8—22no—
196C2×Q8—22no—
197C2×Q8—612no—
198C2×Q8—1221no—
199C2×Q8—1222no—
200C2×Q8—1222no—
201C2×Q8#1175821312yes—
202C22×C4—21no—
203C22×C4—21no—
204C22×C4—611no—
205C22×C4—611no—
206C22×C4—612no—
207C22×C4—1221no—
208C22×C4—1221no—
209C22×C4C22⋊#692312yes—
210C22×C4C22×#692311yescharacteristic
211C2×C8—1224no—
212C2×C8—1228no—
213C2×C8—2442no—
214C2×C8—2444no—
215C4⋊C4—22no—
216C4⋊C4—1228no—
217C4⋊C4—1222no—
218C4⋊C4—2444no—
219C4⋊C4—2442no—
220C4⋊C4—2442no—
221C42—22no—
222C42—612no—
223C42—612no—
224C42—1224no—
225C42—1224no—
226C42—1221no—
227C42—1221no—
228C42—2441no—
229C42—2441no—
230C42—2441no—
231C42—2441no—
232C23C2×C22⋊#692311yescharacteristic
233Q8—24no—
234Q8—42no—
235Q8—1224no—
236Q8—2442no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—22no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4—42no—
245C2×C4—611no—
246C2×C4—611no—
247C2×C4—614no—
248C2×C4—612no—
249C2×C4—614no—
250C2×C4—1222no—
251C2×C4—1222no—
252C2×C4—1222no—
253C2×C4—1222no—
254C2×C4—2441no—
255C2×C4—2442no—
256C2×C4—2441no—
257C2×C4—2441no—
258C2×C4D4×#692312yes—
259C2×C4D61⋊M1611yescharacteristic
260C2×C4C2×#1175821311yescharacteristic
261C2×C4#1451986412yes—
262C8—1228no—
263C8—4882no—
264C22#1684071411yescharacteristic
265C22#1684073311yescharacteristic
266C22#1684073511yescharacteristic
267C22#1684075512yes—
268C22D61⋊#10412yes—
269C4—42no—
270C4—42no—
271C4—81no—
272C4—612no—
273C4—612no—
274C4—1224no—
275C4—1222no—
276C4—4881no—
277C4—2442no—
278C4#1684079112yes—
279C4#1684079412yes—
280C2#2146114112yes—
281C2#2146116212yes—
282C2#2146194411yescharacteristic
283C2#2146195011yescharacteristic
284C2#2146195411yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#391C4
socle, prime radicalC23×C61C2×C22⋊C4
cosocleC2×C4×Dic61C23
hypercenter#391#6923
hypocenterC61#9647
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #391

Complements

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

NH ≅ G/Ntype
163. C61#9647semidirect

Maximal subgroups

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

subgroupindex
#214617342
C4×#145198322
C2×#168406122
C2×Q8⋊#924202
#214483882
#964761