Finite Group Databasebeta

← #30601607

Subgroups — #30601607

Order 15616.

606 conjugacy classes of subgroups; only the 166 normal subgroups are shown.

normal subgroups only

This group has 606 conjugacy classes of subgroups — too many to draw. Only its 166 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#21461752C211yesmaximal, characteristic
2C42×#92420C211yesmaximal, characteristic
3C2×#16840612C212yesmaximal
4C2×Q8⋊#92420C212yesmaximal
5#21448388C211yesmaximal, characteristic
6C2×#14519844—22no—
7C2×C4⋊#92420C2212yes—
8C2×C4×#92420—22no—
9C2×C4×#92420C2212yes—
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—
23#14519844—44no—
24C4⋊#92420—22no—
25C4⋊#92420—22no—
26C4×#92420—28no—
27C4×#92420—22no—
28C4×#92420D414yes—
29C22×Dic122C2×C411yescharacteristic
30#14519775—22no—
31#14519775C814yescomplemented
32Q8×Dic61—22no—
33Q8×Dic61—22no—
34#14519742—22no—
35#14519742—22no—
36C2×C4⋊Dic61—21no—
37C2×C4⋊Dic61C2×C411yescharacteristic
38C2×#11758196—22no—
39C2×#11758196—22no—
40C2×#11758196—21no—
41C2×C4×Dic61—21no—
42C2×C4×Dic61—21no—
43C2×C4×Dic61C2×C411yescharacteristic
44C2×C4×Dic61D412yes—
45C2×C4×Dic61D412yes—
46C2×C4×Dic61C2311yescharacteristic
47#14519684—22no—
48C22×Q8×C61C2×C411yescharacteristic
49C2×C4⋊C4×C61C2×C411yescharacteristic
50C2×C42×C61C2×C411yescharacteristic
51#95×C61—22no—
52C2×Q8×C61—21no—
53C2×Q8×C61—22no—
54C2×Q8×C61—22no—
55C2×Q8×C61C2×C812yes—
56C22×C4×C61—21no—
57C22×C4×C61—21no—
58C22×C4×C61C22⋊C412yes—
59C22×C4×C61C22×C411yescharacteristic
60C22×Dic61—21no—
61C22×Dic61—21no—
62C22×Dic61C22⋊C412yes—
63C22×Dic61C2×D411yescharacteristic
64C22×Dic61C2×D411yescharacteristic
65C2×Dic122—22no—
66C2×Dic122—22no—
67C2×Dic122—21no—
68C2×Dic122C2×C812yes—
69C2×#92420—28no—
70C2×#92420—24no—
71C2×#92420—42no—
72C2×#92420—44no—
73C4⋊C4×C61—22no—
74C42×C61—22no—
75C4⋊Dic61—22no—
76C4⋊Dic61—42no—
77#11758196—28no—
78#11758196—44no—
79#11758196—42no—
80C4×Dic61—24no—
81C4×Dic61—41no—
82C4×Dic61—41no—
83C4×Dic61—41no—
84C4×Dic61—41no—
85C4×Dic61C2×C812yes—
86C4×Dic61M1612yes—
87C4×Dic61SD1614yes—
88C4×Dic61Q1614yes—
89C4×Dic61C2×D412yes—
90C4×Dic61#4112yes—
91C23×C61C2×C22⋊C411yescharacteristic
92Q8×C61—24no—
93Q8×C61—42no—
94C2×C4×C61—22no—
95C2×C4×C61—22no—
96C2×C4×C61—22no—
97C2×C4×C61—41no—
98C2×C4×C61—41no—
99C2×C4×C61—41no—
100C2×C4×C61—42no—
101C2×C4×C61#10314yes—
102C2×C4×C61C4×D412yes—
103C2×C4×C61C22×C811yescharacteristic
104C2×C4×C61C2×M1611yescharacteristic
105C2×C4×C61#13112yes—
106C2×Dic61—22no—
107C2×Dic61—22no—
108C2×Dic61—41no—
109C2×Dic61—41no—
110C2×Dic61—41no—
111C2×Dic61—42no—
112C2×Dic61C22⋊C814yes—
113C2×Dic61#10314yes—
114C2×Dic61#10414yes—
115C2×Dic61#12112yes—
116C2×Dic61#12411yescharacteristic
117C2×Dic61#12711yescharacteristic
118C2×Dic61C2×SD1612yes—
119C2×Dic61C2×Q1612yes—
120Dic122—24no—
121Dic122—42no—
122#92420—28no—
123#92420—82no—
124#9637—611nomaximal, Sylow
125C22×C61#39011yescharacteristic
126C22×C61C2×C22⋊C811yescharacteristic
127C22×C61#40811yescharacteristic
128C22×C61C2×#10312yes—
129C22×C61C2×#10412yes—
130C4×C61—24no—
131C4×C61—42no—
132C4×C61—81no—
133C4×C61C8×D412yes—
134C4×C61#43612yes—
135Dic61—22no—
136Dic61—42no—
137Dic61—81no—
138Dic61Q8⋊C818yescomplemented
139Dic61#48712yes—
140Dic61#49211yescharacteristic
141Dic61#49411yescharacteristic
142C4×C4⋊Q8—611no—
143#1842—611no—
144C42×C8—611no—
145C2×Q8⋊C8—612no—
146C2×Q8⋊C8—612no—
147C2×C61C2×Q8⋊C812yes—
148C2×C61#149312yes—
149C2×C61#195411yescharacteristic
150C2×C61#195611yescharacteristic
151C2×C61#196211yescharacteristic
152C2×C4⋊Q8—611no—
153C2×C4×Q8—611no—
154C2×C4×Q8—611no—
155C2×C4⋊C8—612no—
156C2×C4⋊C8—1222no—
157C2×C4×C8—612no—
158C2×C4×C8—1222no—
159#391—611no—
160#391#692311yescharacteristic
161#389—1222no—
162#384—611no—
163C4×C4⋊C4—1222no—
164C43—611no—
165Q8⋊C8—1224no—
166Q8⋊C8—1224no—
167C61#963711yescharacteristic, complemented, Sylow
168C22×Q8—611no—
169C22×Q8C2×#692311yescharacteristic
170C22×C8—1222no—
171C22×C8—1222no—
172C4⋊Q8—614no—
173C4⋊Q8—1222no—
174C4×Q8—1222no—
175C4×Q8—1222no—
176C4×Q8—1222no—
177C4×Q8—1222no—
178C2×C4⋊C4—611no—
179C2×C4⋊C4—1222no—
180C2×C4⋊C4—1221no—
181C2×C4⋊C4—1221no—
182C2×C4⋊C4—1222no—
183C2×C4⋊C4C2×#692311yescharacteristic
184C2×C42—612no—
185C2×C42—611no—
186C2×C42—611no—
187C2×C42—612no—
188C2×C42—1221no—
189C2×C42—1221no—
190C2×C42C2×#692311yescharacteristic
191C4⋊C8—1222no—
192C4⋊C8—1222no—
193C4⋊C8—2444no—
194C4×C8—614no—
195C4×C8—1222no—
196C4×C8—1228no—
197#95—22no—
198#95—1222no—
199C2×Q8—21no—
200C2×Q8—22no—
201C2×Q8—22no—
202C2×Q8—612no—
203C2×Q8—1221no—
204C2×Q8—1222no—
205C2×Q8—1222no—
206C2×Q8D61⋊C812yes—
207C22×C4—21no—
208C22×C4—21no—
209C22×C4—611no—
210C22×C4—612no—
211C22×C4—611no—
212C22×C4—1221no—
213C22×C4—1221no—
214C22×C4C22⋊#692312yes—
215C22×C4C22×#692311yescharacteristic
216C2×C8—1224no—
217C2×C8—1228no—
218C2×C8—2442no—
219C2×C8—2444no—
220C4⋊C4—22no—
221C4⋊C4—1228no—
222C4⋊C4—1222no—
223C4⋊C4—2444no—
224C4⋊C4—2442no—
225C4⋊C4—2442no—
226C42—22no—
227C42—614no—
228C42—614no—
229C42—612no—
230C42—612no—
231C42—612no—
232C42—612no—
233C42—1224no—
234C42—2441no—
235C42—2441no—
236C42—2441no—
237C42—2441no—
238C23C2×C22⋊#692311yescharacteristic
239Q8—24no—
240Q8—42no—
241Q8—1224no—
242Q8—2442no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—41no—
249C2×C4—42no—
250C2×C4—611no—
251C2×C4—611no—
252C2×C4—614no—
253C2×C4—614no—
254C2×C4—612no—
255C2×C4—612no—
256C2×C4—614no—
257C2×C4—612no—
258C2×C4—1222no—
259C2×C4—1222no—
260C2×C4—2441no—
261C2×C4—2442no—
262C2×C4—2441no—
263C2×C4—2441no—
264C2×C4#1451984014yes—
265C2×C4D4×#692312yes—
266C2×C4C2×D61⋊C811yescharacteristic
267C2×C4D61⋊M1611yescharacteristic
268C2×C4#1451986412yes—
269C8—1228no—
270C8—4882no—
271C22#1684071411yescharacteristic
272C22D61⋊(C22⋊C8)11yescharacteristic
273C22#1684073511yescharacteristic
274C22C2×#1451984012yes—
275C22D61⋊#10412yes—
276C4—24no—
277C4—42no—
278C4—81no—
279C4—618no—
280C4—612no—
281C4—611no—
282C4—611no—
283C4—1222no—
284C4—4881no—
285C4—2442no—
286C4#1684078912yes—
287C4#1684079512yes—
288C2D61⋊(Q8⋊C8)12yes—
289C2#2146116712yes—
290C2#2146194211yescharacteristic
291C2#2146194611yescharacteristic
292C2#2146195411yescharacteristic
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#9637
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
31. #14519775C8semidirect
138. Dic61Q8⋊C8semidirect
167. C61#9637semidirect

Maximal subgroups

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

subgroupindex
#214617522
C42×#924202
C2×#168406122
C2×Q8⋊#924202
#214483882
#963761