Finite Group Databasebeta

← #30604890

Subgroups — #30604890

Order 15616.

402 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 72 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
1C4×#14519838C211yesmaximal, characteristic
2#21461061C211yesmaximal, characteristic
3#21460820C212yesmaximal
4#21460803C212yesmaximal
5#21449110C211yesmaximal, characteristic
6#16840779—21no—
7C2×#14519838—21no—
8C4×#11758217—21no—
9#16840642C2212yes—
10#16840608C2212yes—
11#16840607—21no—
12C2×C4×Dic122C2211yescharacteristic
13#16839693C411yescharacteristic
14#16839693C2211yescharacteristic
15#16839692—21no—
16#16839682—21no—
17#16839681C411yescharacteristic
18#16839681C2211yescharacteristic
19C4×#11758196—21no—
20C4×#11758196—21no—
21#16839608C411yescharacteristic
22C2×C4×Q8×C61C411yescharacteristic
23C2×#11758217—22no—
24#14519844—41no—
25#14519838—24no—
26C22⋊#92420—22no—
27#14519832—41no—
28C4×#92420—41no—
29C4×#92420—41no—
30C22×Dic122D411yescharacteristic
31C4×Dic122—41no—
32C4×Dic122—41no—
33C2×C4⋊Dic61D411yescharacteristic
34C2×#11758196—21no—
35C2×#11758196—21no—
36C2×#11758196—21no—
37C2×#11758196—21no—
38C2×#11758196C2×C411yescharacteristic
39C2×#11758196C2311yescharacteristic
40C2×C4×Dic61—21no—
41C2×C4×Dic61D411yescharacteristic
42C2×C4×Dic61D411yescharacteristic
43#14519684—21no—
44#14519684—21no—
45#14519684—21no—
46#14519684—21no—
47#14519684—21no—
48#14519684C2×C411yescharacteristic
49#14519684C2×C411yescharacteristic
50C22×Q8×C61C2×C411yescharacteristic
51C4×Q8×C61—41no—
52C4×Q8×C61—41no—
53C2×C4⋊C4×C61—21no—
54C2×C4⋊C4×C61C2×C411yescharacteristic
55C2×C42×C61—21no—
56C2×C42×C61C2×C411yescharacteristic
57C2×Q8×C61—42no—
58C2×Q8×C61—41no—
59C22×C4×C61—21no—
60C22×C4×C61—21no—
61C22×C4×C61C22⋊C411yescharacteristic
62C22×C4×C61C22⋊C411yescharacteristic
63C22×C4×C61C22×C411yescharacteristic
64C22×Dic61—21no—
65C22×Dic61—21no—
66C22×Dic61C22⋊C411yescharacteristic
67C22×Dic61C22⋊C411yescharacteristic
68C22×Dic61C2×D411yescharacteristic
69C22×Dic61C2×D411yescharacteristic
70C2×Dic122—22no—
71C2×Dic122—22no—
72C2×Dic122—41no—
73#11758217—24no—
74#11758217—42no—
75C2×#92420—42no—
76C2×#92420—42no—
77C4⋊C4×C61—42no—
78C4⋊C4×C61—41no—
79C42×C61—21no—
80C42×C61—21no—
81C42×C61—41no—
82C42×C61—41no—
83C4⋊Dic61—41no—
84#11758196—41no—
85#11758196—41no—
86#11758196—42no—
87#11758196—42no—
88#11758196—42no—
89#11758196—42no—
90C4×Dic61—24no—
91C4×Dic61—21no—
92C4×Dic61—21no—
93C4×Dic61—21no—
94C4×Dic61—21no—
95C23×C61C2×C22⋊C411yescharacteristic
96Q8×C61—42no—
97Q8×C61—42no—
98C2×C4×C61—22no—
99C2×C4×C61—22no—
100C2×C4×C61—21no—
101C2×C4×C61—21no—
102C2×C4×C61—21no—
103C2×C4×C61—21no—
104C2×C4×C61—41no—
105C2×C4×C61—41no—
106C2×C4×C61—41no—
107C2×C4×C61—41no—
108C2×C4×C61—41no—
109C2×C4×C61—41no—
110C2×C4×C61#9911yescharacteristic
111C2×C4×C61#9911yescharacteristic
112C2×Dic61—21no—
113C2×Dic61—21no—
114C2×Dic61—21no—
115C2×Dic61—21no—
116C2×Dic61—22no—
117C2×Dic61—22no—
118C2×Dic61—21no—
119C2×Dic61—21no—
120C2×Dic61—41no—
121C2×Dic61—41no—
122C2×Dic61—41no—
123C2×Dic61—41no—
124C2×Dic61—41no—
125C2×Dic61—41no—
126C2×Dic61#10412yes—
127C2×Dic61#13512yes—
128Dic122—44no—
129#92420—44no—
130#92420—82no—
131#11736—611nomaximal, Sylow
132C22×C61—21no—
133C22×C61—21no—
134C22×C61C2×#9911yescharacteristic
135C22×C61#41611yescharacteristic
136C22×C61C2×#10411yescharacteristic
137C4×C61—21no—
138C4×C61—42no—
139C4×C61—41no—
140C4×C61—41no—
141C4×C61—81no—
142C4×C61#35612yes—
143Dic61—22no—
144Dic61—22no—
145Dic61—42no—
146Dic61—42no—
147Dic61—41no—
148Dic61—41no—
149#2399—611no—
150C4×#101—611no—
151#1461—611no—
152#1354—612no—
153#1346—612no—
154C2×C61—21no—
155C2×C61—21no—
156C2×C61#150111yescharacteristic
157C2×C61#212011yescharacteristic
158C2×C61C2×#35611yescharacteristic
159C2×C4×Q8—611no—
160C2×C4×Q8#692311yescharacteristic
161#431—1221no—
162C2×#101—1221no—
163C4×M16—1221no—
164#398—611no—
165#398—611no—
166#398—1221no—
167#395—611no—
168#395—611no—
169#395—1221no—
170C4×C4⋊C4—1221no—
171C4×C4⋊C4—1221no—
172#376—611no—
173#343—612no—
174#324—612no—
175#324—1221no—
176C61#1173611yescharacteristic, complemented, Sylow
177C22×Q8—611no—
178C22×Q8C2×#692311yescharacteristic
179C2×M16—1222no—
180C4×Q8—41no—
181C4×Q8—41no—
182C4×Q8—2441no—
183C4×Q8—2441no—
184C2×C4⋊C4—21no—
185C2×C4⋊C4—611no—
186C2×C4⋊C4—611no—
187C2×C4⋊C4—611no—
188C2×C4⋊C4—1221no—
189C2×C4⋊C4—1221no—
190C2×C4⋊C4—1221no—
191C2×C4⋊C4—1221no—
192C2×C4⋊C4C2×#692311yescharacteristic
193C2×C42—21no—
194C2×C42—611no—
195C2×C42—611no—
196C2×C42—1221no—
197C2×C42C2×#692311yescharacteristic
198C4⋊C8—2441no—
199#101—1224no—
200C22⋊C8—1222no—
201#97—2441no—
202C4×C8—2441no—
203C4×C8—2441no—
204#95—611no—
205#95—611no—
206#95—1221no—
207#95—1221no—
208#95—1221no—
209#95—1221no—
210#95—1221no—
211C2×Q8—42no—
212C2×Q8—41no—
213C2×Q8—1222no—
214C2×Q8—1222no—
215C2×Q8—2441no—
216C22×C4—21no—
217C22×C4—21no—
218C22×C4—611no—
219C22×C4—611no—
220C22×C4—611no—
221C22×C4—611no—
222C22×C4—1221no—
223C22×C4—1221no—
224C22×C4C22⋊#692311yescharacteristic
225C22×C4C22⋊#692311yescharacteristic
226C22×C4C22×#692311yescharacteristic
227M16—1224no—
228M16—2442no—
229C2×C8—2442no—
230C2×C8—2442no—
231C4⋊C4—41no—
232C4⋊C4—42no—
233C4⋊C4—2441no—
234C4⋊C4—2441no—
235C4⋊C4—2441no—
236C4⋊C4—2442no—
237C4⋊C4—2442no—
238C4⋊C4—2442no—
239C4⋊C4—2442no—
240C42—21no—
241C42—21no—
242C42—41no—
243C42—41no—
244C42—1224no—
245C42—1221no—
246C42—1221no—
247C42—1221no—
248C42—1221no—
249C23C2×C22⋊#692311yescharacteristic
250Q8—42no—
251Q8—42no—
252Q8—2444no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—612no—
266C2×C4—612no—
267C2×C4—1221no—
268C2×C4—1221no—
269C2×C4—1221no—
270C2×C4—1221no—
271C2×C4—1222no—
272C2×C4—1222no—
273C2×C4—1221no—
274C2×C4—1221no—
275C2×C4—2441no—
276C2×C4—2441no—
277C2×C4—2441no—
278C2×C4—2441no—
279C2×C4—2441no—
280C2×C4—2441no—
281C2×C4#1451983511yescharacteristic
282C2×C4#1451983511yescharacteristic
283C8—4882no—
284C8—2444no—
285C22—21no—
286C22—21no—
287C22C2×#1451983511yescharacteristic
288C22#1684075211yescharacteristic
289C22D61⋊#10411yescharacteristic
290C4—21no—
291C4—42no—
292C4—41no—
293C4—41no—
294C4—81no—
295C4—1222no—
296C4—1222no—
297C4—2442no—
298C4—2442no—
299C4—2441no—
300C4—2441no—
301C4#1684067212yes—
302C2—21no—
303C2—21no—
304C2#2146119411yescharacteristic
305C2#2146207011yescharacteristic
306C2C2×#1684067211yescharacteristic
subgroupG/H
centerC2×C4#14519835
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC2×C4×Q8×C61C4
socleC22×C61C2×#99
prime radicalC23×C61C2×C22⋊C4
cosocleC2×#11758196C23
hypercenterC2×C4×Q8#6923
hypocenterC61#11736
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
176. C61#11736semidirect

Maximal subgroups

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

subgroupindex
C4×#145198382
#214610612
#214608202
#214608032
#214491102
#1173661