Finite Group Databasebeta

← #30604891

Subgroups — #30604891

Order 15616.

402 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 70 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#21461572C211yesmaximal, characteristic
2#21461063C211yesmaximal, characteristic
3#21460819C212yesmaximal
4#21460803C212yesmaximal
5#21449111C211yesmaximal, characteristic
6#16840778—21no—
7C2×#14519838—21no—
8C4×#11758217—21no—
9#16840642C2212yes—
10#16840608—21no—
11#16840608C2212yes—
12C2×#14519742C411yescharacteristic
13C2×#14519742C2211yescharacteristic
14#16839696—21no—
15#16839693C2211yescharacteristic
16#16839683C2211yescharacteristic
17#16839682—21no—
18#16839682C411yescharacteristic
19C4⋊C4×Dic61—21no—
20#16839613—21no—
21#16839607C411yescharacteristic
22C61×#398C411yescharacteristic
23C2×#11758217—22no—
24C4⋊#92420—41no—
25#14519838—24no—
26C22⋊#92420—22no—
27#14519832—41no—
28C4×#92420—41no—
29C4×#92420—41no—
30C22×Dic122C2×C411yescharacteristic
31C22×Dic122D411yescharacteristic
32#14519742—41no—
33#14519742—41no—
34#14519742—41no—
35#14519742—41no—
36C2×C4⋊Dic61—21no—
37C2×#11758196—21no—
38C2×#11758196—21no—
39C2×#11758196—21no—
40C2×#11758196D411yescharacteristic
41C2×#11758196C2311yescharacteristic
42C2×C4×Dic61—21no—
43C2×C4×Dic61—21no—
44C2×C4×Dic61C2×C411yescharacteristic
45C2×C4×Dic61D411yescharacteristic
46C2×C4×Dic61D411yescharacteristic
47#14519684—21no—
48#14519684—21no—
49#14519684—21no—
50#14519684—21no—
51#14519684C2×C411yescharacteristic
52C2×C4⋊C4×C61—21no—
53C2×C4⋊C4×C61C2×C411yescharacteristic
54C2×C4⋊C4×C61C2×C411yescharacteristic
55#95×C61—21no—
56#95×C61C2×C411yescharacteristic
57C22×C4×C61—21no—
58C22×C4×C61—21no—
59C22×C4×C61C22⋊C411yescharacteristic
60C22×C4×C61C22⋊C411yescharacteristic
61C22×C4×C61C22×C411yescharacteristic
62C22×Dic61—21no—
63C22×Dic61—21no—
64C22×Dic61C22⋊C411yescharacteristic
65C22×Dic61C22⋊C411yescharacteristic
66C22×Dic61C2×D411yescharacteristic
67C22×Dic61C2×D411yescharacteristic
68C2×Dic122—22no—
69C2×Dic122—22no—
70C2×Dic122—41no—
71C2×Dic122—41no—
72C2×Dic122—42no—
73#11758217—24no—
74#11758217—42no—
75C2×#92420—42no—
76C2×#92420—42no—
77C4⋊C4×C61—41no—
78C4⋊C4×C61—41no—
79C4⋊C4×C61—42no—
80C4⋊Dic61—42no—
81#11758196—41no—
82#11758196—41no—
83#11758196—42no—
84#11758196—42no—
85#11758196—42no—
86C4×Dic61—24no—
87C4×Dic61—21no—
88C4×Dic61—21no—
89C4×Dic61—21no—
90C4×Dic61—21no—
91C4×Dic61—21no—
92C4×Dic61—21no—
93C4×Dic61—41no—
94C4×Dic61—41no—
95C23×C61C2×C22⋊C411yescharacteristic
96C2×C4×C61—21no—
97C2×C4×C61—21no—
98C2×C4×C61—22no—
99C2×C4×C61—21no—
100C2×C4×C61—21no—
101C2×C4×C61—41no—
102C2×C4×C61—41no—
103C2×C4×C61—41no—
104C2×C4×C61—41no—
105C2×C4×C61—41no—
106C2×C4×C61—41no—
107C2×C4×C61—41no—
108C2×C4×C61#10412yes—
109C2×Dic61—21no—
110C2×Dic61—21no—
111C2×Dic61—22no—
112C2×Dic61—22no—
113C2×Dic61—22no—
114C2×Dic61—21no—
115C2×Dic61—21no—
116C2×Dic61—21no—
117C2×Dic61—21no—
118C2×Dic61—41no—
119C2×Dic61—41no—
120C2×Dic61—41no—
121C2×Dic61—41no—
122C2×Dic61—41no—
123C2×Dic61#9911yescharacteristic
124C2×Dic61#9911yescharacteristic
125C2×Dic61#13512yes—
126Dic122—44no—
127Dic122—42no—
128Dic122—42no—
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—22no—
138C4×C61—42no—
139C4×C61—41no—
140C4×C61—41no—
141C4×C61—81no—
142Dic61—21no—
143Dic61—22no—
144Dic61—42no—
145Dic61—41no—
146Dic61—42no—
147Dic61—41no—
148Dic61#35612yes—
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—611no—
161#431—1221no—
162C2×#101—1221no—
163C4×M16—1221no—
164#398—611no—
165#398—1221no—
166#398#692311yescharacteristic
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×Q8—611no—
179C2×M16—1222no—
180C4×Q8—2441no—
181C4×Q8—2441no—
182C4×Q8—2441no—
183C4×Q8—2441no—
184C2×C4⋊C4—21no—
185C2×C4⋊C4—611no—
186C2×C4⋊C4—611no—
187C2×C4⋊C4—1221no—
188C2×C4⋊C4—1221no—
189C2×C4⋊C4—1221no—
190C2×C4⋊C4—1221no—
191C2×C4⋊C4C2×#692311yescharacteristic
192C2×C4⋊C4C2×#692311yescharacteristic
193C2×C42—611no—
194C2×C42—611no—
195C2×C42—611no—
196C2×C42—1221no—
197C2×C42—1221no—
198C4⋊C8—2441no—
199#101—1224no—
200C22⋊C8—1222no—
201#97—2441no—
202C4×C8—2441no—
203C4×C8—2441no—
204#95—21no—
205#95—611no—
206#95—1221no—
207#95—1221no—
208#95—1221no—
209#95—1221no—
210#95C2×#692311yescharacteristic
211C2×Q8—1222no—
212C2×Q8—1222no—
213C2×Q8—2441no—
214C2×Q8—2441no—
215C2×Q8—2442no—
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—41no—
233C4⋊C4—42no—
234C4⋊C4—2441no—
235C4⋊C4—2441no—
236C4⋊C4—2442no—
237C4⋊C4—2442no—
238C4⋊C4—2442no—
239C4⋊C4—2442no—
240C42—1221no—
241C42—1221no—
242C42—1221no—
243C42—1221no—
244C42—1221no—
245C42—1221no—
246C42—1224no—
247C42—2441no—
248C42—2441no—
249C23C2×C22⋊#692311yescharacteristic
250Q8—2444no—
251Q8—2442no—
252Q8—2442no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—22no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—41no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—611no—
266C2×C4—611no—
267C2×C4—612no—
268C2×C4—1222no—
269C2×C4—1221no—
270C2×C4—1221no—
271C2×C4—1222no—
272C2×C4—1222no—
273C2×C4—1221no—
274C2×C4—1221no—
275C2×C4—1221no—
276C2×C4—1221no—
277C2×C4—2441no—
278C2×C4—2441no—
279C2×C4—2441no—
280C2×C4—2441no—
281C2×C4—2441no—
282C2×C4#1451984112yes—
283C8—4882no—
284C8—2444no—
285C22—21no—
286C22—21no—
287C22D61⋊#9911yescharacteristic
288C22#1684075211yescharacteristic
289C22C2×#1451984111yescharacteristic
290C4—22no—
291C4—42no—
292C4—41no—
293C4—41no—
294C4—81no—
295C4—612no—
296C4—1221no—
297C4—1222no—
298C4—2442no—
299C4—2441no—
300C4—2442no—
301C4—2441no—
302C2—21no—
303C2—21no—
304C2#2146119511yescharacteristic
305C2#2146207311yescharacteristic
306C2D61⋊#35611yescharacteristic
subgroupG/H
centerC22D61⋊#99
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#398C4
socleC22×C61C2×#99
prime radicalC23×C61C2×C22⋊C4
cosocleC2×#11758196C23
hypercenter#398#6923
hypocenterC61#11736
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #398

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
#214615722
#214610632
#214608192
#214608032
#214491112
#1173661