Finite Group Databasebeta

← #30605231

Subgroups — #30605231

Order 15616.

384 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 66 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#21461686C211yesmaximal, characteristic
2#21461083C211yesmaximal, characteristic
3#21460820C212yesmaximal
4#21460804C212yesmaximal
5#21449109C211yesmaximal, characteristic
6#16840782—21no—
7#16840765—21no—
8C2×#14519838—21no—
9#16840642C2212yes—
10#16840608—21no—
11#16840608C2212yes—
12C2×Q8×Dic61C411yescharacteristic
13C2×#14519742C2211yescharacteristic
14#16839695—21no—
15#16839694C2211yescharacteristic
16#16839692C411yescharacteristic
17#16839683—21no—
18#16839681C2211yescharacteristic
19C4⋊C4×Dic61—21no—
20#16839613—21no—
21#16839607C411yescharacteristic
22C61×#395C411yescharacteristic
23C2×#11758217—22no—
24#14519844—41no—
25#14519844—41no—
26C4⋊#92420—41no—
27#14519838—42no—
28C22⋊#92420—22no—
29#14519832—41no—
30C22×Dic122D411yescharacteristic
31Q8×Dic61—41no—
32Q8×Dic61—41no—
33#14519742—41no—
34#14519742—41no—
35C2×C4⋊Dic61—21no—
36C2×C4⋊Dic61—21no—
37C2×C4⋊Dic61C2×C411yescharacteristic
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
52C22×Q8×C61C2×C411yescharacteristic
53C2×C4⋊C4×C61—21no—
54C2×C4⋊C4×C61C2×C411yescharacteristic
55#95×C61—21no—
56#95×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—21no—
71C2×Dic122—21no—
72C2×Dic122—41no—
73C2×Dic122—41no—
74#11758217—42no—
75#11758217—42no—
76C2×#92420—42no—
77C2×#92420—42no—
78C4⋊C4×C61—41no—
79C4⋊C4×C61—42no—
80C4⋊Dic61—42no—
81C4⋊Dic61—41no—
82C4⋊Dic61—41no—
83C4⋊Dic61—41no—
84#11758196—41no—
85#11758196—41no—
86#11758196—42no—
87#11758196—42no—
88C4×Dic61—24no—
89C4×Dic61—21no—
90C4×Dic61—21no—
91C4×Dic61—21no—
92C4×Dic61—21no—
93C4×Dic61—21no—
94C4×Dic61—21no—
95C4×Dic61—41no—
96C4×Dic61—41no—
97C23×C61C2×C22⋊C411yescharacteristic
98Q8×C61—42no—
99Q8×C61—42no—
100C2×C4×C61—22no—
101C2×C4×C61—22no—
102C2×C4×C61—21no—
103C2×C4×C61—21no—
104C2×C4×C61—21no—
105C2×C4×C61—21no—
106C2×C4×C61—21no—
107C2×C4×C61—41no—
108C2×C4×C61—41no—
109C2×C4×C61—41no—
110C2×C4×C61—41no—
111C2×C4×C61—41no—
112C2×C4×C61—41no—
113C2×Dic61—21no—
114C2×Dic61—21no—
115C2×Dic61—22no—
116C2×Dic61—22no—
117C2×Dic61—21no—
118C2×Dic61—21no—
119C2×Dic61—21no—
120C2×Dic61—21no—
121C2×Dic61—41no—
122C2×Dic61—41no—
123C2×Dic61—41no—
124C2×Dic61—41no—
125C2×Dic61—41no—
126C2×Dic61—41no—
127C2×Dic61#9911yescharacteristic
128C2×Dic61#9911yescharacteristic
129C2×Dic61AGL(1,ℤ/8)11yescharacteristic
130C2×Dic61#13711yescharacteristic
131Dic122—42no—
132Dic122—42no—
133#92420—82no—
134#92420—82no—
135#11831—611nomaximal, Sylow
136C22×C61—21no—
137C22×C61—21no—
138C22×C61C2×#9911yescharacteristic
139C22×C61#41711yescharacteristic
140C22×C61#42111yescharacteristic
141C4×C61—42no—
142C4×C61—41no—
143C4×C61—42no—
144C4×C61—41no—
145C4×C61—41no—
146Dic61—21no—
147Dic61—21no—
148Dic61—21no—
149Dic61—42no—
150Dic61—41no—
151Dic61—41no—
152Dic61—81no—
153Dic61#35612yes—
154#2399—611no—
155#1801—611no—
156#1467—611no—
157#1354—612no—
158#1346—612no—
159C2×C61—21no—
160C2×C61—21no—
161C2×C61#151311yescharacteristic
162C2×C61#212011yescharacteristic
163C2×C61C2×#35611yescharacteristic
164C2×C4×Q8—611no—
165C2×C4×Q8—611no—
166#432—1221no—
167#423—1221no—
168C2×#101—1221no—
169#398—611no—
170#398—611no—
171#398—1221no—
172#395—611no—
173#395—1221no—
174#395#692311yescharacteristic
175C4×C4⋊C4—1221no—
176C4×C4⋊C4—1221no—
177#376—611no—
178#343—612no—
179#324—612no—
180#324—1221no—
181C61#1183111yescharacteristic, complemented, Sylow
182C22×Q8—611no—
183C22×Q8C2×#692311yescharacteristic
184C2×M16—1222no—
185C4×Q8—2441no—
186C4×Q8—2441no—
187C4×Q8—2441no—
188C4×Q8—2441no—
189C2×C4⋊C4—21no—
190C2×C4⋊C4—611no—
191C2×C4⋊C4—611no—
192C2×C4⋊C4—611no—
193C2×C4⋊C4—1221no—
194C2×C4⋊C4—1221no—
195C2×C4⋊C4—1221no—
196C2×C4⋊C4—1221no—
197C2×C4⋊C4C2×#692311yescharacteristic
198C2×C42—611no—
199C2×C42—611no—
200C2×C42—611no—
201C2×C42—1221no—
202C2×C42—1221no—
203C4⋊C8—2441no—
204C4⋊C8—2441no—
205C4⋊C8—2441no—
206#101—2442no—
207C22⋊C8—1222no—
208#97—2441no—
209#95—21no—
210#95—611no—
211#95—1221no—
212#95—1221no—
213#95—1221no—
214#95—1221no—
215#95C2×#692311yescharacteristic
216C2×Q8—42no—
217C2×Q8—41no—
218C2×Q8—1221no—
219C2×Q8—1221no—
220C2×Q8—2441no—
221C2×Q8—2441no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—611no—
225C22×C4—611no—
226C22×C4—611no—
227C22×C4—611no—
228C22×C4—1221no—
229C22×C4—1221no—
230C22×C4C22⋊#692311yescharacteristic
231C22×C4C22⋊#692311yescharacteristic
232C22×C4C22×#692311yescharacteristic
233M16—2442no—
234M16—2442no—
235C2×C8—2442no—
236C2×C8—2442no—
237C4⋊C4—41no—
238C4⋊C4—42no—
239C4⋊C4—2441no—
240C4⋊C4—2441no—
241C4⋊C4—2441no—
242C4⋊C4—2442no—
243C4⋊C4—2442no—
244C4⋊C4—2441no—
245C4⋊C4—2441no—
246C4⋊C4—2442no—
247C42—1221no—
248C42—1221no—
249C42—1221no—
250C42—1221no—
251C42—1221no—
252C42—1221no—
253C42—1224no—
254C42—2441no—
255C42—2441no—
256C23C2×C22⋊#692311yescharacteristic
257Q8—42no—
258Q8—42no—
259Q8—2442no—
260Q8—2442no—
261C2×C4—22no—
262C2×C4—22no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—611no—
275C2×C4—611no—
276C2×C4—611no—
277C2×C4—611no—
278C2×C4—1222no—
279C2×C4—1221no—
280C2×C4—1221no—
281C2×C4—1222no—
282C2×C4—1221no—
283C2×C4—1221no—
284C2×C4—1221no—
285C2×C4—1221no—
286C2×C4—2441no—
287C2×C4—2441no—
288C2×C4—2441no—
289C2×C4—2441no—
290C2×C4—2441no—
291C2×C4—2441no—
292C8—4882no—
293C8—4882no—
294C22—21no—
295C22—21no—
296C22D61⋊#9911yescharacteristic
297C22#1684075311yescharacteristic
298C22#1684076111yescharacteristic
299C4—42no—
300C4—41no—
301C4—42no—
302C4—41no—
303C4—41no—
304C4—612no—
305C4—1221no—
306C4—1221no—
307C4—1221no—
308C4—4881no—
309C4—2442no—
310C4—2441no—
311C4—2441no—
312C2—21no—
313C2—21no—
314C2#2146123711yescharacteristic
315C2#2146207111yescharacteristic
316C2D61⋊#35611yescharacteristic
subgroupG/H
centerC22D61⋊#99
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#395C4
socleC22×C61C2×#99
prime radicalC23×C61C2×C22⋊C4
cosocleC2×#11758196C23
hypercenter#395#6923
hypocenterC61#11831
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #395

Complements

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

NH ≅ G/Ntype
181. C61#11831semidirect

Maximal subgroups

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

subgroupindex
#214616862
#214610832
#214608202
#214608042
#214491092
#1183161