Finite Group Databasebeta

← #30605173

Subgroups — #30605173

Order 15616.

388 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 64 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#21461721C211yesmaximal, characteristic
2#21461071C211yesmaximal, characteristic
3#21460819C212yesmaximal, complemented
4#21460818C212yesmaximal, complemented
5#21449088C211yesmaximal, characteristic
6#16840783—21no—
7#16840732—21no—
8#16840642—21no—
9#16840642C2212yes—
10#16840608C2212yes—
11#16840605—21no—
12C2×#14519742C411yescharacteristic
13C2×#14519733C2211yescharacteristic
14#16839700C2211yescharacteristic
15#16839693—21no—
16#16839685—21no—
17#16839683C2211yescharacteristic
18#16839674C411yescharacteristic
19C4⋊C4×Dic61—21no—
20#16839613C411yescharacteristic
21C22⋊C4×Dic61—21no—
22C61×#399C411yescharacteristic
23C2×#11758217—22no—
24C4⋊#92420—41no—
25C22⋊#92420—22no—
26C22⋊#92420—41no—
27C22⋊#92420—41no—
28#14519832—41no—
29C22×Dic122C2×C411yescharacteristic
30C23×Dic61D411yescharacteristic
31#14519742—41no—
32#14519742—41no—
33#14519733—41no—
34#14519733—41no—
35C2×C4⋊Dic61—21no—
36C2×#11758196—21no—
37C2×#11758196—21no—
38C2×#11758196D411yescharacteristic
39C2×#11758196C2311yescharacteristic
40C2×C22⋊Dic61—21no—
41C2×C22⋊Dic61D411yescharacteristic
42C2×C4×Dic61—21no—
43C2×C4×Dic61—21no—
44C2×C4×Dic61C2×C411yescharacteristic
45C2×C4×Dic61D411yescharacteristic
46#14519684—21no—
47#14519684—21no—
48#14519684—21no—
49#14519684—21no—
50#14519684C2×C411yescharacteristic
51C2×C4⋊C4×C61—21no—
52C2×C4⋊C4×C61C2×C411yescharacteristic
53C2×C22⋊C4×C61—21no—
54C2×C22⋊C4×C61C2×C411yescharacteristic
55#95×C61C2×C411yescharacteristic
56C24×C61C22⋊C411yescharacteristic
57C22×C4×C61—21no—
58C22×C4×C61—21no—
59C22×C4×C61C22⋊C411yescharacteristic
60C22×C4×C61C22×C411yescharacteristic
61C22×Dic61—21no—
62C22×Dic61—21no—
63C22×Dic61—21no—
64C22×Dic61—22no—
65C22×Dic61—21no—
66C22×Dic61—41no—
67C22×Dic61C22⋊C411yescharacteristic
68C22×Dic61C22⋊C411yescharacteristic
69C22×Dic61C2×D411yescharacteristic
70C22×Dic61C2×D411yescharacteristic
71C2×Dic122—41no—
72C2×Dic122—42no—
73#11758217—42no—
74#11758217—42no—
75C2×#92420—42no—
76C2×#92420—42no—
77C4⋊C4×C61—42no—
78C4⋊C4×C61—41no—
79C22⋊C4×C61—41no—
80C22⋊C4×C61—42no—
81C22⋊Dic61—41no—
82C22⋊Dic61—42no—
83C4⋊Dic61—42no—
84#11758196—41no—
85#11758196—41no—
86#11758196—42no—
87#11758196—42no—
88C4×Dic61—21no—
89C4×Dic61—21no—
90C4×Dic61—21no—
91C4×Dic61—21no—
92C4×Dic61—42no—
93C4×Dic61—41no—
94C4×Dic61—41no—
95C23×C61—21no—
96C23×C61—21no—
97C23×C61—21no—
98C23×C61—41no—
99C23×C61—41no—
100C23×C61C2×C22⋊C411yescharacteristic
101C2×C4×C61—22no—
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—41no—
111C2×Dic61—21no—
112C2×Dic61—21no—
113C2×Dic61—21no—
114C2×Dic61—21no—
115C2×Dic61—22no—
116C2×Dic61—21no—
117C2×Dic61—21no—
118C2×Dic61—42no—
119C2×Dic61—42no—
120C2×Dic61—41no—
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×Dic61#13712yes—
130Dic122—42no—
131Dic122—42no—
132#92420—82no—
133#92420—82no—
134#11816—611nomaximal, Sylow
135C22×C61—21no—
136C22×C61—21no—
137C22×C61—42no—
138C22×C61—41no—
139C22×C61—41no—
140C22×C61—41no—
141C22×C61—81no—
142C22×C61C2×#9911yescharacteristic
143C22×C61#41911yescharacteristic
144C22×C61#42111yescharacteristic
145C4×C61—42no—
146C4×C61—41no—
147C4×C61—41no—
148C4×C61—81no—
149Dic61—22no—
150Dic61—21no—
151Dic61—21no—
152Dic61—41no—
153Dic61—42no—
154Dic61—41no—
155Dic61—81no—
156#2396—611no—
157#1822—611no—
158#1464—611no—
159#1354—612no—
160#1353—612no—
161C2×C61—21no—
162C2×C61—21no—
163C2×C61—81no—
164C2×C61#151111yescharacteristic
165C2×C61#212011yescharacteristic
166C2×C61#213211yescharacteristic
167C2×C4×Q8—611no—
168C2×#117—611no—
169#432—1221no—
170#407—1221no—
171#400—611no—
172#399#692311yescharacteristic
173#398—1221no—
174#396—1221no—
175#395—611no—
176#393—611no—
177C4×C4⋊C4—611no—
178C4×C4⋊C4—1221no—
179C4×C22⋊C4—1221no—
180#343—612no—
181#343—1221no—
182#324—612no—
183#323—1221no—
184C61#1181611yescharacteristic, complemented, Sylow
185C22×Q8—611no—
186C23×C4—611no—
187C2×M16—1222no—
188C4×Q8—2441no—
189C4×Q8—2441no—
190#117—2441no—
191#117—2441no—
192C2×C4⋊C4—21no—
193C2×C4⋊C4—611no—
194C2×C4⋊C4—611no—
195C2×C4⋊C4—1221no—
196C2×C4⋊C4—1221no—
197C2×C4⋊C4—1221no—
198C2×C4⋊C4C2×#692311yescharacteristic
199C2×C22⋊C4—21no—
200C2×C22⋊C4—611no—
201C2×C22⋊C4—1221no—
202C2×C22⋊C4C2×#692311yescharacteristic
203C2×C42—611no—
204C2×C42—611no—
205C2×C42—1221no—
206C2×C42—1221no—
207C4⋊C8—2441no—
208C22⋊C8—1222no—
209C22⋊C8—2441no—
210C22⋊C8—2441no—
211#97—2441no—
212#95—611no—
213#95—1221no—
214#95—1221no—
215#95—1221no—
216#95—1221no—
217#95C2×#692311yescharacteristic
218C24C22⋊#692311yescharacteristic
219C2×Q8—2441no—
220C2×Q8—2442no—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—611no—
224C22×C4—611no—
225C22×C4—611no—
226C22×C4—611no—
227C22×C4—1221no—
228C22×C4—1221no—
229C22×C4—1222no—
230C22×C4—1221no—
231C22×C4—1221no—
232C22×C4—2441no—
233C22×C4C22⋊#692311yescharacteristic
234C22×C4C22×#692311yescharacteristic
235M16—2442no—
236M16—2442no—
237C2×C8—2442no—
238C2×C8—2442no—
239C4⋊C4—41no—
240C4⋊C4—42no—
241C4⋊C4—2441no—
242C4⋊C4—2441no—
243C4⋊C4—2442no—
244C4⋊C4—2442no—
245C4⋊C4—2442no—
246C22⋊C4—41no—
247C22⋊C4—42no—
248C22⋊C4—2441no—
249C22⋊C4—2442no—
250C42—1221no—
251C42—1221no—
252C42—1221no—
253C42—1221no—
254C42—2441no—
255C42—2441no—
256C42—2442no—
257C23—21no—
258C23—21no—
259C23—21no—
260C23—41no—
261C23—41no—
262C23C2×C22⋊#692311yescharacteristic
263Q8—2442no—
264Q8—2442no—
265C2×C4—22no—
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—41no—
275C2×C4—611no—
276C2×C4—611no—
277C2×C4—612no—
278C2×C4—1221no—
279C2×C4—1221no—
280C2×C4—1221no—
281C2×C4—1221no—
282C2×C4—1222no—
283C2×C4—1221no—
284C2×C4—1221no—
285C2×C4—2442no—
286C2×C4—2442no—
287C2×C4—2441no—
288C2×C4—2441no—
289C2×C4—2441no—
290C2×C4—2441no—
291C2×C4—2441no—
292C2×C4—2441no—
293C2×C4—2441no—
294C8—4882no—
295C8—4882no—
296C22—21no—
297C22—21no—
298C22—42no—
299C22—41no—
300C22—41no—
301C22—41no—
302C22—81no—
303C22D61⋊#9911yescharacteristic
304C22#1684075511yescharacteristic
305C22#1684075911yescharacteristic
306C4—42no—
307C4—41no—
308C4—41no—
309C4—81no—
310C4—1222no—
311C4—1221no—
312C4—1221no—
313C4—4881no—
314C4—2441no—
315C4—2442no—
316C4—2441no—
317C2—21no—
318C2—21no—
319C2—81no—
320C2#2146122811yescharacteristic
321C2#2146207311yescharacteristic
322C2#2146211111yescharacteristic
subgroupG/H
centerC22D61⋊#99
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#399C4
socleC22×C61C2×#99
prime radicalC24×C61C22⋊C4
cosocleC2×#11758196C23
hypercenter#399#6923
hypocenterC61#11816
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #399

Complements

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

NH ≅ G/Ntype
3. #21460819C2semidirect
4. #21460818C2semidirect
184. C61#11816semidirect

Maximal subgroups

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

subgroupindex
#214617212
#214610712
#214608192
#214608182
#214490882
#1181661