Finite Group Databasebeta

← #30604990

Subgroups — #30604990

Order 15616.

428 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 68 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#21461525C211yesmaximal, characteristic
2#21461071C211yesmaximal, characteristic
3#21460819C212yesmaximal, complemented
4#21460803C212yesmaximal, complemented
5#21451397C211yesmaximal, characteristic
6C22×#11758217—21no—
7#16840783—21no—
8#16840642—21no—
9#16840642C2212yes—
10#16840608C2212yes—
11#16840605—21no—
12C2×#14519742C411yescharacteristic
13C2×#14519733C2211yescharacteristic
14#16839693C2211yescharacteristic
15#16839683C2211yescharacteristic
16#16839674C411yescharacteristic
17#16839655—21no—
18#16839645—21no—
19#16839644—21no—
20#16839634—21no—
21#16839629C411yescharacteristic
22C61×#397C411yescharacteristic
23C2×#11758217—24no—
24C2×#11758217—22no—
25C2×#11758217—41no—
26C2×#11758217—42no—
27C22×#92420—41no—
28C4⋊#92420—41no—
29C22⋊#92420—22no—
30#14519832—41no—
31C22×Dic122C2×C411yescharacteristic
32C23×Dic61D411yescharacteristic
33#14519742—41no—
34#14519742—41no—
35#14519733—41no—
36#14519733—41no—
37C2×C4⋊Dic61—21no—
38C2×#11758196—21no—
39C2×#11758196—21no—
40C2×#11758196D411yescharacteristic
41C2×#11758196C2311yescharacteristic
42C2×C22⋊Dic61—21no—
43C2×C22⋊Dic61D411yescharacteristic
44C2×C4×Dic61—21no—
45C2×C4×Dic61C2×C411yescharacteristic
46C2×C4×Dic61D411yescharacteristic
47#14519684—21no—
48#14519684—21no—
49#14519684—21no—
50#14519684—21no—
51#14519684—21no—
52#14519684C2×C411yescharacteristic
53C2×C4⋊C4×C61C2×C411yescharacteristic
54C2×C22⋊C4×C61—21no—
55C2×C22⋊C4×C61C2×C411yescharacteristic
56#95×C61—21no—
57#95×C61C2×C411yescharacteristic
58C24×C61C22⋊C411yescharacteristic
59C22×C4×C61—21no—
60C22×C4×C61—21no—
61C22×C4×C61C22⋊C411yescharacteristic
62C22×C4×C61C22×C411yescharacteristic
63C22×Dic61—22no—
64C22×Dic61—21no—
65C22×Dic61—21no—
66C22×Dic61—21no—
67C22×Dic61—21no—
68C22×Dic61—21no—
69C22×Dic61—21no—
70C22×Dic61C22⋊C411yescharacteristic
71C22×Dic61C22⋊C411yescharacteristic
72C22×Dic61C2×D411yescharacteristic
73C22×Dic61C2×D411yescharacteristic
74C2×Dic122—41no—
75C2×Dic122—42no—
76#11758217—24no—
77#11758217—44no—
78#11758217—42no—
79C2×#92420—44no—
80C2×#92420—42no—
81C2×#92420—42no—
82C4⋊C4×C61—41no—
83C22⋊C4×C61—41no—
84C22⋊C4×C61—42no—
85C22⋊Dic61—41no—
86C22⋊Dic61—42no—
87C4⋊Dic61—42no—
88#11758196—41no—
89#11758196—41no—
90#11758196—41no—
91#11758196—41no—
92#11758196—41no—
93#11758196—41no—
94C4×Dic61—21no—
95C4×Dic61—21no—
96C4×Dic61—21no—
97C4×Dic61—21no—
98C4×Dic61—42no—
99C23×C61—21no—
100C23×C61—21no—
101C23×C61—41no—
102C23×C61—41no—
103C23×C61#10412yes—
104C23×C61C2×C22⋊C411yescharacteristic
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×C4×C61—41no—
114C2×C4×C61—41no—
115C2×Dic61—22no—
116C2×Dic61—22no—
117C2×Dic61—22no—
118C2×Dic61—22no—
119C2×Dic61—21no—
120C2×Dic61—21no—
121C2×Dic61—21no—
122C2×Dic61—21no—
123C2×Dic61—22no—
124C2×Dic61—21no—
125C2×Dic61—21no—
126C2×Dic61—41no—
127C2×Dic61—41no—
128C2×Dic61—41no—
129C2×Dic61—41no—
130C2×Dic61—41no—
131C2×Dic61—41no—
132C2×Dic61—41no—
133C2×Dic61#9911yescharacteristic
134C2×Dic61#9911yescharacteristic
135C2×Dic61AGL(1,ℤ/8)11yescharacteristic
136C2×Dic61#13711yescharacteristic
137Dic122—42no—
138Dic122—42no—
139#92420—44no—
140#92420—82no—
141#11763—611nomaximal, Sylow
142C22×C61—21no—
143C22×C61—21no—
144C22×C61—22no—
145C22×C61—42no—
146C22×C61—41no—
147C22×C61—41no—
148C22×C61—81no—
149C22×C61C2×#9911yescharacteristic
150C22×C61#41711yescharacteristic
151C22×C61C2×#10411yescharacteristic
152C4×C61—41no—
153C4×C61—41no—
154C4×C61—81no—
155C4×C61—81no—
156Dic61—21no—
157Dic61—21no—
158Dic61—21no—
159Dic61—21no—
160Dic61—41no—
161Dic61—42no—
162Dic61—41no—
163Dic61—81no—
164#2599—611no—
165#1742—611no—
166#1464—611no—
167#1354—612no—
168#1346—612no—
169C2×C61—21no—
170C2×C61—21no—
171C2×C61—42no—
172C2×C61#150411yescharacteristic
173C2×C61#212011yescharacteristic
174C2×C61#213511yescharacteristic
175C22×M16—1221no—
176C2×C4×Q8—611no—
177C2×#117—611no—
178#432—1221no—
179#398—611no—
180#397#692311yescharacteristic
181#395—611no—
182#393—611no—
183#388—1221no—
184#387—1221no—
185#387—1221no—
186#385—1221no—
187#383—611no—
188#343—612no—
189#343—1221no—
190#324—612no—
191#323—1221no—
192C61#1176311yescharacteristic, complemented, Sylow
193C22×Q8—611no—
194C23×C4—611no—
195C2×M16—1222no—
196C2×M16—1224no—
197C2×M16—2442no—
198C2×M16—2441no—
199C22×C8—2441no—
200C4×Q8—2441no—
201C4×Q8—2441no—
202#117—2441no—
203#117—2441no—
204C2×C4⋊C4—611no—
205C2×C4⋊C4—611no—
206C2×C4⋊C4—1221no—
207C2×C4⋊C4—1221no—
208C2×C4⋊C4—1221no—
209C2×C4⋊C4C2×#692311yescharacteristic
210C2×C22⋊C4—21no—
211C2×C22⋊C4—611no—
212C2×C22⋊C4—1221no—
213C2×C22⋊C4C2×#692311yescharacteristic
214C2×C42—611no—
215C2×C42—611no—
216C2×C42—1221no—
217C4⋊C8—2441no—
218C22⋊C8—1222no—
219#97—2441no—
220#95—21no—
221#95—611no—
222#95—1221no—
223#95—1221no—
224#95—1221no—
225#95—1221no—
226#95—1221no—
227#95C2×#692311yescharacteristic
228C24C22⋊#692311yescharacteristic
229C2×Q8—2441no—
230C2×Q8—2442no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—611no—
234C22×C4—611no—
235C22×C4—611no—
236C22×C4—611no—
237C22×C4—1221no—
238C22×C4—1221no—
239C22×C4—1221no—
240C22×C4—1221no—
241C22×C4—1222no—
242C22×C4—1221no—
243C22×C4—1221no—
244C22×C4C22⋊#692311yescharacteristic
245C22×C4C22×#692311yescharacteristic
246M16—1224no—
247M16—2442no—
248M16—2444no—
249C2×C8—2442no—
250C2×C8—2444no—
251C2×C8—2442no—
252C4⋊C4—41no—
253C4⋊C4—2441no—
254C4⋊C4—2441no—
255C4⋊C4—2441no—
256C4⋊C4—2441no—
257C4⋊C4—2441no—
258C4⋊C4—2441no—
259C4⋊C4—2442no—
260C22⋊C4—41no—
261C22⋊C4—42no—
262C22⋊C4—2441no—
263C22⋊C4—2442no—
264C42—1221no—
265C42—1221no—
266C42—1221no—
267C42—1221no—
268C42—2442no—
269C23—21no—
270C23—21no—
271C23—41no—
272C23—41no—
273C23#1451984112yes—
274C23C2×C22⋊#692311yescharacteristic
275Q8—2442no—
276Q8—2442no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—611no—
288C2×C4—611no—
289C2×C4—611no—
290C2×C4—611no—
291C2×C4—1222no—
292C2×C4—1222no—
293C2×C4—1222no—
294C2×C4—1222no—
295C2×C4—1221no—
296C2×C4—1221no—
297C2×C4—1221no—
298C2×C4—1221no—
299C2×C4—1222no—
300C2×C4—1221no—
301C2×C4—1221no—
302C2×C4—2441no—
303C2×C4—2441no—
304C2×C4—2441no—
305C2×C4—2441no—
306C2×C4—2441no—
307C2×C4—2441no—
308C2×C4—2441no—
309C8—4882no—
310C8—2444no—
311C22—21no—
312C22—21no—
313C22—22no—
314C22—42no—
315C22—41no—
316C22—41no—
317C22—81no—
318C22D61⋊#9911yescharacteristic
319C22#1684075311yescharacteristic
320C22C2×#1451984111yescharacteristic
321C4—41no—
322C4—41no—
323C4—81no—
324C4—81no—
325C4—1221no—
326C4—1221no—
327C4—1221no—
328C4—1221no—
329C4—4881no—
330C4—2441no—
331C4—2442no—
332C4—2441no—
333C2—21no—
334C2—21no—
335C2—42no—
336C2#2146120411yescharacteristic
337C2#2146207311yescharacteristic
338C2#2146212211yescharacteristic
subgroupG/H
centerC22D61⋊#99
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#397C4
socleC22×C61C2×#99
prime radicalC24×C61C22⋊C4
cosocleC2×#11758196C23
hypercenter#397#6923
hypocenterC61#11763
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #397

Complements

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

NH ≅ G/Ntype
3. #21460819C2semidirect
4. #21460803C2semidirect
192. C61#11763semidirect

Maximal subgroups

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

subgroupindex
#214615252
#214610712
#214608192
#214608032
#214513972
#1176361