Finite Group Databasebeta

← #29590409

Subgroups — #29590409

Order 15616.

358 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 71 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#21451700C211yesmaximal, characteristic
2#21445614C211yesmaximal, characteristic
3#21444141C211yesmaximal, characteristic
4#21443847C211yesmaximal, characteristic
5#21443845C211yesmaximal, characteristic
6#21443825C211yesmaximal, characteristic
7C61×#1346C211yesmaximal, characteristic
8C2×#14519768C411yescharacteristic
9C2×#14519742C2211yescharacteristic
10#16839812—21no—
11C2×#14519695—21no—
12M16×Dic61—21no—
13#16839703—21no—
14#16839702C411yescharacteristic
15#16839701C2211yescharacteristic
16#16839693C411yescharacteristic
17#16839682—21no—
18#16839649—21no—
19#16839648—21no—
20#16839629C411yescharacteristic
21#16839531C2211yescharacteristic
22#16839488C2211yescharacteristic
23#16839487—21no—
24C61×#398C2211yescharacteristic
25C61×#343C2211yescharacteristic
26C61×#324C2211yescharacteristic
27C22×Dic122D411yescharacteristic
28C2×#11758194—21no—
29#14519768—41no—
30#14519768—41no—
31#14519742—41no—
32#14519742—41no—
33C2×C4⋊Dic61—21no—
34C2×C4⋊Dic61C2×C411yescharacteristic
35C2×#11758196—21no—
36C2×#11758196—21no—
37C2×#11758196C2×C411yescharacteristic
38C2×#11758196D411yescharacteristic
39C2×C4×Dic61C2×C411yescharacteristic
40C2×C4×Dic61D411yescharacteristic
41C2×C4×Dic61D411yescharacteristic
42#14519706—41no—
43#14519695—24no—
44C22⋊#92418—21no—
45#14519687—41no—
46C8×Dic61—41no—
47C8×Dic61—41no—
48#14519684—21no—
49#14519684—21no—
50#14519684—21no—
51#14519684—21no—
52#14519684—21no—
53#14519684—21no—
54#14519684—21no—
55#14519684C2×C411yescharacteristic
56C2×M16×C61—21no—
57C2×C4⋊C4×C61—21no—
58C2×C4⋊C4×C61C2×C411yescharacteristic
59C2×C4⋊C4×C61C2311yescharacteristic
60C22⋊C8×C61—21no—
61#95×C61—21no—
62#95×C61C2×C411yescharacteristic
63C22×C4×C61—21no—
64C22×C4×C61—21no—
65C22×C4×C61C22×C411yescharacteristic
66C22×C4×C61C2×D411yescharacteristic
67C22×C4×C61C2×D411yescharacteristic
68C22×Dic61—21no—
69C22×Dic61—21no—
70C22×Dic61C22⋊C411yescharacteristic
71C22×Dic61C22⋊C411yescharacteristic
72C22×Dic61C22⋊C411yescharacteristic
73C22×Dic61C22⋊C411yescharacteristic
74C2×Dic122—21no—
75C2×Dic122—21no—
76C2×Dic122—22no—
77C2×Dic122—41no—
78M16×C61—22no—
79M16×C61—41no—
80C2×C8×C61—41no—
81C2×C8×C61—41no—
82C4⋊C4×C61—41no—
83C4⋊C4×C61—41no—
84C4⋊C4×C61—41no—
85C4⋊C4×C61—41no—
86C4⋊Dic61—41no—
87C4⋊Dic61—41no—
88C4⋊Dic61—41no—
89#11758196—41no—
90#11758196—41no—
91#11758196—42no—
92#11758196—42no—
93C4×Dic61—21no—
94C4×Dic61—21no—
95C4×Dic61—21no—
96C4×Dic61—21no—
97C4×Dic61—21no—
98C4×Dic61—21no—
99#11758194—22no—
100#11758194—41no—
101C2×#92418—41no—
102C2×#92418—41no—
103C23×C61C2×C22⋊C411yescharacteristic
104C2×C4×C61—21no—
105C2×C4×C61—21no—
106C2×C4×C61—21no—
107C2×C4×C61—21no—
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×C4×C61—41no—
116C2×C4×C61#13511yescharacteristic
117C2×C4×C61#13511yescharacteristic
118C2×Dic61—21no—
119C2×Dic61—21no—
120C2×Dic61—21no—
121C2×Dic61—21no—
122C2×Dic61—21no—
123C2×Dic61—21no—
124C2×Dic61—41no—
125C2×Dic61—41no—
126C2×Dic61—41no—
127C2×Dic61—41no—
128C2×Dic61—42no—
129C2×Dic61—41no—
130C2×Dic61—41no—
131C2×Dic61#9911yescharacteristic
132C2×Dic61#9911yescharacteristic
133C2×Dic61#10412yes—
134Dic122—42no—
135Dic122—42no—
136C8×C61—42no—
137C8×C61—81no—
138#92418—42no—
139#92418—81no—
140#11740—611nomaximal, Sylow
141C22×C61—21no—
142C22×C61—21no—
143C22×C61C2×#9911yescharacteristic
144C22×C61#41611yescharacteristic
145C22×C61C2×#10411yescharacteristic
146C4×C61—21no—
147C4×C61—21no—
148C4×C61—41no—
149C4×C61—41no—
150C4×C61—81no—
151C4×C61—81no—
152Dic61—21no—
153Dic61—21no—
154Dic61—22no—
155Dic61—41no—
156Dic61—41no—
157Dic61—81no—
158Dic61—81no—
159#2634—611no—
160C4×#101—611no—
161#1461—611no—
162#1353—611no—
163#1353—611no—
164#1346—611no—
165#1346D6111yescharacteristic
166C2×C61—21no—
167C2×C61—21no—
168C2×C61#150111yescharacteristic
169C2×C61#212311yescharacteristic
170C2×C61#213311yescharacteristic
171C2×#125—611no—
172C2×C4×Q8—611no—
173#431—1221no—
174C2×#101—1221no—
175C4×M16—1221no—
176#400—611no—
177#400—611no—
178#400—1221no—
179#398—611no—
180#398C2×D6111yescharacteristic
181#395—1221no—
182#387—1221no—
183#387—1221no—
184#383—611no—
185#343—611no—
186#343C2×D6111yescharacteristic
187#324—611no—
188#324—1221no—
189#324C2×D6111yescharacteristic
190C61#1174011yescharacteristic, complemented, Sylow
191C22×Q8—611no—
192C2×M16—21no—
193C2×M16—1221no—
194#125—2441no—
195#125—2441no—
196C4×Q8—2441no—
197C4×Q8—2441no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—611no—
200C2×C4⋊C4—611no—
201C2×C4⋊C4—611no—
202C2×C4⋊C4—1221no—
203C2×C4⋊C4—1221no—
204C2×C4⋊C4—1221no—
205C2×C4⋊C4C4×D6111yescharacteristic
206C2×C4⋊C4C22×D6111yescharacteristic
207C2×C42—611no—
208C2×C42—611no—
209C2×C42—611no—
210C4⋊C8—2441no—
211#101—1224no—
212C22⋊C8—21no—
213C22⋊C8—1221no—
214#97—2441no—
215C4×C8—2441no—
216C4×C8—2441no—
217#95—21no—
218#95—611no—
219#95—1221no—
220#95—1221no—
221#95—1221no—
222#95—1221no—
223#95—1221no—
224#95—1221no—
225#95—1221no—
226#95C4×D6111yescharacteristic
227C2×Q8—1222no—
228C2×Q8—1221no—
229C2×Q8—1221no—
230C2×Q8—2441no—
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×C4C2×C4×D6111yescharacteristic
240C22×C4D4×D6111yescharacteristic
241C22×C4D4×D6111yescharacteristic
242M16—22no—
243M16—41no—
244M16—1222no—
245M16—2441no—
246C2×C8—41no—
247C2×C8—41no—
248C2×C8—2441no—
249C2×C8—2441no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—2441no—
255C4⋊C4—2441no—
256C4⋊C4—2441no—
257C4⋊C4—2442no—
258C4⋊C4—2441no—
259C4⋊C4—2441no—
260C4⋊C4—2442no—
261C42—1221no—
262C42—1221no—
263C42—1221no—
264C42—1221no—
265C42—1221no—
266C42—1221no—
267C23C22⋊C4×D6111yescharacteristic
268Q8—2442no—
269Q8—2442no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—611no—
283C2×C4—611no—
284C2×C4—612no—
285C2×C4—1221no—
286C2×C4—1221no—
287C2×C4—1221no—
288C2×C4—1221no—
289C2×C4—1221no—
290C2×C4—1221no—
291C2×C4—2441no—
292C2×C4—2441no—
293C2×C4—2441no—
294C2×C4—2442no—
295C2×C4—2441no—
296C2×C4—2441no—
297C2×C4—2441no—
298C2×C4#1451979611yescharacteristic
299C2×C4#1451979811yescharacteristic
300C8—42no—
301C8—81no—
302C8—4881no—
303C8—2442no—
304C22—21no—
305C22—21no—
306C22#99×D6111yescharacteristic
307C22#1683975511yescharacteristic
308C22#104×D6111yescharacteristic
309C4—21no—
310C4—21no—
311C4—41no—
312C4—41no—
313C4—81no—
314C4—81no—
315C4—1221no—
316C4—1221no—
317C4—1222no—
318C4—4881no—
319C4—4881no—
320C4—2441no—
321C4—2441no—
322C2—21no—
323C2—21no—
324C2#2144430711yescharacteristic
325C2#2144747111yescharacteristic
326C2#2144750711yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C4⋊C4C22×D61
FittingC61×#1346C2
socleC22×C61C2×#99
prime radicalC23×C61C2×C22⋊C4
cosocleC2×C4⋊C4×C61C23
hypercenter#1346D61
hypocenterC61#11740
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1346

Complements

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

NH ≅ G/Ntype
190. C61#11740semidirect

Maximal subgroups

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

subgroupindex
#214517002
#214456142
#214441412
#214438472
#214438452
#214438252
C61×#13462
#1174061