Finite Group Databasebeta

← #29590412

Subgroups — #29590412

Order 15616.

358 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 91 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
1C4×#14519696C211yesmaximal, characteristic
2#21444143C211yesmaximal, characteristic
3#21443846C212yesmaximal
4#21443825C212yesmaximal
5C61×#2634C211yesmaximal, characteristic
6#16839815—21no—
7C2×#14519696—21no—
8C4×#11758194—21no—
9#16839531C2212yes—
10#16839488—21no—
11#16839488C2212yes—
12C2×#125×C61C411yescharacteristic
13C2×C4×Q8×C61C2211yescharacteristic
14C61×#400—21no—
15C61×#400C411yescharacteristic
16C61×#400C2211yescharacteristic
17C61×#398C411yescharacteristic
18C61×#398C2211yescharacteristic
19C61×#395—21no—
20C61×#387—21no—
21C61×#387—21no—
22C61×#383C411yescharacteristic
23C2×#11758194—22no—
24C4⋊#92418—41no—
25#14519696—24no—
26C22⋊#92418—22no—
27#14519688—41no—
28C4×#92418—41no—
29C4×#92418—41no—
30C22×Q8×C61D411yescharacteristic
31#125×C61—41no—
32#125×C61—41no—
33C4×Q8×C61—41no—
34C4×Q8×C61—41no—
35C2×C4⋊C4×C61—21no—
36C2×C4⋊C4×C61—21no—
37C2×C4⋊C4×C61—21no—
38C2×C4⋊C4×C61—21no—
39C2×C4⋊C4×C61C2×C411yescharacteristic
40C2×C4⋊C4×C61C2×C411yescharacteristic
41C2×C4⋊C4×C61C2×C411yescharacteristic
42C2×C4⋊C4×C61D411yescharacteristic
43C2×C4⋊C4×C61C2311yescharacteristic
44C2×C42×C61C2×C411yescharacteristic
45C2×C42×C61D411yescharacteristic
46C2×C42×C61D411yescharacteristic
47#95×C61—21no—
48#95×C61—21no—
49#95×C61—21no—
50#95×C61—21no—
51#95×C61—21no—
52#95×C61—21no—
53#95×C61—21no—
54#95×C61—21no—
55#95×C61C2×C411yescharacteristic
56#95×C61C2×C411yescharacteristic
57C2×Q8×C61—22no—
58C2×Q8×C61—22no—
59C2×Q8×C61—41no—
60C22×C4×C61—21no—
61C22×C4×C61—21no—
62C22×C4×C61—21no—
63C22×C4×C61—21no—
64C22×C4×C61C22⋊C411yescharacteristic
65C22×C4×C61C22⋊C411yescharacteristic
66C22×C4×C61C22⋊C411yescharacteristic
67C22×C4×C61C22⋊C411yescharacteristic
68C22×C4×C61C22×C411yescharacteristic
69C22×C4×C61C2×D411yescharacteristic
70C22×C4×C61C2×D411yescharacteristic
71C4⋊C4×C61—41no—
72C4⋊C4×C61—41no—
73C4⋊C4×C61—41no—
74C4⋊C4×C61—42no—
75C4⋊C4×C61—41no—
76C4⋊C4×C61—41no—
77C4⋊C4×C61—41no—
78C4⋊C4×C61—41no—
79C4⋊C4×C61—42no—
80C4⋊C4×C61—42no—
81C42×C61—21no—
82C42×C61—21no—
83C42×C61—21no—
84C42×C61—21no—
85C42×C61—21no—
86C42×C61—21no—
87#11758194—24no—
88#11758194—42no—
89C2×#92418—42no—
90C2×#92418—42no—
91C23×C61C2×C22⋊C411yescharacteristic
92Q8×C61—44no—
93C2×C4×C61—21no—
94C2×C4×C61—21no—
95C2×C4×C61—21no—
96C2×C4×C61—21no—
97C2×C4×C61—21no—
98C2×C4×C61—21no—
99C2×C4×C61—21no—
100C2×C4×C61—21no—
101C2×C4×C61—21no—
102C2×C4×C61—21no—
103C2×C4×C61—41no—
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×C4×C61—42no—
112C2×C4×C61—41no—
113C2×C4×C61—41no—
114C2×C4×C61—41no—
115C2×C4×C61—41no—
116C2×C4×C61—41no—
117C2×C4×C61—41no—
118C2×C4×C61#9911yescharacteristic
119C2×C4×C61#9911yescharacteristic
120C2×C4×C61#10412yes—
121C2×C4×C61#13512yes—
122#92418—44no—
123#92418—82no—
124#11740—611nomaximal, Sylow
125C22×C61—21no—
126C22×C61—21no—
127C22×C61C2×#9911yescharacteristic
128C22×C61#41611yescharacteristic
129C22×C61C2×#10411yescharacteristic
130C4×C61—21no—
131C4×C61—21no—
132C4×C61—22no—
133C4×C61—22no—
134C4×C61—41no—
135C4×C61—41no—
136C4×C61—41no—
137C4×C61—41no—
138C4×C61—81no—
139C4×C61—81no—
140C4×C61—81no—
141C4×C61—81no—
142#2634D6111yescharacteristic
143C4×#101—611no—
144#1461—611no—
145#1353—612no—
146#1346—612no—
147C2×C61—21no—
148C2×C61—21no—
149C2×C61#150111yescharacteristic
150C2×C61#212311yescharacteristic
151C2×C61#213311yescharacteristic
152C2×#125Dic6111yescharacteristic
153C2×C4×Q8C2×D6111yescharacteristic
154#431—1221no—
155C2×#101—1221no—
156C4×M16—1221no—
157#400—21no—
158#400Dic6111yescharacteristic
159#400C2×D6111yescharacteristic
160#398Dic6111yescharacteristic
161#398C2×D6111yescharacteristic
162#395—21no—
163#387—21no—
164#387—21no—
165#383Dic6111yescharacteristic
166#343—612no—
167#324—612no—
168#324—1221no—
169C61#1174011yescharacteristic, complemented, Sylow
170C22×Q8C22⋊D6111yescharacteristic
171C2×M16—1222no—
172#125—41no—
173#125—41no—
174C4×Q8—41no—
175C4×Q8—41no—
176C2×C4⋊C4—21no—
177C2×C4⋊C4—21no—
178C2×C4⋊C4—21no—
179C2×C4⋊C4—21no—
180C2×C4⋊C4C2×Dic6111yescharacteristic
181C2×C4⋊C4C2×Dic6111yescharacteristic
182C2×C4⋊C4C2×Dic6111yescharacteristic
183C2×C4⋊C4C22⋊D6111yescharacteristic
184C2×C4⋊C4C22×D6111yescharacteristic
185C2×C42C2×Dic6111yescharacteristic
186C2×C42C22⋊D6111yescharacteristic
187C2×C42C22⋊D6111yescharacteristic
188C4⋊C8—2441no—
189#101—1224no—
190C22⋊C8—1222no—
191#97—2441no—
192C4×C8—2441no—
193C4×C8—2441no—
194#95—21no—
195#95—21no—
196#95—21no—
197#95—21no—
198#95—21no—
199#95—21no—
200#95—21no—
201#95—21no—
202#95C2×Dic6111yescharacteristic
203#95C2×Dic6111yescharacteristic
204C2×Q8—22no—
205C2×Q8—22no—
206C2×Q8—41no—
207C22×C4—21no—
208C22×C4—21no—
209C22×C4—21no—
210C22×C4—21no—
211C22×C4C22⋊Dic6111yescharacteristic
212C22×C4C22⋊Dic6111yescharacteristic
213C22×C4C22⋊Dic6111yescharacteristic
214C22×C4C22⋊Dic6111yescharacteristic
215C22×C4C22×Dic6111yescharacteristic
216C22×C4C2×C22⋊D6111yescharacteristic
217C22×C4C2×C22⋊D6111yescharacteristic
218M16—1224no—
219M16—2442no—
220C2×C8—2442no—
221C2×C8—2442no—
222C4⋊C4—41no—
223C4⋊C4—41no—
224C4⋊C4—41no—
225C4⋊C4—41no—
226C4⋊C4—41no—
227C4⋊C4—42no—
228C4⋊C4—41no—
229C4⋊C4—41no—
230C4⋊C4—42no—
231C4⋊C4—42no—
232C42—21no—
233C42—21no—
234C42—21no—
235C42—21no—
236C42—21no—
237C42—21no—
238C23C2×C22⋊Dic6111yescharacteristic
239Q8—44no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—42no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4#1451969211yescharacteristic
266C2×C4#1451969211yescharacteristic
267C2×C4#1451970412yes—
268C2×C4#1451979712yes—
269C8—4882no—
270C8—2444no—
271C22—21no—
272C22—21no—
273C22C2×#1451969211yescharacteristic
274C22#1683975811yescharacteristic
275C22C2×#1451970411yescharacteristic
276C4—21no—
277C4—21no—
278C4—22no—
279C4—22no—
280C4—41no—
281C4—41no—
282C4—41no—
283C4—41no—
284C4—81no—
285C4—81no—
286C4—81no—
287C4—81no—
288C2—21no—
289C2—21no—
290C2#2144431011yescharacteristic
291C2#2144747311yescharacteristic
292C2#2144750811yescharacteristic
subgroupG/H
centerC22C2×#14519692
commutatorC22×C4×C61C22×C4
FrattiniC2×C4⋊C4C22×D61
FittingC61×#2634C2
socleC22×C61C2×#99
prime radicalC23×C61C2×C22⋊C4
cosocleC2×C4⋊C4×C61C23
hypercenter#2634D61
hypocenterC61#11740
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #2634

Complements

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

NH ≅ G/Ntype
169. C61#11740semidirect

Maximal subgroups

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

subgroupindex
C4×#145196962
#214441432
#214438462
#214438252
C61×#26342
#1174061