Finite Group Databasebeta

← #29567310

Subgroups — #29567310

Order 15616.

432 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 67 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#21445743C211yesmaximal, characteristic
2#21445743C211yesmaximal, characteristic
3C61×#1784C211yesmaximal, characteristic
4C2×#14519696—21no—
5C2×#14519696—21no—
6C2×#14519696—21no—
7C2×#14519696C412yes—
8#16839726—21no—
9#16839726C412yes—
10C23×Q8×C61C2211yescharacteristic
11C2×#101×C61—21no—
12C2×#101×C61C412yes—
13C61×#407—21no—
14C2×#11758194—22no—
15C2×#11758194—22no—
16#14519696—42no—
17#14519696—42no—
18#14519696—42no—
19#14519696—42no—
20C22⋊#92418—42no—
21C22⋊#92418—42no—
22C22×Q8×C61—42no—
23C22×Q8×C61—42no—
24C22×Q8×C61—42no—
25C22×Q8×C61C2×C411yescharacteristic
26C22×Q8×C61C2×C411yescharacteristic
27C22×Q8×C61D411yescharacteristic
28C22×Q8×C61D411yescharacteristic
29C23×C4×C61C2×C411yescharacteristic
30C23×C4×C61D411yescharacteristic
31C23×C4×C61Q811yescharacteristic
32C2×M16×C61—22no—
33#101×C61—42no—
34#101×C61—42no—
35C22⋊C8×C61—42no—
36C24×C61C4⋊C411yescharacteristic
37C2×Q8×C61—22no—
38C2×Q8×C61—22no—
39C2×Q8×C61—22no—
40C2×Q8×C61—22no—
41C2×Q8×C61—22no—
42C2×Q8×C61—22no—
43C2×Q8×C61—41no—
44C2×Q8×C61—41no—
45C2×Q8×C61—41no—
46C2×Q8×C61—41no—
47C2×Q8×C61—41no—
48C2×Q8×C61—41no—
49C2×Q8×C61—416no—
50C22×C4×C61—22no—
51C22×C4×C61—22no—
52C22×C4×C61—22no—
53C22×C4×C61—41no—
54C22×C4×C61—41no—
55C22×C4×C61—41no—
56C22×C4×C61—41no—
57C22×C4×C61—41no—
58C22×C4×C61—41no—
59C22×C4×C61C4211yescharacteristic
60C22×C4×C61C22⋊C411yescharacteristic
61C22×C4×C61C22⋊C411yescharacteristic
62C22×C4×C61C22⋊C411yescharacteristic
63C22×C4×C61C4⋊C411yescharacteristic
64C22×C4×C61C4⋊C411yescharacteristic
65M16×C61—42no—
66M16×C61—42no—
67C2×C8×C61—42no—
68#11758194—42no—
69#11758194—42no—
70#11758194—42no—
71#11758194—42no—
72C2×#92418—42no—
73C2×#92418—42no—
74C23×C61—21no—
75C23×C61—21no—
76C23×C61—21no—
77C23×C61—42no—
78C23×C61#9511yescharacteristic
79Q8×C61—44no—
80Q8×C61—44no—
81Q8×C61—44no—
82Q8×C61—44no—
83C2×C4×C61—21no—
84C2×C4×C61—21no—
85C2×C4×C61—21no—
86C2×C4×C61—21no—
87C2×C4×C61—21no—
88C2×C4×C61—21no—
89C2×C4×C61—21no—
90C2×C4×C61—21no—
91C2×C4×C61—21no—
92C2×C4×C61—21no—
93C2×C4×C61—21no—
94C2×C4×C61—21no—
95C2×C4×C61—21no—
96C2×C4×C61—21no—
97C2×C4×C61—21no—
98C2×C4×C61—44no—
99C2×C4×C61—44no—
100C2×C4×C61—44no—
101C2×C4×C61#9912yes—
102C2×C4×C61#9912yes—
103C2×C4×C61#9912yes—
104C8×C61—82no—
105#92418—82no—
106#92418—82no—
107#7315—611nomaximal, Sylow
108C22×C61—22no—
109C22×C61—22no—
110C22×C61—22no—
111C22×C61—41no—
112C22×C61—41no—
113C22×C61—41no—
114C22×C61—41no—
115C22×C61—41no—
116C22×C61#34211yescharacteristic
117C22×C61#34211yescharacteristic
118C22×C61#34211yescharacteristic
119C4×C61—22no—
120C4×C61—22no—
121C4×C61—22no—
122C4×C61—41no—
123C4×C61—41no—
124C4×C61—41no—
125#1784—611no—
126#1784—611no—
127#1784D6111yescharacteristic
128C2×C61—21no—
129C2×C61—21no—
130C2×C61—21no—
131C2×C61—42no—
132C2×C61#130411yescharacteristic
133C23×Q8C2×D6111yescharacteristic
134C2×#101—21no—
135C2×#101—612no—
136C2×#101—1221no—
137C2×#101—1221no—
138C2×#101—1221no—
139C2×#101Dic6112yes—
140#407—21no—
141#407—612no—
142#407—1221no—
143C61#731511yescharacteristic, complemented, Sylow
144C22×Q8—42no—
145C22×Q8—42no—
146C22×Q8—42no—
147C22×Q8C4×D6111yescharacteristic
148C22×Q8D24411yescharacteristic
149C22×Q8C2×Dic6111yescharacteristic
150C22×Q8C22⋊D6111yescharacteristic
151C23×C4Dic12211yescharacteristic
152C23×C4C4×D6111yescharacteristic
153C23×C4C22⋊D6111yescharacteristic
154C2×M16—22no—
155C2×M16—1222no—
156C2×M16—1222no—
157#101—42no—
158#101—42no—
159#101—2442no—
160#101—2442no—
161#101—2442no—
162#101—2442no—
163C22⋊C8—42no—
164C22⋊C8—2442no—
165C22⋊C8—2442no—
166C24#1175819611yescharacteristic
167C2×Q8—22no—
168C2×Q8—22no—
169C2×Q8—22no—
170C2×Q8—22no—
171C2×Q8—22no—
172C2×Q8—22no—
173C2×Q8—41no—
174C2×Q8—41no—
175C2×Q8—41no—
176C2×Q8—41no—
177C2×Q8—41no—
178C2×Q8—41no—
179C2×Q8—416no—
180C22×C4—22no—
181C22×C4—22no—
182C22×C4—22no—
183C22×C4—41no—
184C22×C4—41no—
185C22×C4—41no—
186C22×C4—41no—
187C22×C4—41no—
188C22×C4—41no—
189C22×C4C4×Dic6111yescharacteristic
190C22×C4#1175819611yescharacteristic
191C22×C4C4⋊Dic6111yescharacteristic
192C22×C4#1175819811yescharacteristic
193C22×C4#1175819811yescharacteristic
194C22×C4C22⋊Dic6111yescharacteristic
195M16—42no—
196M16—42no—
197M16—2442no—
198M16—2442no—
199M16—2442no—
200M16—2442no—
201C2×C8—42no—
202C2×C8—2442no—
203C2×C8—2442no—
204C23—21no—
205C23—21no—
206C23—21no—
207C23—42no—
208C23#1451968411yescharacteristic
209Q8—44no—
210Q8—44no—
211Q8—44no—
212Q8—44no—
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—44no—
229C2×C4—44no—
230C2×C4—44no—
231C2×C4#1451969112yes—
232C2×C4#1451969112yes—
233C2×C4#1451969212yes—
234C8—82no—
235C8—4882no—
236C8—4882no—
237C22—22no—
238C22—22no—
239C22—22no—
240C22—41no—
241C22—41no—
242C22—41no—
243C22—41no—
244C22—41no—
245C22#1683952811yescharacteristic
246C22#1683952811yescharacteristic
247C22#1683952911yescharacteristic
248C4—22no—
249C4—22no—
250C4—22no—
251C4—41no—
252C4—41no—
253C4—41no—
254C2—21no—
255C2—21no—
256C2—21no—
257C2—42no—
258C2#2144372311yescharacteristic
subgroupG/H
centerC2#21443723
commutatorC22×C4×C61C42
FrattiniC23×Q8C2×D61
FittingC61×#1784C2
socleC2×C61#1304
prime radicalC24×C61C4⋊C4
cosocleC23×Q8×C61C22
hypercenter#1784D61
hypocenterC61#7315
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C23 ◁ C23×Q8 ◁ #1784

Complements

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

NH ≅ G/Ntype
143. C61#7315semidirect

Maximal subgroups

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

subgroupindex
#214457432
C61×#17842
#731561