Finite Group Databasebeta

← #29577648

Subgroups — #29577648

Order 15616.

456 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 103 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#21448925C211yesmaximal, characteristic, complemented
2#21444446C211yesmaximal, characteristic, complemented
3#21444327C212yesmaximal
4#21443713C212yesmaximal, complemented
5C61×#3142C211yesmaximal, characteristic
6#16839819C2212yes—
7#16839648—22no—
8#16839648—22no—
9C4⋊C4×Dic61—22no—
10#16839608C2212yes—
11#16839504—22no—
12#16839496—22no—
13#16839496—22no—
14C61×#532C2211yescharacteristic
15C2×#125×C61C2211yescharacteristic
16C61×#491C412yescomplemented
17C61×#490C412yescomplemented
18C61×#488—22no—
19C61×#417—22no—
20C4×M16×C61C2211yescharacteristic
21C2×C4⋊Dic61—22no—
22C2×C4×Dic61—22no—
23C2×C4×Dic61—22no—
24C4⋊#92418—22no—
25C22⋊#92418—22no—
26#14519688—22no—
27#14519684—22no—
28#14519684—22no—
29#14519684—22no—
30#14519684D412yes—
31#14519684D412yes—
32C2×#41×C61—21no—
33C2×M16×C61—21no—
34C4⋊Q8×C61C2×C411yescharacteristic
35#127×C61C2×C411yescharacteristic
36#125×C61—22no—
37#125×C61C2×C412yes—
38#125×C61D412yes—
39#124×C61—21no—
40#121×C61—22no—
41C4×D4×C61—22no—
42C2×C4⋊C4×C61—22no—
43C2×C4⋊C4×C61D412yes—
44C2×C42×C61C2311yescharacteristic
45#103×C61—24no—
46#102×C61—24no—
47#97×C61C2×C412yes—
48C4×C8×C61—21no—
49#41×C61—44no—
50C2×Q8×C61—21no—
51C2×D4×C61—21no—
52C2×D4×C61—22no—
53C2×D4×C61—41no—
54C22×C4×C61—22no—
55C22×C4×C61—41no—
56C22×C4×C61C2×D411yescharacteristic
57C22×C4×C61C2×D412yes—
58C22×Dic61—22no—
59C22×Dic61—22no—
60M16×C61—42no—
61C2×C8×C61—22no—
62C4⋊C4×C61—24no—
63C4⋊C4×C61—24no—
64C4⋊C4×C61—22no—
65C4⋊C4×C61—22no—
66C4⋊C4×C61C22⋊C414yes—
67C22⋊C4×C61—42no—
68C42×C61C22×C411yescharacteristic
69C42×C61C2×D411yescharacteristic
70C42×C61#4112yes—
71C4⋊Dic61—44no—
72C4×Dic61—44no—
73C4×Dic61—44no—
74C2×#92418—42no—
75C23×C61—41no—
76C23×C61#12011yescharacteristic
77Q8×C61—42no—
78D4×C61—42no—
79D4×C61—82no—
80D4×C61—82no—
81C2×C4×C61—22no—
82C2×C4×C61—24no—
83C2×C4×C61—42no—
84C2×C4×C61—42no—
85C2×C4×C61—42no—
86C2×C4×C61—41no—
87C2×C4×C61—82no—
88C2×C4×C61C2×C22⋊C411yescharacteristic
89C2×C4×C61C4×D412yes—
90C2×C4×C61#12112yes—
91C2×C4×C61#12311yescharacteristic
92C2×Dic61—24no—
93C2×Dic61—42no—
94C2×Dic61—42no—
95C2×Dic61—42no—
96C2×Dic61—42no—
97C2×Dic61—42no—
98C8×C61—42no—
99#92418—82no—
100#9442—611nomaximal, Sylow
101C22×C61—22no—
102C22×C61—81no—
103C22×C61—82no—
104C22×C61#38611yescharacteristic
105C22×C61#45412yes—
106C4×C61—21no—
107C4×C61—21no—
108C4×C61—22no—
109C4×C61—22no—
110C4×C61—44no—
111C4×C61—81no—
112Dic61—44no—
113Dic61—82no—
114#3142D6111yescharacteristic
115#2371—611no—
116#1534—611no—
117#1505—612no—
118#1300—612no—
119C2×C61—22no—
120C2×C61—161no—
121C2×C61#188811yescharacteristic
122C2×C61#190612yes—
123#532C2×D6111yescharacteristic
124C2×#125C2×D6111yescharacteristic
125#491Dic6112yescomplemented
126#490Dic6112yescomplemented
127#488—22no—
128#432—612no—
129#417—22no—
130C4×M16C2×D6111yescharacteristic
131#387—1222no—
132#387—1222no—
133C4×C4⋊C4—1222no—
134#376—612no—
135#330—1222no—
136#327—1222no—
137#327—1222no—
138C61#944211yescharacteristic, complemented, Sylow
139C2×#41—21no—
140C2×M16—21no—
141C4⋊Q8C2×Dic6111yescharacteristic
142#127C2×Dic6111yescharacteristic
143#125—22no—
144#125C2×Dic6112yes—
145#125C22⋊D6112yes—
146#124—21no—
147#121—22no—
148C4×D4—22no—
149C2×C4⋊C4—22no—
150C2×C4⋊C4—1222no—
151C2×C4⋊C4C22⋊D6112yes—
152C2×C42—1222no—
153C2×C42—1222no—
154C2×C42C22×D6111yescharacteristic
155C4⋊C8—1222no—
156#103—24no—
157#102—24no—
158C22⋊C8—1222no—
159#97—1222no—
160#97C2×Dic6112yes—
161C4×C8—21no—
162#95—612no—
163#95—612no—
164#95—1222no—
165#95—1222no—
166#95—1222no—
167#41—44no—
168C2×Q8—21no—
169C2×D4—21no—
170C2×D4—22no—
171C2×D4—41no—
172C22×C4—22no—
173C22×C4—41no—
174C22×C4—1222no—
175C22×C4—1222no—
176C22×C4D4×D6112yes—
177C22×C4C2×C22⋊D6111yescharacteristic
178M16—42no—
179C2×C8—22no—
180C2×C8—2442no—
181C4⋊C4—24no—
182C4⋊C4—24no—
183C4⋊C4—22no—
184C4⋊C4—22no—
185C4⋊C4—2444no—
186C4⋊C4C22⋊Dic6114yes—
187C22⋊C4—42no—
188C42—2444no—
189C42—2444no—
190C42#1175822412yes—
191C42C22×Dic6111yescharacteristic
192C42C2×C22⋊D6111yescharacteristic
193C23—41no—
194C23#1451974511yescharacteristic
195Q8—42no—
196D4—42no—
197D4—82no—
198D4—82no—
199C2×C4—22no—
200C2×C4—24no—
201C2×C4—42no—
202C2×C4—42no—
203C2×C4—42no—
204C2×C4—41no—
205C2×C4—82no—
206C2×C4—1224no—
207C2×C4—2442no—
208C2×C4—2442no—
209C2×C4—2442no—
210C2×C4—2442no—
211C2×C4—2442no—
212C2×C4C2×C22⋊Dic6111yescharacteristic
213C2×C4D4×Dic6112yes—
214C2×C4#1451974912yes—
215C2×C4#1451975811yescharacteristic
216C8—42no—
217C8—4882no—
218C22—22no—
219C22—81no—
220C22—82no—
221C22#1683964211yescharacteristic
222C22#1683993412yes—
223C4—21no—
224C4—21no—
225C4—22no—
226C4—22no—
227C4—44no—
228C4—81no—
229C4—4882no—
230C4—2444no—
231C2—22no—
232C2—161no—
233C2#2144622311yescharacteristic
234C2#2144632212yes—
subgroupG/H
centerC22#16839642
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#3142C2
socleC22×C61#386
prime radicalC61×#532C22
cosocleC2×C42×C61C23
hypercenter#3142D61
hypocenterC61#9442
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3142

Complements

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

NH ≅ G/Ntype
1. #21448925C2semidirect
2. #21444446C2semidirect
4. #21443713C2semidirect
16. C61×#491C4semidirect
17. C61×#490C4semidirect
125. #491Dic61semidirect
126. #490Dic61semidirect
138. C61#9442semidirect

Maximal subgroups

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

subgroupindex
#214489252
#214444462
#214443272
#214437132
C61×#31422
#944261