Finite Group Databasebeta

← #30595013

Subgroups — #30595013

Order 15616.

236 conjugacy classes of subgroups; only the 36 normal subgroups are shown.

normal subgroups only

This group has 236 conjugacy classes of subgroups — too many to draw. Only its 36 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#21460914C211yesmaximal, characteristic
2#21460636C211yesmaximal, characteristic
3#21446972C211yesmaximal, characteristic
4C2×#14519836—21no—
5#16840628—21no—
6#16839766—21no—
7#16839663C2211yescharacteristic
8#16839531C411yescharacteristic, complemented
9#16839521—21no—
10C61×#544C411yescharacteristic, complemented
11C22×#92420—41no—
12C2×C22⋊#6923—41no—
13#14519836—22no—
14#14519836—41no—
15C22×D244D411yescharacteristic
16C2×#11758194—21no—
17C2×#11758198—41no—
18C2×C4×Dic61D411yescharacteristic
19#14519697—41no—
20#14519697—41no—
21C4⋊Q8×C61—41no—
22#125×C61—41no—
23C22⋊Q8×C61—41no—
24#117×C61—21no—
25C2×C4⋊C4×C61C2×C411yescharacteristic
26C23×D61—21no—
27C22×#6923—81no—
28C2×Q8×C61—41no—
29C22×C4×C61—21no—
30C22×C4×C61C22⋊C411yescharacteristic
31C22×Dic61—21no—
32C2×D244—21no—
33C2×D244—41no—
34C2×D244—41no—
35C2×D244SD1611yescharacteristic
36C2×D244Q1611yescharacteristic
37C22⋊#6923—42no—
38C22⋊#6923—81no—
39C2×#92420—42no—
40C2×#92420—81no—
41C2×#92420—81no—
42C4⋊C4×C61—21no—
43C4⋊C4×C61—21no—
44C4⋊C4×C61—41no—
45C4⋊C4×C61—42no—
46C4⋊C4×C61—41no—
47C22⋊C4×C61—41no—
48C42×C61—41no—
49#11758198—81no—
50#11758198—81no—
51C4×Dic61—41no—
52#11758194—41no—
53#11758194—41no—
54C2×#92418—41no—
55C23×C61#9911yescharacteristic
56C22×D61—21no—
57C22×D61—21no—
58C22×D61—41no—
59C22×D61—41no—
60C22×D61—81no—
61C22×D61—81no—
62C2×#6923—82no—
63C2×#6923—161no—
64C2×#6923—161no—
65Q8×C61—161no—
66C2×C4×C61—21no—
67C2×C4×C61—21no—
68C2×C4×C61—41no—
69C2×C4×C61—41no—
70C2×C4×C61—41no—
71C2×C4×C61—81no—
72C2×C4×C61#10311yescharacteristic
73C2×C4×C61#10411yescharacteristic
74C2×Dic61—21no—
75C2×Dic61—21no—
76C2×Dic61—41no—
77C2×Dic61—41no—
78D244—41no—
79D244—41no—
80D244—81no—
81#92420—82no—
82#92418—81no—
83#7430—611nomaximal, Sylow
84C22×C61—21no—
85C22×C61—21no—
86C22×C61#32811yescharacteristic
87C22×C61AΣL(1,𝔽16)11yescharacteristic
88C22×C61#35411yescharacteristic
89C2×D61—41no—
90C2×D61—41no—
91C2×D61—81no—
92C2×D61—81no—
93C2×D61—81no—
94C2×D61—81no—
95C2×D61—161no—
96#6923—162no—
97C4×C61—21no—
98C4×C61—21no—
99C4×C61—81no—
100C4×C61—81no—
101C4×C61—81no—
102Dic61—41no—
103Dic61—41no—
104#2027—611no—
105#1393—611no—
106#1270—611no—
107C2×C61—21no—
108C2×C61—21no—
109C2×C61#135111yescharacteristic
110C2×C61#140211yescharacteristic
111C2×C61#140411yescharacteristic
112D61—81no—
113D61—81no—
114#544#692311yescharacteristic, complemented
115#418—1221no—
116C2×#99—1221no—
117#390—611no—
118#343—611no—
119#339—1221no—
120#336—1221no—
121C61#743011yescharacteristic, complemented, Sylow
122C22×D4—611no—
123C2×M16—1221no—
124C22×C8—2441no—
125C4⋊Q8—41no—
126#125—41no—
127C22⋊Q8—41no—
128#117—21no—
129C2×C4⋊C4C2×#692311yescharacteristic
130C2×C22⋊C4—2441no—
131C2×C22⋊C4—2441no—
132C2×C42—611no—
133#102—2441no—
134#102—2441no—
135#99—1222no—
136#99—2441no—
137C24—1221no—
138C2×Q8—41no—
139C2×D4—611no—
140C2×D4—611no—
141C2×D4—1221no—
142C2×D4—2441no—
143C2×D4—2441no—
144C22×C4—21no—
145C22×C4—1221no—
146C22×C4—4881no—
147C22×C4C22⋊#692311yescharacteristic
148M16—2441no—
149M16—2441no—
150C2×C8—4881no—
151C2×C8—4881no—
152C2×C8—2441no—
153C2×C8—2442no—
154C4⋊C4—21no—
155C4⋊C4—21no—
156C4⋊C4—41no—
157C4⋊C4—41no—
158C4⋊C4—42no—
159C22⋊C4—41no—
160C22⋊C4—4881no—
161C22⋊C4—4881no—
162C22⋊C4—4881no—
163C22⋊C4—2442no—
164C42—41no—
165C42—2441no—
166C23—1221no—
167C23—1221no—
168C23—4881no—
169C23—4881no—
170C23—2441no—
171C23—2441no—
172C23#1451983511yescharacteristic
173Q8—161no—
174D4—4881no—
175D4—2441no—
176D4—2441no—
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—41no—
180C2×C4—41no—
181C2×C4—41no—
182C2×C4—81no—
183C2×C4—1221no—
184C2×C4—1221no—
185C2×C4—9761no—
186C2×C4—9761no—
187C2×C4—4882no—
188C2×C4—2441no—
189C2×C4—2441no—
190C2×C4#1451984011yescharacteristic
191C2×C4#1451984211yescharacteristic
192C8—4881no—
193C8—4882no—
194C22—21no—
195C22—21no—
196C22—9761no—
197C22—4881no—
198C22—4881no—
199C22—4881no—
200C22—4881no—
201C22—2441no—
202C22—2441no—
203C22#1684061611yescharacteristic
204C22#1684066211yescharacteristic
205C22#1684066811yescharacteristic
206C4—21no—
207C4—21no—
208C4—81no—
209C4—81no—
210C4—81no—
211C4—9762no—
212C4—2441no—
213C4—2441no—
214C2—21no—
215C2—21no—
216C2—4881no—
217C2—4881no—
218C2#2146081411yescharacteristic
219C2#2146093811yescharacteristic
220C2#2146094211yescharacteristic
subgroupG/H
centerC22#16840662
commutatorC2×C4⋊C4×C61C2×C4
FrattiniC2×C4⋊C4C2×#6923
FittingC61×#544C4
socleC22×C61AΣL(1,𝔽16)
prime radicalC22×D244D4
cosocle#16839663C22
hypercenter#544#6923
hypocenterC61#7430
LCSG ▷ C2×C4⋊C4×C61 ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4 ◁ #544

Complements

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

NH ≅ G/Ntype
8. #16839531C4semidirect
10. C61×#544C4semidirect
114. #544#6923semidirect
121. C61#7430semidirect

Maximal subgroups

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

subgroupindex
#214609142
#214606362
#214469722
#743061