Finite Group Databasebeta

← #30594077

Subgroups — #30594077

Order 15616.

264 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 40 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#21460740C211yesmaximal, characteristic
2#21460691C211yesmaximal, characteristic
3#21446826C211yesmaximal, characteristic
4#16840733—21no—
5C22⋊#11758187—21no—
6C2×#14519753—21no—
7C2×#14519701—21no—
8C2×#14519689C2211yescharacteristic
9#16839525C411yescharacteristic
10C22×Q16×C61C411yescharacteristic
11C2×#11758213—41no—
12C2×#11758187—41no—
13#14519834—22no—
14C22⋊#92420—41no—
15C22×C4×D61D411yescharacteristic
16C22×#92418D411yescharacteristic
17#14519753—42no—
18#14519753—42no—
19C2×C4⋊Dic61—21no—
20C2×#11758196—41no—
21C2×#11758198—41no—
22#14519701—42no—
23#14519689—41no—
24C22×Q8×C61—21no—
25C2×Q16×C61—41no—
26C2×Q16×C61—42no—
27C22×C8×C61C2×C411yescharacteristic
28C23×D61SD1611yescharacteristic
29C2×Q8×C61—22no—
30C2×Q8×C61—41no—
31C2×Q8×C61—41no—
32C2×Q8×C61—41no—
33C2×Q8×C61—41no—
34C2×Q8×C61—41no—
35C22×C4×C61—41no—
36C22×C4×C61C22⋊C411yescharacteristic
37C22×Dic61—41no—
38C22×Dic61D811yescharacteristic
39C2×C4×D61—21no—
40C2×C4×D61—21no—
41C2×C4×D61—41no—
42C2×C4×D61—41no—
43C2×#92420—42no—
44#11758213—81no—
45#11758213—81no—
46Q16×C61—42no—
47Q16×C61—42no—
48C2×C8×C61—21no—
49C2×C8×C61—41no—
50#11758198—44no—
51C4⋊Dic61—22no—
52C4⋊Dic61—41no—
53#11758196—44no—
54C2×#92418—21no—
55C2×#92418—41no—
56#11758187—81no—
57C23×C61#10211yescharacteristic
58C22×D61—21no—
59C22×D61—21no—
60C22×D61—21no—
61C22×D61—41no—
62C22×D61—41no—
63Q8×C61—42no—
64Q8×C61—42no—
65Q8×C61—81no—
66Q8×C61—81no—
67C2×C4×C61—21no—
68C2×C4×C61—21no—
69C2×C4×C61—42no—
70C2×C4×C61—81no—
71C2×C4×C61—81no—
72C2×C4×C61#9911yescharacteristic
73C2×C4×C61#10411yescharacteristic
74C2×Dic61—21no—
75C2×Dic61—41no—
76C2×Dic61—42no—
77C2×Dic61—81no—
78C2×Dic61—81no—
79C4×D61—41no—
80C4×D61—41no—
81C4×D61—81no—
82#92420—82no—
83C8×C61—41no—
84#92418—41no—
85#7086—611nomaximal, Sylow
86C22×C61—21no—
87C22×C61—21no—
88C22×C61#32711yescharacteristic
89C22×C61#35911yescharacteristic
90C22×C61#36211yescharacteristic
91C2×D61—42no—
92C2×D61—41no—
93C2×D61—41no—
94C2×D61—41no—
95C2×D61—81no—
96C4×C61—21no—
97C4×C61—82no—
98C4×C61AΣL(1,𝔽16)11yescharacteristic
99C4×C61#35311yescharacteristic
100Dic61—41no—
101Dic61—82no—
102#2001—611no—
103#1314—611no—
104#1293—611no—
105C2×C61—21no—
106C2×C61—21no—
107C2×C61#134211yescharacteristic
108C2×C61#134311yescharacteristic
109C2×C61#135011yescharacteristic
110D61—81no—
111C22×Q16#692311yescharacteristic
112C2×C22⋊Q8—1221no—
113C2×#103—1221no—
114#407—1221no—
115C2×C22⋊C8—611no—
116C22⋊C16—1221no—
117#340—611no—
118C61#708611yescharacteristic, complemented, Sylow
119C22×Q8—21no—
120C23×C4—611no—
121C2×Q16—41no—
122C2×Q16—42no—
123C2×M16—2441no—
124C22×C8—611no—
125C22×C8C2×#692311yescharacteristic
126C22⋊Q8—2442no—
127C22⋊Q8—2442no—
128C2×C4⋊C4—1221no—
129C2×C4⋊C4—2441no—
130C2×C22⋊C4—2441no—
131C2×C16—2441no—
132#103—2442no—
133C22⋊C8—1222no—
134C22⋊C8—2441no—
135C22⋊C8—2441no—
136C24—611no—
137C2×Q8—22no—
138C2×Q8—41no—
139C2×Q8—41no—
140C2×Q8—41no—
141C2×Q8—41no—
142C2×Q8—41no—
143C22×C4—41no—
144C22×C4—611no—
145C22×C4—1221no—
146C22×C4—1221no—
147C22×C4—2441no—
148C22×C4—2441no—
149C22×C4—2441no—
150C22×C4C22⋊#692311yescharacteristic
151Q16—42no—
152Q16—42no—
153M16—4881no—
154M16—4881no—
155C2×C8—21no—
156C2×C8—41no—
157C2×C8—1221no—
158C2×C8—2442no—
159C2×C8—2441no—
160C4⋊C4—1222no—
161C4⋊C4—2441no—
162C4⋊C4—2444no—
163C22⋊C4—2444no—
164C16—4881no—
165C23—1221no—
166C23—1221no—
167C23—1221no—
168C23—2441no—
169C23—2441no—
170C23#1451983911yescharacteristic
171Q8—42no—
172Q8—42no—
173Q8—81no—
174Q8—81no—
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—42no—
178C2×C4—81no—
179C2×C4—81no—
180C2×C4—1221no—
181C2×C4—4881no—
182C2×C4—4881no—
183C2×C4—4881no—
184C2×C4—2442no—
185C2×C4—2441no—
186C2×C4—2441no—
187C2×C4—2441no—
188C2×C4#1451983511yescharacteristic
189C2×C4#1451984111yescharacteristic
190C8—41no—
191C8—4882no—
192C8—2441no—
193C22—21no—
194C22—21no—
195C22—4881no—
196C22—2442no—
197C22—2441no—
198C22—2441no—
199C22—2441no—
200C22#1684061311yescharacteristic
201C22#1684067711yescharacteristic
202C22#1684068111yescharacteristic
203C4—21no—
204C4—82no—
205C4—4882no—
206C4—2441no—
207C4#1684066211yescharacteristic
208C4#1684066611yescharacteristic
209C2—21no—
210C2—21no—
211C2—4881no—
212C2#2146079511yescharacteristic
213C2#2146079711yescharacteristic
214C2#2146081111yescharacteristic
subgroupG/H
centerC22#16840613
commutatorC22×C8×C61C2×C4
FrattiniC22×C8C2×#6923
FittingC22×Q16×C61C4
socleC22×C61#327
prime radicalC23×D61SD16
cosocleC2×#14519689C22
hypercenterC22×Q16#6923
hypocenterC61#7086
LCSG ▷ C22×C8×C61 ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C22×Q16

Complements

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

NH ≅ G/Ntype
118. C61#7086semidirect

Maximal subgroups

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

subgroupindex
#214607402
#214606912
#214468262
#708661