Finite Group Databasebeta

← #30599057

Subgroups — #30599057

Order 15616.

320 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 86 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#21461379C212yesmaximal
2#21461310C212yesmaximal
3#21460725C212yesmaximal
4#21454751C211yesmaximal, characteristic
5#16840783C2214yes—
6#16840626—22no—
7#16840623—22no—
8#16840619—24no—
9#16840315C2211yescharacteristic
10#16839890—22no—
11C8×Dic122—22no—
12#16839790C411yescharacteristic
13#16839789C411yescharacteristic
14#16839785C2211yescharacteristic
15#16839717C411yescharacteristic
16C2×C8×Dic61C2211yescharacteristic
17C61×#405C411yescharacteristic
18C4⋊#92420—24no—
19C22⋊#92420—24no—
20#14519832—24no—
21C2×#11758194C2×C411yescharacteristic
22C22×#92418C2×C411yescharacteristic
23#14519776Q812yes—
24#14519768D412yes—
25#14519754—22no—
26C4×Dic122—22no—
27#14519736C2×C411yescharacteristic
28C2×C4×Dic61C2311yescharacteristic
29C4⋊#92418—22no—
30#14519706—22no—
31#14519706—22no—
32#14519687—21no—
33C8×Dic61—21no—
34C8×Dic61D412yes—
35C8×Dic61D412yes—
36C2×M16×C61C2×C411yescharacteristic
37C22×C8×C61C2×C411yescharacteristic
38#117×C61C2×C411yescharacteristic
39#97×C61—21no—
40C4×C8×C61—21no—
41C22×C4×C61C22×C411yescharacteristic
42C22×Dic61#4112yes—
43C2×Dic122—22no—
44C2×#92420—44no—
45M16×C61—41no—
46C2×C8×C61—22no—
47C2×C8×C61—21no—
48C2×C8×C61C22⋊C411yescharacteristic
49C2×C8×C61C22⋊C411yescharacteristic
50C4⋊C4×C61C4⋊C412yes—
51C22⋊C4×C61—21no—
52C42×C61—21no—
53C22⋊Dic61—21no—
54C4⋊Dic61—22no—
55C4⋊Dic61C4⋊C412yes—
56#11758196—22no—
57#11758196—22no—
58C4×Dic61—21no—
59C4×Dic61C2×D411yescharacteristic
60C4×Dic61C2×D412yes—
61C4×Dic61C2×Q811yescharacteristic
62#11758194—41no—
63C2×#92418—21no—
64C2×#92418—41no—
65C2×#92418C22⋊C412yes—
66C23×C61#11711yescharacteristic
67C2×C4×C61—21no—
68C2×C4×C61—21no—
69C2×C4×C61—22no—
70C2×C4×C61C2×C22⋊C411yescharacteristic
71C2×C4×C61C2×C4⋊C411yescharacteristic
72C2×Dic61—22no—
73C2×Dic61—42no—
74C2×Dic61#12112yes—
75C2×Dic61C22⋊Q812yes—
76Dic122—44no—
77#92420—84no—
78C8×C61—21no—
79C8×C61—41no—
80C8×C61#10112yes—
81#92418—22no—
82#92418—41no—
83#8631—611nomaximal, Sylow
84C22×C61—21no—
85C22×C61—22no—
86C22×C61#38011yescharacteristic
87C4×C61—21no—
88C4×C61—42no—
89C4×C61C2×#10111yescharacteristic
90C4×C61#41311yescharacteristic
91Dic61—22no—
92Dic61—22no—
93Dic61—42no—
94#2960—611no—
95#1568—612no—
96#1537—612no—
97#1307—612no—
98C2×C61—41no—
99C2×C61#180111yescharacteristic
100C2×C61#181412yes—
101#533—611no—
102#446—1222no—
103C8×Q8—1222no—
104#432—614no—
105#424—611no—
106#424—611no—
107#423—611no—
108#405—611no—
109#405#692311yescharacteristic
110C2×C4×C8—611no—
111#335—1222no—
112#334—1222no—
113#330—1224no—
114C61#863111yescharacteristic, complemented, Sylow
115C2×M16—611no—
116C2×M16C2×#692311yescharacteristic
117C22×C8—611no—
118C22×C8C2×#692311yescharacteristic
119C4⋊Q8—612no—
120#125—612no—
121C22⋊Q8—1222no—
122C4×Q8—1222no—
123#117—611no—
124#117C2×#692311yescharacteristic
125C2×C42—611no—
126C4⋊C8—1222no—
127C4⋊C8—1222no—
128C4⋊C8—1224no—
129C4⋊C8—1222no—
130C22⋊C8—1224no—
131#97—21no—
132#97—1224no—
133#97—1221no—
134C4×C8—21no—
135C4×C8—612no—
136C4×C8—612no—
137C4×C8—1221no—
138C2×Q8—1222no—
139C22×C4—612no—
140C22×C4C22×#692311yescharacteristic
141M16—41no—
142M16—2441no—
143C2×C8—22no—
144C2×C8—21no—
145C2×C8—612no—
146C2×C8—1221no—
147C2×C8—2441no—
148C2×C8—2444no—
149C2×C8C22⋊#692311yescharacteristic
150C2×C8C22⋊#692311yescharacteristic
151C4⋊C4—612no—
152C4⋊C4—1222no—
153C4⋊C4—1222no—
154C4⋊C4—1222no—
155C4⋊C4C4⋊#692312yes—
156C22⋊C4—21no—
157C22⋊C4—1221no—
158C42—21no—
159C42—612no—
160C42—611no—
161C42—611no—
162C42—1221no—
163C23#1451985611yescharacteristic
164Q8—2444no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—22no—
168C2×C4—612no—
169C2×C4—612no—
170C2×C4—1222no—
171C2×C4—2442no—
172C2×C4C2×C22⋊#692311yescharacteristic
173C2×C4C2×C4⋊#692311yescharacteristic
174C8—21no—
175C8—41no—
176C8—1222no—
177C8—4884no—
178C8—2441no—
179C8#1451983812yes—
180C22—21no—
181C22—22no—
182C22#1684070411yescharacteristic
183C4—21no—
184C4—42no—
185C4—1222no—
186C4—1222no—
187C4—2442no—
188C4C2×#1451983811yescharacteristic
189C4#1684074811yescharacteristic
190C2—41no—
191C2#2146168511yescharacteristic
192C2#2146170512yes—
subgroupG/H
centerC22#16840704
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#405C4
socleC22×C61#380
prime radicalC23×C61#117
cosocleC2×C4×Dic61C23
hypercenter#405#6923
hypocenterC61#8631
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #405

Complements

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

NH ≅ G/Ntype
114. C61#8631semidirect

Maximal subgroups

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

subgroupindex
#214613792
#214613102
#214607252
#214547512
#863161