Finite Group Databasebeta

← #30599073

Subgroups — #30599073

Order 15616.

336 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 90 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#21461376C212yesmaximal
2#21461358C212yesmaximal
3#21460727C212yesmaximal
4#21454751C211yesmaximal, characteristic
5#16840765C2214yes—
6#16840626—22no—
7#16840625—22no—
8#16840621—24no—
9#16840315C2211yescharacteristic
10#16839890—22no—
11C8×Dic122—22no—
12#16839790C411yescharacteristic
13#16839789C411yescharacteristic
14#16839785C2211yescharacteristic
15#16839717C411yescharacteristic
16C2×C8×Dic61C2211yescharacteristic
17C61×#405C411yescharacteristic
18C2×#11758217—24no—
19#14519844—24no—
20C4⋊#92420—24no—
21C2×#11758194C2×C411yescharacteristic
22C22×#92418C2×C411yescharacteristic
23#14519776D412yes—
24#14519768Q812yes—
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—
44#11758217—84no—
45C2×#92420—44no—
46M16×C61—41no—
47C2×C8×C61—22no—
48C2×C8×C61—21no—
49C2×C8×C61C22⋊C411yescharacteristic
50C2×C8×C61C22⋊C411yescharacteristic
51C4⋊C4×C61C4⋊C412yes—
52C22⋊C4×C61—21no—
53C42×C61—21no—
54C22⋊Dic61—21no—
55C4⋊Dic61—22no—
56C4⋊Dic61C4⋊C412yes—
57#11758196—22no—
58#11758196—22no—
59C4×Dic61—21no—
60C4×Dic61C2×D411yescharacteristic
61C4×Dic61C2×D412yes—
62C4×Dic61C2×Q811yescharacteristic
63#11758194—41no—
64C2×#92418—21no—
65C2×#92418—41no—
66C2×#92418C22⋊C412yes—
67C23×C61#11711yescharacteristic
68C2×C4×C61—21no—
69C2×C4×C61—21no—
70C2×C4×C61—22no—
71C2×C4×C61C2×C22⋊C411yescharacteristic
72C2×C4×C61C2×C4⋊C411yescharacteristic
73C2×Dic61—22no—
74C2×Dic61—22no—
75C2×Dic61—22no—
76C2×Dic61#12112yes—
77C2×Dic61C22⋊Q812yes—
78Dic122—42no—
79Dic122—42no—
80#92420—84no—
81C8×C61—21no—
82C8×C61—41no—
83C8×C61#10112yes—
84#92418—22no—
85#92418—41no—
86#8639—611nomaximal, Sylow
87C22×C61—21no—
88C22×C61—22no—
89C22×C61#38011yescharacteristic
90C4×C61—21no—
91C4×C61—42no—
92C4×C61C2×#10111yescharacteristic
93C4×C61#41311yescharacteristic
94Dic61—22no—
95Dic61—42no—
96Dic61#47212yes—
97Dic61#47312yes—
98#2960—611no—
99#1567—612no—
100#1561—612no—
101#1309—612no—
102C2×C61—41no—
103C2×C61#180111yescharacteristic
104C2×C61#181612yes—
105#533—611no—
106#446—1222no—
107C8×Q8—1222no—
108#424—611no—
109#424—611no—
110#423—611no—
111#423—614no—
112#405—611no—
113#405#692311yescharacteristic
114C2×C4×C8—611no—
115#335—1222no—
116#335—1222no—
117#332—1224no—
118C61#863911yescharacteristic, complemented, Sylow
119C2×M16—611no—
120C2×M16—1224no—
121C2×M16C2×#692311yescharacteristic
122C22×C8—611no—
123C22×C8C2×#692311yescharacteristic
124C4⋊Q8—612no—
125#125—612no—
126C22⋊Q8—1222no—
127C4×Q8—1222no—
128#117—611no—
129#117C2×#692311yescharacteristic
130C2×C42—611no—
131C4⋊C8—1222no—
132C4⋊C8—1222no—
133C4⋊C8—1224no—
134C4⋊C8—1224no—
135C4⋊C8—1222no—
136#97—21no—
137#97—1221no—
138C4×C8—21no—
139C4×C8—612no—
140C4×C8—612no—
141C4×C8—1221no—
142C2×Q8—1222no—
143C22×C4—612no—
144C22×C4C22×#692311yescharacteristic
145M16—41no—
146M16—4884no—
147M16—2441no—
148C2×C8—22no—
149C2×C8—21no—
150C2×C8—612no—
151C2×C8—1221no—
152C2×C8—2441no—
153C2×C8—2444no—
154C2×C8C22⋊#692311yescharacteristic
155C2×C8C22⋊#692311yescharacteristic
156C4⋊C4—612no—
157C4⋊C4—1222no—
158C4⋊C4—1222no—
159C4⋊C4—1222no—
160C4⋊C4C4⋊#692312yes—
161C22⋊C4—21no—
162C22⋊C4—1221no—
163C42—21no—
164C42—612no—
165C42—611no—
166C42—611no—
167C42—1221no—
168C23#1451985611yescharacteristic
169Q8—2442no—
170Q8—2442no—
171C2×C4—21no—
172C2×C4—21no—
173C2×C4—22no—
174C2×C4—612no—
175C2×C4—612no—
176C2×C4—1222no—
177C2×C4—1222no—
178C2×C4—1222no—
179C2×C4C2×C22⋊#692311yescharacteristic
180C2×C4C2×C4⋊#692311yescharacteristic
181C8—21no—
182C8—41no—
183C8—1222no—
184C8—4884no—
185C8—2441no—
186C8#1451983812yes—
187C22—21no—
188C22—22no—
189C22#1684070411yescharacteristic
190C4—21no—
191C4—42no—
192C4—612no—
193C4—612no—
194C4—1222no—
195C4—2442no—
196C4C2×#1451983811yescharacteristic
197C4#1684074811yescharacteristic
198C2—41no—
199C2#2146168511yescharacteristic
200C2#2146170812yes—
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#8639
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
118. C61#8639semidirect

Maximal subgroups

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

subgroupindex
#214613762
#214613582
#214607272
#214547512
#863961