Finite Group Databasebeta

← #30599070

Subgroups — #30599070

Order 15616.

336 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 88 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#21461373C212yesmaximal
2#21461358C212yesmaximal
3#21460727C212yesmaximal
4#21454752C211yesmaximal, characteristic
5#16840765C2214yes—
6#16840624—22no—
7#16840623—22no—
8#16840621—24no—
9#16840315C2211yescharacteristic
10#16839891—22no—
11#16839886—22no—
12#16839788C411yescharacteristic
13#16839785C2211yescharacteristic
14#16839720C411yescharacteristic
15#16839718C411yescharacteristic
16C2×C8×Dic61C2211yescharacteristic
17C61×#424C411yescharacteristic
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
29#14519706—22no—
30#14519706—22no—
31#14519688—21no—
32#14519687—21no—
33C4×#92418—21no—
34C8×Dic61—21no—
35C8×Dic61D412yes—
36C8×Dic61D412yes—
37C2×M16×C61C2×C411yescharacteristic
38C22×C8×C61C2×C411yescharacteristic
39#117×C61C2×C411yescharacteristic
40C4⋊C8×C61—22no—
41C22×C4×C61C22×C411yescharacteristic
42C22×Dic61#4112yes—
43C2×Dic122—22no—
44#11758217—84no—
45C2×#92420—44no—
46M16×C61—41no—
47C2×C8×C61—21no—
48C2×C8×C61—41no—
49C2×C8×C61C22⋊C412yes—
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—22no—
64C2×#92418—21no—
65C2×#92418C22⋊C411yescharacteristic
66C2×#92418C22⋊C411yescharacteristic
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—24no—
74C2×Dic61—22no—
75C2×Dic61#12112yes—
76C2×Dic61C22⋊Q812yes—
77Dic122—44no—
78#92420—84no—
79C8×C61—22no—
80C8×C61—41no—
81#92418—21no—
82#92418—41no—
83#92418#10112yes—
84#8637—611nomaximal, Sylow
85C22×C61—21no—
86C22×C61—22no—
87C22×C61#38011yescharacteristic
88C4×C61—21no—
89C4×C61—42no—
90C4×C61C2×#10111yescharacteristic
91C4×C61#41311yescharacteristic
92Dic61—22no—
93Dic61—42no—
94Dic61#47114yes—
95#2960—611no—
96#1566—612no—
97#1561—612no—
98#1309—612no—
99C2×C61—41no—
100C2×C61#180111yescharacteristic
101C2×C61#181512yes—
102#533—611no—
103#446—1222no—
104C8×Q8—1222no—
105#424—611no—
106#424#692311yescharacteristic
107#423—611no—
108#423—614no—
109#405—611no—
110#405—611no—
111C2×C4×C8—611no—
112#334—1222no—
113#334—1222no—
114#332—1224no—
115C61#863711yescharacteristic, complemented, Sylow
116C2×M16—611no—
117C2×M16—1224no—
118C2×M16C2×#692311yescharacteristic
119C22×C8—611no—
120C22×C8C2×#692311yescharacteristic
121C4⋊Q8—612no—
122#125—612no—
123C22⋊Q8—1222no—
124C4×Q8—1222no—
125#117—611no—
126#117C2×#692311yescharacteristic
127C2×C42—611no—
128C4⋊C8—22no—
129C4⋊C8—1222no—
130C4⋊C8—1224no—
131C4⋊C8—1224no—
132C4⋊C8—1222no—
133#97—1221no—
134#97—1221no—
135C4×C8—612no—
136C4×C8—612no—
137C4×C8—1221no—
138C4×C8—1221no—
139C2×Q8—1222no—
140C22×C4—612no—
141C22×C4C22×#692311yescharacteristic
142M16—41no—
143M16—4884no—
144M16—2441no—
145C2×C8—21no—
146C2×C8—41no—
147C2×C8—611no—
148C2×C8—611no—
149C2×C8—1222no—
150C2×C8—1221no—
151C2×C8—2444no—
152C2×C8C22⋊#692312yes—
153C4⋊C4—612no—
154C4⋊C4—1222no—
155C4⋊C4—1222no—
156C4⋊C4—1222no—
157C4⋊C4C4⋊#692312yes—
158C22⋊C4—21no—
159C22⋊C4—1221no—
160C42—21no—
161C42—612no—
162C42—611no—
163C42—611no—
164C42—1221no—
165C23#1451985611yescharacteristic
166Q8—2444no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—22no—
170C2×C4—612no—
171C2×C4—612no—
172C2×C4—1224no—
173C2×C4—1222no—
174C2×C4C2×C22⋊#692311yescharacteristic
175C2×C4C2×C4⋊#692311yescharacteristic
176C8—22no—
177C8—41no—
178C8—612no—
179C8—1221no—
180C8—4884no—
181C8—2441no—
182C22—21no—
183C22—22no—
184C22#1684070411yescharacteristic
185C4—21no—
186C4—42no—
187C4—614no—
188C4—1222no—
189C4—2442no—
190C4D61⋊#10111yescharacteristic
191C4#1684074911yescharacteristic
192C2—41no—
193C2#2146168611yescharacteristic
194C2#2146170712yes—
subgroupG/H
centerC22#16840704
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#424C4
socleC22×C61#380
prime radicalC23×C61#117
cosocleC2×C4×Dic61C23
hypercenter#424#6923
hypocenterC61#8637
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #424

Complements

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

NH ≅ G/Ntype
115. C61#8637semidirect

Maximal subgroups

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

subgroupindex
#214613732
#214613582
#214607272
#214547522
#863761