Finite Group Databasebeta

← #30602108

Subgroups — #30602108

Order 15616.

390 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 390 conjugacy classes of subgroups — too many to draw. Only its 92 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#21461743C211yesmaximal, characteristic
2#21461169C212yesmaximal
3#21461168C212yesmaximal
4#21461015C211yesmaximal, characteristic
5#21456330C211yesmaximal, characteristic
6#16840766C2212yes—
7C4×D61⋊C8C2211yescharacteristic
8C4×D61⋊C8C2211yescharacteristic
9#16840638—22no—
10#16840612—24no—
11Q8⋊#92420—24no—
12#92420⋊C8—22no—
13#16840317C2212yes—
14#16840167C411yescharacteristic
15#16840163—22no—
16#16840158C412yes—
17#16839799—22no—
18C4×C8×D61C2211yescharacteristic
19C61×#500C411yescharacteristic
20C2×#11758213—22no—
21C2×D61⋊C8—21no—
22C2×D61⋊C8—21no—
23C4⋊#92420—22no—
24C4⋊#92420—22no—
25C4×#92420—21no—
26C4×#92420—21no—
27C4×#92420D412yes—
28C4×#92420D412yes—
29C2×C8×D61D412yes—
30#14519777C2×C412yes—
31#14519768—22no—
32#14519757—22no—
33#14519753—22no—
34Q8×Dic61—22no—
35#14519742—22no—
36#14519735—22no—
37C42×D61C2311yescharacteristic
38#14519711—22no—
39#14519708—24no—
40C4×#92418C2×C411yescharacteristic
41C8×Dic61D412yes—
42C4⋊Q8×C61C2×C412yes—
43#107×C61—22no—
44C4×C8×C61C2×C411yescharacteristic
45C2×Q8×C61—22no—
46C2×C4×D61C2×D411yescharacteristic
47C2×C4×D61#4111yescharacteristic
48C2×C4×D61#4111yescharacteristic
49C2×Dic122—22no—
50C2×#92420—22no—
51C2×#92420—22no—
52C2×#92420—42no—
53#11758213—44no—
54D61⋊C8—24no—
55D61⋊C8—42no—
56C2×C8×C61C22⋊C412yes—
57C4⋊C4×C61—22no—
58C4⋊C4×C61—22no—
59C42×C61C22×C411yescharacteristic
60#11758198—42no—
61C4⋊Dic61—22no—
62C4⋊Dic61—22no—
63C4⋊Dic61—42no—
64#11758196—42no—
65C4×Dic61—42no—
66C4×Dic61C2×D411yescharacteristic
67C4×Dic61C2×D411yescharacteristic
68C4×Dic61C2×D411yescharacteristic
69C2×#92418C22⋊C412yes—
70C8×D61—24no—
71C22×D61#12411yescharacteristic
72Q8×C61—44no—
73C2×C4×C61—42no—
74C2×C4×C61C2×C22⋊C411yescharacteristic
75C2×C4×C61C4×D411yescharacteristic
76C2×C4×C61C4×D411yescharacteristic
77C2×Dic61—42no—
78C2×Dic61#12111yescharacteristic
79C2×Dic61#12111yescharacteristic
80C2×Dic61#12711yescharacteristic
81C4×D61—22no—
82C4×D61—22no—
83C4×D61#13714yes—
84Dic122—44no—
85#92420—24no—
86#92420—42no—
87#92420—82no—
88C8×C61—22no—
89#92418—22no—
90#9859—611nomaximal, Sylow
91C22×C61#39011yescharacteristic
92C2×D61—21no—
93C2×D61—21no—
94C2×D61#49112yes—
95C4×C61—82no—
96C4×C61#41912yes—
97C4×C61#44312yes—
98C4×C61#44412yes—
99Dic61—21no—
100Dic61—21no—
101Dic61—82no—
102Dic61#49712yes—
103#3160—611no—
104#1837—611no—
105#1493—612no—
106#1493—612no—
107C2×#322—611no—
108C2×C61#196011yescharacteristic
109C2×C61#197411yescharacteristic
110C2×C61#197511yescharacteristic
111D61—22no—
112#533—612no—
113#500—611no—
114#500#692311yescharacteristic
115#499—1222no—
116#498—612no—
117#427—1222no—
118#423—612no—
119C2×C4×C8—611no—
120C2×C4×C8—611no—
121C2×C4×C8—611no—
122#341—1222no—
123Q8⋊C8—1224no—
124Q8⋊C8—1224no—
125#322—1222no—
126C61#985911yescharacteristic, complemented, Sylow
127C2×M16—1222no—
128C22×C8—612no—
129C22×C8—1221no—
130C22×C8—1221no—
131C4⋊Q8—612no—
132C4⋊Q8C2×#692312yes—
133#125—1222no—
134C22⋊Q8—1222no—
135C22⋊Q8—1222no—
136C4×Q8—1222no—
137C4×Q8—1222no—
138#117—1222no—
139C2×C42—611no—
140#107—22no—
141#107—1222no—
142#106—1224no—
143C4⋊C8—1222no—
144C4⋊C8—1222no—
145C4×C8—612no—
146C4×C8—612no—
147C4×C8—612no—
148C4×C8—611no—
149C4×C8—1221no—
150C4×C8—1221no—
151C4×C8C2×#692311yescharacteristic
152C2×Q8—22no—
153C2×Q8—1222no—
154C22×C4—611no—
155C22×C4—611no—
156C22×C4—611no—
157M16—2444no—
158C2×C8—612no—
159C2×C8—1224no—
160C2×C8—1222no—
161C2×C8—1224no—
162C2×C8—1222no—
163C2×C8—2442no—
164C2×C8—2442no—
165C2×C8C22⋊#692312yes—
166C4⋊C4—22no—
167C4⋊C4—22no—
168C4⋊C4—1222no—
169C4⋊C4—1222no—
170C4⋊C4—2442no—
171C4⋊C4—2442no—
172C22⋊C4—2442no—
173C42—611no—
174C42—611no—
175C42—611no—
176C42—2442no—
177C42C22×#692311yescharacteristic
178C23—611no—
179Q8—44no—
180Q8—2444no—
181C2×C4—42no—
182C2×C4—611no—
183C2×C4—614no—
184C2×C4—611no—
185C2×C4—611no—
186C2×C4—1222no—
187C2×C4—1222no—
188C2×C4—2442no—
189C2×C4C2×C22⋊#692311yescharacteristic
190C2×C4D4×#692311yescharacteristic
191C2×C4D4×#692311yescharacteristic
192C8—22no—
193C8—1224no—
194C8—1222no—
195C8—4882no—
196C8—2442no—
197C22—612no—
198C22—1221no—
199C22—1221no—
200C22#1684071411yescharacteristic
201C4—82no—
202C4—612no—
203C4—1221no—
204C4—1221no—
205C4—4882no—
206C4#1684075512yes—
207C4#1684080412yes—
208C4#1684080812yes—
209C2—1222no—
210C2#2146195011yescharacteristic
211C2#2146197211yescharacteristic
212C2#2146197311yescharacteristic
subgroupG/H
centerC22#16840714
commutatorC42×C61C22×C4
FrattiniC42C22×#6923
FittingC61×#500C4
socleC22×C61#390
prime radicalC22×D61#124
cosocleC42×D61C23
hypercenter#500#6923
hypocenterC61#9859
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #500

Complements

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

NH ≅ G/Ntype
126. C61#9859semidirect

Maximal subgroups

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

subgroupindex
#214617432
#214611692
#214611682
#214610152
#214563302
#985961