Finite Group Databasebeta

← #30601950

Subgroups — #30601950

Order 15616.

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

normal subgroups only

This group has 390 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#21461744C211yesmaximal, characteristic
2#21461335C212yesmaximal
3#21461333C212yesmaximal
4#21461033C211yesmaximal, characteristic
5#500×D61C211yesmaximal, characteristic
6#16840780C2211yescharacteristic
7#16840780C2211yescharacteristic
8#16840767C2212yes—
9#16840638—22no—
10#16840622—24no—
11#16840621—24no—
12#92420⋊C8—22no—
13C4⋊Q8×D61C2212yes—
14#16840167C411yescharacteristic
15#16840166—22no—
16#16840165C412yes—
17#107×D61—22no—
18C4×C8×D61C2211yescharacteristic
19C61×#500C411yescharacteristic
20C2×#11758213—22no—
21#14519844—22no—
22#14519844—22no—
23#14519844D412yes—
24#14519844D412yes—
25#14519834—21no—
26#14519834—21no—
27C4×#92420—21no—
28C4×#92420—21no—
29C2×Q8×D61—22no—
30C2×C8×D61D412yes—
31#14519777C2×C412yes—
32#14519776—22no—
33#14519776—22no—
34#14519775—22no—
35C4⋊C4×D61—22no—
36C4⋊C4×D61—22no—
37C42×D61C2311yescharacteristic
38#14519711—22no—
39#14519710—24no—
40C4×#92418C2×C411yescharacteristic
41C8×Dic61D412yes—
42C4⋊Q8×C61C2×C412yes—
43#107×C61—22no—
44C4×C8×C61C2×C411yescharacteristic
45C2×Q8×C61—22no—
46Q8×D61—84no—
47C2×C4×D61—42no—
48C2×C4×D61C2×D411yescharacteristic
49C2×C4×D61#4111yescharacteristic
50C2×C4×D61#4111yescharacteristic
51C2×Dic122—22no—
52C2×Dic122—42no—
53C2×#92420—22no—
54C2×#92420—22no—
55C2×#92420—42no—
56#11758213—44no—
57C2×C8×C61C22⋊C412yes—
58C4⋊C4×C61—22no—
59C4⋊C4×C61—22no—
60C42×C61C22×C411yescharacteristic
61C4⋊Dic61—22no—
62C4⋊Dic61—22no—
63#11758196—42no—
64#11758196—42no—
65C4×Dic61C2×D411yescharacteristic
66C4×Dic61C2×D411yescharacteristic
67C4×Dic61C2×D411yescharacteristic
68C2×#92418C22⋊C412yes—
69C8×D61—24no—
70C22×D61#12411yescharacteristic
71Q8×C61—82no—
72C2×C4×C61—42no—
73C2×C4×C61C2×C22⋊C411yescharacteristic
74C2×C4×C61C4×D411yescharacteristic
75C2×C4×C61C4×D411yescharacteristic
76C2×Dic61—42no—
77C2×Dic61#12111yescharacteristic
78C2×Dic61#12111yescharacteristic
79C2×Dic61#12711yescharacteristic
80C4×D61—22no—
81C4×D61—22no—
82C4×D61—84no—
83C4×D61#13714yes—
84Dic122—84no—
85Dic122—82no—
86#92420—42no—
87#92420—42no—
88#92420—82no—
89C8×C61—22no—
90#92418—22no—
91#9778—611nomaximal, Sylow
92C22×C61#39011yescharacteristic
93C2×D61—21no—
94C2×D61—21no—
95C2×D61#49112yes—
96C4×C61—21no—
97C4×C61—21no—
98C4×C61—82no—
99C4×C61#41912yes—
100Dic61—82no—
101Dic61#47212yes—
102Dic61#47312yes—
103Dic61#49712yes—
104C2×#500—611no—
105#1837—611no—
106#1549—612no—
107#1548—612no—
108#1452—611no—
109C2×C61#196011yescharacteristic
110C2×C61#197811yescharacteristic
111C2×C61#197911yescharacteristic
112D61—22no—
113C2×C4⋊Q8—612no—
114#500—612no—
115#500—611no—
116#500—1222no—
117#500#692311yescharacteristic
118#431—611no—
119#431—611no—
120C2×#107—1222no—
121#423—612no—
122C2×C4×C8—611no—
123#341—1222no—
124#333—1224no—
125#332—1224no—
126#322—1222no—
127C61#977811yescharacteristic, complemented, Sylow
128C22×Q8—1222no—
129C2×M16—1222no—
130C22×C8—612no—
131C4⋊Q8—612no—
132C4⋊Q8—1222no—
133C4⋊Q8—1222no—
134C4⋊Q8—1222no—
135C4⋊Q8C2×#692312yes—
136C2×C4⋊C4—1222no—
137C2×C4⋊C4—1222no—
138C2×C42—611no—
139#107—22no—
140#107—1224no—
141#107—1222no—
142C4⋊C8—612no—
143C4⋊C8—612no—
144C4⋊C8—1222no—
145C4⋊C8—1222no—
146C22⋊C8—1221no—
147C22⋊C8—1221no—
148C4×C8—612no—
149C4×C8—611no—
150C4×C8—1221no—
151C4×C8—1221no—
152C4×C8C2×#692311yescharacteristic
153C2×Q8—22no—
154C2×Q8—1222no—
155C2×Q8—4884no—
156C2×Q8—2442no—
157C22×C4—611no—
158C22×C4—611no—
159C22×C4—611no—
160C22×C4—2442no—
161M16—2444no—
162C2×C8—612no—
163C2×C8—1224no—
164C2×C8—1222no—
165C2×C8—1222no—
166C2×C8—2442no—
167C2×C8C22⋊#692312yes—
168C4⋊C4—22no—
169C4⋊C4—22no—
170C4⋊C4—1222no—
171C4⋊C4—1222no—
172C4⋊C4—2442no—
173C4⋊C4—2442no—
174C42—611no—
175C42—611no—
176C42—611no—
177C42C22×#692311yescharacteristic
178C23—611no—
179Q8—82no—
180Q8—4882no—
181Q8—4884no—
182C2×C4—42no—
183C2×C4—611no—
184C2×C4—611no—
185C2×C4—611no—
186C2×C4—614no—
187C2×C4—1222no—
188C2×C4—1222no—
189C2×C4—4884no—
190C2×C4—2442no—
191C2×C4C2×C22⋊#692311yescharacteristic
192C2×C4D4×#692311yescharacteristic
193C2×C4D4×#692311yescharacteristic
194C8—22no—
195C8—1222no—
196C8—4882no—
197C8—2442no—
198C8—2442no—
199C22—612no—
200C22—1221no—
201C22—1221no—
202C22#1684071411yescharacteristic
203C4—21no—
204C4—21no—
205C4—82no—
206C4—612no—
207C4—612no—
208C4—612no—
209C4—4882no—
210C4#1684075512yes—
211C2—1222no—
212C2#2146195011yescharacteristic
213C2#2146198011yescharacteristic
214C2#2146198111yescharacteristic
subgroupG/H
centerC22#16840714
commutatorC42×C61C22×C4
FrattiniC42C22×#6923
FittingC61×#500C4
socleC22×C61#390
prime radicalC22×D61#124
cosocleC42×D61C23
hypercenter#500#6923
hypocenterC61#9778
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #500

Complements

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

NH ≅ G/Ntype
127. C61#9778semidirect

Maximal subgroups

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

subgroupindex
#214617442
#214613352
#214613332
#214610332
#500×D612
#977861