Finite Group Databasebeta

← #30601948

Subgroups — #30601948

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#498×D61C211yesmaximal, characteristic
6#16840780C2212yes—
7#16840767C2211yescharacteristic
8#16840767C2211yescharacteristic
9#16840638—22no—
10#16840622—24no—
11#16840621—24no—
12#92420⋊C8—22no—
13C4⋊Q8×D61C2212yes—
14#16840160C411yescharacteristic
15#16840159—22no—
16#16840158C412yes—
17#106×D61—22no—
18C4×C8×D61C2211yescharacteristic
19C61×#498C411yescharacteristic
20C2×#11758213—21no—
21C2×#11758213—21no—
22#14519844—22no—
23#14519844—22no—
24#14519844D414yes—
25#14519834—22no—
26C4×#92420—22no—
27C2×Q8×D61—22no—
28C2×C8×D61D412yes—
29#14519777C2×C412yes—
30#14519776—22no—
31#14519776—22no—
32#14519775—22no—
33C4⋊C4×D61—22no—
34C4⋊C4×D61—22no—
35C42×D61C2311yescharacteristic
36#14519709—22no—
37#14519708—24no—
38C4×#92418C2×C411yescharacteristic
39C8×Dic61D412yes—
40C4⋊Q8×C61C2×C412yes—
41#106×C61—22no—
42C4×C8×C61C2×C411yescharacteristic
43C2×Q8×C61—22no—
44Q8×D61—84no—
45C2×C4×D61—42no—
46C2×C4×D61C2×D411yescharacteristic
47C2×C4×D61#4112yes—
48C2×Dic122—22no—
49C2×Dic122—42no—
50C2×#92420—24no—
51C2×#92420—41no—
52C2×#92420—41no—
53#11758213—42no—
54#11758213—42no—
55C2×C8×C61C22⋊C412yes—
56C4⋊C4×C61—22no—
57C4⋊C4×C61—22no—
58C42×C61C22×C411yescharacteristic
59C4⋊Dic61—22no—
60C4⋊Dic61—22no—
61#11758196—42no—
62#11758196—42no—
63C4×Dic61C2×D411yescharacteristic
64C4×Dic61C2×D412yes—
65C2×#92418C22⋊C412yes—
66C8×D61—22no—
67C8×D61—22no—
68C22×D61#12411yescharacteristic
69Q8×C61—82no—
70C2×C4×C61—42no—
71C2×C4×C61C2×C22⋊C411yescharacteristic
72C2×C4×C61C4×D412yes—
73C2×Dic61—42no—
74C2×Dic61#12112yes—
75C2×Dic61#12711yescharacteristic
76C4×D61—24no—
77C4×D61—84no—
78C4×D61#13712yes—
79C4×D61#13712yes—
80Dic122—84no—
81Dic122—82no—
82#92420—44no—
83#92420—81no—
84#92420—81no—
85C8×C61—22no—
86#92418—22no—
87#9776—611nomaximal, Sylow
88C22×C61#39011yescharacteristic
89C2×D61—22no—
90C2×D61#49112yes—
91C4×C61—22no—
92C4×C61—82no—
93C4×C61#41912yes—
94Dic61—82no—
95Dic61#47114yes—
96Dic61#49711yescharacteristic
97Dic61#49711yescharacteristic
98C2×#498—611no—
99#1837—611no—
100#1549—612no—
101#1548—612no—
102#1452—611no—
103C2×C61#196011yescharacteristic
104C2×C61#197712yes—
105D61—22no—
106C2×C4⋊Q8—612no—
107#498—612no—
108#498—611no—
109#498—1222no—
110#498#692311yescharacteristic
111#431—612no—
112C2×#106—1222no—
113#423—611no—
114#423—611no—
115C2×C4×C8—611no—
116#341—1222no—
117#333—1224no—
118#332—1224no—
119#322—1222no—
120C61#977611yescharacteristic, complemented, Sylow
121C22×Q8—1222no—
122C2×M16—1221no—
123C2×M16—1221no—
124C22×C8—612no—
125C4⋊Q8—612no—
126C4⋊Q8—1222no—
127C4⋊Q8—1222no—
128C4⋊Q8—1222no—
129C4⋊Q8C2×#692312yes—
130C2×C4⋊C4—1222no—
131C2×C4⋊C4—1222no—
132C2×C42—611no—
133#106—22no—
134#106—1224no—
135#106—1222no—
136C4⋊C8—614no—
137C4⋊C8—1222no—
138C4⋊C8—1222no—
139C22⋊C8—1222no—
140C4×C8—612no—
141C4×C8—611no—
142C4×C8—1222no—
143C4×C8C2×#692311yescharacteristic
144C2×Q8—22no—
145C2×Q8—1222no—
146C2×Q8—4884no—
147C2×Q8—2442no—
148C22×C4—611no—
149C22×C4—612no—
150C22×C4—2442no—
151M16—2442no—
152M16—2442no—
153C2×C8—612no—
154C2×C8—1222no—
155C2×C8—1222no—
156C2×C8—1224no—
157C2×C8—2441no—
158C2×C8—2441no—
159C2×C8C22⋊#692312yes—
160C4⋊C4—22no—
161C4⋊C4—22no—
162C4⋊C4—1222no—
163C4⋊C4—1222no—
164C4⋊C4—2442no—
165C4⋊C4—2442no—
166C42—611no—
167C42—612no—
168C42C22×#692311yescharacteristic
169C23—611no—
170Q8—82no—
171Q8—4882no—
172Q8—4884no—
173C2×C4—42no—
174C2×C4—612no—
175C2×C4—611no—
176C2×C4—612no—
177C2×C4—612no—
178C2×C4—1224no—
179C2×C4—4884no—
180C2×C4—2442no—
181C2×C4C2×C22⋊#692311yescharacteristic
182C2×C4D4×#692312yes—
183C8—22no—
184C8—1222no—
185C8—4881no—
186C8—4881no—
187C8—2444no—
188C22—612no—
189C22—1222no—
190C22#1684071411yescharacteristic
191C4—22no—
192C4—82no—
193C4—611no—
194C4—611no—
195C4—614no—
196C4—4882no—
197C4#1684075512yes—
198C2—1222no—
199C2#2146195011yescharacteristic
200C2#2146197912yes—
subgroupG/H
centerC22#16840714
commutatorC42×C61C22×C4
FrattiniC42C22×#6923
FittingC61×#498C4
socleC22×C61#390
prime radicalC22×D61#124
cosocleC42×D61C23
hypercenter#498#6923
hypocenterC61#9776
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #498

Complements

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

NH ≅ G/Ntype
120. C61#9776semidirect

Maximal subgroups

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

subgroupindex
#214617442
#214613352
#214613332
#214610332
#498×D612
#977661