Finite Group Databasebeta

← #30602115

Subgroups — #30602115

Order 15616.

406 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 112 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#21461760C211yesmaximal, characteristic
2#21461169C212yesmaximal
3#21461168C212yesmaximal
4#21461013C211yesmaximal, characteristic
5#21456328C211yesmaximal, characteristic
6C2×#14519848—22no—
7#16840766C2211yescharacteristic
8#16840766C2211yescharacteristic
9C4×D61⋊C8C2212yes—
10#16840612—24no—
11Q8⋊#92420—24no—
12#16840603—22no—
13#16840317C2212yes—
14#16840165C412yes—
15#16840162—22no—
16#16840160C411yescharacteristic
17#16839797—22no—
18C4×C8×D61C2211yescharacteristic
19C61×#498C411yescharacteristic
20C2×#11758213—21no—
21C2×#11758213—21no—
22C2×D61⋊C8—22no—
23#14519848—44no—
24C4⋊#92420—22no—
25C4⋊#92420—22no—
26C4×#92420—22no—
27C4×#92420D414yes—
28C2×C8×D61D412yes—
29#14519777C2×C412yes—
30#14519768—22no—
31#14519757—22no—
32#14519753—22no—
33Q8×Dic61—22no—
34#14519742—22no—
35#14519735—22no—
36C42×D61C2311yescharacteristic
37#14519710—24no—
38#14519709—22no—
39C4×#92418C2×C411yescharacteristic
40C8×Dic61D412yes—
41C4⋊Q8×C61C2×C412yes—
42#106×C61—22no—
43C4×C8×C61C2×C411yescharacteristic
44C2×Q8×C61—22no—
45C2×C4×D61C2×D411yescharacteristic
46C2×C4×D61#4112yes—
47C2×Dic122—22no—
48C2×#92420—24no—
49C2×#92420—41no—
50C2×#92420—41no—
51#11758213—42no—
52#11758213—42no—
53D61⋊C8—44no—
54C2×C8×C61C22⋊C412yes—
55C4⋊C4×C61—22no—
56C4⋊C4×C61—22no—
57C42×C61C22×C411yescharacteristic
58#11758198—42no—
59C4⋊Dic61—22no—
60C4⋊Dic61—22no—
61C4⋊Dic61—42no—
62#11758196—42no—
63C4×Dic61—42no—
64C4×Dic61C2×D411yescharacteristic
65C4×Dic61C2×D412yes—
66C2×#92418C22⋊C412yes—
67C8×D61SD1614yes—
68C8×D61Q1614yes—
69C22×D61#12411yescharacteristic
70Q8×C61—44no—
71C2×C4×C61—42no—
72C2×C4×C61C2×C22⋊C411yescharacteristic
73C2×C4×C61C4×D412yes—
74C2×Dic61—42no—
75C2×Dic61#12112yes—
76C2×Dic61#12711yescharacteristic
77C4×D61—24no—
78C4×D61C2×SD1612yes—
79C4×D61C2×Q1612yes—
80Dic122—44no—
81#92420—44no—
82#92420—81no—
83#92420—81no—
84C8×C61#10314yes—
85#92418#10314yes—
86#9861—611nomaximal, Sylow
87C22×C61#39011yescharacteristic
88C2×D61—22no—
89C2×D61#48712yes—
90C4×C61—82no—
91C4×C61C2×#10312yes—
92C4×C61#44414yes—
93Dic61—22no—
94Dic61—82no—
95Dic61#49211yescharacteristic
96Dic61#49411yescharacteristic
97#3160—611no—
98#1848—611no—
99#1493—612no—
100#1493—612no—
101C2×#322—611no—
102C2×C61#195611yescharacteristic
103C2×C61#197512yes—
104D61—22no—
105#533—612no—
106#500—612no—
107#499—1222no—
108#498—611no—
109#498#692311yescharacteristic
110C2×#108—1222no—
111#427—1222no—
112#423—611no—
113#423—611no—
114C2×C4×C8—611no—
115C2×C4×C8—612no—
116Q8⋊C8—1224no—
117Q8⋊C8—1224no—
118#322—1222no—
119C61#986111yescharacteristic, complemented, Sylow
120C2×M16—1221no—
121C2×M16—1221no—
122C22×C8—612no—
123C22×C8—1222no—
124C4⋊Q8—612no—
125C4⋊Q8C2×#692312yes—
126#125—1222no—
127C22⋊Q8—1222no—
128C22⋊Q8—1222no—
129C4×Q8—1222no—
130C4×Q8—1222no—
131#117—1222no—
132C2×C42—611no—
133#108—2444no—
134#107—1224no—
135#106—22no—
136#106—1222no—
137C4⋊C8—1222no—
138C4⋊C8—1222no—
139C4×C8—612no—
140C4×C8—614no—
141C4×C8—611no—
142C4×C8—1222no—
143C4×C8C2×#692311yescharacteristic
144C2×Q8—22no—
145C2×Q8—1222no—
146C22×C4—611no—
147C22×C4—612no—
148M16—2442no—
149M16—2442no—
150C2×C8—612no—
151C2×C8—614no—
152C2×C8—614no—
153C2×C8—1224no—
154C2×C8—2441no—
155C2×C8—2441no—
156C2×C8—2444no—
157C2×C8C22⋊#692312yes—
158C4⋊C4—22no—
159C4⋊C4—22no—
160C4⋊C4—1222no—
161C4⋊C4—1222no—
162C4⋊C4—2442no—
163C4⋊C4—2442no—
164C22⋊C4—2442no—
165C42—611no—
166C42—612no—
167C42—2442no—
168C42C22×#692311yescharacteristic
169C23—611no—
170Q8—44no—
171Q8—2444no—
172C2×C4—42no—
173C2×C4—611no—
174C2×C4—612no—
175C2×C4—612no—
176C2×C4—612no—
177C2×C4—1224no—
178C2×C4—2442no—
179C2×C4C2×C22⋊#692311yescharacteristic
180C2×C4D4×#692312yes—
181C8—614no—
182C8—4881no—
183C8—4881no—
184C8—2444no—
185C8#1451984014yes—
186C22—612no—
187C22—1222no—
188C22#1684071411yescharacteristic
189C4—82no—
190C4—611no—
191C4—611no—
192C4—1222no—
193C4—4882no—
194C4C2×#1451984012yes—
195C4#1684080714yes—
196C2—1222no—
197C2#2146194611yescharacteristic
198C2#2146197512yes—
subgroupG/H
centerC22#16840714
commutatorC42×C61C22×C4
FrattiniC42C22×#6923
FittingC61×#498C4
socleC22×C61#390
prime radicalC22×D61#124
cosocleC42×D61C23
hypercenter#498#6923
hypocenterC61#9861
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #498

Complements

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

NH ≅ G/Ntype
119. C61#9861semidirect

Maximal subgroups

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

subgroupindex
#214617602
#214611692
#214611682
#214610132
#214563282
#986161