Finite Group Databasebeta

← #30602114

Subgroups — #30602114

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#21461758C211yesmaximal, characteristic
2#21461169C212yesmaximal
3#21461168C212yesmaximal
4#21461013C211yesmaximal, characteristic
5#21456330C211yesmaximal, characteristic
6C2×#14519847—22no—
7#16840766C2212yes—
8C4×D61⋊C8C2211yescharacteristic
9C4×D61⋊C8C2211yescharacteristic
10#16840612—24no—
11Q8⋊#92420—24no—
12#16840603—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—
23#14519847—44no—
24C4⋊#92420—22no—
25C4⋊#92420—22no—
26C4×#92420—21no—
27C4×#92420—21no—
28C4×#92420D412yes—
29C4×#92420D412yes—
30C2×C8×D61D412yes—
31#14519777C2×C412yes—
32#14519768—22no—
33#14519757—22no—
34#14519753—22no—
35Q8×Dic61—22no—
36#14519742—22no—
37#14519735—22no—
38C42×D61C2311yescharacteristic
39#14519711—22no—
40#14519708—24no—
41C4×#92418C2×C411yescharacteristic
42C8×Dic61D412yes—
43C4⋊Q8×C61C2×C412yes—
44#107×C61—22no—
45C4×C8×C61C2×C411yescharacteristic
46C2×Q8×C61—22no—
47C2×C4×D61C2×D411yescharacteristic
48C2×C4×D61#4111yescharacteristic
49C2×C4×D61#4111yescharacteristic
50C2×Dic122—22no—
51C2×#92420—22no—
52C2×#92420—22no—
53C2×#92420—42no—
54#11758213—44no—
55D61⋊C8—42no—
56D61⋊C8—42no—
57C2×C8×C61C22⋊C412yes—
58C4⋊C4×C61—22no—
59C4⋊C4×C61—22no—
60C42×C61C22×C411yescharacteristic
61#11758198—42no—
62C4⋊Dic61—22no—
63C4⋊Dic61—22no—
64C4⋊Dic61—42no—
65#11758196—42no—
66C4×Dic61—42no—
67C4×Dic61C2×D411yescharacteristic
68C4×Dic61C2×D411yescharacteristic
69C4×Dic61C2×D411yescharacteristic
70C2×#92418C22⋊C412yes—
71C8×D61SD1614yes—
72C8×D61Q1614yes—
73C22×D61#12411yescharacteristic
74Q8×C61—44no—
75C2×C4×C61—42no—
76C2×C4×C61C2×C22⋊C411yescharacteristic
77C2×C4×C61C4×D411yescharacteristic
78C2×C4×C61C4×D411yescharacteristic
79C2×Dic61—42no—
80C2×Dic61#12111yescharacteristic
81C2×Dic61#12111yescharacteristic
82C2×Dic61#12711yescharacteristic
83C4×D61—22no—
84C4×D61—22no—
85C4×D61C2×SD1612yes—
86C4×D61C2×Q1612yes—
87Dic122—44no—
88#92420—42no—
89#92420—42no—
90#92420—82no—
91C8×C61#10314yes—
92#92418#10314yes—
93#9861—611nomaximal, Sylow
94C22×C61#39011yescharacteristic
95C2×D61—21no—
96C2×D61—21no—
97C2×D61#48712yes—
98C4×C61—82no—
99C4×C61C2×#10312yes—
100C4×C61#44412yes—
101C4×C61#44412yes—
102Dic61—21no—
103Dic61—21no—
104Dic61—82no—
105Dic61#49211yescharacteristic
106Dic61#49411yescharacteristic
107#3160—611no—
108#1848—611no—
109#1493—612no—
110#1493—612no—
111C2×#322—611no—
112C2×C61#195611yescharacteristic
113C2×C61#197511yescharacteristic
114C2×C61#197511yescharacteristic
115D61—22no—
116#533—612no—
117#500—611no—
118#500#692311yescharacteristic
119#499—1222no—
120#498—612no—
121C2×#108—1222no—
122#427—1222no—
123#423—612no—
124C2×C4×C8—611no—
125C2×C4×C8—611no—
126C2×C4×C8—611no—
127Q8⋊C8—1224no—
128Q8⋊C8—1224no—
129#322—1222no—
130C61#986111yescharacteristic, complemented, Sylow
131C2×M16—1222no—
132C22×C8—612no—
133C22×C8—1221no—
134C22×C8—1221no—
135C4⋊Q8—612no—
136C4⋊Q8C2×#692312yes—
137#125—1222no—
138C22⋊Q8—1222no—
139C22⋊Q8—1222no—
140C4×Q8—1222no—
141C4×Q8—1222no—
142#117—1222no—
143C2×C42—611no—
144#108—2444no—
145#107—22no—
146#107—1222no—
147#106—1224no—
148C4⋊C8—1222no—
149C4⋊C8—1222no—
150C4×C8—612no—
151C4×C8—612no—
152C4×C8—612no—
153C4×C8—611no—
154C4×C8—1221no—
155C4×C8—1221no—
156C4×C8C2×#692311yescharacteristic
157C2×Q8—22no—
158C2×Q8—1222no—
159C22×C4—611no—
160C22×C4—611no—
161C22×C4—611no—
162M16—2444no—
163C2×C8—612no—
164C2×C8—614no—
165C2×C8—614no—
166C2×C8—1222no—
167C2×C8—1222no—
168C2×C8—2442no—
169C2×C8—2442no—
170C2×C8—2442no—
171C2×C8C22⋊#692312yes—
172C4⋊C4—22no—
173C4⋊C4—22no—
174C4⋊C4—1222no—
175C4⋊C4—1222no—
176C4⋊C4—2442no—
177C4⋊C4—2442no—
178C22⋊C4—2442no—
179C42—611no—
180C42—611no—
181C42—611no—
182C42—2442no—
183C42C22×#692311yescharacteristic
184C23—611no—
185Q8—44no—
186Q8—2444no—
187C2×C4—42no—
188C2×C4—611no—
189C2×C4—612no—
190C2×C4—612no—
191C2×C4—611no—
192C2×C4—611no—
193C2×C4—1222no—
194C2×C4—1222no—
195C2×C4—2442no—
196C2×C4C2×C22⋊#692311yescharacteristic
197C2×C4D4×#692311yescharacteristic
198C2×C4D4×#692311yescharacteristic
199C8—614no—
200C8—4882no—
201C8—2442no—
202C8—2442no—
203C8#1451984014yes—
204C22—612no—
205C22—1221no—
206C22—1221no—
207C22#1684071411yescharacteristic
208C4—82no—
209C4—611no—
210C4—611no—
211C4—1221no—
212C4—1221no—
213C4—4882no—
214C4C2×#1451984012yes—
215C4#1684080812yes—
216C4#1684080912yes—
217C2—1222no—
218C2#2146194611yescharacteristic
219C2#2146197311yescharacteristic
220C2#2146197411yescharacteristic
subgroupG/H
centerC22#16840714
commutatorC42×C61C22×C4
FrattiniC42C22×#6923
FittingC61×#500C4
socleC22×C61#390
prime radicalC22×D61#124
cosocleC42×D61C23
hypercenter#500#6923
hypocenterC61#9861
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #500

Complements

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

NH ≅ G/Ntype
130. C61#9861semidirect

Maximal subgroups

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

subgroupindex
#214617582
#214611692
#214611682
#214610132
#214563302
#986161