Finite Group Databasebeta

← #30607937

Subgroups — #30607937

Order 15616.

280 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 90 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#21462175C212yesmaximal
2#21461759C211yesmaximal, characteristic
3#21461621C211yesmaximal, characteristic
4#21460900C212yesmaximal
5#364×D61C211yesmaximal, characteristic
6C2×#14519848C2212yes—
7D61⋊#108C2211yescharacteristic
8C2×#14519847—21no—
9#16840772C2211yescharacteristic
10#16840767—21no—
11#16840725—21no—
12#16840691—22no—
13#16840690—22no—
14#16840633—21no—
15M32×D61C2212yes—
16C4×C8×D61C2211yescharacteristic
17#16839583C411yescharacteristic, complemented
18#16839582C412yescomplemented
19C61×#364C411yescharacteristic, complemented
20C2×#11758213—22no—
21D61⋊M16—21no—
22#14519856—21no—
23#14519848—22no—
24#14519848—22no—
25#14519848D412yes—
26#14519847—21no—
27#14519847—41no—
28#14519847—41no—
29#14519846—21no—
30#14519845Q812yes—
31#14519844—42no—
32#14519831—41no—
33C8×#6923—41no—
34C2×C8×D61D411yescharacteristic
35C2×C8×D61C2311yescharacteristic
36C42×D61D411yescharacteristic
37#14519717C2×C412yes—
38#14519716—22no—
39C16×D61—22no—
40C4×#92418Q811yescharacteristic
41C8×Dic61C2×C411yescharacteristic
42C8×Dic61Q811yescharacteristic
43M32×C61C2×C412yes—
44C4×C8×C61C2×C411yescharacteristic
45C2×C4×D61—21no—
46C2×C4×D61C2×D411yescharacteristic
47C22⋊#6923—41no—
48#11758217—41no—
49C2×#92420—42no—
50C4⋊#6923—22no—
51C4×#6923—41no—
52#11758213—22no—
53#11758213—42no—
54#11758213—42no—
55D61⋊C8—41no—
56C2×C8×C61C4⋊C411yescharacteristic
57C2×C8×C61C22×C411yescharacteristic
58C42×C61C4⋊C411yescharacteristic
59C4×Dic61—21no—
60C4×Dic61C4⋊C411yescharacteristic
61C2×#92418C4⋊C411yescharacteristic
62C2×#92418C2×Q811yescharacteristic
63C8×D61D811yescharacteristic
64C8×D61D811yescharacteristic
65C8×D61Q1611yescharacteristic
66C8×D61Q1611yescharacteristic
67C8×D61C2×D411yescharacteristic
68C8×D61C2×Q811yescharacteristic
69C8×D61#4111yescharacteristic
70C8×D61#4111yescharacteristic
71C16×C61—22no—
72#11758185—22no—
73C22×D61#13711yescharacteristic
74C2×#6923—42no—
75C2×C4×C61—21no—
76C2×C4×C61C2×C4⋊C411yescharacteristic
77C2×Dic61—21no—
78C2×Dic61AGL(1,ℤ/8)11yescharacteristic
79C4×D61—42no—
80C4×D61#12111yescharacteristic
81C4×D61C22⋊Q811yescharacteristic
82C4×D61C2×D811yescharacteristic
83C4×D61C2×Q1611yescharacteristic
84#92420—42no—
85#92420—82no—
86C8×C61#10711yescharacteristic
87C8×C61#10711yescharacteristic
88C8×C61C4×D411yescharacteristic
89C8×C61C4×Q811yescharacteristic
90#92418#10711yescharacteristic
91#92418#10711yescharacteristic
92#92418#12511yescharacteristic
93#92418C4⋊Q811yescharacteristic
94#13182—611nomaximal, Sylow
95C22×C61#42811yescharacteristic
96C2×D61—41no—
97C2×D61#46211yescharacteristic
98C2×D61#47411yescharacteristic
99#6923—82no—
100C4×C61—41no—
101C4×C61#38911yescharacteristic
102C4×C61C2×#10711yescharacteristic
103Dic61—22no—
104Dic61#45911yescharacteristic
105Dic61#47711yescharacteristic
106#2161—612no—
107C2×#364—611no—
108#1848—611no—
109#1772—611no—
110#1389—612no—
111C2×C61—21no—
112C2×C61#194711yescharacteristic
113D61—21no—
114D61—21no—
115C2×M32—612no—
116C2×#108—611no—
117C2×#108—612no—
118C2×#108—1221no—
119#427—611no—
120#423—1221no—
121#405—1221no—
122C2×C4×C8—611no—
123#368—1222no—
124#368—1222no—
125#364—612no—
126#364—611no—
127#364#692311yescharacteristic, complemented
128#339—1221no—
129C61#1318211yescharacteristic, complemented, Sylow
130C2×M16—1221no—
131C2×M16—1222no—
132C22×C8—611no—
133C22×C8—611no—
134#117—1221no—
135C2×C42—611no—
136M32—612no—
137M32—1222no—
138M32C2×#692312yes—
139C2×C16—1222no—
140#108—612no—
141#108—1221no—
142#108—1222no—
143#108—1222no—
144#108—2441no—
145#108—2441no—
146#107—1221no—
147#106—612no—
148C4⋊C8—2442no—
149#97—2441no—
150C4×C8—611no—
151C4×C8—611no—
152C4×C8—611no—
153C4×C8—2441no—
154C4×C8C2×#692311yescharacteristic
155C22×C4—611no—
156C22×C4—1221no—
157M16—1222no—
158M16—2442no—
159M16—2442no—
160M16—2441no—
161C2×C8—611no—
162C2×C8—611no—
163C2×C8—611no—
164C2×C8—611no—
165C2×C8—611no—
166C2×C8—611no—
167C2×C8—611no—
168C2×C8—611no—
169C2×C8—611no—
170C2×C8—611no—
171C2×C8—2442no—
172C2×C8—2441no—
173C2×C8C4⋊#692311yescharacteristic
174C2×C8C22×#692311yescharacteristic
175C4⋊C4—1222no—
176C22⋊C4—2441no—
177C42—611no—
178C42—1221no—
179C42—2441no—
180C42C4⋊#692311yescharacteristic
181C16—22no—
182C16—1222no—
183C23—611no—
184C2×C4—21no—
185C2×C4—611no—
186C2×C4—611no—
187C2×C4—611no—
188C2×C4—611no—
189C2×C4—611no—
190C2×C4—1221no—
191C2×C4—2442no—
192C2×C4—2442no—
193C2×C4C2×C4⋊#692311yescharacteristic
194C8—611no—
195C8—611no—
196C8—611no—
197C8—611no—
198C8—4882no—
199C8—2442no—
200C8#1451984611yescharacteristic
201C8#1451984611yescharacteristic
202C8D4×#692311yescharacteristic
203C8Q8×#692311yescharacteristic
204C22—611no—
205C22—611no—
206C22—2441no—
207C22#1684077311yescharacteristic
208C4—41no—
209C4—611no—
210C4—611no—
211C4—1222no—
212C4—4882no—
213C4#1684071311yescharacteristic
214C4C2×#1451984611yescharacteristic
215C2—21no—
216C2—1221no—
217C2—1221no—
218C2#2146193011yescharacteristic
subgroupG/H
centerC2#21461930
commutatorC2×C8×C61C22×C4
FrattiniC2×C8C22×#6923
FittingC61×#364C4
socleC2×C61#1947
prime radicalC22×D61#137
cosocleC2×C8×D61C23
hypercenter#364#6923
hypocenterC61#13182
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #364

Complements

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

NH ≅ G/Ntype
17. #16839583C4semidirect
18. #16839582C4semidirect
19. C61×#364C4semidirect
127. #364#6923semidirect
129. C61#13182semidirect

Maximal subgroups

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

subgroupindex
#214621752
#214617592
#214616212
#214609002
#364×D612
#1318261