Finite Group Databasebeta

← #30607938

Subgroups — #30607938

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#21461760C211yesmaximal, characteristic
3#21461621C211yesmaximal, characteristic
4#21460900C212yesmaximal
5#364×D61C211yesmaximal, characteristic
6C2×#14519848—21no—
7C2×#14519848C2212yes—
8D61⋊#108C2211yescharacteristic
9#16840772C2211yescharacteristic
10#16840766—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#14519848—41no—
26#14519848—41no—
27#14519848D411yescharacteristic
28#14519848D411yescharacteristic
29#14519847—21no—
30#14519846—21no—
31#14519845Q812yes—
32C4⋊#92420—42no—
33#14519831—41no—
34C8×#6923—41no—
35C2×C8×D61D411yescharacteristic
36C2×C8×D61C2311yescharacteristic
37C42×D61D411yescharacteristic
38#14519717C2×C412yes—
39#14519716—22no—
40C16×D61—22no—
41C4×#92418Q811yescharacteristic
42C8×Dic61C2×C411yescharacteristic
43C8×Dic61Q811yescharacteristic
44M32×C61C2×C412yes—
45C4×C8×C61C2×C411yescharacteristic
46C2×C4×D61—21no—
47C2×C4×D61C2×D411yescharacteristic
48C22⋊#6923—41no—
49#11758217—41no—
50C2×#92420—42no—
51C4⋊#6923—22no—
52C4×#6923—41no—
53#11758213—21no—
54#11758213—21no—
55#11758213—42no—
56#11758213—42no—
57D61⋊C8—41no—
58C2×C8×C61C4⋊C411yescharacteristic
59C2×C8×C61C22×C411yescharacteristic
60C42×C61C4⋊C411yescharacteristic
61C4×Dic61—21no—
62C4×Dic61C4⋊C411yescharacteristic
63C2×#92418C4⋊C411yescharacteristic
64C2×#92418C2×Q811yescharacteristic
65C8×D61D811yescharacteristic
66C8×D61D811yescharacteristic
67C8×D61Q1611yescharacteristic
68C8×D61Q1611yescharacteristic
69C8×D61C2×D411yescharacteristic
70C8×D61C2×Q811yescharacteristic
71C8×D61#4111yescharacteristic
72C8×D61#4111yescharacteristic
73C16×C61—22no—
74#11758185—22no—
75C22×D61#13711yescharacteristic
76C2×#6923—42no—
77C2×C4×C61—21no—
78C2×C4×C61C2×C4⋊C411yescharacteristic
79C2×Dic61—21no—
80C2×Dic61AGL(1,ℤ/8)11yescharacteristic
81C4×D61—42no—
82C4×D61#12111yescharacteristic
83C4×D61C22⋊Q811yescharacteristic
84C4×D61C2×D811yescharacteristic
85C4×D61C2×Q1611yescharacteristic
86#92420—41no—
87#92420—41no—
88#92420—82no—
89C8×C61#10711yescharacteristic
90C8×C61#10711yescharacteristic
91C8×C61C4×D411yescharacteristic
92C8×C61C4×Q811yescharacteristic
93#92418#10711yescharacteristic
94#92418#10711yescharacteristic
95#92418#12511yescharacteristic
96#92418C4⋊Q811yescharacteristic
97#13182—611nomaximal, Sylow
98C22×C61#42811yescharacteristic
99C2×D61—41no—
100C2×D61#46211yescharacteristic
101C2×D61#47411yescharacteristic
102#6923—82no—
103C4×C61—22no—
104C4×C61#38911yescharacteristic
105C4×C61C2×#10711yescharacteristic
106Dic61—41no—
107Dic61#45911yescharacteristic
108Dic61#47711yescharacteristic
109#2161—612no—
110C2×#364—611no—
111#1848—611no—
112#1772—611no—
113#1389—612no—
114C2×C61—21no—
115C2×C61#194711yescharacteristic
116D61—21no—
117D61—21no—
118C2×M32—612no—
119C2×#108—611no—
120C2×#108—612no—
121C2×#108—1221no—
122#427—611no—
123#423—1221no—
124#405—1221no—
125C2×C4×C8—611no—
126#368—1222no—
127#368—1222no—
128#364—612no—
129#364—611no—
130#364#692311yescharacteristic, complemented
131#339—1221no—
132C61#1318211yescharacteristic, complemented, Sylow
133C2×M16—1221no—
134C2×M16—1222no—
135C22×C8—611no—
136C22×C8—611no—
137#117—1221no—
138C2×C42—611no—
139M32—612no—
140M32—1222no—
141M32C2×#692312yes—
142C2×C16—1222no—
143#108—611no—
144#108—611no—
145#108—1221no—
146#108—1222no—
147#108—1222no—
148#108—2441no—
149#108—2441no—
150#107—1221no—
151#106—612no—
152C4⋊C8—2442no—
153#97—2441no—
154C4×C8—611no—
155C4×C8—611no—
156C4×C8—611no—
157C4×C8—2441no—
158C4×C8C2×#692311yescharacteristic
159C22×C4—611no—
160C22×C4—1221no—
161M16—1221no—
162M16—1221no—
163M16—2442no—
164M16—2442no—
165M16—2441no—
166C2×C8—611no—
167C2×C8—611no—
168C2×C8—611no—
169C2×C8—611no—
170C2×C8—611no—
171C2×C8—611no—
172C2×C8—611no—
173C2×C8—611no—
174C2×C8—611no—
175C2×C8—611no—
176C2×C8—2442no—
177C2×C8—2441no—
178C2×C8C4⋊#692311yescharacteristic
179C2×C8C22×#692311yescharacteristic
180C4⋊C4—1222no—
181C22⋊C4—2441no—
182C42—611no—
183C42—1221no—
184C42—2441no—
185C42C4⋊#692311yescharacteristic
186C16—22no—
187C16—1222no—
188C23—611no—
189C2×C4—21no—
190C2×C4—611no—
191C2×C4—611no—
192C2×C4—611no—
193C2×C4—611no—
194C2×C4—611no—
195C2×C4—1221no—
196C2×C4—2442no—
197C2×C4—2442no—
198C2×C4C2×C4⋊#692311yescharacteristic
199C8—611no—
200C8—611no—
201C8—611no—
202C8—611no—
203C8—4882no—
204C8—2441no—
205C8—2441no—
206C8#1451984611yescharacteristic
207C8#1451984611yescharacteristic
208C8D4×#692311yescharacteristic
209C8Q8×#692311yescharacteristic
210C22—611no—
211C22—611no—
212C22—2441no—
213C22#1684077311yescharacteristic
214C4—22no—
215C4—611no—
216C4—611no—
217C4—4882no—
218C4—2441no—
219C4#1684071311yescharacteristic
220C4C2×#1451984611yescharacteristic
221C2—21no—
222C2—1221no—
223C2—1221no—
224C2#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
130. #364#6923semidirect
132. C61#13182semidirect

Maximal subgroups

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

subgroupindex
#214621752
#214617602
#214616212
#214609002
#364×D612
#1318261