Finite Group Databasebeta

← #30607935

Subgroups — #30607935

Order 15616.

294 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 294 conjugacy classes of subgroups — too many to draw. Only its 92 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#21462171C212yesmaximal
2#21461756C211yesmaximal, characteristic
3#21461621C211yesmaximal, characteristic
4#21460894C212yesmaximal
5#364×D61C211yesmaximal, characteristic
6D61⋊#108C2211yescharacteristic
7#16840772C2211yescharacteristic
8C2×#14519846C2212yes—
9C2×#14519845—21no—
10#16840725—21no—
11#16840706—21no—
12#16840689—22no—
13#16840688—22no—
14#16840633—21no—
15M32×D61C2212yes—
16C4×C8×D61C2211yescharacteristic
17#16839583C411yescharacteristic, complemented
18#16839582C412yescomplemented
19C61×#364C411yescharacteristic, complemented
20D61⋊M16—21no—
21#14519856—21no—
22C2×C4⋊#6923—22no—
23#14519848—21no—
24#14519847Q812yes—
25#14519846—22no—
26#14519846—22no—
27#14519846D412yes—
28#14519845—21no—
29#14519845—41no—
30#14519845—41no—
31#14519831—41no—
32C8×#6923—41no—
33(C2×#6923)⋊C4—42no—
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
45C22×#6923—42no—
46C2×C4×D61—21no—
47C2×C4×D61C2×D411yescharacteristic
48C22⋊#6923—41no—
49#11758217—41no—
50C4⋊#6923—22no—
51C4⋊#6923—42no—
52C4⋊#6923—42no—
53C4×#6923—41no—
54#11758213—22no—
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×D61AGL(1,ℤ/8)11yescharacteristic
74C2×#6923—42no—
75C2×#6923—84no—
76C2×#6923—82no—
77C2×C4×C61—21no—
78C2×C4×C61C2×C4⋊C411yescharacteristic
79C2×Dic61—21no—
80C2×Dic61#13711yescharacteristic
81C4×D61—42no—
82C4×D61#12111yescharacteristic
83C4×D61C22⋊Q811yescharacteristic
84C4×D61C2×D811yescharacteristic
85C4×D61C2×Q1611yescharacteristic
86#92420—42no—
87C8×C61#10711yescharacteristic
88C8×C61#10711yescharacteristic
89C8×C61C4×D411yescharacteristic
90C8×C61C4×Q811yescharacteristic
91#92418#10711yescharacteristic
92#92418#10711yescharacteristic
93#92418#12511yescharacteristic
94#92418C4⋊Q811yescharacteristic
95#13180—611nomaximal, Sylow
96C22×C61#42811yescharacteristic
97C2×D61—22no—
98C2×D61#45911yescharacteristic
99C2×D61#47711yescharacteristic
100#6923—82no—
101#6923—162no—
102C4×C61—41no—
103C4×C61#38911yescharacteristic
104C4×C61C2×#10711yescharacteristic
105Dic61—41no—
106Dic61#46211yescharacteristic
107Dic61#47411yescharacteristic
108#2159—612no—
109C2×#364—611no—
110#1846—611no—
111#1772—611no—
112#1387—612no—
113C2×C61—21no—
114C2×C61#194711yescharacteristic
115D61—21no—
116D61#221212yes—
117C2×M32—612no—
118C2×#108—611no—
119#427—611no—
120C2×#107—612no—
121C2×#106—1221no—
122#405—1221no—
123C2×C4×C8—611no—
124#382—1221no—
125#367—1222no—
126#366—1222no—
127#364—612no—
128#364—611no—
129#364#692311yescharacteristic, complemented
130#339—1221no—
131C61#1318011yescharacteristic, complemented, Sylow
132C2×M16—1221no—
133C22×C8—611no—
134C22×C8—611no—
135#117—1221no—
136C2×C4⋊C4—1222no—
137C2×C42—611no—
138M32—612no—
139M32—1222no—
140M32C2×#692312yes—
141C2×C16—1222no—
142#108—612no—
143#108—1221no—
144#107—612no—
145#107—1222no—
146#107—1222no—
147#106—1221no—
148#106—2441no—
149#106—2441no—
150#97—2441no—
151C4×C8—611no—
152C4×C8—611no—
153C4×C8—611no—
154C4×C8—2441no—
155C4×C8C2×#692311yescharacteristic
156#95—2442no—
157C22×C4—611no—
158C22×C4—1221no—
159C22×C4—2442no—
160M16—1222no—
161M16—2441no—
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—611no—
172C2×C8—2441no—
173C2×C8C4⋊#692311yescharacteristic
174C2×C8C22×#692311yescharacteristic
175C4⋊C4—1222no—
176C4⋊C4—2442no—
177C4⋊C4—2442no—
178C22⋊C4—2441no—
179C42—611no—
180C42—1221no—
181C42—2441no—
182C42C4⋊#692311yescharacteristic
183C16—22no—
184C16—1222no—
185C23—611no—
186C2×C4—21no—
187C2×C4—611no—
188C2×C4—611no—
189C2×C4—611no—
190C2×C4—611no—
191C2×C4—611no—
192C2×C4—1221no—
193C2×C4—4882no—
194C2×C4—4884no—
195C2×C4—2442no—
196C2×C4—2442no—
197C2×C4C2×C4⋊#692311yescharacteristic
198C8—611no—
199C8—611no—
200C8—611no—
201C8—611no—
202C8—2442no—
203C8#1451984611yescharacteristic
204C8#1451984611yescharacteristic
205C8D4×#692311yescharacteristic
206C8Q8×#692311yescharacteristic
207C22—611no—
208C22—611no—
209C22—1222no—
210C22#1684077311yescharacteristic
211C4—41no—
212C4—611no—
213C4—611no—
214C4—9762no—
215C4—4882no—
216C4—2441no—
217C4#1684071311yescharacteristic
218C4C2×#1451984611yescharacteristic
219C2—21no—
220C2—612no—
221C2—1221no—
222C2#2146193011yescharacteristic
subgroupG/H
centerC2#21461930
commutatorC2×C8×C61C22×C4
FrattiniC2×C8C22×#6923
FittingC61×#364C4
socleC2×C61#1947
prime radicalC22×D61AGL(1,ℤ/8)
cosocleC2×C8×D61C23
hypercenter#364#6923
hypocenterC61#13180
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
129. #364#6923semidirect
131. C61#13180semidirect

Maximal subgroups

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

subgroupindex
#214621712
#214617562
#214616212
#214608942
#364×D612
#1318061