Finite Group Databasebeta

← #37526973

Subgroups — #37526973

Order 22976.

234 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 101 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#26040010C211yesmaximal, characteristic, complemented
2#26040008C211yesmaximal, characteristic, complemented
3#26040005C211yesmaximal, characteristic, complemented
4#26040001C211yesmaximal, characteristic, complemented
5#26039999C211yesmaximal, characteristic, complemented
6#26039996C211yesmaximal, characteristic, complemented
7#26039992C211yesmaximal, characteristic, complemented
8#26039987C211yesmaximal, characteristic
9C4×Dic718C211yesmaximal, characteristic, complemented
10C4×C22⋊D359C211yesmaximal, characteristic, complemented
11C4×C22⋊D359C211yesmaximal, characteristic, complemented
12#26039974C211yesmaximal, characteristic, complemented
13#26039972C211yesmaximal, characteristic, complemented
14C2×C4×Dic359C211yesmaximal, characteristic, complemented
15C4×D4×C359C211yesmaximal, characteristic, complemented
16C2×Dic718C2211yescharacteristic
17C2×C22⋊D359C2211yescharacteristic
18C2×C22⋊D359C2211yescharacteristic
19C22×Dic359C2211yescharacteristic
20C22×Dic359C2211yescharacteristic
21C2×C4×D359C2211yescharacteristic
22C4⋊Dic359C2211yescharacteristic
23C4⋊Dic359C2211yescharacteristic
24C4⋊Dic359C2211yescharacteristic
25Dic359⋊C4C2211yescharacteristic
26Dic359⋊C4C2211yescharacteristic
27Dic359⋊C4C2211yescharacteristic
28Dic359⋊C4C2211yescharacteristic
29Dic359⋊C4C2211yescharacteristic
30Dic359⋊C4C2211yescharacteristic
31C22⋊Dic359C2211yescharacteristic
32C22⋊Dic359C2211yescharacteristic
33C22⋊Dic359C2211yescharacteristic
34C22⋊Dic359C2211yescharacteristic
35(C2×D359)⋊C4C2211yescharacteristic
36(C2×D359)⋊C4C2211yescharacteristic
37(C2×D359)⋊C4C2211yescharacteristic
38(C2×D359)⋊C4C2211yescharacteristic
39C4×Dic359C2211yescharacteristic
40C4×Dic359C2211yescharacteristic
41C4×Dic359C2211yescharacteristic
42C4×Dic359C2211yescharacteristic
43C4×Dic359C2211yescharacteristic
44C2×D4×C359C2211yescharacteristic
45C22×C4×C359C2211yescharacteristic
46C22×C4×C359C2211yescharacteristic
47C4⋊C4×C359C2211yescharacteristic
48C22⋊C4×C359C2211yescharacteristic
49C22⋊C4×C359C2211yescharacteristic
50C42×C359C2211yescharacteristic
51C22×D359C2311yescharacteristic
52Dic718—22no—
53C22⋊D359—22no—
54C22⋊D359—22no—
55C2×Dic359—22no—
56C2×Dic359—22no—
57C2×Dic359C2311yescharacteristic
58C2×Dic359C2311yescharacteristic
59C2×Dic359C2311yescharacteristic
60C2×Dic359C2311yescharacteristic
61C2×Dic359C2311yescharacteristic
62C2×Dic359C2311yescharacteristic
63C2×Dic359C2311yescharacteristic
64C4×D359—22no—
65C23×C359C2311yescharacteristic
66C23×C359C2311yescharacteristic
67D4×C359—22no—
68C2×C4×C359—22no—
69C2×C4×C359—22no—
70C2×C4×C359C2311yescharacteristic
71C2×C4×C359C2311yescharacteristic
72C2×C4×C359C2311yescharacteristic
73C2×C4×C359C2311yescharacteristic
74C2×C4×C359C2311yescharacteristic
75C22×C359—21no—
76C22×C359—21no—
77C22×C359—21no—
78C22×C359—21no—
79C22×C359—21no—
80C22×C359#4112yes—
81C22×C359C2411yescharacteristic
82C2×D359—21no—
83C2×D359—21no—
84C2×D359—21no—
85C4×C359—21no—
86C4×C359—21no—
87C4×C359—21no—
88C4×C359—21no—
89C4×C359#4112yes—
90Dic359—21no—
91Dic359—21no—
92Dic359—21no—
93Dic359—21no—
94Dic359—21no—
95Dic359—21no—
96Dic359#4112yes—
97C2×C359—22no—
98C2×C359—41no—
99C2×C359C2×#4111yescharacteristic
100C2×C359C2×#4111yescharacteristic
101C2×C359C2×#4111yescharacteristic
102D359—41no—
103C359#52911yescharacteristic, complemented, Sylow
104#529—3591nomaximal, Sylow
105#126—3591no—
106#126—3591no—
107#125—3591no—
108#124—3591no—
109#123—3591no—
110#123—3591no—
111C22⋊Q8—3591no—
112#121—3591no—
113C4×Q8—3591no—
114C4×D4—3591no—
115C4×D4—3591no—
116C4×D4D35911yescharacteristic, complemented
117#117—3591no—
118#117—3591no—
119C2×C42—3591no—
120C2×Q8—3591no—
121C2×D4—3591no—
122C2×D4—3591no—
123C2×D4C2×D35911yescharacteristic
124C22×C4—3591no—
125C22×C4—3591no—
126C22×C4—3591no—
127C22×C4C2×D35911yescharacteristic
128C22×C4C2×D35911yescharacteristic
129C4⋊C4—3591no—
130C4⋊C4—3591no—
131C4⋊C4—3591no—
132C4⋊C4—3591no—
133C4⋊C4—3591no—
134C4⋊C4—3591no—
135C4⋊C4—3591no—
136C4⋊C4—3591no—
137C4⋊C4—3591no—
138C4⋊C4C2×D35911yescharacteristic
139C22⋊C4—3591no—
140C22⋊C4—3591no—
141C22⋊C4—3591no—
142C22⋊C4—3591no—
143C22⋊C4—3591no—
144C22⋊C4—3591no—
145C22⋊C4—3591no—
146C22⋊C4—3591no—
147C22⋊C4C2×D35911yescharacteristic
148C22⋊C4C2×D35911yescharacteristic
149C42—3591no—
150C42—3591no—
151C42—3591no—
152C42—3591no—
153C42—3591no—
154C42C2×D35911yescharacteristic
155C23—3591no—
156C23C22×D35911yescharacteristic
157C23C22×D35911yescharacteristic
158Q8—7182no—
159D4—22no—
160D4—7182no—
161D4—7182no—
162C2×C4—22no—
163C2×C4—22no—
164C2×C4—3591no—
165C2×C4—3591no—
166C2×C4—3591no—
167C2×C4—3591no—
168C2×C4—3591no—
169C2×C4—3591no—
170C2×C4—3591no—
171C2×C4—7182no—
172C2×C4—7182no—
173C2×C4—7182no—
174C2×C4C22×D35911yescharacteristic
175C2×C4C22×D35911yescharacteristic
176C2×C4C22×D35911yescharacteristic
177C2×C4C22×D35911yescharacteristic
178C2×C4C22×D35911yescharacteristic
179C22—21no—
180C22—21no—
181C22—21no—
182C22—21no—
183C22—21no—
184C22—7181no—
185C22—7181no—
186C22—7181no—
187C22#1915334112yes—
188C22C23×D35911yescharacteristic
189C4—21no—
190C4—21no—
191C4—21no—
192C4—21no—
193C4—3592no—
194C4—7181no—
195C4—7181no—
196C4—7181no—
197C4—7181no—
198C4—7181no—
199C4—7181no—
200C4#1915334012yes—
201C2—22no—
202C2—41no—
203C2—14361no—
204C2#41×D35911yescharacteristic
205C2C2×#1915334011yescharacteristic
206C2C2×#1915334111yescharacteristic
subgroupG/H
centerC2×C4C22×D359
commutator, socle, cosocleC22×C359C24
FrattiniC22C23×D359
FittingC4×D4×C359C2
prime radical#26039987C2
hypercenterC4×D4D359
hypocenterC359#529
LCSG ▷ C22×C359 ▷ C359
UCSC1 ◁ C2×C4 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. #26040010C2semidirect
2. #26040008C2semidirect
3. #26040005C2semidirect
4. #26040001C2semidirect
5. #26039999C2semidirect
6. #26039996C2semidirect
7. #26039992C2semidirect
9. C4×Dic718C2semidirect
10. C4×C22⋊D359C2semidirect
11. C4×C22⋊D359C2semidirect
12. #26039974C2semidirect
13. #26039972C2semidirect
14. C2×C4×Dic359C2semidirect
15. C4×D4×C359C2semidirect
103. C359#529semidirect
116. C4×D4D359semidirect

Maximal subgroups

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

subgroupindex
#260400102
#260400082
#260400052
#260400012
#260399992
#260399962
#260399922
#260399872
C4×Dic7182
C4×C22⋊D3592
#260399742
#260399722
C2×C4×Dic3592
C4×D4×C3592
#529359