Finite Group Databasebeta

← C2×#31826759 #49131031

Subgroups — C2×#31826759 #49131031

Order 36224.

416 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 157 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
1C2×#22583609C211yesmaximal, characteristic
2C2×#22583575C211yesmaximal, characteristic
3#31826759C218yesmaximal, direct product factor
4C2×#22583543C211yesmaximal, characteristic
5C2×Dic283⋊C8C211yesmaximal, characteristic
6C2×#22583535C211yesmaximal, characteristic
7C2×#22583533C211yesmaximal, characteristic
8C2×#107×C283C211yesmaximal, characteristic
9C22×Dic566—21no—
10C22×Dic566C2211yescharacteristic
11C22×C283⋊C8C2211yescharacteristic
12#22583609—22no—
13#22583609C2214yes—
14#22583575—22no—
15#22583575C2214yes—
16C2×C4⋊Dic283C2211yescharacteristic
17C2×Dic283⋊C4—21no—
18C2×Dic283⋊C4—21no—
19C2×C4×Dic283—21no—
20C2×C4×Dic283C2211yescharacteristic
21#22583543C2214yes—
22Dic283⋊C8C2214yes—
23#22583535C2214yes—
24#22583533C2214yes—
25C22×C8×C283C2211yescharacteristic
26C2×C4⋊C4×C283C2211yescharacteristic
27C2×C4⋊C4×C283C2211yescharacteristic
28#107×C283C2214yes—
29C2×Dic566—24no—
30C2×Dic566—21no—
31C2×Dic566—22no—
32C2×Dic566—44no—
33C2×Dic566Q814yescomplemented
34C2×Dic566C2312yes—
35C22×Dic283—21no—
36C22×Dic283—21no—
37C22×Dic283D411yescharacteristic
38C22×Dic283D411yescharacteristic
39C2×C283⋊C8—22no—
40C2×C283⋊C8C2312yes—
41C4⋊Dic283—21no—
42C4⋊Dic283C2312yes—
43Dic283⋊C4—24no—
44Dic283⋊C4—24no—
45C4×Dic283—24no—
46C4×Dic283D412yes—
47C4×Dic283C2312yes—
48C22×C4×C283—21no—
49C22×C4×C283—21no—
50C22×C4×C283C2311yescharacteristic
51C2×C8×C283—22no—
52C2×C8×C283C2312yes—
53C4⋊C4×C283—21no—
54C4⋊C4×C283—21no—
55C4⋊C4×C283C2312yes—
56C4⋊C4×C283C2312yes—
57Dic566—24no—
58Dic566—22no—
59Dic566—48no—
60Dic566C2×Q814yescomplemented
61C2×Dic283—24no—
62C2×Dic283—22no—
63C2×Dic283—22no—
64C2×Dic283—22no—
65C2×Dic283—42no—
66C2×Dic283Q1614yes—
67C2×Dic283C2×D412yes—
68C2×Dic283C2×D412yes—
69C283⋊C8—22no—
70C23×C283C2×D411yescharacteristic
71C2×C4×C283—22no—
72C2×C4×C283—22no—
73C2×C4×C283—42no—
74C2×C4×C283—42no—
75C2×C4×C283C2×D411yescharacteristic
76C2×C4×C283C2×Q812yes—
77C2×C4×C283#4112yes—
78C2×C4×C283C2411yescharacteristic
79C8×C283—22no—
80C22×C283C22⋊Q812yes—
81C22×C283C2×Q1612yes—
82C22×C283AGL(1,ℤ/8)12yes—
83C22×C283C22×D411yescharacteristic
84C4×C283—42no—
85C4×C283—42no—
86C4×C283C22⋊Q812yes—
87C4×C283C22×Q811yescharacteristic
88C4×C283C2×#4111yescharacteristic
89Dic283—24no—
90Dic283—22no—
91Dic283—42no—
92Dic283C2×Q1614yes—
93C2×C283#47714yescomplemented
94C2×C283C2×C22⋊Q811yescharacteristic
95C2×C283C22×Q1611yescharacteristic
96C2×C283C2×AGL(1,ℤ/8)11yescharacteristic
97C283C2×#47711yescharacteristic, complemented, Sylow
98C2×#477—2831nomaximal, Sylow
99C2×C4⋊Q8—2831no—
100C2×C4×Q8—2831no—
101#477—2838no—
102C2×#107—2831no—
103C2×#107D28311yescharacteristic
104C2×C4⋊C8—2831no—
105C2×#103—2831no—
106C2×#103—2831no—
107C22×Q8—2831no—
108C22×Q8—5661no—
109C22×C8—2831no—
110C22×C8C2×D28311yescharacteristic
111C4⋊Q8—2834no—
112C4⋊Q8—5662no—
113C4×Q8—2834no—
114C4×Q8—5662no—
115C2×C4⋊C4—2831no—
116C2×C4⋊C4—5661no—
117C2×C4⋊C4—5661no—
118C2×C4⋊C4C2×D28311yescharacteristic
119C2×C4⋊C4C2×D28311yescharacteristic
120C2×C42—2831no—
121C2×C42—5661no—
122#107—2834no—
123#107C2×D28314yes—
124C4⋊C8—2834no—
125#103—2834no—
126#103—2834no—
127C2×Q8—2834no—
128C2×Q8—2832no—
129C2×Q8—5664no—
130C2×Q8—5661no—
131C2×Q8—5662no—
132C2×Q8—11324no—
133C22×C4—21no—
134C22×C4—21no—
135C22×C4—2831no—
136C22×C4—2831no—
137C22×C4—5661no—
138C22×C4—5661no—
139C22×C4C22×D28311yescharacteristic
140C2×C8—22no—
141C2×C8—2832no—
142C2×C8—5662no—
143C2×C8C22×D28312yes—
144C4⋊C4—21no—
145C4⋊C4—21no—
146C4⋊C4—2832no—
147C4⋊C4—5664no—
148C4⋊C4—5664no—
149C4⋊C4—5661no—
150C4⋊C4C22×D28312yes—
151C4⋊C4C22×D28312yes—
152C42—2832no—
153C42—2832no—
154C42—5664no—
155C23D4×D28311yescharacteristic
156Q8—2834no—
157Q8—5664no—
158Q8—5662no—
159Q8—11328no—
160C2×C4—22no—
161C2×C4—22no—
162C2×C4—42no—
163C2×C4—42no—
164C2×C4—2834no—
165C2×C4—2832no—
166C2×C4—2832no—
167C2×C4—5664no—
168C2×C4—5662no—
169C2×C4—5662no—
170C2×C4—5662no—
171C2×C4—11322no—
172C2×C4D4×D28311yescharacteristic
173C2×C4Q8×D28312yes—
174C2×C4#1798539212yes—
175C2×C4C23×D28311yescharacteristic
176C8—22no—
177C8—5662no—
178C22#2258358812yes—
179C22Q16×D28312yes—
180C22#2258363412yes—
181C22C2×D4×D28311yescharacteristic
182C4—42no—
183C4—42no—
184C4—2834no—
185C4—5664no—
186C4—5662no—
187C4—11322no—
188C4#2258358812yes—
189C4C2×Q8×D28311yescharacteristic
190C4C2×#1798539211yescharacteristic
191C2#3182675914yesdirect product factor
192C2C2×#2258358811yescharacteristic
193C2C2×Q16×D28311yescharacteristic
194C2C2×#2258363411yescharacteristic
subgroupG/H
centerC23D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
FittingC2×#107×C283C2
socle, prime radicalC23×C283C2×D4
hypercenterC2×#107D283
hypocenterC283C2×#477
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
3. #31826759C2direct (N × H)
33. C2×Dic566Q8semidirect
60. Dic566C2×Q8semidirect
93. C2×C283#477semidirect
97. C283C2×#477semidirect
191. C2#31826759direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#225836092
C2×#225835752
#318267592
C2×#225835432
C2×Dic283⋊C82
C2×#225835352
C2×#225835332
C2×#107×C2832
C2×#477283