Finite Group Databasebeta

← C2×#31826794 #49131137

Subgroups — C2×#31826794 #49131137

Order 36224.

460 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 149 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×#22583586C211yesmaximal, characteristic
2C2×C4⋊C4×D283C211yesmaximal, characteristic
3#31826794C218yesmaximal, direct product factor
4C2×#22583542C211yesmaximal, characteristic, complemented
5C2×#22583541C211yesmaximal, characteristic, complemented
6C2×#22583534C211yesmaximal, characteristic, complemented
7C2×(C2×D283)⋊C8C211yesmaximal, characteristic
8C2×#103×C283C211yesmaximal, characteristic, complemented
9C22×C4×D283—21no—
10C22×C4×D283C2211yescharacteristic
11C22×C283⋊C8C2211yescharacteristic
12#22583586—22no—
13#22583586C2214yes—
14C2×C4⋊Dic283C2211yescharacteristic
15C2×C4⋊Dic283C2211yescharacteristic
16C2×Dic283⋊C4—21no—
17C2×Dic283⋊C4—21no—
18C4⋊C4×D283—22no—
19C4⋊C4×D283C2214yes—
20C2×(C2×D283)⋊C4—21no—
21#22583542C2214yescomplemented
22#22583541C2214yescomplemented
23#22583534C2214yescomplemented
24(C2×D283)⋊C8C2214yes—
25C22×Q8×C283C2211yescharacteristic
26C22×C8×C283C2211yescharacteristic
27C2×C4⋊C4×C283C2211yescharacteristic
28#103×C283C2214yescomplemented
29C23×D283D411yescharacteristic
30C22×Dic283—21no—
31C22×Dic283—21no—
32C22×Dic283D411yescharacteristic
33C2×C4×D283—24no—
34C2×C4×D283—22no—
35C2×C4×D283—22no—
36C2×C4×D283—44no—
37C2×C4×D283D412yes—
38C2×C4×D283C2312yes—
39C2×C283⋊C8—22no—
40C2×C283⋊C8C2312yes—
41C4⋊Dic283—21no—
42C4⋊Dic283—21no—
43C4⋊Dic283C2312yes—
44C4⋊Dic283C2312yes—
45Dic283⋊C4—24no—
46Dic283⋊C4—24no—
47(C2×D283)⋊C4—24no—
48C2×Q8×C283—21no—
49C2×Q8×C283—22no—
50C2×Q8×C283—22no—
51C2×Q8×C283C2312yes—
52C22×C4×C283—21no—
53C22×C4×C283—21no—
54C22×C4×C283C2311yescharacteristic
55C2×C8×C283—22no—
56C2×C8×C283C2312yes—
57C4⋊C4×C283—21no—
58C4⋊C4×C283C2312yes—
59C22×D283—22no—
60C22×D283—22no—
61C22×D283SD1614yes—
62C22×D283C2×D412yes—
63C2×Dic283—22no—
64C2×Dic283—22no—
65C2×Dic283—22no—
66C2×Dic283—42no—
67C2×Dic283—42no—
68C2×Dic283C2×D412yes—
69C4×D283—24no—
70C4×D283—22no—
71C4×D283—22no—
72C4×D283—48no—
73C283⋊C8—22no—
74C23×C283C2×D411yescharacteristic
75Q8×C283—22no—
76Q8×C283—22no—
77Q8×C283—42no—
78C2×C4×C283—22no—
79C2×C4×C283—22no—
80C2×C4×C283—42no—
81C2×C4×C283—42no—
82C2×C4×C283C2×D411yescharacteristic
83C2×C4×C283#4112yes—
84C2×C4×C283#4112yes—
85C2×C4×C283C2411yescharacteristic
86C8×C283—22no—
87C22×C283#12312yes—
88C22×C283C2×SD1612yes—
89C22×C283#13712yes—
90C22×C283C22×D411yescharacteristic
91C2×D283—22no—
92C2×D283—22no—
93C2×D283—28no—
94C2×D283C2×SD1614yes—
95C4×C283—42no—
96C4×C283—42no—
97C4×C283#12312yes—
98C4×C283C2×#4111yescharacteristic
99C4×C283C2×#4111yescharacteristic
100Dic283—22no—
101Dic283—42no—
102Dic283—42no—
103C2×C283#48314yescomplemented
104C2×C283C2×#12311yescharacteristic
105C2×C283C22×SD1611yescharacteristic
106C2×C283C2×#13711yescharacteristic
107D283—24no—
108C283C2×#48311yescharacteristic, complemented, Sylow
109C2×#483—2831nomaximal, Sylow
110C2×C22⋊Q8—2831no—
111C22×C4⋊C4—2831no—
112#483—2838no—
113C2×#106—2831no—
114C2×#106—2831no—
115C2×#103—2831no—
116C2×#103D28311yescharacteristic, complemented
117C2×C22⋊C8—2831no—
118C22×Q8C2×D28311yescharacteristic
119C23×C4—2831no—
120C23×C4—5661no—
121C22×C8—2831no—
122C22×C8C2×D28311yescharacteristic
123C22⋊Q8—2834no—
124C22⋊Q8—5662no—
125C2×C4⋊C4—2831no—
126C2×C4⋊C4—2831no—
127C2×C4⋊C4—2834no—
128C2×C4⋊C4—5662no—
129C2×C4⋊C4—5661no—
130C2×C4⋊C4—5661no—
131C2×C4⋊C4C2×D28311yescharacteristic
132C2×C22⋊C4—5661no—
133#106—2834no—
134#106—2834no—
135#103—2834no—
136#103C2×D28314yescomplemented
137C22⋊C8—2834no—
138C24—2831no—
139C2×Q8—21no—
140C2×Q8—22no—
141C2×Q8—22no—
142C2×Q8C22×D28312yes—
143C22×C4—21no—
144C22×C4—21no—
145C22×C4—2831no—
146C22×C4—2832no—
147C22×C4—2832no—
148C22×C4—5664no—
149C22×C4—5662no—
150C22×C4—5662no—
151C22×C4—5661no—
152C22×C4—5661no—
153C22×C4—11324no—
154C22×C4C22×D28311yescharacteristic
155C2×C8—22no—
156C2×C8—2832no—
157C2×C8—5662no—
158C2×C8C22×D28312yes—
159C4⋊C4—21no—
160C4⋊C4—2832no—
161C4⋊C4—2832no—
162C4⋊C4—5664no—
163C4⋊C4—5664no—
164C4⋊C4—5661no—
165C4⋊C4—5661no—
166C4⋊C4C22×D28312yes—
167C22⋊C4—5664no—
168C23—2834no—
169C23—2832no—
170C23—5662no—
171C23—5662no—
172C23D4×D28311yescharacteristic
173Q8—22no—
174Q8—22no—
175Q8—42no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—42no—
179C2×C4—42no—
180C2×C4—2832no—
181C2×C4—5662no—
182C2×C4—5664no—
183C2×C4—5662no—
184C2×C4—5662no—
185C2×C4—5662no—
186C2×C4—5662no—
187C2×C4—11328no—
188C2×C4—11322no—
189C2×C4—11322no—
190C2×C4D4×D28311yescharacteristic
191C2×C4#1798539112yes—
192C2×C4#1798539212yes—
193C2×C4C23×D28311yescharacteristic
194C8—22no—
195C8—5662no—
196C22—2834no—
197C22—5662no—
198C22—5662no—
199C22—5668no—
200C22#2258359212yes—
201C22SD16×D28312yes—
202C22#2258364212yes—
203C22C2×D4×D28311yescharacteristic
204C4—42no—
205C4—42no—
206C4—5662no—
207C4—11322no—
208C4—11322no—
209C4#2258359212yes—
210C4C2×#1798539111yescharacteristic
211C4C2×#1798539211yescharacteristic
212C2—5664no—
213C2#3182679414yesdirect product factor
214C2C2×#2258359211yescharacteristic
215C2C2×SD16×D28311yescharacteristic
216C2C2×#2258364211yescharacteristic
subgroupG/H
centerC23D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
FittingC2×#103×C283C2
socleC23×C283C2×D4
prime radicalC23×D283D4
hypercenterC2×#103D283
hypocenterC283C2×#483
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
3. #31826794C2direct (N × H)
4. C2×#22583542C2semidirect
5. C2×#22583541C2semidirect
6. C2×#22583534C2semidirect
8. C2×#103×C283C2semidirect
21. #22583542C22semidirect
22. #22583541C22semidirect
23. #22583534C22semidirect
28. #103×C283C22semidirect
103. C2×C283#483semidirect
108. C283C2×#483semidirect
116. C2×#103D283semidirect
136. #103C2×D283semidirect
213. C2#31826794direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#225835862
C2×C4⋊C4×D2832
#318267942
C2×#225835422
C2×#225835412
C2×#225835342
C2×(C2×D283)⋊C82
C2×#103×C2832
C2×#483283