Finite Group Databasebeta

← C2×#31826785 #49131162

Subgroups — C2×#31826785 #49131162

Order 36224.

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

normal subgroups only

This group has 512 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×#22583585C211yesmaximal, characteristic
2C2×C4⋊C4×D283C211yesmaximal, characteristic, complemented
3#31826785C218yesmaximal, direct product factor
4C2×#22583541C211yesmaximal, characteristic, complemented
5C2×#22583532C211yesmaximal, characteristic, complemented
6C2×#22583530C211yesmaximal, characteristic, complemented
7C2×(C2×D283)⋊C8C211yesmaximal, characteristic, complemented
8C2×#106×C283C211yesmaximal, characteristic, complemented
9C22×D1132—21no—
10C22×D1132C2211yescharacteristic
11C22×C4×D283—21no—
12C22×C4×D283C2211yescharacteristic
13C22×C283⋊C8C2211yescharacteristic
14#22583585—22no—
15#22583585C2214yes—
16C2×C4⋊Dic283C2211yescharacteristic
17C2×Dic283⋊C4—21no—
18C4⋊C4×D283—22no—
19C4⋊C4×D283C2214yescomplemented
20C2×(C2×D283)⋊C4—21no—
21#22583541C2214yescomplemented
22#22583532C2214yescomplemented
23#22583530C2214yescomplemented
24(C2×D283)⋊C8C2214yescomplemented
25C22×C8×C283C2211yescharacteristic
26C2×C4⋊C4×C283C2211yescharacteristic
27C2×C4⋊C4×C283C2211yescharacteristic
28#106×C283C2214yescomplemented
29C23×D283—21no—
30C23×D283D411yescharacteristic
31C2×D1132—24no—
32C2×D1132—21no—
33C2×D1132—22no—
34C2×D1132—22no—
35C2×D1132—44no—
36C2×D1132C2312yes—
37C22×Dic283—21no—
38C22×Dic283D411yescharacteristic
39C2×C4×D283—24no—
40C2×C4×D283—22no—
41C2×C4×D283—22no—
42C2×C4×D283—44no—
43C2×C4×D283D412yes—
44C2×C4×D283C2312yes—
45C2×C283⋊C8—22no—
46C2×C283⋊C8C2312yes—
47C4⋊Dic283—21no—
48C4⋊Dic283C2312yes—
49Dic283⋊C4—24no—
50(C2×D283)⋊C4—24no—
51C22×C4×C283—21no—
52C22×C4×C283—21no—
53C22×C4×C283C2311yescharacteristic
54C2×C8×C283—22no—
55C2×C8×C283C2312yes—
56C4⋊C4×C283—21no—
57C4⋊C4×C283—21no—
58C4⋊C4×C283C2312yes—
59C4⋊C4×C283C2312yes—
60C22×D283—22no—
61C22×D283—22no—
62C22×D283—22no—
63C22×D283—42no—
64C22×D283—42no—
65C22×D283—42no—
66C22×D283SD1614yes—
67C22×D283C2×D412yes—
68D1132—22no—
69D1132—22no—
70D1132—48no—
71D1132—42no—
72C2×Dic283—22no—
73C2×Dic283—22no—
74C2×Dic283—42no—
75C2×Dic283C2×D412yes—
76C4×D283—24no—
77C4×D283—22no—
78C4×D283—22no—
79C4×D283—48no—
80C283⋊C8—22no—
81C23×C283C2×D411yescharacteristic
82C2×C4×C283—22no—
83C2×C4×C283—22no—
84C2×C4×C283—42no—
85C2×C4×C283—42no—
86C2×C4×C283C2×D411yescharacteristic
87C2×C4×C283#4112yes—
88C2×C4×C283#4112yes—
89C2×C4×C283C2411yescharacteristic
90C8×C283—22no—
91C22×C283#12312yes—
92C22×C283C2×SD1612yes—
93C22×C283AGL(1,ℤ/8)12yes—
94C22×C283C22×D411yescharacteristic
95C2×D283—22no—
96C2×D283—22no—
97C2×D283—28no—
98C2×D283—42no—
99C2×D283—42no—
100C2×D283—42no—
101C2×D283—84no—
102C2×D283C2×SD1614yes—
103C4×C283—42no—
104C4×C283—42no—
105C4×C283#12312yes—
106C4×C283C2×#4111yescharacteristic
107C4×C283C2×#4111yescharacteristic
108Dic283—22no—
109Dic283—42no—
110C2×C283#48114yescomplemented
111C2×C283C2×#12311yescharacteristic
112C2×C283C22×SD1611yescharacteristic
113C2×C283C2×AGL(1,ℤ/8)11yescharacteristic
114D283—24no—
115D283—82no—
116C283C2×#48111yescharacteristic, complemented, Sylow
117C2×#481—2831nomaximal, Sylow
118C2×#121—2831no—
119C22×C4⋊C4—2831no—
120#481—2838no—
121C2×#106—2831no—
122C2×#106D28311yescharacteristic, complemented
123C2×#102—2831no—
124C2×#102—2831no—
125C2×C22⋊C8—2831no—
126C22×D4—2831no—
127C22×D4—5661no—
128C23×C4—2831no—
129C23×C4—5661no—
130C22×C8—2831no—
131C22×C8C2×D28311yescharacteristic
132#121—2834no—
133#121—5662no—
134C2×C4⋊C4—2831no—
135C2×C4⋊C4—2834no—
136C2×C4⋊C4—5662no—
137C2×C4⋊C4—5661no—
138C2×C4⋊C4C2×D28311yescharacteristic
139C2×C4⋊C4C2×D28311yescharacteristic
140C2×C22⋊C4—5661no—
141#106—2834no—
142#106C2×D28314yescomplemented
143#102—2834no—
144#102—2834no—
145C22⋊C8—2834no—
146C24—2831no—
147C24—5661no—
148C2×D4—2832no—
149C2×D4—5664no—
150C2×D4—5661no—
151C2×D4—5662no—
152C2×D4—5662no—
153C2×D4—11324no—
154C22×C4—21no—
155C22×C4—21no—
156C22×C4—2831no—
157C22×C4—2832no—
158C22×C4—2832no—
159C22×C4—5664no—
160C22×C4—5662no—
161C22×C4—5662no—
162C22×C4—5661no—
163C22×C4—11324no—
164C22×C4C22×D28311yescharacteristic
165C2×C8—22no—
166C2×C8—2832no—
167C2×C8—5662no—
168C2×C8C22×D28312yes—
169C4⋊C4—21no—
170C4⋊C4—21no—
171C4⋊C4—2832no—
172C4⋊C4—5664no—
173C4⋊C4—5661no—
174C4⋊C4C22×D28312yes—
175C4⋊C4C22×D28312yes—
176C22⋊C4—5664no—
177C23—2834no—
178C23—2832no—
179C23—5662no—
180C23—5662no—
181C23—5662no—
182C23—11322no—
183C23—11322no—
184C23—11322no—
185C23D4×D28311yescharacteristic
186D4—5662no—
187D4—5662no—
188D4—11328no—
189D4—11322no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—42no—
193C2×C4—42no—
194C2×C4—2832no—
195C2×C4—5662no—
196C2×C4—5664no—
197C2×C4—5662no—
198C2×C4—5662no—
199C2×C4—5662no—
200C2×C4—11328no—
201C2×C4—11322no—
202C2×C4D4×D28311yescharacteristic
203C2×C4#1798539212yes—
204C2×C4#1798539312yes—
205C2×C4C23×D28311yescharacteristic
206C8—22no—
207C8—5662no—
208C22—2834no—
209C22—5662no—
210C22—5662no—
211C22—5668no—
212C22—11322no—
213C22—11322no—
214C22—11322no—
215C22—22644no—
216C22#2258359512yes—
217C22SD16×D28312yes—
218C22#2258363712yes—
219C22C2×D4×D28311yescharacteristic
220C4—42no—
221C4—42no—
222C4—5662no—
223C4—11322no—
224C4#2258359512yes—
225C4C2×#1798539211yescharacteristic
226C4C2×#1798539311yescharacteristic
227C2—5664no—
228C2—22642no—
229C2#3182678514yesdirect product factor
230C2C2×#2258359511yescharacteristic
231C2C2×SD16×D28311yescharacteristic
232C2C2×#2258363711yescharacteristic
subgroupG/H
centerC23D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
FittingC2×#106×C283C2
socleC23×C283C2×D4
prime radicalC2×#22583585C2
hypercenterC2×#106D283
hypocenterC283C2×#481
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#106

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C4×D283C2semidirect
3. #31826785C2direct (N × H)
4. C2×#22583541C2semidirect
5. C2×#22583532C2semidirect
6. C2×#22583530C2semidirect
7. C2×(C2×D283)⋊C8C2semidirect
8. C2×#106×C283C2semidirect
19. C4⋊C4×D283C22semidirect
21. #22583541C22semidirect
22. #22583532C22semidirect
23. #22583530C22semidirect
24. (C2×D283)⋊C8C22semidirect
28. #106×C283C22semidirect
110. C2×C283#481semidirect
116. C283C2×#481semidirect
122. C2×#106D283semidirect
142. #106C2×D283semidirect
229. C2#31826785direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#225835852
C2×C4⋊C4×D2832
#318267852
C2×#225835412
C2×#225835322
C2×#225835302
C2×(C2×D283)⋊C82
C2×#106×C2832
C2×#481283