Finite Group Databasebeta

← #49131782

Subgroups — #49131782

Order 36224.

348 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 137 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#31827021C211yesmaximal, characteristic
2#31827020C211yesmaximal, characteristic
3#31826875C211yesmaximal, characteristic, complemented
4#31826874C211yesmaximal, characteristic, complemented
5#31826873C212yesmaximal, complemented
6#31826872C212yesmaximal, complemented
7#31826871C211yesmaximal, characteristic, complemented
8#31826502C212yesmaximal
9#31826500C212yesmaximal
10#97×D283C211yesmaximal, characteristic
11#501×C283C211yesmaximal, characteristic, complemented
12C2×C8×D283C2212yes—
13#22583610C2211yescharacteristic
14#22583609C2211yescharacteristic
15#22583609C2211yescharacteristic
16#22583602C2211yescharacteristic
17#22583601C2212yes—
18#22583590—21no—
19#22583588—21no—
20#22583588—21no—
21#22583586—21no—
22Q8×Dic283—21no—
23#22583575—21no—
24#22583575—21no—
25#22583575—21no—
26#22583568C2211yescharacteristic
27#22583568C2212yes—
28#22583568C2211yescharacteristic
29C42×D283C2211yescharacteristic
30#22583544C2212yes—
31#22583543C2212yes—
32#22583543C2212yes—
33#22583542C2212yes—
34#22583541C2212yes—
35#22583541C2212yes—
36#22583521C2211yescharacteristic
37#22583520C2212yes—
38C4⋊Q8×C283C2211yescharacteristic
39#125×C283C2211yescharacteristic
40#107×C283C2212yes—
41#106×C283C2212yes—
42#97×C283C2211yescharacteristic
43C2×Dic566—21no—
44C2×Dic566—21no—
45C2×Dic566—21no—
46C2×C4×D283D411yescharacteristic
47C2×C4×D283D411yescharacteristic
48C2×C4×D283C2311yescharacteristic
49C2×C283⋊C8C2312yes—
50C8×D283Q818yescomplemented
51C4⋊Dic283—22no—
52C4⋊Dic283—21no—
53C4⋊Dic283C2312yes—
54C4⋊Dic283C2311yescharacteristic
55C4⋊Dic283C2311yescharacteristic
56Dic283⋊C4—22no—
57Dic283⋊C4—21no—
58Dic283⋊C4—21no—
59Dic283⋊C4—21no—
60Dic283⋊C4—21no—
61(C2×D283)⋊C4—22no—
62(C2×D283)⋊C4—21no—
63(C2×D283)⋊C4—21no—
64C4×Dic283—21no—
65C4×Dic283—21no—
66C4×Dic283—22no—
67C4×Dic283D411yescharacteristic
68C4×Dic283D411yescharacteristic
69C4×Dic283C2311yescharacteristic
70C2×Q8×C283—21no—
71C2×C8×C283C2312yes—
72C4⋊C4×C283—21no—
73C4⋊C4×C283—21no—
74C4⋊C4×C283—21no—
75C4⋊C4×C283C2312yes—
76C4⋊C4×C283C2311yescharacteristic
77C4⋊C4×C283C2311yescharacteristic
78C42×C283C2311yescharacteristic
79C22×D283C2×D411yescharacteristic
80Dic566—42no—
81Dic566—42no—
82Dic566—42no—
83C2×Dic283—21no—
84C2×Dic283—21no—
85C2×Dic283—22no—
86C2×Dic283C2×D411yescharacteristic
87C2×Dic283C2×D411yescharacteristic
88C2×Dic283C2×D411yescharacteristic
89C4×D283—41no—
90C4×D283—41no—
91C4×D283C2×Q814yes—
92C283⋊C8C2×Q814yes—
93Q8×C283—42no—
94C2×C4×C283—21no—
95C2×C4×C283—21no—
96C2×C4×C283—22no—
97C2×C4×C283C2×D411yescharacteristic
98C2×C4×C283C2×D411yescharacteristic
99C2×C4×C283C2411yescharacteristic
100C8×C283C2×Q814yes—
101C22×C283C22×D411yescharacteristic
102C2×D283—21no—
103C2×D283—21no—
104C2×D283C4⋊Q812yes—
105C4×C283—21no—
106C4×C283—21no—
107C4×C283—42no—
108C4×C283—41no—
109C4×C283—41no—
110C4×C283C22×Q812yes—
111Dic283—21no—
112Dic283—21no—
113Dic283—41no—
114Dic283—41no—
115Dic283—42no—
116Dic283C4⋊Q812yes—
117C2×C283C2×C4⋊Q811yescharacteristic
118C2×C283#57511yescharacteristic
119C2×C283#57511yescharacteristic
120D283—22no—
121C283#316211yescharacteristic, complemented, Sylow
122#3162—2831nomaximal, Sylow
123#533—2831no—
124#533—2831no—
125#501—2831no—
126#501—2831no—
127#501—2832no—
128#501—2832no—
129#501—2831no—
130#501D28311yescharacteristic, complemented
131#427—2832no—
132#427—2832no—
133C2×#97—2831no—
134C22×C8—2832no—
135C4⋊Q8—2831no—
136C4⋊Q8—2831no—
137C4⋊Q8—2831no—
138C4⋊Q8C2×D28311yescharacteristic
139#125—2832no—
140#125—2831no—
141#125C2×D28311yescharacteristic
142C22⋊Q8—5661no—
143C22⋊Q8—5661no—
144C22⋊Q8—5661no—
145C22⋊Q8—5661no—
146C4×Q8—5661no—
147C4×Q8—5661no—
148C4×Q8—5661no—
149C4×Q8—5661no—
150#117—2831no—
151#117—2832no—
152#117—2831no—
153C2×C42—2831no—
154#107—2832no—
155#107—2832no—
156#107—2832no—
157#107C2×D28312yes—
158#106—2832no—
159#106—2832no—
160#106—2832no—
161#106C2×D28312yes—
162#97—2832no—
163#97—2831no—
164#97C2×D28311yescharacteristic
165C2×Q8—21no—
166C2×Q8—5661no—
167C2×Q8—5661no—
168C2×Q8—5661no—
169C22×C4—2831no—
170C22×C4—2831no—
171C22×C4—2831no—
172C2×C8—2832no—
173C2×C8—2838no—
174C2×C8C22×D28312yes—
175C4⋊C4—21no—
176C4⋊C4—21no—
177C4⋊C4—21no—
178C4⋊C4—2832no—
179C4⋊C4—2831no—
180C4⋊C4—2831no—
181C4⋊C4—5662no—
182C4⋊C4—5661no—
183C4⋊C4—5661no—
184C4⋊C4—5662no—
185C4⋊C4—5661no—
186C4⋊C4—5661no—
187C4⋊C4—5661no—
188C4⋊C4C22×D28311yescharacteristic
189C4⋊C4C22×D28312yes—
190C4⋊C4C22×D28311yescharacteristic
191C22⋊C4—5661no—
192C22⋊C4—5661no—
193C22⋊C4—5662no—
194C42—2831no—
195C42—2831no—
196C42—2831no—
197C42—5661no—
198C42—5661no—
199C42—5662no—
200C42C22×D28311yescharacteristic
201C23—2831no—
202Q8—42no—
203Q8—11322no—
204Q8—11322no—
205Q8—11322no—
206C2×C4—21no—
207C2×C4—21no—
208C2×C4—22no—
209C2×C4—2831no—
210C2×C4—2834no—
211C2×C4—2831no—
212C2×C4—2831no—
213C2×C4—5661no—
214C2×C4—5662no—
215C2×C4—5661no—
216C2×C4—11321no—
217C2×C4—11321no—
218C2×C4D4×D28311yescharacteristic
219C2×C4D4×D28311yescharacteristic
220C2×C4C23×D28311yescharacteristic
221C8—2834no—
222C8Q8×D28314yes—
223C22—2832no—
224C22—5661no—
225C22—5661no—
226C22C2×D4×D28311yescharacteristic
227C4—21no—
228C4—21no—
229C4—42no—
230C4—41no—
231C4—41no—
232C4—2832no—
233C4—5661no—
234C4—5661no—
235C4—11321no—
236C4—11322no—
237C4—11321no—
238C4C2×Q8×D28312yes—
239C2—5662no—
240C2C4⋊Q8×D28311yescharacteristic
241C2#3182726111yescharacteristic
242C2#3182726411yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#501×C283C2
socleC22×C283C22×D4
prime radicalC22×D283C2×D4
hypercenter#501D283
hypocenterC283#3162
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #501

Complements

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

NH ≅ G/Ntype
3. #31826875C2semidirect
4. #31826874C2semidirect
5. #31826873C2semidirect
6. #31826872C2semidirect
7. #31826871C2semidirect
11. #501×C283C2semidirect
50. C8×D283Q8semidirect
121. C283#3162semidirect
130. #501D283semidirect

Maximal subgroups

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

subgroupindex
#318270212
#318270202
#318268752
#318268742
#318268732
#318268722
#318268712
#318265022
#318265002
#97×D2832
#501×C2832
#3162283