Finite Group Databasebeta

← #49133873

Subgroups — #49133873

Order 36224.

342 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 115 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#31827189C211yesmaximal, characteristic
2#31827175C211yesmaximal, characteristic
3#31826861C211yesmaximal, characteristic, complemented
4#31826805C212yesmaximal, complemented
5#31826797C212yesmaximal, complemented
6#31826761C211yesmaximal, characteristic, complemented
7#31826722C212yesmaximal, complemented
8C4×#17985382C211yesmaximal, characteristic, complemented
9#31826542C211yesmaximal, characteristic
10#31826504C212yesmaximal, complemented
11#475×C283C211yesmaximal, characteristic, complemented
12C2×#17985382C2211yescharacteristic
13C2×#17985375C2212yes—
14#22583610C2211yescharacteristic
15#22583605—22no—
16#22583602—21no—
17#22583599—21no—
18#22583590C2212yes—
19#22583588—22no—
20#22583586C2212yes—
21Q8×Dic283—21no—
22C4×Dic566C2211yescharacteristic
23C4×D1132—21no—
24C4×D1132C2211yescharacteristic
25#22583568C2212yes—
26C4⋊C4×D283C2212yes—
27#22583544C2212yes—
28#22583543C2211yescharacteristic
29#22583541C2212yes—
30#22583541C2212yes—
31#22583535C2212yes—
32#22583534C2211yescharacteristic
33#22583533C2211yescharacteristic
34(C2×D283)⋊C8C2212yes—
35C4×C283⋊C8C2211yescharacteristic
36C4⋊Q8×C283C2211yescharacteristic
37C4×Q8×C283C2211yescharacteristic
38#106×C283C2212yes—
39C4⋊C8×C283C2211yescharacteristic
40#103×C283C2212yes—
41C2×Dic566—21no—
42C2×Dic566C2311yescharacteristic
43C2×D1132D411yescharacteristic
44C2×C4×D283—22no—
45C2×C4×D283C2312yes—
46#17985382—22no—
47#17985375—24no—
48C2×C283⋊C8C2311yescharacteristic
49C2×C283⋊C8C2311yescharacteristic
50C4⋊Dic283—22no—
51C4⋊Dic283—21no—
52C4⋊Dic283D411yescharacteristic
53C4⋊Dic283C2312yes—
54C4⋊Dic283C2311yescharacteristic
55Dic283⋊C4—22no—
56Dic283⋊C4—22no—
57Dic283⋊C4—21no—
58(C2×D283)⋊C4—22no—
59(C2×D283)⋊C4—22no—
60(C2×D283)⋊C4—22no—
61(C2×D283)⋊C4D412yes—
62C4×Dic283—22no—
63C4×Dic283—21no—
64C2×Q8×C283—21no—
65C2×Q8×C283C2311yescharacteristic
66C2×C8×C283C2312yes—
67C4⋊C4×C283—21no—
68C4⋊C4×C283—21no—
69C4⋊C4×C283C2311yescharacteristic
70C4⋊C4×C283C2312yes—
71C42×C283—21no—
72C42×C283C2311yescharacteristic
73C22×D283C2×D412yes—
74Dic566—21no—
75Dic566—21no—
76Dic566—81no—
77D1132—22no—
78C2×Dic283—21no—
79C2×Dic283—21no—
80C2×Dic283—22no—
81C2×Dic283C2×D412yes—
82C4×D283—22no—
83C4×D283—22no—
84C4×D283—82no—
85C283⋊C8—21no—
86C283⋊C8#4112yes—
87Q8×C283—21no—
88Q8×C283—21no—
89Q8×C283—42no—
90C2×C4×C283—21no—
91C2×C4×C283—21no—
92C2×C4×C283—22no—
93C2×C4×C283C2×D411yescharacteristic
94C2×C4×C283C2×D411yescharacteristic
95C2×C4×C283C2411yescharacteristic
96C8×C283—22no—
97C22×C283C22×D411yescharacteristic
98C2×D283—22no—
99C2×D283—22no—
100C2×D283—22no—
101C4×C283—21no—
102C4×C283—41no—
103C4×C283—42no—
104C4×C283—41no—
105C4×C283#13712yes—
106C4×C283C2×#4111yescharacteristic
107C4×C2832−1+411yescharacteristic
108Dic283—22no—
109Dic283—41no—
110Dic283—42no—
111Dic283—41no—
112C2×C283#54711yescharacteristic
113C2×C283C2×#13711yescharacteristic
114C2×C283#57711yescharacteristic
115D283—42no—
116C283#335611yescharacteristic, complemented, Sylow
117#3356—2831nomaximal, Sylow
118#556—2831no—
119#554—2831no—
120#498—2831no—
121#485—2832no—
122#483—2832no—
123#477—2831no—
124#475D28311yescharacteristic, complemented
125#470—2832no—
126C4×Q16—2831no—
127#436—2831no—
128#428—2832no—
129C2×Q16—2831no—
130C2×M16—2832no—
131C4⋊Q8—2831no—
132C4⋊Q8C2×D28311yescharacteristic
133#126—5662no—
134#125—5661no—
135#124—5661no—
136C22⋊Q8—2832no—
137C22⋊Q8—2832no—
138C22⋊Q8—5662no—
139C4×Q8—2831no—
140C4×Q8—5661no—
141C4×Q8C2×D28311yescharacteristic
142C4×D4—2831no—
143C4×D4—5661no—
144#117—2832no—
145C2×C4⋊C4—2832no—
146#107—2832no—
147#107—2831no—
148#106—2832no—
149#106—2832no—
150#106C2×D28312yes—
151C4⋊C8C2×D28311yescharacteristic
152#103—2831no—
153#103—2832no—
154#103—2831no—
155#103C2×D28312yes—
156C22⋊C8—2832no—
157C4×C8—2831no—
158C2×Q8—21no—
159C2×Q8—2831no—
160C2×Q8—5661no—
161C2×Q8C22×D28311yescharacteristic
162C2×D4—2831no—
163C22×C4—2832no—
164C22×C4—5662no—
165Q16—5662no—
166M16—5664no—
167C2×C8—2831no—
168C2×C8—2831no—
169C2×C8C22×D28312yes—
170C4⋊C4—21no—
171C4⋊C4—21no—
172C4⋊C4—2831no—
173C4⋊C4—2832no—
174C4⋊C4—2831no—
175C4⋊C4—5662no—
176C4⋊C4—5662no—
177C4⋊C4—5662no—
178C4⋊C4—5661no—
179C4⋊C4—5661no—
180C4⋊C4C22×D28311yescharacteristic
181C4⋊C4C22×D28312yes—
182C22⋊C4—2832no—
183C22⋊C4—5662no—
184C22⋊C4—5662no—
185C22⋊C4—5662no—
186C42—21no—
187C42—5662no—
188C42—5661no—
189C42C22×D28311yescharacteristic
190C23—2832no—
191Q8—21no—
192Q8—21no—
193Q8—42no—
194Q8—5661no—
195Q8—5661no—
196Q8—22641no—
197D4—5662no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—22no—
201C2×C4—2832no—
202C2×C4—5662no—
203C2×C4—5662no—
204C2×C4—5661no—
205C2×C4—5661no—
206C2×C4—5662no—
207C2×C4—22642no—
208C2×C4D4×D28311yescharacteristic
209C2×C4D4×D28311yescharacteristic
210C2×C4C23×D28311yescharacteristic
211C8—22no—
212C8—2832no—
213C8—5661no—
214C22—5662no—
215C22—5662no—
216C22—5662no—
217C22C2×D4×D28311yescharacteristic
218C4—21no—
219C4—42no—
220C4—41no—
221C4—41no—
222C4—5662no—
223C4—11322no—
224C4—11321no—
225C4—11321no—
226C4#2258363912yes—
227C4#41×D28311yescharacteristic
228C4#2258365811yescharacteristic
229C2—11322no—
230C2#3182711711yescharacteristic
231C2C2×#2258363911yescharacteristic
232C2#3182727411yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#475×C283C2
socleC22×C283C22×D4
prime radicalC2×D1132D4
hypercenter#475D283
hypocenterC283#3356
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #475

Complements

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

NH ≅ G/Ntype
3. #31826861C2semidirect
4. #31826805C2semidirect
5. #31826797C2semidirect
6. #31826761C2semidirect
7. #31826722C2semidirect
8. C4×#17985382C2semidirect
10. #31826504C2semidirect
11. #475×C283C2semidirect
116. C283#3356semidirect
124. #475D283semidirect

Maximal subgroups

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

subgroupindex
#318271892
#318271752
#318268612
#318268052
#318267972
#318267612
#318267222
C4×#179853822
#318265422
#318265042
#475×C2832
#3356283