Finite Group Databasebeta

← #49133140

Subgroups — #49133140

Order 36224.

388 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 123 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#31827175C211yesmaximal, characteristic
2#31827130C211yesmaximal, characteristic
3#31826815C211yesmaximal, characteristic, complemented
4#31826799C212yesmaximal, complemented
5#31826761C211yesmaximal, characteristic, complemented
6#31826703C212yesmaximal, complemented
7#31826619C212yesmaximal, complemented
8C4×#17985382C211yesmaximal, characteristic, complemented
9#31826530C211yesmaximal, characteristic
10#103×D283C212yesmaximal, complemented
11#462×C283C211yesmaximal, characteristic, complemented
12C2×Q8×D283C2212yes—
13C2×#17985382C2211yescharacteristic
14C2×C8×D283C2212yes—
15#22583610C2211yescharacteristic
16#22583609—21no—
17#22583602—21no—
18#22583588—22no—
19#22583588—22no—
20#22583586C2212yes—
21#22583586C2212yes—
22C4×Dic566C2211yescharacteristic
23C4×D1132—21no—
24C4×D1132C2211yescharacteristic
25#22583572—21no—
26C4⋊C4×D283C2212yes—
27#22583544C2212yes—
28#22583543C2211yescharacteristic
29#22583535C2212yes—
30#22583534C2211yescharacteristic
31#22583534C2212yes—
32#22583534C2212yes—
33#22583533C2211yescharacteristic
34(C2×D283)⋊C8C2212yes—
35C4×C283⋊C8C2211yescharacteristic
36C2×Q16×C283C2212yes—
37C4⋊Q8×C283C2211yescharacteristic
38C4×Q8×C283C2211yescharacteristic
39C4⋊C8×C283C2211yescharacteristic
40#103×C283C2212yes—
41C2×Dic566—22no—
42C2×Dic566—21no—
43C2×Dic566C2311yescharacteristic
44Q8×D283—24no—
45Q8×D283—42no—
46C2×D1132D411yescharacteristic
47C2×C4×D283—22no—
48C2×C4×D283—22no—
49C2×C4×D283C2312yes—
50#17985382—22no—
51C2×C283⋊C8C2311yescharacteristic
52C2×C283⋊C8C2311yescharacteristic
53C8×D283—42no—
54C4⋊Dic283—21no—
55C4⋊Dic283D411yescharacteristic
56C4⋊Dic283C2312yes—
57C4⋊Dic283C2311yescharacteristic
58Dic283⋊C4—22no—
59Dic283⋊C4—22no—
60Dic283⋊C4—22no—
61Dic283⋊C4—21no—
62(C2×D283)⋊C4—22no—
63(C2×D283)⋊C4—22no—
64(C2×D283)⋊C4D412yes—
65C4×Dic283—21no—
66C2×Q8×C283C2311yescharacteristic
67C2×Q8×C283C2312yes—
68Q16×C283—42no—
69C2×C8×C283C2312yes—
70C4⋊C4×C283—21no—
71C4⋊C4×C283—21no—
72C4⋊C4×C283—21no—
73C4⋊C4×C283C2311yescharacteristic
74C42×C283—21no—
75C42×C283C2311yescharacteristic
76C22×D283C2×D412yes—
77Dic566—21no—
78Dic566—44no—
79Dic566—81no—
80Dic566#4112yes—
81D1132Q1614yescomplemented
82C2×Dic283—21no—
83C2×Dic283—21no—
84C2×Dic283—22no—
85C2×Dic283C2×D412yes—
86C4×D283—22no—
87C4×D283—22no—
88C4×D283—44no—
89C4×D283—82no—
90C283⋊C8—21no—
91C283⋊C8—21no—
92Q8×C283—21no—
93Q8×C283—22no—
94Q8×C283—21no—
95Q8×C283—22no—
96C2×C4×C283—21no—
97C2×C4×C283—21no—
98C2×C4×C283—22no—
99C2×C4×C283C2×D411yescharacteristic
100C2×C4×C283C2×D411yescharacteristic
101C2×C4×C283C2411yescharacteristic
102C8×C283—22no—
103C22×C283C22×D411yescharacteristic
104C2×D283—22no—
105C2×D283—22no—
106C2×D283C2×Q1614yes—
107C4×C283—21no—
108C4×C283—41no—
109C4×C283—42no—
110C4×C283—41no—
111C4×C283C2×Q1612yes—
112C4×C283C2×#4111yescharacteristic
113C4×C283H(5,𝔽2)11yescharacteristic
114Dic283—22no—
115Dic283—22no—
116Dic283—42no—
117Dic283—41no—
118C2×C283#54611yescharacteristic
119C2×C283C22×Q1611yescharacteristic
120C2×C283#57711yescharacteristic
121D283—24no—
122C283#329911yescharacteristic, complemented, Sylow
123#3299—2831nomaximal, Sylow
124#554—2831no—
125D4×Q8—2831no—
126#487—2831no—
127#484—2832no—
128#477—2831no—
129#467—2832no—
130#462D28311yescharacteristic, complemented
131#451—2832no—
132C4×Q16—2831no—
133C8×D4—2831no—
134C2×#103—2832no—
135C22×Q8—2832no—
136C2×Q16—2831no—
137C2×Q16C2×D28312yes—
138C22×C8—2832no—
139C4⋊Q8—2831no—
140C4⋊Q8—5661no—
141C4⋊Q8C2×D28311yescharacteristic
142#125—5661no—
143C22⋊Q8—2832no—
144C22⋊Q8—2832no—
145C22⋊Q8—5662no—
146C22⋊Q8—5662no—
147C4×Q8—2831no—
148C4×Q8C2×D28311yescharacteristic
149C4×D4—2831no—
150C4×D4—5661no—
151C4×D4—5661no—
152C2×C4⋊C4—2832no—
153#107—2832no—
154#107—2831no—
155C4⋊C8C2×D28311yescharacteristic
156#103—2832no—
157#103—2831no—
158#103—2832no—
159#103—2832no—
160#103—2831no—
161#103C2×D28312yes—
162C22⋊C8—2832no—
163C4×C8—2831no—
164C2×Q8—2831no—
165C2×Q8—5662no—
166C2×Q8—5661no—
167C2×Q8—5664no—
168C2×Q8—11322no—
169C2×Q8C22×D28312yes—
170C2×Q8C22×D28311yescharacteristic
171C2×D4—2831no—
172C22×C4—2832no—
173C22×C4—5662no—
174C22×C4—5662no—
175Q16—42no—
176Q16—5662no—
177C2×C8—2831no—
178C2×C8—2831no—
179C2×C8—11322no—
180C2×C8C22×D28312yes—
181C4⋊C4—21no—
182C4⋊C4—21no—
183C4⋊C4—21no—
184C4⋊C4—2831no—
185C4⋊C4—2832no—
186C4⋊C4—2831no—
187C4⋊C4—5662no—
188C4⋊C4—5662no—
189C4⋊C4—5662no—
190C4⋊C4—5661no—
191C4⋊C4—5661no—
192C4⋊C4C22×D28311yescharacteristic
193C22⋊C4—2832no—
194C22⋊C4—5662no—
195C22⋊C4—5662no—
196C42—21no—
197C42—5661no—
198C42C22×D28311yescharacteristic
199C23—2832no—
200Q8—21no—
201Q8—22no—
202Q8—21no—
203Q8—22no—
204Q8—2832no—
205Q8—5661no—
206Q8—11324no—
207Q8—22641no—
208D4—2834no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—22no—
212C2×C4—2832no—
213C2×C4—5661no—
214C2×C4—5662no—
215C2×C4—5662no—
216C2×C4—5661no—
217C2×C4—5662no—
218C2×C4—11324no—
219C2×C4—22642no—
220C2×C4D4×D28311yescharacteristic
221C2×C4D4×D28311yescharacteristic
222C2×C4C23×D28311yescharacteristic
223C8—22no—
224C8—5661no—
225C8—5661no—
226C22—2834no—
227C22—5662no—
228C22—5662no—
229C22C2×D4×D28311yescharacteristic
230C4—21no—
231C4—41no—
232C4—42no—
233C4—41no—
234C4—5662no—
235C4—5662no—
236C4—11322no—
237C4—11321no—
238C4Q16×D28312yes—
239C4#41×D28311yescharacteristic
240C4#2258365511yescharacteristic
241C2—5664no—
242C2#3182711211yescharacteristic
243C2C2×Q16×D28311yescharacteristic
244C2#3182727411yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#462×C283C2
socleC22×C283C22×D4
prime radicalC2×D1132D4
hypercenter#462D283
hypocenterC283#3299
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #462

Complements

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

NH ≅ G/Ntype
3. #31826815C2semidirect
4. #31826799C2semidirect
5. #31826761C2semidirect
6. #31826703C2semidirect
7. #31826619C2semidirect
8. C4×#17985382C2semidirect
10. #103×D283C2semidirect
11. #462×C283C2semidirect
81. D1132Q16semidirect
122. C283#3299semidirect
130. #462D283semidirect

Maximal subgroups

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

subgroupindex
#318271752
#318271302
#318268152
#318267992
#318267612
#318267032
#318266192
C4×#179853822
#318265302
#103×D2832
#462×C2832
#3299283