Finite Group Databasebeta

← #49131832

Subgroups — #49131832

Order 36224.

380 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 121 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#31827001C212yesmaximal, complemented
2#31826866C211yesmaximal, characteristic, complemented
3#31826850C211yesmaximal, characteristic, complemented
4#31826821C212yesmaximal, complemented
5#31826701C211yesmaximal, characteristic
6#31826696C212yesmaximal, complemented
7Q16×Dic283C211yesmaximal, characteristic, complemented
8#31826550C212yesmaximal, complemented
9#31826547C211yesmaximal, characteristic, complemented
10C2×C8×Dic283C211yesmaximal, characteristic, complemented
11#467×C283C211yesmaximal, characteristic, complemented
12C2×#17985379C2212yes—
13C2×D2264C2211yescharacteristic
14C22×C283⋊C8C2211yescharacteristic
15#22583605—22no—
16#22583601C2212yes—
17#22583599C2212yes—
18#22583594—22no—
19#22583584C2212yes—
20Q8×Dic283C2212yes—
21#22583572C2212yes—
22(C22⋊D283)⋊C4—22no—
23#22583568—22no—
24C2×C4×Dic283C2211yescharacteristic
25#22583544C2211yescharacteristic
26#22583541C2212yes—
27#22583534C2212yes—
28#22583532C2212yes—
29#22583530C2212yes—
30C8×Dic283C2211yescharacteristic
31C8×Dic283C2211yescharacteristic
32C8×Dic283C2211yescharacteristic
33C8×Dic283C2211yescharacteristic
34C2×Q16×C283C2211yescharacteristic
35C22×C8×C283C2211yescharacteristic
36C22⋊Q8×C283C2212yes—
37#107×C283C2211yescharacteristic
38#103×C283C2212yes—
39C2×D1132C2312yes—
40C2×C22⋊D283—22no—
41C22×Dic283D411yescharacteristic
42C22×Dic283D411yescharacteristic
43C2×C4×D283—22no—
44#17985379—24no—
45D2264—22no—
46C2×C283⋊C8—22no—
47C2×C283⋊C8C2311yescharacteristic
48C2×C283⋊C8C2311yescharacteristic
49C4⋊Dic283—22no—
50C4⋊Dic283—22no—
51C4⋊Dic283C2312yes—
52Dic283⋊C4—22no—
53(C2×D283)⋊C4—22no—
54(C2×D283)⋊C4—22no—
55(C2×D283)⋊C4—22no—
56(C2×D283)⋊C4—22no—
57C4×Dic283—22no—
58C4×Dic283D411yescharacteristic
59C4×Dic283D411yescharacteristic
60C4×Dic283C2311yescharacteristic
61C4×Dic283C2311yescharacteristic
62C2×Q8×C283C2312yes—
63C22×C4×C283C2311yescharacteristic
64Q16×C283—22no—
65C2×C8×C283—22no—
66C2×C8×C283C2311yescharacteristic
67C2×C8×C283C2311yescharacteristic
68C4⋊C4×C283—22no—
69C4⋊C4×C283C2312yes—
70C22⋊C4×C283—22no—
71C22×D283—22no—
72D1132—22no—
73D1132—22no—
74C22⋊D283—44no—
75C2×Dic283—22no—
76C2×Dic283—22no—
77C2×Dic283—22no—
78C2×Dic283C2×D411yescharacteristic
79C2×Dic283C2×D411yescharacteristic
80C2×Dic283C2×D411yescharacteristic
81C2×Dic283C2×D411yescharacteristic
82C4×D283—44no—
83C283⋊C8—21no—
84C283⋊C8#4112yes—
85C23×C283C2×D411yescharacteristic
86Q8×C283—22no—
87Q8×C283—22no—
88C2×C4×C283—21no—
89C2×C4×C283—21no—
90C2×C4×C283—22no—
91C2×C4×C283—22no—
92C2×C4×C283C2×D411yescharacteristic
93C2×C4×C283C2411yescharacteristic
94C8×C283—21no—
95C8×C283#4112yes—
96C22×C283—21no—
97C22×C283—21no—
98C22×C283#13512yes—
99C22×C283C22×D411yescharacteristic
100C2×D283—42no—
101C2×D283—42no—
102C2×D283—42no—
103C4×C283—21no—
104C4×C283—42no—
105C4×C283—42no—
106C4×C283C2×#4111yescharacteristic
107C4×C283C2×#4111yescharacteristic
108Dic283—21no—
109Dic283—21no—
110Dic283—21no—
111Dic283—42no—
112Dic283#13512yes—
113C2×C283—22no—
114C2×C283#53211yescharacteristic
115C2×C283C2×#13511yescharacteristic
116C2×C283C2×#13511yescharacteristic
117D283—82no—
118C283#316811yescharacteristic, complemented, Sylow
119#3168—2831nomaximal, Sylow
120#529—2832no—
121#499—2831no—
122#495—2831no—
123#488—2832no—
124#467D28311yescharacteristic, complemented
125#466—2831no—
126#465—2832no—
127C4×Q16—2831no—
128C4×SD16—2832no—
129C4×D8—2831no—
130C2×C4×C8—2831no—
131C2×Q16C2×D28311yescharacteristic
132C2×SD16—2832no—
133C2×D8—2831no—
134C22×C8—2831no—
135C22×C8C2×D28311yescharacteristic
136#126—5662no—
137#125—2832no—
138#124—2832no—
139#123—5662no—
140C22⋊Q8C2×D28312yes—
141#121—2832no—
142C4×Q8—2832no—
143C4×D4—2832no—
144C4×D4—5662no—
145#117—5662no—
146C2×C42—2831no—
147#107—2831no—
148#107C2×D28311yescharacteristic
149#106—2832no—
150#103—2832no—
151#103C2×D28312yes—
152#102—2832no—
153#102—2832no—
154C4×C8—2831no—
155C4×C8—2831no—
156C4×C8—2831no—
157C4×C8—2831no—
158C2×Q8C22×D28312yes—
159C2×D4—2832no—
160C2×D4—5662no—
161C22×C4—2831no—
162C22×C4—2831no—
163C22×C4—5662no—
164C22×C4C22×D28311yescharacteristic
165Q16—22no—
166SD16—5664no—
167D8—5662no—
168C2×C8—22no—
169C2×C8—2831no—
170C2×C8—2831no—
171C2×C8—5662no—
172C2×C8C22×D28311yescharacteristic
173C2×C8C22×D28311yescharacteristic
174C4⋊C4—22no—
175C4⋊C4—2832no—
176C4⋊C4—5662no—
177C4⋊C4—5662no—
178C4⋊C4—5662no—
179C4⋊C4C22×D28312yes—
180C22⋊C4—22no—
181C22⋊C4—5662no—
182C22⋊C4—5662no—
183C22⋊C4—5662no—
184C22⋊C4—5662no—
185C42—2831no—
186C42—2831no—
187C42—2831no—
188C42—2831no—
189C42—5662no—
190C23—5662no—
191C23D4×D28311yescharacteristic
192Q8—22no—
193Q8—22no—
194D4—5662no—
195D4—5662no—
196D4—11324no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—2831no—
202C2×C4—2831no—
203C2×C4—2831no—
204C2×C4—2831no—
205C2×C4—5662no—
206C2×C4—5662no—
207C2×C4—5662no—
208C2×C4—11324no—
209C2×C4D4×D28311yescharacteristic
210C2×C4C23×D28311yescharacteristic
211C8—21no—
212C8—2832no—
213C8—5661no—
214C8#1798539112yes—
215C22—21no—
216C22—21no—
217C22—11322no—
218C22—11322no—
219C22—11322no—
220C22#2258363312yes—
221C22C2×D4×D28311yescharacteristic
222C4—21no—
223C4—42no—
224C4—42no—
225C4—2832no—
226C4—5661no—
227C4—5661no—
228C4—5661no—
229C4—11322no—
230C4#41×D28311yescharacteristic
231C4C2×#1798539111yescharacteristic
232C2—22no—
233C2—22642no—
234C2#3182701011yescharacteristic
235C2#135×D28311yescharacteristic
236C2C2×#2258363311yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#467×C283C2
socleC22×C283C22×D4
prime radical#31826701C2
hypercenter#467D283
hypocenterC283#3168
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ #467

Complements

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

NH ≅ G/Ntype
1. #31827001C2semidirect
2. #31826866C2semidirect
3. #31826850C2semidirect
4. #31826821C2semidirect
6. #31826696C2semidirect
7. Q16×Dic283C2semidirect
8. #31826550C2semidirect
9. #31826547C2semidirect
10. C2×C8×Dic283C2semidirect
11. #467×C283C2semidirect
118. C283#3168semidirect
124. #467D283semidirect

Maximal subgroups

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

subgroupindex
#318270012
#318268662
#318268502
#318268212
#318267012
#318266962
Q16×Dic2832
#318265502
#318265472
C2×C8×Dic2832
#467×C2832
#3168283