Finite Group Databasebeta

← #49133956

Subgroups — #49133956

Order 36224.

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

normal subgroups only

This group has 348 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#31827200C211yesmaximal, characteristic
2#31827190C211yesmaximal, characteristic, complemented
3#31826821C212yesmaximal, complemented
4#31826813C211yesmaximal, characteristic
5#31826764C212yesmaximal, complemented
6#31826690C212yesmaximal, complemented
7#31826666C211yesmaximal, characteristic
8#31826589C211yesmaximal, characteristic, complemented
9C4×#17985382C211yesmaximal, characteristic, complemented
10#31826552C212yesmaximal, complemented
11#475×C283C211yesmaximal, characteristic, complemented
12C2×#17985382C2211yescharacteristic
13C2×#17985381C2212yes—
14#22583608—21no—
15#22583607C2211yescharacteristic
16#22583601C2212yes—
17#22583600—22no—
18#22583599C2212yes—
19#22583598—21no—
20#22583595—22no—
21Q8×Dic283—21no—
22C4×Dic566C2211yescharacteristic
23C4×Dic566C2211yescharacteristic
24#22583575C2212yes—
25C4×D1132—21no—
26#22583572C2212yes—
27#22583543C2211yescharacteristic
28Dic283⋊C8C2212yes—
29#22583534C2211yescharacteristic
30#22583533C2211yescharacteristic
31#22583532C2212yes—
32#22583530C2212yes—
33#22583530C2212yes—
34C4×C283⋊C8C2211yescharacteristic
35C8×Dic283C2212yes—
36C4⋊Q8×C283C2211yescharacteristic
37C4×Q8×C283C2211yescharacteristic
38#106×C283C2212yes—
39C4⋊C8×C283C2211yescharacteristic
40#103×C283C2212yes—
41C2×Dic566D411yescharacteristic
42C2×Dic566C2311yescharacteristic
43C2×D1132—21no—
44C2×D1132—21no—
45C2×D1132C2312yes—
46C2×C4×D283—22no—
47#17985382—22no—
48#17985381—24no—
49C2×C283⋊C8C2311yescharacteristic
50C2×C283⋊C8C2311yescharacteristic
51C4⋊Dic283—22no—
52C4⋊Dic283D411yescharacteristic
53C4⋊Dic283C2311yescharacteristic
54Dic283⋊C4—22no—
55Dic283⋊C4—22no—
56Dic283⋊C4—21no—
57Dic283⋊C4D412yes—
58(C2×D283)⋊C4—22no—
59(C2×D283)⋊C4—22no—
60(C2×D283)⋊C4—22no—
61C4×Dic283—22no—
62C4×Dic283—21no—
63C4×Dic283C2312yes—
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×D283—22no—
74Dic566—22no—
75Dic566—21no—
76Dic566#4112yes—
77D1132—22no—
78D1132—22no—
79D1132—42no—
80D1132—81no—
81C2×Dic283—21no—
82C2×Dic283—21no—
83C2×Dic283C2×D412yes—
84C2×Dic283C2×D412yes—
85C4×D283—82no—
86C283⋊C8—21no—
87C283⋊C8—21no—
88Q8×C283—21no—
89Q8×C283—21no—
90Q8×C283—42no—
91C2×C4×C283—21no—
92C2×C4×C283—21no—
93C2×C4×C283—22no—
94C2×C4×C283C2×D411yescharacteristic
95C2×C4×C283C2×D411yescharacteristic
96C2×C4×C283C2411yescharacteristic
97C8×C283—22no—
98C22×C283C22×D411yescharacteristic
99C2×D283—42no—
100C2×D283—42no—
101C2×D283—42no—
102C4×C283—21no—
103C4×C283—41no—
104C4×C283—42no—
105C4×C283—41no—
106C4×C283#13512yes—
107C4×C283C2×#4111yescharacteristic
108C4×C2832−1+411yescharacteristic
109Dic283—22no—
110Dic283—22no—
111Dic283—22no—
112Dic283—41no—
113C2×C283#54811yescharacteristic
114C2×C283C2×#13511yescharacteristic
115C2×C283#57711yescharacteristic
116D283—82no—
117C283#336511yescharacteristic, complemented, Sylow
118#3365—2831nomaximal, Sylow
119#559—2831no—
120#557—2831no—
121#488—2832no—
122#486—2831no—
123#478—2832no—
124#475D28311yescharacteristic, complemented
125#464—2832no—
126#460—2831no—
127C8×Q8—2831no—
128C4×Q16—2831no—
129C4×SD16—2832no—
130C2×Q16—2831no—
131C2×SD16—2832no—
132C4⋊Q8—5661no—
133C4⋊Q8C2×D28311yescharacteristic
134#127—2831no—
135#125—2832no—
136#125—5662no—
137#124—2832no—
138#124—5661no—
139#123—5662no—
140C4×Q8—2831no—
141C4×Q8—2832no—
142C4×Q8—2831no—
143C4×Q8—5661no—
144C4×Q8C2×D28311yescharacteristic
145C4×D4—2832no—
146C4×D4—5661no—
147#107—2831no—
148#106C2×D28312yes—
149C4⋊C8—2832no—
150C4⋊C8C2×D28311yescharacteristic
151#103—2831no—
152#103—2831no—
153#103C2×D28312yes—
154#102—2832no—
155#102—2832no—
156#102—2832no—
157C4×C8—2832no—
158C4×C8—2831no—
159C2×Q8—21no—
160C2×Q8—2831no—
161C2×Q8—2831no—
162C2×Q8C22×D28311yescharacteristic
163C2×D4—2832no—
164C2×D4—5661no—
165C2×D4—5661no—
166C22×C4—5662no—
167Q16—5662no—
168SD16—5664no—
169C2×C8—2831no—
170C2×C8—2831no—
171C2×C8C22×D28312yes—
172C4⋊C4—21no—
173C4⋊C4—21no—
174C4⋊C4—2832no—
175C4⋊C4—2831no—
176C4⋊C4—2831no—
177C4⋊C4—5662no—
178C4⋊C4—5662no—
179C4⋊C4—5662no—
180C4⋊C4—5661no—
181C4⋊C4C22×D28312yes—
182C4⋊C4C22×D28311yescharacteristic
183C22⋊C4—5662no—
184C22⋊C4—5662no—
185C22⋊C4—5662no—
186C42—21no—
187C42—2832no—
188C42—5662no—
189C42—5661no—
190C42C22×D28311yescharacteristic
191C23—5662no—
192Q8—21no—
193Q8—21no—
194Q8—42no—
195Q8—2832no—
196Q8—5662no—
197Q8—5661no—
198D4—5662no—
199D4—5662no—
200D4—11322no—
201D4—22641no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—22no—
205C2×C4—2832no—
206C2×C4—2832no—
207C2×C4—5661no—
208C2×C4—5661no—
209C2×C4—22642no—
210C2×C4D4×D28311yescharacteristic
211C2×C4D4×D28311yescharacteristic
212C2×C4C23×D28311yescharacteristic
213C8—22no—
214C8—5661no—
215C8—5661no—
216C22—11322no—
217C22—11322no—
218C22—11322no—
219C22C2×D4×D28311yescharacteristic
220C4—21no—
221C4—42no—
222C4—41no—
223C4—41no—
224C4—5662no—
225C4—5662no—
226C4—5662no—
227C4—11321no—
228C4#2258363112yes—
229C4#41×D28311yescharacteristic
230C4#2258365811yescharacteristic
231C2—22642no—
232C2#3182712511yescharacteristic
233C2C2×#2258363111yescharacteristic
234C2#3182727411yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#475×C283C2
socleC22×C283C22×D4
prime radical#22583607C22
hypercenter#475D283
hypocenterC283#3365
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
2. #31827190C2semidirect
3. #31826821C2semidirect
5. #31826764C2semidirect
6. #31826690C2semidirect
8. #31826589C2semidirect
9. C4×#17985382C2semidirect
10. #31826552C2semidirect
11. #475×C283C2semidirect
117. C283#3365semidirect
124. #475D283semidirect

Maximal subgroups

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

subgroupindex
#318272002
#318271902
#318268212
#318268132
#318267642
#318266902
#318266662
#318265892
C4×#179853822
#318265522
#475×C2832
#3365283