Finite Group Databasebeta

← #49121676

Subgroups — #49121676

Order 36224.

342 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 79 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#31827231C211yesmaximal, characteristic, complemented
2#31826976C211yesmaximal, characteristic
3#31826447C211yesmaximal, characteristic, complemented
4#31826429C211yesmaximal, characteristic, complemented
5#31826237C211yesmaximal, characteristic, complemented
6#31826236C211yesmaximal, characteristic, complemented
7#407×C283C211yesmaximal, characteristic, complemented
8C2×#17985392C2211yescharacteristic
9#22583618—22no—
10#22583616—22no—
11C2×#17985376C2211yescharacteristic
12C2×#17985376C2211yescharacteristic
13M16×D283—22no—
14#22583593C412yes—
15#22583589—21no—
16#22583584—21no—
17#22583579C412yes—
18C4×C22⋊D283—22no—
19#22583569C2211yescharacteristic
20#22583528—21no—
21#22583526—21no—
22C22⋊(C283⋊C8)—22no—
23C23×C4×C283C2211yescharacteristic
24C2×M16×C283C2211yescharacteristic
25C2×M16×C283C2211yescharacteristic
26C22⋊C8×C283—22no—
27#17985392—21no—
28#17985392—21no—
29#17985392—21no—
30#17985392—21no—
31C2×Dic566D411yescharacteristic
32C2×D1132D411yescharacteristic
33C2×C22⋊D283—22no—
34C2×C22⋊D283C2×C412yes—
35C2×C4×D283D412yes—
36#17985376—21no—
37#17985376—21no—
38#17985376—21no—
39#17985376—21no—
40#17985375—24no—
41C2×C283⋊C8—21no—
42C2×C283⋊C8D412yescomplemented
43C8×D283—24no—
44C4⋊Dic283—21no—
45Dic283⋊C4—22no—
46C22⋊Dic283—22no—
47C22⋊Dic283C2×C412yes—
48(C2×D283)⋊C4—22no—
49C4×Dic283—21no—
50C24×C283C2×C411yescharacteristic
51C22×C4×C283—21no—
52C22×C4×C283—21no—
53C22×C4×C283—21no—
54C22×C4×C283—21no—
55C22×C4×C283—21no—
56C22×C4×C283—21no—
57C22×C4×C283C2×C411yescharacteristic
58C22×C4×C283C2311yescharacteristic
59M16×C283—21no—
60M16×C283—21no—
61M16×C283—21no—
62M16×C283—21no—
63C2×C8×C283—21no—
64C2×C8×C283D412yescomplemented
65C22×D283C22⋊C412yes—
66Dic566—21no—
67Dic566—21no—
68D1132—21no—
69D1132—21no—
70C22⋊D283—22no—
71C22⋊D283—22no—
72C22⋊D283—44no—
73C2×Dic283—22no—
74C2×Dic283C22⋊C412yes—
75C4×D283—22no—
76C4×D283—22no—
77C283⋊C8—22no—
78C283⋊C8—41no—
79C23×C283—21no—
80C23×C283—21no—
81C23×C283—21no—
82C23×C283—42no—
83C23×C283C22×C411yescharacteristic
84C2×C4×C283—21no—
85C2×C4×C283—21no—
86C2×C4×C283—21no—
87C2×C4×C283—41no—
88C2×C4×C283—41no—
89C2×C4×C283—41no—
90C2×C4×C283—41no—
91C2×C4×C283C2×D411yescharacteristic
92C2×C4×C283C2×D411yescharacteristic
93C2×C4×C283C2×D411yescharacteristic
94C2×C4×C283C2×D411yescharacteristic
95C2×C4×C283#4111yescharacteristic
96C2×C4×C283#4111yescharacteristic
97C8×C283—22no—
98C8×C283—41no—
99C22×C283—22no—
100C22×C283—22no—
101C22×C283—22no—
102C22×C283—41no—
103C22×C283—41no—
104C22×C283—41no—
105C22×C283—41no—
106C22×C283—41no—
107C22×C283C2×C22⋊C411yescharacteristic
108C22×C283C4×D411yescharacteristic
109C22×C283C4×D411yescharacteristic
110C2×D283—22no—
111C2×D283—42no—
112C4×C283—41no—
113C4×C283#12011yescharacteristic
114C4×C283#12111yescharacteristic
115C4×C283#12111yescharacteristic
116C4×C283#12311yescharacteristic
117Dic283—22no—
118Dic283—42no—
119C2×C283—21no—
120C2×C283—21no—
121C2×C283—21no—
122C2×C283—42no—
123C2×C283#38611yescharacteristic
124D283—42no—
125C283#189111yescharacteristic, complemented, Sylow
126#1891—2831nomaximal, Sylow
127#568—2831no—
128#525—2831no—
129#413—2831no—
130#407—2831no—
131#407D28311yescharacteristic, complemented
132#344—2831no—
133#344—2831no—
134C2×#41—2831no—
135C23×C4C2×D28311yescharacteristic
136#131—5662no—
137#131—5662no—
138C2×M16—2831no—
139C2×M16—2831no—
140C2×M16—5662no—
141C2×M16C2×D28311yescharacteristic
142C2×M16C2×D28311yescharacteristic
143#123—2832no—
144C22⋊Q8—5661no—
145#121—5661no—
146#120—2832no—
147C4×D4—5662no—
148#117—2831no—
149#101—5661no—
150#100—5661no—
151C22⋊C8—22no—
152C22⋊C8—5662no—
153C24C4×D28311yescharacteristic
154#41—5661no—
155#41—5661no—
156#41—5661no—
157#41—5661no—
158C2×Q8—2831no—
159C2×D4—2832no—
160C2×D4—2831no—
161C2×D4—5662no—
162C22×C4—21no—
163C22×C4—21no—
164C22×C4—21no—
165C22×C4—21no—
166C22×C4—21no—
167C22×C4—21no—
168C22×C4—2832no—
169C22×C4C4×D28311yescharacteristic
170C22×C4C22×D28311yescharacteristic
171M16—21no—
172M16—21no—
173M16—21no—
174M16—21no—
175M16—5664no—
176M16—5661no—
177M16—5661no—
178M16—5661no—
179M16—5661no—
180C2×C8—21no—
181C2×C8—2832no—
182C2×C8—5664no—
183C2×C8—5661no—
184C2×C8C22⋊D28312yescomplemented
185C4⋊C4—5662no—
186C4⋊C4—5661no—
187C22⋊C4—2832no—
188C22⋊C4—5662no—
189C22⋊C4—5662no—
190C42—5661no—
191C23—21no—
192C23—21no—
193C23—21no—
194C23—42no—
195C23—2832no—
196C23C2×C4×D28311yescharacteristic
197Q8—5661no—
198Q8—5661no—
199D4—5662no—
200D4—5662no—
201D4—5661no—
202D4—5661no—
203D4—11324no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—41no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—2832no—
212C2×C4—5662no—
213C2×C4—5662no—
214C2×C4—5662no—
215C2×C4D4×D28311yescharacteristic
216C2×C4D4×D28311yescharacteristic
217C2×C4D4×D28311yescharacteristic
218C2×C4C2×C22⋊D28311yescharacteristic
219C2×C4#1798539111yescharacteristic
220C2×C4#1798539211yescharacteristic
221C8—22no—
222C8—41no—
223C8—5662no—
224C8—11321no—
225C22—22no—
226C22—22no—
227C22—22no—
228C22—41no—
229C22—41no—
230C22—41no—
231C22—41no—
232C22—41no—
233C22—5662no—
234C22—11322no—
235C22C22⋊C4×D28311yescharacteristic
236C22(C22⋊D283)⋊C411yescharacteristic
237C22C4×C22⋊D28311yescharacteristic
238C4—41no—
239C4—5662no—
240C4—11322no—
241C4#2258357811yescharacteristic
242C4#2258358111yescharacteristic
243C4#2258358311yescharacteristic
244C4#2258359211yescharacteristic
245C2—21no—
246C2—21no—
247C2—21no—
248C2—42no—
249C2—11322no—
250C2#3182634111yescharacteristic
subgroupG/H
centerC4#22583578
commutatorC23×C283C22×C4
FrattiniC22×C4C22×D283
Fitting#407×C283C2
socleC2×C283#386
prime radical#31826976C2
cosocleC22×C4×C283C23
hypercenter#407D283
hypocenterC283#1891
LCSG ▷ C23×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C4 ◁ C22×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
1. #31827231C2semidirect
3. #31826447C2semidirect
4. #31826429C2semidirect
5. #31826237C2semidirect
6. #31826236C2semidirect
7. #407×C283C2semidirect
42. C2×C283⋊C8D4semidirect
64. C2×C8×C283D4semidirect
125. C283#1891semidirect
131. #407D283semidirect
184. C2×C8C22⋊D283semidirect

Maximal subgroups

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

subgroupindex
#318272312
#318269762
#318264472
#318264292
#318262372
#318262362
#407×C2832
#1891283