Finite Group Databasebeta

← #49133978

Subgroups — #49133978

Order 36224.

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

normal subgroups only

This group has 372 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#31827185C211yesmaximal, characteristic, complemented
2#31827130C211yesmaximal, characteristic, complemented
3#31826823C212yesmaximal, complemented
4#31826817C211yesmaximal, characteristic, complemented
5#31826759C212yesmaximal, complemented
6#31826679C212yesmaximal
7#31826671C211yesmaximal, characteristic, complemented
8#31826592C211yesmaximal, characteristic, complemented
9#31826564C212yesmaximal, complemented
10C4×#17985377C211yesmaximal, characteristic
11#474×C283C211yesmaximal, characteristic, complemented
12C2×Q8×D283—21no—
13C2×#17985381C2212yes—
14C2×#17985377C2211yescharacteristic
15#22583610C2211yescharacteristic
16#22583609C2212yes—
17#22583603—22no—
18#22583597C2212yes—
19#22583589—21no—
20#22583588—22no—
21#22583586—21no—
22C4×Dic566C2211yescharacteristic
23#22583575C2212yes—
24C4×D1132C2211yescharacteristic
25#22583572C2212yes—
26#22583569—21no—
27#22583543C2211yescharacteristic
28Dic283⋊C8C2212yes—
29#22583535C2212yes—
30#22583533C2212yes—
31#22583533C2212yes—
32#22583531C2211yescharacteristic
33#22583530C2211yescharacteristic
34#22583520C2212yes—
35C4×C283⋊C8C2211yescharacteristic
36C4⋊Q8×C283C2211yescharacteristic
37C4×D4×C283C2211yescharacteristic
38#107×C283C2212yes—
39C4⋊C8×C283C2211yescharacteristic
40#102×C283C2212yes—
41C2×Dic566—22no—
42C2×Dic566D411yescharacteristic
43C2×Dic566C2312yes—
44Q8×D283—44no—
45C2×D1132C2311yescharacteristic
46C2×C4×D283—22no—
47C2×C4×D283—21no—
48#17985381—24no—
49#17985377—22no—
50C2×C283⋊C8C2311yescharacteristic
51C2×C283⋊C8C2311yescharacteristic
52C4⋊Dic283—21no—
53C4⋊Dic283—21no—
54C4⋊Dic283D411yescharacteristic
55C4⋊Dic283C2311yescharacteristic
56Dic283⋊C4—22no—
57Dic283⋊C4—22no—
58Dic283⋊C4D412yes—
59C22⋊Dic283—22no—
60C22⋊Dic283—22no—
61(C2×D283)⋊C4—22no—
62(C2×D283)⋊C4—21no—
63C4×Dic283—22no—
64C4×Dic283C2312yes—
65C2×Q8×C283—21no—
66C2×D4×C283C2311yescharacteristic
67C22×C4×C283—21no—
68C2×C8×C283C2312yes—
69C4⋊C4×C283—21no—
70C4⋊C4×C283C2312yes—
71C4⋊C4×C283C2311yescharacteristic
72C22⋊C4×C283—21no—
73C42×C283C2311yescharacteristic
74C22×D283—21no—
75Dic566—22no—
76Dic566—22no—
77Dic566—22no—
78Dic566—44no—
79D1132—21no—
80D1132#4112yes—
81C2×Dic283—22no—
82C2×Dic283—21no—
83C2×Dic283C2×D412yes—
84C2×Dic283C2×D412yes—
85C4×D283—44no—
86C4×D283—42no—
87C283⋊C8—21no—
88C283⋊C8—21no—
89C23×C283—21no—
90Q8×C283—42no—
91D4×C283—21no—
92D4×C283—21no—
93C2×C4×C283—21no—
94C2×C4×C283—22no—
95C2×C4×C283—42no—
96C2×C4×C283C2×D411yescharacteristic
97C2×C4×C283C2×D411yescharacteristic
98C2×C4×C283C2411yescharacteristic
99C8×C283—22no—
100C22×C283—41no—
101C22×C283—41no—
102C22×C283—41no—
103C22×C283C22×D411yescharacteristic
104C2×D283—22no—
105C2×D283—41no—
106C2×D283—41no—
107C4×C283—21no—
108C4×C283—41no—
109C4×C283—42no—
110C4×C283AGL(1,ℤ/8)12yes—
111C4×C283C2×#4111yescharacteristic
112C4×C2832−1+411yescharacteristic
113Dic283—22no—
114Dic283—22no—
115Dic283—42no—
116Dic283—41no—
117C2×C283—81no—
118C2×C283#54811yescharacteristic
119C2×C283C2×AGL(1,ℤ/8)11yescharacteristic
120C2×C283#57811yescharacteristic
121D283—42no—
122C283#336711yescharacteristic, complemented, Sylow
123#3367—2831nomaximal, Sylow
124#556—2831no—
125D4×Q8—2831no—
126#489—2832no—
127#487—2831no—
128#477—2832no—
129#474D28311yescharacteristic, complemented
130#463—2832no—
131#461—2831no—
132#446—2831no—
133#440—2832no—
134C4×D8—2831no—
135C22×Q8—5661no—
136C2×SD16—2832no—
137C2×D8—2831no—
138C4⋊Q8—2832no—
139C4⋊Q8—2831no—
140C4⋊Q8C2×D28311yescharacteristic
141#126—5662no—
142#124—2832no—
143C22⋊Q8—5662no—
144C22⋊Q8—5661no—
145C22⋊Q8—5661no—
146C4×Q8—2831no—
147C4×Q8—2832no—
148C4×D4—2832no—
149C4×D4—2831no—
150C4×D4C2×D28311yescharacteristic
151#117—5661no—
152#107—2831no—
153#107C2×D28312yes—
154C4⋊C8—2832no—
155C4⋊C8C2×D28311yescharacteristic
156#103—2832no—
157#103—2832no—
158#103—2832no—
159#102—2831no—
160#102—2831no—
161#102C2×D28312yes—
162#97—2832no—
163C4×C8—2831no—
164C2×Q8—21no—
165C2×Q8—2831no—
166C2×Q8—2832no—
167C2×Q8—5662no—
168C2×Q8—11324no—
169C2×D4—2831no—
170C2×D4C22×D28311yescharacteristic
171C22×C4—21no—
172C22×C4—5662no—
173C22×C4—5661no—
174SD16—5664no—
175D8—5662no—
176C2×C8—2831no—
177C2×C8—2831no—
178C2×C8C22×D28312yes—
179C4⋊C4—21no—
180C4⋊C4—2832no—
181C4⋊C4—2831no—
182C4⋊C4—2831no—
183C4⋊C4—5662no—
184C4⋊C4—5662no—
185C4⋊C4—5661no—
186C4⋊C4—5661no—
187C4⋊C4C22×D28311yescharacteristic
188C4⋊C4C22×D28312yes—
189C22⋊C4—21no—
190C22⋊C4—5662no—
191C22⋊C4—5662no—
192C22⋊C4—5662no—
193C22⋊C4—5661no—
194C42—2832no—
195C42—5662no—
196C42C22×D28311yescharacteristic
197C23—21no—
198C23—5661no—
199Q8—42no—
200Q8—5662no—
201Q8—5662no—
202Q8—5662no—
203Q8—11324no—
204D4—21no—
205D4—21no—
206D4—2832no—
207D4—5661no—
208C2×C4—21no—
209C2×C4—22no—
210C2×C4—42no—
211C2×C4—2832no—
212C2×C4—2832no—
213C2×C4—5662no—
214C2×C4—5661no—
215C2×C4—11324no—
216C2×C4—11322no—
217C2×C4D4×D28311yescharacteristic
218C2×C4D4×D28311yescharacteristic
219C2×C4C23×D28311yescharacteristic
220C8—22no—
221C8—5661no—
222C8—5661no—
223C22—41no—
224C22—41no—
225C22—41no—
226C22—5662no—
227C22—11321no—
228C22—11321no—
229C22C2×D4×D28311yescharacteristic
230C4—21no—
231C4—41no—
232C4—42no—
233C4—5662no—
234C4—5662no—
235C4—11321no—
236C4—11322no—
237C4#2258363412yes—
238C4#41×D28311yescharacteristic
239C4#2258365811yescharacteristic
240C2—81no—
241C2—11322no—
242C2#3182712511yescharacteristic
243C2C2×#2258363411yescharacteristic
244C2#3182728111yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#474×C283C2
socleC22×C283C22×D4
prime radicalC2×#17985377C22
hypercenter#474D283
hypocenterC283#3367
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
1. #31827185C2semidirect
2. #31827130C2semidirect
3. #31826823C2semidirect
4. #31826817C2semidirect
5. #31826759C2semidirect
7. #31826671C2semidirect
8. #31826592C2semidirect
9. #31826564C2semidirect
11. #474×C283C2semidirect
122. C283#3367semidirect
129. #474D283semidirect

Maximal subgroups

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

subgroupindex
#318271852
#318271302
#318268232
#318268172
#318267592
#318266792
#318266712
#318265922
#318265642
C4×#179853772
#474×C2832
#3367283