Finite Group Databasebeta

← #49133983

Subgroups — #49133983

Order 36224.

372 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 372 conjugacy classes of subgroups — too many to draw. Only its 117 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#31827189C211yesmaximal, characteristic, complemented
2D4×Dic566C211yesmaximal, characteristic, complemented
3#31826826C212yesmaximal, complemented
4#31826815C211yesmaximal, characteristic, complemented
5#31826758C212yesmaximal, complemented
6#31826746C211yesmaximal, characteristic, complemented
7#31826682C212yesmaximal
8#31826592C211yesmaximal, characteristic, complemented
9#31826566C212yesmaximal, complemented
10C4×#17985377C211yesmaximal, characteristic
11#461×C283C211yesmaximal, characteristic, complemented
12C22×Dic566—21no—
13C2×#17985377C2211yescharacteristic
14#22583610C2211yescharacteristic
15#22583609C2212yes—
16#22583605—22no—
17#22583599C2212yes—
18#22583590—21no—
19#22583589—21no—
20#22583587—22no—
21Q8×Dic283C2212yes—
22C4×Dic566C2211yescharacteristic
23C4×D1132C2211yescharacteristic
24D4×Dic283C2212yes—
25#22583568—21no—
26#22583544C2212yes—
27#22583543C2211yescharacteristic
28Dic283⋊C8C2212yes—
29#22583534C2212yes—
30#22583534C2212yes—
31#22583532C2212yes—
32#22583531C2211yescharacteristic
33#22583530C2211yescharacteristic
34#22583520C2212yes—
35C4×C283⋊C8C2211yescharacteristic
36C2×SD16×C283C2212yes—
37C4⋊Q8×C283C2211yescharacteristic
38C4×D4×C283C2211yescharacteristic
39C4⋊C8×C283C2211yescharacteristic
40#103×C283C2212yes—
41C2×Dic566—22no—
42C2×Dic566—21no—
43C2×Dic566—44no—
44C2×Dic566D411yescharacteristic
45C2×D1132C2311yescharacteristic
46C22×Dic283—22no—
47C2×C4×D283—21no—
48#17985377—22no—
49C2×C283⋊C8C2311yescharacteristic
50C2×C283⋊C8C2311yescharacteristic
51C4⋊Dic283—22no—
52C4⋊Dic283—21no—
53C4⋊Dic283D411yescharacteristic
54C4⋊Dic283C2312yes—
55C4⋊Dic283C2311yescharacteristic
56Dic283⋊C4—22no—
57Dic283⋊C4D412yes—
58C22⋊Dic283—22no—
59(C2×D283)⋊C4—22no—
60(C2×D283)⋊C4—22no—
61(C2×D283)⋊C4—21no—
62C4×Dic283—22no—
63C4×Dic283C2312yes—
64C2×Q8×C283C2312yes—
65C2×D4×C283C2311yescharacteristic
66C22×C4×C283—21no—
67SD16×C283—24no—
68C2×C8×C283C2312yes—
69C4⋊C4×C283—21no—
70C4⋊C4×C283—21no—
71C4⋊C4×C283C2311yescharacteristic
72C22⋊C4×C283—21no—
73C42×C283C2311yescharacteristic
74C22×D283—21no—
75Dic566—22no—
76Dic566—44no—
77Dic566—42no—
78D1132—21no—
79D1132—21no—
80C2×Dic283—21no—
81C2×Dic283—22no—
82C2×Dic283—44no—
83C2×Dic283C2×D412yes—
84C2×Dic283C2×D412yes—
85C4×D283—42no—
86C283⋊C8—21no—
87C283⋊C8—21no—
88C23×C283—21no—
89Q8×C283—22no—
90Q8×C283—22no—
91D4×C283—21no—
92D4×C283#4112yes—
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—22no—
101C22×C283—41no—
102C22×C283—41no—
103C22×C283C22×D411yescharacteristic
104C2×D283—41no—
105C2×D283—41no—
106C2×D283—41no—
107C4×C283—21no—
108C4×C283—42no—
109C4×C283—41no—
110C4×C283AGL(1,ℤ/8)12yes—
111C4×C283C2×#4111yescharacteristic
112C4×C2832−1+411yescharacteristic
113Dic283—22no—
114Dic283—22no—
115Dic283—41no—
116Dic283—42no—
117C2×C283—42no—
118C2×C283#54811yescharacteristic
119C2×C283C2×AGL(1,ℤ/8)11yescharacteristic
120C2×C283#57811yescharacteristic
121D283—81no—
122C283#336711yescharacteristic, complemented, Sylow
123#3367—2831nomaximal, Sylow
124#556—2831no—
125D4×Q8—2831no—
126#489—2832no—
127#487—2831no—
128#477—2832no—
129#474—2831no—
130#463—2832no—
131#461D28311yescharacteristic, complemented
132#446—2831no—
133#440—2832no—
134C4×D8—2831no—
135C22×Q8—5661no—
136C2×SD16C2×D28312yes—
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—2832no—
153#107—2831no—
154C4⋊C8—2832no—
155C4⋊C8C2×D28311yescharacteristic
156#103—2832no—
157#103—2832no—
158#103C2×D28312yes—
159#102—2831no—
160#102—2832no—
161#102—2831no—
162#97—2832no—
163C4×C8—2831no—
164C2×Q8—2831no—
165C2×Q8—5662no—
166C2×Q8—5661no—
167C2×Q8—11324no—
168C2×Q8C22×D28312yes—
169C2×D4—2831no—
170C2×D4C22×D28311yescharacteristic
171C22×C4—21no—
172C22×C4—5662no—
173C22×C4—5661no—
174SD16—24no—
175D8—5662no—
176C2×C8—2831no—
177C2×C8—2831no—
178C2×C8C22×D28312yes—
179C4⋊C4—21no—
180C4⋊C4—21no—
181C4⋊C4—2832no—
182C4⋊C4—2831no—
183C4⋊C4—2832no—
184C4⋊C4—2831no—
185C4⋊C4—5662no—
186C4⋊C4—5662no—
187C4⋊C4—5661no—
188C4⋊C4C22×D28311yescharacteristic
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—22no—
200Q8—22no—
201Q8—5662no—
202Q8—11324no—
203Q8—11322no—
204D4—21no—
205D4—5661no—
206D4—5661no—
207D4#1798539112yes—
208C2×C4—22no—
209C2×C4—21no—
210C2×C4—42no—
211C2×C4—2832no—
212C2×C4—2832no—
213C2×C4—5661no—
214C2×C4—5662no—
215C2×C4—11324no—
216C2×C4—11322no—
217C2×C4D4×D28311yescharacteristic
218C2×C4D4×D28311yescharacteristic
219C2×C4C23×D28311yescharacteristic
220C8—22no—
221C8—5661no—
222C8—5661no—
223C22—22no—
224C22—41no—
225C22—41no—
226C22—11321no—
227C22—11321no—
228C22—11321no—
229C22C2×D4×D28311yescharacteristic
230C4—21no—
231C4—41no—
232C4—42no—
233C4—5662no—
234C4—5662no—
235C4—11322no—
236C4—11321no—
237C4#2258363712yes—
238C4C2×#1798539111yescharacteristic
239C4#2258365711yescharacteristic
240C2—42no—
241C2—22641no—
242C2#3182712111yescharacteristic
243C2C2×#2258363711yescharacteristic
244C2#3182728111yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#461×C283C2
socleC22×C283C22×D4
prime radicalC2×#17985377C22
hypercenter#461D283
hypocenterC283#3367
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
1. #31827189C2semidirect
2. D4×Dic566C2semidirect
3. #31826826C2semidirect
4. #31826815C2semidirect
5. #31826758C2semidirect
6. #31826746C2semidirect
8. #31826592C2semidirect
9. #31826566C2semidirect
11. #461×C283C2semidirect
122. C283#3367semidirect
131. #461D283semidirect

Maximal subgroups

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

subgroupindex
#318271892
D4×Dic5662
#318268262
#318268152
#318267582
#318267462
#318266822
#318265922
#318265662
C4×#179853772
#461×C2832
#3367283