Finite Group Databasebeta

← #49134296

Subgroups — #49134296

Order 36224.

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

normal subgroups only

This group has 350 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#31827190C211yesmaximal, characteristic, complemented
2#31827185C211yesmaximal, characteristic
3#31826856C212yesmaximal
4#31826844C211yesmaximal, characteristic, complemented
5#31826685C212yesmaximal
6#31826676C211yesmaximal, characteristic, complemented
7#31826674C212yesmaximal, complemented
8#31826592C211yesmaximal, characteristic, complemented
9#31826569C212yesmaximal, complemented
10C4×#17985380C211yesmaximal, characteristic
11#461×C283C211yesmaximal, characteristic
12C2×Dic1132C2212yes—
13C2×#17985382C2212yes—
14C2×#17985382C2212yes—
15C2×#17985380C2211yescharacteristic
16#22583610C2211yescharacteristic
17#22583608C2212yes—
18#22583603—22no—
19#22583601—21no—
20#22583600—22no—
21#22583597C2212yes—
22#22583589—21no—
23Q8×Dic283C2212yes—
24C4×Dic566C2211yescharacteristic
25C4×Dic566C2211yescharacteristic
26#22583575—21no—
27#22583575C2212yes—
28#22583569—21no—
29#22583541C2211yescharacteristic
30Dic283⋊C8C2212yes—
31#22583535C2212yes—
32#22583533C2211yescharacteristic
33#22583531C2211yescharacteristic
34#22583520C2212yes—
35C4×C283⋊C8C2211yescharacteristic
36C2×SD16×C283C2212yes—
37C4⋊Q8×C283C2211yescharacteristic
38C4×D4×C283C2211yescharacteristic
39C4⋊C8×C283C2211yescharacteristic
40#103×C283C2212yes—
41C2×Dic566D411yescharacteristic
42C2×Dic566C2312yes—
43C2×Dic566C2311yescharacteristic
44Dic1132—42no—
45#17985382—24no—
46#17985382—42no—
47#17985380—22no—
48C2×C283⋊C8C2311yescharacteristic
49C2×C283⋊C8C2311yescharacteristic
50C4⋊Dic283—22no—
51C4⋊Dic283—21no—
52C4⋊Dic283—21no—
53C4⋊Dic283D411yescharacteristic
54C4⋊Dic283C2311yescharacteristic
55Dic283⋊C4—22no—
56Dic283⋊C4—22no—
57Dic283⋊C4—22no—
58Dic283⋊C4—21no—
59Dic283⋊C4D412yes—
60C22⋊Dic283—22no—
61C22⋊Dic283—22no—
62C4×Dic283—22no—
63C4×Dic283—22no—
64C4×Dic283—21no—
65C4×Dic283C2312yes—
66C2×Q8×C283C2312yes—
67C2×D4×C283C2311yescharacteristic
68C22×C4×C283—21no—
69SD16×C283—42no—
70C2×C8×C283C2312yes—
71C4⋊C4×C283—21no—
72C4⋊C4×C283—21no—
73C4⋊C4×C283C2311yescharacteristic
74C22⋊C4×C283—21no—
75C42×C283C2311yescharacteristic
76Dic566—22no—
77Dic566—21no—
78Dic566—22no—
79Dic566—22no—
80Dic566—21no—
81C2×Dic283—21no—
82C2×Dic283—22no—
83C2×Dic283—21no—
84C2×Dic283C2×D412yes—
85C2×Dic283C2×D412yes—
86C283⋊C8—21no—
87C283⋊C8#4112yes—
88C23×C283—21no—
89Q8×C283—22no—
90Q8×C283—22no—
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
104C4×C283—21no—
105C4×C283—42no—
106C4×C283—41no—
107C4×C283#13712yes—
108C4×C283C2×#4111yescharacteristic
109C4×C283H(5,𝔽2)11yescharacteristic
110Dic283—22no—
111Dic283—22no—
112Dic283—42no—
113Dic283—41no—
114Dic283—41no—
115C2×C283—81no—
116C2×C283#55011yescharacteristic
117C2×C283C2×#13711yescharacteristic
118C2×C283#57811yescharacteristic
119C283#339811yescharacteristic, complemented, Sylow
120#3398—2831nomaximal, Sylow
121#557—2831no—
122#556—2831no—
123#497—2832no—
124#494—2831no—
125#464—2832no—
126#462—2831no—
127#462—2832no—
128#461D28311yescharacteristic
129#446—2831no—
130#441—2832no—
131C4×SD16—2831no—
132C2×Q16—2832no—
133C2×Q16—2832no—
134C2×Q16—2832no—
135C2×SD16—2831no—
136C2×SD16C2×D28312yes—
137C4⋊Q8—2832no—
138C4⋊Q8—2831no—
139C4⋊Q8C2×D28311yescharacteristic
140#126—5662no—
141#125—5662no—
142#125—5661no—
143#124—2832no—
144C22⋊Q8—5661no—
145C4×Q8—2831no—
146C4×Q8—2832no—
147C4×Q8—2832no—
148C4×Q8—2831no—
149C4×Q8—5661no—
150C4×D4C2×D28311yescharacteristic
151#117—5661no—
152#106—2831no—
153C4⋊C8—2832no—
154C4⋊C8C2×D28311yescharacteristic
155#103—2832no—
156#103—2831no—
157#103C2×D28312yes—
158#102—2831no—
159#97—2832no—
160C4×C8—2831no—
161C2×Q8—2831no—
162C2×Q8—2832no—
163C2×Q8—2831no—
164C2×Q8C22×D28312yes—
165C2×D4C22×D28311yescharacteristic
166C22×C4—21no—
167Q16—5664no—
168Q16—11322no—
169Q16—11322no—
170SD16—42no—
171SD16—5662no—
172C2×C8—2831no—
173C2×C8—2831no—
174C2×C8C22×D28312yes—
175C4⋊C4—21no—
176C4⋊C4—21no—
177C4⋊C4—2832no—
178C4⋊C4—2831no—
179C4⋊C4—2831no—
180C4⋊C4—5662no—
181C4⋊C4—5662no—
182C4⋊C4—5662no—
183C4⋊C4—5662no—
184C4⋊C4—5661no—
185C4⋊C4—5661no—
186C4⋊C4—5661no—
187C4⋊C4C22×D28311yescharacteristic
188C22⋊C4—21no—
189C22⋊C4—5662no—
190C22⋊C4—5662no—
191C42—2832no—
192C42—5662no—
193C42—5662no—
194C42—5661no—
195C42C22×D28311yescharacteristic
196C23—21no—
197Q8—22no—
198Q8—22no—
199Q8—5662no—
200Q8—5661no—
201Q8—5662no—
202Q8—5661no—
203Q8—5662no—
204D4—21no—
205D4—21no—
206C2×C4—21no—
207C2×C4—22no—
208C2×C4—42no—
209C2×C4—2832no—
210C2×C4—2832no—
211C2×C4—5661no—
212C2×C4—5662no—
213C2×C4—5661no—
214C2×C4D4×D28311yescharacteristic
215C2×C4D4×D28311yescharacteristic
216C2×C4C23×D28311yescharacteristic
217C8—22no—
218C8—2832no—
219C8—5661no—
220C22—41no—
221C22—41no—
222C22—41no—
223C22C2×D4×D28311yescharacteristic
224C4—21no—
225C4—41no—
226C4—42no—
227C4—5662no—
228C4—5662no—
229C4—11321no—
230C4—11322no—
231C4—11321no—
232C4#2258363912yes—
233C4#41×D28311yescharacteristic
234C4#2258365511yescharacteristic
235C2—81no—
236C2#3182713311yescharacteristic
237C2C2×#2258363911yescharacteristic
238C2#3182728111yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#461×C283C2
socleC22×C283C22×D4
prime radicalC2×D4×C283C23
hypercenter#461D283
hypocenterC283#3398
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. #31827190C2semidirect
4. #31826844C2semidirect
6. #31826676C2semidirect
7. #31826674C2semidirect
8. #31826592C2semidirect
9. #31826569C2semidirect
119. C283#3398semidirect

Maximal subgroups

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

subgroupindex
#318271902
#318271852
#318268562
#318268442
#318266852
#318266762
#318266742
#318265922
#318265692
C4×#179853802
#461×C2832
#3398283