Finite Group Databasebeta

← #49134297

Subgroups — #49134297

Order 36224.

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

normal subgroups only

This group has 350 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#31827190C211yesmaximal, characteristic, complemented
2#31827189C211yesmaximal, characteristic
3#31826858C212yesmaximal
4#31826689C212yesmaximal
5#31826673C212yesmaximal, complemented
6#31826672C211yesmaximal, characteristic, complemented
7#31826667C211yesmaximal, characteristic
8#31826595C211yesmaximal, characteristic, complemented
9#31826572C212yesmaximal, complemented
10C4×#17985381C211yesmaximal, characteristic
11#494×C283C211yesmaximal, characteristic, complemented
12C2×#17985382C2212yes—
13C2×#17985381C2211yescharacteristic
14C2×#17985379C2212yes—
15#22583608C2212yes—
16#22583605—22no—
17#22583601—21no—
18#22583600—22no—
19#22583599C2212yes—
20#22583590—21no—
21Q8×Dic283C2212yes—
22Q8×Dic283C2212yes—
23C4×Dic566C2211yescharacteristic
24C4×Dic566C2211yescharacteristic
25#22583575—21no—
26C4×D1132C2211yescharacteristic
27#22583568—21no—
28#22583542C2211yescharacteristic
29C4⋊(C283⋊C8)C2211yescharacteristic
30Dic283⋊C8C2212yes—
31#22583535C2211yescharacteristic
32#22583534C2212yes—
33#22583534C2212yes—
34#22583532C2211yescharacteristic
35#22583520C2212yes—
36C2×Q16×C283C2212yes—
37C2×Q16×C283C2212yes—
38C4⋊Q8×C283C2211yescharacteristic
39C4⋊Q8×C283C2211yescharacteristic
40C4×C8×C283C2211yescharacteristic
41C2×Dic566D411yescharacteristic
42C2×Dic566C2311yescharacteristic
43C2×D1132C2311yescharacteristic
44C2×C4×D283—21no—
45#17985382—42no—
46#17985381—22no—
47#17985379—42no—
48C2×C283⋊C8C2312yes—
49C4⋊Dic283—22no—
50C4⋊Dic283—22no—
51C4⋊Dic283D411yescharacteristic
52C4⋊Dic283C2311yescharacteristic
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—21no—
61C4×Dic283—22no—
62C4×Dic283—22no—
63C4×Dic283—21no—
64C4×Dic283C2312yes—
65C2×Q8×C283C2312yes—
66C2×Q8×C283C2312yes—
67Q16×C283—24no—
68Q16×C283—42no—
69C2×C8×C283C2311yescharacteristic
70C2×C8×C283C2311yescharacteristic
71C4⋊C4×C283—21no—
72C4⋊C4×C283—21no—
73C4⋊C4×C283—21no—
74C4⋊C4×C283—21no—
75C42×C283C2311yescharacteristic
76C22×D283—21no—
77Dic566—22no—
78Dic566—21no—
79Dic566—21no—
80D1132—21no—
81D1132—21no—
82C2×Dic283—21no—
83C2×Dic283—21no—
84C2×Dic283—21no—
85C2×Dic283C2×D412yes—
86C2×Dic283C2×D412yes—
87C4×D283—42no—
88C283⋊C8—22no—
89Q8×C283—22no—
90Q8×C283—22no—
91Q8×C283—22no—
92Q8×C283—22no—
93C2×C4×C283—22no—
94C2×C4×C283—22no—
95C2×C4×C283C2×D411yescharacteristic
96C2×C4×C283C2×D411yescharacteristic
97C2×C4×C283C2411yescharacteristic
98C8×C283—21no—
99C8×C283#4112yes—
100C22×C283C22×D411yescharacteristic
101C2×D283—41no—
102C2×D283—41no—
103C2×D283—41no—
104C4×C283—21no—
105C4×C283—42no—
106C4×C283—42no—
107C4×C283#13712yes—
108C4×C283C2×#4111yescharacteristic
109C4×C283H(5,𝔽2)11yescharacteristic
110Dic283—22no—
111Dic283—22no—
112Dic283—41no—
113Dic283—41no—
114Dic283—41no—
115C2×C283#55011yescharacteristic
116C2×C283C2×#13711yescharacteristic
117C2×C283#57811yescharacteristic
118D283—81no—
119C283#339811yescharacteristic, complemented, Sylow
120#3398—2831nomaximal, Sylow
121#557—2831no—
122#556—2831no—
123#497—2832no—
124#494D28311yescharacteristic, complemented
125#464—2832no—
126#462—2832no—
127#462—2831no—
128#461—2831no—
129#446—2831no—
130#441—2832no—
131C4×SD16—2831no—
132C2×Q16—2832no—
133C2×Q16C2×D28312yes—
134C2×Q16C2×D28312yes—
135C2×SD16—2832no—
136C2×SD16—2831no—
137C4⋊Q8—2832no—
138C4⋊Q8C2×D28311yescharacteristic
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×D4—2831no—
151#117—5661no—
152#106—2831no—
153C4⋊C8—2832no—
154C4⋊C8—2831no—
155#103—2832no—
156#103—2832no—
157#103—2831no—
158#102—2831no—
159#97—2832no—
160C4×C8C2×D28311yescharacteristic
161C2×Q8—2831no—
162C2×Q8—2831no—
163C2×Q8C22×D28312yes—
164C2×Q8C22×D28312yes—
165C2×D4—2831no—
166C22×C4—5661no—
167Q16—24no—
168Q16—42no—
169Q16—11322no—
170SD16—5662no—
171SD16—11322no—
172C2×C8—2832no—
173C2×C8C22×D28311yescharacteristic
174C2×C8C22×D28311yescharacteristic
175C4⋊C4—21no—
176C4⋊C4—21no—
177C4⋊C4—21no—
178C4⋊C4—21no—
179C4⋊C4—2832no—
180C4⋊C4—2831no—
181C4⋊C4—2831no—
182C4⋊C4—2831no—
183C4⋊C4—5662no—
184C4⋊C4—5662no—
185C4⋊C4—5662no—
186C4⋊C4—5662no—
187C4⋊C4—5661no—
188C22⋊C4—5662no—
189C22⋊C4—5662no—
190C22⋊C4—5661no—
191C42—2832no—
192C42—5662no—
193C42—5662no—
194C42—5661no—
195C42C22×D28311yescharacteristic
196C23—5661no—
197Q8—22no—
198Q8—22no—
199Q8—22no—
200Q8—22no—
201Q8—5662no—
202Q8—5661no—
203Q8—5661no—
204D4—5661no—
205D4—5661no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—2832no—
209C2×C4—2832no—
210C2×C4—5661no—
211C2×C4—5661no—
212C2×C4—5661no—
213C2×C4—11322no—
214C2×C4D4×D28311yescharacteristic
215C2×C4D4×D28311yescharacteristic
216C2×C4C23×D28311yescharacteristic
217C8—21no—
218C8—5662no—
219C8#1798539112yes—
220C22—11321no—
221C22—11321no—
222C22—11321no—
223C22C2×D4×D28311yescharacteristic
224C4—21no—
225C4—42no—
226C4—42no—
227C4—5662no—
228C4—5662no—
229C4—11321no—
230C4—11321no—
231C4—11321no—
232C4#2258364212yes—
233C4C2×#1798539111yescharacteristic
234C4#2258365511yescharacteristic
235C2—22641no—
236C2#3182713511yescharacteristic
237C2C2×#2258364211yescharacteristic
238C2#3182727811yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#494×C283C2
socleC22×C283C22×D4
prime radicalC2×D1132C23
hypercenter#494D283
hypocenterC283#3398
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #494

Complements

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

NH ≅ G/Ntype
1. #31827190C2semidirect
5. #31826673C2semidirect
6. #31826672C2semidirect
8. #31826595C2semidirect
9. #31826572C2semidirect
11. #494×C283C2semidirect
119. C283#3398semidirect
124. #494D283semidirect

Maximal subgroups

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

subgroupindex
#318271902
#318271892
#318268582
#318266892
#318266732
#318266722
#318266672
#318265952
#318265722
C4×#179853812
#494×C2832
#3398283