Finite Group Databasebeta

← #49134316

Subgroups — #49134316

Order 36224.

362 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 125 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#31827200C211yesmaximal, characteristic
2#31827194C211yesmaximal, characteristic, complemented
3#31826859C212yesmaximal, complemented
4#31826838C211yesmaximal, characteristic
5#31826688C212yesmaximal, complemented
6#31826676C211yesmaximal, characteristic, complemented
7#31826671C212yesmaximal, complemented
8#31826666C211yesmaximal, characteristic
9#31826567C212yesmaximal, complemented
10C4×Dic1132C211yesmaximal, characteristic, complemented
11#446×C283C211yesmaximal, characteristic, complemented
12C2×Dic1132C2211yescharacteristic
13C2×Dic1132C2212yes—
14C2×#17985381C2212yes—
15C2×#17985381C2212yes—
16C2×#17985381C2212yes—
17#22583610C2211yescharacteristic
18#22583610C2212yes—
19#22583607C2211yescharacteristic
20#22583601—21no—
21#22583601—22no—
22#22583599—21no—
23#22583598C2212yes—
24#22583595—22no—
25Q8×Dic283—21no—
26C4×Dic566C2212yes—
27C4×Dic566C2211yescharacteristic
28C4×Dic566C2211yescharacteristic
29C4×D1132C2212yes—
30#22583572—21no—
31#22583544C2211yescharacteristic
32#22583535C2211yescharacteristic
33#22583535C2211yescharacteristic
34#22583535C2212yes—
35#22583532C2212yes—
36C4×Q8×C283C2211yescharacteristic
37C4⋊C8×C283C2212yes—
38C4⋊C8×C283C2211yescharacteristic
39#97×C283C2212yes—
40C4×C8×C283C2211yescharacteristic
41C2×Dic566C2311yescharacteristic
42C2×Dic566C2312yes—
43C2×Dic566C2311yescharacteristic
44C2×D1132—21no—
45C2×D1132—21no—
46C2×D1132C2312yes—
47C2×C4×D283—22no—
48Dic1132—22no—
49Dic1132—42no—
50#17985381—24no—
51#17985381—42no—
52#17985381—42no—
53C4⋊Dic283—22no—
54C4⋊Dic283—21no—
55C4⋊Dic283—22no—
56C4⋊Dic283—21no—
57C4⋊Dic283C2311yescharacteristic
58C4⋊Dic283C2311yescharacteristic
59Dic283⋊C4—21no—
60Dic283⋊C4—22no—
61Dic283⋊C4—21no—
62(C2×D283)⋊C4—22no—
63(C2×D283)⋊C4—22no—
64(C2×D283)⋊C4—22no—
65C4×Dic283—21no—
66C4×Dic283—22no—
67C4×Dic283—21no—
68C2×Q8×C283D411yescharacteristic
69C2×C8×C283C2311yescharacteristic
70C2×C8×C283C2312yes—
71C2×C8×C283C2311yescharacteristic
72C4⋊C4×C283D411yescharacteristic
73C4⋊C4×C283D412yes—
74C42×C283C2312yes—
75C42×C283C2311yescharacteristic
76C22×D283—22no—
77Dic566—22no—
78Dic566—21no—
79Dic566—21no—
80Dic566—21no—
81Dic566—22no—
82Dic566—21no—
83D1132—22no—
84D1132—22no—
85D1132—42no—
86D1132—81no—
87C2×Dic283—21no—
88C2×Dic283—21no—
89C2×Dic283—21no—
90C2×Dic283—22no—
91C2×Dic283—21no—
92C4×D283—82no—
93Q8×C283—22no—
94C2×C4×C283C2×D412yes—
95C2×C4×C283C2×D411yescharacteristic
96C2×C4×C283C2×D412yes—
97C2×C4×C283C2×D411yescharacteristic
98C2×C4×C283C2411yescharacteristic
99C8×C283—21no—
100C8×C283—22no—
101C8×C283#4112yes—
102C22×C283C22×D411yescharacteristic
103C2×D283—42no—
104C2×D283—42no—
105C2×D283—42no—
106C4×C283—22no—
107C4×C283—22no—
108C4×C283—21no—
109C4×C283#13712yes—
110C4×C283C2×#4111yescharacteristic
111C4×C283H(5,𝔽2)11yescharacteristic
112Dic283—41no—
113Dic283—42no—
114Dic283—41no—
115Dic283—41no—
116Dic283—41no—
117C2×C283#55011yescharacteristic
118C2×C283C2×#13711yescharacteristic
119C2×C283#57711yescharacteristic
120D283—82no—
121C283#340011yescharacteristic, complemented, Sylow
122#3400—2831nomaximal, Sylow
123#559—2831no—
124#557—2831no—
125#497—2832no—
126#492—2831no—
127#464—2832no—
128#462—2831no—
129#461—2832no—
130#460—2831no—
131#446D28311yescharacteristic, complemented
132#440—2832no—
133C4×Q16—2831no—
134C2×Q16—2831no—
135C2×Q16—2832no—
136C2×SD16—2832no—
137C2×SD16—2832no—
138C2×SD16—2832no—
139C4⋊Q8—2832no—
140C4⋊Q8—2831no—
141#127—2831no—
142#125—5661no—
143#125—5662no—
144#124—2832no—
145#124—5661no—
146#123—5662no—
147C4×Q8—2831no—
148C4×Q8—2832no—
149C4×Q8—2831no—
150C4×Q8—5661no—
151C4×Q8C2×D28311yescharacteristic
152C4×D4—2832no—
153C4×D4—5661no—
154#107—2831no—
155C4⋊C8C2×D28311yescharacteristic
156C4⋊C8C2×D28312yes—
157#103—2831no—
158#103—2831no—
159#103—2832no—
160#102—2832no—
161#97C2×D28312yes—
162C4×C8C2×D28311yescharacteristic
163C2×Q8—2831no—
164C2×Q8—2832no—
165C2×Q8—2831no—
166C2×Q8D113211yescharacteristic
167C2×D4—2832no—
168C2×D4—5661no—
169C2×D4—5661no—
170C22×C4—5662no—
171Q16—5662no—
172Q16—11322no—
173SD16—5664no—
174SD16—11322no—
175SD16—11322no—
176C2×C8C22×D28311yescharacteristic
177C2×C8C22×D28312yes—
178C2×C8C22×D28311yescharacteristic
179C4⋊C4—2831no—
180C4⋊C4—2831no—
181C4⋊C4—5661no—
182C4⋊C4—5662no—
183C4⋊C4—5661no—
184C4⋊C4—5662no—
185C4⋊C4—5661no—
186C4⋊C4—5662no—
187C4⋊C4—5661no—
188C4⋊C4D113211yescharacteristic
189C4⋊C4D113212yes—
190C22⋊C4—5662no—
191C22⋊C4—5662no—
192C22⋊C4—5662no—
193C42—5661no—
194C42—5662no—
195C42—5661no—
196C42C22×D28311yescharacteristic
197C42C22×D28312yes—
198C23—5662no—
199Q8—22no—
200Q8—5662no—
201Q8—5661no—
202Q8—5661no—
203Q8—5661no—
204Q8—5662no—
205Q8—5661no—
206D4—5662no—
207D4—5662no—
208D4—11322no—
209D4—22641no—
210C2×C4—5661no—
211C2×C4—5661no—
212C2×C4—5661no—
213C2×C4—5662no—
214C2×C4—5661no—
215C2×C4—22642no—
216C2×C4C2×D113212yes—
217C2×C4C2×D113212yes—
218C2×C4C2×D113211yescharacteristic
219C2×C4C2×D113211yescharacteristic
220C2×C4C23×D28311yescharacteristic
221C8—21no—
222C8—22no—
223C8#1798539312yes—
224C22—11322no—
225C22—11322no—
226C22—11322no—
227C22C22×D113211yescharacteristic
228C4—22no—
229C4—22no—
230C4—21no—
231C4—11321no—
232C4—11321no—
233C4—11321no—
234C4—11322no—
235C4—11321no—
236C4#2258364312yes—
237C4C2×#1798539311yescharacteristic
238C4#2258365611yescharacteristic
239C2—22642no—
240C2#3182713711yescharacteristic
241C2C2×#2258364311yescharacteristic
242C2#3182727711yescharacteristic
subgroupG/H
centerC22C22×D1132
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#446×C283C2
socleC22×C283C22×D4
prime radical#22583607C22
hypercenter#446D283
hypocenterC283#3400
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #446

Complements

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

NH ≅ G/Ntype
2. #31827194C2semidirect
3. #31826859C2semidirect
5. #31826688C2semidirect
6. #31826676C2semidirect
7. #31826671C2semidirect
9. #31826567C2semidirect
10. C4×Dic1132C2semidirect
11. #446×C283C2semidirect
121. C283#3400semidirect
131. #446D283semidirect

Maximal subgroups

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

subgroupindex
#318272002
#318271942
#318268592
#318268382
#318266882
#318266762
#318266712
#318266662
#318265672
C4×Dic11322
#446×C2832
#3400283