Finite Group Databasebeta

← #49134312

Subgroups — #49134312

Order 36224.

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

normal subgroups only

This group has 362 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#31827200C211yesmaximal, characteristic
2#31827193C211yesmaximal, characteristic, complemented
3#31826858C212yesmaximal, complemented
4#31826838C211yesmaximal, characteristic
5#31826690C212yesmaximal, complemented
6#31826675C211yesmaximal, characteristic, complemented
7#31826669C212yesmaximal, complemented
8#31826665C211yesmaximal, characteristic
9#31826595C211yesmaximal, characteristic, complemented
10#31826564C212yesmaximal, complemented
11C4×Q16×C283C211yesmaximal, characteristic, complemented
12C2×#17985382C2212yes—
13C2×#17985381C2212yes—
14C2×#17985381C2212yes—
15C2×#17985379C2212yes—
16#22583610C2211yescharacteristic
17#22583608C2212yes—
18#22583607C2211yescharacteristic
19#22583602—21no—
20#22583600—22no—
21#22583599C2212yes—
22#22583598—21no—
23#22583595—22no—
24C4×Dic566—21no—
25C4×Dic566C2211yescharacteristic
26#22583575C2212yes—
27C4×D1132—21no—
28#22583572C2212yes—
29C4⋊(C283⋊C8)C2211yescharacteristic
30Dic283⋊C8C2212yes—
31#22583533C2212yes—
32#22583530C2212yes—
33#22583520C2212yes—
34C2×Q16×C283C2211yescharacteristic
35C4×Q8×C283C2211yescharacteristic
36C4×Q8×C283C2211yescharacteristic
37#107×C283C2211yescharacteristic
38#103×C283C2211yescharacteristic
39#103×C283C2211yescharacteristic
40C4×C8×C283C2211yescharacteristic
41C2×Dic566D411yescharacteristic
42C2×Dic566C2312yes—
43C2×D1132—21no—
44C2×D1132—21no—
45C2×D1132C2312yes—
46C2×C4×D283—22no—
47#17985382—42no—
48#17985381—24no—
49#17985381—42no—
50#17985379—42no—
51C2×C283⋊C8C2312yes—
52C4⋊Dic283—21no—
53C4⋊Dic283—21no—
54C4⋊Dic283D411yescharacteristic
55Dic283⋊C4—22no—
56Dic283⋊C4—22no—
57Dic283⋊C4—22no—
58Dic283⋊C4D412yes—
59(C2×D283)⋊C4—22no—
60(C2×D283)⋊C4—22no—
61(C2×D283)⋊C4—22no—
62C4×Dic283—22no—
63C4×Dic283C2312yes—
64C2×Q8×C283C2311yescharacteristic
65C2×Q8×C283C2311yescharacteristic
66Q16×C283—22no—
67C2×C8×C283C2311yescharacteristic
68C2×C8×C283C2311yescharacteristic
69C4⋊C4×C283—21no—
70C4⋊C4×C283—21no—
71C4⋊C4×C283C2311yescharacteristic
72C4⋊C4×C283C2311yescharacteristic
73C42×C283—21no—
74C42×C283—21no—
75C42×C283C2311yescharacteristic
76C22×D283—22no—
77Dic566—22no—
78Dic566—22no—
79Dic566—22no—
80D1132—22no—
81D1132—22no—
82D1132—42no—
83D1132—81no—
84C2×Dic283—22no—
85C2×Dic283C2×D412yes—
86C2×Dic283C2×D412yes—
87C4×D283—82no—
88C283⋊C8—22no—
89Q8×C283—21no—
90Q8×C283—21no—
91Q8×C283—21no—
92Q8×C283—21no—
93C2×C4×C283—21no—
94C2×C4×C283—21no—
95C2×C4×C283—21no—
96C2×C4×C283—21no—
97C2×C4×C283C2×D411yescharacteristic
98C2×C4×C283C2×D411yescharacteristic
99C2×C4×C283C2411yescharacteristic
100C8×C283—21no—
101C8×C283#4112yes—
102C22×C283C22×D411yescharacteristic
103C2×D283—42no—
104C2×D283—42no—
105C2×D283—42no—
106C4×C283—21no—
107C4×C283—41no—
108C4×C283—41no—
109C4×C283—41no—
110C4×C283—41no—
111C4×C283#13712yes—
112C4×C283C2×#4111yescharacteristic
113C4×C283H(5,𝔽2)11yescharacteristic
114Dic283—22no—
115Dic283—22no—
116Dic283—42no—
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#446—2831no—
132#440—2832no—
133C4×Q16D28311yescharacteristic, complemented
134C2×Q16—2832no—
135C2×Q16C2×D28311yescharacteristic
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—5661no—
150C4×Q8C2×D28311yescharacteristic
151C4×Q8C2×D28311yescharacteristic
152C4×D4—2832no—
153C4×D4—5661no—
154#107C2×D28311yescharacteristic
155C4⋊C8—2832no—
156C4⋊C8—2831no—
157#103—2832no—
158#103C2×D28311yescharacteristic
159#103C2×D28311yescharacteristic
160#102—2832no—
161#97—2832no—
162C4×C8C2×D28311yescharacteristic
163C2×Q8—2831no—
164C2×Q8—2832no—
165C2×Q8C22×D28311yescharacteristic
166C2×Q8C22×D28311yescharacteristic
167C2×D4—2832no—
168C2×D4—5661no—
169C2×D4—5661no—
170C22×C4—5662no—
171Q16—22no—
172Q16—11322no—
173SD16—5664no—
174SD16—11322no—
175SD16—11322no—
176C2×C8—2832no—
177C2×C8C22×D28311yescharacteristic
178C2×C8C22×D28311yescharacteristic
179C4⋊C4—21no—
180C4⋊C4—21no—
181C4⋊C4—2832no—
182C4⋊C4—2831no—
183C4⋊C4—5662no—
184C4⋊C4—5662no—
185C4⋊C4—5662no—
186C4⋊C4—5661no—
187C4⋊C4—5661no—
188C4⋊C4C22×D28311yescharacteristic
189C4⋊C4C22×D28311yescharacteristic
190C22⋊C4—5662no—
191C22⋊C4—5662no—
192C22⋊C4—5662no—
193C42—21no—
194C42—21no—
195C42—2832no—
196C42—5662no—
197C42C22×D28311yescharacteristic
198C23—5662no—
199Q8—21no—
200Q8—21no—
201Q8—21no—
202Q8—21no—
203Q8—5662no—
204Q8—5662no—
205Q8—5662no—
206D4—5662no—
207D4—5662no—
208D4—11322no—
209D4—22641no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—2832no—
215C2×C4—2832no—
216C2×C4—5662no—
217C2×C4—22642no—
218C2×C4D4×D28311yescharacteristic
219C2×C4D4×D28311yescharacteristic
220C2×C4C23×D28311yescharacteristic
221C8—21no—
222C8—5662no—
223C8#1798539212yes—
224C22—11322no—
225C22—11322no—
226C22—11322no—
227C22C2×D4×D28311yescharacteristic
228C4—21no—
229C4—41no—
230C4—41no—
231C4—41no—
232C4—41no—
233C4—5662no—
234C4—5662no—
235C4—11322no—
236C4#2258364212yes—
237C4C2×#1798539211yescharacteristic
238C4#2258365611yescharacteristic
239C2—22642no—
240C2#3182713611yescharacteristic
241C2C2×#2258364211yescharacteristic
242C2#3182727211yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
FittingC4×Q16×C283C2
socleC22×C283C22×D4
prime radical#22583607C22
hypercenterC4×Q16D283
hypocenterC283#3400
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q16

Complements

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

NH ≅ G/Ntype
2. #31827193C2semidirect
3. #31826858C2semidirect
5. #31826690C2semidirect
6. #31826675C2semidirect
7. #31826669C2semidirect
9. #31826595C2semidirect
10. #31826564C2semidirect
11. C4×Q16×C283C2semidirect
121. C283#3400semidirect
133. C4×Q16D283semidirect

Maximal subgroups

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

subgroupindex
#318272002
#318271932
#318268582
#318268382
#318266902
#318266752
#318266692
#318266652
#318265952
#318265642
C4×Q16×C2832
#3400283