Finite Group Databasebeta

← #49134318

Subgroups — #49134318

Order 36224.

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

normal subgroups only

This group has 362 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#31827200C211yesmaximal, characteristic
2#31827190C211yesmaximal, characteristic, complemented
3#31826858C212yesmaximal, complemented
4#31826839C211yesmaximal, characteristic
5#31826689C212yesmaximal, complemented
6#31826669C212yesmaximal, complemented
7#31826666C211yesmaximal, characteristic
8#31826592C211yesmaximal, characteristic, complemented
9#31826568C212yesmaximal, complemented
10C4×#17985382C211yesmaximal, characteristic, complemented
11#462×C283C211yesmaximal, characteristic, complemented
12C2×#17985382C2211yescharacteristic
13C2×#17985381C2212yes—
14C2×#17985379C2212yes—
15C2×#17985379C2212yes—
16#22583608C2212yes—
17#22583607C2211yescharacteristic
18#22583601—21no—
19#22583600—22no—
20#22583599C2212yes—
21#22583598—21no—
22#22583595—22no—
23Q8×Dic283C2212yes—
24C4×Dic566C2211yescharacteristic
25C4×Dic566C2211yescharacteristic
26#22583575—21no—
27C4×D1132—21no—
28#22583572C2212yes—
29#22583543C2211yescharacteristic
30Dic283⋊C8C2212yes—
31#22583534C2211yescharacteristic
32#22583533C2211yescharacteristic
33#22583532C2212yes—
34#22583520C2212yes—
35C4×C283⋊C8C2211yescharacteristic
36C2×Q16×C283C2212yes—
37C4⋊Q8×C283C2211yescharacteristic
38C4×Q8×C283C2211yescharacteristic
39C4⋊C8×C283C2211yescharacteristic
40#103×C283C2212yes—
41C2×Dic566D411yescharacteristic
42C2×Dic566C2311yescharacteristic
43C2×D1132—21no—
44C2×D1132—21no—
45C2×D1132C2312yes—
46C2×C4×D283—22no—
47#17985382—22no—
48#17985381—42no—
49#17985379—24no—
50#17985379—42no—
51C2×C283⋊C8C2311yescharacteristic
52C2×C283⋊C8C2311yescharacteristic
53C4⋊Dic283—22no—
54C4⋊Dic283D411yescharacteristic
55C4⋊Dic283C2311yescharacteristic
56Dic283⋊C4—22no—
57Dic283⋊C4—22no—
58Dic283⋊C4—21no—
59Dic283⋊C4D412yes—
60(C2×D283)⋊C4—22no—
61(C2×D283)⋊C4—22no—
62(C2×D283)⋊C4—22no—
63C4×Dic283—22no—
64C4×Dic283—21no—
65C4×Dic283C2312yes—
66C2×Q8×C283C2312yes—
67C2×Q8×C283C2311yescharacteristic
68Q16×C283—42no—
69C2×C8×C283C2312yes—
70C4⋊C4×C283—21no—
71C4⋊C4×C283—21no—
72C4⋊C4×C283—21no—
73C4⋊C4×C283C2311yescharacteristic
74C42×C283—21no—
75C42×C283C2311yescharacteristic
76C22×D283—22no—
77Dic566—22no—
78Dic566—21no—
79Dic566—21no—
80D1132—22no—
81D1132—22no—
82D1132—42no—
83D1132—81no—
84C2×Dic283—21no—
85C2×Dic283—21no—
86C2×Dic283C2×D412yes—
87C2×Dic283C2×D412yes—
88C4×D283—82no—
89C283⋊C8—21no—
90C283⋊C8#4112yes—
91Q8×C283—22no—
92Q8×C283—21no—
93Q8×C283—21no—
94Q8×C283—22no—
95C2×C4×C283—21no—
96C2×C4×C283—21no—
97C2×C4×C283—22no—
98C2×C4×C283C2×D411yescharacteristic
99C2×C4×C283C2×D411yescharacteristic
100C2×C4×C283C2411yescharacteristic
101C8×C283—22no—
102C22×C283C22×D411yescharacteristic
103C2×D283—42no—
104C2×D283—42no—
105C2×D283—42no—
106C4×C283—21no—
107C4×C283—41no—
108C4×C283—42no—
109C4×C283—41no—
110C4×C283#13712yes—
111C4×C283C2×#4111yescharacteristic
112C4×C283H(5,𝔽2)11yescharacteristic
113Dic283—22no—
114Dic283—22no—
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#462D28311yescharacteristic, complemented
129#461—2832no—
130#460—2831no—
131#446—2831no—
132#440—2832no—
133C4×Q16—2831no—
134C2×Q16—2831no—
135C2×Q16C2×D28312yes—
136C2×SD16—2832no—
137C2×SD16—2832no—
138C2×SD16—2832no—
139C4⋊Q8—2832no—
140C4⋊Q8C2×D28311yescharacteristic
141#127—2831no—
142#125—5662no—
143#125—5661no—
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⋊C8—2832no—
156C4⋊C8C2×D28311yescharacteristic
157#103—2831no—
158#103—2831no—
159#103C2×D28312yes—
160#102—2832no—
161#97—2832no—
162C4×C8—2831no—
163C2×Q8—2831no—
164C2×Q8—2831no—
165C2×Q8C22×D28311yescharacteristic
166C2×Q8C22×D28312yes—
167C2×D4—2832no—
168C2×D4—5661no—
169C2×D4—5661no—
170C22×C4—5662no—
171Q16—42no—
172Q16—5662no—
173SD16—5664no—
174SD16—11322no—
175SD16—11322no—
176C2×C8—2831no—
177C2×C8—2831no—
178C2×C8C22×D28312yes—
179C4⋊C4—21no—
180C4⋊C4—21no—
181C4⋊C4—21no—
182C4⋊C4—2832no—
183C4⋊C4—2831no—
184C4⋊C4—2831no—
185C4⋊C4—5662no—
186C4⋊C4—5662no—
187C4⋊C4—5662no—
188C4⋊C4—5661no—
189C4⋊C4C22×D28311yescharacteristic
190C22⋊C4—5662no—
191C22⋊C4—5662no—
192C22⋊C4—5662no—
193C42—21no—
194C42—2832no—
195C42—5662no—
196C42—5661no—
197C42C22×D28311yescharacteristic
198C23—5662no—
199Q8—22no—
200Q8—21no—
201Q8—22no—
202Q8—21no—
203Q8—5662no—
204Q8—5661no—
205Q8—5661no—
206D4—5662no—
207D4—5662no—
208D4—11322no—
209D4—22641no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—22no—
213C2×C4—2832no—
214C2×C4—2832no—
215C2×C4—5661no—
216C2×C4—5661no—
217C2×C4—22642no—
218C2×C4D4×D28311yescharacteristic
219C2×C4D4×D28311yescharacteristic
220C2×C4C23×D28311yescharacteristic
221C8—22no—
222C8—2832no—
223C8—5661no—
224C22—11322no—
225C22—11322no—
226C22—11322no—
227C22C2×D4×D28311yescharacteristic
228C4—21no—
229C4—41no—
230C4—41no—
231C4—42no—
232C4—5662no—
233C4—5662no—
234C4—11321no—
235C4—11321no—
236C4#2258364212yes—
237C4#41×D28311yescharacteristic
238C4#2258365511yescharacteristic
239C2—22642no—
240C2#3182713311yescharacteristic
241C2C2×#2258364211yescharacteristic
242C2#3182727411yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#462×C283C2
socleC22×C283C22×D4
prime radical#22583607C22
hypercenter#462D283
hypocenterC283#3400
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #462

Complements

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

NH ≅ G/Ntype
2. #31827190C2semidirect
3. #31826858C2semidirect
5. #31826689C2semidirect
6. #31826669C2semidirect
8. #31826592C2semidirect
9. #31826568C2semidirect
10. C4×#17985382C2semidirect
11. #462×C283C2semidirect
121. C283#3400semidirect
128. #462D283semidirect

Maximal subgroups

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

subgroupindex
#318272002
#318271902
#318268582
#318268392
#318266892
#318266692
#318266662
#318265922
#318265682
C4×#179853822
#462×C2832
#3400283