Finite Group Databasebeta

← #49133129

Subgroups — #49133129

Order 36224.

420 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 123 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#31827130C211yesmaximal, characteristic, complemented
2#31827120C211yesmaximal, characteristic
3#31826815C211yesmaximal, characteristic, complemented
4#31826794C212yesmaximal, complemented
5#31826751C211yesmaximal, characteristic, complemented
6#31826691C212yesmaximal, complemented
7#31826602C212yesmaximal, complemented
8C4×#17985380C211yesmaximal, characteristic, complemented
9#31826530C211yesmaximal, characteristic, complemented
10#103×D283C212yesmaximal, complemented
11#461×C283C211yesmaximal, characteristic, complemented
12C2×#17985392—21no—
13C2×Q8×D283C2212yes—
14C2×#17985380C2211yescharacteristic
15C2×C8×D283C2212yes—
16#22583610C2211yescharacteristic
17#22583609—21no—
18#22583592—22no—
19#22583589—21no—
20#22583588—22no—
21#22583586C2212yes—
22#22583581C2212yes—
23C4×Dic566C2211yescharacteristic
24C4×D1132C2211yescharacteristic
25#22583572—21no—
26C4⋊C4×D283C2212yes—
27#22583542C2212yes—
28#22583541C2211yescharacteristic
29#22583535C2212yes—
30#22583534C2212yes—
31#22583534C2212yes—
32#22583533C2211yescharacteristic
33#22583531C2211yescharacteristic
34(C2×D283)⋊C8C2212yes—
35C4×C283⋊C8C2211yescharacteristic
36C2×SD16×C283C2212yes—
37C4⋊Q8×C283C2211yescharacteristic
38C4×D4×C283C2211yescharacteristic
39C4⋊C8×C283C2211yescharacteristic
40#103×C283C2212yes—
41#17985392—44no—
42C2×Dic566—22no—
43C2×Dic566—21no—
44C2×Dic566C2311yescharacteristic
45Q8×D283—24no—
46Q8×D283—42no—
47C2×D1132D411yescharacteristic
48C2×C22⋊D283—22no—
49C2×C4×D283—22no—
50C2×C4×D283—22no—
51C2×C4×D283C2312yes—
52#17985380—22no—
53C2×C283⋊C8C2311yescharacteristic
54C2×C283⋊C8C2311yescharacteristic
55C8×D283—42no—
56C4⋊Dic283—21no—
57C4⋊Dic283D411yescharacteristic
58C4⋊Dic283C2312yes—
59C4⋊Dic283C2311yescharacteristic
60Dic283⋊C4—22no—
61Dic283⋊C4—22no—
62Dic283⋊C4—21no—
63C22⋊Dic283—22no—
64(C2×D283)⋊C4—22no—
65(C2×D283)⋊C4D412yes—
66C4×Dic283—21no—
67C2×Q8×C283C2312yes—
68C2×D4×C283C2311yescharacteristic
69C22×C4×C283—21no—
70SD16×C283—42no—
71C2×C8×C283C2312yes—
72C4⋊C4×C283—21no—
73C4⋊C4×C283—21no—
74C4⋊C4×C283C2311yescharacteristic
75C22⋊C4×C283—21no—
76C42×C283C2311yescharacteristic
77C22×D283C2×D412yes—
78Dic566—21no—
79Dic566—44no—
80Dic566—42no—
81Dic566#4112yescomplemented
82D1132SD1614yescomplemented
83C22⋊D283—44no—
84C2×Dic283—21no—
85C2×Dic283—21no—
86C2×Dic283—22no—
87C2×Dic283C2×D412yes—
88C4×D283—22no—
89C4×D283—22no—
90C4×D283—44no—
91C4×D283—44no—
92C283⋊C8—21no—
93C283⋊C8—21no—
94C23×C283—21no—
95Q8×C283—22no—
96Q8×C283—22no—
97D4×C283—21no—
98D4×C283—21no—
99C2×C4×C283—21no—
100C2×C4×C283—22no—
101C2×C4×C283—42no—
102C2×C4×C283C2×D411yescharacteristic
103C2×C4×C283C2×D411yescharacteristic
104C2×C4×C283C2411yescharacteristic
105C8×C283—22no—
106C22×C283—41no—
107C22×C283—41no—
108C22×C283—41no—
109C22×C283C22×D411yescharacteristic
110C2×D283—22no—
111C2×D283—22no—
112C2×D283C2×SD1614yes—
113C4×C283—21no—
114C4×C283—42no—
115C4×C283—41no—
116C4×C283C2×SD1612yes—
117C4×C283C2×#4111yescharacteristic
118C4×C283H(5,𝔽2)11yescharacteristic
119Dic283—22no—
120Dic283—22no—
121Dic283—42no—
122Dic283—41no—
123C2×C283—81no—
124C2×C283#54611yescharacteristic
125C2×C283C22×SD1611yescharacteristic
126C2×C283#57811yescharacteristic
127D283—24no—
128C283#329811yescharacteristic, complemented, Sylow
129#3298—2831nomaximal, Sylow
130D4×Q8—2831no—
131#547—2831no—
132#487—2831no—
133#483—2832no—
134#475—2831no—
135#465—2832no—
136#461D28311yescharacteristic, complemented
137#448—2832no—
138C4×SD16—2831no—
139C8×D4—2831no—
140C2×#103—2832no—
141C2×#41—5661no—
142C22×Q8—2832no—
143C2×SD16—2831no—
144C2×SD16C2×D28312yes—
145C22×C8—2832no—
146C4⋊Q8—2831no—
147C4⋊Q8—5661no—
148C4⋊Q8C2×D28311yescharacteristic
149#123—5662no—
150C22⋊Q8—2832no—
151C22⋊Q8—5662no—
152C22⋊Q8—5661no—
153#121—2832no—
154C4×Q8—2831no—
155C4×D4—2831no—
156C4×D4—5661no—
157C4×D4C2×D28311yescharacteristic
158C2×C4⋊C4—2832no—
159#106—2832no—
160#106—2831no—
161C4⋊C8C2×D28311yescharacteristic
162#103—2832no—
163#103—2832no—
164#103—2832no—
165#103—2831no—
166#103C2×D28312yes—
167#102—2831no—
168C22⋊C8—2832no—
169C4×C8—2831no—
170#41—11324no—
171C2×Q8—2831no—
172C2×Q8—5662no—
173C2×Q8—5661no—
174C2×Q8—5664no—
175C2×Q8—11322no—
176C2×Q8C22×D28312yes—
177C2×D4—2831no—
178C2×D4—5662no—
179C2×D4C22×D28311yescharacteristic
180C22×C4—21no—
181C22×C4—2832no—
182C22×C4—5662no—
183C22×C4—5662no—
184SD16—42no—
185SD16—5662no—
186C2×C8—2831no—
187C2×C8—2831no—
188C2×C8—11322no—
189C2×C8C22×D28312yes—
190C4⋊C4—21no—
191C4⋊C4—21no—
192C4⋊C4—2831no—
193C4⋊C4—2831no—
194C4⋊C4—2832no—
195C4⋊C4—5662no—
196C4⋊C4—5662no—
197C4⋊C4—5661no—
198C4⋊C4—5661no—
199C4⋊C4C22×D28311yescharacteristic
200C22⋊C4—21no—
201C22⋊C4—2832no—
202C22⋊C4—5662no—
203C22⋊C4—5662no—
204C42—5661no—
205C42C22×D28311yescharacteristic
206C23—21no—
207C23—2832no—
208Q8—22no—
209Q8—22no—
210Q8—2832no—
211Q8—5661no—
212Q8—11324no—
213Q8—11322no—
214D4—21no—
215D4—21no—
216D4—2834no—
217D4—11324no—
218C2×C4—21no—
219C2×C4—22no—
220C2×C4—42no—
221C2×C4—2832no—
222C2×C4—5661no—
223C2×C4—5662no—
224C2×C4—5662no—
225C2×C4—5661no—
226C2×C4—5662no—
227C2×C4—11324no—
228C2×C4—11324no—
229C2×C4D4×D28311yescharacteristic
230C2×C4D4×D28311yescharacteristic
231C2×C4C23×D28311yescharacteristic
232C8—22no—
233C8—5661no—
234C8—5661no—
235C22—41no—
236C22—41no—
237C22—41no—
238C22—2834no—
239C22—5662no—
240C22—5662no—
241C22C2×D4×D28311yescharacteristic
242C4—21no—
243C4—41no—
244C4—42no—
245C4—5662no—
246C4—5662no—
247C4—11322no—
248C4—11321no—
249C4SD16×D28312yes—
250C4#41×D28311yescharacteristic
251C4#2258365511yescharacteristic
252C2—81no—
253C2—5664no—
254C2#3182711211yescharacteristic
255C2C2×SD16×D28311yescharacteristic
256C2#3182728111yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#461×C283C2
socleC22×C283C22×D4
prime radical#31827120C2
hypercenter#461D283
hypocenterC283#3298
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. #31827130C2semidirect
3. #31826815C2semidirect
4. #31826794C2semidirect
5. #31826751C2semidirect
6. #31826691C2semidirect
7. #31826602C2semidirect
8. C4×#17985380C2semidirect
9. #31826530C2semidirect
10. #103×D283C2semidirect
11. #461×C283C2semidirect
81. Dic566#41semidirect
82. D1132SD16semidirect
128. C283#3298semidirect
136. #461D283semidirect

Maximal subgroups

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

subgroupindex
#318271302
#318271202
#318268152
#318267942
#318267512
#318266912
#318266022
C4×#179853802
#318265302
#103×D2832
#461×C2832
#3298283