Finite Group Databasebeta

← #49131222

Subgroups — #49131222

Order 36224.

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

normal subgroups only

This group has 418 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#31827034C211yesmaximal, characteristic
2#31826945C211yesmaximal, characteristic, complemented
3#31826792C212yesmaximal, complemented
4#31826791C212yesmaximal, complemented
5#31826785C212yesmaximal, complemented
6#31826780C212yesmaximal, complemented
7#31826508C211yesmaximal, characteristic, complemented
8#31826469C211yesmaximal, characteristic, complemented
9C2×#22583532C211yesmaximal, characteristic, complemented
10#31826431C211yesmaximal, characteristic, complemented
11#427×C283C211yesmaximal, characteristic, complemented
12C2×#17985392C2211yescharacteristic
13C22×D1132C2211yescharacteristic
14C2×#17985376C2211yescharacteristic
15#22583607—21no—
16#22583598—21no—
17#22583585C2212yes—
18#22583585C2212yes—
19#22583580—22no—
20C4×Dic566—21no—
21C4×D1132—21no—
22(C22⋊D283)⋊C4—22no—
23#22583568C2212yescomplemented
24C2×C4⋊Dic283C2211yescharacteristic
25C4⋊C4×D283C2212yescomplemented
26#22583543C2212yescomplemented
27#22583541C2212yescomplemented
28#22583532C2212yes—
29#22583532C2212yes—
30#22583530C2212yes—
31#22583530C2212yes—
32(C2×D283)⋊C8C2212yescomplemented
33(C2×D283)⋊C8C2212yescomplemented
34C22×C8×C283C2211yescharacteristic
35#117×C283C2211yescharacteristic
36#117×C283C2211yescharacteristic
37#107×C283C2211yescharacteristic, complemented
38#107×C283C2211yescharacteristic, complemented
39#106×C283C2211yescharacteristic, complemented
40#106×C283C2211yescharacteristic, complemented
41C23×D283—21no—
42#17985392—22no—
43#17985392—22no—
44C2×Dic566D411yescharacteristic
45C2×D1132—22no—
46C2×D1132—22no—
47C2×D1132—21no—
48C2×D1132—22no—
49C2×D1132—22no—
50C2×D1132D411yescharacteristic
51C2×D1132C2312yes—
52C2×C22⋊D283D412yes—
53C22×Dic283—21no—
54C2×C4×D283—22no—
55C2×C4×D283C2312yes—
56#17985376—22no—
57C2×C283⋊C8C2312yes—
58C4⋊Dic283—21no—
59C4⋊Dic283C2312yes—
60Dic283⋊C4—22no—
61(C2×D283)⋊C4—22no—
62(C2×D283)⋊C4—22no—
63(C2×D283)⋊C4—22no—
64C4×Dic283—22no—
65C22×C4×C283C2311yescharacteristic
66C2×C8×C283—22no—
67C2×C8×C283C2311yescharacteristic
68C2×C8×C283C2311yescharacteristic
69C4⋊C4×C283C2311yescharacteristic
70C4⋊C4×C283C2311yescharacteristic
71C4⋊C4×C283C2311yescharacteristic
72C4⋊C4×C283C2311yescharacteristic
73C22⋊C4×C283—21no—
74C22⋊C4×C283—21no—
75C42×C283—21no—
76C42×C283—21no—
77C22×D283—22no—
78C22×D283—42no—
79C22×D283—81no—
80C22×D283—81no—
81C22×D283C2×D412yes—
82Dic566—22no—
83D1132—22no—
84D1132—22no—
85D1132—22no—
86D1132—42no—
87D1132—82no—
88D1132—82no—
89C22⋊D283—24no—
90C2×Dic283—22no—
91C2×Dic283—81no—
92C2×Dic283C2×D412yes—
93C4×D283—22no—
94C4×D283—22no—
95C4×D283—82no—
96C283⋊C8—22no—
97C23×C283C2×D411yescharacteristic
98C2×C4×C283—21no—
99C2×C4×C283—21no—
100C2×C4×C283—21no—
101C2×C4×C283—21no—
102C2×C4×C283C2×D411yescharacteristic
103C2×C4×C283#4112yes—
104C2×C4×C283#4112yes—
105C2×C4×C283C2411yescharacteristic
106C8×C283—21no—
107C8×C283—21no—
108C22×C283—21no—
109C22×C283—21no—
110C22×C283#12312yes—
111C22×C283C22×D411yescharacteristic
112C2×D283—22no—
113C2×D283—22no—
114C2×D283—22no—
115C2×D283—42no—
116C2×D283—42no—
117C2×D283—42no—
118C2×D283—84no—
119C4×C283—41no—
120C4×C283—41no—
121C4×C283—41no—
122C4×C283—41no—
123C4×C283#12312yes—
124C4×C283C2×#4111yescharacteristic
125C4×C283C2×#4111yescharacteristic
126Dic283—22no—
127Dic283—42no—
128C2×C283—22no—
129C2×C283C2×#12311yescharacteristic
130C2×C283#57611yescharacteristic
131C2×C283#57711yescharacteristic
132D283—42no—
133D283—82no—
134C283#309611yescharacteristic, complemented, Sylow
135#3096—2831nomaximal, Sylow
136#535—2831no—
137#520—2831no—
138#482—2832no—
139#482—2832no—
140#481—2832no—
141#480—2832no—
142#428—2831no—
143#427D28311yescharacteristic, complemented
144#418—2831no—
145C2×#102—2831no—
146#408—2831no—
147C2×#41—2831no—
148C22×D4—2831no—
149C2×M16—2831no—
150C22×C8C2×D28311yescharacteristic
151#127—5661no—
152#124—5661no—
153#121—2832no—
154#121—2832no—
155#120—5662no—
156C4×Q8—5661no—
157C4×D4—5661no—
158C4×D4—5662no—
159#117—2832no—
160#117C2×D28311yescharacteristic
161#117C2×D28311yescharacteristic
162C2×C4⋊C4—2831no—
163C2×C4⋊C4—2832no—
164#107—2832no—
165#107C2×D28311yescharacteristic, complemented
166#107C2×D28311yescharacteristic, complemented
167#106—2832no—
168#106C2×D28311yescharacteristic, complemented
169#106C2×D28311yescharacteristic, complemented
170#102—2832no—
171#102—2832no—
172#102—2832no—
173#102—2832no—
174C22⋊C8—2832no—
175C22⋊C8—2832no—
176C24—5661no—
177#41—5662no—
178#41—5662no—
179C2×Q8—2831no—
180C2×D4—2832no—
181C2×D4—2831no—
182C2×D4—2832no—
183C2×D4—5662no—
184C2×D4—5662no—
185C2×D4—5661no—
186C2×D4—5662no—
187C2×D4—5662no—
188C22×C4—2832no—
189C22×C4—5662no—
190C22×C4—5661no—
191C22×C4C22×D28311yescharacteristic
192M16—5662no—
193C2×C8—22no—
194C2×C8—2832no—
195C2×C8C22×D28311yescharacteristic
196C2×C8C22×D28311yescharacteristic
197C4⋊C4—2832no—
198C4⋊C4—5662no—
199C4⋊C4—5661no—
200C4⋊C4C22×D28311yescharacteristic
201C4⋊C4C22×D28311yescharacteristic
202C4⋊C4C22×D28311yescharacteristic
203C4⋊C4C22×D28311yescharacteristic
204C22⋊C4—21no—
205C22⋊C4—21no—
206C22⋊C4—5662no—
207C22⋊C4—5662no—
208C22⋊C4—5662no—
209C42—21no—
210C42—21no—
211C42—5662no—
212C23—2832no—
213C23—5662no—
214C23—11322no—
215C23—22641no—
216C23—22641no—
217C23D4×D28311yescharacteristic
218Q8—5662no—
219D4—5664no—
220D4—5662no—
221D4—5662no—
222D4—5662no—
223D4—11322no—
224D4—22642no—
225D4—22642no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—2832no—
231C2×C4—5662no—
232C2×C4—5662no—
233C2×C4—5662no—
234C2×C4—22642no—
235C2×C4—22641no—
236C2×C4D4×D28311yescharacteristic
237C2×C4#1798539212yes—
238C2×C4#1798539312yes—
239C2×C4C23×D28311yescharacteristic
240C8—21no—
241C8—21no—
242C8—5662no—
243C22—21no—
244C22—21no—
245C22—5662no—
246C22—5662no—
247C22—5662no—
248C22—11322no—
249C22—11322no—
250C22—11322no—
251C22—22644no—
252C22#2258359512yes—
253C22C2×D4×D28311yescharacteristic
254C4—41no—
255C4—41no—
256C4—41no—
257C4—41no—
258C4—5662no—
259C4—11322no—
260C4#2258359512yes—
261C4C2×#1798539211yescharacteristic
262C4C2×#1798539311yescharacteristic
263C2—22no—
264C2—11322no—
265C2—22642no—
266C2C2×#2258359511yescharacteristic
267C2#3182726711yescharacteristic
268C2#3182727211yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#427×C283C2
socleC22×C283C22×D4
prime radical#31827034C2
hypercenter#427D283
hypocenterC283#3096
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ #427

Complements

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

NH ≅ G/Ntype
2. #31826945C2semidirect
3. #31826792C2semidirect
4. #31826791C2semidirect
5. #31826785C2semidirect
6. #31826780C2semidirect
7. #31826508C2semidirect
8. #31826469C2semidirect
9. C2×#22583532C2semidirect
10. #31826431C2semidirect
11. #427×C283C2semidirect
23. #22583568C22semidirect
25. C4⋊C4×D283C22semidirect
26. #22583543C22semidirect
27. #22583541C22semidirect
32. (C2×D283)⋊C8C22semidirect
33. (C2×D283)⋊C8C22semidirect
37. #107×C283C22semidirect
38. #107×C283C22semidirect
39. #106×C283C22semidirect
40. #106×C283C22semidirect
134. C283#3096semidirect
143. #427D283semidirect
165. #107C2×D283semidirect
166. #107C2×D283semidirect
168. #106C2×D283semidirect
169. #106C2×D283semidirect

Maximal subgroups

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

subgroupindex
#318270342
#318269452
#318267922
#318267912
#318267852
#318267802
#318265082
#318264692
C2×#225835322
#318264312
#427×C2832
#3096283