Finite Group Databasebeta

← #49131401

Subgroups — #49131401

Order 36224.

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

normal subgroups only

This group has 450 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#31826999C211yesmaximal, characteristic, complemented
2C2×C4×D1132C211yesmaximal, characteristic, complemented
3#31826796C211yesmaximal, characteristic, complemented
4#31826779C211yesmaximal, characteristic, complemented
5#31826766C212yesmaximal, complemented
6#31826681C212yesmaximal, complemented
7#31826618C211yesmaximal, characteristic, complemented
8#31826601C211yesmaximal, characteristic
9#31826578C212yesmaximal, complemented
10#31826567C212yesmaximal, complemented
11#432×C283C211yesmaximal, characteristic, complemented
12C22×D1132C2211yescharacteristic
13C22×C4×D283—21no—
14C2×#17985381C2212yes—
15C2×D2264C2212yes—
16#22583604—21no—
17#22583602C2211yescharacteristic, complemented
18#22583598C2211yescharacteristic, complemented
19#22583593—21no—
20#22583589C2211yescharacteristic
21#22583584C2211yescharacteristic
22C4×Dic566C2211yescharacteristic, complemented
23C4×D1132—21no—
24C4×D1132—21no—
25C4×D1132C2212yes—
26C4×D1132C2212yes—
27C4×D1132C2211yescharacteristic, complemented
28C4×C22⋊D283—21no—
29#22583567—21no—
30C2×C4⋊Dic283C2211yescharacteristic
31C2×(C2×D283)⋊C4—21no—
32#22583544C2212yescomplemented
33#22583542C2212yescomplemented
34#22583535C2212yescomplemented
35#22583532C2212yes—
36#22583532C2212yes—
37#22583532C2212yescomplemented
38C2×C42×C283C2211yescharacteristic
39C4⋊C8×C283C2212yescomplemented
40C22⋊C8×C283C2211yescharacteristic
41C22⋊C8×C283C2211yescharacteristic
42#97×C283C2212yescomplemented
43C23×D283—21no—
44C2×Dic566C2311yescharacteristic
45C2×D1132—24no—
46C2×D1132—21no—
47C2×D1132C2311yescharacteristic
48C2×D1132C2312yes—
49C2×C22⋊D283—21no—
50C22×Dic283—21no—
51C2×C4×D283—21no—
52C2×C4×D283—22no—
53C2×C4×D283—22no—
54C2×C4×D283—44no—
55#17985381—24no—
56D2264—24no—
57C4⋊Dic283—21no—
58C4⋊Dic283C2312yes—
59C4⋊Dic283C2311yescharacteristic
60C4⋊Dic283C2311yescharacteristic
61Dic283⋊C4—21no—
62Dic283⋊C4—21no—
63Dic283⋊C4—21no—
64Dic283⋊C4—21no—
65C22⋊Dic283—21no—
66(C2×D283)⋊C4—22no—
67(C2×D283)⋊C4—22no—
68(C2×D283)⋊C4—21no—
69(C2×D283)⋊C4—21no—
70(C2×D283)⋊C4—21no—
71(C2×D283)⋊C4—21no—
72C4×Dic283—21no—
73C22×C4×C283D411yescharacteristic
74C22×C4×C283D411yescharacteristic
75C22×C4×C283C2311yescharacteristic
76C2×C8×C283C2312yes—
77C2×C8×C283C2312yes—
78C42×C283D411yescharacteristic
79C42×C283D411yescharacteristic
80C42×C283C2311yescharacteristic
81C42×C283C2311yescharacteristic
82C22×D283—24no—
83C22×D283—22no—
84C22×D283—21no—
85C22×D283—42no—
86C22×D283—42no—
87Dic566—22no—
88D1132—24no—
89D1132—22no—
90D1132—22no—
91D1132#4114yes—
92C22⋊D283—42no—
93C2×Dic283—21no—
94C2×Dic283—21no—
95C2×Dic283—22no—
96C2×Dic283—21no—
97C2×Dic283—42no—
98C4×D283—42no—
99C4×D283—44no—
100C4×D283—44no—
101C23×C283C2×D411yescharacteristic
102C2×C4×C283—22no—
103C2×C4×C283—22no—
104C2×C4×C283—41no—
105C2×C4×C283C2×D411yescharacteristic
106C2×C4×C283C2×D411yescharacteristic
107C2×C4×C283C2×D411yescharacteristic
108C2×C4×C283C2×D411yescharacteristic
109C2×C4×C283C2×D411yescharacteristic
110C2×C4×C283C2411yescharacteristic
111C8×C283—22no—
112C8×C283—22no—
113C22×C283—21no—
114C22×C283—21no—
115C22×C283AGL(1,ℤ/8)12yes—
116C22×C283C22×D411yescharacteristic
117C2×D283—24no—
118C2×D283—48no—
119C2×D283—42no—
120C2×D283—42no—
121C2×D283—41no—
122C2×D283—41no—
123C2×D283—41no—
124C4×C283—21no—
125C4×C283—21no—
126C4×C283—21no—
127C4×C283—21no—
128C4×C283—21no—
129C4×C283C2×#4112yes—
130Dic283—41no—
131Dic283—42no—
132Dic283—41no—
133Dic283—41no—
134C2×C283—22no—
135C2×C283#52511yescharacteristic
136C2×C283C2×AGL(1,ℤ/8)11yescharacteristic
137C2×C283#57511yescharacteristic
138D283—44no—
139D283—81no—
140C283#311411yescharacteristic, complemented, Sylow
141#3114—2831nomaximal, Sylow
142#529—2831no—
143C2×C4×D4—2831no—
144#483—2831no—
145#480—2831no—
146#478—2832no—
147#463—2832no—
148#450—2831no—
149#447—2831no—
150#442—2832no—
151#440—2832no—
152#432D28311yescharacteristic, complemented
153C22×D4—2831no—
154C23×C4—5661no—
155C2×SD16—2832no—
156C2×D8—2832no—
157#126—5661no—
158#125—2831no—
159#124—2831no—
160#123—5661no—
161C22⋊Q8—2831no—
162#121—2831no—
163C4×Q8—2831no—
164C4×D4—2832no—
165C4×D4—2832no—
166C4×D4—2831no—
167C4×D4—5661no—
168C4×D4—5661no—
169C4×D4—5661no—
170#117—5661no—
171C2×C4⋊C4—2831no—
172C2×C22⋊C4—5661no—
173C2×C42C2×D28311yescharacteristic
174#107—2832no—
175#106—2832no—
176C4⋊C8C2×D28312yescomplemented
177#103—2832no—
178#102—2832no—
179#102—2832no—
180#102—2832no—
181C22⋊C8C2×D28311yescharacteristic
182C22⋊C8C2×D28311yescharacteristic
183#97C2×D28312yescomplemented
184C24—5661no—
185C2×Q8—2831no—
186C2×D4—2832no—
187C2×D4—2831no—
188C2×D4—5664no—
189C2×D4—5661no—
190C2×D4—5661no—
191C22×C4—5661no—
192C22×C4—5661no—
193C22×C4—5662no—
194C22×C4—5662no—
195C22×C4—11324no—
196C22×C4D113211yescharacteristic
197C22×C4D113211yescharacteristic
198C22×C4C22×D28311yescharacteristic
199SD16—5664no—
200D8—5664no—
201C2×C8C22×D28312yes—
202C2×C8C22×D28312yes—
203C4⋊C4—2831no—
204C4⋊C4—2831no—
205C4⋊C4—2832no—
206C4⋊C4—5661no—
207C4⋊C4—5661no—
208C4⋊C4—5661no—
209C4⋊C4—5661no—
210C4⋊C4—5661no—
211C22⋊C4—5661no—
212C22⋊C4—5662no—
213C22⋊C4—5662no—
214C22⋊C4—5661no—
215C22⋊C4—5661no—
216C22⋊C4—5661no—
217C22⋊C4—5661no—
218C42—5661no—
219C42D113211yescharacteristic
220C42D113211yescharacteristic
221C42C22×D28311yescharacteristic
222C42C22×D28311yescharacteristic
223C23—5664no—
224C23—5662no—
225C23—5661no—
226C23—11322no—
227C23—11322no—
228C23C2×D113211yescharacteristic
229Q8—5662no—
230D4—2834no—
231D4—5664no—
232D4—5662no—
233D4—5662no—
234D4—11322no—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—41no—
238C2×C4—5661no—
239C2×C4—5661no—
240C2×C4—5661no—
241C2×C4—5662no—
242C2×C4—11324no—
243C2×C4—11324no—
244C2×C4—11322no—
245C2×C4—11322no—
246C2×C4C2×D113211yescharacteristic
247C2×C4C2×D113211yescharacteristic
248C2×C4C2×D113211yescharacteristic
249C2×C4C2×D113211yescharacteristic
250C2×C4C2×D113211yescharacteristic
251C2×C4C23×D28311yescharacteristic
252C8—22no—
253C8—22no—
254C22—21no—
255C22—21no—
256C22—5664no—
257C22—11328no—
258C22—11322no—
259C22—11322no—
260C22—11321no—
261C22—11321no—
262C22—11321no—
263C22#2258363812yes—
264C22C22×D113211yescharacteristic
265C4—21no—
266C4—21no—
267C4—21no—
268C4—21no—
269C4—21no—
270C4—11321no—
271C4—11322no—
272C4—11321no—
273C4—11321no—
274C4#41×D28312yes—
275C2—22no—
276C2—11324no—
277C2—22641no—
278C2#3182697711yescharacteristic
279C2C2×#2258363811yescharacteristic
280C2#3182726511yescharacteristic
subgroupG/H
centerC22C22×D1132
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#432×C283C2
socleC22×C283C22×D4
prime radical#31826601C2
hypercenter#432D283
hypocenterC283#3114
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
1. #31826999C2semidirect
2. C2×C4×D1132C2semidirect
3. #31826796C2semidirect
4. #31826779C2semidirect
5. #31826766C2semidirect
6. #31826681C2semidirect
7. #31826618C2semidirect
9. #31826578C2semidirect
10. #31826567C2semidirect
11. #432×C283C2semidirect
17. #22583602C22semidirect
18. #22583598C22semidirect
22. C4×Dic566C22semidirect
27. C4×D1132C22semidirect
32. #22583544C22semidirect
33. #22583542C22semidirect
34. #22583535C22semidirect
37. #22583532C22semidirect
39. C4⋊C8×C283C22semidirect
42. #97×C283C22semidirect
140. C283#3114semidirect
152. #432D283semidirect
176. C4⋊C8C2×D283semidirect
183. #97C2×D283semidirect

Maximal subgroups

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

subgroupindex
#318269992
C2×C4×D11322
#318267962
#318267792
#318267662
#318266812
#318266182
#318266012
#318265782
#318265672
#432×C2832
#3114283