Finite Group Databasebeta

← #49130740

Subgroups — #49130740

Order 36224.

584 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 584 conjugacy classes of subgroups — too many to draw. Only its 137 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
1C2×#22583638C211yesmaximal, characteristic, complemented
2C2×#22583636C211yesmaximal, characteristic, complemented
3C2×#22583606C211yesmaximal, characteristic, complemented
4#31826933C211yesmaximal, characteristic, complemented
5#31826664C214yesmaximal, complemented
6#31826659C214yesmaximal, complemented
7#31826488C211yesmaximal, characteristic, complemented
8#31826469C211yesmaximal, characteristic, complemented
9#418×C283C211yesmaximal, characteristic, complemented
10C2×#17985392C2211yescharacteristic
11C22×D1132C2211yescharacteristic
12C22×C22⋊D283—22no—
13#22583638—24no—
14#22583636—24no—
15C2×#17985381C2212yescomplemented
16C2×#17985380C2212yescomplemented
17C2×D2264C2212yescomplemented
18C2×#17985377C2212yescomplemented
19C2×#17985376C2211yescharacteristic
20#22583606—21no—
21#22583606—21no—
22#22583606C2214yes—
23#22583575C2212yescomplemented
24#22583572C2212yescomplemented
25(C22⋊D283)⋊C4—22no—
26#22583567—21no—
27C2×C4×Dic283C2211yescharacteristic
28C42×D283—21no—
29Dic283⋊C8C2214yescomplemented
30#22583530C2214yescomplemented
31C22×D4×C283C2211yescharacteristic
32C2×M16×C283C2211yescharacteristic
33#117×C283C2211yescharacteristic
34#102×C283C2214yescomplemented
35C23×D283—21no—
36#17985392—22no—
37#17985392D414yescomplemented
38C2×Dic566C2311yescharacteristic
39C2×D1132—22no—
40C2×D1132—21no—
41C2×D1132—22no—
42C2×D1132C2312yes—
43C2×D1132C2311yescharacteristic
44C2×C22⋊D283—24no—
45C2×C22⋊D283—24no—
46C2×C22⋊D283—21no—
47C2×C22⋊D283—48no—
48C22×Dic283D412yes—
49C2×C4×D283—22no—
50C2×C4×D283—21no—
51#17985381—24no—
52#17985380—24no—
53D2264—24no—
54#17985377—24no—
55#17985376—22no—
56C2×C283⋊C8C2312yes—
57Dic283⋊C4—22no—
58(C2×D283)⋊C4—22no—
59C4×Dic283—22no—
60C4×Dic283D411yescharacteristic
61C4×Dic283D411yescharacteristic
62C4×Dic283C2312yes—
63C24×C283—21no—
64C2×D4×C283—22no—
65C2×D4×C283—21no—
66C2×D4×C283—22no—
67C2×D4×C283C2312yes—
68C22×C4×C283C2311yescharacteristic
69M16×C283—22no—
70C2×C8×C283C2312yes—
71C4⋊C4×C283C2312yes—
72C22⋊C4×C283—21no—
73C42×C283—21no—
74C22×D283—21no—
75C22×D283—22no—
76C22×D283—44no—
77C22×D283—42no—
78Dic566—21no—
79Dic566C2×D412yescomplemented
80D1132—22no—
81D1132—21no—
82D1132—22no—
83D1132—42no—
84D1132C2×D412yescomplemented
85C22⋊D283—24no—
86C22⋊D283—48no—
87C22⋊D283—48no—
88C2×Dic283—21no—
89C2×Dic283—24no—
90C2×Dic283C2×D412yes—
91C2×Dic283C2×D412yes—
92C4×D283—24no—
93C4×D283—44no—
94C283⋊C8—22no—
95C23×C283—22no—
96C23×C283—44no—
97C23×C283—42no—
98C23×C283C2×D411yescharacteristic
99D4×C283—22no—
100D4×C283—22no—
101D4×C283—42no—
102C2×C4×C283—22no—
103C2×C4×C283C2×D411yescharacteristic
104C2×C4×C283C2×D412yes—
105C2×C4×C283#4112yes—
106C2×C4×C283C2411yescharacteristic
107C8×C283—22no—
108C22×C283—22no—
109C22×C283—42no—
110C22×C283—44no—
111C22×C283—84no—
112C22×C283#12112yes—
113C22×C283C22×D411yescharacteristic
114C2×D283—22no—
115C2×D283—42no—
116C2×D283—42no—
117C2×D283—44no—
118C2×D283—84no—
119C4×C283—42no—
120C4×C283#12112yes—
121C4×C283C22×D411yescharacteristic
122C4×C283C2×#4111yescharacteristic
123Dic283—22no—
124Dic283—22no—
125Dic283AGL(1,ℤ/8)14yescomplemented
126C2×C283—22no—
127C2×C283—82no—
128C2×C283C2×#12111yescharacteristic
129C2×C283C2×AGL(1,ℤ/8)12yes—
130D283—42no—
131D283—82no—
132C283#303811yescharacteristic, complemented, Sylow
133#3038—2831nomaximal, Sylow
134C2×AGL(1,ℤ/8)—2831no—
135C2×AGL(1,ℤ/8)—2831no—
136C2×#127—2831no—
137C4×#41—2831no—
138#460—2834no—
139#459—2834no—
140#423—2831no—
141#418—2831no—
142#418D28311yescharacteristic, complemented
143C2×#41—2831no—
144C22×D4—2831no—
145C22×D4—5662no—
146C22×D4C2×D28311yescharacteristic
147AGL(1,ℤ/8)—5664no—
148AGL(1,ℤ/8)—5664no—
149C2×SD16—2832no—
150C2×SD16—2832no—
151C2×D8—2832no—
152C2×D8—2832no—
153C2×M16—2831no—
154C2×M16C2×D28311yescharacteristic
155#127—2834no—
156#127—5661no—
157#127—5661no—
158C4×Q8—2832no—
159C4×D4—2832no—
160C4×D4—5662no—
161#117—5661no—
162#117C2×D28311yescharacteristic
163C2×C42—2831no—
164C2×C42—5661no—
165C4⋊C8—2834no—
166#102—2834no—
167#102C2×D28314yescomplemented
168C24—21no—
169C24—5661no—
170#41—2834no—
171#41—5662no—
172C2×Q8—2831no—
173C2×D4—22no—
174C2×D4—21no—
175C2×D4—22no—
176C2×D4—2831no—
177C2×D4—2832no—
178C2×D4—5664no—
179C2×D4—5664no—
180C2×D4—5661no—
181C2×D4—5662no—
182C2×D4—5661no—
183C2×D4—5662no—
184C2×D4—11328no—
185C2×D4C22×D28312yes—
186C22×C4—2832no—
187C22×C4—5662no—
188C22×C4—5661no—
189C22×C4C22×D28311yescharacteristic
190SD16—5664no—
191SD16—5664no—
192D8—5664no—
193D8—5664no—
194M16—22no—
195M16—5662no—
196C2×C8—2832no—
197C2×C8C22×D28312yes—
198C4⋊C4—5662no—
199C4⋊C4C22×D28312yes—
200C22⋊C4—21no—
201C22⋊C4—5662no—
202C42—21no—
203C42—2831no—
204C42—2831no—
205C42—2832no—
206C42—5662no—
207C23—22no—
208C23—44no—
209C23—42no—
210C23—5661no—
211C23—5662no—
212C23—11324no—
213C23—11322no—
214C23D4×D28311yescharacteristic
215Q8—2832no—
216Q8—5661no—
217D4—22no—
218D4—22no—
219D4—42no—
220D4—2832no—
221D4—5664no—
222D4—5662no—
223D4—5661no—
224D4—5662no—
225D4—11328no—
226D4—11328no—
227D4—11322no—
228C2×C4—22no—
229C2×C4—2832no—
230C2×C4—2832no—
231C2×C4—5664no—
232C2×C4—5661no—
233C2×C4—5664no—
234C2×C4—11324no—
235C2×C4D4×D28311yescharacteristic
236C2×C4D4×D28312yes—
237C2×C4#1798539212yes—
238C2×C4C23×D28311yescharacteristic
239C8—22no—
240C8—5662no—
241C22—22no—
242C22—42no—
243C22—44no—
244C22—84no—
245C22—5662no—
246C22—11322no—
247C22—11322no—
248C22—11324no—
249C22—22644no—
250C22#2258358312yes—
251C22C2×D4×D28311yescharacteristic
252C4—42no—
253C4—2834no—
254C4—5662no—
255C4—5662no—
256C4#2258358312yes—
257C4C2×D4×D28311yescharacteristic
258C4C2×#1798539211yescharacteristic
259C2—22no—
260C2—82no—
261C2—11322no—
262C2—22642no—
263C2C2×#2258358311yescharacteristic
264C2AGL(1,ℤ/8)×D28312yes—
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#418×C283C2
socleC22×C283C22×D4
hypercenter#418D283
hypocenterC283#3038
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
1. C2×#22583638C2semidirect
2. C2×#22583636C2semidirect
3. C2×#22583606C2semidirect
4. #31826933C2semidirect
5. #31826664C2semidirect
6. #31826659C2semidirect
7. #31826488C2semidirect
8. #31826469C2semidirect
9. #418×C283C2semidirect
15. C2×#17985381C22semidirect
16. C2×#17985380C22semidirect
17. C2×D2264C22semidirect
18. C2×#17985377C22semidirect
23. #22583575C22semidirect
24. #22583572C22semidirect
29. Dic283⋊C8C22semidirect
30. #22583530C22semidirect
34. #102×C283C22semidirect
37. #17985392D4semidirect
79. Dic566C2×D4semidirect
84. D1132C2×D4semidirect
125. Dic283AGL(1,ℤ/8)semidirect
132. C283#3038semidirect
142. #418D283semidirect
167. #102C2×D283semidirect

Maximal subgroups

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

subgroupindex
C2×#225836382
C2×#225836362
C2×#225836062
#318269332
#318266642
#318266592
#318264882
#318264692
#418×C2832
#3038283