Finite Group Databasebeta

← #44560609

Subgroups — #44560609

Order 32128.

418 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 121 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#30632292C211yesmaximal, characteristic, complemented
2#30632161C211yesmaximal, characteristic, complemented
3#30632012C212yesmaximal, complemented
4#30631988C212yesmaximal, complemented
5#30631883C212yesmaximal, complemented
6#30631823C212yesmaximal, complemented
7#30631800C212yesmaximal, complemented
8C4×D2008C212yesmaximal, complemented
9#433×C251C211yesmaximal, characteristic, complemented
10C22×D1004C2211yescharacteristic
11C2×D2008C2212yes—
12C2×D2008C2212yes—
13#22548712C2211yescharacteristic, complemented
14#22548707C2211yescharacteristic, complemented
15#22548700—22no—
16#22548689C2212yes—
17#22548688—22no—
18C4×D1004C2212yes—
19C4×D1004C2212yes—
20C4×D1004C2212yescomplemented
21#22548677—22no—
22#22548674C2211yescharacteristic
23C22⋊C4×D251—22no—
24#22548649C2212yescomplemented
25#22548647C2212yescomplemented
26#22548637C2212yes—
27#22548637C2212yes—
28#22548637C2212yescomplemented
29#22548637C2212yescomplemented
30#117×C251C2211yescharacteristic
31C4⋊C8×C251C2212yescomplemented
32C22⋊C8×C251C2212yes—
33#97×C251C2211yescharacteristic, complemented
34C4×C8×C251C2211yescharacteristic, complemented
35C23×D251—21no—
36C2×D1004—24no—
37C2×D1004—21no—
38C2×D1004—22no—
39C2×D1004C2312yes—
40C2×D1004C2312yes—
41C2×C22⋊D251—22no—
42C2×C4×D251—22no—
43C2×C4×D251—22no—
44C2×C4×D251—22no—
45D2008—24no—
46D2008—24no—
47C4⋊Dic251C2312yes—
48C4⋊Dic251C2312yes—
49Dic251⋊C4—22no—
50C22⋊Dic251—21no—
51(C2×D251)⋊C4—22no—
52(C2×D251)⋊C4—22no—
53(C2×D251)⋊C4—22no—
54(C2×D251)⋊C4—22no—
55C4×Dic251—21no—
56C22×C4×C251C2311yescharacteristic
57C2×C8×C251C2312yes—
58C2×C8×C251C2312yes—
59C4⋊C4×C251D412yes—
60C22⋊C4×C251D412yes—
61C42×C251C2311yescharacteristic
62C42×C251C2311yescharacteristic
63C22×D251—22no—
64C22×D251—24no—
65C22×D251—22no—
66C22×D251—82no—
67D1004—24no—
68D1004—22no—
69D1004—22no—
70D1004—22no—
71D1004—82no—
72D1004#4114yes—
73C22⋊D251—82no—
74C2×Dic251—22no—
75C2×Dic251—22no—
76C4×D251—82no—
77C4×D251—82no—
78C4×D251—82no—
79C23×C251C2×D411yescharacteristic
80C2×C4×C251—22no—
81C2×C4×C251C2×D412yes—
82C2×C4×C251C2×D412yes—
83C2×C4×C251C2×D411yescharacteristic
84C2×C4×C251C2411yescharacteristic
85C8×C251—22no—
86C8×C251—22no—
87C22×C251—21no—
88C22×C251—22no—
89C22×C251C22×D411yescharacteristic
90C2×D251—24no—
91C2×D251—42no—
92C2×D251—42no—
93C2×D251—42no—
94C2×D251—42no—
95C2×D251—42no—
96C2×D251—84no—
97C4×C251—21no—
98C4×C251—22no—
99C4×C251—22no—
100C4×C251C2×#4112yes—
101Dic251—42no—
102Dic251—42no—
103C2×C251—41no—
104C2×C251#52511yescharacteristic
105C2×C251#57612yes—
106D251—44no—
107D251—82no—
108C251#312211yescharacteristic, complemented, Sylow
109#3122—2511nomaximal, Sylow
110#540—2511no—
111#518—2511no—
112#482—2512no—
113#478—2512no—
114#459—2512no—
115#447—2512no—
116#442—2512no—
117C4×D8—2512no—
118#433D25111yescharacteristic, complemented
119C22×D4—2511no—
120C2×D8—2512no—
121C2×D8—2512no—
122#127—2511no—
123#125—2511no—
124#123—5022no—
125#121—5022no—
126#121—2512no—
127C4×D4—5022no—
128C4×D4—2512no—
129C4×D4—2512no—
130C4×D4—2512no—
131#117—2511no—
132#117C2×D25111yescharacteristic
133C2×C22⋊C4—5022no—
134#107—2512no—
135#106—2512no—
136C4⋊C8C2×D25112yescomplemented
137#102—2512no—
138#102—2512no—
139#102—2512no—
140#102—2512no—
141C22⋊C8C2×D25112yes—
142#97C2×D25111yescharacteristic, complemented
143C4×C8C2×D25111yescharacteristic, complemented
144C24—5021no—
145C2×D4—5024no—
146C2×D4—5022no—
147C2×D4—5022no—
148C2×D4—5021no—
149C2×D4—2512no—
150C2×D4—2512no—
151C22×C4—5022no—
152C22×C4—5022no—
153C22×C4—5022no—
154C22×C4C22×D25111yescharacteristic
155D8—5024no—
156D8—5024no—
157C2×C8C22×D25112yes—
158C2×C8C22×D25112yes—
159C4⋊C4—5022no—
160C4⋊C4—2512no—
161C4⋊C4—2512no—
162C4⋊C4D100412yes—
163C22⋊C4—5021no—
164C22⋊C4—5022no—
165C22⋊C4—5022no—
166C22⋊C4—5022no—
167C22⋊C4—5022no—
168C22⋊C4D100412yes—
169C42—5021no—
170C42C22×D25111yescharacteristic
171C42C22×D25111yescharacteristic
172C23—20082no—
173C23—5024no—
174C23—5022no—
175C23—5022no—
176C23C2×D100411yescharacteristic
177D4—20082no—
178D4—20082no—
179D4—5024no—
180D4—5022no—
181D4—5022no—
182D4—5022no—
183D4—2514no—
184C2×C4—22no—
185C2×C4—20082no—
186C2×C4—20082no—
187C2×C4—20082no—
188C2×C4—5022no—
189C2×C4—5022no—
190C2×C4C2×D100411yescharacteristic
191C2×C4C2×D100412yes—
192C2×C4C2×D100412yes—
193C2×C4C23×D25111yescharacteristic
194C8—22no—
195C8—22no—
196C22—21no—
197C22—22no—
198C22—20084no—
199C22—10042no—
200C22—10042no—
201C22—10042no—
202C22—10042no—
203C22—10042no—
204C22—5024no—
205C22C22×D100411yescharacteristic
206C4—21no—
207C4—22no—
208C4—22no—
209C4—10042no—
210C4—10042no—
211C4#41×D25112yes—
212C2—41no—
213C2—20082no—
214C2—10044no—
215C2#3063219911yescharacteristic
216C2#3063249212yes—
subgroupG/H
centerC22C22×D1004
commutator, cosocleC2×C4×C251C24
FrattiniC2×C4C23×D251
Fitting#433×C251C2
socleC22×C251C22×D4
hypercenter#433D251
hypocenterC251#3122
LCSG ▷ C2×C4×C251 ▷ C2×C251 ▷ C251
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #30632292C2semidirect
2. #30632161C2semidirect
3. #30632012C2semidirect
4. #30631988C2semidirect
5. #30631883C2semidirect
6. #30631823C2semidirect
7. #30631800C2semidirect
8. C4×D2008C2semidirect
9. #433×C251C2semidirect
13. #22548712C22semidirect
14. #22548707C22semidirect
20. C4×D1004C22semidirect
24. #22548649C22semidirect
25. #22548647C22semidirect
28. #22548637C22semidirect
29. #22548637C22semidirect
31. C4⋊C8×C251C22semidirect
33. #97×C251C22semidirect
34. C4×C8×C251C22semidirect
108. C251#3122semidirect
118. #433D251semidirect
136. C4⋊C8C2×D251semidirect
142. #97C2×D251semidirect
143. C4×C8C2×D251semidirect

Maximal subgroups

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

subgroupindex
#306322922
#306321612
#306320122
#306319882
#306318832
#306318232
#306318002
C4×D20082
#433×C2512
#3122251