Finite Group Databasebeta

← #44560618

Subgroups — #44560618

Order 32128.

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

normal subgroups only

This group has 394 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#30632299C211yesmaximal, characteristic, complemented
2#30632161C211yesmaximal, characteristic
3#30632029C212yesmaximal, complemented
4#30631988C212yesmaximal, complemented
5#30631893C212yesmaximal, complemented
6#30631840C212yesmaximal
7#30631789C212yesmaximal, complemented
8C4×#16860799C212yesmaximal, complemented
9#433×C251C211yesmaximal, characteristic, complemented
10C22×D1004C2211yescharacteristic
11C2×#16860799C2212yes—
12C2×#16860799C2212yes—
13#22548715C2211yescharacteristic, complemented
14#22548708—22no—
15#22548707C2211yescharacteristic, complemented
16#22548705—22no—
17#22548694C2212yes—
18C4×Dic502C2212yescomplemented
19C4×D1004C2212yes—
20C4×D1004C2212yes—
21#22548677—22no—
22#22548674C2211yescharacteristic
23C22⋊C4×D251—22no—
24#22548649C2212yescomplemented
25#22548647C2212yescomplemented
26#22548640C2212yescomplemented
27#22548640C2212yescomplemented
28#22548637C2212yes—
29#22548637C2212yes—
30#117×C251C2211yescharacteristic
31C4⋊C8×C251C2212yescomplemented
32C22⋊C8×C251C2212yes—
33#97×C251C2211yescharacteristic, complemented
34C4×C8×C251C2211yescharacteristic, complemented
35C23×D251—21no—
36C2×Dic502C2312yes—
37C2×D1004—24no—
38C2×D1004—21no—
39C2×D1004C2312yes—
40C2×C4×D251—22no—
41C2×C4×D251—22no—
42#16860799—24no—
43#16860799—24no—
44C4⋊Dic251—22no—
45C4⋊Dic251C2312yes—
46C4⋊Dic251C2312yes—
47Dic251⋊C4—22no—
48Dic251⋊C4—22no—
49Dic251⋊C4—22no—
50C22⋊Dic251—21no—
51C22⋊Dic251—22no—
52(C2×D251)⋊C4—22no—
53(C2×D251)⋊C4—22no—
54C4×Dic251—21no—
55C4×Dic251—22no—
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—82no—
66Dic502—22no—
67Dic502—22no—
68D1004—24no—
69D1004—22no—
70D1004#4114yes—
71C2×Dic251—22no—
72C2×Dic251—22no—
73C2×Dic251—22no—
74C4×D251—82no—
75C4×D251—82no—
76C23×C251C2×D411yescharacteristic
77C2×C4×C251—22no—
78C2×C4×C251C2×D412yes—
79C2×C4×C251C2×D412yes—
80C2×C4×C251C2×D411yescharacteristic
81C2×C4×C251C2411yescharacteristic
82C8×C251—22no—
83C8×C251—22no—
84C22×C251—21no—
85C22×C251—22no—
86C22×C251C22×D411yescharacteristic
87C2×D251—24no—
88C2×D251—42no—
89C2×D251—42no—
90C2×D251—84no—
91C4×C251—21no—
92C4×C251—22no—
93C4×C251—22no—
94C4×C251C2×#4112yes—
95Dic251—42no—
96Dic251—42no—
97Dic251—42no—
98C2×C251—41no—
99C2×C251#52511yescharacteristic
100C2×C251#57712yes—
101D251—44no—
102C251#312311yescharacteristic, complemented, Sylow
103#3123—2511nomaximal, Sylow
104#541—2511no—
105#518—2511no—
106#485—2512no—
107#478—2512no—
108#461—2512no—
109#450—2512no—
110#440—2512no—
111C4×SD16—2512no—
112#433D25111yescharacteristic, complemented
113C22×D4—2511no—
114C2×SD16—2512no—
115C2×SD16—2512no—
116C4⋊Q8—2511no—
117#126—5022no—
118#125—5022no—
119#125—2511no—
120C22⋊Q8—2512no—
121C4×Q8—2512no—
122C4×D4—5022no—
123C4×D4—2512no—
124C4×D4—2512no—
125#117—2511no—
126#117C2×D25111yescharacteristic
127C2×C22⋊C4—5022no—
128#107—2512no—
129#106—2512no—
130C4⋊C8C2×D25112yescomplemented
131#103—2512no—
132#103—2512no—
133#102—2512no—
134#102—2512no—
135C22⋊C8C2×D25112yes—
136#97C2×D25111yescharacteristic, complemented
137C4×C8C2×D25111yescharacteristic, complemented
138C24—5021no—
139C2×Q8—2512no—
140C2×D4—5024no—
141C2×D4—5021no—
142C2×D4—2512no—
143C22×C4—5022no—
144C22×C4—5022no—
145C22×C4C22×D25111yescharacteristic
146SD16—5024no—
147SD16—5024no—
148C2×C8C22×D25112yes—
149C2×C8C22×D25112yes—
150C4⋊C4—5022no—
151C4⋊C4—5022no—
152C4⋊C4—5022no—
153C4⋊C4—5022no—
154C4⋊C4—2512no—
155C4⋊C4—2512no—
156C4⋊C4D100412yes—
157C22⋊C4—5021no—
158C22⋊C4—5022no—
159C22⋊C4—5022no—
160C22⋊C4—5022no—
161C22⋊C4D100412yes—
162C42—5021no—
163C42—5022no—
164C42C22×D25111yescharacteristic
165C42C22×D25111yescharacteristic
166C23—20082no—
167C23—5024no—
168C23—5022no—
169C23C2×D100411yescharacteristic
170Q8—5022no—
171Q8—5022no—
172D4—5024no—
173D4—5022no—
174D4—2514no—
175C2×C4—22no—
176C2×C4—20082no—
177C2×C4—20082no—
178C2×C4—5022no—
179C2×C4—5022no—
180C2×C4—5022no—
181C2×C4C2×D100412yes—
182C2×C4C2×D100411yescharacteristic
183C2×C4C2×D100412yes—
184C2×C4C23×D25111yescharacteristic
185C8—22no—
186C8—22no—
187C22—21no—
188C22—22no—
189C22—20084no—
190C22—10042no—
191C22—10042no—
192C22—5024no—
193C22C22×D100411yescharacteristic
194C4—21no—
195C4—22no—
196C4—22no—
197C4—10042no—
198C4—10042no—
199C4—10042no—
200C4#41×D25112yes—
201C2—41no—
202C2—10044no—
203C2#3063219911yescharacteristic
204C2#3063249912yes—
subgroupG/H
centerC22C22×D1004
commutator, cosocleC2×C4×C251C24
FrattiniC2×C4C23×D251
Fitting#433×C251C2
socleC22×C251C22×D4
prime radicalC22×D1004C22
hypercenter#433D251
hypocenterC251#3123
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. #30632299C2semidirect
3. #30632029C2semidirect
4. #30631988C2semidirect
5. #30631893C2semidirect
7. #30631789C2semidirect
8. C4×#16860799C2semidirect
9. #433×C251C2semidirect
13. #22548715C22semidirect
15. #22548707C22semidirect
18. C4×Dic502C22semidirect
24. #22548649C22semidirect
25. #22548647C22semidirect
26. #22548640C22semidirect
27. #22548640C22semidirect
31. C4⋊C8×C251C22semidirect
33. #97×C251C22semidirect
34. C4×C8×C251C22semidirect
102. C251#3123semidirect
112. #433D251semidirect
130. C4⋊C8C2×D251semidirect
136. #97C2×D251semidirect
137. C4×C8C2×D251semidirect

Maximal subgroups

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

subgroupindex
#306322992
#306321612
#306320292
#306319882
#306318932
#306318402
#306317892
C4×#168607992
#433×C2512
#3123251