Finite Group Databasebeta

← #44560657

Subgroups — #44560657

Order 32128.

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

normal subgroups only

This group has 382 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
2#30632164C211yesmaximal, characteristic, complemented
3#30632012C212yesmaximal, complemented
4#30631995C212yesmaximal, complemented
5#30631888C212yesmaximal, complemented
6#30631828C212yesmaximal, complemented
7#30631789C212yesmaximal, complemented
8C4×#16860799C212yesmaximal, complemented
9#433×C251C211yesmaximal, characteristic, complemented
10C22×Dic502C2211yescharacteristic
11C2×#16860799C2212yes—
12C2×#16860799C2212yes—
13#22548712C2211yescharacteristic
14#22548707C2211yescharacteristic
15#22548700—22no—
16#22548689C2212yes—
17#22548688—22no—
18C4×Dic502C2212yes—
19C4×Dic502C2212yes—
20#22548680—22no—
21C4×D1004C2212yes—
22#22548674C2211yescharacteristic
23#22548671—22no—
24#22548649C2212yes—
25#22548647C2212yes—
26#22548640C2212yes—
27#22548640C2212yes—
28#22548637C2212yes—
29#22548637C2212yes—
30#117×C251C2211yescharacteristic
31C4⋊C8×C251C2212yes—
32C22⋊C8×C251C2212yes—
33#97×C251C2211yescharacteristic
34C4×C8×C251C2211yescharacteristic
35C2×Dic502—24no—
36C2×Dic502—21no—
37C2×Dic502C2312yes—
38C2×D1004—22no—
39C2×D1004C2312yes—
40C2×C22⋊D251—22no—
41C22×Dic251—21no—
42C2×C4×D251—22no—
43#16860799—24no—
44#16860799—24no—
45C4⋊Dic251C2312yes—
46C4⋊Dic251C2312yes—
47Dic251⋊C4—22no—
48Dic251⋊C4—22no—
49Dic251⋊C4—22no—
50C22⋊Dic251—21no—
51(C2×D251)⋊C4—22no—
52(C2×D251)⋊C4—22no—
53C4×Dic251—22no—
54C4×Dic251—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—
64Dic502—24no—
65Dic502—22no—
66Dic502#4114yes—
67D1004—22no—
68D1004—22no—
69D1004—82no—
70C22⋊D251—82no—
71C2×Dic251—24no—
72C2×Dic251—22no—
73C2×Dic251—22no—
74C2×Dic251—22no—
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—42no—
88C2×D251—42no—
89C2×D251—42no—
90C4×C251—21no—
91C4×C251—22no—
92C4×C251—22no—
93C4×C251C2×#4112yes—
94Dic251—24no—
95Dic251—42no—
96Dic251—42no—
97C2×C251—41no—
98C2×C251#52511yescharacteristic
99C2×C251#57712yes—
100D251—82no—
101C251#312611yescharacteristic, complemented, Sylow
102#3126—2511nomaximal, Sylow
103#540—2511no—
104#519—2511no—
105#482—2512no—
106#479—2512no—
107#460—2512no—
108#448—2512no—
109#440—2512no—
110C4×SD16—2512no—
111#433D25111yescharacteristic, complemented
112C22×Q8—2511no—
113C2×SD16—2512no—
114C2×SD16—2512no—
115#127—2511no—
116#125—2511no—
117#123—5022no—
118#121—5022no—
119#121—2512no—
120C4×Q8—5022no—
121C4×Q8—2512no—
122C4×Q8—2512no—
123C4×D4—2512no—
124#117—5022no—
125#117—2511no—
126#117C2×D25111yescharacteristic
127#107—2512no—
128#106—2512no—
129C4⋊C8C2×D25112yes—
130#103—2512no—
131#103—2512no—
132#102—2512no—
133#102—2512no—
134C22⋊C8C2×D25112yes—
135#97C2×D25111yescharacteristic
136C4×C8C2×D25111yescharacteristic
137C2×Q8—5024no—
138C2×Q8—5021no—
139C2×Q8—2512no—
140C2×D4—5022no—
141C2×D4—5022no—
142C2×D4—2512no—
143C22×C4—5022no—
144C22×C4—5021no—
145C22×C4C22×D25111yescharacteristic
146SD16—5024no—
147SD16—5024no—
148C2×C8C22×D25112yes—
149C2×C8C22×D25112yes—
150C4⋊C4—5022no—
151C4⋊C4—5022no—
152C4⋊C4—5022no—
153C4⋊C4—2512no—
154C4⋊C4—2512no—
155C4⋊C4D100412yes—
156C22⋊C4—5021no—
157C22⋊C4—5022no—
158C22⋊C4—5022no—
159C22⋊C4D100412yes—
160C42—5022no—
161C42—5022no—
162C42—5021no—
163C42C22×D25111yescharacteristic
164C42C22×D25111yescharacteristic
165C23—5022no—
166C23C2×D100411yescharacteristic
167Q8—5024no—
168Q8—5022no—
169Q8—2514no—
170D4—20082no—
171D4—20082no—
172D4—5022no—
173D4—5022no—
174C2×C4—22no—
175C2×C4—20082no—
176C2×C4—5022no—
177C2×C4—5022no—
178C2×C4—5024no—
179C2×C4—5022no—
180C2×C4C2×D100412yes—
181C2×C4C2×D100412yes—
182C2×C4C2×D100411yescharacteristic
183C2×C4C23×D25111yescharacteristic
184C8—22no—
185C8—22no—
186C22—21no—
187C22—22no—
188C22—10042no—
189C22—10042no—
190C22—10042no—
191C22C22×D100411yescharacteristic
192C4—21no—
193C4—22no—
194C4—22no—
195C4—10042no—
196C4—10042no—
197C4—5024no—
198C4#41×D25112yes—
199C2—41no—
200C2—20082no—
201C2#3063219911yescharacteristic
202C2#3063249912yes—
subgroupG/H
centerC22C22×D1004
commutator, cosocleC2×C4×C251C24
FrattiniC2×C4C23×D251
Fitting#433×C251C2
socleC22×C251C22×D4
prime radical#30632292C2
hypercenter#433D251
hypocenterC251#3126
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
2. #30632164C2semidirect
3. #30632012C2semidirect
4. #30631995C2semidirect
5. #30631888C2semidirect
6. #30631828C2semidirect
7. #30631789C2semidirect
8. C4×#16860799C2semidirect
9. #433×C251C2semidirect
101. C251#3126semidirect
111. #433D251semidirect

Maximal subgroups

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

subgroupindex
#306322922
#306321642
#306320122
#306319952
#306318882
#306318282
#306317892
C4×#168607992
#433×C2512
#3126251