Finite Group Databasebeta

← #44549629

Subgroups — #44549629

Order 32128.

234 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 57 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#30632352C211yesmaximal, characteristic
2#30632083C211yesmaximal, characteristic, complemented
3#30631973C211yesmaximal, characteristic, complemented
4#30631893C211yesmaximal, characteristic
5#30631417C211yesmaximal, characteristic, complemented
6#30631414C211yesmaximal, characteristic
7#332×C251C211yesmaximal, characteristic, complemented
8C2×Q8×D251—21no—
9C2×#16860799—21no—
10#22548715C2211yescharacteristic
11#22548714—21no—
12#22548693—22no—
13#22548691—21no—
14C4×Dic502C2211yescharacteristic
15C4×D1004C2211yescharacteristic
16#22548677—21no—
17#22548647—21no—
18#22548646—22no—
19#22548640—21no—
20#22548640—21no—
21C4×C251⋊C8C2211yescharacteristic
22C4⋊Q8×C251C2211yescharacteristic
23C4⋊C8×C251C2211yescharacteristic
24C4⋊C8×C251C2211yescharacteristic
25C2×Dic502—22no—
26C2×Dic502—21no—
27C2×Dic502D411yescharacteristic
28Q8×D251—42no—
29Q8×D251—42no—
30C2×D1004D411yescharacteristic
31C2×C4×D251—22no—
32C2×C4×D251—21no—
33#16860799—42no—
34C2×C251⋊C8—21no—
35C4⋊Dic251—21no—
36C4⋊Dic251—21no—
37C4⋊Dic251D411yescharacteristic
38C4⋊Dic251D411yescharacteristic
39Dic251⋊C4—22no—
40Dic251⋊C4—21no—
41(C2×D251)⋊C4—22no—
42(C2×D251)⋊C4—21no—
43C4×Dic251—21no—
44C2×Q8×C251—21no—
45C2×C8×C251—21no—
46C2×C8×C251—21no—
47C4⋊C4×C251—21no—
48C4⋊C4×C251D412yes—
49C42×C251C2311yescharacteristic
50C22×D251—21no—
51Dic502—21no—
52Dic502—44no—
53Dic502—41no—
54Dic502—41no—
55Dic502SD1612yescomplemented
56D1004—21no—
57D1004SD1612yes—
58C2×Dic251—21no—
59C2×Dic251—21no—
60C2×Dic251—21no—
61C2×Dic251—41no—
62C4×D251—44no—
63C4×D251—41no—
64C4×D251—41no—
65C251⋊C8—22no—
66Q8×C251—41no—
67Q8×C251—41no—
68C2×C4×C251—22no—
69C2×C4×C251C2×D411yescharacteristic
70C2×C4×C251C2×D411yescharacteristic
71C2×C4×C251C2×D411yescharacteristic
72C8×C251—41no—
73C8×C251—41no—
74C22×C251#12011yescharacteristic
75C2×D251—22no—
76C2×D251—41no—
77C2×D251—41no—
78C4×C251—21no—
79C4×C251—42no—
80C4×C251C2×SD1611yescharacteristic
81C4×C251C2×SD1611yescharacteristic
82C4×C251AGL(1,ℤ/8)11yescharacteristic
83C4×C251#13711yescharacteristic
84Dic251—22no—
85Dic251—41no—
86Dic251—41no—
87Dic251—81no—
88C2×C251#44811yescharacteristic
89C2×C251#45011yescharacteristic
90C2×C251#45611yescharacteristic
91D251—42no—
92C251#165111yescharacteristic, complemented, Sylow
93#1651—2511nomaximal, Sylow
94D4×Q8—2511no—
95#498—2511no—
96#475—2511no—
97#461—2511no—
98#332D25111yescharacteristic, complemented
99Q8⋊C8—2511no—
100D4⋊C8—2511no—
101C22×Q8—5021no—
102C2×SD16—5021no—
103C4⋊Q8—5021no—
104C4⋊Q8—2511no—
105C4⋊Q8C2×D25111yescharacteristic
106C22⋊Q8—5021no—
107C22⋊Q8—5022no—
108C4×Q8—2511no—
109C4×D4—5021no—
110C4×D4—2511no—
111#106—5021no—
112#106—5022no—
113C4⋊C8C2×D25111yescharacteristic
114C4⋊C8C2×D25111yescharacteristic
115#103—5021no—
116#103—5021no—
117C4×C8—2511no—
118C2×Q8—21no—
119C2×Q8—10042no—
120C2×Q8—10042no—
121C2×Q8—5022no—
122C2×Q8—5021no—
123C2×Q8—2511no—
124C2×D4—2511no—
125C22×C4—5022no—
126C22×C4—5021no—
127SD16—10042no—
128C2×C8—21no—
129C2×C8—21no—
130C2×C8—5021no—
131C4⋊C4—21no—
132C4⋊C4—5022no—
133C4⋊C4—5021no—
134C4⋊C4—5021no—
135C4⋊C4—5021no—
136C4⋊C4—2511no—
137C4⋊C4—2511no—
138C4⋊C4D100412yes—
139C22⋊C4—5022no—
140C22⋊C4—5021no—
141C42—5021no—
142C42C22×D25111yescharacteristic
143C23—5021no—
144Q8—41no—
145Q8—41no—
146Q8—10044no—
147Q8—10041no—
148Q8—10041no—
149Q8—5021no—
150Q8—2512no—
151D4—5021no—
152D4—2512no—
153C2×C4—22no—
154C2×C4—10044no—
155C2×C4—10041no—
156C2×C4—10041no—
157C2×C4—10041no—
158C2×C4—5021no—
159C2×C4—5021no—
160C2×C4—5021no—
161C2×C4D4×D25111yescharacteristic
162C2×C4D4×D25111yescharacteristic
163C2×C4C2×D100411yescharacteristic
164C8—41no—
165C8—41no—
166C8—5022no—
167C22—10041no—
168C22—10041no—
169C22—5022no—
170C22#2254868511yescharacteristic
171C4—21no—
172C4—42no—
173C4—20081no—
174C4—10041no—
175C4—10041no—
176C4—5022no—
177C4SD16×D25111yescharacteristic
178C4SD16×D25111yescharacteristic
179C4#2254873911yescharacteristic
180C4#2254874711yescharacteristic
181C2—10042no—
182C2#3063182711yescharacteristic
183C2#3063183911yescharacteristic
184C2#3063187211yescharacteristic
subgroupG/H
centerC22#22548685
commutator, cosocleC42×C251C23
FrattiniC42C22×D251
Fitting#332×C251C2
socleC22×C251#120
prime radicalC2×D1004D4
hypercenter#332D251
hypocenterC251#1651
LCSG ▷ C42×C251 ▷ C22×C251 ▷ C251
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
2. #30632083C2semidirect
3. #30631973C2semidirect
5. #30631417C2semidirect
7. #332×C251C2semidirect
55. Dic502SD16semidirect
92. C251#1651semidirect
98. #332D251semidirect

Maximal subgroups

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

subgroupindex
#306323522
#306320832
#306319732
#306318932
#306314172
#306314142
#332×C2512
#1651251