Finite Group Databasebeta

← #26137108

Subgroups — #26137108

Order 12032.

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

normal subgroups only

This group has 214 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
1C2×#15688958C211yesmaximal, characteristic, complemented
2C2×C32×D47C211yesmaximal, characteristic, complemented
3#20245475C211yesmaximal, characteristic, complemented
4#20245471C211yesmaximal, characteristic, complemented
5#20241587C211yesmaximal, characteristic, complemented
6#20241567C211yesmaximal, characteristic, complemented
7C47×#1415C211yesmaximal, characteristic, complemented
8C2×D752C2211yescharacteristic
9C2×C16×D47C2211yescharacteristic
10#15689360—21no—
11#15689356—21no—
12#15688958—22no—
13C2×C47⋊C32C2211yescharacteristic
14C32×D47—22no—
15#15688949C2211yescharacteristic
16#15688924—21no—
17#15688923—21no—
18C2×D16×C47C2211yescharacteristic
19C2×C32×C47C2211yescharacteristic
20C47×#366C2211yescharacteristic
21C2×D376—21no—
22C2×C8×D47D411yescharacteristic
23#13093999—41no—
24#13093995—41no—
25D752—21no—
26D752—21no—
27C2×C47⋊C16D411yescharacteristic
28C16×D47—21no—
29C16×D47—21no—
30#13093958—21no—
31#13093945—41no—
32#13093944—41no—
33C47⋊C32D412yescomplemented
34C2×D8×C47—21no—
35D16×C47—21no—
36D16×C47—21no—
37C2×C16×C47C2311yescharacteristic
38#107×C47—21no—
39C32×C47—21no—
40C2×D4×C47—41no—
41C2×C22⋊D47—81no—
42C2×D188—41no—
43C2×D188—81no—
44C2×C4×D47D811yescharacteristic
45D8×C47—41no—
46D8×C47—41no—
47C2×C8×C47C2×D411yescharacteristic
48C4⋊C4×C47—41no—
49C22⋊Dic47—81no—
50(C2×D47)⋊C4—81no—
51C4⋊Dic47—41no—
52C2×C47⋊C8D811yescharacteristic
53D376—41no—
54D376—41no—
55C8×D47—21no—
56C8×D47—21no—
57C16×C47C2×D411yescharacteristic
58C16×C47#4111yescharacteristic
59C47⋊C16—21no—
60C23×C47—81no—
61C22×D47—81no—
62C22×D47D1611yescharacteristic
63D4×C47—81no—
64D4×C47—81no—
65C2×C4×C47—81no—
66C2×C4×C47C2×D811yescharacteristic
67C22⋊D47—162no—
68C2×Dic47—81no—
69C2×Dic47D1611yescharacteristic
70D188—81no—
71D188—81no—
72D188—162no—
73C4×D47—21no—
74C4×D47—21no—
75C8×C47#12111yescharacteristic
76C8×C47#13511yescharacteristic
77C47⋊C8—21no—
78#13694—471nomaximal, Sylow
79C22×C47—161no—
80C22×C47—161no—
81C22×C47—161no—
82C22×C47C2×D1611yescharacteristic
83C2×D47—21no—
84C2×D47—21no—
85C2×D47—161no—
86C2×D47—161no—
87C2×D47—161no—
88C2×D47D3212yescomplemented
89C4×C47—161no—
90C4×C47#46611yescharacteristic
91C4×C47#50811yescharacteristic
92Dic47—21no—
93Dic47—161no—
94C2×D32—471no—
95C22×C32—471no—
96#2215—471no—
97#2215—471no—
98#1423—471no—
99#1415—471no—
100#1415D4711yescharacteristic, complemented
101C2×C47—321no—
102C2×C47#221511yescharacteristic
103C2×C47C2×D3211yescharacteristic
104C2×C47#226211yescharacteristic
105D47—22no—
106D47—321no—
107C2×D16—471no—
108C2×D16C2×D4711yescharacteristic
109C22×C16—471no—
110#466—941no—
111#466—941no—
112D32—942no—
113C2×C32—471no—
114C2×C32—942no—
115C2×C32C2×D4711yescharacteristic
116#366—471no—
117#366C2×D4711yescharacteristic
118#357—941no—
119#357—941no—
120C47#1369411yescharacteristic, complemented, Sylow
121C2×D8—21no—
122C2×D8—941no—
123C22×C8—471no—
124#121—1881no—
125#121—1881no—
126D16—21no—
127D16—21no—
128D16—941no—
129D16—941no—
130C2×C16—471no—
131C2×C16—941no—
132C2×C16—941no—
133C2×C16C22×D4711yescharacteristic
134#107—21no—
135#107—941no—
136#102—1881no—
137#102—1881no—
138C32—21no—
139C32—472no—
140C2×D4—41no—
141C2×D4—3761no—
142C2×D4—3761no—
143C2×D4—1881no—
144C22×C4—471no—
145D8—41no—
146D8—41no—
147D8—1881no—
148D8—1881no—
149C2×C8—471no—
150C2×C8—941no—
151C2×C8—941no—
152C2×C8D4×D4711yescharacteristic
153C4⋊C4—41no—
154C4⋊C4—1881no—
155C22⋊C4—3761no—
156C22⋊C4—3761no—
157C16—941no—
158C16#1062535011yescharacteristic
159C16D4×D4711yescharacteristic
160C23—81no—
161C23—471no—
162C23—3761no—
163D4—81no—
164D4—81no—
165D4—3761no—
166D4—3761no—
167D4—7522no—
168D4—7522no—
169C2×C4—81no—
170C2×C4—471no—
171C2×C4—941no—
172C2×C4—941no—
173C2×C4—3761no—
174C2×C4D8×D4711yescharacteristic
175C8—941no—
176C8#1309399711yescharacteristic
177C8#1309404511yescharacteristic
178C22—161no—
179C22—161no—
180C22—161no—
181C22—472no—
182C22—941no—
183C22—941no—
184C22—7521no—
185C22—7521no—
186C22—7521no—
187C22D16×D4711yescharacteristic
188C4—161no—
189C4—941no—
190C4—7521no—
191C4#1568935811yescharacteristic
192C4#1568955411yescharacteristic
193C2—321no—
194C2—942no—
195C2—15041no—
196C2#2024547311yescharacteristic
197C2D32×D4711yescharacteristic
198C2#2024569611yescharacteristic
subgroupG/H
centerC22D16×D47
commutator, cosocleC2×C16×C47C23
FrattiniC2×C16C22×D47
FittingC47×#1415C2
socleC22×C47C2×D16
hypercenter#1415D47
hypocenterC47#13694
LCSG ▷ C2×C16×C47 ▷ C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ #1415

Complements

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

NH ≅ G/Ntype
1. C2×#15688958C2semidirect
2. C2×C32×D47C2semidirect
3. #20245475C2semidirect
4. #20245471C2semidirect
5. #20241587C2semidirect
6. #20241567C2semidirect
7. C47×#1415C2semidirect
33. C47⋊C32D4semidirect
88. C2×D47D32semidirect
100. #1415D47semidirect
120. C47#13694semidirect

Maximal subgroups

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

subgroupindex
C2×#156889582
C2×C32×D472
#202454752
#202454712
#202415872
#202415672
C47×#14152
#1369447