Finite Group Databasebeta

← #37571509

Subgroups — #37571509

Order 24448.

228 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 51 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#27133288C211yesmaximal, characteristic
2#27132993C211yesmaximal, characteristic, complemented
3#27132589C211yesmaximal, characteristic
4#27132401C211yesmaximal, characteristic, complemented
5#27132400C211yesmaximal, characteristic, complemented
6#27132386C211yesmaximal, characteristic
7#483×C191C211yesmaximal, characteristic, complemented
8#20259302—21no—
9#20259301C2211yescharacteristic
10#20259300—21no—
11#20259300—21no—
12#20259299—21no—
13#20259298—21no—
14C2×(C2×D191)⋊C4—21no—
15C2×(C2×D191)⋊C4C2211yescharacteristic
16C22⋊C4×D191—21no—
17#20259253—21no—
18#20259245—21no—
19C22⋊(C191⋊C8)C2211yescharacteristic
20C191⋊#95—21no—
21C191⋊#95C2211yescharacteristic
22C22⋊Q8×C191C2211yescharacteristic
23C2×C4⋊C4×C191C2211yescharacteristic
24#106×C191—21no—
25#103×C191—21no—
26C22⋊C8×C191C2211yescharacteristic
27C23×D191D411yescharacteristic
28C2×Dic382—21no—
29C2×Dic382D411yescharacteristic
30C22×Dic191—21no—
31C22×Dic191D411yescharacteristic
32C2×C4×D191—21no—
33C2×C4×D191—21no—
34C2×C191⋊C8—21no—
35C4⋊Dic191—21no—
36C4⋊Dic191D411yescharacteristic
37Dic191⋊C4—21no—
38Dic191⋊C4—21no—
39Dic191⋊C4—21no—
40C22⋊Dic191—21no—
41(C2×D191)⋊C4—21no—
42(C2×D191)⋊C4—21no—
43(C2×D191)⋊C4—21no—
44(C2×D191)⋊C4—21no—
45(C2×D191)⋊C4—42no—
46C2×Q8×C191D411yescharacteristic
47C22×C4×C191—21no—
48C22×C4×C191C2311yescharacteristic
49C2×C8×C191—21no—
50C4⋊C4×C191—21no—
51C4⋊C4×C191—21no—
52C4⋊C4×C191—21no—
53C4⋊C4×C191D411yescharacteristic
54C22⋊C4×C191—21no—
55C22×D191—21no—
56C22×D191—21no—
57C22×D191—41no—
58C22×D191—41no—
59C22×D191SD1612yes—
60Dic382—41no—
61Dic382—81no—
62C2×Dic191—21no—
63C2×Dic191—21no—
64C2×Dic191—21no—
65C2×Dic191—41no—
66C2×Dic191—41no—
67C2×Dic191—41no—
68C2×Dic191—41no—
69C4×D191—81no—
70C4×D191—81no—
71C191⋊C8—41no—
72C23×C191C2×D411yescharacteristic
73Q8×C191—41no—
74C2×C4×C191—21no—
75C2×C4×C191—21no—
76C2×C4×C191—41no—
77C2×C4×C191—41no—
78C2×C4×C191—41no—
79C2×C4×C191—41no—
80C2×C4×C191C2×D411yescharacteristic
81C2×C4×C191C2×D411yescharacteristic
82C8×C191—41no—
83C22×C191—21no—
84C22×C191—21no—
85C22×C191#12011yescharacteristic
86C22×C191C2×SD1611yescharacteristic
87C22×C191#13711yescharacteristic
88C2×D191—22no—
89C2×D191—41no—
90C2×D191—41no—
91C2×D191—42no—
92C2×D191—81no—
93C4×C191—21no—
94C4×C191—21no—
95C4×C191—41no—
96C4×C191—41no—
97C4×C191—81no—
98Dic191—41no—
99Dic191—41no—
100Dic191—41no—
101Dic191—81no—
102C2×C191—21no—
103C2×C191—21no—
104C2×C191#44811yescharacteristic
105C2×C191#45511yescharacteristic
106C2×C191#45811yescharacteristic
107D191—42no—
108C191#160811yescharacteristic, complemented, Sylow
109#1608—1911nomaximal, Sylow
110#543—1911no—
111#483—1911no—
112#483D19111yescharacteristic, complemented
113#397—1911no—
114#328—1911no—
115#328—1911no—
116#323—1911no—
117C22⋊Q8—3821no—
118C22⋊Q8—3821no—
119C22⋊Q8—3821no—
120C22⋊Q8—3821no—
121C22⋊Q8—3821no—
122C22⋊Q8—1911no—
123C22⋊Q8C2×D19111yescharacteristic
124C2×C4⋊C4C2×D19111yescharacteristic
125C2×C22⋊C4—3821no—
126C2×C22⋊C4—3821no—
127C2×C22⋊C4—1911no—
128#106—21no—
129#106—3821no—
130#103—21no—
131#103—3821no—
132C22⋊C8—1911no—
133C22⋊C8C2×D19111yescharacteristic
134#95—3821no—
135#95—1911no—
136C24—1911no—
137C2×Q8—3821no—
138C2×Q8—1911no—
139C2×Q8C22⋊D19111yescharacteristic
140C22×C4—21no—
141C22×C4—3821no—
142C22×C4—3821no—
143C22×C4—3821no—
144C22×C4—1911no—
145C22×C4C22×D19111yescharacteristic
146C2×C8—21no—
147C2×C8—3821no—
148C4⋊C4—21no—
149C4⋊C4—21no—
150C4⋊C4—21no—
151C4⋊C4—3821no—
152C4⋊C4—3821no—
153C4⋊C4—3821no—
154C4⋊C4—3821no—
155C4⋊C4—1911no—
156C4⋊C4C22⋊D19111yescharacteristic
157C22⋊C4—21no—
158C22⋊C4—3821no—
159C22⋊C4—3821no—
160C22⋊C4—3821no—
161C22⋊C4—3821no—
162C22⋊C4—3821no—
163C22⋊C4—7642no—
164C23—3821no—
165C23—3821no—
166C23—1912no—
167C23—7641no—
168C23—7641no—
169C23D4×D19111yescharacteristic
170Q8—41no—
171Q8—15281no—
172Q8—7641no—
173C2×C4—21no—
174C2×C4—21no—
175C2×C4—41no—
176C2×C4—41no—
177C2×C4—41no—
178C2×C4—41no—
179C2×C4—3821no—
180C2×C4—3821no—
181C2×C4—3821no—
182C2×C4—15281no—
183C2×C4—15281no—
184C2×C4—7641no—
185C2×C4—7641no—
186C2×C4—7641no—
187C2×C4—7641no—
188C2×C4D4×D19111yescharacteristic
189C2×C4C2×C22⋊D19111yescharacteristic
190C8—41no—
191C8—7641no—
192C22—21no—
193C22—21no—
194C22—3822no—
195C22—15281no—
196C22—7642no—
197C22—7641no—
198C22—7641no—
199C22#2025929011yescharacteristic
200C22SD16×D19111yescharacteristic
201C22#2025935111yescharacteristic
202C4—21no—
203C4—21no—
204C4—41no—
205C4—41no—
206C4—81no—
207C4—15281no—
208C4—7641no—
209C4—7641no—
210C4—7641no—
211C2—21no—
212C2—21no—
213C2—7642no—
214C2#2713280011yescharacteristic
215C2#2713283911yescharacteristic
216C2#2713285211yescharacteristic
subgroupG/H
centerC22#20259290
commutator, cosocleC22×C4×C191C23
FrattiniC22×C4C22×D191
Fitting#483×C191C2
socleC22×C191#120
prime radicalC23×D191D4
hypercenter#483D191
hypocenterC191#1608
LCSG ▷ C22×C4×C191 ▷ C22×C191 ▷ C191
UCSC1 ◁ C22 ◁ C22×C4 ◁ #483

Complements

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

NH ≅ G/Ntype
2. #27132993C2semidirect
4. #27132401C2semidirect
5. #27132400C2semidirect
7. #483×C191C2semidirect
108. C191#1608semidirect
112. #483D191semidirect

Maximal subgroups

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

subgroupindex
#271332882
#271329932
#271325892
#271324012
#271324002
#271323862
#483×C1912
#1608191