Finite Group Databasebeta

← #37571567

Subgroups — #37571567

Order 24448.

240 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 49 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#27133253C211yesmaximal, characteristic
2#27132981C211yesmaximal, characteristic, complemented
3#27132598C211yesmaximal, characteristic, complemented
4#27132400C211yesmaximal, characteristic, complemented
5#27132398C211yesmaximal, characteristic, complemented
6#27132386C211yesmaximal, characteristic, complemented
7#484×C191C211yesmaximal, characteristic, complemented
8#20259317—21no—
9#20259311—21no—
10#20259307—21no—
11#20259297—21no—
12#20259296C2211yescharacteristic
13#20259292—21no—
14(C22⋊D191)⋊C4—21no—
15C2×Dic191⋊C4—21no—
16C2×(C2×D191)⋊C4—21no—
17C2×(C2×D191)⋊C4C2211yescharacteristic
18#20259253—21no—
19#20259242—21no—
20C22⋊(C191⋊C8)C2211yescharacteristic
21C191⋊#95C2211yescharacteristic
22C22⋊Q8×C191C2211yescharacteristic
23C2×C4⋊C4×C191C2211yescharacteristic
24#107×C191—21no—
25#103×C191—21no—
26C22⋊C8×C191C2211yescharacteristic
27C23×D191D411yescharacteristic
28C2×D764—21no—
29C2×D764—21no—
30C2×D764D411yescharacteristic
31C2×C22⋊D191—21no—
32C22×Dic191—21no—
33C22×Dic191D411yescharacteristic
34C2×C4×D191—21no—
35C2×C191⋊C8—21no—
36C4⋊Dic191D411yescharacteristic
37Dic191⋊C4—21no—
38Dic191⋊C4—42no—
39(C2×D191)⋊C4—21no—
40(C2×D191)⋊C4—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—
46C4×Dic191—21no—
47C2×Q8×C191D411yescharacteristic
48C22×C4×C191—21no—
49C22×C4×C191C2311yescharacteristic
50C2×C8×C191—21no—
51C4⋊C4×C191—21no—
52C4⋊C4×C191—21no—
53C4⋊C4×C191—21no—
54C4⋊C4×C191D411yescharacteristic
55C22⋊C4×C191—21no—
56C22×D191—21no—
57C22×D191—21no—
58C22×D191—21no—
59C22×D191—21no—
60C22×D191—41no—
61C22×D191—41no—
62D764—41no—
63D764—81no—
64D764—81no—
65C22⋊D191—41no—
66C22⋊D191—41no—
67C2×Dic191—22no—
68C2×Dic191—21no—
69C2×Dic191—21no—
70C2×Dic191—41no—
71C2×Dic191—41no—
72C2×Dic191—41no—
73C4×D191—81no—
74C191⋊C8—41no—
75C23×C191C2×D411yescharacteristic
76Q8×C191—41no—
77C2×C4×C191—21no—
78C2×C4×C191—21no—
79C2×C4×C191—41no—
80C2×C4×C191—41no—
81C2×C4×C191—41no—
82C2×C4×C191—41no—
83C2×C4×C191C2×D411yescharacteristic
84C2×C4×C191C2×D411yescharacteristic
85C8×C191—41no—
86C22×C191—21no—
87C22×C191—21no—
88C22×C191#12011yescharacteristic
89C22×C191#13511yescharacteristic
90C22×C191#13711yescharacteristic
91C2×D191—42no—
92C2×D191—41no—
93C2×D191—41no—
94C2×D191—41no—
95C2×D191—41no—
96C2×D191—41no—
97C2×D191—41no—
98C2×D191—81no—
99C4×C191—21no—
100C4×C191—21no—
101C4×C191—41no—
102C4×C191—41no—
103C4×C191—81no—
104Dic191—42no—
105Dic191—41no—
106Dic191—41no—
107C2×C191—21no—
108C2×C191—21no—
109C2×C191#45211yescharacteristic
110C2×C191#45311yescharacteristic
111C2×C191#45811yescharacteristic
112D191—81no—
113D191—81no—
114C191#161811yescharacteristic, complemented, Sylow
115#1618—1911nomaximal, Sylow
116#538—1911no—
117#484D19111yescharacteristic, complemented
118#481—1911no—
119#399—1911no—
120#328—1911no—
121#327—1911no—
122#323—1911no—
123#126—3821no—
124#124—3821no—
125#123—3821no—
126C22⋊Q8C2×D19111yescharacteristic
127#121—3821no—
128#121—1911no—
129#120—3821no—
130C4×D4—3821no—
131C2×C4⋊C4—3821no—
132C2×C4⋊C4C2×D19111yescharacteristic
133C2×C22⋊C4—3821no—
134C2×C22⋊C4—1911no—
135#107—21no—
136#106—3821no—
137#103—21no—
138#102—3821no—
139C22⋊C8—1911no—
140C22⋊C8C2×D19111yescharacteristic
141#95—1911no—
142C24—1911no—
143C2×Q8C22⋊D19111yescharacteristic
144C2×D4—3821no—
145C2×D4—3821no—
146C2×D4—3821no—
147C2×D4—1911no—
148C22×C4—21no—
149C22×C4—3821no—
150C22×C4—3821no—
151C22×C4—1911no—
152C22×C4C22×D19111yescharacteristic
153C2×C8—21no—
154C2×C8—3821no—
155C4⋊C4—21no—
156C4⋊C4—21no—
157C4⋊C4—21no—
158C4⋊C4—3821no—
159C4⋊C4—1911no—
160C4⋊C4—7642no—
161C4⋊C4C22⋊D19111yescharacteristic
162C22⋊C4—21no—
163C22⋊C4—3821no—
164C22⋊C4—3821no—
165C22⋊C4—3821no—
166C22⋊C4—3821no—
167C22⋊C4—3821no—
168C22⋊C4—3821no—
169C22⋊C4—7642no—
170C42—3821no—
171C23—3821no—
172C23—3821no—
173C23—3821no—
174C23—3821no—
175C23—7641no—
176C23—7641no—
177C23D4×D19111yescharacteristic
178Q8—41no—
179D4—15281no—
180D4—15281no—
181D4—7641no—
182D4—7641no—
183D4—7641no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—41no—
190C2×C4—3822no—
191C2×C4—3821no—
192C2×C4—3821no—
193C2×C4—15281no—
194C2×C4—7641no—
195C2×C4—7641no—
196C2×C4—7641no—
197C2×C4D4×D19111yescharacteristic
198C2×C4C2×C22⋊D19111yescharacteristic
199C8—41no—
200C8—7641no—
201C22—21no—
202C22—21no—
203C22—15281no—
204C22—7642no—
205C22—7641no—
206C22—7641no—
207C22—7641no—
208C22—7641no—
209C22—7641no—
210C22—7641no—
211C22#2025929011yescharacteristic
212C22#2025934511yescharacteristic
213C22#2025935411yescharacteristic
214C4—21no—
215C4—21no—
216C4—41no—
217C4—41no—
218C4—81no—
219C4—7642no—
220C4—7641no—
221C4—7641no—
222C2—21no—
223C2—21no—
224C2—15281no—
225C2—15281no—
226C2#2713282411yescharacteristic
227C2#2713282911yescharacteristic
228C2#2713285211yescharacteristic
subgroupG/H
centerC22#20259290
commutator, cosocleC22×C4×C191C23
FrattiniC22×C4C22×D191
Fitting#484×C191C2
socleC22×C191#120
prime radical#27133253C2
hypercenter#484D191
hypocenterC191#1618
LCSG ▷ C22×C4×C191 ▷ C22×C191 ▷ C191
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
2. #27132981C2semidirect
3. #27132598C2semidirect
4. #27132400C2semidirect
5. #27132398C2semidirect
6. #27132386C2semidirect
7. #484×C191C2semidirect
114. C191#1618semidirect
117. #484D191semidirect

Maximal subgroups

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

subgroupindex
#271332532
#271329812
#271325982
#271324002
#271323982
#271323862
#484×C1912
#1618191