Finite Group Databasebeta

← #37571005

Subgroups — #37571005

Order 24448.

238 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 63 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#27133199C211yesmaximal, characteristic
2#27132713C211yesmaximal, characteristic, complemented
3#27132508C211yesmaximal, characteristic, complemented
4#27132400C211yesmaximal, characteristic, complemented
5#27132398C211yesmaximal, characteristic
6#27132396C211yesmaximal, characteristic
7#328×C191C211yesmaximal, characteristic, complemented
8#20259317—21no—
9#20259313C411yescharacteristic, complemented
10#20259311C411yescharacteristic, complemented
11#20259306—21no—
12#20259296C2211yescharacteristic
13Q8×Dic191C411yescharacteristic, complemented
14#20259284C411yescharacteristic, complemented
15(C22⋊D191)⋊C4—21no—
16#20259280—21no—
17C2×C4×Dic191—21no—
18C2×C4×Dic191C2211yescharacteristic
19Dic191⋊C8—21no—
20C22⋊(C191⋊C8)C2211yescharacteristic
21C8×Dic191—21no—
22C191⋊#95—21no—
23C191⋊#95C2211yescharacteristic
24C22⋊Q8×C191C2211yescharacteristic
25C22⋊C8×C191C2211yescharacteristic
26#95×C191C2211yescharacteristic
27C2×D764C2×C411yescharacteristic
28C2×C22⋊D191—21no—
29C22×Dic191—21no—
30C22×Dic191D411yescharacteristic
31C22×Dic191D411yescharacteristic
32C2×C4×D191—21no—
33C2×C191⋊C8—21no—
34C4⋊Dic191—21no—
35C4⋊Dic191—21no—
36C4⋊Dic191C2×C411yescharacteristic
37Dic191⋊C4—21no—
38(C2×D191)⋊C4—21no—
39(C2×D191)⋊C4—21no—
40(C2×D191)⋊C4—21no—
41(C2×D191)⋊C4—21no—
42C4×Dic191—24no—
43C4×Dic191—21no—
44C4×Dic191C2×C411yescharacteristic
45C4×Dic191C2×C411yescharacteristic
46C4×Dic191D411yescharacteristic
47C4×Dic191D411yescharacteristic
48C2×Q8×C191C2×C411yescharacteristic
49C22×C4×C191—21no—
50C22×C4×C191C2311yescharacteristic
51C2×C8×C191—21no—
52C4⋊C4×C191—21no—
53C4⋊C4×C191C2×C411yescharacteristic
54C22⋊C4×C191—21no—
55C22×D191—21no—
56D764—41no—
57C22⋊D191—41no—
58C22⋊D191—41no—
59C2×Dic191—21no—
60C2×Dic191—21no—
61C2×Dic191—22no—
62C2×Dic191—22no—
63C2×Dic191—21no—
64C2×Dic191—41no—
65C2×Dic191—41no—
66C2×Dic191C22⋊C411yescharacteristic
67C2×Dic191C22⋊C411yescharacteristic
68C2×Dic191C22⋊C411yescharacteristic
69C2×Dic191C22⋊C411yescharacteristic
70C4×D191—42no—
71C191⋊C8—41no—
72C23×C191C2×D411yescharacteristic
73Q8×C191—41no—
74C2×C4×C191—22no—
75C2×C4×C191—21no—
76C2×C4×C191—21no—
77C2×C4×C191—41no—
78C2×C4×C191—41no—
79C2×C4×C191—41no—
80C2×C4×C191C22×C411yescharacteristic
81C2×C4×C191C2×D411yescharacteristic
82C8×C191—41no—
83C22×C191—21no—
84C22×C191—21no—
85C22×C191C2×C22⋊C411yescharacteristic
86C22×C191#13511yescharacteristic
87C22×C191#13511yescharacteristic
88C2×D191—41no—
89C2×D191—41no—
90C2×D191—41no—
91C4×C191—21no—
92C4×C191—21no—
93C4×C191—42no—
94C4×C191—41no—
95C4×C191—41no—
96Dic191—21no—
97Dic191—21no—
98Dic191—21no—
99Dic191—42no—
100Dic191—41no—
101Dic191#10412yes—
102C2×C191—21no—
103C2×C191—21no—
104C2×C191#41011yescharacteristic
105C2×C191#41611yescharacteristic
106C2×C191C2×#10411yescharacteristic
107D191—81no—
108C191#150011yescharacteristic, complemented, Sylow
109#1500—1911nomaximal, Sylow
110#529—1911no—
111#431—1911no—
112#376—1911no—
113#328—1911no—
114#328D19111yescharacteristic, complemented
115#327—1911no—
116#327—1911no—
117#126—3821no—
118#125—1911no—
119#124—1911no—
120#123—3821no—
121C22⋊Q8C2×D19111yescharacteristic
122#121—1911no—
123C4×Q8—1911no—
124C4×D4—3821no—
125C4×D4—1911no—
126#117—3821no—
127C2×C42—3821no—
128C2×C42—1911no—
129C4⋊C8—3821no—
130C22⋊C8—1911no—
131C22⋊C8C2×D19111yescharacteristic
132C4×C8—3821no—
133#95—3821no—
134#95—1911no—
135#95C2×D19111yescharacteristic
136C2×Q8C4×D19111yescharacteristic
137C2×D4—3821no—
138C2×D4—1911no—
139C22×C4—21no—
140C22×C4—3821no—
141C22×C4—3821no—
142C22×C4—1911no—
143C22×C4—1911no—
144C22×C4C22×D19111yescharacteristic
145C2×C8—21no—
146C2×C8—3821no—
147C4⋊C4—21no—
148C4⋊C4—3821no—
149C4⋊C4—3821no—
150C4⋊C4—3821no—
151C4⋊C4—1911no—
152C4⋊C4C4×D19111yescharacteristic
153C22⋊C4—21no—
154C22⋊C4—3821no—
155C22⋊C4—3821no—
156C22⋊C4—3821no—
157C22⋊C4—3821no—
158C42—3824no—
159C42—3821no—
160C42—1911no—
161C42—1911no—
162C42—1911no—
163C42—1911no—
164C23—3821no—
165C23D4×D19111yescharacteristic
166Q8—41no—
167D4—7641no—
168D4—7641no—
169D4—7641no—
170C2×C4—22no—
171C2×C4—21no—
172C2×C4—21no—
173C2×C4—41no—
174C2×C4—41no—
175C2×C4—41no—
176C2×C4—3821no—
177C2×C4—3821no—
178C2×C4—3822no—
179C2×C4—3822no—
180C2×C4—3821no—
181C2×C4—1911no—
182C2×C4—1911no—
183C2×C4—1911no—
184C2×C4—1911no—
185C2×C4—7642no—
186C2×C4—7641no—
187C2×C4—7641no—
188C2×C4C2×C4×D19111yescharacteristic
189C2×C4D4×D19111yescharacteristic
190C8—41no—
191C8—7641no—
192C22—21no—
193C22—21no—
194C22—7641no—
195C22—7641no—
196C22—7641no—
197C22C22⋊C4×D19111yescharacteristic
198C22#2025934311yescharacteristic
199C22#2025934511yescharacteristic
200C4—21no—
201C4—21no—
202C4—42no—
203C4—41no—
204C4—41no—
205C4—3821no—
206C4—3821no—
207C4—3821no—
208C4—1912no—
209C4—7642no—
210C4—7641no—
211C2—21no—
212C2—21no—
213C2—15281no—
214C2#2713263511yescharacteristic
215C2#2713265811yescharacteristic
216C2#104×D19111yescharacteristic
subgroupG/H
centerC22C22⋊C4×D191
commutatorC2×C4×C191C22×C4
FrattiniC22×C4C22×D191
Fitting#328×C191C2
socleC22×C191C2×C22⋊C4
prime radical#20259296C22
cosocleC22×C4×C191C23
hypercenter#328D191
hypocenterC191#1500
LCSG ▷ C2×C4×C191 ▷ C22×C191 ▷ C191
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
2. #27132713C2semidirect
3. #27132508C2semidirect
4. #27132400C2semidirect
7. #328×C191C2semidirect
9. #20259313C4semidirect
10. #20259311C4semidirect
13. Q8×Dic191C4semidirect
14. #20259284C4semidirect
108. C191#1500semidirect
114. #328D191semidirect

Maximal subgroups

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

subgroupindex
#271331992
#271327132
#271325082
#271324002
#271323982
#271323962
#328×C1912
#1500191