Finite Group Databasebeta

← #37583981

Subgroups — #37583981

Order 24448.

346 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 117 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#27133284C212yesmaximal, complemented
2#27132959C212yesmaximal, complemented
3#27132944C212yesmaximal, complemented
4#27132909C212yesmaximal, complemented
5#27132904C211yesmaximal, characteristic, complemented
6#27132899C211yesmaximal, characteristic
7#27132886C212yesmaximal, complemented
8#27132879C212yesmaximal, complemented
9#424×C191C211yesmaximal, characteristic, complemented
10C2×Dic764C2211yescharacteristic
11C2×#15690276C2212yes—
12C2×D1528C2211yescharacteristic
13#20259322C2212yes—
14#20259317—22no—
15#20259310C2212yes—
16#20259308—22no—
17#20259304—22no—
18#20259301C2212yes—
19#20259300—22no—
20#20259296C2212yes—
21C4×Dic382C2212yes—
22C4×D764C2212yes—
23#20259256C2211yescharacteristic
24#20259256C2212yes—
25#20259256C2211yescharacteristic
26#20259247C2212yes—
27#20259247C2212yes—
28#20259244C2212yes—
29#20259244C2212yes—
30C2×M16×C191C2211yescharacteristic
31C22×C8×C191C2211yescharacteristic
32#117×C191C2211yescharacteristic
33C4⋊C8×C191C2212yes—
34C4⋊C8×C191C2212yes—
35C2×Dic382—22no—
36C2×Dic382C2312yes—
37C2×D764C2312yes—
38C2×C22⋊D191—22no—
39C2×C4×D191—22no—
40Dic764—41no—
41#15690276—42no—
42D1528—41no—
43C4⋊Dic191—22no—
44C4⋊Dic191C2312yes—
45C4⋊Dic191C2312yes—
46Dic191⋊C4—22no—
47Dic191⋊C4—22no—
48C22⋊Dic191—22no—
49(C2×D191)⋊C4—22no—
50(C2×D191)⋊C4—22no—
51(C2×D191)⋊C4—22no—
52(C2×D191)⋊C4—22no—
53C4×Dic191—22no—
54C22×C4×C191C2311yescharacteristic
55M16×C191—41no—
56C2×C8×C191—41no—
57C2×C8×C191C2311yescharacteristic
58C2×C8×C191C2312yes—
59C2×C8×C191C2311yescharacteristic
60C4⋊C4×C191D411yescharacteristic
61C4⋊C4×C191D411yescharacteristic
62C22⋊C4×C191D412yes—
63C42×C191C2312yes—
64C22×D191—22no—
65Dic382—22no—
66Dic382—22no—
67Dic382—82no—
68D764—22no—
69D764—22no—
70C22⋊D191—82no—
71C2×Dic191—22no—
72C2×Dic191—22no—
73C2×Dic191—22no—
74C4×D191—82no—
75C23×C191C2×D411yescharacteristic
76C2×C4×C191—21no—
77C2×C4×C191—21no—
78C2×C4×C191C2×D412yes—
79C2×C4×C191C2×D412yes—
80C2×C4×C191C2×D411yescharacteristic
81C2×C4×C191C2411yescharacteristic
82C8×C191—21no—
83C8×C191—21no—
84C8×C191—22no—
85C22×C191—21no—
86C22×C191—21no—
87C22×C191—21no—
88C22×C191C22×D411yescharacteristic
89C2×D191—42no—
90C2×D191—42no—
91C2×D191—42no—
92C4×C191—21no—
93C4×C191—22no—
94C4×C191—22no—
95C4×C191H(5,𝔽2)11yescharacteristic
96C4×C1912−1+411yescharacteristic
97Dic191—42no—
98Dic191—42no—
99Dic191—42no—
100C2×C191—41no—
101C2×C191#53711yescharacteristic
102C2×C191#57611yescharacteristic
103C2×C191#57811yescharacteristic
104D191—82no—
105C191#326211yescharacteristic, complemented, Sylow
106#3262—1911nomaximal, Sylow
107#542—1912no—
108#477—1912no—
109#474—1912no—
110#468—1912no—
111#467—1911no—
112#466—1911no—
113#464—1912no—
114#463—1912no—
115#424D19111yescharacteristic, complemented
116C2×Q16—1911no—
117C2×SD16—1912no—
118C2×D8—1911no—
119C2×M16C2×D19111yescharacteristic
120C22×C8C2×D19111yescharacteristic
121C4⋊Q8—1912no—
122#126—3822no—
123#124—3822no—
124#124—1912no—
125#123—3822no—
126C22⋊Q8—3822no—
127C22⋊Q8—1912no—
128#121—1912no—
129C4×Q8—1912no—
130C4×D4—1912no—
131#117C2×D19111yescharacteristic
132#107—1911no—
133#107—1911no—
134#107—1912no—
135C4⋊C8C2×D19112yes—
136C4⋊C8C2×D19112yes—
137#103—1912no—
138#103—1912no—
139#102—1912no—
140#102—1912no—
141C2×Q8—3822no—
142C2×Q8—1912no—
143C2×D4—3822no—
144C2×D4—1912no—
145C22×C4—3822no—
146C22×C4C22×D19111yescharacteristic
147Q16—7641no—
148SD16—7642no—
149D8—7641no—
150M16—41no—
151C2×C8—41no—
152C2×C8C22×D19111yescharacteristic
153C2×C8C22×D19112yes—
154C2×C8C22×D19111yescharacteristic
155C4⋊C4—3822no—
156C4⋊C4—3822no—
157C4⋊C4—3822no—
158C4⋊C4—1912no—
159C4⋊C4—1912no—
160C4⋊C4D76411yescharacteristic
161C4⋊C4D76411yescharacteristic
162C22⋊C4—3822no—
163C22⋊C4—3822no—
164C22⋊C4—3822no—
165C22⋊C4—3822no—
166C22⋊C4—3822no—
167C22⋊C4D76412yes—
168C42—3822no—
169C42C22×D19112yes—
170C23—3822no—
171C23C2×D76411yescharacteristic
172Q8—3822no—
173Q8—3822no—
174Q8—15282no—
175D4—3822no—
176D4—3822no—
177D4—15282no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—3822no—
181C2×C4—3822no—
182C2×C4—3822no—
183C2×C4—15282no—
184C2×C4C2×D76412yes—
185C2×C4C2×D76412yes—
186C2×C4C2×D76411yescharacteristic
187C2×C4C23×D19111yescharacteristic
188C8—21no—
189C8—21no—
190C8—22no—
191C22—21no—
192C22—21no—
193C22—21no—
194C22—7642no—
195C22—7642no—
196C22—7642no—
197C22C22×D76411yescharacteristic
198C4—22no—
199C4—22no—
200C4—21no—
201C4—7642no—
202C4—7642no—
203C4—7642no—
204C4#2025936711yescharacteristic
205C4#2025937011yescharacteristic
206C2—41no—
207C2—15282no—
208C2#2713324411yescharacteristic
209C2#2713346811yescharacteristic
210C2#2713348011yescharacteristic
subgroupG/H
centerC22C22×D764
commutator, cosocleC2×C4×C191C24
FrattiniC2×C4C23×D191
Fitting#424×C191C2
socleC22×C191C22×D4
prime radical#27132899C2
hypercenter#424D191
hypocenterC191#3262
LCSG ▷ C2×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C22 ◁ #117 ◁ #424

Complements

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

NH ≅ G/Ntype
1. #27133284C2semidirect
2. #27132959C2semidirect
3. #27132944C2semidirect
4. #27132909C2semidirect
5. #27132904C2semidirect
7. #27132886C2semidirect
8. #27132879C2semidirect
9. #424×C191C2semidirect
105. C191#3262semidirect
115. #424D191semidirect

Maximal subgroups

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

subgroupindex
#271332842
#271329592
#271329442
#271329092
#271329042
#271328992
#271328862
#271328792
#424×C1912
#3262191