Finite Group Databasebeta

← #37583982

Subgroups — #37583982

Order 24448.

346 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 109 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#27133286C212yesmaximal, complemented
2#27132956C212yesmaximal, complemented
3#27132942C212yesmaximal, complemented
4#27132911C212yesmaximal, complemented
5#27132899C211yesmaximal, characteristic
6#27132887C212yesmaximal, complemented
7#27132881C212yesmaximal, complemented
8#27132689C211yesmaximal, characteristic, complemented
9#467×C191C211yesmaximal, characteristic, complemented
10C2×#15690274C2212yes—
11C2×D1528C2211yescharacteristic
12C2×#15690271C2211yescharacteristic
13#20259321C2212yes—
14#20259317—22no—
15#20259311C2212yes—
16#20259308—22no—
17#20259304—22no—
18#20259302—22no—
19#20259296C2212yes—
20Q8×Dic191C2212yes—
21#20259284C2212yes—
22#20259281C2211yescharacteristic
23#20259256C2211yescharacteristic
24#20259255C2212yes—
25Dic191⋊C8C2212yes—
26Dic191⋊C8C2212yes—
27#20259246C2212yes—
28#20259244C2212yes—
29#20259242C2212yes—
30C2×Q16×C191C2211yescharacteristic
31C22×C8×C191C2211yescharacteristic
32C22⋊Q8×C191C2212yes—
33#107×C191C2211yescharacteristic
34#103×C191C2212yes—
35C2×Dic382—22no—
36C2×D764C2312yes—
37C2×C22⋊D191—22no—
38C2×C4×D191—22no—
39#15690274—42no—
40D1528—41no—
41#15690271—41no—
42C2×C191⋊C8C2312yes—
43C4⋊Dic191—22no—
44C4⋊Dic191D411yescharacteristic
45C4⋊Dic191D411yescharacteristic
46C4⋊Dic191C2312yes—
47Dic191⋊C4—22no—
48C22⋊Dic191D412yes—
49(C2×D191)⋊C4—22no—
50(C2×D191)⋊C4—22no—
51(C2×D191)⋊C4—22no—
52(C2×D191)⋊C4—22no—
53C4×Dic191—22no—
54C4×Dic191C2312yes—
55C2×Q8×C191C2312yes—
56C22×C4×C191C2311yescharacteristic
57Q16×C191—41no—
58C2×C8×C191—41no—
59C2×C8×C191C2311yescharacteristic
60C2×C8×C191C2311yescharacteristic
61C4⋊C4×C191—22no—
62C4⋊C4×C191C2312yes—
63C22⋊C4×C191—22no—
64C22×D191—22no—
65Dic382—82no—
66D764—22no—
67D764—22no—
68C22⋊D191—82no—
69C2×Dic191—22no—
70C2×Dic191C2×D412yes—
71C2×Dic191C2×D412yes—
72C4×D191—82no—
73C191⋊C8—22no—
74C23×C191C2×D411yescharacteristic
75Q8×C191—22no—
76Q8×C191—22no—
77C2×C4×C191—21no—
78C2×C4×C191—21no—
79C2×C4×C191—22no—
80C2×C4×C191—22no—
81C2×C4×C191C2×D411yescharacteristic
82C2×C4×C191C2411yescharacteristic
83C8×C191—21no—
84C8×C191—21no—
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—42no—
94C4×C191—42no—
95C4×C191H(5,𝔽2)11yescharacteristic
96C4×C1912−1+411yescharacteristic
97Dic191—22no—
98Dic191—22no—
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#467D19111yescharacteristic, complemented
112#466—1911no—
113#464—1912no—
114#463—1912no—
115#424—1911no—
116C2×Q16C2×D19111yescharacteristic
117C2×SD16—1912no—
118C2×D8—1911no—
119C2×M16—1911no—
120C22×C8C2×D19111yescharacteristic
121C4⋊Q8—1912no—
122#126—3822no—
123#124—3822no—
124#124—1912no—
125#123—3822no—
126C22⋊Q8—3822no—
127C22⋊Q8C2×D19112yes—
128#121—1912no—
129C4×Q8—1912no—
130C4×D4—1912no—
131#117—1911no—
132#107—1911no—
133#107—1912no—
134#107C2×D19111yescharacteristic
135C4⋊C8—1912no—
136C4⋊C8—1912no—
137#103—1912no—
138#103C2×D19112yes—
139#102—1912no—
140#102—1912no—
141C2×Q8—3822no—
142C2×Q8C22×D19112yes—
143C2×D4—3822no—
144C2×D4—1912no—
145C22×C4—3822no—
146C22×C4C22×D19111yescharacteristic
147Q16—41no—
148SD16—7642no—
149D8—7641no—
150M16—7641no—
151C2×C8—41no—
152C2×C8—1912no—
153C2×C8C22×D19111yescharacteristic
154C2×C8C22×D19111yescharacteristic
155C4⋊C4—22no—
156C4⋊C4—3822no—
157C4⋊C4—3822no—
158C4⋊C4—1912no—
159C4⋊C4—1911no—
160C4⋊C4—1911no—
161C4⋊C4C22×D19112yes—
162C22⋊C4—22no—
163C22⋊C4—3822no—
164C22⋊C4—3822no—
165C22⋊C4—3822no—
166C22⋊C4—3822no—
167C22⋊C4—1912no—
168C42—3822no—
169C42—1912no—
170C23—3822no—
171C23D4×D19111yescharacteristic
172Q8—22no—
173Q8—22no—
174Q8—15282no—
175D4—3822no—
176D4—3822no—
177D4—15282no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—3822no—
183C2×C4—1912no—
184C2×C4—1912no—
185C2×C4—15282no—
186C2×C4D4×D19111yescharacteristic
187C2×C4C23×D19111yescharacteristic
188C8—21no—
189C8—21no—
190C8—3822no—
191C22—21no—
192C22—21no—
193C22—21no—
194C22—7642no—
195C22—7642no—
196C22—7642no—
197C22C2×D4×D19111yescharacteristic
198C4—21no—
199C4—42no—
200C4—42no—
201C4—3822no—
202C4—3822no—
203C4—7642no—
204C4#2025936711yescharacteristic
205C4#2025936911yescharacteristic
206C2—41no—
207C2—15282no—
208C2#2713324011yescharacteristic
209C2#2713346511yescharacteristic
210C2#2713347611yescharacteristic
subgroupG/H
centerC22C2×D4×D191
commutator, cosocleC2×C4×C191C24
FrattiniC2×C4C23×D191
Fitting#467×C191C2
socleC22×C191C22×D4
prime radical#27132899C2
hypercenter#467D191
hypocenterC191#3262
LCSG ▷ C2×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C22 ◁ C22×C4 ◁ #467

Complements

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

NH ≅ G/Ntype
1. #27133286C2semidirect
2. #27132956C2semidirect
3. #27132942C2semidirect
4. #27132911C2semidirect
6. #27132887C2semidirect
7. #27132881C2semidirect
8. #27132689C2semidirect
9. #467×C191C2semidirect
105. C191#3262semidirect
111. #467D191semidirect

Maximal subgroups

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

subgroupindex
#271332862
#271329562
#271329422
#271329112
#271328992
#271328872
#271328812
#271326892
#467×C1912
#3262191