Finite Group Databasebeta

← #37580894

Subgroups — #37580894

Order 24448.

524 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 524 conjugacy classes of subgroups — too many to draw. Only its 153 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
1C2×#20259313C211yesmaximal, characteristic, complemented
2C2×#20259311C211yesmaximal, characteristic
3#27132570C211yesmaximal, characteristic, complemented
4#27132565C211yesmaximal, characteristic
5#27132564C211yesmaximal, characteristic
6#27132555C214yesmaximal, complemented
7#27132552C214yesmaximal, complemented
8C42×Dic191C211yesmaximal, characteristic, complemented
9#391×C191C211yesmaximal, characteristic, complemented
10C22×D764C2211yescharacteristic
11#20259313—24no—
12#20259311—24no—
13C2×C4⋊Dic191C2212yes—
14C2×C4⋊Dic191C2211yescharacteristic
15C2×Dic191⋊C4C2212yes—
16C2×(C2×D191)⋊C4C2212yes—
17C2×(C2×D191)⋊C4C2214yes—
18C2×(C2×D191)⋊C4C2214yes—
19C2×(C2×D191)⋊C4C2212yes—
20C2×C4×Dic191C2212yes—
21C2×C4×Dic191C2212yes—
22C2×C4×Dic191C2211yescharacteristic
23C2×C4×Dic191C2211yescharacteristic
24C191⋊#95C2214yes—
25C22×Q8×C191C2211yescharacteristic
26C2×C4⋊C4×C191C2211yescharacteristic
27C2×C42×C191C2211yescharacteristic
28#95×C191C2214yes—
29C23×D191C2312yes—
30C2×D764—22no—
31C2×D764—22no—
32C2×D764—22no—
33C22×Dic191C2312yes—
34C22×Dic191C2311yescharacteristic
35C22×Dic191C2311yescharacteristic
36C22×Dic191C2312yes—
37C4⋊Dic191—24no—
38C4⋊Dic191—22no—
39Dic191⋊C4—24no—
40(C2×D191)⋊C4—24no—
41(C2×D191)⋊C4—24no—
42(C2×D191)⋊C4—28no—
43(C2×D191)⋊C4—28no—
44C4×Dic191—24no—
45C4×Dic191—22no—
46C4×Dic191—24no—
47C4×Dic191D414yes—
48C2×Q8×C191—22no—
49C2×Q8×C191—22no—
50C2×Q8×C191—22no—
51C22×C4×C191C2312yes—
52C22×C4×C191C2312yes—
53C22×C4×C191C2312yes—
54C22×C4×C191C2311yescharacteristic
55C4⋊C4×C191—22no—
56C42×C191—22no—
57C22×D191—22no—
58C22×D191—24no—
59C22×D191—24no—
60C22×D191—22no—
61C22×D191—22no—
62D764—44no—
63C2×Dic191—22no—
64C2×Dic191—22no—
65C2×Dic191—22no—
66C2×Dic191—22no—
67C2×Dic191—22no—
68C2×Dic191—24no—
69C2×Dic191C2×D412yes—
70C2×Dic191C2×D412yes—
71C2×Dic191#4114yes—
72C23×C191C2411yescharacteristic
73Q8×C191—44no—
74C2×C4×C191—22no—
75C2×C4×C191—22no—
76C2×C4×C191—22no—
77C2×C4×C191—22no—
78C2×C4×C191—22no—
79C2×C4×C191—22no—
80C2×C4×C191—24no—
81C2×C4×C191C2×D412yes—
82C2×C4×C191#4112yes—
83C2×C4×C191#4112yes—
84C2×C4×C191#4114yes—
85C22×C191C22×D411yescharacteristic
86C22×C191C2×#4112yes—
87C22×C191C2×#4111yescharacteristic
88C22×C191C2×#4111yescharacteristic
89C22×C191C2×#4112yes—
90C2×D191—42no—
91C2×D191—44no—
92C2×D191—44no—
93C2×D191—42no—
94C2×D191—42no—
95C4×C191—24no—
96C4×C191—42no—
97C4×C191—42no—
98C4×C191#12414yes—
99Dic191—24no—
100Dic191—22no—
101Dic191—22no—
102Dic191—42no—
103C2×C191C2×#12411yescharacteristic
104C2×C191#52912yes—
105C2×C191#52912yes—
106C2×C191#53211yescharacteristic
107C2×C191#53211yescharacteristic
108D191—82no—
109C191#286111yescharacteristic, complemented, Sylow
110#2861—1911nomaximal, Sylow
111C2×#125—1911no—
112C2×#124—1911no—
113#391—1911no—
114#391D19111yescharacteristic, complemented
115#390—1911no—
116#390—1911no—
117#388—1914no—
118#388—1914no—
119C43—1911no—
120C22×Q8C2×D19111yescharacteristic
121C22×D4—1911no—
122#125—3824no—
123#124—3824no—
124C2×C4⋊C4—1912no—
125C2×C4⋊C4—1912no—
126C2×C4⋊C4—1911no—
127C2×C4⋊C4C2×D19111yescharacteristic
128C2×C22⋊C4—1912no—
129C2×C22⋊C4—1912no—
130C2×C22⋊C4—1914no—
131C2×C22⋊C4—1914no—
132C2×C42—1912no—
133C2×C42—1912no—
134C2×C42—1911no—
135C2×C42—1911no—
136C2×C42C2×D19111yescharacteristic
137#95—1914no—
138#95C2×D19114yes—
139C24—1912no—
140C2×Q8—22no—
141C2×Q8—22no—
142C2×Q8—22no—
143C2×D4—3822no—
144C2×D4—3822no—
145C2×D4—3822no—
146C22×C4—1912no—
147C22×C4—1912no—
148C22×C4—1911no—
149C22×C4—1911no—
150C22×C4C22×D19112yes—
151C22×C4C22×D19112yes—
152C22×C4C22×D19112yes—
153C22×C4C22×D19111yescharacteristic
154C4⋊C4—22no—
155C4⋊C4—3824no—
156C4⋊C4—3824no—
157C4⋊C4—3822no—
158C22⋊C4—3828no—
159C22⋊C4—3824no—
160C22⋊C4—3824no—
161C22⋊C4—3828no—
162C42—22no—
163C42—3824no—
164C42—3822no—
165C42—3824no—
166C42—1914no—
167C23—3822no—
168C23—3824no—
169C23—3822no—
170C23—3822no—
171C23—3824no—
172C23C23×D19111yescharacteristic
173Q8—44no—
174D4—7644no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—24no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—3822no—
183C2×C4—3822no—
184C2×C4—3822no—
185C2×C4—3822no—
186C2×C4—3822no—
187C2×C4—3824no—
188C2×C4—1912no—
189C2×C4—1912no—
190C2×C4—1914no—
191C2×C4D4×D19112yes—
192C2×C4#1569028612yes—
193C2×C4#1569028712yes—
194C2×C4#1569028814yes—
195C22—7644no—
196C22—7644no—
197C22—7642no—
198C22—7642no—
199C22—7642no—
200C22C2×D4×D19111yescharacteristic
201C22#41×D19112yes—
202C22C2×#1569028611yescharacteristic
203C22C2×#1569028711yescharacteristic
204C22C2×#1569028812yes—
205C4—24no—
206C4—42no—
207C4—42no—
208C4—3824no—
209C4—3822no—
210C4—3822no—
211C4—7642no—
212C4#2025930814yes—
213C2—15282no—
214C2C2×#2025930811yescharacteristic
215C2#2713319912yes—
216C2#2713320012yes—
217C2#2713321211yescharacteristic
218C2#2713321411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D191
commutator, socle, cosocleC23×C191C24
Fitting#391×C191C2
prime radicalC22×D764C22
hypercenter#391D191
hypocenterC191#2861
LCSG ▷ C23×C191 ▷ C191
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
1. C2×#20259313C2semidirect
3. #27132570C2semidirect
6. #27132555C2semidirect
7. #27132552C2semidirect
8. C42×Dic191C2semidirect
9. #391×C191C2semidirect
109. C191#2861semidirect
114. #391D191semidirect

Maximal subgroups

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

subgroupindex
C2×#202593132
C2×#202593112
#271325702
#271325652
#271325642
#271325552
#271325522
C42×Dic1912
#391×C1912
#2861191