Finite Group Databasebeta

← #37582052

Subgroups — #37582052

Order 24448.

458 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 141 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
1C22×#15690277C211yesmaximal, characteristic, complemented
2#27133234C211yesmaximal, characteristic
3#27133141C211yesmaximal, characteristic, complemented
4#27132883C214yesmaximal, complemented
5#27132871C214yesmaximal, complemented
6#27132691C211yesmaximal, characteristic, complemented
7#27132673C211yesmaximal, characteristic, complemented
8#27132659C211yesmaximal, characteristic
9C2×#137×C191C211yesmaximal, characteristic
10C22×Dic382C2211yescharacteristic
11C2×#15690277—24no—
12C2×#15690277C2214yes—
13C22×C191⋊C8C2211yescharacteristic
14#20259320C2212yes—
15#20259309C2212yes—
16#20259303—22no—
17#20259301—22no—
18Q8×Dic191—22no—
19Q8×Dic191C2214yes—
20#20259281—22no—
21#20259281C2211yescharacteristic
22#20259281C2211yescharacteristic
23Dic191⋊C8C2214yes—
24#20259247C2214yes—
25#20259246C2212yes—
26#20259243C2212yes—
27C2×#41×C191C2211yescharacteristic
28C22×Q8×C191C2211yescharacteristic
29#137×C191—24no—
30C2×Q16×C191C2212yes—
31C2×SD16×C191C2212yes—
32C2×M16×C191C2211yescharacteristic
33C2×Dic382—21no—
34C2×Dic382—22no—
35C2×Dic382—22no—
36C2×Dic382C2312yes—
37C22×Dic191—21no—
38#15690277—28no—
39C2×C191⋊C8—22no—
40C2×C191⋊C8C2312yes—
41C4⋊Dic191—24no—
42C4⋊Dic191D412yes—
43C4⋊Dic191C2312yes—
44Dic191⋊C4—24no—
45C22⋊Dic191—24no—
46C22⋊Dic191—21no—
47C22⋊Dic191D412yes—
48C4×Dic191—24no—
49C4×Dic191—21no—
50C4×Dic191C2312yes—
51#41×C191—22no—
52#41×C191—22no—
53C2×Q8×C191—21no—
54C2×Q8×C191—22no—
55C2×Q8×C191D414yes—
56C2×Q8×C191C2311yescharacteristic
57C2×Q8×C191C2312yes—
58C2×D4×C191—21no—
59C2×D4×C191C2311yescharacteristic
60C22×C4×C191—21no—
61C22×C4×C191—21no—
62C22×C4×C191C2311yescharacteristic
63Q16×C191—24no—
64SD16×C191—24no—
65M16×C191—22no—
66C2×C8×C191C2312yes—
67Dic382—22no—
68Dic382—22no—
69Dic382—42no—
70C2×Dic191—22no—
71C2×Dic191—22no—
72C2×Dic191—42no—
73C2×Dic191C2×D414yes—
74C191⋊C8—22no—
75C23×C191—21no—
76C23×C191C2×D411yescharacteristic
77Q8×C191—24no—
78Q8×C191—22no—
79Q8×C191—21no—
80Q8×C191—21no—
81Q8×C191C2×D414yes—
82D4×C191—21no—
83D4×C191—21no—
84D4×C191—42no—
85C2×C4×C191—24no—
86C2×C4×C191—22no—
87C2×C4×C191—21no—
88C2×C4×C191—42no—
89C2×C4×C191C2×D411yescharacteristic
90C2×C4×C191C2×D412yes—
91C2×C4×C191#4112yes—
92C2×C4×C191C2411yescharacteristic
93C8×C191—22no—
94C22×C191—22no—
95C22×C191—41no—
96C22×C191—42no—
97C22×C191#12112yes—
98C22×C191C22×D411yescharacteristic
99C4×C191—24no—
100C4×C191—41no—
101C4×C191#12112yes—
102C4×C191C22×D411yescharacteristic
103C4×C191C2×#4111yescharacteristic
104Dic191—24no—
105Dic191—42no—
106Dic191—42no—
107C2×C191—22no—
108C2×C191—81no—
109C2×C191C2×#12111yescharacteristic
110C2×C191#57812yes—
111C191#304411yescharacteristic, complemented, Sylow
112#3044—1911nomaximal, Sylow
113C2×#137D19111yescharacteristic
114C22×Q16—1911no—
115#536—1911no—
116#519—1911no—
117#464—1914no—
118#462—1914no—
119#424—1911no—
120#419—1911no—
121#416—1911no—
122C2×#41C2×D19111yescharacteristic
123C22×Q8—1911no—
124C22×Q8C2×D19111yescharacteristic
125#137—24no—
126C2×Q16—3824no—
127C2×Q16—1914no—
128C2×Q16C2×D19112yes—
129C2×SD16C2×D19112yes—
130C2×M16C2×D19111yescharacteristic
131C22×C8—1911no—
132C4⋊Q8—1912no—
133#124—1912no—
134#123—3822no—
135C22⋊Q8—3822no—
136C4×Q8—3822no—
137C4×Q8—1914no—
138#117—3822no—
139#117—1911no—
140#117—1911no—
141C4⋊C8—1914no—
142#103—1912no—
143#103—1914no—
144#102—1912no—
145#41—22no—
146#41—22no—
147C2×Q8—21no—
148C2×Q8—22no—
149C2×Q8—3821no—
150C2×Q8—3822no—
151C2×Q8—3822no—
152C2×Q8—1912no—
153C2×Q8C22⋊D19114yes—
154C2×Q8C22×D19111yescharacteristic
155C2×Q8C22×D19112yes—
156C2×D4—21no—
157C2×D4C22×D19111yescharacteristic
158C22×C4—21no—
159C22×C4—21no—
160C22×C4—3821no—
161C22×C4C22×D19111yescharacteristic
162Q16—24no—
163Q16—3828no—
164SD16—24no—
165M16—22no—
166C2×C8—3822no—
167C2×C8—1912no—
168C2×C8C22×D19112yes—
169C4⋊C4—3824no—
170C4⋊C4—3824no—
171C4⋊C4—1912no—
172C4⋊C4—1912no—
173C22⋊C4—3821no—
174C22⋊C4—3824no—
175C22⋊C4—1912no—
176C42—3824no—
177C42—3821no—
178C42—1912no—
179C23—21no—
180C23D4×D19111yescharacteristic
181Q8—22no—
182Q8—24no—
183Q8—21no—
184Q8—21no—
185Q8—3822no—
186Q8—3822no—
187Q8—7642no—
188Q8C2×C22⋊D19114yes—
189D4—21no—
190D4—21no—
191D4—42no—
192C2×C4—22no—
193C2×C4—24no—
194C2×C4—21no—
195C2×C4—42no—
196C2×C4—3822no—
197C2×C4—3822no—
198C2×C4—1914no—
199C2×C4—7642no—
200C2×C4D4×D19111yescharacteristic
201C2×C4C2×C22⋊D19112yes—
202C2×C4#1569028612yes—
203C2×C4C23×D19111yescharacteristic
204C8—22no—
205C8—3822no—
206C22—22no—
207C22—42no—
208C22—41no—
209C22#2025929412yes—
210C22C2×D4×D19111yescharacteristic
211C4—24no—
212C4—41no—
213C4—3824no—
214C4—7642no—
215C4—7642no—
216C4#2025929412yes—
217C4C22×C22⋊D19111yescharacteristic
218C4C2×#1569028611yescharacteristic
219C2—22no—
220C2—81no—
221C2C2×#2025929411yescharacteristic
222C2#2713347912yes—
subgroupG/H
centerC22C2×D4×D191
commutator, cosocleC2×C4×C191C24
FrattiniC2×C4C23×D191
FittingC2×#137×C191C2
socleC22×C191C22×D4
prime radicalC2×#41×C191C22
hypercenterC2×#137D191
hypocenterC191#3044
LCSG ▷ C2×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
1. C22×#15690277C2semidirect
3. #27133141C2semidirect
4. #27132883C2semidirect
5. #27132871C2semidirect
6. #27132691C2semidirect
7. #27132673C2semidirect
111. C191#3044semidirect

Maximal subgroups

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

subgroupindex
C22×#156902772
#271332342
#271331412
#271328832
#271328712
#271326912
#271326732
#271326592
C2×#137×C1912
#3044191