Finite Group Databasebeta

← #37583142

Subgroups — #37583142

Order 24448.

362 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 121 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#27133275C211yesmaximal, characteristic, complemented
2#27133062C211yesmaximal, characteristic, complemented
3#27133035C211yesmaximal, characteristic, complemented
4#27133033C211yesmaximal, characteristic, complemented
5#27133027C211yesmaximal, characteristic, complemented
6#27132907C212yesmaximal, complemented
7#27132890C212yesmaximal, complemented
8#27132763C212yesmaximal, complemented
9C4×#15690275C212yesmaximal, complemented
10#27132619C211yesmaximal, characteristic, complemented
11#540×C191C211yesmaximal, characteristic
12C2×#15690275C2212yes—
13C2×#15690275C2212yes—
14C2×#15690271C2211yescharacteristic
15C22×C191⋊C8C2211yescharacteristic
16#20259322C2211yescharacteristic
17#20259315—22no—
18#20259314C2211yescharacteristic
19#20259312—22no—
20#20259301C2212yes—
21C4×Dic382C2212yes—
22#20259255C2212yes—
23#20259253C2212yes—
24#20259245C2212yes—
25#20259245C2212yes—
26#20259243C2212yes—
27#20259243C2212yes—
28#20259233C2211yescharacteristic
29#20259233C2211yescharacteristic
30C4×C191⋊C8C2211yescharacteristic
31C4×C191⋊C8C2211yescharacteristic
32#127×C191C2211yescharacteristic
33#125×C191C2211yescharacteristic
34#123×C191—22no—
35#121×C191—22no—
36#121×C191C2212yes—
37C4×D4×C191C2212yes—
38#117×C191C2211yescharacteristic
39C2×Dic382C2312yes—
40#15690275—24no—
41#15690275—24no—
42#15690271—22no—
43C2×C191⋊C8—22no—
44C2×C191⋊C8C2311yescharacteristic
45C2×C191⋊C8C2311yescharacteristic
46C2×C191⋊C8C2311yescharacteristic
47C2×C191⋊C8C2311yescharacteristic
48C4⋊Dic191—22no—
49C4⋊Dic191C2312yes—
50Dic191⋊C4—22no—
51Dic191⋊C4—22no—
52Dic191⋊C4—22no—
53C22⋊Dic191—22no—
54C4×Dic191—22no—
55C2×D4×C191—22no—
56C2×D4×C191—22no—
57C2×D4×C191C2312yes—
58C22×C4×C191—22no—
59C22×C4×C191C2311yescharacteristic
60C4⋊C4×C191—22no—
61C4⋊C4×C191D412yes—
62C4⋊C4×C191C2312yes—
63C22⋊C4×C191—22no—
64C22⋊C4×C191—22no—
65C22⋊C4×C191D412yes—
66C42×C191C2311yescharacteristic
67C42×C191C2311yescharacteristic
68Dic382—22no—
69Dic382—22no—
70C2×Dic191—22no—
71C2×Dic191—22no—
72C191⋊C8—21no—
73C191⋊C8—21no—
74C191⋊C8#4112yes—
75C191⋊C8#4112yes—
76C23×C191—22no—
77C23×C191C2×D411yescharacteristic
78D4×C191—22no—
79D4×C191—22no—
80D4×C191—82no—
81D4×C191—82no—
82C2×C4×C191—21no—
83C2×C4×C191—21no—
84C2×C4×C191—22no—
85C2×C4×C191—82no—
86C2×C4×C191C2×D412yes—
87C2×C4×C191C2×D412yes—
88C2×C4×C191C2×D411yescharacteristic
89C2×C4×C191C2411yescharacteristic
90C22×C191—21no—
91C22×C191—22no—
92C22×C191—42no—
93C22×C191—42no—
94C22×C191—42no—
95C22×C191C22×D411yescharacteristic
96C4×C191—21no—
97C4×C191—22no—
98C4×C191—22no—
99C4×C191—42no—
100C4×C191C2×#4111yescharacteristic
101C4×C191C2×#4111yescharacteristic
102Dic191—42no—
103Dic191—42no—
104C2×C191—41no—
105C2×C191—82no—
106C2×C191#53211yescharacteristic
107C2×C191#57712yes—
108C191#317411yescharacteristic, complemented, Sylow
109#3174—1911nomaximal, Sylow
110#541—1911no—
111#540D19111yescharacteristic
112#499—1911no—
113#492—1911no—
114#491—1911no—
115#490—1911no—
116#468—1912no—
117#465—1912no—
118#440—1912no—
119C4×SD16—1912no—
120#405—1911no—
121C2×SD16—1912no—
122C2×SD16—1912no—
123C2×M16—1911no—
124C22×C8—1911no—
125C4⋊Q8—1911no—
126#127C2×D19111yescharacteristic
127#126—3822no—
128#125—3822no—
129#125—1911no—
130#125C2×D19111yescharacteristic
131#123—22no—
132C22⋊Q8—1912no—
133#121—22no—
134#121C2×D19112yes—
135C4×Q8—1912no—
136C4×D4C2×D19112yes—
137#117C2×D19111yescharacteristic
138#107—1912no—
139#106—1912no—
140#103—1912no—
141#103—1912no—
142#102—1912no—
143#102—1912no—
144#97—1911no—
145#97—1911no—
146C4×C8—1911no—
147C4×C8—1911no—
148C2×Q8—1912no—
149C2×D4—22no—
150C2×D4—22no—
151C2×D4C22×D19112yes—
152C22×C4—22no—
153C22×C4C22×D19111yescharacteristic
154SD16—3824no—
155SD16—3824no—
156M16—3822no—
157C2×C8—3822no—
158C2×C8—1911no—
159C2×C8—1911no—
160C2×C8—1911no—
161C2×C8—1911no—
162C4⋊C4—22no—
163C4⋊C4—3822no—
164C4⋊C4—3822no—
165C4⋊C4—3822no—
166C4⋊C4—3822no—
167C4⋊C4—1912no—
168C4⋊C4C22⋊D19112yes—
169C4⋊C4C22×D19112yes—
170C22⋊C4—22no—
171C22⋊C4—22no—
172C22⋊C4—3822no—
173C22⋊C4C22⋊D19112yes—
174C42—3822no—
175C42C22×D19111yescharacteristic
176C42C22×D19111yescharacteristic
177C23—22no—
178C23C2×C22⋊D19111yescharacteristic
179Q8—3822no—
180Q8—3822no—
181D4—22no—
182D4—22no—
183D4—82no—
184D4—82no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—22no—
188C2×C4—82no—
189C2×C4—3822no—
190C2×C4—3822no—
191C2×C4C2×C22⋊D19112yes—
192C2×C4C2×C22⋊D19112yes—
193C2×C4C2×C22⋊D19111yescharacteristic
194C2×C4C23×D19111yescharacteristic
195C8—3821no—
196C8—3821no—
197C8—1912no—
198C8—1912no—
199C22—21no—
200C22—22no—
201C22—42no—
202C22—42no—
203C22—42no—
204C22C22×C22⋊D19111yescharacteristic
205C4—21no—
206C4—22no—
207C4—22no—
208C4—42no—
209C4—7642no—
210C4—7642no—
211C4#41×D19111yescharacteristic
212C4#41×D19111yescharacteristic
213C2—41no—
214C2—82no—
215C2#2713320911yescharacteristic
216C2#2713347412yes—
subgroupG/H
centerC22C22×C22⋊D191
commutator, cosocleC2×C4×C191C24
FrattiniC2×C4C23×D191
Fitting, prime radical#540×C191C2
socleC22×C191C22×D4
hypercenter#540D191
hypocenterC191#3174
LCSG ▷ C2×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C22 ◁ #117 ◁ #540

Complements

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

NH ≅ G/Ntype
1. #27133275C2semidirect
2. #27133062C2semidirect
3. #27133035C2semidirect
4. #27133033C2semidirect
5. #27133027C2semidirect
6. #27132907C2semidirect
7. #27132890C2semidirect
8. #27132763C2semidirect
9. C4×#15690275C2semidirect
10. #27132619C2semidirect
108. C191#3174semidirect

Maximal subgroups

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

subgroupindex
#271332752
#271330622
#271330352
#271330332
#271330272
#271329072
#271328902
#271327632
C4×#156902752
#271326192
#540×C1912
#3174191