Finite Group Databasebeta

← #37582915

Subgroups — #37582915

Order 24448.

424 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 125 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#27133214C211yesmaximal, characteristic
2C4⋊Q8×D191C211yesmaximal, characteristic, complemented
3#27133024C214yesmaximal, complemented
4#27133013C211yesmaximal, characteristic, complemented
5#27133011C211yesmaximal, characteristic, complemented
6#27133010C211yesmaximal, characteristic, complemented
7#27132663C214yesmaximal, complemented
8C4×#15690270C211yesmaximal, characteristic, complemented
9#487×C191C211yesmaximal, characteristic, complemented
10C2×#15690288C2212yes—
11C2×Q8×D191—21no—
12C2×#15690270C2212yes—
13#20259322C2211yescharacteristic
14#20259321—21no—
15#20259321C2212yes—
16#20259320—21no—
17#20259319C2211yescharacteristic
18#20259311C2212yes—
19#20259297—21no—
20#20259297—21no—
21#20259284—21no—
22#20259284—21no—
23C4⋊C4×D191—21no—
24C4⋊C4×D191C2212yes—
25C42×D191C2211yescharacteristic
26#20259246C2214yes—
27#20259244C2214yes—
28#20259242C2214yes—
29#20259232C2212yes—
30C4×C191⋊C8C2211yescharacteristic
31C4⋊Q8×C191C2211yescharacteristic
32C4⋊Q8×C191C2211yescharacteristic
33#103×C191C2214yes—
34C4×C8×C191C2211yescharacteristic
35#15690288—28no—
36C2×Dic382—22no—
37C2×Dic382—21no—
38Q8×D191—44no—
39C2×D764—22no—
40C2×D764—21no—
41C2×D764—21no—
42C2×D764C2312yes—
43C2×C4×D191—22no—
44C2×C4×D191—22no—
45C2×C4×D191D411yescharacteristic
46C2×C4×D191D411yescharacteristic
47C2×C4×D191C2311yescharacteristic
48#15690270—24no—
49C2×C191⋊C8C2312yes—
50C4⋊Dic191—21no—
51C4⋊Dic191C2312yes—
52Dic191⋊C4—22no—
53Dic191⋊C4—22no—
54(C2×D191)⋊C4—22no—
55(C2×D191)⋊C4—22no—
56C4×Dic191D411yescharacteristic
57C4×Dic191D411yescharacteristic
58C4×Dic191C2311yescharacteristic
59C2×Q8×C191—21no—
60C2×Q8×C191C2312yes—
61C2×C8×C191C2312yes—
62C4⋊C4×C191—21no—
63C4⋊C4×C191—21no—
64C4⋊C4×C191—21no—
65C4⋊C4×C191C2312yes—
66C42×C191C2311yescharacteristic
67C22×D191—22no—
68C22×D191C2×D411yescharacteristic
69Dic382—44no—
70Dic382—42no—
71D764—24no—
72D764—44no—
73D764—42no—
74D764—42no—
75C2×Dic191—22no—
76C2×Dic191C2×D411yescharacteristic
77C2×Dic191C2×D411yescharacteristic
78C2×Dic191C2×D411yescharacteristic
79C4×D191—22no—
80C4×D191—22no—
81C4×D191—44no—
82C4×D191—44no—
83C4×D191#4114yes—
84C191⋊C8—22no—
85Q8×C191—24no—
86Q8×C191—42no—
87C2×C4×C191—22no—
88C2×C4×C191—22no—
89C2×C4×C191C2×D411yescharacteristic
90C2×C4×C191C2×D411yescharacteristic
91C2×C4×C191C2411yescharacteristic
92C8×C191—22no—
93C22×C191C22×D411yescharacteristic
94C2×D191—21no—
95C2×D191—21no—
96C2×D191—42no—
97C2×D191—42no—
98C2×D191—42no—
99C2×D191#12412yes—
100C4×C191—42no—
101C4×C191—42no—
102C4×C191AGL(1,ℤ/8)12yes—
103C4×C191#13712yes—
104C4×C191C2×#4112yes—
105Dic191—21no—
106Dic191—21no—
107Dic191—42no—
108Dic191#12412yes—
109C2×C191C2×#12411yescharacteristic
110C2×C191C2×AGL(1,ℤ/8)11yescharacteristic
111C2×C191C2×#13711yescharacteristic
112D191—22no—
113D191—82no—
114C191#314111yescharacteristic, complemented, Sylow
115#3141—1911nomaximal, Sylow
116#532—1911no—
117C2×C4⋊Q8—1911no—
118#489—1914no—
119#487—1911no—
120#487D19111yescharacteristic, complemented
121#486—1911no—
122#486—1911no—
123#417—1914no—
124C4×M16—1911no—
125C2×#41—1912no—
126C22×Q8—3821no—
127C2×M16—1912no—
128C4⋊Q8—3821no—
129C4⋊Q8—3821no—
130C4⋊Q8—1912no—
131C4⋊Q8—1911no—
132C4⋊Q8C2×D19111yescharacteristic
133C4⋊Q8C2×D19111yescharacteristic
134#127—1911no—
135#124—1912no—
136#121—3821no—
137#121—3821no—
138C4×D4—3821no—
139C4×D4—3821no—
140C2×C4⋊C4—3821no—
141C2×C4⋊C4—1912no—
142C2×C42—1911no—
143#103—1914no—
144#103C2×D19114yes—
145#102—1914no—
146#102—1914no—
147#97—1912no—
148C4×C8—1911no—
149C4×C8C2×D19111yescharacteristic
150#41—3828no—
151C2×Q8—21no—
152C2×Q8—3822no—
153C2×Q8—3821no—
154C2×Q8—7644no—
155C2×Q8C22×D19112yes—
156C2×D4—3822no—
157C2×D4—3821no—
158C2×D4—3821no—
159C2×D4—1912no—
160C22×C4—3822no—
161C22×C4—3822no—
162C22×C4—1911no—
163C22×C4—1911no—
164C22×C4—1911no—
165M16—3824no—
166C2×C8—1912no—
167C2×C8C22×D19112yes—
168C4⋊C4—21no—
169C4⋊C4—21no—
170C4⋊C4—21no—
171C4⋊C4—3822no—
172C4⋊C4—3822no—
173C4⋊C4—3821no—
174C4⋊C4—1912no—
175C4⋊C4C22×D19112yes—
176C22⋊C4—3822no—
177C22⋊C4—3822no—
178C42—1911no—
179C42—1911no—
180C42—1911no—
181C42C22×D19111yescharacteristic
182C23—3822no—
183C23—1911no—
184Q8—24no—
185Q8—42no—
186Q8—7644no—
187Q8—7642no—
188D4—3824no—
189D4—7644no—
190D4—7642no—
191D4—7642no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—3822no—
195C2×C4—3822no—
196C2×C4—3822no—
197C2×C4—1911no—
198C2×C4—1911no—
199C2×C4—1911no—
200C2×C4—1914no—
201C2×C4—7644no—
202C2×C4—7644no—
203C2×C4D4×D19111yescharacteristic
204C2×C4D4×D19111yescharacteristic
205C2×C4C23×D19111yescharacteristic
206C8—22no—
207C8—3822no—
208C22—3821no—
209C22—3821no—
210C22—1912no—
211C22—7642no—
212C22—7642no—
213C22—7642no—
214C22C2×D4×D19111yescharacteristic
215C4—42no—
216C4—42no—
217C4—3821no—
218C4—3821no—
219C4—1912no—
220C4—7642no—
221C4#2025934912yes—
222C4#2025935412yes—
223C4#41×D19112yes—
224C2—3822no—
225C2—15282no—
226C2#124×D19111yescharacteristic
227C2C2×#2025934911yescharacteristic
228C2C2×#2025935411yescharacteristic
subgroupG/H
centerC22C2×D4×D191
commutator, cosocleC2×C4×C191C24
FrattiniC2×C4C23×D191
Fitting#487×C191C2
socleC22×C191C22×D4
prime radical#27133214C2
hypercenter#487D191
hypocenterC191#3141
LCSG ▷ C2×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
2. C4⋊Q8×D191C2semidirect
3. #27133024C2semidirect
4. #27133013C2semidirect
5. #27133011C2semidirect
6. #27133010C2semidirect
7. #27132663C2semidirect
8. C4×#15690270C2semidirect
9. #487×C191C2semidirect
114. C191#3141semidirect
120. #487D191semidirect

Maximal subgroups

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

subgroupindex
#271332142
C4⋊Q8×D1912
#271330242
#271330132
#271330112
#271330102
#271326632
C4×#156902702
#487×C1912
#3141191