Finite Group Databasebeta

← #487×D191 #37582828

Subgroups — #487×D191 #37582828

Order 24448.

424 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 145 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
1C4⋊Q8×D191C211yesmaximal, characteristic
2C4⋊Q8×D191C211yesmaximal, characteristic
3#27133015C211yesmaximal, characteristic, complemented
4#27133014C211yesmaximal, characteristic, complemented
5#27133013C211yesmaximal, characteristic, complemented
6#27133012C214yesmaximal, complemented
7#103×D191C214yesmaximal
8C4×C8×D191C211yesmaximal, characteristic
9#487×C191C211yesmaximal, characteristic, complemented
10C2×Q8×D191—21no—
11C2×Q8×D191C2212yes—
12C2×C8×D191C2212yes—
13#20259322C2211yescharacteristic
14#20259322C2211yescharacteristic
15#20259321—21no—
16#20259321—21no—
17#20259321—21no—
18#20259321C2212yes—
19#20259320—21no—
20#20259320C2212yes—
21C4⋊C4×D191—21no—
22C4⋊C4×D191—21no—
23C4⋊C4×D191—21no—
24C4⋊C4×D191C2212yes—
25C42×D191C2211yescharacteristic
26#20259247C2214yes—
27#20259246C2214yes—
28#20259245C2214yes—
29C4×C191⋊C8C2211yescharacteristic
30C8×Dic191C2212yes—
31C4⋊Q8×C191C2211yescharacteristic
32C4⋊Q8×C191C2211yescharacteristic
33#103×C191C2214yes—
34C4×C8×C191C2211yescharacteristic
35C2×Dic382—22no—
36C2×Dic382—22no—
37C2×Dic382—21no—
38C2×Dic382C2312yes—
39Q8×D191—28no—
40Q8×D191—44no—
41C2×C4×D191—22no—
42C2×C4×D191—22no—
43C2×C4×D191D411yescharacteristic
44C2×C4×D191D411yescharacteristic
45C2×C4×D191C2311yescharacteristic
46C2×C191⋊C8C2312yes—
47C8×D191—24no—
48C4⋊Dic191—21no—
49C4⋊Dic191—21no—
50C4⋊Dic191—21no—
51C4⋊Dic191C2312yes—
52Dic191⋊C4—22no—
53Dic191⋊C4—22no—
54Dic191⋊C4—22no—
55Dic191⋊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×D191C2×D411yescharacteristic
68Dic382—24no—
69Dic382—42no—
70Dic382—44no—
71Dic382—44no—
72C2×Dic191—22no—
73C2×Dic191—22no—
74C2×Dic191C2×D411yescharacteristic
75C2×Dic191C2×D411yescharacteristic
76C2×Dic191C2×D411yescharacteristic
77C4×D191—44no—
78C4×D191—44no—
79C4×D191SD1614yes—
80C4×D191Q1614yes—
81C4×D191#4114yes—
82C191⋊C8—22no—
83Q8×C191—24no—
84Q8×C191—42no—
85C2×C4×C191—22no—
86C2×C4×C191—22no—
87C2×C4×C191C2×D411yescharacteristic
88C2×C4×C191C2×D411yescharacteristic
89C2×C4×C191C2411yescharacteristic
90C8×C191—22no—
91C22×C191C22×D411yescharacteristic
92C2×D191#12412yes—
93C2×D191C2×SD1612yes—
94C2×D191C2×Q1612yes—
95C4×C191—42no—
96C4×C191—42no—
97C4×C191C2×SD1612yes—
98C4×C191C2×Q1612yes—
99C4×C191C2×#4112yes—
100Dic191—42no—
101Dic191—42no—
102Dic191#12412yes—
103Dic191C2×SD1612yes—
104Dic191C2×Q1612yes—
105C2×C191C2×#12411yescharacteristic
106C2×C191C22×SD1611yescharacteristic
107C2×C191C22×Q1611yescharacteristic
108D191#48714yesdirect product factor
109C191C2×#48711yescharacteristic, complemented, Sylow
110C2×#487—1911nomaximal, Sylow
111C2×C4⋊Q8—1911no—
112C2×C4⋊Q8—1911no—
113#487—1911no—
114#487—1911no—
115#487—1914no—
116#487—1911no—
117#487D19111yescharacteristic, direct product factor
118C2×#103—1914no—
119C2×C4×C8—1911no—
120C22×Q8—3821no—
121C22×Q8—1912no—
122C22×C8—1912no—
123C4⋊Q8—3821no—
124C4⋊Q8—3821no—
125C4⋊Q8—3821no—
126C4⋊Q8—3821no—
127C4⋊Q8—1912no—
128C4⋊Q8—1912no—
129C4⋊Q8—1911no—
130C4⋊Q8—1911no—
131C4⋊Q8C2×D19111yescharacteristic
132C4⋊Q8C2×D19111yescharacteristic
133C2×C4⋊C4—3821no—
134C2×C4⋊C4—3821no—
135C2×C4⋊C4—3821no—
136C2×C4⋊C4—1912no—
137C2×C42—1911no—
138#103—1914no—
139#103—1914no—
140#103—1914no—
141#103C2×D19114yes—
142C4×C8—1912no—
143C4×C8—1911no—
144C4×C8C2×D19111yescharacteristic
145C2×Q8—21no—
146C2×Q8—3822no—
147C2×Q8—3822no—
148C2×Q8—3821no—
149C2×Q8—3828no—
150C2×Q8—1912no—
151C2×Q8—7644no—
152C2×Q8C22×D19112yes—
153C22×C4—3822no—
154C22×C4—3822no—
155C22×C4—1911no—
156C22×C4—1911no—
157C22×C4—1911no—
158C2×C8—3824no—
159C2×C8—1912no—
160C2×C8C22×D19112yes—
161C4⋊C4—21no—
162C4⋊C4—21no—
163C4⋊C4—21no—
164C4⋊C4—3822no—
165C4⋊C4—3822no—
166C4⋊C4—3822no—
167C4⋊C4—3822no—
168C4⋊C4—3821no—
169C4⋊C4—3821no—
170C4⋊C4—3821no—
171C4⋊C4—1912no—
172C4⋊C4C22×D19112yes—
173C42—1911no—
174C42—1911no—
175C42—1911no—
176C42C22×D19111yescharacteristic
177C23—1911no—
178Q8—24no—
179Q8—42no—
180Q8—3824no—
181Q8—7644no—
182Q8—7644no—
183Q8—7642no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—3822no—
187C2×C4—3822no—
188C2×C4—1911no—
189C2×C4—1911no—
190C2×C4—1911no—
191C2×C4—1914no—
192C2×C4—1914no—
193C2×C4—1914no—
194C2×C4—7644no—
195C2×C4—7644no—
196C2×C4D4×D19111yescharacteristic
197C2×C4D4×D19111yescharacteristic
198C2×C4C23×D19111yescharacteristic
199C8—22no—
200C8—3822no—
201C22—1912no—
202C22—1912no—
203C22—1912no—
204C22C2×D4×D19111yescharacteristic
205C4—42no—
206C4—42no—
207C4—1912no—
208C4—1912no—
209C4—1912no—
210C4—7642no—
211C4—7642no—
212C4SD16×D19112yes—
213C4Q16×D19112yes—
214C4#41×D19112yes—
215C2—1914no—
216C2#124×D19111yescharacteristic
217C2C2×SD16×D19111yescharacteristic
218C2C2×Q16×D19111yescharacteristic
subgroupG/H
centerC22C2×D4×D191
commutator, cosocleC2×C4×C191C24
FrattiniC2×C4C23×D191
Fitting#487×C191C2
socleC22×C191C22×D4
prime radicalC22×D191C2×D4
hypercenter#487D191
hypocenterC191C2×#487
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
3. #27133015C2semidirect
4. #27133014C2semidirect
5. #27133013C2semidirect
6. #27133012C2semidirect
9. #487×C191C2semidirect
108. D191#487direct (N × H)
109. C191C2×#487semidirect
117. #487D191direct (N × H)

Maximal subgroups

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

subgroupindex
C4⋊Q8×D1912
#271330152
#271330142
#271330132
#271330122
#103×D1912
C4×C8×D1912
#487×C1912
C2×#487191