Finite Group Databasebeta

← #37573718

Subgroups — #37573718

Order 24448.

316 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 87 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×#20259302C211yesmaximal, characteristic
2C2×#20259247C211yesmaximal, characteristic, complemented
3C2×#20259245C211yesmaximal, characteristic, complemented
4C2×(C2×D191)⋊C8C211yesmaximal, characteristic
5#27132520C211yesmaximal, characteristic
6#27132425C211yesmaximal, characteristic, complemented
7C2×#106×C191C211yesmaximal, characteristic, complemented
8C22×Dic382C2211yescharacteristic
9C22×C4×D191C2211yescharacteristic
10C22×C191⋊C8C2211yescharacteristic
11#20259302—22no—
12#20259302—22no—
13C2×C4⋊Dic191—21no—
14C2×C4⋊Dic191C2211yescharacteristic
15C2×(C2×D191)⋊C4—21no—
16C2×(C2×D191)⋊C4—21no—
17#20259247—22no—
18#20259245—22no—
19(C2×D191)⋊C8—22no—
20C191⋊#95—21no—
21C22×C8×C191C2211yescharacteristic
22C2×C4⋊C4×C191C2211yescharacteristic
23C2×C4⋊C4×C191C2211yescharacteristic
24#106×C191—22no—
25C23×D191D411yescharacteristic
26C2×Dic382—21no—
27C2×Dic382—21no—
28C2×Dic382—21no—
29C2×Dic382—21no—
30C2×Dic382—21no—
31C2×Dic382D412yes—
32C22×Dic191—21no—
33C22×Dic191—21no—
34C22×Dic191D411yescharacteristic
35C2×C4×D191—21no—
36C2×C4×D191—21no—
37C2×C4×D191—21no—
38C2×C4×D191—21no—
39C2×C4×D191—21no—
40C2×C4×D191—21no—
41C2×C191⋊C8—21no—
42C2×C191⋊C8—21no—
43C2×C191⋊C8—21no—
44C4⋊Dic191—24no—
45C4⋊Dic191—21no—
46C4⋊Dic191—21no—
47(C2×D191)⋊C4—24no—
48(C2×D191)⋊C4—42no—
49C22×C4×C191—21no—
50C22×C4×C191—21no—
51C22×C4×C191C2311yescharacteristic
52C2×C8×C191—21no—
53C2×C8×C191—21no—
54C2×C8×C191D412yes—
55C4⋊C4×C191—21no—
56C4⋊C4×C191—21no—
57C4⋊C4×C191—21no—
58C4⋊C4×C191D412yes—
59C22×D191—21no—
60C22×D191—21no—
61C22×D191—21no—
62C22×D191—21no—
63C22×D191—21no—
64C22×D191—21no—
65C22×D191SD1612yes—
66Dic382—22no—
67Dic382—22no—
68Dic382—41no—
69Dic382—41no—
70C2×Dic191—22no—
71C2×Dic191—21no—
72C2×Dic191—21no—
73C2×Dic191—21no—
74C2×Dic191—41no—
75C2×Dic191—41no—
76C2×Dic191—41no—
77C2×Dic191—41no—
78C2×Dic191—41no—
79C4×D191—41no—
80C4×D191—41no—
81C4×D191—41no—
82C4×D191—41no—
83C191⋊C8—41no—
84C23×C191C2×D411yescharacteristic
85C2×C4×C191—22no—
86C2×C4×C191—41no—
87C2×C4×C191—41no—
88C2×C4×C191—41no—
89C2×C4×C191—41no—
90C2×C4×C191—41no—
91C2×C4×C191C2×D411yescharacteristic
92C2×C4×C191C2×D411yescharacteristic
93C2×C4×C191C2×D411yescharacteristic
94C2×C4×C191#4111yescharacteristic
95C2×C4×C191#4111yescharacteristic
96C2×C4×C191#4111yescharacteristic
97C8×C191—22no—
98C22×C191#12011yescharacteristic
99C22×C191#12111yescharacteristic
100C22×C191#12311yescharacteristic
101C22×C191C2×SD1611yescharacteristic
102C22×C191#13511yescharacteristic
103C22×C191#13711yescharacteristic
104C22×C191#13711yescharacteristic
105C2×D191—22no—
106C2×D191—22no—
107C2×D191—22no—
108C2×D191—41no—
109C2×D191—41no—
110C2×D191—41no—
111C2×D191—41no—
112C4×C191—42no—
113C4×C191—81no—
114C4×C191#12111yescharacteristic
115C4×C191#12111yescharacteristic
116C4×C191#12311yescharacteristic
117C4×C191#12411yescharacteristic
118Dic191—41no—
119Dic191—42no—
120Dic191—81no—
121C2×C191#39411yescharacteristic
122C2×C191#44811yescharacteristic
123C2×C191#45211yescharacteristic
124C2×C191#46511yescharacteristic
125C2×C191#47011yescharacteristic
126C2×C191#48311yescharacteristic
127C2×C191#48511yescharacteristic
128D191—42no—
129C191#203511yescharacteristic, complemented, Sylow
130#2035—1911nomaximal, Sylow
131C2×C22⋊Q8—1911no—
132C2×#106D19111yescharacteristic, complemented
133C2×#103—1911no—
134C2×#103—1911no—
135C2×C22⋊C8—1911no—
136#380—1911no—
137#340—1911no—
138C22×Q8—1911no—
139C23×C4—1911no—
140C22×C8—1911no—
141C22×C8C2×D19111yescharacteristic
142C22⋊Q8—3822no—
143C22⋊Q8—3822no—
144C2×C4⋊C4—3821no—
145C2×C4⋊C4—1911no—
146C2×C4⋊C4C2×D19111yescharacteristic
147C2×C4⋊C4C2×D19111yescharacteristic
148C2×C22⋊C4—3821no—
149C2×C22⋊C4—3821no—
150#106—22no—
151#103—3822no—
152#103—3822no—
153C22⋊C8—3822no—
154#95—3821no—
155C24—1911no—
156C2×Q8—3821no—
157C2×Q8—3821no—
158C2×Q8—3821no—
159C2×Q8—3821no—
160C2×Q8—3821no—
161C2×Q8—1912no—
162C22×C4—21no—
163C22×C4—21no—
164C22×C4—3821no—
165C22×C4—3821no—
166C22×C4—3821no—
167C22×C4—3821no—
168C22×C4—3821no—
169C22×C4—3821no—
170C22×C4—3821no—
171C22×C4—3821no—
172C22×C4—1911no—
173C22×C4C22×D19111yescharacteristic
174C2×C8—21no—
175C2×C8—21no—
176C2×C8—3821no—
177C2×C8—3821no—
178C2×C8—3821no—
179C2×C8D76412yes—
180C4⋊C4—21no—
181C4⋊C4—21no—
182C4⋊C4—21no—
183C4⋊C4—3824no—
184C4⋊C4—3821no—
185C4⋊C4—3821no—
186C4⋊C4C22⋊D19112yes—
187C22⋊C4—3824no—
188C22⋊C4—7642no—
189C23—3821no—
190C23—3821no—
191C23—3821no—
192C23—3821no—
193C23—3821no—
194C23—3821no—
195C23—1912no—
196C23D4×D19111yescharacteristic
197Q8—3822no—
198Q8—3822no—
199Q8—7641no—
200Q8—7641no—
201C2×C4—22no—
202C2×C4—41no—
203C2×C4—41no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—41no—
207C2×C4—3822no—
208C2×C4—3821no—
209C2×C4—3821no—
210C2×C4—3821no—
211C2×C4—7641no—
212C2×C4—7641no—
213C2×C4—7641no—
214C2×C4—7641no—
215C2×C4—7641no—
216C2×C4—7641no—
217C2×C4—7641no—
218C2×C4—7641no—
219C2×C4—7641no—
220C2×C4D4×D19111yescharacteristic
221C2×C4C2×C22⋊D19111yescharacteristic
222C2×C4C2×D76411yescharacteristic
223C2×C4#1569028711yescharacteristic
224C2×C4#1569028811yescharacteristic
225C2×C4#1569028811yescharacteristic
226C8—22no—
227C8—7641no—
228C22—3822no—
229C22—3822no—
230C22—3822no—
231C22—7641no—
232C22—7641no—
233C22—7641no—
234C22—7641no—
235C22#2025929011yescharacteristic
236C22#2025929711yescharacteristic
237C22#2025930711yescharacteristic
238C22SD16×D19111yescharacteristic
239C22#2025934311yescharacteristic
240C22#2025935111yescharacteristic
241C22#2025935111yescharacteristic
242C4—42no—
243C4—81no—
244C4—15281no—
245C4—7641no—
246C4—7642no—
247C4#2025929611yescharacteristic
248C4#2025929711yescharacteristic
249C4#2025930711yescharacteristic
250C4#2025931111yescharacteristic
251C2—7642no—
252C2#2713258011yescharacteristic
253C2#2713280011yescharacteristic
254C2#2713282211yescharacteristic
255C2#2713289311yescharacteristic
256C2#2713292211yescharacteristic
257C2#2713299511yescharacteristic
258C2#2713300711yescharacteristic
subgroupG/H
centerC23D4×D191
commutator, cosocleC22×C4×C191C23
FrattiniC22×C4C22×D191
FittingC2×#106×C191C2
socleC23×C191C2×D4
prime radicalC23×D191D4
hypercenterC2×#106D191
hypocenterC191#2035
LCSG ▷ C22×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#106

Complements

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

NH ≅ G/Ntype
2. C2×#20259247C2semidirect
3. C2×#20259245C2semidirect
6. #27132425C2semidirect
7. C2×#106×C191C2semidirect
129. C191#2035semidirect
132. C2×#106D191semidirect

Maximal subgroups

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

subgroupindex
C2×#202593022
C2×#202592472
C2×#202592452
C2×(C2×D191)⋊C82
#271325202
#271324252
C2×#106×C1912
#2035191