Finite Group Databasebeta

← #37573604

Subgroups — #37573604

Order 24448.

406 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 93 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×#15690276C211yesmaximal, characteristic
2C22×#15690274C211yesmaximal, characteristic
3C2×#20259320C211yesmaximal, characteristic, complemented
4C2×#20259245C211yesmaximal, characteristic, complemented
5#27132564C211yesmaximal, characteristic
6#27132417C211yesmaximal, characteristic, complemented
7C2×#103×C191C211yesmaximal, characteristic, complemented
8C22×Dic382C2211yescharacteristic
9C22×D764C2211yescharacteristic
10C2×#15690276—22no—
11C2×#15690276—22no—
12C2×#15690276—22no—
13C2×#15690274—22no—
14C2×#15690274—22no—
15C2×#15690274—22no—
16C22×C191⋊C8C2211yescharacteristic
17#20259320—22no—
18#20259320—22no—
19C2×Dic191⋊C4—22no—
20C2×(C2×D191)⋊C4—22no—
21C2×C4×Dic191C2211yescharacteristic
22#20259245—22no—
23C22×Q8×C191C2211yescharacteristic
24C22×C8×C191C2211yescharacteristic
25C2×C4⋊C4×C191C2211yescharacteristic
26#103×C191—22no—
27C23×D191—21no—
28C2×Dic382—21no—
29C2×Dic382—21no—
30C2×Dic382—21no—
31C2×Dic382—21no—
32C2×Dic382—21no—
33C2×Dic382D412yes—
34C2×D764—21no—
35C2×D764—21no—
36C2×D764—21no—
37C2×D764—21no—
38C2×D764—21no—
39C2×D764D412yes—
40C22×Dic191—21no—
41C22×Dic191D412yes—
42#15690276—28no—
43#15690274—28no—
44C2×C191⋊C8—21no—
45C2×C191⋊C8—21no—
46C2×C191⋊C8D412yes—
47Dic191⋊C4—28no—
48(C2×D191)⋊C4—44no—
49C4×Dic191—21no—
50C4×Dic191—21no—
51C2×Q8×C191—21no—
52C2×Q8×C191—21no—
53C2×Q8×C191—21no—
54C2×Q8×C191—21no—
55C2×Q8×C191—21no—
56C2×Q8×C191D412yes—
57C22×C4×C191—21no—
58C22×C4×C191—21no—
59C22×C4×C191C2311yescharacteristic
60C2×C8×C191—21no—
61C2×C8×C191—21no—
62C2×C8×C191D412yes—
63C4⋊C4×C191—21no—
64C4⋊C4×C191—21no—
65C22×D191—22no—
66C22×D191—41no—
67C22×D191—41no—
68C22×D191—42no—
69C22×D191—42no—
70Dic382—22no—
71Dic382—22no—
72Dic382—41no—
73Dic382—41no—
74D764—22no—
75D764—22no—
76D764—41no—
77D764—41no—
78C2×Dic191—22no—
79C2×Dic191—22no—
80C2×Dic191—22no—
81C2×Dic191—41no—
82C2×Dic191—41no—
83C2×Dic191SD1614yescomplemented
84C191⋊C8—22no—
85C23×C191C2×D411yescharacteristic
86Q8×C191—22no—
87Q8×C191—22no—
88Q8×C191—41no—
89Q8×C191—41no—
90C2×C4×C191—22no—
91C2×C4×C191—41no—
92C2×C4×C191—41no—
93C2×C4×C191—41no—
94C2×C4×C191—42no—
95C2×C4×C191C2×D411yescharacteristic
96C2×C4×C191C2×D411yescharacteristic
97C2×C4×C191C2×D411yescharacteristic
98C2×C4×C191C2×D411yescharacteristic
99C2×C4×C191C2×D411yescharacteristic
100C2×C4×C191#4111yescharacteristic
101C8×C191—22no—
102C22×C191#12011yescharacteristic
103C22×C191#12111yescharacteristic
104C22×C191#12711yescharacteristic
105C22×C191C2×SD1612yes—
106C22×C191#13712yes—
107C2×D191—42no—
108C2×D191—44no—
109C2×D191—82no—
110C2×D191—81no—
111C2×D191—81no—
112C4×C191—42no—
113C4×C191—81no—
114C4×C191#12011yescharacteristic
115C4×C191#12011yescharacteristic
116C4×C191#12111yescharacteristic
117C4×C191#12111yescharacteristic
118Dic191—24no—
119Dic191—42no—
120C2×C191#39211yescharacteristic
121C2×C191#44812yes—
122C2×C191#46112yes—
123C2×C191#49211yescharacteristic
124C2×C191#49711yescharacteristic
125D191—82no—
126C191#201311yescharacteristic, complemented, Sylow
127#2013—1911nomaximal, Sylow
128C22×SD16—1911no—
129C22×SD16—1911no—
130C2×C4⋊Q8—1911no—
131C2×#103—1911no—
132C2×#103D19111yescharacteristic, complemented
133#390—1911no—
134#336—1911no—
135C22×Q8—1911no—
136C22×Q8C2×D19111yescharacteristic
137C22×D4—1911no—
138C2×SD16—3822no—
139C2×SD16—3822no—
140C2×SD16—3822no—
141C2×SD16—3822no—
142C2×SD16—3822no—
143C2×SD16—3822no—
144C22×C8—1911no—
145C22×C8C2×D19111yescharacteristic
146C4⋊Q8—3822no—
147C4⋊Q8—3822no—
148C2×C4⋊C4—3822no—
149C2×C4⋊C4C2×D19111yescharacteristic
150C2×C22⋊C4—3822no—
151C2×C42—1911no—
152#103—22no—
153#103—3822no—
154C24—3821no—
155C2×Q8—21no—
156C2×Q8—21no—
157C2×Q8—21no—
158C2×Q8—21no—
159C2×Q8—21no—
160C2×Q8—3821no—
161C2×Q8—3821no—
162C2×Q8—3821no—
163C2×Q8—3821no—
164C2×Q8—3821no—
165C2×Q8—1912no—
166C2×Q8D76412yes—
167C2×D4—3821no—
168C2×D4—3821no—
169C2×D4—3821no—
170C2×D4—3821no—
171C2×D4—3821no—
172C2×D4—1912no—
173C22×C4—21no—
174C22×C4—21no—
175C22×C4—3821no—
176C22×C4—1912no—
177C22×C4C22×D19111yescharacteristic
178SD16—3828no—
179SD16—3828no—
180C2×C8—21no—
181C2×C8—21no—
182C2×C8—3821no—
183C2×C8—3821no—
184C2×C8—1912no—
185C2×C8C22⋊D19112yes—
186C4⋊C4—21no—
187C4⋊C4—21no—
188C4⋊C4—3828no—
189C22⋊C4—7644no—
190C42—3821no—
191C42—3821no—
192C23—3822no—
193C23—7642no—
194C23—7642no—
195C23—7641no—
196C23—7641no—
197C23D4×D19111yescharacteristic
198Q8—22no—
199Q8—22no—
200Q8—41no—
201Q8—41no—
202Q8—3822no—
203Q8—3822no—
204Q8—7641no—
205Q8—7641no—
206D4—3822no—
207D4—3822no—
208D4—7641no—
209D4—7641no—
210C2×C4—22no—
211C2×C4—41no—
212C2×C4—41no—
213C2×C4—42no—
214C2×C4—41no—
215C2×C4—3822no—
216C2×C4—3822no—
217C2×C4—3822no—
218C2×C4—1914no—
219C2×C4—7641no—
220C2×C4—7641no—
221C2×C4D4×D19111yescharacteristic
222C2×C4D4×D19111yescharacteristic
223C2×C4D4×D19111yescharacteristic
224C2×C4C2×C22⋊D19111yescharacteristic
225C2×C4C2×D76411yescharacteristic
226C2×C4#1569028711yescharacteristic
227C8—22no—
228C8—3822no—
229C22—15281no—
230C22—15281no—
231C22—15282no—
232C22—7642no—
233C22—7644no—
234C22#2025929211yescharacteristic
235C22#2025929511yescharacteristic
236C22#2025931811yescharacteristic
237C22SD16×D19112yes—
238C22#2025935412yes—
239C4—42no—
240C4—81no—
241C4—3824no—
242C4—7642no—
243C4#2025929011yescharacteristic
244C4#2025929211yescharacteristic
245C4#2025929511yescharacteristic
246C4#2025929611yescharacteristic
247C2—15282no—
248C2#2713257211yescharacteristic
249C2#2713280312yes—
250C2#2713286712yes—
251C2#2713303411yescharacteristic
252C2#2713305611yescharacteristic
subgroupG/H
centerC23D4×D191
commutator, cosocleC22×C4×C191C23
FrattiniC22×C4C22×D191
FittingC2×#103×C191C2
socleC23×C191C2×D4
prime radicalC22×D764C22
hypercenterC2×#103D191
hypocenterC191#2013
LCSG ▷ C22×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
3. C2×#20259320C2semidirect
4. C2×#20259245C2semidirect
6. #27132417C2semidirect
7. C2×#103×C191C2semidirect
83. C2×Dic191SD16semidirect
126. C191#2013semidirect
132. C2×#103D191semidirect

Maximal subgroups

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

subgroupindex
C22×#156902762
C22×#156902742
C2×#202593202
C2×#202592452
#271325642
#271324172
C2×#103×C1912
#2013191