Finite Group Databasebeta

← #37576144

Subgroups — #37576144

Order 24448.

836 conjugacy classes of subgroups; only the 185 normal subgroups are shown.

normal subgroups only

This group has 836 conjugacy classes of subgroups — too many to draw. Only its 185 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×#20259320C211yesmaximal, characteristic, complemented
2C2×#20259309C211yesmaximal, characteristic, complemented
3C2×#20259301C211yesmaximal, characteristic, complemented
4#27132577C214yesmaximal, complemented
5#27132570C211yesmaximal, characteristic, complemented
6#27132566C211yesmaximal, characteristic, complemented
7#27132536C214yesmaximal, complemented
8C4×C22⋊Dic191C211yesmaximal, characteristic, complemented
9C22×#41×C191C211yesmaximal, characteristic
10C22×Dic382C2211yescharacteristic
11#20259320—24no—
12#20259309—24no—
13#20259301—24no—
14C2×C4⋊Dic191C2211yescharacteristic
15C2×Dic191⋊C4C2214yes—
16C2×Dic191⋊C4C2212yes—
17C2×C22⋊Dic191C2212yes—
18C2×C22⋊Dic191C2214yes—
19C2×C22⋊Dic191C2214yes—
20C2×C22⋊Dic191C2212yes—
21C2×C4×Dic191C2211yescharacteristic
22C2×C4×Dic191C2211yescharacteristic
23C191⋊#95C2212yes—
24C191⋊#95C2214yes—
25C2×#41×C191—24no—
26C2×#41×C191—24no—
27C2×#41×C191—24no—
28C22×Q8×C191C2211yescharacteristic
29C22×D4×C191C2212yes—
30C22×D4×C191C2211yescharacteristic
31C23×C4×C191C2212yes—
32C23×C4×C191C2211yescharacteristic
33C2×Dic382—22no—
34C2×Dic382—22no—
35C2×Dic382—22no—
36C22×Dic191C2312yes—
37C22×Dic191C2312yes—
38C22×Dic191C2312yes—
39C22×Dic191C2312yes—
40C4⋊Dic191—22no—
41Dic191⋊C4—24no—
42Dic191⋊C4—28no—
43C22⋊Dic191—24no—
44C22⋊Dic191—28no—
45C22⋊Dic191—24no—
46C22⋊Dic191—28no—
47C4×Dic191—22no—
48C4×Dic191—22no—
49C24×C191C2312yes—
50C24×C191C2311yescharacteristic
51#41×C191—232no—
52C2×Q8×C191—22no—
53C2×Q8×C191—22no—
54C2×Q8×C191D414yes—
55C2×D4×C191—24no—
56C2×D4×C191—24no—
57C2×D4×C191—24no—
58C2×D4×C191—22no—
59C2×D4×C191—22no—
60C2×D4×C191D414yes—
61C22×C4×C191—24no—
62C22×C4×C191—24no—
63C22×C4×C191—24no—
64C22×C4×C191—22no—
65C22×C4×C191—22no—
66C22×C4×C191D414yes—
67C22×C4×C191C2311yescharacteristic
68C22×C4×C191C2312yes—
69C22×C4×C191C2311yescharacteristic
70Dic382—44no—
71C2×Dic191—22no—
72C2×Dic191—22no—
73C2×Dic191—22no—
74C2×Dic191—22no—
75C2×Dic191—22no—
76C2×Dic191—22no—
77C2×Dic191—22no—
78C2×Dic191—24no—
79C2×Dic191—22no—
80C2×Dic191—22no—
81C2×Dic191#4114yescomplemented
82C23×C191—22no—
83C23×C191—21no—
84C23×C191—22no—
85C23×C191—21no—
86C23×C191—22no—
87C23×C191—24no—
88C23×C191—22no—
89C23×C191—24no—
90C23×C191C2×D414yes—
91C23×C191C2×D412yes—
92C23×C191C2411yescharacteristic
93Q8×C191—28no—
94D4×C191—216no—
95D4×C191—28no—
96C2×C4×C191—216no—
97C2×C4×C191—21no—
98C2×C4×C191—21no—
99C2×C4×C191—22no—
100C2×C4×C191—22no—
101C2×C4×C191—28no—
102C2×C4×C191C2×D412yes—
103C2×C4×C191C2×D414yes—
104C2×C4×C191C2×D412yes—
105C2×C4×C191C2×D412yes—
106C2×C4×C191C2×D412yes—
107C22×C191—24no—
108C22×C191—22no—
109C22×C191—22no—
110C22×C191—22no—
111C22×C191—28no—
112C22×C191—42no—
113C22×C191—42no—
114C22×C191—42no—
115C22×C191—42no—
116C22×C191—44no—
117C22×C191C22×D411yescharacteristic
118C22×C191C22×D411yescharacteristic
119C22×C191C22×D411yescharacteristic
120C22×C191C2×#4112yes—
121C22×C1912−1+412yes—
122C4×C191—22no—
123C4×C191—24no—
124C4×C191#12014yes—
125Dic191—24no—
126Dic191—42no—
127Dic191—42no—
128Dic191—42no—
129C2×C191—42no—
130C2×C191—44no—
131C2×C191C2×#12011yescharacteristic
132C2×C191#53211yescharacteristic
133C2×C191#53611yescharacteristic
134C2×C191#54712yes—
135C2×C191#54812yes—
136C191#243211yescharacteristic, complemented, Sylow
137#2432—1911nomaximal, Sylow
138C22×#41D19111yescharacteristic
139C2×C4⋊Q8—1911no—
140C2×#124—1911no—
141C2×C22⋊Q8—1911no—
142#394—1914no—
143#391—1911no—
144#390—1911no—
145#385—1914no—
146C4×C22⋊C4—1911no—
147C2×#41—24no—
148C2×#41—24no—
149C2×#41—24no—
150C22×Q8—1911no—
151C22×Q8C2×D19111yescharacteristic
152C22×D4C2×D19112yes—
153C22×D4C2×D19111yescharacteristic
154C23×C4C2×D19112yes—
155C23×C4C2×D19111yescharacteristic
156C4⋊Q8—3824no—
157#124—3824no—
158C22⋊Q8—3824no—
159C2×C4⋊C4—1912no—
160C2×C4⋊C4—1911no—
161C2×C4⋊C4—1914no—
162C2×C22⋊C4—1912no—
163C2×C22⋊C4—1914no—
164C2×C22⋊C4—1912no—
165C2×C22⋊C4—1914no—
166C2×C42—1911no—
167C2×C42—1911no—
168#95—1912no—
169#95—1914no—
170C24C22×D19112yes—
171C24C22×D19111yescharacteristic
172#41—232no—
173C2×Q8—22no—
174C2×Q8—22no—
175C2×Q8—3822no—
176C2×Q8—3822no—
177C2×Q8—3822no—
178C2×Q8C22⋊D19114yes—
179C2×D4—24no—
180C2×D4—24no—
181C2×D4—24no—
182C2×D4—22no—
183C2×D4—22no—
184C2×D4C22⋊D19114yes—
185C22×C4—24no—
186C22×C4—24no—
187C22×C4—24no—
188C22×C4—22no—
189C22×C4—22no—
190C22×C4—1912no—
191C22×C4—1912no—
192C22×C4—1912no—
193C22×C4—1912no—
194C22×C4C22⋊D19114yes—
195C22×C4C22×D19111yescharacteristic
196C22×C4C22×D19112yes—
197C22×C4C22×D19111yescharacteristic
198C4⋊C4—3824no—
199C4⋊C4—3828no—
200C4⋊C4—3822no—
201C22⋊C4—3824no—
202C22⋊C4—3828no—
203C22⋊C4—3824no—
204C22⋊C4—3828no—
205C42—3822no—
206C42—3822no—
207C23—22no—
208C23—21no—
209C23—22no—
210C23—21no—
211C23—22no—
212C23—24no—
213C23—22no—
214C23—24no—
215C23C2×C22⋊D19114yes—
216C23C2×C22⋊D19112yes—
217C23C23×D19111yescharacteristic
218Q8—28no—
219Q8—7644no—
220D4—216no—
221D4—28no—
222C2×C4—216no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—22no—
226C2×C4—22no—
227C2×C4—28no—
228C2×C4—3822no—
229C2×C4—3822no—
230C2×C4—3822no—
231C2×C4—3822no—
232C2×C4—3822no—
233C2×C4—3822no—
234C2×C4—3822no—
235C2×C4—3824no—
236C2×C4—3822no—
237C2×C4—3822no—
238C2×C4—1914no—
239C2×C4C2×C22⋊D19112yes—
240C2×C4C2×C22⋊D19114yes—
241C2×C4C2×C22⋊D19112yes—
242C2×C4C2×C22⋊D19112yes—
243C2×C4C2×C22⋊D19112yes—
244C22—22no—
245C22—22no—
246C22—28no—
247C22—24no—
248C22—22no—
249C22—42no—
250C22—42no—
251C22—42no—
252C22—42no—
253C22—44no—
254C22C22×C22⋊D19111yescharacteristic
255C22C22×C22⋊D19111yescharacteristic
256C22C22×C22⋊D19111yescharacteristic
257C22#41×D19112yes—
258C22#2025936912yes—
259C4—22no—
260C4—24no—
261C4—3824no—
262C4—7642no—
263C4—7642no—
264C4—7642no—
265C4#2025929114yes—
266C2—42no—
267C2—44no—
268C2C2×#2025929111yescharacteristic
269C2#2713320911yescharacteristic
270C2#2713323411yescharacteristic
271C2#2713331212yes—
272C2#2713332012yes—
subgroupG/H
center, FrattiniC23C23×D191
commutator, socle, cosocleC23×C191C24
Fitting, prime radicalC22×#41×C191C2
hypercenterC22×#41D191
hypocenterC191#2432
LCSG ▷ C23×C191 ▷ C191
UCSC1 ◁ C23 ◁ C22×#41

Complements

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

NH ≅ G/Ntype
1. C2×#20259320C2semidirect
2. C2×#20259309C2semidirect
3. C2×#20259301C2semidirect
4. #27132577C2semidirect
5. #27132570C2semidirect
6. #27132566C2semidirect
7. #27132536C2semidirect
8. C4×C22⋊Dic191C2semidirect
81. C2×Dic191#41semidirect
136. C191#2432semidirect

Maximal subgroups

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

subgroupindex
C2×#202593202
C2×#202593092
C2×#202593012
#271325772
#271325702
#271325662
#271325362
C4×C22⋊Dic1912
C22×#41×C1912
#2432191