Finite Group Databasebeta

← #37573698

Subgroups — #37573698

Order 24448.

278 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 278 conjugacy classes of subgroups — too many to draw. Only its 63 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#27133289C211yesmaximal, characteristic, complemented
2C2×#20259236C211yesmaximal, characteristic
3C2×#20259236C211yesmaximal, characteristic
4C2×#20259236C211yesmaximal, characteristic
5#27132430C211yesmaximal, characteristic, complemented
6#27132429C211yesmaximal, characteristic, complemented
7#342×C191C211yesmaximal, characteristic, complemented
8C22×C22⋊D191C2211yescharacteristic
9#20259301—22no—
10#20259299—22no—
11#20259299—22no—
12C2×C22⋊Dic191C2211yescharacteristic
13C2×C22⋊Dic191C2211yescharacteristic
14C2×C22⋊Dic191C2211yescharacteristic
15#20259236—22no—
16#20259236—22no—
17#20259236—22no—
18C2×C22⋊C4×C191C2211yescharacteristic
19C2×C22⋊C4×C191C2211yescharacteristic
20C2×C22⋊C4×C191C2211yescharacteristic
21C23×D191Q811yescharacteristic, complemented
22C2×Dic382—22no—
23C2×C22⋊D191—21no—
24C2×C22⋊D191—21no—
25C2×C22⋊D191—21no—
26C2×C22⋊D191—21no—
27C2×C22⋊D191—21no—
28C2×C22⋊D191—21no—
29C22×Dic191—21no—
30C22×Dic191—21no—
31C22×Dic191—21no—
32C22×Dic191Q811yescharacteristic, complemented
33C4⋊Dic191—22no—
34Dic191⋊C4—24no—
35C22⋊Dic191—21no—
36C22⋊Dic191—21no—
37C22⋊Dic191—21no—
38C22⋊Dic191—21no—
39C22⋊Dic191D412yes—
40C22⋊Dic191D412yes—
41C24×C191C2311yescharacteristic
42C22×C4×C191—21no—
43C22×C4×C191—21no—
44C22×C4×C191—21no—
45C22⋊C4×C191—21no—
46C22⋊C4×C191—21no—
47C22⋊C4×C191—21no—
48C22⋊C4×C191—21no—
49C22⋊C4×C191—21no—
50C22⋊C4×C191D412yes—
51C22×D191—21no—
52C22×D191—21no—
53C22×D191—21no—
54C22×D191—81no—
55Dic382—82no—
56C22⋊D191—41no—
57C22⋊D191—41no—
58C22⋊D191—41no—
59C22⋊D191—41no—
60C2×Dic191—22no—
61C2×Dic191—22no—
62C2×Dic191—21no—
63C2×Dic191—21no—
64C2×Dic191—21no—
65C2×Dic191—41no—
66C2×Dic191—81no—
67C2×Dic191—81no—
68C2×Dic191—81no—
69C23×C191—81no—
70C23×C191C2×D411yescharacteristic
71C23×C191C2×D411yescharacteristic
72C23×C191C2×D411yescharacteristic
73C23×C191C2×Q811yescharacteristic
74C23×C191#4111yescharacteristic
75C23×C191#4111yescharacteristic
76C23×C191#4111yescharacteristic
77C2×C4×C191—22no—
78C2×C4×C191—41no—
79C2×C4×C191—41no—
80C2×C4×C191—81no—
81C2×C4×C191—81no—
82C2×C4×C191—81no—
83C22×C191—41no—
84C22×C191—41no—
85C22×C191—41no—
86C22×C191—41no—
87C22×C191—41no—
88C22×C191—41no—
89C22×C191—41no—
90C22×C191#12011yescharacteristic
91C22×C191C22⋊Q811yescharacteristic
92C22×C191C22⋊Q811yescharacteristic
93C22×C191C22⋊Q811yescharacteristic
94C22×C191#12411yescharacteristic
95C22×C191#12411yescharacteristic
96C22×C191#12411yescharacteristic
97C2×D191—41no—
98C2×D191—81no—
99C2×D191—81no—
100C2×D191—81no—
101C4×C191—42no—
102C4×C191—81no—
103C4×C191—81no—
104Dic191—42no—
105Dic191—42no—
106Dic191—41no—
107Dic191—81no—
108C2×C191—21no—
109C2×C191—21no—
110C2×C191—21no—
111C2×C191—21no—
112C2×C191—21no—
113C2×C191—21no—
114C2×C191—21no—
115C2×C191#39311yescharacteristic
116D191—81no—
117C191#203211yescharacteristic, complemented, Sylow
118#2032—1911nomaximal, Sylow
119#543—1911no—
120C2×#99—1911no—
121C2×#99—1911no—
122C2×#99—1911no—
123#342—1911no—
124#342—1911no—
125#342D19111yescharacteristic, complemented
126C22×D4—1911no—
127C22⋊Q8—3822no—
128C22⋊Q8—3822no—
129C22⋊Q8—3822no—
130C2×C22⋊C4—1911no—
131C2×C22⋊C4—1911no—
132C2×C22⋊C4—1911no—
133C2×C22⋊C4C2×D19111yescharacteristic
134C2×C22⋊C4C2×D19111yescharacteristic
135C2×C22⋊C4C2×D19111yescharacteristic
136#99—3822no—
137#99—3822no—
138#99—3822no—
139C24—1911no—
140C24C22×D19111yescharacteristic
141C2×Q8—3822no—
142C2×D4—3821no—
143C2×D4—3821no—
144C2×D4—3821no—
145C2×D4—3821no—
146C2×D4—3821no—
147C2×D4—3821no—
148C22×C4—21no—
149C22×C4—21no—
150C22×C4—21no—
151C22×C4—3821no—
152C22×C4—3821no—
153C22×C4—3821no—
154C22×C4—1911no—
155C4⋊C4—3824no—
156C4⋊C4—3822no—
157C22⋊C4—21no—
158C22⋊C4—21no—
159C22⋊C4—21no—
160C22⋊C4—21no—
161C22⋊C4—21no—
162C22⋊C4—3821no—
163C22⋊C4—3821no—
164C22⋊C4—3821no—
165C22⋊C4—3821no—
166C22⋊C4—1912no—
167C22⋊C4—1912no—
168C22⋊C4D76412yes—
169C23—81no—
170C23—3821no—
171C23—3821no—
172C23—3821no—
173C23—15281no—
174C23D4×D19111yescharacteristic
175C23D4×D19111yescharacteristic
176C23C2×D76411yescharacteristic
177C23Q8×D19111yescharacteristic
178C23#1569028611yescharacteristic
179C23#1569028711yescharacteristic
180C23#1569028711yescharacteristic
181Q8—15282no—
182D4—7641no—
183D4—7641no—
184D4—7641no—
185D4—7641no—
186C2×C4—22no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—81no—
190C2×C4—81no—
191C2×C4—81no—
192C2×C4—3822no—
193C2×C4—3822no—
194C2×C4—3821no—
195C2×C4—3821no—
196C2×C4—3821no—
197C2×C4—15281no—
198C2×C4—15281no—
199C2×C4—15281no—
200C2×C4—7641no—
201C22—41no—
202C22—41no—
203C22—41no—
204C22—41no—
205C22—41no—
206C22—41no—
207C22—41no—
208C22—15281no—
209C22—15281no—
210C22—15281no—
211C22—7641no—
212C22#2025929211yescharacteristic
213C22#2025930011yescharacteristic
214C22#2025930011yescharacteristic
215C22#2025930211yescharacteristic
216C22#2025930811yescharacteristic
217C22#2025930811yescharacteristic
218C22#2025931011yescharacteristic
219C4—42no—
220C4—81no—
221C4—81no—
222C4—15281no—
223C4—7642no—
224C4—7642no—
225C4—7641no—
226C2—21no—
227C2—21no—
228C2—21no—
229C2—21no—
230C2—21no—
231C2—21no—
232C2—21no—
233C2—15281no—
234C2#2713257611yescharacteristic
subgroupG/H
centerC2#27132576
commutator, cosocleC24×C191C23
FrattiniC24C22×D191
Fitting#342×C191C2
socleC2×C191#393
prime radicalC22×C22⋊D191C22
hypercenter#342D191
hypocenterC191#2032
LCSG ▷ C24×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C2 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
1. #27133289C2semidirect
5. #27132430C2semidirect
6. #27132429C2semidirect
7. #342×C191C2semidirect
21. C23×D191Q8semidirect
32. C22×Dic191Q8semidirect
117. C191#2032semidirect
125. #342D191semidirect

Maximal subgroups

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

subgroupindex
#271332892
C2×#202592362
#271324302
#271324292
#342×C1912
#2032191