Finite Group Databasebeta

← #37571073

Subgroups — #37571073

Order 24448.

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

normal subgroups only

This group has 284 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#27133173C211yesmaximal, characteristic
2C22⋊C8×D191C211yesmaximal, characteristic, complemented
3#27132525C211yesmaximal, characteristic, complemented
4#27132401C211yesmaximal, characteristic, complemented
5#27132399C211yesmaximal, characteristic, complemented
6#27132397C211yesmaximal, characteristic, complemented
7#327×C191C211yesmaximal, characteristic, complemented
8C2×#15690286C411yescharacteristic, complemented
9C22×C4×D191C2211yescharacteristic
10C2×C8×D191—21no—
11#20259304—21no—
12#20259302C411yescharacteristic, complemented
13#20259301C2211yescharacteristic
14#20259293C411yescharacteristic, complemented
15#20259290—21no—
16D4×Dic191—21no—
17(C22⋊D191)⋊C4—21no—
18#20259280C411yescharacteristic, complemented
19C2×(C2×D191)⋊C4—21no—
20C22⋊(C191⋊C8)C2211yescharacteristic
21(C2×D191)⋊C8—21no—
22C191⋊#95—21no—
23C191⋊#95C2211yescharacteristic
24#121×C191C2211yescharacteristic
25C22⋊C8×C191C2211yescharacteristic
26#95×C191C2211yescharacteristic
27C23×D191D411yescharacteristic
28#15690286—42no—
29C2×Dic382C2×C411yescharacteristic
30C2×C22⋊D191—21no—
31C2×C22⋊D191—21no—
32C22×Dic191—21no—
33C22×Dic191—21no—
34C22×Dic191D411yescharacteristic
35C2×C4×D191—42no—
36C2×C4×D191C2×C411yescharacteristic
37C2×C4×D191C2×C411yescharacteristic
38C2×C4×D191D411yescharacteristic
39C2×C4×D191D411yescharacteristic
40C2×C191⋊C8—21no—
41C8×D191—42no—
42C4⋊Dic191—21no—
43C4⋊Dic191C2×C411yescharacteristic
44Dic191⋊C4—21no—
45C22⋊Dic191—21no—
46C22⋊Dic191—21no—
47(C2×D191)⋊C4—21no—
48(C2×D191)⋊C4—21no—
49(C2×D191)⋊C4—42no—
50C4×Dic191—21no—
51C2×D4×C191—21no—
52C2×D4×C191C2×C411yescharacteristic
53C22×C4×C191—21no—
54C22×C4×C191C2311yescharacteristic
55C2×C8×C191—21no—
56C4⋊C4×C191C2×C411yescharacteristic
57C22⋊C4×C191—21no—
58C22×D191—21no—
59C22×D191—21no—
60C22×D191—22no—
61C22×D191—41no—
62C22×D191C22⋊C411yescharacteristic
63C22×D191C22⋊C411yescharacteristic
64Dic382—41no—
65C22⋊D191—42no—
66C22⋊D191—42no—
67C2×Dic191—21no—
68C2×Dic191—21no—
69C2×Dic191—41no—
70C2×Dic191—42no—
71C2×Dic191—41no—
72C2×Dic191—41no—
73C2×Dic191—41no—
74C2×Dic191C22⋊C411yescharacteristic
75C2×Dic191C22⋊C411yescharacteristic
76C4×D191—22no—
77C4×D191—22no—
78C4×D191—41no—
79C4×D191—41no—
80C191⋊C8—41no—
81C23×C191—21no—
82C23×C191C2×D411yescharacteristic
83D4×C191—41no—
84D4×C191—41no—
85D4×C191—41no—
86C2×C4×C191—21no—
87C2×C4×C191—41no—
88C2×C4×C191—41no—
89C2×C4×C191—41no—
90C2×C4×C191—41no—
91C2×C4×C191C22×C411yescharacteristic
92C2×C4×C191C2×D411yescharacteristic
93C8×C191—41no—
94C22×C191—21no—
95C22×C191—21no—
96C22×C191—41no—
97C22×C191—41no—
98C22×C191—41no—
99C22×C191C2×C22⋊C411yescharacteristic
100C22×C191#13511yescharacteristic
101C22×C191#13511yescharacteristic
102C2×D191—21no—
103C2×D191—21no—
104C2×D191—21no—
105C2×D191—21no—
106C2×D191—21no—
107C2×D191—42no—
108C2×D191—42no—
109C2×D191#9912yes—
110C4×C191—21no—
111C4×C191—21no—
112C4×C191—41no—
113C4×C191—81no—
114Dic191—21no—
115Dic191—21no—
116Dic191—41no—
117Dic191—41no—
118Dic191—81no—
119C2×C191—21no—
120C2×C191—21no—
121C2×C191—81no—
122C2×C191C2×#9911yescharacteristic
123C2×C191#41611yescharacteristic
124C2×C191#42111yescharacteristic
125D191—22no—
126D191—41no—
127C191#151611yescharacteristic, complemented, Sylow
128#1516—1911nomaximal, Sylow
129#525—1911no—
130C2×C22⋊C8—1911no—
131#381—1911no—
132#328—1911no—
133#328—1911no—
134#327—1911no—
135#327D19111yescharacteristic, complemented
136C2×#41—1911no—
137C23×C4—1911no—
138C22×C8—3821no—
139#123—3821no—
140C22⋊Q8—1911no—
141C22⋊Q8—1911no—
142#121—1911no—
143#121C2×D19111yescharacteristic
144#120—3821no—
145C4×D4—3821no—
146C4×D4—3821no—
147#117—1911no—
148C2×C22⋊C4—3821no—
149C22⋊C8—3821no—
150C22⋊C8—1911no—
151C22⋊C8C2×D19111yescharacteristic
152#95—3821no—
153#95—1911no—
154#95C2×D19111yescharacteristic
155C24—1911no—
156#41—7642no—
157C2×Q8—1911no—
158C2×D4—21no—
159C2×D4—3821no—
160C2×D4—3821no—
161C2×D4C4×D19111yescharacteristic
162C22×C4—21no—
163C22×C4—3821no—
164C22×C4—3821no—
165C22×C4—1911no—
166C22×C4—1911no—
167C22×C4—1911no—
168C22×C4—1911no—
169C22×C4—1911no—
170C22×C4—7642no—
171C22×C4C22×D19111yescharacteristic
172C2×C8—21no—
173C2×C8—3821no—
174C2×C8—7642no—
175C4⋊C4—3821no—
176C4⋊C4—3821no—
177C4⋊C4—1911no—
178C4⋊C4C4×D19111yescharacteristic
179C22⋊C4—21no—
180C22⋊C4—3821no—
181C22⋊C4—3821no—
182C22⋊C4—3821no—
183C22⋊C4—3821no—
184C22⋊C4—7642no—
185C42—3821no—
186C23—21no—
187C23—3822no—
188C23—3821no—
189C23—3821no—
190C23—1911no—
191C23—1911no—
192C23—7641no—
193C23D4×D19111yescharacteristic
194Q8—7641no—
195D4—41no—
196D4—41no—
197D4—41no—
198D4—7642no—
199D4—7642no—
200C2×C4—21no—
201C2×C4—41no—
202C2×C4—41no—
203C2×C4—41no—
204C2×C4—41no—
205C2×C4—3822no—
206C2×C4—3822no—
207C2×C4—3821no—
208C2×C4—3821no—
209C2×C4—1911no—
210C2×C4—1911no—
211C2×C4—7641no—
212C2×C4—7641no—
213C2×C4—7641no—
214C2×C4—7642no—
215C2×C4—7641no—
216C2×C4—7641no—
217C2×C4—7641no—
218C2×C4C2×C4×D19111yescharacteristic
219C2×C4D4×D19111yescharacteristic
220C8—41no—
221C8—7641no—
222C22—21no—
223C22—21no—
224C22—41no—
225C22—41no—
226C22—41no—
227C22—3821no—
228C22—3821no—
229C22—3821no—
230C22—3821no—
231C22—3821no—
232C22—1912no—
233C22—7642no—
234C22—7642no—
235C22C22⋊C4×D19111yescharacteristic
236C22#2025934111yescharacteristic
237C22#2025934311yescharacteristic
238C4—21no—
239C4—21no—
240C4—41no—
241C4—81no—
242C4—3821no—
243C4—3821no—
244C4—15281no—
245C4—7641no—
246C4—7641no—
247C2—21no—
248C2—21no—
249C2—81no—
250C2—3822no—
251C2—7641no—
252C2#99×D19111yescharacteristic
253C2#2713265611yescharacteristic
254C2#2713267811yescharacteristic
subgroupG/H
centerC22C22⋊C4×D191
commutatorC2×C4×C191C22×C4
FrattiniC22×C4C22×D191
Fitting#327×C191C2
socleC22×C191C2×C22⋊C4
prime radical#27133173C2
cosocleC22×C4×C191C23
hypercenter#327D191
hypocenterC191#1516
LCSG ▷ C2×C4×C191 ▷ C22×C191 ▷ C191
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

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

NH ≅ G/Ntype
2. C22⋊C8×D191C2semidirect
3. #27132525C2semidirect
4. #27132401C2semidirect
5. #27132399C2semidirect
6. #27132397C2semidirect
7. #327×C191C2semidirect
8. C2×#15690286C4semidirect
12. #20259302C4semidirect
14. #20259293C4semidirect
18. #20259280C4semidirect
127. C191#1516semidirect
135. #327D191semidirect

Maximal subgroups

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

subgroupindex
#271331732
C22⋊C8×D1912
#271325252
#271324012
#271323992
#271323972
#327×C1912
#1516191