Finite Group Databasebeta

← #37571507

Subgroups — #37571507

Order 24448.

280 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 51 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#27133221C211yesmaximal, characteristic
2#27132977C211yesmaximal, characteristic, complemented
3#27132974C211yesmaximal, characteristic, complemented
4#27132590C211yesmaximal, characteristic, complemented
5#27132396C211yesmaximal, characteristic, complemented
6#27132386C211yesmaximal, characteristic, complemented
7#327×C191C211yesmaximal, characteristic, complemented
8C2×D4×D191—21no—
9#20259307—21no—
10#20259304—21no—
11#20259296C2211yescharacteristic
12#20259294—21no—
13#20259292—21no—
14#20259290—21no—
15C2×C4⋊Dic191C2211yescharacteristic, complemented
16C2×(C2×D191)⋊C4—21no—
17C2×(C2×D191)⋊C4C2211yescharacteristic
18#20259256—21no—
19#20259255—21no—
20#20259244—21no—
21#20259243—21no—
22C22⋊(C191⋊C8)C2211yescharacteristic, complemented
23C191⋊#95—21no—
24#121×C191C2211yescharacteristic
25C22⋊C8×C191C2211yescharacteristic, complemented
26#95×C191C2211yescharacteristic, complemented
27C23×D191—21no—
28C23×D191D411yescharacteristic
29C2×D764—21no—
30C2×D764D411yescharacteristic
31C2×C22⋊D191—21no—
32C2×C22⋊D191—21no—
33C2×C22⋊D191—21no—
34D4×D191—42no—
35D4×D191—42no—
36C22×Dic191—21no—
37C22×Dic191D411yescharacteristic
38C2×C4×D191—21no—
39C2×C191⋊C8—21no—
40C4⋊Dic191—21no—
41C4⋊Dic191—21no—
42C4⋊Dic191D411yescharacteristic
43Dic191⋊C4—21no—
44C22⋊Dic191—21no—
45(C2×D191)⋊C4—21no—
46(C2×D191)⋊C4—21no—
47(C2×D191)⋊C4—21no—
48(C2×D191)⋊C4—21no—
49(C2×D191)⋊C4—42no—
50C2×D4×C191—21no—
51C2×D4×C191D411yescharacteristic
52C22×C4×C191—21no—
53C22×C4×C191C2311yescharacteristic
54C2×C8×C191—21no—
55C4⋊C4×C191D411yescharacteristic
56C22⋊C4×C191—21no—
57C22×D191—21no—
58C22×D191—21no—
59C22×D191—21no—
60C22×D191—42no—
61C22×D191—41no—
62C22×D191—41no—
63C22×D191—81no—
64C22×D191—81no—
65C22×D191D812yes—
66D764—41no—
67D764—42no—
68C22⋊D191—42no—
69C22⋊D191—41no—
70C22⋊D191—41no—
71C22⋊D191—81no—
72C2×Dic191—21no—
73C2×Dic191—21no—
74C2×Dic191—41no—
75C2×Dic191—41no—
76C2×Dic191—41no—
77C2×Dic191—41no—
78C4×D191—42no—
79C191⋊C8—41no—
80C23×C191—21no—
81C23×C191C2×D411yescharacteristic
82D4×C191—41no—
83D4×C191—41no—
84D4×C191—41no—
85C2×C4×C191—21no—
86C2×C4×C191—41no—
87C2×C4×C191—41no—
88C2×C4×C191—41no—
89C2×C4×C191—41no—
90C2×C4×C191C2×D411yescharacteristic
91C2×C4×C191C2×D411yescharacteristic
92C8×C191—41no—
93C22×C191—21no—
94C22×C191—21no—
95C22×C191—41no—
96C22×C191—41no—
97C22×C191—41no—
98C22×C191#12011yescharacteristic
99C22×C191C2×D811yescharacteristic
100C22×C191AGL(1,ℤ/8)11yescharacteristic
101C2×D191—22no—
102C2×D191—41no—
103C2×D191—41no—
104C2×D191—42no—
105C2×D191—41no—
106C2×D191—41no—
107C2×D191—41no—
108C2×D191—81no—
109C2×D191—84no—
110C4×C191—21no—
111C4×C191—21no—
112C4×C191—41no—
113C4×C191—81no—
114Dic191—41no—
115Dic191—41no—
116Dic191—81no—
117C2×C191—21no—
118C2×C191—21no—
119C2×C191—81no—
120C2×C191#44711yescharacteristic
121C2×C191#45511yescharacteristic
122C2×C191#45811yescharacteristic
123D191—42no—
124D191—81no—
125C191#160711yescharacteristic, complemented, Sylow
126#1607—1911nomaximal, Sylow
127#534—1911no—
128#480—1911no—
129#480—1911no—
130#397—1911no—
131#327—1911no—
132#327D19111yescharacteristic, complemented
133#323—1911no—
134C22×D4—3821no—
135#123—3821no—
136#123—3821no—
137#121—3821no—
138#121—1911no—
139#121C2×D19111yescharacteristic
140#120—3821no—
141#120—3821no—
142C2×C4⋊C4—1911no—
143C2×C22⋊C4—3821no—
144C2×C22⋊C4—1911no—
145#107—3821no—
146#107—3821no—
147#102—3821no—
148#102—3821no—
149C22⋊C8—1911no—
150C22⋊C8C2×D19111yescharacteristic, complemented
151#95—3821no—
152#95C2×D19111yescharacteristic, complemented
153C24—3821no—
154C24—1911no—
155C2×D4—21no—
156C2×D4—3821no—
157C2×D4—3821no—
158C2×D4—3821no—
159C2×D4—3821no—
160C2×D4—1911no—
161C2×D4—7642no—
162C2×D4—7642no—
163C2×D4D76411yescharacteristic
164C22×C4—21no—
165C22×C4—3821no—
166C22×C4—3821no—
167C22×C4—1911no—
168C22×C4C22×D19111yescharacteristic
169C2×C8—21no—
170C2×C8—3821no—
171C4⋊C4—3821no—
172C4⋊C4—3821no—
173C4⋊C4—3821no—
174C4⋊C4—1911no—
175C4⋊C4D76411yescharacteristic
176C22⋊C4—21no—
177C22⋊C4—3821no—
178C22⋊C4—3821no—
179C22⋊C4—3821no—
180C22⋊C4—3821no—
181C22⋊C4—3821no—
182C22⋊C4—7642no—
183C23—21no—
184C23—3821no—
185C23—3821no—
186C23—3821no—
187C23—1912no—
188C23—15281no—
189C23—15281no—
190C23—7641no—
191C23—7641no—
192C23—7642no—
193C23D4×D19111yescharacteristic
194D4—41no—
195D4—41no—
196D4—41no—
197D4—15281no—
198D4—7641no—
199D4—7642no—
200D4—7642no—
201D4—7641no—
202D4—7641no—
203C2×C4—21no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—41no—
207C2×C4—41no—
208C2×C4—3821no—
209C2×C4—3821no—
210C2×C4—7642no—
211C2×C4—7641no—
212C2×C4—7641no—
213C2×C4—7641no—
214C2×C4—7641no—
215C2×C4D4×D19111yescharacteristic
216C2×C4C2×D76411yescharacteristic
217C8—41no—
218C8—7641no—
219C22—21no—
220C22—21no—
221C22—41no—
222C22—41no—
223C22—41no—
224C22—3822no—
225C22—15281no—
226C22—15284no—
227C22—7642no—
228C22—7641no—
229C22—7641no—
230C22—7641no—
231C22—7641no—
232C22—7641no—
233C22#2025929211yescharacteristic
234C22D8×D19111yescharacteristic
235C22#2025934911yescharacteristic
236C4—21no—
237C4—21no—
238C4—41no—
239C4—81no—
240C4—15281no—
241C4—7641no—
242C4—7641no—
243C2—21no—
244C2—21no—
245C2—81no—
246C2—15281no—
247C2—7642no—
248C2#2713279811yescharacteristic
249C2#2713284211yescharacteristic
250C2#2713285411yescharacteristic
subgroupG/H
centerC22#20259292
commutator, cosocleC22×C4×C191C23
FrattiniC22×C4C22×D191
Fitting#327×C191C2
socleC22×C191#120
prime radical#27133221C2
hypercenter#327D191
hypocenterC191#1607
LCSG ▷ C22×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. #27132977C2semidirect
3. #27132974C2semidirect
4. #27132590C2semidirect
5. #27132396C2semidirect
6. #27132386C2semidirect
7. #327×C191C2semidirect
15. C2×C4⋊Dic191C22semidirect
22. C22⋊(C191⋊C8)C22semidirect
25. C22⋊C8×C191C22semidirect
26. #95×C191C22semidirect
125. C191#1607semidirect
132. #327D191semidirect
150. C22⋊C8C2×D191semidirect
152. #95C2×D191semidirect

Maximal subgroups

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

subgroupindex
#271332212
#271329772
#271329742
#271325902
#271323962
#271323862
#327×C1912
#1607191