Finite Group Databasebeta

← #37571558

Subgroups — #37571558

Order 24448.

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

normal subgroups only

This group has 246 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#27133240C211yesmaximal, characteristic
2#27132982C211yesmaximal, characteristic, complemented
3#27132979C211yesmaximal, characteristic, complemented
4#27132603C211yesmaximal, characteristic, complemented
5#27132396C211yesmaximal, characteristic, complemented
6#27132388C211yesmaximal, characteristic, complemented
7#327×C191C211yesmaximal, characteristic, complemented
8C2×#15690286—21no—
9#20259300—21no—
10#20259299—21no—
11#20259296C2211yescharacteristic
12#20259295—21no—
13#20259294—21no—
14#20259294—21no—
15C2×C4⋊Dic191C2211yescharacteristic
16C2×Dic191⋊C4C2211yescharacteristic
17#20259254—21no—
18#20259253—21no—
19#20259244—21no—
20#20259243—21no—
21C22⋊(C191⋊C8)C2211yescharacteristic
22C191⋊#95—21no—
23C191⋊#95—21no—
24#121×C191C2211yescharacteristic
25C22⋊C8×C191C2211yescharacteristic
26#95×C191C2211yescharacteristic
27#15690286—42no—
28#15690286—42no—
29C2×Dic382—21no—
30C2×D764D411yescharacteristic
31C2×C22⋊D191—21no—
32C2×C22⋊D191—21no—
33C2×C22⋊D191—21no—
34C22×Dic191—21no—
35C22×Dic191—21no—
36C22×Dic191D411yescharacteristic
37C22×Dic191D411yescharacteristic
38C2×C4×D191—21no—
39C2×C191⋊C8—21no—
40C4⋊Dic191—21no—
41C4⋊Dic191—21no—
42C4⋊Dic191D411yescharacteristic
43Dic191⋊C4—21no—
44Dic191⋊C4—21no—
45Dic191⋊C4—21no—
46C22⋊Dic191—21no—
47(C2×D191)⋊C4—21no—
48(C2×D191)⋊C4—21no—
49C2×D4×C191—21no—
50C2×D4×C191D411yescharacteristic
51C22×C4×C191—21no—
52C22×C4×C191C2311yescharacteristic
53C2×C8×C191—21no—
54C4⋊C4×C191D411yescharacteristic
55C22⋊C4×C191—21no—
56C22×D191—21no—
57Dic382—42no—
58D764—41no—
59C22⋊D191—42no—
60C22⋊D191—41no—
61C22⋊D191—41no—
62C22⋊D191—81no—
63C2×Dic191—21no—
64C2×Dic191—21no—
65C2×Dic191—21no—
66C2×Dic191—21no—
67C2×Dic191—42no—
68C2×Dic191—41no—
69C2×Dic191—42no—
70C2×Dic191—41no—
71C2×Dic191SD1612yes—
72C4×D191—42no—
73C191⋊C8—41no—
74C23×C191—21no—
75C23×C191C2×D411yescharacteristic
76D4×C191—41no—
77D4×C191—41no—
78D4×C191—41no—
79C2×C4×C191—21no—
80C2×C4×C191—41no—
81C2×C4×C191—41no—
82C2×C4×C191—41no—
83C2×C4×C191—41no—
84C2×C4×C191C2×D411yescharacteristic
85C2×C4×C191C2×D411yescharacteristic
86C8×C191—41no—
87C22×C191—21no—
88C22×C191—21no—
89C22×C191—41no—
90C22×C191—41no—
91C22×C191—41no—
92C22×C191#12011yescharacteristic
93C22×C191C2×SD1611yescharacteristic
94C22×C191AGL(1,ℤ/8)11yescharacteristic
95C2×D191—41no—
96C2×D191—41no—
97C2×D191—41no—
98C4×C191—21no—
99C4×C191—21no—
100C4×C191—41no—
101C4×C191—81no—
102Dic191—22no—
103Dic191—41no—
104Dic191—41no—
105Dic191—81no—
106C2×C191—21no—
107C2×C191—21no—
108C2×C191—81no—
109C2×C191#45011yescharacteristic
110C2×C191#45411yescharacteristic
111C2×C191#45811yescharacteristic
112D191—81no—
113C191#161611yescharacteristic, complemented, Sylow
114#1616—1911nomaximal, Sylow
115#537—1911no—
116#481—1911no—
117#481—1911no—
118#400—1911no—
119#327—1911no—
120#327D19111yescharacteristic, complemented
121#324—1911no—
122C2×#41—3821no—
123C22⋊Q8—3821no—
124C22⋊Q8—3821no—
125#121—3821no—
126#121—3821no—
127#121—3821no—
128#121—1911no—
129#121C2×D19111yescharacteristic
130C2×C4⋊C4—1911no—
131C2×C4⋊C4—1911no—
132#106—3821no—
133#106—3821no—
134#102—3821no—
135#102—3821no—
136C22⋊C8—1911no—
137C22⋊C8C2×D19111yescharacteristic
138#95—3821no—
139#95—3821no—
140#95C2×D19111yescharacteristic
141#41—7642no—
142#41—7642no—
143C2×Q8—3821no—
144C2×D4—21no—
145C2×D4—3821no—
146C2×D4—3821no—
147C2×D4—3821no—
148C2×D4—1911no—
149C2×D4D76411yescharacteristic
150C22×C4—21no—
151C22×C4—3821no—
152C22×C4—3821no—
153C22×C4—3821no—
154C22×C4—1911no—
155C22×C4—1911no—
156C22×C4C22×D19111yescharacteristic
157C2×C8—21no—
158C2×C8—3821no—
159C4⋊C4—3821no—
160C4⋊C4—3821no—
161C4⋊C4—3821no—
162C4⋊C4—3821no—
163C4⋊C4—3821no—
164C4⋊C4—1911no—
165C4⋊C4D76411yescharacteristic
166C22⋊C4—21no—
167C22⋊C4—3821no—
168C22⋊C4—3821no—
169C22⋊C4—3821no—
170C23—21no—
171C23—3821no—
172C23D4×D19111yescharacteristic
173Q8—7642no—
174D4—41no—
175D4—41no—
176D4—41no—
177D4—15281no—
178D4—7641no—
179D4—7642no—
180D4—7641no—
181D4—7641no—
182C2×C4—21no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—3821no—
188C2×C4—3821no—
189C2×C4—3821no—
190C2×C4—3821no—
191C2×C4—1912no—
192C2×C4—7642no—
193C2×C4—7642no—
194C2×C4—7642no—
195C2×C4—7641no—
196C2×C4—7641no—
197C2×C4D4×D19111yescharacteristic
198C2×C4C2×D76411yescharacteristic
199C8—41no—
200C8—7641no—
201C22—21no—
202C22—21no—
203C22—41no—
204C22—41no—
205C22—41no—
206C22—7641no—
207C22—7641no—
208C22—7641no—
209C22#2025929211yescharacteristic
210C22SD16×D19111yescharacteristic
211C22#2025934611yescharacteristic
212C4—21no—
213C4—21no—
214C4—41no—
215C4—81no—
216C4—3822no—
217C4—15281no—
218C4—7641no—
219C4—7641no—
220C2—21no—
221C2—21no—
222C2—81no—
223C2—15281no—
224C2#2713281511yescharacteristic
225C2#2713283711yescharacteristic
226C2#2713285411yescharacteristic
subgroupG/H
centerC22#20259292
commutator, cosocleC22×C4×C191C23
FrattiniC22×C4C22×D191
Fitting#327×C191C2
socleC22×C191#120
prime radical#27133240C2
hypercenter#327D191
hypocenterC191#1616
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. #27132982C2semidirect
3. #27132979C2semidirect
4. #27132603C2semidirect
5. #27132396C2semidirect
6. #27132388C2semidirect
7. #327×C191C2semidirect
113. C191#1616semidirect
120. #327D191semidirect

Maximal subgroups

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

subgroupindex
#271332402
#271329822
#271329792
#271326032
#271323962
#271323882
#327×C1912
#1616191