Finite Group Databasebeta

← #37571825

Subgroups — #37571825

Order 24448.

228 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 45 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#27133405C211yesmaximal, characteristic
2#27133055C211yesmaximal, characteristic, complemented
3#27133025C211yesmaximal, characteristic, complemented
4#27132403C211yesmaximal, characteristic, complemented
5#27132402C211yesmaximal, characteristic, complemented
6#27132402C211yesmaximal, characteristic, complemented
7#489×C191C211yesmaximal, characteristic, complemented
8C2×#15690277—21no—
9C2×#15690274—21no—
10#20259311—21no—
11#20259310C2211yescharacteristic
12#20259310C2211yescharacteristic
13#20259308—21no—
14#20259308—21no—
15#20259292—21no—
16#20259292—21no—
17#20259290—21no—
18#20259245—21no—
19#20259242—21no—
20#20259233C2211yescharacteristic, complemented
21#20259233C2211yescharacteristic, complemented
22C4⋊Q8×C191C2211yescharacteristic, complemented
23#124×C191C2211yescharacteristic
24#103×C191—21no—
25#102×C191—21no—
26#97×C191C2211yescharacteristic, complemented
27C23×D191—21no—
28C2×Dic382D411yescharacteristic
29C2×Dic382D411yescharacteristic
30C2×D764—21no—
31C2×D764D411yescharacteristic
32C2×D764D411yescharacteristic
33C2×C22⋊D191—21no—
34C2×C22⋊D191—21no—
35#15690277—42no—
36#15690274—42no—
37C2×C191⋊C8—21no—
38C2×C191⋊C8—21no—
39C22⋊Dic191—21no—
40(C2×D191)⋊C4—21no—
41(C2×D191)⋊C4—21no—
42(C2×D191)⋊C4—21no—
43(C2×D191)⋊C4—21no—
44(C2×D191)⋊C4—21no—
45(C2×D191)⋊C4—21no—
46C4×Dic191—21no—
47C2×Q8×C191—21no—
48C2×Q8×C191D411yescharacteristic
49C2×D4×C191D411yescharacteristic
50C2×C8×C191—21no—
51C4⋊C4×C191—21no—
52C4⋊C4×C191—21no—
53C22⋊C4×C191—21no—
54C22⋊C4×C191—21no—
55C42×C191C2311yescharacteristic
56C22×D191—21no—
57C22×D191—21no—
58C22×D191—81no—
59C22×D191—81no—
60C22×D191—81no—
61Dic382—41no—
62Dic382—41no—
63D764—41no—
64D764—41no—
65D764—81no—
66C22⋊D191—81no—
67C22⋊D191—81no—
68C2×Dic191—21no—
69C2×Dic191—21no—
70C191⋊C8—22no—
71C191⋊C8—41no—
72C23×C191—21no—
73Q8×C191—41no—
74Q8×C191—41no—
75Q8×C191—41no—
76D4×C191—41no—
77C2×C4×C191—21no—
78C2×C4×C191—41no—
79C2×C4×C191C2×D411yescharacteristic
80C2×C4×C191C2×D411yescharacteristic
81C2×C4×C191C2×D411yescharacteristic
82C8×C191—41no—
83C22×C191—41no—
84C22×C191—41no—
85C22×C191—41no—
86C22×C191#12011yescharacteristic
87C2×D191—41no—
88C2×D191—41no—
89C2×D191—41no—
90C2×D191—41no—
91C2×D191—41no—
92C2×D191—41no—
93C2×D191—84no—
94C4×C191—21no—
95C4×C191—21no—
96C4×C191—21no—
97C4×C191—41no—
98C4×C191—81no—
99Dic191—41no—
100Dic191—41no—
101C2×C191—81no—
102C2×C191#45311yescharacteristic
103C2×C191#45511yescharacteristic
104C2×C191#45511yescharacteristic
105D191—81no—
106D191—81no—
107C191#165911yescharacteristic, complemented, Sylow
108#1659—1911nomaximal, Sylow
109H(3,𝔽4)—1911no—
110#497—1911no—
111#489—1911no—
112#489D19111yescharacteristic, complemented
113#329—1911no—
114#329—1911no—
115#329—1911no—
116C2×Q16—3821no—
117C2×SD16—3821no—
118C4⋊Q8C2×D19111yescharacteristic, complemented
119#124—3821no—
120#124—3821no—
121#124—3821no—
122#124—1911no—
123#124—1911no—
124#124C2×D19111yescharacteristic
125#120—3821no—
126#120—3821no—
127#120—3821no—
128#103—21no—
129#103—3821no—
130#102—21no—
131#102—3821no—
132#97—1911no—
133#97—1911no—
134#97C2×D19111yescharacteristic, complemented
135C24—3821no—
136C2×Q8—21no—
137C2×Q8—1911no—
138C2×Q8—1911no—
139C2×Q8C22⋊D19111yescharacteristic
140C2×D4—3821no—
141C2×D4—3821no—
142C2×D4—3821no—
143C2×D4—1911no—
144C2×D4—1911no—
145C2×D4C22⋊D19111yescharacteristic
146Q16—7642no—
147SD16—7642no—
148C2×C8—21no—
149C2×C8—3821no—
150C2×C8—3821no—
151C4⋊C4—21no—
152C4⋊C4—21no—
153C22⋊C4—21no—
154C22⋊C4—21no—
155C22⋊C4—3821no—
156C22⋊C4—3821no—
157C22⋊C4—3821no—
158C22⋊C4—3821no—
159C22⋊C4—3821no—
160C22⋊C4—3821no—
161C22⋊C4—3821no—
162C42—3821no—
163C42C22×D19111yescharacteristic
164C23—21no—
165C23—3821no—
166C23—3821no—
167C23—15281no—
168C23—15281no—
169C23—15281no—
170Q8—41no—
171Q8—41no—
172Q8—41no—
173Q8—7641no—
174Q8—7641no—
175D4—41no—
176D4—15281no—
177D4—15281no—
178D4—15281no—
179D4—7641no—
180D4—7641no—
181C2×C4—21no—
182C2×C4—41no—
183C2×C4—3821no—
184C2×C4—3821no—
185C2×C4D4×D19111yescharacteristic
186C2×C4D4×D19111yescharacteristic
187C2×C4C2×C22⋊D19111yescharacteristic
188C8—41no—
189C8—3822no—
190C8—7641no—
191C22—41no—
192C22—41no—
193C22—41no—
194C22—15284no—
195C22—7641no—
196C22—7641no—
197C22—7641no—
198C22—7641no—
199C22—7641no—
200C22—7641no—
201C22#2025929011yescharacteristic
202C4—21no—
203C4—21no—
204C4—21no—
205C4—41no—
206C4—81no—
207C4—7641no—
208C4—7641no—
209C2—81no—
210C2—15281no—
211C2—15281no—
212C2#2713282911yescharacteristic
213C2#2713283911yescharacteristic
214C2#2713284011yescharacteristic
subgroupG/H
centerC22#20259290
commutator, cosocleC42×C191C23
FrattiniC42C22×D191
Fitting#489×C191C2
socleC22×C191#120
prime radical#27133405C2
hypercenter#489D191
hypocenterC191#1659
LCSG ▷ C42×C191 ▷ C22×C191 ▷ C191
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
2. #27133055C2semidirect
3. #27133025C2semidirect
4. #27132403C2semidirect
5. #27132402C2semidirect
6. #27132402C2semidirect
7. #489×C191C2semidirect
20. #20259233C22semidirect
21. #20259233C22semidirect
22. C4⋊Q8×C191C22semidirect
26. #97×C191C22semidirect
107. C191#1659semidirect
112. #489D191semidirect
118. C4⋊Q8C2×D191semidirect
134. #97C2×D191semidirect

Maximal subgroups

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

subgroupindex
#271334052
#271330552
#271330252
#271324032
#271324022
#489×C1912
#1659191