Finite Group Databasebeta

← #37571814

Subgroups — #37571814

Order 24448.

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

normal subgroups only

This group has 230 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#27133407C211yesmaximal, characteristic, complemented
2#27133053C211yesmaximal, characteristic, complemented
3#27133052C211yesmaximal, characteristic, complemented
4#27133028C211yesmaximal, characteristic, complemented
5#27132404C211yesmaximal, characteristic, complemented
6#27132402C211yesmaximal, characteristic, complemented
7#329×C191C211yesmaximal, characteristic, complemented
8C2×#15690276—21no—
9C2×#15690274—21no—
10C2×D1528—21no—
11C2×#15690272—21no—
12#20259319C2211yescharacteristic
13#20259314C2211yescharacteristic
14#20259310C2211yescharacteristic
15#20259306—21no—
16#20259304—21no—
17#20259299—21no—
18#20259298—21no—
19#20259295—21no—
20#20259294—21no—
21#20259244—21no—
22#20259244—21no—
23#20259233C2211yescharacteristic
24#124×C191C2211yescharacteristic
25#97×C191C2211yescharacteristic
26#97×C191C2211yescharacteristic
27C2×Dic382D411yescharacteristic
28C2×D764—21no—
29C2×D764—21no—
30C2×D764—21no—
31C2×D764D411yescharacteristic
32C2×C22⋊D191—21no—
33C2×C22⋊D191—21no—
34C22×Dic191—21no—
35C2×C4×D191—21no—
36#15690276—42no—
37#15690274—42no—
38D1528—42no—
39#15690272—42no—
40C2×C191⋊C8—21no—
41C4⋊Dic191—21no—
42C4⋊Dic191D411yescharacteristic
43C4⋊Dic191D411yescharacteristic
44Dic191⋊C4—21no—
45Dic191⋊C4—21no—
46Dic191⋊C4—21no—
47C22⋊Dic191—21no—
48(C2×D191)⋊C4—21no—
49(C2×D191)⋊C4—21no—
50(C2×D191)⋊C4—21no—
51C2×Q8×C191D411yescharacteristic
52C2×D4×C191D411yescharacteristic
53C2×C8×C191—21no—
54C2×C8×C191—21no—
55C22⋊C4×C191—21no—
56C22⋊C4×C191—21no—
57C42×C191C2311yescharacteristic
58C22×D191—21no—
59C22×D191—41no—
60Dic382—41no—
61D764—41no—
62D764—41no—
63D764—41no—
64D764—41no—
65D764—41no—
66D764—42no—
67C22⋊D191—81no—
68C22⋊D191—81no—
69C2×Dic191—21no—
70C2×Dic191—21no—
71C2×Dic191—21no—
72C2×Dic191—81no—
73C4×D191—81no—
74C191⋊C8—22no—
75C23×C191—21no—
76Q8×C191—41no—
77D4×C191—41no—
78C2×C4×C191—21no—
79C2×C4×C191C2×D411yescharacteristic
80C2×C4×C191C2×D411yescharacteristic
81C2×C4×C191C2×D411yescharacteristic
82C8×C191—22no—
83C8×C191—41no—
84C22×C191—41no—
85C22×C191—41no—
86C22×C191—41no—
87C22×C191#12011yescharacteristic
88C2×D191—41no—
89C2×D191—41no—
90C2×D191—41no—
91C2×D191—81no—
92C2×D191—81no—
93C2×D191—81no—
94C4×C191—21no—
95C4×C191—21no—
96C4×C191—21no—
97C4×C191—41no—
98Dic191—41no—
99Dic191—41no—
100Dic191—41no—
101C2×C191—81no—
102C2×C191#45311yescharacteristic
103C2×C191#45311yescharacteristic
104C2×C191#45411yescharacteristic
105D191—81no—
106D191—161no—
107C191#165611yescharacteristic, complemented, Sylow
108#1656—1911nomaximal, Sylow
109#562—1911no—
110#496—1911no—
111#496—1911no—
112#490—1911no—
113#330—1911no—
114#329—1911no—
115#329D19111yescharacteristic, complemented
116C2×SD16—3821no—
117C2×SD16—3821no—
118C2×D8—3821no—
119C2×D8—3821no—
120#127—1911no—
121#125—1911no—
122#124—1911no—
123#124C2×D19111yescharacteristic
124#123—3821no—
125#123—3821no—
126C22⋊Q8—3821no—
127C22⋊Q8—3821no—
128#121—3821no—
129#121—3821no—
130#102—3821no—
131#102—3821no—
132#97—1911no—
133#97C2×D19111yescharacteristic
134#97C2×D19111yescharacteristic
135C2×Q8—1911no—
136C2×Q8D76411yescharacteristic
137C2×D4—3821no—
138C2×D4—3821no—
139C2×D4—3821no—
140C2×D4—3821no—
141C2×D4—3821no—
142C2×D4—1911no—
143C2×D4D76411yescharacteristic
144C22×C4—3821no—
145C22×C4—3821no—
146SD16—7642no—
147SD16—7642no—
148D8—7642no—
149D8—7642no—
150C2×C8—21no—
151C2×C8—21no—
152C2×C8—3821no—
153C4⋊C4—3821no—
154C4⋊C4—3821no—
155C4⋊C4—3821no—
156C4⋊C4—3821no—
157C4⋊C4—1911no—
158C4⋊C4—1911no—
159C22⋊C4—21no—
160C22⋊C4—21no—
161C22⋊C4—3821no—
162C22⋊C4—3821no—
163C22⋊C4—3821no—
164C22⋊C4—3821no—
165C42C22×D19111yescharacteristic
166C23—21no—
167C23—3821no—
168C23—7641no—
169Q8—41no—
170Q8—7641no—
171D4—41no—
172D4—15281no—
173D4—15281no—
174D4—7641no—
175D4—7641no—
176D4—7641no—
177D4—7641no—
178D4—7642no—
179D4—7641no—
180C2×C4—21no—
181C2×C4—3821no—
182C2×C4—3821no—
183C2×C4—3821no—
184C2×C4—15281no—
185C2×C4—15281no—
186C2×C4D4×D19111yescharacteristic
187C2×C4D4×D19111yescharacteristic
188C2×C4C2×D76411yescharacteristic
189C8—22no—
190C8—41no—
191C8—3822no—
192C22—41no—
193C22—41no—
194C22—41no—
195C22—15281no—
196C22—15281no—
197C22—15281no—
198C22—7641no—
199C22—7641no—
200C22—7641no—
201C22#2025929211yescharacteristic
202C4—21no—
203C4—21no—
204C4—21no—
205C4—41no—
206C4—7641no—
207C4—7641no—
208C4—7641no—
209C2—81no—
210C2—30561no—
211C2—15281no—
212C2#2713283211yescharacteristic
213C2#2713283311yescharacteristic
214C2#2713283711yescharacteristic
subgroupG/H
centerC22#20259292
commutator, cosocleC42×C191C23
FrattiniC42C22×D191
Fitting#329×C191C2
socleC22×C191#120
hypercenter#329D191
hypocenterC191#1656
LCSG ▷ C42×C191 ▷ C22×C191 ▷ C191
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
1. #27133407C2semidirect
2. #27133053C2semidirect
3. #27133052C2semidirect
4. #27133028C2semidirect
5. #27132404C2semidirect
6. #27132402C2semidirect
7. #329×C191C2semidirect
107. C191#1656semidirect
115. #329D191semidirect

Maximal subgroups

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

subgroupindex
#271334072
#271330532
#271330522
#271330282
#271324042
#271324022
#329×C1912
#1656191