Finite Group Databasebeta

← #37571586

Subgroups — #37571586

Order 24448.

278 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 278 conjugacy classes of subgroups — too many to draw. Only its 55 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#27133333C211yesmaximal, characteristic, complemented
2#27133039C211yesmaximal, characteristic, complemented
3#27132864C211yesmaximal, characteristic, complemented
4#27132859C211yesmaximal, characteristic, complemented
5#27132393C211yesmaximal, characteristic, complemented
6#27132390C211yesmaximal, characteristic, complemented
7#331×C191C211yesmaximal, characteristic, complemented
8C2×#15690286—21no—
9C2×#15690276—21no—
10C2×D1528—21no—
11C2×#15690272—22no—
12#20259319C2211yescharacteristic
13#20259318—21no—
14#20259294—22no—
15#20259293—21no—
16C4×Dic382C2211yescharacteristic
17C4×D764C2211yescharacteristic
18D4×Dic191—21no—
19#20259244—21no—
20#20259244—21no—
21C4×C191⋊C8C2211yescharacteristic
22#127×C191C2211yescharacteristic
23C4⋊C8×C191C2211yescharacteristic
24C4⋊C8×C191C2211yescharacteristic
25#15690286—42no—
26#15690286—42no—
27C2×Dic382D411yescharacteristic
28C2×D764—21no—
29C2×D764—21no—
30C2×D764—21no—
31C2×D764D411yescharacteristic
32C2×C22⋊D191—22no—
33C2×C22⋊D191—22no—
34C22×Dic191—22no—
35C2×C4×D191—21no—
36#15690276—42no—
37D1528—42no—
38#15690272—44no—
39C2×C191⋊C8—21no—
40C4⋊Dic191D411yescharacteristic
41C4⋊Dic191D411yescharacteristic
42Dic191⋊C4—21no—
43C22⋊Dic191—22no—
44(C2×D191)⋊C4—21no—
45C4×Dic191—21no—
46C2×D4×C191—21no—
47C2×D4×C191—21no—
48C2×D4×C191D412yes—
49C2×C8×C191—21no—
50C2×C8×C191—21no—
51C42×C191C2311yescharacteristic
52C22×D191—21no—
53C22×D191—41no—
54Dic382—21no—
55Dic382D812yescomplemented
56D764—21no—
57D764—21no—
58D764—42no—
59D764—41no—
60D764—41no—
61D764—41no—
62D764—41no—
63C22⋊D191—44no—
64C22⋊D191—82no—
65C2×Dic191—21no—
66C2×Dic191—21no—
67C2×Dic191—21no—
68C2×Dic191—44no—
69C4×D191—41no—
70C4×D191—41no—
71C191⋊C8—22no—
72C23×C191—22no—
73D4×C191—42no—
74D4×C191—41no—
75D4×C191—41no—
76D4×C191—41no—
77D4×C191—41no—
78C2×C4×C191C2×D411yescharacteristic
79C2×C4×C191C2×D411yescharacteristic
80C2×C4×C191C2×D411yescharacteristic
81C8×C191—41no—
82C8×C191—41no—
83C22×C191—42no—
84C22×C191—42no—
85C22×C191—42no—
86C22×C191#12011yescharacteristic
87C2×D191—41no—
88C2×D191—41no—
89C2×D191—41no—
90C2×D191—81no—
91C2×D191—81no—
92C2×D191—81no—
93C4×C191—21no—
94C4×C191C2×D811yescharacteristic
95C4×C191#13511yescharacteristic
96C4×C191AGL(1,ℤ/8)11yescharacteristic
97C4×C191AGL(1,ℤ/8)11yescharacteristic
98Dic191—22no—
99Dic191—41no—
100Dic191—41no—
101C2×C191—82no—
102C2×C191#44711yescharacteristic
103C2×C191#44911yescharacteristic
104C2×C191#45311yescharacteristic
105D191—81no—
106D191—161no—
107C191#162111yescharacteristic, complemented, Sylow
108#1621—1911nomaximal, Sylow
109#550—1911no—
110#493—1911no—
111#460—1911no—
112#459—1911no—
113#331D19111yescharacteristic, complemented
114Q8⋊C8—1911no—
115D4⋊C8—1911no—
116C2×#41—3821no—
117C2×SD16—3821no—
118C2×D8—3821no—
119C2×D8—3822no—
120#127—3821no—
121#127—1911no—
122#127C2×D19111yescharacteristic
123#121—3822no—
124#121—3821no—
125C4×Q8—1911no—
126C4×D4—3821no—
127C4×D4—1911no—
128C4⋊C8C2×D19111yescharacteristic
129C4⋊C8C2×D19111yescharacteristic
130#102—3821no—
131#102—3821no—
132C4×C8—1911no—
133#41—7642no—
134#41—7642no—
135C2×Q8—1911no—
136C2×D4—21no—
137C2×D4—21no—
138C2×D4—3822no—
139C2×D4—3822no—
140C2×D4—3821no—
141C2×D4—3821no—
142C2×D4—3821no—
143C2×D4—1911no—
144C2×D4D76412yes—
145C22×C4—3822no—
146C22×C4—3821no—
147SD16—7642no—
148D8—7642no—
149D8—7644no—
150C2×C8—21no—
151C2×C8—21no—
152C2×C8—3821no—
153C4⋊C4—3821no—
154C4⋊C4—1911no—
155C4⋊C4—1911no—
156C22⋊C4—3822no—
157C22⋊C4—3821no—
158C42—3821no—
159C42C22×D19111yescharacteristic
160C23—22no—
161C23—3821no—
162C23—7641no—
163Q8—3821no—
164Q8—1912no—
165D4—42no—
166D4—41no—
167D4—41no—
168D4—41no—
169D4—41no—
170D4—3821no—
171D4—3821no—
172D4—15282no—
173D4—7642no—
174D4—7644no—
175D4—7641no—
176D4—7641no—
177D4—7641no—
178D4—7641no—
179C2×C4—3821no—
180C2×C4—3821no—
181C2×C4—3821no—
182C2×C4—7644no—
183C2×C4—7641no—
184C2×C4—7641no—
185C2×C4D4×D19111yescharacteristic
186C2×C4D4×D19111yescharacteristic
187C2×C4C2×D76411yescharacteristic
188C8—41no—
189C8—41no—
190C8—3822no—
191C22—42no—
192C22—42no—
193C22—42no—
194C22—15281no—
195C22—15281no—
196C22—15281no—
197C22—7641no—
198C22—7641no—
199C22—7641no—
200C22#2025929211yescharacteristic
201C4—21no—
202C4—3822no—
203C4—7641no—
204C4—7641no—
205C4D8×D19111yescharacteristic
206C4#2025934311yescharacteristic
207C4#2025934611yescharacteristic
208C4#2025934911yescharacteristic
209C2—82no—
210C2—30561no—
211C2—15281no—
212C2#2713279811yescharacteristic
213C2#2713280911yescharacteristic
214C2#2713283311yescharacteristic
subgroupG/H
centerC22#20259292
commutator, cosocleC42×C191C23
FrattiniC42C22×D191
Fitting#331×C191C2
socleC22×C191#120
hypercenter#331D191
hypocenterC191#1621
LCSG ▷ C42×C191 ▷ C22×C191 ▷ C191
UCSC1 ◁ C22 ◁ C42 ◁ #331

Complements

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

NH ≅ G/Ntype
1. #27133333C2semidirect
2. #27133039C2semidirect
3. #27132864C2semidirect
4. #27132859C2semidirect
5. #27132393C2semidirect
6. #27132390C2semidirect
7. #331×C191C2semidirect
55. Dic382D8semidirect
107. C191#1621semidirect
113. #331D191semidirect

Maximal subgroups

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

subgroupindex
#271333332
#271330392
#271328642
#271328592
#271323932
#271323902
#331×C1912
#1621191