Finite Group Databasebeta

← #37571582

Subgroups — #37571582

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#27132860C211yesmaximal, characteristic, complemented
3#27132855C211yesmaximal, characteristic, complemented
4#27132407C211yesmaximal, characteristic, complemented
5#27132395C211yesmaximal, characteristic, complemented
6#27132392C211yesmaximal, characteristic, complemented
7#493×C191C211yesmaximal, characteristic, complemented
8C2×#15690286—21no—
9C2×#15690275—21no—
10C2×#15690272—21no—
11#20259318—21no—
12#20259294—22no—
13#20259293—21no—
14C4×Dic382C2211yescharacteristic
15C4×D764C2211yescharacteristic
16D4×Dic191—21no—
17C4⋊(C191⋊C8)C2211yescharacteristic
18C4⋊(C191⋊C8)C2211yescharacteristic
19#20259243—21no—
20#20259243—21no—
21C2×D8×C191—22no—
22#127×C191C2211yescharacteristic
23#127×C191C2211yescharacteristic
24C4×C8×C191C2211yescharacteristic
25#15690286—42no—
26#15690286—42no—
27C2×Dic382D411yescharacteristic
28C2×D764D411yescharacteristic
29C2×C22⋊D191—22no—
30C2×C22⋊D191—22no—
31C22×Dic191—22no—
32C2×C4×D191—21no—
33#15690275—42no—
34#15690272—42no—
35C2×C191⋊C8—21no—
36C2×C191⋊C8—21no—
37C4⋊Dic191D411yescharacteristic
38C4⋊Dic191D411yescharacteristic
39Dic191⋊C4—21no—
40C22⋊Dic191—22no—
41(C2×D191)⋊C4—21no—
42C4×Dic191—21no—
43C2×D4×C191—21no—
44C2×D4×C191—21no—
45C2×D4×C191—21no—
46C2×D4×C191—21no—
47C2×D4×C191—21no—
48C2×D4×C191D412yes—
49D8×C191—44no—
50C2×C8×C191—21no—
51C42×C191C2311yescharacteristic
52C22×D191—21no—
53Dic382—21no—
54Dic382D812yescomplemented
55D764—21no—
56D764—21no—
57C22⋊D191—44no—
58C22⋊D191—82no—
59C2×Dic191—21no—
60C2×Dic191—21no—
61C2×Dic191—21no—
62C2×Dic191—44no—
63C4×D191—41no—
64C4×D191—41no—
65C191⋊C8—41no—
66C191⋊C8—41no—
67C23×C191—22no—
68C23×C191—41no—
69D4×C191—42no—
70D4×C191—42no—
71D4×C191—41no—
72D4×C191—41no—
73D4×C191—41no—
74D4×C191—41no—
75D4×C191—41no—
76D4×C191—41no—
77D4×C191—41no—
78D4×C191—41no—
79C2×C4×C191C2×D411yescharacteristic
80C2×C4×C191C2×D411yescharacteristic
81C2×C4×C191C2×D411yescharacteristic
82C8×C191—22no—
83C22×C191—42no—
84C22×C191—42no—
85C22×C191—42no—
86C22×C191—81no—
87C22×C191—81no—
88C22×C191—81no—
89C22×C191#12011yescharacteristic
90C2×D191—41no—
91C2×D191—41no—
92C2×D191—41no—
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—161no—
103C2×C191#44711yescharacteristic
104C2×C191#44911yescharacteristic
105C2×C191#45311yescharacteristic
106D191—81no—
107C191#162111yescharacteristic, complemented, Sylow
108#1621—1911nomaximal, Sylow
109#550—1911no—
110#493D19111yescharacteristic, complemented
111#460—1911no—
112#459—1911no—
113#331—1911no—
114Q8⋊C8—1911no—
115D4⋊C8—1911no—
116C2×#41—3821no—
117C2×SD16—3821no—
118C2×D8—22no—
119C2×D8—3821no—
120#127—3821no—
121#127C2×D19111yescharacteristic
122#127C2×D19111yescharacteristic
123#121—3822no—
124#121—3821no—
125C4×Q8—1911no—
126C4×D4—3821no—
127C4×D4—1911no—
128C4⋊C8—1911no—
129C4⋊C8—1911no—
130#102—3821no—
131#102—3821no—
132C4×C8C2×D19111yescharacteristic
133#41—7642no—
134#41—7642no—
135C2×Q8—1911no—
136C2×D4—21no—
137C2×D4—21no—
138C2×D4—21no—
139C2×D4—21no—
140C2×D4—21no—
141C2×D4—3822no—
142C2×D4—3822no—
143C2×D4—1911no—
144C2×D4C22⋊D19112yes—
145C22×C4—3822no—
146C22×C4—3821no—
147SD16—7642no—
148D8—44no—
149D8—7642no—
150C2×C8—21no—
151C2×C8—3821no—
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—41no—
162C23—3821no—
163Q8—3821no—
164Q8—1912no—
165D4—42no—
166D4—42no—
167D4—41no—
168D4—41no—
169D4—41no—
170D4—41no—
171D4—41no—
172D4—41no—
173D4—41no—
174D4—41no—
175D4—3821no—
176D4—3821no—
177D4—15282no—
178D4—7644no—
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×C22⋊D19111yescharacteristic
188C8—22no—
189C8—7641no—
190C8—7641no—
191C22—42no—
192C22—42no—
193C22—42no—
194C22—81no—
195C22—81no—
196C22—81no—
197C22—7641no—
198C22—7641no—
199C22—7641no—
200C22#2025929011yescharacteristic
201C4—21no—
202C4—3822no—
203C4—7641no—
204C4—7641no—
205C4D8×D19111yescharacteristic
206C4#2025934111yescharacteristic
207C4#2025934611yescharacteristic
208C4#2025934611yescharacteristic
209C2—82no—
210C2—161no—
211C2—15281no—
212C2#2713279511yescharacteristic
213C2#2713280511yescharacteristic
214C2#2713283011yescharacteristic
subgroupG/H
centerC22#20259290
commutator, cosocleC42×C191C23
FrattiniC42C22×D191
Fitting#493×C191C2
socleC22×C191#120
hypercenter#493D191
hypocenterC191#1621
LCSG ▷ C42×C191 ▷ C22×C191 ▷ C191
UCSC1 ◁ C22 ◁ C42 ◁ #493

Complements

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

NH ≅ G/Ntype
1. #27133333C2semidirect
2. #27132860C2semidirect
3. #27132855C2semidirect
4. #27132407C2semidirect
5. #27132395C2semidirect
6. #27132392C2semidirect
7. #493×C191C2semidirect
54. Dic382D8semidirect
107. C191#1621semidirect
110. #493D191semidirect

Maximal subgroups

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

subgroupindex
#271333332
#271328602
#271328552
#271324072
#271323952
#271323922
#493×C1912
#1621191