Finite Group Databasebeta

← #37571668

Subgroups — #37571668

Order 24448.

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

normal subgroups only

This group has 234 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#27133316C211yesmaximal, characteristic
2#27132950C211yesmaximal, characteristic, complemented
3#27132950C211yesmaximal, characteristic, complemented
4#27132409C211yesmaximal, characteristic, complemented
5#27132392C211yesmaximal, characteristic, complemented
6#27132392C211yesmaximal, characteristic, complemented
7#487×C191C211yesmaximal, characteristic, complemented
8C2×#15690288—21no—
9#20259307—22no—
10#20259298—21no—
11#20259297—21no—
12C4×D764C2211yescharacteristic
13C4×D764C2211yescharacteristic
14C4⋊C4×D191—21no—
15#20259253—21no—
16#20259253—21no—
17C4⋊(C191⋊C8)C2211yescharacteristic
18C4⋊(C191⋊C8)C2211yescharacteristic
19#20259242—21no—
20#20259242—21no—
21C4⋊Q8×C191C2211yescharacteristic
22C4⋊Q8×C191C2211yescharacteristic
23#103×C191—22no—
24C4×C8×C191C2211yescharacteristic
25#15690288—42no—
26#15690288—42no—
27C2×D764—22no—
28C2×D764D411yescharacteristic
29C2×D764D411yescharacteristic
30C2×C4×D191—22no—
31C2×C4×D191—21no—
32C2×C4×D191—21no—
33C2×C191⋊C8—21no—
34C2×C191⋊C8—21no—
35C4⋊Dic191D411yescharacteristic
36C4⋊Dic191D411yescharacteristic
37Dic191⋊C4—22no—
38(C2×D191)⋊C4—22no—
39(C2×D191)⋊C4—21no—
40(C2×D191)⋊C4—21no—
41C2×Q8×C191—21no—
42C2×Q8×C191—21no—
43C2×C8×C191—21no—
44C4⋊C4×C191—21no—
45C4⋊C4×C191—21no—
46C4⋊C4×C191—21no—
47C4⋊C4×C191D412yes—
48C42×C191C2311yescharacteristic
49C22×D191—21no—
50C22×D191—21no—
51D764—21no—
52D764—21no—
53D764—21no—
54D764—44no—
55D764SD1612yes—
56C2×Dic191—21no—
57C2×Dic191—21no—
58C4×D191—44no—
59C4×D191—41no—
60C4×D191—41no—
61C4×D191—41no—
62C4×D191—41no—
63C191⋊C8—41no—
64C191⋊C8—41no—
65Q8×C191—42no—
66Q8×C191—41no—
67Q8×C191—41no—
68C2×C4×C191—22no—
69C2×C4×C191—41no—
70C2×C4×C191C2×D411yescharacteristic
71C2×C4×C191C2×D411yescharacteristic
72C2×C4×C191C2×D411yescharacteristic
73C8×C191—41no—
74C22×C191#12011yescharacteristic
75C2×D191—22no—
76C2×D191—41no—
77C2×D191—41no—
78C2×D191—41no—
79C2×D191—41no—
80C2×D191—41no—
81C4×C191—21no—
82C4×C191—42no—
83C4×C191—81no—
84C4×C191C2×SD1611yescharacteristic
85C4×C191#13511yescharacteristic
86C4×C191AGL(1,ℤ/8)11yescharacteristic
87C4×C191#13711yescharacteristic
88Dic191—41no—
89Dic191—41no—
90C2×C191#45011yescharacteristic
91C2×C191#45211yescharacteristic
92C2×C191#45411yescharacteristic
93D191—42no—
94D191—81no—
95C191#163511yescharacteristic, complemented, Sylow
96#1635—1911nomaximal, Sylow
97#547—1911no—
98#487D19111yescharacteristic, complemented
99#476—1911no—
100#476—1911no—
101#332—1911no—
102D4⋊C8—1911no—
103D4⋊C8—1911no—
104C2×#41—3821no—
105C4⋊Q8C2×D19111yescharacteristic
106C4⋊Q8C2×D19111yescharacteristic
107#123—3822no—
108C22⋊Q8—3821no—
109#121—3821no—
110C4×D4—1911no—
111C4×D4—1911no—
112C2×C4⋊C4—3821no—
113#106—3821no—
114#106—3821no—
115C4⋊C8—1911no—
116C4⋊C8—1911no—
117#103—22no—
118#102—3821no—
119#102—3821no—
120C4×C8C2×D19111yescharacteristic
121#41—7642no—
122#41—7642no—
123C2×Q8—21no—
124C2×Q8—21no—
125C2×D4—3822no—
126C2×D4—1911no—
127C2×D4—1911no—
128C22×C4—3822no—
129C22×C4—3821no—
130C22×C4—3821no—
131C2×C8—21no—
132C2×C8—3821no—
133C2×C8—3821no—
134C4⋊C4—21no—
135C4⋊C4—21no—
136C4⋊C4—21no—
137C4⋊C4—3822no—
138C4⋊C4—1911no—
139C4⋊C4—1911no—
140C4⋊C4C22⋊D19112yes—
141C22⋊C4—3822no—
142C22⋊C4—3821no—
143C22⋊C4—3821no—
144C42C22×D19111yescharacteristic
145C23—3821no—
146C23—3821no—
147Q8—42no—
148Q8—41no—
149Q8—41no—
150D4—3821no—
151D4—3821no—
152D4—3821no—
153D4—1912no—
154D4—7644no—
155C2×C4—22no—
156C2×C4—41no—
157C2×C4—3821no—
158C2×C4—3821no—
159C2×C4—7644no—
160C2×C4—7641no—
161C2×C4—7641no—
162C2×C4—7641no—
163C2×C4—7641no—
164C2×C4D4×D19111yescharacteristic
165C2×C4D4×D19111yescharacteristic
166C2×C4C2×C22⋊D19111yescharacteristic
167C8—41no—
168C8—7641no—
169C8—7641no—
170C22—3822no—
171C22—7641no—
172C22—7641no—
173C22—7641no—
174C22—7641no—
175C22—7641no—
176C22#2025929011yescharacteristic
177C4—21no—
178C4—42no—
179C4—81no—
180C4—7641no—
181C4—7641no—
182C4SD16×D19111yescharacteristic
183C4#2025934511yescharacteristic
184C4#2025934911yescharacteristic
185C4#2025935411yescharacteristic
186C2—15281no—
187C2—7642no—
188C2#2713281211yescharacteristic
189C2#2713282411yescharacteristic
190C2#2713283511yescharacteristic
subgroupG/H
centerC22#20259290
commutator, cosocleC42×C191C23
FrattiniC42C22×D191
Fitting#487×C191C2
socleC22×C191#120
prime radical#27133316C2
hypercenter#487D191
hypocenterC191#1635
LCSG ▷ C42×C191 ▷ C22×C191 ▷ C191
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
2. #27132950C2semidirect
3. #27132950C2semidirect
4. #27132409C2semidirect
5. #27132392C2semidirect
6. #27132392C2semidirect
7. #487×C191C2semidirect
95. C191#1635semidirect
98. #487D191semidirect

Maximal subgroups

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

subgroupindex
#271333162
#271329502
#271324092
#271323922
#487×C1912
#1635191