Finite Group Databasebeta

← #37574490

Subgroups — #37574490

Order 24448.

216 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 47 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#27133464C211yesmaximal, characteristic
2#27133104C211yesmaximal, characteristic, complemented
3#27132935C211yesmaximal, characteristic, complemented
4#27132476C211yesmaximal, characteristic, complemented
5#27132471C211yesmaximal, characteristic, complemented
6#27132446C211yesmaximal, characteristic, complemented
7C2×SD32×C191C211yesmaximal, characteristic, complemented
8#20259367—21no—
9#20259353—21no—
10#20259348—21no—
11#20259346—22no—
12#20259344C2211yescharacteristic
13#20259341—21no—
14D8×D191—21no—
15#20259328C2211yescharacteristic
16#20259268—21no—
17#20259265—21no—
18#20259262C2211yescharacteristic, complemented
19#20259258C2211yescharacteristic, complemented
20#20259241—21no—
21C2×Q16×C191C2211yescharacteristic, complemented
22C2×D8×C191C2211yescharacteristic
23SD32×C191—22no—
24C2×C16×C191C2211yescharacteristic, complemented
25#15690287—21no—
26#15690287D411yescharacteristic
27#15690286—22no—
28#15690286—41no—
29C2×C22⋊D191—42no—
30D4×D191—22no—
31D4×D191—41no—
32Dic764D411yescharacteristic
33#15690277—41no—
34#15690276—21no—
35#15690275—22no—
36#15690274—41no—
37D1528D411yescharacteristic
38#15690272—22no—
39#15690271—21no—
40#15690271D411yescharacteristic
41#15690270—21no—
42C8×D191—21no—
43C191⋊C16—21no—
44C2×Q8×C191—21no—
45C2×D4×C191—21no—
46Q16×C191—21no—
47Q16×C191—21no—
48D8×C191—21no—
49D8×C191D412yes—
50C2×C8×C191C2311yescharacteristic
51C16×C191—21no—
52C22×D191—42no—
53Dic382—21no—
54Dic382D811yescharacteristic
55D764—21no—
56D764D811yescharacteristic
57C22⋊D191—21no—
58C22⋊D191—42no—
59C22⋊D191—42no—
60C22⋊D191—41no—
61C2×Dic191—42no—
62C4×D191—21no—
63C4×D191—41no—
64C191⋊C8—21no—
65C191⋊C8—41no—
66C23×C191—41no—
67Q8×C191—41no—
68Q8×C191—41no—
69D4×C191—22no—
70D4×C191—41no—
71C2×C4×C191—41no—
72C2×C4×C191C2×D411yescharacteristic
73C8×C191C2×D411yescharacteristic
74C8×C191C2×D411yescharacteristic
75C22×C191—42no—
76C22×C191—161no—
77C22×C191AGL(1,ℤ/8)11yescharacteristic
78C2×D191—21no—
79C2×D191—41no—
80C2×D191—162no—
81C4×C191—81no—
82C4×C191#12011yescharacteristic
83C4×C191C2×D811yescharacteristic
84Dic191—21no—
85Dic191—41no—
86C2×C191—21no—
87C2×C191—82no—
88C2×C191#44711yescharacteristic
89D191—41no—
90D191—81no—
91C191#219411yescharacteristic, complemented, Sylow
92#2194—1911nomaximal, Sylow
93#576—1911no—
94#510—1911no—
95C2×SD32D19111yescharacteristic, complemented
96#473—1911no—
97#361—1911no—
98#359—1911no—
99#350—1911no—
100H(5,𝔽2)—3821no—
101#137—3821no—
102AGL(1,ℤ/8)—3822no—
103AGL(1,ℤ/8)—3821no—
104#135—3821no—
105#135—1911no—
106C2×Q16C2×D19111yescharacteristic, complemented
107C2×D8—3821no—
108C2×D8C2×D19111yescharacteristic
109#131—1911no—
110Q32—3821no—
111SD32—22no—
112SD32—3821no—
113M32—1911no—
114C2×C16C2×D19111yescharacteristic, complemented
115#108—1911no—
116#101—3821no—
117#41—3822no—
118#41—3821no—
119#41—1911no—
120#41—7641no—
121C2×Q8—21no—
122C2×D4—21no—
123C2×D4—3822no—
124C2×D4—7641no—
125C2×D4—7642no—
126Q16—21no—
127Q16—21no—
128Q16—1911no—
129Q16—7641no—
130SD16—3822no—
131SD16—3821no—
132SD16—7641no—
133D8—21no—
134D8—3822no—
135D8—1911no—
136D8C22⋊D19112yes—
137M16—3821no—
138M16—3821no—
139M16—1911no—
140C2×C8—3821no—
141C2×C8C22×D19111yescharacteristic
142C16—21no—
143C16—3821no—
144C23—41no—
145C23—7642no—
146Q8—41no—
147Q8—41no—
148Q8—3821no—
149Q8—1911no—
150D4—22no—
151D4—41no—
152D4—3821no—
153D4—3821no—
154D4—1911no—
155D4—7642no—
156D4—7642no—
157D4—7641no—
158C2×C4—41no—
159C2×C4—3821no—
160C2×C4—7642no—
161C2×C4—7641no—
162C2×C4D4×D19111yescharacteristic
163C8—3821no—
164C8—7641no—
165C8D4×D19111yescharacteristic
166C8C2×C22⋊D19111yescharacteristic
167C22—42no—
168C22—161no—
169C22—3821no—
170C22—30562no—
171C22—7641no—
172C22#2025934611yescharacteristic
173C4—81no—
174C4—3821no—
175C4—7641no—
176C4#2025929011yescharacteristic
177C4D8×D19111yescharacteristic
178C2—21no—
179C2—82no—
180C2—15281no—
181C2—7641no—
182C2#2713279511yescharacteristic
subgroupG/H
centerC2#27132795
commutator, cosocleC2×C8×C191C23
FrattiniC2×C8C22×D191
FittingC2×SD32×C191C2
socleC2×C191#447
prime radical#27133464C2
hypercenterC2×SD32D191
hypocenterC191#2194
LCSG ▷ C2×C8×C191 ▷ C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×SD32

Complements

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

NH ≅ G/Ntype
2. #27133104C2semidirect
3. #27132935C2semidirect
4. #27132476C2semidirect
5. #27132471C2semidirect
6. #27132446C2semidirect
7. C2×SD32×C191C2semidirect
18. #20259262C22semidirect
19. #20259258C22semidirect
21. C2×Q16×C191C22semidirect
24. C2×C16×C191C22semidirect
91. C191#2194semidirect
95. C2×SD32D191semidirect
106. C2×Q16C2×D191semidirect
114. C2×C16C2×D191semidirect

Maximal subgroups

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

subgroupindex
#271334642
#271331042
#271329352
#271324762
#271324712
#271324462
C2×SD32×C1912
#2194191