Finite Group Databasebeta

← #37574464

Subgroups — #37574464

Order 24448.

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

normal subgroups only

This group has 226 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#27133460C211yesmaximal, characteristic, complemented
2#27133099C211yesmaximal, characteristic, complemented
3#27132913C211yesmaximal, characteristic, complemented
4#27132474C211yesmaximal, characteristic, complemented
5#27132473C211yesmaximal, characteristic, complemented
6#27132444C211yesmaximal, characteristic, complemented
7#509×C191C211yesmaximal, characteristic, complemented
8#41×D191—21no—
9#20259354—21no—
10#20259351—21no—
11#20259349—21no—
12#20259346—21no—
13#20259344C2211yescharacteristic
14#20259342—21no—
15C2×#15690270C2211yescharacteristic
16#20259293—21no—
17#20259266—21no—
18#20259263—21no—
19#20259262C2211yescharacteristic, complemented
20#20259254C2211yescharacteristic, complemented
21#20259243—21no—
22#135×C191C2211yescharacteristic
23C2×D8×C191C2211yescharacteristic, complemented
24SD32×C191—21no—
25D16×C191—21no—
26M32×C191C2211yescharacteristic, complemented
27#15690288—21no—
28#15690287—21no—
29#15690287—41no—
30#15690286—21no—
31#15690286—41no—
32Q8×D191—21no—
33C2×C22⋊D191—41no—
34D4×D191—21no—
35D4×D191—41no—
36C2×C4×D191—41no—
37C2×C4×D191D411yescharacteristic
38Dic764D411yescharacteristic, complemented
39#15690277—21no—
40#15690276—21no—
41#15690275—21no—
42#15690274—21no—
43D1528D411yescharacteristic, complemented
44#15690272—21no—
45#15690270—21no—
46#15690270—21no—
47C2×C191⋊C8D411yescharacteristic
48C4⋊Dic191—21no—
49C22⋊Dic191—41no—
50C191⋊C16—21no—
51#41×C191—21no—
52C2×D4×C191—21no—
53Q16×C191D411yescharacteristic, complemented
54SD16×C191—21no—
55D8×C191—21no—
56D8×C191—21no—
57D8×C191D411yescharacteristic, complemented
58C2×C8×C191C2311yescharacteristic
59C16×C191—21no—
60C22×D191—41no—
61C22×D191D811yescharacteristic
62Dic382—21no—
63Dic382—41no—
64D764—21no—
65D764—41no—
66C22⋊D191—41no—
67C22⋊D191—41no—
68C22⋊D191—41no—
69C22⋊D191—82no—
70C2×Dic191—41no—
71C2×Dic191—41no—
72C2×Dic191D811yescharacteristic
73C4×D191—21no—
74C4×D191—21no—
75C4×D191—41no—
76C4×D191—41no—
77C4×D191—41no—
78C191⋊C8—21no—
79C23×C191—41no—
80Q8×C191—21no—
81D4×C191—21no—
82D4×C191—41no—
83D4×C191—41no—
84D4×C191—41no—
85C2×C4×C191—41no—
86C2×C4×C191C2×D411yescharacteristic
87C8×C191C2×D411yescharacteristic
88C8×C191C2×D411yescharacteristic
89C22×C191—41no—
90C22×C191—81no—
91C22×C191—81no—
92C22×C191—81no—
93C22×C191C2×D811yescharacteristic
94C2×D191—21no—
95C2×D191—41no—
96C2×D191—41no—
97C2×D191—82no—
98C4×C191—41no—
99C4×C191#12011yescharacteristic
100C4×C191AGL(1,ℤ/8)11yescharacteristic
101Dic191—21no—
102Dic191—41no—
103Dic191—81no—
104C2×C191—21no—
105C2×C191—81no—
106C2×C191—161no—
107C2×C191#44711yescharacteristic
108D191—41no—
109D191—81no—
110C191#219011yescharacteristic, complemented, Sylow
111#2190—1911nomaximal, Sylow
112#575—1911no—
113#509—1911no—
114#509D19111yescharacteristic, complemented
115#469—1911no—
116#360—1911no—
117#360—1911no—
118#349—1911no—
119C2×#41—3821no—
120#137—3821no—
121#137—3821no—
122AGL(1,ℤ/8)—3821no—
123AGL(1,ℤ/8)—3821no—
124#135—3821no—
125#135—1911no—
126#135C2×D19111yescharacteristic
127C2×D8C2×D19111yescharacteristic, complemented
128C2×M16—1911no—
129#121—3821no—
130SD32—21no—
131SD32—3821no—
132D16—21no—
133D16—3821no—
134M32—1911no—
135M32C2×D19111yescharacteristic, complemented
136#106—1911no—
137#102—3821no—
138#41—21no—
139#41—3821no—
140#41—3821no—
141#41—3821no—
142#41—7641no—
143#41—7641no—
144C2×Q8—3821no—
145C2×D4—21no—
146C2×D4—3821no—
147C2×D4—7641no—
148C2×D4—7641no—
149C22×C4—1911no—
150C22×C4—7641no—
151Q16—3821no—
152Q16—1911no—
153Q16C22⋊D19111yescharacteristic, complemented
154SD16—21no—
155SD16—3821no—
156SD16—3821no—
157SD16—3821no—
158D8—21no—
159D8—21no—
160D8—3821no—
161D8—1911no—
162D8C22⋊D19111yescharacteristic, complemented
163M16—3821no—
164M16—3821no—
165C2×C8—1911no—
166C2×C8C22×D19111yescharacteristic
167C4⋊C4—3821no—
168C22⋊C4—7641no—
169C16—21no—
170C16—3821no—
171C23—41no—
172C23—1911no—
173C23—7641no—
174Q8—21no—
175Q8—3821no—
176Q8—7641no—
177D4—21no—
178D4—41no—
179D4—41no—
180D4—41no—
181D4—3821no—
182D4—15282no—
183D4—7641no—
184D4—7641no—
185D4—7641no—
186D4—7641no—
187C2×C4—41no—
188C2×C4—3821no—
189C2×C4—3821no—
190C2×C4—1911no—
191C2×C4—7641no—
192C2×C4—7641no—
193C2×C4—7641no—
194C2×C4—7641no—
195C2×C4—7641no—
196C2×C4D4×D19111yescharacteristic
197C8—3821no—
198C8D4×D19111yescharacteristic
199C8C2×C22⋊D19111yescharacteristic
200C22—41no—
201C22—81no—
202C22—81no—
203C22—81no—
204C22—3821no—
205C22—15282no—
206C22—7641no—
207C22—7641no—
208C22D8×D19111yescharacteristic
209C4—41no—
210C4—3821no—
211C4—15281no—
212C4—7641no—
213C4#2025929011yescharacteristic
214C4#2025934611yescharacteristic
215C2—21no—
216C2—81no—
217C2—161no—
218C2—15281no—
219C2—7641no—
220C2#2713279511yescharacteristic
subgroupG/H
centerC2#27132795
commutator, cosocleC2×C8×C191C23
FrattiniC2×C8C22×D191
Fitting#509×C191C2
socleC2×C191#447
hypercenter#509D191
hypocenterC191#2190
LCSG ▷ C2×C8×C191 ▷ C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #509

Complements

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

NH ≅ G/Ntype
1. #27133460C2semidirect
2. #27133099C2semidirect
3. #27132913C2semidirect
4. #27132474C2semidirect
5. #27132473C2semidirect
6. #27132444C2semidirect
7. #509×C191C2semidirect
19. #20259262C22semidirect
20. #20259254C22semidirect
23. C2×D8×C191C22semidirect
26. M32×C191C22semidirect
38. Dic764D4semidirect
43. D1528D4semidirect
53. Q16×C191D4semidirect
57. D8×C191D4semidirect
110. C191#2190semidirect
114. #509D191semidirect
127. C2×D8C2×D191semidirect
135. M32C2×D191semidirect
153. Q16C22⋊D191semidirect
162. D8C22⋊D191semidirect

Maximal subgroups

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

subgroupindex
#271334602
#271330992
#271329132
#271324742
#271324732
#271324442
#509×C1912
#2190191