Finite Group Databasebeta

← #15675344

Subgroups — #15675344

Order 2944.

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#13093214C211yesmaximal, characteristic, complemented
2#13092855C211yesmaximal, characteristic, complemented
3#13092852C211yesmaximal, characteristic, complemented
4#13092671C211yesmaximal, characteristic, complemented
5#13092226C211yesmaximal, characteristic, complemented
6#13092198C211yesmaximal, characteristic, complemented
7C23×#360C211yesmaximal, characteristic, complemented
8#41×D23—21no—
9C23×#135C2211yescharacteristic
10#10625121—21no—
11#10625089—21no—
12#10625086—21no—
13#10625085—21no—
14#10625082—21no—
15#10625075C2211yescharacteristic
16C2×D184C2211yescharacteristic, complemented
17C2×#67262C2211yescharacteristic
18#10625066—21no—
19C23×M32C2211yescharacteristic, complemented
20C23×#106C2211yescharacteristic, complemented
21#10625010—21no—
22#10625008—21no—
23#10624994C2211yescharacteristic, complemented
24#10624991—21no—
25#10624982—21no—
26D368—21no—
27#41×C23—21no—
28#67292—21no—
29Q8×D23—21no—
30#67290—21no—
31#67290—41no—
32D4×D23—21no—
33D4×D23—41no—
34#67288—21no—
35#67288—41no—
36C2×D92—21no—
37C2×D92—41no—
38C2×C4×D23—41no—
39C2×C4×D23D411yescharacteristic
40Q16×C23D411yescharacteristic, complemented
41SD16×C23—21no—
42D8×C23D411yescharacteristic, complemented
43C2×C8×C23C2311yescharacteristic
44C4⋊C4×C23—21no—
45#67275—21no—
46#67274—21no—
47#67273—21no—
48#67272—21no—
49(C2×D23)⋊C4—41no—
50C2×C23⋊C8D411yescharacteristic
51Dic92D411yescharacteristic, complemented
52D184—21no—
53D184—21no—
54D184D411yescharacteristic, complemented
55#67263—21no—
56#67262—21no—
57#67262—21no—
58C16×C23—21no—
59C23⋊C16—21no—
60C22×D23—41no—
61C22×D23—41no—
62C22×D23D811yescharacteristic
63Q8×C23—21no—
64D4×C23—21no—
65D4×C23—41no—
66C2×C4×C23—41no—
67C2×C4×C23—41no—
68C2×C4×C23C2×D411yescharacteristic
69C22⋊D23—41no—
70C22⋊D23—41no—
71C22⋊D23—41no—
72C2×Dic23—41no—
73C2×Dic23D811yescharacteristic
74D92—21no—
75D92—41no—
76D92—41no—
77D92—41no—
78D92—82no—
79C4×D23—21no—
80C4×D23—21no—
81C4×D23—41no—
82C4×D23—41no—
83C4×D23—41no—
84Dic46—21no—
85Dic46—41no—
86C8×C23C2×D411yescharacteristic
87C8×C23C2×D411yescharacteristic
88C23⋊C8—21no—
89#2190—231nomaximal, Sylow
90C22×C23—41no—
91C22×C23C2×D811yescharacteristic
92C2×D23—21no—
93C2×D23—41no—
94C2×D23—41no—
95C2×D23—82no—
96C2×D23—81no—
97C2×D23—81no—
98C2×D23—81no—
99C4×C23—41no—
100C4×C23—81no—
101C4×C23#12011yescharacteristic
102C4×C23AGL(1,ℤ/8)11yescharacteristic
103Dic23—21no—
104Dic23—41no—
105#575—231no—
106#509—231no—
107#509—231no—
108#469—231no—
109#360—231no—
110#360D2311yescharacteristic, complemented
111#349—231no—
112C2×C23—21no—
113C2×C23—81no—
114C2×C23#44711yescharacteristic
115D23—41no—
116D23—81no—
117D23—161no—
118C2×#41—461no—
119#137—461no—
120#137—461no—
121AGL(1,ℤ/8)—461no—
122AGL(1,ℤ/8)—461no—
123#135—231no—
124#135—461no—
125#135C2×D2311yescharacteristic
126C2×D8—231no—
127C2×M16—231no—
128#121—461no—
129SD32—461no—
130SD32—461no—
131D16—461no—
132D16—461no—
133M32—231no—
134M32C2×D2311yescharacteristic, complemented
135#106C2×D2311yescharacteristic, complemented
136#102—461no—
137C23#219011yescharacteristic, complemented, Sylow
138#41—21no—
139#41—461no—
140#41—461no—
141#41—461no—
142#41—921no—
143#41—921no—
144C2×Q8—461no—
145C2×D4—461no—
146C2×D4—461no—
147C2×D4—921no—
148C2×D4—921no—
149C22×C4—231no—
150C22×C4—921no—
151Q16—231no—
152Q16—461no—
153Q16D9211yescharacteristic, complemented
154SD16—21no—
155SD16—461no—
156SD16—461no—
157SD16—461no—
158D8—231no—
159D8—461no—
160D8—461no—
161D8—461no—
162D8D9211yescharacteristic, complemented
163M16—461no—
164M16—461no—
165C2×C8—231no—
166C2×C8C22×D2311yescharacteristic
167C4⋊C4—21no—
168C22⋊C4—921no—
169C16—21no—
170C16—461no—
171C23—231no—
172C23—921no—
173C23—921no—
174Q8—21no—
175Q8—461no—
176Q8—921no—
177D4—21no—
178D4—41no—
179D4—461no—
180D4—921no—
181D4—921no—
182D4—921no—
183D4—921no—
184D4—921no—
185D4—921no—
186D4—1842no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—231no—
190C2×C4—461no—
191C2×C4—461no—
192C2×C4—921no—
193C2×C4—921no—
194C2×C4—921no—
195C2×C4—921no—
196C2×C4D4×D2311yescharacteristic
197C8—461no—
198C8C2×D9211yescharacteristic
199C8D4×D2311yescharacteristic
200C22—41no—
201C22—461no—
202C22—921no—
203C22—921no—
204C22—1841no—
205C22—1841no—
206C22—1842no—
207C22—1841no—
208C22D8×D2311yescharacteristic
209C4—41no—
210C4—81no—
211C4—461no—
212C4—921no—
213C4#1062505311yescharacteristic
214C4#1062508511yescharacteristic
215C2—21no—
216C2—81no—
217C2—921no—
218C2—3681no—
219C2—1841no—
220C2#1309255211yescharacteristic
subgroupG/H
centerC2#13092552
commutator, cosocleC2×C8×C23C23
FrattiniC2×C8C22×D23
FittingC23×#360C2
socleC2×C23#447
hypercenter#360D23
hypocenterC23#2190
LCSG ▷ C2×C8×C23 ▷ C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #360

Complements

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

NH ≅ G/Ntype
1. #13093214C2semidirect
2. #13092855C2semidirect
3. #13092852C2semidirect
4. #13092671C2semidirect
5. #13092226C2semidirect
6. #13092198C2semidirect
7. C23×#360C2semidirect
16. C2×D184C22semidirect
19. C23×M32C22semidirect
20. C23×#106C22semidirect
23. #10624994C22semidirect
40. Q16×C23D4semidirect
42. D8×C23D4semidirect
51. Dic92D4semidirect
54. D184D4semidirect
110. #360D23semidirect
134. M32C2×D23semidirect
135. #106C2×D23semidirect
137. C23#2190semidirect
153. Q16D92semidirect
162. D8D92semidirect

Maximal subgroups

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

subgroupindex
#130932142
#130928552
#130928522
#130926712
#130922262
#130921982
C23×#3602
#219023