Finite Group Databasebeta

← #15673879

Subgroups — #15673879

Order 2944.

324 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 93 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#13093184C211yesmaximal, characteristic, complemented
2#13092434C211yesmaximal, characteristic, complemented
3#13092422C211yesmaximal, characteristic, complemented
4C2×#10625015C211yesmaximal, characteristic, complemented
5#13092188C211yesmaximal, characteristic, complemented
6C23⋊#338C211yesmaximal, characteristic, complemented
7C2×C23×AGL(1,ℤ/8)C211yesmaximal, characteristic
8C2×#41×C23C2211yescharacteristic
9C22×D4×C23C2211yescharacteristic
10C23×AGL(1,ℤ/8)—22no—
11C23×AGL(1,ℤ/8)—22no—
12C2×SD16×C23C412yescomplemented
13C2×D8×C23C412yescomplemented
14C2×M16×C23C2211yescharacteristic
15#10625119—22no—
16#10625119—22no—
17#10625097C2211yescharacteristic
18C2×#67267—22no—
19C2×#67267C2211yescharacteristic
20C2×#67267C2211yescharacteristic
21C2×#67267C2211yescharacteristic
22#10625019—22no—
23#10625015—22no—
24#10625014—22no—
25C24×C23—21no—
26#41×C23—21no—
27#41×C23—21no—
28#41×C23D412yes—
29#41×C23D412yes—
30C2×Q8×C23C2×C411yescharacteristic
31C2×D4×C23—21no—
32C2×D4×C23—21no—
33C2×D4×C23—21no—
34C2×D4×C23—21no—
35C2×D4×C23—21no—
36C2×D4×C23—21no—
37C2×D4×C23C2×C412yes—
38C2×D4×C23C2×C411yescharacteristic
39C22×C4×C23—21no—
40C22×C4×C23C2311yescharacteristic
41SD16×C23—24no—
42D8×C23—24no—
43M16×C23—21no—
44M16×C23—21no—
45C2×C8×C23C2×C412yes—
46C22⋊Dic23—21no—
47C4⋊Dic23—21no—
48C4×Dic23—21no—
49#67267—24no—
50#67267—21no—
51#67267—21no—
52#67267—21no—
53#67267—21no—
54#67267—21no—
55#67267D412yes—
56C2×C23⋊C8—24no—
57C2×C23⋊C8—21no—
58C2×C23⋊C8—21no—
59C2×C23⋊C8D412yes—
60C23×C23—21no—
61C23×C23—22no—
62C23×C23—41no—
63C23×C23—41no—
64C23×C23—82no—
65C23×C23#4111yescharacteristic
66Q8×C23—21no—
67Q8×C23C22⋊C412yes—
68D4×C23—22no—
69D4×C23—22no—
70D4×C23—22no—
71D4×C23—21no—
72D4×C23—22no—
73D4×C23—41no—
74D4×C23—41no—
75D4×C23C22⋊C412yes—
76C2×C4×C23—21no—
77C2×C4×C23—22no—
78C2×C4×C23—22no—
79C2×C4×C23C22×C411yescharacteristic
80C2×C4×C23C2×D411yescharacteristic
81C2×C4×C23C2×D411yescharacteristic
82C2×C4×C23C2×D411yescharacteristic
83C2×C4×C23C2×D411yescharacteristic
84C2×C4×C23#4111yescharacteristic
85C2×Dic23—41no—
86C8×C23—22no—
87C23⋊C8—22no—
88C23⋊C8—22no—
89C23⋊C8—41no—
90#1903—231nomaximal, Sylow
91C22×C23—22no—
92C22×C23—41no—
93C22×C23—42no—
94C22×C23—81no—
95C22×C23—82no—
96C22×C23—82no—
97C22×C23—82no—
98C22×C23C4×D411yescharacteristic
99C22×C23#12111yescharacteristic
100C22×C23#12311yescharacteristic
101C4×C23—22no—
102C4×C23C2×C22⋊C411yescharacteristic
103C4×C23C4×D411yescharacteristic
104C4×C23#12011yescharacteristic
105C4×C23#12111yescharacteristic
106Dic23—81no—
107C2×AGL(1,ℤ/8)D2311yescharacteristic
108#568—231no—
109#421—231no—
110#418—231no—
111C2×#100—231no—
112#344—231no—
113#338—231no—
114C2×C23—21no—
115C2×C23—21no—
116C2×C23—21no—
117C2×C23—42no—
118C2×C23—82no—
119C2×C23#38611yescharacteristic
120C2×#41C2×D2311yescharacteristic
121C22×D4C2×D2311yescharacteristic
122AGL(1,ℤ/8)—22no—
123AGL(1,ℤ/8)—22no—
124C2×SD16Dic2312yescomplemented
125C2×D8Dic2312yescomplemented
126#131—462no—
127#131—462no—
128C2×M16—231no—
129C2×M16—231no—
130C2×M16—231no—
131C2×M16—462no—
132C2×M16C2×D2311yescharacteristic
133#117—231no—
134#104—462no—
135#102—462no—
136#100—462no—
137C23#190311yescharacteristic, complemented, Sylow
138C24—21no—
139#41—21no—
140#41—21no—
141#41C22⋊D2312yes—
142#41C22⋊D2312yes—
143C2×Q8C2×Dic2311yescharacteristic
144C2×D4—21no—
145C2×D4—21no—
146C2×D4—21no—
147C2×D4—21no—
148C2×D4—21no—
149C2×D4—21no—
150C2×D4C2×Dic2312yes—
151C2×D4C2×Dic2311yescharacteristic
152C22×C4—21no—
153C22×C4C22×D2311yescharacteristic
154SD16—24no—
155D8—24no—
156M16—21no—
157M16—21no—
158M16—232no—
159M16—464no—
160M16—461no—
161M16—461no—
162M16—461no—
163M16—461no—
164M16—461no—
165C2×C8—232no—
166C2×C8—464no—
167C2×C8—461no—
168C2×C8—461no—
169C2×C8C2×Dic2312yes—
170C4⋊C4—461no—
171C22⋊C4—461no—
172C42—461no—
173C23—21no—
174C23—22no—
175C23—41no—
176C23—41no—
177C23—82no—
178C23#6729011yescharacteristic
179Q8—21no—
180Q8C22⋊Dic2312yes—
181D4—22no—
182D4—22no—
183D4—21no—
184D4—22no—
185D4—22no—
186D4—41no—
187D4—41no—
188D4C22⋊Dic2312yes—
189C2×C4—21no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—921no—
193C2×C4D4×D2311yescharacteristic
194C2×C4D4×D2311yescharacteristic
195C2×C4#6729011yescharacteristic
196C2×C4C22×Dic2311yescharacteristic
197C2×C4C2×C22⋊D2311yescharacteristic
198C2×C4C2×C22⋊D2311yescharacteristic
199C8—22no—
200C8—462no—
201C8—462no—
202C8—921no—
203C22—22no—
204C22—41no—
205C22—42no—
206C22—81no—
207C22—82no—
208C22—82no—
209C22—82no—
210C22D4×Dic2311yescharacteristic
211C22#1062510611yescharacteristic
212C22#1062511011yescharacteristic
213C4—22no—
214C4—1841no—
215C4D4×Dic2311yescharacteristic
216C4#1062510811yescharacteristic
217C4#1062511011yescharacteristic
218C4C2×C22⋊Dic2311yescharacteristic
219C2—21no—
220C2—21no—
221C2—21no—
222C2—42no—
223C2—82no—
224C2#1309229711yescharacteristic
subgroupG/H
centerC2#13092297
commutatorC2×C4×C23C22×C4
FrattiniC22×C4C22×D23
Fitting, prime radicalC2×C23×AGL(1,ℤ/8)C2
socleC2×C23#386
cosocleC22×C4×C23C23
hypercenterC2×AGL(1,ℤ/8)D23
hypocenterC23#1903
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. #13093184C2semidirect
2. #13092434C2semidirect
3. #13092422C2semidirect
4. C2×#10625015C2semidirect
5. #13092188C2semidirect
6. C23⋊#338C2semidirect
12. C2×SD16×C23C4semidirect
13. C2×D8×C23C4semidirect
124. C2×SD16Dic23semidirect
125. C2×D8Dic23semidirect
137. C23#1903semidirect

Maximal subgroups

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

subgroupindex
#130931842
#130924342
#130924222
C2×#106250152
#130921882
C23⋊#3382
C2×C23×AGL(1,ℤ/8)2
#190323