Finite Group Databasebeta

← #15675080

Subgroups — #15675080

Order 2944.

250 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 65 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#13092963C211yesmaximal, characteristic
2#13092401C211yesmaximal, characteristic, complemented
3#13092215C212yesmaximal, complemented
4#13092213C212yesmaximal, complemented
5C23×#413C211yesmaximal, characteristic, complemented
6C2×#41×C23C2211yescharacteristic
7C2×#67288C411yescharacteristic
8C2×M16×C23—21no—
9#10625118C2211yescharacteristic
10#10625115C2211yescharacteristic
11#10625111C411yescharacteristic
12#10625110—21no—
13#10625110—21no—
14#10625107C411yescharacteristic
15C4×C22⋊D23—21no—
16C4×C22⋊D23—21no—
17C2×C4×Dic23C411yescharacteristic
18C2×#67267—21no—
19C23×#101C2212yes—
20C23×#100—21no—
21#10625018C2212yes—
22#10625015—21no—
23#41×C23—41no—
24#41×C23—41no—
25C2×Q8×C23C2311yescharacteristic
26C2×D4×C23C2×C411yescharacteristic
27C2×D4×C23D411yescharacteristic
28C2×D4×C23D411yescharacteristic
29C22×C4×C23C2×C411yescharacteristic
30C22×C4×C23D411yescharacteristic
31C22×C4×C23D411yescharacteristic
32C2×C22⋊D23—21no—
33C2×C22⋊D23—21no—
34C2×C22⋊D23—21no—
35C22×Dic23—21no—
36#67288—41no—
37#67288—41no—
38C2×D92C2×C411yescharacteristic
39C2×C4×D23—21no—
40C2×Dic46C2×C411yescharacteristic
41M16×C23—22no—
42M16×C23—41no—
43C2×C8×C23—41no—
44C22⋊Dic23—21no—
45C22⋊Dic23—21no—
46(C2×D23)⋊C4—21no—
47(C2×D23)⋊C4—21no—
48Dic23⋊C4—21no—
49Dic23⋊C4—21no—
50C4×Dic23—21no—
51C4×Dic23C2×C411yescharacteristic
52C4×Dic23C2×C411yescharacteristic
53#67267—22no—
54#67267—41no—
55C2×C23⋊C8—41no—
56C23×C23C22⋊C411yescharacteristic
57C23×C23C22⋊C411yescharacteristic
58C23×C23C22⋊C411yescharacteristic
59C22×D23—21no—
60Q8×C23—41no—
61D4×C23—41no—
62D4×C23—41no—
63D4×C23—41no—
64C2×C4×C23—21no—
65C2×C4×C23—21no—
66C2×C4×C23—21no—
67C2×C4×C23—21no—
68C2×C4×C23—21no—
69C2×C4×C23—21no—
70C2×C4×C23C22⋊C411yescharacteristic
71C2×C4×C23C22×C411yescharacteristic
72C2×C4×C23C2×D411yescharacteristic
73C2×C4×C23C2×D411yescharacteristic
74C22⋊D23—42no—
75C22⋊D23—42no—
76C22⋊D23—42no—
77C2×Dic23—21no—
78C2×Dic23—21no—
79C2×Dic23—21no—
80C2×Dic23—42no—
81D92—41no—
82C4×D23—41no—
83C4×D23—41no—
84Dic46—41no—
85C8×C23—42no—
86C23⋊C8—42no—
87#2132—231nomaximal, Sylow
88C22×C23—21no—
89C22×C23—21no—
90C22×C23—21no—
91C22×C23—41no—
92C22×C23—41no—
93C22×C23—41no—
94C22×C23C2×C22⋊C411yescharacteristic
95C2×D23—41no—
96C2×D23—41no—
97C2×D23—41no—
98C4×C23—21no—
99C4×C23—21no—
100C4×C23—21no—
101C4×C23#9911yescharacteristic
102C4×C23#9911yescharacteristic
103Dic23—22no—
104Dic23—41no—
105Dic23—41no—
106#532—231no—
107#413—231no—
108#413D2311yescharacteristic, complemented
109#356—232no—
110#355—232no—
111C2×C23—21no—
112C2×C23—41no—
113C2×C23—41no—
114C2×C23—41no—
115C2×C23C2×#9911yescharacteristic
116D23—81no—
117C2×#41—231no—
118C2×#41C2×D2311yescharacteristic
119C2×M16—21no—
120C2×M16—461no—
121C4⋊Q8—231no—
122#127—231no—
123#124—231no—
124#124—231no—
125#121—461no—
126#121—461no—
127C4×D4—461no—
128C4×D4—461no—
129C2×C42—231no—
130#101—232no—
131#101C2×D2312yes—
132#100—21no—
133#100—461no—
134C23#213211yescharacteristic, complemented, Sylow
135#41—41no—
136#41—41no—
137#41—921no—
138#41—921no—
139C2×Q8—231no—
140C2×Q8C22×D2311yescharacteristic
141C2×D4—231no—
142C2×D4—461no—
143C2×D4—461no—
144C2×D4—461no—
145C2×D4C4×D2311yescharacteristic
146C2×D4D9211yescharacteristic
147C2×D4C22⋊D2311yescharacteristic
148C22×C4—461no—
149C22×C4—461no—
150C22×C4C4×D2311yescharacteristic
151C22×C4D9211yescharacteristic
152C22×C4C22⋊D2311yescharacteristic
153M16—22no—
154M16—41no—
155M16—462no—
156M16—921no—
157C2×C8—41no—
158C2×C8—921no—
159C4⋊C4—461no—
160C4⋊C4—461no—
161C22⋊C4—461no—
162C22⋊C4—461no—
163C22⋊C4—461no—
164C22⋊C4—461no—
165C42—231no—
166C42—231no—
167C42—461no—
168C23—461no—
169C23(C2×D23)⋊C411yescharacteristic
170C23(C2×D23)⋊C411yescharacteristic
171C23(C2×D23)⋊C411yescharacteristic
172Q8—41no—
173Q8—921no—
174D4—41no—
175D4—41no—
176D4—41no—
177D4—921no—
178D4—922no—
179D4—922no—
180D4—922no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—461no—
188C2×C4—461no—
189C2×C4—461no—
190C2×C4—922no—
191C2×C4—921no—
192C2×C4—921no—
193C2×C4(C2×D23)⋊C411yescharacteristic
194C2×C4C2×C4×D2311yescharacteristic
195C2×C4C2×D9211yescharacteristic
196C2×C4C2×C22⋊D2311yescharacteristic
197C8—42no—
198C8—922no—
199C22—21no—
200C22—21no—
201C22—21no—
202C22—41no—
203C22—41no—
204C22—41no—
205C22—921no—
206C22—921no—
207C22—921no—
208C22C2×(C2×D23)⋊C411yescharacteristic
209C4—21no—
210C4—21no—
211C4—21no—
212C4—462no—
213C4—921no—
214C4—921no—
215C4#1062498811yescharacteristic
216C4#1062498811yescharacteristic
217C2—21no—
218C2—41no—
219C2—41no—
220C2—41no—
221C2—1841no—
222C2C2×#1062498811yescharacteristic
subgroupG/H
centerC4#10624988
commutatorC2×C4×C23C22×C4
FrattiniC2×Q8C22×D23
FittingC23×#413C2
socleC2×C23C2×#99
prime radical#13092963C2
cosocleC2×Q8×C23C23
hypercenter#413D23
hypocenterC23#2132
LCSG ▷ C2×C4×C23 ▷ C22×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×#41 ◁ #413

Complements

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

NH ≅ G/Ntype
2. #13092401C2semidirect
3. #13092215C2semidirect
4. #13092213C2semidirect
5. C23×#413C2semidirect
108. #413D23semidirect
134. C23#2132semidirect

Maximal subgroups

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

subgroupindex
#130929632
#130924012
#130922152
#130922132
C23×#4132
#213223