Finite Group Databasebeta

← #15675060

Subgroups — #15675060

Order 2944.

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

normal subgroups only

This group has 258 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#13092391C211yesmaximal, characteristic, complemented
3#13092211C212yesmaximal, complemented
4#13092209C212yesmaximal, complemented
5C23×#410C211yesmaximal, characteristic, complemented
6C2×#41×C23C2211yescharacteristic
7C2×#67288C411yescharacteristic, complemented
8C23×#117—21no—
9#10625118C411yescharacteristic, complemented
10#10625115C411yescharacteristic, complemented
11#10625111C2211yescharacteristic
12#10625110—21no—
13#10625110—21no—
14#10625107C2211yescharacteristic
15C4×C22⋊D23—21no—
16C4×C22⋊D23—21no—
17#10625097—21no—
18C2×C4×Dic23C411yescharacteristic, complemented
19C23×#99—21no—
20C23×#99C2212yes—
21#10625016—21no—
22#10625016C2212yes—
23#41×C23—41no—
24#41×C23—41no—
25C2×Q8×C23C2×C411yescharacteristic
26C2×D4×C23D411yescharacteristic
27C2×D4×C23D411yescharacteristic
28C2×D4×C23C2311yescharacteristic
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
41C4⋊C4×C23—41no—
42C22⋊C4×C23—22no—
43C42×C23—41no—
44C22⋊Dic23—21no—
45C22⋊Dic23—21no—
46C22⋊Dic23—22no—
47(C2×D23)⋊C4—21no—
48(C2×D23)⋊C4—21no—
49C4⋊Dic23—41no—
50Dic23⋊C4—21no—
51Dic23⋊C4—21no—
52C4×Dic23—21no—
53C4×Dic23—41no—
54C4×Dic23C2×C411yescharacteristic
55C4×Dic23C2×C411yescharacteristic
56C23×C23C22⋊C411yescharacteristic
57C23×C23C2×D411yescharacteristic
58C23×C23C2×D411yescharacteristic
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×C23—42no—
71C2×C4×C23C22⋊C411yescharacteristic
72C2×C4×C23C22⋊C411yescharacteristic
73C2×C4×C23C22⋊C411yescharacteristic
74C2×C4×C23C22×C411yescharacteristic
75C22⋊D23—42no—
76C22⋊D23—42no—
77C22⋊D23—42no—
78C2×Dic23—21no—
79C2×Dic23—21no—
80C2×Dic23—21no—
81C2×Dic23—42no—
82C2×Dic23—42no—
83D92—41no—
84C4×D23—41no—
85C4×D23—41no—
86Dic46—41no—
87#2126—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—82no—
102C4×C23#9911yescharacteristic
103C4×C23#9911yescharacteristic
104Dic23—22no—
105Dic23—41no—
106Dic23—41no—
107Dic23—82no—
108#532—231no—
109#410—231no—
110#410D2311yescharacteristic, complemented
111#354—232no—
112#353—232no—
113C2×C23—21no—
114C2×C23—41no—
115C2×C23—41no—
116C2×C23—41no—
117C2×C23C2×#9911yescharacteristic
118D23—81no—
119C2×#41—231no—
120C2×#41C2×D2311yescharacteristic
121C4⋊Q8—231no—
122#127—231no—
123#124—231no—
124#124—231no—
125#121—461no—
126#121—461no—
127C4×D4—461no—
128C4×D4—461no—
129#117—21no—
130#117—461no—
131C2×C42—231no—
132#99—21no—
133#99—232no—
134#99—461no—
135#99C2×D2312yes—
136C23#212611yescharacteristic, complemented, Sylow
137#41—41no—
138#41—41no—
139#41—921no—
140#41—921no—
141C2×Q8—231no—
142C2×Q8C4×D2311yescharacteristic
143C2×D4—231no—
144C2×D4—461no—
145C2×D4—461no—
146C2×D4—461no—
147C2×D4D9211yescharacteristic
148C2×D4C22⋊D2311yescharacteristic
149C2×D4C22×D2311yescharacteristic
150C22×C4—461no—
151C22×C4—461no—
152C22×C4C4×D2311yescharacteristic
153C22×C4D9211yescharacteristic
154C22×C4C22⋊D2311yescharacteristic
155C4⋊C4—41no—
156C4⋊C4—461no—
157C4⋊C4—461no—
158C4⋊C4—921no—
159C22⋊C4—22no—
160C22⋊C4—461no—
161C22⋊C4—461no—
162C22⋊C4—461no—
163C22⋊C4—461no—
164C22⋊C4—462no—
165C42—41no—
166C42—231no—
167C42—231no—
168C42—461no—
169C42—921no—
170C23—461no—
171C23(C2×D23)⋊C411yescharacteristic
172C23C2×D9211yescharacteristic
173C23C2×C22⋊D2311yescharacteristic
174Q8—41no—
175Q8—921no—
176D4—41no—
177D4—41no—
178D4—41no—
179D4—921no—
180D4—922no—
181D4—922no—
182D4—922no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—42no—
190C2×C4—461no—
191C2×C4—461no—
192C2×C4—461no—
193C2×C4—922no—
194C2×C4—921no—
195C2×C4—921no—
196C2×C4—922no—
197C2×C4(C2×D23)⋊C411yescharacteristic
198C2×C4(C2×D23)⋊C411yescharacteristic
199C2×C4(C2×D23)⋊C411yescharacteristic
200C2×C4C2×C4×D2311yescharacteristic
201C22—21no—
202C22—21no—
203C22—21no—
204C22—41no—
205C22—41no—
206C22—41no—
207C22—921no—
208C22—921no—
209C22—921no—
210C22C2×(C2×D23)⋊C411yescharacteristic
211C4—21no—
212C4—21no—
213C4—21no—
214C4—82no—
215C4—462no—
216C4—921no—
217C4—921no—
218C4—1842no—
219C4#1062498811yescharacteristic
220C4#1062498811yescharacteristic
221C2—21no—
222C2—41no—
223C2—41no—
224C2—41no—
225C2—1841no—
226C2C2×#1062498811yescharacteristic
subgroupG/H
centerC4#10624988
commutatorC2×C4×C23C22×C4
FrattiniC2×D4C22×D23
FittingC23×#410C2
socleC2×C23C2×#99
prime radical#13092963C2
cosocleC2×D4×C23C23
hypercenter#410D23
hypocenterC23#2126
LCSG ▷ C2×C4×C23 ▷ C22×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×#41 ◁ #410

Complements

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

NH ≅ G/Ntype
2. #13092391C2semidirect
3. #13092211C2semidirect
4. #13092209C2semidirect
5. C23×#410C2semidirect
7. C2×#67288C4semidirect
9. #10625118C4semidirect
10. #10625115C4semidirect
18. C2×C4×Dic23C4semidirect
110. #410D23semidirect
136. C23#2126semidirect

Maximal subgroups

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

subgroupindex
#130929632
#130923912
#130922112
#130922092
C23×#4102
#212623