Finite Group Databasebeta

← #15673890

Subgroups — #15673890

Order 2944.

310 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 310 conjugacy classes of subgroups — too many to draw. Only its 79 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
1C2×#10625080C211yesmaximal, characteristic
2#13092894C211yesmaximal, characteristic, complemented
3#13092433C211yesmaximal, characteristic
4#13092427C211yesmaximal, characteristic, complemented
5#13092390C211yesmaximal, characteristic
6#13092174C211yesmaximal, characteristic, complemented
7C23×#344C211yesmaximal, characteristic, complemented
8C2×#67288C2211yescharacteristic
9C22×Dic46C2211yescharacteristic
10C2×M16×C23C2211yescharacteristic
11C2×M16×C23C2211yescharacteristic
12C23×#117C2211yescharacteristic
13#10625097C2211yescharacteristic
14#10625097C2211yescharacteristic
15#10625080—22no—
16#10625080—22no—
17C2×Dic92C412yescomplemented
18C2×#67263C412yescomplemented
19#10625058—22no—
20#10625048—22no—
21C4×Dic46—22no—
22#10625007—22no—
23#10624998—22no—
24#10624988—22no—
25C22×C4×C23C2311yescharacteristic
26C2×C22⋊D23—21no—
27C22×Dic23—21no—
28#67288—21no—
29#67288—21no—
30#67288—21no—
31#67288—21no—
32C2×D92C2×C411yescharacteristic
33C2×C4×D23—21no—
34C2×Dic46—21no—
35C2×Dic46—21no—
36C2×Dic46—21no—
37C2×Dic46C2×C411yescharacteristic
38C2×Dic46C2×C412yes—
39C2×Dic46D412yes—
40C2×Dic46D412yes—
41M16×C23—21no—
42M16×C23—21no—
43M16×C23—21no—
44M16×C23—21no—
45C2×C8×C23—21no—
46C2×C8×C23C2×C412yes—
47C4⋊C4×C23—21no—
48C22⋊C4×C23D412yes—
49C42×C23—21no—
50C22⋊Dic23—21no—
51C22⋊Dic23—21no—
52C4⋊Dic23—21no—
53C4⋊Dic23—21no—
54Dic23⋊C4—24no—
55C4×Dic23—24no—
56C4×Dic23—21no—
57C4×Dic23D412yes—
58Dic92—24no—
59#67263—24no—
60C23×C23C2×D411yescharacteristic
61C22×D23—21no—
62C2×C4×C23—22no—
63C2×C4×C23C22×C411yescharacteristic
64C2×C4×C23C2×D411yescharacteristic
65C2×C4×C23C2×D411yescharacteristic
66C2×C4×C23C2×D411yescharacteristic
67C2×C4×C23#4111yescharacteristic
68C2×C4×C23#4111yescharacteristic
69C22⋊D23—41no—
70C22⋊D23—41no—
71C2×Dic23—22no—
72C2×Dic23—22no—
73C2×Dic23—22no—
74C2×Dic23—21no—
75C2×Dic23—22no—
76C2×Dic23—41no—
77D92—21no—
78D92—21no—
79C4×D23—41no—
80C4×D23—41no—
81Dic46—22no—
82Dic46—22no—
83Dic46—22no—
84Dic46—21no—
85Dic46—21no—
86Dic46C22⋊C414yes—
87C8×C23—22no—
88C8×C23—41no—
89#1905—231nomaximal, Sylow
90C22×C23—41no—
91C22×C23C4×D411yescharacteristic
92C22×C23#12011yescharacteristic
93C22×C23#12111yescharacteristic
94C2×D23—41no—
95C2×D23—81no—
96C4×C23—42no—
97C4×C23C2×C22⋊C411yescharacteristic
98C4×C23C4×D411yescharacteristic
99C4×C23#12111yescharacteristic
100C4×C23#12311yescharacteristic
101Dic23—24no—
102Dic23—42no—
103Dic23—41no—
104Dic23—81no—
105C2×#137—231no—
106#519—231no—
107#421—231no—
108#419—231no—
109#410—231no—
110#344D2311yescharacteristic, complemented
111H(3,ℤ/4)—231no—
112C2×C23—21no—
113C2×C23—21no—
114C2×C23—21no—
115C2×C23#38611yescharacteristic
116D23—81no—
117C2×#41—231no—
118C22×Q8—231no—
119#137—462no—
120#137—462no—
121C2×Q16—232no—
122C2×SD16—232no—
123C2×M16C2×D2311yescharacteristic
124C2×M16C2×D2311yescharacteristic
125C4×Q8—462no—
126C4×Q8—462no—
127#117—231no—
128#117—231no—
129#117—462no—
130#117C2×D2311yescharacteristic
131#104—462no—
132#103—462no—
133#99—462no—
134C23#190511yescharacteristic, complemented, Sylow
135#41—461no—
136#41—461no—
137#41—461no—
138#41—461no—
139C2×Q8—232no—
140C2×Q8—231no—
141C2×Q8—232no—
142C2×Q8—232no—
143C2×Q8—461no—
144C2×Q8—461no—
145C2×Q8—461no—
146C2×D4—231no—
147C2×D4—461no—
148C22×C4—461no—
149C22×C4—461no—
150C22×C4C22×D2311yescharacteristic
151Q16—464no—
152SD16—464no—
153M16—21no—
154M16—21no—
155M16—21no—
156M16—21no—
157C2×C8—21no—
158C2×C8C4×D2312yes—
159C4⋊C4—21no—
160C4⋊C4—464no—
161C4⋊C4—461no—
162C4⋊C4—461no—
163C22⋊C4—461no—
164C22⋊C4—461no—
165C22⋊C4D9212yes—
166C42—21no—
167C42—232no—
168C42—464no—
169C42—461no—
170C23—461no—
171C23C2×D9211yescharacteristic
172Q8—234no—
173Q8—462no—
174Q8—462no—
175Q8—462no—
176Q8—461no—
177Q8—461no—
178D4—461no—
179D4—461no—
180D4—921no—
181D4—921no—
182C2×C4—22no—
183C2×C4—462no—
184C2×C4—462no—
185C2×C4—462no—
186C2×C4—461no—
187C2×C4—462no—
188C2×C4—921no—
189C2×C4—921no—
190C2×C4—921no—
191C2×C4C2×C4×D2311yescharacteristic
192C2×C4#6728811yescharacteristic
193C2×C4D4×D2311yescharacteristic
194C2×C4D4×D2311yescharacteristic
195C2×C4D4×D2311yescharacteristic
196C2×C4#6729211yescharacteristic
197C8—22no—
198C8—41no—
199C22—41no—
200C22—921no—
201C22—1841no—
202C22C4×D9211yescharacteristic
203C22#1062505311yescharacteristic
204C22#1062506611yescharacteristic
205C4—42no—
206C4—464no—
207C4—922no—
208C4—921no—
209C4—1841no—
210C4C22⋊C4×D2311yescharacteristic
211C4#1062505511yescharacteristic
212C4#1062506411yescharacteristic
213C4#1062506511yescharacteristic
214C2—21no—
215C2—21no—
216C2—21no—
217C2—1841no—
218C2#1309229511yescharacteristic
subgroupG/H
centerC2#13092295
commutatorC2×C4×C23C22×C4
FrattiniC22×C4C22×D23
FittingC23×#344C2
socleC2×C23#386
prime radicalC2×#67288C22
cosocleC22×C4×C23C23
hypercenter#344D23
hypocenterC23#1905
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2 ◁ C22×C4 ◁ #344

Complements

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

NH ≅ G/Ntype
2. #13092894C2semidirect
4. #13092427C2semidirect
6. #13092174C2semidirect
7. C23×#344C2semidirect
17. C2×Dic92C4semidirect
18. C2×#67263C4semidirect
110. #344D23semidirect
134. C23#1905semidirect

Maximal subgroups

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

subgroupindex
C2×#106250802
#130928942
#130924332
#130924272
#130923902
#130921742
C23×#3442
#190523