Finite Group Databasebeta

← #15673913

Subgroups — #15673913

Order 2944.

312 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 83 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
2C2×#10625078C211yesmaximal, characteristic
3#13092416C211yesmaximal, characteristic
4C2×#10624992C211yesmaximal, characteristic, complemented
5C2×#10625006C211yesmaximal, characteristic, complemented
6#13092181C211yesmaximal, characteristic, complemented
7C23×#343C211yesmaximal, characteristic, complemented
8C2×#67288C2211yescharacteristic
9C22×Dic46C2211yescharacteristic
10C2×M16×C23C2211yescharacteristic
11C2×M16×C23C2211yescharacteristic
12C2×C4⋊C4×C23C2211yescharacteristic
13C2×#67267C2211yescharacteristic
14C22×C23⋊C8C2211yescharacteristic
15#10625080—22no—
16#10625080C414yescomplemented
17#10625078—22no—
18#10625078—22no—
19C2×Dic92—21no—
20C2×#67263—21no—
21C2×#67262—21no—
22C2×C8×D23—21no—
23#10625006—22no—
24#10624992—21no—
25#10624992—21no—
26#10624992—21no—
27#10624991—21no—
28C22×C4×C23—21no—
29C22×C4×C23C2311yescharacteristic
30C2×C22⋊D23—21no—
31C22×Dic23—21no—
32#67288—21no—
33#67288—21no—
34#67288C2×C412yes—
35#67288D412yes—
36C2×D92D411yescharacteristic
37C2×C4×D23—21no—
38C2×Dic46—21no—
39C2×Dic46—21no—
40C2×Dic46—21no—
41C2×Dic46—21no—
42C2×Dic46—21no—
43C2×Dic46C2×C412yes—
44C2×Dic46D411yescharacteristic
45M16×C23—21no—
46M16×C23—21no—
47M16×C23C2×C412yes—
48M16×C23D412yes—
49C2×C8×C23—21no—
50C2×C8×C23—21no—
51C4⋊C4×C23—21no—
52C4⋊C4×C23—21no—
53#67267—21no—
54#67267—21no—
55C2×C23⋊C8—21no—
56C2×C23⋊C8—21no—
57C2×C23⋊C8—21no—
58C2×C23⋊C8D411yescharacteristic
59C2×C23⋊C8D411yescharacteristic
60Dic92—24no—
61#67263—24no—
62#67262—24no—
63C8×D23—24no—
64C23×C23#4111yescharacteristic
65C22×D23—21no—
66C2×C4×C23—41no—
67C2×C4×C23—81no—
68C2×C4×C23C22×C411yescharacteristic
69C2×C4×C23C2×D411yescharacteristic
70C2×C4×C23C2×D411yescharacteristic
71C2×C4×C23C2×D411yescharacteristic
72C2×C4×C23C2×D411yescharacteristic
73C2×C4×C23#4111yescharacteristic
74C22⋊D23—22no—
75C22⋊D23—22no—
76C2×Dic23—21no—
77C2×Dic23—22no—
78C2×Dic23—41no—
79C2×Dic23—41no—
80D92—21no—
81D92C22⋊C412yes—
82C4×D23—22no—
83C4×D23—22no—
84Dic46—21no—
85Dic46—22no—
86Dic46—22no—
87Dic46—41no—
88Dic46—41no—
89Dic46C22⋊C412yes—
90C8×C23—22no—
91C8×C23—22no—
92C23⋊C8—21no—
93C23⋊C8—21no—
94C23⋊C8—41no—
95#1908—231nomaximal, Sylow
96C22×C23—21no—
97C22×C23—21no—
98C22×C23C4×D411yescharacteristic
99C22×C23#12111yescharacteristic
100C22×C23#12311yescharacteristic
101C2×D23—22no—
102C2×D23—41no—
103C2×D23—41no—
104C4×C23—81no—
105C4×C23C2×C22⋊C411yescharacteristic
106C4×C23C4×D411yescharacteristic
107C4×C23#12011yescharacteristic
108C4×C23#12111yescharacteristic
109Dic23—22no—
110Dic23—42no—
111C2×#137—231no—
112C2×#131—231no—
113#417—231no—
114C2×#103—231no—
115C2×#101—231no—
116#343D2311yescharacteristic, complemented
117#341—231no—
118C2×C23—21no—
119C2×C23—21no—
120C2×C23#38611yescharacteristic
121C2×C23#47111yescharacteristic
122C2×C23#47311yescharacteristic
123D23—42no—
124C2×#41—231no—
125C22×Q8—231no—
126#137—234no—
127#137—462no—
128C2×Q16—461no—
129C2×SD16—461no—
130#131—462no—
131#131—462no—
132C2×M16—231no—
133C2×M16—461no—
134C2×M16C2×D2311yescharacteristic
135C2×M16C2×D2311yescharacteristic
136C22×C8—231no—
137C22×C8—461no—
138C2×C4⋊C4C2×D2311yescharacteristic
139#103—461no—
140#103—461no—
141#103—461no—
142#102—461no—
143#101—462no—
144C23#190811yescharacteristic, complemented, Sylow
145#41—232no—
146#41—232no—
147#41—461no—
148#41—461no—
149C2×Q8—232no—
150C2×Q8—231no—
151C2×Q8—461no—
152C2×Q8—461no—
153C2×Q8—461no—
154C2×Q8—461no—
155C2×Q8—461no—
156C2×D4—231no—
157C2×D4—461no—
158C22×C4—21no—
159C22×C4—461no—
160C22×C4—461no—
161C22×C4C22×D2311yescharacteristic
162Q16—464no—
163SD16—464no—
164M16—21no—
165M16—21no—
166M16—464no—
167M16—461no—
168M16—461no—
169M16C4×D2312yes—
170M16D9212yes—
171C2×C8—21no—
172C2×C8—21no—
173C2×C8—231no—
174C2×C8—231no—
175C2×C8—464no—
176C2×C8—461no—
177C2×C8—461no—
178C2×C8—461no—
179C4⋊C4—21no—
180C4⋊C4—21no—
181C23—461no—
182C23#6728811yescharacteristic
183Q8—232no—
184Q8—461no—
185Q8—462no—
186Q8—462no—
187Q8—921no—
188Q8—921no—
189D4—232no—
190D4—462no—
191D4—462no—
192D4—461no—
193C2×C4—41no—
194C2×C4—81no—
195C2×C4—461no—
196C2×C4—462no—
197C2×C4—462no—
198C2×C4—462no—
199C2×C4—921no—
200C2×C4—921no—
201C2×C4C2×C4×D2311yescharacteristic
202C2×C4C2×D9211yescharacteristic
203C2×C4D4×D2311yescharacteristic
204C2×C4D4×D2311yescharacteristic
205C2×C4D4×D2311yescharacteristic
206C2×C4#6729211yescharacteristic
207C8—22no—
208C8—22no—
209C8—461no—
210C8—461no—
211C8—921no—
212C22—21no—
213C22—21no—
214C22—462no—
215C22—921no—
216C22—921no—
217C22C4×D9211yescharacteristic
218C22#1062505511yescharacteristic
219C22#1062506511yescharacteristic
220C4—81no—
221C4—462no—
222C4—922no—
223C4C22⋊C4×D2311yescharacteristic
224C4#1062505311yescharacteristic
225C4#1062506411yescharacteristic
226C4#1062506611yescharacteristic
227C2—21no—
228C2—21no—
229C2—922no—
230C2#1309229511yescharacteristic
231C2#1309267911yescharacteristic
232C2#1309269111yescharacteristic
subgroupG/H
centerC22#10625055
commutatorC2×C4×C23C22×C4
FrattiniC22×C4C22×D23
FittingC23×#343C2
socleC22×C23#121
prime radicalC2×#67288C22
cosocleC22×C4×C23C23
hypercenter#343D23
hypocenterC23#1908
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #343

Complements

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

NH ≅ G/Ntype
4. C2×#10624992C2semidirect
5. C2×#10625006C2semidirect
6. #13092181C2semidirect
7. C23×#343C2semidirect
16. #10625080C4semidirect
116. #343D23semidirect
144. C23#1908semidirect

Maximal subgroups

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

subgroupindex
C2×#106250802
C2×#106250782
#130924162
C2×#106249922
C2×#106250062
#130921812
C23×#3432
#190823