Finite Group Databasebeta

← #15674532

Subgroups — #15674532

Order 2944.

326 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 87 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×#10625059C211yesmaximal, characteristic, complemented
2C2×#10625003C211yesmaximal, characteristic
3C2×#10624991C211yesmaximal, characteristic
4#13092318C211yesmaximal, characteristic
5#13092179C211yesmaximal, characteristic, complemented
6#13092171C211yesmaximal, characteristic, complemented
7C23×#340C211yesmaximal, characteristic, complemented
8C22×D92C2211yescharacteristic
9C22×Dic46—21no—
10C22×C8×C23C2211yescharacteristic
11C2×C4⋊C4×C23C2211yescharacteristic
12C2×C4⋊C4×C23C2211yescharacteristic
13C2×(C2×D23)⋊C4—21no—
14C2×(C2×D23)⋊C4—21no—
15C2×C4⋊Dic23C2211yescharacteristic
16C2×Dic23⋊C4—21no—
17C2×C4×Dic23C2211yescharacteristic
18C22×C23⋊C8C2211yescharacteristic
19#10625059—22no—
20#10625059—22no—
21#10625003—22no—
22#10624991—22no—
23C23×D23—21no—
24C22×C4×C23—21no—
25C22×C4×C23—21no—
26C22×C4×C23C2311yescharacteristic
27C22×Dic23—21no—
28C22×Dic23D411yescharacteristic
29C22×Dic23D411yescharacteristic
30C2×D92—21no—
31C2×D92—21no—
32C2×D92—21no—
33C2×D92—21no—
34C2×D92—21no—
35C2×D92Q812yescomplemented
36C2×Dic46—24no—
37C2×Dic46—42no—
38C2×Dic46—42no—
39C2×C8×C23—21no—
40C2×C8×C23—21no—
41C2×C8×C23—21no—
42C4⋊C4×C23—21no—
43C4⋊C4×C23—21no—
44C4⋊C4×C23—21no—
45C4⋊C4×C23D412yes—
46(C2×D23)⋊C4—42no—
47(C2×D23)⋊C4—42no—
48C4⋊Dic23—21no—
49C4⋊Dic23D412yes—
50Dic23⋊C4—24no—
51C4×Dic23—21no—
52C4×Dic23—21no—
53C2×C23⋊C8—21no—
54C2×C23⋊C8—21no—
55C2×C23⋊C8—21no—
56C23×C23C2×D411yescharacteristic
57C22×D23—22no—
58C22×D23—41no—
59C22×D23—41no—
60C22×D23—41no—
61C22×D23—41no—
62C22×D23—41no—
63C22×D23—41no—
64C2×C4×C23—22no—
65C2×C4×C23—41no—
66C2×C4×C23—41no—
67C2×C4×C23—41no—
68C2×C4×C23—41no—
69C2×C4×C23—41no—
70C2×C4×C23C2×D411yescharacteristic
71C2×C4×C23C2×D411yescharacteristic
72C2×C4×C23C2×Q811yescharacteristic
73C2×C4×C23#4111yescharacteristic
74C2×C4×C23#4111yescharacteristic
75C2×C4×C23#4111yescharacteristic
76C2×Dic23—21no—
77C2×Dic23—21no—
78C2×Dic23—21no—
79C2×Dic23—21no—
80C2×Dic23—22no—
81C2×Dic23—41no—
82C2×Dic23—41no—
83C2×Dic23D812yes—
84C2×Dic23SD1612yes—
85D92—22no—
86D92—22no—
87D92—41no—
88D92—41no—
89Dic46—48no—
90C8×C23—41no—
91C23⋊C8—41no—
92#2023—231nomaximal, Sylow
93C22×C23#12011yescharacteristic
94C22×C23C22⋊Q811yescharacteristic
95C22×C23#12411yescharacteristic
96C22×C23C2×D811yescharacteristic
97C22×C23C2×SD1611yescharacteristic
98C22×C23AGL(1,ℤ/8)11yescharacteristic
99C22×C23#13711yescharacteristic
100C2×D23—42no—
101C2×D23—42no—
102C2×D23—42no—
103C2×D23—81no—
104C2×D23—81no—
105C2×D23—81no—
106C2×D23—81no—
107C4×C23—42no—
108C4×C23—81no—
109C4×C23C22⋊Q811yescharacteristic
110C4×C23C22⋊Q811yescharacteristic
111C4×C23#12411yescharacteristic
112C4×C23#12411yescharacteristic
113Dic23—22no—
114Dic23—22no—
115Dic23—42no—
116C2×C4⋊Q8—231no—
117C2×#102—231no—
118C2×#102—231no—
119#390—231no—
120#340—231no—
121#340D2311yescharacteristic, complemented
122#336—231no—
123C2×C23#39311yescharacteristic
124C2×C23#44711yescharacteristic
125C2×C23#44811yescharacteristic
126C2×C23#47411yescharacteristic
127C2×C23#47611yescharacteristic
128C2×C23#48611yescharacteristic
129C2×C23#48911yescharacteristic
130D23—82no—
131C22×Q8—461no—
132C22×D4—231no—
133C22×C8—231no—
134C22×C8C2×D2311yescharacteristic
135C4⋊Q8—462no—
136C4⋊Q8—462no—
137C2×C4⋊C4—231no—
138C2×C4⋊C4—461no—
139C2×C4⋊C4C2×D2311yescharacteristic
140C2×C4⋊C4C2×D2311yescharacteristic
141C2×C22⋊C4—461no—
142C2×C22⋊C4—461no—
143C2×C42—231no—
144#102—462no—
145#102—462no—
146C23#202311yescharacteristic, complemented, Sylow
147C24—461no—
148C2×Q8—464no—
149C2×Q8—922no—
150C2×Q8—922no—
151C2×D4—232no—
152C2×D4—461no—
153C2×D4—461no—
154C2×D4—461no—
155C2×D4—461no—
156C2×D4—461no—
157C22×C4—21no—
158C22×C4—21no—
159C22×C4—231no—
160C22×C4—231no—
161C22×C4—461no—
162C22×C4C22×D2311yescharacteristic
163C2×C8—21no—
164C2×C8—21no—
165C2×C8—21no—
166C2×C8—461no—
167C2×C8—461no—
168C2×C8—461no—
169C4⋊C4—21no—
170C4⋊C4—21no—
171C4⋊C4—21no—
172C4⋊C4—232no—
173C4⋊C4—464no—
174C4⋊C4—461no—
175C4⋊C4D9212yes—
176C22⋊C4—922no—
177C22⋊C4—922no—
178C42—461no—
179C42—461no—
180C23—462no—
181C23—921no—
182C23—921no—
183C23—921no—
184C23—921no—
185C23—921no—
186C23—921no—
187C23D4×D2311yescharacteristic
188Q8—928no—
189D4—462no—
190D4—462no—
191D4—921no—
192D4—921no—
193C2×C4—22no—
194C2×C4—41no—
195C2×C4—41no—
196C2×C4—41no—
197C2×C4—41no—
198C2×C4—41no—
199C2×C4—232no—
200C2×C4—232no—
201C2×C4—461no—
202C2×C4—461no—
203C2×C4—461no—
204C2×C4—461no—
205C2×C4—462no—
206C2×C4—921no—
207C2×C4—921no—
208C2×C4C2×D9211yescharacteristic
209C2×C4#6728811yescharacteristic
210C2×C4#6728811yescharacteristic
211C2×C4D4×D2311yescharacteristic
212C2×C4#6729011yescharacteristic
213C2×C4Q8×D2311yescharacteristic
214C8—41no—
215C8—921no—
216C22—922no—
217C22—922no—
218C22—922no—
219C22—1841no—
220C22—1841no—
221C22—1841no—
222C22—1841no—
223C22#1062505311yescharacteristic
224C22#1062505611yescharacteristic
225C22#1062506711yescharacteristic
226C22D8×D2311yescharacteristic
227C22SD16×D2311yescharacteristic
228C22#1062508511yescharacteristic
229C22#1062508911yescharacteristic
230C4—42no—
231C4—81no—
232C4—462no—
233C4—462no—
234C4—922no—
235C4#1062504611yescharacteristic
236C4#1062505611yescharacteristic
237C4#1062506711yescharacteristic
238C4#1062506811yescharacteristic
239C2—1842no—
240C2#1309233011yescharacteristic
241C2#1309255211yescharacteristic
242C2#1309255711yescharacteristic
243C2#1309269611yescharacteristic
244C2#1309270611yescharacteristic
245C2#1309276211yescharacteristic
246C2#1309277811yescharacteristic
subgroupG/H
centerC23D4×D23
commutator, cosocleC22×C4×C23C23
FrattiniC22×C4C22×D23
FittingC23×#340C2
socleC23×C23C2×D4
prime radicalC22×D92C22
hypercenter#340D23
hypocenterC23#2023
LCSG ▷ C22×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
1. C2×#10625059C2semidirect
5. #13092179C2semidirect
6. #13092171C2semidirect
7. C23×#340C2semidirect
35. C2×D92Q8semidirect
121. #340D23semidirect
146. C23#2023semidirect

Maximal subgroups

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

subgroupindex
C2×#106250592
C2×#106250032
C2×#106249912
#130923182
#130921792
#130921712
C23×#3402
#202323