Finite Group Databasebeta

← #15674617

Subgroups — #15674617

Order 2944.

278 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 278 conjugacy classes of subgroups — too many to draw. Only its 67 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#13092993C211yesmaximal, characteristic
2#13092460C211yesmaximal, characteristic, complemented
3C2×#10624987C211yesmaximal, characteristic
4#13092419C211yesmaximal, characteristic
5C2×#10625006C211yesmaximal, characteristic, complemented
6#13092323C211yesmaximal, characteristic, complemented
7C23×#339C211yesmaximal, characteristic, complemented
8C2×#67288C2211yescharacteristic
9C22×Dic46C2211yescharacteristic
10C2×M16×C23C2211yescharacteristic
11C23×#117C2211yescharacteristic
12C2×C42×C23C2211yescharacteristic
13C2×C4⋊Dic23C2211yescharacteristic
14C2×#67267C2211yescharacteristic
15#10625068—21no—
16#10625068—21no—
17#10625057—22no—
18#10625046—21no—
19#10625040—21no—
20C23⋊#95—22no—
21#10625006—22no—
22#10625003—21no—
23#10624998—21no—
24#10624990—21no—
25#10624989—21no—
26#10624987—22no—
27C22×C4×C23—21no—
28C22×C4×C23C2311yescharacteristic
29C2×C22⋊D23—21no—
30C22×Dic23—21no—
31C22×Dic23D412yes—
32#67288—21no—
33#67288—21no—
34#67288—21no—
35#67288—21no—
36C2×D92D411yescharacteristic
37C2×C4×D23—21no—
38C2×Dic46—21no—
39C2×Dic46—21no—
40C2×Dic46—21no—
41C2×Dic46—21no—
42C2×Dic46—21no—
43C2×Dic46—21no—
44C2×Dic46D411yescharacteristic
45M16×C23—21no—
46M16×C23—21no—
47C2×C8×C23—21no—
48C4⋊C4×C23D411yescharacteristic
49C4⋊C4×C23D411yescharacteristic
50C22⋊C4×C23—21no—
51C42×C23—21no—
52C42×C23—21no—
53C42×C23—21no—
54(C2×D23)⋊C4—22no—
55(C2×D23)⋊C4—22no—
56C4⋊Dic23—22no—
57C4⋊Dic23—22no—
58C4⋊Dic23—21no—
59C4⋊Dic23—21no—
60#67267—21no—
61#67267D412yes—
62C2×C23⋊C8—21no—
63C23×C23C2×D411yescharacteristic
64C22×D23—21no—
65C2×C4×C23—22no—
66C2×C4×C23—21no—
67C2×C4×C23—21no—
68C2×C4×C23—41no—
69C2×C4×C23—41no—
70C2×C4×C23C2×D411yescharacteristic
71C2×C4×C23C2×D411yescharacteristic
72C2×C4×C23C2×D411yescharacteristic
73C2×C4×C23#4111yescharacteristic
74C2×C4×C23#4111yescharacteristic
75C2×C4×C23#4111yescharacteristic
76C22⋊D23—41no—
77C22⋊D23—41no—
78C2×Dic23—21no—
79C2×Dic23—22no—
80C2×Dic23—22no—
81C2×Dic23—22no—
82C2×Dic23—42no—
83C2×Dic23—41no—
84D92—21no—
85D92—21no—
86C4×D23—41no—
87C4×D23—41no—
88Dic46—21no—
89Dic46—21no—
90Dic46—41no—
91Dic46—41no—
92Dic46—41no—
93Dic46—41no—
94C8×C23—41no—
95C23⋊C8—22no—
96#2038—231nomaximal, Sylow
97C22×C23—21no—
98C22×C23—21no—
99C22×C23#12011yescharacteristic
100C22×C23#12111yescharacteristic
101C22×C23#12311yescharacteristic
102C2×D23—41no—
103C2×D23—41no—
104C2×D23—41no—
105C4×C23—42no—
106C4×C23—41no—
107C4×C23—41no—
108C4×C23#12111yescharacteristic
109C4×C23#12111yescharacteristic
110C4×C23#12311yescharacteristic
111C4×C23#12411yescharacteristic
112Dic23—41no—
113Dic23—42no—
114Dic23—81no—
115#536—231no—
116#428—231no—
117C2×#104—231no—
118#417—231no—
119C2×#101—231no—
120#391—231no—
121#339D2311yescharacteristic, complemented
122C2×C23—21no—
123C2×C23—21no—
124C2×C23#39411yescharacteristic
125C2×C23#45411yescharacteristic
126C2×C23#45611yescharacteristic
127D23—81no—
128C2×#41—231no—
129C22×Q8—231no—
130C2×M16—231no—
131C2×M16C2×D2311yescharacteristic
132C4⋊Q8—461no—
133#124—461no—
134#123—462no—
135C22⋊Q8—461no—
136C22⋊Q8—461no—
137#117C2×D2311yescharacteristic
138C2×C4⋊C4—231no—
139C2×C42C2×D2311yescharacteristic
140#107—461no—
141#106—461no—
142#104—462no—
143#103—461no—
144#102—461no—
145#101—462no—
146#95—462no—
147C23#203811yescharacteristic, complemented, Sylow
148#41—461no—
149#41—461no—
150#41—461no—
151#41—461no—
152C2×Q8—231no—
153C2×Q8—461no—
154C2×Q8—461no—
155C2×Q8—461no—
156C2×Q8—461no—
157C2×Q8—461no—
158C2×Q8—461no—
159C2×D4—231no—
160C2×D4—461no—
161C22×C4—21no—
162C22×C4—232no—
163C22×C4—461no—
164C22×C4—461no—
165C22×C4C22×D2311yescharacteristic
166M16—21no—
167M16—21no—
168M16—232no—
169M16—461no—
170C2×C8—21no—
171C2×C8—461no—
172C4⋊C4—462no—
173C4⋊C4—462no—
174C4⋊C4—461no—
175C4⋊C4—461no—
176C4⋊C4D9211yescharacteristic
177C4⋊C4D9211yescharacteristic
178C22⋊C4—21no—
179C22⋊C4—462no—
180C22⋊C4—462no—
181C42—21no—
182C42—21no—
183C42—21no—
184C23—461no—
185C23D4×D2311yescharacteristic
186Q8—461no—
187Q8—461no—
188Q8—921no—
189Q8—921no—
190Q8—921no—
191Q8—921no—
192D4—461no—
193D4—461no—
194D4—921no—
195D4—921no—
196C2×C4—22no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—41no—
200C2×C4—41no—
201C2×C4—462no—
202C2×C4—461no—
203C2×C4—462no—
204C2×C4—462no—
205C2×C4—921no—
206C2×C4—921no—
207C2×C4—922no—
208C2×C4—921no—
209C2×C4C2×D9211yescharacteristic
210C2×C4#6728811yescharacteristic
211C2×C4#6728811yescharacteristic
212C2×C4D4×D2311yescharacteristic
213C2×C4D4×D2311yescharacteristic
214C2×C4#6729211yescharacteristic
215C8—41no—
216C8—462no—
217C22—21no—
218C22—21no—
219C22—921no—
220C22—921no—
221C22—921no—
222C22#1062505311yescharacteristic
223C22#1062505511yescharacteristic
224C22#1062506511yescharacteristic
225C4—42no—
226C4—41no—
227C4—41no—
228C4—922no—
229C4—921no—
230C4—1841no—
231C4#1062504611yescharacteristic
232C4#1062505511yescharacteristic
233C4#1062506511yescharacteristic
234C4#1062506611yescharacteristic
235C2—21no—
236C2—21no—
237C2—1841no—
238C2#1309233511yescharacteristic
239C2#1309259111yescharacteristic
240C2#1309260111yescharacteristic
subgroupG/H
centerC22#10625053
commutator, cosocleC22×C4×C23C23
FrattiniC22×C4C22×D23
FittingC23×#339C2
socleC22×C23#120
prime radicalC2×#67288C22
hypercenter#339D23
hypocenterC23#2038
LCSG ▷ C22×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
2. #13092460C2semidirect
5. C2×#10625006C2semidirect
6. #13092323C2semidirect
7. C23×#339C2semidirect
121. #339D23semidirect
147. C23#2038semidirect

Maximal subgroups

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

subgroupindex
#130929932
#130924602
C2×#106249872
#130924192
C2×#106250062
#130923232
C23×#3392
#203823