Finite Group Databasebeta

← #15674648

Subgroups — #15674648

Order 2944.

382 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 69 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#13092979C211yesmaximal, characteristic
2C2×#10624988C212yesmaximal, complemented
3#13092296C212yesmaximal, complemented
4#13092184C211yesmaximal, characteristic, complemented
5C23×#385C211yesmaximal, characteristic, complemented
6C23×C4×C23C2211yescharacteristic
7C22×C22⋊D23C2212yes—
8C2×C4⋊C4×C23—21no—
9C2×C22⋊C4×C23C2211yescharacteristic
10C2×C22⋊C4×C23C2211yescharacteristic
11C2×C22⋊Dic23C2212yes—
12#10625101—21no—
13#10625101—21no—
14C2×(C2×D23)⋊C4—22no—
15#10625057—22no—
16#10625053—22no—
17C23×#95—21no—
18C23⋊#95—22no—
19#10624988—24no—
20C24×C23C2311yescharacteristic
21C23×D23D412yes—
22C22×C4×C23—22no—
23C22×C4×C23—21no—
24C22×C4×C23—21no—
25C22×C4×C23—42no—
26C22×C4×C23D411yescharacteristic
27C22×C4×C23D411yescharacteristic
28C2×C22⋊D23—22no—
29C2×C22⋊D23—22no—
30C2×C22⋊D23—22no—
31C2×C22⋊D23—22no—
32C2×C22⋊D23—22no—
33C2×C22⋊D23—22no—
34C22×Dic23—22no—
35C22×Dic23D412yes—
36C2×D92—21no—
37C2×D92—21no—
38C4⋊C4×C23—42no—
39C22⋊C4×C23—22no—
40C22⋊C4×C23—21no—
41C22⋊C4×C23D412yescomplemented
42C22⋊Dic23—22no—
43C22⋊Dic23—22no—
44(C2×D23)⋊C4—22no—
45(C2×D23)⋊C4—22no—
46(C2×D23)⋊C4—44no—
47C4⋊Dic23—21no—
48C4⋊Dic23—21no—
49C23×C23—41no—
50C23×C23—41no—
51C23×C23C2×D411yescharacteristic
52C23×C23C2×D412yes—
53C23×C23C2×D411yescharacteristic
54C23×C23#4111yescharacteristic
55C23×C23#4112yes—
56C22×D23—22no—
57C22×D23—22no—
58C22×D23—22no—
59C22×D23—42no—
60C22×D23—42no—
61C2×C4×C23—24no—
62C2×C4×C23—22no—
63C2×C4×C23—21no—
64C2×C4×C23—21no—
65C2×C4×C23—22no—
66C2×C4×C23—41no—
67C2×C4×C23—41no—
68C2×C4×C23—42no—
69C2×C4×C23—41no—
70C2×C4×C23—41no—
71C2×C4×C23—41no—
72C2×C4×C23—41no—
73C22⋊D23—42no—
74C22⋊D23—42no—
75C22⋊D23—42no—
76C22⋊D23—42no—
77C2×Dic23—22no—
78C2×Dic23—22no—
79C2×Dic23—22no—
80C2×Dic23—42no—
81C2×Dic23—42no—
82C2×Dic23—42no—
83D92—81no—
84D92—81no—
85#2044—231nomaximal, Sylow
86C22×C23—22no—
87C22×C23—21no—
88C22×C23—22no—
89C22×C23—21no—
90C22×C23—41no—
91C22×C23—41no—
92C22×C23—42no—
93C22×C23#12011yescharacteristic
94C22×C23#12112yes—
95C22×C23#12111yescharacteristic
96C22×C23#12312yes—
97C22×C23#12411yescharacteristic
98C2×D23—44no—
99C2×D23—42no—
100C2×D23—42no—
101C2×D23—42no—
102C2×D23—82no—
103C4×C23—42no—
104C4×C23—41no—
105C4×C23—42no—
106C4×C23—41no—
107Dic23—42no—
108Dic23—82no—
109#534—231no—
110C2×#99—232no—
111#386—232no—
112#385D2311yescharacteristic, complemented
113#342—231no—
114C2×C23—22no—
115C2×C23—21no—
116C2×C23—22no—
117C2×C23—21no—
118C2×C23#39411yescharacteristic
119C2×C23B(4,𝔽2)11yescharacteristic
120C2×C23#45811yescharacteristic
121D23—82no—
122C22×D4—232no—
123C23×C4C2×D2311yescharacteristic
124#123—462no—
125#121—461no—
126#121—461no—
127#120—462no—
128C2×C4⋊C4—21no—
129C2×C22⋊C4—232no—
130C2×C22⋊C4—462no—
131C2×C22⋊C4C2×D2311yescharacteristic
132C2×C22⋊C4C2×D2311yescharacteristic
133#99—464no—
134#95—21no—
135#95—462no—
136C23#204411yescharacteristic, complemented, Sylow
137C24—232no—
138C24C22×D2311yescharacteristic
139C2×D4—461no—
140C2×D4—461no—
141C2×D4—462no—
142C2×D4—462no—
143C2×D4—462no—
144C2×D4—462no—
145C2×D4—462no—
146C2×D4—462no—
147C22×C4—22no—
148C22×C4—21no—
149C22×C4—21no—
150C22×C4—42no—
151C22×C4—232no—
152C22×C4—462no—
153C22×C4C22⋊D2311yescharacteristic
154C22×C4C22⋊D2311yescharacteristic
155C4⋊C4—42no—
156C4⋊C4—461no—
157C4⋊C4—461no—
158C22⋊C4—21no—
159C22⋊C4—22no—
160C22⋊C4—462no—
161C22⋊C4—462no—
162C22⋊C4—462no—
163C22⋊C4—462no—
164C22⋊C4—924no—
165C22⋊C4D9212yescomplemented
166C23—41no—
167C23—41no—
168C23—462no—
169C23—462no—
170C23—462no—
171C23—922no—
172C23—922no—
173C23C2×D9211yescharacteristic
174C23#6728811yescharacteristic
175C23D4×D2312yes—
176C23#6729212yes—
177C23C2×C22⋊D2311yescharacteristic
178D4—922no—
179D4—922no—
180D4—922no—
181D4—922no—
182D4—1841no—
183D4—1841no—
184C2×C4—24no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—41no—
190C2×C4—41no—
191C2×C4—42no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—41no—
195C2×C4—41no—
196C2×C4—462no—
197C2×C4—462no—
198C2×C4—462no—
199C2×C4—922no—
200C2×C4—922no—
201C2×C4—922no—
202C22—21no—
203C22—22no—
204C22—21no—
205C22—22no—
206C22—41no—
207C22—41no—
208C22—42no—
209C22—924no—
210C22—922no—
211C22—922no—
212C22—922no—
213C22—1842no—
214C22#1062506512yes—
215C22#1062506612yes—
216C22#1062510111yescharacteristic
217C22#1062510811yescharacteristic
218C22#1062511811yescharacteristic
219C4—42no—
220C4—42no—
221C4—41no—
222C4—41no—
223C4—922no—
224C4—1842no—
225C2—21no—
226C2—22no—
227C2—22no—
228C2—21no—
229C2—1842no—
230C2#1309233411yescharacteristic
231C2#1309260311yescharacteristic
232C2#1309260611yescharacteristic
subgroupG/H
centerC22#10625108
commutator, cosocleC24×C23C23
FrattiniC24C22×D23
FittingC23×#385C2
socleC22×C23#120
prime radical#13092979C2
hypercenter#385D23
hypocenterC23#2044
LCSG ▷ C24×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C24 ◁ #385

Complements

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

NH ≅ G/Ntype
2. C2×#10624988C2semidirect
3. #13092296C2semidirect
4. #13092184C2semidirect
5. C23×#385C2semidirect
41. C22⋊C4×C23D4semidirect
112. #385D23semidirect
136. C23#2044semidirect
165. C22⋊C4D92semidirect

Maximal subgroups

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

subgroupindex
#130929792
C2×#106249882
#130922962
#130921842
C23×#3852
#204423