Finite Group Databasebeta

← #15674441

Subgroups — #15674441

Order 2944.

406 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 75 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×#10625079C212yesmaximal, complemented
2#13092998C211yesmaximal, characteristic, complemented
3C2×#10625007C212yesmaximal, complemented
4#13092318C211yesmaximal, characteristic, complemented
5C23×#343C211yesmaximal, characteristic, complemented
6C2×#67288C2212yes—
7C22×D92C2211yescharacteristic
8C2×M16×C23C2212yes—
9C2×C4⋊C4×C23C2211yescharacteristic
10#10625101—22no—
11C2×(C2×D23)⋊C4—22no—
12C2×C4×Dic23C2211yescharacteristic
13#10625079—24no—
14#10625079—24no—
15C2×D184—22no—
16C2×#67263—22no—
17#10625068—22no—
18#10625066—22no—
19#10625007—24no—
20C23×D23—21no—
21C22×C4×C23D412yes—
22C22×C4×C23C2311yescharacteristic
23C2×C22⋊D23—22no—
24C22×Dic23—21no—
25#67288—22no—
26#67288—22no—
27#67288—22no—
28#67288—22no—
29C2×D92—22no—
30C2×D92—22no—
31C2×D92—21no—
32C2×D92—22no—
33C2×D92D412yes—
34C2×D92D412yescomplemented
35C2×C4×D23—22no—
36C2×Dic46D412yes—
37M16×C23—22no—
38M16×C23D414yescomplemented
39C2×C8×C23—22no—
40C4⋊C4×C23—22no—
41(C2×D23)⋊C4—24no—
42(C2×D23)⋊C4—44no—
43C4⋊Dic23—22no—
44C4×Dic23—22no—
45D184—28no—
46#67263—28no—
47C23×C23C2×D411yescharacteristic
48C22×D23—22no—
49C22×D23—22no—
50C22×D23—42no—
51C22×D23—42no—
52C22×D23—41no—
53C22×D23—41no—
54C2×C4×C23—22no—
55C2×C4×C23—42no—
56C2×C4×C23C2×D412yes—
57C2×C4×C23C2×D411yescharacteristic
58C2×C4×C23C2×D412yes—
59C2×C4×C23#4111yescharacteristic
60C22⋊D23—42no—
61C22⋊D23—42no—
62C2×Dic23—22no—
63C2×Dic23—22no—
64C2×Dic23—41no—
65C2×Dic23—41no—
66D92—24no—
67D92—22no—
68D92—22no—
69D92—42no—
70D92—82no—
71C4×D23—42no—
72C4×D23—42no—
73Dic46—22no—
74Dic46—22no—
75C8×C23—24no—
76#2006—231nomaximal, Sylow
77C22×C23—21no—
78C22×C23—21no—
79C22×C23#12011yescharacteristic
80C22×C23#12111yescharacteristic
81C22×C23#12711yescharacteristic
82C2×D23—44no—
83C2×D23—42no—
84C2×D23—42no—
85C2×D23—42no—
86C2×D23—42no—
87C2×D23—82no—
88C2×D23—81no—
89C2×D23—81no—
90C4×C23—42no—
91C4×C23#12012yes—
92C4×C23#12112yes—
93Dic23—42no—
94Dic23—42no—
95C2×AGL(1,ℤ/8)—232no—
96#537—231no—
97C2×#104—232no—
98#390—231no—
99#343D2311yescharacteristic, complemented
100C2×C23—21no—
101C2×C23—21no—
102C2×C23#39211yescharacteristic
103C2×C23#45311yescharacteristic
104C2×C23#45411yescharacteristic
105D23—82no—
106D23—82no—
107C2×#41—232no—
108C22×D4—231no—
109AGL(1,ℤ/8)—464no—
110AGL(1,ℤ/8)—464no—
111C2×SD16—462no—
112C2×D8—462no—
113C2×M16C2×D2312yes—
114C22⋊Q8—462no—
115#121—462no—
116#121—462no—
117C2×C4⋊C4C2×D2311yescharacteristic
118C2×C22⋊C4—462no—
119C2×C42—231no—
120#104—464no—
121C23#200611yescharacteristic, complemented, Sylow
122C24—461no—
123#41—462no—
124#41—462no—
125#41—462no—
126#41—462no—
127C2×Q8—232no—
128C2×D4—232no—
129C2×D4—232no—
130C2×D4—462no—
131C2×D4—462no—
132C2×D4—462no—
133C2×D4—462no—
134C2×D4—461no—
135C22×C4—461no—
136C22×C4—462no—
137C22×C4D9212yes—
138C22×C4C22×D2311yescharacteristic
139SD16—468no—
140D8—468no—
141M16—22no—
142M16D9214yescomplemented
143C2×C8—22no—
144C4⋊C4—22no—
145C4⋊C4—462no—
146C22⋊C4—464no—
147C22⋊C4—924no—
148C42—462no—
149C23—462no—
150C23—462no—
151C23—922no—
152C23—922no—
153C23—921no—
154C23—921no—
155C23C2×D9211yescharacteristic
156Q8—462no—
157Q8—462no—
158D4—462no—
159D4—464no—
160D4—462no—
161D4—922no—
162D4—922no—
163D4—922no—
164D4—1842no—
165C2×C4—22no—
166C2×C4—42no—
167C2×C4—462no—
168C2×C4—462no—
169C2×C4—921no—
170C2×C4—921no—
171C2×C4—922no—
172C2×C4—922no—
173C2×C4C2×D9212yes—
174C2×C4D4×D2311yescharacteristic
175C2×C4D4×D2312yes—
176C2×C4#6729211yescharacteristic
177C8—24no—
178C22—21no—
179C22—21no—
180C22—924no—
181C22—922no—
182C22—922no—
183C22—922no—
184C22—922no—
185C22—1842no—
186C22—1841no—
187C22—1841no—
188C22#1062504511yescharacteristic
189C22#1062505311yescharacteristic
190C22#1062506611yescharacteristic
191C4—42no—
192C4—922no—
193C4—922no—
194C4#1062505312yes—
195C4#1062506612yes—
196C2—21no—
197C2—21no—
198C2—1842no—
199C2—1842no—
200C2#1309232711yescharacteristic
201C2#1309258711yescharacteristic
202C2#1309259211yescharacteristic
subgroupG/H
centerC22#10625053
commutator, cosocleC22×C4×C23C23
FrattiniC22×C4C22×D23
FittingC23×#343C2
socleC22×C23#120
hypercenter#343D23
hypocenterC23#2006
LCSG ▷ C22×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #343

Complements

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

NH ≅ G/Ntype
1. C2×#10625079C2semidirect
2. #13092998C2semidirect
3. C2×#10625007C2semidirect
4. #13092318C2semidirect
5. C23×#343C2semidirect
34. C2×D92D4semidirect
38. M16×C23D4semidirect
99. #343D23semidirect
121. C23#2006semidirect
142. M16D92semidirect

Maximal subgroups

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

subgroupindex
C2×#106250792
#130929982
C2×#106250072
#130923182
C23×#3432
#200623