Finite Group Databasebeta

← #15683688

Subgroups — #15683688

Order 2944.

382 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 125 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#13093022C211yesmaximal, characteristic
2#13092741C212yesmaximal, complemented
3#13092724C212yesmaximal, complemented
4#13092617C212yesmaximal, complemented
5#13092556C212yesmaximal, complemented
6#13092515C212yesmaximal, complemented
7C4×#67274C212yesmaximal, complemented
8#13092478C211yesmaximal, characteristic, complemented
9C23×#519C211yesmaximal, characteristic, complemented
10C22×Q8×C23C2211yescharacteristic
11C4×Q8×C23—22no—
12C4×Q8×C23C2212yes—
13C4×Q8×C23C2212yes—
14C23×#117—22no—
15C23×#117C2211yescharacteristic
16C23×#117C2211yescharacteristic
17C2×#67274C2212yes—
18C2×#67274C2212yes—
19#10625101C2212yes—
20#10625065—22no—
21#10625055—22no—
22#10625045C2211yescharacteristic
23C4×D92C2212yes—
24#10625041C2211yescharacteristic
25#10625017C2212yes—
26#10625017C2212yes—
27C22⋊(C23⋊C8)C2212yes—
28#10624991C2212yes—
29#10624991C2212yes—
30#10624990C2212yes—
31#10624989C2212yes—
32C4⋊(C23⋊C8)C2212yes—
33#10624985C2211yescharacteristic
34C4×C23⋊C8C2211yescharacteristic
35C2×Q8×C23—24no—
36C2×Q8×C23—21no—
37C2×Q8×C23C2312yes—
38C22×C4×C23—21no—
39C22×C4×C23C2311yescharacteristic
40C2×C22⋊D23—22no—
41C2×D92—22no—
42C2×D92C2312yes—
43C2×C4×D23—22no—
44C4⋊C4×C23—22no—
45C4⋊C4×C23—22no—
46C4⋊C4×C23D412yes—
47C4⋊C4×C23C2312yes—
48C22⋊C4×C23—21no—
49C22⋊C4×C23D412yes—
50C42×C23—22no—
51C42×C23—22no—
52C42×C23—21no—
53C42×C23C2311yescharacteristic
54C42×C23C2311yescharacteristic
55#67274—24no—
56#67274—24no—
57(C2×D23)⋊C4—22no—
58(C2×D23)⋊C4—22no—
59C4⋊Dic23C2312yes—
60Dic23⋊C4—22no—
61C2×C23⋊C8C2312yes—
62C2×C23⋊C8C2312yes—
63C23×C23C2×D411yescharacteristic
64C22×D23—22no—
65Q8×C23—24no—
66Q8×C23—22no—
67Q8×C23#4114yes—
68C2×C4×C23—24no—
69C2×C4×C23—22no—
70C2×C4×C23—22no—
71C2×C4×C23—22no—
72C2×C4×C23C2×D412yes—
73C2×C4×C23C2×D411yescharacteristic
74C2×C4×C23C2×D412yes—
75C2×C4×C23C2411yescharacteristic
76C22⋊D23—82no—
77C2×Dic23—22no—
78D92—22no—
79D92—22no—
80D92—82no—
81C4×D23—82no—
82C23⋊C8—22no—
83C23⋊C8—22no—
84#3126—231nomaximal, Sylow
85C22×C23—21no—
86C22×C23—22no—
87C22×C23C22×D411yescharacteristic
88C2×D23—42no—
89C2×D23—42no—
90C2×D23—42no—
91C4×C23—24no—
92C4×C23—21no—
93C4×C23—22no—
94C4×C23—22no—
95C4×C23—42no—
96C4×C23C2×#4112yes—
97Dic23—42no—
98#540—231no—
99#519D2311yescharacteristic, complemented
100#482—232no—
101#479—232no—
102#460—232no—
103#448—232no—
104#440—232no—
105C4×SD16—232no—
106#433—231no—
107C2×C23—41no—
108C2×C23#52511yescharacteristic
109C2×C23#57712yes—
110D23—82no—
111C22×Q8C2×D2311yescharacteristic
112C2×SD16—232no—
113C2×SD16—232no—
114#127—231no—
115#125—231no—
116#123—462no—
117#121—232no—
118#121—462no—
119C4×Q8—22no—
120C4×Q8C2×D2312yes—
121C4×Q8C2×D2312yes—
122C4×D4—232no—
123#117—22no—
124#117C2×D2311yescharacteristic
125#117C2×D2311yescharacteristic
126#107—232no—
127#106—232no—
128C4⋊C8—232no—
129#103—232no—
130#103—232no—
131#102—232no—
132#102—232no—
133C22⋊C8—232no—
134#97—231no—
135C4×C8—231no—
136C23#312611yescharacteristic, complemented, Sylow
137C2×Q8—24no—
138C2×Q8—21no—
139C2×Q8C22×D2312yes—
140C2×D4—232no—
141C2×D4—462no—
142C2×D4—462no—
143C22×C4—21no—
144C22×C4—462no—
145C22×C4C22×D2311yescharacteristic
146SD16—464no—
147SD16—464no—
148C2×C8—232no—
149C2×C8—232no—
150C4⋊C4—22no—
151C4⋊C4—22no—
152C4⋊C4—232no—
153C4⋊C4—462no—
154C4⋊C4C22⋊D2312yes—
155C4⋊C4C22×D2312yes—
156C22⋊C4—21no—
157C22⋊C4—462no—
158C22⋊C4—462no—
159C22⋊C4C22⋊D2312yes—
160C42—22no—
161C42—22no—
162C42—21no—
163C42C22×D2311yescharacteristic
164C42C22×D2311yescharacteristic
165C23—462no—
166C23C2×C22⋊D2311yescharacteristic
167Q8—24no—
168Q8—22no—
169Q8#6728814yes—
170D4—462no—
171D4—462no—
172D4—1842no—
173D4—1842no—
174C2×C4—24no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—462no—
179C2×C4—1842no—
180C2×C4C2×C22⋊D2312yes—
181C2×C4C2×C22⋊D2312yes—
182C2×C4C2×C22⋊D2311yescharacteristic
183C2×C4C23×D2311yescharacteristic
184C8—462no—
185C8—462no—
186C22—21no—
187C22—22no—
188C22—922no—
189C22—922no—
190C22—922no—
191C22C22×C22⋊D2311yescharacteristic
192C4—24no—
193C4—21no—
194C4—22no—
195C4—22no—
196C4—42no—
197C4—922no—
198C4C2×#6728812yes—
199C2—41no—
200C2—1842no—
201C2#1309292811yescharacteristic
202C2#1309322512yes—
subgroupG/H
centerC22C22×C22⋊D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#519C2
socleC22×C23C22×D4
prime radical#13093022C2
hypercenter#519D23
hypocenterC23#3126
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ #117 ◁ #519

Complements

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

NH ≅ G/Ntype
2. #13092741C2semidirect
3. #13092724C2semidirect
4. #13092617C2semidirect
5. #13092556C2semidirect
6. #13092515C2semidirect
7. C4×#67274C2semidirect
8. #13092478C2semidirect
9. C23×#519C2semidirect
99. #519D23semidirect
136. C23#3126semidirect

Maximal subgroups

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

subgroupindex
#130930222
#130927412
#130927242
#130926172
#130925562
#130925152
C4×#672742
#130924782
C23×#5192
#312623