Finite Group Databasebeta

← #15673368

Subgroups — #15673368

Order 2944.

588 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 588 conjugacy classes of subgroups — too many to draw. Only its 97 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×#10625160C211yesmaximal, characteristic
2#13092433C212yesmaximal, complemented
3#13092423C212yesmaximal, complemented
4#13092391C211yesmaximal, characteristic, complemented
5C23×#413C211yesmaximal, characteristic, complemented
6C2×#41×C23C2211yescharacteristic
7#10625160—24no—
8#10625160—24no—
9C2×#67292—21no—
10C2×D4×D23—22no—
11C2×D4×D23—21no—
12C2×#67288C412yescomplemented
13C2×#67288C2211yescharacteristic
14C22×D92C412yescomplemented
15C22×D92C2211yescharacteristic
16C2×M16×C23C2212yescomplemented
17#10625097C2212yescomplemented
18C23×#101—21no—
19C23×#100—21no—
20#10625016—22no—
21#10625007—24no—
22#10625003—24no—
23C23×D23—22no—
24C23×D23—21no—
25#41×C23—22no—
26#41×C23—22no—
27C2×Q8×C23D411yescharacteristic
28C2×D4×C23D412yes—
29C2×D4×C23D411yescharacteristic
30C22×C4×C23C2×C412yes—
31C22×C4×C23C2311yescharacteristic
32C2×C22⋊D23—22no—
33C2×C22⋊D23—21no—
34#67292—28no—
35D4×D23—216no—
36D4×D23—28no—
37#67288—22no—
38#67288—24no—
39#67288—24no—
40#67288D414yes—
41C2×D92—22no—
42C2×D92—21no—
43C2×D92—22no—
44C2×D92—24no—
45C2×D92—24no—
46C2×D92C2×C411yescharacteristic
47C2×D92C2×C412yes—
48C2×D92D414yes—
49C2×C4×D23—22no—
50C2×C4×D23—21no—
51C2×Dic46C2×C411yescharacteristic
52M16×C23—22no—
53M16×C23—22no—
54C2×C8×C23—22no—
55C22⋊Dic23—22no—
56C4⋊Dic23—22no—
57C4×Dic23—22no—
58C23×C23C22⋊C412yes—
59C23×C23C2×D411yescharacteristic
60C22×D23—22no—
61C22×D23—21no—
62C22×D23—28no—
63C22×D23—24no—
64C22×D23—82no—
65C22×D23—84no—
66Q8×C23—22no—
67D4×C23—24no—
68D4×C23—22no—
69C2×C4×C23—22no—
70C2×C4×C23—22no—
71C2×C4×C23C22⋊C412yes—
72C2×C4×C23C22×C411yescharacteristic
73C2×C4×C23C2×D412yes—
74C2×C4×C23C2×D412yes—
75C2×C4×C23C2×D411yescharacteristic
76C22⋊D23—28no—
77C22⋊D23—24no—
78C2×Dic23—21no—
79C2×Dic23—42no—
80D92—28no—
81D92—21no—
82D92—22no—
83D92—24no—
84D92C22⋊C412yes—
85D92C22⋊C414yes—
86C4×D23—28no—
87C4×D23—24no—
88Dic46—21no—
89Dic46C22⋊C412yes—
90C8×C23—42no—
91#1795—231nomaximal, Sylow
92C22×C23—22no—
93C22×C23—41no—
94C22×C23—42no—
95C22×C23C2×C22⋊C411yescharacteristic
96C22×C23#12012yes—
97C2×D23—24no—
98C2×D23—22no—
99C2×D23—44no—
100C2×D23—42no—
101C2×D23—84no—
102C2×D23—88no—
103C4×C23—22no—
104C4×C23C2×C22⋊C411yescharacteristic
105C4×C23C2×C22⋊C411yescharacteristic
106C4×C23#12012yes—
107Dic23—22no—
108Dic23—82no—
109C2×H(5,𝔽2)—231no—
110#421—232no—
111#418—232no—
112#413D2311yescharacteristic, complemented
113#410—231no—
114C2×C23—22no—
115C2×C23—21no—
116C2×C23—42no—
117C2×C23#37911yescharacteristic
118D23—44no—
119D23—42no—
120H(5,𝔽2)—464no—
121H(5,𝔽2)—464no—
122C2×#41—232no—
123C2×#41—231no—
124C2×#41—461no—
125C2×#41C2×D2311yescharacteristic
126C22×D4—232no—
127C22×D4—231no—
128C22×D4—462no—
129C22×D4—461no—
130C2×M16C2×D2312yescomplemented
131#117—232no—
132#104—464no—
133#102—464no—
134#101—21no—
135#100—21no—
136#99—462no—
137C23#179511yescharacteristic, complemented, Sylow
138C24—462no—
139C24—461no—
140#41—22no—
141#41—22no—
142#41—234no—
143#41—464no—
144#41—464no—
145#41—468no—
146#41—462no—
147C2×Q8—231no—
148C2×Q8C22⋊D2311yescharacteristic
149C2×D4—232no—
150C2×D4—231no—
151C2×D4—234no—
152C2×D4—464no—
153C2×D4—464no—
154C2×D4—4616no—
155C2×D4—468no—
156C2×D4—462no—
157C2×D4—461no—
158C2×D4—462no—
159C2×D4—462no—
160C2×D4—461no—
161C2×D4D9212yes—
162C2×D4C22⋊D2311yescharacteristic
163C22×C4—462no—
164C22×C4—461no—
165C22×C4C4×D2312yes—
166C22×C4C22×D2311yescharacteristic
167M16—22no—
168M16—22no—
169C2×C8—22no—
170C4⋊C4—462no—
171C22⋊C4—462no—
172C42—462no—
173C23—468no—
174C23—462no—
175C23—461no—
176C23—464no—
177C23—1842no—
178C23—1844no—
179C23(C2×D23)⋊C412yes—
180C23C2×D9211yescharacteristic
181Q8—22no—
182Q8—232no—
183Q8—461no—
184D4—24no—
185D4—22no—
186D4—234no—
187D4—232no—
188D4—468no—
189D4—468no—
190D4—464no—
191D4—461no—
192D4—462no—
193D4—464no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—468no—
197C2×C4—461no—
198C2×C4—464no—
199C2×C4—922no—
200C2×C4(C2×D23)⋊C412yes—
201C2×C4C2×C4×D2311yescharacteristic
202C2×C4D4×D2312yes—
203C2×C4D4×D2312yes—
204C2×C4C2×C22⋊D2311yescharacteristic
205C8—42no—
206C22—22no—
207C22—41no—
208C22—42no—
209C22—464no—
210C22—462no—
211C22—924no—
212C22—922no—
213C22—1844no—
214C22—1848no—
215C22#1062505312yes—
216C22C2×(C2×D23)⋊C411yescharacteristic
217C4—22no—
218C4—462no—
219C4—1842no—
220C4C22⋊C4×D2311yescharacteristic
221C4C22⋊C4×D2311yescharacteristic
222C4#1062510812yes—
223C2—22no—
224C2—21no—
225C2—42no—
226C2—924no—
227C2—922no—
228C2#1309227211yescharacteristic
subgroupG/H
centerC2#13092272
commutatorC2×C4×C23C22×C4
FrattiniC22×C4C22×D23
FittingC23×#413C2
socleC2×C23#379
prime radicalC2×#10625160C2
cosocleC22×C4×C23C23
hypercenter#413D23
hypocenterC23#1795
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2 ◁ C22×C4 ◁ #413

Complements

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

NH ≅ G/Ntype
2. #13092433C2semidirect
3. #13092423C2semidirect
4. #13092391C2semidirect
5. C23×#413C2semidirect
12. C2×#67288C4semidirect
14. C22×D92C4semidirect
16. C2×M16×C23C22semidirect
17. #10625097C22semidirect
112. #413D23semidirect
130. C2×M16C2×D23semidirect
137. C23#1795semidirect

Maximal subgroups

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

subgroupindex
C2×#106251602
#130924332
#130924232
#130923912
C23×#4132
#179523