Finite Group Databasebeta

← #15683795

Subgroups — #15683795

Order 2944.

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

normal subgroups only

This group has 392 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#13092963C211yesmaximal, characteristic
2C2×#10625061C211yesmaximal, characteristic, complemented
3#13092784C212yesmaximal, complemented
4#13092780C212yesmaximal, complemented
5#13092773C212yesmaximal, complemented
6#13092770C212yesmaximal, complemented
7#13092419C211yesmaximal, characteristic, complemented
8#13092418C211yesmaximal, characteristic, complemented
9#13092416C211yesmaximal, characteristic, complemented
10M16×Dic23C211yesmaximal, characteristic, complemented
11C23×#417C211yesmaximal, characteristic, complemented
12C2×#41×C23C2211yescharacteristic
13C2×#67288C2211yescharacteristic
14C2×M16×C23C2211yescharacteristic
15C2×C4⋊C4×C23C2211yescharacteristic
16#10625118C2211yescharacteristic
17#10625115C2211yescharacteristic
18#10625111C2211yescharacteristic
19#10625110—21no—
20#10625110—21no—
21#10625107C2211yescharacteristic
22C4×C22⋊D23—21no—
23C4×C22⋊D23—21no—
24C2×C4⋊Dic23—21no—
25C2×C4⋊Dic23C2211yescharacteristic
26C2×Dic23⋊C4—21no—
27C2×C4×Dic23C2211yescharacteristic
28C2×#67267C2211yescharacteristic
29#10625061—21no—
30#10625061—21no—
31#10625061C2212yes—
32#10625061C2212yes—
33C23×#103C2212yes—
34C23×#102C2212yes—
35#10625017C2212yes—
36#10625014C2212yes—
37#10625003C2212yes—
38#10624998C2212yes—
39#10624997C2212yes—
40C8×Dic23C2212yes—
41#10624992C2212yes—
42#10624991C2212yes—
43#41×C23—22no—
44#41×C23—22no—
45C2×Q8×C23C2311yescharacteristic
46C2×D4×C23—21no—
47C2×D4×C23C2311yescharacteristic
48C22×C4×C23—21no—
49C22×C4×C23—21no—
50C22×C4×C23C2311yescharacteristic
51C2×C22⋊D23—21no—
52C2×C22⋊D23—21no—
53C2×C22⋊D23—21no—
54C22×Dic23—21no—
55C22×Dic23D411yescharacteristic
56C22×Dic23D411yescharacteristic
57#67288—22no—
58#67288—22no—
59C2×D92C2311yescharacteristic
60C2×C4×D23—21no—
61C2×Dic46C2311yescharacteristic
62M16×C23—22no—
63C2×C8×C23C2312yes—
64C4⋊C4×C23—21no—
65C4⋊C4×C23C2312yes—
66C22⋊Dic23—21no—
67C22⋊Dic23—21no—
68(C2×D23)⋊C4—21no—
69(C2×D23)⋊C4—21no—
70C4⋊Dic23—21no—
71C4⋊Dic23—22no—
72C4⋊Dic23—22no—
73C4⋊Dic23C2312yes—
74Dic23⋊C4—22no—
75Dic23⋊C4—22no—
76Dic23⋊C4—21no—
77Dic23⋊C4—21no—
78C4×Dic23D411yescharacteristic
79C4×Dic23D411yescharacteristic
80C4×Dic23C2311yescharacteristic
81C4×Dic23C2311yescharacteristic
82#67267—22no—
83C2×C23⋊C8C2312yes—
84C23×C23—21no—
85C23×C23C2×D411yescharacteristic
86C22×D23—21no—
87Q8×C23—21no—
88Q8×C23—21no—
89D4×C23—21no—
90D4×C23—21no—
91D4×C23—42no—
92C2×C4×C23—22no—
93C2×C4×C23—21no—
94C2×C4×C23—42no—
95C2×C4×C23—42no—
96C2×C4×C23C2×D411yescharacteristic
97C2×C4×C23#4112yes—
98C2×C4×C23#4112yes—
99C2×C4×C23C2411yescharacteristic
100C22⋊D23—42no—
101C22⋊D23—42no—
102C22⋊D23—42no—
103C2×Dic23—22no—
104C2×Dic23—21no—
105C2×Dic23—41no—
106C2×Dic23—41no—
107C2×Dic23—42no—
108C2×Dic23C2×D411yescharacteristic
109C2×Dic23C2×D411yescharacteristic
110C2×Dic23C2×D411yescharacteristic
111C2×Dic23C2×D411yescharacteristic
112D92—21no—
113D92—21no—
114C4×D23—42no—
115Dic46—21no—
116Dic46—21no—
117C8×C23—22no—
118C23⋊C8—22no—
119#3142—231nomaximal, Sylow
120C22×C23—21no—
121C22×C23—21no—
122C22×C23—41no—
123C22×C23—41no—
124C22×C23—41no—
125C22×C23#12412yes—
126C22×C23C22×D411yescharacteristic
127C2×D23—41no—
128C2×D23—41no—
129C2×D23—41no—
130C4×C23—41no—
131C4×C23—42no—
132C4×C23#12412yes—
133C4×C23C2×#4111yescharacteristic
134C4×C23C2×#4111yescharacteristic
135Dic23—21no—
136Dic23—21no—
137Dic23—21no—
138Dic23—21no—
139Dic23—41no—
140Dic23—42no—
141#532—231no—
142C2×#125—231no—
143#491—232no—
144#490—232no—
145#488—232no—
146#488—232no—
147#417—231no—
148#417—231no—
149#417—231no—
150#417D2311yescharacteristic, complemented
151C4×M16—231no—
152C2×C23—22no—
153C2×C23—81no—
154C2×C23C2×#12411yescharacteristic
155C2×C23#57511yescharacteristic
156C2×C23#57511yescharacteristic
157D23—81no—
158C2×#41—231no—
159C2×#41C2×D2311yescharacteristic
160C2×M16—231no—
161C2×M16C2×D2311yescharacteristic
162C4⋊Q8—231no—
163#127—231no—
164#125—232no—
165#125—232no—
166#125—461no—
167#125—461no—
168#124—231no—
169#124—231no—
170#121—461no—
171#121—461no—
172C4×D4—461no—
173C4×D4—461no—
174C2×C4⋊C4—231no—
175C2×C4⋊C4—461no—
176C2×C4⋊C4—461no—
177C2×C4⋊C4C2×D2311yescharacteristic
178C2×C42—231no—
179#103—232no—
180#103—232no—
181#103—232no—
182#103C2×D2312yes—
183#102—232no—
184#102—232no—
185#102—232no—
186#102C2×D2312yes—
187#97—232no—
188C4×C8—232no—
189C23#314211yescharacteristic, complemented, Sylow
190#41—22no—
191#41—22no—
192#41—462no—
193#41—462no—
194C2×Q8—231no—
195C2×Q8C22×D2311yescharacteristic
196C2×D4—21no—
197C2×D4—231no—
198C2×D4—461no—
199C2×D4—461no—
200C2×D4—461no—
201C2×D4C22×D2311yescharacteristic
202C22×C4—21no—
203C22×C4—21no—
204C22×C4—231no—
205C22×C4—231no—
206C22×C4—461no—
207C22×C4—461no—
208C22×C4C22×D2311yescharacteristic
209M16—22no—
210M16—462no—
211C2×C8—232no—
212C2×C8C22×D2312yes—
213C4⋊C4—21no—
214C4⋊C4—232no—
215C4⋊C4—462no—
216C4⋊C4—462no—
217C4⋊C4—462no—
218C4⋊C4—462no—
219C4⋊C4—461no—
220C4⋊C4—461no—
221C4⋊C4—461no—
222C4⋊C4C22×D2312yes—
223C22⋊C4—461no—
224C22⋊C4—461no—
225C22⋊C4—461no—
226C22⋊C4—461no—
227C42—231no—
228C42—231no—
229C42—231no—
230C42—231no—
231C23—21no—
232C23—461no—
233C23D4×D2311yescharacteristic
234Q8—21no—
235Q8—21no—
236Q8—461no—
237Q8—461no—
238D4—21no—
239D4—21no—
240D4—42no—
241D4—461no—
242D4—461no—
243D4—922no—
244D4—922no—
245D4—922no—
246C2×C4—21no—
247C2×C4—22no—
248C2×C4—42no—
249C2×C4—42no—
250C2×C4—231no—
251C2×C4—231no—
252C2×C4—231no—
253C2×C4—231no—
254C2×C4—461no—
255C2×C4—462no—
256C2×C4—921no—
257C2×C4—921no—
258C2×C4—922no—
259C2×C4—922no—
260C2×C4#6728812yes—
261C2×C4D4×D2311yescharacteristic
262C2×C4#6729012yes—
263C2×C4C23×D2311yescharacteristic
264C8—22no—
265C8—462no—
266C22—21no—
267C22—21no—
268C22—41no—
269C22—41no—
270C22—41no—
271C22—921no—
272C22—921no—
273C22—921no—
274C22#1062505612yes—
275C22C2×D4×D2311yescharacteristic
276C4—41no—
277C4—42no—
278C4—461no—
279C4—461no—
280C4—461no—
281C4—461no—
282C4—921no—
283C4—922no—
284C4#1062505612yes—
285C4C2×#6728811yescharacteristic
286C4C2×#6729011yescharacteristic
287C2—22no—
288C2—81no—
289C2—1841no—
290C2C2×#1062505611yescharacteristic
291C2#1309321311yescharacteristic
292C2#1309321611yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#417C2
socleC22×C23C22×D4
prime radical#13092963C2
hypercenter#417D23
hypocenterC23#3142
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

Complements

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

NH ≅ G/Ntype
2. C2×#10625061C2semidirect
3. #13092784C2semidirect
4. #13092780C2semidirect
5. #13092773C2semidirect
6. #13092770C2semidirect
7. #13092419C2semidirect
8. #13092418C2semidirect
9. #13092416C2semidirect
10. M16×Dic23C2semidirect
11. C23×#417C2semidirect
150. #417D23semidirect
189. C23#3142semidirect

Maximal subgroups

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

subgroupindex
#130929632
C2×#106250612
#130927842
#130927802
#130927732
#130927702
#130924192
#130924182
#130924162
M16×Dic232
C23×#4172
#314223