Finite Group Databasebeta

← #15682672

Subgroups — #15682672

Order 2944.

752 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 752 conjugacy classes of subgroups — too many to draw. Only its 149 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
2C2×#10625113C211yesmaximal, characteristic, complemented
3C22×#67274C211yesmaximal, characteristic, complemented
4#13092577C214yesmaximal, complemented
5#13092567C214yesmaximal, complemented
6#13092421C211yesmaximal, characteristic, complemented
7#13092411C211yesmaximal, characteristic, complemented
8#13092384C211yesmaximal, characteristic, complemented
9C23×#536C211yesmaximal, characteristic, complemented
10C2×#41×C23C2211yescharacteristic
11C22×Q8×C23C2211yescharacteristic, complemented
12#10625160—24no—
13#10625160—24no—
14C2×#67292—21no—
15C2×D4×D23—22no—
16C2×D4×D23—21no—
17C2×#67288C2212yes—
18C2×#67288C2211yescharacteristic
19C22×D92C2212yes—
20C22×D92C2211yescharacteristic
21C23×C4⋊Q8—21no—
22C23×#124—21no—
23C23×#123—22no—
24C23×C22⋊Q8C2214yescomplemented
25C23×#117C2211yescharacteristic, complemented
26C2×#67275C2212yescomplemented
27#10625113—24no—
28C2×#67274—24no—
29C2×#67274C2214yescomplemented
30C2×#67274C2212yescomplemented
31C2×#67267C2211yescharacteristic, complemented
32C22×C23⋊C8C2211yescharacteristic, complemented
33C22⋊(C23⋊C8)C2214yescomplemented
34#10624992C2212yescomplemented
35#10624991C2212yescomplemented
36#10624991C2214yescomplemented
37C23×D23—22no—
38C23×D23—21no—
39#41×C23—22no—
40#41×C23—22no—
41C2×Q8×C23—21no—
42C2×Q8×C23—22no—
43C2×Q8×C23—22no—
44C2×Q8×C23D411yescharacteristic
45C2×Q8×C23C2312yes—
46C2×D4×C23D412yes—
47C2×D4×C23D411yescharacteristic
48C22×C4×C23—21no—
49C22×C4×C23C2312yes—
50C22×C4×C23C2311yescharacteristic
51C2×C22⋊D23—22no—
52C2×C22⋊D23—21no—
53#67292—28no—
54D4×D23—216no—
55D4×D23—28no—
56#67288—22no—
57#67288—24no—
58#67288—24no—
59#67288D414yes—
60C2×D92—22no—
61C2×D92—21no—
62C2×D92—22no—
63C2×D92—24no—
64C2×D92—24no—
65C2×D92D414yes—
66C2×D92C2311yescharacteristic
67C2×D92C2312yes—
68C2×C4×D23—22no—
69C2×C4×D23—21no—
70C2×Dic46C2311yescharacteristic
71C4⋊C4×C23—24no—
72C4⋊C4×C23C2312yes—
73C22⋊C4×C23—21no—
74C22⋊C4×C23—24no—
75C42×C23—21no—
76#67275—24no—
77#67274—28no—
78#67274—24no—
79#67267—22no—
80C2×C23⋊C8—22no—
81C2×C23⋊C8C2312yes—
82C2×C23⋊C8C2312yes—
83C23×C23C2×D412yes—
84C23×C23C2×D411yescharacteristic
85C22×D23—22no—
86C22×D23—21no—
87C22×D23—28no—
88C22×D23—24no—
89C22×D23—82no—
90C22×D23—84no—
91Q8×C23—22no—
92Q8×C23—22no—
93Q8×C23—22no—
94Q8×C23—42no—
95D4×C23—24no—
96D4×C23—22no—
97C2×C4×C23—22no—
98C2×C4×C23—22no—
99C2×C4×C23—22no—
100C2×C4×C23—22no—
101C2×C4×C23—42no—
102C2×C4×C23C2×D412yes—
103C2×C4×C23C2×D412yes—
104C2×C4×C23C2×D412yes—
105C2×C4×C23C2×D411yescharacteristic
106C2×C4×C23C2411yescharacteristic
107C22⋊D23—28no—
108C22⋊D23—24no—
109C2×Dic23—21no—
110D92—28no—
111D92—24no—
112D92—21no—
113D92—22no—
114D92C2×D412yes—
115D92C2×D414yes—
116C4×D23—28no—
117C4×D23—24no—
118Dic46—21no—
119Dic46C2×D412yes—
120C23⋊C8—22no—
121C23⋊C8—22no—
122#3009—231nomaximal, Sylow
123C22×C23—22no—
124C22×C23—22no—
125C22×C23—24no—
126C22×C23#12012yes—
127C22×C23C22×D411yescharacteristic
128C2×D23—24no—
129C2×D23—22no—
130C2×D23—44no—
131C2×D23—42no—
132C2×D23—84no—
133C2×D23—88no—
134C4×C23—22no—
135C4×C23—42no—
136C4×C23—42no—
137C4×C23#12012yes—
138C4×C23C22×D411yescharacteristic
139C4×C23C22×D411yescharacteristic
140Dic23—22no—
141C2×H(5,𝔽2)—231no—
142C2×#137—231no—
143C22×SD16—231no—
144#536D2311yescharacteristic, complemented
145#452—234no—
146#450—234no—
147#418—231no—
148#416—231no—
149#408—231no—
150C2×C23—22no—
151C2×C23—42no—
152C2×C23C2×#12011yescharacteristic
153C2×C23#57712yes—
154D23—44no—
155D23—42no—
156H(5,𝔽2)—464no—
157H(5,𝔽2)—464no—
158C2×#41—231no—
159C2×#41—232no—
160C2×#41—461no—
161C2×#41C2×D2311yescharacteristic
162C22×Q8C2×D2311yescharacteristic, complemented
163C22×D4—231no—
164C22×D4—232no—
165C22×D4—462no—
166C22×D4—461no—
167#137—464no—
168C2×Q16—232no—
169C2×SD16—234no—
170C2×SD16—232no—
171C2×SD16—464no—
172C2×M16—231no—
173C22×C8—231no—
174C4⋊Q8—21no—
175#124—21no—
176#123—22no—
177C22⋊Q8C2×D2314yescomplemented
178#117C2×D2311yescharacteristic, complemented
179#103—232no—
180#102—232no—
181#102—234no—
182C22⋊C8—234no—
183C23#300911yescharacteristic, complemented, Sylow
184C24—462no—
185C24—461no—
186#41—22no—
187#41—22no—
188#41—234no—
189#41—464no—
190#41—464no—
191#41—468no—
192#41—462no—
193C2×Q8—21no—
194C2×Q8—22no—
195C2×Q8—22no—
196C2×Q8—231no—
197C2×Q8C22⋊D2311yescharacteristic
198C2×Q8C22×D2312yes—
199C2×D4—234no—
200C2×D4—232no—
201C2×D4—231no—
202C2×D4—464no—
203C2×D4—464no—
204C2×D4—4616no—
205C2×D4—468no—
206C2×D4—462no—
207C2×D4—461no—
208C2×D4—462no—
209C2×D4—462no—
210C2×D4—461no—
211C2×D4C22⋊D2312yes—
212C2×D4C22⋊D2311yescharacteristic
213C22×C4—21no—
214C22×C4—462no—
215C22×C4—461no—
216C22×C4C22×D2312yes—
217C22×C4C22×D2311yescharacteristic
218Q16—464no—
219SD16—468no—
220SD16—464no—
221M16—462no—
222C2×C8—232no—
223C2×C8—232no—
224C2×C8—462no—
225C4⋊C4—24no—
226C4⋊C4C22×D2312yes—
227C22⋊C4—21no—
228C22⋊C4—24no—
229C42—21no—
230C23—468no—
231C23—462no—
232C23—461no—
233C23—464no—
234C23—1842no—
235C23—1844no—
236C23C2×C22⋊D2312yes—
237C23C2×C22⋊D2311yescharacteristic
238Q8—22no—
239Q8—22no—
240Q8—22no—
241Q8—42no—
242Q8—232no—
243Q8—461no—
244D4—24no—
245D4—22no—
246D4—234no—
247D4—232no—
248D4—468no—
249D4—468no—
250D4—464no—
251D4—464no—
252D4—461no—
253D4—462no—
254C2×C4—22no—
255C2×C4—22no—
256C2×C4—22no—
257C2×C4—22no—
258C2×C4—42no—
259C2×C4—468no—
260C2×C4—461no—
261C2×C4—464no—
262C2×C4D4×D2312yes—
263C2×C4D4×D2312yes—
264C2×C4C2×C22⋊D2312yes—
265C2×C4C2×C22⋊D2311yescharacteristic
266C2×C4C23×D2311yescharacteristic
267C8—462no—
268C8—462no—
269C22—22no—
270C22—22no—
271C22—24no—
272C22—464no—
273C22—462no—
274C22—924no—
275C22—922no—
276C22—1844no—
277C22—1848no—
278C22#1062510812yes—
279C22C22×C22⋊D2311yescharacteristic
280C4—22no—
281C4—42no—
282C4—42no—
283C4—462no—
284C4#1062510812yes—
285C4C2×D4×D2311yescharacteristic
286C4C2×D4×D2311yescharacteristic
287C2—22no—
288C2—42no—
289C2—924no—
290C2—922no—
291C2C2×#1062510811yescharacteristic
292C2#1309322512yes—
subgroupG/H
centerC22C22×C22⋊D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#536C2
socleC22×C23C22×D4
prime radicalC2×#10625160C2
hypercenter#536D23
hypocenterC23#3009
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C2×#41 ◁ #536

Complements

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

NH ≅ G/Ntype
2. C2×#10625113C2semidirect
3. C22×#67274C2semidirect
4. #13092577C2semidirect
5. #13092567C2semidirect
6. #13092421C2semidirect
7. #13092411C2semidirect
8. #13092384C2semidirect
9. C23×#536C2semidirect
11. C22×Q8×C23C22semidirect
24. C23×C22⋊Q8C22semidirect
25. C23×#117C22semidirect
26. C2×#67275C22semidirect
29. C2×#67274C22semidirect
30. C2×#67274C22semidirect
31. C2×#67267C22semidirect
32. C22×C23⋊C8C22semidirect
33. C22⋊(C23⋊C8)C22semidirect
34. #10624992C22semidirect
35. #10624991C22semidirect
36. #10624991C22semidirect
144. #536D23semidirect
162. C22×Q8C2×D23semidirect
177. C22⋊Q8C2×D23semidirect
178. #117C2×D23semidirect
183. C23#3009semidirect

Maximal subgroups

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

subgroupindex
C2×#106251602
C2×#106251132
C22×#672742
#130925772
#130925672
#130924212
#130924112
#130923842
C23×#5362
#300923