Finite Group Databasebeta

← #15683880

Subgroups — #15683880

Order 2944.

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

normal subgroups only

This group has 596 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×#10625103C211yesmaximal, characteristic, complemented
2C2×#10625120C211yesmaximal, characteristic, complemented
3C2×#10625121C211yesmaximal, characteristic, complemented
4C22×#67272C211yesmaximal, characteristic, complemented
5#13092986C211yesmaximal, characteristic, complemented
6#13092807C212yesmaximal, complemented
7#13092804C212yesmaximal, complemented
8#13092799C212yesmaximal, complemented
9#13092793C212yesmaximal, complemented
10#13092373C211yesmaximal, characteristic, complemented
11C23×#535C211yesmaximal, characteristic, complemented
12C2×#41×C23C2211yescharacteristic
13C22×D4×C23C2211yescharacteristic
14C2×#67288C2211yescharacteristic
15C22×D92C2211yescharacteristic
16C23×#127C2212yescomplemented
17C23×#124C2212yescomplemented
18C23×#121—22no—
19C23×#120—22no—
20C23×#117C2211yescharacteristic
21#10625121—24no—
22#10625120—24no—
23C2×#67275C2211yescharacteristic, complemented
24C2×#67274C2211yescharacteristic, complemented
25C2×#67274C2212yescomplemented
26C2×#67273C2211yescharacteristic, complemented
27C2×#67273C2212yescomplemented
28#10625103—24no—
29C2×#67272—24no—
30C2×#67272C2212yes—
31C2×#67272C2212yes—
32C2×#67272C2211yescharacteristic, complemented
33C2×#67272C2212yescomplemented
34C2×#67272C2212yescomplemented
35C2×#67267C2211yescharacteristic
36C22×C23⋊C8C2211yescharacteristic
37#10625066—22no—
38#10625053—22no—
39#10625046C2212yescomplemented
40#10625045C2212yescomplemented
41#10624985C2212yescomplemented
42C4×C23⋊C8C2212yescomplemented
43C24×C23—21no—
44C23×D23—21no—
45#41×C23—22no—
46#41×C23—22no—
47C2×Q8×C23C2311yescharacteristic
48C2×D4×C23—21no—
49C2×D4×C23—22no—
50C2×D4×C23—22no—
51C2×D4×C23—21no—
52C2×D4×C23—24no—
53C2×D4×C23C2312yes—
54C2×D4×C23C2311yescharacteristic
55C22×C4×C23—21no—
56C22×C4×C23C2311yescharacteristic
57C2×C22⋊D23—21no—
58#67288—22no—
59#67288—22no—
60C2×D92—22no—
61C2×D92—22no—
62C2×D92—21no—
63C2×D92—24no—
64C2×D92C2311yescharacteristic
65C2×D92C2312yes—
66C2×C4×D23—21no—
67C2×Dic46C2311yescharacteristic
68C4⋊C4×C23D412yes—
69C22⋊C4×C23—24no—
70C22⋊C4×C23D412yes—
71C42×C23C2312yes—
72#67275—22no—
73#67274—24no—
74#67274—22no—
75#67273—24no—
76#67273—22no—
77#67272—24no—
78#67272—24no—
79#67272—24no—
80#67272—24no—
81#67272—22no—
82(C2×D23)⋊C4—24no—
83#67267D414yescomplemented
84C2×C23⋊C8D414yescomplemented
85C2×C23⋊C8C2311yescharacteristic
86C2×C23⋊C8C2311yescharacteristic
87C2×C23⋊C8C2312yes—
88C23×C23—22no—
89C23×C23—21no—
90C23×C23—42no—
91C23×C23—82no—
92C23×C23C2×D411yescharacteristic
93C22×D23—22no—
94C22×D23—21no—
95C22×D23—42no—
96C22×D23—82no—
97Q8×C23—21no—
98Q8×C23—21no—
99D4×C23—22no—
100D4×C23—21no—
101D4×C23—22no—
102D4×C23—21no—
103D4×C23—42no—
104D4×C23—42no—
105D4×C23—84no—
106C2×C4×C23—21no—
107C2×C4×C23—42no—
108C2×C4×C23C2×D412yes—
109C2×C4×C23C2×D412yes—
110C2×C4×C23C2×D414yes—
111C2×C4×C23C2×D411yescharacteristic
112C2×C4×C23C2411yescharacteristic
113C22⋊D23—42no—
114C2×Dic23—21no—
115D92—22no—
116D92—21no—
117D92—22no—
118D92—21no—
119D92—42no—
120D92—84no—
121C4×D23—42no—
122Dic46—21no—
123Dic46—21no—
124C23⋊C8C2×D412yes—
125C23⋊C8C2×D412yes—
126C23⋊C8C2×D414yes—
127#3155—231nomaximal, Sylow
128C22×C23—22no—
129C22×C23—41no—
130C22×C23—42no—
131C22×C23—42no—
132C22×C23—44no—
133C22×C23—84no—
134C22×C23#12712yes—
135C22×C23C22×D411yescharacteristic
136C2×D23—41no—
137C2×D23—42no—
138C2×D23—42no—
139C2×D23—44no—
140C2×D23—84no—
141C4×C23—24no—
142C4×C23—41no—
143C4×C23#12712yes—
144C4×C23C22×D411yescharacteristic
145C4×C23C22×D411yescharacteristic
146Dic23—41no—
147C2×AGL(1,ℤ/8)—231no—
148C2×AGL(1,ℤ/8)—231no—
149C2×#135—231no—
150C22×D8—231no—
151#535—231no—
152#535D2311yescharacteristic, complemented
153#496—232no—
154#496—232no—
155#495—232no—
156#493—232no—
157#405—231no—
158C2×C23—22no—
159C2×C23—81no—
160C2×C23—82no—
161C2×C23C2×#12711yescharacteristic
162C2×C23#57612yes—
163D23—81no—
164D23—82no—
165C2×#41—231no—
166C2×#41C2×D2311yescharacteristic
167C22×D4—231no—
168C22×D4C2×D2311yescharacteristic
169AGL(1,ℤ/8)—464no—
170AGL(1,ℤ/8)—464no—
171#135—464no—
172C2×Q16—231no—
173C2×SD16—231no—
174C2×SD16—232no—
175C2×SD16—231no—
176C2×SD16—232no—
177C2×D8—232no—
178C2×D8—232no—
179C2×D8—231no—
180C2×D8—232no—
181C2×D8—232no—
182C2×D8—464no—
183C2×M16—231no—
184C22×C8—231no—
185#127—232no—
186#127C2×D2312yescomplemented
187#124—232no—
188#124C2×D2312yescomplemented
189#121—22no—
190#121—462no—
191#120—22no—
192#120—462no—
193#117C2×D2311yescharacteristic
194#97—232no—
195C4×C8—232no—
196C23#315511yescharacteristic, complemented, Sylow
197C24—21no—
198C24—461no—
199#41—22no—
200#41—22no—
201#41—462no—
202#41—462no—
203C2×Q8—231no—
204C2×Q8C22×D2311yescharacteristic
205C2×D4—21no—
206C2×D4—22no—
207C2×D4—22no—
208C2×D4—21no—
209C2×D4—24no—
210C2×D4—232no—
211C2×D4—231no—
212C2×D4—461no—
213C2×D4—462no—
214C2×D4—462no—
215C2×D4—461no—
216C2×D4—464no—
217C2×D4C22×D2312yes—
218C2×D4C22×D2311yescharacteristic
219C22×C4—21no—
220C22×C4—461no—
221C22×C4C22×D2311yescharacteristic
222Q16—462no—
223SD16—462no—
224SD16—464no—
225SD16—462no—
226SD16—464no—
227D8—464no—
228D8—464no—
229D8—462no—
230D8—464no—
231D8—464no—
232M16—234no—
233C2×C8—234no—
234C2×C8—231no—
235C2×C8—232no—
236C2×C8—231no—
237C4⋊C4C22⋊D2312yes—
238C22⋊C4—24no—
239C22⋊C4—464no—
240C22⋊C4C22⋊D2312yes—
241C42C22×D2312yes—
242C23—22no—
243C23—21no—
244C23—42no—
245C23—82no—
246C23—462no—
247C23—461no—
248C23—922no—
249C23—1842no—
250C23C2×C22⋊D2311yescharacteristic
251Q8—21no—
252Q8—21no—
253Q8—461no—
254Q8—461no—
255D4—22no—
256D4—21no—
257D4—22no—
258D4—21no—
259D4—42no—
260D4—42no—
261D4—84no—
262D4—462no—
263D4—461no—
264D4—462no—
265D4—461no—
266D4—922no—
267D4—922no—
268D4—1844no—
269C2×C4—21no—
270C2×C4—42no—
271C2×C4—461no—
272C2×C4—922no—
273C2×C4D4×D2312yes—
274C2×C4D4×D2312yes—
275C2×C4C2×C22⋊D2314yes—
276C2×C4C2×C22⋊D2311yescharacteristic
277C2×C4C23×D2311yescharacteristic
278C8—232no—
279C8—232no—
280C8—234no—
281C22—22no—
282C22—41no—
283C22—42no—
284C22—42no—
285C22—44no—
286C22—84no—
287C22—921no—
288C22—922no—
289C22—922no—
290C22—924no—
291C22—1844no—
292C22#1062511112yes—
293C22C22×C22⋊D2311yescharacteristic
294C4—24no—
295C4—41no—
296C4—921no—
297C4#1062511112yes—
298C4C2×D4×D2311yescharacteristic
299C4C2×D4×D2311yescharacteristic
300C2—22no—
301C2—82no—
302C2—81no—
303C2—1842no—
304C2—1841no—
305C2C2×#1062511111yescharacteristic
306C2#1309322012yes—
subgroupG/H
centerC22C22×C22⋊D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#535C2
socleC22×C23C22×D4
hypercenter#535D23
hypocenterC23#3155
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ #117 ◁ #535

Complements

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

NH ≅ G/Ntype
1. C2×#10625103C2semidirect
2. C2×#10625120C2semidirect
3. C2×#10625121C2semidirect
4. C22×#67272C2semidirect
5. #13092986C2semidirect
6. #13092807C2semidirect
7. #13092804C2semidirect
8. #13092799C2semidirect
9. #13092793C2semidirect
10. #13092373C2semidirect
11. C23×#535C2semidirect
16. C23×#127C22semidirect
17. C23×#124C22semidirect
23. C2×#67275C22semidirect
24. C2×#67274C22semidirect
25. C2×#67274C22semidirect
26. C2×#67273C22semidirect
27. C2×#67273C22semidirect
32. C2×#67272C22semidirect
33. C2×#67272C22semidirect
34. C2×#67272C22semidirect
39. #10625046C22semidirect
40. #10625045C22semidirect
41. #10624985C22semidirect
42. C4×C23⋊C8C22semidirect
83. #67267D4semidirect
84. C2×C23⋊C8D4semidirect
152. #535D23semidirect
186. #127C2×D23semidirect
188. #124C2×D23semidirect
196. C23#3155semidirect

Maximal subgroups

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

subgroupindex
C2×#106251032
C2×#106251202
C2×#106251212
C22×#672722
#130929862
#130928072
#130928042
#130927992
#130927932
#130923732
C23×#5352
#315523