Finite Group Databasebeta

← #15683078

Subgroups — #15683078

Order 2944.

504 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 141 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×#10625079C211yesmaximal, characteristic, complemented
2C2×#10625078C211yesmaximal, characteristic, complemented
3#13092998C211yesmaximal, characteristic, complemented
4#13092986C211yesmaximal, characteristic, complemented
5#13092671C212yesmaximal, complemented
6#13092664C212yesmaximal, complemented
7#13092654C212yesmaximal, complemented
8#13092647C212yesmaximal, complemented
9#13092411C211yesmaximal, characteristic, complemented
10C2×#10624991C211yesmaximal, characteristic, complemented
11C23×#428C211yesmaximal, characteristic, complemented
12C2×#67288C2211yescharacteristic
13C2×#67288C2211yescharacteristic
14C22×D92C2211yescharacteristic
15C2×M16×C23C2211yescharacteristic
16C23×#117C2211yescharacteristic
17C2×C4⋊C4×C23C2211yescharacteristic
18#10625101—22no—
19C22×C23⋊C8C2211yescharacteristic
20#10625079—24no—
21#10625078—24no—
22C2×D184C2212yes—
23C2×#67263C2212yes—
24C2×#67262C2212yescomplemented
25C2×C8×D23C2212yescomplemented
26#10625068—21no—
27#10625068C2212yescomplemented
28#10625066—21no—
29#10625066C2212yes—
30#10625066C2212yes—
31#10625066C2212yescomplemented
32#10625053—22no—
33#10625046—21no—
34#10625045—21no—
35C23×#107C2212yescomplemented
36C23×#106C2212yescomplemented
37#10624992C2211yescharacteristic, complemented
38#10624992C2211yescharacteristic, complemented
39#10624991C2212yes—
40#10624991C2212yes—
41#10624991C2211yescharacteristic, complemented
42#10624991C2211yescharacteristic, complemented
43C23×D23—21no—
44C22×C4×C23—21no—
45C22×C4×C23C2311yescharacteristic
46C2×C22⋊D23—21no—
47C2×C22⋊D23D412yes—
48#67288—22no—
49#67288—22no—
50#67288—22no—
51#67288—22no—
52C2×D92—22no—
53C2×D92—22no—
54C2×D92—21no—
55C2×D92—22no—
56C2×D92—22no—
57C2×D92—22no—
58C2×D92D411yescharacteristic
59C2×D92C2312yes—
60C2×D92C2311yescharacteristic
61C2×C4×D23—21no—
62C2×C4×D23C2312yes—
63C2×Dic46D411yescharacteristic
64C2×Dic46C2311yescharacteristic
65M16×C23D414yescomplemented
66C2×C8×C23C2312yes—
67C4⋊C4×C23—21no—
68C4⋊C4×C23C2311yescharacteristic
69C4⋊C4×C23C2312yes—
70C4⋊C4×C23C2311yescharacteristic
71C22⋊C4×C23—21no—
72C42×C23—21no—
73(C2×D23)⋊C4—22no—
74(C2×D23)⋊C4—22no—
75(C2×D23)⋊C4—22no—
76(C2×D23)⋊C4—22no—
77C4⋊Dic23—22no—
78C2×C23⋊C8—22no—
79C2×C23⋊C8C2311yescharacteristic
80C2×C23⋊C8C2311yescharacteristic
81D184—24no—
82#67263—24no—
83#67262—24no—
84C8×D23—24no—
85C23×C23C2×D411yescharacteristic
86C22×D23—21no—
87C22×D23—22no—
88C22×D23—42no—
89C22×D23—81no—
90C22×D23—81no—
91C22×D23C2×D412yes—
92C2×C4×C23—22no—
93C2×C4×C23—21no—
94C2×C4×C23—21no—
95C2×C4×C23—81no—
96C2×C4×C23C2×D412yes—
97C2×C4×C23C2×D411yescharacteristic
98C2×C4×C23#4112yes—
99C2×C4×C23C2411yescharacteristic
100C22⋊D23—24no—
101C22⋊D23—42no—
102C2×Dic23—21no—
103C2×Dic23C2×D412yes—
104D92—22no—
105D92—22no—
106D92—21no—
107D92—22no—
108D92—21no—
109D92—42no—
110D92—82no—
111D92—82no—
112D92—82no—
113C4×D23—22no—
114C4×D23—22no—
115C4×D23—42no—
116Dic46—22no—
117Dic46—21no—
118Dic46—21no—
119C8×C23C2×D414yes—
120C23⋊C8—21no—
121C23⋊C8—21no—
122#3062—231nomaximal, Sylow
123C22×C23—21no—
124C22×C23—21no—
125C22×C23#12112yes—
126C22×C23C22×D411yescharacteristic
127C2×D23—22no—
128C2×D23—22no—
129C2×D23—22no—
130C2×D23—41no—
131C2×D23—42no—
132C2×D23—41no—
133C2×D23—42no—
134C2×D23—42no—
135C2×D23—41no—
136C2×D23—84no—
137C4×C23—41no—
138C4×C23—42no—
139C4×C23—41no—
140C4×C23#12112yes—
141C4×C23C22×D411yescharacteristic
142C4×C23C2×#4111yescharacteristic
143Dic23—22no—
144Dic23—41no—
145C2×AGL(1,ℤ/8)—231no—
146C2×#131—231no—
147#537—231no—
148#535—231no—
149#469—232no—
150#468—232no—
151#466—232no—
152#465—232no—
153#428D2311yescharacteristic, complemented
154#416—231no—
155C2×#102—231no—
156C2×C23—22no—
157C2×C23C2×#12111yescharacteristic
158C2×C23#57611yescharacteristic
159C2×C23#57711yescharacteristic
160D23—42no—
161D23—81no—
162D23—82no—
163C2×#41—231no—
164C2×#41—231no—
165C22×D4—231no—
166AGL(1,ℤ/8)—464no—
167C2×SD16—232no—
168C2×D8—232no—
169#131—464no—
170C2×M16—232no—
171C2×M16C2×D2311yescharacteristic
172C22×C8—231no—
173C22×C8—232no—
174#127—461no—
175#124—461no—
176C22⋊Q8—232no—
177C22⋊Q8—461no—
178#121—232no—
179#121—232no—
180#121—232no—
181#121—461no—
182#121—462no—
183#120—462no—
184#117C2×D2311yescharacteristic
185C2×C4⋊C4C2×D2311yescharacteristic
186#107C2×D2312yescomplemented
187#106C2×D2312yescomplemented
188#103—231no—
189#103—231no—
190#102—232no—
191#102—232no—
192#102—231no—
193#102—231no—
194C23#306211yescharacteristic, complemented, Sylow
195C24—461no—
196#41—462no—
197#41—462no—
198#41—462no—
199#41—462no—
200C2×Q8—231no—
201C2×Q8—231no—
202C2×D4—232no—
203C2×D4—231no—
204C2×D4—231no—
205C2×D4—232no—
206C2×D4—462no—
207C2×D4—462no—
208C2×D4—462no—
209C2×D4—461no—
210C2×D4—462no—
211C2×D4—461no—
212C2×D4—462no—
213C22×C4—21no—
214C22×C4—232no—
215C22×C4—461no—
216C22×C4C22×D2311yescharacteristic
217SD16—464no—
218D8—464no—
219M16—464no—
220M16D9214yescomplemented
221C2×C8—231no—
222C2×C8—231no—
223C2×C8—462no—
224C2×C8—464no—
225C2×C8C22×D2312yes—
226C4⋊C4—21no—
227C4⋊C4—462no—
228C4⋊C4C22×D2312yes—
229C4⋊C4C22×D2311yescharacteristic
230C4⋊C4C22×D2311yescharacteristic
231C22⋊C4—21no—
232C22⋊C4—462no—
233C22⋊C4—462no—
234C22⋊C4—462no—
235C22⋊C4—462no—
236C42—21no—
237C23—232no—
238C23—461no—
239C23—462no—
240C23—922no—
241C23—1841no—
242C23—1841no—
243C23D4×D2311yescharacteristic
244Q8—462no—
245Q8—461no—
246Q8—461no—
247D4—464no—
248D4—462no—
249D4—461no—
250D4—462no—
251D4—462no—
252D4—461no—
253D4—922no—
254D4—922no—
255D4—1842no—
256D4—1842no—
257D4—1842no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—22no—
261C2×C4—81no—
262C2×C4—232no—
263C2×C4—462no—
264C2×C4—462no—
265C2×C4—461no—
266C2×C4—922no—
267C2×C4C2×D9212yes—
268C2×C4D4×D2311yescharacteristic
269C2×C4#6729212yes—
270C2×C4C23×D2311yescharacteristic
271C8—461no—
272C8—461no—
273C8C2×D9214yes—
274C22—21no—
275C22—21no—
276C22—462no—
277C22—462no—
278C22—462no—
279C22—921no—
280C22—922no—
281C22—921no—
282C22—922no—
283C22—922no—
284C22—921no—
285C22—1844no—
286C22#1062506612yes—
287C22C2×D4×D2311yescharacteristic
288C4—42no—
289C4—41no—
290C4—41no—
291C4—462no—
292C4—921no—
293C4#1062506612yes—
294C4C22×D9211yescharacteristic
295C4C2×#6729211yescharacteristic
296C2—22no—
297C2—922no—
298C2—1842no—
299C2—1841no—
300C2C2×#1062506611yescharacteristic
301C2#1309322111yescharacteristic
302C2#1309322611yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#428C2
socleC22×C23C22×D4
hypercenter#428D23
hypocenterC23#3062
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
1. C2×#10625079C2semidirect
2. C2×#10625078C2semidirect
3. #13092998C2semidirect
4. #13092986C2semidirect
5. #13092671C2semidirect
6. #13092664C2semidirect
7. #13092654C2semidirect
8. #13092647C2semidirect
9. #13092411C2semidirect
10. C2×#10624991C2semidirect
11. C23×#428C2semidirect
24. C2×#67262C22semidirect
25. C2×C8×D23C22semidirect
27. #10625068C22semidirect
31. #10625066C22semidirect
35. C23×#107C22semidirect
36. C23×#106C22semidirect
37. #10624992C22semidirect
38. #10624992C22semidirect
41. #10624991C22semidirect
42. #10624991C22semidirect
65. M16×C23D4semidirect
153. #428D23semidirect
186. #107C2×D23semidirect
187. #106C2×D23semidirect
194. C23#3062semidirect
220. M16D92semidirect

Maximal subgroups

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

subgroupindex
C2×#106250792
C2×#106250782
#130929982
#130929862
#130926712
#130926642
#130926542
#130926472
#130924112
C2×#106249912
C23×#4282
#306223