Finite Group Databasebeta

← #15683019

Subgroups — #15683019

Order 2944.

548 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 548 conjugacy classes of subgroups — too many to draw. Only its 135 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×#10625120C211yesmaximal, characteristic, complemented
2C2×M16×D23C211yesmaximal, characteristic, complemented
3#13092924C211yesmaximal, characteristic, complemented
4C2×#10625066C211yesmaximal, characteristic, complemented
5#13092669C212yesmaximal, complemented
6#13092666C212yesmaximal, complemented
7#13092652C212yesmaximal, complemented
8#13092649C212yesmaximal, complemented
9#13092457C211yesmaximal, characteristic, complemented
10#13092423C211yesmaximal, characteristic, complemented
11C23×#417C211yesmaximal, characteristic, complemented
12C2×#41×C23C2211yescharacteristic
13C22×D92—21no—
14C22×D92C2211yescharacteristic
15C22×C4×D23C2211yescharacteristic
16C2×M16×C23C2211yescharacteristic
17C2×C4⋊C4×C23C2211yescharacteristic
18#10625120—24no—
19#10625117C2211yescharacteristic, complemented
20#10625117C2211yescharacteristic, complemented
21C2×#67274C2212yescomplemented
22#10625109C2211yescharacteristic, complemented
23#10625109C2211yescharacteristic, complemented
24#10625108—21no—
25#10625106—21no—
26C2×#67272C2212yescomplemented
27C4×C22⋊D23—21no—
28C4×C22⋊D23—21no—
29C2×(C2×D23)⋊C4—21no—
30#10625097C2211yescharacteristic
31C2×#67267C2211yescharacteristic
32M16×D23—24no—
33C2×#67262C2212yescomplemented
34C2×C8×D23C2212yescomplemented
35#10625066—21no—
36#10625066—21no—
37#10625066C2212yes—
38#10625066C2212yes—
39C23×#103C2212yescomplemented
40C23×#102C2212yescomplemented
41#10625003C2212yescomplemented
42#10625003C2212yescomplemented
43#10624990C2212yescomplemented
44#10624989C2212yescomplemented
45C23×D23—21no—
46C23×D23D411yescharacteristic
47#41×C23—22no—
48#41×C23—22no—
49C2×Q8×C23C2311yescharacteristic
50C2×D4×C23—21no—
51C2×D4×C23C2311yescharacteristic
52C22×C4×C23—21no—
53C22×C4×C23—21no—
54C22×C4×C23C2311yescharacteristic
55C2×C22⋊D23—21no—
56C2×C22⋊D23—21no—
57C22×Dic23D411yescharacteristic
58C2×D92—22no—
59C2×D92—22no—
60C2×D92—22no—
61C2×D92—22no—
62C2×D92—21no—
63C2×D92—44no—
64C2×D92C2312yes—
65C2×C4×D23—22no—
66C2×C4×D23—22no—
67C2×C4×D23D411yescharacteristic
68C2×C4×D23D411yescharacteristic
69C2×C4×D23C2311yescharacteristic
70C2×C4×D23C2311yescharacteristic
71M16×C23—22no—
72C2×C8×C23C2312yes—
73C4⋊C4×C23—21no—
74C4⋊C4×C23C2312yes—
75C22⋊Dic23—21no—
76C22⋊Dic23—21no—
77C22⋊Dic23—21no—
78#67274—24no—
79#67272—24no—
80(C2×D23)⋊C4—21no—
81(C2×D23)⋊C4—21no—
82(C2×D23)⋊C4—22no—
83(C2×D23)⋊C4—22no—
84C4⋊Dic23C2311yescharacteristic
85C4⋊Dic23C2311yescharacteristic
86Dic23⋊C4—21no—
87Dic23⋊C4—21no—
88C4×Dic23—21no—
89#67267D414yescomplemented
90C2×C23⋊C8C2312yes—
91#67262—24no—
92C8×D23—24no—
93C23×C23—21no—
94C23×C23C2×D411yescharacteristic
95C22×D23—22no—
96C22×D23—22no—
97C22×D23—22no—
98C22×D23—41no—
99C22×D23—42no—
100C22×D23—42no—
101C22×D23—42no—
102C22×D23C2×D411yescharacteristic
103C22×D23C2×D411yescharacteristic
104Q8×C23—21no—
105Q8×C23—21no—
106D4×C23—21no—
107D4×C23—21no—
108D4×C23—42no—
109C2×C4×C23—21no—
110C2×C4×C23—22no—
111C2×C4×C23—42no—
112C2×C4×C23—42no—
113C2×C4×C23C2×D411yescharacteristic
114C2×C4×C23C2×D412yes—
115C2×C4×C23#4112yes—
116C2×C4×C23C2411yescharacteristic
117C22⋊D23—42no—
118C22⋊D23—42no—
119C2×Dic23—22no—
120C2×Dic23—21no—
121C2×Dic23—21no—
122C2×Dic23C2×D411yescharacteristic
123C2×Dic23C2×D411yescharacteristic
124D92—22no—
125D92—22no—
126D92—44no—
127D92—44no—
128D92—42no—
129C4×D23—22no—
130C4×D23—22no—
131C4×D23—21no—
132C4×D23—21no—
133C4×D23—21no—
134C4×D23—21no—
135C8×C23—22no—
136C23⋊C8C2×D414yescomplemented
137#3055—231nomaximal, Sylow
138C22×C23—21no—
139C22×C23—21no—
140C22×C23—41no—
141C22×C23—41no—
142C22×C23—41no—
143C22×C23#12112yes—
144C22×C23C22×D411yescharacteristic
145C2×D23—21no—
146C2×D23—21no—
147C2×D23—21no—
148C2×D23—21no—
149C2×D23—21no—
150C2×D23—44no—
151C2×D23—42no—
152C2×D23—42no—
153C2×D23—42no—
154C2×D23—84no—
155C2×D23AGL(1,ℤ/8)12yescomplemented
156C4×C23—41no—
157C4×C23—42no—
158C4×C23#12112yes—
159C4×C23C22×D411yescharacteristic
160C4×C23C2×#4111yescharacteristic
161Dic23—21no—
162Dic23—21no—
163Dic23—41no—
164Dic23—41no—
165C2×AGL(1,ℤ/8)—231no—
166C22×M16—231no—
167#525—231no—
168C2×#121—231no—
169#469—232no—
170#468—232no—
171#466—232no—
172#465—232no—
173#428—231no—
174#418—231no—
175#417D2311yescharacteristic, complemented
176C2×C23—22no—
177C2×C23—81no—
178C2×C23C2×#12111yescharacteristic
179C2×C23C2×AGL(1,ℤ/8)11yescharacteristic
180C2×C23#57511yescharacteristic
181D23—22no—
182D23—41no—
183D23—82no—
184C2×#41C2×D2311yescharacteristic
185C22×D4—231no—
186C22×D4—461no—
187C23×C4—231no—
188AGL(1,ℤ/8)—464no—
189C2×SD16—232no—
190C2×D8—232no—
191C2×M16—231no—
192C2×M16—232no—
193C2×M16—464no—
194C2×M16C2×D2311yescharacteristic
195C22×C8—232no—
196#123—461no—
197C22⋊Q8—231no—
198C22⋊Q8—231no—
199#121—231no—
200#121—231no—
201#121—232no—
202#121—232no—
203#121—461no—
204#121—461no—
205#120—461no—
206C4×D4—461no—
207C4×D4—461no—
208#117—231no—
209C2×C4⋊C4C2×D2311yescharacteristic
210C2×C22⋊C4—461no—
211#107—232no—
212#106—232no—
213#103C2×D2312yescomplemented
214#102—232no—
215#102—232no—
216#102C2×D2312yescomplemented
217C23#305511yescharacteristic, complemented, Sylow
218C24—231no—
219C24—461no—
220#41—22no—
221#41—22no—
222C2×Q8C22×D2311yescharacteristic
223C2×D4—21no—
224C2×D4—232no—
225C2×D4—462no—
226C2×D4—462no—
227C2×D4—461no—
228C2×D4—461no—
229C2×D4—462no—
230C2×D4—462no—
231C2×D4—461no—
232C2×D4—924no—
233C2×D4C22×D2311yescharacteristic
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—231no—
237C22×C4—231no—
238C22×C4—231no—
239C22×C4—231no—
240C22×C4—231no—
241C22×C4—462no—
242C22×C4—462no—
243C22×C4C22×D2311yescharacteristic
244SD16—464no—
245D8—464no—
246M16—22no—
247M16—234no—
248M16—464no—
249C2×C8—232no—
250C2×C8—464no—
251C2×C8C22×D2312yes—
252C4⋊C4—21no—
253C4⋊C4—231no—
254C4⋊C4—231no—
255C4⋊C4—461no—
256C4⋊C4—461no—
257C4⋊C4C22×D2312yes—
258C22⋊C4—462no—
259C22⋊C4—462no—
260C22⋊C4—461no—
261C22⋊C4—461no—
262C22⋊C4—461no—
263C22⋊C4—461no—
264C22⋊C4—461no—
265C42—461no—
266C23—21no—
267C23—231no—
268C23—231no—
269C23—462no—
270C23—462no—
271C23—462no—
272C23—921no—
273C23—922no—
274C23—922no—
275C23—922no—
276C23D4×D2311yescharacteristic
277Q8—21no—
278Q8—21no—
279D4—21no—
280D4—21no—
281D4—42no—
282D4—462no—
283D4—462no—
284D4—924no—
285D4—924no—
286D4—922no—
287D4—922no—
288D4—922no—
289C2×C4—22no—
290C2×C4—21no—
291C2×C4—42no—
292C2×C4—42no—
293C2×C4—231no—
294C2×C4—231no—
295C2×C4—462no—
296C2×C4—462no—
297C2×C4—462no—
298C2×C4—461no—
299C2×C4—461no—
300C2×C4—461no—
301C2×C4—461no—
302C2×C4—461no—
303C2×C4—461no—
304C2×C4#6728812yes—
305C2×C4D4×D2311yescharacteristic
306C2×C4D4×D2312yes—
307C2×C4C23×D2311yescharacteristic
308C8—22no—
309C8—234no—
310C22—21no—
311C22—21no—
312C22—41no—
313C22—41no—
314C22—41no—
315C22—232no—
316C22—461no—
317C22—461no—
318C22—461no—
319C22—461no—
320C22—461no—
321C22—924no—
322C22—922no—
323C22—922no—
324C22—922no—
325C22—1844no—
326C22#1062505512yes—
327C22C2×D4×D2311yescharacteristic
328C4—41no—
329C4—42no—
330C4—461no—
331C4—461no—
332C4—921no—
333C4—921no—
334C4#1062505512yes—
335C4C2×#6728811yescharacteristic
336C4C2×D4×D2311yescharacteristic
337C2—22no—
338C2—81no—
339C2—462no—
340C2—921no—
341C2—1842no—
342C2C2×#1062505511yescharacteristic
343C2AGL(1,ℤ/8)×D2311yescharacteristic
344C2#1309321611yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#417C2
socleC22×C23C22×D4
hypercenter#417D23
hypocenterC23#3055
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
1. C2×#10625120C2semidirect
2. C2×M16×D23C2semidirect
3. #13092924C2semidirect
4. C2×#10625066C2semidirect
5. #13092669C2semidirect
6. #13092666C2semidirect
7. #13092652C2semidirect
8. #13092649C2semidirect
9. #13092457C2semidirect
10. #13092423C2semidirect
11. C23×#417C2semidirect
19. #10625117C22semidirect
20. #10625117C22semidirect
21. C2×#67274C22semidirect
22. #10625109C22semidirect
23. #10625109C22semidirect
26. C2×#67272C22semidirect
33. C2×#67262C22semidirect
34. C2×C8×D23C22semidirect
39. C23×#103C22semidirect
40. C23×#102C22semidirect
41. #10625003C22semidirect
42. #10625003C22semidirect
43. #10624990C22semidirect
44. #10624989C22semidirect
89. #67267D4semidirect
136. C23⋊C8C2×D4semidirect
155. C2×D23AGL(1,ℤ/8)semidirect
175. #417D23semidirect
213. #103C2×D23semidirect
216. #102C2×D23semidirect
217. C23#3055semidirect

Maximal subgroups

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

subgroupindex
C2×#106251202
C2×M16×D232
#130929242
C2×#106250662
#130926692
#130926662
#130926522
#130926492
#130924572
#130924232
C23×#4172
#305523