Finite Group Databasebeta

← #15682796

Subgroups — #15682796

Order 2944.

800 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 800 conjugacy classes of subgroups — too many to draw. Only its 145 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×#10625155C211yesmaximal, characteristic, complemented
2#13092979C212yesmaximal, complemented
3#13092976C211yesmaximal, characteristic, complemented
4#13092608C214yesmaximal, complemented
5#13092605C214yesmaximal, complemented
6C2×#10624988C212yesmaximal, complemented
7C2×C23×#99C211yesmaximal, characteristic, complemented
8C22×D4×C23C2211yescharacteristic
9C22×C22⋊D23—21no—
10C22×C22⋊D23C2212yes—
11C22×C22⋊D23C2211yescharacteristic, complemented
12#10625155—22no—
13#10625155—24no—
14#10625155C2214yes—
15C2×#67290—22no—
16C2×D4×D23—22no—
17C2×#67288—21no—
18C2×C22⋊C4×C23C2212yescomplemented
19#10625124—21no—
20C2×C22⋊Dic23C2211yescharacteristic, complemented
21#10625110—22no—
22#10625108C2212yescomplemented
23#10625106C2212yescomplemented
24#10625101—24no—
25#10625100—21no—
26#10625057—22no—
27#10625057C2214yescomplemented
28#10625053—22no—
29#10625053C2214yescomplemented
30C23×#99C2214yescomplemented
31#10624988C2218yescomplemented
32C24×C23D411yescharacteristic, complemented
33C24×C23C2311yescharacteristic
34C23×D23—21no—
35C23×D23D412yescomplemented
36C23×D23C2311yescharacteristic, complemented
37C2×D4×C23—22no—
38C2×D4×C23—22no—
39C2×D4×C23D412yescomplemented
40C2×D4×C23C2312yes—
41C22×C4×C23—22no—
42C22×C4×C23D411yescharacteristic, complemented
43C2×C22⋊D23—22no—
44C2×C22⋊D23—24no—
45C2×C22⋊D23—22no—
46C2×C22⋊D23—22no—
47C2×C22⋊D23—22no—
48C2×C22⋊D23—22no—
49C2×C22⋊D23—24no—
50C2×C22⋊D23—22no—
51C2×C22⋊D23—21no—
52C2×C22⋊D23—22no—
53C2×C22⋊D23—21no—
54C2×C22⋊D23—22no—
55C2×C22⋊D23D414yescomplemented
56C2×C22⋊D23C2314yes—
57C22×Dic23—21no—
58C22×Dic23—21no—
59C22×Dic23D412yescomplemented
60C22×Dic23C2311yescharacteristic, complemented
61#67290—28no—
62#67290—28no—
63D4×D23—28no—
64D4×D23—28no—
65#67288—24no—
66#67288—24no—
67C2×D92—21no—
68C2×D92—24no—
69C2×C4×D23—22no—
70C2×Dic46—21no—
71C22⋊C4×C23—22no—
72C22⋊C4×C23C2314yescomplemented
73C22⋊Dic23—21no—
74C22⋊Dic23—22no—
75C22⋊Dic23C2312yescomplemented
76(C2×D23)⋊C4—24no—
77(C2×D23)⋊C4—22no—
78(C2×D23)⋊C4—24no—
79C4⋊Dic23—24no—
80Dic23⋊C4—22no—
81C23×C23—21no—
82C23×C23—21no—
83C23×C23—81no—
84C23×C23—81no—
85C23×C23C2×D412yes—
86C23×C23C2×D411yescharacteristic
87C23×C23C2×D411yescharacteristic
88C23×C23C2×D412yes—
89C23×C23C2×D412yes—
90C23×C23C2411yescharacteristic
91C22×D23—22no—
92C22×D23—24no—
93C22×D23—22no—
94C22×D23—22no—
95C22×D23—21no—
96C22×D23—81no—
97C22×D23—82no—
98C22×D23—82no—
99C22×D23C2×D414yes—
100D4×C23—24no—
101D4×C23—24no—
102C2×C4×C23—21no—
103C2×C4×C23—21no—
104C2×C4×C23—24no—
105C2×C4×C23—82no—
106C2×C4×C23C2×D412yes—
107C22⋊D23—28no—
108C22⋊D23—24no—
109C22⋊D23—24no—
110C22⋊D23—24no—
111C22⋊D23—24no—
112C22⋊D23—41no—
113C22⋊D23—42no—
114C22⋊D23—41no—
115C22⋊D23—82no—
116C2×Dic23—24no—
117C2×Dic23—22no—
118C2×Dic23—22no—
119C2×Dic23—21no—
120C2×Dic23—22no—
121C2×Dic23—22no—
122C2×Dic23—81no—
123C2×Dic23C2×D414yes—
124D92—24no—
125D92—84no—
126C4×D23—28no—
127Dic46—24no—
128#3026—231nomaximal, Sylow
129C22×C23—22no—
130C22×C23—41no—
131C22×C23—42no—
132C22×C23—42no—
133C22×C23—41no—
134C22×C23—41no—
135C22×C23—42no—
136C22×C23—42no—
137C22×C23—81no—
138C22×C23#12011yescharacteristic
139C22×C23#12012yes—
140C22×C23#12011yescharacteristic
141C22×C23C22×D411yescharacteristic
142C22×C23C22×D412yes—
143C2×D23—24no—
144C2×D23—44no—
145C2×D23—44no—
146C2×D23—44no—
147C2×D23—42no—
148C2×D23—41no—
149C2×D23—82no—
150C2×D23—84no—
151C4×C23—22no—
152C4×C23—44no—
153Dic23—24no—
154Dic23—42no—
155Dic23—41no—
156C2×H(5,𝔽2)—231no—
157#534—231no—
158#534—232no—
159#458—234no—
160B(4,𝔽2)—234no—
161C2×#99—232no—
162C2×#99D2311yescharacteristic, complemented
163C2×C23—21no—
164C2×C23—22no—
165C2×C23—21no—
166C2×C23—22no—
167C2×C23—21no—
168C2×C23—42no—
169C2×C23C2×#12011yescharacteristic
170D23—44no—
171D23—81no—
172H(5,𝔽2)—234no—
173H(5,𝔽2)—464no—
174H(5,𝔽2)—462no—
175C2×#41—462no—
176C2×#41—461no—
177C22×D4—232no—
178C22×D4—231no—
179C22×D4—462no—
180C22×D4—461no—
181C22×D4C2×D2311yescharacteristic
182#123—232no—
183#123—234no—
184#123—462no—
185#123—461no—
186#121—464no—
187#121—462no—
188#120—232no—
189#120—234no—
190#120—462no—
191#120—461no—
192C2×C22⋊C4—231no—
193C2×C22⋊C4C2×D2312yescomplemented
194#99—238no—
195#99C2×D2314yescomplemented
196C23#302611yescharacteristic, complemented, Sylow
197C24—232no—
198C24—231no—
199C24—461no—
200C24D9211yescharacteristic, complemented
201C24C22×D2311yescharacteristic
202#41—464no—
203#41—468no—
204#41—468no—
205#41—464no—
206C2×Q8—461no—
207C2×D4—22no—
208C2×D4—22no—
209C2×D4—234no—
210C2×D4—234no—
211C2×D4—461no—
212C2×D4—464no—
213C2×D4—468no—
214C2×D4—468no—
215C2×D4—462no—
216C2×D4—464no—
217C2×D4—462no—
218C2×D4—462no—
219C2×D4—464no—
220C2×D4—462no—
221C2×D4—462no—
222C2×D4—461no—
223C2×D4—461no—
224C2×D4—462no—
225C2×D4—462no—
226C2×D4—462no—
227C2×D4D9212yescomplemented
228C2×D4C22×D2312yes—
229C22×C4—22no—
230C22×C4—232no—
231C22×C4—231no—
232C22×C4—462no—
233C22×C4—461no—
234C22×C4—461no—
235C22×C4D9211yescharacteristic, complemented
236C4⋊C4—464no—
237C4⋊C4—462no—
238C22⋊C4—22no—
239C22⋊C4—232no—
240C22⋊C4—464no—
241C22⋊C4—464no—
242C22⋊C4—461no—
243C22⋊C4—462no—
244C22⋊C4—462no—
245C22⋊C4C22×D2314yescomplemented
246C23—21no—
247C23—21no—
248C23—81no—
249C23—81no—
250C23—234no—
251C23—464no—
252C23—462no—
253C23—462no—
254C23—461no—
255C23—462no—
256C23—1841no—
257C23—1842no—
258C23—1842no—
259C23C2×D9212yes—
260C23C2×D9211yescharacteristic
261C23C2×D9211yescharacteristic
262C23D4×D2312yes—
263C23D4×D2312yes—
264C23C23×D2311yescharacteristic
265Q8—464no—
266D4—24no—
267D4—24no—
268D4—464no—
269D4—468no—
270D4—464no—
271D4—464no—
272D4—464no—
273D4—464no—
274D4—921no—
275D4—921no—
276D4—922no—
277D4—1844no—
278D4—1842no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—24no—
282C2×C4—82no—
283C2×C4—234no—
284C2×C4—468no—
285C2×C4—464no—
286C2×C4—462no—
287C2×C4—462no—
288C2×C4—462no—
289C2×C4—461no—
290C2×C4—462no—
291C2×C4—1841no—
292C2×C4C2×D9212yes—
293C22—22no—
294C22—42no—
295C22—41no—
296C22—41no—
297C22—42no—
298C22—41no—
299C22—42no—
300C22—42no—
301C22—81no—
302C22—464no—
303C22—924no—
304C22—924no—
305C22—924no—
306C22—922no—
307C22—921no—
308C22—1842no—
309C22—1844no—
310C22#1062505311yescharacteristic
311C22#1062505311yescharacteristic
312C22#1062505312yes—
313C22C22×D9211yescharacteristic
314C22C2×D4×D2312yes—
315C4—22no—
316C4—44no—
317C4—464no—
318C4—922no—
319C4—921no—
320C2—22no—
321C2—21no—
322C2—21no—
323C2—21no—
324C2—22no—
325C2—42no—
326C2—924no—
327C2—1841no—
328C2C2×#1062505311yescharacteristic
subgroupG/H
centerC2C2×#10625053
commutator, cosocleC23×C23C24
FrattiniC23C23×D23
FittingC2×C23×#99C2
socleC2×C23C2×#120
hypercenterC2×#99D23
hypocenterC23#3026
LCSG ▷ C23×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2 ◁ C24 ◁ C2×#99

Complements

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

NH ≅ G/Ntype
1. C2×#10625155C2semidirect
2. #13092979C2semidirect
3. #13092976C2semidirect
4. #13092608C2semidirect
5. #13092605C2semidirect
6. C2×#10624988C2semidirect
7. C2×C23×#99C2semidirect
11. C22×C22⋊D23C22semidirect
18. C2×C22⋊C4×C23C22semidirect
20. C2×C22⋊Dic23C22semidirect
22. #10625108C22semidirect
23. #10625106C22semidirect
27. #10625057C22semidirect
29. #10625053C22semidirect
30. C23×#99C22semidirect
31. #10624988C22semidirect
32. C24×C23D4semidirect
35. C23×D23D4semidirect
36. C23×D23C23semidirect
39. C2×D4×C23D4semidirect
42. C22×C4×C23D4semidirect
55. C2×C22⋊D23D4semidirect
59. C22×Dic23D4semidirect
60. C22×Dic23C23semidirect
72. C22⋊C4×C23C23semidirect
75. C22⋊Dic23C23semidirect
162. C2×#99D23semidirect
193. C2×C22⋊C4C2×D23semidirect
195. #99C2×D23semidirect
196. C23#3026semidirect
200. C24D92semidirect
227. C2×D4D92semidirect
235. C22×C4D92semidirect
245. C22⋊C4C22×D23semidirect

Maximal subgroups

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

subgroupindex
C2×#106251552
#130929792
#130929762
#130926082
#130926052
C2×#106249882
C2×C23×#992
#302623