Finite Group Databasebeta

← #15682706

Subgroups — #15682706

Order 2944.

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

normal subgroups only

This group has 764 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×#10625155C211yesmaximal, characteristic, complemented
2C2×#10625103C211yesmaximal, characteristic, complemented
3C2×#10625075C211yesmaximal, characteristic, complemented
4#13092998C211yesmaximal, characteristic, complemented
5#13092580C212yesmaximal, complemented
6#13092569C212yesmaximal, complemented
7#13092563C212yesmaximal, complemented
8#13092552C212yesmaximal, complemented
9#13092416C211yesmaximal, characteristic, complemented
10#13092383C211yesmaximal, characteristic, complemented
11C2×C23×#102C211yesmaximal, characteristic, complemented
12C22×D4×C23C2211yescharacteristic
13C22×C22⋊D23—22no—
14#10625155—24no—
15#10625155—24no—
16C2×#67290—21no—
17C2×#67290C2212yes—
18C2×D4×D23—21no—
19C2×D4×D23C2212yes—
20C2×#67288C2211yescharacteristic
21C2×#67288C2211yescharacteristic
22C2×#67288C2211yescharacteristic, complemented
23C22×C8×C23C2211yescharacteristic, complemented
24C2×C4⋊C4×C23C2211yescharacteristic, complemented
25C2×#67273C2212yescomplemented
26#10625103—24no—
27C2×#67272C2212yescomplemented
28#10625101—22no—
29C2×#67267C2211yescharacteristic, complemented
30C2×Dic92C2211yescharacteristic, complemented
31#10625075—24no—
32C2×D184C2211yescharacteristic, complemented
33C2×#67263C2211yescharacteristic, complemented
34C2×#67263C2211yescharacteristic, complemented
35#10625068—21no—
36#10625068C2212yescomplemented
37#10625066—21no—
38#10625066C2212yescomplemented
39C23×#102C2212yescomplemented
40C23×#102C2212yescomplemented
41(C2×D23)⋊C8C2212yescomplemented
42(C2×D23)⋊C8C2212yescomplemented
43#10624992C2212yescomplemented
44#10624991C2212yescomplemented
45C24×C23—21no—
46C23×D23—22no—
47C2×D4×C23—21no—
48C2×D4×C23—22no—
49C2×D4×C23D414yescomplemented
50C2×D4×C23C2312yes—
51C22×C4×C23—21no—
52C22×C4×C23C2311yescharacteristic
53C2×C22⋊D23—216no—
54C2×C22⋊D23—21no—
55C2×C22⋊D23—22no—
56C2×C22⋊D23—21no—
57C2×C22⋊D23—22no—
58C2×C22⋊D23D412yes—
59C22×Dic23—22no—
60#67290—28no—
61#67290—24no—
62#67290—24no—
63D4×D23—28no—
64D4×D23—24no—
65D4×D23—24no—
66#67288—22no—
67#67288—22no—
68#67288—22no—
69#67288—22no—
70#67288—22no—
71#67288D414yescomplemented
72C2×D92—22no—
73C2×D92D411yescharacteristic
74C2×D92C2311yescharacteristic
75C2×D92C2311yescharacteristic
76C2×C4×D23—21no—
77C2×C4×D23—21no—
78C2×C4×D23C2312yes—
79C2×Dic46D411yescharacteristic
80C2×Dic46C2311yescharacteristic
81C2×Dic46C2311yescharacteristic
82C2×C8×C23—22no—
83C2×C8×C23C2311yescharacteristic
84C2×C8×C23C2311yescharacteristic
85C4⋊C4×C23—21no—
86C4⋊C4×C23C2312yes—
87#67273—24no—
88#67272—24no—
89(C2×D23)⋊C4—22no—
90(C2×D23)⋊C4—22no—
91C4⋊Dic23—22no—
92#67267—22no—
93C2×C23⋊C8C2312yes—
94Dic92—22no—
95D184—22no—
96#67263—22no—
97#67263—22no—
98C23×C23—22no—
99C23×C23—24no—
100C23×C23—81no—
101C23×C23—81no—
102C23×C23C2×D411yescharacteristic
103C22×D23—21no—
104C22×D23—28no—
105C22×D23—21no—
106C22×D23—82no—
107C22×D23—82no—
108C22×D23C2×D412yes—
109D4×C23—24no—
110D4×C23—22no—
111D4×C23C2×D414yes—
112C2×C4×C23—22no—
113C2×C4×C23—81no—
114C2×C4×C23C2×D412yes—
115C2×C4×C23C2×D411yescharacteristic
116C2×C4×C23C2×D412yes—
117C2×C4×C23C2411yescharacteristic
118C22⋊D23—28no—
119C22⋊D23—28no—
120C22⋊D23—24no—
121C22⋊D23—24no—
122C22⋊D23—42no—
123C2×Dic23—28no—
124C2×Dic23—21no—
125C2×Dic23—21no—
126C2×Dic23C2×D412yes—
127D92—22no—
128D92—21no—
129D92—21no—
130D92—21no—
131D92—82no—
132D92C2×D412yes—
133C4×D23—24no—
134C4×D23—22no—
135C4×D23—22no—
136C4×D23—42no—
137Dic46—22no—
138Dic46—21no—
139Dic46—21no—
140Dic46—21no—
141Dic46C2×D412yes—
142C8×C23—21no—
143C8×C23—21no—
144C23⋊C8—22no—
145#3012—231nomaximal, Sylow
146C22×C23—21no—
147C22×C23—21no—
148C22×C23—24no—
149C22×C23—42no—
150C22×C23—42no—
151C22×C23—84no—
152C22×C23#12012yes—
153C22×C23C22×D411yescharacteristic
154C2×D23—22no—
155C2×D23—22no—
156C2×D23—22no—
157C2×D23—22no—
158C2×D23—41no—
159C2×D23—41no—
160C2×D23—41no—
161C2×D23—41no—
162C2×D23—41no—
163C2×D23—88no—
164C4×C23—42no—
165C4×C23#12012yes—
166C4×C23C22×D411yescharacteristic
167C4×C23C22×D411yescharacteristic
168Dic23—22no—
169Dic23—22no—
170Dic23—41no—
171C2×H(5,𝔽2)—231no—
172C2×AGL(1,ℤ/8)—231no—
173C2×#135—231no—
174#537—231no—
175#452—232no—
176#450—232no—
177#449—232no—
178#447—232no—
179#417—231no—
180C2×#102D2311yescharacteristic, complemented
181#408—231no—
182C2×C23—22no—
183C2×C23—44no—
184C2×C23C2×#12011yescharacteristic
185C2×C23#57611yescharacteristic
186C2×C23#57711yescharacteristic
187D23—42no—
188D23—42no—
189D23—81no—
190H(5,𝔽2)—464no—
191H(5,𝔽2)—464no—
192C2×#41—231no—
193C2×#41—232no—
194C2×#41—231no—
195C2×#41—231no—
196C2×#41—461no—
197C22×D4—232no—
198C22×D4—461no—
199C22×D4—462no—
200C22×D4C2×D2311yescharacteristic
201AGL(1,ℤ/8)—464no—
202#135—464no—
203C2×Q16—231no—
204C2×SD16—232no—
205C2×SD16—231no—
206C2×SD16—231no—
207C2×D8—232no—
208C2×D8—231no—
209C2×M16—231no—
210C22×C8C2×D2311yescharacteristic, complemented
211C22⋊Q8—232no—
212C22⋊Q8—461no—
213#121—232no—
214#121—461no—
215#121—462no—
216C2×C4⋊C4C2×D2311yescharacteristic, complemented
217#103—232no—
218#102—232no—
219#102C2×D2312yescomplemented
220#102C2×D2312yescomplemented
221C22⋊C8—232no—
222C22⋊C8—232no—
223C23#301211yescharacteristic, complemented, Sylow
224C24—21no—
225C24—462no—
226#41—234no—
227#41—464no—
228#41—468no—
229#41—464no—
230#41—462no—
231#41—462no—
232#41—462no—
233#41—462no—
234#41—462no—
235C2×Q8—231no—
236C2×Q8—231no—
237C2×Q8—231no—
238C2×D4—21no—
239C2×D4—22no—
240C2×D4—232no—
241C2×D4—231no—
242C2×D4—231no—
243C2×D4—231no—
244C2×D4—462no—
245C2×D4—462no—
246C2×D4—464no—
247C2×D4—468no—
248C2×D4—462no—
249C2×D4—4616no—
250C2×D4—461no—
251C2×D4—464no—
252C2×D4—461no—
253C2×D4D9214yescomplemented
254C2×D4C22×D2312yes—
255C22×C4—21no—
256C22×C4—232no—
257C22×C4—462no—
258C22×C4—461no—
259C22×C4—461no—
260C22×C4C22×D2311yescharacteristic
261Q16—462no—
262SD16—462no—
263SD16—462no—
264SD16—464no—
265D8—462no—
266D8—464no—
267M16—462no—
268C2×C8—22no—
269C2×C8—232no—
270C2×C8C22×D2311yescharacteristic
271C2×C8C22×D2311yescharacteristic
272C4⋊C4—21no—
273C4⋊C4—462no—
274C4⋊C4C22×D2312yes—
275C22⋊C4—462no—
276C22⋊C4—462no—
277C23—22no—
278C23—24no—
279C23—81no—
280C23—81no—
281C23—232no—
282C23—468no—
283C23—461no—
284C23—461no—
285C23—1842no—
286C23—1842no—
287C23D4×D2311yescharacteristic
288Q8—232no—
289Q8—462no—
290Q8—461no—
291Q8—461no—
292Q8—461no—
293D4—24no—
294D4—22no—
295D4—232no—
296D4—468no—
297D4—468no—
298D4—464no—
299D4—464no—
300D4—462no—
301D4—461no—
302D4—461no—
303D4—461no—
304D4—922no—
305D4—1842no—
306D4C2×D9214yes—
307C2×C4—22no—
308C2×C4—81no—
309C2×C4—232no—
310C2×C4—468no—
311C2×C4—461no—
312C2×C4—464no—
313C2×C4—462no—
314C2×C4—462no—
315C2×C4—461no—
316C2×C4—922no—
317C2×C4C2×D9212yes—
318C2×C4D4×D2311yescharacteristic
319C2×C4D4×D2312yes—
320C2×C4C23×D2311yescharacteristic
321C8—21no—
322C8—21no—
323C8—462no—
324C22—21no—
325C22—21no—
326C22—24no—
327C22—42no—
328C22—42no—
329C22—84no—
330C22—462no—
331C22—462no—
332C22—462no—
333C22—462no—
334C22—921no—
335C22—921no—
336C22—921no—
337C22—921no—
338C22—921no—
339C22—1848no—
340C22#1062505312yes—
341C22C2×D4×D2311yescharacteristic
342C4—42no—
343C4—462no—
344C4—462no—
345C4—921no—
346C4#1062505312yes—
347C4C22×D9211yescharacteristic
348C4C2×D4×D2311yescharacteristic
349C2—22no—
350C2—44no—
351C2—922no—
352C2—922no—
353C2—1841no—
354C2C2×#1062505311yescharacteristic
355C2#1309321811yescharacteristic
356C2#1309322311yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC2×C23×#102C2
socleC22×C23C22×D4
hypercenterC2×#102D23
hypocenterC23#3012
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
1. C2×#10625155C2semidirect
2. C2×#10625103C2semidirect
3. C2×#10625075C2semidirect
4. #13092998C2semidirect
5. #13092580C2semidirect
6. #13092569C2semidirect
7. #13092563C2semidirect
8. #13092552C2semidirect
9. #13092416C2semidirect
10. #13092383C2semidirect
11. C2×C23×#102C2semidirect
22. C2×#67288C22semidirect
23. C22×C8×C23C22semidirect
24. C2×C4⋊C4×C23C22semidirect
25. C2×#67273C22semidirect
27. C2×#67272C22semidirect
29. C2×#67267C22semidirect
30. C2×Dic92C22semidirect
32. C2×D184C22semidirect
33. C2×#67263C22semidirect
34. C2×#67263C22semidirect
36. #10625068C22semidirect
38. #10625066C22semidirect
39. C23×#102C22semidirect
40. C23×#102C22semidirect
41. (C2×D23)⋊C8C22semidirect
42. (C2×D23)⋊C8C22semidirect
43. #10624992C22semidirect
44. #10624991C22semidirect
49. C2×D4×C23D4semidirect
71. #67288D4semidirect
180. C2×#102D23semidirect
210. C22×C8C2×D23semidirect
216. C2×C4⋊C4C2×D23semidirect
219. #102C2×D23semidirect
220. #102C2×D23semidirect
223. C23#3012semidirect
253. C2×D4D92semidirect

Maximal subgroups

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

subgroupindex
C2×#106251552
C2×#106251032
C2×#106250752
#130929982
#130925802
#130925692
#130925632
#130925522
#130924162
#130923832
C2×C23×#1022
#301223