Finite Group Databasebeta

← #15682703

Subgroups — #15682703

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×#10625160C211yesmaximal, characteristic, complemented
2C2×#10625079C211yesmaximal, characteristic, complemented
3C2×#10625121C211yesmaximal, characteristic, complemented
4#13092998C211yesmaximal, characteristic, complemented
5#13092582C212yesmaximal, complemented
6#13092569C212yesmaximal, complemented
7#13092565C212yesmaximal, complemented
8#13092552C212yesmaximal, complemented
9C2×#10624991C211yesmaximal, characteristic, complemented
10#13092385C211yesmaximal, characteristic, complemented
11C23×#417C211yesmaximal, characteristic, complemented
12C2×#41×C23C2211yescharacteristic
13#10625160—24no—
14#10625160—24no—
15C2×#67292C2212yes—
16C2×D4×D23—22no—
17C2×D4×D23C2212yes—
18C2×#67288—21no—
19C2×#67288C2211yescharacteristic
20C2×#67288C2211yescharacteristic, complemented
21C22×D92—21no—
22C22×D92C2211yescharacteristic
23C2×M16×C23C2211yescharacteristic, complemented
24C2×C4⋊C4×C23C2211yescharacteristic, complemented
25#10625121—24no—
26C2×#67275C2211yescharacteristic, complemented
27C2×#67274C2211yescharacteristic, complemented
28C2×#67273C2211yescharacteristic, complemented
29C2×#67272C2211yescharacteristic, complemented
30#10625101—22no—
31C22×C23⋊C8C2211yescharacteristic, complemented
32#10625079—24no—
33C2×D184C2212yescomplemented
34C2×#67263C2212yescomplemented
35#10625068—21no—
36#10625068C2212yescomplemented
37#10625066—21no—
38#10625066C2212yescomplemented
39C23×#103C2212yescomplemented
40C23×#102C2212yescomplemented
41(C2×D23)⋊C8C2212yescomplemented
42(C2×D23)⋊C8C2212yescomplemented
43#10624991C2212yescomplemented
44#10624991C2212yescomplemented
45C23×D23—21no—
46C23×D23—22no—
47#41×C23—22no—
48#41×C23D414yescomplemented
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—22no—
57C2×C22⋊D23D412yes—
58#67292—24no—
59#67292—24no—
60D4×D23—216no—
61D4×D23—24no—
62D4×D23—24no—
63#67288—28no—
64#67288—22no—
65#67288—22no—
66#67288—22no—
67#67288—22no—
68C2×D92—28no—
69C2×D92—22no—
70C2×D92—21no—
71C2×D92—22no—
72C2×D92—22no—
73C2×D92D411yescharacteristic
74C2×D92D414yescomplemented
75C2×D92C2311yescharacteristic
76C2×D92C2312yes—
77C2×C4×D23—22no—
78C2×C4×D23—21no—
79C2×C4×D23C2312yes—
80C2×Dic46D411yescharacteristic
81C2×Dic46C2311yescharacteristic
82M16×C23—22no—
83C2×C8×C23C2312yes—
84C4⋊C4×C23—21no—
85C4⋊C4×C23C2312yes—
86#67275—22no—
87#67274—22no—
88#67273—22no—
89#67272—22no—
90(C2×D23)⋊C4—22no—
91(C2×D23)⋊C4—22no—
92C4⋊Dic23—22no—
93C2×C23⋊C8—22no—
94C2×C23⋊C8C2311yescharacteristic
95C2×C23⋊C8C2311yescharacteristic
96D184—24no—
97#67263—24no—
98C23×C23—21no—
99C23×C23C2×D411yescharacteristic
100C22×D23—22no—
101C22×D23—28no—
102C22×D23—24no—
103C22×D23—21no—
104C22×D23—82no—
105C22×D23—82no—
106C22×D23—81no—
107C22×D23—81no—
108C22×D23C2×D412yes—
109Q8×C23—21no—
110Q8×C23C2×D412yes—
111D4×C23—24no—
112D4×C23—21no—
113D4×C23C2×D412yes—
114C2×C4×C23—21no—
115C2×C4×C23—24no—
116C2×C4×C23—22no—
117C2×C4×C23—81no—
118C2×C4×C23C2×D412yes—
119C2×C4×C23C2×D411yescharacteristic
120C2×C4×C23C2×D412yes—
121C2×C4×C23C2411yescharacteristic
122C22⋊D23—28no—
123C22⋊D23—24no—
124C22⋊D23—42no—
125C2×Dic23—21no—
126C2×Dic23C2×D412yes—
127D92—28no—
128D92—22no—
129D92—24no—
130D92—22no—
131D92—21no—
132D92—21no—
133D92—82no—
134D92C2×D414yes—
135C4×D23—28no—
136C4×D23—22no—
137C4×D23—22no—
138C4×D23—42no—
139Dic46—22no—
140Dic46—21no—
141Dic46—21no—
142C8×C23—22no—
143C23⋊C8—21no—
144C23⋊C8—21no—
145#3012—231nomaximal, Sylow
146C22×C23—21no—
147C22×C23—21no—
148C22×C23—22no—
149C22×C23—41no—
150C22×C23—41no—
151C22×C23#12012yes—
152C22×C23C22×D411yescharacteristic
153C2×D23—22no—
154C2×D23—24no—
155C2×D23—22no—
156C2×D23—22no—
157C2×D23—42no—
158C2×D23—42no—
159C2×D23—41no—
160C2×D23—41no—
161C2×D23—41no—
162C2×D23—84no—
163C2×D23—88no—
164C4×C23—22no—
165C4×C23—42no—
166C4×C23#12012yes—
167C4×C23C22×D411yescharacteristic
168C4×C23C22×D411yescharacteristic
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#417D2311yescharacteristic, complemented
180C2×#102—231no—
181#408—231no—
182C2×C23—22no—
183C2×C23—42no—
184C2×C23C2×#12011yescharacteristic
185C2×C23#57611yescharacteristic
186C2×C23#57711yescharacteristic
187D23—42no—
188D23—44no—
189D23—81no—
190H(5,𝔽2)—464no—
191H(5,𝔽2)—464no—
192C2×#41—231no—
193C2×#41—232no—
194C2×#41—231no—
195C2×#41—461no—
196C2×#41C2×D2311yescharacteristic
197C22×D4—232no—
198C22×D4—231no—
199C22×D4—461no—
200C22×D4—462no—
201AGL(1,ℤ/8)—464no—
202#135—464no—
203C2×Q16—231no—
204C2×SD16—231no—
205C2×SD16—231no—
206C2×SD16—232no—
207C2×D8—231no—
208C2×D8—232no—
209C2×M16C2×D2311yescharacteristic, complemented
210C22×C8—231no—
211C22⋊Q8—232no—
212C22⋊Q8—461no—
213#121—232no—
214#121—461no—
215#121—462no—
216C2×C4⋊C4C2×D2311yescharacteristic, complemented
217#103C2×D2312yescomplemented
218#102—232no—
219#102—232no—
220#102C2×D2312yescomplemented
221C22⋊C8—232no—
222C22⋊C8—232no—
223C23#301211yescharacteristic, complemented, Sylow
224C24—462no—
225C24—461no—
226#41—22no—
227#41—468no—
228#41—464no—
229#41—464no—
230#41—462no—
231#41—462no—
232#41—462no—
233#41—462no—
234#41D9214yescomplemented
235C2×Q8—231no—
236C2×Q8—231no—
237C2×Q8C22×D2311yescharacteristic
238C2×D4—21no—
239C2×D4—232no—
240C2×D4—234no—
241C2×D4—231no—
242C2×D4—232no—
243C2×D4—231no—
244C2×D4—462no—
245C2×D4—468no—
246C2×D4—462no—
247C2×D4—462no—
248C2×D4—464no—
249C2×D4—4616no—
250C2×D4—464no—
251C2×D4—461no—
252C2×D4—462no—
253C2×D4—461no—
254C2×D4C22×D2311yescharacteristic
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—232no—
258C22×C4—462no—
259C22×C4—461no—
260C22×C4C22×D2311yescharacteristic
261Q16—462no—
262SD16—464no—
263SD16—462no—
264SD16—462no—
265D8—464no—
266D8—462no—
267M16—22no—
268C2×C8—231no—
269C2×C8—231no—
270C2×C8—462no—
271C2×C8C22×D2312yes—
272C4⋊C4—21no—
273C4⋊C4—462no—
274C4⋊C4C22×D2312yes—
275C22⋊C4—462no—
276C22⋊C4—462no—
277C23—21no—
278C23—232no—
279C23—468no—
280C23—462no—
281C23—464no—
282C23—461no—
283C23—1841no—
284C23—1841no—
285C23—1842no—
286C23—1842no—
287C23D4×D2311yescharacteristic
288Q8—21no—
289Q8—462no—
290Q8—461no—
291Q8—461no—
292Q8C2×D9212yes—
293D4—24no—
294D4—21no—
295D4—234no—
296D4—468no—
297D4—468no—
298D4—464no—
299D4—464no—
300D4—462no—
301D4—462no—
302D4—461no—
303D4—461no—
304D4—922no—
305D4—1842no—
306D4C2×D9212yes—
307C2×C4—21no—
308C2×C4—24no—
309C2×C4—22no—
310C2×C4—81no—
311C2×C4—232no—
312C2×C4—468no—
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—22no—
322C8—461no—
323C8—461no—
324C22—21no—
325C22—21no—
326C22—22no—
327C22—41no—
328C22—41no—
329C22—464no—
330C22—462no—
331C22—462no—
332C22—462no—
333C22—922no—
334C22—922no—
335C22—921no—
336C22—921no—
337C22—921no—
338C22—1844no—
339C22—1848no—
340C22#1062505312yes—
341C22C2×D4×D2311yescharacteristic
342C4—22no—
343C4—42no—
344C4—462no—
345C4—921no—
346C4#1062505312yes—
347C4C22×D9211yescharacteristic
348C4C2×D4×D2311yescharacteristic
349C2—22no—
350C2—42no—
351C2—922no—
352C2—924no—
353C2—1841no—
354C2C2×#1062505311yescharacteristic
355C2#1309322111yescharacteristic
356C2#1309322611yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#417C2
socleC22×C23C22×D4
hypercenter#417D23
hypocenterC23#3012
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×#10625160C2semidirect
2. C2×#10625079C2semidirect
3. C2×#10625121C2semidirect
4. #13092998C2semidirect
5. #13092582C2semidirect
6. #13092569C2semidirect
7. #13092565C2semidirect
8. #13092552C2semidirect
9. C2×#10624991C2semidirect
10. #13092385C2semidirect
11. C23×#417C2semidirect
20. C2×#67288C22semidirect
23. C2×M16×C23C22semidirect
24. C2×C4⋊C4×C23C22semidirect
26. C2×#67275C22semidirect
27. C2×#67274C22semidirect
28. C2×#67273C22semidirect
29. C2×#67272C22semidirect
31. C22×C23⋊C8C22semidirect
33. C2×D184C22semidirect
34. C2×#67263C22semidirect
36. #10625068C22semidirect
38. #10625066C22semidirect
39. C23×#103C22semidirect
40. C23×#102C22semidirect
41. (C2×D23)⋊C8C22semidirect
42. (C2×D23)⋊C8C22semidirect
43. #10624991C22semidirect
44. #10624991C22semidirect
48. #41×C23D4semidirect
74. C2×D92D4semidirect
179. #417D23semidirect
209. C2×M16C2×D23semidirect
216. C2×C4⋊C4C2×D23semidirect
217. #103C2×D23semidirect
220. #102C2×D23semidirect
223. C23#3012semidirect
234. #41D92semidirect

Maximal subgroups

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

subgroupindex
C2×#106251602
C2×#106250792
C2×#106251212
#130929982
#130925822
#130925692
#130925652
#130925522
C2×#106249912
#130923852
C23×#4172
#301223