Finite Group Databasebeta

← #15682752

Subgroups — #15682752

Order 2944.

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

normal subgroups only

This group has 762 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×#10625160C211yesmaximal, characteristic, complemented
2#13093215C211yesmaximal, characteristic, complemented
3#13092981C211yesmaximal, characteristic, complemented
4#13092593C214yesmaximal, complemented
5#13092583C214yesmaximal, complemented
6#13092434C211yesmaximal, characteristic, complemented
7#13092433C211yesmaximal, characteristic, complemented
8C2×#10625005C211yesmaximal, characteristic, complemented
9C23×#575C211yesmaximal, characteristic, complemented
10C2×#41×C23C2211yescharacteristic
11C2×#41×C23C2211yescharacteristic, complemented
12#10625160—22no—
13#10625160—22no—
14#10625160—22no—
15#10625160C2214yes—
16C2×#67292—21no—
17C2×D4×D23—22no—
18C2×D4×D23—21no—
19C2×#67288—21no—
20C2×#67288C2211yescharacteristic
21C22×D92—21no—
22C22×D92C2211yescharacteristic
23C23×#137—21no—
24C23×#137C2212yescomplemented
25C23×AGL(1,ℤ/8)—21no—
26C23×AGL(1,ℤ/8)C2212yescomplemented
27C23×#135—22no—
28C2×M16×C23C2211yescharacteristic, complemented
29#10625122—21no—
30#10625121—22no—
31#10625120—21no—
32#10625118C2212yescomplemented
33#10625113C2212yescomplemented
34#10625111C2212yescomplemented
35#10625108—22no—
36#10625103C2212yescomplemented
37#10625101—22no—
38#10625097C2211yescharacteristic, complemented
39C2×#67267C2211yescharacteristic, complemented
40#10625019C2214yescomplemented
41#10625007C2214yescomplemented
42#10625005C2214yescomplemented
43C23×D23—22no—
44C23×D23D412yes—
45#41×C23—21no—
46#41×C23—21no—
47#41×C23—21no—
48#41×C23—21no—
49#41×C23—21no—
50#41×C23—21no—
51#41×C23D412yescomplemented
52#41×C23C2312yes—
53C2×Q8×C23D411yescharacteristic, complemented
54C2×Q8×C23C2311yescharacteristic, complemented
55C2×D4×C23—21no—
56C2×D4×C23—21no—
57C2×D4×C23D411yescharacteristic, complemented
58C2×D4×C23C2311yescharacteristic, complemented
59C22×C4×C23—21no—
60C22×C4×C23—21no—
61C22×C4×C23C2311yescharacteristic
62C2×C22⋊D23—22no—
63C2×C22⋊D23—21no—
64C2×C22⋊D23—24no—
65#67292—24no—
66#67292—24no—
67D4×D23—28no—
68D4×D23—24no—
69D4×D23—28no—
70D4×D23—24no—
71#67288—24no—
72#67288—21no—
73#67288—21no—
74#67288—24no—
75#67288D412yescomplemented
76#67288C2312yes—
77C2×D92—22no—
78C2×D92—24no—
79C2×D92—21no—
80C2×D92—21no—
81C2×D92—21no—
82C2×D92—21no—
83C2×D92—24no—
84C2×D92D412yes—
85C2×D92D411yescharacteristic, complemented
86C2×D92C2312yes—
87C2×C4×D23—22no—
88C2×C4×D23—21no—
89C2×Dic46D411yescharacteristic, complemented
90Q16×C23—22no—
91SD16×C23—22no—
92SD16×C23—22no—
93D8×C23—22no—
94M16×C23—21no—
95M16×C23C2312yescomplemented
96C2×C8×C23—21no—
97C22⋊Dic23—21no—
98#67275—22no—
99#67274—22no—
100#67273—22no—
101#67272—22no—
102(C2×D23)⋊C4—24no—
103C4⋊Dic23—21no—
104C4×Dic23C2312yescomplemented
105#67267—21no—
106#67267C2312yescomplemented
107C2×C23⋊C8—21no—
108C23×C23—21no—
109C23×C23—21no—
110C23×C23C2×D411yescharacteristic
111C22×D23—22no—
112C22×D23—21no—
113C22×D23—28no—
114C22×D23—22no—
115C22×D23—82no—
116C22×D23—84no—
117C22×D23C2×D414yes—
118Q8×C23—21no—
119Q8×C23—21no—
120Q8×C23—21no—
121Q8×C23C2×D412yes—
122D4×C23—22no—
123D4×C23—22no—
124D4×C23—21no—
125D4×C23—21no—
126D4×C23—21no—
127D4×C23—41no—
128D4×C23—41no—
129D4×C23C2×D412yes—
130C2×C4×C23—21no—
131C2×C4×C23—22no—
132C2×C4×C23—22no—
133C2×C4×C23—21no—
134C2×C4×C23—41no—
135C2×C4×C23—41no—
136C2×C4×C23C2×D411yescharacteristic
137C2×C4×C23C2×D411yescharacteristic
138C2×C4×C23C2×D411yescharacteristic
139C2×C4×C23C2×D411yescharacteristic
140C2×C4×C23C2×D411yescharacteristic
141C2×C4×C23C2411yescharacteristic
142C22⋊D23—28no—
143C22⋊D23—22no—
144C22⋊D23—22no—
145C22⋊D23—84no—
146C2×Dic23—21no—
147C2×Dic23—22no—
148D92—28no—
149D92—22no—
150D92—21no—
151D92—22no—
152D92—22no—
153D92—22no—
154D92C2×D412yes—
155C4×D23—28no—
156C4×D23—22no—
157C4×D23—22no—
158Dic46—21no—
159Dic46C2×D412yes—
160C8×C23—22no—
161C23⋊C8—22no—
162#3019—231nomaximal, Sylow
163C22×C23—22no—
164C22×C23—41no—
165C22×C23—42no—
166C22×C23—42no—
167C22×C23—41no—
168C22×C23#12011yescharacteristic
169C22×C23#12011yescharacteristic
170C22×C23C22×D411yescharacteristic
171C2×D23—24no—
172C2×D23—22no—
173C2×D23—44no—
174C2×D23—42no—
175C2×D23—44no—
176C2×D23—82no—
177C2×D23—88no—
178C4×C23—22no—
179C4×C23—41no—
180C4×C23#12011yescharacteristic
181C4×C23#12011yescharacteristic
182C4×C23C22×D411yescharacteristic
183C4×C23C22×D411yescharacteristic
184Dic23—22no—
185Dic23—42no—
186C2×H(5,𝔽2)—231no—
187#575—231no—
188#575D2311yescharacteristic, complemented
189#535—231no—
190#455—234no—
191#453—234no—
192#421—231no—
193#421—231no—
194C2×#100—231no—
195C2×C23—21no—
196C2×C23—21no—
197C2×C23—21no—
198C2×C23—42no—
199C2×C23—81no—
200C2×C23C2×#12011yescharacteristic
201D23—44no—
202D23—42no—
203H(5,𝔽2)—234no—
204H(5,𝔽2)—462no—
205H(5,𝔽2)—462no—
206H(5,𝔽2)—462no—
207C2×#41—231no—
208C2×#41—461no—
209C2×#41—461no—
210C2×#41C2×D2311yescharacteristic
211C2×#41C2×D2311yescharacteristic, complemented
212C22×D4—231no—
213C22×D4—461no—
214C22×D4—462no—
215C22×D4—461no—
216#137—21no—
217#137—232no—
218#137—461no—
219#137C2×D2312yescomplemented
220AGL(1,ℤ/8)—21no—
221AGL(1,ℤ/8)—232no—
222AGL(1,ℤ/8)—461no—
223AGL(1,ℤ/8)C2×D2312yescomplemented
224#135—22no—
225#135—462no—
226C2×M16—231no—
227C2×M16C2×D2311yescharacteristic, complemented
228#127—232no—
229#124—232no—
230#121—462no—
231#120—462no—
232#117—231no—
233#104—234no—
234#104—234no—
235#100—234no—
236C23#301911yescharacteristic, complemented, Sylow
237C24—232no—
238C24—462no—
239#41—21no—
240#41—21no—
241#41—21no—
242#41—21no—
243#41—21no—
244#41—21no—
245#41—232no—
246#41—232no—
247#41—464no—
248#41—464no—
249#41—464no—
250#41—464no—
251#41—461no—
252#41—461no—
253#41C22⋊D2312yescomplemented
254#41C22×D2312yes—
255C2×Q8—231no—
256C2×Q8C22⋊D2311yescharacteristic, complemented
257C2×Q8C22×D2311yescharacteristic, complemented
258C2×D4—21no—
259C2×D4—21no—
260C2×D4—231no—
261C2×D4—232no—
262C2×D4—232no—
263C2×D4—464no—
264C2×D4—462no—
265C2×D4—464no—
266C2×D4—468no—
267C2×D4—468no—
268C2×D4—464no—
269C2×D4—462no—
270C2×D4—461no—
271C2×D4—464no—
272C2×D4—464no—
273C2×D4—461no—
274C2×D4—461no—
275C2×D4—461no—
276C2×D4—461no—
277C2×D4C22⋊D2311yescharacteristic, complemented
278C2×D4C22×D2311yescharacteristic, complemented
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—462no—
282C22×C4—461no—
283C22×C4C22×D2311yescharacteristic
284Q16—22no—
285Q16—462no—
286SD16—22no—
287SD16—22no—
288SD16—462no—
289SD16—462no—
290D8—22no—
291D8—462no—
292M16—21no—
293M16—232no—
294M16—461no—
295M16C22×D2312yescomplemented
296C2×C8—21no—
297C2×C8—461no—
298C4⋊C4—461no—
299C22⋊C4—464no—
300C22⋊C4—461no—
301C42—232no—
302C23—21no—
303C23—21no—
304C23—234no—
305C23—468no—
306C23—461no—
307C23—462no—
308C23—462no—
309C23—1842no—
310C23—1844no—
311C23D4×D2311yescharacteristic
312Q8—21no—
313Q8—21no—
314Q8—21no—
315Q8—232no—
316Q8—461no—
317Q8C2×C22⋊D2312yes—
318D4—22no—
319D4—22no—
320D4—21no—
321D4—21no—
322D4—21no—
323D4—41no—
324D4—41no—
325D4—232no—
326D4—468no—
327D4—468no—
328D4—462no—
329D4—462no—
330D4—461no—
331D4—462no—
332D4—462no—
333D4—462no—
334D4—462no—
335D4—1844no—
336D4C2×C22⋊D2312yes—
337C2×C4—21no—
338C2×C4—22no—
339C2×C4—22no—
340C2×C4—21no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—468no—
344C2×C4—461no—
345C2×C4—462no—
346C2×C4—462no—
347C2×C4—462no—
348C2×C4D4×D2311yescharacteristic
349C2×C4D4×D2311yescharacteristic
350C2×C4D4×D2311yescharacteristic
351C2×C4C2×C22⋊D2311yescharacteristic
352C2×C4C2×C22⋊D2311yescharacteristic
353C2×C4C23×D2311yescharacteristic
354C8—22no—
355C8—462no—
356C22—22no—
357C22—41no—
358C22—42no—
359C22—42no—
360C22—41no—
361C22—462no—
362C22—464no—
363C22—924no—
364C22—924no—
365C22—922no—
366C22—1842no—
367C22—1848no—
368C22#1062510811yescharacteristic
369C22#1062510811yescharacteristic
370C22C2×D4×D2311yescharacteristic
371C4—22no—
372C4—41no—
373C4—462no—
374C4—922no—
375C4#1062510811yescharacteristic
376C4#1062510811yescharacteristic
377C4C2×D4×D2311yescharacteristic
378C4C22×C22⋊D2311yescharacteristic
379C2—21no—
380C2—21no—
381C2—21no—
382C2—42no—
383C2—81no—
384C2—924no—
385C2—922no—
386C2C2×#1062510811yescharacteristic
subgroupG/H
centerC2C2×#10625108
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#575C2
socleC2×C23C2×#120
hypercenter#575D23
hypocenterC23#3019
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2 ◁ C22×C4 ◁ #575

Complements

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

NH ≅ G/Ntype
1. C2×#10625160C2semidirect
2. #13093215C2semidirect
3. #13092981C2semidirect
4. #13092593C2semidirect
5. #13092583C2semidirect
6. #13092434C2semidirect
7. #13092433C2semidirect
8. C2×#10625005C2semidirect
9. C23×#575C2semidirect
11. C2×#41×C23C22semidirect
24. C23×#137C22semidirect
26. C23×AGL(1,ℤ/8)C22semidirect
28. C2×M16×C23C22semidirect
32. #10625118C22semidirect
33. #10625113C22semidirect
34. #10625111C22semidirect
36. #10625103C22semidirect
38. #10625097C22semidirect
39. C2×#67267C22semidirect
40. #10625019C22semidirect
41. #10625007C22semidirect
42. #10625005C22semidirect
51. #41×C23D4semidirect
53. C2×Q8×C23D4semidirect
54. C2×Q8×C23C23semidirect
57. C2×D4×C23D4semidirect
58. C2×D4×C23C23semidirect
75. #67288D4semidirect
85. C2×D92D4semidirect
89. C2×Dic46D4semidirect
95. M16×C23C23semidirect
104. C4×Dic23C23semidirect
106. #67267C23semidirect
188. #575D23semidirect
211. C2×#41C2×D23semidirect
219. #137C2×D23semidirect
223. AGL(1,ℤ/8)C2×D23semidirect
227. C2×M16C2×D23semidirect
236. C23#3019semidirect
253. #41C22⋊D23semidirect
256. C2×Q8C22⋊D23semidirect
257. C2×Q8C22×D23semidirect
277. C2×D4C22⋊D23semidirect
278. C2×D4C22×D23semidirect
295. M16C22×D23semidirect

Maximal subgroups

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

subgroupindex
C2×#106251602
#130932152
#130929812
#130925932
#130925832
#130924342
#130924332
C2×#106250052
C23×#5752
#301923