Finite Group Databasebeta

← #15682755

Subgroups — #15682755

Order 2944.

762 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 762 conjugacy classes of subgroups — too many to draw. Only its 133 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
1H(5,𝔽2)×D23C211yesmaximal, characteristic, complemented
2#13093216C212yesmaximal, complemented
3#13092985C211yesmaximal, characteristic, complemented
4#13092594C211yesmaximal, characteristic, complemented
5#13092593C212yesmaximal, complemented
6#13092587C211yesmaximal, characteristic, complemented
7#13092586C212yesmaximal, complemented
8#13092585C211yesmaximal, characteristic, complemented
9#13092432C212yesmaximal, complemented
10#100×D23C211yesmaximal, characteristic, complemented
11C23×#455C211yesmaximal, characteristic, complemented
12C23×H(5,𝔽2)C2211yescharacteristic
13#10625160—22no—
14#10625160C2212yes—
15#41×D23—22no—
16#41×D23C2212yes—
17C2×#67292C2211yescharacteristic, complemented
18#10625155—22no—
19#10625155—22no—
20#10625155C2211yescharacteristic
21C2×D4×D23—22no—
22C2×D4×D23—22no—
23C2×D4×D23C2211yescharacteristic
24C23×#137C2212yescomplemented
25C23×#124C2211yescharacteristic, complemented
26#10625120C2212yescomplemented
27#10625118C2211yescharacteristic, complemented
28#10625113C2212yescomplemented
29#10625111C2211yescharacteristic, complemented
30#10625090—22no—
31#10625089—22no—
32#10625087—22no—
33#10625085—22no—
34#10625079C2212yescomplemented
35M16×D23C2212yescomplemented
36#10625055—22no—
37#10625053—22no—
38#10625045C2211yescharacteristic, complemented
39#10625043C2211yescharacteristic, complemented
40C23×#104C2212yescomplemented
41C23×#100C2211yescharacteristic, complemented
42#10625019C2212yescomplemented
43#10625015C2211yescharacteristic, complemented
44#10625007C2212yescomplemented
45#10625005C2212yescomplemented
46#10624987C2212yescomplemented
47C23×D23—22no—
48C23×D23D412yes—
49#41×C23—22no—
50#41×C23C2312yes—
51C2×Q8×C23C2311yescharacteristic, complemented
52C2×D4×C23—22no—
53C2×D4×C23—22no—
54C2×D4×C23C2311yescharacteristic
55C2×C22⋊D23—22no—
56C2×C22⋊D23—24no—
57C2×C22⋊D23—22no—
58C2×C22⋊D23—22no—
59C2×C22⋊D23D412yes—
60#67292—22no—
61#67292—22no—
62#67292—22no—
63#67292D412yescomplemented
64Q8×D23D412yescomplemented
65#67290—24no—
66#67290—22no—
67#67290—22no—
68#67290D412yescomplemented
69D4×D23—24no—
70D4×D23—24no—
71D4×D23—24no—
72D4×D23—22no—
73D4×D23—24no—
74D4×D23—22no—
75D4×D23—22no—
76D4×D23—22no—
77D4×D23—22no—
78D4×D23D412yescomplemented
79#67288—24no—
80#67288—22no—
81#67288—22no—
82#67288C2312yes—
83C2×D92—22no—
84C2×D92—22no—
85C2×D92—21no—
86C2×D92—22no—
87C2×D92C2311yescharacteristic
88C2×D92C2311yescharacteristic, complemented
89C2×C4×D23—22no—
90C2×C4×D23—22no—
91C2×C4×D23—21no—
92C2×C4×D23C2311yescharacteristic
93Q16×C23—22no—
94SD16×C23—22no—
95M16×C23C2312yescomplemented
96C22⋊C4×C23—22no—
97C42×C23C2311yescharacteristic, complemented
98#67275—22no—
99#67274—22no—
100#67274—22no—
101#67272—22no—
102(C2×D23)⋊C4—21no—
103(C2×D23)⋊C4—22no—
104Dic23⋊C4—21no—
105C4×Dic23C2311yescharacteristic, complemented
106#67267C2312yescomplemented
107D184—22no—
108#67263—22no—
109#67262—22no—
110C8×D23—22no—
111C23×C23—22no—
112C23×C23C2×D412yes—
113C22×D23—24no—
114C22×D23—22no—
115C22×D23—22no—
116C22×D23—22no—
117C22×D23—22no—
118C22×D23—21no—
119C22×D23—82no—
120C22×D23—84no—
121C22×D23C2×D412yes—
122C22×D23C2×D411yescharacteristic
123Q8×C23—22no—
124Q8×C23C2×D412yes—
125D4×C23—24no—
126D4×C23—22no—
127D4×C23—22no—
128D4×C23C2×D412yes—
129C2×C4×C23—22no—
130C2×C4×C23—22no—
131C2×C4×C23—21no—
132C2×C4×C23—21no—
133C2×C4×C23C2411yescharacteristic
134C22⋊D23—24no—
135C22⋊D23—24no—
136C22⋊D23—22no—
137C22⋊D23—22no—
138C22⋊D23—24no—
139C22⋊D23—22no—
140C22⋊D23—82no—
141C2×Dic23—22no—
142C2×Dic23—22no—
143C2×Dic23—21no—
144C2×Dic23C2×D411yescharacteristic
145D92—24no—
146D92—22no—
147D92—22no—
148D92—22no—
149D92—41no—
150D92—41no—
151D92—82no—
152D92C2×D412yes—
153C4×D23—24no—
154C4×D23—22no—
155C4×D23—22no—
156C4×D23—22no—
157C4×D23—42no—
158C4×D23C2×D412yes—
159C4×D23C2×D412yes—
160Dic46—22no—
161Dic46C2×D412yes—
162C8×C23—22no—
163C23⋊C8—22no—
164#3019—231nomaximal, Sylow
165C22×C23—22no—
166C22×C23—22no—
167C22×C23—42no—
168C22×C23—82no—
169C22×C23C22×D411yescharacteristic
170C2×D23—22no—
171C2×D23—22no—
172C2×D23—41no—
173C2×D23—44no—
174C2×D23—44no—
175C2×D23—42no—
176C2×D23—42no—
177C2×D23—41no—
178C2×D23—82no—
179C2×D23—84no—
180C2×D23—82no—
181C2×D23#12011yescharacteristic
182C2×D23#12011yescharacteristic
183C4×C23—22no—
184C4×C23—41no—
185C4×C23—41no—
186C4×C23C22×D412yes—
187Dic23—22no—
188Dic23—41no—
189Dic23#12012yes—
190C2×H(5,𝔽2)—231no—
191#575—232no—
192#535—231no—
193#455—232no—
194#455—231no—
195#455D2311yescharacteristic, complemented
196#453—231no—
197#453—232no—
198#453—231no—
199#421—232no—
200C2×#100—231no—
201C2×C23—21no—
202C2×C23—42no—
203C2×C23—42no—
204C2×C23C2×#12011yescharacteristic
205D23—21no—
206D23—21no—
207D23—42no—
208D23—42no—
209D23—81no—
210H(5,𝔽2)—232no—
211H(5,𝔽2)—231no—
212H(5,𝔽2)—462no—
213H(5,𝔽2)—462no—
214H(5,𝔽2)—462no—
215H(5,𝔽2)C2×D2311yescharacteristic
216C2×#41—232no—
217C2×#41—231no—
218C2×#41—462no—
219C22×D4—231no—
220C22×D4—462no—
221C22×D4—462no—
222#137—232no—
223#137—462no—
224#137C2×D2312yescomplemented
225AGL(1,ℤ/8)—232no—
226AGL(1,ℤ/8)—232no—
227AGL(1,ℤ/8)—462no—
228#135—462no—
229#135—462no—
230C2×M16—232no—
231#127—231no—
232#127—231no—
233#124—231no—
234#124C2×D2311yescharacteristic, complemented
235#121—462no—
236#120—462no—
237#117—231no—
238#104—232no—
239#104—232no—
240#104—232no—
241#104C2×D2312yescomplemented
242#100—231no—
243#100—232no—
244#100C2×D2311yescharacteristic, complemented
245C23#301911yescharacteristic, complemented, Sylow
246C24—232no—
247C24—462no—
248#41—22no—
249#41—232no—
250#41—232no—
251#41—232no—
252#41—462no—
253#41—462no—
254#41—464no—
255#41—462no—
256#41—462no—
257#41—462no—
258#41—462no—
259#41—464no—
260#41—462no—
261#41C22×D2312yes—
262C2×Q8—232no—
263C2×Q8C22×D2311yescharacteristic, complemented
264C2×D4—22no—
265C2×D4—22no—
266C2×D4—232no—
267C2×D4—232no—
268C2×D4—231no—
269C2×D4—231no—
270C2×D4—462no—
271C2×D4—462no—
272C2×D4—461no—
273C2×D4—462no—
274C2×D4—462no—
275C2×D4—462no—
276C2×D4—462no—
277C2×D4—462no—
278C2×D4—464no—
279C2×D4—464no—
280C2×D4—464no—
281C2×D4—464no—
282C2×D4—464no—
283C2×D4—462no—
284C2×D4—462no—
285C2×D4—462no—
286C2×D4—462no—
287C2×D4C22×D2311yescharacteristic
288C22×C4—231no—
289C22×C4—462no—
290C22×C4—461no—
291C22×C4—462no—
292Q16—22no—
293Q16—462no—
294SD16—22no—
295SD16—462no—
296SD16—462no—
297SD16—462no—
298D8—462no—
299D8—462no—
300M16—232no—
301M16—462no—
302M16C22×D2312yescomplemented
303C2×C8—462no—
304C4⋊C4—461no—
305C22⋊C4—22no—
306C22⋊C4—461no—
307C22⋊C4—462no—
308C42—231no—
309C42C22×D2311yescharacteristic, complemented
310C23—22no—
311C23—231no—
312C23—232no—
313C23—462no—
314C23—462no—
315C23—462no—
316C23—462no—
317C23—464no—
318C23—461no—
319C23—1842no—
320C23—1844no—
321C23D4×D2312yes—
322Q8—22no—
323Q8—232no—
324Q8—462no—
325Q8D4×D2312yes—
326D4—24no—
327D4—22no—
328D4—22no—
329D4—232no—
330D4—462no—
331D4—464no—
332D4—464no—
333D4—462no—
334D4—462no—
335D4—464no—
336D4—464no—
337D4—462no—
338D4—462no—
339D4—462no—
340D4—921no—
341D4—921no—
342D4—1842no—
343D4—1842no—
344D4D4×D2312yes—
345C2×C4—22no—
346C2×C4—22no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—231no—
350C2×C4—232no—
351C2×C4—232no—
352C2×C4—462no—
353C2×C4—462no—
354C2×C4—464no—
355C2×C4—462no—
356C2×C4—462no—
357C2×C4—462no—
358C2×C4—461no—
359C2×C4—922no—
360C2×C4C23×D2311yescharacteristic
361C8—22no—
362C8—462no—
363C22—22no—
364C22—22no—
365C22—42no—
366C22—82no—
367C22—231no—
368C22—231no—
369C22—462no—
370C22—462no—
371C22—921no—
372C22—922no—
373C22—922no—
374C22—924no—
375C22—924no—
376C22—921no—
377C22—1842no—
378C22—1842no—
379C22—1844no—
380C22C2×D4×D2311yescharacteristic
381C4—22no—
382C4—41no—
383C4—41no—
384C4—232no—
385C4—462no—
386C4—921no—
387C4C2×D4×D2312yes—
388C2—21no—
389C2—42no—
390C2—42no—
391C2—461no—
392C2—461no—
393C2—922no—
394C2—922no—
395C2—1841no—
396C2#120×D2311yescharacteristic
subgroupG/H
centerC2#120×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#455C2
socleC2×C23C2×#120
hypercenter#455D23
hypocenterC23#3019
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2 ◁ C2×C4 ◁ #455

Complements

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

NH ≅ G/Ntype
1. H(5,𝔽2)×D23C2semidirect
2. #13093216C2semidirect
3. #13092985C2semidirect
4. #13092594C2semidirect
5. #13092593C2semidirect
6. #13092587C2semidirect
7. #13092586C2semidirect
8. #13092585C2semidirect
9. #13092432C2semidirect
10. #100×D23C2semidirect
11. C23×#455C2semidirect
17. C2×#67292C22semidirect
24. C23×#137C22semidirect
25. C23×#124C22semidirect
26. #10625120C22semidirect
27. #10625118C22semidirect
28. #10625113C22semidirect
29. #10625111C22semidirect
34. #10625079C22semidirect
35. M16×D23C22semidirect
38. #10625045C22semidirect
39. #10625043C22semidirect
40. C23×#104C22semidirect
41. C23×#100C22semidirect
42. #10625019C22semidirect
43. #10625015C22semidirect
44. #10625007C22semidirect
45. #10625005C22semidirect
46. #10624987C22semidirect
51. C2×Q8×C23C23semidirect
63. #67292D4semidirect
64. Q8×D23D4semidirect
68. #67290D4semidirect
78. D4×D23D4semidirect
88. C2×D92C23semidirect
95. M16×C23C23semidirect
97. C42×C23C23semidirect
105. C4×Dic23C23semidirect
106. #67267C23semidirect
195. #455D23semidirect
224. #137C2×D23semidirect
234. #124C2×D23semidirect
241. #104C2×D23semidirect
244. #100C2×D23semidirect
245. C23#3019semidirect
263. C2×Q8C22×D23semidirect
302. M16C22×D23semidirect
309. C42C22×D23semidirect

Maximal subgroups

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

subgroupindex
H(5,𝔽2)×D232
#130932162
#130929852
#130925942
#130925932
#130925872
#130925862
#130925852
#130924322
#100×D232
C23×#4552
#301923