Finite Group Databasebeta

← #15685171

Subgroups — #15685171

Order 2944.

448 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13093233C211yesmaximal, characteristic, complemented
2#13093230C211yesmaximal, characteristic, complemented
3#13093229C211yesmaximal, characteristic, complemented
4#13093226C211yesmaximal, characteristic, complemented
5#13092810C211yesmaximal, characteristic, complemented
6#13092691C211yesmaximal, characteristic, complemented
7#13092683C211yesmaximal, characteristic, complemented
8#13092681C211yesmaximal, characteristic, complemented
9#13092602C211yesmaximal, characteristic, complemented
10#13092598C211yesmaximal, characteristic, complemented
11#13092593C211yesmaximal, characteristic, complemented
12#13092592C211yesmaximal, characteristic, complemented
13#13092538C211yesmaximal, characteristic, complemented
14#13092537C211yesmaximal, characteristic, complemented
15C23×#473C211yesmaximal, characteristic, complemented
16#10625161C2211yescharacteristic
17#10625160C2211yescharacteristic
18#10625158C2211yescharacteristic
19#10625158C2211yescharacteristic, complemented
20C23×#137C2211yescharacteristic
21C23×#137C2211yescharacteristic
22C2×Q16×C23C2211yescharacteristic, complemented
23C23×#131C2211yescharacteristic
24#10625121C2211yescharacteristic
25#10625118C2211yescharacteristic
26#10625115C2211yescharacteristic, complemented
27C2×#67275C2211yescharacteristic, complemented
28#10625113C2211yescharacteristic
29#10625113C2211yescharacteristic, complemented
30C2×#67274C2211yescharacteristic
31#10625090—21no—
32#10625090—21no—
33#10625089—21no—
34#10625089—21no—
35#10625089—21no—
36#10625089—21no—
37Q16×D23—21no—
38Q16×D23—21no—
39#10625087—21no—
40#10625086—21no—
41#10625085—21no—
42SD16×D23—21no—
43#10625080—21no—
44#10625080C2211yescharacteristic
45#10625080C2211yescharacteristic, complemented
46#10625079—21no—
47#10625079C2211yescharacteristic
48#10625079C2211yescharacteristic
49#10625078C2211yescharacteristic
50#10625078C2211yescharacteristic, complemented
51#10625075—21no—
52#10625075C2211yescharacteristic
53C2×#67263—21no—
54C2×#67263C2211yescharacteristic
55#10625072C2211yescharacteristic, complemented
56C23×#108C2211yescharacteristic, complemented
57C23×#101C2211yescharacteristic, complemented
58C23×#101C2211yescharacteristic, complemented
59#10625019C2211yescharacteristic
60#10625007C2211yescharacteristic
61#10625007C2211yescharacteristic, complemented
62#10625007C2211yescharacteristic, complemented
63#10625006C2211yescharacteristic, complemented
64#10625005C2211yescharacteristic
65#10625004C2211yescharacteristic, complemented
66#10624997C2211yescharacteristic, complemented
67#41×C23C2311yescharacteristic
68C2×Q8×C23C2311yescharacteristic
69C2×Q8×C23C2311yescharacteristic
70#67292—21no—
71#67292—21no—
72#67292—21no—
73#67292—21no—
74#67292—21no—
75Q8×D23—21no—
76Q8×D23—21no—
77Q8×D23—21no—
78Q8×D23—21no—
79Q8×D23—21no—
80#67290—21no—
81#67290—41no—
82D4×D23—21no—
83D4×D23—41no—
84#67288—21no—
85#67288—21no—
86#67288—41no—
87#67288—41no—
88#67288C2311yescharacteristic
89#67288C2311yescharacteristic
90#67288C2311yescharacteristic
91C2×D92—21no—
92C2×D92C2311yescharacteristic
93C2×Dic46—21no—
94C2×Dic46C2311yescharacteristic
95Q16×C23—21no—
96Q16×C23—21no—
97Q16×C23—21no—
98Q16×C23—21no—
99SD16×C23—21no—
100SD16×C23—21no—
101M16×C23—21no—
102M16×C23C2311yescharacteristic
103M16×C23C2311yescharacteristic
104M16×C23C2311yescharacteristic
105C2×C8×C23—21no—
106C2×C8×C23C2311yescharacteristic
107#67275—21no—
108#67275—21no—
109#67275—21no—
110#67275—21no—
111#67275D411yescharacteristic
112#67274—21no—
113#67274—21no—
114#67274—21no—
115#67274—21no—
116#67274D411yescharacteristic
117#67273D411yescharacteristic
118#67272D411yescharacteristic
119(C2×D23)⋊C4—41no—
120Dic23⋊C4—41no—
121C4×Dic23C2311yescharacteristic
122#67267C2311yescharacteristic
123C2×C23⋊C8C2311yescharacteristic
124Dic92—21no—
125Dic92—21no—
126Dic92D411yescharacteristic
127D184—21no—
128D184—21no—
129D184D411yescharacteristic
130#67263—21no—
131#67263—21no—
132#67263—21no—
133#67263—21no—
134#67263—21no—
135#67263—21no—
136#67263D411yescharacteristic
137#67263D411yescharacteristic
138#67262—21no—
139#67262—21no—
140#67262—21no—
141C8×D23—21no—
142C8×D23—21no—
143C8×D23—21no—
144C22×D23—21no—
145C22×D23—41no—
146Q8×C23—21no—
147Q8×C23—21no—
148Q8×C23—21no—
149Q8×C23—21no—
150Q8×C23C2×D411yescharacteristic
151D4×C23—21no—
152D4×C23C2×D411yescharacteristic
153C2×C4×C23—21no—
154C2×C4×C23—21no—
155C2×C4×C23—21no—
156C2×C4×C23C2411yescharacteristic
157C22⋊D23—21no—
158C22⋊D23—21no—
159C22⋊D23—21no—
160C22⋊D23—41no—
161C22⋊D23—41no—
162C2×Dic23—21no—
163C2×Dic23—21no—
164C2×Dic23—41no—
165D92—21no—
166D92—21no—
167D92—41no—
168D92—41no—
169D92—41no—
170D92C2×D411yescharacteristic
171D92C2×D411yescharacteristic
172D92C2×D411yescharacteristic
173C4×D23—21no—
174C4×D23—21no—
175C4×D23—21no—
176C4×D23—41no—
177C4×D23—41no—
178C4×D23—41no—
179C4×D23—41no—
180C4×D23—41no—
181C4×D23—41no—
182Dic46—21no—
183Dic46—21no—
184Dic46—41no—
185Dic46—41no—
186Dic46—41no—
187Dic46C2×D411yescharacteristic
188Dic46C2×D411yescharacteristic
189Dic46C2×D411yescharacteristic
190C8×C23—21no—
191C8×C23—21no—
192C8×C23—21no—
193C8×C23C2×D411yescharacteristic
194C8×C23C2×D411yescharacteristic
195C23⋊C8—21no—
196C23⋊C8C2×D411yescharacteristic
197C23⋊C8C2×D411yescharacteristic
198#3289—231nomaximal, Sylow
199C22×C23—21no—
200C22×C23H(5,𝔽2)11yescharacteristic
201C2×D23—21no—
202C2×D23—21no—
203C2×D23—21no—
204C2×D23—41no—
205C2×D23—81no—
206C2×D23—161no—
207C4×C23—21no—
208C4×C23—41no—
209C4×C23—41no—
210C4×C23C22×D411yescharacteristic
211C4×C23C22×D411yescharacteristic
212Dic23—21no—
213Dic23—21no—
214Dic23—21no—
215Dic23—41no—
216Dic23—41no—
217#578—231no—
218#578—231no—
219#577—231no—
220#577—231no—
221#497—231no—
222#473—231no—
223#473D2311yescharacteristic, complemented
224#471—231no—
225#471—231no—
226#456—231no—
227#456—231no—
228#455—231no—
229#454—231no—
230#444—231no—
231#444—231no—
232C2×C23—21no—
233C2×C23—41no—
234C2×C23D4211yescharacteristic
235D23—41no—
236D23—41no—
237D23—41no—
238D23—81no—
2392−1+4—231no—
2402−1+4—231no—
2412−1+4—231no—
242H(5,𝔽2)—231no—
243#137—231no—
244#137—231no—
245#137—231no—
246#137—231no—
247#137—461no—
248#137—461no—
249#137—461no—
250#137—461no—
251#137—461no—
252#137—461no—
253#137C2×D2311yescharacteristic
254#137C2×D2311yescharacteristic
255AGL(1,ℤ/8)—231no—
256AGL(1,ℤ/8)—231no—
257AGL(1,ℤ/8)—461no—
258AGL(1,ℤ/8)—461no—
259#135—231no—
260#135—231no—
261#135—461no—
262#135—461no—
263#135—461no—
264#135—461no—
265C2×Q16—231no—
266C2×Q16—461no—
267C2×Q16—461no—
268C2×Q16C2×D2311yescharacteristic, complemented
269C2×SD16—231no—
270C2×SD16—231no—
271C2×SD16—461no—
272C2×SD16—461no—
273#131—231no—
274#131—231no—
275#131—231no—
276#131C2×D2311yescharacteristic
277C4⋊Q8—231no—
278#124—231no—
279#108—231no—
280#108C2×D2311yescharacteristic, complemented
281#104—231no—
282#104—231no—
283#104—231no—
284#104—231no—
285#101—231no—
286#101C2×D2311yescharacteristic, complemented
287#101C2×D2311yescharacteristic, complemented
288#100—231no—
289#97—231no—
290C23#328911yescharacteristic, complemented, Sylow
291#41—231no—
292#41—231no—
293#41—231no—
294#41—461no—
295#41—461no—
296#41—461no—
297#41—461no—
298#41—461no—
299#41—461no—
300#41—461no—
301#41—461no—
302#41—921no—
303#41—921no—
304#41—921no—
305#41C22×D2311yescharacteristic
306C2×Q8—231no—
307C2×Q8—461no—
308C2×Q8—461no—
309C2×Q8—461no—
310C2×Q8—461no—
311C2×Q8—461no—
312C2×Q8—461no—
313C2×Q8C22×D2311yescharacteristic
314C2×Q8C22×D2311yescharacteristic
315C2×D4—231no—
316C2×D4—461no—
317C2×D4—461no—
318C2×D4—921no—
319Q16—21no—
320Q16—21no—
321Q16—21no—
322Q16—21no—
323Q16—231no—
324Q16—231no—
325Q16—461no—
326Q16—461no—
327Q16—461no—
328Q16—461no—
329Q16—461no—
330Q16—461no—
331SD16—21no—
332SD16—21no—
333SD16—231no—
334SD16—231no—
335SD16—231no—
336SD16—231no—
337SD16—461no—
338SD16—461no—
339SD16—461no—
340SD16—461no—
341SD16—461no—
342SD16—461no—
343SD16—461no—
344SD16—461no—
345SD16—461no—
346SD16—461no—
347D8—231no—
348D8—231no—
349D8—461no—
350D8—461no—
351M16—21no—
352M16—231no—
353M16—461no—
354M16—461no—
355M16—461no—
356M16C22×D2311yescharacteristic
357M16C22×D2311yescharacteristic
358M16C22×D2311yescharacteristic
359C2×C8—21no—
360C2×C8—231no—
361C2×C8—461no—
362C2×C8—461no—
363C2×C8—461no—
364C2×C8C22×D2311yescharacteristic
365C4⋊C4—921no—
366C22⋊C4—921no—
367C42—231no—
368C23—461no—
369C23—921no—
370Q8—21no—
371Q8—21no—
372Q8—21no—
373Q8—21no—
374Q8—231no—
375Q8—231no—
376Q8—231no—
377Q8—461no—
378Q8—461no—
379Q8—921no—
380Q8—921no—
381Q8—921no—
382Q8D4×D2311yescharacteristic
383D4—21no—
384D4—231no—
385D4—231no—
386D4—231no—
387D4—461no—
388D4—461no—
389D4—461no—
390D4—461no—
391D4—461no—
392D4—921no—
393D4—921no—
394D4—921no—
395D4—921no—
396D4—921no—
397D4D4×D2311yescharacteristic
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—461no—
402C2×C4—461no—
403C2×C4—461no—
404C2×C4—461no—
405C2×C4—461no—
406C2×C4—921no—
407C2×C4—921no—
408C2×C4—921no—
409C2×C4—921no—
410C2×C4—921no—
411C2×C4—921no—
412C2×C4—921no—
413C2×C4C23×D2311yescharacteristic
414C8—21no—
415C8—21no—
416C8—21no—
417C8—231no—
418C8—231no—
419C8—461no—
420C8D4×D2311yescharacteristic
421C8D4×D2311yescharacteristic
422C22—21no—
423C22—461no—
424C22—461no—
425C22—461no—
426C22—921no—
427C22—3681no—
428C22—1841no—
429C22#1062516011yescharacteristic
430C4—21no—
431C4—41no—
432C4—41no—
433C4—461no—
434C4—461no—
435C4—461no—
436C4—921no—
437C4—921no—
438C4C2×D4×D2311yescharacteristic
439C4C2×D4×D2311yescharacteristic
440C2—21no—
441C2—41no—
442C2—921no—
443C2—921no—
444C2—921no—
445C2—1841no—
446C2#1309305111yescharacteristic
subgroupG/H
centerC2#13093051
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#473C2
socleC2×C23D42
hypercenter#473D23
hypocenterC23#3289
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2 ◁ C2×C4 ◁ #473

Complements

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

NH ≅ G/Ntype
1. #13093233C2semidirect
2. #13093230C2semidirect
3. #13093229C2semidirect
4. #13093226C2semidirect
5. #13092810C2semidirect
6. #13092691C2semidirect
7. #13092683C2semidirect
8. #13092681C2semidirect
9. #13092602C2semidirect
10. #13092598C2semidirect
11. #13092593C2semidirect
12. #13092592C2semidirect
13. #13092538C2semidirect
14. #13092537C2semidirect
15. C23×#473C2semidirect
19. #10625158C22semidirect
22. C2×Q16×C23C22semidirect
26. #10625115C22semidirect
27. C2×#67275C22semidirect
29. #10625113C22semidirect
45. #10625080C22semidirect
50. #10625078C22semidirect
55. #10625072C22semidirect
56. C23×#108C22semidirect
57. C23×#101C22semidirect
58. C23×#101C22semidirect
61. #10625007C22semidirect
62. #10625007C22semidirect
63. #10625006C22semidirect
65. #10625004C22semidirect
66. #10624997C22semidirect
223. #473D23semidirect
268. C2×Q16C2×D23semidirect
280. #108C2×D23semidirect
286. #101C2×D23semidirect
287. #101C2×D23semidirect
290. C23#3289semidirect

Maximal subgroups

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

subgroupindex
#130932332
#130932302
#130932292
#130932262
#130928102
#130926912
#130926832
#130926812
#130926022
#130925982
#130925932
#130925922
#130925382
#130925372
C23×#4732
#328923