Finite Group Databasebeta

← #15684890

Subgroups — #15684890

Order 2944.

546 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10625103C211yesmaximal, characteristic, complemented
2C2×SD16×D23C211yesmaximal, characteristic, complemented
3#13093077C211yesmaximal, characteristic, complemented
4D4×C22⋊D23C211yesmaximal, characteristic, complemented
5#13092803C211yesmaximal, characteristic, complemented
6#13092665C211yesmaximal, characteristic, complemented
7#13092652C211yesmaximal, characteristic, complemented
8#13092634C211yesmaximal, characteristic, complemented
9#13092616C211yesmaximal, characteristic, complemented
10#13092564C211yesmaximal, characteristic, complemented
11#13092554C211yesmaximal, characteristic, complemented
12#13092552C211yesmaximal, characteristic, complemented
13#13092514C211yesmaximal, characteristic, complemented
14#13092491C211yesmaximal, characteristic, complemented
15C23×#450C211yesmaximal, characteristic, complemented
16C22×D4×C23C2211yescharacteristic
17C22×C22⋊D23—21no—
18C2×Q8×D23C2211yescharacteristic, complemented
19C2×D4×D23C2211yescharacteristic
20C2×#67288C2211yescharacteristic, complemented
21C2×SD16×C23C2211yescharacteristic
22C2×SD16×C23C2211yescharacteristic, complemented
23C23×C22⋊Q8C2211yescharacteristic, complemented
24#10625124—21no—
25#10625118C2211yescharacteristic, complemented
26C2×#67274C2211yescharacteristic, complemented
27#10625111C2211yescharacteristic
28#10625110—21no—
29#10625109C2211yescharacteristic
30#10625108—21no—
31D4×Dic23C2211yescharacteristic
32C2×#67273C2211yescharacteristic
33C2×#67273C2211yescharacteristic, complemented
34#10625103—24no—
35C2×#67272C2211yescharacteristic
36C2×#67272C2211yescharacteristic, complemented
37#10625101C2211yescharacteristic
38C4×C22⋊D23C2211yescharacteristic
39C2×#67267C2211yescharacteristic, complemented
40SD16×D23—24no—
41C2×D184C2211yescharacteristic, complemented
42C2×#67263C2211yescharacteristic, complemented
43C2×C8×D23C2211yescharacteristic, complemented
44#10625067—21no—
45#10625066C2211yescharacteristic, complemented
46#10625064—21no—
47#10625058C2211yescharacteristic, complemented
48#10625056—21no—
49#10625055—21no—
50C23×#102C2211yescharacteristic
51C23×#102C2211yescharacteristic, complemented
52C23×C22⋊C8C2211yescharacteristic, complemented
53#10625017C2211yescharacteristic, complemented
54#10625003C2211yescharacteristic, complemented
55(C2×D23)⋊C8C2211yescharacteristic, complemented
56#10624998C2211yescharacteristic, complemented
57#10624997C2211yescharacteristic, complemented
58Dic23⋊C8C2211yescharacteristic, complemented
59#10624991C2211yescharacteristic, complemented
60#10624989C2211yescharacteristic, complemented
61C24×C23—21no—
62C23×D23—21no—
63C2×Q8×C23C2311yescharacteristic
64C2×D4×C23—22no—
65C2×D4×C23—21no—
66C2×D4×C23—41no—
67C2×D4×C23C2311yescharacteristic
68C2×D4×C23C2311yescharacteristic
69C22×C4×C23C2311yescharacteristic
70C2×C22⋊D23—21no—
71C2×C22⋊D23—21no—
72C2×C22⋊D23—21no—
73C2×C22⋊D23—21no—
74C2×C22⋊D23—21no—
75C2×C22⋊D23—21no—
76C2×C22⋊D23—44no—
77C2×C22⋊D23D411yescharacteristic
78C22×Dic23—21no—
79Q8×D23—22no—
80Q8×D23—41no—
81D4×D23—22no—
82D4×D23—41no—
83#67288—22no—
84#67288—41no—
85C2×D92—21no—
86C2×D92C2311yescharacteristic
87C2×D92C2311yescharacteristic
88C2×C4×D23—21no—
89C2×C4×D23—21no—
90C2×C4×D23C2311yescharacteristic
91C2×Dic46—21no—
92C2×Dic46C2311yescharacteristic
93SD16×C23—22no—
94SD16×C23—41no—
95C2×C8×C23C2311yescharacteristic
96C2×C8×C23C2311yescharacteristic
97C4⋊C4×C23—21no—
98C4⋊C4×C23C2311yescharacteristic
99C22⋊C4×C23—21no—
100C22⋊Dic23—21no—
101C22⋊Dic23—21no—
102C22⋊Dic23D411yescharacteristic
103#67274—22no—
104#67273—22no—
105#67273D414yescomplemented
106#67272—22no—
107#67272—22no—
108(C2×D23)⋊C4—21no—
109(C2×D23)⋊C4—21no—
110(C2×D23)⋊C4—21no—
111(C2×D23)⋊C4—21no—
112(C2×D23)⋊C4D411yescharacteristic
113C4⋊Dic23C2311yescharacteristic
114Dic23⋊C4—21no—
115Dic23⋊C4D411yescharacteristic
116C4×Dic23—21no—
117C4×Dic23C2311yescharacteristic
118#67267—22no—
119C2×C23⋊C8C2311yescharacteristic
120C2×C23⋊C8C2311yescharacteristic
121D184—41no—
122#67263—22no—
123C8×D23—22no—
124C23×C23—21no—
125C23×C23—21no—
126C23×C23—42no—
127C23×C23—42no—
128C23×C23—81no—
129C23×C23C2×D411yescharacteristic
130C22×D23—21no—
131C22×D23—21no—
132C22×D23—42no—
133C22×D23—42no—
134C22×D23—81no—
135C22×D23C2×D411yescharacteristic
136Q8×C23—21no—
137Q8×C23—21no—
138D4×C23—21no—
139D4×C23—21no—
140D4×C23—21no—
141D4×C23—42no—
142D4×C23C2×D412yes—
143C2×C4×C23—21no—
144C2×C4×C23—21no—
145C2×C4×C23—21no—
146C2×C4×C23—21no—
147C2×C4×C23C2×D411yescharacteristic
148C2×C4×C23C2411yescharacteristic
149C22⋊D23—22no—
150C22⋊D23—42no—
151C22⋊D23—42no—
152C22⋊D23—42no—
153C22⋊D23—42no—
154C22⋊D23—42no—
155C22⋊D23—81no—
156C2×Dic23—21no—
157C2×Dic23—21no—
158C2×Dic23—42no—
159C2×Dic23C2×D411yescharacteristic
160C2×Dic23C2×D411yescharacteristic
161C2×Dic23C2×D411yescharacteristic
162D92—21no—
163D92—21no—
164D92—21no—
165D92—21no—
166D92—42no—
167C4×D23—21no—
168C4×D23—21no—
169C4×D23—42no—
170C4×D23—42no—
171Dic46—21no—
172Dic46—42no—
173Dic46C2×D412yescomplemented
174C8×C23—21no—
175C8×C23—21no—
176C23⋊C8—21no—
177C23⋊C8C2×D412yescomplemented
178#3265—231nomaximal, Sylow
179C22×C23—21no—
180C22×C23—22no—
181C22×C23—21no—
182C22×C23—21no—
183C22×C23—41no—
184C22×C23—41no—
185C22×C23—41no—
186C22×C23—41no—
187C22×C23—41no—
188C22×C23—84no—
189C22×C23C22×D411yescharacteristic
190C2×D23—21no—
191C2×D23—21no—
192C2×D23—41no—
193C2×D23—41no—
194C2×D23—41no—
195C2×D23—41no—
196C2×D23—41no—
197C2×D23—41no—
198C2×D23—84no—
199C2×D23AGL(1,ℤ/8)12yescomplemented
200C4×C23—21no—
201C4×C23—41no—
202C4×C23—41no—
203C4×C23C22×D411yescharacteristic
204C4×C23H(5,𝔽2)11yescharacteristic
205Dic23—22no—
206Dic23—21no—
207Dic23—21no—
208Dic23—21no—
209Dic23—41no—
210C2×AGL(1,ℤ/8)—231no—
211C22×SD16—231no—
212#548—231no—
213D42—231no—
214#496—231no—
215#468—231no—
216#466—231no—
217#463—231no—
218#460—231no—
219#450D2311yescharacteristic, complemented
220#449—231no—
221#448—231no—
222#447—231no—
223#440—231no—
224#435—231no—
225C2×C23—42no—
226C2×C23—41no—
227C2×C23—81no—
228C2×C23D4211yescharacteristic
229C2×C23C2×AGL(1,ℤ/8)11yescharacteristic
230C2×C23#57711yescharacteristic
231D23—22no—
232D23—81no—
233D23—81no—
234C2×#41—231no—
235C22×Q8—231no—
236C22×D4—231no—
237C22×D4—461no—
238C22×D4C2×D2311yescharacteristic
239AGL(1,ℤ/8)—464no—
240C2×SD16—231no—
241C2×SD16—231no—
242C2×SD16—231no—
243C2×SD16—231no—
244C2×SD16—464no—
245C2×SD16C2×D2311yescharacteristic
246C2×SD16C2×D2311yescharacteristic, complemented
247C2×D8—231no—
248C2×D8—231no—
249C2×D8—231no—
250C2×M16—231no—
251C22×C8—231no—
252#127—231no—
253#124—231no—
254#124—461no—
255C22⋊Q8—461no—
256C22⋊Q8C2×D2311yescharacteristic, complemented
257#121—231no—
258#121—231no—
259#121—231no—
260#121—461no—
261#121—461no—
262#120—461no—
263#120—461no—
264C4×Q8—231no—
265C4×D4—231no—
266C4×D4—231no—
267C4×D4—461no—
268#107—231no—
269C4⋊C8—231no—
270#103—231no—
271#103—231no—
272#102—231no—
273#102—231no—
274#102C2×D2311yescharacteristic
275#102C2×D2311yescharacteristic, complemented
276C22⋊C8—231no—
277C22⋊C8C2×D2311yescharacteristic, complemented
278#97—231no—
279C23#326511yescharacteristic, complemented, Sylow
280C24—21no—
281C24—461no—
282#41—462no—
283#41—921no—
284C2×Q8—231no—
285C2×Q8—461no—
286C2×Q8—462no—
287C2×Q8—921no—
288C2×Q8C22×D2311yescharacteristic
289C2×D4—22no—
290C2×D4—21no—
291C2×D4—41no—
292C2×D4—231no—
293C2×D4—231no—
294C2×D4—231no—
295C2×D4—461no—
296C2×D4—461no—
297C2×D4—461no—
298C2×D4—461no—
299C2×D4—462no—
300C2×D4—461no—
301C2×D4—461no—
302C2×D4—461no—
303C2×D4—921no—
304C2×D4—924no—
305C2×D4C22×D2311yescharacteristic
306C2×D4C22×D2311yescharacteristic
307C22×C4—231no—
308C22×C4—461no—
309C22×C4—461no—
310C22×C4—461no—
311C22×C4C22×D2311yescharacteristic
312SD16—22no—
313SD16—41no—
314SD16—234no—
315SD16—462no—
316SD16—462no—
317SD16—462no—
318D8—462no—
319D8—462no—
320D8—921no—
321M16—462no—
322C2×C8—231no—
323C2×C8—231no—
324C2×C8—462no—
325C2×C8C22×D2311yescharacteristic
326C2×C8C22×D2311yescharacteristic
327C4⋊C4—21no—
328C4⋊C4—231no—
329C4⋊C4—231no—
330C4⋊C4—461no—
331C4⋊C4C22×D2311yescharacteristic
332C22⋊C4—21no—
333C22⋊C4—231no—
334C22⋊C4—231no—
335C22⋊C4—461no—
336C22⋊C4—461no—
337C22⋊C4—461no—
338C22⋊C4—461no—
339C22⋊C4—461no—
340C22⋊C4—461no—
341C42—231no—
342C42—461no—
343C23—21no—
344C23—21no—
345C23—42no—
346C23—42no—
347C23—81no—
348C23—231no—
349C23—461no—
350C23—461no—
351C23—922no—
352C23—922no—
353C23—1841no—
354C23D4×D2311yescharacteristic
355Q8—21no—
356Q8—21no—
357Q8—232no—
358Q8—461no—
359Q8—922no—
360D4—21no—
361D4—21no—
362D4—21no—
363D4—42no—
364D4—462no—
365D4—461no—
366D4—461no—
367D4—461no—
368D4—461no—
369D4—922no—
370D4—922no—
371D4—922no—
372D4—922no—
373D4—922no—
374D4—922no—
375D4—1841no—
376D4D4×D2312yes—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—231no—
382C2×C4—231no—
383C2×C4—231no—
384C2×C4—461no—
385C2×C4—461no—
386C2×C4—461no—
387C2×C4—461no—
388C2×C4—922no—
389C2×C4—922no—
390C2×C4—922no—
391C2×C4D4×D2311yescharacteristic
392C2×C4C23×D2311yescharacteristic
393C8—21no—
394C8—21no—
395C8—232no—
396C8—461no—
397C22—21no—
398C22—21no—
399C22—21no—
400C22—22no—
401C22—41no—
402C22—41no—
403C22—41no—
404C22—41no—
405C22—41no—
406C22—84no—
407C22—232no—
408C22—461no—
409C22—461no—
410C22—921no—
411C22—921no—
412C22—921no—
413C22—921no—
414C22—921no—
415C22—921no—
416C22—1844no—
417C22C2×D4×D2311yescharacteristic
418C4—21no—
419C4—41no—
420C4—41no—
421C4—461no—
422C4—461no—
423C4—461no—
424C4—462no—
425C4—921no—
426C4C2×D4×D2311yescharacteristic
427C4#1062515511yescharacteristic
428C2—41no—
429C2—42no—
430C2—81no—
431C2—462no—
432C2—1841no—
433C2—1841no—
434C2#1309304911yescharacteristic
435C2AGL(1,ℤ/8)×D2311yescharacteristic
436C2#1309322311yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#450C2
socleC22×C23C22×D4
hypercenter#450D23
hypocenterC23#3265
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. C2×#10625103C2semidirect
2. C2×SD16×D23C2semidirect
3. #13093077C2semidirect
4. D4×C22⋊D23C2semidirect
5. #13092803C2semidirect
6. #13092665C2semidirect
7. #13092652C2semidirect
8. #13092634C2semidirect
9. #13092616C2semidirect
10. #13092564C2semidirect
11. #13092554C2semidirect
12. #13092552C2semidirect
13. #13092514C2semidirect
14. #13092491C2semidirect
15. C23×#450C2semidirect
18. C2×Q8×D23C22semidirect
20. C2×#67288C22semidirect
22. C2×SD16×C23C22semidirect
23. C23×C22⋊Q8C22semidirect
25. #10625118C22semidirect
26. C2×#67274C22semidirect
33. C2×#67273C22semidirect
36. C2×#67272C22semidirect
39. C2×#67267C22semidirect
41. C2×D184C22semidirect
42. C2×#67263C22semidirect
43. C2×C8×D23C22semidirect
45. #10625066C22semidirect
47. #10625058C22semidirect
51. C23×#102C22semidirect
52. C23×C22⋊C8C22semidirect
53. #10625017C22semidirect
54. #10625003C22semidirect
55. (C2×D23)⋊C8C22semidirect
56. #10624998C22semidirect
57. #10624997C22semidirect
58. Dic23⋊C8C22semidirect
59. #10624991C22semidirect
60. #10624989C22semidirect
105. #67273D4semidirect
173. Dic46C2×D4semidirect
177. C23⋊C8C2×D4semidirect
199. C2×D23AGL(1,ℤ/8)semidirect
219. #450D23semidirect
246. C2×SD16C2×D23semidirect
256. C22⋊Q8C2×D23semidirect
275. #102C2×D23semidirect
277. C22⋊C8C2×D23semidirect
279. C23#3265semidirect

Maximal subgroups

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

subgroupindex
C2×#106251032
C2×SD16×D232
#130930772
D4×C22⋊D232
#130928032
#130926652
#130926522
#130926342
#130926162
#130925642
#130925542
#130925522
#130925142
#130924912
C23×#4502
#326523