Finite Group Databasebeta

← #15684884

Subgroups — #15684884

Order 2944.

568 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10625079C211yesmaximal, characteristic, complemented
2C2×D8×D23C211yesmaximal, characteristic, complemented
3#13093064C211yesmaximal, characteristic, complemented
4#13093051C211yesmaximal, characteristic, complemented
5#13092805C211yesmaximal, characteristic, complemented
6#13092647C211yesmaximal, characteristic, complemented
7#13092631C211yesmaximal, characteristic, complemented
8#13092611C211yesmaximal, characteristic, complemented
9#13092569C211yesmaximal, characteristic, complemented
10#13092560C211yesmaximal, characteristic, complemented
11#13092552C211yesmaximal, characteristic, complemented
12#13092550C211yesmaximal, characteristic, complemented
13#13092528C211yesmaximal, characteristic, complemented
14#13092486C211yesmaximal, characteristic, complemented
15C23×#469C211yesmaximal, characteristic, complemented
16C2×D4×D23—21no—
17C2×D4×D23C2211yescharacteristic
18C2×D4×D23C2211yescharacteristic, complemented
19C2×#67288C2211yescharacteristic, complemented
20C22×D92C2211yescharacteristic, complemented
21C2×D8×C23C2211yescharacteristic, complemented
22C2×M16×C23C2211yescharacteristic, complemented
23C23×#121C2211yescharacteristic, complemented
24C23×#121C2211yescharacteristic, complemented
25#10625111C2211yescharacteristic, complemented
26#10625109—21no—
27#10625108—21no—
28#10625108—21no—
29#10625107C2211yescharacteristic, complemented
30C2×#67273C2211yescharacteristic, complemented
31C2×#67272C2211yescharacteristic
32C2×#67272C2211yescharacteristic, complemented
33C2×#67272C2211yescharacteristic, complemented
34C4×C22⋊D23C2211yescharacteristic
35D8×D23—24no—
36#10625079—24no—
37C2×D184C2211yescharacteristic
38C2×D184C2211yescharacteristic, complemented
39C2×#67263C2211yescharacteristic, complemented
40C2×#67263C2211yescharacteristic, complemented
41C2×C8×D23C2211yescharacteristic, complemented
42#10625068C2211yescharacteristic, complemented
43#10625066C2211yescharacteristic
44#10625064C2211yescharacteristic, complemented
45#10625064C2211yescharacteristic, complemented
46#10625055—21no—
47#10625054—21no—
48#10625053—21no—
49C22⋊C4×D23—21no—
50C23×#106C2211yescharacteristic, complemented
51C23×#102C2211yescharacteristic, complemented
52C23×#102C2211yescharacteristic, complemented
53C22⋊(C23⋊C8)C2211yescharacteristic, complemented
54(C2×D23)⋊C8C2211yescharacteristic, complemented
55#10624997C2211yescharacteristic, complemented
56Dic23⋊C8C2211yescharacteristic, complemented
57#10624992C2211yescharacteristic, complemented
58#10624991C2211yescharacteristic, complemented
59#10624991C2211yescharacteristic, complemented
60#10624991C2211yescharacteristic, complemented
61C23×D23—21no—
62C23×D23—21no—
63C23×D23—21no—
64C2×D4×C23—21no—
65C2×D4×C23—21no—
66C2×D4×C23C2311yescharacteristic
67C2×D4×C23C2311yescharacteristic
68C22×C4×C23C2311yescharacteristic
69C2×C22⋊D23—21no—
70C2×C22⋊D23—21no—
71C2×C22⋊D23—21no—
72C2×C22⋊D23—21no—
73C2×C22⋊D23—21no—
74C2×C22⋊D23D411yescharacteristic
75D4×D23—22no—
76D4×D23—22no—
77D4×D23—41no—
78D4×D23—41no—
79D4×D23—44no—
80#67288—22no—
81#67288—41no—
82C2×D92—22no—
83C2×D92—21no—
84C2×D92—21no—
85C2×D92—41no—
86C2×D92C2311yescharacteristic
87C2×D92C2311yescharacteristic
88C2×D92C2311yescharacteristic
89C2×C4×D23—21no—
90C2×C4×D23—21no—
91C2×C4×D23—21no—
92C2×C4×D23C2311yescharacteristic
93C2×Dic46C2311yescharacteristic
94D8×C23—22no—
95M16×C23—22no—
96C2×C8×C23C2311yescharacteristic
97C2×C8×C23C2311yescharacteristic
98C4⋊C4×C23C2311yescharacteristic
99C4⋊C4×C23C2311yescharacteristic
100C22⋊C4×C23—21no—
101C22⋊C4×C23—21no—
102C22⋊Dic23—21no—
103C22⋊Dic23—21no—
104C22⋊Dic23D411yescharacteristic
105#67273—41no—
106#67272—22no—
107#67272—22no—
108#67272—41no—
109(C2×D23)⋊C4—21no—
110(C2×D23)⋊C4—21no—
111(C2×D23)⋊C4—21no—
112(C2×D23)⋊C4—21no—
113(C2×D23)⋊C4D411yescharacteristic
114C4⋊Dic23—21no—
115Dic23⋊C4D411yescharacteristic
116C4×Dic23C2311yescharacteristic
117C2×C23⋊C8C2311yescharacteristic
118C2×C23⋊C8C2311yescharacteristic
119D184—22no—
120D184D414yescomplemented
121#67263—22no—
122#67263—22no—
123C8×D23—22no—
124C23×C23—21no—
125C23×C23—21no—
126C23×C23C2×D411yescharacteristic
127C22×D23—21no—
128C22×D23—21no—
129C22×D23—21no—
130C22×D23—42no—
131C22×D23—42no—
132C22×D23—42no—
133C22×D23—42no—
134C22×D23—42no—
135C22×D23—42no—
136C22×D23—81no—
137C22×D23—81no—
138C22×D23—81no—
139C22×D23C2×D411yescharacteristic
140D4×C23—21no—
141D4×C23—21no—
142D4×C23—21no—
143D4×C23—21no—
144D4×C23—42no—
145D4×C23—81no—
146C2×C4×C23—21no—
147C2×C4×C23—21no—
148C2×C4×C23—21no—
149C2×C4×C23—21no—
150C2×C4×C23C2×D411yescharacteristic
151C2×C4×C23C2411yescharacteristic
152C22⋊D23—22no—
153C22⋊D23—42no—
154C22⋊D23—42no—
155C22⋊D23—42no—
156C22⋊D23—42no—
157C22⋊D23—81no—
158C2×Dic23—21no—
159C2×Dic23C2×D411yescharacteristic
160C2×Dic23C2×D411yescharacteristic
161C2×Dic23C2×D411yescharacteristic
162D92—21no—
163D92—21no—
164D92—21no—
165D92—21no—
166D92—42no—
167D92—42no—
168D92C2×D412yes—
169D92C2×D412yescomplemented
170C4×D23—21no—
171C4×D23—21no—
172C4×D23—42no—
173C4×D23—42no—
174C4×D23—81no—
175Dic46—21no—
176Dic46—21no—
177C8×C23—21no—
178C8×C23C2×D412yescomplemented
179C23⋊C8—21no—
180C23⋊C8—21no—
181#3264—231nomaximal, Sylow
182C22×C23—21no—
183C22×C23—21no—
184C22×C23—21no—
185C22×C23—41no—
186C22×C23—41no—
187C22×C23—41no—
188C22×C23—41no—
189C22×C23—41no—
190C22×C23—41no—
191C22×C23C22×D411yescharacteristic
192C2×D23—21no—
193C2×D23—21no—
194C2×D23—22no—
195C2×D23—22no—
196C2×D23—41no—
197C2×D23—41no—
198C2×D23—41no—
199C2×D23—41no—
200C2×D23—41no—
201C2×D23—41no—
202C2×D23—41no—
203C2×D23—84no—
204C2×D23—84no—
205C2×D23—84no—
206C2×D23AGL(1,ℤ/8)12yescomplemented
207C4×C23—21no—
208C4×C23—41no—
209C4×C23—41no—
210C4×C23C22×D411yescharacteristic
211C4×C23H(5,𝔽2)11yescharacteristic
212Dic23—21no—
213Dic23—21no—
214Dic23—21no—
215Dic23—41no—
216C2×AGL(1,ℤ/8)—231no—
217C22×D8—231no—
218#546—231no—
219D42—231no—
220#496—231no—
221#469D2311yescharacteristic, complemented
222#465—231no—
223#463—231no—
224#459—231no—
225#450—231no—
226#449—231no—
227#447—231no—
228#447—231no—
229#442—231no—
230#435—231no—
231C2×C23—41no—
232C2×C23—81no—
233C2×C23—81no—
234C2×C23D4211yescharacteristic
235C2×C23C2×AGL(1,ℤ/8)11yescharacteristic
236C2×C23#57611yescharacteristic
237D23—22no—
238D23—42no—
239D23—42no—
240D23—81no—
241C2×#41—231no—
242C22×D4—231no—
243C22×D4—231no—
244C22×D4—231no—
245C22×D4—461no—
246AGL(1,ℤ/8)—464no—
247C2×SD16—231no—
248C2×SD16—231no—
249C2×SD16—231no—
250C2×D8—231no—
251C2×D8—231no—
252C2×D8—231no—
253C2×D8—231no—
254C2×D8—231no—
255C2×D8—464no—
256C2×D8C2×D2311yescharacteristic, complemented
257C2×M16C2×D2311yescharacteristic, complemented
258C22×C8—231no—
259#127—231no—
260#124—231no—
261#123—461no—
262C22⋊Q8—231no—
263#121—231no—
264#121—461no—
265#121—461no—
266#121C2×D2311yescharacteristic, complemented
267#121C2×D2311yescharacteristic, complemented
268#120—461no—
269#120—461no—
270#120—461no—
271C4×D4—231no—
272C4×D4—231no—
273C4×D4—231no—
274C2×C22⋊C4—461no—
275#106C2×D2311yescharacteristic, complemented
276C4⋊C8—231no—
277#103—231no—
278#102—231no—
279#102—231no—
280#102—231no—
281#102C2×D2311yescharacteristic, complemented
282#102C2×D2311yescharacteristic, complemented
283C22⋊C8—231no—
284C22⋊C8—231no—
285#97—231no—
286C23#326411yescharacteristic, complemented, Sylow
287C24—461no—
288C24—461no—
289C24—461no—
290#41—462no—
291#41—921no—
292C2×Q8—231no—
293C2×D4—21no—
294C2×D4—21no—
295C2×D4—231no—
296C2×D4—231no—
297C2×D4—231no—
298C2×D4—231no—
299C2×D4—462no—
300C2×D4—461no—
301C2×D4—461no—
302C2×D4—461no—
303C2×D4—461no—
304C2×D4—461no—
305C2×D4—462no—
306C2×D4—462no—
307C2×D4—461no—
308C2×D4—461no—
309C2×D4—921no—
310C2×D4—921no—
311C2×D4—921no—
312C2×D4—924no—
313C2×D4C22×D2311yescharacteristic
314C2×D4C22×D2311yescharacteristic
315C22×C4—231no—
316C22×C4—461no—
317C22×C4—461no—
318C22×C4—461no—
319C22×C4C22×D2311yescharacteristic
320SD16—462no—
321SD16—462no—
322SD16—921no—
323D8—22no—
324D8—234no—
325D8—462no—
326D8—462no—
327D8—462no—
328D8—921no—
329M16—22no—
330C2×C8—231no—
331C2×C8—231no—
332C2×C8—462no—
333C2×C8C22×D2311yescharacteristic
334C2×C8C22×D2311yescharacteristic
335C4⋊C4—231no—
336C4⋊C4—461no—
337C4⋊C4C22×D2311yescharacteristic
338C4⋊C4C22×D2311yescharacteristic
339C22⋊C4—21no—
340C22⋊C4—21no—
341C22⋊C4—231no—
342C22⋊C4—231no—
343C22⋊C4—461no—
344C22⋊C4—461no—
345C22⋊C4—461no—
346C22⋊C4—461no—
347C22⋊C4—461no—
348C22⋊C4—461no—
349C42—231no—
350C23—21no—
351C23—21no—
352C23—231no—
353C23—461no—
354C23—461no—
355C23—461no—
356C23—922no—
357C23—922no—
358C23—922no—
359C23—922no—
360C23—922no—
361C23—922no—
362C23—1841no—
363C23—1841no—
364C23—1841no—
365C23D4×D2311yescharacteristic
366Q8—461no—
367Q8—461no—
368D4—21no—
369D4—21no—
370D4—21no—
371D4—21no—
372D4—42no—
373D4—81no—
374D4—232no—
375D4—232no—
376D4—462no—
377D4—461no—
378D4—461no—
379D4—461no—
380D4—461no—
381D4—922no—
382D4—922no—
383D4—922no—
384D4—922no—
385D4—922no—
386D4—922no—
387D4—1841no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—231no—
393C2×C4—231no—
394C2×C4—231no—
395C2×C4—461no—
396C2×C4—461no—
397C2×C4—461no—
398C2×C4—922no—
399C2×C4—922no—
400C2×C4—1841no—
401C2×C4D4×D2311yescharacteristic
402C2×C4C23×D2311yescharacteristic
403C8—21no—
404C8—461no—
405C8—461no—
406C8D4×D2312yescomplemented
407C22—21no—
408C22—21no—
409C22—21no—
410C22—41no—
411C22—41no—
412C22—41no—
413C22—41no—
414C22—41no—
415C22—41no—
416C22—232no—
417C22—461no—
418C22—461no—
419C22—462no—
420C22—462no—
421C22—921no—
422C22—921no—
423C22—921no—
424C22—921no—
425C22—921no—
426C22—921no—
427C22—921no—
428C22—1844no—
429C22—1844no—
430C22—1844no—
431C22C2×D4×D2311yescharacteristic
432C4—21no—
433C4—41no—
434C4—41no—
435C4—461no—
436C4—461no—
437C4—461no—
438C4—921no—
439C4C2×D4×D2311yescharacteristic
440C4#1062516011yescharacteristic
441C2—41no—
442C2—81no—
443C2—81no—
444C2—462no—
445C2—922no—
446C2—922no—
447C2—1841no—
448C2#1309305111yescharacteristic
449C2AGL(1,ℤ/8)×D2311yescharacteristic
450C2#1309322111yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#469C2
socleC22×C23C22×D4
hypercenter#469D23
hypocenterC23#3264
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #469

Complements

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

NH ≅ G/Ntype
1. C2×#10625079C2semidirect
2. C2×D8×D23C2semidirect
3. #13093064C2semidirect
4. #13093051C2semidirect
5. #13092805C2semidirect
6. #13092647C2semidirect
7. #13092631C2semidirect
8. #13092611C2semidirect
9. #13092569C2semidirect
10. #13092560C2semidirect
11. #13092552C2semidirect
12. #13092550C2semidirect
13. #13092528C2semidirect
14. #13092486C2semidirect
15. C23×#469C2semidirect
18. C2×D4×D23C22semidirect
19. C2×#67288C22semidirect
20. C22×D92C22semidirect
21. C2×D8×C23C22semidirect
22. C2×M16×C23C22semidirect
23. C23×#121C22semidirect
24. C23×#121C22semidirect
25. #10625111C22semidirect
29. #10625107C22semidirect
30. C2×#67273C22semidirect
32. C2×#67272C22semidirect
33. C2×#67272C22semidirect
38. C2×D184C22semidirect
39. C2×#67263C22semidirect
40. C2×#67263C22semidirect
41. C2×C8×D23C22semidirect
42. #10625068C22semidirect
44. #10625064C22semidirect
45. #10625064C22semidirect
50. C23×#106C22semidirect
51. C23×#102C22semidirect
52. C23×#102C22semidirect
53. C22⋊(C23⋊C8)C22semidirect
54. (C2×D23)⋊C8C22semidirect
55. #10624997C22semidirect
56. Dic23⋊C8C22semidirect
57. #10624992C22semidirect
58. #10624991C22semidirect
59. #10624991C22semidirect
60. #10624991C22semidirect
120. D184D4semidirect
169. D92C2×D4semidirect
178. C8×C23C2×D4semidirect
206. C2×D23AGL(1,ℤ/8)semidirect
221. #469D23semidirect
256. C2×D8C2×D23semidirect
257. C2×M16C2×D23semidirect
266. #121C2×D23semidirect
267. #121C2×D23semidirect
275. #106C2×D23semidirect
281. #102C2×D23semidirect
282. #102C2×D23semidirect
286. C23#3264semidirect
406. C8D4×D23semidirect

Maximal subgroups

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

subgroupindex
C2×#106250792
C2×D8×D232
#130930642
#130930512
#130928052
#130926472
#130926312
#130926112
#130925692
#130925602
#130925522
#130925502
#130925282
#130924862
C23×#4692
#326423