Finite Group Databasebeta

← #15684879

Subgroups — #15684879

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×#10625082C211yesmaximal, characteristic, complemented
2C2×D8×D23C211yesmaximal, characteristic, complemented
3#13093062C211yesmaximal, characteristic, complemented
4D4×D92C211yesmaximal, characteristic, complemented
5#13092806C211yesmaximal, characteristic, complemented
6#13092671C211yesmaximal, characteristic, complemented
7#13092647C211yesmaximal, characteristic, complemented
8#13092632C211yesmaximal, characteristic, complemented
9#13092612C211yesmaximal, characteristic, complemented
10#13092569C211yesmaximal, characteristic, complemented
11#13092563C211yesmaximal, characteristic, complemented
12#13092552C211yesmaximal, characteristic, complemented
13#13092552C211yesmaximal, characteristic, complemented
14#13092490C211yesmaximal, characteristic, complemented
15C23×#442C211yesmaximal, characteristic, complemented
16C2×#67290C2211yescharacteristic, complemented
17C2×D4×D23C2211yescharacteristic
18C2×D4×D23C2211yescharacteristic, complemented
19C2×D4×D23C2211yescharacteristic, complemented
20C22×D92—21no—
21C2×D8×C23C2211yescharacteristic
22C4×D4×C23C2211yescharacteristic, complemented
23C4×D4×C23C2211yescharacteristic, complemented
24C2×#67273C2211yescharacteristic, complemented
25C2×#67272C2211yescharacteristic
26C2×#67272C2211yescharacteristic, complemented
27C2×#67272C2211yescharacteristic, complemented
28#10625101—21no—
29#10625101—21no—
30C2×(C2×D23)⋊C4—21no—
31#10625082—24no—
32D8×D23—24no—
33C2×D184C2211yescharacteristic, complemented
34C2×D184C2211yescharacteristic, complemented
35C2×#67263C2211yescharacteristic, complemented
36C2×#67263C2211yescharacteristic, complemented
37C2×#67262C2211yescharacteristic, complemented
38C2×C8×D23C2211yescharacteristic, complemented
39#10625068C2211yescharacteristic, complemented
40#10625066C2211yescharacteristic
41#10625066C2211yescharacteristic, complemented
42#10625066C2211yescharacteristic, complemented
43#10625057—21no—
44#10625053—21no—
45#10625053—21no—
46#10625053—21no—
47#10625046C2211yescharacteristic, complemented
48#10625045C2211yescharacteristic, complemented
49C4×D92C2211yescharacteristic
50C23×#106C2211yescharacteristic, complemented
51C23×#102C2211yescharacteristic, complemented
52C23×#102C2211yescharacteristic, complemented
53C23×#97C2211yescharacteristic, complemented
54(C2×D23)⋊C8C2211yescharacteristic, complemented
55(C2×D23)⋊C8C2211yescharacteristic, complemented
56#10624992C2211yescharacteristic, complemented
57#10624991C2211yescharacteristic, complemented
58#10624991C2211yescharacteristic, complemented
59#10624991C2211yescharacteristic, complemented
60C4⋊(C23⋊C8)C2211yescharacteristic, complemented
61C23×D23—21no—
62C23×D23—21no—
63C23×D23—21no—
64C2×D4×C23C2311yescharacteristic
65C2×D4×C23C2311yescharacteristic
66C22×C4×C23—21no—
67C22×C4×C23—21no—
68C2×C22⋊D23—21no—
69C2×C22⋊D23—21no—
70C2×C22⋊D23—21no—
71C2×C22⋊D23—21no—
72C22×Dic23—21no—
73#67290—22no—
74#67290—41no—
75D4×D23—22no—
76D4×D23—22no—
77D4×D23—22no—
78D4×D23—41no—
79D4×D23—41no—
80D4×D23—41no—
81C2×D92—21no—
82C2×D92—21no—
83C2×D92—21no—
84C2×D92—21no—
85C2×D92—21no—
86C2×D92—44no—
87C2×D92D411yescharacteristic
88C2×D92C2311yescharacteristic
89C2×D92C2311yescharacteristic
90C2×D92C2311yescharacteristic
91C2×C4×D23C2311yescharacteristic
92C2×C4×D23C2311yescharacteristic
93C2×Dic46C2311yescharacteristic
94D8×C23D414yescomplemented
95C2×C8×C23C2311yescharacteristic
96C2×C8×C23C2311yescharacteristic
97C4⋊C4×C23C2311yescharacteristic
98C4⋊C4×C23C2311yescharacteristic
99C22⋊C4×C23—21no—
100C22⋊C4×C23—21no—
101C42×C23C2311yescharacteristic
102#67273—22no—
103#67272—22no—
104#67272—22no—
105#67272—22no—
106(C2×D23)⋊C4—21no—
107(C2×D23)⋊C4—21no—
108(C2×D23)⋊C4—21no—
109(C2×D23)⋊C4—21no—
110(C2×D23)⋊C4—21no—
111(C2×D23)⋊C4—21no—
112(C2×D23)⋊C4D411yescharacteristic
113(C2×D23)⋊C4D411yescharacteristic
114C4⋊Dic23—21no—
115C4⋊Dic23D411yescharacteristic
116C2×C23⋊C8C2311yescharacteristic
117C2×C23⋊C8C2311yescharacteristic
118D184—22no—
119D184—41no—
120#67263—22no—
121#67263—41no—
122#67262—22no—
123C8×D23—22no—
124C23×C23—21no—
125C23×C23—21no—
126C22×D23—21no—
127C22×D23—21no—
128C22×D23—21no—
129C22×D23—42no—
130C22×D23—42no—
131C22×D23—42no—
132C22×D23—42no—
133C22×D23—42no—
134C22×D23—42no—
135C22×D23—81no—
136C22×D23—81no—
137C22×D23—81no—
138C22×D23C2×D411yescharacteristic
139C22×D23C2×D411yescharacteristic
140D4×C23—21no—
141D4×C23—21no—
142D4×C23C2×D412yes—
143D4×C23C2×D412yescomplemented
144C2×C4×C23—21no—
145C2×C4×C23—21no—
146C2×C4×C23—42no—
147C2×C4×C23—81no—
148C2×C4×C23C2×D411yescharacteristic
149C2×C4×C23C2×D411yescharacteristic
150C2×C4×C23C2411yescharacteristic
151C22⋊D23—42no—
152C22⋊D23—42no—
153C22⋊D23—42no—
154C22⋊D23—42no—
155C2×Dic23—21no—
156C2×Dic23—42no—
157C2×Dic23C2×D411yescharacteristic
158C2×Dic23C2×D411yescharacteristic
159D92—22no—
160D92—21no—
161D92—21no—
162D92—21no—
163D92—21no—
164D92—21no—
165D92—21no—
166D92—42no—
167D92—42no—
168D92—42no—
169D92—81no—
170D92—81no—
171C4×D23—21no—
172C4×D23—21no—
173C4×D23—21no—
174C4×D23—21no—
175Dic46—21no—
176Dic46—21no—
177C8×C23—21no—
178C8×C23C2×D412yescomplemented
179C23⋊C8—21no—
180C23⋊C8—21no—
181#3264—231nomaximal, Sylow
182C22×C23—22no—
183C22×C23—22no—
184C22×C23—41no—
185C22×C23—41no—
186C22×C23—41no—
187C22×C23—41no—
188C22×C23C22×D411yescharacteristic
189C2×D23—21no—
190C2×D23—21no—
191C2×D23—21no—
192C2×D23—21no—
193C2×D23—21no—
194C2×D23—41no—
195C2×D23—41no—
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—21no—
209C4×C23—41no—
210C4×C23—41no—
211C4×C23C22×D411yescharacteristic
212C4×C23H(5,𝔽2)11yescharacteristic
213Dic23—21no—
214Dic23—21no—
215Dic23—41no—
216C2×AGL(1,ℤ/8)—231no—
217C22×D8—231no—
218#546—231no—
219D42—231no—
220#496—231no—
221#469—231no—
222#465—231no—
223#463—231no—
224#459—231no—
225#450—231no—
226#449—231no—
227#447—231no—
228#447—231no—
229#442D2311yescharacteristic, complemented
230#435—231no—
231C2×C23—42no—
232C2×C23—42no—
233C2×C23D4211yescharacteristic
234C2×C23C2×AGL(1,ℤ/8)11yescharacteristic
235C2×C23#57611yescharacteristic
236D23—22no—
237D23—41no—
238D23—81no—
239D23—81no—
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
257C2×M16—231no—
258C22×C8—231no—
259#127—231no—
260#124—231no—
261#123—461no—
262C22⋊Q8—231no—
263#121—231no—
264#121—231no—
265#121—231no—
266#121—461no—
267#121—461no—
268#120—461no—
269#120—461no—
270#120—461no—
271C4×D4—231no—
272C4×D4C2×D2311yescharacteristic, complemented
273C4×D4C2×D2311yescharacteristic, complemented
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#97C2×D2311yescharacteristic, complemented
286C23#326411yescharacteristic, complemented, Sylow
287C24—461no—
288C24—461no—
289C24—461no—
290#41—462no—
291#41—921no—
292C2×Q8—231no—
293C2×D4—231no—
294C2×D4—231no—
295C2×D4—231no—
296C2×D4—231no—
297C2×D4—461no—
298C2×D4—461no—
299C2×D4—461no—
300C2×D4—461no—
301C2×D4—461no—
302C2×D4—461no—
303C2×D4—462no—
304C2×D4—462no—
305C2×D4—462no—
306C2×D4—461no—
307C2×D4—461no—
308C2×D4—461no—
309C2×D4—924no—
310C2×D4—921no—
311C2×D4—921no—
312C2×D4—921no—
313C2×D4C22×D2311yescharacteristic
314C2×D4C22×D2311yescharacteristic
315C22×C4—21no—
316C22×C4—21no—
317C22×C4—231no—
318C22×C4—231no—
319C22×C4—461no—
320SD16—462no—
321SD16—462no—
322SD16—921no—
323D8—462no—
324D8—462no—
325D8—462no—
326D8—462no—
327D8—921no—
328D8D9214yescomplemented
329M16—462no—
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—
349C42C22×D2311yescharacteristic
350C23—21no—
351C23—21no—
352C23—231no—
353C23—231no—
354C23—461no—
355C23—461no—
356C23—461no—
357C23—922no—
358C23—922no—
359C23—922no—
360C23—922no—
361C23—922no—
362C23—922no—
363C23—1841no—
364C23—1841no—
365C23—1841no—
366Q8—461no—
367Q8—461no—
368D4—21no—
369D4—21no—
370D4—462no—
371D4—461no—
372D4—461no—
373D4—461no—
374D4—461no—
375D4—461no—
376D4—461no—
377D4—922no—
378D4—922no—
379D4—922no—
380D4—922no—
381D4—922no—
382D4—922no—
383D4—922no—
384D4—1841no—
385D4—1841no—
386D4C2×D9212yes—
387D4C2×D9212yescomplemented
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—42no—
391C2×C4—81no—
392C2×C4—231no—
393C2×C4—231no—
394C2×C4—461no—
395C2×C4—461no—
396C2×C4—461no—
397C2×C4—461no—
398C2×C4—461no—
399C2×C4—922no—
400C2×C4D4×D2311yescharacteristic
401C2×C4D4×D2311yescharacteristic
402C2×C4C23×D2311yescharacteristic
403C8—21no—
404C8—461no—
405C8—461no—
406C8C2×D9212yescomplemented
407C22—22no—
408C22—22no—
409C22—41no—
410C22—41no—
411C22—41no—
412C22—41no—
413C22—232no—
414C22—461no—
415C22—461no—
416C22—461no—
417C22—461no—
418C22—461no—
419C22—921no—
420C22—921no—
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—21no—
434C4—41no—
435C4—41no—
436C4—461no—
437C4—461no—
438C4—921no—
439C4C22×D9211yescharacteristic
440C4#1062516011yescharacteristic
441C2—42no—
442C2—42no—
443C2—462no—
444C2—921no—
445C2—1841no—
446C2—1841no—
447C2—1841no—
448C2D4×D9211yescharacteristic
449C2AGL(1,ℤ/8)×D2311yescharacteristic
450C2#1309322111yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#442C2
socleC22×C23C22×D4
hypercenter#442D23
hypocenterC23#3264
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
1. C2×#10625082C2semidirect
2. C2×D8×D23C2semidirect
3. #13093062C2semidirect
4. D4×D92C2semidirect
5. #13092806C2semidirect
6. #13092671C2semidirect
7. #13092647C2semidirect
8. #13092632C2semidirect
9. #13092612C2semidirect
10. #13092569C2semidirect
11. #13092563C2semidirect
12. #13092552C2semidirect
13. #13092552C2semidirect
14. #13092490C2semidirect
15. C23×#442C2semidirect
16. C2×#67290C22semidirect
18. C2×D4×D23C22semidirect
19. C2×D4×D23C22semidirect
22. C4×D4×C23C22semidirect
23. C4×D4×C23C22semidirect
24. C2×#67273C22semidirect
26. C2×#67272C22semidirect
27. C2×#67272C22semidirect
33. C2×D184C22semidirect
34. C2×D184C22semidirect
35. C2×#67263C22semidirect
36. C2×#67263C22semidirect
37. C2×#67262C22semidirect
38. C2×C8×D23C22semidirect
39. #10625068C22semidirect
41. #10625066C22semidirect
42. #10625066C22semidirect
47. #10625046C22semidirect
48. #10625045C22semidirect
50. C23×#106C22semidirect
51. C23×#102C22semidirect
52. C23×#102C22semidirect
53. C23×#97C22semidirect
54. (C2×D23)⋊C8C22semidirect
55. (C2×D23)⋊C8C22semidirect
56. #10624992C22semidirect
57. #10624991C22semidirect
58. #10624991C22semidirect
59. #10624991C22semidirect
60. C4⋊(C23⋊C8)C22semidirect
94. D8×C23D4semidirect
143. D4×C23C2×D4semidirect
178. C8×C23C2×D4semidirect
206. C2×D23AGL(1,ℤ/8)semidirect
229. #442D23semidirect
272. C4×D4C2×D23semidirect
273. C4×D4C2×D23semidirect
275. #106C2×D23semidirect
281. #102C2×D23semidirect
282. #102C2×D23semidirect
285. #97C2×D23semidirect
286. C23#3264semidirect
328. D8D92semidirect
387. D4C2×D92semidirect
406. C8C2×D92semidirect

Maximal subgroups

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

subgroupindex
C2×#106250822
C2×D8×D232
#130930622
D4×D922
#130928062
#130926712
#130926472
#130926322
#130926122
#130925692
#130925632
#130925522
#130924902
C23×#4422
#326423