Finite Group Databasebeta

← #15685359

Subgroups — #15685359

Order 2944.

442 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13093068C211yesmaximal, characteristic, complemented
2#13093055C211yesmaximal, characteristic, complemented
3#13092778C211yesmaximal, characteristic, complemented
4#13092746C211yesmaximal, characteristic, complemented
5#13092735C211yesmaximal, characteristic, complemented
6#13092705C211yesmaximal, characteristic, complemented
7#13092670C211yesmaximal, characteristic, complemented
8#13092649C211yesmaximal, characteristic, complemented
9#13092635C211yesmaximal, characteristic, complemented
10#13092562C211yesmaximal, characteristic, complemented
11#13092552C211yesmaximal, characteristic, complemented
12#13092526C211yesmaximal, characteristic, complemented
13#13092486C211yesmaximal, characteristic, complemented
14#102×D23C211yesmaximal, characteristic, complemented
15C23×#417C211yesmaximal, characteristic, complemented
16C2×#41×C23C2211yescharacteristic
17C2×D4×D23C2211yescharacteristic
18C2×#67288—21no—
19C2×M16×C23C2211yescharacteristic, complemented
20C2×C4⋊C4×C23C2211yescharacteristic, complemented
21#10625118C2211yescharacteristic
22#10625117C2211yescharacteristic
23C2×#67274C2211yescharacteristic, complemented
24#10625110—21no—
25#10625108—21no—
26D4×Dic23C2211yescharacteristic
27C2×#67272C2211yescharacteristic
28#10625101C2211yescharacteristic
29#10625101C2211yescharacteristic, complemented
30#10625100—21no—
31#10625100—21no—
32C4×C22⋊D23C2211yescharacteristic
33C2×(C2×D23)⋊C4—21no—
34C2×D184C2211yescharacteristic
35C2×C8×D23C2211yescharacteristic
36#10625067—21no—
37#10625066C2211yescharacteristic
38#10625065—21no—
39#10625064C2211yescharacteristic, complemented
40C4⋊C4×D23C2211yescharacteristic
41#10625059C2211yescharacteristic, complemented
42C23×#103C2211yescharacteristic, complemented
43C23×#103C2211yescharacteristic, complemented
44C23×#102C2211yescharacteristic
45C23×#102C2211yescharacteristic
46#10625017C2211yescharacteristic, complemented
47#10625014C2211yescharacteristic
48C22⋊(C23⋊C8)C2211yescharacteristic, complemented
49#10625003C2211yescharacteristic
50#10625003C2211yescharacteristic, complemented
51(C2×D23)⋊C8C2211yescharacteristic
52#10624999C2211yescharacteristic, complemented
53#10624997C2211yescharacteristic, complemented
54Dic23⋊C8C2211yescharacteristic, complemented
55#10624991C2211yescharacteristic
56#10624991C2211yescharacteristic
57#10624990C2211yescharacteristic, complemented
58#10624990C2211yescharacteristic, complemented
59C23×D23—21no—
60#41×C23—22no—
61#41×C23—41no—
62C2×Q8×C23C2311yescharacteristic
63C2×D4×C23—21no—
64C2×D4×C23C2311yescharacteristic
65C22×C4×C23—21no—
66C22×C4×C23—21no—
67C22×C4×C23C2311yescharacteristic
68C2×C22⋊D23—21no—
69C2×C22⋊D23—21no—
70C2×C22⋊D23—21no—
71C2×C22⋊D23D411yescharacteristic
72C22×Dic23—21no—
73D4×D23—22no—
74D4×D23—41no—
75#67288—44no—
76C2×D92—21no—
77C2×D92C2311yescharacteristic
78C2×D92C2311yescharacteristic
79C2×C4×D23—21no—
80C2×C4×D23—21no—
81C2×C4×D23C2311yescharacteristic
82C2×Dic46—21no—
83M16×C23—41no—
84C2×C8×C23C2311yescharacteristic
85C2×C8×C23C2311yescharacteristic
86C4⋊C4×C23—21no—
87C4⋊C4×C23C2311yescharacteristic
88C4⋊C4×C23C2311yescharacteristic
89C22⋊Dic23—21no—
90C22⋊Dic23D411yescharacteristic
91#67274—41no—
92#67272—22no—
93(C2×D23)⋊C4—21no—
94(C2×D23)⋊C4—21no—
95(C2×D23)⋊C4—21no—
96(C2×D23)⋊C4—21no—
97(C2×D23)⋊C4—21no—
98(C2×D23)⋊C4—21no—
99(C2×D23)⋊C4—21no—
100(C2×D23)⋊C4D411yescharacteristic
101C4⋊Dic23C2311yescharacteristic
102C4⋊Dic23C2311yescharacteristic
103Dic23⋊C4—21no—
104Dic23⋊C4—21no—
105Dic23⋊C4—21no—
106Dic23⋊C4D411yescharacteristic
107C4×Dic23C2311yescharacteristic
108C2×C23⋊C8C2311yescharacteristic
109C2×C23⋊C8C2311yescharacteristic
110D184—41no—
111C8×D23—41no—
112C23×C23—21no—
113C23×C23C2×D411yescharacteristic
114C22×D23—21no—
115C22×D23—21no—
116C22×D23—42no—
117C22×D23—42no—
118C22×D23—81no—
119C22×D23C2×D411yescharacteristic
120Q8×C23—21no—
121Q8×C23—21no—
122D4×C23—21no—
123D4×C23—42no—
124D4×C23#4112yescomplemented
125C2×C4×C23—21no—
126C2×C4×C23—21no—
127C2×C4×C23—21no—
128C2×C4×C23—21no—
129C2×C4×C23—21no—
130C2×C4×C23—42no—
131C2×C4×C23—42no—
132C2×C4×C23C2×D411yescharacteristic
133C2×C4×C23C2411yescharacteristic
134C22⋊D23—22no—
135C22⋊D23—42no—
136C22⋊D23—42no—
137C22⋊D23—81no—
138C2×Dic23—21no—
139C2×Dic23—21no—
140C2×Dic23—81no—
141C2×Dic23C2×D411yescharacteristic
142C2×Dic23C2×D411yescharacteristic
143C2×Dic23C2×D411yescharacteristic
144D92—21no—
145D92—21no—
146D92—21no—
147D92—21no—
148D92—42no—
149C4×D23—21no—
150C4×D23—21no—
151C4×D23—42no—
152C4×D23—42no—
153Dic46—42no—
154C8×C23—21no—
155C8×C23—21no—
156C23⋊C8—21no—
157C23⋊C8—21no—
158#3306—231nomaximal, Sylow
159C22×C23—22no—
160C22×C23—21no—
161C22×C23—21no—
162C22×C23—21no—
163C22×C23—41no—
164C22×C23—41no—
165C22×C23C22×D411yescharacteristic
166C2×D23—21no—
167C2×D23—21no—
168C2×D23—41no—
169C2×D23—41no—
170C2×D23—41no—
171C2×D23—41no—
172C2×D23—41no—
173C2×D23—41no—
174C2×D23—84no—
175C2×D23AGL(1,ℤ/8)12yes—
176C4×C23—21no—
177C4×C23—41no—
178C4×C23—41no—
179C4×C23—41no—
180C4×C23C2×#4111yescharacteristic
181C4×C23H(5,𝔽2)11yescharacteristic
182Dic23—21no—
183Dic23—21no—
184Dic23—21no—
185Dic23—41no—
186Dic23—41no—
187#547—231no—
188#546—231no—
189#489—231no—
190#483—231no—
191#481—231no—
192#476—231no—
193#469—231no—
194#465—231no—
195#463—231no—
196#449—231no—
197#447—231no—
198#442—231no—
199#435—231no—
200#417D2311yescharacteristic, complemented
201C2×#102—231no—
202C2×C23—42no—
203C2×C23—41no—
204C2×C23#54611yescharacteristic
205C2×C23C2×AGL(1,ℤ/8)11yescharacteristic
206C2×C23#57711yescharacteristic
207D23—22no—
208D23—81no—
209D23—81no—
210C2×#41—461no—
211C2×#41C2×D2311yescharacteristic
212C22×D4—231no—
213C2×SD16—231no—
214C2×D8—231no—
215C2×D8—231no—
216C2×M16C2×D2311yescharacteristic, complemented
217C22×C8—231no—
218C4⋊Q8—231no—
219#124—231no—
220#123—461no—
221#123—461no—
222#123—461no—
223C22⋊Q8—231no—
224C22⋊Q8—461no—
225#121—231no—
226#121—231no—
227#121—231no—
228#121—461no—
229#120—461no—
230C4×D4—231no—
231C4×D4—231no—
232C4×D4—231no—
233C2×C4⋊C4—231no—
234C2×C4⋊C4C2×D2311yescharacteristic, complemented
235C2×C22⋊C4—461no—
236#106—231no—
237#106—231no—
238#106—231no—
239C4⋊C8—231no—
240#103—231no—
241#103C2×D2311yescharacteristic, complemented
242#103C2×D2311yescharacteristic, complemented
243#102—231no—
244#102—231no—
245#102—231no—
246#102—231no—
247#102—231no—
248#102C2×D2311yescharacteristic
249#102C2×D2311yescharacteristic
250C22⋊C8—231no—
251C22⋊C8—231no—
252#97—231no—
253C23#330611yescharacteristic, complemented, Sylow
254C24—461no—
255#41—22no—
256#41—41no—
257#41—924no—
258C2×Q8—461no—
259C2×Q8C22×D2311yescharacteristic
260C2×D4—21no—
261C2×D4—231no—
262C2×D4—231no—
263C2×D4—231no—
264C2×D4—461no—
265C2×D4—461no—
266C2×D4—462no—
267C2×D4—461no—
268C2×D4—461no—
269C2×D4—921no—
270C2×D4C22×D2311yescharacteristic
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—231no—
274C22×C4—461no—
275C22×C4—461no—
276C22×C4—461no—
277C22×C4C22×D2311yescharacteristic
278SD16—921no—
279D8—462no—
280D8—921no—
281M16—41no—
282C2×C8—231no—
283C2×C8—231no—
284C2×C8—921no—
285C2×C8C22×D2311yescharacteristic
286C2×C8C22×D2311yescharacteristic
287C4⋊C4—21no—
288C4⋊C4—231no—
289C4⋊C4—231no—
290C4⋊C4—231no—
291C4⋊C4—461no—
292C4⋊C4—461no—
293C4⋊C4—461no—
294C4⋊C4C22×D2311yescharacteristic
295C4⋊C4C22×D2311yescharacteristic
296C22⋊C4—231no—
297C22⋊C4—231no—
298C22⋊C4—461no—
299C22⋊C4—461no—
300C22⋊C4—461no—
301C22⋊C4—461no—
302C22⋊C4—461no—
303C22⋊C4—461no—
304C22⋊C4—461no—
305C22⋊C4—461no—
306C42—231no—
307C23—21no—
308C23—231no—
309C23—461no—
310C23—461no—
311C23—922no—
312C23—922no—
313C23—1841no—
314C23D4×D2311yescharacteristic
315Q8—21no—
316Q8—21no—
317Q8—922no—
318D4—21no—
319D4—42no—
320D4—462no—
321D4—461no—
322D4—461no—
323D4—461no—
324D4—461no—
325D4—922no—
326D4—922no—
327D4—922no—
328D4—1841no—
329D4#6728812yescomplemented
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—42no—
336C2×C4—42no—
337C2×C4—231no—
338C2×C4—231no—
339C2×C4—231no—
340C2×C4—461no—
341C2×C4—461no—
342C2×C4—461no—
343C2×C4—461no—
344C2×C4—922no—
345C2×C4—922no—
346C2×C4—1841no—
347C2×C4D4×D2311yescharacteristic
348C2×C4C23×D2311yescharacteristic
349C8—21no—
350C8—21no—
351C8—461no—
352C8—461no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—22no—
357C22—41no—
358C22—41no—
359C22—232no—
360C22—461no—
361C22—461no—
362C22—921no—
363C22—921no—
364C22—921no—
365C22—921no—
366C22—921no—
367C22—921no—
368C22—1844no—
369C22C2×D4×D2311yescharacteristic
370C4—21no—
371C4—41no—
372C4—41no—
373C4—41no—
374C4—461no—
375C4—461no—
376C4—461no—
377C4—921no—
378C4—921no—
379C4C2×#6728811yescharacteristic
380C4#1062515511yescharacteristic
381C2—41no—
382C2—42no—
383C2—462no—
384C2—1841no—
385C2—1841no—
386C2#1309305711yescharacteristic
387C2AGL(1,ℤ/8)×D2311yescharacteristic
388C2#1309322611yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#417C2
socleC22×C23C22×D4
hypercenter#417D23
hypocenterC23#3306
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

Complements

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

NH ≅ G/Ntype
1. #13093068C2semidirect
2. #13093055C2semidirect
3. #13092778C2semidirect
4. #13092746C2semidirect
5. #13092735C2semidirect
6. #13092705C2semidirect
7. #13092670C2semidirect
8. #13092649C2semidirect
9. #13092635C2semidirect
10. #13092562C2semidirect
11. #13092552C2semidirect
12. #13092526C2semidirect
13. #13092486C2semidirect
14. #102×D23C2semidirect
15. C23×#417C2semidirect
19. C2×M16×C23C22semidirect
20. C2×C4⋊C4×C23C22semidirect
23. C2×#67274C22semidirect
29. #10625101C22semidirect
39. #10625064C22semidirect
41. #10625059C22semidirect
42. C23×#103C22semidirect
43. C23×#103C22semidirect
46. #10625017C22semidirect
48. C22⋊(C23⋊C8)C22semidirect
50. #10625003C22semidirect
52. #10624999C22semidirect
53. #10624997C22semidirect
54. Dic23⋊C8C22semidirect
57. #10624990C22semidirect
58. #10624990C22semidirect
124. D4×C23#41semidirect
200. #417D23semidirect
216. C2×M16C2×D23semidirect
234. C2×C4⋊C4C2×D23semidirect
241. #103C2×D23semidirect
242. #103C2×D23semidirect
253. C23#3306semidirect
329. D4#67288semidirect

Maximal subgroups

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

subgroupindex
#130930682
#130930552
#130927782
#130927462
#130927352
#130927052
#130926702
#130926492
#130926352
#130925622
#130925522
#130925262
#130924862
#102×D232
C23×#4172
#330623