Finite Group Databasebeta

← #15685358

Subgroups — #15685358

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#13093071C211yesmaximal, characteristic, complemented
2#13092776C211yesmaximal, characteristic, complemented
3#13092745C211yesmaximal, characteristic, complemented
4#13092733C211yesmaximal, characteristic, complemented
5#13092707C211yesmaximal, characteristic, complemented
6#13092668C211yesmaximal, characteristic, complemented
7#13092648C211yesmaximal, characteristic, complemented
8#13092629C211yesmaximal, characteristic, complemented
9#13092562C211yesmaximal, characteristic, complemented
10#13092551C211yesmaximal, characteristic, complemented
11#13092527C211yesmaximal, characteristic, complemented
12#13092489C211yesmaximal, characteristic, complemented
13#13092418C211yesmaximal, characteristic, complemented
14C2×#10625014C211yesmaximal, characteristic, complemented
15C23×#546C211yesmaximal, characteristic, complemented
16C2×#41×C23C2211yescharacteristic
17C22×D4×C23C2211yescharacteristic
18C2×#67290—21no—
19C23×#124C2211yescharacteristic
20C23×#123—21no—
21C23×C22⋊Q8C2211yescharacteristic
22C23×#121—21no—
23C23×#121C2211yescharacteristic
24C23×#120—21no—
25C4×D4×C23C2211yescharacteristic
26C4×D4×C23C2211yescharacteristic
27C2×C22⋊C4×C23—21no—
28C2×#67274C2211yescharacteristic, complemented
29C2×#67272C2211yescharacteristic
30C2×#67272C2211yescharacteristic
31#10625101C2211yescharacteristic
32#10625101C2211yescharacteristic, complemented
33C2×C4⋊Dic23C2211yescharacteristic
34C2×C4⋊Dic23C2211yescharacteristic, complemented
35C2×#67267C2211yescharacteristic, complemented
36C22×C23⋊C8C2211yescharacteristic
37#10625068—21no—
38#10625057—21no—
39#10625057—21no—
40C4×D92C2211yescharacteristic, complemented
41#10625040C2211yescharacteristic, complemented
42#10625017C2211yescharacteristic, complemented
43#10625017C2211yescharacteristic, complemented
44#10625017C2211yescharacteristic, complemented
45#10625014C2211yescharacteristic
46#10625014C2211yescharacteristic
47#10625014C2211yescharacteristic
48#10625014C2211yescharacteristic
49#10625014C2211yescharacteristic
50#10625014C2211yescharacteristic
51C22⋊(C23⋊C8)C2211yescharacteristic
52C22⋊(C23⋊C8)C2211yescharacteristic, complemented
53#10624991C2211yescharacteristic, complemented
54#10624990C2211yescharacteristic, complemented
55#10624990C2211yescharacteristic, complemented
56#10624990C2211yescharacteristic, complemented
57C4⋊(C23⋊C8)C2211yescharacteristic, complemented
58#10624985C2211yescharacteristic, complemented
59C24×C23—21no—
60#41×C23—22no—
61#41×C23—41no—
62C2×Q8×C23C2311yescharacteristic
63C2×D4×C23—22no—
64C2×D4×C23—21no—
65C2×D4×C23—21no—
66C2×D4×C23—21no—
67C2×D4×C23—41no—
68C2×D4×C23D411yescharacteristic
69C2×D4×C23C2311yescharacteristic
70C2×D4×C23C2311yescharacteristic
71C22×C4×C23—21no—
72C22×C4×C23—21no—
73C22×C4×C23C2311yescharacteristic
74C22×C4×C23C2311yescharacteristic
75C2×C22⋊D23—21no—
76C2×C22⋊D23—21no—
77C22×Dic23—21no—
78C22×Dic23—21no—
79#67290—44no—
80C2×D92C2311yescharacteristic
81C2×C4×D23—21no—
82C2×Dic46—21no—
83C4⋊C4×C23—21no—
84C4⋊C4×C23D411yescharacteristic
85C4⋊C4×C23C2311yescharacteristic
86C22⋊C4×C23—21no—
87C22⋊C4×C23—21no—
88C22⋊C4×C23—21no—
89C22⋊C4×C23—21no—
90C22⋊C4×C23—21no—
91C22⋊C4×C23D411yescharacteristic
92C22⋊C4×C23D411yescharacteristic
93C42×C23C2311yescharacteristic
94#67274—41no—
95#67272—22no—
96#67272—41no—
97(C2×D23)⋊C4—21no—
98(C2×D23)⋊C4—21no—
99(C2×D23)⋊C4—21no—
100C4⋊Dic23—21no—
101C4⋊Dic23—21no—
102C4⋊Dic23—21no—
103C4⋊Dic23C2311yescharacteristic
104C4⋊Dic23C2311yescharacteristic
105C4⋊Dic23C2311yescharacteristic
106#67267—41no—
107C2×C23⋊C8—41no—
108C2×C23⋊C8C2311yescharacteristic
109C2×C23⋊C8C2311yescharacteristic
110C2×C23⋊C8C2311yescharacteristic
111C2×C23⋊C8C2311yescharacteristic
112C23×C23—21no—
113C23×C23—21no—
114C23×C23—42no—
115C23×C23—42no—
116C23×C23—81no—
117C23×C23C2×D411yescharacteristic
118C23×C23C2×D411yescharacteristic
119C22×D23—21no—
120Q8×C23—21no—
121Q8×C23—21no—
122D4×C23—22no—
123D4×C23—21no—
124D4×C23—21no—
125D4×C23—21no—
126D4×C23—42no—
127D4×C23—42no—
128D4×C23—81no—
129D4×C23#4112yescomplemented
130C2×C4×C23—21no—
131C2×C4×C23—21no—
132C2×C4×C23—21no—
133C2×C4×C23—21no—
134C2×C4×C23—21no—
135C2×C4×C23—21no—
136C2×C4×C23—42no—
137C2×C4×C23—81no—
138C2×C4×C23C2×D411yescharacteristic
139C2×C4×C23C2×D411yescharacteristic
140C2×C4×C23C2×D411yescharacteristic
141C2×C4×C23C2×D411yescharacteristic
142C2×C4×C23C2411yescharacteristic
143C22⋊D23—42no—
144C22⋊D23—42no—
145C2×Dic23—21no—
146C2×Dic23—21no—
147C2×Dic23—21no—
148C2×Dic23—42no—
149C2×Dic23—42no—
150D92—21no—
151D92—21no—
152C4×D23—42no—
153Dic46—42no—
154C23⋊C8—21no—
155C23⋊C8—21no—
156C23⋊C8—21no—
157C23⋊C8—21no—
158#3306—231nomaximal, Sylow
159C22×C23—21no—
160C22×C23—21no—
161C22×C23—21no—
162C22×C23—22no—
163C22×C23—21no—
164C22×C23—21no—
165C22×C23—41no—
166C22×C23—41no—
167C22×C23—41no—
168C22×C23—41no—
169C22×C23—41no—
170C22×C23—84no—
171C22×C23AGL(1,ℤ/8)12yes—
172C22×C23C22×D411yescharacteristic
173C2×D23—41no—
174C2×D23—41no—
175C2×D23—41no—
176C4×C23—21no—
177C4×C23—21no—
178C4×C23—21no—
179C4×C23—21no—
180C4×C23—41no—
181C4×C23—41no—
182C4×C23C2×#4111yescharacteristic
183C4×C23H(5,𝔽2)11yescharacteristic
184Dic23—41no—
185Dic23—41no—
186Dic23—41no—
187#547—231no—
188#546D2311yescharacteristic, complemented
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#417—231no—
201C2×#102—231no—
202C2×C23—22no—
203C2×C23—41no—
204C2×C23—42no—
205C2×C23—81no—
206C2×C23#54611yescharacteristic
207C2×C23C2×AGL(1,ℤ/8)11yescharacteristic
208C2×C23#57711yescharacteristic
209D23—81no—
210C2×#41—461no—
211C2×#41C2×D2311yescharacteristic
212C22×D4C2×D2311yescharacteristic
213C2×SD16—231no—
214C2×D8—231no—
215C2×D8—231no—
216C2×M16—231no—
217C22×C8—231no—
218C4⋊Q8—231no—
219#124C2×D2311yescharacteristic
220#123—21no—
221#123—461no—
222#123—461no—
223C22⋊Q8—461no—
224C22⋊Q8C2×D2311yescharacteristic
225#121—21no—
226#121—231no—
227#121—231no—
228#121C2×D2311yescharacteristic
229#120—21no—
230C4×D4—231no—
231C4×D4C2×D2311yescharacteristic
232C4×D4C2×D2311yescharacteristic
233C2×C4⋊C4—231no—
234C2×C4⋊C4—231no—
235C2×C22⋊C4—21no—
236#106—231no—
237#106—231no—
238#106—231no—
239C4⋊C8—231no—
240#103—231no—
241#103—231no—
242#103—231no—
243#102—231no—
244#102—231no—
245#102—231no—
246#102—231no—
247#102—231no—
248#102—231no—
249#102—231no—
250C22⋊C8—231no—
251C22⋊C8—231no—
252#97—231no—
253C23#330611yescharacteristic, complemented, Sylow
254C24—21no—
255#41—22no—
256#41—41no—
257#41—924no—
258C2×Q8—461no—
259C2×Q8C22×D2311yescharacteristic
260C2×D4—22no—
261C2×D4—21no—
262C2×D4—21no—
263C2×D4—21no—
264C2×D4—41no—
265C2×D4—231no—
266C2×D4—461no—
267C2×D4—461no—
268C2×D4C22⋊D2311yescharacteristic
269C2×D4C22×D2311yescharacteristic
270C2×D4C22×D2311yescharacteristic
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—461no—
274C22×C4—461no—
275C22×C4—461no—
276C22×C4C22×D2311yescharacteristic
277C22×C4C22×D2311yescharacteristic
278SD16—921no—
279D8—462no—
280D8—921no—
281M16—921no—
282C2×C8—231no—
283C2×C8—231no—
284C2×C8—231no—
285C2×C8—231no—
286C2×C8—921no—
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—21no—
297C22⋊C4—21no—
298C22⋊C4—21no—
299C22⋊C4—21no—
300C22⋊C4—21no—
301C22⋊C4—461no—
302C22⋊C4—461no—
303C22⋊C4—461no—
304C22⋊C4C22⋊D2311yescharacteristic
305C22⋊C4C22⋊D2311yescharacteristic
306C42C22×D2311yescharacteristic
307C23—21no—
308C23—21no—
309C23—42no—
310C23—42no—
311C23—81no—
312C23—461no—
313C23C2×C22⋊D2311yescharacteristic
314C23C2×C22⋊D2311yescharacteristic
315Q8—21no—
316Q8—21no—
317Q8—922no—
318D4—22no—
319D4—21no—
320D4—21no—
321D4—21no—
322D4—42no—
323D4—42no—
324D4—81no—
325D4—461no—
326D4—461no—
327D4—922no—
328D4—922no—
329D4#6729012yescomplemented
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—42no—
337C2×C4—81no—
338C2×C4—461no—
339C2×C4—461no—
340C2×C4—461no—
341C2×C4—922no—
342C2×C4—922no—
343C2×C4—922no—
344C2×C4C2×C22⋊D2311yescharacteristic
345C2×C4C2×C22⋊D2311yescharacteristic
346C2×C4C2×C22⋊D2311yescharacteristic
347C2×C4C2×C22⋊D2311yescharacteristic
348C2×C4C23×D2311yescharacteristic
349C8—461no—
350C8—461no—
351C8—461no—
352C8—461no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—22no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—84no—
365C22—921no—
366C22—921no—
367C22—921no—
368C22#1062512012yes—
369C22C22×C22⋊D2311yescharacteristic
370C4—21no—
371C4—21no—
372C4—21no—
373C4—21no—
374C4—41no—
375C4—41no—
376C4—921no—
377C4—921no—
378C4—921no—
379C4C2×#6729011yescharacteristic
380C4#1062515511yescharacteristic
381C2—22no—
382C2—41no—
383C2—42no—
384C2—81no—
385C2—1841no—
386C2#1309306111yescharacteristic
387C2C2×#1062512011yescharacteristic
388C2#1309322811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#546C2
socleC22×C23C22×D4
hypercenter#546D23
hypocenterC23#3306
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C4×D4 ◁ #546

Complements

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

NH ≅ G/Ntype
1. #13093071C2semidirect
2. #13092776C2semidirect
3. #13092745C2semidirect
4. #13092733C2semidirect
5. #13092707C2semidirect
6. #13092668C2semidirect
7. #13092648C2semidirect
8. #13092629C2semidirect
9. #13092562C2semidirect
10. #13092551C2semidirect
11. #13092527C2semidirect
12. #13092489C2semidirect
13. #13092418C2semidirect
14. C2×#10625014C2semidirect
15. C23×#546C2semidirect
28. C2×#67274C22semidirect
32. #10625101C22semidirect
34. C2×C4⋊Dic23C22semidirect
35. C2×#67267C22semidirect
40. C4×D92C22semidirect
41. #10625040C22semidirect
42. #10625017C22semidirect
43. #10625017C22semidirect
44. #10625017C22semidirect
52. C22⋊(C23⋊C8)C22semidirect
53. #10624991C22semidirect
54. #10624990C22semidirect
55. #10624990C22semidirect
56. #10624990C22semidirect
57. C4⋊(C23⋊C8)C22semidirect
58. #10624985C22semidirect
129. D4×C23#41semidirect
188. #546D23semidirect
253. C23#3306semidirect
329. D4#67290semidirect

Maximal subgroups

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

subgroupindex
#130930712
#130927762
#130927452
#130927332
#130927072
#130926682
#130926482
#130926292
#130925622
#130925512
#130925272
#130924892
#130924182
C2×#106250142
C23×#5462
#330623