Finite Group Databasebeta

← #15685243

Subgroups — #15685243

Order 2944.

420 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13093115C211yesmaximal, characteristic, complemented
2#13093061C211yesmaximal, characteristic, complemented
3#13092770C211yesmaximal, characteristic, complemented
4#13092752C211yesmaximal, characteristic, complemented
5#13092740C211yesmaximal, characteristic, complemented
6#13092719C211yesmaximal, characteristic, complemented
7#13092652C211yesmaximal, characteristic, complemented
8#13092646C211yesmaximal, characteristic, complemented
9#13092631C211yesmaximal, characteristic, complemented
10#13092563C211yesmaximal, characteristic, complemented
11#13092551C211yesmaximal, characteristic, complemented
12#13092497C211yesmaximal, characteristic, complemented
13C8×C22⋊D23C211yesmaximal, characteristic, complemented
14#13092410C211yesmaximal, characteristic, complemented
15C2×C23×#102C211yesmaximal, characteristic, complemented
16C22×D4×C23C2211yescharacteristic
17C2×#67290C2211yescharacteristic
18C22×C8×C23C2211yescharacteristic
19C2×C4⋊C4×C23C2211yescharacteristic
20#10625124—21no—
21C2×C22⋊Dic23—21no—
22#10625110—21no—
23#10625109C2211yescharacteristic
24#10625107C2211yescharacteristic
25#10625106—21no—
26D4×Dic23C2211yescharacteristic
27C2×#67272C2211yescharacteristic
28C2×#67272C2211yescharacteristic
29#10625101—21no—
30#10625101C2211yescharacteristic
31C4×C22⋊D23—21no—
32C4×C22⋊D23C2211yescharacteristic
33#10625095C2211yescharacteristic
34C2×#67263C2211yescharacteristic, complemented
35C2×C8×D23C2211yescharacteristic, complemented
36#10625069—21no—
37#10625066C2211yescharacteristic, complemented
38#10625065—21no—
39#10625064C2211yescharacteristic, complemented
40#10625063C2211yescharacteristic, complemented
41#10625061C2211yescharacteristic, complemented
42C23×#102C2211yescharacteristic
43C23×#102C2211yescharacteristic
44C23×#102C2211yescharacteristic
45C23×#102C2211yescharacteristic
46#10625014C2211yescharacteristic
47#10625014C2211yescharacteristic
48C22⋊(C23⋊C8)C2211yescharacteristic
49#10625003C2211yescharacteristic, complemented
50(C2×D23)⋊C8C2211yescharacteristic, complemented
51#10624999C2211yescharacteristic, complemented
52#10624998C2211yescharacteristic, complemented
53Dic23⋊C8C2211yescharacteristic, complemented
54C8×Dic23C2211yescharacteristic, complemented
55#10624992C2211yescharacteristic, complemented
56#10624992C2211yescharacteristic, complemented
57#10624989C2211yescharacteristic, complemented
58#10624989C2211yescharacteristic, complemented
59C24×C23—21no—
60C2×D4×C23—22no—
61C2×D4×C23—21no—
62C2×D4×C23—41no—
63C2×D4×C23C2311yescharacteristic
64C2×D4×C23C2311yescharacteristic
65C22×C4×C23—21no—
66C22×C4×C23C2311yescharacteristic
67C2×C22⋊D23—21no—
68C2×C22⋊D23—21no—
69C2×C22⋊D23—21no—
70C2×C22⋊D23D411yescharacteristic
71C22×Dic23—21no—
72C22×Dic23—21no—
73#67290—22no—
74#67290—41no—
75C2×D92—21no—
76C2×D92C2311yescharacteristic
77C2×C4×D23—21no—
78C2×C4×D23C2311yescharacteristic
79C2×Dic46C2311yescharacteristic
80C2×C8×C23—41no—
81C2×C8×C23C2311yescharacteristic
82C2×C8×C23C2311yescharacteristic
83C4⋊C4×C23—21no—
84C4⋊C4×C23C2311yescharacteristic
85C4⋊C4×C23C2311yescharacteristic
86C22⋊Dic23—21no—
87C22⋊Dic23—21no—
88C22⋊Dic23—21no—
89C22⋊Dic23—21no—
90C22⋊Dic23—21no—
91C22⋊Dic23D411yescharacteristic
92#67272—22no—
93#67272—41no—
94(C2×D23)⋊C4—21no—
95(C2×D23)⋊C4—21no—
96(C2×D23)⋊C4—21no—
97(C2×D23)⋊C4—21no—
98(C2×D23)⋊C4D411yescharacteristic
99C4⋊Dic23—21no—
100C4⋊Dic23C2311yescharacteristic
101C4⋊Dic23C2311yescharacteristic
102Dic23⋊C4—21no—
103Dic23⋊C4—21no—
104Dic23⋊C4D411yescharacteristic
105C4×Dic23—21no—
106C4×Dic23C2311yescharacteristic
107C2×C23⋊C8C2311yescharacteristic
108C2×C23⋊C8C2311yescharacteristic
109#67263—41no—
110C8×D23—41no—
111C23×C23—21no—
112C23×C23—21no—
113C23×C23—42no—
114C23×C23—42no—
115C23×C23—81no—
116C23×C23C2×D411yescharacteristic
117C22×D23—21no—
118C22×D23C2×D411yescharacteristic
119D4×C23—21no—
120D4×C23—21no—
121D4×C23—21no—
122D4×C23—42no—
123D4×C23#4112yes—
124C2×C4×C23—21no—
125C2×C4×C23—21no—
126C2×C4×C23—21no—
127C2×C4×C23—21no—
128C2×C4×C23—81no—
129C2×C4×C23C2×D411yescharacteristic
130C2×C4×C23C2411yescharacteristic
131C22⋊D23—22no—
132C22⋊D23—42no—
133C22⋊D23—42no—
134C22⋊D23—81no—
135C2×Dic23—21no—
136C2×Dic23—21no—
137C2×Dic23—21no—
138C2×Dic23—42no—
139C2×Dic23—81no—
140C2×Dic23C2×D411yescharacteristic
141C2×Dic23C2×D411yescharacteristic
142C2×Dic23C2×D411yescharacteristic
143D92—21no—
144D92—21no—
145D92—81no—
146C4×D23—21no—
147C4×D23—21no—
148C4×D23—81no—
149Dic46—21no—
150Dic46—21no—
151C8×C23—21no—
152C8×C23—21no—
153C23⋊C8—21no—
154C23⋊C8—21no—
155#3297—231nomaximal, Sylow
156C22×C23—21no—
157C22×C23—21no—
158C22×C23—22no—
159C22×C23—41no—
160C22×C23—41no—
161C22×C23—41no—
162C22×C23—41no—
163C22×C23—41no—
164C22×C23—84no—
165C22×C23#13512yes—
166C22×C23C22×D411yescharacteristic
167C2×D23—21no—
168C2×D23—21no—
169C2×D23—21no—
170C2×D23—41no—
171C2×D23—41no—
172C2×D23—41no—
173C4×C23—21no—
174C4×C23—41no—
175C4×C23—41no—
176C4×C23C2×#4111yescharacteristic
177C4×C23H(5,𝔽2)11yescharacteristic
178Dic23—21no—
179Dic23—21no—
180Dic23—21no—
181Dic23—41no—
182Dic23—41no—
183Dic23—41no—
184#553—231no—
185#546—231no—
186#488—231no—
187#484—231no—
188#482—231no—
189#478—231no—
190#466—231no—
191#465—231no—
192#463—231no—
193#449—231no—
194#447—231no—
195C4×D8—231no—
196C8×D4—231no—
197#416—231no—
198C2×#102D2311yescharacteristic, complemented
199C2×C23—22no—
200C2×C23—42no—
201C2×C23—81no—
202C2×C23#54611yescharacteristic
203C2×C23C2×#13511yescharacteristic
204C2×C23#57611yescharacteristic
205D23—41no—
206D23—81no—
207C2×#41—231no—
208C22×D4C2×D2311yescharacteristic
209C2×SD16—231no—
210C2×D8—231no—
211C2×D8—231no—
212C22×C8—231no—
213C22×C8C2×D2311yescharacteristic
214#126—461no—
215#125—231no—
216#124—231no—
217#123—461no—
218#123—461no—
219C22⋊Q8—231no—
220#121—231no—
221#121—231no—
222#121—231no—
223#121—461no—
224#121—461no—
225#120—461no—
226C4×D4—231no—
227C4×D4—231no—
228C4×D4—231no—
229C4×D4—461no—
230#117—231no—
231C2×C4⋊C4C2×D2311yescharacteristic
232C2×C22⋊C4—461no—
233#107—231no—
234#107—231no—
235#106—231no—
236C4⋊C8—231no—
237#103—231no—
238#103—231no—
239#103—231no—
240#102—231no—
241#102—231no—
242#102—231no—
243#102C2×D2311yescharacteristic
244#102C2×D2311yescharacteristic
245#102C2×D2311yescharacteristic
246#102C2×D2311yescharacteristic
247C22⋊C8—231no—
248C22⋊C8—231no—
249C4×C8—231no—
250C23#329711yescharacteristic, complemented, Sylow
251C24—21no—
252#41—462no—
253#41—921no—
254C2×Q8—231no—
255C2×D4—22no—
256C2×D4—21no—
257C2×D4—41no—
258C2×D4—231no—
259C2×D4—231no—
260C2×D4—461no—
261C2×D4—461no—
262C2×D4—461no—
263C2×D4—461no—
264C2×D4C22×D2311yescharacteristic
265C2×D4C22×D2311yescharacteristic
266C22×C4—21no—
267C22×C4—231no—
268C22×C4—461no—
269C22×C4—461no—
270C22×C4—461no—
271C22×C4C22×D2311yescharacteristic
272SD16—921no—
273D8—462no—
274D8—921no—
275C2×C8—41no—
276C2×C8—231no—
277C2×C8—231no—
278C2×C8—921no—
279C2×C8C22×D2311yescharacteristic
280C2×C8C22×D2311yescharacteristic
281C4⋊C4—21no—
282C4⋊C4—231no—
283C4⋊C4—231no—
284C4⋊C4—231no—
285C4⋊C4—461no—
286C4⋊C4—461no—
287C4⋊C4—461no—
288C4⋊C4C22×D2311yescharacteristic
289C4⋊C4C22×D2311yescharacteristic
290C22⋊C4—231no—
291C22⋊C4—231no—
292C22⋊C4—461no—
293C22⋊C4—461no—
294C22⋊C4—461no—
295C22⋊C4—461no—
296C22⋊C4—461no—
297C22⋊C4—461no—
298C22⋊C4—461no—
299C22⋊C4—461no—
300C22⋊C4—461no—
301C42—231no—
302C42—461no—
303C23—21no—
304C23—21no—
305C23—42no—
306C23—42no—
307C23—81no—
308C23—231no—
309C23—461no—
310C23D4×D2311yescharacteristic
311Q8—461no—
312Q8—461no—
313D4—21no—
314D4—21no—
315D4—21no—
316D4—42no—
317D4—462no—
318D4—461no—
319D4—461no—
320D4—922no—
321D4—922no—
322D4—1841no—
323D4—1841no—
324D4#6728812yes—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—81no—
330C2×C4—231no—
331C2×C4—231no—
332C2×C4—231no—
333C2×C4—461no—
334C2×C4—461no—
335C2×C4—461no—
336C2×C4—461no—
337C2×C4—461no—
338C2×C4—922no—
339C2×C4—1841no—
340C2×C4—1841no—
341C2×C4D4×D2311yescharacteristic
342C2×C4C23×D2311yescharacteristic
343C8—21no—
344C8—21no—
345C8—461no—
346C8—461no—
347C22—21no—
348C22—21no—
349C22—22no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—84no—
356C22—461no—
357C22—461no—
358C22—461no—
359C22—921no—
360C22—921no—
361C22—921no—
362C22#1062508712yes—
363C22C2×D4×D2311yescharacteristic
364C4—21no—
365C4—41no—
366C4—41no—
367C4—461no—
368C4—461no—
369C4—461no—
370C4—921no—
371C4—921no—
372C4—921no—
373C4C2×#6728811yescharacteristic
374C4#1062515511yescharacteristic
375C2—22no—
376C2—42no—
377C2—81no—
378C2—921no—
379C2—1841no—
380C2#1309305711yescharacteristic
381C2C2×#1062508711yescharacteristic
382C2#1309321811yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC2×C23×#102C2
socleC22×C23C22×D4
hypercenterC2×#102D23
hypocenterC23#3297
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
1. #13093115C2semidirect
2. #13093061C2semidirect
3. #13092770C2semidirect
4. #13092752C2semidirect
5. #13092740C2semidirect
6. #13092719C2semidirect
7. #13092652C2semidirect
8. #13092646C2semidirect
9. #13092631C2semidirect
10. #13092563C2semidirect
11. #13092551C2semidirect
12. #13092497C2semidirect
13. C8×C22⋊D23C2semidirect
14. #13092410C2semidirect
15. C2×C23×#102C2semidirect
34. C2×#67263C22semidirect
35. C2×C8×D23C22semidirect
37. #10625066C22semidirect
39. #10625064C22semidirect
40. #10625063C22semidirect
41. #10625061C22semidirect
49. #10625003C22semidirect
50. (C2×D23)⋊C8C22semidirect
51. #10624999C22semidirect
52. #10624998C22semidirect
53. Dic23⋊C8C22semidirect
54. C8×Dic23C22semidirect
55. #10624992C22semidirect
56. #10624992C22semidirect
57. #10624989C22semidirect
58. #10624989C22semidirect
198. C2×#102D23semidirect
250. C23#3297semidirect

Maximal subgroups

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

subgroupindex
#130931152
#130930612
#130927702
#130927522
#130927402
#130927192
#130926522
#130926462
#130926312
#130925632
#130925512
#130924972
C8×C22⋊D232
#130924102
C2×C23×#1022
#329723