Finite Group Databasebeta

← #15683575

Subgroups — #15683575

Order 2944.

406 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13092891C211yesmaximal, characteristic, complemented
2#13092755C211yesmaximal, characteristic, complemented
3#13092738C211yesmaximal, characteristic, complemented
4#13092704C211yesmaximal, characteristic, complemented
5#13092694C211yesmaximal, characteristic, complemented
6#13092629C211yesmaximal, characteristic, complemented
7#13092629C211yesmaximal, characteristic, complemented
8#13092567C211yesmaximal, characteristic, complemented
9#13092550C211yesmaximal, characteristic
10#13092527C211yesmaximal, characteristic, complemented
11#13092515C211yesmaximal, characteristic, complemented
12C4×#67274C211yesmaximal, characteristic, complemented
13C4×#67272C211yesmaximal, characteristic, complemented
14#13092478C211yesmaximal, characteristic, complemented
15C23×#542C211yesmaximal, characteristic, complemented
16C22×D92C2211yescharacteristic
17C23×C4⋊Q8C2211yescharacteristic, complemented
18C23×#126—21no—
19C23×#124—21no—
20C23×#124C2211yescharacteristic, complemented
21C23×#123—21no—
22C23×C22⋊Q8—21no—
23C23×C22⋊Q8C2211yescharacteristic
24C23×#121C2211yescharacteristic
25C4×Q8×C23C2211yescharacteristic, complemented
26C4×D4×C23C2211yescharacteristic, complemented
27C23×#117C2211yescharacteristic
28C2×#67274C2211yescharacteristic
29C2×#67274C2211yescharacteristic
30C2×#67272C2211yescharacteristic
31C2×#67272C2211yescharacteristic
32#10625097C2211yescharacteristic
33#10625064—21no—
34#10625064—21no—
35C22⋊C4×D23—21no—
36C22⋊C4×D23—21no—
37C4×D92C2211yescharacteristic
38C4×D92C2211yescharacteristic
39C4×D92C2211yescharacteristic
40C4×D92C2211yescharacteristic
41#10625017C2211yescharacteristic, complemented
42#10625017C2211yescharacteristic, complemented
43#10625014C2211yescharacteristic, complemented
44#10625014C2211yescharacteristic, complemented
45C22⋊(C23⋊C8)C2211yescharacteristic
46C22⋊(C23⋊C8)C2211yescharacteristic
47#10624991C2211yescharacteristic
48#10624991C2211yescharacteristic
49#10624991C2211yescharacteristic
50#10624991C2211yescharacteristic
51#10624990C2211yescharacteristic, complemented
52#10624990C2211yescharacteristic, complemented
53#10624989C2211yescharacteristic, complemented
54#10624989C2211yescharacteristic, complemented
55C4⋊(C23⋊C8)C2211yescharacteristic, complemented
56C4⋊(C23⋊C8)C2211yescharacteristic, complemented
57#10624985C2211yescharacteristic, complemented
58C4×C23⋊C8C2211yescharacteristic, complemented
59C23×D23—21no—
60C2×Q8×C23—21no—
61C2×Q8×C23C2311yescharacteristic
62C2×D4×C23—21no—
63C2×D4×C23C2311yescharacteristic
64C22×C4×C23—21no—
65C22×C4×C23C2311yescharacteristic
66C2×D92—21no—
67C2×D92—22no—
68C2×D92—22no—
69C2×D92C2311yescharacteristic
70C2×D92C2311yescharacteristic
71C2×C4×D23—21no—
72C2×C4×D23—21no—
73C2×C4×D23—21no—
74C2×C4×D23—21no—
75C4⋊C4×C23—21no—
76C4⋊C4×C23—21no—
77C4⋊C4×C23—21no—
78C4⋊C4×C23D411yescharacteristic
79C4⋊C4×C23D411yescharacteristic
80C4⋊C4×C23C2311yescharacteristic
81C4⋊C4×C23C2311yescharacteristic
82C22⋊C4×C23—21no—
83C22⋊C4×C23—21no—
84C22⋊C4×C23—21no—
85C22⋊C4×C23—21no—
86C22⋊C4×C23—21no—
87C22⋊C4×C23D411yescharacteristic
88C22⋊C4×C23D411yescharacteristic
89C42×C23—21no—
90C42×C23C2311yescharacteristic
91C42×C23C2311yescharacteristic
92C22⋊Dic23—21no—
93#67274—22no—
94#67274—22no—
95#67272—22no—
96#67272—22no—
97(C2×D23)⋊C4—21no—
98(C2×D23)⋊C4—21no—
99(C2×D23)⋊C4—21no—
100(C2×D23)⋊C4—21no—
101C4⋊Dic23C2311yescharacteristic
102C4⋊Dic23C2311yescharacteristic
103C4×Dic23—21no—
104C2×C23⋊C8C2311yescharacteristic
105C2×C23⋊C8C2311yescharacteristic
106C2×C23⋊C8C2311yescharacteristic
107C2×C23⋊C8C2311yescharacteristic
108C23×C23—21no—
109C23×C23C2×D411yescharacteristic
110C22×D23—21no—
111C22×D23—21no—
112C22×D23—24no—
113C22×D23—81no—
114C22×D23—81no—
115Q8×C23—21no—
116Q8×C23—21no—
117Q8×C23—81no—
118D4×C23—21no—
119D4×C23—21no—
120D4×C23—81no—
121C2×C4×C23—21no—
122C2×C4×C23—21no—
123C2×C4×C23—21no—
124C2×C4×C23—21no—
125C2×C4×C23—21no—
126C2×C4×C23—81no—
127C2×C4×C23C2×D411yescharacteristic
128C2×C4×C23C2×D411yescharacteristic
129C2×C4×C23C2×D411yescharacteristic
130C2×C4×C23C2×D411yescharacteristic
131C2×C4×C23C2×D411yescharacteristic
132C2×C4×C23C2411yescharacteristic
133C2×Dic23—21no—
134C2×Dic23—21no—
135D92—24no—
136D92—21no—
137D92—21no—
138D92#4112yes—
139D92#4112yes—
140C4×D23—81no—
141C4×D23—81no—
142C4×D23—81no—
143C4×D23—81no—
144C23⋊C8—21no—
145C23⋊C8—21no—
146C23⋊C8—21no—
147C23⋊C8—21no—
148#3118—231nomaximal, Sylow
149C22×C23—21no—
150C22×C23—21no—
151C22×C23—21no—
152C22×C23—41no—
153C22×C23—41no—
154C22×C23—41no—
155C22×C23C22×D411yescharacteristic
156C2×D23—22no—
157C2×D23—22no—
158C2×D23—41no—
159C2×D23—41no—
160C2×D23—41no—
161C2×D23—41no—
162C2×D23—84no—
163C4×C23—21no—
164C4×C23—21no—
165C4×C23—21no—
166C4×C23—21no—
167C4×C23—21no—
168C4×C23—41no—
169C4×C23—41no—
170C4×C23—41no—
171C4×C23C2×#4111yescharacteristic
172C4×C23C2×#4111yescharacteristic
173Dic23—41no—
174Dic23—41no—
175#542D2311yescharacteristic, complemented
176#518—231no—
177#485—231no—
178#482—231no—
179#476—231no—
180#474—231no—
181#463—231no—
182#463—231no—
183#450—231no—
184#447—231no—
185#442—231no—
186#440—231no—
187C4×SD16—231no—
188C4×D8—231no—
189#433—231no—
190C2×C23—41no—
191C2×C23—81no—
192C2×C23#52511yescharacteristic
193C2×C23#57611yescharacteristic
194C2×C23#57711yescharacteristic
195D23—42no—
196D23—42no—
197C22×D4—231no—
198C2×SD16—231no—
199C2×SD16—231no—
200C2×D8—231no—
201C2×D8—231no—
202C4⋊Q8C2×D2311yescharacteristic, complemented
203#126—21no—
204#124—21no—
205#124C2×D2311yescharacteristic, complemented
206#123—21no—
207C22⋊Q8—21no—
208C22⋊Q8C2×D2311yescharacteristic
209#121C2×D2311yescharacteristic
210C4×Q8C2×D2311yescharacteristic, complemented
211C4×D4—231no—
212C4×D4—231no—
213C4×D4—231no—
214C4×D4—231no—
215C4×D4—461no—
216C4×D4—461no—
217C4×D4C2×D2311yescharacteristic, complemented
218#117—231no—
219#117C2×D2311yescharacteristic
220C2×C22⋊C4—461no—
221C2×C22⋊C4—461no—
222#107—231no—
223#107—231no—
224#106—231no—
225#106—231no—
226C4⋊C8—231no—
227C4⋊C8—231no—
228#103—231no—
229#103—231no—
230#102—231no—
231#102—231no—
232#102—231no—
233#102—231no—
234#102—231no—
235#102—231no—
236C22⋊C8—231no—
237C22⋊C8—231no—
238#97—231no—
239C4×C8—231no—
240C23#311811yescharacteristic, complemented, Sylow
241C24—461no—
242C2×Q8—21no—
243C2×Q8C22×D2311yescharacteristic
244C2×D4—21no—
245C2×D4—231no—
246C2×D4—231no—
247C2×D4—462no—
248C2×D4—462no—
249C2×D4—461no—
250C2×D4C22×D2311yescharacteristic
251C22×C4—21no—
252C22×C4—461no—
253C22×C4—461no—
254C22×C4—461no—
255C22×C4—461no—
256C22×C4C22×D2311yescharacteristic
257SD16—462no—
258SD16—462no—
259D8—462no—
260D8—462no—
261C2×C8—231no—
262C2×C8—231no—
263C2×C8—231no—
264C2×C8—231no—
265C4⋊C4—21no—
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—231no—
269C4⋊C4—231no—
270C4⋊C4C22⋊D2311yescharacteristic
271C4⋊C4C22⋊D2311yescharacteristic
272C4⋊C4C22×D2311yescharacteristic
273C4⋊C4C22×D2311yescharacteristic
274C22⋊C4—21no—
275C22⋊C4—21no—
276C22⋊C4—21no—
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—461no—
280C22⋊C4—461no—
281C22⋊C4—461no—
282C22⋊C4—461no—
283C22⋊C4—461no—
284C22⋊C4C22⋊D2311yescharacteristic
285C22⋊C4C22⋊D2311yescharacteristic
286C42—21no—
287C42—461no—
288C42C22×D2311yescharacteristic
289C42C22×D2311yescharacteristic
290C23—21no—
291C23—464no—
292C23—461no—
293C23—461no—
294C23—1841no—
295C23—1841no—
296C23C2×C22⋊D2311yescharacteristic
297Q8—21no—
298Q8—21no—
299Q8—81no—
300D4—21no—
301D4—21no—
302D4—81no—
303D4—232no—
304D4—232no—
305D4—464no—
306D4—461no—
307D4—461no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—81no—
314C2×C4—461no—
315C2×C4—461no—
316C2×C4—1841no—
317C2×C4—1841no—
318C2×C4—1841no—
319C2×C4—1841no—
320C2×C4C2×C22⋊D2311yescharacteristic
321C2×C4C2×C22⋊D2311yescharacteristic
322C2×C4C2×C22⋊D2311yescharacteristic
323C2×C4C2×C22⋊D2311yescharacteristic
324C2×C4C2×C22⋊D2311yescharacteristic
325C2×C4C23×D2311yescharacteristic
326C8—461no—
327C8—461no—
328C8—461no—
329C8—461no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—462no—
337C22—462no—
338C22—921no—
339C22—921no—
340C22—921no—
341C22—921no—
342C22—1844no—
343C22C22×C22⋊D2311yescharacteristic
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—21no—
349C4—41no—
350C4—41no—
351C4—41no—
352C4—921no—
353C4—921no—
354C4#41×D2311yescharacteristic
355C4#41×D2311yescharacteristic
356C2—41no—
357C2—81no—
358C2—922no—
359C2—922no—
360C2#1309292411yescharacteristic
361C2#1309322011yescharacteristic
362C2#1309322511yescharacteristic
subgroupG/H
centerC22C22×C22⋊D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#542C2
socleC22×C23C22×D4
prime radical#13092550C2
hypercenter#542D23
hypocenterC23#3118
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ #117 ◁ #542

Complements

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

NH ≅ G/Ntype
1. #13092891C2semidirect
2. #13092755C2semidirect
3. #13092738C2semidirect
4. #13092704C2semidirect
5. #13092694C2semidirect
6. #13092629C2semidirect
7. #13092629C2semidirect
8. #13092567C2semidirect
10. #13092527C2semidirect
11. #13092515C2semidirect
12. C4×#67274C2semidirect
13. C4×#67272C2semidirect
14. #13092478C2semidirect
15. C23×#542C2semidirect
17. C23×C4⋊Q8C22semidirect
20. C23×#124C22semidirect
25. C4×Q8×C23C22semidirect
26. C4×D4×C23C22semidirect
41. #10625017C22semidirect
42. #10625017C22semidirect
43. #10625014C22semidirect
44. #10625014C22semidirect
51. #10624990C22semidirect
52. #10624990C22semidirect
53. #10624989C22semidirect
54. #10624989C22semidirect
55. C4⋊(C23⋊C8)C22semidirect
56. C4⋊(C23⋊C8)C22semidirect
57. #10624985C22semidirect
58. C4×C23⋊C8C22semidirect
175. #542D23semidirect
202. C4⋊Q8C2×D23semidirect
205. #124C2×D23semidirect
210. C4×Q8C2×D23semidirect
217. C4×D4C2×D23semidirect
240. C23#3118semidirect

Maximal subgroups

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

subgroupindex
#130928912
#130927552
#130927382
#130927042
#130926942
#130926292
#130925672
#130925502
#130925272
#130925152
C4×#672742
C4×#672722
#130924782
C23×#5422
#311823