Finite Group Databasebeta

← #15683579

Subgroups — #15683579

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#13093032C211yesmaximal, characteristic, complemented
2#13092889C211yesmaximal, characteristic, complemented
3#13092761C211yesmaximal, characteristic, complemented
4#13092739C211yesmaximal, characteristic, complemented
5#13092706C211yesmaximal, characteristic, complemented
6#13092695C211yesmaximal, characteristic, complemented
7#13092631C211yesmaximal, characteristic, complemented
8#13092630C211yesmaximal, characteristic, complemented
9#13092569C211yesmaximal, characteristic, complemented
10#13092549C211yesmaximal, characteristic
11#13092519C211yesmaximal, characteristic, complemented
12C4×#67273C211yesmaximal, characteristic, complemented
13C4×#67272C211yesmaximal, characteristic, complemented
14#13092479C211yesmaximal, characteristic, complemented
15C23×#442C211yesmaximal, characteristic, complemented
16C2×D4×D23C2211yescharacteristic
17C2×D8×C23C2211yescharacteristic
18C4×D4×C23C2211yescharacteristic
19C4×D4×C23C2211yescharacteristic, complemented
20#10625109C2211yescharacteristic
21#10625107C2211yescharacteristic, complemented
22D4×Dic23C2211yescharacteristic
23C2×#67273C2211yescharacteristic
24C2×#67272C2211yescharacteristic
25#10625100—21no—
26C4×C22⋊D23—21no—
27C2×(C2×D23)⋊C4—21no—
28#10625095—21no—
29C2×#67263C2211yescharacteristic
30#10625068C2211yescharacteristic
31#10625064C2211yescharacteristic
32#10625063C2211yescharacteristic
33#10625059C2211yescharacteristic, complemented
34#10625056—21no—
35(C22⋊D23)⋊C4—21no—
36C22⋊C4×D23—21no—
37#10625050—21no—
38C4×D92C2211yescharacteristic
39#10625043C2211yescharacteristic
40C4×Dic46C2211yescharacteristic, complemented
41C23×#106C2211yescharacteristic, complemented
42C23×#102C2211yescharacteristic
43C23×#102C2211yescharacteristic, complemented
44C23×#97C2211yescharacteristic, complemented
45#10625014C2211yescharacteristic
46#10625014C2211yescharacteristic, complemented
47#10625003C2211yescharacteristic
48(C2×D23)⋊C8C2211yescharacteristic
49(C2×D23)⋊C8C2211yescharacteristic
50#10625000C2211yescharacteristic, complemented
51#10624998C2211yescharacteristic, complemented
52Dic23⋊C8C2211yescharacteristic, complemented
53Dic23⋊C8C2211yescharacteristic, complemented
54#10624992C2211yescharacteristic, complemented
55#10624991C2211yescharacteristic
56#10624990C2211yescharacteristic, complemented
57#10624989C2211yescharacteristic, complemented
58C4×C23⋊C8C2211yescharacteristic, complemented
59C23×D23—21no—
60C2×D4×C23C2311yescharacteristic
61C2×D4×C23C2311yescharacteristic
62C22×C4×C23—21no—
63C22×C4×C23—21no—
64C2×C22⋊D23—21no—
65C2×C22⋊D23—21no—
66C22×Dic23—21no—
67D4×D23—22no—
68D4×D23—22no—
69C2×D92C2311yescharacteristic
70C2×C4×D23—21no—
71C2×C4×D23—21no—
72C2×C4×D23C2311yescharacteristic
73C2×Dic46—21no—
74C2×Dic46C2311yescharacteristic
75D8×C23—22no—
76C2×C8×C23C2311yescharacteristic
77C2×C8×C23C2311yescharacteristic
78C4⋊C4×C23C2311yescharacteristic
79C4⋊C4×C23C2311yescharacteristic
80C22⋊C4×C23—21no—
81C22⋊C4×C23—21no—
82C42×C23C2311yescharacteristic
83C22⋊Dic23—21no—
84C22⋊Dic23—21no—
85C22⋊Dic23—21no—
86C22⋊Dic23—21no—
87#67273—22no—
88#67272—22no—
89(C2×D23)⋊C4—21no—
90(C2×D23)⋊C4—21no—
91(C2×D23)⋊C4—21no—
92(C2×D23)⋊C4—21no—
93(C2×D23)⋊C4D411yescharacteristic
94(C2×D23)⋊C4D411yescharacteristic
95C4⋊Dic23—21no—
96C4⋊Dic23C2311yescharacteristic
97C4⋊Dic23C2311yescharacteristic
98Dic23⋊C4—21no—
99Dic23⋊C4—21no—
100Dic23⋊C4D411yescharacteristic
101Dic23⋊C4D411yescharacteristic
102C4×Dic23—21no—
103C4×Dic23—21no—
104C4×Dic23C2311yescharacteristic
105C2×C23⋊C8C2311yescharacteristic
106C2×C23⋊C8C2311yescharacteristic
107#67263—22no—
108C23×C23—21no—
109C23×C23—21no—
110C22×D23—21no—
111C22×D23—24no—
112C22×D23—81no—
113C22×D23—81no—
114C22×D23C2×D411yescharacteristic
115D4×C23—21no—
116D4×C23—21no—
117D4×C23—21no—
118D4×C23#4112yes—
119C2×C4×C23—21no—
120C2×C4×C23—21no—
121C2×C4×C23—81no—
122C2×C4×C23—81no—
123C2×C4×C23C2×D411yescharacteristic
124C2×C4×C23C2×D411yescharacteristic
125C2×C4×C23C2411yescharacteristic
126C22⋊D23—24no—
127C22⋊D23—81no—
128C2×Dic23—21no—
129C2×Dic23—21no—
130C2×Dic23—21no—
131C2×Dic23—81no—
132C2×Dic23C2×D411yescharacteristic
133C2×Dic23C2×D411yescharacteristic
134C2×Dic23C2×D411yescharacteristic
135D92—21no—
136D92#4112yes—
137C4×D23—21no—
138C4×D23—21no—
139C4×D23—81no—
140C4×D23—81no—
141Dic46—21no—
142Dic46—21no—
143Dic46—81no—
144C8×C23—21no—
145C8×C23—21no—
146C23⋊C8—21no—
147C23⋊C8—21no—
148#3118—231nomaximal, Sylow
149C22×C23—22no—
150C22×C23—41no—
151C22×C23—41no—
152C22×C23—41no—
153C22×C23—41no—
154C22×C23—41no—
155C22×C23C22×D411yescharacteristic
156C2×D23—21no—
157C2×D23—22no—
158C2×D23—21no—
159C2×D23—21no—
160C2×D23—41no—
161C2×D23—41no—
162C2×D23—84no—
163C4×C23—21no—
164C4×C23—21no—
165C4×C23—41no—
166C4×C23—41no—
167C4×C23C2×#4111yescharacteristic
168C4×C23C2×#4111yescharacteristic
169Dic23—21no—
170Dic23—21no—
171Dic23—21no—
172Dic23—41no—
173Dic23—41no—
174Dic23—41no—
175#542—231no—
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#442D2311yescharacteristic, complemented
186#440—231no—
187C4×SD16—231no—
188C4×D8—231no—
189#433—231no—
190C2×C23—42no—
191C2×C23—81no—
192C2×C23#52511yescharacteristic
193C2×C23#57611yescharacteristic
194C2×C23#57711yescharacteristic
195D23—41no—
196D23—42no—
197C22×D4—231no—
198C2×SD16—231no—
199C2×SD16—231no—
200C2×D8—231no—
201C2×D8C2×D2311yescharacteristic
202C4⋊Q8—231no—
203#126—461no—
204#124—231no—
205#124—461no—
206#123—461no—
207C22⋊Q8—231no—
208C22⋊Q8—461no—
209#121—231no—
210C4×Q8—231no—
211C4×D4—231no—
212C4×D4—231no—
213C4×D4—231no—
214C4×D4—461no—
215C4×D4—461no—
216C4×D4C2×D2311yescharacteristic
217C4×D4C2×D2311yescharacteristic, complemented
218#117—231no—
219#117—231no—
220C2×C22⋊C4—461no—
221C2×C22⋊C4—461no—
222#107—231no—
223#107—231no—
224#106—231no—
225#106C2×D2311yescharacteristic, complemented
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#102C2×D2311yescharacteristic
235#102C2×D2311yescharacteristic, complemented
236C22⋊C8—231no—
237C22⋊C8—231no—
238#97C2×D2311yescharacteristic, complemented
239C4×C8—231no—
240C23#311811yescharacteristic, complemented, Sylow
241C24—461no—
242C2×Q8—231no—
243C2×Q8—461no—
244C2×D4—231no—
245C2×D4—461no—
246C2×D4—462no—
247C2×D4—462no—
248C2×D4—461no—
249C2×D4C22×D2311yescharacteristic
250C2×D4C22×D2311yescharacteristic
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—231no—
254C22×C4—461no—
255C22×C4—461no—
256C22×C4—461no—
257SD16—462no—
258SD16—462no—
259D8—22no—
260D8—462no—
261C2×C8—231no—
262C2×C8—231no—
263C2×C8C22×D2311yescharacteristic
264C2×C8C22×D2311yescharacteristic
265C4⋊C4—231no—
266C4⋊C4—231no—
267C4⋊C4—231no—
268C4⋊C4—231no—
269C4⋊C4—461no—
270C4⋊C4—461no—
271C4⋊C4—461no—
272C4⋊C4C22×D2311yescharacteristic
273C4⋊C4C22×D2311yescharacteristic
274C22⋊C4—21no—
275C22⋊C4—21no—
276C22⋊C4—231no—
277C22⋊C4—231no—
278C22⋊C4—461no—
279C22⋊C4—461no—
280C22⋊C4—461no—
281C22⋊C4—461no—
282C22⋊C4—461no—
283C22⋊C4—461no—
284C22⋊C4—461no—
285C22⋊C4—461no—
286C42—231no—
287C42—461no—
288C42—461no—
289C42C22×D2311yescharacteristic
290C23—21no—
291C23—21no—
292C23—231no—
293C23—464no—
294C23—461no—
295C23—1841no—
296C23—1841no—
297Q8—461no—
298Q8—461no—
299Q8—1841no—
300D4—21no—
301D4—21no—
302D4—21no—
303D4—232no—
304D4—464no—
305D4—461no—
306D4—1841no—
307D4#6728812yes—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—81no—
311C2×C4—81no—
312C2×C4—231no—
313C2×C4—231no—
314C2×C4—231no—
315C2×C4—461no—
316C2×C4—461no—
317C2×C4—461no—
318C2×C4—461no—
319C2×C4—461no—
320C2×C4—1841no—
321C2×C4—1841no—
322C2×C4—1841no—
323C2×C4D4×D2311yescharacteristic
324C2×C4D4×D2311yescharacteristic
325C2×C4C23×D2311yescharacteristic
326C8—21no—
327C8—21no—
328C8—461no—
329C8—461no—
330C22—22no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—461no—
337C22—462no—
338C22—461no—
339C22—461no—
340C22—921no—
341C22—921no—
342C22—1844no—
343C22C2×D4×D2311yescharacteristic
344C4—21no—
345C4—21no—
346C4—41no—
347C4—41no—
348C4—461no—
349C4—461no—
350C4—461no—
351C4—921no—
352C4—921no—
353C4—921no—
354C4C2×#6728811yescharacteristic
355C4#41×D2311yescharacteristic
356C2—42no—
357C2—81no—
358C2—921no—
359C2—922no—
360C2#1309292611yescharacteristic
361C2#1309322111yescharacteristic
362C2#1309322711yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#442C2
socleC22×C23C22×D4
prime radical#13092549C2
hypercenter#442D23
hypocenterC23#3118
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. #13093032C2semidirect
2. #13092889C2semidirect
3. #13092761C2semidirect
4. #13092739C2semidirect
5. #13092706C2semidirect
6. #13092695C2semidirect
7. #13092631C2semidirect
8. #13092630C2semidirect
9. #13092569C2semidirect
11. #13092519C2semidirect
12. C4×#67273C2semidirect
13. C4×#67272C2semidirect
14. #13092479C2semidirect
15. C23×#442C2semidirect
19. C4×D4×C23C22semidirect
21. #10625107C22semidirect
33. #10625059C22semidirect
40. C4×Dic46C22semidirect
41. C23×#106C22semidirect
43. C23×#102C22semidirect
44. C23×#97C22semidirect
46. #10625014C22semidirect
50. #10625000C22semidirect
51. #10624998C22semidirect
52. Dic23⋊C8C22semidirect
53. Dic23⋊C8C22semidirect
54. #10624992C22semidirect
56. #10624990C22semidirect
57. #10624989C22semidirect
58. C4×C23⋊C8C22semidirect
185. #442D23semidirect
217. C4×D4C2×D23semidirect
225. #106C2×D23semidirect
235. #102C2×D23semidirect
238. #97C2×D23semidirect
240. C23#3118semidirect

Maximal subgroups

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

subgroupindex
#130930322
#130928892
#130927612
#130927392
#130927062
#130926952
#130926312
#130926302
#130925692
#130925492
#130925192
C4×#672732
C4×#672722
#130924792
C23×#4422
#311823