Finite Group Databasebeta

← #15683588

Subgroups — #15683588

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#13093041C211yesmaximal, characteristic, complemented
2#13092889C211yesmaximal, characteristic, complemented
3#13092760C211yesmaximal, characteristic, complemented
4#13092744C211yesmaximal, characteristic, complemented
5#13092704C211yesmaximal, characteristic, complemented
6#13092633C211yesmaximal, characteristic, complemented
7#13092632C211yesmaximal, characteristic, complemented
8#13092569C211yesmaximal, characteristic, complemented
9#13092552C211yesmaximal, characteristic
10#13092526C211yesmaximal, characteristic, complemented
11#13092516C211yesmaximal, characteristic, complemented
12#13092508C211yesmaximal, characteristic, complemented
13#13092499C211yesmaximal, characteristic, complemented
14#13092477C211yesmaximal, characteristic, complemented
15C23×#474C211yesmaximal, characteristic, complemented
16C2×D4×D23C2211yescharacteristic
17C23×C4⋊Q8C2211yescharacteristic, complemented
18C4×D4×C23C2211yescharacteristic
19#10625118—21no—
20#10625117—21no—
21D4×Dic23C2211yescharacteristic
22C2×#67273C2211yescharacteristic
23C2×#67272C2211yescharacteristic
24C4×C22⋊D23—21no—
25C2×(C2×D23)⋊C4—21no—
26C2×D184C2211yescharacteristic
27C2×#67263C2211yescharacteristic
28#10625069—21no—
29#10625068C2211yescharacteristic
30#10625066C2211yescharacteristic
31#10625065—21no—
32#10625064C2211yescharacteristic
33#10625064C2211yescharacteristic, complemented
34#10625063C2211yescharacteristic
35#10625058C2211yescharacteristic, complemented
36(C22⋊D23)⋊C4—21no—
37C22⋊C4×D23—21no—
38#10625046C2211yescharacteristic, complemented
39C4×D92C2211yescharacteristic
40#10625043C2211yescharacteristic
41C23×#107C2211yescharacteristic, complemented
42C23×#107C2211yescharacteristic, complemented
43C23×C4⋊C8C2211yescharacteristic, complemented
44C23×#102C2211yescharacteristic
45C23×#102C2211yescharacteristic
46#10625003C2211yescharacteristic, complemented
47(C2×D23)⋊C8C2211yescharacteristic
48(C2×D23)⋊C8C2211yescharacteristic
49#10624998C2211yescharacteristic, complemented
50#10624997C2211yescharacteristic, complemented
51C8×Dic23C2211yescharacteristic, complemented
52#10624992C2211yescharacteristic, complemented
53#10624991C2211yescharacteristic
54#10624991C2211yescharacteristic
55#10624991C2211yescharacteristic, complemented
56#10624990C2211yescharacteristic, complemented
57#10624990C2211yescharacteristic, complemented
58C4⋊(C23⋊C8)C2211yescharacteristic, complemented
59C23×D23—21no—
60C2×Q8×C23—21no—
61C2×D4×C23C2311yescharacteristic
62C22×C4×C23—21no—
63C2×C22⋊D23—21no—
64C22×Dic23—21no—
65D4×D23—22no—
66D4×D23—22no—
67C2×D92—21no—
68C2×D92C2311yescharacteristic
69C2×D92C2311yescharacteristic
70C2×C4×D23—21no—
71C2×C4×D23—21no—
72C2×C4×D23—21no—
73C2×C4×D23C2311yescharacteristic
74C2×Dic46C2311yescharacteristic
75C2×C8×C23C2311yescharacteristic
76C2×C8×C23C2311yescharacteristic
77C4⋊C4×C23—21no—
78C4⋊C4×C23C2311yescharacteristic
79C4⋊C4×C23C2311yescharacteristic
80C4⋊C4×C23C2311yescharacteristic
81C22⋊C4×C23—21no—
82C42×C23C2311yescharacteristic
83C22⋊Dic23—21no—
84#67273—22no—
85#67272—22no—
86(C2×D23)⋊C4—21no—
87(C2×D23)⋊C4—21no—
88(C2×D23)⋊C4—21no—
89(C2×D23)⋊C4—21no—
90(C2×D23)⋊C4—21no—
91(C2×D23)⋊C4—21no—
92(C2×D23)⋊C4—21no—
93(C2×D23)⋊C4—21no—
94(C2×D23)⋊C4D411yescharacteristic
95(C2×D23)⋊C4D411yescharacteristic
96C4⋊Dic23—21no—
97C4⋊Dic23C2311yescharacteristic
98Dic23⋊C4—21no—
99Dic23⋊C4D411yescharacteristic
100Dic23⋊C4D411yescharacteristic
101C4×Dic23—21no—
102C4×Dic23—21no—
103C4×Dic23C2311yescharacteristic
104C2×C23⋊C8C2311yescharacteristic
105C2×C23⋊C8C2311yescharacteristic
106D184—22no—
107#67263—22no—
108C23×C23—21no—
109C22×D23—21no—
110C22×D23—24no—
111C22×D23—21no—
112C22×D23—81no—
113C22×D23—81no—
114C22×D23C2×D411yescharacteristic
115Q8×C23—81no—
116D4×C23—21no—
117D4×C23#4112yes—
118C2×C4×C23—21no—
119C2×C4×C23—21no—
120C2×C4×C23—21no—
121C2×C4×C23—81no—
122C2×C4×C23C2×D411yescharacteristic
123C2×C4×C23C2×D411yescharacteristic
124C2×C4×C23C2411yescharacteristic
125C22⋊D23—24no—
126C2×Dic23—21no—
127C2×Dic23—21no—
128C2×Dic23—81no—
129C2×Dic23C2×D411yescharacteristic
130C2×Dic23C2×D411yescharacteristic
131C2×Dic23C2×D411yescharacteristic
132D92—21no—
133D92—21no—
134D92—21no—
135D92—81no—
136D92#4112yes—
137C4×D23—21no—
138C4×D23—21no—
139C4×D23—81no—
140C4×D23—81no—
141C4×D23—81no—
142Dic46—21no—
143Dic46—21no—
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×C23C22×D411yescharacteristic
153C2×D23—21no—
154C2×D23—22no—
155C2×D23—21no—
156C2×D23—21no—
157C2×D23—41no—
158C2×D23—41no—
159C2×D23—41no—
160C2×D23—41no—
161C2×D23—41no—
162C2×D23—84no—
163C4×C23—21no—
164C4×C23—21no—
165C4×C23—41no—
166C4×C23—41no—
167C4×C23—41no—
168C4×C23C2×#4111yescharacteristic
169C4×C23C2×#4111yescharacteristic
170Dic23—21no—
171Dic23—21no—
172Dic23—21no—
173Dic23—41no—
174Dic23—41no—
175#542—231no—
176#518—231no—
177#485—231no—
178#482—231no—
179#476—231no—
180#474D2311yescharacteristic, complemented
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—42no—
191C2×C23#52511yescharacteristic
192C2×C23#57611yescharacteristic
193C2×C23#57711yescharacteristic
194D23—41no—
195D23—42no—
196D23—81no—
197C22×D4—231no—
198C2×SD16—231no—
199C2×SD16—231no—
200C2×D8—231no—
201C2×D8—231no—
202C4⋊Q8C2×D2311yescharacteristic, complemented
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—231no—
215C4×D4—461no—
216C4×D4—461no—
217C4×D4C2×D2311yescharacteristic
218#117—231no—
219#117—231no—
220C2×C22⋊C4—461no—
221C2×C22⋊C4—461no—
222#107C2×D2311yescharacteristic, complemented
223#107C2×D2311yescharacteristic, complemented
224#106—231no—
225#106—231no—
226C4⋊C8—231no—
227C4⋊C8C2×D2311yescharacteristic, complemented
228#103—231no—
229#103—231no—
230#102—231no—
231#102—231no—
232#102—231no—
233#102—231no—
234#102C2×D2311yescharacteristic
235#102C2×D2311yescharacteristic
236C22⋊C8—231no—
237C22⋊C8—231no—
238#97—231no—
239C4×C8—231no—
240C23#311811yescharacteristic, complemented, Sylow
241C24—461no—
242C2×Q8—21no—
243C2×Q8—231no—
244C2×D4—231no—
245C2×D4—231no—
246C2×D4—461no—
247C2×D4—461no—
248C2×D4—462no—
249C2×D4—462no—
250C2×D4C22×D2311yescharacteristic
251C22×C4—21no—
252C22×C4—231no—
253C22×C4—461no—
254C22×C4—461no—
255C22×C4—461no—
256C22×C4—461no—
257SD16—462no—
258SD16—462no—
259D8—462no—
260D8—462no—
261C2×C8—231no—
262C2×C8—231no—
263C2×C8C22×D2311yescharacteristic
264C2×C8C22×D2311yescharacteristic
265C4⋊C4—21no—
266C4⋊C4—231no—
267C4⋊C4—231no—
268C4⋊C4—231no—
269C4⋊C4—461no—
270C4⋊C4—461no—
271C4⋊C4C22×D2311yescharacteristic
272C4⋊C4C22×D2311yescharacteristic
273C4⋊C4C22×D2311yescharacteristic
274C22⋊C4—21no—
275C22⋊C4—231no—
276C22⋊C4—231no—
277C22⋊C4—461no—
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—231no—
292C23—464no—
293C23—461no—
294C23—461no—
295C23—1841no—
296C23—1841no—
297Q8—81no—
298Q8—461no—
299Q8—461no—
300D4—21no—
301D4—232no—
302D4—464no—
303D4—461no—
304D4—461no—
305D4—461no—
306D4—1841no—
307D4#6729212yes—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
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—1841no—
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—461no—
334C22—462no—
335C22—461no—
336C22—461no—
337C22—921no—
338C22—921no—
339C22—921no—
340C22—921no—
341C22—921no—
342C22—1844no—
343C22C2×D4×D2311yescharacteristic
344C4—21no—
345C4—21no—
346C4—41no—
347C4—41no—
348C4—41no—
349C4—461no—
350C4—461no—
351C4—461no—
352C4—921no—
353C4—921no—
354C4C2×#6729211yescharacteristic
355C4#41×D2311yescharacteristic
356C2—42no—
357C2—921no—
358C2—922no—
359C2—1841no—
360C2#1309293011yescharacteristic
361C2#1309321811yescharacteristic
362C2#1309322611yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#474C2
socleC22×C23C22×D4
prime radical#13092552C2
hypercenter#474D23
hypocenterC23#3118
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
1. #13093041C2semidirect
2. #13092889C2semidirect
3. #13092760C2semidirect
4. #13092744C2semidirect
5. #13092704C2semidirect
6. #13092633C2semidirect
7. #13092632C2semidirect
8. #13092569C2semidirect
10. #13092526C2semidirect
11. #13092516C2semidirect
12. #13092508C2semidirect
13. #13092499C2semidirect
14. #13092477C2semidirect
15. C23×#474C2semidirect
17. C23×C4⋊Q8C22semidirect
33. #10625064C22semidirect
35. #10625058C22semidirect
38. #10625046C22semidirect
41. C23×#107C22semidirect
42. C23×#107C22semidirect
43. C23×C4⋊C8C22semidirect
46. #10625003C22semidirect
49. #10624998C22semidirect
50. #10624997C22semidirect
51. C8×Dic23C22semidirect
52. #10624992C22semidirect
55. #10624991C22semidirect
56. #10624990C22semidirect
57. #10624990C22semidirect
58. C4⋊(C23⋊C8)C22semidirect
180. #474D23semidirect
202. C4⋊Q8C2×D23semidirect
222. #107C2×D23semidirect
223. #107C2×D23semidirect
227. C4⋊C8C2×D23semidirect
240. C23#3118semidirect

Maximal subgroups

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

subgroupindex
#130930412
#130928892
#130927602
#130927442
#130927042
#130926332
#130926322
#130925692
#130925522
#130925262
#130925162
#130925082
#130924992
#130924772
C23×#4742
#311823