Finite Group Databasebeta

← #15683642

Subgroups — #15683642

Order 2944.

418 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13093023C211yesmaximal, characteristic, complemented
2#13092889C211yesmaximal, characteristic, complemented
3#13092744C211yesmaximal, characteristic, complemented
4#13092743C211yesmaximal, characteristic, complemented
5#13092714C211yesmaximal, characteristic, complemented
6#13092613C211yesmaximal, characteristic, complemented
7#13092612C211yesmaximal, characteristic, complemented
8#13092552C211yesmaximal, characteristic, complemented
9#13092552C211yesmaximal, characteristic, complemented
10#13092528C211yesmaximal, characteristic, complemented
11#13092526C211yesmaximal, characteristic, complemented
12#13092499C211yesmaximal, characteristic, complemented
13#13092497C211yesmaximal, characteristic, complemented
14#13092477C211yesmaximal, characteristic, complemented
15C23×#478C211yesmaximal, characteristic, complemented
16C2×D4×D23C2211yescharacteristic
17C23×#125C2211yescharacteristic, complemented
18C4×D4×C23C2211yescharacteristic
19D4×Dic23C2211yescharacteristic
20C2×#67272C2211yescharacteristic
21C2×#67272C2211yescharacteristic
22C4×C22⋊D23—21no—
23C2×(C2×D23)⋊C4—21no—
24C2×D184C2211yescharacteristic
25C2×D184C2211yescharacteristic
26#10625066—21no—
27#10625066—21no—
28#10625066C2211yescharacteristic
29#10625066C2211yescharacteristic
30#10625065—21no—
31#10625065—21no—
32#10625064C2211yescharacteristic
33#10625064C2211yescharacteristic, complemented
34#10625064C2211yescharacteristic, complemented
35#10625063C2211yescharacteristic
36(C22⋊D23)⋊C4—21no—
37C22⋊C4×D23—21no—
38#10625045C2211yescharacteristic, complemented
39C4×D92C2211yescharacteristic
40#10625043C2211yescharacteristic
41C23×#107C2211yescharacteristic, complemented
42C23×#106C2211yescharacteristic, complemented
43C23×C4⋊C8C2211yescharacteristic, complemented
44C23×#102C2211yescharacteristic
45C23×#102C2211yescharacteristic
46#10625003C2211yescharacteristic, complemented
47#10625003C2211yescharacteristic, complemented
48(C2×D23)⋊C8C2211yescharacteristic
49(C2×D23)⋊C8C2211yescharacteristic
50#10624997C2211yescharacteristic, complemented
51C8×Dic23C2211yescharacteristic, complemented
52#10624991C2211yescharacteristic
53#10624991C2211yescharacteristic
54#10624991C2211yescharacteristic, complemented
55#10624991C2211yescharacteristic, complemented
56#10624990C2211yescharacteristic, complemented
57#10624989C2211yescharacteristic, complemented
58C4⋊(C23⋊C8)C2211yescharacteristic, complemented
59C23×D23—21no—
60C2×D4×C23C2311yescharacteristic
61C22×C4×C23—21no—
62C2×C22⋊D23—21no—
63C22×Dic23—21no—
64D4×D23—22no—
65D4×D23—22no—
66C2×D92—21no—
67C2×D92—21no—
68C2×D92—21no—
69C2×D92—21no—
70C2×D92C2311yescharacteristic
71C2×D92C2311yescharacteristic
72C2×D92C2311yescharacteristic
73C2×C4×D23—21no—
74C2×C4×D23—21no—
75C2×C4×D23—21no—
76C2×C4×D23—21no—
77C2×C4×D23C2311yescharacteristic
78C2×C8×C23C2311yescharacteristic
79C2×C8×C23C2311yescharacteristic
80C4⋊C4×C23—21no—
81C4⋊C4×C23—21no—
82C4⋊C4×C23C2311yescharacteristic
83C4⋊C4×C23C2311yescharacteristic
84C4⋊C4×C23C2311yescharacteristic
85C22⋊C4×C23—21no—
86C42×C23C2311yescharacteristic
87C22⋊Dic23—21no—
88#67272—22no—
89#67272—22no—
90(C2×D23)⋊C4—21no—
91(C2×D23)⋊C4—21no—
92(C2×D23)⋊C4—21no—
93(C2×D23)⋊C4—21no—
94(C2×D23)⋊C4—21no—
95(C2×D23)⋊C4—21no—
96(C2×D23)⋊C4—21no—
97(C2×D23)⋊C4D411yescharacteristic
98(C2×D23)⋊C4D411yescharacteristic
99C4⋊Dic23C2311yescharacteristic
100Dic23⋊C4D411yescharacteristic
101Dic23⋊C4D411yescharacteristic
102C4×Dic23—21no—
103C4×Dic23C2311yescharacteristic
104C2×C23⋊C8C2311yescharacteristic
105C2×C23⋊C8C2311yescharacteristic
106D184—22no—
107D184—22no—
108C23×C23—21no—
109C22×D23—21no—
110C22×D23—24no—
111C22×D23—21no—
112C22×D23—21no—
113C22×D23—81no—
114C22×D23—81no—
115C22×D23C2×D411yescharacteristic
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—81no—
128C2×Dic23C2×D411yescharacteristic
129C2×Dic23C2×D411yescharacteristic
130C2×Dic23C2×D411yescharacteristic
131D92—21no—
132D92—21no—
133D92—21no—
134D92—21no—
135D92—21no—
136D92—81no—
137D92—81no—
138D92—81no—
139D92—81no—
140D92#4112yes—
141C4×D23—21no—
142C4×D23—21no—
143C4×D23—81no—
144C4×D23—81no—
145C4×D23—81no—
146C4×D23—81no—
147C8×C23—21no—
148C8×C23—21no—
149C23⋊C8—21no—
150C23⋊C8—21no—
151#3122—231nomaximal, Sylow
152C22×C23—22no—
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—41no—
163C2×D23—41no—
164C2×D23—41no—
165C2×D23—41no—
166C2×D23—41no—
167C2×D23—41no—
168C2×D23—84no—
169C4×C23—21no—
170C4×C23—21no—
171C4×C23—41no—
172C4×C23—41no—
173C4×C23—41no—
174C4×C23C2×#4111yescharacteristic
175C4×C23C2×#4111yescharacteristic
176Dic23—21no—
177Dic23—21no—
178Dic23—21no—
179Dic23—41no—
180#540—231no—
181#518—231no—
182#482—231no—
183#482—231no—
184#478—231no—
185#478D2311yescharacteristic, complemented
186#459—231no—
187#459—231no—
188#447—231no—
189#447—231no—
190#442—231no—
191#442—231no—
192C4×D8—231no—
193C4×D8—231no—
194#433—231no—
195C2×C23—42no—
196C2×C23#52511yescharacteristic
197C2×C23#57611yescharacteristic
198C2×C23#57611yescharacteristic
199D23—41no—
200D23—42no—
201D23—81no—
202D23—81no—
203C22×D4—231no—
204C2×D8—231no—
205C2×D8—231no—
206C2×D8—231no—
207C2×D8—231no—
208#127—231no—
209#125C2×D2311yescharacteristic, complemented
210#123—461no—
211#123—461no—
212#121—231no—
213#121—231no—
214#121—461no—
215#121—461no—
216C4×D4—231no—
217C4×D4—231no—
218C4×D4—231no—
219C4×D4—231no—
220C4×D4—231no—
221C4×D4—461no—
222C4×D4—461no—
223C4×D4C2×D2311yescharacteristic
224#117—231no—
225#117—231no—
226C2×C22⋊C4—461no—
227C2×C22⋊C4—461no—
228#107—231no—
229#107C2×D2311yescharacteristic, complemented
230#106—231no—
231#106C2×D2311yescharacteristic, complemented
232C4⋊C8—231no—
233C4⋊C8C2×D2311yescharacteristic, complemented
234#102—231no—
235#102—231no—
236#102—231no—
237#102—231no—
238#102—231no—
239#102—231no—
240#102C2×D2311yescharacteristic
241#102C2×D2311yescharacteristic
242C22⋊C8—231no—
243C22⋊C8—231no—
244#97—231no—
245C4×C8—231no—
246C23#312211yescharacteristic, complemented, Sylow
247C24—461no—
248C2×D4—231no—
249C2×D4—231no—
250C2×D4—231no—
251C2×D4—461no—
252C2×D4—461no—
253C2×D4—461no—
254C2×D4—462no—
255C2×D4—462no—
256C2×D4—461no—
257C2×D4—461no—
258C2×D4C22×D2311yescharacteristic
259C22×C4—21no—
260C22×C4—231no—
261C22×C4—461no—
262C22×C4—461no—
263C22×C4—461no—
264C22×C4—461no—
265C22×C4—461no—
266D8—462no—
267D8—462no—
268D8—462no—
269D8—462no—
270C2×C8—231no—
271C2×C8—231no—
272C2×C8C22×D2311yescharacteristic
273C2×C8C22×D2311yescharacteristic
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—231no—
277C4⋊C4—231no—
278C4⋊C4—231no—
279C4⋊C4C22×D2311yescharacteristic
280C4⋊C4C22×D2311yescharacteristic
281C4⋊C4C22×D2311yescharacteristic
282C22⋊C4—21no—
283C22⋊C4—231no—
284C22⋊C4—231no—
285C22⋊C4—461no—
286C22⋊C4—461no—
287C22⋊C4—461no—
288C22⋊C4—461no—
289C22⋊C4—461no—
290C22⋊C4—461no—
291C22⋊C4—461no—
292C22⋊C4—461no—
293C42—231no—
294C42—461no—
295C42C22×D2311yescharacteristic
296C23—21no—
297C23—231no—
298C23—464no—
299C23—461no—
300C23—461no—
301C23—461no—
302C23—1841no—
303C23—1841no—
304D4—21no—
305D4—232no—
306D4—464no—
307D4—461no—
308D4—461no—
309D4—461no—
310D4—461no—
311D4—461no—
312D4—1841no—
313D4—1841no—
314D4—1841no—
315D4—1841no—
316D4#6729212yes—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—81no—
321C2×C4—231no—
322C2×C4—231no—
323C2×C4—231no—
324C2×C4—461no—
325C2×C4—461no—
326C2×C4—461no—
327C2×C4—1841no—
328C2×C4—1841no—
329C2×C4—1841no—
330C2×C4—1841no—
331C2×C4—1841no—
332C2×C4D4×D2311yescharacteristic
333C2×C4D4×D2311yescharacteristic
334C2×C4C23×D2311yescharacteristic
335C8—21no—
336C8—21no—
337C8—461no—
338C8—461no—
339C22—22no—
340C22—41no—
341C22—41no—
342C22—461no—
343C22—462no—
344C22—461no—
345C22—461no—
346C22—921no—
347C22—921no—
348C22—921no—
349C22—921no—
350C22—921no—
351C22—921no—
352C22—921no—
353C22—921no—
354C22—1844no—
355C22C2×D4×D2311yescharacteristic
356C4—21no—
357C4—21no—
358C4—41no—
359C4—41no—
360C4—41no—
361C4—461no—
362C4—461no—
363C4—461no—
364C4—921no—
365C4C2×#6729211yescharacteristic
366C4#41×D2311yescharacteristic
367C2—42no—
368C2—921no—
369C2—922no—
370C2—1841no—
371C2—1841no—
372C2#1309293011yescharacteristic
373C2#1309321911yescharacteristic
374C2#1309322111yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#478C2
socleC22×C23C22×D4
hypercenter#478D23
hypocenterC23#3122
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #13093023C2semidirect
2. #13092889C2semidirect
3. #13092744C2semidirect
4. #13092743C2semidirect
5. #13092714C2semidirect
6. #13092613C2semidirect
7. #13092612C2semidirect
8. #13092552C2semidirect
9. #13092552C2semidirect
10. #13092528C2semidirect
11. #13092526C2semidirect
12. #13092499C2semidirect
13. #13092497C2semidirect
14. #13092477C2semidirect
15. C23×#478C2semidirect
17. C23×#125C22semidirect
33. #10625064C22semidirect
34. #10625064C22semidirect
38. #10625045C22semidirect
41. C23×#107C22semidirect
42. C23×#106C22semidirect
43. C23×C4⋊C8C22semidirect
46. #10625003C22semidirect
47. #10625003C22semidirect
50. #10624997C22semidirect
51. C8×Dic23C22semidirect
54. #10624991C22semidirect
55. #10624991C22semidirect
56. #10624990C22semidirect
57. #10624989C22semidirect
58. C4⋊(C23⋊C8)C22semidirect
185. #478D23semidirect
209. #125C2×D23semidirect
229. #107C2×D23semidirect
231. #106C2×D23semidirect
233. C4⋊C8C2×D23semidirect
246. C23#3122semidirect

Maximal subgroups

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

subgroupindex
#130930232
#130928892
#130927442
#130927432
#130927142
#130926132
#130926122
#130925522
#130925282
#130925262
#130924992
#130924972
#130924772
C23×#4782
#312223