Finite Group Databasebeta

← #15683634

Subgroups — #15683634

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#13093020C211yesmaximal, characteristic, complemented
2#13092892C211yesmaximal, characteristic, complemented
3#13092742C211yesmaximal, characteristic, complemented
4#13092738C211yesmaximal, characteristic, complemented
5#13092719C211yesmaximal, characteristic, complemented
6#13092715C211yesmaximal, characteristic, complemented
7#13092610C211yesmaximal, characteristic, complemented
8#13092610C211yesmaximal, characteristic, complemented
9#13092551C211yesmaximal, characteristic, complemented
10#13092529C211yesmaximal, characteristic, complemented
11#13092526C211yesmaximal, characteristic, complemented
12D8×Dic23C211yesmaximal, characteristic, complemented
13#13092497C211yesmaximal, characteristic, complemented
14#13092475C211yesmaximal, characteristic, complemented
15C23×#447C211yesmaximal, characteristic, complemented
16C22×D4×C23C2211yescharacteristic
17C2×D8×C23C2211yescharacteristic
18C2×D8×C23C2211yescharacteristic
19C23×#121C2211yescharacteristic
20C2×C22⋊Dic23—21no—
21C2×C22⋊Dic23—21no—
22#10625111C2211yescharacteristic, complemented
23#10625110—21no—
24#10625109—21no—
25D4×Dic23—21no—
26D4×Dic23—21no—
27D4×Dic23C2211yescharacteristic
28D4×Dic23C2211yescharacteristic
29D4×Dic23C2211yescharacteristic
30D4×Dic23C2211yescharacteristic
31D4×Dic23C2211yescharacteristic, complemented
32C2×#67272C2211yescharacteristic
33C2×#67272C2211yescharacteristic
34#10625101C2211yescharacteristic
35#10625097C2211yescharacteristic
36#10625097C2211yescharacteristic
37#10625064C2211yescharacteristic, complemented
38#10625061C2211yescharacteristic, complemented
39#10625057—21no—
40#10625054—21no—
41C23×#102C2211yescharacteristic
42C23×#102C2211yescharacteristic
43C23×C22⋊C8C2211yescharacteristic
44#10625014C2211yescharacteristic
45#10625014C2211yescharacteristic
46#10625014C2211yescharacteristic, complemented
47#10625014C2211yescharacteristic, complemented
48C22⋊(C23⋊C8)C2211yescharacteristic
49#10625003C2211yescharacteristic, complemented
50#10625003C2211yescharacteristic, complemented
51#10625000C2211yescharacteristic, complemented
52#10624999C2211yescharacteristic, complemented
53#10624997C2211yescharacteristic, complemented
54Dic23⋊C8C2211yescharacteristic, complemented
55Dic23⋊C8C2211yescharacteristic, complemented
56C8×Dic23C2211yescharacteristic, complemented
57#10624990C2211yescharacteristic, complemented
58#10624989C2211yescharacteristic, complemented
59C24×C23—21no—
60C2×D4×C23—22no—
61C2×D4×C23—22no—
62C2×D4×C23—21no—
63C2×D4×C23—21no—
64C2×D4×C23C2311yescharacteristic
65C2×D4×C23C2311yescharacteristic
66C2×D4×C23C2311yescharacteristic
67C22×C4×C23C2311yescharacteristic
68C2×C22⋊D23—21no—
69C2×C22⋊D23—21no—
70C2×C22⋊D23—21no—
71C22×Dic23—21no—
72C22×Dic23—21no—
73C22×Dic23—21no—
74C22×Dic23—21no—
75C22×Dic23—21no—
76C2×D92C2311yescharacteristic
77C2×C4×D23—21no—
78D8×C23—22no—
79D8×C23—22no—
80C2×C8×C23C2311yescharacteristic
81C2×C8×C23C2311yescharacteristic
82C4⋊C4×C23C2311yescharacteristic
83C22⋊C4×C23—21no—
84C22⋊Dic23—21no—
85C22⋊Dic23—21no—
86C22⋊Dic23—21no—
87C22⋊Dic23—21no—
88C22⋊Dic23—21no—
89C22⋊Dic23—21no—
90C22⋊Dic23D411yescharacteristic
91C22⋊Dic23D411yescharacteristic
92#67272—22no—
93#67272—22no—
94(C2×D23)⋊C4—21no—
95(C2×D23)⋊C4—21no—
96C4⋊Dic23—21no—
97C4⋊Dic23D411yescharacteristic
98C4⋊Dic23D411yescharacteristic
99C4⋊Dic23C2311yescharacteristic
100C4⋊Dic23C2311yescharacteristic
101C4⋊Dic23C2311yescharacteristic
102Dic23⋊C4—21no—
103C4×Dic23—21no—
104C4×Dic23C2311yescharacteristic
105C4×Dic23C2311yescharacteristic
106C2×C23⋊C8C2311yescharacteristic
107C2×C23⋊C8C2311yescharacteristic
108C23×C23—24no—
109C23×C23—21no—
110C23×C23—21no—
111C23×C23—21no—
112C23×C23—81no—
113C23×C23—81no—
114C23×C23C2×D411yescharacteristic
115C22×D23—21no—
116D4×C23—24no—
117D4×C23—21no—
118D4×C23—21no—
119D4×C23—21no—
120D4×C23—21no—
121D4×C23—81no—
122D4×C23#4112yes—
123D4×C23#4112yes—
124C2×C4×C23—21no—
125C2×C4×C23—21no—
126C2×C4×C23—21no—
127C2×C4×C23C2×D411yescharacteristic
128C2×C4×C23C2411yescharacteristic
129C22⋊D23—81no—
130C22⋊D23—81no—
131C22⋊D23—81no—
132C2×Dic23—21no—
133C2×Dic23—21no—
134C2×Dic23—21no—
135C2×Dic23—81no—
136C2×Dic23—81no—
137C2×Dic23—81no—
138C2×Dic23—81no—
139C2×Dic23—81no—
140C2×Dic23C2×D411yescharacteristic
141C2×Dic23C2×D411yescharacteristic
142C2×Dic23C2×D411yescharacteristic
143C2×Dic23C2×D411yescharacteristic
144D92—21no—
145D92—21no—
146C4×D23—81no—
147C8×C23—21no—
148C8×C23—21no—
149C23⋊C8—21no—
150C23⋊C8—21no—
151#3122—231nomaximal, Sylow
152C22×C23—21no—
153C22×C23—22no—
154C22×C23—22no—
155C22×C23—21no—
156C22×C23—21no—
157C22×C23—41no—
158C22×C23—41no—
159C22×C23—41no—
160C22×C23—41no—
161C22×C23—41no—
162C22×C23—41no—
163C22×C23—41no—
164C22×C23—84no—
165C22×C23C22×D411yescharacteristic
166C2×D23—41no—
167C2×D23—41no—
168C2×D23—41no—
169C4×C23—21no—
170C4×C23—41no—
171C4×C23C2×#4111yescharacteristic
172C4×C23C2×#4111yescharacteristic
173Dic23—21no—
174Dic23—21no—
175Dic23—21no—
176Dic23—21no—
177Dic23—41no—
178Dic23—41no—
179Dic23—41no—
180#540—231no—
181#518—231no—
182#482—231no—
183#482—231no—
184#478—231no—
185#478—231no—
186#459—231no—
187#459—231no—
188#447—231no—
189#447D2311yescharacteristic, complemented
190#442—231no—
191#442—231no—
192C4×D8—231no—
193C4×D8—231no—
194#433—231no—
195C2×C23—41no—
196C2×C23—42no—
197C2×C23—42no—
198C2×C23—81no—
199C2×C23#52511yescharacteristic
200C2×C23#57611yescharacteristic
201C2×C23#57611yescharacteristic
202D23—81no—
203C22×D4C2×D2311yescharacteristic
204C2×D8—231no—
205C2×D8—231no—
206C2×D8C2×D2311yescharacteristic
207C2×D8C2×D2311yescharacteristic
208#127—231no—
209#125—231no—
210#123—461no—
211#123—461no—
212#121—231no—
213#121—461no—
214#121—461no—
215#121C2×D2311yescharacteristic
216C4×D4—231no—
217C4×D4—231no—
218C4×D4—231no—
219C4×D4—231no—
220C4×D4—231no—
221C4×D4—231no—
222C4×D4—461no—
223C4×D4—461no—
224#117—231no—
225#117—231no—
226C2×C22⋊C4—461no—
227C2×C22⋊C4—461no—
228#107—231no—
229#107—231no—
230#106—231no—
231#106—231no—
232C4⋊C8—231no—
233C4⋊C8—231no—
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⋊C8C2×D2311yescharacteristic
244#97—231no—
245C4×C8—231no—
246C23#312211yescharacteristic, complemented, Sylow
247C24—21no—
248C2×D4—22no—
249C2×D4—22no—
250C2×D4—21no—
251C2×D4—21no—
252C2×D4—231no—
253C2×D4—461no—
254C2×D4—461no—
255C2×D4—461no—
256C2×D4C22×D2311yescharacteristic
257C2×D4C22×D2311yescharacteristic
258C2×D4C22×D2311yescharacteristic
259C22×C4—461no—
260C22×C4—461no—
261C22×C4—461no—
262C22×C4—461no—
263C22×C4—461no—
264C22×C4—461no—
265C22×C4C22×D2311yescharacteristic
266D8—22no—
267D8—22no—
268D8—462no—
269D8—462no—
270C2×C8—231no—
271C2×C8—231no—
272C2×C8C22×D2311yescharacteristic
273C2×C8C22×D2311yescharacteristic
274C4⋊C4—231no—
275C4⋊C4—231no—
276C4⋊C4—231no—
277C4⋊C4—231no—
278C4⋊C4—231no—
279C4⋊C4—461no—
280C4⋊C4—461no—
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—231no—
295C42—461no—
296C23—24no—
297C23—21no—
298C23—21no—
299C23—21no—
300C23—81no—
301C23—81no—
302C23—461no—
303C23D4×D2311yescharacteristic
304D4—24no—
305D4—21no—
306D4—21no—
307D4—21no—
308D4—21no—
309D4—81no—
310D4—461no—
311D4—461no—
312D4—1841no—
313D4—1841no—
314D4—1841no—
315D4#6729012yes—
316D4#6729012yes—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—231no—
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×C4—1841no—
333C2×C4D4×D2311yescharacteristic
334C2×C4C23×D2311yescharacteristic
335C8—21no—
336C8—21no—
337C8—461no—
338C8—461no—
339C22—21no—
340C22—22no—
341C22—22no—
342C22—21no—
343C22—21no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—41no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—84no—
352C22—921no—
353C22—921no—
354C22—921no—
355C22C2×D4×D2311yescharacteristic
356C4—21no—
357C4—41no—
358C4—461no—
359C4—461no—
360C4—461no—
361C4—461no—
362C4—921no—
363C4—921no—
364C4—921no—
365C4C2×#6729011yescharacteristic
366C4C2×#6729011yescharacteristic
367C2—41no—
368C2—42no—
369C2—42no—
370C2—81no—
371C2—1841no—
372C2#1309292311yescharacteristic
373C2#1309321811yescharacteristic
374C2#1309322111yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#447C2
socleC22×C23C22×D4
hypercenter#447D23
hypocenterC23#3122
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. #13093020C2semidirect
2. #13092892C2semidirect
3. #13092742C2semidirect
4. #13092738C2semidirect
5. #13092719C2semidirect
6. #13092715C2semidirect
7. #13092610C2semidirect
8. #13092610C2semidirect
9. #13092551C2semidirect
10. #13092529C2semidirect
11. #13092526C2semidirect
12. D8×Dic23C2semidirect
13. #13092497C2semidirect
14. #13092475C2semidirect
15. C23×#447C2semidirect
22. #10625111C22semidirect
31. D4×Dic23C22semidirect
37. #10625064C22semidirect
38. #10625061C22semidirect
46. #10625014C22semidirect
47. #10625014C22semidirect
49. #10625003C22semidirect
50. #10625003C22semidirect
51. #10625000C22semidirect
52. #10624999C22semidirect
53. #10624997C22semidirect
54. Dic23⋊C8C22semidirect
55. Dic23⋊C8C22semidirect
56. C8×Dic23C22semidirect
57. #10624990C22semidirect
58. #10624989C22semidirect
189. #447D23semidirect
246. C23#3122semidirect

Maximal subgroups

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

subgroupindex
#130930202
#130928922
#130927422
#130927382
#130927192
#130927152
#130926102
#130925512
#130925292
#130925262
D8×Dic232
#130924972
#130924752
C23×#4472
#312223