Finite Group Databasebeta

← #15686482

Subgroups — #15686482

Order 2944.

380 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13093153C211yesmaximal, characteristic, complemented
2#13093149C211yesmaximal, characteristic, complemented
3#13092805C211yesmaximal, characteristic, complemented
4#13092798C211yesmaximal, characteristic, complemented
5#13092637C211yesmaximal, characteristic, complemented
6#13092636C211yesmaximal, characteristic, complemented
7#13092634C211yesmaximal, characteristic, complemented
8#13092630C211yesmaximal, characteristic, complemented
9#13092610C211yesmaximal, characteristic, complemented
10#13092609C211yesmaximal, characteristic, complemented
11#13092545C211yesmaximal, characteristic, complemented
12#13092519C211yesmaximal, characteristic, complemented
13#13092518C211yesmaximal, characteristic, complemented
14D8×Dic23C211yesmaximal, characteristic, complemented
15C23×#496C211yesmaximal, characteristic, complemented
16C2×SD16×C23C2211yescharacteristic
17C2×SD16×C23C2211yescharacteristic
18C2×D8×C23C2211yescharacteristic
19C2×D8×C23C2211yescharacteristic
20C23×#127C2211yescharacteristic
21C23×#124C2211yescharacteristic
22#10625118C2211yescharacteristic
23Q8×Dic23C2211yescharacteristic
24C2×#67275C2211yescharacteristic
25#10625111C2211yescharacteristic
26#10625107—21no—
27#10625107C2211yescharacteristic
28#10625107C2211yescharacteristic
29#10625106—21no—
30#10625106—21no—
31D4×Dic23—21no—
32D4×Dic23C2211yescharacteristic
33D4×Dic23C2211yescharacteristic
34D4×Dic23C2211yescharacteristic
35C2×#67273C2211yescharacteristic
36C2×#67272C2211yescharacteristic
37C2×#67272C2211yescharacteristic
38C2×#67263C2211yescharacteristic
39#10625057—21no—
40#10625056—21no—
41#10625054—21no—
42(C22⋊D23)⋊C4—21no—
43C4×D92C2211yescharacteristic
44C4×Dic46C2211yescharacteristic
45C4×Dic46C2211yescharacteristic
46C23×#97C2211yescharacteristic
47#10625017C2211yescharacteristic
48#10625014C2211yescharacteristic
49#10625014C2211yescharacteristic
50#10625014C2211yescharacteristic
51#10625003C2211yescharacteristic
52#10625000C2211yescharacteristic
53#10624998C2211yescharacteristic
54#10624997C2211yescharacteristic
55Dic23⋊C8C2211yescharacteristic
56Dic23⋊C8C2211yescharacteristic
57C8×Dic23C2211yescharacteristic
58C4⋊(C23⋊C8)C2211yescharacteristic
59C2×Q8×C23C2311yescharacteristic
60C2×D4×C23—21no—
61C2×D4×C23—21no—
62C2×D4×C23C2311yescharacteristic
63C2×D4×C23C2311yescharacteristic
64C2×D4×C23C2311yescharacteristic
65C2×C22⋊D23—21no—
66C2×C22⋊D23—21no—
67C22×Dic23—21no—
68C22×Dic23—21no—
69C22×Dic23—21no—
70C2×D92C2311yescharacteristic
71C2×C4×D23—21no—
72C2×Dic46D411yescharacteristic
73C2×Dic46C2311yescharacteristic
74SD16×C23—22no—
75SD16×C23—41no—
76D8×C23—22no—
77D8×C23—41no—
78C2×C8×C23C2311yescharacteristic
79C2×C8×C23C2311yescharacteristic
80C22⋊C4×C23—21no—
81C22⋊C4×C23—21no—
82C42×C23C2311yescharacteristic
83C22⋊Dic23—21no—
84C22⋊Dic23—21no—
85C22⋊Dic23—21no—
86C22⋊Dic23—21no—
87C22⋊Dic23—21no—
88C22⋊Dic23—21no—
89C22⋊Dic23—21no—
90#67275—41no—
91#67273—41no—
92#67272—41no—
93#67272—41no—
94(C2×D23)⋊C4—21no—
95(C2×D23)⋊C4—21no—
96(C2×D23)⋊C4—21no—
97C4⋊Dic23—21no—
98C4⋊Dic23D411yescharacteristic
99C4⋊Dic23C2311yescharacteristic
100C4⋊Dic23C2311yescharacteristic
101Dic23⋊C4—21no—
102Dic23⋊C4D411yescharacteristic
103Dic23⋊C4D411yescharacteristic
104C4×Dic23—21no—
105C4×Dic23—21no—
106C4×Dic23C2311yescharacteristic
107C4×Dic23C2311yescharacteristic
108C2×C23⋊C8C2311yescharacteristic
109C2×C23⋊C8C2311yescharacteristic
110#67263—22no—
111C23×C23—21no—
112C23×C23—21no—
113C23×C23—21no—
114C22×D23—21no—
115Q8×C23—21no—
116Q8×C23—21no—
117D4×C23—21no—
118D4×C23—21no—
119D4×C23—21no—
120D4×C23—21no—
121D4×C23—21no—
122D4×C23—21no—
123D4×C23—42no—
124D4×C23—81no—
125C2×C4×C23—21no—
126C2×C4×C23C2×D411yescharacteristic
127C2×C4×C23C2×D411yescharacteristic
128C2×C4×C23C2411yescharacteristic
129C22⋊D23—42no—
130C22⋊D23—81no—
131C2×Dic23—21no—
132C2×Dic23—21no—
133C2×Dic23—21no—
134C2×Dic23—81no—
135C2×Dic23—81no—
136C2×Dic23—81no—
137C2×Dic23C2×D411yescharacteristic
138C2×Dic23C2×D411yescharacteristic
139C2×Dic23C2×D411yescharacteristic
140C2×Dic23C2×D411yescharacteristic
141D92—21no—
142D92—21no—
143C4×D23—81no—
144Dic46—21no—
145Dic46—21no—
146Dic46—41no—
147C8×C23—21no—
148C8×C23#4112yes—
149C23⋊C8—21no—
150C23⋊C8—21no—
151#3403—231nomaximal, Sylow
152C22×C23—41no—
153C22×C23—41no—
154C22×C23—41no—
155C22×C23—41no—
156C22×C23—41no—
157C22×C23—41no—
158C22×C23—41no—
159C22×C23—41no—
160C22×C23—41no—
161C22×C23C22×D411yescharacteristic
162C2×D23—41no—
163C2×D23—41no—
164C2×D23—41no—
165C4×C23—21no—
166C4×C23—21no—
167C4×C23—41no—
168C4×C23C2×#4111yescharacteristic
169C4×C23H(5,𝔽2)11yescharacteristic
170Dic23—21no—
171Dic23—21no—
172Dic23—21no—
173Dic23—21no—
174Dic23—41no—
175Dic23—41no—
176Dic23—41no—
177#559—231no—
178#559—231no—
179#496—231no—
180#496D2311yescharacteristic, complemented
181#495—231no—
182#464—231no—
183#464—231no—
184#463—231no—
185#463—231no—
186#459—231no—
187#459—231no—
188#446—231no—
189#440—231no—
190#440—231no—
191C4×D8—231no—
192C2×C23—81no—
193C2×C23—81no—
194C2×C23—81no—
195C2×C23#55011yescharacteristic
196C2×C23#57511yescharacteristic
197C2×C23#57611yescharacteristic
198D23—81no—
199C2×Q16—231no—
200C2×SD16—231no—
201C2×SD16—231no—
202C2×SD16C2×D2311yescharacteristic
203C2×SD16C2×D2311yescharacteristic
204C2×D8—231no—
205C2×D8—231no—
206C2×D8C2×D2311yescharacteristic
207C2×D8C2×D2311yescharacteristic
208#127—231no—
209#127C2×D2311yescharacteristic
210#124—231no—
211#124—231no—
212#124—231no—
213#124—461no—
214#124—461no—
215#124C2×D2311yescharacteristic
216#123—461no—
217#123—461no—
218#123—461no—
219#123—461no—
220C4×Q8—231no—
221C4×Q8—231no—
222C4×Q8—231no—
223C4×D4—231no—
224C4×D4—231no—
225C4×D4—231no—
226C4×D4—231no—
227C4×D4—461no—
228C4×D4—461no—
229#107—231no—
230C4⋊C8—231no—
231C4⋊C8—231no—
232C4⋊C8—231no—
233#103—231no—
234#103—231no—
235#102—231no—
236#102—231no—
237#102—231no—
238#102—231no—
239#97—231no—
240#97C2×D2311yescharacteristic
241C4×C8—231no—
242C23#340311yescharacteristic, complemented, Sylow
243C2×Q8—231no—
244C2×Q8—231no—
245C2×Q8C22×D2311yescharacteristic
246C2×D4—21no—
247C2×D4—21no—
248C2×D4—231no—
249C2×D4—461no—
250C2×D4—461no—
251C2×D4C22×D2311yescharacteristic
252C2×D4C22×D2311yescharacteristic
253C2×D4C22×D2311yescharacteristic
254C22×C4—461no—
255C22×C4—461no—
256C22×C4—461no—
257C22×C4—461no—
258Q16—921no—
259SD16—22no—
260SD16—41no—
261SD16—462no—
262SD16—921no—
263D8—22no—
264D8—41no—
265D8—921no—
266D8—921no—
267C2×C8—231no—
268C2×C8—231no—
269C2×C8C22×D2311yescharacteristic
270C2×C8C22×D2311yescharacteristic
271C4⋊C4—231no—
272C4⋊C4—231no—
273C4⋊C4—231no—
274C4⋊C4—231no—
275C4⋊C4—231no—
276C4⋊C4—461no—
277C4⋊C4—461no—
278C22⋊C4—21no—
279C22⋊C4—21no—
280C22⋊C4—461no—
281C22⋊C4—461no—
282C22⋊C4—461no—
283C22⋊C4—461no—
284C22⋊C4—461no—
285C22⋊C4—461no—
286C22⋊C4—461no—
287C22⋊C4—461no—
288C22⋊C4—461no—
289C22⋊C4—461no—
290C42—231no—
291C42—231no—
292C42—461no—
293C42—461no—
294C42C22×D2311yescharacteristic
295C23—21no—
296C23—21no—
297C23—21no—
298C23—461no—
299Q8—21no—
300Q8—21no—
301Q8—461no—
302Q8—461no—
303Q8—921no—
304D4—21no—
305D4—21no—
306D4—21no—
307D4—21no—
308D4—21no—
309D4—21no—
310D4—42no—
311D4—81no—
312D4—461no—
313D4—461no—
314D4—922no—
315D4—1841no—
316C2×C4—21no—
317C2×C4—231no—
318C2×C4—231no—
319C2×C4—231no—
320C2×C4—231no—
321C2×C4—461no—
322C2×C4—461no—
323C2×C4—461no—
324C2×C4—1841no—
325C2×C4—1841no—
326C2×C4—1841no—
327C2×C4—1841no—
328C2×C4D4×D2311yescharacteristic
329C2×C4D4×D2311yescharacteristic
330C2×C4C23×D2311yescharacteristic
331C8—21no—
332C8—461no—
333C8—461no—
334C8#6729012yes—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—921no—
345C22—921no—
346C22—921no—
347C22C2×D4×D2311yescharacteristic
348C4—21no—
349C4—21no—
350C4—41no—
351C4—461no—
352C4—461no—
353C4—461no—
354C4—461no—
355C4—921no—
356C4—921no—
357C4—921no—
358C4C2×#6729011yescharacteristic
359C4#1062515511yescharacteristic
360C2—81no—
361C2—81no—
362C2—81no—
363C2—1841no—
364C2#1309308711yescharacteristic
365C2#1309321311yescharacteristic
366C2#1309322111yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#496C2
socleC22×C23C22×D4
hypercenter#496D23
hypocenterC23#3403
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ #496

Complements

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

NH ≅ G/Ntype
1. #13093153C2semidirect
2. #13093149C2semidirect
3. #13092805C2semidirect
4. #13092798C2semidirect
5. #13092637C2semidirect
6. #13092636C2semidirect
7. #13092634C2semidirect
8. #13092630C2semidirect
9. #13092610C2semidirect
10. #13092609C2semidirect
11. #13092545C2semidirect
12. #13092519C2semidirect
13. #13092518C2semidirect
14. D8×Dic23C2semidirect
15. C23×#496C2semidirect
180. #496D23semidirect
242. C23#3403semidirect

Maximal subgroups

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

subgroupindex
#130931532
#130931492
#130928052
#130927982
#130926372
#130926362
#130926342
#130926302
#130926102
#130926092
#130925452
#130925192
#130925182
D8×Dic232
C23×#4962
#340323