Finite Group Databasebeta

← #15686484

Subgroups — #15686484

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#13093152C211yesmaximal, characteristic, complemented
2#13093149C211yesmaximal, characteristic, complemented
3#13092807C211yesmaximal, characteristic, complemented
4#13092803C211yesmaximal, characteristic, complemented
5#13092802C211yesmaximal, characteristic, complemented
6#13092641C211yesmaximal, characteristic, complemented
7#13092635C211yesmaximal, characteristic, complemented
8#13092634C211yesmaximal, characteristic, complemented
9#13092613C211yesmaximal, characteristic, complemented
10#13092611C211yesmaximal, characteristic, complemented
11#13092546C211yesmaximal, characteristic, complemented
12#13092520C211yesmaximal, characteristic, complemented
13#13092515C211yesmaximal, characteristic, complemented
14#13092497C211yesmaximal, characteristic, complemented
15C23×#464C211yesmaximal, characteristic, complemented
16C2×Q16×C23C2211yescharacteristic
17C2×SD16×C23C2211yescharacteristic
18C23×#124C2211yescharacteristic
19C4×Q8×C23C2211yescharacteristic
20#10625118C2211yescharacteristic
21#10625118C2211yescharacteristic
22#10625118C2211yescharacteristic
23Q8×Dic23C2211yescharacteristic
24C2×#67274C2211yescharacteristic
25C2×#67274C2211yescharacteristic
26C2×#67274C2211yescharacteristic
27#10625111C2211yescharacteristic
28D4×Dic23C2211yescharacteristic
29C2×#67272C2211yescharacteristic
30C2×#67272C2211yescharacteristic
31C2×D184C2211yescharacteristic
32C2×D184C2211yescharacteristic
33#10625065—21no—
34#10625065—21no—
35#10625064C2211yescharacteristic
36#10625064C2211yescharacteristic
37#10625057—21no—
38#10625056—21no—
39#10625054—21no—
40(C22⋊D23)⋊C4—21no—
41#10625046—21no—
42#10625045C2211yescharacteristic
43C4×D92—21no—
44C4×D92C2211yescharacteristic
45C4×Dic46C2211yescharacteristic
46C23×C4⋊C8C2211yescharacteristic
47C23×#103C2211yescharacteristic
48C23×#102C2211yescharacteristic
49#10625017C2211yescharacteristic
50#10625003C2211yescharacteristic
51#10625003C2211yescharacteristic
52#10624997C2211yescharacteristic
53Dic23⋊C8C2211yescharacteristic
54Dic23⋊C8C2211yescharacteristic
55C8×Dic23C2211yescharacteristic
56#10624991C2211yescharacteristic
57#10624989C2211yescharacteristic
58#10624985C2211yescharacteristic
59C2×Q8×C23C2311yescharacteristic
60C2×Q8×C23C2311yescharacteristic
61C2×D4×C23C2311yescharacteristic
62C2×C22⋊D23—21no—
63C2×C22⋊D23—21no—
64C22×Dic23—21no—
65C2×D92—21no—
66C2×D92—21no—
67C2×D92C2311yescharacteristic
68C2×D92C2311yescharacteristic
69C2×D92C2311yescharacteristic
70C2×C4×D23—21no—
71C2×C4×D23—21no—
72C2×C4×D23—21no—
73C2×Dic46D411yescharacteristic
74Q16×C23—41no—
75SD16×C23—41no—
76C2×C8×C23C2311yescharacteristic
77C2×C8×C23C2311yescharacteristic
78C4⋊C4×C23—21no—
79C4⋊C4×C23C2311yescharacteristic
80C22⋊C4×C23—21no—
81C22⋊C4×C23—21no—
82C42×C23—21no—
83C42×C23C2311yescharacteristic
84C22⋊Dic23—21no—
85#67274—22no—
86#67274—22no—
87#67274—41no—
88#67272—22no—
89#67272—41no—
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)⋊C4—21no—
98(C2×D23)⋊C4—21no—
99C4⋊Dic23—21no—
100C4⋊Dic23D411yescharacteristic
101C4⋊Dic23C2311yescharacteristic
102Dic23⋊C4D411yescharacteristic
103Dic23⋊C4D411yescharacteristic
104C4×Dic23—21no—
105C4×Dic23C2311yescharacteristic
106C4×Dic23C2311yescharacteristic
107C2×C23⋊C8C2311yescharacteristic
108C2×C23⋊C8C2311yescharacteristic
109D184—41no—
110D184—41no—
111C23×C23—21no—
112C22×D23—21no—
113C22×D23—21no—
114C22×D23—21no—
115Q8×C23—21no—
116Q8×C23—21no—
117Q8×C23—21no—
118Q8×C23—21no—
119D4×C23—21no—
120D4×C23—21no—
121C2×C4×C23—21no—
122C2×C4×C23—21no—
123C2×C4×C23—21no—
124C2×C4×C23C2×D411yescharacteristic
125C2×C4×C23C2×D411yescharacteristic
126C2×C4×C23C2411yescharacteristic
127C22⋊D23—42no—
128C22⋊D23—81no—
129C2×Dic23—21no—
130C2×Dic23—81no—
131C2×Dic23C2×D411yescharacteristic
132C2×Dic23C2×D411yescharacteristic
133C2×Dic23C2×D411yescharacteristic
134C2×Dic23C2×D411yescharacteristic
135D92—21no—
136D92—21no—
137D92—21no—
138D92—21no—
139D92—21no—
140D92—21no—
141D92—42no—
142D92—81no—
143C4×D23—81no—
144C4×D23—81no—
145C4×D23—81no—
146Dic46—41no—
147C8×C23—21no—
148C8×C23—21no—
149C23⋊C8—21no—
150C23⋊C8#4112yes—
151#3403—231nomaximal, Sylow
152C22×C23—41no—
153C22×C23—41no—
154C22×C23—41no—
155C22×C23C22×D411yescharacteristic
156C2×D23—41no—
157C2×D23—41no—
158C2×D23—41no—
159C2×D23—41no—
160C2×D23—41no—
161C2×D23—41no—
162C2×D23—41no—
163C2×D23—41no—
164C2×D23—41no—
165C4×C23—21no—
166C4×C23—21no—
167C4×C23—41no—
168C4×C23—41no—
169C4×C23—41no—
170C4×C23C2×#4111yescharacteristic
171C4×C23H(5,𝔽2)11yescharacteristic
172Dic23—21no—
173Dic23—21no—
174Dic23—21no—
175Dic23—21no—
176Dic23—41no—
177#559—231no—
178#559—231no—
179#496—231no—
180#496—231no—
181#495—231no—
182#464—231no—
183#464D2311yescharacteristic, complemented
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#55011yescharacteristic
194C2×C23#57511yescharacteristic
195C2×C23#57611yescharacteristic
196D23—81no—
197D23—81no—
198D23—81no—
199C2×Q16C2×D2311yescharacteristic
200C2×SD16—231no—
201C2×SD16—231no—
202C2×SD16—231no—
203C2×SD16C2×D2311yescharacteristic
204C2×D8—231no—
205C2×D8—231no—
206C2×D8—231no—
207C2×D8—231no—
208#127—231no—
209#127—231no—
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×Q8C2×D2311yescharacteristic
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⋊C8C2×D2311yescharacteristic
233#103—231no—
234#103C2×D2311yescharacteristic
235#102—231no—
236#102—231no—
237#102—231no—
238#102C2×D2311yescharacteristic
239#97—231no—
240#97—231no—
241C4×C8—231no—
242C23#340311yescharacteristic, complemented, Sylow
243C2×Q8—231no—
244C2×Q8C22×D2311yescharacteristic
245C2×Q8C22×D2311yescharacteristic
246C2×D4—231no—
247C2×D4—231no—
248C2×D4—231no—
249C2×D4—461no—
250C2×D4—461no—
251C2×D4—461no—
252C2×D4—461no—
253C2×D4C22×D2311yescharacteristic
254C22×C4—461no—
255C22×C4—461no—
256C22×C4—461no—
257C22×C4—461no—
258Q16—41no—
259SD16—41no—
260SD16—462no—
261SD16—462no—
262SD16—921no—
263D8—462no—
264D8—921no—
265D8—921no—
266D8—921no—
267C2×C8—231no—
268C2×C8—231no—
269C2×C8C22×D2311yescharacteristic
270C2×C8C22×D2311yescharacteristic
271C4⋊C4—21no—
272C4⋊C4—231no—
273C4⋊C4—231no—
274C4⋊C4—231no—
275C4⋊C4—231no—
276C4⋊C4—461no—
277C4⋊C4C22×D2311yescharacteristic
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—21no—
291C42—231no—
292C42—231no—
293C42—461no—
294C42C22×D2311yescharacteristic
295C23—21no—
296C23—461no—
297C23—461no—
298C23—461no—
299Q8—21no—
300Q8—21no—
301Q8—21no—
302Q8—21no—
303Q8—921no—
304D4—21no—
305D4—21no—
306D4—461no—
307D4—461no—
308D4—461no—
309D4—461no—
310D4—461no—
311D4—461no—
312D4—922no—
313D4—922no—
314D4—1841no—
315D4—1841no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—231no—
320C2×C4—231no—
321C2×C4—231no—
322C2×C4—231no—
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—21no—
333C8—232no—
334C8—461no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—921no—
339C22—921no—
340C22—921no—
341C22—921no—
342C22—921no—
343C22—921no—
344C22—921no—
345C22—921no—
346C22—921no—
347C22C2×D4×D2311yescharacteristic
348C4—21no—
349C4—21no—
350C4—41no—
351C4—41no—
352C4—41no—
353C4—461no—
354C4—461no—
355C4—461no—
356C4—461no—
357C4—921no—
358C4#1062515511yescharacteristic
359C4#41×D2311yescharacteristic
360C2—81no—
361C2—1841no—
362C2—1841no—
363C2—1841no—
364C2#1309308511yescharacteristic
365C2#1309321611yescharacteristic
366C2#1309321911yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#464C2
socleC22×C23C22×D4
hypercenter#464D23
hypocenterC23#3403
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

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

NH ≅ G/Ntype
1. #13093152C2semidirect
2. #13093149C2semidirect
3. #13092807C2semidirect
4. #13092803C2semidirect
5. #13092802C2semidirect
6. #13092641C2semidirect
7. #13092635C2semidirect
8. #13092634C2semidirect
9. #13092613C2semidirect
10. #13092611C2semidirect
11. #13092546C2semidirect
12. #13092520C2semidirect
13. #13092515C2semidirect
14. #13092497C2semidirect
15. C23×#464C2semidirect
183. #464D23semidirect
242. C23#3403semidirect

Maximal subgroups

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

subgroupindex
#130931522
#130931492
#130928072
#130928032
#130928022
#130926412
#130926352
#130926342
#130926132
#130926112
#130925462
#130925202
#130925152
#130924972
C23×#4642
#340323