Finite Group Databasebeta

← #15686480

Subgroups — #15686480

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#13093150C211yesmaximal, characteristic, complemented
3#13092805C211yesmaximal, characteristic, complemented
4#13092804C211yesmaximal, characteristic, complemented
5#13092800C211yesmaximal, characteristic, complemented
6#13092640C211yesmaximal, characteristic, complemented
7#13092638C211yesmaximal, characteristic, complemented
8#13092631C211yesmaximal, characteristic, complemented
9#13092630C211yesmaximal, characteristic, complemented
10#13092610C211yesmaximal, characteristic, complemented
11#13092546C211yesmaximal, characteristic, complemented
12#13092517C211yesmaximal, characteristic, complemented
13#13092514C211yesmaximal, characteristic, complemented
14#13092497C211yesmaximal, characteristic, complemented
15C23×#459C211yesmaximal, characteristic, complemented
16C2×D8×C23C2211yescharacteristic
17C2×D8×C23C2211yescharacteristic
18C23×#127C2211yescharacteristic
19C4×D4×C23C2211yescharacteristic
20#10625111C2211yescharacteristic
21#10625107—21no—
22#10625107C2211yescharacteristic
23#10625107C2211yescharacteristic
24#10625107C2211yescharacteristic
25#10625106—21no—
26#10625106—21no—
27D4×Dic23—21no—
28D4×Dic23C2211yescharacteristic
29D4×Dic23C2211yescharacteristic
30C2×#67273C2211yescharacteristic
31C2×#67273C2211yescharacteristic
32C2×#67273C2211yescharacteristic
33C2×#67272C2211yescharacteristic
34C2×#67272C2211yescharacteristic
35#10625100—21no—
36C4×C22⋊D23—21no—
37C2×Dic92C2211yescharacteristic
38C2×#67263C2211yescharacteristic
39#10625064C2211yescharacteristic
40#10625058C2211yescharacteristic
41#10625056—21no—
42#10625054—21no—
43#10625046C2211yescharacteristic
44C4×Dic46C2211yescharacteristic
45C4×Dic46C2211yescharacteristic
46C23×C4⋊C8C2211yescharacteristic
47C23×#102C2211yescharacteristic
48C23×#102C2211yescharacteristic
49#10625014C2211yescharacteristic
50#10625003C2211yescharacteristic
51#10624998C2211yescharacteristic
52#10624997C2211yescharacteristic
53Dic23⋊C8C2211yescharacteristic
54Dic23⋊C8C2211yescharacteristic
55C8×Dic23C2211yescharacteristic
56#10624992C2211yescharacteristic
57#10624989C2211yescharacteristic
58#10624985C2211yescharacteristic
59C2×D4×C23—21no—
60C2×D4×C23—21no—
61C2×D4×C23C2311yescharacteristic
62C2×D4×C23C2311yescharacteristic
63C2×D4×C23C2311yescharacteristic
64C22×C4×C23—21no—
65C2×C22⋊D23—21no—
66C2×C22⋊D23—21no—
67C22×Dic23—21no—
68C22×Dic23—21no—
69C2×D92C2311yescharacteristic
70C2×C4×D23—21no—
71C2×Dic46D411yescharacteristic
72C2×Dic46C2311yescharacteristic
73C2×Dic46C2311yescharacteristic
74D8×C23—41no—
75D8×C23—41no—
76C2×C8×C23C2311yescharacteristic
77C2×C8×C23C2311yescharacteristic
78C4⋊C4×C23C2311yescharacteristic
79C22⋊C4×C23—21no—
80C42×C23C2311yescharacteristic
81C22⋊Dic23—21no—
82C22⋊Dic23—21no—
83C22⋊Dic23—21no—
84C22⋊Dic23—21no—
85C22⋊Dic23—21no—
86C22⋊Dic23—21no—
87C22⋊Dic23—21no—
88C22⋊Dic23—21no—
89#67273—22no—
90#67273—22no—
91#67273—41no—
92#67272—22no—
93#67272—41no—
94(C2×D23)⋊C4—21no—
95(C2×D23)⋊C4—21no—
96(C2×D23)⋊C4—21no—
97C4⋊Dic23D411yescharacteristic
98C4⋊Dic23C2311yescharacteristic
99Dic23⋊C4—21no—
100Dic23⋊C4—21no—
101Dic23⋊C4D411yescharacteristic
102Dic23⋊C4D411yescharacteristic
103C4×Dic23—21no—
104C4×Dic23—21no—
105C4×Dic23C2311yescharacteristic
106C4×Dic23C2311yescharacteristic
107C2×C23⋊C8C2311yescharacteristic
108C2×C23⋊C8C2311yescharacteristic
109Dic92—41no—
110#67263—41no—
111C23×C23—21no—
112C23×C23—21no—
113C23×C23—21no—
114C22×D23—21no—
115D4×C23—21no—
116D4×C23—21no—
117D4×C23—21no—
118D4×C23—21no—
119D4×C23—21no—
120D4×C23—21no—
121D4×C23—42no—
122D4×C23—81no—
123C2×C4×C23—21no—
124C2×C4×C23—81no—
125C2×C4×C23C2×D411yescharacteristic
126C2×C4×C23C2×D411yescharacteristic
127C2×C4×C23C2411yescharacteristic
128C22⋊D23—42no—
129C22⋊D23—81no—
130C2×Dic23—21no—
131C2×Dic23—21no—
132C2×Dic23—21no—
133C2×Dic23—81no—
134C2×Dic23—81no—
135C2×Dic23C2×D411yescharacteristic
136C2×Dic23C2×D411yescharacteristic
137C2×Dic23C2×D411yescharacteristic
138C2×Dic23C2×D411yescharacteristic
139D92—21no—
140D92—21no—
141C4×D23—81no—
142Dic46—21no—
143Dic46—21no—
144Dic46—21no—
145Dic46—21no—
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×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#496—231no—
181#495—231no—
182#464—231no—
183#464—231no—
184#463—231no—
185#463—231no—
186#459—231no—
187#459D2311yescharacteristic, complemented
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×SD16—231no—
203C2×SD16—231no—
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—231no—
214#124—461no—
215#124—461no—
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—461no—
227C4×D4—461no—
228C4×D4C2×D2311yescharacteristic
229#107—231no—
230C4⋊C8—231no—
231C4⋊C8—231no—
232C4⋊C8C2×D2311yescharacteristic
233#103—231no—
234#103—231no—
235#102—231no—
236#102—231no—
237#102C2×D2311yescharacteristic
238#102C2×D2311yescharacteristic
239#97—231no—
240#97—231no—
241C4×C8—231no—
242C23#340311yescharacteristic, complemented, Sylow
243C2×Q8—231no—
244C2×Q8—231no—
245C2×Q8—231no—
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—21no—
255C22×C4—461no—
256C22×C4—461no—
257C22×C4—461no—
258Q16—921no—
259SD16—462no—
260SD16—462no—
261SD16—921no—
262SD16—921no—
263D8—41no—
264D8—41no—
265D8—462no—
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—461no—
276C4⋊C4—461no—
277C4⋊C4C22×D2311yescharacteristic
278C22⋊C4—21no—
279C22⋊C4—461no—
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—461no—
300Q8—461no—
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—81no—
318C2×C4—231no—
319C2×C4—231no—
320C2×C4—231no—
321C2×C4—231no—
322C2×C4—461no—
323C2×C4—461no—
324C2×C4—461no—
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—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—
358C4#1062515511yescharacteristic
359C4#41×D2311yescharacteristic
360C2—81no—
361C2—81no—
362C2—81no—
363C2—1841no—
364C2#1309308511yescharacteristic
365C2#1309321311yescharacteristic
366C2#1309321811yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#459C2
socleC22×C23C22×D4
hypercenter#459D23
hypocenterC23#3403
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #13093153C2semidirect
2. #13093150C2semidirect
3. #13092805C2semidirect
4. #13092804C2semidirect
5. #13092800C2semidirect
6. #13092640C2semidirect
7. #13092638C2semidirect
8. #13092631C2semidirect
9. #13092630C2semidirect
10. #13092610C2semidirect
11. #13092546C2semidirect
12. #13092517C2semidirect
13. #13092514C2semidirect
14. #13092497C2semidirect
15. C23×#459C2semidirect
187. #459D23semidirect
242. C23#3403semidirect

Maximal subgroups

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

subgroupindex
#130931532
#130931502
#130928052
#130928042
#130928002
#130926402
#130926382
#130926312
#130926302
#130926102
#130925462
#130925172
#130925142
#130924972
C23×#4592
#340323