Finite Group Databasebeta

← #15686486

Subgroups — #15686486

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#13093150C211yesmaximal, characteristic, complemented
3#13092806C211yesmaximal, characteristic, complemented
4#13092803C211yesmaximal, characteristic, complemented
5#13092798C211yesmaximal, characteristic, complemented
6#13092642C211yesmaximal, characteristic, complemented
7#13092639C211yesmaximal, characteristic, complemented
8#13092635C211yesmaximal, characteristic, complemented
9#13092631C211yesmaximal, characteristic, complemented
10#13092612C211yesmaximal, characteristic, complemented
11#13092611C211yesmaximal, characteristic, complemented
12#13092545C211yesmaximal, characteristic, complemented
13#13092516C211yesmaximal, characteristic, complemented
14#13092499C211yesmaximal, characteristic, complemented
15C23×#440C211yesmaximal, characteristic, complemented
16C2×SD16×C23C2211yescharacteristic
17C4×Q8×C23C2211yescharacteristic
18C4×D4×C23C2211yescharacteristic
19#10625118C2211yescharacteristic
20#10625118C2211yescharacteristic
21C2×#67275C2211yescharacteristic
22C2×#67274C2211yescharacteristic
23#10625111C2211yescharacteristic
24#10625107C2211yescharacteristic
25C2×#67272C2211yescharacteristic
26C2×#67272C2211yescharacteristic
27#10625100—21no—
28C4×C22⋊D23—21no—
29C2×D184C2211yescharacteristic
30C2×D184C2211yescharacteristic
31C2×#67263C2211yescharacteristic
32C2×#67263C2211yescharacteristic
33#10625065—21no—
34#10625065—21no—
35#10625064C2211yescharacteristic
36#10625064C2211yescharacteristic
37#10625064C2211yescharacteristic
38#10625058C2211yescharacteristic
39#10625056—21no—
40#10625054—21no—
41#10625046—21no—
42#10625046C2211yescharacteristic
43#10625045C2211yescharacteristic
44C4×D92—21no—
45C4×Dic46C2211yescharacteristic
46C23×#107C2211yescharacteristic
47C23×#103C2211yescharacteristic
48C23×#102C2211yescharacteristic
49C23×#97C2211yescharacteristic
50#10624997C2211yescharacteristic
51Dic23⋊C8C2211yescharacteristic
52Dic23⋊C8C2211yescharacteristic
53C8×Dic23C2211yescharacteristic
54#10624992C2211yescharacteristic
55#10624991C2211yescharacteristic
56#10624991C2211yescharacteristic
57#10624991C2211yescharacteristic
58C4⋊(C23⋊C8)C2211yescharacteristic
59C2×Q8×C23C2311yescharacteristic
60C2×D4×C23C2311yescharacteristic
61C22×C4×C23—21no—
62C2×C22⋊D23—21no—
63C2×C22⋊D23—21no—
64C2×D92—21no—
65C2×D92—21no—
66C2×D92C2311yescharacteristic
67C2×D92C2311yescharacteristic
68C2×D92C2311yescharacteristic
69C2×C4×D23—21no—
70C2×C4×D23—21no—
71C2×C4×D23—21no—
72C2×Dic46D411yescharacteristic
73C2×Dic46C2311yescharacteristic
74SD16×C23—22no—
75C2×C8×C23C2311yescharacteristic
76C2×C8×C23C2311yescharacteristic
77C4⋊C4×C23—21no—
78C4⋊C4×C23C2311yescharacteristic
79C4⋊C4×C23C2311yescharacteristic
80C22⋊C4×C23—21no—
81C42×C23—21no—
82C42×C23C2311yescharacteristic
83C22⋊Dic23—21no—
84C22⋊Dic23—21no—
85#67275—41no—
86#67274—41no—
87#67272—41no—
88#67272—41no—
89(C2×D23)⋊C4—21no—
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—
98C4⋊Dic23D411yescharacteristic
99Dic23⋊C4—21no—
100Dic23⋊C4D411yescharacteristic
101Dic23⋊C4D411yescharacteristic
102C4×Dic23—21no—
103C4×Dic23C2311yescharacteristic
104C4×Dic23C2311yescharacteristic
105C2×C23⋊C8C2311yescharacteristic
106C2×C23⋊C8C2311yescharacteristic
107D184—22no—
108D184—41no—
109#67263—22no—
110#67263—41no—
111C23×C23—21no—
112C22×D23—21no—
113C22×D23—21no—
114C22×D23—21no—
115Q8×C23—21no—
116Q8×C23—21no—
117D4×C23—21no—
118D4×C23—21no—
119C2×C4×C23—21no—
120C2×C4×C23—21no—
121C2×C4×C23—21no—
122C2×C4×C23—81no—
123C2×C4×C23C2×D411yescharacteristic
124C2×C4×C23C2×D411yescharacteristic
125C2×C4×C23C2411yescharacteristic
126C22⋊D23—42no—
127C22⋊D23—81no—
128C2×Dic23—21no—
129C2×Dic23C2×D411yescharacteristic
130C2×Dic23C2×D411yescharacteristic
131C2×Dic23C2×D411yescharacteristic
132C2×Dic23C2×D411yescharacteristic
133D92—21no—
134D92—21no—
135D92—21no—
136D92—21no—
137D92—21no—
138D92—21no—
139D92—42no—
140D92—81no—
141C4×D23—81no—
142C4×D23—81no—
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×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#464—231no—
184#463—231no—
185#463—231no—
186#459—231no—
187#459—231no—
188#446—231no—
189#440—231no—
190#440D2311yescharacteristic, complemented
191C4×D8—231no—
192C2×C23—81no—
193C2×C23#55011yescharacteristic
194C2×C23#57511yescharacteristic
195C2×C23#57611yescharacteristic
196D23—81no—
197D23—81no—
198D23—81no—
199C2×Q16—231no—
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—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×Q8C2×D2311yescharacteristic
223C4×D4—231no—
224C4×D4—231no—
225C4×D4—231no—
226C4×D4—461no—
227C4×D4—461no—
228C4×D4C2×D2311yescharacteristic
229#107C2×D2311yescharacteristic
230C4⋊C8—231no—
231C4⋊C8—231no—
232C4⋊C8—231no—
233#103—231no—
234#103C2×D2311yescharacteristic
235#102—231no—
236#102—231no—
237#102—231no—
238#102C2×D2311yescharacteristic
239#97—231no—
240#97C2×D2311yescharacteristic
241C4×C8—231no—
242C23#340311yescharacteristic, complemented, Sylow
243C2×Q8—231no—
244C2×Q8—231no—
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—21no—
255C22×C4—461no—
256C22×C4—461no—
257C22×C4—461no—
258Q16—921no—
259SD16—22no—
260SD16—462no—
261SD16—921no—
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—461no—
276C4⋊C4C22×D2311yescharacteristic
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—21no—
291C42—231no—
292C42—231no—
293C42—461no—
294C42C22×D2311yescharacteristic
295C23—21no—
296C23—461no—
297C23—461no—
298C23—461no—
299Q8—21no—
300Q8—21no—
301Q8—461no—
302Q8—461no—
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—81no—
320C2×C4—231no—
321C2×C4—231no—
322C2×C4—231no—
323C2×C4—231no—
324C2×C4—461no—
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#6728812yes—
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—
358C4C2×#6728811yescharacteristic
359C4#1062516011yescharacteristic
360C2—81no—
361C2—1841no—
362C2—1841no—
363C2—1841no—
364C2#1309308811yescharacteristic
365C2#1309321611yescharacteristic
366C2#1309322111yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#440C2
socleC22×C23C22×D4
hypercenter#440D23
hypocenterC23#3403
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
1. #13093152C2semidirect
2. #13093150C2semidirect
3. #13092806C2semidirect
4. #13092803C2semidirect
5. #13092798C2semidirect
6. #13092642C2semidirect
7. #13092639C2semidirect
8. #13092635C2semidirect
9. #13092631C2semidirect
10. #13092612C2semidirect
11. #13092611C2semidirect
12. #13092545C2semidirect
13. #13092516C2semidirect
14. #13092499C2semidirect
15. C23×#440C2semidirect
190. #440D23semidirect
242. C23#3403semidirect

Maximal subgroups

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

subgroupindex
#130931522
#130931502
#130928062
#130928032
#130927982
#130926422
#130926392
#130926352
#130926312
#130926122
#130926112
#130925452
#130925162
#130924992
C23×#4402
#340323