Finite Group Databasebeta

← #15683961

Subgroups — #15683961

Order 2944.

380 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13092951C211yesmaximal, characteristic, complemented
2#13092816C211yesmaximal, characteristic, complemented
3#13092799C211yesmaximal, characteristic, complemented
4#13092774C211yesmaximal, characteristic, complemented
5#13092771C211yesmaximal, characteristic, complemented
6#13092656C211yesmaximal, characteristic, complemented
7#13092651C211yesmaximal, characteristic
8#13092648C211yesmaximal, characteristic, complemented
9#13092644C211yesmaximal, characteristic, complemented
10C4×#67275C211yesmaximal, characteristic, complemented
11C4×#67274C211yesmaximal, characteristic, complemented
12C4×#67273C211yesmaximal, characteristic, complemented
13C4×#67272C211yesmaximal, characteristic, complemented
14C2×C4×C23⋊C8C211yesmaximal, characteristic, complemented
15C23×#529C211yesmaximal, characteristic, complemented
16C23×#126—21no—
17C23×#125C2211yescharacteristic
18C23×#124C2211yescharacteristic
19C23×#123—21no—
20C23×C22⋊Q8C2211yescharacteristic
21C23×#121C2211yescharacteristic
22C4×Q8×C23C2211yescharacteristic
23C4×D4×C23—21no—
24C4×D4×C23C2211yescharacteristic
25C23×#117—21no—
26C2×C42×C23C2211yescharacteristic
27C2×#67275C2211yescharacteristic
28C2×#67274C2211yescharacteristic
29C2×#67273C2211yescharacteristic
30C2×#67272C2211yescharacteristic
31#10625101C2211yescharacteristic
32#10625100—21no—
33C4×C22⋊D23—21no—
34#10625095C2211yescharacteristic
35C22×C23⋊C8C2211yescharacteristic
36C22×C23⋊C8C2211yescharacteristic
37#10625047—21no—
38#10625046C2211yescharacteristic
39C4×D92C2211yescharacteristic
40#10625043—21no—
41#10625041C2211yescharacteristic
42C4×Dic46C2211yescharacteristic
43#10625017C2211yescharacteristic
44#10625017C2211yescharacteristic
45#10625014C2211yescharacteristic
46#10625014C2211yescharacteristic
47#10624992C2211yescharacteristic
48#10624992C2211yescharacteristic
49#10624991C2211yescharacteristic
50#10624991C2211yescharacteristic
51#10624990C2211yescharacteristic
52#10624990C2211yescharacteristic
53#10624989C2211yescharacteristic
54#10624989C2211yescharacteristic
55C4×C23⋊C8C2211yescharacteristic
56C4×C23⋊C8C2211yescharacteristic
57C4×C23⋊C8C2211yescharacteristic
58C4×C23⋊C8C2211yescharacteristic
59C2×Q8×C23C2311yescharacteristic
60C2×D4×C23—21no—
61C2×D4×C23C2311yescharacteristic
62C22×C4×C23—21no—
63C22×C4×C23D411yescharacteristic
64C22×C4×C23D411yescharacteristic
65C22×C4×C23C2311yescharacteristic
66C2×C22⋊D23—21no—
67C2×D92C2311yescharacteristic
68C2×C4×D23—21no—
69C2×Dic46C2311yescharacteristic
70C4⋊C4×C23—21no—
71C4⋊C4×C23—21no—
72C4⋊C4×C23—21no—
73C4⋊C4×C23—21no—
74C4⋊C4×C23C2311yescharacteristic
75C4⋊C4×C23C2311yescharacteristic
76C22⋊C4×C23—21no—
77C22⋊C4×C23—21no—
78C22⋊C4×C23—21no—
79C22⋊C4×C23—21no—
80C22⋊C4×C23—21no—
81C42×C23—21no—
82C42×C23D411yescharacteristic
83C42×C23D411yescharacteristic
84C42×C23C2311yescharacteristic
85C42×C23C2311yescharacteristic
86C22⋊Dic23—21no—
87#67275—22no—
88#67274—22no—
89#67273—22no—
90#67272—22no—
91(C2×D23)⋊C4—21no—
92(C2×D23)⋊C4—21no—
93(C2×D23)⋊C4—21no—
94(C2×D23)⋊C4—21no—
95C4⋊Dic23C2311yescharacteristic
96C4⋊Dic23C2311yescharacteristic
97Dic23⋊C4—21no—
98Dic23⋊C4—21no—
99Dic23⋊C4—21no—
100Dic23⋊C4—21no—
101C4×Dic23—21no—
102C2×C23⋊C8—22no—
103C2×C23⋊C8—22no—
104C2×C23⋊C8C2311yescharacteristic
105C2×C23⋊C8C2311yescharacteristic
106C2×C23⋊C8C2311yescharacteristic
107C2×C23⋊C8C2311yescharacteristic
108C23×C23—21no—
109C23×C23C2×D411yescharacteristic
110C22×D23—21no—
111Q8×C23—21no—
112Q8×C23—21no—
113D4×C23—21no—
114D4×C23—21no—
115D4×C23—42no—
116C2×C4×C23—22no—
117C2×C4×C23—22no—
118C2×C4×C23—21no—
119C2×C4×C23—21no—
120C2×C4×C23—21no—
121C2×C4×C23—21no—
122C2×C4×C23—21no—
123C2×C4×C23—42no—
124C2×C4×C23C2×D411yescharacteristic
125C2×C4×C23C2×D411yescharacteristic
126C2×C4×C23C2×D411yescharacteristic
127C2×C4×C23C2×D411yescharacteristic
128C2×C4×C23C2×D411yescharacteristic
129C2×C4×C23C2411yescharacteristic
130C22⋊D23—42no—
131C2×Dic23—21no—
132C2×Dic23—21no—
133C2×Dic23—21no—
134D92—21no—
135D92—21no—
136C4×D23—42no—
137Dic46—21no—
138Dic46—21no—
139C23⋊C8—21no—
140C23⋊C8—21no—
141C23⋊C8#4112yes—
142C23⋊C8#4112yes—
143#3168—231nomaximal, Sylow
144C22×C23—21no—
145C22×C23—21no—
146C22×C23—41no—
147C22×C23—41no—
148C22×C23—41no—
149C22×C23#13512yes—
150C22×C23C22×D411yescharacteristic
151C2×D23—41no—
152C2×D23—41no—
153C2×D23—41no—
154C4×C23—21no—
155C4×C23—21no—
156C4×C23—21no—
157C4×C23—21no—
158C4×C23—41no—
159C4×C23—41no—
160C4×C23—41no—
161C4×C23#13512yes—
162C4×C23C2×#4111yescharacteristic
163C4×C23C2×#4111yescharacteristic
164Dic23—41no—
165Dic23—41no—
166Dic23—41no—
167#529—231no—
168#529D2311yescharacteristic, complemented
169#499—231no—
170#495—231no—
171#488—231no—
172#488—231no—
173#467—231no—
174#466—231no—
175#465—231no—
176#465—231no—
177C4×Q16—231no—
178C4×SD16—231no—
179C4×SD16—231no—
180C4×D8—231no—
181C2×C4×C8—231no—
182C2×C23—22no—
183C2×C23—81no—
184C2×C23#53211yescharacteristic
185C2×C23C2×#13511yescharacteristic
186C2×C23C2×#13511yescharacteristic
187D23—81no—
188C2×Q16—231no—
189C2×SD16—231no—
190C2×SD16—231no—
191C2×D8—231no—
192C22×C8—231no—
193C22×C8—231no—
194#126—21no—
195#126—461no—
196#125—231no—
197#125C2×D2311yescharacteristic
198#124—231no—
199#124C2×D2311yescharacteristic
200#123—21no—
201#123—461no—
202C22⋊Q8—231no—
203C22⋊Q8C2×D2311yescharacteristic
204#121—231no—
205#121C2×D2311yescharacteristic
206C4×Q8—231no—
207C4×Q8C2×D2311yescharacteristic
208C4×D4—21no—
209C4×D4—231no—
210C4×D4—461no—
211C4×D4C2×D2311yescharacteristic
212#117—21no—
213#117—461no—
214C2×C42C2×D2311yescharacteristic
215#107—231no—
216#107—231no—
217#106—231no—
218#106—231no—
219#103—231no—
220#103—231no—
221#103—231no—
222#103—231no—
223#102—231no—
224#102—231no—
225#102—231no—
226#102—231no—
227C4×C8—231no—
228C4×C8—231no—
229C4×C8—231no—
230C4×C8—231no—
231C23#316811yescharacteristic, complemented, Sylow
232C2×Q8—231no—
233C2×Q8C22×D2311yescharacteristic
234C2×D4—21no—
235C2×D4—231no—
236C2×D4—461no—
237C2×D4C22×D2311yescharacteristic
238C22×C4—21no—
239C22×C4—461no—
240C22×C4C22⋊D2311yescharacteristic
241C22×C4C22⋊D2311yescharacteristic
242C22×C4C22×D2311yescharacteristic
243Q16—462no—
244SD16—462no—
245SD16—462no—
246D8—462no—
247C2×C8—231no—
248C2×C8—231no—
249C2×C8—231no—
250C2×C8—231no—
251C2×C8—462no—
252C2×C8—462no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—21no—
257C4⋊C4—231no—
258C4⋊C4—231no—
259C4⋊C4—461no—
260C4⋊C4—461no—
261C4⋊C4—461no—
262C4⋊C4—461no—
263C4⋊C4C22×D2311yescharacteristic
264C4⋊C4C22×D2311yescharacteristic
265C22⋊C4—21no—
266C22⋊C4—21no—
267C22⋊C4—21no—
268C22⋊C4—21no—
269C22⋊C4—21no—
270C22⋊C4—461no—
271C22⋊C4—461no—
272C22⋊C4—461no—
273C22⋊C4—461no—
274C22⋊C4—461no—
275C42—21no—
276C42—461no—
277C42C22⋊D2311yescharacteristic
278C42C22⋊D2311yescharacteristic
279C42C22×D2311yescharacteristic
280C42C22×D2311yescharacteristic
281C23—21no—
282C23—461no—
283C23C2×C22⋊D2311yescharacteristic
284Q8—21no—
285Q8—21no—
286Q8—461no—
287Q8—461no—
288D4—21no—
289D4—21no—
290D4—42no—
291D4—461no—
292D4—461no—
293D4—922no—
294C2×C4—22no—
295C2×C4—22no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—42no—
302C2×C4—461no—
303C2×C4—461no—
304C2×C4—461no—
305C2×C4—922no—
306C2×C4C2×C22⋊D2311yescharacteristic
307C2×C4C2×C22⋊D2311yescharacteristic
308C2×C4C2×C22⋊D2311yescharacteristic
309C2×C4C2×C22⋊D2311yescharacteristic
310C2×C4C2×C22⋊D2311yescharacteristic
311C2×C4C23×D2311yescharacteristic
312C8—232no—
313C8—232no—
314C8—461no—
315C8—461no—
316C22—21no—
317C22—21no—
318C22—41no—
319C22—41no—
320C22—41no—
321C22—921no—
322C22—921no—
323C22—921no—
324C22#1062512112yes—
325C22C22×C22⋊D2311yescharacteristic
326C4—21no—
327C4—21no—
328C4—21no—
329C4—21no—
330C4—41no—
331C4—41no—
332C4—41no—
333C4—921no—
334C4—921no—
335C4—921no—
336C4#1062512112yes—
337C4#41×D2311yescharacteristic
338C4#41×D2311yescharacteristic
339C2—22no—
340C2—81no—
341C2—1841no—
342C2#1309296311yescharacteristic
343C2C2×#1062512111yescharacteristic
344C2C2×#1062512111yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#529C2
socleC22×C23C22×D4
prime radical#13092651C2
hypercenter#529D23
hypocenterC23#3168
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #529

Complements

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

NH ≅ G/Ntype
1. #13092951C2semidirect
2. #13092816C2semidirect
3. #13092799C2semidirect
4. #13092774C2semidirect
5. #13092771C2semidirect
6. #13092656C2semidirect
8. #13092648C2semidirect
9. #13092644C2semidirect
10. C4×#67275C2semidirect
11. C4×#67274C2semidirect
12. C4×#67273C2semidirect
13. C4×#67272C2semidirect
14. C2×C4×C23⋊C8C2semidirect
15. C23×#529C2semidirect
168. #529D23semidirect
231. C23#3168semidirect

Maximal subgroups

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

subgroupindex
#130929512
#130928162
#130927992
#130927742
#130927712
#130926562
#130926512
#130926482
#130926442
C4×#672752
C4×#672742
C4×#672732
C4×#672722
C2×C4×C23⋊C82
C23×#5292
#316823