Finite Group Databasebeta

← #15683645

Subgroups — #15683645

Order 2944.

394 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13093027C211yesmaximal, characteristic, complemented
2#13092891C211yesmaximal, characteristic
3#13092758C211yesmaximal, characteristic, complemented
4#13092720C211yesmaximal, characteristic, complemented
5#13092716C211yesmaximal, characteristic, complemented
6#13092621C211yesmaximal, characteristic, complemented
7#13092621C211yesmaximal, characteristic, complemented
8#13092570C211yesmaximal, characteristic
9#13092567C211yesmaximal, characteristic
10#13092520C211yesmaximal, characteristic, complemented
11#13092516C211yesmaximal, characteristic, complemented
12#13092504C211yesmaximal, characteristic, complemented
13#13092502C211yesmaximal, characteristic, complemented
14#13092475C211yesmaximal, characteristic, complemented
15C23×#485C211yesmaximal, characteristic, complemented
16C22×D92C2211yescharacteristic
17C23×C22⋊Q8C2211yescharacteristic
18C23×#117C2211yescharacteristic
19Q8×Dic23C2211yescharacteristic, complemented
20#10625115C2211yescharacteristic, complemented
21C2×#67274C2211yescharacteristic
22C2×#67274C2211yescharacteristic
23#10625097C2211yescharacteristic
24#10625095C2211yescharacteristic
25C2×#67263C2211yescharacteristic
26C2×#67263C2211yescharacteristic
27#10625064C2211yescharacteristic
28#10625064C2211yescharacteristic
29#10625064C2211yescharacteristic
30#10625064C2211yescharacteristic
31#10625061—21no—
32#10625061C2211yescharacteristic, complemented
33#10625060—21no—
34#10625058C2211yescharacteristic, complemented
35C22⋊C4×D23—21no—
36C22⋊C4×D23—21no—
37#10625050—21no—
38#10625050—21no—
39C4×D92—21no—
40C4×D92—21no—
41C23×#107C2211yescharacteristic, complemented
42C23×#106C2211yescharacteristic, complemented
43C23×#103C2211yescharacteristic, complemented
44C23×#103C2211yescharacteristic, complemented
45C23×C22⋊C8C2211yescharacteristic
46C22⋊(C23⋊C8)C2211yescharacteristic
47#10625003C2211yescharacteristic
48#10625003C2211yescharacteristic
49#10624997C2211yescharacteristic, complemented
50Dic23⋊C8C2211yescharacteristic, complemented
51Dic23⋊C8C2211yescharacteristic, complemented
52C8×Dic23C2211yescharacteristic, complemented
53#10624992C2211yescharacteristic, complemented
54#10624992C2211yescharacteristic, complemented
55#10624991C2211yescharacteristic
56#10624991C2211yescharacteristic
57#10624990C2211yescharacteristic, complemented
58#10624989C2211yescharacteristic, complemented
59C23×D23—21no—
60C2×Q8×C23C2311yescharacteristic
61C22×C4×C23C2311yescharacteristic
62C2×D92—21no—
63C2×D92—22no—
64C2×D92—22no—
65C2×D92C2311yescharacteristic
66C2×D92C2311yescharacteristic
67C2×C4×D23—21no—
68C2×C4×D23—21no—
69C2×C4×D23—21no—
70C2×C4×D23—21no—
71C2×Dic46C2311yescharacteristic
72C2×C8×C23C2311yescharacteristic
73C2×C8×C23C2311yescharacteristic
74C4⋊C4×C23—21no—
75C4⋊C4×C23C2311yescharacteristic
76C4⋊C4×C23C2311yescharacteristic
77C4⋊C4×C23C2311yescharacteristic
78C22⋊C4×C23—21no—
79C22⋊C4×C23—21no—
80C42×C23—21no—
81C22⋊Dic23—21no—
82C22⋊Dic23D411yescharacteristic
83C22⋊Dic23D411yescharacteristic
84#67274—22no—
85#67274—22no—
86(C2×D23)⋊C4—21no—
87(C2×D23)⋊C4—21no—
88(C2×D23)⋊C4—21no—
89(C2×D23)⋊C4—21no—
90C4⋊Dic23—21no—
91C4⋊Dic23—21no—
92C4⋊Dic23D411yescharacteristic
93C4⋊Dic23D411yescharacteristic
94C4⋊Dic23C2311yescharacteristic
95Dic23⋊C4—21no—
96Dic23⋊C4—21no—
97Dic23⋊C4—21no—
98Dic23⋊C4—21no—
99Dic23⋊C4—21no—
100C4×Dic23—21no—
101C4×Dic23—21no—
102C4×Dic23C2311yescharacteristic
103C4×Dic23C2311yescharacteristic
104C2×C23⋊C8C2311yescharacteristic
105C2×C23⋊C8C2311yescharacteristic
106#67263—22no—
107#67263—22no—
108C23×C23C2×D411yescharacteristic
109C22×D23—21no—
110C22×D23—21no—
111C22×D23—24no—
112C22×D23—81no—
113C22×D23—81no—
114Q8×C23—21no—
115Q8×C23—21no—
116C2×C4×C23—21no—
117C2×C4×C23—21no—
118C2×C4×C23—21no—
119C2×C4×C23—21no—
120C2×C4×C23—21no—
121C2×C4×C23—21no—
122C2×C4×C23C2×D411yescharacteristic
123C2×C4×C23C2411yescharacteristic
124C2×Dic23—21no—
125C2×Dic23—21no—
126C2×Dic23C2×D411yescharacteristic
127C2×Dic23C2×D411yescharacteristic
128C2×Dic23C2×D411yescharacteristic
129C2×Dic23C2×D411yescharacteristic
130D92—24no—
131D92—21no—
132D92—21no—
133D92#4112yes—
134D92#4112yes—
135C4×D23—81no—
136C4×D23—81no—
137C4×D23—81no—
138C4×D23—81no—
139Dic46—21no—
140Dic46—21no—
141C8×C23—21no—
142C8×C23—21no—
143C23⋊C8—21no—
144C23⋊C8—21no—
145#3123—231nomaximal, Sylow
146C22×C23—21no—
147C22×C23—21no—
148C22×C23—21no—
149C22×C23C22×D411yescharacteristic
150C2×D23—22no—
151C2×D23—22no—
152C2×D23—41no—
153C2×D23—41no—
154C2×D23—41no—
155C2×D23—41no—
156C2×D23—84no—
157C4×C23—21no—
158C4×C23—41no—
159C4×C23—41no—
160C4×C23—41no—
161C4×C23—41no—
162C4×C23C2×#4111yescharacteristic
163C4×C23C2×#4111yescharacteristic
164Dic23—21no—
165Dic23—21no—
166Dic23—21no—
167Dic23—21no—
168Dic23—41no—
169Dic23—41no—
170#541—231no—
171#518—231no—
172#485—231no—
173#485D2311yescharacteristic, complemented
174#478—231no—
175#478—231no—
176#461—231no—
177#461—231no—
178#450—231no—
179#450—231no—
180#440—231no—
181#440—231no—
182C4×SD16—231no—
183C4×SD16—231no—
184#433—231no—
185C2×C23—41no—
186C2×C23#52511yescharacteristic
187C2×C23#57711yescharacteristic
188C2×C23#57711yescharacteristic
189D23—42no—
190D23—42no—
191C22×D4—231no—
192C2×SD16—231no—
193C2×SD16—231no—
194C2×SD16—231no—
195C2×SD16—231no—
196C4⋊Q8—231no—
197#126—461no—
198#126—461no—
199#125—231no—
200#125—461no—
201#125—461no—
202C22⋊Q8—231no—
203C22⋊Q8C2×D2311yescharacteristic
204C4×Q8—231no—
205C4×Q8—231no—
206C4×D4—231no—
207C4×D4—231no—
208C4×D4—231no—
209C4×D4—231no—
210C4×D4—461no—
211C4×D4—461no—
212#117—231no—
213#117C2×D2311yescharacteristic
214C2×C22⋊C4—461no—
215C2×C22⋊C4—461no—
216#107—231no—
217#107C2×D2311yescharacteristic, complemented
218#106—231no—
219#106C2×D2311yescharacteristic, complemented
220C4⋊C8—231no—
221C4⋊C8—231no—
222#103—231no—
223#103—231no—
224#103C2×D2311yescharacteristic, complemented
225#103C2×D2311yescharacteristic, complemented
226#102—231no—
227#102—231no—
228#102—231no—
229#102—231no—
230C22⋊C8—231no—
231C22⋊C8C2×D2311yescharacteristic
232#97—231no—
233C4×C8—231no—
234C23#312311yescharacteristic, complemented, Sylow
235C24—461no—
236C2×Q8—231no—
237C2×Q8C22×D2311yescharacteristic
238C2×D4—231no—
239C2×D4—231no—
240C2×D4—462no—
241C2×D4—462no—
242C2×D4—461no—
243C22×C4—461no—
244C22×C4—461no—
245C22×C4—461no—
246C22×C4—461no—
247C22×C4C22×D2311yescharacteristic
248SD16—462no—
249SD16—462no—
250SD16—462no—
251SD16—462no—
252C2×C8—231no—
253C2×C8—231no—
254C2×C8C22×D2311yescharacteristic
255C2×C8C22×D2311yescharacteristic
256C4⋊C4—21no—
257C4⋊C4—231no—
258C4⋊C4—231no—
259C4⋊C4—231no—
260C4⋊C4—461no—
261C4⋊C4—461no—
262C4⋊C4—461no—
263C4⋊C4—461no—
264C4⋊C4—461no—
265C4⋊C4—461no—
266C4⋊C4—461no—
267C4⋊C4C22×D2311yescharacteristic
268C4⋊C4C22×D2311yescharacteristic
269C4⋊C4C22×D2311yescharacteristic
270C22⋊C4—21no—
271C22⋊C4—21no—
272C22⋊C4—231no—
273C22⋊C4—231no—
274C22⋊C4—461no—
275C22⋊C4—461no—
276C22⋊C4—461no—
277C22⋊C4—461no—
278C22⋊C4—461no—
279C42—21no—
280C42—231no—
281C42—231no—
282C42—461no—
283C42—461no—
284C23—464no—
285C23—461no—
286C23—461no—
287C23—1841no—
288C23—1841no—
289C23D4×D2311yescharacteristic
290Q8—21no—
291Q8—21no—
292Q8—461no—
293Q8—461no—
294D4—232no—
295D4—232no—
296D4—464no—
297D4—461no—
298D4—461no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—231no—
306C2×C4—231no—
307C2×C4—231no—
308C2×C4—231no—
309C2×C4—461no—
310C2×C4—461no—
311C2×C4—1841no—
312C2×C4—1841no—
313C2×C4—1841no—
314C2×C4—1841no—
315C2×C4D4×D2311yescharacteristic
316C2×C4C23×D2311yescharacteristic
317C8—21no—
318C8—21no—
319C8—461no—
320C8—461no—
321C22—21no—
322C22—21no—
323C22—21no—
324C22—462no—
325C22—462no—
326C22—921no—
327C22—921no—
328C22—921no—
329C22—921no—
330C22—1844no—
331C22C2×D4×D2311yescharacteristic
332C4—21no—
333C4—41no—
334C4—41no—
335C4—41no—
336C4—41no—
337C4—461no—
338C4—461no—
339C4—461no—
340C4—461no—
341C4—921no—
342C4—921no—
343C4#41×D2311yescharacteristic
344C4#41×D2311yescharacteristic
345C2—41no—
346C2—922no—
347C2—922no—
348C2#1309292511yescharacteristic
349C2#1309322411yescharacteristic
350C2#1309322611yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#485C2
socleC22×C23C22×D4
prime radicalC22×D92C22
hypercenter#485D23
hypocenterC23#3123
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
1. #13093027C2semidirect
3. #13092758C2semidirect
4. #13092720C2semidirect
5. #13092716C2semidirect
6. #13092621C2semidirect
7. #13092621C2semidirect
10. #13092520C2semidirect
11. #13092516C2semidirect
12. #13092504C2semidirect
13. #13092502C2semidirect
14. #13092475C2semidirect
15. C23×#485C2semidirect
19. Q8×Dic23C22semidirect
20. #10625115C22semidirect
32. #10625061C22semidirect
34. #10625058C22semidirect
41. C23×#107C22semidirect
42. C23×#106C22semidirect
43. C23×#103C22semidirect
44. C23×#103C22semidirect
49. #10624997C22semidirect
50. Dic23⋊C8C22semidirect
51. Dic23⋊C8C22semidirect
52. C8×Dic23C22semidirect
53. #10624992C22semidirect
54. #10624992C22semidirect
57. #10624990C22semidirect
58. #10624989C22semidirect
173. #485D23semidirect
217. #107C2×D23semidirect
219. #106C2×D23semidirect
224. #103C2×D23semidirect
225. #103C2×D23semidirect
234. C23#3123semidirect

Maximal subgroups

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

subgroupindex
#130930272
#130928912
#130927582
#130927202
#130927162
#130926212
#130925702
#130925672
#130925202
#130925162
#130925042
#130925022
#130924752
C23×#4852
#312323