Finite Group Databasebeta

← #15685226

Subgroups — #15685226

Order 2944.

408 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13093063C211yesmaximal, characteristic
2#13092774C211yesmaximal, characteristic, complemented
3#13092747C211yesmaximal, characteristic, complemented
4#13092741C211yesmaximal, characteristic, complemented
5#13092714C211yesmaximal, characteristic, complemented
6#13092656C211yesmaximal, characteristic, complemented
7#13092648C211yesmaximal, characteristic, complemented
8#13092639C211yesmaximal, characteristic, complemented
9#13092577C211yesmaximal, characteristic, complemented
10#13092567C211yesmaximal, characteristic, complemented
11C4×#67274C211yesmaximal, characteristic, complemented
12D4×C23⋊C8C211yesmaximal, characteristic, complemented
13#13092411C211yesmaximal, characteristic, complemented
14C2×#10624991C211yesmaximal, characteristic, complemented
15C23×#552C211yesmaximal, characteristic, complemented
16C2×#67288C2211yescharacteristic
17C22×D92C2211yescharacteristic
18C23×#126—21no—
19C23×#125—21no—
20C23×#125C2211yescharacteristic, complemented
21C23×#123—21no—
22C23×C22⋊Q8C2211yescharacteristic
23C23×C22⋊Q8C2211yescharacteristic, complemented
24C4×Q8×C23C2211yescharacteristic, complemented
25C4×D4×C23C2211yescharacteristic
26C23×#117—21no—
27C23×#117C2211yescharacteristic, complemented
28C2×C4⋊C4×C23C2211yescharacteristic
29C2×#67275C2211yescharacteristic, complemented
30C2×#67274C2211yescharacteristic
31C2×#67274C2211yescharacteristic
32#10625108—21no—
33#10625101C2211yescharacteristic
34#10625095C2211yescharacteristic
35C22×C23⋊C8C2211yescharacteristic
36C22×C23⋊C8C2211yescharacteristic, complemented
37#10625065—21no—
38#10625055—21no—
39C22⋊C4×D23—21no—
40#10625046C2211yescharacteristic
41C4×D92C2211yescharacteristic
42#10625017C2211yescharacteristic, complemented
43C22⋊(C23⋊C8)C2211yescharacteristic
44C22⋊(C23⋊C8)C2211yescharacteristic, complemented
45#10624992C2211yescharacteristic, complemented
46#10624992C2211yescharacteristic, complemented
47#10624992C2211yescharacteristic, complemented
48#10624991C2211yescharacteristic
49#10624991C2211yescharacteristic
50#10624991C2211yescharacteristic
51#10624991C2211yescharacteristic
52#10624991C2211yescharacteristic
53#10624991C2211yescharacteristic
54#10624990C2211yescharacteristic, complemented
55#10624990C2211yescharacteristic, complemented
56#10624989C2211yescharacteristic, complemented
57C4⋊(C23⋊C8)C2211yescharacteristic, complemented
58C4×C23⋊C8C2211yescharacteristic, complemented
59C23×D23—21no—
60C2×Q8×C23C2311yescharacteristic
61C2×D4×C23D411yescharacteristic
62C22×C4×C23—21no—
63C22×C4×C23C2311yescharacteristic
64C22×C4×C23C2311yescharacteristic
65C2×C22⋊D23—21no—
66C2×C22⋊D23—21no—
67#67288—22no—
68#67288—41no—
69C2×D92—22no—
70C2×D92—21no—
71C2×D92—41no—
72C2×D92C2311yescharacteristic
73C2×D92C2311yescharacteristic
74C2×C4×D23—21no—
75C2×C4×D23—21no—
76C2×Dic46C2311yescharacteristic
77C4⋊C4×C23—21no—
78C4⋊C4×C23—21no—
79C4⋊C4×C23—21no—
80C4⋊C4×C23—21no—
81C4⋊C4×C23—21no—
82C4⋊C4×C23—21no—
83C4⋊C4×C23D411yescharacteristic
84C4⋊C4×C23C2311yescharacteristic
85C4⋊C4×C23C2311yescharacteristic
86C4⋊C4×C23C2311yescharacteristic
87C22⋊C4×C23—21no—
88C22⋊C4×C23—21no—
89C22⋊C4×C23—21no—
90C22⋊C4×C23D411yescharacteristic
91C22⋊C4×C23D411yescharacteristic
92C42×C23—21no—
93C42×C23—21no—
94C42×C23C2311yescharacteristic
95C22⋊Dic23—21no—
96#67275—41no—
97#67274—22no—
98#67274—41no—
99(C2×D23)⋊C4—21no—
100(C2×D23)⋊C4—21no—
101(C2×D23)⋊C4—21no—
102(C2×D23)⋊C4—21no—
103C4⋊Dic23C2311yescharacteristic
104Dic23⋊C4—21no—
105C2×C23⋊C8—41no—
106C2×C23⋊C8—41no—
107C2×C23⋊C8C2311yescharacteristic
108C2×C23⋊C8C2311yescharacteristic
109C2×C23⋊C8C2311yescharacteristic
110C2×C23⋊C8C2311yescharacteristic
111C23×C23C2×D411yescharacteristic
112C23×C23C2×D411yescharacteristic
113C22×D23—21no—
114C22×D23—21no—
115C22×D23—42no—
116C22×D23—42no—
117C22×D23—81no—
118Q8×C23—21no—
119Q8×C23—21no—
120D4×C23—22no—
121C2×C4×C23—21no—
122C2×C4×C23—21no—
123C2×C4×C23—21no—
124C2×C4×C23—21no—
125C2×C4×C23—21no—
126C2×C4×C23—21no—
127C2×C4×C23—21no—
128C2×C4×C23—21no—
129C2×C4×C23—42no—
130C2×C4×C23C2×D411yescharacteristic
131C2×C4×C23C2×D411yescharacteristic
132C2×C4×C23C2×D411yescharacteristic
133C2×C4×C23C2×D411yescharacteristic
134C2×C4×C23C2411yescharacteristic
135C22⋊D23—42no—
136C22⋊D23—81no—
137C2×Dic23—21no—
138C2×Dic23—21no—
139D92—21no—
140D92—21no—
141D92—21no—
142D92—42no—
143D92#4112yes—
144C4×D23—42no—
145C4×D23—81no—
146Dic46—21no—
147Dic46—21no—
148C23⋊C8—21no—
149C23⋊C8—21no—
150C23⋊C8—21no—
151C23⋊C8—21no—
152#3296—231nomaximal, Sylow
153C22×C23—21no—
154C22×C23—21no—
155C22×C23—21no—
156C22×C23—21no—
157C22×C23—21no—
158C22×C23#13512yes—
159C22×C23C22×D411yescharacteristic
160C2×D23—22no—
161C2×D23—41no—
162C2×D23—41no—
163C2×D23—41no—
164C2×D23—41no—
165C2×D23—41no—
166C2×D23—84no—
167C4×C23—21no—
168C4×C23—21no—
169C4×C23—21no—
170C4×C23—21no—
171C4×C23—41no—
172C4×C23—41no—
173C4×C23—41no—
174C4×C23—41no—
175C4×C23C2×#4111yescharacteristic
176C4×C23H(5,𝔽2)11yescharacteristic
177Dic23—41no—
178Dic23—41no—
179#552D2311yescharacteristic, complemented
180#546—231no—
181#488—231no—
182#483—231no—
183#482—231no—
184#478—231no—
185#467—231no—
186#465—231no—
187#464—231no—
188#452—231no—
189#450—231no—
190C4×SD16—231no—
191C8×D4—231no—
192#416—231no—
193C2×#102—231no—
194C2×C23—22no—
195C2×C23—41no—
196C2×C23#54611yescharacteristic
197C2×C23C2×#13511yescharacteristic
198C2×C23#57711yescharacteristic
199D23—42no—
200D23—81no—
201C2×#41—231no—
202C22×D4—231no—
203C2×Q16—231no—
204C2×SD16—231no—
205C2×SD16—231no—
206C22×C8—231no—
207C22×C8—231no—
208#126—21no—
209#125—21no—
210#125C2×D2311yescharacteristic, complemented
211#124—231no—
212#123—21no—
213#123—461no—
214C22⋊Q8—231no—
215C22⋊Q8C2×D2311yescharacteristic
216C22⋊Q8C2×D2311yescharacteristic, complemented
217#121—231no—
218#121—461no—
219#120—461no—
220C4×Q8C2×D2311yescharacteristic, complemented
221C4×D4—231no—
222C4×D4C2×D2311yescharacteristic
223#117—21no—
224#117C2×D2311yescharacteristic, complemented
225C2×C4⋊C4C2×D2311yescharacteristic
226C2×C22⋊C4—461no—
227#107—231no—
228#106—231no—
229#106—231no—
230C4⋊C8—231no—
231#103—231no—
232#103—231no—
233#103—231no—
234#103—231no—
235#102—231no—
236#102—231no—
237#102—231no—
238#102—231no—
239#102—231no—
240#102—231no—
241C22⋊C8—231no—
242C22⋊C8—231no—
243C4×C8—231no—
244C23#329611yescharacteristic, complemented, Sylow
245C24—461no—
246#41—462no—
247#41—921no—
248C2×Q8—231no—
249C2×Q8C22×D2311yescharacteristic
250C2×D4—231no—
251C2×D4—231no—
252C2×D4—462no—
253C2×D4—461no—
254C2×D4—461no—
255C2×D4—461no—
256C2×D4—921no—
257C2×D4C22⋊D2311yescharacteristic
258C22×C4—21no—
259C22×C4—461no—
260C22×C4—461no—
261C22×C4C22×D2311yescharacteristic
262C22×C4C22×D2311yescharacteristic
263Q16—921no—
264SD16—462no—
265SD16—921no—
266C2×C8—231no—
267C2×C8—231no—
268C2×C8—231no—
269C2×C8—231no—
270C2×C8—921no—
271C2×C8—921no—
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—21no—
277C4⋊C4—21no—
278C4⋊C4—231no—
279C4⋊C4—461no—
280C4⋊C4C22⋊D2311yescharacteristic
281C4⋊C4C22×D2311yescharacteristic
282C4⋊C4C22×D2311yescharacteristic
283C4⋊C4C22×D2311yescharacteristic
284C22⋊C4—21no—
285C22⋊C4—21no—
286C22⋊C4—21no—
287C22⋊C4—461no—
288C22⋊C4—461no—
289C22⋊C4—461no—
290C22⋊C4—461no—
291C22⋊C4—461no—
292C22⋊C4C22⋊D2311yescharacteristic
293C22⋊C4C22⋊D2311yescharacteristic
294C42—21no—
295C42—21no—
296C42C22×D2311yescharacteristic
297C23—461no—
298C23—461no—
299C23—922no—
300C23—922no—
301C23—1841no—
302C23C2×C22⋊D2311yescharacteristic
303C23C2×C22⋊D2311yescharacteristic
304Q8—21no—
305Q8—21no—
306Q8—461no—
307Q8—461no—
308D4—22no—
309D4—232no—
310D4—461no—
311D4—461no—
312D4—461no—
313D4—922no—
314D4—922no—
315D4—1841no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—42no—
325C2×C4—461no—
326C2×C4—461no—
327C2×C4—922no—
328C2×C4—1841no—
329C2×C4C2×C22⋊D2311yescharacteristic
330C2×C4C2×C22⋊D2311yescharacteristic
331C2×C4C2×C22⋊D2311yescharacteristic
332C2×C4C2×C22⋊D2311yescharacteristic
333C2×C4C23×D2311yescharacteristic
334C8—461no—
335C8—461no—
336C8—461no—
337C8—461no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—462no—
344C22—921no—
345C22—921no—
346C22—921no—
347C22—921no—
348C22—921no—
349C22—1844no—
350C22#1062512112yes—
351C22C22×C22⋊D2311yescharacteristic
352C4—21no—
353C4—21no—
354C4—21no—
355C4—21no—
356C4—41no—
357C4—41no—
358C4—41no—
359C4—41no—
360C4—921no—
361C4—921no—
362C4#41×D2311yescharacteristic
363C4#1062516011yescharacteristic
364C2—22no—
365C2—41no—
366C2—922no—
367C2—1841no—
368C2#1309305511yescharacteristic
369C2C2×#1062512111yescharacteristic
370C2#1309322511yescharacteristic
subgroupG/H
centerC22C22×C22⋊D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#552C2
socleC22×C23C22×D4
prime radical#13093063C2
hypercenter#552D23
hypocenterC23#3296
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C4×D4 ◁ #552

Complements

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

NH ≅ G/Ntype
2. #13092774C2semidirect
3. #13092747C2semidirect
4. #13092741C2semidirect
5. #13092714C2semidirect
6. #13092656C2semidirect
7. #13092648C2semidirect
8. #13092639C2semidirect
9. #13092577C2semidirect
10. #13092567C2semidirect
11. C4×#67274C2semidirect
12. D4×C23⋊C8C2semidirect
13. #13092411C2semidirect
14. C2×#10624991C2semidirect
15. C23×#552C2semidirect
20. C23×#125C22semidirect
23. C23×C22⋊Q8C22semidirect
24. C4×Q8×C23C22semidirect
27. C23×#117C22semidirect
29. C2×#67275C22semidirect
36. C22×C23⋊C8C22semidirect
42. #10625017C22semidirect
44. C22⋊(C23⋊C8)C22semidirect
45. #10624992C22semidirect
46. #10624992C22semidirect
47. #10624992C22semidirect
54. #10624990C22semidirect
55. #10624990C22semidirect
56. #10624989C22semidirect
57. C4⋊(C23⋊C8)C22semidirect
58. C4×C23⋊C8C22semidirect
179. #552D23semidirect
210. #125C2×D23semidirect
216. C22⋊Q8C2×D23semidirect
220. C4×Q8C2×D23semidirect
224. #117C2×D23semidirect
244. C23#3296semidirect

Maximal subgroups

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

subgroupindex
#130930632
#130927742
#130927472
#130927412
#130927142
#130926562
#130926482
#130926392
#130925772
#130925672
C4×#672742
D4×C23⋊C82
#130924112
C2×#106249912
C23×#5522
#329623