Finite Group Databasebeta

← #15685203

Subgroups — #15685203

Order 2944.

494 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13093067C211yesmaximal, characteristic, complemented
2D4×C22⋊D23C211yesmaximal, characteristic, complemented
3#13092762C211yesmaximal, characteristic, complemented
4#13092731C211yesmaximal, characteristic, complemented
5#13092729C211yesmaximal, characteristic, complemented
6#13092695C211yesmaximal, characteristic, complemented
7#13092651C211yesmaximal, characteristic, complemented
8#13092650C211yesmaximal, characteristic, complemented
9#13092610C211yesmaximal, characteristic, complemented
10#13092549C211yesmaximal, characteristic, complemented
11D8×Dic23C211yesmaximal, characteristic, complemented
12(C22⋊D23)⋊C8C211yesmaximal, characteristic, complemented
13C2×#10625014C211yesmaximal, characteristic, complemented
14#102×D23C211yesmaximal, characteristic, complemented
15C23×#447C211yesmaximal, characteristic, complemented
16C22×D4×C23C2211yescharacteristic
17C22×C22⋊D23—21no—
18C2×#67290—21no—
19C2×D4×D23C2211yescharacteristic
20C2×D8×C23C2211yescharacteristic
21C2×D8×C23C2211yescharacteristic, complemented
22C23×#121C2211yescharacteristic, complemented
23#10625124—21no—
24#10625111C2211yescharacteristic
25#10625110—21no—
26#10625109C2211yescharacteristic
27#10625109C2211yescharacteristic, complemented
28#10625108—21no—
29#10625106—21no—
30D4×Dic23C2211yescharacteristic
31D4×Dic23C2211yescharacteristic, complemented
32C2×#67272C2211yescharacteristic, complemented
33#10625101C2211yescharacteristic
34C4×C22⋊D23C2211yescharacteristic
35C2×C4⋊Dic23C2211yescharacteristic, complemented
36C22×C23⋊C8C2211yescharacteristic, complemented
37C2×C8×D23C2211yescharacteristic, complemented
38C4⋊C4×D23C2211yescharacteristic, complemented
39#10625059C2211yescharacteristic, complemented
40#10625054—21no—
41#10625049—21no—
42C23×#102C2211yescharacteristic
43C23×#102C2211yescharacteristic, complemented
44C23×C22⋊C8C2211yescharacteristic, complemented
45#10625014C2211yescharacteristic
46#10625014C2211yescharacteristic
47#10625014C2211yescharacteristic, complemented
48#10625014C2211yescharacteristic, complemented
49#10625014C2211yescharacteristic, complemented
50#10625003C2211yescharacteristic, complemented
51#10625003C2211yescharacteristic, complemented
52(C2×D23)⋊C8C2211yescharacteristic, complemented
53#10625000C2211yescharacteristic, complemented
54#10625000C2211yescharacteristic, complemented
55Dic23⋊C8C2211yescharacteristic, complemented
56C8×Dic23C2211yescharacteristic, complemented
57#10624991C2211yescharacteristic, complemented
58#10624989C2211yescharacteristic, complemented
59C24×C23—21no—
60C23×D23—21no—
61C2×D4×C23—22no—
62C2×D4×C23—21no—
63C2×D4×C23—21no—
64C2×D4×C23—41no—
65C2×D4×C23C2311yescharacteristic
66C2×D4×C23C2311yescharacteristic
67C2×D4×C23C2311yescharacteristic
68C22×C4×C23C2311yescharacteristic
69C2×C22⋊D23—21no—
70C2×C22⋊D23—21no—
71C2×C22⋊D23—21no—
72C2×C22⋊D23—21no—
73C2×C22⋊D23—21no—
74C2×C22⋊D23—21no—
75C2×C22⋊D23—44no—
76C2×C22⋊D23D411yescharacteristic
77C22×Dic23—21no—
78C22×Dic23—21no—
79C22×Dic23—21no—
80#67290—44no—
81D4×D23—22no—
82D4×D23—41no—
83C2×D92C2311yescharacteristic
84C2×C4×D23—21no—
85C2×C4×D23C2311yescharacteristic
86C2×Dic46—21no—
87D8×C23—22no—
88D8×C23—41no—
89C2×C8×C23C2311yescharacteristic
90C2×C8×C23C2311yescharacteristic
91C4⋊C4×C23C2311yescharacteristic
92C22⋊C4×C23—21no—
93C22⋊Dic23—21no—
94C22⋊Dic23—21no—
95C22⋊Dic23—21no—
96C22⋊Dic23—21no—
97C22⋊Dic23D411yescharacteristic
98#67272—41no—
99(C2×D23)⋊C4—21no—
100(C2×D23)⋊C4D411yescharacteristic
101C4⋊Dic23—21no—
102C4⋊Dic23C2311yescharacteristic
103C4⋊Dic23C2311yescharacteristic
104C4⋊Dic23C2311yescharacteristic
105Dic23⋊C4—21no—
106Dic23⋊C4—21no—
107Dic23⋊C4D411yescharacteristic
108C4×Dic23C2311yescharacteristic
109C2×C23⋊C8—41no—
110C2×C23⋊C8C2311yescharacteristic
111C2×C23⋊C8C2311yescharacteristic
112C8×D23—41no—
113C23×C23—21no—
114C23×C23—21no—
115C23×C23—21no—
116C23×C23—42no—
117C23×C23—42no—
118C23×C23—81no—
119C23×C23C2×D411yescharacteristic
120C22×D23—21no—
121C22×D23—42no—
122C22×D23—42no—
123C22×D23—81no—
124C22×D23C2×D411yescharacteristic
125D4×C23—21no—
126D4×C23—21no—
127D4×C23—21no—
128D4×C23—21no—
129D4×C23—21no—
130D4×C23—42no—
131D4×C23—42no—
132D4×C23#4112yescomplemented
133C2×C4×C23—21no—
134C2×C4×C23—21no—
135C2×C4×C23—21no—
136C2×C4×C23C2×D411yescharacteristic
137C2×C4×C23C2411yescharacteristic
138C22⋊D23—42no—
139C22⋊D23—42no—
140C22⋊D23—42no—
141C22⋊D23—42no—
142C22⋊D23—42no—
143C22⋊D23—81no—
144C22⋊D23D814yescomplemented
145C2×Dic23—21no—
146C2×Dic23—21no—
147C2×Dic23—21no—
148C2×Dic23—42no—
149C2×Dic23—42no—
150C2×Dic23—42no—
151C2×Dic23C2×D411yescharacteristic
152C2×Dic23C2×D411yescharacteristic
153C2×Dic23C2×D411yescharacteristic
154D92—21no—
155D92—21no—
156C4×D23—21no—
157C4×D23—21no—
158C4×D23—42no—
159Dic46—42no—
160C8×C23—21no—
161C8×C23—21no—
162C23⋊C8—21no—
163C23⋊C8—21no—
164#3294—231nomaximal, Sylow
165C22×C23—21no—
166C22×C23—21no—
167C22×C23—22no—
168C22×C23—41no—
169C22×C23—41no—
170C22×C23—41no—
171C22×C23—41no—
172C22×C23—41no—
173C22×C23—41no—
174C22×C23—41no—
175C22×C23—41no—
176C22×C23—84no—
177C22×C23C2×D812yes—
178C22×C23C22×D411yescharacteristic
179C2×D23—21no—
180C2×D23—21no—
181C2×D23—41no—
182C2×D23—41no—
183C2×D23—41no—
184C2×D23—84no—
185C2×D23C2×D812yes—
186C4×C23—21no—
187C4×C23—41no—
188C4×C23C2×#4111yescharacteristic
189C4×C23H(5,𝔽2)11yescharacteristic
190Dic23—21no—
191Dic23—21no—
192Dic23—41no—
193Dic23—41no—
194Dic23—41no—
195Dic23C2×D812yes—
196#547—231no—
197D42—231no—
198#486—231no—
199#480—231no—
200#480—231no—
201#474—231no—
202#466—231no—
203#466—231no—
204#459—231no—
205#447—231no—
206#447D2311yescharacteristic, complemented
207C4×D8—231no—
208C8×D4—231no—
209C2×#102—231no—
210C2×#102—231no—
211C2×C23—22no—
212C2×C23—42no—
213C2×C23—81no—
214C2×C23—81no—
215C2×C23#54611yescharacteristic
216C2×C23C22×D811yescharacteristic
217C2×C23#57711yescharacteristic
218D23—22no—
219D23—81no—
220C2×#41—461no—
221C22×D4—231no—
222C22×D4—461no—
223C22×D4C2×D2311yescharacteristic
224C2×D8—231no—
225C2×D8C2×D2311yescharacteristic
226C2×D8C2×D2311yescharacteristic, complemented
227C22×C8—231no—
228C22×C8—231no—
229C4⋊Q8—231no—
230#127—231no—
231#123—461no—
232#123—461no—
233C22⋊Q8—461no—
234#121—231no—
235#121—231no—
236#121—231no—
237#121—461no—
238#121C2×D2311yescharacteristic, complemented
239#120—461no—
240#120—461no—
241C4×D4—231no—
242C4×D4—231no—
243C4×D4—231no—
244C2×C4⋊C4—231no—
245C2×C4⋊C4—231no—
246#107—231no—
247#107—231no—
248#107—231no—
249C4⋊C8—231no—
250#102—231no—
251#102—231no—
252#102—231no—
253#102—231no—
254#102—231no—
255#102—231no—
256#102—231no—
257#102—231no—
258#102C2×D2311yescharacteristic
259#102C2×D2311yescharacteristic, complemented
260C22⋊C8—231no—
261C22⋊C8C2×D2311yescharacteristic, complemented
262C4×C8—231no—
263C23#329411yescharacteristic, complemented, Sylow
264C24—21no—
265C24—461no—
266#41—924no—
267C2×Q8—461no—
268C2×D4—22no—
269C2×D4—21no—
270C2×D4—21no—
271C2×D4—41no—
272C2×D4—231no—
273C2×D4—231no—
274C2×D4—461no—
275C2×D4—461no—
276C2×D4—461no—
277C2×D4—462no—
278C2×D4—461no—
279C2×D4—461no—
280C2×D4—461no—
281C2×D4—921no—
282C2×D4—924no—
283C2×D4C22×D2311yescharacteristic
284C2×D4C22×D2311yescharacteristic
285C2×D4C22×D2311yescharacteristic
286C22×C4—231no—
287C22×C4—461no—
288C22×C4—461no—
289C22×C4—461no—
290C22×C4—461no—
291C22×C4C22×D2311yescharacteristic
292D8—22no—
293D8—41no—
294D8—921no—
295C2×C8—231no—
296C2×C8—231no—
297C2×C8—921no—
298C2×C8—921no—
299C2×C8C22×D2311yescharacteristic
300C2×C8C22×D2311yescharacteristic
301C4⋊C4—231no—
302C4⋊C4—231no—
303C4⋊C4—231no—
304C4⋊C4—231no—
305C4⋊C4—461no—
306C4⋊C4—461no—
307C4⋊C4—461no—
308C4⋊C4C22×D2311yescharacteristic
309C22⋊C4—21no—
310C22⋊C4—231no—
311C22⋊C4—231no—
312C22⋊C4—461no—
313C22⋊C4—461no—
314C22⋊C4—461no—
315C22⋊C4—461no—
316C22⋊C4—461no—
317C42—231no—
318C23—21no—
319C23—21no—
320C23—21no—
321C23—42no—
322C23—42no—
323C23—81no—
324C23—231no—
325C23—461no—
326C23—922no—
327C23—922no—
328C23—1841no—
329C23D4×D2311yescharacteristic
330Q8—922no—
331D4—21no—
332D4—21no—
333D4—21no—
334D4—21no—
335D4—21no—
336D4—42no—
337D4—42no—
338D4—234no—
339D4—461no—
340D4—461no—
341D4—922no—
342D4—922no—
343D4—922no—
344D4—922no—
345D4—922no—
346D4—1841no—
347D4#6729012yescomplemented
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—231no—
352C2×C4—231no—
353C2×C4—231no—
354C2×C4—461no—
355C2×C4—461no—
356C2×C4—461no—
357C2×C4—461no—
358C2×C4—461no—
359C2×C4—922no—
360C2×C4—922no—
361C2×C4—922no—
362C2×C4—922no—
363C2×C4D4×D2311yescharacteristic
364C2×C4C23×D2311yescharacteristic
365C8—21no—
366C8—21no—
367C8—461no—
368C8—461no—
369C22—21no—
370C22—21no—
371C22—22no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—41no—
378C22—41no—
379C22—41no—
380C22—84no—
381C22—232no—
382C22—461no—
383C22—461no—
384C22—921no—
385C22—921no—
386C22—921no—
387C22—1844no—
388C22D8×D2312yes—
389C22C2×D4×D2311yescharacteristic
390C4—21no—
391C4—41no—
392C4—232no—
393C4—461no—
394C4—461no—
395C4—921no—
396C4—921no—
397C4—921no—
398C4C2×#6729011yescharacteristic
399C4#1062515511yescharacteristic
400C2—22no—
401C2—42no—
402C2—81no—
403C2—81no—
404C2—462no—
405C2—1841no—
406C2#1309305411yescharacteristic
407C2C2×D8×D2311yescharacteristic
408C2#1309322711yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#447C2
socleC22×C23C22×D4
hypercenter#447D23
hypocenterC23#3294
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. #13093067C2semidirect
2. D4×C22⋊D23C2semidirect
3. #13092762C2semidirect
4. #13092731C2semidirect
5. #13092729C2semidirect
6. #13092695C2semidirect
7. #13092651C2semidirect
8. #13092650C2semidirect
9. #13092610C2semidirect
10. #13092549C2semidirect
11. D8×Dic23C2semidirect
12. (C22⋊D23)⋊C8C2semidirect
13. C2×#10625014C2semidirect
14. #102×D23C2semidirect
15. C23×#447C2semidirect
21. C2×D8×C23C22semidirect
22. C23×#121C22semidirect
27. #10625109C22semidirect
31. D4×Dic23C22semidirect
32. C2×#67272C22semidirect
35. C2×C4⋊Dic23C22semidirect
36. C22×C23⋊C8C22semidirect
37. C2×C8×D23C22semidirect
38. C4⋊C4×D23C22semidirect
39. #10625059C22semidirect
43. C23×#102C22semidirect
44. C23×C22⋊C8C22semidirect
47. #10625014C22semidirect
48. #10625014C22semidirect
49. #10625014C22semidirect
50. #10625003C22semidirect
51. #10625003C22semidirect
52. (C2×D23)⋊C8C22semidirect
53. #10625000C22semidirect
54. #10625000C22semidirect
55. Dic23⋊C8C22semidirect
56. C8×Dic23C22semidirect
57. #10624991C22semidirect
58. #10624989C22semidirect
132. D4×C23#41semidirect
144. C22⋊D23D8semidirect
206. #447D23semidirect
226. C2×D8C2×D23semidirect
238. #121C2×D23semidirect
259. #102C2×D23semidirect
261. C22⋊C8C2×D23semidirect
263. C23#3294semidirect
347. D4#67290semidirect

Maximal subgroups

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

subgroupindex
#130930672
D4×C22⋊D232
#130927622
#130927312
#130927292
#130926952
#130926512
#130926502
#130926102
#130925492
D8×Dic232
(C22⋊D23)⋊C82
C2×#106250142
#102×D232
C23×#4472
#329423