Finite Group Databasebeta

← #46822691

Subgroups — #46822691

Order 34432.

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#31771255C211yesmaximal, characteristic, complemented
2D4×C22⋊D269C211yesmaximal, characteristic, complemented
3#31770950C211yesmaximal, characteristic, complemented
4#31770919C211yesmaximal, characteristic, complemented
5#31770917C211yesmaximal, characteristic, complemented
6#31770883C211yesmaximal, characteristic, complemented
7#31770839C211yesmaximal, characteristic, complemented
8#31770838C211yesmaximal, characteristic, complemented
9#31770798C211yesmaximal, characteristic, complemented
10#31770737C211yesmaximal, characteristic, complemented
11D8×Dic269C211yesmaximal, characteristic, complemented
12#31770668C211yesmaximal, characteristic, complemented
13C2×#22575374C211yesmaximal, characteristic, complemented
14#102×D269C211yesmaximal, characteristic, complemented
15#447×C269C211yesmaximal, characteristic, complemented
16C2×#16864401—21no—
17C22×C22⋊D269—21no—
18C2×D4×D269C2211yescharacteristic
19C2×#16864387C2211yescharacteristic, complemented
20C22×#14524130C2211yescharacteristic, complemented
21C2×C8×D269C2211yescharacteristic, complemented
22#22575452C2211yescharacteristic, complemented
23#22575449C2211yescharacteristic
24#22575435—21no—
25#22575434—21no—
26#22575430—21no—
27#22575427C2211yescharacteristic
28#22575425—21no—
29#22575424C2211yescharacteristic
30#22575424C2211yescharacteristic, complemented
31#22575422—21no—
32#22575421—21no—
33D4×Dic269C2211yescharacteristic
34D4×Dic269C2211yescharacteristic, complemented
35C4×C22⋊D269C2211yescharacteristic
36C2×C4⋊Dic269C2211yescharacteristic, complemented
37C4⋊C4×D269C2211yescharacteristic, complemented
38#22575387C2211yescharacteristic, complemented
39#22575387C2211yescharacteristic, complemented
40#22575386C2211yescharacteristic, complemented
41#22575382C2211yescharacteristic, complemented
42#22575375C2211yescharacteristic, complemented
43#22575375C2211yescharacteristic, complemented
44#22575374C2211yescharacteristic
45#22575374C2211yescharacteristic
46#22575374C2211yescharacteristic, complemented
47#22575374C2211yescharacteristic, complemented
48#22575374C2211yescharacteristic, complemented
49#22575373C2211yescharacteristic, complemented
50#22575365C2211yescharacteristic, complemented
51C8×Dic269C2211yescharacteristic, complemented
52C22×D4×C269C2211yescharacteristic
53C2×D8×C269C2211yescharacteristic
54C2×D8×C269C2211yescharacteristic, complemented
55#121×C269C2211yescharacteristic, complemented
56#102×C269C2211yescharacteristic
57#102×C269C2211yescharacteristic, complemented
58C22⋊C8×C269C2211yescharacteristic, complemented
59C23×D269—21no—
60#16864401—44no—
61C2×Dic538—21no—
62C2×D1076C2311yescharacteristic
63C2×C22⋊D269—21no—
64C2×C22⋊D269—21no—
65C2×C22⋊D269—21no—
66C2×C22⋊D269—21no—
67C2×C22⋊D269—21no—
68C2×C22⋊D269—21no—
69C2×C22⋊D269—44no—
70C2×C22⋊D269D411yescharacteristic
71D4×D269—22no—
72D4×D269—41no—
73C22×Dic269—21no—
74C22×Dic269—21no—
75C22×Dic269—21no—
76C2×C4×D269—21no—
77C2×C4×D269C2311yescharacteristic
78#16864387—41no—
79C2×#14524130—41no—
80C2×#14524130C2311yescharacteristic
81C2×#14524130C2311yescharacteristic
82C8×D269—41no—
83C4⋊Dic269—21no—
84C4⋊Dic269C2311yescharacteristic
85C4⋊Dic269C2311yescharacteristic
86C4⋊Dic269C2311yescharacteristic
87#16864381—21no—
88#16864381—21no—
89#16864381D411yescharacteristic
90C22⋊Dic269—21no—
91C22⋊Dic269—21no—
92C22⋊Dic269—21no—
93C22⋊Dic269—21no—
94C22⋊Dic269D411yescharacteristic
95#16864379—21no—
96#16864379D411yescharacteristic
97C4×Dic269C2311yescharacteristic
98C24×C269—21no—
99C2×D4×C269—22no—
100C2×D4×C269—21no—
101C2×D4×C269—21no—
102C2×D4×C269—41no—
103C2×D4×C269C2311yescharacteristic
104C2×D4×C269C2311yescharacteristic
105C2×D4×C269C2311yescharacteristic
106C22×C4×C269C2311yescharacteristic
107D8×C269—22no—
108D8×C269—41no—
109C2×C8×C269C2311yescharacteristic
110C2×C8×C269C2311yescharacteristic
111C4⋊C4×C269C2311yescharacteristic
112C22⋊C4×C269—21no—
113C22×D269—21no—
114C22×D269—42no—
115C22×D269—42no—
116C22×D269—81no—
117C22×D269C2×D411yescharacteristic
118Dic538—42no—
119D1076—21no—
120D1076—21no—
121C22⋊D269—42no—
122C22⋊D269—42no—
123C22⋊D269—42no—
124C22⋊D269—42no—
125C22⋊D269—42no—
126C22⋊D269—81no—
127C22⋊D269D814yescomplemented
128C2×Dic269—21no—
129C2×Dic269—21no—
130C2×Dic269—21no—
131C2×Dic269—42no—
132C2×Dic269—42no—
133C2×Dic269—42no—
134C2×Dic269C2×D411yescharacteristic
135C2×Dic269C2×D411yescharacteristic
136C2×Dic269C2×D411yescharacteristic
137C4×D269—21no—
138C4×D269—21no—
139C4×D269—42no—
140#14524130—21no—
141#14524130—21no—
142C23×C269—21no—
143C23×C269—21no—
144C23×C269—21no—
145C23×C269—42no—
146C23×C269—42no—
147C23×C269—81no—
148C23×C269C2×D411yescharacteristic
149D4×C269—21no—
150D4×C269—21no—
151D4×C269—21no—
152D4×C269—21no—
153D4×C269—21no—
154D4×C269—42no—
155D4×C269—42no—
156D4×C269#4112yescomplemented
157C2×C4×C269—21no—
158C2×C4×C269—21no—
159C2×C4×C269—21no—
160C2×C4×C269C2×D411yescharacteristic
161C2×C4×C269C2411yescharacteristic
162C8×C269—21no—
163C8×C269—21no—
164C22×C269—21no—
165C22×C269—21no—
166C22×C269—22no—
167C22×C269—41no—
168C22×C269—41no—
169C22×C269—41no—
170C22×C269—41no—
171C22×C269—41no—
172C22×C269—41no—
173C22×C269—41no—
174C22×C269—41no—
175C22×C269—84no—
176C22×C269C2×D812yes—
177C22×C269C22×D411yescharacteristic
178C2×D269—21no—
179C2×D269—21no—
180C2×D269—41no—
181C2×D269—41no—
182C2×D269—41no—
183C2×D269—84no—
184C2×D269C2×D812yes—
185C4×C269—21no—
186C4×C269—41no—
187C4×C269C2×#4111yescharacteristic
188C4×C269H(5,𝔽2)11yescharacteristic
189Dic269—21no—
190Dic269—21no—
191Dic269—41no—
192Dic269—41no—
193Dic269—41no—
194Dic269C2×D812yes—
195C2×C269—22no—
196C2×C269—42no—
197C2×C269—81no—
198C2×C269—81no—
199C2×C269#54611yescharacteristic
200C2×C269C22×D811yescharacteristic
201C2×C269#57711yescharacteristic
202D269—22no—
203D269—81no—
204C269#329411yescharacteristic, complemented, Sylow
205#3294—2691nomaximal, Sylow
206#547—2691no—
207D42—2691no—
208#486—2691no—
209#480—2691no—
210#480—2691no—
211#474—2691no—
212#466—2691no—
213#466—2691no—
214#459—2691no—
215#447—2691no—
216#447D26911yescharacteristic, complemented
217C4×D8—2691no—
218C8×D4—2691no—
219C2×#102—2691no—
220C2×#102—2691no—
221C2×#41—5381no—
222C22×D4—2691no—
223C22×D4—5381no—
224C22×D4C2×D26911yescharacteristic
225C2×D8—2691no—
226C2×D8C2×D26911yescharacteristic
227C2×D8C2×D26911yescharacteristic, complemented
228C22×C8—2691no—
229C22×C8—2691no—
230C4⋊Q8—2691no—
231#127—2691no—
232#123—5381no—
233#123—5381no—
234C22⋊Q8—5381no—
235#121—2691no—
236#121—2691no—
237#121—2691no—
238#121—5381no—
239#121C2×D26911yescharacteristic, complemented
240#120—5381no—
241#120—5381no—
242C4×D4—2691no—
243C4×D4—2691no—
244C4×D4—2691no—
245C2×C4⋊C4—2691no—
246C2×C4⋊C4—2691no—
247#107—2691no—
248#107—2691no—
249#107—2691no—
250C4⋊C8—2691no—
251#102—2691no—
252#102—2691no—
253#102—2691no—
254#102—2691no—
255#102—2691no—
256#102—2691no—
257#102—2691no—
258#102—2691no—
259#102C2×D26911yescharacteristic
260#102C2×D26911yescharacteristic, complemented
261C22⋊C8—2691no—
262C22⋊C8C2×D26911yescharacteristic, complemented
263C4×C8—2691no—
264C24—21no—
265C24—5381no—
266#41—10764no—
267C2×Q8—5381no—
268C2×D4—22no—
269C2×D4—21no—
270C2×D4—21no—
271C2×D4—41no—
272C2×D4—2691no—
273C2×D4—2691no—
274C2×D4—5381no—
275C2×D4—5381no—
276C2×D4—5381no—
277C2×D4—5382no—
278C2×D4—5381no—
279C2×D4—5381no—
280C2×D4—5381no—
281C2×D4—10761no—
282C2×D4—10764no—
283C2×D4C22×D26911yescharacteristic
284C2×D4C22×D26911yescharacteristic
285C2×D4C22×D26911yescharacteristic
286C22×C4—2691no—
287C22×C4—5381no—
288C22×C4—5381no—
289C22×C4—5381no—
290C22×C4—5381no—
291C22×C4C22×D26911yescharacteristic
292D8—22no—
293D8—41no—
294D8—10761no—
295C2×C8—2691no—
296C2×C8—2691no—
297C2×C8—10761no—
298C2×C8—10761no—
299C2×C8C22×D26911yescharacteristic
300C2×C8C22×D26911yescharacteristic
301C4⋊C4—2691no—
302C4⋊C4—2691no—
303C4⋊C4—2691no—
304C4⋊C4—2691no—
305C4⋊C4—5381no—
306C4⋊C4—5381no—
307C4⋊C4—5381no—
308C4⋊C4C22×D26911yescharacteristic
309C22⋊C4—21no—
310C22⋊C4—2691no—
311C22⋊C4—2691no—
312C22⋊C4—5381no—
313C22⋊C4—5381no—
314C22⋊C4—5381no—
315C22⋊C4—5381no—
316C22⋊C4—5381no—
317C42—2691no—
318C23—21no—
319C23—21no—
320C23—21no—
321C23—42no—
322C23—42no—
323C23—81no—
324C23—2691no—
325C23—5381no—
326C23—10762no—
327C23—10762no—
328C23—21521no—
329C23D4×D26911yescharacteristic
330Q8—10762no—
331D4—21no—
332D4—21no—
333D4—21no—
334D4—21no—
335D4—21no—
336D4—42no—
337D4—42no—
338D4—2694no—
339D4—5381no—
340D4—5381no—
341D4—10762no—
342D4—10762no—
343D4—10762no—
344D4—10762no—
345D4—10762no—
346D4—21521no—
347D4#1686440112yescomplemented
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—2691no—
352C2×C4—2691no—
353C2×C4—2691no—
354C2×C4—5381no—
355C2×C4—5381no—
356C2×C4—5381no—
357C2×C4—5381no—
358C2×C4—5381no—
359C2×C4—10762no—
360C2×C4—10762no—
361C2×C4—10762no—
362C2×C4—10762no—
363C2×C4D4×D26911yescharacteristic
364C2×C4C23×D26911yescharacteristic
365C8—21no—
366C8—21no—
367C8—5381no—
368C8—5381no—
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—2692no—
382C22—5381no—
383C22—5381no—
384C22—10761no—
385C22—10761no—
386C22—10761no—
387C22—21524no—
388C22D8×D26912yes—
389C22C2×D4×D26911yescharacteristic
390C4—21no—
391C4—41no—
392C4—2692no—
393C4—5381no—
394C4—5381no—
395C4—10761no—
396C4—10761no—
397C4—10761no—
398C4C2×#1686440111yescharacteristic
399C4#2257549811yescharacteristic
400C2—22no—
401C2—42no—
402C2—81no—
403C2—81no—
404C2—5382no—
405C2—21521no—
406C2#3177124211yescharacteristic
407C2C2×D8×D26911yescharacteristic
408C2#3177141511yescharacteristic
subgroupG/H
centerC22C2×D4×D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#447×C269C2
socleC22×C269C22×D4
hypercenter#447D269
hypocenterC269#3294
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. #31771255C2semidirect
2. D4×C22⋊D269C2semidirect
3. #31770950C2semidirect
4. #31770919C2semidirect
5. #31770917C2semidirect
6. #31770883C2semidirect
7. #31770839C2semidirect
8. #31770838C2semidirect
9. #31770798C2semidirect
10. #31770737C2semidirect
11. D8×Dic269C2semidirect
12. #31770668C2semidirect
13. C2×#22575374C2semidirect
14. #102×D269C2semidirect
15. #447×C269C2semidirect
19. C2×#16864387C22semidirect
20. C22×#14524130C22semidirect
21. C2×C8×D269C22semidirect
22. #22575452C22semidirect
30. #22575424C22semidirect
34. D4×Dic269C22semidirect
36. C2×C4⋊Dic269C22semidirect
37. C4⋊C4×D269C22semidirect
38. #22575387C22semidirect
39. #22575387C22semidirect
40. #22575386C22semidirect
41. #22575382C22semidirect
42. #22575375C22semidirect
43. #22575375C22semidirect
46. #22575374C22semidirect
47. #22575374C22semidirect
48. #22575374C22semidirect
49. #22575373C22semidirect
50. #22575365C22semidirect
51. C8×Dic269C22semidirect
54. C2×D8×C269C22semidirect
55. #121×C269C22semidirect
57. #102×C269C22semidirect
58. C22⋊C8×C269C22semidirect
127. C22⋊D269D8semidirect
156. D4×C269#41semidirect
204. C269#3294semidirect
216. #447D269semidirect
227. C2×D8C2×D269semidirect
239. #121C2×D269semidirect
260. #102C2×D269semidirect
262. C22⋊C8C2×D269semidirect
347. D4#16864401semidirect

Maximal subgroups

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

subgroupindex
#317712552
D4×C22⋊D2692
#317709502
#317709192
#317709172
#317708832
#317708392
#317708382
#317707982
#317707372
D8×Dic2692
#317706682
C2×#225753742
#102×D2692
#447×C2692
#3294269