Finite Group Databasebeta

← #46821122

Subgroups — #46821122

Order 34432.

418 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31771208C211yesmaximal, characteristic, complemented
2#31771080C211yesmaximal, characteristic, complemented
3#31770930C211yesmaximal, characteristic, complemented
4#31770926C211yesmaximal, characteristic, complemented
5#31770907C211yesmaximal, characteristic, complemented
6#31770903C211yesmaximal, characteristic, complemented
7#31770798C211yesmaximal, characteristic, complemented
8#31770798C211yesmaximal, characteristic, complemented
9#31770739C211yesmaximal, characteristic, complemented
10#31770717C211yesmaximal, characteristic, complemented
11#31770714C211yesmaximal, characteristic, complemented
12D8×Dic269C211yesmaximal, characteristic, complemented
13#31770685C211yesmaximal, characteristic, complemented
14#31770663C211yesmaximal, characteristic, complemented
15#447×C269C211yesmaximal, characteristic, complemented
16C2×#16864387C2211yescharacteristic
17C2×#16864387C2211yescharacteristic
18#22575449C2211yescharacteristic, complemented
19#22575444C2211yescharacteristic, complemented
20#22575437—21no—
21#22575435—21no—
22#22575427C2211yescharacteristic
23#22575425—21no—
24#22575424—21no—
25D4×Dic269—21no—
26D4×Dic269—21no—
27D4×Dic269C2211yescharacteristic
28D4×Dic269C2211yescharacteristic
29D4×Dic269C2211yescharacteristic
30D4×Dic269C2211yescharacteristic
31D4×Dic269C2211yescharacteristic, complemented
32#22575415C2211yescharacteristic, complemented
33#22575412C2211yescharacteristic
34#22575412C2211yescharacteristic
35C2×C22⋊Dic269—21no—
36C2×C22⋊Dic269—21no—
37#22575387C2211yescharacteristic, complemented
38#22575386C2211yescharacteristic, complemented
39#22575385C2211yescharacteristic, complemented
40#22575384C2211yescharacteristic, complemented
41#22575382C2211yescharacteristic, complemented
42#22575382C2211yescharacteristic, complemented
43#22575375C2211yescharacteristic, complemented
44#22575375C2211yescharacteristic, complemented
45#22575374C2211yescharacteristic
46#22575374C2211yescharacteristic
47#22575374C2211yescharacteristic, complemented
48#22575374C2211yescharacteristic, complemented
49C22⋊#14524130C2211yescharacteristic
50#22575363C2211yescharacteristic, complemented
51C8×Dic269C2211yescharacteristic, complemented
52C22×D4×C269C2211yescharacteristic
53C2×D8×C269C2211yescharacteristic
54C2×D8×C269C2211yescharacteristic
55#121×C269C2211yescharacteristic
56#102×C269C2211yescharacteristic
57#102×C269C2211yescharacteristic
58C22⋊C8×C269C2211yescharacteristic
59C2×D1076C2311yescharacteristic
60C2×C22⋊D269—21no—
61C2×C22⋊D269—21no—
62C2×C22⋊D269—21no—
63C22×Dic269—21no—
64C22×Dic269—21no—
65C22×Dic269—21no—
66C22×Dic269—21no—
67C22×Dic269—21no—
68C2×C4×D269—21no—
69#16864387—22no—
70#16864387—22no—
71C2×#14524130C2311yescharacteristic
72C2×#14524130C2311yescharacteristic
73C4⋊Dic269—21no—
74C4⋊Dic269D411yescharacteristic
75C4⋊Dic269D411yescharacteristic
76C4⋊Dic269C2311yescharacteristic
77C4⋊Dic269C2311yescharacteristic
78C4⋊Dic269C2311yescharacteristic
79#16864381—21no—
80C22⋊Dic269—21no—
81C22⋊Dic269—21no—
82C22⋊Dic269—21no—
83C22⋊Dic269—21no—
84C22⋊Dic269—21no—
85C22⋊Dic269—21no—
86C22⋊Dic269D411yescharacteristic
87C22⋊Dic269D411yescharacteristic
88#16864379—21no—
89#16864379—21no—
90C4×Dic269—21no—
91C4×Dic269C2311yescharacteristic
92C4×Dic269C2311yescharacteristic
93C24×C269—21no—
94C2×D4×C269—22no—
95C2×D4×C269—22no—
96C2×D4×C269—21no—
97C2×D4×C269—21no—
98C2×D4×C269C2311yescharacteristic
99C2×D4×C269C2311yescharacteristic
100C2×D4×C269C2311yescharacteristic
101C22×C4×C269C2311yescharacteristic
102D8×C269—22no—
103D8×C269—22no—
104C2×C8×C269C2311yescharacteristic
105C2×C8×C269C2311yescharacteristic
106C4⋊C4×C269C2311yescharacteristic
107C22⋊C4×C269—21no—
108C22×D269—21no—
109D1076—21no—
110D1076—21no—
111C22⋊D269—81no—
112C22⋊D269—81no—
113C22⋊D269—81no—
114C2×Dic269—21no—
115C2×Dic269—21no—
116C2×Dic269—21no—
117C2×Dic269—81no—
118C2×Dic269—81no—
119C2×Dic269—81no—
120C2×Dic269—81no—
121C2×Dic269—81no—
122C2×Dic269C2×D411yescharacteristic
123C2×Dic269C2×D411yescharacteristic
124C2×Dic269C2×D411yescharacteristic
125C2×Dic269C2×D411yescharacteristic
126C4×D269—81no—
127#14524130—21no—
128#14524130—21no—
129C23×C269—24no—
130C23×C269—21no—
131C23×C269—21no—
132C23×C269—21no—
133C23×C269—81no—
134C23×C269—81no—
135C23×C269C2×D411yescharacteristic
136D4×C269—24no—
137D4×C269—21no—
138D4×C269—21no—
139D4×C269—21no—
140D4×C269—21no—
141D4×C269—81no—
142D4×C269#4112yes—
143D4×C269#4112yes—
144C2×C4×C269—21no—
145C2×C4×C269—21no—
146C2×C4×C269—21no—
147C2×C4×C269C2×D411yescharacteristic
148C2×C4×C269C2411yescharacteristic
149C8×C269—21no—
150C8×C269—21no—
151C22×C269—21no—
152C22×C269—22no—
153C22×C269—22no—
154C22×C269—21no—
155C22×C269—21no—
156C22×C269—41no—
157C22×C269—41no—
158C22×C269—41no—
159C22×C269—41no—
160C22×C269—41no—
161C22×C269—41no—
162C22×C269—41no—
163C22×C269—84no—
164C22×C269C22×D411yescharacteristic
165C2×D269—41no—
166C2×D269—41no—
167C2×D269—41no—
168C4×C269—21no—
169C4×C269—41no—
170C4×C269C2×#4111yescharacteristic
171C4×C269C2×#4111yescharacteristic
172Dic269—21no—
173Dic269—21no—
174Dic269—21no—
175Dic269—21no—
176Dic269—41no—
177Dic269—41no—
178Dic269—41no—
179C2×C269—41no—
180C2×C269—42no—
181C2×C269—42no—
182C2×C269—81no—
183C2×C269#52511yescharacteristic
184C2×C269#57611yescharacteristic
185C2×C269#57611yescharacteristic
186D269—81no—
187C269#312211yescharacteristic, complemented, Sylow
188#3122—2691nomaximal, Sylow
189#540—2691no—
190#518—2691no—
191#482—2691no—
192#482—2691no—
193#478—2691no—
194#478—2691no—
195#459—2691no—
196#459—2691no—
197#447—2691no—
198#447D26911yescharacteristic, complemented
199#442—2691no—
200#442—2691no—
201C4×D8—2691no—
202C4×D8—2691no—
203#433—2691no—
204C22×D4C2×D26911yescharacteristic
205C2×D8—2691no—
206C2×D8—2691no—
207C2×D8C2×D26911yescharacteristic
208C2×D8C2×D26911yescharacteristic
209#127—2691no—
210#125—2691no—
211#123—5381no—
212#123—5381no—
213#121—2691no—
214#121—5381no—
215#121—5381no—
216#121C2×D26911yescharacteristic
217C4×D4—2691no—
218C4×D4—2691no—
219C4×D4—2691no—
220C4×D4—2691no—
221C4×D4—2691no—
222C4×D4—2691no—
223C4×D4—5381no—
224C4×D4—5381no—
225#117—2691no—
226#117—2691no—
227C2×C22⋊C4—5381no—
228C2×C22⋊C4—5381no—
229#107—2691no—
230#107—2691no—
231#106—2691no—
232#106—2691no—
233C4⋊C8—2691no—
234C4⋊C8—2691no—
235#102—2691no—
236#102—2691no—
237#102—2691no—
238#102—2691no—
239#102—2691no—
240#102—2691no—
241#102C2×D26911yescharacteristic
242#102C2×D26911yescharacteristic
243C22⋊C8—2691no—
244C22⋊C8C2×D26911yescharacteristic
245#97—2691no—
246C4×C8—2691no—
247C24—21no—
248C2×D4—22no—
249C2×D4—22no—
250C2×D4—21no—
251C2×D4—21no—
252C2×D4—2691no—
253C2×D4—5381no—
254C2×D4—5381no—
255C2×D4—5381no—
256C2×D4C22×D26911yescharacteristic
257C2×D4C22×D26911yescharacteristic
258C2×D4C22×D26911yescharacteristic
259C22×C4—5381no—
260C22×C4—5381no—
261C22×C4—5381no—
262C22×C4—5381no—
263C22×C4—5381no—
264C22×C4—5381no—
265C22×C4C22×D26911yescharacteristic
266D8—22no—
267D8—22no—
268D8—5382no—
269D8—5382no—
270C2×C8—2691no—
271C2×C8—2691no—
272C2×C8C22×D26911yescharacteristic
273C2×C8C22×D26911yescharacteristic
274C4⋊C4—2691no—
275C4⋊C4—2691no—
276C4⋊C4—2691no—
277C4⋊C4—2691no—
278C4⋊C4—2691no—
279C4⋊C4—5381no—
280C4⋊C4—5381no—
281C4⋊C4C22×D26911yescharacteristic
282C22⋊C4—21no—
283C22⋊C4—2691no—
284C22⋊C4—2691no—
285C22⋊C4—5381no—
286C22⋊C4—5381no—
287C22⋊C4—5381no—
288C22⋊C4—5381no—
289C22⋊C4—5381no—
290C22⋊C4—5381no—
291C22⋊C4—5381no—
292C22⋊C4—5381no—
293C42—2691no—
294C42—2691no—
295C42—5381no—
296C23—24no—
297C23—21no—
298C23—21no—
299C23—21no—
300C23—81no—
301C23—81no—
302C23—5381no—
303C23D4×D26911yescharacteristic
304D4—24no—
305D4—21no—
306D4—21no—
307D4—21no—
308D4—21no—
309D4—81no—
310D4—5381no—
311D4—5381no—
312D4—21521no—
313D4—21521no—
314D4—21521no—
315D4#1686440112yes—
316D4#1686440112yes—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—2691no—
321C2×C4—2691no—
322C2×C4—2691no—
323C2×C4—2691no—
324C2×C4—5381no—
325C2×C4—5381no—
326C2×C4—5381no—
327C2×C4—21521no—
328C2×C4—21521no—
329C2×C4—21521no—
330C2×C4—21521no—
331C2×C4—21521no—
332C2×C4—21521no—
333C2×C4D4×D26911yescharacteristic
334C2×C4C23×D26911yescharacteristic
335C8—21no—
336C8—21no—
337C8—5381no—
338C8—5381no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—22no—
343C22—22no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—41no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—84no—
352C22—10761no—
353C22—10761no—
354C22—10761no—
355C22C2×D4×D26911yescharacteristic
356C4—21no—
357C4—41no—
358C4—5381no—
359C4—5381no—
360C4—5381no—
361C4—5381no—
362C4—10761no—
363C4—10761no—
364C4—10761no—
365C4C2×#1686440111yescharacteristic
366C4C2×#1686440111yescharacteristic
367C2—41no—
368C2—42no—
369C2—42no—
370C2—81no—
371C2—21521no—
372C2#3177111111yescharacteristic
373C2#3177140611yescharacteristic
374C2#3177140911yescharacteristic
subgroupG/H
centerC22C2×D4×D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#447×C269C2
socleC22×C269C22×D4
hypercenter#447D269
hypocenterC269#3122
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. #31771208C2semidirect
2. #31771080C2semidirect
3. #31770930C2semidirect
4. #31770926C2semidirect
5. #31770907C2semidirect
6. #31770903C2semidirect
7. #31770798C2semidirect
8. #31770798C2semidirect
9. #31770739C2semidirect
10. #31770717C2semidirect
11. #31770714C2semidirect
12. D8×Dic269C2semidirect
13. #31770685C2semidirect
14. #31770663C2semidirect
15. #447×C269C2semidirect
18. #22575449C22semidirect
19. #22575444C22semidirect
31. D4×Dic269C22semidirect
32. #22575415C22semidirect
37. #22575387C22semidirect
38. #22575386C22semidirect
39. #22575385C22semidirect
40. #22575384C22semidirect
41. #22575382C22semidirect
42. #22575382C22semidirect
43. #22575375C22semidirect
44. #22575375C22semidirect
47. #22575374C22semidirect
48. #22575374C22semidirect
50. #22575363C22semidirect
51. C8×Dic269C22semidirect
187. C269#3122semidirect
198. #447D269semidirect

Maximal subgroups

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

subgroupindex
#317712082
#317710802
#317709302
#317709262
#317709072
#317709032
#317707982
#317707392
#317707172
#317707142
D8×Dic2692
#317706852
#317706632
#447×C2692
#3122269