Finite Group Databasebeta

← #46822922

Subgroups — #46822922

Order 34432.

402 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#31771323C211yesmaximal, characteristic, complemented
2#31771249C211yesmaximal, characteristic
3#31770963C211yesmaximal, characteristic, complemented
4#31770946C211yesmaximal, characteristic, complemented
5#31770928C211yesmaximal, characteristic, complemented
6#31770893C211yesmaximal, characteristic, complemented
7#31770863C211yesmaximal, characteristic, complemented
8#31770833C211yesmaximal, characteristic, complemented
9#31770826C211yesmaximal, characteristic, complemented
10#31770768C211yesmaximal, characteristic, complemented
11#31770756C211yesmaximal, characteristic, complemented
12#31770702C211yesmaximal, characteristic, complemented
13#31770674C211yesmaximal, characteristic, complemented
14#31770598C211yesmaximal, characteristic, complemented
15#418×C269C211yesmaximal, characteristic, complemented
16C2×#16864401C2211yescharacteristic
17C2×Dic1076C2211yescharacteristic, complemented
18C2×#16864390C2211yescharacteristic
19C2×#16864390C2211yescharacteristic
20C2×C8×D269C2211yescharacteristic, complemented
21#22575452C2211yescharacteristic, complemented
22#22575447—21no—
23#22575446—21no—
24#22575440C2211yescharacteristic
25#22575439—21no—
26#22575434—21no—
27#22575433C2211yescharacteristic, complemented
28#22575432C2211yescharacteristic
29#22575432C2211yescharacteristic
30#22575425—21no—
31#22575424C2211yescharacteristic
32#22575422—21no—
33C4×Dic538—21no—
34#22575418C2211yescharacteristic, complemented
35D4×Dic269C2211yescharacteristic
36C4×C22⋊D269C2211yescharacteristic
37#22575411C2211yescharacteristic, complemented
38C2×C22⋊Dic269—21no—
39#22575386C2211yescharacteristic, complemented
40#22575385C2211yescharacteristic, complemented
41#22575384C2211yescharacteristic, complemented
42#22575382C2211yescharacteristic, complemented
43#22575378C2211yescharacteristic, complemented
44#22575378C2211yescharacteristic, complemented
45#22575376C2211yescharacteristic, complemented
46#22575376C2211yescharacteristic, complemented
47#22575374C2211yescharacteristic
48#22575374C2211yescharacteristic
49C22⋊#14524130C2211yescharacteristic
50#22575365C2211yescharacteristic, complemented
51#22575363C2211yescharacteristic, complemented
52C22×D4×C269C2211yescharacteristic
53C2×M16×C269C2211yescharacteristic
54#117×C269C2211yescharacteristic
55#102×C269C2211yescharacteristic
56#102×C269C2211yescharacteristic
57#102×C269C2211yescharacteristic
58#102×C269C2211yescharacteristic
59#16864401—22no—
60#16864401—41no—
61C2×Dic538—21no—
62C2×Dic538C2311yescharacteristic
63C2×Dic538C2311yescharacteristic
64C2×C22⋊D269—21no—
65C2×C22⋊D269—21no—
66C2×C22⋊D269D411yescharacteristic
67C22×Dic269—21no—
68C22×Dic269—21no—
69C2×C4×D269C2311yescharacteristic
70Dic1076—41no—
71#16864390—22no—
72#16864390—41no—
73C2×#14524130C2311yescharacteristic
74C2×#14524130C2311yescharacteristic
75C8×D269—41no—
76C4⋊Dic269—21no—
77C4⋊Dic269C2311yescharacteristic
78C4⋊Dic269C2311yescharacteristic
79#16864381—21no—
80#16864381—21no—
81#16864381—21no—
82#16864381—21no—
83#16864381D411yescharacteristic
84C22⋊Dic269—21no—
85C22⋊Dic269—21no—
86C22⋊Dic269—21no—
87C22⋊Dic269—21no—
88C22⋊Dic269—21no—
89C22⋊Dic269—21no—
90C22⋊Dic269D411yescharacteristic
91#16864379—21no—
92#16864379—21no—
93#16864379D411yescharacteristic
94C4×Dic269—21no—
95C4×Dic269—21no—
96C4×Dic269C2311yescharacteristic
97C24×C269—21no—
98C2×D4×C269—22no—
99C2×D4×C269—21no—
100C2×D4×C269—41no—
101C2×D4×C269C2311yescharacteristic
102C2×D4×C269C2311yescharacteristic
103C22×C4×C269C2311yescharacteristic
104M16×C269—41no—
105C2×C8×C269C2311yescharacteristic
106C2×C8×C269C2311yescharacteristic
107C4⋊C4×C269C2311yescharacteristic
108C4⋊C4×C269C2311yescharacteristic
109C22⋊C4×C269—21no—
110C42×C269—21no—
111C22×D269C2×D411yescharacteristic
112Dic538—21no—
113Dic538—21no—
114Dic538—21no—
115Dic538—21no—
116Dic538—42no—
117C22⋊D269—41no—
118C22⋊D269—42no—
119C22⋊D269—81no—
120C2×Dic269—21no—
121C2×Dic269—21no—
122C2×Dic269—21no—
123C2×Dic269—21no—
124C2×Dic269—42no—
125C2×Dic269—81no—
126C2×Dic269C2×D411yescharacteristic
127C2×Dic269C2×D411yescharacteristic
128C2×Dic269C2×D411yescharacteristic
129C4×D269—21no—
130C4×D269—21no—
131#14524130—21no—
132#14524130—21no—
133C23×C269—21no—
134C23×C269—21no—
135C23×C269—42no—
136C23×C269—42no—
137C23×C269—81no—
138C23×C269C2×D411yescharacteristic
139D4×C269—21no—
140D4×C269—21no—
141D4×C269—21no—
142D4×C269—42no—
143D4×C269#4112yes—
144C2×C4×C269—21no—
145C2×C4×C269—21no—
146C2×C4×C269—21no—
147C2×C4×C269—21no—
148C2×C4×C269C2×D411yescharacteristic
149C2×C4×C269C2411yescharacteristic
150C8×C269—21no—
151C8×C269—21no—
152C22×C269—21no—
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—84no—
162C22×C269C22×D411yescharacteristic
163C2×D269—21no—
164C2×D269—21no—
165C2×D269—21no—
166C4×C269—21no—
167C4×C269—41no—
168C4×C269—41no—
169C4×C269C2×#4111yescharacteristic
170C4×C269H(5,𝔽2)11yescharacteristic
171Dic269—21no—
172Dic269—21no—
173Dic269—21no—
174Dic269—41no—
175Dic269—41no—
176Dic269—41no—
177Dic269—41no—
178C2×C269—41no—
179C2×C269—42no—
180C2×C269—81no—
181C2×C269#54611yescharacteristic
182C2×C269#57511yescharacteristic
183C2×C269#57711yescharacteristic
184D269—41no—
185C269#331111yescharacteristic, complemented, Sylow
186#3311—2691nomaximal, Sylow
187#556—2691no—
188#546—2691no—
189#489—2691no—
190#485—2691no—
191#482—2691no—
192#476—2691no—
193#470—2691no—
194#465—2691no—
195#464—2691no—
196#452—2691no—
197#450—2691no—
198#440—2691no—
199#435—2691no—
200#418D26911yescharacteristic, complemented
201#416—2691no—
202C2×#41—2691no—
203C22×D4C2×D26911yescharacteristic
204C2×Q16—2691no—
205C2×SD16—2691no—
206C2×SD16—2691no—
207C2×M16C2×D26911yescharacteristic
208C22×C8—2691no—
209C4⋊Q8—2691no—
210#126—5381no—
211#126—5381no—
212#124—2691no—
213#124—5381no—
214#123—5381no—
215C22⋊Q8—2691no—
216C22⋊Q8—2691no—
217C22⋊Q8—2691no—
218#121—2691no—
219#121—5381no—
220#120—5381no—
221C4×Q8—2691no—
222C4×Q8—5381no—
223C4×D4—2691no—
224C4×D4—2691no—
225#117—2691no—
226#117C2×D26911yescharacteristic
227C2×C22⋊C4—5381no—
228#107—2691no—
229#106—2691no—
230#106—2691no—
231C4⋊C8—2691no—
232#103—2691no—
233#103—2691no—
234#103—2691no—
235#103—2691no—
236#102—2691no—
237#102—2691no—
238#102C2×D26911yescharacteristic
239#102C2×D26911yescharacteristic
240#102C2×D26911yescharacteristic
241#102C2×D26911yescharacteristic
242C22⋊C8—2691no—
243C22⋊C8—2691no—
244#97—2691no—
245C24—21no—
246#41—5382no—
247#41—10761no—
248C2×Q8—2691no—
249C2×Q8—2691no—
250C2×Q8—5381no—
251C2×D4—22no—
252C2×D4—21no—
253C2×D4—41no—
254C2×D4—2691no—
255C2×D4—5381no—
256C2×D4—5381no—
257C2×D4C22×D26911yescharacteristic
258C2×D4C22×D26911yescharacteristic
259C22×C4—2691no—
260C22×C4—5381no—
261C22×C4—5381no—
262C22×C4C22×D26911yescharacteristic
263Q16—10761no—
264SD16—5382no—
265SD16—10761no—
266M16—41no—
267C2×C8—2691no—
268C2×C8—2691no—
269C2×C8—10761no—
270C2×C8C22×D26911yescharacteristic
271C2×C8C22×D26911yescharacteristic
272C4⋊C4—2691no—
273C4⋊C4—2691no—
274C4⋊C4—2691no—
275C4⋊C4—5381no—
276C4⋊C4—5381no—
277C4⋊C4—5381no—
278C4⋊C4—5381no—
279C4⋊C4—5381no—
280C4⋊C4C22×D26911yescharacteristic
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—21no—
294C42—2691no—
295C42—5381no—
296C42—5381no—
297C23—21no—
298C23—21no—
299C23—42no—
300C23—42no—
301C23—81no—
302C23—2691no—
303C23D4×D26911yescharacteristic
304Q8—5381no—
305Q8—5381no—
306Q8—5381no—
307Q8—5381no—
308Q8—10762no—
309D4—21no—
310D4—21no—
311D4—21no—
312D4—42no—
313D4—10761no—
314D4—10762no—
315D4—21521no—
316D4#1686440212yes—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—2691no—
322C2×C4—2691no—
323C2×C4—2691no—
324C2×C4—5381no—
325C2×C4—5381no—
326C2×C4—5381no—
327C2×C4—5381no—
328C2×C4—5381no—
329C2×C4—5381no—
330C2×C4—10762no—
331C2×C4—21521no—
332C2×C4D4×D26911yescharacteristic
333C2×C4C23×D26911yescharacteristic
334C8—21no—
335C8—21no—
336C8—5381no—
337C8—5381no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—22no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—84no—
348C22—5381no—
349C22—5381no—
350C22—5381no—
351C22C2×D4×D26911yescharacteristic
352C4—21no—
353C4—41no—
354C4—41no—
355C4—5381no—
356C4—5381no—
357C4—5381no—
358C4—10761no—
359C4—10761no—
360C4—10761no—
361C4—10761no—
362C4C2×#1686440211yescharacteristic
363C4#2257549811yescharacteristic
364C2—41no—
365C2—42no—
366C2—81no—
367C2—10761no—
368C2#3177124511yescharacteristic
369C2#3177140111yescharacteristic
370C2#3177141511yescharacteristic
subgroupG/H
centerC22C2×D4×D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#418×C269C2
socleC22×C269C22×D4
prime radical#31771249C2
hypercenter#418D269
hypocenterC269#3311
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
1. #31771323C2semidirect
3. #31770963C2semidirect
4. #31770946C2semidirect
5. #31770928C2semidirect
6. #31770893C2semidirect
7. #31770863C2semidirect
8. #31770833C2semidirect
9. #31770826C2semidirect
10. #31770768C2semidirect
11. #31770756C2semidirect
12. #31770702C2semidirect
13. #31770674C2semidirect
14. #31770598C2semidirect
15. #418×C269C2semidirect
17. C2×Dic1076C22semidirect
20. C2×C8×D269C22semidirect
21. #22575452C22semidirect
27. #22575433C22semidirect
34. #22575418C22semidirect
37. #22575411C22semidirect
39. #22575386C22semidirect
40. #22575385C22semidirect
41. #22575384C22semidirect
42. #22575382C22semidirect
43. #22575378C22semidirect
44. #22575378C22semidirect
45. #22575376C22semidirect
46. #22575376C22semidirect
50. #22575365C22semidirect
51. #22575363C22semidirect
185. C269#3311semidirect
200. #418D269semidirect

Maximal subgroups

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

subgroupindex
#317713232
#317712492
#317709632
#317709462
#317709282
#317708932
#317708632
#317708332
#317708262
#317707682
#317707562
#317707022
#317706742
#317705982
#418×C2692
#3311269