Finite Group Databasebeta

← #46823587

Subgroups — #46823587

Order 34432.

396 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31771314C211yesmaximal, characteristic, complemented
2#31771275C211yesmaximal, characteristic, complemented
3#31770969C211yesmaximal, characteristic, complemented
4#31770968C211yesmaximal, characteristic, complemented
5#31770950C211yesmaximal, characteristic, complemented
6#31770906C211yesmaximal, characteristic, complemented
7#31770903C211yesmaximal, characteristic, complemented
8#31770893C211yesmaximal, characteristic, complemented
9#31770798C211yesmaximal, characteristic, complemented
10#31770798C211yesmaximal, characteristic, complemented
11#31770734C211yesmaximal, characteristic, complemented
12#31770717C211yesmaximal, characteristic, complemented
13#31770715C211yesmaximal, characteristic, complemented
14D8×Dic269C211yesmaximal, characteristic, complemented
15#459×C269C211yesmaximal, characteristic, complemented
16C2×#16864401—21no—
17C2×#16864387C2211yescharacteristic
18#22575452C2211yescharacteristic
19#22575449C2211yescharacteristic
20#22575449C2211yescharacteristic
21#22575445C2211yescharacteristic
22#22575444C2211yescharacteristic
23#22575432—21no—
24#22575430—21no—
25#22575430—21no—
26#22575425—21no—
27#22575425—21no—
28#22575424—21no—
29C4×Dic538C2211yescharacteristic
30C4×D1076C2211yescharacteristic
31D4×Dic269C2211yescharacteristic
32D4×Dic269C2211yescharacteristic
33D4×Dic269C2211yescharacteristic
34D4×Dic269C2211yescharacteristic
35C2×#16864381—21no—
36#22575387C2211yescharacteristic
37#22575385C2211yescharacteristic
38#22575384C2211yescharacteristic
39#22575382C2211yescharacteristic
40#22575382C2211yescharacteristic
41#22575375C2211yescharacteristic
42#22575375C2211yescharacteristic
43#22575374C2211yescharacteristic
44#22575374C2211yescharacteristic
45#22575374C2211yescharacteristic
46#22575374C2211yescharacteristic
47#22575374C2211yescharacteristic
48#22575373C2211yescharacteristic
49#22575364C2211yescharacteristic
50#22575363C2211yescharacteristic
51C8×Dic269C2211yescharacteristic
52C2×D8×C269C2211yescharacteristic
53C2×D8×C269C2211yescharacteristic
54#127×C269C2211yescharacteristic
55C4×D4×C269C2211yescharacteristic
56C4⋊C8×C269C2211yescharacteristic
57#102×C269C2211yescharacteristic
58#102×C269C2211yescharacteristic
59#16864401—44no—
60C2×Dic538—21no—
61C2×Dic538D411yescharacteristic
62C2×D1076C2311yescharacteristic
63C2×C22⋊D269—21no—
64C2×C22⋊D269—21no—
65C2×C22⋊D269—21no—
66C2×C22⋊D269—21no—
67C22×Dic269—21no—
68C22×Dic269—21no—
69C22×Dic269—21no—
70C22×Dic269—21no—
71C2×C4×D269—21no—
72#16864387—22no—
73C2×#14524130C2311yescharacteristic
74C2×#14524130C2311yescharacteristic
75C4⋊Dic269—21no—
76C4⋊Dic269D411yescharacteristic
77C4⋊Dic269C2311yescharacteristic
78C4⋊Dic269C2311yescharacteristic
79C4⋊Dic269C2311yescharacteristic
80#16864381—21no—
81#16864381—21no—
82#16864381—21no—
83#16864381—21no—
84#16864381D411yescharacteristic
85#16864381D411yescharacteristic
86C22⋊Dic269—21no—
87C22⋊Dic269—21no—
88C22⋊Dic269—21no—
89C22⋊Dic269—21no—
90#16864379—21no—
91C4×Dic269C2311yescharacteristic
92C4×Dic269C2311yescharacteristic
93C2×D4×C269—21no—
94C2×D4×C269—21no—
95C2×D4×C269C2311yescharacteristic
96C2×D4×C269C2311yescharacteristic
97C2×D4×C269C2311yescharacteristic
98C22×C4×C269—21no—
99D8×C269—22no—
100D8×C269—22no—
101C2×C8×C269C2311yescharacteristic
102C2×C8×C269C2311yescharacteristic
103C4⋊C4×C269C2311yescharacteristic
104C22⋊C4×C269—21no—
105C42×C269C2311yescharacteristic
106C22×D269—21no—
107Dic538—22no—
108Dic538—81no—
109D1076—21no—
110D1076—21no—
111C22⋊D269—42no—
112C22⋊D269—42no—
113C22⋊D269—81no—
114C22⋊D269—81no—
115C2×Dic269—21no—
116C2×Dic269—21no—
117C2×Dic269—21no—
118C2×Dic269—42no—
119C2×Dic269—42no—
120C2×Dic269—42no—
121C2×Dic269—81no—
122C2×Dic269C2×D411yescharacteristic
123C2×Dic269C2×D411yescharacteristic
124C2×Dic269C2×D411yescharacteristic
125C2×Dic269C2×D411yescharacteristic
126C4×D269—42no—
127#14524130—21no—
128#14524130—21no—
129C23×C269—21no—
130C23×C269—21no—
131C23×C269—21no—
132D4×C269—21no—
133D4×C269—21no—
134D4×C269—21no—
135D4×C269—21no—
136D4×C269—21no—
137D4×C269—42no—
138D4×C269—81no—
139D4×C269#4112yescomplemented
140C2×C4×C269—21no—
141C2×C4×C269—81no—
142C2×C4×C269C2×D411yescharacteristic
143C2×C4×C269C2×D411yescharacteristic
144C2×C4×C269C2411yescharacteristic
145C8×C269—21no—
146C8×C269—21no—
147C22×C269—22no—
148C22×C269—41no—
149C22×C269—41no—
150C22×C269—41no—
151C22×C269—41no—
152C22×C269—41no—
153C22×C269—41no—
154C22×C269—41no—
155C22×C269—41no—
156C22×C269C22×D411yescharacteristic
157C2×D269—41no—
158C2×D269—41no—
159C2×D269—41no—
160C4×C269—21no—
161C4×C269—21no—
162C4×C269—41no—
163C4×C269C2×#4111yescharacteristic
164C4×C2692−1+411yescharacteristic
165Dic269—21no—
166Dic269—21no—
167Dic269—21no—
168Dic269—41no—
169Dic269—41no—
170Dic269—41no—
171Dic269AGL(1,ℤ/8)12yes—
172C2×C269—42no—
173C2×C269—81no—
174C2×C269—81no—
175C2×C269#54811yescharacteristic
176C2×C269C2×AGL(1,ℤ/8)11yescharacteristic
177C2×C269#57611yescharacteristic
178D269—81no—
179C269#336611yescharacteristic, complemented, Sylow
180#3366—2691nomaximal, Sylow
181#554—2691no—
182#550—2691no—
183#490—2691no—
184#490—2691no—
185#486—2691no—
186#478—2691no—
187#478—2691no—
188#476—2691no—
189#459—2691no—
190#459—2691no—
191#459D26911yescharacteristic, complemented
192#446—2691no—
193#442—2691no—
194#442—2691no—
195C4×D8—2691no—
196C2×#41—5381no—
197C2×D8—2691no—
198C2×D8C2×D26911yescharacteristic
199C2×D8C2×D26911yescharacteristic
200C4⋊Q8—2691no—
201#127—2691no—
202#127—2691no—
203#127C2×D26911yescharacteristic
204#125—2691no—
205#125—2691no—
206C22⋊Q8—5381no—
207C22⋊Q8—5381no—
208C22⋊Q8—5381no—
209#121—5381no—
210#121—5381no—
211#121—5381no—
212C4×Q8—2691no—
213C4×D4—2691no—
214C4×D4—2691no—
215C4×D4—2691no—
216C4×D4—2691no—
217C4×D4—2691no—
218C4×D4C2×D26911yescharacteristic
219C2×C4⋊C4—5381no—
220#107—2691no—
221#106—2691no—
222#106—2691no—
223C4⋊C8—2691no—
224C4⋊C8—2691no—
225C4⋊C8C2×D26911yescharacteristic
226#102—2691no—
227#102—2691no—
228#102—2691no—
229#102—2691no—
230#102—2691no—
231#102—2691no—
232#102—2691no—
233#102—2691no—
234#102C2×D26911yescharacteristic
235#102C2×D26911yescharacteristic
236#97—2691no—
237#97—2691no—
238C4×C8—2691no—
239#41—10764no—
240C2×Q8—2691no—
241C2×Q8—5381no—
242C2×D4—21no—
243C2×D4—21no—
244C2×D4—2691no—
245C2×D4—5381no—
246C2×D4—5381no—
247C2×D4—5381no—
248C2×D4—5381no—
249C2×D4C22×D26911yescharacteristic
250C2×D4C22×D26911yescharacteristic
251C2×D4C22×D26911yescharacteristic
252C22×C4—21no—
253C22×C4—5381no—
254C22×C4—5381no—
255C22×C4—5381no—
256C22×C4—5381no—
257C22×C4—5381no—
258D8—22no—
259D8—22no—
260D8—5382no—
261C2×C8—2691no—
262C2×C8—2691no—
263C2×C8C22×D26911yescharacteristic
264C2×C8C22×D26911yescharacteristic
265C4⋊C4—2691no—
266C4⋊C4—2691no—
267C4⋊C4—2691no—
268C4⋊C4—2691no—
269C4⋊C4—2691no—
270C4⋊C4—2691no—
271C4⋊C4—5381no—
272C4⋊C4—5381no—
273C4⋊C4—5381no—
274C4⋊C4—5381no—
275C4⋊C4—5381no—
276C4⋊C4C22×D26911yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—5381no—
279C22⋊C4—5381no—
280C22⋊C4—5381no—
281C22⋊C4—5381no—
282C22⋊C4—5381no—
283C42—2691no—
284C42—2691no—
285C42C22×D26911yescharacteristic
286C23—21no—
287C23—21no—
288C23—21no—
289C23—5381no—
290Q8—5382no—
291Q8—21521no—
292D4—21no—
293D4—21no—
294D4—21no—
295D4—21no—
296D4—21no—
297D4—42no—
298D4—81no—
299D4—5381no—
300D4—5381no—
301D4—10762no—
302D4—10762no—
303D4—21521no—
304D4—21521no—
305D4#1686440112yescomplemented
306C2×C4—21no—
307C2×C4—81no—
308C2×C4—2691no—
309C2×C4—2691no—
310C2×C4—2691no—
311C2×C4—2691no—
312C2×C4—5381no—
313C2×C4—5381no—
314C2×C4—5381no—
315C2×C4—10762no—
316C2×C4—10762no—
317C2×C4—10762no—
318C2×C4—10762no—
319C2×C4—21521no—
320C2×C4D4×D26911yescharacteristic
321C2×C4D4×D26911yescharacteristic
322C2×C4C23×D26911yescharacteristic
323C8—21no—
324C8—21no—
325C8—5381no—
326C8—5381no—
327C22—22no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—10761no—
337C22—10761no—
338C22—10761no—
339C22C2×D4×D26911yescharacteristic
340C4—21no—
341C4—21no—
342C4—41no—
343C4—2692no—
344C4—5381no—
345C4—5381no—
346C4—5381no—
347C4—10761no—
348C4—10761no—
349C4—10761no—
350C4C2×#1686440111yescharacteristic
351C4#2257550011yescharacteristic
352C2—42no—
353C2—81no—
354C2—81no—
355C2—21521no—
356C2#3177126111yescharacteristic
357C2AGL(1,ℤ/8)×D26911yescharacteristic
358C2#3177140611yescharacteristic
subgroupG/H
centerC22C2×D4×D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#459×C269C2
socleC22×C269C22×D4
hypercenter#459D269
hypocenterC269#3366
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #31771314C2semidirect
2. #31771275C2semidirect
3. #31770969C2semidirect
4. #31770968C2semidirect
5. #31770950C2semidirect
6. #31770906C2semidirect
7. #31770903C2semidirect
8. #31770893C2semidirect
9. #31770798C2semidirect
10. #31770798C2semidirect
11. #31770734C2semidirect
12. #31770717C2semidirect
13. #31770715C2semidirect
14. D8×Dic269C2semidirect
15. #459×C269C2semidirect
139. D4×C269#41semidirect
179. C269#3366semidirect
191. #459D269semidirect
305. D4#16864401semidirect

Maximal subgroups

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

subgroupindex
#317713142
#317712752
#317709692
#317709682
#317709502
#317709062
#317709032
#317708932
#317707982
#317707342
#317707172
#317707152
D8×Dic2692
#459×C2692
#3366269