Finite Group Databasebeta

← #46823589

Subgroups — #46823589

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#31771311C211yesmaximal, characteristic, complemented
2#31771275C211yesmaximal, characteristic, complemented
3#31770968C211yesmaximal, characteristic, complemented
4#31770950C211yesmaximal, characteristic, complemented
5#31770907C211yesmaximal, characteristic, complemented
6#31770902C211yesmaximal, characteristic, complemented
7#31770893C211yesmaximal, characteristic, complemented
8#31770799C211yesmaximal, characteristic, complemented
9#31770799C211yesmaximal, characteristic, complemented
10#31770797C211yesmaximal, characteristic, complemented
11#31770733C211yesmaximal, characteristic, complemented
12#31770718C211yesmaximal, characteristic, complemented
13#31770714C211yesmaximal, characteristic, complemented
14#31770685C211yesmaximal, characteristic, complemented
15#490×C269C211yesmaximal, characteristic, complemented
16C2×#16864401—21no—
17C2×D2152C2211yescharacteristic
18C2×#16864387C2211yescharacteristic
19C2×#16864387C2211yescharacteristic
20#22575452C2211yescharacteristic
21#22575449C2211yescharacteristic
22#22575449C2211yescharacteristic
23#22575444C2211yescharacteristic
24#22575433—21no—
25#22575431—21no—
26#22575431—21no—
27#22575425—21no—
28#22575425—21no—
29#22575424—21no—
30C4×Dic538C2211yescharacteristic
31C4×D1076C2211yescharacteristic
32C4×D1076C2211yescharacteristic
33D4×Dic269C2211yescharacteristic
34D4×Dic269C2211yescharacteristic
35#22575415C2211yescharacteristic
36#22575415C2211yescharacteristic
37C4⋊C4×D269—21no—
38#22575386C2211yescharacteristic
39#22575385C2211yescharacteristic
40#22575384C2211yescharacteristic
41C4⋊#14524130C2211yescharacteristic
42#22575382C2211yescharacteristic
43#22575382C2211yescharacteristic
44#22575375C2211yescharacteristic
45#22575375C2211yescharacteristic
46#22575374C2211yescharacteristic
47#22575374C2211yescharacteristic
48#22575373C2211yescharacteristic
49#22575373C2211yescharacteristic
50#22575363C2211yescharacteristic
51C8×Dic269C2211yescharacteristic
52#127×C269C2211yescharacteristic
53#125×C269C2211yescharacteristic
54#102×C269C2211yescharacteristic
55#102×C269C2211yescharacteristic
56#102×C269C2211yescharacteristic
57#102×C269C2211yescharacteristic
58#97×C269C2211yescharacteristic
59#16864401—44no—
60C2×Dic538—21no—
61C2×Dic538D411yescharacteristic
62C2×D1076C2311yescharacteristic
63C2×D1076C2311yescharacteristic
64C2×C22⋊D269—21no—
65C2×C22⋊D269—21no—
66C2×C22⋊D269—21no—
67C2×C22⋊D269—21no—
68C22×Dic269—21no—
69C22×Dic269—21no—
70C2×C4×D269—21no—
71C2×C4×D269—21no—
72C2×C4×D269—21no—
73C2×C4×D269—21no—
74D2152—22no—
75#16864387—22no—
76#16864387—22no—
77C2×#14524130C2311yescharacteristic
78C2×#14524130C2311yescharacteristic
79C4⋊Dic269—21no—
80C4⋊Dic269D411yescharacteristic
81C4⋊Dic269C2311yescharacteristic
82C4⋊Dic269C2311yescharacteristic
83#16864381—21no—
84#16864381—21no—
85#16864381D411yescharacteristic
86#16864381D411yescharacteristic
87C22⋊Dic269—21no—
88C22⋊Dic269—21no—
89#16864379—21no—
90#16864379—21no—
91#16864379—21no—
92#16864379—21no—
93C4×Dic269C2311yescharacteristic
94C4×Dic269C2311yescharacteristic
95C2×D4×C269—21no—
96C2×D4×C269—21no—
97C2×D4×C269C2311yescharacteristic
98C2×D4×C269C2311yescharacteristic
99C2×C8×C269C2311yescharacteristic
100C2×C8×C269C2311yescharacteristic
101C4⋊C4×C269—21no—
102C4⋊C4×C269—21no—
103C4⋊C4×C269C2311yescharacteristic
104C4⋊C4×C269C2311yescharacteristic
105C42×C269C2311yescharacteristic
106C22×D269—21no—
107C22×D269—21no—
108Dic538—22no—
109Dic538—81no—
110D1076—21no—
111D1076—21no—
112D1076—21no—
113D1076#4112yescomplemented
114C22⋊D269—42no—
115C22⋊D269—42no—
116C22⋊D269—81no—
117C22⋊D269—81no—
118C2×Dic269—21no—
119C2×Dic269—21no—
120C2×Dic269—42no—
121C2×Dic269—42no—
122C2×Dic269C2×D411yescharacteristic
123C2×Dic269C2×D411yescharacteristic
124C2×Dic269C2×D411yescharacteristic
125C2×Dic269C2×D411yescharacteristic
126C4×D269—42no—
127C4×D269—42no—
128C4×D269—81no—
129C4×D269—81no—
130#14524130—21no—
131#14524130—21no—
132C23×C269—21no—
133C23×C269—21no—
134D4×C269—21no—
135D4×C269—21no—
136D4×C269—21no—
137D4×C269—21no—
138D4×C269—42no—
139D4×C269—81no—
140C2×C4×C269—21no—
141C2×C4×C269—21no—
142C2×C4×C269C2×D411yescharacteristic
143C2×C4×C269C2×D411yescharacteristic
144C2×C4×C269C2411yescharacteristic
145C8×C269—21no—
146C8×C269—21no—
147C22×C269—41no—
148C22×C269—41no—
149C22×C269—41no—
150C22×C269—41no—
151C22×C269—41no—
152C22×C269—41no—
153C22×C269C22×D411yescharacteristic
154C2×D269—22no—
155C2×D269—41no—
156C2×D269—41no—
157C2×D269—41no—
158C2×D269—41no—
159C2×D269—41no—
160C4×C269—21no—
161C4×C269—21no—
162C4×C269—41no—
163C4×C269—41no—
164C4×C269C2×#4111yescharacteristic
165C4×C2692−1+411yescharacteristic
166Dic269—21no—
167Dic269—21no—
168Dic269—21no—
169Dic269—41no—
170Dic269—41no—
171Dic269AGL(1,ℤ/8)12yes—
172C2×C269—81no—
173C2×C269—81no—
174C2×C269#54811yescharacteristic
175C2×C269C2×AGL(1,ℤ/8)11yescharacteristic
176C2×C269#57611yescharacteristic
177D269—42no—
178D269—81no—
179C269#336611yescharacteristic, complemented, Sylow
180#3366—2691nomaximal, Sylow
181#554—2691no—
182#550—2691no—
183#490—2691no—
184#490D26911yescharacteristic, complemented
185#486—2691no—
186#478—2691no—
187#478—2691no—
188#476—2691no—
189#459—2691no—
190#459—2691no—
191#459—2691no—
192#446—2691no—
193#442—2691no—
194#442—2691no—
195C4×D8—2691no—
196C2×#41—5381no—
197C2×D8—2691no—
198C2×D8—2691no—
199C2×D8—2691no—
200C4⋊Q8—2691no—
201#127—2691no—
202#127—2691no—
203#127C2×D26911yescharacteristic
204#125—2691no—
205#125C2×D26911yescharacteristic
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×D4—2691no—
219C2×C4⋊C4—5381no—
220#107—2691no—
221#106—2691no—
222#106—2691no—
223C4⋊C8—2691no—
224C4⋊C8—2691no—
225C4⋊C8—2691no—
226#102—2691no—
227#102—2691no—
228#102—2691no—
229#102—2691no—
230#102—2691no—
231#102—2691no—
232#102C2×D26911yescharacteristic
233#102C2×D26911yescharacteristic
234#102C2×D26911yescharacteristic
235#102C2×D26911yescharacteristic
236#97—2691no—
237#97C2×D26911yescharacteristic
238C4×C8—2691no—
239#41—10764no—
240C2×Q8—2691no—
241C2×Q8—5381no—
242C2×D4—21no—
243C2×D4—21no—
244C2×D4—2691no—
245C2×D4—2691no—
246C2×D4—5381no—
247C2×D4—5381no—
248C2×D4—5381no—
249C2×D4—5381no—
250C2×D4C22×D26911yescharacteristic
251C2×D4C22×D26911yescharacteristic
252C22×C4—5381no—
253C22×C4—5381no—
254C22×C4—5381no—
255C22×C4—5381no—
256C22×C4—5381no—
257C22×C4—5381no—
258D8—5382no—
259D8—5382no—
260D8—5382no—
261C2×C8—2691no—
262C2×C8—2691no—
263C2×C8C22×D26911yescharacteristic
264C2×C8C22×D26911yescharacteristic
265C4⋊C4—21no—
266C4⋊C4—21no—
267C4⋊C4—2691no—
268C4⋊C4—2691no—
269C4⋊C4—2691no—
270C4⋊C4—2691no—
271C4⋊C4—2691no—
272C4⋊C4—5381no—
273C4⋊C4—5381no—
274C4⋊C4—5381no—
275C4⋊C4C22×D26911yescharacteristic
276C4⋊C4C22×D26911yescharacteristic
277C22⋊C4—5381no—
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—5381no—
289C23—5381no—
290Q8—5382no—
291Q8—21521no—
292D4—21no—
293D4—21no—
294D4—21no—
295D4—21no—
296D4—42no—
297D4—81no—
298D4—2692no—
299D4—5381no—
300D4—5381no—
301D4—5381no—
302D4—10762no—
303D4—10762no—
304D4—21521no—
305D4—21521no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—2691no—
309C2×C4—2691no—
310C2×C4—2691no—
311C2×C4—2691no—
312C2×C4—5381no—
313C2×C4—5381no—
314C2×C4—10762no—
315C2×C4—10762no—
316C2×C4—10762no—
317C2×C4—10762no—
318C2×C4—21521no—
319C2×C4—21521no—
320C2×C4D4×D26911yescharacteristic
321C2×C4D4×D26911yescharacteristic
322C2×C4C23×D26911yescharacteristic
323C8—21no—
324C8—21no—
325C8—5381no—
326C8—5381no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—5382no—
334C22—10761no—
335C22—10761no—
336C22—10761no—
337C22—10761no—
338C22—10761no—
339C22C2×D4×D26911yescharacteristic
340C4—21no—
341C4—21no—
342C4—41no—
343C4—41no—
344C4—2692no—
345C4—5381no—
346C4—5381no—
347C4—5381no—
348C4—10761no—
349C4—10761no—
350C4#41×D26911yescharacteristic
351C4#2257550011yescharacteristic
352C2—81no—
353C2—81no—
354C2—10762no—
355C2—21521no—
356C2#3177126311yescharacteristic
357C2AGL(1,ℤ/8)×D26911yescharacteristic
358C2#3177140911yescharacteristic
subgroupG/H
centerC22C2×D4×D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#490×C269C2
socleC22×C269C22×D4
hypercenter#490D269
hypocenterC269#3366
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
1. #31771311C2semidirect
2. #31771275C2semidirect
3. #31770968C2semidirect
4. #31770950C2semidirect
5. #31770907C2semidirect
6. #31770902C2semidirect
7. #31770893C2semidirect
8. #31770799C2semidirect
9. #31770799C2semidirect
10. #31770797C2semidirect
11. #31770733C2semidirect
12. #31770718C2semidirect
13. #31770714C2semidirect
14. #31770685C2semidirect
15. #490×C269C2semidirect
113. D1076#41semidirect
179. C269#3366semidirect
184. #490D269semidirect

Maximal subgroups

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

subgroupindex
#317713112
#317712752
#317709682
#317709502
#317709072
#317709022
#317708932
#317707992
#317707972
#317707332
#317707182
#317707142
#317706852
#490×C2692
#3366269