Finite Group Databasebeta

← #46822350

Subgroups — #46822350

Order 34432.

346 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31771226C211yesmaximal, characteristic, complemented
2#31770895C211yesmaximal, characteristic, complemented
3#31770892C211yesmaximal, characteristic, complemented
4#31770890C211yesmaximal, characteristic, complemented
5#31770887C211yesmaximal, characteristic, complemented
6#31770861C211yesmaximal, characteristic, complemented
7#31770856C211yesmaximal, characteristic
8#31770836C211yesmaximal, characteristic, complemented
9#31770832C211yesmaximal, characteristic, complemented
10#31770827C211yesmaximal, characteristic, complemented
11#31770824C211yesmaximal, characteristic, complemented
12#31770820C211yesmaximal, characteristic, complemented
13#31770817C211yesmaximal, characteristic, complemented
14#31770632C211yesmaximal, characteristic, complemented
15#542×C269C211yesmaximal, characteristic, complemented
16C2×#16864392C2211yescharacteristic
17C2×#16864390C2211yescharacteristic
18C2×#16864389C2211yescharacteristic
19C2×#16864387C2211yescharacteristic
20C2×#16864386C2211yescharacteristic
21C22×#14524130C2211yescharacteristic
22#22575453C2211yescharacteristic
23#22575448—21no—
24#22575441C2211yescharacteristic
25#22575439—21no—
26#22575435—21no—
27#22575432C2211yescharacteristic
28#22575431—21no—
29#22575427C2211yescharacteristic
30C4×Dic538C2211yescharacteristic
31C4×D1076C2211yescharacteristic
32#22575384C2211yescharacteristic
33#22575384C2211yescharacteristic
34#22575384C2211yescharacteristic
35#22575384C2211yescharacteristic
36C4⋊#14524130C2211yescharacteristic
37C4⋊#14524130C2211yescharacteristic
38C4⋊#14524130C2211yescharacteristic
39C4⋊#14524130C2211yescharacteristic
40#22575377C2211yescharacteristic
41#22575377C2211yescharacteristic
42#22575376C2211yescharacteristic
43#22575376C2211yescharacteristic
44#22575374C2211yescharacteristic
45#22575374C2211yescharacteristic
46#22575373C2211yescharacteristic
47#22575373C2211yescharacteristic
48C4⋊Q8×C269C2211yescharacteristic
49#126×C269—21no—
50#124×C269—21no—
51#124×C269C2211yescharacteristic
52#123×C269—21no—
53C22⋊Q8×C269—21no—
54C22⋊Q8×C269C2211yescharacteristic
55#121×C269C2211yescharacteristic
56C4×Q8×C269C2211yescharacteristic
57C4×D4×C269C2211yescharacteristic
58#117×C269C2211yescharacteristic
59C2×Dic538—21no—
60C2×Dic538C2311yescharacteristic
61C2×D1076C2311yescharacteristic
62C2×C22⋊D269—21no—
63C2×C4×D269—21no—
64#16864392—41no—
65#16864390—41no—
66#16864389—41no—
67#16864387—41no—
68#16864386—41no—
69C2×#14524130—41no—
70C2×#14524130C2311yescharacteristic
71C2×#14524130C2311yescharacteristic
72C2×#14524130C2311yescharacteristic
73C2×#14524130C2311yescharacteristic
74C4⋊Dic269—21no—
75C4⋊Dic269C2311yescharacteristic
76C4⋊Dic269C2311yescharacteristic
77#16864381—21no—
78#16864381—21no—
79C22⋊Dic269—21no—
80#16864379—21no—
81#16864379—21no—
82#16864379—21no—
83#16864379—21no—
84C4×Dic269—21no—
85C2×Q8×C269—21no—
86C2×Q8×C269C2311yescharacteristic
87C2×D4×C269—21no—
88C2×D4×C269C2311yescharacteristic
89C22×C4×C269—21no—
90C22×C4×C269C2311yescharacteristic
91C4⋊C4×C269—21no—
92C4⋊C4×C269—21no—
93C4⋊C4×C269—21no—
94C4⋊C4×C269D411yescharacteristic
95C4⋊C4×C269D411yescharacteristic
96C4⋊C4×C269C2311yescharacteristic
97C4⋊C4×C269C2311yescharacteristic
98C22⋊C4×C269—21no—
99C22⋊C4×C269—21no—
100C22⋊C4×C269—21no—
101C22⋊C4×C269—21no—
102C22⋊C4×C269—21no—
103C22⋊C4×C269D411yescharacteristic
104C22⋊C4×C269D411yescharacteristic
105C42×C269—21no—
106C42×C269C2311yescharacteristic
107C42×C269C2311yescharacteristic
108C22×D269—21no—
109Dic538—21no—
110Dic538—21no—
111Dic538—81no—
112D1076—21no—
113D1076—21no—
114C22⋊D269—81no—
115C2×Dic269—21no—
116C2×Dic269—21no—
117C2×Dic269—21no—
118C4×D269—81no—
119#14524130—21no—
120#14524130—21no—
121#14524130—21no—
122#14524130—21no—
123C23×C269—21no—
124C23×C269C2×D411yescharacteristic
125Q8×C269—21no—
126Q8×C269—21no—
127Q8×C269—81no—
128D4×C269—21no—
129D4×C269—21no—
130D4×C269—81no—
131C2×C4×C269—21no—
132C2×C4×C269—21no—
133C2×C4×C269—21no—
134C2×C4×C269—21no—
135C2×C4×C269—21no—
136C2×C4×C269—81no—
137C2×C4×C269C2×D411yescharacteristic
138C2×C4×C269C2×D411yescharacteristic
139C2×C4×C269C2×D411yescharacteristic
140C2×C4×C269C2×D411yescharacteristic
141C2×C4×C269C2×D411yescharacteristic
142C2×C4×C269C2411yescharacteristic
143C22×C269—21no—
144C22×C269—21no—
145C22×C269—21no—
146C22×C269—41no—
147C22×C269—41no—
148C22×C269—41no—
149C22×C269C22×D411yescharacteristic
150C2×D269—41no—
151C2×D269—41no—
152C2×D269—41no—
153C4×C269—21no—
154C4×C269—21no—
155C4×C269—21no—
156C4×C269—21no—
157C4×C269—21no—
158C4×C269—41no—
159C4×C269—41no—
160C4×C269—41no—
161C4×C269H(5,𝔽2)11yescharacteristic
162C4×C2692−1+411yescharacteristic
163Dic269—41no—
164Dic269—41no—
165Dic269—41no—
166C2×C269—41no—
167C2×C269—81no—
168C2×C269#53711yescharacteristic
169C2×C269#57711yescharacteristic
170C2×C269#57711yescharacteristic
171D269—81no—
172C269#326311yescharacteristic, complemented, Sylow
173#3263—2691nomaximal, Sylow
174#542—2691no—
175#542D26911yescharacteristic, complemented
176#476—2691no—
177#476—2691no—
178#475—2691no—
179#475—2691no—
180#470—2691no—
181#469—2691no—
182#465—2691no—
183#465—2691no—
184#464—2691no—
185#464—2691no—
186#463—2691no—
187#463—2691no—
188#424—2691no—
189C2×Q16—2691no—
190C2×SD16—2691no—
191C2×SD16—2691no—
192C2×D8—2691no—
193C2×M16—2691no—
194C22×C8—2691no—
195C4⋊Q8—2691no—
196C4⋊Q8C2×D26911yescharacteristic
197#126—21no—
198#126—5381no—
199#124—21no—
200#124—2691no—
201#124—5381no—
202#124C2×D26911yescharacteristic
203#123—21no—
204#123—5381no—
205C22⋊Q8—21no—
206C22⋊Q8—2691no—
207C22⋊Q8—5381no—
208C22⋊Q8C2×D26911yescharacteristic
209#121—2691no—
210#121C2×D26911yescharacteristic
211C4×Q8—2691no—
212C4×Q8C2×D26911yescharacteristic
213C4×D4—2691no—
214C4×D4C2×D26911yescharacteristic
215#117C2×D26911yescharacteristic
216#106—2691no—
217#106—2691no—
218#106—2691no—
219#106—2691no—
220C4⋊C8—2691no—
221C4⋊C8—2691no—
222C4⋊C8—2691no—
223C4⋊C8—2691no—
224#103—2691no—
225#103—2691no—
226#103—2691no—
227#103—2691no—
228#102—2691no—
229#102—2691no—
230#102—2691no—
231#102—2691no—
232C2×Q8—21no—
233C2×Q8—2691no—
234C2×Q8—5381no—
235C2×Q8C22×D26911yescharacteristic
236C2×D4—21no—
237C2×D4—2691no—
238C2×D4—5381no—
239C2×D4C22×D26911yescharacteristic
240C22×C4—21no—
241C22×C4—5381no—
242C22×C4C22×D26911yescharacteristic
243Q16—10761no—
244SD16—10761no—
245SD16—10761no—
246D8—10761no—
247M16—10761no—
248C2×C8—2691no—
249C2×C8—2691no—
250C2×C8—2691no—
251C2×C8—2691no—
252C2×C8—10761no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—2691no—
257C4⋊C4—2691no—
258C4⋊C4—5381no—
259C4⋊C4—5381no—
260C4⋊C4—5381no—
261C4⋊C4C22⋊D26911yescharacteristic
262C4⋊C4C22⋊D26911yescharacteristic
263C4⋊C4C22×D26911yescharacteristic
264C4⋊C4C22×D26911yescharacteristic
265C22⋊C4—21no—
266C22⋊C4—21no—
267C22⋊C4—21no—
268C22⋊C4—21no—
269C22⋊C4—21no—
270C22⋊C4—5381no—
271C22⋊C4—5381no—
272C22⋊C4—5381no—
273C22⋊C4—5381no—
274C22⋊C4—5381no—
275C22⋊C4C22⋊D26911yescharacteristic
276C22⋊C4C22⋊D26911yescharacteristic
277C42—21no—
278C42—5381no—
279C42C22×D26911yescharacteristic
280C42C22×D26911yescharacteristic
281C23—21no—
282C23—5381no—
283C23C2×C22⋊D26911yescharacteristic
284Q8—21no—
285Q8—21no—
286Q8—81no—
287Q8—5381no—
288Q8—5381no—
289Q8—21521no—
290D4—21no—
291D4—21no—
292D4—81no—
293D4—5381no—
294D4—5381no—
295D4—21521no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—81no—
302C2×C4—5381no—
303C2×C4—5381no—
304C2×C4—5381no—
305C2×C4—21521no—
306C2×C4C2×C22⋊D26911yescharacteristic
307C2×C4C2×C22⋊D26911yescharacteristic
308C2×C4C2×C22⋊D26911yescharacteristic
309C2×C4C2×C22⋊D26911yescharacteristic
310C2×C4C2×C22⋊D26911yescharacteristic
311C2×C4C23×D26911yescharacteristic
312C8—5381no—
313C8—5381no—
314C8—5381no—
315C8—5381no—
316C22—21no—
317C22—21no—
318C22—21no—
319C22—41no—
320C22—41no—
321C22—41no—
322C22—10761no—
323C22—10761no—
324C22—10761no—
325C22C22×C22⋊D26911yescharacteristic
326C4—21no—
327C4—21no—
328C4—21no—
329C4—21no—
330C4—21no—
331C4—41no—
332C4—41no—
333C4—41no—
334C4—10761no—
335C4—10761no—
336C4—10761no—
337C4#2257549911yescharacteristic
338C4#2257550011yescharacteristic
339C2—41no—
340C2—81no—
341C2—21521no—
342C2#3177118311yescharacteristic
343C2#3177141311yescharacteristic
344C2#3177141611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#542×C269C2
socleC22×C269C22×D4
prime radical#31770856C2
hypercenter#542D269
hypocenterC269#3263
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ #117 ◁ #542

Complements

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

NH ≅ G/Ntype
1. #31771226C2semidirect
2. #31770895C2semidirect
3. #31770892C2semidirect
4. #31770890C2semidirect
5. #31770887C2semidirect
6. #31770861C2semidirect
8. #31770836C2semidirect
9. #31770832C2semidirect
10. #31770827C2semidirect
11. #31770824C2semidirect
12. #31770820C2semidirect
13. #31770817C2semidirect
14. #31770632C2semidirect
15. #542×C269C2semidirect
172. C269#3263semidirect
175. #542D269semidirect

Maximal subgroups

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

subgroupindex
#317712262
#317708952
#317708922
#317708902
#317708872
#317708612
#317708562
#317708362
#317708322
#317708272
#317708242
#317708202
#317708172
#317706322
#542×C2692
#3263269