Finite Group Databasebeta

← #46823491

Subgroups — #46823491

Order 34432.

360 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31771303C211yesmaximal, characteristic, complemented
2#31771302C211yesmaximal, characteristic, complemented
3#31771006C211yesmaximal, characteristic, complemented
4#31770930C211yesmaximal, characteristic, complemented
5#31770927C211yesmaximal, characteristic, complemented
6#31770920C211yesmaximal, characteristic, complemented
7#31770908C211yesmaximal, characteristic, complemented
8#31770907C211yesmaximal, characteristic, complemented
9#31770857C211yesmaximal, characteristic, complemented
10#31770856C211yesmaximal, characteristic, complemented
11#31770685C211yesmaximal, characteristic, complemented
12#31770680C211yesmaximal, characteristic, complemented
13#31770646C211yesmaximal, characteristic, complemented
14#31770645C211yesmaximal, characteristic, complemented
15#480×C269C211yesmaximal, characteristic, complemented
16C2×#16864387C2211yescharacteristic
17C2×#16864386C2211yescharacteristic
18C2×#16864385C2211yescharacteristic
19#22575448—21no—
20#22575446—21no—
21#22575444C2211yescharacteristic
22#22575444C2211yescharacteristic
23#22575438—21no—
24#22575434—21no—
25#22575428C2211yescharacteristic
26#22575427—21no—
27#22575427C2211yescharacteristic
28#22575424—21no—
29#22575424C2211yescharacteristic
30D4×Dic269C2211yescharacteristic
31#22575415C2211yescharacteristic
32C4×C22⋊D269—21no—
33C4×C22⋊D269C2211yescharacteristic
34#22575413—21no—
35#22575412C2211yescharacteristic
36#22575411C2211yescharacteristic
37C4⋊C4×D269C2211yescharacteristic
38#22575387C2211yescharacteristic
39#22575386C2211yescharacteristic
40#22575386C2211yescharacteristic
41#22575385C2211yescharacteristic
42#22575384C2211yescharacteristic
43#22575384C2211yescharacteristic
44#22575384C2211yescharacteristic
45#22575382C2211yescharacteristic
46#22575375C2211yescharacteristic
47#22575375C2211yescharacteristic
48#22575374C2211yescharacteristic
49#22575373C2211yescharacteristic
50#22575365C2211yescharacteristic
51C8×Dic269C2211yescharacteristic
52#121×C269C2211yescharacteristic
53C2×C4⋊C4×C269C2211yescharacteristic
54#107×C269C2211yescharacteristic
55#107×C269C2211yescharacteristic
56#102×C269C2211yescharacteristic
57#102×C269C2211yescharacteristic
58C22⋊C8×C269C2211yescharacteristic
59C2×D1076—21no—
60C2×D1076C2311yescharacteristic
61C2×C22⋊D269—21no—
62C2×C22⋊D269—21no—
63C2×C22⋊D269D411yescharacteristic
64C22×Dic269—21no—
65C2×C4×D269—21no—
66C2×C4×D269—21no—
67C2×C4×D269C2311yescharacteristic
68#16864387—22no—
69#16864386—22no—
70#16864385—22no—
71C2×#14524130C2311yescharacteristic
72C2×#14524130C2311yescharacteristic
73C4⋊Dic269—21no—
74C4⋊Dic269—21no—
75C4⋊Dic269C2311yescharacteristic
76C4⋊Dic269C2311yescharacteristic
77C4⋊Dic269C2311yescharacteristic
78#16864381—21no—
79#16864381—21no—
80#16864381—21no—
81#16864381D411yescharacteristic
82C22⋊Dic269—21no—
83C22⋊Dic269—21no—
84C22⋊Dic269—21no—
85C22⋊Dic269D411yescharacteristic
86#16864379—21no—
87#16864379—21no—
88#16864379—21no—
89#16864379—21no—
90#16864379D411yescharacteristic
91C4×Dic269—21no—
92C4×Dic269—21no—
93C4×Dic269C2311yescharacteristic
94C2×D4×C269—21no—
95C2×D4×C269C2311yescharacteristic
96C22×C4×C269—21no—
97C22×C4×C269C2311yescharacteristic
98C2×C8×C269C2311yescharacteristic
99C2×C8×C269C2311yescharacteristic
100C4⋊C4×C269—21no—
101C4⋊C4×C269C2311yescharacteristic
102C4⋊C4×C269C2311yescharacteristic
103C4⋊C4×C269C2311yescharacteristic
104C22⋊C4×C269—21no—
105C22×D269—21no—
106C22×D269C2×D411yescharacteristic
107D1076—21no—
108D1076—21no—
109D1076—81no—
110C22⋊D269—41no—
111C22⋊D269—42no—
112C22⋊D269—42no—
113C2×Dic269—21no—
114C2×Dic269—21no—
115C2×Dic269—21no—
116C2×Dic269—81no—
117C2×Dic269C2×D411yescharacteristic
118C2×Dic269C2×D411yescharacteristic
119C2×Dic269C2×D411yescharacteristic
120C4×D269—21no—
121C4×D269—21no—
122C4×D269—81no—
123C4×D269—81no—
124#14524130—21no—
125#14524130#4112yes—
126C23×C269—21no—
127C23×C269C2×D411yescharacteristic
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×C269C2411yescharacteristic
139C8×C269—21no—
140C8×C269—21no—
141C22×C269—21no—
142C22×C269—21no—
143C22×C269—21no—
144C22×C269—41no—
145C22×C269—41no—
146C22×C269—41no—
147C22×C269C22×D411yescharacteristic
148C2×D269—21no—
149C2×D269—21no—
150C2×D269—21no—
151C2×D269—41no—
152C2×D269—41no—
153C2×D269—41no—
154C4×C269—21no—
155C4×C269—41no—
156C4×C269—41no—
157C4×C269—41no—
158C4×C269C2×#4111yescharacteristic
159C4×C2692−1+411yescharacteristic
160Dic269—21no—
161Dic269—21no—
162Dic269—21no—
163Dic269—41no—
164Dic269—41no—
165Dic269—41no—
166C2×C269—41no—
167C2×C269—81no—
168C2×C269#54711yescharacteristic
169C2×C269#57511yescharacteristic
170C2×C269#57611yescharacteristic
171D269—41no—
172D269—81no—
173C269#335511yescharacteristic, complemented, Sylow
174#3355—2691nomaximal, Sylow
175#553—2691no—
176#553—2691no—
177#499—2691no—
178#482—2691no—
179#482—2691no—
180#480—2691no—
181#480D26911yescharacteristic, complemented
182#478—2691no—
183#478—2691no—
184#469—2691no—
185#469—2691no—
186C4×D8—2691no—
187#436—2691no—
188#428—2691no—
189#428—2691no—
190C2×D8—2691no—
191C2×M16—2691no—
192C2×M16—2691no—
193#126—5381no—
194#126—5381no—
195#125—2691no—
196#125—2691no—
197#123—5381no—
198#123—5381no—
199#121—2691no—
200#121—2691no—
201#121—2691no—
202#121—5381no—
203#121—5381no—
204#121C2×D26911yescharacteristic
205C4×D4—2691no—
206C4×D4—2691no—
207C4×D4—2691no—
208C4×D4—5381no—
209C4×D4—5381no—
210#117—2691no—
211#117—2691no—
212C2×C4⋊C4—2691no—
213C2×C4⋊C4C2×D26911yescharacteristic
214#107—2691no—
215#107—2691no—
216#107—2691no—
217#107C2×D26911yescharacteristic
218#107C2×D26911yescharacteristic
219#106—2691no—
220#106—2691no—
221#106—2691no—
222#106—2691no—
223C4⋊C8—2691no—
224#102—2691no—
225#102—2691no—
226#102—2691no—
227#102—2691no—
228#102C2×D26911yescharacteristic
229#102C2×D26911yescharacteristic
230C22⋊C8—2691no—
231C22⋊C8C2×D26911yescharacteristic
232C4×C8—2691no—
233C2×D4—21no—
234C2×D4—2691no—
235C2×D4—2691no—
236C2×D4—5381no—
237C2×D4—5381no—
238C2×D4—5381no—
239C2×D4C22×D26911yescharacteristic
240C22×C4—21no—
241C22×C4—2691no—
242C22×C4—5381no—
243C22×C4—5381no—
244C22×C4—5381no—
245C22×C4C22×D26911yescharacteristic
246D8—5382no—
247M16—5382no—
248M16—5382no—
249C2×C8—2691no—
250C2×C8—2691no—
251C2×C8C22×D26911yescharacteristic
252C2×C8C22×D26911yescharacteristic
253C4⋊C4—21no—
254C4⋊C4—2691no—
255C4⋊C4—2691no—
256C4⋊C4—2691no—
257C4⋊C4—2691no—
258C4⋊C4—5381no—
259C4⋊C4—5381no—
260C4⋊C4—5381no—
261C4⋊C4—5381no—
262C4⋊C4—5381no—
263C4⋊C4C22×D26911yescharacteristic
264C4⋊C4C22×D26911yescharacteristic
265C4⋊C4C22×D26911yescharacteristic
266C22⋊C4—21no—
267C22⋊C4—2691no—
268C22⋊C4—2691no—
269C22⋊C4—5381no—
270C22⋊C4—5381no—
271C22⋊C4—5381no—
272C22⋊C4—5381no—
273C22⋊C4—5381no—
274C22⋊C4—5381no—
275C22⋊C4—5381no—
276C42—2691no—
277C42—5381no—
278C42—5381no—
279C23—21no—
280C23—2691no—
281C23—5381no—
282C23D4×D26911yescharacteristic
283D4—21no—
284D4—21no—
285D4—81no—
286D4—5381no—
287D4—5381no—
288D4—10761no—
289D4—10762no—
290D4—10762no—
291D4—21521no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—81no—
298C2×C4—2691no—
299C2×C4—2691no—
300C2×C4—2691no—
301C2×C4—5381no—
302C2×C4—5381no—
303C2×C4—5381no—
304C2×C4—5381no—
305C2×C4—5381no—
306C2×C4—21521no—
307C2×C4—21521no—
308C2×C4—21521no—
309C2×C4D4×D26911yescharacteristic
310C2×C4C23×D26911yescharacteristic
311C8—21no—
312C8—21no—
313C8—2692no—
314C8—5381no—
315C22—21no—
316C22—21no—
317C22—21no—
318C22—41no—
319C22—41no—
320C22—41no—
321C22—5381no—
322C22—5381no—
323C22—5381no—
324C22—10761no—
325C22—10761no—
326C22—10761no—
327C22C2×D4×D26911yescharacteristic
328C4—21no—
329C4—41no—
330C4—41no—
331C4—41no—
332C4—5381no—
333C4—5381no—
334C4—5381no—
335C4—10761no—
336C4—10761no—
337C4—10761no—
338C4#41×D26911yescharacteristic
339C4#2257550011yescharacteristic
340C2—41no—
341C2—81no—
342C2—10761no—
343C2—21521no—
344C2#3177125311yescharacteristic
345C2#3177140411yescharacteristic
346C2#3177140611yescharacteristic
subgroupG/H
centerC22C2×D4×D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#480×C269C2
socleC22×C269C22×D4
hypercenter#480D269
hypocenterC269#3355
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
1. #31771303C2semidirect
2. #31771302C2semidirect
3. #31771006C2semidirect
4. #31770930C2semidirect
5. #31770927C2semidirect
6. #31770920C2semidirect
7. #31770908C2semidirect
8. #31770907C2semidirect
9. #31770857C2semidirect
10. #31770856C2semidirect
11. #31770685C2semidirect
12. #31770680C2semidirect
13. #31770646C2semidirect
14. #31770645C2semidirect
15. #480×C269C2semidirect
173. C269#3355semidirect
181. #480D269semidirect

Maximal subgroups

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

subgroupindex
#317713032
#317713022
#317710062
#317709302
#317709272
#317709202
#317709082
#317709072
#317708572
#317708562
#317706852
#317706802
#317706462
#317706452
#480×C2692
#3355269