Finite Group Databasebeta

← #46820680

Subgroups — #46820680

Order 34432.

440 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31771161C211yesmaximal, characteristic, complemented
2C4×D4×D269C211yesmaximal, characteristic
3#31770906C211yesmaximal, characteristic, complemented
4#31770905C211yesmaximal, characteristic, complemented
5#31770902C211yesmaximal, characteristic, complemented
6#31770894C211yesmaximal, characteristic, complemented
7#31770893C211yesmaximal, characteristic, complemented
8#31770884C211yesmaximal, characteristic, complemented
9#31770883C211yesmaximal, characteristic, complemented
10#31770646C211yesmaximal, characteristic, complemented
11#31770644C211yesmaximal, characteristic, complemented
12#31770627C211yesmaximal, characteristic, complemented
13#31770608C211yesmaximal, characteristic
14#31770608C211yesmaximal, characteristic
15#478×C269C211yesmaximal, characteristic, complemented
16C2×D4×D269C2211yescharacteristic
17C22×C4×D269—21no—
18C2×#16864385C2211yescharacteristic
19C2×#16864385C2211yescharacteristic
20#22575452C2211yescharacteristic, complemented
21#22575452C2211yescharacteristic, complemented
22#22575445C2211yescharacteristic, complemented
23#22575431—21no—
24#22575431—21no—
25#22575418—21no—
26#22575418—21no—
27C4×D1076C2211yescharacteristic
28D4×Dic269C2211yescharacteristic
29#22575415C2211yescharacteristic
30C4×C22⋊D269—21no—
31#22575413—21no—
32#22575411C2211yescharacteristic
33#22575411C2211yescharacteristic
34C4⋊C4×D269C2211yescharacteristic
35C22⋊C4×D269—21no—
36C42×D269C2211yescharacteristic
37#22575387C2211yescharacteristic, complemented
38#22575386C2211yescharacteristic, complemented
39#22575386C2211yescharacteristic, complemented
40#22575385C2211yescharacteristic, complemented
41#22575384C2211yescharacteristic, complemented
42#22575384C2211yescharacteristic, complemented
43C4⋊#14524130C2211yescharacteristic, complemented
44#22575382C2211yescharacteristic, complemented
45#22575382C2211yescharacteristic, complemented
46#22575375C2211yescharacteristic
47#22575375C2211yescharacteristic
48#22575374C2211yescharacteristic
49#22575374C2211yescharacteristic
50#22575373C2211yescharacteristic
51#22575373C2211yescharacteristic
52#125×C269C2211yescharacteristic, complemented
53C4×D4×C269C2211yescharacteristic
54#107×C269C2211yescharacteristic, complemented
55#106×C269C2211yescharacteristic, complemented
56C4⋊C8×C269C2211yescharacteristic, complemented
57#102×C269C2211yescharacteristic
58#102×C269C2211yescharacteristic
59C23×D269—21no—
60C2×Dic538—21no—
61C2×Dic538—21no—
62C2×D1076C2311yescharacteristic
63C2×C22⋊D269—21no—
64D4×D269—22no—
65D4×D269Q814yescomplemented
66C22×Dic269—21no—
67C2×C4×D269—21no—
68C2×C4×D269—21no—
69C2×C4×D269—21no—
70C2×C4×D269—44no—
71C2×C4×D269D411yescharacteristic
72C2×C4×D269D411yescharacteristic
73C2×C4×D269C2311yescharacteristic
74#16864385—22no—
75#16864385—22no—
76C2×#14524130C2311yescharacteristic
77C2×#14524130C2311yescharacteristic
78C4⋊Dic269C2311yescharacteristic
79C4⋊Dic269C2311yescharacteristic
80C4⋊Dic269C2311yescharacteristic
81#16864381—21no—
82#16864381—21no—
83#16864381—21no—
84#16864381—21no—
85#16864381—21no—
86C22⋊Dic269—21no—
87#16864379—21no—
88#16864379—21no—
89#16864379—21no—
90#16864379—21no—
91C4×Dic269—21no—
92C4×Dic269—21no—
93C4×Dic269D411yescharacteristic
94C4×Dic269D411yescharacteristic
95C4×Dic269C2311yescharacteristic
96C2×D4×C269C2311yescharacteristic
97C22×C4×C269—21no—
98C2×C8×C269C2311yescharacteristic
99C2×C8×C269C2311yescharacteristic
100C4⋊C4×C269—21no—
101C4⋊C4×C269—21no—
102C4⋊C4×C269C2311yescharacteristic
103C4⋊C4×C269C2311yescharacteristic
104C4⋊C4×C269C2311yescharacteristic
105C22⋊C4×C269—21no—
106C42×C269C2311yescharacteristic
107C22×D269—21no—
108C22×D269—24no—
109C22×D269—42no—
110C22×D269—42no—
111C22×D269C2×D411yescharacteristic
112Dic538—42no—
113Dic538—42no—
114D1076—21no—
115D1076C2×Q812yes—
116C22⋊D269—24no—
117C2×Dic269—21no—
118C2×Dic269—21no—
119C2×Dic269—21no—
120C2×Dic269—42no—
121C2×Dic269C2×D411yescharacteristic
122C2×Dic269C2×D411yescharacteristic
123C2×Dic269C2×D411yescharacteristic
124C4×D269—22no—
125C4×D269—41no—
126C4×D269—42no—
127C4×D269—42no—
128C4×D269—42no—
129C4×D269C2×Q812yes—
130C4×D269#4112yes—
131#14524130—21no—
132#14524130—21no—
133C23×C269—21no—
134D4×C269—21no—
135D4×C269C2×Q812yes—
136C2×C4×C269—21no—
137C2×C4×C269—21no—
138C2×C4×C269—21no—
139C2×C4×C269—42no—
140C2×C4×C269C2×D411yescharacteristic
141C2×C4×C269C2×D411yescharacteristic
142C2×C4×C269C2411yescharacteristic
143C8×C269—21no—
144C8×C269—21no—
145C22×C269—22no—
146C22×C269—41no—
147C22×C269—41no—
148C22×C269C22×D411yescharacteristic
149C2×D269—21no—
150C2×D269—21no—
151C2×D269—22no—
152C2×D269—48no—
153C2×D269—41no—
154C2×D269—41no—
155C2×D269C22⋊Q812yes—
156C4×C269—21no—
157C4×C269—21no—
158C4×C269—41no—
159C4×C269—41no—
160C4×C269—41no—
161C4×C269C22×Q811yescharacteristic
162C4×C269C2×#4111yescharacteristic
163Dic269—21no—
164Dic269—41no—
165Dic269—41no—
166Dic269—41no—
167Dic269C22⋊Q812yes—
168Dic269AGL(1,ℤ/8)12yes—
169C2×C269—42no—
170C2×C269C2×C22⋊Q811yescharacteristic
171C2×C269C2×AGL(1,ℤ/8)11yescharacteristic
172C2×C269#57511yescharacteristic
173D269—22no—
174D269—42no—
175C269#307711yescharacteristic, complemented, Sylow
176#3077—2691nomaximal, Sylow
177#533—2691no—
178C2×C4×D4—2691no—
179#478—2691no—
180#478—2691no—
181#478—2691no—
182#478D26911yescharacteristic, complemented
183#476—2691no—
184#476—2691no—
185#474—2691no—
186#474—2691no—
187#428—2691no—
188#428—2691no—
189#423—2691no—
190#418—2691no—
191#418—2691no—
192C22×D4—2691no—
193C23×C4—5381no—
194C2×M16—2691no—
195C2×M16—2691no—
196C4⋊Q8—2691no—
197C4⋊Q8—2691no—
198#125—2691no—
199#125C2×D26911yescharacteristic, complemented
200C22⋊Q8—5381no—
201C22⋊Q8—5381no—
202C4×Q8—5381no—
203C4×Q8—5381no—
204C4×D4—2691no—
205C4×D4—2691no—
206C4×D4—2691no—
207C4×D4—5381no—
208C4×D4—5381no—
209C4×D4C2×D26911yescharacteristic
210#117—2691no—
211#117—2691no—
212C2×C4⋊C4—2691no—
213C2×C22⋊C4—5381no—
214C2×C42—2691no—
215#107—2691no—
216#107—2691no—
217#107—2691no—
218#107C2×D26911yescharacteristic, complemented
219#106—2691no—
220#106—2691no—
221#106—2691no—
222#106C2×D26911yescharacteristic, complemented
223C4⋊C8—2691no—
224C4⋊C8—2691no—
225C4⋊C8—2691no—
226C4⋊C8C2×D26911yescharacteristic, complemented
227#102—2691no—
228#102—2691no—
229#102—2691no—
230#102—2691no—
231#102—2691no—
232#102—2691no—
233#102C2×D26911yescharacteristic
234#102C2×D26911yescharacteristic
235C24—5381no—
236C2×Q8—5381no—
237C2×Q8—5381no—
238C2×D4—2694no—
239C2×D4—2691no—
240C2×D4—5382no—
241C2×D4—5381no—
242C2×D4C22×D26911yescharacteristic
243C22×C4—21no—
244C22×C4—2691no—
245C22×C4—2691no—
246C22×C4—2691no—
247C22×C4—5381no—
248C22×C4—5381no—
249C22×C4—5381no—
250C22×C4—5381no—
251C22×C4—10764no—
252M16—5382no—
253M16—5382no—
254C2×C8—2691no—
255C2×C8—2691no—
256C2×C8C22×D26911yescharacteristic
257C2×C8C22×D26911yescharacteristic
258C4⋊C4—21no—
259C4⋊C4—21no—
260C4⋊C4—2691no—
261C4⋊C4—2691no—
262C4⋊C4—2691no—
263C4⋊C4—5381no—
264C4⋊C4—5381no—
265C4⋊C4—5381no—
266C4⋊C4—5381no—
267C4⋊C4—5381no—
268C4⋊C4C22×D26911yescharacteristic
269C4⋊C4C22×D26911yescharacteristic
270C4⋊C4C22×D26911yescharacteristic
271C22⋊C4—21no—
272C22⋊C4—5381no—
273C22⋊C4—5381no—
274C22⋊C4—5381no—
275C22⋊C4—5381no—
276C22⋊C4—5381no—
277C42—2691no—
278C42—2691no—
279C42—2691no—
280C42—5381no—
281C42—5381no—
282C42C22×D26911yescharacteristic
283C23—21no—
284C23—2691no—
285C23—5384no—
286C23—5381no—
287C23—10762no—
288C23—10762no—
289Q8—10762no—
290Q8—10762no—
291D4—21no—
292D4—2692no—
293D4—5384no—
294D4—5381no—
295D4Q8×D26912yes—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—42no—
300C2×C4—2691no—
301C2×C4—2691no—
302C2×C4—2692no—
303C2×C4—2692no—
304C2×C4—2691no—
305C2×C4—5382no—
306C2×C4—5381no—
307C2×C4—5381no—
308C2×C4—5381no—
309C2×C4—10761no—
310C2×C4—10762no—
311C2×C4—10762no—
312C2×C4—10762no—
313C2×C4—10762no—
314C2×C4D4×D26911yescharacteristic
315C2×C4D4×D26911yescharacteristic
316C2×C4C23×D26911yescharacteristic
317C8—21no—
318C8—21no—
319C8—5381no—
320C8—5381no—
321C22—22no—
322C22—41no—
323C22—41no—
324C22—2692no—
325C22—5381no—
326C22—5381no—
327C22—5382no—
328C22—10768no—
329C22—10761no—
330C22—10761no—
331C22C2×D4×D26911yescharacteristic
332C4—21no—
333C4—21no—
334C4—41no—
335C4—41no—
336C4—41no—
337C4—2692no—
338C4—2692no—
339C4—5381no—
340C4—10761no—
341C4—10761no—
342C4—10761no—
343C4C2×Q8×D26911yescharacteristic
344C4#41×D26911yescharacteristic
345C2—42no—
346C2—5382no—
347C2—10762no—
348C2C22⋊Q8×D26911yescharacteristic
349C2AGL(1,ℤ/8)×D26911yescharacteristic
350C2#3177140211yescharacteristic
subgroupG/H
centerC22C2×D4×D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#478×C269C2
socleC22×C269C22×D4
prime radicalC2×D4×D269C22
hypercenter#478D269
hypocenterC269#3077
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #31771161C2semidirect
3. #31770906C2semidirect
4. #31770905C2semidirect
5. #31770902C2semidirect
6. #31770894C2semidirect
7. #31770893C2semidirect
8. #31770884C2semidirect
9. #31770883C2semidirect
10. #31770646C2semidirect
11. #31770644C2semidirect
12. #31770627C2semidirect
15. #478×C269C2semidirect
20. #22575452C22semidirect
21. #22575452C22semidirect
22. #22575445C22semidirect
37. #22575387C22semidirect
38. #22575386C22semidirect
39. #22575386C22semidirect
40. #22575385C22semidirect
41. #22575384C22semidirect
42. #22575384C22semidirect
43. C4⋊#14524130C22semidirect
44. #22575382C22semidirect
45. #22575382C22semidirect
52. #125×C269C22semidirect
54. #107×C269C22semidirect
55. #106×C269C22semidirect
56. C4⋊C8×C269C22semidirect
65. D4×D269Q8semidirect
175. C269#3077semidirect
182. #478D269semidirect
199. #125C2×D269semidirect
218. #107C2×D269semidirect
222. #106C2×D269semidirect
226. C4⋊C8C2×D269semidirect

Maximal subgroups

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

subgroupindex
#317711612
C4×D4×D2692
#317709062
#317709052
#317709022
#317708942
#317708932
#317708842
#317708832
#317706462
#317706442
#317706272
#317706082
#478×C2692
#3077269