Finite Group Databasebeta

← #46820711

Subgroups — #46820711

Order 34432.

398 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#31771232C211yesmaximal, characteristic, complemented
2#31771077C211yesmaximal, characteristic
3#31770907C211yesmaximal, characteristic, complemented
4#31770906C211yesmaximal, characteristic, complemented
5#31770905C211yesmaximal, characteristic, complemented
6#31770904C211yesmaximal, characteristic, complemented
7#31770894C211yesmaximal, characteristic, complemented
8#31770883C211yesmaximal, characteristic, complemented
9#31770882C211yesmaximal, characteristic, complemented
10#31770644C211yesmaximal, characteristic, complemented
11#31770640C211yesmaximal, characteristic, complemented
12#31770630C211yesmaximal, characteristic, complemented
13#31770608C211yesmaximal, characteristic
14#102×D269C211yesmaximal, characteristic
15#476×C269C211yesmaximal, characteristic, complemented
16C2×D4×D269C2211yescharacteristic
17C2×#16864385C2211yescharacteristic
18C2×C8×D269C2211yescharacteristic
19#22575452C2211yescharacteristic, complemented
20#22575451—21no—
21#22575445C2211yescharacteristic, complemented
22#22575444C2211yescharacteristic, complemented
23#22575443—21no—
24#22575431—21no—
25#22575429—21no—
26C4×D1076C2211yescharacteristic
27D4×Dic269C2211yescharacteristic
28#22575415C2211yescharacteristic
29C4×C22⋊D269—21no—
30#22575413—21no—
31#22575411C2211yescharacteristic
32#22575411C2211yescharacteristic
33#22575410C2211yescharacteristic
34C4⋊C4×D269C2211yescharacteristic
35C2×#16864379—21no—
36C22⋊C4×D269—21no—
37#22575387C2211yescharacteristic, complemented
38#22575386C2211yescharacteristic, complemented
39#22575386C2211yescharacteristic, complemented
40#22575386C2211yescharacteristic, complemented
41#22575385C2211yescharacteristic, 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
52C4⋊Q8×C269C2211yescharacteristic, complemented
53C4×D4×C269C2211yescharacteristic
54#106×C269C2211yescharacteristic, complemented
55#106×C269C2211yescharacteristic, complemented
56C4⋊C8×C269C2211yescharacteristic, complemented
57#102×C269C2211yescharacteristic
58#102×C269C2211yescharacteristic
59C23×D269—21no—
60C2×Dic538—21no—
61C2×D1076C2311yescharacteristic
62C2×C22⋊D269—21no—
63D4×D269—22no—
64D4×D269Q814yescomplemented
65C22×Dic269—21no—
66C2×C4×D269—21no—
67C2×C4×D269—21no—
68C2×C4×D269—21no—
69C2×C4×D269C2311yescharacteristic
70#16864385—22no—
71C2×#14524130C2311yescharacteristic
72C2×#14524130C2311yescharacteristic
73C8×D269—22no—
74C4⋊Dic269—21no—
75C4⋊Dic269C2311yescharacteristic
76C4⋊Dic269C2311yescharacteristic
77C4⋊Dic269C2311yescharacteristic
78#16864381—21no—
79#16864381—21no—
80#16864381—21no—
81#16864381—21no—
82#16864381—21no—
83#16864381D411yescharacteristic
84#16864381D411yescharacteristic
85C22⋊Dic269—21no—
86#16864379—21no—
87#16864379—21no—
88#16864379—21no—
89#16864379—21no—
90#16864379D411yescharacteristic
91#16864379D411yescharacteristic
92C4×Dic269—21no—
93C4×Dic269—21no—
94C4×Dic269C2311yescharacteristic
95C2×Q8×C269—21no—
96C2×D4×C269C2311yescharacteristic
97C22×C4×C269—21no—
98C2×C8×C269C2311yescharacteristic
99C2×C8×C269C2311yescharacteristic
100C4⋊C4×C269—21no—
101C4⋊C4×C269C2311yescharacteristic
102C4⋊C4×C269C2311yescharacteristic
103C4⋊C4×C269C2311yescharacteristic
104C22⋊C4×C269—21no—
105C42×C269C2311yescharacteristic
106C22×D269—21no—
107C22×D269—24no—
108C22×D269—81no—
109C22×D269—81no—
110C22×D269C2×D411yescharacteristic
111Dic538—81no—
112D1076—21no—
113D1076C2×Q812yes—
114C22⋊D269—24no—
115C2×Dic269—21no—
116C2×Dic269—21no—
117C2×Dic269—21no—
118C2×Dic269—81no—
119C2×Dic269C2×D411yescharacteristic
120C2×Dic269C2×D411yescharacteristic
121C2×Dic269C2×D411yescharacteristic
122C4×D269—81no—
123C4×D269—81no—
124C4×D269—81no—
125C4×D269C2×Q812yes—
126C4×D269#4112yes—
127#14524130—21no—
128#14524130—21no—
129C23×C269—21no—
130Q8×C269—81no—
131D4×C269—21no—
132D4×C269C2×Q812yes—
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×C269C2411yescharacteristic
140C8×C269—21no—
141C8×C269—21no—
142C22×C269—22no—
143C22×C269—41no—
144C22×C269—41no—
145C22×C269C22×D411yescharacteristic
146C2×D269—21no—
147C2×D269—21no—
148C2×D269—22no—
149C2×D269—41no—
150C2×D269—41no—
151C2×D269—84no—
152C2×D269C22⋊Q812yes—
153C4×C269—21no—
154C4×C269—21no—
155C4×C269—41no—
156C4×C269—41no—
157C4×C269—41no—
158C4×C269C22×Q811yescharacteristic
159C4×C269C2×#4111yescharacteristic
160Dic269—21no—
161Dic269—21no—
162Dic269—41no—
163Dic269—41no—
164Dic269—41no—
165Dic269C22⋊Q812yes—
166C2×C269—42no—
167C2×C269C2×C22⋊Q811yescharacteristic
168C2×C269#57611yescharacteristic
169C2×C269#57711yescharacteristic
170D269—22no—
171D269—42no—
172C269#308111yescharacteristic, complemented, Sylow
173#3081—2691nomaximal, Sylow
174#544—2691no—
175#518—2691no—
176#478—2691no—
177#478—2691no—
178#478—2691no—
179#478—2691no—
180#476—2691no—
181#476D26911yescharacteristic, complemented
182#474—2691no—
183#474—2691no—
184#428—2691no—
185#427—2691no—
186#424—2691no—
187#418—2691no—
188C2×#102—2691no—
189C22×D4—2691no—
190C2×M16—2691no—
191C22×C8—2691no—
192C4⋊Q8—2691no—
193C4⋊Q8—5381no—
194C4⋊Q8C2×D26911yescharacteristic, complemented
195#125—2691no—
196#125—2691no—
197#125—5381no—
198C22⋊Q8—5381no—
199C22⋊Q8—5381no—
200C4×D4—2691no—
201C4×D4—2691no—
202C4×D4—2691no—
203C4×D4—5381no—
204C4×D4—5381no—
205C4×D4C2×D26911yescharacteristic
206#117—2691no—
207#117—2691no—
208#117—2691no—
209C2×C4⋊C4—2691no—
210C2×C22⋊C4—5381no—
211C2×C22⋊C4—5381no—
212#107—2691no—
213#107—2691no—
214#107—2691no—
215#107—2691no—
216#106—2691no—
217#106—2691no—
218#106C2×D26911yescharacteristic, complemented
219#106C2×D26911yescharacteristic, complemented
220C4⋊C8—2691no—
221C4⋊C8—2691no—
222C4⋊C8—2691no—
223C4⋊C8C2×D26911yescharacteristic, complemented
224#102—2691no—
225#102—2691no—
226#102—2691no—
227#102—2691no—
228#102—2691no—
229#102—2691no—
230#102C2×D26911yescharacteristic
231#102C2×D26911yescharacteristic
232C24—5381no—
233C2×Q8—21no—
234C2×Q8—5381no—
235C2×D4—2694no—
236C2×D4—2691no—
237C2×D4—5382no—
238C2×D4—5381no—
239C2×D4C22×D26911yescharacteristic
240C22×C4—21no—
241C22×C4—2691no—
242C22×C4—5381no—
243C22×C4—5381no—
244C22×C4—5381no—
245C22×C4—5381no—
246M16—5382no—
247C2×C8—2691no—
248C2×C8—2691no—
249C2×C8—5382no—
250C2×C8C22×D26911yescharacteristic
251C2×C8C22×D26911yescharacteristic
252C4⋊C4—21no—
253C4⋊C4—2691no—
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⋊C4—5381no—
264C4⋊C4C22×D26911yescharacteristic
265C4⋊C4C22×D26911yescharacteristic
266C4⋊C4C22×D26911yescharacteristic
267C22⋊C4—21no—
268C22⋊C4—2691no—
269C22⋊C4—2691no—
270C22⋊C4—5381no—
271C22⋊C4—5381no—
272C22⋊C4—5381no—
273C22⋊C4—5381no—
274C22⋊C4—5381no—
275C42—2691no—
276C42—5381no—
277C42—5381no—
278C42C22×D26911yescharacteristic
279C23—21no—
280C23—2691no—
281C23—5384no—
282C23—5381no—
283C23—21521no—
284C23—21521no—
285Q8—81no—
286Q8—21521no—
287D4—21no—
288D4—2692no—
289D4—5384no—
290D4—5381no—
291D4Q8×D26912yes—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—81no—
296C2×C4—2691no—
297C2×C4—2692no—
298C2×C4—2692no—
299C2×C4—2691no—
300C2×C4—2691no—
301C2×C4—5381no—
302C2×C4—5381no—
303C2×C4—5381no—
304C2×C4—21521no—
305C2×C4—21521no—
306C2×C4—21521no—
307C2×C4—21521no—
308C2×C4D4×D26911yescharacteristic
309C2×C4D4×D26911yescharacteristic
310C2×C4C23×D26911yescharacteristic
311C8—21no—
312C8—21no—
313C8—5381no—
314C8—5381no—
315C22—22no—
316C22—41no—
317C22—41no—
318C22—2692no—
319C22—5381no—
320C22—5381no—
321C22—5382no—
322C22—10761no—
323C22—10761no—
324C22—21524no—
325C22C2×D4×D26911yescharacteristic
326C4—21no—
327C4—21no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—2692no—
332C4—5381no—
333C4—5381no—
334C4—10761no—
335C4—10761no—
336C4—10761no—
337C4C2×Q8×D26911yescharacteristic
338C4#41×D26911yescharacteristic
339C2—42no—
340C2—5382no—
341C2—10762no—
342C2C22⋊Q8×D26911yescharacteristic
343C2#3177140911yescharacteristic
344C2#3177141111yescharacteristic
subgroupG/H
centerC22C2×D4×D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#476×C269C2
socleC22×C269C22×D4
prime radicalC2×D4×D269C22
hypercenter#476D269
hypocenterC269#3081
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
1. #31771232C2semidirect
3. #31770907C2semidirect
4. #31770906C2semidirect
5. #31770905C2semidirect
6. #31770904C2semidirect
7. #31770894C2semidirect
8. #31770883C2semidirect
9. #31770882C2semidirect
10. #31770644C2semidirect
11. #31770640C2semidirect
12. #31770630C2semidirect
15. #476×C269C2semidirect
19. #22575452C22semidirect
21. #22575445C22semidirect
22. #22575444C22semidirect
37. #22575387C22semidirect
38. #22575386C22semidirect
39. #22575386C22semidirect
40. #22575386C22semidirect
41. #22575385C22semidirect
42. #22575384C22semidirect
43. C4⋊#14524130C22semidirect
44. #22575382C22semidirect
45. #22575382C22semidirect
52. C4⋊Q8×C269C22semidirect
54. #106×C269C22semidirect
55. #106×C269C22semidirect
56. C4⋊C8×C269C22semidirect
64. D4×D269Q8semidirect
172. C269#3081semidirect
181. #476D269semidirect
194. C4⋊Q8C2×D269semidirect
218. #106C2×D269semidirect
219. #106C2×D269semidirect
223. C4⋊C8C2×D269semidirect

Maximal subgroups

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

subgroupindex
#317712322
#317710772
#317709072
#317709062
#317709052
#317709042
#317708942
#317708832
#317708822
#317706442
#317706402
#317706302
#317706082
#102×D2692
#476×C2692
#3081269