Finite Group Databasebeta

← #46822738

Subgroups — #46822738

Order 34432.

420 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31771299C211yesmaximal, characteristic, complemented
2#31771252C211yesmaximal, characteristic, complemented
3#31770958C211yesmaximal, characteristic, complemented
4#31770942C211yesmaximal, characteristic, complemented
5#31770904C211yesmaximal, characteristic, complemented
6#31770839C211yesmaximal, characteristic, complemented
7#31770835C211yesmaximal, characteristic, complemented
8#31770819C211yesmaximal, characteristic, complemented
9#31770752C211yesmaximal, characteristic, complemented
10#31770740C211yesmaximal, characteristic, complemented
11#31770687C211yesmaximal, characteristic, complemented
12#31770668C211yesmaximal, characteristic, complemented
13#31770599C211yesmaximal, characteristic, complemented
14#102×D269C211yesmaximal, characteristic, complemented
15#482×C269C211yesmaximal, characteristic, complemented
16C2×#16864402C2211yescharacteristic
17C2×D4×D269C2211yescharacteristic
18C2×#16864391C2211yescharacteristic, complemented
19C2×D2152C2211yescharacteristic
20C2×#16864387C2211yescharacteristic
21C22×#14524130C2211yescharacteristic, complemented
22C2×C8×D269C2211yescharacteristic
23#22575447—21no—
24#22575444C2211yescharacteristic, complemented
25#22575440C2211yescharacteristic
26#22575435—21no—
27#22575435—21no—
28#22575433C2211yescharacteristic
29#22575428C2211yescharacteristic
30#22575427C2211yescharacteristic, complemented
31#22575426—21no—
32#22575424—21no—
33#22575421—21no—
34C4×D1076—21no—
35#22575415C2211yescharacteristic
36#22575415C2211yescharacteristic, complemented
37C4×C22⋊D269C2211yescharacteristic
38C4⋊C4×D269C2211yescharacteristic
39C22⋊C4×D269—21no—
40#22575386C2211yescharacteristic, complemented
41#22575382C2211yescharacteristic, complemented
42#22575378C2211yescharacteristic, complemented
43#22575376C2211yescharacteristic, complemented
44#22575376C2211yescharacteristic, complemented
45#22575375C2211yescharacteristic
46#22575374C2211yescharacteristic
47#22575373C2211yescharacteristic
48#22575373C2211yescharacteristic
49#22575373C2211yescharacteristic, complemented
50#22575365C2211yescharacteristic
51C8×Dic269C2211yescharacteristic, complemented
52#121×C269C2211yescharacteristic
53#117×C269C2211yescharacteristic, complemented
54#107×C269C2211yescharacteristic, complemented
55#106×C269C2211yescharacteristic, complemented
56#102×C269C2211yescharacteristic
57#102×C269C2211yescharacteristic
58C22⋊C8×C269C2211yescharacteristic, complemented
59C23×D269—21no—
60#16864402—22no—
61#16864402—41no—
62C2×Dic538C2311yescharacteristic
63C2×D1076—21no—
64C2×D1076C2311yescharacteristic
65C2×D1076C2311yescharacteristic
66C2×C22⋊D269—21no—
67C2×C22⋊D269—21no—
68C2×C22⋊D269—21no—
69C2×C22⋊D269D411yescharacteristic
70D4×D269—22no—
71D4×D269—41no—
72C2×C4×D269—21no—
73C2×C4×D269—21no—
74C2×C4×D269—21no—
75C2×C4×D269—21no—
76C2×C4×D269C2311yescharacteristic
77#16864391—41no—
78D2152—22no—
79#16864387—41no—
80C2×#14524130—41no—
81C2×#14524130C2311yescharacteristic
82C2×#14524130C2311yescharacteristic
83C8×D269—41no—
84C4⋊Dic269—21no—
85C4⋊Dic269—21no—
86C4⋊Dic269C2311yescharacteristic
87#16864381—21no—
88#16864381—21no—
89#16864381D411yescharacteristic
90C22⋊Dic269—21no—
91C22⋊Dic269—21no—
92C22⋊Dic269D411yescharacteristic
93#16864379—21no—
94#16864379—21no—
95#16864379—21no—
96#16864379—21no—
97#16864379—21no—
98#16864379D411yescharacteristic
99C4×Dic269C2311yescharacteristic
100C2×D4×C269—21no—
101C2×D4×C269C2311yescharacteristic
102C22×C4×C269C2311yescharacteristic
103C2×C8×C269C2311yescharacteristic
104C2×C8×C269C2311yescharacteristic
105C4⋊C4×C269C2311yescharacteristic
106C4⋊C4×C269C2311yescharacteristic
107C4⋊C4×C269C2311yescharacteristic
108C22⋊C4×C269—21no—
109C22⋊C4×C269—21no—
110C42×C269—21no—
111C22×D269—21no—
112C22×D269—21no—
113C22×D269—42no—
114C22×D269—42no—
115C22×D269—81no—
116C22×D269C2×D411yescharacteristic
117Dic538—21no—
118Dic538—21no—
119D1076—21no—
120D1076—21no—
121D1076—21no—
122D1076—42no—
123D1076#4112yes—
124C22⋊D269—22no—
125C22⋊D269—42no—
126C22⋊D269—42no—
127C22⋊D269—81no—
128C2×Dic269—21no—
129C2×Dic269—21no—
130C2×Dic269C2×D411yescharacteristic
131C2×Dic269C2×D411yescharacteristic
132C2×Dic269C2×D411yescharacteristic
133C4×D269—21no—
134C4×D269—21no—
135C4×D269—42no—
136C4×D269—81no—
137C4×D269—81no—
138C4×D269—81no—
139#14524130—21no—
140#14524130—21no—
141C23×C269—21no—
142C23×C269C2×D411yescharacteristic
143D4×C269—21no—
144D4×C269—21no—
145D4×C269—81no—
146C2×C4×C269—21no—
147C2×C4×C269—21no—
148C2×C4×C269—21no—
149C2×C4×C269—21no—
150C2×C4×C269—21no—
151C2×C4×C269C2×D411yescharacteristic
152C2×C4×C269C2411yescharacteristic
153C8×C269—21no—
154C8×C269—21no—
155C22×C269—21no—
156C22×C269—21no—
157C22×C269—21no—
158C22×C269—41no—
159C22×C269—41no—
160C22×C269—41no—
161C22×C269C22×D411yescharacteristic
162C2×D269—21no—
163C2×D269—21no—
164C2×D269—22no—
165C2×D269—41no—
166C2×D269—41no—
167C2×D269—41no—
168C2×D269—41no—
169C2×D269—41no—
170C2×D269—84no—
171C2×D269#13512yes—
172C4×C269—21no—
173C4×C269—41no—
174C4×C269—41no—
175C4×C269—41no—
176C4×C269C2×#4111yescharacteristic
177C4×C269H(5,𝔽2)11yescharacteristic
178Dic269—21no—
179Dic269—21no—
180Dic269—21no—
181Dic269—41no—
182Dic269—41no—
183C2×C269—41no—
184C2×C269—81no—
185C2×C269#54611yescharacteristic
186C2×C269C2×#13511yescharacteristic
187C2×C269#57611yescharacteristic
188D269—22no—
189D269—42no—
190D269—81no—
191C269#329711yescharacteristic, complemented, Sylow
192#3297—2691nomaximal, Sylow
193#553—2691no—
194#546—2691no—
195#488—2691no—
196#484—2691no—
197#482D26911yescharacteristic, complemented
198#478—2691no—
199#466—2691no—
200#465—2691no—
201#463—2691no—
202#449—2691no—
203#447—2691no—
204C4×D8—2691no—
205C8×D4—2691no—
206#416—2691no—
207C2×#102—2691no—
208C2×#41—2691no—
209C22×D4—2691no—
210C2×SD16—2691no—
211C2×D8—2691no—
212C2×D8—2691no—
213C22×C8—2691no—
214C22×C8—2691no—
215#126—5381no—
216#125—2691no—
217#124—2691no—
218#123—5381no—
219#123—5381no—
220C22⋊Q8—2691no—
221#121—2691no—
222#121—2691no—
223#121—5381no—
224#121—5381no—
225#121C2×D26911yescharacteristic
226#120—5381no—
227C4×D4—2691no—
228C4×D4—2691no—
229C4×D4—2691no—
230C4×D4—5381no—
231#117C2×D26911yescharacteristic, complemented
232C2×C4⋊C4—2691no—
233C2×C22⋊C4—5381no—
234#107—2691no—
235#107C2×D26911yescharacteristic, complemented
236#106C2×D26911yescharacteristic, complemented
237C4⋊C8—2691no—
238#103—2691no—
239#103—2691no—
240#103—2691no—
241#102—2691no—
242#102—2691no—
243#102—2691no—
244#102—2691no—
245#102—2691no—
246#102C2×D26911yescharacteristic
247#102C2×D26911yescharacteristic
248C22⋊C8—2691no—
249C22⋊C8C2×D26911yescharacteristic, complemented
250C4×C8—2691no—
251C24—5381no—
252#41—5382no—
253#41—10761no—
254C2×Q8—2691no—
255C2×D4—21no—
256C2×D4—2691no—
257C2×D4—2691no—
258C2×D4—2691no—
259C2×D4—5381no—
260C2×D4—5381no—
261C2×D4—5382no—
262C2×D4—5381no—
263C2×D4—5381no—
264C2×D4—10761no—
265C2×D4C22×D26911yescharacteristic
266C22×C4—2691no—
267C22×C4—5381no—
268C22×C4—5381no—
269C22×C4—5381no—
270C22×C4—5381no—
271C22×C4C22×D26911yescharacteristic
272SD16—10761no—
273D8—5382no—
274D8—10761no—
275C2×C8—2691no—
276C2×C8—2691no—
277C2×C8—10761no—
278C2×C8—10761no—
279C2×C8C22×D26911yescharacteristic
280C2×C8C22×D26911yescharacteristic
281C4⋊C4—2691no—
282C4⋊C4—2691no—
283C4⋊C4—5381no—
284C4⋊C4—5381no—
285C4⋊C4—5381no—
286C4⋊C4—5381no—
287C4⋊C4C22×D26911yescharacteristic
288C4⋊C4C22×D26911yescharacteristic
289C4⋊C4C22×D26911yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—2691no—
293C22⋊C4—2691no—
294C22⋊C4—5381no—
295C22⋊C4—5381no—
296C22⋊C4—5381no—
297C22⋊C4—5381no—
298C22⋊C4—5381no—
299C22⋊C4—5381no—
300C22⋊C4—5381no—
301C42—21no—
302C42—2691no—
303C23—21no—
304C23—2691no—
305C23—5381no—
306C23—5381no—
307C23—10762no—
308C23—10762no—
309C23—21521no—
310C23D4×D26911yescharacteristic
311Q8—5381no—
312Q8—5381no—
313D4—21no—
314D4—21no—
315D4—81no—
316D4—2692no—
317D4—5382no—
318D4—5381no—
319D4—5381no—
320D4—5381no—
321D4—10762no—
322D4—10762no—
323D4—10762no—
324D4—21521no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—2691no—
331C2×C4—2691no—
332C2×C4—2691no—
333C2×C4—5381no—
334C2×C4—5381no—
335C2×C4—5381no—
336C2×C4—5381no—
337C2×C4—10762no—
338C2×C4—21521no—
339C2×C4—21521no—
340C2×C4—21521no—
341C2×C4D4×D26911yescharacteristic
342C2×C4C23×D26911yescharacteristic
343C8—21no—
344C8—21no—
345C8—5381no—
346C8—5381no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—2692no—
354C22—5381no—
355C22—5381no—
356C22—5382no—
357C22—10761no—
358C22—10761no—
359C22—10761no—
360C22—10761no—
361C22—10761no—
362C22—21524no—
363C22C2×D4×D26911yescharacteristic
364C4—21no—
365C4—41no—
366C4—41no—
367C4—41no—
368C4—5381no—
369C4—5381no—
370C4—5381no—
371C4—10761no—
372C4—10761no—
373C4#41×D26911yescharacteristic
374C4#2257549911yescharacteristic
375C2—41no—
376C2—81no—
377C2—5382no—
378C2—10762no—
379C2—21521no—
380C2#3177124711yescharacteristic
381C2#135×D26911yescharacteristic
382C2#3177140911yescharacteristic
subgroupG/H
centerC22C2×D4×D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#482×C269C2
socleC22×C269C22×D4
hypercenter#482D269
hypocenterC269#3297
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
1. #31771299C2semidirect
2. #31771252C2semidirect
3. #31770958C2semidirect
4. #31770942C2semidirect
5. #31770904C2semidirect
6. #31770839C2semidirect
7. #31770835C2semidirect
8. #31770819C2semidirect
9. #31770752C2semidirect
10. #31770740C2semidirect
11. #31770687C2semidirect
12. #31770668C2semidirect
13. #31770599C2semidirect
14. #102×D269C2semidirect
15. #482×C269C2semidirect
18. C2×#16864391C22semidirect
21. C22×#14524130C22semidirect
24. #22575444C22semidirect
30. #22575427C22semidirect
36. #22575415C22semidirect
40. #22575386C22semidirect
41. #22575382C22semidirect
42. #22575378C22semidirect
43. #22575376C22semidirect
44. #22575376C22semidirect
49. #22575373C22semidirect
51. C8×Dic269C22semidirect
53. #117×C269C22semidirect
54. #107×C269C22semidirect
55. #106×C269C22semidirect
58. C22⋊C8×C269C22semidirect
191. C269#3297semidirect
197. #482D269semidirect
231. #117C2×D269semidirect
235. #107C2×D269semidirect
236. #106C2×D269semidirect
249. C22⋊C8C2×D269semidirect

Maximal subgroups

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

subgroupindex
#317712992
#317712522
#317709582
#317709422
#317709042
#317708392
#317708352
#317708192
#317707522
#317707402
#317706872
#317706682
#317705992
#102×D2692
#482×C2692
#3297269