Finite Group Databasebeta

← #46821069

Subgroups — #46821069

Order 34432.

406 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31771226C211yesmaximal, characteristic, complemented
2#31770946C211yesmaximal, characteristic, complemented
3#31770929C211yesmaximal, characteristic, complemented
4#31770895C211yesmaximal, characteristic, complemented
5#31770885C211yesmaximal, characteristic, complemented
6#31770820C211yesmaximal, characteristic, complemented
7#31770820C211yesmaximal, characteristic, complemented
8#31770756C211yesmaximal, characteristic, complemented
9#31770739C211yesmaximal, characteristic
10#31770715C211yesmaximal, characteristic, complemented
11#31770705C211yesmaximal, characteristic, complemented
12C4×#16864390C211yesmaximal, characteristic, complemented
13C4×#16864387C211yesmaximal, characteristic, complemented
14#31770666C211yesmaximal, characteristic, complemented
15#518×C269C211yesmaximal, characteristic, complemented
16C2×#16864390C2211yescharacteristic
17C2×#16864390C2211yescharacteristic
18C2×#16864387C2211yescharacteristic
19C2×#16864387C2211yescharacteristic
20#22575453C2211yescharacteristic, complemented
21#22575448—21no—
22#22575441C2211yescharacteristic, complemented
23#22575439—21no—
24#22575435—21no—
25#22575432C2211yescharacteristic
26#22575431—21no—
27#22575427C2211yescharacteristic
28C4×Dic538C2211yescharacteristic, complemented
29C4×D1076C2211yescharacteristic, complemented
30#22575386C2211yescharacteristic, complemented
31#22575386C2211yescharacteristic, complemented
32#22575384C2211yescharacteristic, complemented
33#22575384C2211yescharacteristic, complemented
34C4⋊#14524130C2211yescharacteristic, complemented
35C4⋊#14524130C2211yescharacteristic, complemented
36#22575376C2211yescharacteristic, complemented
37#22575376C2211yescharacteristic, complemented
38#22575374C2211yescharacteristic
39#22575374C2211yescharacteristic
40#22575374C2211yescharacteristic
41#22575374C2211yescharacteristic
42#22575373C2211yescharacteristic, complemented
43#22575373C2211yescharacteristic, complemented
44C22⋊#14524130C2211yescharacteristic
45C22⋊#14524130C2211yescharacteristic
46#22575364C2211yescharacteristic, complemented
47C4×#14524130C2211yescharacteristic, complemented
48C22×D4×C269C2211yescharacteristic
49C4×D4×C269—21no—
50C4×D4×C269—21no—
51C4×D4×C269C2211yescharacteristic
52C4×D4×C269C2211yescharacteristic
53C4×D4×C269C2211yescharacteristic
54C4×D4×C269C2211yescharacteristic
55#117×C269C2211yescharacteristic
56#117×C269C2211yescharacteristic
57C2×C22⋊C4×C269—21no—
58C2×C22⋊C4×C269—21no—
59C2×Dic538—21no—
60C2×Dic538C2311yescharacteristic
61C2×D1076C2311yescharacteristic
62C2×C22⋊D269—21no—
63C2×C4×D269—21no—
64#16864390—22no—
65#16864390—22no—
66#16864387—22no—
67#16864387—22no—
68C2×#14524130C2311yescharacteristic
69C2×#14524130C2311yescharacteristic
70C2×#14524130C2311yescharacteristic
71C2×#14524130C2311yescharacteristic
72C4⋊Dic269—21no—
73C4⋊Dic269C2311yescharacteristic
74C4⋊Dic269C2311yescharacteristic
75#16864381—21no—
76#16864381—21no—
77C22⋊Dic269—21no—
78#16864379—21no—
79#16864379—21no—
80#16864379—21no—
81#16864379—21no—
82C4×Dic269—21no—
83C24×C269—21no—
84C2×D4×C269—22no—
85C2×D4×C269—22no—
86C2×D4×C269—21no—
87C2×D4×C269C2311yescharacteristic
88C2×D4×C269C2311yescharacteristic
89C22×C4×C269—21no—
90C22×C4×C269—21no—
91C22×C4×C269—21no—
92C22×C4×C269—21no—
93C22×C4×C269C2311yescharacteristic
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—24no—
124C23×C269—21no—
125C23×C269—21no—
126C23×C269—81no—
127C23×C269—81no—
128C23×C269C2×D411yescharacteristic
129D4×C269—24no—
130D4×C269—21no—
131D4×C269—21no—
132D4×C269#4112yes—
133D4×C269#4112yes—
134C2×C4×C269—21no—
135C2×C4×C269—21no—
136C2×C4×C269—21no—
137C2×C4×C269—21no—
138C2×C4×C269—81no—
139C2×C4×C269—81no—
140C2×C4×C269—81no—
141C2×C4×C269—81no—
142C2×C4×C269C2×D411yescharacteristic
143C2×C4×C269C2×D411yescharacteristic
144C2×C4×C269C2×D411yescharacteristic
145C2×C4×C269C2×D411yescharacteristic
146C2×C4×C269C2×D411yescharacteristic
147C2×C4×C269C2411yescharacteristic
148C22×C269—21no—
149C22×C269—22no—
150C22×C269—22no—
151C22×C269—21no—
152C22×C269—21no—
153C22×C269—41no—
154C22×C269—41no—
155C22×C269—41no—
156C22×C269—41no—
157C22×C269—84no—
158C22×C269C22×D411yescharacteristic
159C2×D269—41no—
160C2×D269—41no—
161C2×D269—41no—
162C4×C269—21no—
163C4×C269—21no—
164C4×C269—21no—
165C4×C269—21no—
166C4×C269—21no—
167C4×C269—41no—
168C4×C269—41no—
169C4×C269C2×#4111yescharacteristic
170C4×C269C2×#4111yescharacteristic
171Dic269—41no—
172Dic269—41no—
173Dic269—41no—
174C2×C269—41no—
175C2×C269—42no—
176C2×C269—42no—
177C2×C269#52511yescharacteristic
178C2×C269#57611yescharacteristic
179C2×C269#57711yescharacteristic
180D269—81no—
181C269#311811yescharacteristic, complemented, Sylow
182#3118—2691nomaximal, Sylow
183#542—2691no—
184#518D26911yescharacteristic, complemented
185#485—2691no—
186#482—2691no—
187#476—2691no—
188#474—2691no—
189#463—2691no—
190#463—2691no—
191#450—2691no—
192#447—2691no—
193#442—2691no—
194#440—2691no—
195C4×SD16—2691no—
196C4×D8—2691no—
197#433—2691no—
198C22×D4C2×D26911yescharacteristic
199C2×SD16—2691no—
200C2×SD16—2691no—
201C2×D8—2691no—
202C2×D8—2691no—
203C4⋊Q8—2691no—
204#126—5381no—
205#124—2691no—
206#124—5381no—
207#123—5381no—
208C22⋊Q8—2691no—
209C22⋊Q8—5381no—
210#121—2691no—
211C4×Q8—2691no—
212C4×D4—21no—
213C4×D4—21no—
214C4×D4—2691no—
215C4×D4C2×D26911yescharacteristic
216C4×D4C2×D26911yescharacteristic
217C4×D4C2×D26911yescharacteristic
218C4×D4C2×D26911yescharacteristic
219#117C2×D26911yescharacteristic
220#117C2×D26911yescharacteristic
221C2×C22⋊C4—21no—
222C2×C22⋊C4—21no—
223#107—2691no—
224#107—2691no—
225#106—2691no—
226#106—2691no—
227C4⋊C8—2691no—
228C4⋊C8—2691no—
229#103—2691no—
230#103—2691no—
231#102—2691no—
232#102—2691no—
233#102—2691no—
234#102—2691no—
235#102—2691no—
236#102—2691no—
237C22⋊C8—2691no—
238C22⋊C8—2691no—
239#97—2691no—
240C4×C8—2691no—
241C24—21no—
242C2×Q8—2691no—
243C2×Q8—5381no—
244C2×D4—22no—
245C2×D4—22no—
246C2×D4—21no—
247C2×D4—2691no—
248C2×D4—5381no—
249C2×D4C22×D26911yescharacteristic
250C2×D4C22×D26911yescharacteristic
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—5381no—
256C22×C4C22×D26911yescharacteristic
257SD16—5382no—
258SD16—5382no—
259D8—5382no—
260D8—5382no—
261C2×C8—2691no—
262C2×C8—2691no—
263C2×C8—2691no—
264C2×C8—2691no—
265C4⋊C4—2691no—
266C4⋊C4—2691no—
267C4⋊C4—5381no—
268C4⋊C4—5381no—
269C4⋊C4—5381no—
270C4⋊C4C22⋊D26911yescharacteristic
271C4⋊C4C22⋊D26911yescharacteristic
272C4⋊C4C22×D26911yescharacteristic
273C4⋊C4C22×D26911yescharacteristic
274C22⋊C4—21no—
275C22⋊C4—21no—
276C22⋊C4—21no—
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—5381no—
280C22⋊C4—5381no—
281C22⋊C4—5381no—
282C22⋊C4—5381no—
283C22⋊C4—5381no—
284C22⋊C4C22⋊D26911yescharacteristic
285C22⋊C4C22⋊D26911yescharacteristic
286C42—21no—
287C42—5381no—
288C42C22×D26911yescharacteristic
289C42C22×D26911yescharacteristic
290C23—24no—
291C23—21no—
292C23—21no—
293C23—81no—
294C23—81no—
295C23—5381no—
296C23C2×C22⋊D26911yescharacteristic
297Q8—5381no—
298Q8—5381no—
299Q8—21521no—
300D4—24no—
301D4—21no—
302D4—21no—
303D4—5381no—
304D4—5381no—
305D4—21521no—
306D4#1686440212yes—
307D4#1686440212yes—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—81no—
313C2×C4—81no—
314C2×C4—81no—
315C2×C4—81no—
316C2×C4—5381no—
317C2×C4—5381no—
318C2×C4—5381no—
319C2×C4—21521no—
320C2×C4C2×C22⋊D26911yescharacteristic
321C2×C4C2×C22⋊D26911yescharacteristic
322C2×C4C2×C22⋊D26911yescharacteristic
323C2×C4C2×C22⋊D26911yescharacteristic
324C2×C4C2×C22⋊D26911yescharacteristic
325C2×C4C23×D26911yescharacteristic
326C8—5381no—
327C8—5381no—
328C8—5381no—
329C8—5381no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—22no—
334C22—22no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—84no—
340C22—10761no—
341C22—10761no—
342C22—10761no—
343C22C22×C22⋊D26911yescharacteristic
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—21no—
349C4—41no—
350C4—41no—
351C4—10761no—
352C4—10761no—
353C4—10761no—
354C4C2×#1686440211yescharacteristic
355C4C2×#1686440211yescharacteristic
356C2—41no—
357C2—42no—
358C2—42no—
359C2—21521no—
360C2#3177111611yescharacteristic
361C2#3177140811yescharacteristic
362C2#3177141611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#518×C269C2
socleC22×C269C22×D4
prime radical#31770739C2
hypercenter#518D269
hypocenterC269#3118
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ #117 ◁ #518

Complements

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

NH ≅ G/Ntype
1. #31771226C2semidirect
2. #31770946C2semidirect
3. #31770929C2semidirect
4. #31770895C2semidirect
5. #31770885C2semidirect
6. #31770820C2semidirect
7. #31770820C2semidirect
8. #31770756C2semidirect
10. #31770715C2semidirect
11. #31770705C2semidirect
12. C4×#16864390C2semidirect
13. C4×#16864387C2semidirect
14. #31770666C2semidirect
15. #518×C269C2semidirect
20. #22575453C22semidirect
22. #22575441C22semidirect
28. C4×Dic538C22semidirect
29. C4×D1076C22semidirect
30. #22575386C22semidirect
31. #22575386C22semidirect
32. #22575384C22semidirect
33. #22575384C22semidirect
34. C4⋊#14524130C22semidirect
35. C4⋊#14524130C22semidirect
36. #22575376C22semidirect
37. #22575376C22semidirect
42. #22575373C22semidirect
43. #22575373C22semidirect
46. #22575364C22semidirect
47. C4×#14524130C22semidirect
181. C269#3118semidirect
184. #518D269semidirect

Maximal subgroups

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

subgroupindex
#317712262
#317709462
#317709292
#317708952
#317708852
#317708202
#317707562
#317707392
#317707152
#317707052
C4×#168643902
C4×#168643872
#317706662
#518×C2692
#3118269