Finite Group Databasebeta

← #46822705

Subgroups — #46822705

Order 34432.

462 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31771310C211yesmaximal, characteristic, complemented
2D4×C22⋊D269C211yesmaximal, characteristic
3#31770950C211yesmaximal, characteristic, complemented
4#31770923C211yesmaximal, characteristic, complemented
5#31770922C211yesmaximal, characteristic, complemented
6#31770893C211yesmaximal, characteristic, complemented
7#31770834C211yesmaximal, characteristic, complemented
8#31770833C211yesmaximal, characteristic, complemented
9#31770804C211yesmaximal, characteristic, complemented
10#31770757C211yesmaximal, characteristic, complemented
11#31770756C211yesmaximal, characteristic, complemented
12#31770696C211yesmaximal, characteristic, complemented
13C8×C22⋊D269C211yesmaximal, characteristic, complemented
14#102×D269C211yesmaximal, characteristic, complemented
15C2×#102×C269C211yesmaximal, characteristic, complemented
16C22×C22⋊D269—21no—
17C2×D4×D269C2211yescharacteristic
18C2×#16864391C2211yescharacteristic, complemented
19C2×#16864390C2211yescharacteristic
20C2×#16864390C2211yescharacteristic, complemented
21C2×C8×D269C2211yescharacteristic, complemented
22#22575452C2211yescharacteristic, complemented
23#22575449C2211yescharacteristic
24#22575443—21no—
25#22575433C2211yescharacteristic, complemented
26#22575432—21no—
27#22575432C2211yescharacteristic, complemented
28#22575431—21no—
29#22575427C2211yescharacteristic
30#22575425—21no—
31#22575424C2211yescharacteristic
32#22575422—21no—
33#22575421—21no—
34#22575418C2211yescharacteristic, complemented
35D4×Dic269C2211yescharacteristic
36C4×C22⋊D269—21no—
37C4×C22⋊D269C2211yescharacteristic
38C4⋊C4×D269C2211yescharacteristic, complemented
39#22575385C2211yescharacteristic, complemented
40#22575384C2211yescharacteristic, complemented
41#22575384C2211yescharacteristic, complemented
42#22575382C2211yescharacteristic, complemented
43#22575378C2211yescharacteristic, complemented
44#22575375C2211yescharacteristic, complemented
45#22575374C2211yescharacteristic
46#22575374C2211yescharacteristic, complemented
47#22575373C2211yescharacteristic, complemented
48#22575373C2211yescharacteristic, complemented
49C22⋊#14524130C2211yescharacteristic, complemented
50#22575365C2211yescharacteristic, complemented
51C8×Dic269C2211yescharacteristic, complemented
52C22×D4×C269C2211yescharacteristic
53C22×C8×C269C2211yescharacteristic, complemented
54C2×C4⋊C4×C269C2211yescharacteristic, complemented
55#102×C269C2211yescharacteristic
56#102×C269C2211yescharacteristic
57#102×C269C2211yescharacteristic, complemented
58#102×C269C2211yescharacteristic, complemented
59C23×D269—21no—
60C2×Dic538—21no—
61C2×Dic538C2311yescharacteristic
62C2×D1076C2311yescharacteristic
63C2×C22⋊D269—21no—
64C2×C22⋊D269—21no—
65C2×C22⋊D269—21no—
66C2×C22⋊D269—21no—
67C2×C22⋊D269—21no—
68C2×C22⋊D269—44no—
69C2×C22⋊D269D411yescharacteristic
70D4×D269—22no—
71D4×D269—41no—
72C22×Dic269—21no—
73C2×C4×D269—21no—
74C2×C4×D269C2311yescharacteristic
75#16864391—41no—
76#16864390—22no—
77#16864390—41no—
78C2×#14524130C2311yescharacteristic
79C2×#14524130C2311yescharacteristic
80C8×D269—41no—
81C4⋊Dic269—21no—
82C4⋊Dic269C2311yescharacteristic
83C4⋊Dic269C2311yescharacteristic
84#16864381—21no—
85#16864381—21no—
86#16864381—21no—
87#16864381—21no—
88#16864381D411yescharacteristic
89C22⋊Dic269—21no—
90C22⋊Dic269—21no—
91C22⋊Dic269—21no—
92C22⋊Dic269D411yescharacteristic
93#16864379—21no—
94#16864379—21no—
95#16864379D411yescharacteristic
96C4×Dic269—21no—
97C4×Dic269C2311yescharacteristic
98C24×C269—21no—
99C2×D4×C269—22no—
100C2×D4×C269—21no—
101C2×D4×C269—41no—
102C2×D4×C269C2311yescharacteristic
103C2×D4×C269C2311yescharacteristic
104C22×C4×C269—21no—
105C22×C4×C269C2311yescharacteristic
106C2×C8×C269—41no—
107C2×C8×C269C2311yescharacteristic
108C2×C8×C269C2311yescharacteristic
109C4⋊C4×C269—21no—
110C4⋊C4×C269C2311yescharacteristic
111C4⋊C4×C269C2311yescharacteristic
112C22×D269—21no—
113C22×D269—42no—
114C22×D269—42no—
115C22×D269—81no—
116C22×D269C2×D411yescharacteristic
117Dic538—21no—
118Dic538—21no—
119Dic538—81no—
120D1076—21no—
121D1076—21no—
122C22⋊D269—42no—
123C22⋊D269—42no—
124C22⋊D269—42no—
125C22⋊D269—42no—
126C22⋊D269—81no—
127C22⋊D269SD1614yescomplemented
128C2×Dic269—21no—
129C2×Dic269—21no—
130C2×Dic269—21no—
131C2×Dic269—42no—
132C2×Dic269C2×D411yescharacteristic
133C2×Dic269C2×D411yescharacteristic
134C2×Dic269C2×D411yescharacteristic
135C4×D269—21no—
136C4×D269—21no—
137C4×D269—81no—
138#14524130—21no—
139#14524130—21no—
140C23×C269—21no—
141C23×C269—21no—
142C23×C269—42no—
143C23×C269—42no—
144C23×C269—81no—
145C23×C269C2×D411yescharacteristic
146D4×C269—21no—
147D4×C269—21no—
148D4×C269—21no—
149D4×C269—42no—
150D4×C269#4112yes—
151C2×C4×C269—21no—
152C2×C4×C269—21no—
153C2×C4×C269—21no—
154C2×C4×C269—21no—
155C2×C4×C269—81no—
156C2×C4×C269C2×D411yescharacteristic
157C2×C4×C269C2411yescharacteristic
158C8×C269—21no—
159C8×C269—21no—
160C22×C269—21no—
161C22×C269—21no—
162C22×C269—22no—
163C22×C269—41no—
164C22×C269—41no—
165C22×C269—41no—
166C22×C269—41no—
167C22×C269—41no—
168C22×C269—84no—
169C22×C269C2×SD1612yes—
170C22×C269C22×D411yescharacteristic
171C2×D269—21no—
172C2×D269—21no—
173C2×D269—41no—
174C2×D269—41no—
175C2×D269—41no—
176C2×D269—84no—
177C2×D269C2×SD1612yes—
178C4×C269—21no—
179C4×C269—41no—
180C4×C269—41no—
181C4×C269C2×#4111yescharacteristic
182C4×C269H(5,𝔽2)11yescharacteristic
183Dic269—21no—
184Dic269—21no—
185Dic269—41no—
186Dic269—41no—
187Dic269—41no—
188Dic269C2×SD1612yes—
189C2×C269—22no—
190C2×C269—42no—
191C2×C269—81no—
192C2×C269#54611yescharacteristic
193C2×C269C22×SD1611yescharacteristic
194C2×C269#57611yescharacteristic
195D269—22no—
196D269—81no—
197C269#329511yescharacteristic, complemented, Sylow
198#3295—2691nomaximal, Sylow
199#554—2691no—
200D42—2691no—
201#486—2691no—
202#481—2691no—
203#481—2691no—
204#476—2691no—
205#465—2691no—
206#465—2691no—
207#460—2691no—
208#450—2691no—
209#450—2691no—
210C4×SD16—2691no—
211C8×D4—2691no—
212C2×#102—2691no—
213C2×#102D26911yescharacteristic, complemented
214C22×D4—2691no—
215C22×D4—5381no—
216C22×D4C2×D26911yescharacteristic
217C2×SD16—2691no—
218C2×SD16—2691no—
219C2×SD16—2691no—
220C22×C8—2691no—
221C22×C8C2×D26911yescharacteristic, complemented
222C4⋊Q8—2691no—
223#127—2691no—
224#125—5381no—
225C22⋊Q8—2691no—
226C22⋊Q8—2691no—
227C22⋊Q8—5381no—
228C22⋊Q8—5381no—
229#121—2691no—
230#121—2691no—
231#121—5381no—
232#120—5381no—
233#120—5381no—
234C4×Q8—2691no—
235C4×D4—2691no—
236C4×D4—2691no—
237C4×D4—5381no—
238C2×C4⋊C4—2691no—
239C2×C4⋊C4C2×D26911yescharacteristic, complemented
240#106—2691no—
241#106—2691no—
242#106—2691no—
243C4⋊C8—2691no—
244#103—2691no—
245#102—2691no—
246#102—2691no—
247#102—2691no—
248#102—2691no—
249#102—2691no—
250#102C2×D26911yescharacteristic
251#102C2×D26911yescharacteristic
252#102C2×D26911yescharacteristic, complemented
253#102C2×D26911yescharacteristic, complemented
254C22⋊C8—2691no—
255C22⋊C8—2691no—
256C4×C8—2691no—
257C24—21no—
258C24—5381no—
259C2×Q8—2691no—
260C2×Q8—5381no—
261C2×D4—22no—
262C2×D4—21no—
263C2×D4—41no—
264C2×D4—2691no—
265C2×D4—2691no—
266C2×D4—5381no—
267C2×D4—5381no—
268C2×D4—5381no—
269C2×D4—5382no—
270C2×D4—5381no—
271C2×D4—5381no—
272C2×D4—10761no—
273C2×D4—10764no—
274C2×D4C22×D26911yescharacteristic
275C2×D4C22×D26911yescharacteristic
276C22×C4—21no—
277C22×C4—2691no—
278C22×C4—5381no—
279C22×C4—5381no—
280C22×C4C22×D26911yescharacteristic
281SD16—5382no—
282SD16—10761no—
283SD16—10761no—
284C2×C8—41no—
285C2×C8—2691no—
286C2×C8—2691no—
287C2×C8—10761no—
288C2×C8C22×D26911yescharacteristic
289C2×C8C22×D26911yescharacteristic
290C4⋊C4—21no—
291C4⋊C4—2691no—
292C4⋊C4—2691no—
293C4⋊C4—2691no—
294C4⋊C4—5381no—
295C4⋊C4—5381no—
296C4⋊C4—5381no—
297C4⋊C4—5381no—
298C4⋊C4—5381no—
299C4⋊C4C22×D26911yescharacteristic
300C4⋊C4C22×D26911yescharacteristic
301C22⋊C4—2691no—
302C22⋊C4—2691no—
303C22⋊C4—5381no—
304C22⋊C4—5381no—
305C22⋊C4—5381no—
306C22⋊C4—5381no—
307C22⋊C4—5381no—
308C42—2691no—
309C42—5381no—
310C23—21no—
311C23—21no—
312C23—42no—
313C23—42no—
314C23—81no—
315C23—2691no—
316C23—5381no—
317C23—10762no—
318C23—10762no—
319C23—21521no—
320C23D4×D26911yescharacteristic
321Q8—5381no—
322Q8—5381no—
323Q8—21521no—
324D4—21no—
325D4—21no—
326D4—21no—
327D4—42no—
328D4—2694no—
329D4—5381no—
330D4—5381no—
331D4—10762no—
332D4—10762no—
333D4—10762no—
334D4—10762no—
335D4—21521no—
336D4#1686440212yes—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—81no—
342C2×C4—2691no—
343C2×C4—2691no—
344C2×C4—2691no—
345C2×C4—5381no—
346C2×C4—5381no—
347C2×C4—5381no—
348C2×C4—5381no—
349C2×C4—5381no—
350C2×C4—10762no—
351C2×C4—21521no—
352C2×C4D4×D26911yescharacteristic
353C2×C4C23×D26911yescharacteristic
354C8—21no—
355C8—21no—
356C8—5381no—
357C8—5381no—
358C22—21no—
359C22—21no—
360C22—22no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—84no—
367C22—2692no—
368C22—5381no—
369C22—5381no—
370C22—10761no—
371C22—10761no—
372C22—10761no—
373C22—21524no—
374C22SD16×D26912yes—
375C22C2×D4×D26911yescharacteristic
376C4—21no—
377C4—41no—
378C4—41no—
379C4—2692no—
380C4—5381no—
381C4—5381no—
382C4—10761no—
383C4—10761no—
384C4—10761no—
385C4C2×#1686440211yescharacteristic
386C4#2257549811yescharacteristic
387C2—22no—
388C2—42no—
389C2—81no—
390C2—5382no—
391C2—21521no—
392C2#3177124511yescharacteristic
393C2C2×SD16×D26911yescharacteristic
394C2#3177140611yescharacteristic
subgroupG/H
centerC22C2×D4×D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
FittingC2×#102×C269C2
socleC22×C269C22×D4
prime radicalD4×C22⋊D269C2
hypercenterC2×#102D269
hypocenterC269#3295
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
1. #31771310C2semidirect
3. #31770950C2semidirect
4. #31770923C2semidirect
5. #31770922C2semidirect
6. #31770893C2semidirect
7. #31770834C2semidirect
8. #31770833C2semidirect
9. #31770804C2semidirect
10. #31770757C2semidirect
11. #31770756C2semidirect
12. #31770696C2semidirect
13. C8×C22⋊D269C2semidirect
14. #102×D269C2semidirect
15. C2×#102×C269C2semidirect
18. C2×#16864391C22semidirect
20. C2×#16864390C22semidirect
21. C2×C8×D269C22semidirect
22. #22575452C22semidirect
25. #22575433C22semidirect
27. #22575432C22semidirect
34. #22575418C22semidirect
38. C4⋊C4×D269C22semidirect
39. #22575385C22semidirect
40. #22575384C22semidirect
41. #22575384C22semidirect
42. #22575382C22semidirect
43. #22575378C22semidirect
44. #22575375C22semidirect
46. #22575374C22semidirect
47. #22575373C22semidirect
48. #22575373C22semidirect
49. C22⋊#14524130C22semidirect
50. #22575365C22semidirect
51. C8×Dic269C22semidirect
53. C22×C8×C269C22semidirect
54. C2×C4⋊C4×C269C22semidirect
57. #102×C269C22semidirect
58. #102×C269C22semidirect
127. C22⋊D269SD16semidirect
197. C269#3295semidirect
213. C2×#102D269semidirect
221. C22×C8C2×D269semidirect
239. C2×C4⋊C4C2×D269semidirect
252. #102C2×D269semidirect
253. #102C2×D269semidirect

Maximal subgroups

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

subgroupindex
#317713102
D4×C22⋊D2692
#317709502
#317709232
#317709222
#317708932
#317708342
#317708332
#317708042
#317707572
#317707562
#317706962
C8×C22⋊D2692
#102×D2692
C2×#102×C2692
#3295269