Finite Group Databasebeta

← #46813439

Subgroups — #46813439

Order 34432.

516 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22575446C211yesmaximal, characteristic
2#31770499C211yesmaximal, characteristic
3#31770493C211yesmaximal, characteristic
4#31770489C211yesmaximal, characteristic, complemented
5#31770488C211yesmaximal, characteristic, complemented
6#31770486C211yesmaximal, characteristic, complemented
7#31770472C211yesmaximal, characteristic, complemented
8C4⋊C4×Dic269C211yesmaximal, characteristic, complemented
9#31770456C211yesmaximal, characteristic, complemented
10#31770456C211yesmaximal, characteristic, complemented
11C22⋊C4×Dic269C211yesmaximal, characteristic
12C22⋊C4×Dic269C211yesmaximal, characteristic
13C22⋊C4×Dic269C211yesmaximal, characteristic
14C42×Dic269C211yesmaximal, characteristic, complemented
15#388×C269C211yesmaximal, characteristic
16C23×Dic269C2211yescharacteristic
17#22575446C418yescomplemented
18C2×C4⋊Dic269C2211yescharacteristic
19C2×#16864381C2211yescharacteristic
20C2×#16864381C2211yescharacteristic
21C2×#16864381C2211yescharacteristic
22C2×#16864381C2211yescharacteristic
23C2×C22⋊Dic269C2211yescharacteristic
24C2×C22⋊Dic269C2211yescharacteristic
25C2×C22⋊Dic269C2211yescharacteristic
26C2×C4×Dic269C2211yescharacteristic
27C2×C4×Dic269C2211yescharacteristic
28C2×C4×Dic269C2211yescharacteristic
29C2×C4×Dic269C2211yescharacteristic
30C2×C4×Dic269C2211yescharacteristic
31C2×C4×Dic269C2211yescharacteristic
32C2×C4×Dic269C2211yescharacteristic
33C2×C4×Dic269C2211yescharacteristic
34C2×C4×Dic269C2211yescharacteristic
35#22575360C2211yescharacteristic
36#22575360C2211yescharacteristic
37#22575360C2211yescharacteristic
38#22575360C2211yescharacteristic
39#22575360C2211yescharacteristic
40#22575360C2211yescharacteristic
41#22575360C2211yescharacteristic
42#22575360C2211yescharacteristic
43#22575360C2211yescharacteristic
44#22575360C2211yescharacteristic
45C2×C4⋊C4×C269C2211yescharacteristic
46C2×C22⋊C4×C269C2211yescharacteristic
47C2×C22⋊C4×C269C2211yescharacteristic
48C2×C22⋊C4×C269C2211yescharacteristic
49C2×C42×C269C2211yescharacteristic
50#95×C269C2211yescharacteristic
51#95×C269C2211yescharacteristic
52C22×Dic269—22no—
53C22×Dic269—22no—
54C22×Dic269—22no—
55C22×Dic269C2311yescharacteristic
56C22×Dic269C2311yescharacteristic
57C22×Dic269C2311yescharacteristic
58C22×Dic269C2311yescharacteristic
59C22×Dic269C2311yescharacteristic
60C22×Dic269C2311yescharacteristic
61C22×Dic269C2311yescharacteristic
62C22×Dic269C2311yescharacteristic
63C4⋊Dic269C2×C414yescomplemented
64#16864381—22no—
65#16864381—22no—
66#16864381C2×C414yescomplemented
67#16864381C2×C414yescomplemented
68C22⋊Dic269—22no—
69C22⋊Dic269C2×C414yes—
70C22⋊Dic269C2×C414yes—
71C4×Dic269—22no—
72C4×Dic269—22no—
73C4×Dic269—22no—
74C4×Dic269—22no—
75C4×Dic269—22no—
76C4×Dic269—22no—
77C4×Dic269—22no—
78C4×Dic269—22no—
79C4×Dic269C2×C414yescomplemented
80C24×C269C2311yescharacteristic
81C22×C4×C269C2311yescharacteristic
82C22×C4×C269C2311yescharacteristic
83C22×C4×C269C2311yescharacteristic
84C22×C4×C269C2311yescharacteristic
85C22×C4×C269C2311yescharacteristic
86C22×C4×C269C2311yescharacteristic
87C4⋊C4×C269—22no—
88C22⋊C4×C269—22no—
89C22⋊C4×C269—22no—
90C22⋊C4×C269C2×C414yes—
91C42×C269—22no—
92C2×Dic269—21no—
93C2×Dic269—21no—
94C2×Dic269—21no—
95C2×Dic269—21no—
96C2×Dic269—21no—
97C2×Dic269—21no—
98C2×Dic269—21no—
99C2×Dic269—21no—
100C2×Dic269—21no—
101C2×Dic269—21no—
102C2×Dic269—21no—
103C2×Dic269—21no—
104C2×Dic269—21no—
105C2×Dic269—21no—
106C2×Dic269—21no—
107C2×Dic269—21no—
108C2×Dic269—44no—
109C2×Dic269C22×C412yes—
110C2×Dic269C22×C412yes—
111C2×Dic269C22×C412yes—
112C2×Dic269C22×C412yes—
113C2×Dic269#4112yes—
114C2×Dic269#4112yes—
115C2×Dic269#4112yes—
116C2×Dic269#4112yes—
117C23×C269—21no—
118C23×C269—21no—
119C23×C269—21no—
120C23×C269—21no—
121C23×C269—21no—
122C23×C269—21no—
123C23×C269C22×C412yes—
124C23×C269C2411yescharacteristic
125C2×C4×C269—21no—
126C2×C4×C269—21no—
127C2×C4×C269—21no—
128C2×C4×C269—21no—
129C2×C4×C269—21no—
130C2×C4×C269—21no—
131C2×C4×C269—21no—
132C2×C4×C269—21no—
133C2×C4×C269—21no—
134C2×C4×C269—21no—
135C2×C4×C269—21no—
136C2×C4×C269—21no—
137C2×C4×C269—21no—
138C2×C4×C269—21no—
139C2×C4×C269C22×C412yes—
140C2×C4×C269C22×C412yes—
141C2×C4×C269#4112yes—
142C2×C4×C269#4112yes—
143C22×C269—22no—
144C22×C269—22no—
145C22×C269—22no—
146C22×C269—41no—
147C22×C269—41no—
148C22×C269—41no—
149C22×C269—41no—
150C22×C269C23×C411yescharacteristic
151C22×C269C2×#4111yescharacteristic
152C22×C269C2×#4111yescharacteristic
153C22×C269C2×#4111yescharacteristic
154C22×C269C2×#4111yescharacteristic
155C22×C269C2×#4111yescharacteristic
156C22×C269C2×#4111yescharacteristic
157C4×C269—22no—
158C4×C269—22no—
159C4×C269—22no—
160C4×C269—22no—
161C4×C269—41no—
162C4×C269—41no—
163Dic269—22no—
164Dic269—22no—
165Dic269—22no—
166Dic269—22no—
167Dic269—22no—
168Dic269—41no—
169Dic269—41no—
170Dic269#12614yescomplemented
171C2×C269—42no—
172C2×C269C4×#4111yescharacteristic
173C2×C269C4×#4111yescharacteristic
174C2×C269C4×#4111yescharacteristic
175C2×C269C2×#12611yescharacteristic
176C2×C269#52911yescharacteristic
177C2×C269#52911yescharacteristic
178C2×C269#52911yescharacteristic
179C269C4×#12611yescharacteristic, complemented, Sylow
180C4×#126—2691nomaximal, Sylow
181C2×#126—2691no—
182#388—2691no—
183#388—2691no—
184#388D26911yescharacteristic
185#387—2691no—
186#387—2691no—
187#387—2691no—
188#383—2691no—
189C4×C4⋊C4—2691no—
190C4×C4⋊C4—2691no—
191C4×C4⋊C4—2691no—
192C4×C22⋊C4—2691no—
193C4×C22⋊C4—2691no—
194C4×C22⋊C4—2691no—
195C43—2691no—
196C23×C4—2691no—
197#126—2698no—
198C2×C4⋊C4—2691no—
199C2×C4⋊C4—2691no—
200C2×C4⋊C4—2691no—
201C2×C4⋊C4—2691no—
202C2×C4⋊C4—2691no—
203C2×C4⋊C4C2×D26911yescharacteristic
204C2×C22⋊C4—2691no—
205C2×C22⋊C4—2691no—
206C2×C22⋊C4—2691no—
207C2×C22⋊C4C2×D26911yescharacteristic
208C2×C22⋊C4C2×D26911yescharacteristic
209C2×C22⋊C4C2×D26911yescharacteristic
210C2×C42—2691no—
211C2×C42—2691no—
212C2×C42—2691no—
213C2×C42—2691no—
214C2×C42—2691no—
215C2×C42—2691no—
216C2×C42—2691no—
217C2×C42—2691no—
218C2×C42—2691no—
219C2×C42C2×D26911yescharacteristic
220#95—2691no—
221#95—2691no—
222#95—2691no—
223#95—2691no—
224#95—2691no—
225#95—2691no—
226#95—2691no—
227#95—2691no—
228#95—2691no—
229#95—2691no—
230#95C2×D26911yescharacteristic
231#95C2×D26911yescharacteristic
232C24C22×D26911yescharacteristic
233C22×C4—2691no—
234C22×C4—2691no—
235C22×C4—2691no—
236C22×C4—2691no—
237C22×C4—2691no—
238C22×C4—2691no—
239C22×C4—2691no—
240C22×C4—2691no—
241C22×C4—5382no—
242C22×C4—5382no—
243C22×C4—5382no—
244C22×C4C22×D26911yescharacteristic
245C22×C4C22×D26911yescharacteristic
246C22×C4C22×D26911yescharacteristic
247C22×C4C22×D26911yescharacteristic
248C22×C4C22×D26911yescharacteristic
249C22×C4C22×D26911yescharacteristic
250C4⋊C4—22no—
251C4⋊C4—2694no—
252C4⋊C4—2694no—
253C4⋊C4—2694no—
254C4⋊C4—5382no—
255C4⋊C4—5382no—
256C22⋊C4—22no—
257C22⋊C4—22no—
258C22⋊C4—2694no—
259C22⋊C4—2694no—
260C22⋊C4—5382no—
261C22⋊C4C4×D26914yes—
262C42—22no—
263C42—2694no—
264C42—5382no—
265C42—5382no—
266C42—5382no—
267C42—5382no—
268C42—5382no—
269C42—5382no—
270C42—5382no—
271C42—5382no—
272C23—21no—
273C23—21no—
274C23—21no—
275C23—21no—
276C23—21no—
277C23—21no—
278C23C2×C4×D26912yes—
279C23C23×D26911yescharacteristic
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—2692no—
295C2×C4—2692no—
296C2×C4—2692no—
297C2×C4—2692no—
298C2×C4—2692no—
299C2×C4—2692no—
300C2×C4—2692no—
301C2×C4—2692no—
302C2×C4—5381no—
303C2×C4—5381no—
304C2×C4—5381no—
305C2×C4—5381no—
306C2×C4—5381no—
307C2×C4—5381no—
308C2×C4—5381no—
309C2×C4—5381no—
310C2×C4—5381no—
311C2×C4—5381no—
312C2×C4—5381no—
313C2×C4—5381no—
314C2×C4—5381no—
315C2×C4—5381no—
316C2×C4—5381no—
317C2×C4—5381no—
318C2×C4—10764no—
319C2×C4C2×C4×D26912yes—
320C2×C4C2×C4×D26912yes—
321C2×C4#1686440112yes—
322C2×C4#1686440112yes—
323C22—22no—
324C22—22no—
325C22—22no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22C22×C4×D26911yescharacteristic
331C22#41×D26911yescharacteristic
332C22#41×D26911yescharacteristic
333C22#41×D26911yescharacteristic
334C22#41×D26911yescharacteristic
335C22C2×#1686440111yescharacteristic
336C22C2×#1686440111yescharacteristic
337C4—22no—
338C4—22no—
339C4—22no—
340C4—22no—
341C4—41no—
342C4—41no—
343C4—2694no—
344C4—5382no—
345C4—5382no—
346C4—5382no—
347C4—5382no—
348C4—5382no—
349C4—10761no—
350C4—10761no—
351C2—42no—
352C2C4×#1686440111yescharacteristic
353C2C4×#1686440111yescharacteristic
354C2#3177107311yescharacteristic
355C2#126×D26911yescharacteristic
356C2#3177113211yescharacteristic
357C2#3177113411yescharacteristic
358C2#3177113611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D269
commutatorC22×C269C23×C4
Fitting#388×C269C2
socle, cosocleC23×C269C24
prime radicalC24×C269C23
hypercenter#388D269
hypocenterC269C4×#126
LCSG ▷ C22×C269 ▷ C269
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
4. #31770489C2semidirect
5. #31770488C2semidirect
6. #31770486C2semidirect
7. #31770472C2semidirect
8. C4⋊C4×Dic269C2semidirect
9. #31770456C2semidirect
10. #31770456C2semidirect
14. C42×Dic269C2semidirect
17. #22575446C4semidirect
63. C4⋊Dic269C2×C4semidirect
66. #16864381C2×C4semidirect
67. #16864381C2×C4semidirect
79. C4×Dic269C2×C4semidirect
170. Dic269#126semidirect
179. C269C4×#126semidirect

Maximal subgroups

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

subgroupindex
C2×#225754462
#317704992
#317704932
#317704892
#317704882
#317704862
#317704722
C4⋊C4×Dic2692
#317704562
C22⋊C4×Dic2692
C42×Dic2692
#388×C2692
C4×#126269