Finite Group Databasebeta

← #46813613

Subgroups — #46813613

Order 34432.

528 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22575430C211yesmaximal, characteristic
2#31770511C211yesmaximal, characteristic, complemented
3#31770509C211yesmaximal, characteristic, complemented
4#31770503C211yesmaximal, characteristic, complemented
5#31770502C211yesmaximal, characteristic, complemented
6#31770492C211yesmaximal, characteristic, complemented
7#31770489C211yesmaximal, characteristic, complemented
8#31770489C211yesmaximal, characteristic, complemented
9#31770488C211yesmaximal, characteristic, complemented
10#31770480C211yesmaximal, characteristic
11#31770477C211yesmaximal, characteristic
12#31770463C211yesmaximal, characteristic
13C4×C22⋊Dic269C211yesmaximal, characteristic
14C2×#22575360C211yesmaximal, characteristic
15C4×C22⋊C4×C269C211yesmaximal, characteristic
16C22×Dic538C2211yescharacteristic
17C23×Dic269C2211yescharacteristic
18C23×Dic269C2211yescharacteristic
19#22575430C418yescomplemented
20C2×C4⋊Dic269C2211yescharacteristic
21C2×C4⋊Dic269C2211yescharacteristic
22C2×C4⋊Dic269C2211yescharacteristic
23C2×#16864381C2211yescharacteristic
24C2×#16864381C2211yescharacteristic
25C2×#16864381C2211yescharacteristic
26C2×#16864381C2211yescharacteristic
27C2×#16864381C2211yescharacteristic
28C2×#16864381C2211yescharacteristic
29C2×C22⋊Dic269C2211yescharacteristic
30C2×C22⋊Dic269C2211yescharacteristic
31C2×C4×Dic269C2211yescharacteristic
32C2×C4×Dic269C2211yescharacteristic
33#22575360C2211yescharacteristic
34#22575360C2211yescharacteristic
35#22575360C2211yescharacteristic
36#22575360C2211yescharacteristic
37#22575360C2211yescharacteristic
38#22575360C2211yescharacteristic
39#22575360C2211yescharacteristic
40#22575360C2211yescharacteristic
41#22575360C2211yescharacteristic
42#22575360C2211yescharacteristic
43#22575360C2211yescharacteristic
44#22575360C2211yescharacteristic
45C23×C4×C269C2211yescharacteristic
46C2×C22⋊C4×C269C2211yescharacteristic
47C2×C22⋊C4×C269C2211yescharacteristic
48C2×C42×C269C2211yescharacteristic
49C2×C42×C269C2211yescharacteristic
50#95×C269C2211yescharacteristic
51#95×C269C2211yescharacteristic
52C2×Dic538—41no—
53C2×Dic538—41no—
54C2×Dic538C2×C414yescomplemented
55C22×Dic269—22no—
56C22×Dic269—41no—
57C22×Dic269—41no—
58C22×Dic269—41no—
59C22×Dic269—41no—
60C22×Dic269C2×C414yes—
61C22×Dic269C2311yescharacteristic
62C22×Dic269C2311yescharacteristic
63C22×Dic269C2311yescharacteristic
64C22×Dic269C2311yescharacteristic
65C22×Dic269C2311yescharacteristic
66C22×Dic269C2311yescharacteristic
67C22×Dic269C2311yescharacteristic
68C22×Dic269C2311yescharacteristic
69C4⋊Dic269—41no—
70C4⋊Dic269—41no—
71C4⋊Dic269C2×C414yescomplemented
72#16864381—41no—
73#16864381—41no—
74#16864381—41no—
75#16864381—41no—
76#16864381C2×C414yescomplemented
77#16864381C2×C414yescomplemented
78C22⋊Dic269—22no—
79C22⋊Dic269C2×C414yes—
80C4×Dic269—41no—
81C4×Dic269—41no—
82C24×C269C2311yescharacteristic
83C22×C4×C269—41no—
84C22×C4×C269—41no—
85C22×C4×C269Q814yescomplemented
86C22×C4×C269C2311yescharacteristic
87C22×C4×C269C2311yescharacteristic
88C22×C4×C269C2311yescharacteristic
89C22×C4×C269C2311yescharacteristic
90C22×C4×C269C2311yescharacteristic
91C22×C4×C269C2311yescharacteristic
92C22⋊C4×C269—22no—
93C22⋊C4×C269C2×C414yes—
94C42×C269—41no—
95C42×C269—41no—
96Dic538—44no—
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—21no—
109C2×Dic269—21no—
110C2×Dic269—21no—
111C2×Dic269—21no—
112C2×Dic269—21no—
113C2×Dic269—21no—
114C2×Dic269—21no—
115C2×Dic269—21no—
116C2×Dic269—21no—
117C2×Dic269—44no—
118C2×Dic269—44no—
119C2×Dic269C22×C412yes—
120C2×Dic269C22×C412yes—
121C2×Dic269C22×C412yes—
122C2×Dic269C22×C412yes—
123C23×C269—21no—
124C23×C269—21no—
125C23×C269—21no—
126C23×C269—21no—
127C23×C269C22×C412yes—
128C23×C269C2×Q812yes—
129C23×C269#4112yes—
130C23×C269C2411yescharacteristic
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×C269—21no—
140C2×C4×C269—21no—
141C2×C4×C269—21no—
142C2×C4×C269—21no—
143C2×C4×C269—21no—
144C2×C4×C269—21no—
145C2×C4×C269—44no—
146C2×C4×C269C22×C412yes—
147C2×C4×C269C22×C412yes—
148C2×C4×C269C2×Q812yes—
149C2×C4×C269C2×Q812yes—
150C22×C269—22no—
151C22×C269—22no—
152C22×C269—22no—
153C22×C269—22no—
154C22×C269—22no—
155C22×C269—22no—
156C22×C269C4×Q814yes—
157C22×C269C23×C411yescharacteristic
158C22×C269C22×Q811yescharacteristic
159C22×C269C2×#4111yescharacteristic
160C22×C269H(5,𝔽2)11yescharacteristic
161C22×C269H(5,𝔽2)11yescharacteristic
162C22×C269H(5,𝔽2)11yescharacteristic
163C22×C2692−1+411yescharacteristic
164C4×C269—22no—
165C4×C269—22no—
166C4×C269—22no—
167C4×C269—22no—
168C4×C269—41no—
169C4×C269—41no—
170Dic269—22no—
171Dic269—22no—
172Dic269—22no—
173Dic269—22no—
174Dic269—41no—
175Dic269—41no—
176Dic269—41no—
177Dic269—41no—
178C2×C269—24no—
179C2×C269C2×C4×Q811yescharacteristic
180C2×C269#51811yescharacteristic
181C2×C269#52011yescharacteristic
182C2×C269#53811yescharacteristic
183C2×C269#53911yescharacteristic
184C2×C269#54311yescharacteristic
185C2×C269#54411yescharacteristic
186C269#232911yescharacteristic, complemented, Sylow
187#2329—2691nomaximal, Sylow
188C2×C22⋊Q8—2691no—
189#391—2691no—
190#391—2691no—
191#389—2691no—
192#389—2691no—
193#387—2691no—
194#387—2691no—
195#387—2691no—
196#387—2691no—
197#385—2691no—
198#385—2691no—
199#380—2691no—
200C4×C22⋊C4—2691no—
201C4×C22⋊C4D26911yescharacteristic
202C2×#95—2691no—
203C22×Q8—2691no—
204C23×C4—2691no—
205C23×C4—2691no—
206C23×C4C2×D26911yescharacteristic
207C22⋊Q8—2698no—
208C2×C4⋊C4—2691no—
209C2×C4⋊C4—2691no—
210C2×C4⋊C4—2691no—
211C2×C4⋊C4—2691no—
212C2×C4⋊C4—2691no—
213C2×C4⋊C4—2691no—
214C2×C4⋊C4—2691no—
215C2×C4⋊C4—2691no—
216C2×C4⋊C4—2691no—
217C2×C22⋊C4—2691no—
218C2×C22⋊C4—2691no—
219C2×C22⋊C4C2×D26911yescharacteristic
220C2×C22⋊C4C2×D26911yescharacteristic
221C2×C42—2691no—
222C2×C42—2691no—
223C2×C42C2×D26911yescharacteristic
224C2×C42C2×D26911yescharacteristic
225#95—2691no—
226#95—2691no—
227#95—2691no—
228#95—2691no—
229#95—2691no—
230#95—2691no—
231#95—2691no—
232#95—2691no—
233#95—2691no—
234#95—2691no—
235#95—2691no—
236#95—2691no—
237#95C2×D26911yescharacteristic
238#95C2×D26911yescharacteristic
239C24C22×D26911yescharacteristic
240C2×Q8—2694no—
241C2×Q8—10761no—
242C2×Q8—10761no—
243C22×C4—41no—
244C22×C4—41no—
245C22×C4—2691no—
246C22×C4—2691no—
247C22×C4—2691no—
248C22×C4—2691no—
249C22×C4—2694no—
250C22×C4—2691no—
251C22×C4—2691no—
252C22×C4—2691no—
253C22×C4—2691no—
254C22×C4—5382no—
255C22×C4—10761no—
256C22×C4—10761no—
257C22×C4—10761no—
258C22×C4—10761no—
259C22×C4Dic53814yescomplemented
260C22×C4C22×D26911yescharacteristic
261C22×C4C22×D26911yescharacteristic
262C22×C4C22×D26911yescharacteristic
263C22×C4C22×D26911yescharacteristic
264C22×C4C22×D26911yescharacteristic
265C22×C4C22×D26911yescharacteristic
266C4⋊C4—2694no—
267C4⋊C4—2694no—
268C4⋊C4—2694no—
269C4⋊C4—10761no—
270C4⋊C4—10761no—
271C4⋊C4—10761no—
272C4⋊C4—10761no—
273C4⋊C4—10761no—
274C4⋊C4—10761no—
275C22⋊C4—22no—
276C22⋊C4—2694no—
277C22⋊C4—5382no—
278C22⋊C4C4×D26914yes—
279C42—41no—
280C42—41no—
281C42—10761no—
282C42—10761no—
283C23—21no—
284C23—21no—
285C23—21no—
286C23—21no—
287C23C2×C4×D26912yes—
288C23C2×Dic53812yes—
289C23#1686440212yes—
290C23C23×D26911yescharacteristic
291Q8—10764no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—44no—
307C2×C4—2692no—
308C2×C4—2692no—
309C2×C4—2692no—
310C2×C4—2692no—
311C2×C4—5381no—
312C2×C4—5381no—
313C2×C4—5381no—
314C2×C4—5381no—
315C2×C4—5381no—
316C2×C4—5381no—
317C2×C4—5381no—
318C2×C4—5381no—
319C2×C4—5381no—
320C2×C4—5381no—
321C2×C4—5381no—
322C2×C4—5381no—
323C2×C4—5381no—
324C2×C4—5381no—
325C2×C4—5381no—
326C2×C4—5381no—
327C2×C4—5381no—
328C2×C4—5381no—
329C2×C4—5381no—
330C2×C4—5381no—
331C2×C4—10764no—
332C2×C4—10764no—
333C2×C4C2×C4×D26912yes—
334C2×C4C2×C4×D26912yes—
335C2×C4C2×Dic53812yes—
336C2×C4C2×Dic53812yes—
337C22—22no—
338C22—22no—
339C22—22no—
340C22—22no—
341C22—22no—
342C22—22no—
343C22C4×Dic53814yes—
344C22C22×C4×D26911yescharacteristic
345C22C22×Dic53811yescharacteristic
346C22C2×#1686440211yescharacteristic
347C22#2257549811yescharacteristic
348C22#2257549811yescharacteristic
349C22#2257549911yescharacteristic
350C22#2257550011yescharacteristic
351C4—22no—
352C4—22no—
353C4—22no—
354C4—22no—
355C4—41no—
356C4—41no—
357C4—5382no—
358C4—5382no—
359C4—5382no—
360C4—5382no—
361C4—10761no—
362C4—10761no—
363C4—10761no—
364C4—10761no—
365C2—24no—
366C2C2×C4×Dic53811yescharacteristic
367C2#3177107711yescharacteristic
368C2#3177108411yescharacteristic
369C2#3177118811yescharacteristic
370C2#3177119711yescharacteristic
371C2#3177123111yescharacteristic
372C2#3177123311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D269
commutatorC22×C269C23×C4
FittingC4×C22⋊C4×C269C2
socle, cosocleC23×C269C24
prime radicalC24×C269C23
hypercenterC4×C22⋊C4D269
hypocenterC269#2329
LCSG ▷ C22×C269 ▷ C269
UCSC1 ◁ C23 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #31770511C2semidirect
3. #31770509C2semidirect
4. #31770503C2semidirect
5. #31770502C2semidirect
6. #31770492C2semidirect
7. #31770489C2semidirect
8. #31770489C2semidirect
9. #31770488C2semidirect
19. #22575430C4semidirect
54. C2×Dic538C2×C4semidirect
71. C4⋊Dic269C2×C4semidirect
76. #16864381C2×C4semidirect
77. #16864381C2×C4semidirect
85. C22×C4×C269Q8semidirect
186. C269#2329semidirect
259. C22×C4Dic538semidirect

Maximal subgroups

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

subgroupindex
C2×#225754302
#317705112
#317705092
#317705032
#317705022
#317704922
#317704892
#317704882
#317704802
#317704772
#317704632
C4×C22⋊Dic2692
C2×#225753602
C4×C22⋊C4×C2692
#2329269