Finite Group Databasebeta

← #46813740

Subgroups — #46813740

Order 34432.

532 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
1C2×#22575411C211yesmaximal, characteristic
2#31770491C211yesmaximal, characteristic, complemented
3#31770490C211yesmaximal, characteristic, complemented
4#31770488C211yesmaximal, characteristic, complemented
5#31770479C211yesmaximal, characteristic
6#31770476C211yesmaximal, characteristic
7#31770472C211yesmaximal, characteristic, complemented
8#31770469C211yesmaximal, characteristic, complemented
9#31770467C211yesmaximal, characteristic
10C4⋊C4×Dic269C211yesmaximal, characteristic, complemented
11C4×#16864379C211yesmaximal, characteristic
12#31770452C211yesmaximal, characteristic
13#31770451C211yesmaximal, characteristic, complemented
14#95×D269C211yesmaximal, characteristic
15#387×C269C211yesmaximal, characteristic, complemented
16C22×C4×D269C2211yescharacteristic
17C22×C4×D269C2211yescharacteristic
18C22×C4×D269C2211yescharacteristic
19#22575411C418yescomplemented
20C2×C4⋊Dic269C2211yescharacteristic
21C2×C4⋊Dic269C2211yescharacteristic
22C2×#16864381C2211yescharacteristic
23C2×#16864381C2211yescharacteristic
24C2×#16864379C2211yescharacteristic
25C2×#16864379C2211yescharacteristic
26C2×#16864379C2211yescharacteristic
27C2×#16864379C2211yescharacteristic
28C2×C4×Dic269C2211yescharacteristic
29C2×C4×Dic269C2211yescharacteristic
30C2×C4×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
45C2×C4⋊C4×C269C2211yescharacteristic
46C2×C4⋊C4×C269C2211yescharacteristic
47C2×C42×C269C2211yescharacteristic
48#95×C269C2211yescharacteristic
49#95×C269C2211yescharacteristic
50#95×C269C2211yescharacteristic
51#95×C269C2211yescharacteristic
52C23×D269C2311yescharacteristic
53C22×Dic269C2311yescharacteristic
54C22×Dic269C2311yescharacteristic
55C22×Dic269C2311yescharacteristic
56C22×Dic269C2311yescharacteristic
57C22×Dic269C2311yescharacteristic
58C22×Dic269C2311yescharacteristic
59C22×Dic269C2311yescharacteristic
60C2×C4×D269—22no—
61C2×C4×D269—22no—
62C2×C4×D269—22no—
63C2×C4×D269—22no—
64C2×C4×D269—22no—
65C2×C4×D269—22no—
66C2×C4×D269—41no—
67C2×C4×D269—41no—
68C2×C4×D269C2×C414yes—
69C4⋊Dic269—22no—
70C4⋊Dic269C2×C414yescomplemented
71#16864381—41no—
72#16864381—41no—
73#16864379—22no—
74#16864379—22no—
75#16864379C2×C414yes—
76#16864379C2×C414yes—
77C4×Dic269—22no—
78C4×Dic269—41no—
79C4×Dic269—41no—
80C4×Dic269C2×C414yescomplemented
81C4×Dic269C2×C414yescomplemented
82C22×C4×C269C2311yescharacteristic
83C22×C4×C269C2311yescharacteristic
84C22×C4×C269C2311yescharacteristic
85C22×C4×C269C2311yescharacteristic
86C22×C4×C269C2311yescharacteristic
87C22×C4×C269C2311yescharacteristic
88C22×C4×C269C2311yescharacteristic
89C4⋊C4×C269—22no—
90C4⋊C4×C269C2×C414yescomplemented
91C42×C269—22no—
92C22×D269—21no—
93C22×D269—21no—
94C22×D269—21no—
95C22×D269—21no—
96C22×D269C22×C412yes—
97C22×D269#4112yes—
98C22×D269#4112yes—
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×Dic269C22×C412yes—
117C2×Dic269C22×C412yes—
118C2×Dic269C22×C412yes—
119C2×Dic269#4112yes—
120C4×D269—28no—
121C4×D269—44no—
122C4×D269—44no—
123C23×C269C2411yescharacteristic
124C2×C4×C269—21no—
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×C269—21no—
140C2×C4×C269—21no—
141C2×C4×C269C22×C412yes—
142C2×C4×C269C22×C412yes—
143C2×C4×C269C22×C412yes—
144C2×C4×C269#4112yes—
145C22×C269C23×C411yescharacteristic
146C22×C269C2×#4111yescharacteristic
147C22×C269C2×#4111yescharacteristic
148C22×C269C2×#4111yescharacteristic
149C22×C269C2×#4111yescharacteristic
150C22×C269H(5,𝔽2)11yescharacteristic
151C22×C2692−1+411yescharacteristic
152C2×D269—22no—
153C2×D269—22no—
154C2×D269—22no—
155C2×D269—22no—
156C2×D269—22no—
157C2×D269—22no—
158C2×D269#11714yes—
159C4×C269—22no—
160C4×C269—22no—
161C4×C269—22no—
162C4×C269—22no—
163C4×C269—41no—
164C4×C269—41no—
165C4×C269—41no—
166Dic269—22no—
167Dic269—22no—
168Dic269—22no—
169Dic269—22no—
170Dic269—41no—
171Dic269—41no—
172Dic269—41no—
173C2×C269C2×#11711yescharacteristic
174C2×C269C4×#4111yescharacteristic
175C2×C269#52011yescharacteristic
176C2×C269#55111yescharacteristic
177C2×C269#55111yescharacteristic
178C2×C269#55211yescharacteristic
179C2×C269#55211yescharacteristic
180D269—24no—
181C269#234311yescharacteristic, complemented, Sylow
182#2343—2691nomaximal, Sylow
183C2×#117—2691no—
184#387—2691no—
185#387—2691no—
186#387—2691no—
187#387D26911yescharacteristic, complemented
188#385—2691no—
189#385—2691no—
190#383—2691no—
191#382—2691no—
192#381—2691no—
193C4×C4⋊C4—2691no—
194C4×C22⋊C4—2691no—
195C4×C22⋊C4—2691no—
196#376—2691no—
197C2×#95—2691no—
198C23×C4—2691no—
199C23×C4—2691no—
200C23×C4—2691no—
201#117—2698no—
202C2×C4⋊C4—2691no—
203C2×C4⋊C4—2691no—
204C2×C4⋊C4—2691no—
205C2×C4⋊C4—2691no—
206C2×C4⋊C4C2×D26911yescharacteristic
207C2×C4⋊C4C2×D26911yescharacteristic
208C2×C22⋊C4—2691no—
209C2×C22⋊C4—2691no—
210C2×C22⋊C4—2691no—
211C2×C22⋊C4—2691no—
212C2×C42—2691no—
213C2×C42—2691no—
214C2×C42—2691no—
215C2×C42—2691no—
216C2×C42—2691no—
217C2×C42C2×D26911yescharacteristic
218#95—2691no—
219#95—2691no—
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
232#95C2×D26911yescharacteristic
233#95C2×D26911yescharacteristic
234C24—2691no—
235C22×C4—2691no—
236C22×C4—2691no—
237C22×C4—2691no—
238C22×C4—2691no—
239C22×C4—2694no—
240C22×C4—2691no—
241C22×C4—2691no—
242C22×C4—2691no—
243C22×C4—5382no—
244C22×C4—5382no—
245C22×C4—5382no—
246C22×C4—5382no—
247C22×C4—5382no—
248C22×C4—5382no—
249C22×C4—10761no—
250C22×C4—10761no—
251C22×C4C22×D26911yescharacteristic
252C22×C4C22×D26911yescharacteristic
253C22×C4C22×D26911yescharacteristic
254C22×C4C22×D26911yescharacteristic
255C22×C4C22×D26911yescharacteristic
256C22×C4C22×D26911yescharacteristic
257C22×C4C22×D26911yescharacteristic
258C4⋊C4—22no—
259C4⋊C4—2694no—
260C4⋊C4—5382no—
261C4⋊C4—10761no—
262C4⋊C4—10761no—
263C4⋊C4C4×D26914yescomplemented
264C22⋊C4—2694no—
265C22⋊C4—2694no—
266C22⋊C4—5382no—
267C22⋊C4—5382no—
268C42—22no—
269C42—2694no—
270C42—2694no—
271C42—5382no—
272C42—10761no—
273C42—10761no—
274C23—2692no—
275C23—2692no—
276C23—2692no—
277C23—5381no—
278C23—5381no—
279C23—5381no—
280C23—5381no—
281C23C23×D26911yescharacteristic
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—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—2692no—
300C2×C4—2692no—
301C2×C4—2692no—
302C2×C4—2692no—
303C2×C4—5388no—
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—5381no—
319C2×C4—5381no—
320C2×C4—5381no—
321C2×C4—10764no—
322C2×C4—10764no—
323C2×C4C2×C4×D26912yes—
324C2×C4C2×C4×D26912yes—
325C2×C4C2×C4×D26912yes—
326C2×C4#1686440112yes—
327C22—2694no—
328C22—5382no—
329C22—5382no—
330C22—5382no—
331C22—5382no—
332C22—5382no—
333C22—5382no—
334C22C22×C4×D26911yescharacteristic
335C22#41×D26911yescharacteristic
336C22#41×D26911yescharacteristic
337C22#41×D26911yescharacteristic
338C22C2×#1686440111yescharacteristic
339C22#2257549911yescharacteristic
340C22#2257550111yescharacteristic
341C4—22no—
342C4—22no—
343C4—22no—
344C4—22no—
345C4—41no—
346C4—41no—
347C4—41no—
348C4—5382no—
349C4—5382no—
350C4—5382no—
351C4—5382no—
352C4—10761no—
353C4—10761no—
354C4—10761no—
355C2—5384no—
356C2#117×D26911yescharacteristic
357C2C4×#1686440111yescharacteristic
358C2#3177108711yescharacteristic
359C2#3177127811yescharacteristic
360C2#3177128011yescharacteristic
361C2#3177128711yescharacteristic
362C2#3177128911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D269
commutatorC22×C269C23×C4
Fitting#387×C269C2
socle, cosocleC23×C269C24
prime radicalC23×D269C23
hypercenter#387D269
hypocenterC269#2343
LCSG ▷ C22×C269 ▷ C269
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
2. #31770491C2semidirect
3. #31770490C2semidirect
4. #31770488C2semidirect
7. #31770472C2semidirect
8. #31770469C2semidirect
10. C4⋊C4×Dic269C2semidirect
13. #31770451C2semidirect
15. #387×C269C2semidirect
19. #22575411C4semidirect
70. C4⋊Dic269C2×C4semidirect
80. C4×Dic269C2×C4semidirect
81. C4×Dic269C2×C4semidirect
90. C4⋊C4×C269C2×C4semidirect
181. C269#2343semidirect
187. #387D269semidirect
263. C4⋊C4C4×D269semidirect

Maximal subgroups

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

subgroupindex
C2×#225754112
#317704912
#317704902
#317704882
#317704792
#317704762
#317704722
#317704692
#317704672
C4⋊C4×Dic2692
C4×#168643792
#317704522
#317704512
#95×D2692
#387×C2692
#2343269