Finite Group Databasebeta

← #46822808

Subgroups — #46822808

Order 34432.

398 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31771319C211yesmaximal, characteristic, complemented
2#31771257C211yesmaximal, characteristic, complemented
3#31770954C211yesmaximal, characteristic, complemented
4#31770949C211yesmaximal, characteristic, complemented
5#31770943C211yesmaximal, characteristic, complemented
6#31770894C211yesmaximal, characteristic, complemented
7#31770833C211yesmaximal, characteristic, complemented
8#31770808C211yesmaximal, characteristic, complemented
9#31770749C211yesmaximal, characteristic, complemented
10#31770748C211yesmaximal, characteristic, complemented
11#31770685C211yesmaximal, characteristic, complemented
12C8×C22⋊D269C211yesmaximal, characteristic, complemented
13#31770602C211yesmaximal, characteristic, complemented
14#31770600C211yesmaximal, characteristic, complemented
15#465×C269C211yesmaximal, characteristic, complemented
16C2×#16864403C2211yescharacteristic
17C2×#16864402C2211yescharacteristic
18C2×#16864390C2211yescharacteristic
19C2×#16864387C2211yescharacteristic
20C2×C8×D269C2211yescharacteristic
21#22575452C2211yescharacteristic
22#22575451C2211yescharacteristic
23#22575440—21no—
24#22575439—21no—
25#22575438—21no—
26#22575435—21no—
27#22575433C2211yescharacteristic
28#22575426—21no—
29#22575425—21no—
30#22575424C2211yescharacteristic
31D4×Dic269C2211yescharacteristic
32#22575415C2211yescharacteristic
33C4×C22⋊D269C2211yescharacteristic
34#22575412C2211yescharacteristic
35#22575411C2211yescharacteristic
36#22575409—21no—
37C4⋊C4×D269—21no—
38#22575386C2211yescharacteristic
39#22575384C2211yescharacteristic
40#22575382C2211yescharacteristic
41#22575378C2211yescharacteristic
42#22575378C2211yescharacteristic
43#22575377C2211yescharacteristic
44#22575377C2211yescharacteristic
45#22575376C2211yescharacteristic
46#22575375C2211yescharacteristic
47#22575375C2211yescharacteristic
48#22575373C2211yescharacteristic
49C22⋊#14524130C2211yescharacteristic
50#22575365C2211yescharacteristic
51C8×Dic269C2211yescharacteristic
52C2×SD16×C269C2211yescharacteristic
53C22×C8×C269C2211yescharacteristic
54C22⋊Q8×C269C2211yescharacteristic
55#121×C269C2211yescharacteristic
56#106×C269C2211yescharacteristic
57#103×C269C2211yescharacteristic
58#102×C269C2211yescharacteristic
59#16864403—22no—
60#16864403—41no—
61#16864402—22no—
62#16864402—41no—
63C2×Dic538—21no—
64C2×Dic538C2311yescharacteristic
65C2×D1076—21no—
66C2×D1076C2311yescharacteristic
67C2×C22⋊D269—21no—
68C2×C22⋊D269—21no—
69C2×C22⋊D269D411yescharacteristic
70C22×Dic269—21no—
71C2×C4×D269—21no—
72C2×C4×D269—21no—
73C2×C4×D269—21no—
74C2×C4×D269C2311yescharacteristic
75#16864390—41no—
76#16864387—22no—
77C2×#14524130C2311yescharacteristic
78C2×#14524130C2311yescharacteristic
79C8×D269—41no—
80C4⋊Dic269—21no—
81C4⋊Dic269C2311yescharacteristic
82C4⋊Dic269C2311yescharacteristic
83#16864381—21no—
84#16864381—21no—
85#16864381—21no—
86#16864381D411yescharacteristic
87C22⋊Dic269—21no—
88C22⋊Dic269—21no—
89C22⋊Dic269—21no—
90C22⋊Dic269D411yescharacteristic
91#16864379—21no—
92#16864379—21no—
93#16864379—21no—
94#16864379D411yescharacteristic
95C4×Dic269—21no—
96C4×Dic269—21no—
97C4×Dic269C2311yescharacteristic
98C2×Q8×C269C2311yescharacteristic
99C2×D4×C269—21no—
100C2×D4×C269C2311yescharacteristic
101C22×C4×C269C2311yescharacteristic
102SD16×C269—41no—
103C2×C8×C269—41no—
104C2×C8×C269C2311yescharacteristic
105C2×C8×C269C2311yescharacteristic
106C4⋊C4×C269—21no—
107C4⋊C4×C269C2311yescharacteristic
108C4⋊C4×C269C2311yescharacteristic
109C22⋊C4×C269—21no—
110C22⋊C4×C269—21no—
111C22×D269—21no—
112C22×D269C2×D411yescharacteristic
113Dic538—21no—
114Dic538—21no—
115Dic538—81no—
116D1076—21no—
117D1076—42no—
118D1076#4112yes—
119C22⋊D269—22no—
120C22⋊D269—42no—
121C22⋊D269—81no—
122C2×Dic269—21no—
123C2×Dic269—21no—
124C2×Dic269—21no—
125C2×Dic269—42no—
126C2×Dic269C2×D411yescharacteristic
127C2×Dic269C2×D411yescharacteristic
128C2×Dic269C2×D411yescharacteristic
129C4×D269—21no—
130C4×D269—21no—
131C4×D269—42no—
132C4×D269—42no—
133C4×D269—42no—
134#14524130—21no—
135#14524130—21no—
136C23×C269—21no—
137C23×C269C2×D411yescharacteristic
138Q8×C269—21no—
139Q8×C269—21no—
140D4×C269—21no—
141D4×C269—21no—
142D4×C269—81no—
143C2×C4×C269—21no—
144C2×C4×C269—21no—
145C2×C4×C269—21no—
146C2×C4×C269—21no—
147C2×C4×C269—21no—
148C2×C4×C269C2×D411yescharacteristic
149C2×C4×C269C2411yescharacteristic
150C8×C269—21no—
151C8×C269—21no—
152C22×C269—21no—
153C22×C269—21no—
154C22×C269—21no—
155C22×C269—41no—
156C22×C269—41no—
157C22×C269—41no—
158C22×C269C22×D411yescharacteristic
159C2×D269—21no—
160C2×D269—22no—
161C2×D269—21no—
162C2×D269—21no—
163C2×D269—41no—
164C2×D269—41no—
165C4×C269—21no—
166C4×C269—41no—
167C4×C269—41no—
168C4×C269—41no—
169C4×C269C2×#4111yescharacteristic
170C4×C269H(5,𝔽2)11yescharacteristic
171Dic269—21no—
172Dic269—21no—
173Dic269—41no—
174Dic269—41no—
175Dic269—41no—
176Dic269#13512yes—
177C2×C269—41no—
178C2×C269—81no—
179C2×C269#54611yescharacteristic
180C2×C269C2×#13511yescharacteristic
181C2×C269#57711yescharacteristic
182D269—41no—
183D269—42no—
184C269#330311yescharacteristic, complemented, Sylow
185#3303—2691nomaximal, Sylow
186#555—2691no—
187#547—2691no—
188#487—2691no—
189#485—2691no—
190#485—2691no—
191#476—2691no—
192#465—2691no—
193#465D26911yescharacteristic, complemented
194#461—2691no—
195#449—2691no—
196#449—2691no—
197C4×D8—2691no—
198C8×D4—2691no—
199#416—2691no—
200#416—2691no—
201C2×#41—2691no—
202C2×#41—2691no—
203C2×SD16—2691no—
204C2×SD16C2×D26911yescharacteristic
205C2×D8—2691no—
206C22×C8—2691no—
207C22×C8C2×D26911yescharacteristic
208C4⋊Q8—2691no—
209C4⋊Q8—2691no—
210#124—5381no—
211#124—5381no—
212#123—5381no—
213#123—5381no—
214C22⋊Q8—2691no—
215C22⋊Q8C2×D26911yescharacteristic
216#121—2691no—
217#121—5381no—
218#121—5381no—
219#121C2×D26911yescharacteristic
220C4×D4—2691no—
221C4×D4—2691no—
222C4×D4—2691no—
223#117—2691no—
224#117—2691no—
225#117—5381no—
226C2×C4⋊C4—5381no—
227#107—2691no—
228#106—2691no—
229#106C2×D26911yescharacteristic
230C4⋊C8—2691no—
231#103—2691no—
232#103—2691no—
233#103—2691no—
234#103—2691no—
235#103—2691no—
236#103C2×D26911yescharacteristic
237#102—2691no—
238#102—2691no—
239#102—2691no—
240#102C2×D26911yescharacteristic
241C22⋊C8—2691no—
242C22⋊C8—2691no—
243C4×C8—2691no—
244#41—5382no—
245#41—5382no—
246#41—10761no—
247#41—10761no—
248C2×Q8—2691no—
249C2×Q8—5381no—
250C2×Q8C22×D26911yescharacteristic
251C2×D4—21no—
252C2×D4—2691no—
253C2×D4—2691no—
254C2×D4—5381no—
255C2×D4—5381no—
256C2×D4—5381no—
257C2×D4C22×D26911yescharacteristic
258C22×C4—2691no—
259C22×C4—5381no—
260C22×C4—5381no—
261C22×C4—5381no—
262C22×C4—5381no—
263C22×C4C22×D26911yescharacteristic
264SD16—41no—
265SD16—10761no—
266D8—5382no—
267C2×C8—41no—
268C2×C8—2691no—
269C2×C8—2691no—
270C2×C8—10761no—
271C2×C8C22×D26911yescharacteristic
272C2×C8C22×D26911yescharacteristic
273C4⋊C4—21no—
274C4⋊C4—2691no—
275C4⋊C4—2691no—
276C4⋊C4—2691no—
277C4⋊C4—5381no—
278C4⋊C4—5381no—
279C4⋊C4—5381no—
280C4⋊C4—5381no—
281C4⋊C4C22×D26911yescharacteristic
282C4⋊C4C22×D26911yescharacteristic
283C22⋊C4—21no—
284C22⋊C4—21no—
285C22⋊C4—2691no—
286C22⋊C4—2691no—
287C22⋊C4—5381no—
288C22⋊C4—5381no—
289C22⋊C4—5381no—
290C22⋊C4—5381no—
291C22⋊C4—5381no—
292C22⋊C4—5381no—
293C42—2691no—
294C42—5381no—
295C42—5381no—
296C23—21no—
297C23—2691no—
298C23—5381no—
299C23D4×D26911yescharacteristic
300Q8—21no—
301Q8—21no—
302Q8—5381no—
303Q8—5381no—
304Q8—21521no—
305D4—21no—
306D4—21no—
307D4—81no—
308D4—2692no—
309D4—5382no—
310D4—5381no—
311D4—10762no—
312D4—10762no—
313D4—21521no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—2691no—
320C2×C4—2691no—
321C2×C4—2691no—
322C2×C4—5381no—
323C2×C4—5381no—
324C2×C4—5381no—
325C2×C4—5381no—
326C2×C4—5381no—
327C2×C4—10762no—
328C2×C4—10762no—
329C2×C4—10762no—
330C2×C4—10762no—
331C2×C4D4×D26911yescharacteristic
332C2×C4C23×D26911yescharacteristic
333C8—21no—
334C8—21no—
335C8—5381no—
336C8—5381no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—5381no—
344C22—5381no—
345C22—5382no—
346C22—5381no—
347C22—10761no—
348C22—10761no—
349C22C2×D4×D26911yescharacteristic
350C4—21no—
351C4—41no—
352C4—41no—
353C4—41no—
354C4—2692no—
355C4—5381no—
356C4—5381no—
357C4—10761no—
358C4—10761no—
359C4—10761no—
360C4#41×D26911yescharacteristic
361C4#2257549811yescharacteristic
362C2—41no—
363C2—81no—
364C2—10761no—
365C2—10762no—
366C2#3177124411yescharacteristic
367C2#135×D26911yescharacteristic
368C2#3177141111yescharacteristic
subgroupG/H
centerC22C2×D4×D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#465×C269C2
socleC22×C269C22×D4
hypercenter#465D269
hypocenterC269#3303
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. #31771319C2semidirect
2. #31771257C2semidirect
3. #31770954C2semidirect
4. #31770949C2semidirect
5. #31770943C2semidirect
6. #31770894C2semidirect
7. #31770833C2semidirect
8. #31770808C2semidirect
9. #31770749C2semidirect
10. #31770748C2semidirect
11. #31770685C2semidirect
12. C8×C22⋊D269C2semidirect
13. #31770602C2semidirect
14. #31770600C2semidirect
15. #465×C269C2semidirect
184. C269#3303semidirect
193. #465D269semidirect

Maximal subgroups

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

subgroupindex
#317713192
#317712572
#317709542
#317709492
#317709432
#317708942
#317708332
#317708082
#317707492
#317707482
#317706852
C8×C22⋊D2692
#317706022
#317706002
#465×C2692
#3303269