Finite Group Databasebeta

← #46822793

Subgroups — #46822793

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#31771307C211yesmaximal, characteristic, complemented
2#31771261C211yesmaximal, characteristic, complemented
3#31770958C211yesmaximal, characteristic, complemented
4#31770948C211yesmaximal, characteristic, complemented
5#31770921C211yesmaximal, characteristic, complemented
6#31770911C211yesmaximal, characteristic, complemented
7#31770833C211yesmaximal, characteristic, complemented
8#31770818C211yesmaximal, characteristic, complemented
9#31770747C211yesmaximal, characteristic, complemented
10#31770743C211yesmaximal, characteristic, complemented
11#31770696C211yesmaximal, characteristic, complemented
12C8×C22⋊D269C211yesmaximal, characteristic, complemented
13#31770598C211yesmaximal, characteristic, complemented
14C2×#22575378C211yesmaximal, characteristic, complemented
15#466×C269C211yesmaximal, characteristic, complemented
16C2×#16864401C2211yescharacteristic
17C22×Dic538C2211yescharacteristic
18C2×#16864390C2211yescharacteristic
19C2×#16864390C2211yescharacteristic
20C2×C8×D269C2211yescharacteristic
21#22575446—21no—
22#22575444C2211yescharacteristic
23#22575440C2211yescharacteristic
24#22575439—21no—
25#22575437—21no—
26#22575433C2211yescharacteristic
27#22575430—21no—
28#22575425—21no—
29#22575425—21no—
30#22575424C2211yescharacteristic
31#22575418C2211yescharacteristic
32D4×Dic269—21no—
33D4×Dic269—21no—
34D4×Dic269C2211yescharacteristic
35C4×C22⋊D269C2211yescharacteristic
36#22575411C2211yescharacteristic
37C2×C4⋊Dic269C2211yescharacteristic
38#22575384C2211yescharacteristic
39#22575384C2211yescharacteristic
40#22575382C2211yescharacteristic
41#22575378C2211yescharacteristic
42#22575378C2211yescharacteristic
43#22575378C2211yescharacteristic
44#22575378C2211yescharacteristic
45#22575376C2211yescharacteristic
46#22575376C2211yescharacteristic
47#22575374C2211yescharacteristic
48#22575374C2211yescharacteristic
49C22⋊#14524130C2211yescharacteristic
50#22575365C2211yescharacteristic
51C8×Dic269C2211yescharacteristic
52C2×D8×C269C2211yescharacteristic
53C22×C8×C269C2211yescharacteristic
54#121×C269C2211yescharacteristic
55#121×C269C2211yescharacteristic
56#107×C269C2211yescharacteristic
57#102×C269C2211yescharacteristic
58#102×C269C2211yescharacteristic
59#16864401—22no—
60#16864401—41no—
61C2×Dic538—22no—
62C2×Dic538—21no—
63C2×Dic538—41no—
64C2×Dic538C2311yescharacteristic
65C2×Dic538C2311yescharacteristic
66C2×C22⋊D269—21no—
67C2×C22⋊D269—21no—
68C2×C22⋊D269D411yescharacteristic
69C22×Dic269—21no—
70C22×Dic269—21no—
71C22×Dic269—21no—
72C22×Dic269—21no—
73C2×C4×D269C2311yescharacteristic
74#16864390—22no—
75#16864390—41no—
76C2×#14524130C2311yescharacteristic
77C2×#14524130C2311yescharacteristic
78C8×D269—41no—
79C4⋊Dic269—21no—
80C4⋊Dic269—21no—
81C4⋊Dic269—21no—
82C4⋊Dic269C2311yescharacteristic
83C4⋊Dic269C2311yescharacteristic
84#16864381—21no—
85#16864381—21no—
86#16864381D411yescharacteristic
87C22⋊Dic269—21no—
88C22⋊Dic269—21no—
89C22⋊Dic269—21no—
90C22⋊Dic269—21no—
91C22⋊Dic269D411yescharacteristic
92#16864379—21no—
93#16864379—21no—
94#16864379D411yescharacteristic
95C4×Dic269—21no—
96C4×Dic269—21no—
97C4×Dic269C2311yescharacteristic
98C2×D4×C269—21no—
99C2×D4×C269—21no—
100C2×D4×C269C2311yescharacteristic
101C2×D4×C269C2311yescharacteristic
102C22×C4×C269C2311yescharacteristic
103D8×C269—41no—
104C2×C8×C269—41no—
105C2×C8×C269C2311yescharacteristic
106C2×C8×C269C2311yescharacteristic
107C4⋊C4×C269C2311yescharacteristic
108C4⋊C4×C269C2311yescharacteristic
109C22⋊C4×C269—21no—
110C22⋊C4×C269—21no—
111C22×D269C2×D411yescharacteristic
112Dic538—21no—
113Dic538—21no—
114Dic538—21no—
115Dic538—42no—
116Dic538#4112yes—
117C22⋊D269—22no—
118C22⋊D269—42no—
119C22⋊D269—81no—
120C2×Dic269—21no—
121C2×Dic269—21no—
122C2×Dic269—21no—
123C2×Dic269—21no—
124C2×Dic269—42no—
125C2×Dic269—42no—
126C2×Dic269—81no—
127C2×Dic269—81no—
128C2×Dic269C2×D411yescharacteristic
129C2×Dic269C2×D411yescharacteristic
130C2×Dic269C2×D411yescharacteristic
131C4×D269—21no—
132C4×D269—21no—
133#14524130—21no—
134#14524130—21no—
135C23×C269—21no—
136C23×C269—21no—
137C23×C269C2×D411yescharacteristic
138D4×C269—21no—
139D4×C269—21no—
140D4×C269—21no—
141D4×C269—21no—
142D4×C269—42no—
143D4×C269—42no—
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—41no—
155C22×C269—41no—
156C22×C269—41no—
157C22×C269—41no—
158C22×C269—41no—
159C22×C269—41no—
160C22×C269#13512yes—
161C22×C269C22×D411yescharacteristic
162C2×D269—21no—
163C2×D269—21no—
164C2×D269—21no—
165C4×C269—21no—
166C4×C269—41no—
167C4×C269—41no—
168C4×C269C2×#4111yescharacteristic
169C4×C269H(5,𝔽2)11yescharacteristic
170Dic269—21no—
171Dic269—22no—
172Dic269—21no—
173Dic269—21no—
174Dic269—41no—
175Dic269—41no—
176Dic269—41no—
177C2×C269—22no—
178C2×C269—81no—
179C2×C269—81no—
180C2×C269#54611yescharacteristic
181C2×C269C2×#13511yescharacteristic
182C2×C269#57711yescharacteristic
183D269—41no—
184C269#330111yescharacteristic, complemented, Sylow
185#3301—2691nomaximal, Sylow
186#553—2691no—
187#548—2691no—
188#488—2691no—
189#485—2691no—
190#481—2691no—
191#479—2691no—
192#466D26911yescharacteristic, complemented
193#465—2691no—
194#463—2691no—
195#449—2691no—
196#448—2691no—
197C4×SD16—2691no—
198C8×D4—2691no—
199#416—2691no—
200C2×#103—2691no—
201C2×#41—2691no—
202C22×Q8—2691no—
203C2×SD16—2691no—
204C2×SD16—2691no—
205C2×D8C2×D26911yescharacteristic
206C22×C8—2691no—
207C22×C8C2×D26911yescharacteristic
208#126—5381no—
209#125—2691no—
210#124—2691no—
211#124—5381no—
212#123—5381no—
213C22⋊Q8—2691no—
214C22⋊Q8—5381no—
215#121—2691no—
216#121—5381no—
217#121—5381no—
218#121C2×D26911yescharacteristic
219#121C2×D26911yescharacteristic
220C4×Q8—2691no—
221C4×D4—2691no—
222C4×D4—2691no—
223C4×D4—5381no—
224C4×D4—5381no—
225#117—2691no—
226C2×C4⋊C4—2691no—
227#107C2×D26911yescharacteristic
228#106—2691no—
229#106—2691no—
230C4⋊C8—2691no—
231#103—2691no—
232#103—2691no—
233#103—2691no—
234#103—2691no—
235#103—2691no—
236#103—2691no—
237#102—2691no—
238#102—2691no—
239#102C2×D26911yescharacteristic
240#102C2×D26911yescharacteristic
241C22⋊C8—2691no—
242C22⋊C8—2691no—
243C4×C8—2691no—
244#41—5382no—
245#41—10761no—
246C2×Q8—2691no—
247C2×Q8—2691no—
248C2×Q8—5382no—
249C2×Q8—5381no—
250C2×Q8—10761no—
251C2×D4—21no—
252C2×D4—21no—
253C2×D4—2691no—
254C2×D4—5381no—
255C2×D4—5381no—
256C2×D4C22×D26911yescharacteristic
257C2×D4C22×D26911yescharacteristic
258C22×C4—2691no—
259C22×C4—5381no—
260C22×C4—5381no—
261C22×C4—5381no—
262C22×C4—5381no—
263C22×C4C22×D26911yescharacteristic
264SD16—5382no—
265SD16—10761no—
266D8—41no—
267C2×C8—41no—
268C2×C8—2691no—
269C2×C8—2691no—
270C2×C8—10761no—
271C2×C8C22×D26911yescharacteristic
272C2×C8C22×D26911yescharacteristic
273C4⋊C4—2691no—
274C4⋊C4—2691no—
275C4⋊C4—2691no—
276C4⋊C4—5381no—
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—21no—
298C23—2691no—
299C23D4×D26911yescharacteristic
300Q8—2692no—
301Q8—5381no—
302Q8—5381no—
303Q8—5381no—
304Q8—10762no—
305D4—21no—
306D4—21no—
307D4—21no—
308D4—21no—
309D4—42no—
310D4—42no—
311D4—5382no—
312D4—10762no—
313D4—21521no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—2691no—
319C2×C4—2691no—
320C2×C4—2691no—
321C2×C4—5381no—
322C2×C4—5381no—
323C2×C4—5381no—
324C2×C4—5381no—
325C2×C4—5381no—
326C2×C4—5381no—
327C2×C4—10762no—
328C2×C4—10762no—
329C2×C4—21521no—
330C2×C4—21521no—
331C2×C4D4×D26911yescharacteristic
332C2×C4C23×D26911yescharacteristic
333C8—21no—
334C8—21no—
335C8—5381no—
336C8—5381no—
337C22—21no—
338C22—21no—
339C22—41no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—5381no—
346C22—5381no—
347C22—5381no—
348C22#2257547212yes—
349C22C2×D4×D26911yescharacteristic
350C4—21no—
351C4—41no—
352C4—41no—
353C4—5381no—
354C4—5381no—
355C4—5382no—
356C4—5381no—
357C4—10761no—
358C4—10761no—
359C4—10761no—
360C4#41×D26911yescharacteristic
361C4#2257549811yescharacteristic
362C2—22no—
363C2—81no—
364C2—81no—
365C2—10761no—
366C2#3177124411yescharacteristic
367C2C2×#2257547211yescharacteristic
368C2#3177141211yescharacteristic
subgroupG/H
centerC22C2×D4×D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#466×C269C2
socleC22×C269C22×D4
hypercenter#466D269
hypocenterC269#3301
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C22×C4 ◁ #466

Complements

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

NH ≅ G/Ntype
1. #31771307C2semidirect
2. #31771261C2semidirect
3. #31770958C2semidirect
4. #31770948C2semidirect
5. #31770921C2semidirect
6. #31770911C2semidirect
7. #31770833C2semidirect
8. #31770818C2semidirect
9. #31770747C2semidirect
10. #31770743C2semidirect
11. #31770696C2semidirect
12. C8×C22⋊D269C2semidirect
13. #31770598C2semidirect
14. C2×#22575378C2semidirect
15. #466×C269C2semidirect
184. C269#3301semidirect
192. #466D269semidirect

Maximal subgroups

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

subgroupindex
#317713072
#317712612
#317709582
#317709482
#317709212
#317709112
#317708332
#317708182
#317707472
#317707432
#317706962
C8×C22⋊D2692
#317705982
C2×#225753782
#466×C2692
#3301269