Finite Group Databasebeta

← #46822828

Subgroups — #46822828

Order 34432.

408 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31771319C211yesmaximal, characteristic, complemented
2#31771274C211yesmaximal, characteristic, complemented
3#31770950C211yesmaximal, characteristic, complemented
4#31770930C211yesmaximal, characteristic, complemented
5#31770928C211yesmaximal, characteristic, complemented
6#31770898C211yesmaximal, characteristic, complemented
7#31770839C211yesmaximal, characteristic, complemented
8#31770838C211yesmaximal, characteristic, complemented
9#31770798C211yesmaximal, characteristic, complemented
10#31770749C211yesmaximal, characteristic, complemented
11SD16×Dic269C211yesmaximal, characteristic, complemented
12#31770668C211yesmaximal, characteristic, complemented
13#31770601C211yesmaximal, characteristic, complemented
14#31770600C211yesmaximal, characteristic, complemented
15#449×C269C211yesmaximal, characteristic, complemented
16C2×#16864403C2211yescharacteristic
17C2×#16864387C2211yescharacteristic
18C22×#14524130C2211yescharacteristic
19C2×C8×D269C2211yescharacteristic
20#22575452C2211yescharacteristic
21#22575449—21no—
22#22575449C2211yescharacteristic
23#22575440—21no—
24#22575439—21no—
25#22575427—21no—
26#22575427C2211yescharacteristic
27#22575425—21no—
28#22575424—21no—
29#22575424C2211yescharacteristic
30#22575424C2211yescharacteristic
31Q8×Dic269C2211yescharacteristic
32D4×Dic269C2211yescharacteristic
33C4×C22⋊D269—21no—
34C4×C22⋊D269C2211yescharacteristic
35#22575412C2211yescharacteristic
36#22575411C2211yescharacteristic
37#22575409—21no—
38#22575387C2211yescharacteristic
39#22575386C2211yescharacteristic
40#22575385C2211yescharacteristic
41#22575382C2211yescharacteristic
42#22575377C2211yescharacteristic
43#22575377C2211yescharacteristic
44#22575375C2211yescharacteristic
45#22575375C2211yescharacteristic
46#22575374C2211yescharacteristic
47#22575374C2211yescharacteristic
48#22575374C2211yescharacteristic
49#22575373C2211yescharacteristic
50#22575365C2211yescharacteristic
51C8×Dic269C2211yescharacteristic
52C2×#41×C269C2211yescharacteristic
53C2×SD16×C269C2211yescharacteristic
54C2×D8×C269C2211yescharacteristic
55#121×C269C2211yescharacteristic
56#103×C269C2211yescharacteristic
57#102×C269C2211yescharacteristic
58C22⋊C8×C269C2211yescharacteristic
59#16864403—22no—
60#16864403—41no—
61C2×Dic538—21no—
62C2×D1076—21no—
63C2×D1076C2311yescharacteristic
64C2×C22⋊D269—21no—
65C2×C22⋊D269—21no—
66C2×C22⋊D269—21no—
67C2×C22⋊D269—21no—
68C2×C22⋊D269—21no—
69C2×C22⋊D269D411yescharacteristic
70C22×Dic269—21no—
71C2×C4×D269—21no—
72C2×C4×D269C2311yescharacteristic
73#16864387—41no—
74C2×#14524130—41no—
75C2×#14524130C2311yescharacteristic
76C2×#14524130C2311yescharacteristic
77C8×D269—41no—
78C4⋊Dic269—21no—
79C4⋊Dic269C2311yescharacteristic
80C4⋊Dic269C2311yescharacteristic
81C4⋊Dic269C2311yescharacteristic
82#16864381—21no—
83#16864381D411yescharacteristic
84C22⋊Dic269—21no—
85C22⋊Dic269—21no—
86C22⋊Dic269—21no—
87C22⋊Dic269—21no—
88C22⋊Dic269D411yescharacteristic
89#16864379—21no—
90#16864379—21no—
91#16864379D411yescharacteristic
92C4×Dic269—21no—
93C4×Dic269—21no—
94C4×Dic269—21no—
95C4×Dic269C2311yescharacteristic
96#41×C269—22no—
97#41×C269—41no—
98C2×Q8×C269C2311yescharacteristic
99C2×D4×C269—21no—
100C2×D4×C269—21no—
101C2×D4×C269C2311yescharacteristic
102C2×D4×C269C2311yescharacteristic
103C22×C4×C269—21no—
104C22×C4×C269C2311yescharacteristic
105SD16×C269—22no—
106D8×C269—41no—
107C2×C8×C269C2311yescharacteristic
108C2×C8×C269C2311yescharacteristic
109C4⋊C4×C269C2311yescharacteristic
110C22⋊C4×C269—21no—
111C22×D269—21no—
112C22×D269C2×D411yescharacteristic
113Dic538—81no—
114D1076—21no—
115D1076—21no—
116D1076—42no—
117C22⋊D269—22no—
118C22⋊D269—42no—
119C22⋊D269—81no—
120C22⋊D269—81no—
121C22⋊D269—81no—
122C22⋊D269—81no—
123C2×Dic269—21no—
124C2×Dic269—21no—
125C2×Dic269—21no—
126C2×Dic269—42no—
127C2×Dic269C2×D411yescharacteristic
128C2×Dic269C2×D411yescharacteristic
129C2×Dic269C2×D411yescharacteristic
130C4×D269—21no—
131C4×D269—21no—
132C4×D269—42no—
133#14524130—21no—
134#14524130—21no—
135C23×C269—21no—
136C23×C269—21no—
137C23×C269C2×D411yescharacteristic
138Q8×C269—21no—
139Q8×C269#4112yes—
140D4×C269—21no—
141D4×C269—21no—
142D4×C269—21no—
143D4×C269—21no—
144D4×C269—42no—
145D4×C269—81no—
146C2×C4×C269—21no—
147C2×C4×C269—21no—
148C2×C4×C269—21no—
149C2×C4×C269—21no—
150C2×C4×C269—42no—
151C2×C4×C269C2×D411yescharacteristic
152C2×C4×C269C2411yescharacteristic
153C8×C269—21no—
154C8×C269—21no—
155C22×C269—21no—
156C22×C269—21no—
157C22×C269—21no—
158C22×C269—41no—
159C22×C269—41no—
160C22×C269—41no—
161C22×C269—41no—
162C22×C269—41no—
163C22×C269—41no—
164C22×C269C22×D411yescharacteristic
165C2×D269—21no—
166C2×D269—21no—
167C2×D269—21no—
168C2×D269—41no—
169C2×D269—41no—
170C2×D269—41no—
171C4×C269—21no—
172C4×C269—22no—
173C4×C269—41no—
174C4×C269C2×#4111yescharacteristic
175C4×C269H(5,𝔽2)11yescharacteristic
176Dic269—21no—
177Dic269—21no—
178Dic269—41no—
179Dic269—41no—
180Dic269—41no—
181Dic269#13512yes—
182C2×C269—41no—
183C2×C269—81no—
184C2×C269—81no—
185C2×C269#54611yescharacteristic
186C2×C269C2×#13511yescharacteristic
187C2×C269#57611yescharacteristic
188D269—41no—
189D269—81no—
190C269#330511yescharacteristic, complemented, Sylow
191#3305—2691nomaximal, Sylow
192#555—2691no—
193#550—2691no—
194#486—2691no—
195#482—2691no—
196#482—2691no—
197#477—2691no—
198#466—2691no—
199#466—2691no—
200#459—2691no—
201#449—2691no—
202#449D26911yescharacteristic, complemented
203C4×SD16—2691no—
204C8×D4—2691no—
205#416—2691no—
206#416—2691no—
207C2×#41—2691no—
208C2×#41C2×D26911yescharacteristic
209C2×SD16C2×D26911yescharacteristic
210C2×D8—2691no—
211C2×D8C2×D26911yescharacteristic
212C22×C8—2691no—
213C22×C8—2691no—
214C4⋊Q8—2691no—
215#127—2691no—
216#127—5381no—
217#124—5381no—
218#124—5381no—
219#121—2691no—
220#121—2691no—
221#121—2691no—
222#121—5381no—
223#121—5381no—
224#121—5381no—
225#121C2×D26911yescharacteristic
226C4×Q8—2691no—
227C4×D4—2691no—
228C4×D4—2691no—
229C4×D4—5381no—
230#117—2691no—
231#117—2691no—
232#117—5381no—
233#107—2691no—
234#107—2691no—
235#106—2691no—
236C4⋊C8—2691no—
237#103—2691no—
238#103—2691no—
239#103C2×D26911yescharacteristic
240#102—2691no—
241#102—2691no—
242#102—2691no—
243#102—2691no—
244#102—2691no—
245#102—2691no—
246#102C2×D26911yescharacteristic
247C22⋊C8—2691no—
248C22⋊C8C2×D26911yescharacteristic
249C4×C8—2691no—
250#41—22no—
251#41—41no—
252#41—5382no—
253#41—10761no—
254C2×Q8—5381no—
255C2×Q8C22×D26911yescharacteristic
256C2×D4—21no—
257C2×D4—21no—
258C2×D4—2691no—
259C2×D4—2691no—
260C2×D4—5381no—
261C2×D4—5381no—
262C2×D4—5381no—
263C2×D4—5381no—
264C2×D4—5381no—
265C2×D4—5381no—
266C2×D4C22×D26911yescharacteristic
267C2×D4C22×D26911yescharacteristic
268C22×C4—21no—
269C22×C4—2691no—
270C22×C4—5381no—
271C22×C4—5381no—
272C22×C4C22×D26911yescharacteristic
273SD16—22no—
274D8—41no—
275D8—10761no—
276C2×C8—2691no—
277C2×C8—2691no—
278C2×C8—10761no—
279C2×C8—10761no—
280C2×C8C22×D26911yescharacteristic
281C2×C8C22×D26911yescharacteristic
282C4⋊C4—2691no—
283C4⋊C4—2691no—
284C4⋊C4—2691no—
285C4⋊C4—2691no—
286C4⋊C4—5381no—
287C4⋊C4—5381no—
288C4⋊C4C22×D26911yescharacteristic
289C22⋊C4—21no—
290C22⋊C4—2691no—
291C22⋊C4—2691no—
292C22⋊C4—5381no—
293C22⋊C4—5381no—
294C22⋊C4—5381no—
295C22⋊C4—5381no—
296C22⋊C4—5381no—
297C22⋊C4—5381no—
298C42—2691no—
299C42—5381no—
300C42—5381no—
301C42—5381no—
302C23—21no—
303C23—21no—
304C23—2691no—
305C23—5381no—
306C23D4×D26911yescharacteristic
307Q8—21no—
308Q8—21521no—
309Q8#1686440112yes—
310D4—21no—
311D4—21no—
312D4—21no—
313D4—21no—
314D4—42no—
315D4—81no—
316D4—5382no—
317D4—5381no—
318D4—5381no—
319D4—10762no—
320D4—10762no—
321D4—21521no—
322D4—21521no—
323D4—21521no—
324D4—21521no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—42no—
330C2×C4—2691no—
331C2×C4—2691no—
332C2×C4—2691no—
333C2×C4—5381no—
334C2×C4—5381no—
335C2×C4—5381no—
336C2×C4—5381no—
337C2×C4—5381no—
338C2×C4—10762no—
339C2×C4—10762no—
340C2×C4D4×D26911yescharacteristic
341C2×C4C23×D26911yescharacteristic
342C8—21no—
343C8—21no—
344C8—5381no—
345C8—5381no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—5381no—
356C22—5381no—
357C22—5381no—
358C22—10761no—
359C22—10761no—
360C22—10761no—
361C22C2×D4×D26911yescharacteristic
362C4—21no—
363C4—22no—
364C4—41no—
365C4—2692no—
366C4—5381no—
367C4—5381no—
368C4—10761no—
369C4—10761no—
370C4—10761no—
371C4C2×#1686440111yescharacteristic
372C4#2257549811yescharacteristic
373C2—41no—
374C2—81no—
375C2—81no—
376C2—10761no—
377C2—21521no—
378C2#3177124211yescharacteristic
379C2#135×D26911yescharacteristic
380C2#3177140911yescharacteristic
subgroupG/H
centerC22C2×D4×D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#449×C269C2
socleC22×C269C22×D4
hypercenter#449D269
hypocenterC269#3305
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #31771319C2semidirect
2. #31771274C2semidirect
3. #31770950C2semidirect
4. #31770930C2semidirect
5. #31770928C2semidirect
6. #31770898C2semidirect
7. #31770839C2semidirect
8. #31770838C2semidirect
9. #31770798C2semidirect
10. #31770749C2semidirect
11. SD16×Dic269C2semidirect
12. #31770668C2semidirect
13. #31770601C2semidirect
14. #31770600C2semidirect
15. #449×C269C2semidirect
190. C269#3305semidirect
202. #449D269semidirect

Maximal subgroups

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

subgroupindex
#317713192
#317712742
#317709502
#317709302
#317709282
#317708982
#317708392
#317708382
#317707982
#317707492
SD16×Dic2692
#317706682
#317706012
#317706002
#449×C2692
#3305269