Finite Group Databasebeta

← #46822885

Subgroups — #46822885

Order 34432.

404 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#31771276C211yesmaximal, characteristic, complemented
2#31770971C211yesmaximal, characteristic, complemented
3#31770929C211yesmaximal, characteristic, complemented
4#31770918C211yesmaximal, characteristic, complemented
5#31770909C211yesmaximal, characteristic, complemented
6#31770856C211yesmaximal, characteristic, complemented
7#31770839C211yesmaximal, characteristic, complemented
8#31770800C211yesmaximal, characteristic, complemented
9#31770748C211yesmaximal, characteristic, complemented
10#31770748C211yesmaximal, characteristic, complemented
11#31770705C211yesmaximal, characteristic, complemented
12#31770677C211yesmaximal, characteristic, complemented
13#31770604C211yesmaximal, characteristic, complemented
14#31770599C211yesmaximal, characteristic, complemented
15#553×C269C211yesmaximal, characteristic, complemented
16C2×#16864402C2211yescharacteristic
17C2×#16864402C2211yescharacteristic
18C2×#16864390C2211yescharacteristic
19C2×#16864387C2211yescharacteristic
20C2×#16864387C2211yescharacteristic
21C2×#16864386C2211yescharacteristic
22C22×#14524130C2211yescharacteristic
23#22575450C2211yescharacteristic
24#22575449—21no—
25#22575427C2211yescharacteristic
26#22575427C2211yescharacteristic
27#22575426—21no—
28#22575426—21no—
29C4×Dic538C2211yescharacteristic
30#22575415—21no—
31#22575386C2211yescharacteristic
32#22575386C2211yescharacteristic
33#22575384C2211yescharacteristic
34C4⋊#14524130C2211yescharacteristic
35#22575376C2211yescharacteristic
36#22575376C2211yescharacteristic
37#22575376C2211yescharacteristic
38#22575374C2211yescharacteristic
39#22575373C2211yescharacteristic
40#22575373C2211yescharacteristic
41#22575373C2211yescharacteristic
42#22575373C2211yescharacteristic
43#22575373C2211yescharacteristic
44#22575373C2211yescharacteristic
45C22⋊#14524130C2211yescharacteristic
46C22⋊#14524130C2211yescharacteristic
47#22575364C2211yescharacteristic
48#126×C269—21no—
49#125×C269C2211yescharacteristic
50#123×C269—21no—
51#121×C269—21no—
52#121×C269C2211yescharacteristic
53#121×C269C2211yescharacteristic
54C4×D4×C269—21no—
55C4×D4×C269C2211yescharacteristic
56C4×D4×C269C2211yescharacteristic
57#117×C269C2211yescharacteristic
58C2×C4⋊C4×C269C2211yescharacteristic
59#16864402—22no—
60#16864402—22no—
61#16864402—41no—
62#16864402—41no—
63C2×Dic538C2311yescharacteristic
64C2×D1076—21no—
65C2×D1076—21no—
66C2×D1076C2311yescharacteristic
67C2×D1076C2311yescharacteristic
68C2×C22⋊D269—21no—
69C2×C22⋊D269—21no—
70C2×C22⋊D269—21no—
71C2×C22⋊D269—21no—
72C2×C4×D269—21no—
73C2×C4×D269—21no—
74#16864390—22no—
75#16864387—41no—
76#16864387—41no—
77#16864386—41no—
78C2×#14524130—41no—
79C2×#14524130C2311yescharacteristic
80C2×#14524130C2311yescharacteristic
81C2×#14524130C2311yescharacteristic
82C2×#14524130C2311yescharacteristic
83C4⋊Dic269C2311yescharacteristic
84#16864381—21no—
85#16864379—21no—
86#16864379—21no—
87C4×Dic269—21no—
88C2×D4×C269—21no—
89C2×D4×C269—21no—
90C2×D4×C269D411yescharacteristic
91C2×D4×C269C2311yescharacteristic
92C22×C4×C269—21no—
93C22×C4×C269—21no—
94C22×C4×C269C2311yescharacteristic
95C22×C4×C269C2311yescharacteristic
96C4⋊C4×C269—21no—
97C4⋊C4×C269—21no—
98C4⋊C4×C269—21no—
99C4⋊C4×C269D411yescharacteristic
100C4⋊C4×C269C2311yescharacteristic
101C4⋊C4×C269C2311yescharacteristic
102C4⋊C4×C269C2311yescharacteristic
103C22⋊C4×C269—21no—
104C22⋊C4×C269—21no—
105C22⋊C4×C269—21no—
106C22⋊C4×C269—21no—
107C22⋊C4×C269D411yescharacteristic
108C22⋊C4×C269D411yescharacteristic
109C42×C269—21no—
110C42×C269C2311yescharacteristic
111C22×D269—21no—
112C22×D269—21no—
113Dic538—21no—
114Dic538#4112yes—
115D1076—21no—
116D1076—21no—
117D1076—21no—
118D1076—21no—
119D1076—42no—
120D1076—81no—
121C22⋊D269—42no—
122C22⋊D269—42no—
123C22⋊D269—81no—
124C22⋊D269—81no—
125C2×Dic269—21no—
126C2×Dic269—21no—
127C4×D269—42no—
128C4×D269—42no—
129#14524130—21no—
130#14524130—21no—
131#14524130—21no—
132#14524130—21no—
133C23×C269—21no—
134C23×C269C2×D411yescharacteristic
135C23×C269C2×D411yescharacteristic
136D4×C269—21no—
137D4×C269—21no—
138D4×C269—41no—
139D4×C269—42no—
140D4×C269—81no—
141C2×C4×C269—21no—
142C2×C4×C269—21no—
143C2×C4×C269—21no—
144C2×C4×C269—21no—
145C2×C4×C269—21no—
146C2×C4×C269—21no—
147C2×C4×C269—21no—
148C2×C4×C269—81no—
149C2×C4×C269—81no—
150C2×C4×C269C2×D411yescharacteristic
151C2×C4×C269C2×D411yescharacteristic
152C2×C4×C269C2×D411yescharacteristic
153C2×C4×C269C2×D411yescharacteristic
154C2×C4×C269C2411yescharacteristic
155C22×C269—21no—
156C22×C269—21no—
157C22×C269—21no—
158C22×C269—21no—
159C22×C269—21no—
160C22×C269—21no—
161C22×C269—41no—
162C22×C269—41no—
163C22×C269—41no—
164C22×C269C22×D411yescharacteristic
165C2×D269—41no—
166C2×D269—41no—
167C2×D269—41no—
168C2×D269—41no—
169C2×D269—41no—
170C2×D269—41no—
171C4×C269—21no—
172C4×C269—21no—
173C4×C269—21no—
174C4×C269—21no—
175C4×C269—41no—
176C4×C269—41no—
177C4×C269—41no—
178C4×C269C2×#4111yescharacteristic
179C4×C269H(5,𝔽2)11yescharacteristic
180Dic269—22no—
181Dic269—41no—
182C2×C269—41no—
183C2×C269—41no—
184C2×C269—81no—
185C2×C269#54611yescharacteristic
186C2×C269#57511yescharacteristic
187C2×C269#57611yescharacteristic
188D269—81no—
189D269—81no—
190C269#330911yescharacteristic, complemented, Sylow
191#3309—2691nomaximal, Sylow
192#553D26911yescharacteristic, complemented
193#550—2691no—
194#490—2691no—
195#482—2691no—
196#480—2691no—
197#479—2691no—
198#469—2691no—
199#466—2691no—
200#459—2691no—
201#449—2691no—
202#449—2691no—
203#440—2691no—
204#435—2691no—
205#417—2691no—
206#416—2691no—
207C2×#41—2691no—
208C2×#41—2691no—
209C2×SD16—2691no—
210C2×D8—2691no—
211C2×D8—2691no—
212C2×M16—2691no—
213C22×C8—2691no—
214#127—2691no—
215#127—5381no—
216#126—21no—
217#125C2×D26911yescharacteristic
218#123—21no—
219#121—21no—
220#121—2691no—
221#121—2691no—
222#121—5381no—
223#121—5381no—
224#121C2×D26911yescharacteristic
225#121C2×D26911yescharacteristic
226C4×Q8—2691no—
227C4×D4—21no—
228C4×D4—5381no—
229C4×D4C2×D26911yescharacteristic
230C4×D4C2×D26911yescharacteristic
231#117C2×D26911yescharacteristic
232C2×C4⋊C4C2×D26911yescharacteristic
233#107—2691no—
234#107—2691no—
235#106—2691no—
236C4⋊C8—2691no—
237#103—2691no—
238#103—2691no—
239#103—2691no—
240#102—2691no—
241#102—2691no—
242#102—2691no—
243#102—2691no—
244#102—2691no—
245#102—2691no—
246#102—2691no—
247C22⋊C8—2691no—
248C22⋊C8—2691no—
249#97—2691no—
250#41—5382no—
251#41—5382no—
252#41—10761no—
253#41—10761no—
254C2×Q8—2691no—
255C2×D4—21no—
256C2×D4—21no—
257C2×D4—2691no—
258C2×D4—2691no—
259C2×D4—5381no—
260C2×D4—5381no—
261C2×D4—5381no—
262C2×D4—5381no—
263C2×D4—5381no—
264C2×D4—5381no—
265C2×D4C22⋊D26911yescharacteristic
266C2×D4C22×D26911yescharacteristic
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—5381no—
270C22×C4—5381no—
271C22×C4C22×D26911yescharacteristic
272C22×C4C22×D26911yescharacteristic
273SD16—5382no—
274D8—10761no—
275D8—10761no—
276M16—10761no—
277C2×C8—2691no—
278C2×C8—2691no—
279C2×C8—2691no—
280C2×C8—2691no—
281C2×C8—10761no—
282C4⋊C4—21no—
283C4⋊C4—21no—
284C4⋊C4—21no—
285C4⋊C4—2691no—
286C4⋊C4—5381no—
287C4⋊C4C22⋊D26911yescharacteristic
288C4⋊C4C22×D26911yescharacteristic
289C4⋊C4C22×D26911yescharacteristic
290C4⋊C4C22×D26911yescharacteristic
291C22⋊C4—21no—
292C22⋊C4—21no—
293C22⋊C4—21no—
294C22⋊C4—21no—
295C22⋊C4—5381no—
296C22⋊C4—5381no—
297C22⋊C4C22⋊D26911yescharacteristic
298C22⋊C4C22⋊D26911yescharacteristic
299C42—21no—
300C42—5381no—
301C42C22×D26911yescharacteristic
302C23—21no—
303C23—5381no—
304C23—5381no—
305C23C2×C22⋊D26911yescharacteristic
306C23C2×C22⋊D26911yescharacteristic
307Q8—2692no—
308Q8—5381no—
309D4—21no—
310D4—21no—
311D4—41no—
312D4—42no—
313D4—81no—
314D4—5381no—
315D4—5381no—
316D4—5381no—
317D4—5381no—
318D4—10762no—
319D4—10762no—
320D4—10762no—
321D4—21521no—
322D4—21521no—
323D4—21521no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—81no—
332C2×C4—81no—
333C2×C4—5381no—
334C2×C4—5381no—
335C2×C4—10762no—
336C2×C4—10762no—
337C2×C4C2×C22⋊D26911yescharacteristic
338C2×C4C2×C22⋊D26911yescharacteristic
339C2×C4C2×C22⋊D26911yescharacteristic
340C2×C4C2×C22⋊D26911yescharacteristic
341C2×C4C23×D26911yescharacteristic
342C8—5381no—
343C8—5381no—
344C8—5381no—
345C8—5381no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—10761no—
356C22—10761no—
357C22—10761no—
358C22—10761no—
359C22—10761no—
360C22—10761no—
361C22C22×C22⋊D26911yescharacteristic
362C4—21no—
363C4—21no—
364C4—21no—
365C4—21no—
366C4—41no—
367C4—41no—
368C4—41no—
369C4—5382no—
370C4—10761no—
371C4#41×D26911yescharacteristic
372C4#2257549911yescharacteristic
373C2—41no—
374C2—41no—
375C2—81no—
376C2—21521no—
377C2—21521no—
378C2#3177124311yescharacteristic
379C2#3177140311yescharacteristic
380C2#3177140811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#553×C269C2
socleC22×C269C22×D4
hypercenter#553D269
hypocenterC269#3309
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C4×D4 ◁ #553

Complements

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

NH ≅ G/Ntype
1. #31771276C2semidirect
2. #31770971C2semidirect
3. #31770929C2semidirect
4. #31770918C2semidirect
5. #31770909C2semidirect
6. #31770856C2semidirect
7. #31770839C2semidirect
8. #31770800C2semidirect
9. #31770748C2semidirect
10. #31770748C2semidirect
11. #31770705C2semidirect
12. #31770677C2semidirect
13. #31770604C2semidirect
14. #31770599C2semidirect
15. #553×C269C2semidirect
190. C269#3309semidirect
192. #553D269semidirect

Maximal subgroups

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

subgroupindex
#317712762
#317709712
#317709292
#317709182
#317709092
#317708562
#317708392
#317708002
#317707482
#317707052
#317706772
#317706042
#317705992
#553×C2692
#3309269