Finite Group Databasebeta

← #46822891

Subgroups — #46822891

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#31771301C211yesmaximal, characteristic, complemented
2#31770969C211yesmaximal, characteristic, complemented
3#31770926C211yesmaximal, characteristic, complemented
4#31770916C211yesmaximal, characteristic, complemented
5#31770912C211yesmaximal, characteristic, complemented
6#31770856C211yesmaximal, characteristic, complemented
7#31770839C211yesmaximal, characteristic, complemented
8#31770797C211yesmaximal, characteristic, complemented
9#31770750C211yesmaximal, characteristic, complemented
10#31770750C211yesmaximal, characteristic, complemented
11#31770703C211yesmaximal, characteristic, complemented
12#31770677C211yesmaximal, characteristic, complemented
13#31770606C211yesmaximal, characteristic, complemented
14#31770601C211yesmaximal, characteristic, complemented
15#550×C269C211yesmaximal, characteristic, complemented
16C2×#16864389C2211yescharacteristic
17C2×#16864387C2211yescharacteristic
18C2×#16864387C2211yescharacteristic
19C2×#16864386C2211yescharacteristic
20C22×#14524130C2211yescharacteristic
21#22575448—21no—
22#22575445C2211yescharacteristic
23#22575435—21no—
24#22575427C2211yescharacteristic
25#22575427C2211yescharacteristic
26#22575425—21no—
27C4×D1076C2211yescharacteristic
28#22575413—21no—
29#22575412C2211yescharacteristic
30C2×C4⋊Dic269C2211yescharacteristic
31#22575386C2211yescharacteristic
32#22575386C2211yescharacteristic
33#22575384C2211yescharacteristic
34C4⋊#14524130C2211yescharacteristic
35#22575377C2211yescharacteristic
36#22575377C2211yescharacteristic
37#22575377C2211yescharacteristic
38#22575374C2211yescharacteristic
39#22575374C2211yescharacteristic
40#22575374C2211yescharacteristic
41#22575374C2211yescharacteristic
42#22575374C2211yescharacteristic
43#22575374C2211yescharacteristic
44#22575373C2211yescharacteristic
45C22⋊#14524130C2211yescharacteristic
46C22⋊#14524130C2211yescharacteristic
47#22575364C2211yescharacteristic
48C2×#41×C269C2211yescharacteristic
49C2×#41×C269C2211yescharacteristic
50#127×C269—21no—
51#127×C269C2211yescharacteristic
52#121×C269—21no—
53#121×C269—21no—
54#121×C269C2211yescharacteristic
55#121×C269C2211yescharacteristic
56C4×Q8×C269C2211yescharacteristic
57C4×D4×C269—21no—
58C4×D4×C269C2211yescharacteristic
59C2×D1076C2311yescharacteristic
60C2×C22⋊D269—21no—
61C2×C22⋊D269—21no—
62C22×Dic269—21no—
63C2×C4×D269—21no—
64#16864389—22no—
65#16864387—41no—
66#16864387—41no—
67#16864386—41no—
68C2×#14524130—41no—
69C2×#14524130C2311yescharacteristic
70C2×#14524130C2311yescharacteristic
71C2×#14524130C2311yescharacteristic
72C2×#14524130C2311yescharacteristic
73C4⋊Dic269—21no—
74C4⋊Dic269C2311yescharacteristic
75C4⋊Dic269C2311yescharacteristic
76C4⋊Dic269C2311yescharacteristic
77#16864381—21no—
78#16864381—21no—
79C22⋊Dic269—21no—
80#16864379—21no—
81#16864379—21no—
82#16864379—21no—
83C4×Dic269—21no—
84#41×C269—22no—
85#41×C269—22no—
86#41×C269—41no—
87#41×C269—41no—
88C2×Q8×C269C2311yescharacteristic
89C2×D4×C269—21no—
90C2×D4×C269—21no—
91C2×D4×C269—21no—
92C2×D4×C269—21no—
93C2×D4×C269—21no—
94C2×D4×C269—21no—
95C2×D4×C269D411yescharacteristic
96C2×D4×C269C2311yescharacteristic
97C2×D4×C269C2311yescharacteristic
98C22×C4×C269—21no—
99C22×C4×C269—21no—
100C22×C4×C269C2311yescharacteristic
101C22×C4×C269C2311yescharacteristic
102C4⋊C4×C269—21no—
103C4⋊C4×C269D411yescharacteristic
104C4⋊C4×C269C2311yescharacteristic
105C22⋊C4×C269—21no—
106C22⋊C4×C269—21no—
107C22⋊C4×C269D411yescharacteristic
108C22⋊C4×C269D411yescharacteristic
109C42×C269—21no—
110C42×C269C2311yescharacteristic
111C22×D269—21no—
112D1076—21no—
113D1076—21no—
114C22⋊D269—42no—
115C22⋊D269—81no—
116C2×Dic269—21no—
117C2×Dic269—21no—
118C2×Dic269—21no—
119C2×Dic269—81no—
120C4×D269—81no—
121#14524130—21no—
122#14524130—21no—
123#14524130—21no—
124#14524130—21no—
125C23×C269—21no—
126C23×C269—21no—
127C23×C269C2×D411yescharacteristic
128C23×C269C2×D411yescharacteristic
129Q8×C269—21no—
130Q8×C269#4112yes—
131D4×C269—21no—
132D4×C269—21no—
133D4×C269—21no—
134D4×C269—21no—
135D4×C269—41no—
136D4×C269—42no—
137D4×C269—42no—
138D4×C269—42no—
139D4×C269—81no—
140D4×C269—81no—
141D4×C269—81no—
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—42no—
149C2×C4×C269—42no—
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×C269—41no—
165C22×C269—41no—
166C22×C269—41no—
167C22×C269C22×D411yescharacteristic
168C2×D269—41no—
169C2×D269—41no—
170C2×D269—41no—
171C4×C269—21no—
172C4×C269—21no—
173C4×C269—22no—
174C4×C269—21no—
175C4×C269—21no—
176C4×C269—41no—
177C4×C269C2×#4111yescharacteristic
178C4×C269H(5,𝔽2)11yescharacteristic
179Dic269—41no—
180Dic269—41no—
181Dic269—41no—
182C2×C269—41no—
183C2×C269—41no—
184C2×C269—81no—
185C2×C269—81no—
186C2×C269#54611yescharacteristic
187C2×C269#57511yescharacteristic
188C2×C269#57611yescharacteristic
189D269—81no—
190C269#330911yescharacteristic, complemented, Sylow
191#3309—2691nomaximal, Sylow
192#553—2691no—
193#550D26911yescharacteristic, complemented
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×#41C2×D26911yescharacteristic
208C2×#41C2×D26911yescharacteristic
209C2×SD16—2691no—
210C2×D8—2691no—
211C2×D8—2691no—
212C2×M16—2691no—
213C22×C8—2691no—
214#127—21no—
215#127C2×D26911yescharacteristic
216#126—5381no—
217#125—2691no—
218#123—5381no—
219#121—21no—
220#121—21no—
221#121—2691no—
222#121—2691no—
223#121—5381no—
224#121C2×D26911yescharacteristic
225#121C2×D26911yescharacteristic
226C4×Q8C2×D26911yescharacteristic
227C4×D4—21no—
228C4×D4—2691no—
229C4×D4—5381no—
230C4×D4C2×D26911yescharacteristic
231#117—2691no—
232C2×C4⋊C4—2691no—
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—22no—
251#41—22no—
252#41—41no—
253#41—41no—
254C2×Q8C22×D26911yescharacteristic
255C2×D4—21no—
256C2×D4—21no—
257C2×D4—21no—
258C2×D4—21no—
259C2×D4—21no—
260C2×D4—21no—
261C2×D4—2691no—
262C2×D4—5381no—
263C2×D4—5381no—
264C2×D4C22⋊D26911yescharacteristic
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—2691no—
284C4⋊C4—2691no—
285C4⋊C4—2691no—
286C4⋊C4—5381no—
287C4⋊C4—5381no—
288C4⋊C4—5381no—
289C4⋊C4C22⋊D26911yescharacteristic
290C4⋊C4C22×D26911yescharacteristic
291C22⋊C4—21no—
292C22⋊C4—21no—
293C22⋊C4—5381no—
294C22⋊C4—5381no—
295C22⋊C4—5381no—
296C22⋊C4—5381no—
297C22⋊C4C22⋊D26911yescharacteristic
298C22⋊C4C22⋊D26911yescharacteristic
299C42—21no—
300C42—5381no—
301C42C22×D26911yescharacteristic
302C23—21no—
303C23—21no—
304C23—5381no—
305C23C2×C22⋊D26911yescharacteristic
306C23C2×C22⋊D26911yescharacteristic
307Q8—21no—
308Q8#1686440112yes—
309D4—21no—
310D4—21no—
311D4—21no—
312D4—21no—
313D4—41no—
314D4—42no—
315D4—42no—
316D4—42no—
317D4—81no—
318D4—81no—
319D4—81no—
320D4—5381no—
321D4—5381no—
322D4—10762no—
323D4—21521no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—42no—
331C2×C4—42no—
332C2×C4—5381no—
333C2×C4—5381no—
334C2×C4—5381no—
335C2×C4—21521no—
336C2×C4—21521no—
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—41no—
356C22—41no—
357C22—41no—
358C22—10761no—
359C22—10761no—
360C22—10761no—
361C22C22×C22⋊D26911yescharacteristic
362C4—21no—
363C4—21no—
364C4—21no—
365C4—21no—
366C4—22no—
367C4—41no—
368C4—10761no—
369C4—10761no—
370C4—10761no—
371C4C2×#1686440111yescharacteristic
372C4#2257549811yescharacteristic
373C2—41no—
374C2—41no—
375C2—81no—
376C2—81no—
377C2—21521no—
378C2#3177124911yescharacteristic
379C2#3177140311yescharacteristic
380C2#3177140811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#550×C269C2
socleC22×C269C22×D4
hypercenter#550D269
hypocenterC269#3309
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C4×D4 ◁ #550

Complements

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

NH ≅ G/Ntype
1. #31771301C2semidirect
2. #31770969C2semidirect
3. #31770926C2semidirect
4. #31770916C2semidirect
5. #31770912C2semidirect
6. #31770856C2semidirect
7. #31770839C2semidirect
8. #31770797C2semidirect
9. #31770750C2semidirect
10. #31770750C2semidirect
11. #31770703C2semidirect
12. #31770677C2semidirect
13. #31770606C2semidirect
14. #31770601C2semidirect
15. #550×C269C2semidirect
190. C269#3309semidirect
193. #550D269semidirect

Maximal subgroups

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

subgroupindex
#317713012
#317709692
#317709262
#317709162
#317709122
#317708562
#317708392
#317707972
#317707502
#317707032
#317706772
#317706062
#317706012
#550×C2692
#3309269