Finite Group Databasebeta

← #46848364

Subgroups — #46848364

Order 34688.

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#31774568C211yesmaximal, characteristic, complemented
2#31774263C211yesmaximal, characteristic, complemented
3#31774221C211yesmaximal, characteristic, complemented
4#31774210C211yesmaximal, characteristic, complemented
5#31774201C211yesmaximal, characteristic, complemented
6#31774148C211yesmaximal, characteristic, complemented
7#31774131C211yesmaximal, characteristic, complemented
8#31774092C211yesmaximal, characteristic, complemented
9#31774040C211yesmaximal, characteristic, complemented
10#31774040C211yesmaximal, characteristic, complemented
11#31773997C211yesmaximal, characteristic, complemented
12#31773969C211yesmaximal, characteristic, complemented
13#31773896C211yesmaximal, characteristic, complemented
14#31773891C211yesmaximal, characteristic, complemented
15#553×C271C211yesmaximal, characteristic, complemented
16C2×#16864654C2211yescharacteristic
17C2×#16864654C2211yescharacteristic
18C2×#16864642C2211yescharacteristic
19C2×#16864639C2211yescharacteristic
20C2×#16864639C2211yescharacteristic
21C2×#16864638C2211yescharacteristic
22C22×C271⋊C8C2211yescharacteristic
23#22576157C2211yescharacteristic
24#22576156—21no—
25#22576134C2211yescharacteristic
26#22576134C2211yescharacteristic
27#22576133—21no—
28#22576133—21no—
29C4×Dic542C2211yescharacteristic
30#22576122—21no—
31#22576093C2211yescharacteristic
32#22576093C2211yescharacteristic
33#22576091C2211yescharacteristic
34C4⋊(C271⋊C8)C2211yescharacteristic
35#22576083C2211yescharacteristic
36#22576083C2211yescharacteristic
37#22576083C2211yescharacteristic
38#22576081C2211yescharacteristic
39#22576080C2211yescharacteristic
40#22576080C2211yescharacteristic
41#22576080C2211yescharacteristic
42#22576080C2211yescharacteristic
43#22576080C2211yescharacteristic
44#22576080C2211yescharacteristic
45C22⋊(C271⋊C8)C2211yescharacteristic
46C22⋊(C271⋊C8)C2211yescharacteristic
47#22576071C2211yescharacteristic
48#126×C271—21no—
49#125×C271C2211yescharacteristic
50#123×C271—21no—
51#121×C271—21no—
52#121×C271C2211yescharacteristic
53#121×C271C2211yescharacteristic
54C4×D4×C271—21no—
55C4×D4×C271C2211yescharacteristic
56C4×D4×C271C2211yescharacteristic
57#117×C271C2211yescharacteristic
58C2×C4⋊C4×C271C2211yescharacteristic
59#16864654—22no—
60#16864654—22no—
61#16864654—41no—
62#16864654—41no—
63C2×Dic542C2311yescharacteristic
64C2×D1084—21no—
65C2×D1084—21no—
66C2×D1084C2311yescharacteristic
67C2×D1084C2311yescharacteristic
68C2×C22⋊D271—21no—
69C2×C22⋊D271—21no—
70C2×C22⋊D271—21no—
71C2×C22⋊D271—21no—
72C2×C4×D271—21no—
73C2×C4×D271—21no—
74#16864642—22no—
75#16864639—41no—
76#16864639—41no—
77#16864638—41no—
78C2×C271⋊C8—41no—
79C2×C271⋊C8C2311yescharacteristic
80C2×C271⋊C8C2311yescharacteristic
81C2×C271⋊C8C2311yescharacteristic
82C2×C271⋊C8C2311yescharacteristic
83C4⋊Dic271C2311yescharacteristic
84Dic271⋊C4—21no—
85(C2×D271)⋊C4—21no—
86(C2×D271)⋊C4—21no—
87C4×Dic271—21no—
88C2×D4×C271—21no—
89C2×D4×C271—21no—
90C2×D4×C271D411yescharacteristic
91C2×D4×C271C2311yescharacteristic
92C22×C4×C271—21no—
93C22×C4×C271—21no—
94C22×C4×C271C2311yescharacteristic
95C22×C4×C271C2311yescharacteristic
96C4⋊C4×C271—21no—
97C4⋊C4×C271—21no—
98C4⋊C4×C271—21no—
99C4⋊C4×C271D411yescharacteristic
100C4⋊C4×C271C2311yescharacteristic
101C4⋊C4×C271C2311yescharacteristic
102C4⋊C4×C271C2311yescharacteristic
103C22⋊C4×C271—21no—
104C22⋊C4×C271—21no—
105C22⋊C4×C271—21no—
106C22⋊C4×C271—21no—
107C22⋊C4×C271D411yescharacteristic
108C22⋊C4×C271D411yescharacteristic
109C42×C271—21no—
110C42×C271C2311yescharacteristic
111C22×D271—21no—
112C22×D271—21no—
113Dic542—21no—
114Dic542#4112yes—
115D1084—21no—
116D1084—21no—
117D1084—21no—
118D1084—21no—
119D1084—42no—
120D1084—81no—
121C22⋊D271—42no—
122C22⋊D271—42no—
123C22⋊D271—81no—
124C22⋊D271—81no—
125C2×Dic271—21no—
126C2×Dic271—21no—
127C4×D271—42no—
128C4×D271—42no—
129C271⋊C8—21no—
130C271⋊C8—21no—
131C271⋊C8—21no—
132C271⋊C8—21no—
133C23×C271—21no—
134C23×C271C2×D411yescharacteristic
135C23×C271C2×D411yescharacteristic
136D4×C271—21no—
137D4×C271—21no—
138D4×C271—41no—
139D4×C271—42no—
140D4×C271—81no—
141C2×C4×C271—21no—
142C2×C4×C271—21no—
143C2×C4×C271—21no—
144C2×C4×C271—21no—
145C2×C4×C271—21no—
146C2×C4×C271—21no—
147C2×C4×C271—21no—
148C2×C4×C271—81no—
149C2×C4×C271—81no—
150C2×C4×C271C2×D411yescharacteristic
151C2×C4×C271C2×D411yescharacteristic
152C2×C4×C271C2×D411yescharacteristic
153C2×C4×C271C2×D411yescharacteristic
154C2×C4×C271C2411yescharacteristic
155C22×C271—21no—
156C22×C271—21no—
157C22×C271—21no—
158C22×C271—21no—
159C22×C271—21no—
160C22×C271—21no—
161C22×C271—41no—
162C22×C271—41no—
163C22×C271—41no—
164C22×C271C22×D411yescharacteristic
165C2×D271—41no—
166C2×D271—41no—
167C2×D271—41no—
168C2×D271—41no—
169C2×D271—41no—
170C2×D271—41no—
171C4×C271—21no—
172C4×C271—21no—
173C4×C271—21no—
174C4×C271—21no—
175C4×C271—41no—
176C4×C271—41no—
177C4×C271—41no—
178C4×C271C2×#4111yescharacteristic
179C4×C271H(5,𝔽2)11yescharacteristic
180Dic271—22no—
181Dic271—41no—
182C2×C271—41no—
183C2×C271—41no—
184C2×C271—81no—
185C2×C271#54611yescharacteristic
186C2×C271#57511yescharacteristic
187C2×C271#57611yescharacteristic
188D271—81no—
189D271—81no—
190C271#330911yescharacteristic, complemented, Sylow
191#3309—2711nomaximal, Sylow
192#553D27111yescharacteristic, complemented
193#550—2711no—
194#490—2711no—
195#482—2711no—
196#480—2711no—
197#479—2711no—
198#469—2711no—
199#466—2711no—
200#459—2711no—
201#449—2711no—
202#449—2711no—
203#440—2711no—
204#435—2711no—
205#417—2711no—
206#416—2711no—
207C2×#41—2711no—
208C2×#41—2711no—
209C2×SD16—2711no—
210C2×D8—2711no—
211C2×D8—2711no—
212C2×M16—2711no—
213C22×C8—2711no—
214#127—2711no—
215#127—5421no—
216#126—21no—
217#125C2×D27111yescharacteristic
218#123—21no—
219#121—21no—
220#121—2711no—
221#121—2711no—
222#121—5421no—
223#121—5421no—
224#121C2×D27111yescharacteristic
225#121C2×D27111yescharacteristic
226C4×Q8—2711no—
227C4×D4—21no—
228C4×D4—5421no—
229C4×D4C2×D27111yescharacteristic
230C4×D4C2×D27111yescharacteristic
231#117C2×D27111yescharacteristic
232C2×C4⋊C4C2×D27111yescharacteristic
233#107—2711no—
234#107—2711no—
235#106—2711no—
236C4⋊C8—2711no—
237#103—2711no—
238#103—2711no—
239#103—2711no—
240#102—2711no—
241#102—2711no—
242#102—2711no—
243#102—2711no—
244#102—2711no—
245#102—2711no—
246#102—2711no—
247C22⋊C8—2711no—
248C22⋊C8—2711no—
249#97—2711no—
250#41—5422no—
251#41—5422no—
252#41—10841no—
253#41—10841no—
254C2×Q8—2711no—
255C2×D4—21no—
256C2×D4—21no—
257C2×D4—2711no—
258C2×D4—2711no—
259C2×D4—5421no—
260C2×D4—5421no—
261C2×D4—5421no—
262C2×D4—5421no—
263C2×D4—5421no—
264C2×D4—5421no—
265C2×D4C22⋊D27111yescharacteristic
266C2×D4C22×D27111yescharacteristic
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—5421no—
270C22×C4—5421no—
271C22×C4C22×D27111yescharacteristic
272C22×C4C22×D27111yescharacteristic
273SD16—5422no—
274D8—10841no—
275D8—10841no—
276M16—10841no—
277C2×C8—2711no—
278C2×C8—2711no—
279C2×C8—2711no—
280C2×C8—2711no—
281C2×C8—10841no—
282C4⋊C4—21no—
283C4⋊C4—21no—
284C4⋊C4—21no—
285C4⋊C4—2711no—
286C4⋊C4—5421no—
287C4⋊C4C22⋊D27111yescharacteristic
288C4⋊C4C22×D27111yescharacteristic
289C4⋊C4C22×D27111yescharacteristic
290C4⋊C4C22×D27111yescharacteristic
291C22⋊C4—21no—
292C22⋊C4—21no—
293C22⋊C4—21no—
294C22⋊C4—21no—
295C22⋊C4—5421no—
296C22⋊C4—5421no—
297C22⋊C4C22⋊D27111yescharacteristic
298C22⋊C4C22⋊D27111yescharacteristic
299C42—21no—
300C42—5421no—
301C42C22×D27111yescharacteristic
302C23—21no—
303C23—5421no—
304C23—5421no—
305C23C2×C22⋊D27111yescharacteristic
306C23C2×C22⋊D27111yescharacteristic
307Q8—2712no—
308Q8—5421no—
309D4—21no—
310D4—21no—
311D4—41no—
312D4—42no—
313D4—81no—
314D4—5421no—
315D4—5421no—
316D4—5421no—
317D4—5421no—
318D4—10842no—
319D4—10842no—
320D4—10842no—
321D4—21681no—
322D4—21681no—
323D4—21681no—
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—5421no—
334C2×C4—5421no—
335C2×C4—10842no—
336C2×C4—10842no—
337C2×C4C2×C22⋊D27111yescharacteristic
338C2×C4C2×C22⋊D27111yescharacteristic
339C2×C4C2×C22⋊D27111yescharacteristic
340C2×C4C2×C22⋊D27111yescharacteristic
341C2×C4C23×D27111yescharacteristic
342C8—5421no—
343C8—5421no—
344C8—5421no—
345C8—5421no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—10841no—
356C22—10841no—
357C22—10841no—
358C22—10841no—
359C22—10841no—
360C22—10841no—
361C22C22×C22⋊D27111yescharacteristic
362C4—21no—
363C4—21no—
364C4—21no—
365C4—21no—
366C4—41no—
367C4—41no—
368C4—41no—
369C4—5422no—
370C4—10841no—
371C4#41×D27111yescharacteristic
372C4#2257620611yescharacteristic
373C2—41no—
374C2—41no—
375C2—81no—
376C2—21681no—
377C2—21681no—
378C2#3177453511yescharacteristic
379C2#3177469511yescharacteristic
380C2#3177470011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D271
commutator, cosocleC2×C4×C271C24
FrattiniC2×C4C23×D271
Fitting#553×C271C2
socleC22×C271C22×D4
hypercenter#553D271
hypocenterC271#3309
LCSG ▷ C2×C4×C271 ▷ C2×C271 ▷ C271
UCSC1 ◁ C22 ◁ C4×D4 ◁ #553

Complements

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

NH ≅ G/Ntype
1. #31774568C2semidirect
2. #31774263C2semidirect
3. #31774221C2semidirect
4. #31774210C2semidirect
5. #31774201C2semidirect
6. #31774148C2semidirect
7. #31774131C2semidirect
8. #31774092C2semidirect
9. #31774040C2semidirect
10. #31774040C2semidirect
11. #31773997C2semidirect
12. #31773969C2semidirect
13. #31773896C2semidirect
14. #31773891C2semidirect
15. #553×C271C2semidirect
190. C271#3309semidirect
192. #553D271semidirect

Maximal subgroups

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

subgroupindex
#317745682
#317742632
#317742212
#317742102
#317742012
#317741482
#317741312
#317740922
#317740402
#317739972
#317739692
#317738962
#317738912
#553×C2712
#3309271