Finite Group Databasebeta

← #46846604

Subgroups — #46846604

Order 34688.

418 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31774498C211yesmaximal, characteristic, complemented
2#31774369C211yesmaximal, characteristic, complemented
3#31774224C211yesmaximal, characteristic, complemented
4#31774219C211yesmaximal, characteristic, complemented
5#31774200C211yesmaximal, characteristic, complemented
6#31774195C211yesmaximal, characteristic, complemented
7#31774091C211yesmaximal, characteristic, complemented
8#31774090C211yesmaximal, characteristic, complemented
9#31774032C211yesmaximal, characteristic, complemented
10#31774029C211yesmaximal, characteristic, complemented
11#31774007C211yesmaximal, characteristic, complemented
12#31774007C211yesmaximal, characteristic, complemented
13C4×D2168C211yesmaximal, characteristic, complemented
14#31773956C211yesmaximal, characteristic, complemented
15C4×D8×C271C211yesmaximal, characteristic, complemented
16C2×D4×D271C2211yescharacteristic
17C2×D2168C2211yescharacteristic
18C2×#16864639C2211yescharacteristic
19C2×#16864639C2211yescharacteristic
20#22576156C2211yescharacteristic, complemented
21#22576151C2211yescharacteristic, complemented
22#22576143—21no—
23#22576142—21no—
24#22576135C2211yescharacteristic
25#22576134—21no—
26#22576133—21no—
27#22576131C2211yescharacteristic
28C4×D1084C2211yescharacteristic
29C4×D1084C2211yescharacteristic, complemented
30D4×Dic271C2211yescharacteristic
31#22576122C2211yescharacteristic
32C4×C22⋊D271—21no—
33(C22⋊D271)⋊C4—21no—
34#22576118C2211yescharacteristic
35#22576117C2211yescharacteristic
36C2×(C2×D271)⋊C4—21no—
37C22⋊C4×D271—21no—
38#22576094C2211yescharacteristic, complemented
39#22576091C2211yescharacteristic, complemented
40#22576091C2211yescharacteristic, complemented
41Dic271⋊C8C2211yescharacteristic, complemented
42Dic271⋊C8C2211yescharacteristic, complemented
43#22576082C2211yescharacteristic
44#22576082C2211yescharacteristic, complemented
45#22576081C2211yescharacteristic
46#22576081C2211yescharacteristic, complemented
47#22576080C2211yescharacteristic
48#22576080C2211yescharacteristic, complemented
49(C2×D271)⋊C8C2211yescharacteristic
50(C2×D271)⋊C8C2211yescharacteristic
51#22576071C2211yescharacteristic, complemented
52C2×D8×C271C2211yescharacteristic
53C4×D4×C271C2211yescharacteristic
54C4×D4×C271C2211yescharacteristic, complemented
55#107×C271C2211yescharacteristic, complemented
56#102×C271C2211yescharacteristic
57#102×C271C2211yescharacteristic, complemented
58C4×C8×C271C2211yescharacteristic, complemented
59C23×D271—21no—
60C2×D1084—21no—
61C2×D1084C2311yescharacteristic
62C2×D1084C2311yescharacteristic
63C2×C22⋊D271—21no—
64C2×C22⋊D271—21no—
65C2×C22⋊D271—21no—
66C2×C22⋊D271—21no—
67D4×D271—22no—
68D4×D271—22no—
69C22×Dic271—21no—
70C2×C4×D271—21no—
71C2×C4×D271—21no—
72C2×C4×D271—21no—
73C2×C4×D271C2311yescharacteristic
74D2168—22no—
75#16864639—22no—
76#16864639—22no—
77C2×C271⋊C8C2311yescharacteristic
78C2×C271⋊C8C2311yescharacteristic
79C4⋊Dic271—21no—
80C4⋊Dic271C2311yescharacteristic
81C4⋊Dic271C2311yescharacteristic
82Dic271⋊C4—21no—
83Dic271⋊C4D411yescharacteristic
84Dic271⋊C4D411yescharacteristic
85C22⋊Dic271—21no—
86C22⋊Dic271—21no—
87(C2×D271)⋊C4—21no—
88(C2×D271)⋊C4—21no—
89(C2×D271)⋊C4—21no—
90(C2×D271)⋊C4—21no—
91(C2×D271)⋊C4—21no—
92(C2×D271)⋊C4D411yescharacteristic
93(C2×D271)⋊C4D411yescharacteristic
94C4×Dic271—21no—
95C4×Dic271C2311yescharacteristic
96C2×D4×C271C2311yescharacteristic
97C2×D4×C271C2311yescharacteristic
98C22×C4×C271—21no—
99C22×C4×C271—21no—
100D8×C271—22no—
101C2×C8×C271C2311yescharacteristic
102C2×C8×C271C2311yescharacteristic
103C4⋊C4×C271C2311yescharacteristic
104C4⋊C4×C271C2311yescharacteristic
105C22⋊C4×C271—21no—
106C22⋊C4×C271—21no—
107C42×C271C2311yescharacteristic
108C22×D271—21no—
109C22×D271—24no—
110C22×D271—21no—
111C22×D271—81no—
112C22×D271—81no—
113C22×D271C2×D411yescharacteristic
114D1084—21no—
115D1084—21no—
116D1084—21no—
117D1084—81no—
118D1084#4112yes—
119C22⋊D271—24no—
120C22⋊D271—81no—
121C22⋊D271—81no—
122C22⋊D271—81no—
123C2×Dic271—21no—
124C2×Dic271—21no—
125C2×Dic271—81no—
126C2×Dic271C2×D411yescharacteristic
127C2×Dic271C2×D411yescharacteristic
128C2×Dic271C2×D411yescharacteristic
129C4×D271—21no—
130C4×D271—21no—
131C4×D271—81no—
132C4×D271—81no—
133C4×D271—81no—
134C271⋊C8—21no—
135C271⋊C8—21no—
136C23×C271—21no—
137C23×C271—21no—
138D4×C271—21no—
139D4×C271—21no—
140D4×C271—21no—
141D4×C271#4112yes—
142C2×C4×C271—21no—
143C2×C4×C271—21no—
144C2×C4×C271—81no—
145C2×C4×C271—81no—
146C2×C4×C271C2×D411yescharacteristic
147C2×C4×C271C2×D411yescharacteristic
148C2×C4×C271C2411yescharacteristic
149C8×C271—21no—
150C8×C271—21no—
151C22×C271—22no—
152C22×C271—41no—
153C22×C271—41no—
154C22×C271—41no—
155C22×C271—41no—
156C22×C271—41no—
157C22×C271C22×D411yescharacteristic
158C2×D271—21no—
159C2×D271—22no—
160C2×D271—21no—
161C2×D271—21no—
162C2×D271—41no—
163C2×D271—41no—
164C2×D271—41no—
165C2×D271—41no—
166C2×D271—41no—
167C2×D271—84no—
168C4×C271—21no—
169C4×C271—21no—
170C4×C271—41no—
171C4×C271—41no—
172C4×C271C2×#4111yescharacteristic
173C4×C271C2×#4111yescharacteristic
174Dic271—21no—
175Dic271—21no—
176Dic271—21no—
177Dic271—41no—
178Dic271—41no—
179C2×C271—42no—
180C2×C271—81no—
181C2×C271#52511yescharacteristic
182C2×C271#57611yescharacteristic
183C2×C271#57611yescharacteristic
184D271—41no—
185D271—42no—
186D271—81no—
187C271#312211yescharacteristic, complemented, Sylow
188#3122—2711nomaximal, Sylow
189#540—2711no—
190#518—2711no—
191#482—2711no—
192#482—2711no—
193#478—2711no—
194#478—2711no—
195#459—2711no—
196#459—2711no—
197#447—2711no—
198#447—2711no—
199#442—2711no—
200#442—2711no—
201C4×D8—2711no—
202C4×D8D27111yescharacteristic, complemented
203#433—2711no—
204C22×D4—2711no—
205C2×D8—2711no—
206C2×D8—2711no—
207C2×D8—2711no—
208C2×D8C2×D27111yescharacteristic
209#127—2711no—
210#125—2711no—
211#123—5421no—
212#123—5421no—
213#121—2711no—
214#121—2711no—
215#121—5421no—
216#121—5421no—
217C4×D4—2711no—
218C4×D4—2711no—
219C4×D4—2711no—
220C4×D4—2711no—
221C4×D4—5421no—
222C4×D4—5421no—
223C4×D4C2×D27111yescharacteristic
224C4×D4C2×D27111yescharacteristic, complemented
225#117—2711no—
226#117—2711no—
227C2×C22⋊C4—5421no—
228C2×C22⋊C4—5421no—
229#107—2711no—
230#107C2×D27111yescharacteristic, complemented
231#106—2711no—
232#106—2711no—
233C4⋊C8—2711no—
234C4⋊C8—2711no—
235#102—2711no—
236#102—2711no—
237#102—2711no—
238#102—2711no—
239#102—2711no—
240#102—2711no—
241#102C2×D27111yescharacteristic
242#102C2×D27111yescharacteristic, complemented
243C22⋊C8—2711no—
244C22⋊C8—2711no—
245#97—2711no—
246C4×C8C2×D27111yescharacteristic, complemented
247C24—5421no—
248C2×D4—2711no—
249C2×D4—2711no—
250C2×D4—5421no—
251C2×D4—5421no—
252C2×D4—5421no—
253C2×D4—5421no—
254C2×D4—5422no—
255C2×D4—5422no—
256C2×D4—5421no—
257C2×D4C22×D27111yescharacteristic
258C2×D4C22×D27111yescharacteristic
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—2711no—
262C22×C4—5421no—
263C22×C4—5421no—
264C22×C4—5421no—
265C22×C4—5421no—
266D8—22no—
267D8—5422no—
268D8—5422no—
269D8—5422no—
270C2×C8—2711no—
271C2×C8—2711no—
272C2×C8C22×D27111yescharacteristic
273C2×C8C22×D27111yescharacteristic
274C4⋊C4—2711no—
275C4⋊C4—2711no—
276C4⋊C4—2711no—
277C4⋊C4—2711no—
278C4⋊C4—5421no—
279C4⋊C4—5421no—
280C4⋊C4C22×D27111yescharacteristic
281C4⋊C4C22×D27111yescharacteristic
282C22⋊C4—21no—
283C22⋊C4—21no—
284C22⋊C4—2711no—
285C22⋊C4—2711no—
286C22⋊C4—5421no—
287C22⋊C4—5421no—
288C22⋊C4—5421no—
289C22⋊C4—5421no—
290C22⋊C4—5421no—
291C22⋊C4—5421no—
292C22⋊C4—5421no—
293C42—2711no—
294C42—5421no—
295C42C22×D27111yescharacteristic
296C23—21no—
297C23—21no—
298C23—2711no—
299C23—5424no—
300C23—5421no—
301C23—5421no—
302C23—21681no—
303C23—21681no—
304D4—21no—
305D4—21no—
306D4—21no—
307D4—2712no—
308D4—5424no—
309D4—5421no—
310D4—5421no—
311D4—5421no—
312D4—21681no—
313D4—21681no—
314D4—21681no—
315D4—21681no—
316D4#1686465412yes—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—81no—
320C2×C4—81no—
321C2×C4—2711no—
322C2×C4—2711no—
323C2×C4—2711no—
324C2×C4—5421no—
325C2×C4—5421no—
326C2×C4—5421no—
327C2×C4—5421no—
328C2×C4—21681no—
329C2×C4—21681no—
330C2×C4—21681no—
331C2×C4—21681no—
332C2×C4D4×D27111yescharacteristic
333C2×C4D4×D27111yescharacteristic
334C2×C4C23×D27111yescharacteristic
335C8—21no—
336C8—21no—
337C8—5421no—
338C8—5421no—
339C22—22no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—5421no—
346C22—5422no—
347C22—5421no—
348C22—5421no—
349C22—10841no—
350C22—10841no—
351C22—10841no—
352C22—10841no—
353C22—10841no—
354C22—21684no—
355C22C2×D4×D27111yescharacteristic
356C4—21no—
357C4—21no—
358C4—41no—
359C4—41no—
360C4—5421no—
361C4—5421no—
362C4—5421no—
363C4—10841no—
364C4—10841no—
365C4#41×D27111yescharacteristic
366C4C2×#1686465411yescharacteristic
367C2—42no—
368C2—81no—
369C2—10841no—
370C2—10842no—
371C2—21681no—
372C2#3177440611yescharacteristic
373C2#3177469811yescharacteristic
374C2#3177469911yescharacteristic
subgroupG/H
centerC22C2×D4×D271
commutator, cosocleC2×C4×C271C24
FrattiniC2×C4C23×D271
FittingC4×D8×C271C2
socleC22×C271C22×D4
hypercenterC4×D8D271
hypocenterC271#3122
LCSG ▷ C2×C4×C271 ▷ C2×C271 ▷ C271
UCSC1 ◁ C22 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. #31774498C2semidirect
2. #31774369C2semidirect
3. #31774224C2semidirect
4. #31774219C2semidirect
5. #31774200C2semidirect
6. #31774195C2semidirect
7. #31774091C2semidirect
8. #31774090C2semidirect
9. #31774032C2semidirect
10. #31774029C2semidirect
11. #31774007C2semidirect
12. #31774007C2semidirect
13. C4×D2168C2semidirect
14. #31773956C2semidirect
15. C4×D8×C271C2semidirect
20. #22576156C22semidirect
21. #22576151C22semidirect
29. C4×D1084C22semidirect
38. #22576094C22semidirect
39. #22576091C22semidirect
40. #22576091C22semidirect
41. Dic271⋊C8C22semidirect
42. Dic271⋊C8C22semidirect
44. #22576082C22semidirect
46. #22576081C22semidirect
48. #22576080C22semidirect
51. #22576071C22semidirect
54. C4×D4×C271C22semidirect
55. #107×C271C22semidirect
57. #102×C271C22semidirect
58. C4×C8×C271C22semidirect
187. C271#3122semidirect
202. C4×D8D271semidirect
224. C4×D4C2×D271semidirect
230. #107C2×D271semidirect
242. #102C2×D271semidirect
246. C4×C8C2×D271semidirect

Maximal subgroups

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

subgroupindex
#317744982
#317743692
#317742242
#317742192
#317742002
#317741952
#317740912
#317740902
#317740322
#317740292
#317740072
C4×D21682
#317739562
C4×D8×C2712
#3122271