Finite Group Databasebeta

← #46846603

Subgroups — #46846603

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#31774500C211yesmaximal, characteristic, complemented
2#31774371C211yesmaximal, characteristic, complemented
3#31774221C211yesmaximal, characteristic, complemented
4#31774200C211yesmaximal, characteristic, complemented
5#31774196C211yesmaximal, characteristic, complemented
6#31774091C211yesmaximal, characteristic, complemented
7#31774091C211yesmaximal, characteristic, complemented
8#31774033C211yesmaximal, characteristic, complemented
9#31774030C211yesmaximal, characteristic, complemented
10#31774008C211yesmaximal, characteristic, complemented
11#31774006C211yesmaximal, characteristic, complemented
12#31773979C211yesmaximal, characteristic, complemented
13#31773977C211yesmaximal, characteristic, complemented
14#31773955C211yesmaximal, characteristic, complemented
15#482×C271C211yesmaximal, characteristic, complemented
16C22×D1084C2211yescharacteristic
17C2×D2168C2211yescharacteristic
18C2×D2168C2211yescharacteristic
19C2×#16864639C2211yescharacteristic
20C2×#16864639C2211yescharacteristic
21#22576156C2211yescharacteristic, complemented
22#22576151C2211yescharacteristic, complemented
23#22576144—21no—
24#22576142—21no—
25#22576134C2211yescharacteristic
26#22576132—21no—
27#22576131—21no—
28C4×D1084—21no—
29C4×D1084—21no—
30D4×Dic271C2211yescharacteristic, complemented
31#22576122C2211yescharacteristic
32#22576122C2211yescharacteristic
33#22576122C2211yescharacteristic
34#22576122C2211yescharacteristic
35#22576122C2211yescharacteristic, complemented
36#22576119C2211yescharacteristic
37C22⋊C4×D271—21no—
38C22⋊C4×D271—21no—
39#22576093C2211yescharacteristic, complemented
40#22576091C2211yescharacteristic, complemented
41Dic271⋊C8C2211yescharacteristic, complemented
42Dic271⋊C8C2211yescharacteristic, complemented
43#22576082C2211yescharacteristic
44#22576082C2211yescharacteristic
45#22576080C2211yescharacteristic
46#22576080C2211yescharacteristic
47#22576080C2211yescharacteristic, complemented
48#22576080C2211yescharacteristic, complemented
49C22⋊(C271⋊C8)C2211yescharacteristic
50#22576070C2211yescharacteristic, complemented
51C8×Dic271C2211yescharacteristic, complemented
52#121×C271C2211yescharacteristic
53#117×C271C2211yescharacteristic
54#107×C271C2211yescharacteristic, complemented
55#106×C271C2211yescharacteristic, complemented
56#102×C271C2211yescharacteristic, complemented
57#102×C271C2211yescharacteristic, complemented
58C22⋊C8×C271C2211yescharacteristic
59C23×D271—21no—
60C2×D1084—22no—
61C2×D1084—22no—
62C2×D1084—21no—
63C2×D1084C2311yescharacteristic
64C2×D1084C2311yescharacteristic
65C2×D1084C2311yescharacteristic
66C2×C22⋊D271—21no—
67C2×C22⋊D271—21no—
68C2×C22⋊D271—21no—
69C22×Dic271—21no—
70C2×C4×D271—21no—
71C2×C4×D271—21no—
72C2×C4×D271—21no—
73C2×C4×D271—21no—
74C2×C4×D271—21no—
75D2168—22no—
76D2168—22no—
77#16864639—22no—
78#16864639—22no—
79C2×C271⋊C8C2311yescharacteristic
80C2×C271⋊C8C2311yescharacteristic
81C4⋊Dic271—21no—
82C4⋊Dic271D411yescharacteristic
83C4⋊Dic271D411yescharacteristic
84C4⋊Dic271C2311yescharacteristic
85Dic271⋊C4—21no—
86C22⋊Dic271—21no—
87C22⋊Dic271D411yescharacteristic
88C22⋊Dic271D411yescharacteristic
89(C2×D271)⋊C4—21no—
90(C2×D271)⋊C4—21no—
91(C2×D271)⋊C4—21no—
92(C2×D271)⋊C4—21no—
93(C2×D271)⋊C4—21no—
94(C2×D271)⋊C4—21no—
95C4×Dic271C2311yescharacteristic
96C4×Dic271C2311yescharacteristic
97C2×D4×C271—21no—
98C2×D4×C271C2311yescharacteristic
99C22×C4×C271C2311yescharacteristic
100C2×C8×C271C2311yescharacteristic
101C2×C8×C271C2311yescharacteristic
102C4⋊C4×C271C2311yescharacteristic
103C4⋊C4×C271C2311yescharacteristic
104C4⋊C4×C271C2311yescharacteristic
105C22⋊C4×C271—21no—
106C22⋊C4×C271—21no—
107C42×C271—21no—
108C22×D271—21no—
109C22×D271—21no—
110C22×D271—24no—
111C22×D271—21no—
112C22×D271—81no—
113C22×D271—81no—
114D1084—24no—
115D1084—21no—
116D1084—21no—
117D1084—21no—
118D1084—21no—
119D1084#4112yes—
120D1084#4112yes—
121C22⋊D271—81no—
122C22⋊D271—81no—
123C22⋊D271—81no—
124C2×Dic271—21no—
125C2×Dic271—81no—
126C2×Dic271C2×D411yescharacteristic
127C2×Dic271C2×D411yescharacteristic
128C2×Dic271C2×D411yescharacteristic
129C2×Dic271C2×D411yescharacteristic
130C4×D271—81no—
131C4×D271—81no—
132C4×D271—81no—
133C4×D271—81no—
134C4×D271—81no—
135C271⋊C8—21no—
136C271⋊C8—21no—
137C23×C271—21no—
138C23×C271C2×D411yescharacteristic
139D4×C271—21no—
140D4×C271—21no—
141D4×C271—81no—
142C2×C4×C271—21no—
143C2×C4×C271—21no—
144C2×C4×C271—21no—
145C2×C4×C271—21no—
146C2×C4×C271—21no—
147C2×C4×C271C2×D411yescharacteristic
148C2×C4×C271C2411yescharacteristic
149C8×C271—21no—
150C8×C271—21no—
151C22×C271—21no—
152C22×C271—21no—
153C22×C271—21no—
154C22×C271—41no—
155C22×C271—41no—
156C22×C271—41no—
157C22×C271C22×D411yescharacteristic
158C2×D271—22no—
159C2×D271—22no—
160C2×D271—41no—
161C2×D271—41no—
162C2×D271—41no—
163C2×D271—41no—
164C2×D271—41no—
165C2×D271—41no—
166C2×D271—41no—
167C2×D271—84no—
168C4×C271—21no—
169C4×C271—41no—
170C4×C271—41no—
171C4×C271—41no—
172C4×C271C2×#4111yescharacteristic
173C4×C271C2×#4111yescharacteristic
174Dic271—21no—
175Dic271—21no—
176Dic271—21no—
177Dic271—21no—
178Dic271—41no—
179C2×C271—41no—
180C2×C271—81no—
181C2×C271#52511yescharacteristic
182C2×C271#57611yescharacteristic
183C2×C271#57611yescharacteristic
184D271—42no—
185D271—42no—
186D271—81no—
187C271#312211yescharacteristic, complemented, Sylow
188#3122—2711nomaximal, Sylow
189#540—2711no—
190#518—2711no—
191#482—2711no—
192#482D27111yescharacteristic, complemented
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×D8—2711no—
203#433—2711no—
204C22×D4—2711no—
205C2×D8—2711no—
206C2×D8—2711no—
207C2×D8—2711no—
208C2×D8—2711no—
209#127—2711no—
210#125—2711no—
211#123—5421no—
212#123—5421no—
213#121—2711no—
214#121—5421no—
215#121—5421no—
216#121C2×D27111yescharacteristic
217C4×D4—2711no—
218C4×D4—2711no—
219C4×D4—2711no—
220C4×D4—2711no—
221C4×D4—2711no—
222C4×D4—2711no—
223C4×D4—5421no—
224C4×D4—5421no—
225#117—2711no—
226#117C2×D27111yescharacteristic
227C2×C22⋊C4—5421no—
228C2×C22⋊C4—5421no—
229#107—2711no—
230#107C2×D27111yescharacteristic, complemented
231#106—2711no—
232#106C2×D27111yescharacteristic, complemented
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, complemented
242#102C2×D27111yescharacteristic, complemented
243C22⋊C8—2711no—
244C22⋊C8C2×D27111yescharacteristic
245#97—2711no—
246C4×C8—2711no—
247C24—5421no—
248C2×D4—21no—
249C2×D4—2711no—
250C2×D4—2711no—
251C2×D4—2711no—
252C2×D4—5422no—
253C2×D4—5422no—
254C2×D4—5421no—
255C2×D4—5421no—
256C2×D4—5421no—
257C2×D4—5421no—
258C2×D4C22×D27111yescharacteristic
259C22×C4—5421no—
260C22×C4—5421no—
261C22×C4—5421no—
262C22×C4—5421no—
263C22×C4—5421no—
264C22×C4—5421no—
265C22×C4C22×D27111yescharacteristic
266D8—5422no—
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—5421no—
278C4⋊C4—5421no—
279C4⋊C4C22×D27111yescharacteristic
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—21no—
294C42—2711no—
295C42—2711no—
296C23—21no—
297C23—5424no—
298C23—5421no—
299C23—5421no—
300C23—5421no—
301C23—21681no—
302C23—21681no—
303C23D4×D27111yescharacteristic
304D4—21no—
305D4—21no—
306D4—81no—
307D4—2712no—
308D4—2712no—
309D4—5424no—
310D4—5421no—
311D4—5421no—
312D4—5421no—
313D4—5421no—
314D4—21681no—
315D4—21681no—
316D4—21681no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—2711no—
323C2×C4—2711no—
324C2×C4—2711no—
325C2×C4—2711no—
326C2×C4—5421no—
327C2×C4—21681no—
328C2×C4—21681no—
329C2×C4—21681no—
330C2×C4—21681no—
331C2×C4—21681no—
332C2×C4—21681no—
333C2×C4D4×D27111yescharacteristic
334C2×C4C23×D27111yescharacteristic
335C8—21no—
336C8—21no—
337C8—5421no—
338C8—5421no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—5422no—
346C22—5422no—
347C22—10841no—
348C22—10841no—
349C22—10841no—
350C22—10841no—
351C22—10841no—
352C22—10841no—
353C22—10841no—
354C22—21684no—
355C22C2×D4×D27111yescharacteristic
356C4—21no—
357C4—41no—
358C4—41no—
359C4—41no—
360C4—5421no—
361C4—5421no—
362C4—5421no—
363C4—5421no—
364C4—10841no—
365C4#41×D27111yescharacteristic
366C4#41×D27111yescharacteristic
367C2—41no—
368C2—81no—
369C2—10842no—
370C2—10842no—
371C2—21681no—
372C2#3177440511yescharacteristic
373C2#3177469911yescharacteristic
374C2#3177470111yescharacteristic
subgroupG/H
centerC22C2×D4×D271
commutator, cosocleC2×C4×C271C24
FrattiniC2×C4C23×D271
Fitting#482×C271C2
socleC22×C271C22×D4
hypercenter#482D271
hypocenterC271#3122
LCSG ▷ C2×C4×C271 ▷ C2×C271 ▷ C271
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
1. #31774500C2semidirect
2. #31774371C2semidirect
3. #31774221C2semidirect
4. #31774200C2semidirect
5. #31774196C2semidirect
6. #31774091C2semidirect
7. #31774091C2semidirect
8. #31774033C2semidirect
9. #31774030C2semidirect
10. #31774008C2semidirect
11. #31774006C2semidirect
12. #31773979C2semidirect
13. #31773977C2semidirect
14. #31773955C2semidirect
15. #482×C271C2semidirect
21. #22576156C22semidirect
22. #22576151C22semidirect
30. D4×Dic271C22semidirect
35. #22576122C22semidirect
39. #22576093C22semidirect
40. #22576091C22semidirect
41. Dic271⋊C8C22semidirect
42. Dic271⋊C8C22semidirect
47. #22576080C22semidirect
48. #22576080C22semidirect
50. #22576070C22semidirect
51. C8×Dic271C22semidirect
54. #107×C271C22semidirect
55. #106×C271C22semidirect
56. #102×C271C22semidirect
57. #102×C271C22semidirect
187. C271#3122semidirect
192. #482D271semidirect
230. #107C2×D271semidirect
232. #106C2×D271semidirect
241. #102C2×D271semidirect
242. #102C2×D271semidirect

Maximal subgroups

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

subgroupindex
#317745002
#317743712
#317742212
#317742002
#317741962
#317740912
#317740332
#317740302
#317740082
#317740062
#317739792
#317739772
#317739552
#482×C2712
#3122271