Finite Group Databasebeta

← #46848338

Subgroups — #46848338

Order 34688.

394 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31774591C211yesmaximal, characteristic, complemented
2#31774549C211yesmaximal, characteristic, complemented
3#31774264C211yesmaximal, characteristic, complemented
4#31774229C211yesmaximal, characteristic, complemented
5#31774200C211yesmaximal, characteristic, complemented
6#31774144C211yesmaximal, characteristic, complemented
7#31774128C211yesmaximal, characteristic, complemented
8#31774101C211yesmaximal, characteristic, complemented
9#31774045C211yesmaximal, characteristic, complemented
10#31774044C211yesmaximal, characteristic, complemented
11#31774008C211yesmaximal, characteristic, complemented
12#31773965C211yesmaximal, characteristic, complemented
13#31773897C211yesmaximal, characteristic, complemented
14#31773891C211yesmaximal, characteristic, complemented
15#485×C271C211yesmaximal, characteristic, complemented
16C2×#16864655C2211yescharacteristic
17C2×#16864654C2211yescharacteristic
18C2×#16864643C2211yescharacteristic
19C2×#16864641C2211yescharacteristic
20C2×D2168C2211yescharacteristic
21C2×#16864637C2211yescharacteristic
22C22×C271⋊C8C2211yescharacteristic
23#22576158C2211yescharacteristic
24#22576154—21no—
25#22576151C2211yescharacteristic
26#22576145—21no—
27#22576142—21no—
28#22576142—21no—
29#22576140C2211yescharacteristic
30#22576135C2211yescharacteristic
31#22576134C2211yescharacteristic
32#22576133—21no—
33#22576133—21no—
34C4×D1084—21no—
35#22576122C2211yescharacteristic
36#22576122C2211yescharacteristic
37C4×C22⋊D271C2211yescharacteristic
38C4⋊C4×D271—21no—
39C4⋊C4×D271C2211yescharacteristic
40#22576091C2211yescharacteristic
41Dic271⋊C8C2211yescharacteristic
42#22576085C2211yescharacteristic
43#22576084C2211yescharacteristic
44#22576083C2211yescharacteristic
45#22576083C2211yescharacteristic
46#22576082C2211yescharacteristic
47#22576080C2211yescharacteristic
48#22576080C2211yescharacteristic
49#22576080C2211yescharacteristic
50(C2×D271)⋊C8C2211yescharacteristic
51#22576070C2211yescharacteristic
52C22⋊Q8×C271C2211yescharacteristic
53#117×C271C2211yescharacteristic
54#107×C271C2211yescharacteristic
55#106×C271C2211yescharacteristic
56#103×C271C2211yescharacteristic
57#103×C271C2211yescharacteristic
58C22⋊C8×C271C2211yescharacteristic
59#16864655—22no—
60#16864655—41no—
61#16864654—22no—
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⋊D271D411yescharacteristic
71C2×C4×D271—21no—
72C2×C4×D271—21no—
73C2×C4×D271—21no—
74C2×C4×D271—21no—
75C2×C4×D271—21no—
76C2×C4×D271C2311yescharacteristic
77#16864643—41no—
78#16864641—41no—
79D2168—22no—
80#16864637—41no—
81C2×C271⋊C8—41no—
82C2×C271⋊C8C2311yescharacteristic
83C2×C271⋊C8C2311yescharacteristic
84C4⋊Dic271—21no—
85C4⋊Dic271—21no—
86C4⋊Dic271C2311yescharacteristic
87Dic271⋊C4—21no—
88Dic271⋊C4—21no—
89Dic271⋊C4—21no—
90Dic271⋊C4—21no—
91Dic271⋊C4D411yescharacteristic
92C22⋊Dic271D411yescharacteristic
93(C2×D271)⋊C4—21no—
94(C2×D271)⋊C4—21no—
95(C2×D271)⋊C4—21no—
96(C2×D271)⋊C4—21no—
97(C2×D271)⋊C4—21no—
98(C2×D271)⋊C4D411yescharacteristic
99C4×Dic271C2311yescharacteristic
100C2×Q8×C271C2311yescharacteristic
101C22×C4×C271C2311yescharacteristic
102C2×C8×C271C2311yescharacteristic
103C2×C8×C271C2311yescharacteristic
104C4⋊C4×C271—21no—
105C4⋊C4×C271C2311yescharacteristic
106C4⋊C4×C271C2311yescharacteristic
107C4⋊C4×C271C2311yescharacteristic
108C22⋊C4×C271—21no—
109C22⋊C4×C271—21no—
110C42×C271—21no—
111C22×D271—21no—
112C22×D271—21no—
113C22×D271C2×D411yescharacteristic
114Dic542—21no—
115Dic542—21no—
116D1084—21no—
117D1084—21no—
118D1084—21no—
119D1084—42no—
120D1084—42no—
121D1084#4112yes—
122C22⋊D271—41no—
123C22⋊D271—42no—
124C22⋊D271—81no—
125C2×Dic271—21no—
126C2×Dic271—21no—
127C2×Dic271C2×D411yescharacteristic
128C2×Dic271C2×D411yescharacteristic
129C2×Dic271C2×D411yescharacteristic
130C4×D271—21no—
131C4×D271—21no—
132C4×D271—42no—
133C4×D271—42no—
134C4×D271—42no—
135C4×D271—81no—
136C4×D271—81no—
137C271⋊C8—21no—
138C271⋊C8—21no—
139C23×C271C2×D411yescharacteristic
140Q8×C271—21no—
141Q8×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×C271C2×D411yescharacteristic
149C2×C4×C271C2411yescharacteristic
150C8×C271—21no—
151C8×C271—21no—
152C22×C271—21no—
153C22×C271—21no—
154C22×C271—21no—
155C22×C271C22×D411yescharacteristic
156C2×D271—21no—
157C2×D271—22no—
158C2×D271—21no—
159C2×D271—21no—
160C2×D271—41no—
161C2×D271—41no—
162C2×D271—41no—
163C2×D271—41no—
164C2×D271—41no—
165C4×C271—21no—
166C4×C271—41no—
167C4×C271—41no—
168C4×C271—41no—
169C4×C271—41no—
170C4×C271C2×#4111yescharacteristic
171C4×C271H(5,𝔽2)11yescharacteristic
172Dic271—21no—
173Dic271—21no—
174Dic271—21no—
175Dic271—41no—
176Dic271—41no—
177C2×C271—41no—
178C2×C271#54611yescharacteristic
179C2×C271#57511yescharacteristic
180C2×C271#57711yescharacteristic
181D271—41no—
182D271—42no—
183D271—81no—
184C271#330711yescharacteristic, complemented, Sylow
185#3307—2711nomaximal, Sylow
186#553—2711no—
187#547—2711no—
188#491—2711no—
189#485D27111yescharacteristic, complemented
190#483—2711no—
191#478—2711no—
192#468—2711no—
193#465—2711no—
194#461—2711no—
195#449—2711no—
196#449—2711no—
197#442—2711no—
198#435—2711no—
199#417—2711no—
200#416—2711no—
201C2×#41—2711no—
202C2×#41—2711no—
203C2×SD16—2711no—
204C2×SD16—2711no—
205C2×D8—2711no—
206C2×M16—2711no—
207C22×C8—2711no—
208C4⋊Q8—2711no—
209#126—5421no—
210#125—2711no—
211#123—5421no—
212#123—5421no—
213#123—5421no—
214C22⋊Q8—2711no—
215C22⋊Q8C2×D27111yescharacteristic
216#121—2711no—
217#121—2711no—
218#121—5421no—
219#121—5421no—
220C4×D4—2711no—
221C4×D4—2711no—
222C4×D4—2711no—
223C4×D4—5421no—
224#117C2×D27111yescharacteristic
225C2×C4⋊C4—2711no—
226C2×C4⋊C4—5421no—
227#107C2×D27111yescharacteristic
228#106—2711no—
229#106C2×D27111yescharacteristic
230C4⋊C8—2711no—
231#103—2711no—
232#103—2711no—
233#103—2711no—
234#103—2711no—
235#103C2×D27111yescharacteristic
236#103C2×D27111yescharacteristic
237#102—2711no—
238#102—2711no—
239#102—2711no—
240#102—2711no—
241C22⋊C8—2711no—
242C22⋊C8C2×D27111yescharacteristic
243#97—2711no—
244#41—5422no—
245#41—5422no—
246#41—10841no—
247#41—10841no—
248C2×Q8—2711no—
249C2×Q8C22×D27111yescharacteristic
250C2×D4—2711no—
251C2×D4—2711no—
252C2×D4—2711no—
253C2×D4—5421no—
254C2×D4—5421no—
255C2×D4—5421no—
256C2×D4—5421no—
257C22×C4—2711no—
258C22×C4—5421no—
259C22×C4—5421no—
260C22×C4—5421no—
261C22×C4—5421no—
262C22×C4—5421no—
263C22×C4C22×D27111yescharacteristic
264SD16—10841no—
265SD16—10841no—
266D8—5422no—
267M16—10841no—
268C2×C8—2711no—
269C2×C8—2711no—
270C2×C8—10841no—
271C2×C8C22×D27111yescharacteristic
272C2×C8C22×D27111yescharacteristic
273C4⋊C4—21no—
274C4⋊C4—2711no—
275C4⋊C4—2711no—
276C4⋊C4—5421no—
277C4⋊C4—5421no—
278C4⋊C4—5421no—
279C4⋊C4—5421no—
280C4⋊C4—5421no—
281C4⋊C4—5421no—
282C4⋊C4C22×D27111yescharacteristic
283C4⋊C4C22×D27111yescharacteristic
284C4⋊C4C22×D27111yescharacteristic
285C22⋊C4—21no—
286C22⋊C4—21no—
287C22⋊C4—2711no—
288C22⋊C4—2711no—
289C22⋊C4—5421no—
290C22⋊C4—5421no—
291C22⋊C4—5421no—
292C22⋊C4—5421no—
293C22⋊C4—5421no—
294C42—21no—
295C42—2711no—
296C23—2711no—
297C23—5421no—
298C23—5421no—
299C23D4×D27111yescharacteristic
300Q8—21no—
301Q8—21no—
302Q8—5421no—
303Q8—5421no—
304D4—2712no—
305D4—5421no—
306D4—5421no—
307D4—5421no—
308D4—10842no—
309D4—10842no—
310D4—10841no—
311D4—10842no—
312D4—21681no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—2711no—
320C2×C4—2711no—
321C2×C4—2711no—
322C2×C4—5421no—
323C2×C4—5421no—
324C2×C4—5421no—
325C2×C4—5421no—
326C2×C4—10842no—
327C2×C4—10842no—
328C2×C4—10842no—
329C2×C4—21681no—
330C2×C4—21681no—
331C2×C4D4×D27111yescharacteristic
332C2×C4C23×D27111yescharacteristic
333C8—21no—
334C8—21no—
335C8—5421no—
336C8—5421no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—5421no—
341C22—5422no—
342C22—5421no—
343C22—5421no—
344C22—10841no—
345C22—10841no—
346C22—10841no—
347C22—10841no—
348C22—10841no—
349C22C2×D4×D27111yescharacteristic
350C4—21no—
351C4—41no—
352C4—41no—
353C4—41no—
354C4—41no—
355C4—5421no—
356C4—5421no—
357C4—5421no—
358C4—10841no—
359C4—10841no—
360C4#41×D27111yescharacteristic
361C4#2257620611yescharacteristic
362C2—41no—
363C2—10841no—
364C2—10842no—
365C2—21681no—
366C2#3177453911yescharacteristic
367C2#3177469411yescharacteristic
368C2#3177470611yescharacteristic
subgroupG/H
centerC22C2×D4×D271
commutator, cosocleC2×C4×C271C24
FrattiniC2×C4C23×D271
Fitting#485×C271C2
socleC22×C271C22×D4
hypercenter#485D271
hypocenterC271#3307
LCSG ▷ C2×C4×C271 ▷ C2×C271 ▷ C271
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
1. #31774591C2semidirect
2. #31774549C2semidirect
3. #31774264C2semidirect
4. #31774229C2semidirect
5. #31774200C2semidirect
6. #31774144C2semidirect
7. #31774128C2semidirect
8. #31774101C2semidirect
9. #31774045C2semidirect
10. #31774044C2semidirect
11. #31774008C2semidirect
12. #31773965C2semidirect
13. #31773897C2semidirect
14. #31773891C2semidirect
15. #485×C271C2semidirect
184. C271#3307semidirect
189. #485D271semidirect

Maximal subgroups

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

subgroupindex
#317745912
#317745492
#317742642
#317742292
#317742002
#317741442
#317741282
#317741012
#317740452
#317740442
#317740082
#317739652
#317738972
#317738912
#485×C2712
#3307271