Finite Group Databasebeta

← #46848357

Subgroups — #46848357

Order 34688.

420 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#31774556C211yesmaximal, characteristic, complemented
2#31774551C211yesmaximal, characteristic, complemented
3#31774257C211yesmaximal, characteristic, complemented
4#31774233C211yesmaximal, characteristic, complemented
5#31774211C211yesmaximal, characteristic, complemented
6#31774193C211yesmaximal, characteristic, complemented
7#31774143C211yesmaximal, characteristic, complemented
8#31774133C211yesmaximal, characteristic, complemented
9#31774113C211yesmaximal, characteristic, complemented
10#31774044C211yesmaximal, characteristic, complemented
11#31774038C211yesmaximal, characteristic, complemented
12#31773999C211yesmaximal, characteristic, complemented
13#31773899C211yesmaximal, characteristic, complemented
14C2×#22576085C211yesmaximal, characteristic, complemented
15#435×C271C211yesmaximal, characteristic, complemented
16C2×#16864654C2211yescharacteristic
17C2×#16864653—21no—
18C22×Dic542C2211yescharacteristic
19C2×#16864643C2211yescharacteristic
20C2×#16864643C2211yescharacteristic
21C2×D2168C2211yescharacteristic
22#22576160C2211yescharacteristic
23#22576148C2211yescharacteristic
24#22576146—21no—
25#22576144—21no—
26#22576144—21no—
27#22576140—21no—
28#22576139C2211yescharacteristic
29#22576138—21no—
30#22576134C2211yescharacteristic
31#22576134C2211yescharacteristic
32#22576134C2211yescharacteristic
33#22576132—21no—
34C4×Dic542C2211yescharacteristic
35C4×D1084C2211yescharacteristic
36(C22⋊D271)⋊C4—21no—
37C2×C4⋊Dic271C2211yescharacteristic
38C2×C4⋊Dic271C2211yescharacteristic
39#22576094C2211yescharacteristic
40#22576094C2211yescharacteristic
41#22576094C2211yescharacteristic
42#22576085C2211yescharacteristic
43#22576085C2211yescharacteristic
44#22576085C2211yescharacteristic
45#22576085C2211yescharacteristic
46#22576085C2211yescharacteristic
47#22576085C2211yescharacteristic
48#22576082C2211yescharacteristic
49#22576082C2211yescharacteristic
50#22576082C2211yescharacteristic
51#22576082C2211yescharacteristic
52C2×M16×C271C2211yescharacteristic
53C22×C8×C271C2211yescharacteristic
54C4×D4×C271C2211yescharacteristic
55C4⋊C8×C271C2211yescharacteristic
56C22⋊C8×C271C2211yescharacteristic
57C22⋊C8×C271C2211yescharacteristic
58#97×C271C2211yescharacteristic
59#16864654—22no—
60#16864654—41no—
61#16864653—44no—
62C2×Dic542—22no—
63C2×Dic542—21no—
64C2×Dic542—21no—
65C2×Dic542—41no—
66C2×Dic542C2311yescharacteristic
67C2×Dic542C2311yescharacteristic
68C2×D1084C2311yescharacteristic
69C2×D1084C2311yescharacteristic
70C2×C22⋊D271—21no—
71C2×C22⋊D271—21no—
72C2×C22⋊D271—21no—
73C2×C22⋊D271—21no—
74C22×Dic271—21no—
75C22×Dic271—21no—
76C22×Dic271—21no—
77C2×C4×D271—21no—
78C2×C4×D271—21no—
79#16864643—22no—
80#16864643—41no—
81D2168—41no—
82C4⋊Dic271—21no—
83C4⋊Dic271—21no—
84C4⋊Dic271—21no—
85C4⋊Dic271C2311yescharacteristic
86C4⋊Dic271C2311yescharacteristic
87C4⋊Dic271C2311yescharacteristic
88C4⋊Dic271C2311yescharacteristic
89Dic271⋊C4—21no—
90Dic271⋊C4—21no—
91C22⋊Dic271—21no—
92(C2×D271)⋊C4—21no—
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—
98C4×Dic271—21no—
99C2×D4×C271D411yescharacteristic
100C22×C4×C271C2311yescharacteristic
101C22×C4×C271C2311yescharacteristic
102M16×C271—41no—
103C2×C8×C271—41no—
104C2×C8×C271C2311yescharacteristic
105C2×C8×C271C2311yescharacteristic
106C2×C8×C271C2311yescharacteristic
107C2×C8×C271C2311yescharacteristic
108C4⋊C4×C271D411yescharacteristic
109C22⋊C4×C271D411yescharacteristic
110C22⋊C4×C271D411yescharacteristic
111C42×C271C2311yescharacteristic
112C22×D271—21no—
113C22×D271—21no—
114Dic542—21no—
115Dic542—21no—
116Dic542—21no—
117Dic542—42no—
118Dic542—42no—
119Dic542#4112yescomplemented
120D1084—21no—
121D1084—21no—
122D1084—21no—
123D1084—21no—
124C22⋊D271—42no—
125C22⋊D271—42no—
126C22⋊D271—42no—
127C22⋊D271—42no—
128C2×Dic271—21no—
129C2×Dic271—21no—
130C2×Dic271—21no—
131C2×Dic271—21no—
132C2×Dic271—21no—
133C2×Dic271—21no—
134C2×Dic271—42no—
135C2×Dic271—42no—
136C2×Dic271—42no—
137C4×D271—42no—
138C4×D271—42no—
139C23×C271C2×D411yescharacteristic
140C23×C271C2×D411yescharacteristic
141D4×C271—22no—
142C2×C4×C271—21no—
143C2×C4×C271—21no—
144C2×C4×C271—21no—
145C2×C4×C271—21no—
146C2×C4×C271C2×D411yescharacteristic
147C2×C4×C271C2×D411yescharacteristic
148C2×C4×C271C2×D411yescharacteristic
149C2×C4×C271C2×D411yescharacteristic
150C2×C4×C271C2411yescharacteristic
151C8×C271—21no—
152C8×C271—21no—
153C8×C271—21no—
154C8×C271—21no—
155C22×C271—21no—
156C22×C271—21no—
157C22×C271—21no—
158C22×C271—21no—
159C22×C271—21no—
160C22×C271AGL(1,ℤ/8)12yes—
161C22×C271C22×D411yescharacteristic
162C2×D271—41no—
163C2×D271—41no—
164C2×D271—41no—
165C2×D271—41no—
166C2×D271—41no—
167C2×D271—41no—
168C4×C271—21no—
169C4×C271—21no—
170C4×C271—21no—
171C4×C271—21no—
172C4×C271C2×#4111yescharacteristic
173C4×C271H(5,𝔽2)11yescharacteristic
174Dic271—22no—
175Dic271—41no—
176Dic271—41no—
177Dic271—41no—
178Dic271—41no—
179Dic271—41no—
180C2×C271—22no—
181C2×C271—41no—
182C2×C271#54611yescharacteristic
183C2×C271C2×AGL(1,ℤ/8)11yescharacteristic
184C2×C271#57811yescharacteristic
185D271—81no—
186D271—81no—
187C271#330811yescharacteristic, complemented, Sylow
188#3308—2711nomaximal, Sylow
189#548—2711no—
190#547—2711no—
191#489—2711no—
192#484—2711no—
193#480—2711no—
194#477—2711no—
195#468—2711no—
196#466—2711no—
197#463—2711no—
198#449—2711no—
199#448—2711no—
200#440—2711no—
201#435D27111yescharacteristic, complemented
202#417—2711no—
203C2×#103—2711no—
204C2×#41—2711no—
205C2×#41—5421no—
206C22×Q8—2711no—
207C2×SD16—2711no—
208C2×SD16—2711no—
209C2×D8—2711no—
210C2×M16C2×D27111yescharacteristic
211C22×C8C2×D27111yescharacteristic
212C4⋊Q8—2711no—
213#124—2711no—
214#124—5421no—
215#123—5421no—
216#123—5421no—
217C22⋊Q8—2711no—
218C22⋊Q8—5421no—
219C22⋊Q8—5421no—
220#121—2711no—
221#121—2711no—
222#121—2711no—
223#121—5421no—
224C4×Q8—2711no—
225C4×D4—2711no—
226C4×D4—5421no—
227C4×D4C2×D27111yescharacteristic
228C2×C4⋊C4—2711no—
229C2×C4⋊C4—2711no—
230#107—2711no—
231#107—2711no—
232#107—2711no—
233C4⋊C8C2×D27111yescharacteristic
234#103—2711no—
235#103—2711no—
236#103—2711no—
237#103—2711no—
238#103—2711no—
239#103—2711no—
240#102—2711no—
241#102—2711no—
242#102—2711no—
243#102—2711no—
244C22⋊C8C2×D27111yescharacteristic
245C22⋊C8C2×D27111yescharacteristic
246#97C2×D27111yescharacteristic
247#41—5422no—
248#41—10841no—
249#41—10844no—
250C2×Q8—2711no—
251C2×Q8—2711no—
252C2×Q8—5422no—
253C2×Q8—5421no—
254C2×Q8—5421no—
255C2×Q8—10841no—
256C2×D4—2711no—
257C2×D4—2711no—
258C2×D4—5421no—
259C2×D4—5421no—
260C2×D4—5421no—
261C2×D4—5421no—
262C2×D4D108411yescharacteristic
263C22×C4—5421no—
264C22×C4—5421no—
265C22×C4—5421no—
266C22×C4—5421no—
267C22×C4—5421no—
268C22×C4C22×D27111yescharacteristic
269C22×C4C22×D27111yescharacteristic
270SD16—5422no—
271SD16—10841no—
272D8—10841no—
273M16—41no—
274C2×C8—41no—
275C2×C8C22×D27111yescharacteristic
276C2×C8C22×D27111yescharacteristic
277C2×C8C22×D27111yescharacteristic
278C2×C8C22×D27111yescharacteristic
279C4⋊C4—2711no—
280C4⋊C4—2711no—
281C4⋊C4—2711no—
282C4⋊C4—2711no—
283C4⋊C4—5421no—
284C4⋊C4—5421no—
285C4⋊C4—5421no—
286C4⋊C4—5421no—
287C4⋊C4—5421no—
288C4⋊C4D108411yescharacteristic
289C22⋊C4—5421no—
290C22⋊C4—5421no—
291C22⋊C4—5421no—
292C22⋊C4—5421no—
293C22⋊C4—5421no—
294C22⋊C4—5421no—
295C22⋊C4—5421no—
296C22⋊C4D108411yescharacteristic
297C22⋊C4D108411yescharacteristic
298C42—5421no—
299C42C22×D27111yescharacteristic
300C23—5421no—
301C23—5421no—
302C23C2×D108411yescharacteristic
303C23C2×D108411yescharacteristic
304Q8—2712no—
305Q8—5421no—
306Q8—5421no—
307Q8—5421no—
308Q8—10842no—
309Q8—10842no—
310D4—22no—
311D4—5421no—
312D4—5421no—
313D4—5421no—
314D4—5421no—
315D4—10842no—
316D4—10842no—
317D4—10842no—
318D4—10842no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—5421no—
324C2×C4—5421no—
325C2×C4—5421no—
326C2×C4—5421no—
327C2×C4—5421no—
328C2×C4—5421no—
329C2×C4—10842no—
330C2×C4—10842no—
331C2×C4—10842no—
332C2×C4—10842no—
333C2×C4—10842no—
334C2×C4C2×D108411yescharacteristic
335C2×C4C2×D108411yescharacteristic
336C2×C4C2×D108411yescharacteristic
337C2×C4C2×D108411yescharacteristic
338C2×C4C23×D27111yescharacteristic
339C8—21no—
340C8—21no—
341C8—21no—
342C8—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—21no—
348C22—10841no—
349C22—10841no—
350C22—10841no—
351C22—10841no—
352C22—10841no—
353C22—10841no—
354C22#2257618812yes—
355C22C22×D108411yescharacteristic
356C4—21no—
357C4—21no—
358C4—21no—
359C4—21no—
360C4—5422no—
361C4—10841no—
362C4—10841no—
363C4—10841no—
364C4—10841no—
365C4—10841no—
366C4#41×D27111yescharacteristic
367C4#2257620511yescharacteristic
368C2—22no—
369C2—41no—
370C2—21681no—
371C2—21681no—
372C2#3177454211yescharacteristic
373C2C2×#2257618811yescharacteristic
374C2#3177471411yescharacteristic
subgroupG/H
centerC22C22×D1084
commutator, cosocleC2×C4×C271C24
FrattiniC2×C4C23×D271
Fitting#435×C271C2
socleC22×C271C22×D4
hypercenter#435D271
hypocenterC271#3308
LCSG ▷ C2×C4×C271 ▷ C2×C271 ▷ C271
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. #31774556C2semidirect
2. #31774551C2semidirect
3. #31774257C2semidirect
4. #31774233C2semidirect
5. #31774211C2semidirect
6. #31774193C2semidirect
7. #31774143C2semidirect
8. #31774133C2semidirect
9. #31774113C2semidirect
10. #31774044C2semidirect
11. #31774038C2semidirect
12. #31773999C2semidirect
13. #31773899C2semidirect
14. C2×#22576085C2semidirect
15. #435×C271C2semidirect
119. Dic542#41semidirect
187. C271#3308semidirect
201. #435D271semidirect

Maximal subgroups

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

subgroupindex
#317745562
#317745512
#317742572
#317742332
#317742112
#317741932
#317741432
#317741332
#317741132
#317740442
#317740382
#317739992
#317738992
C2×#225760852
#435×C2712
#3308271