Finite Group Databasebeta

← #46848372

Subgroups — #46848372

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#31774593C211yesmaximal, characteristic, complemented
2#31774568C211yesmaximal, characteristic, complemented
3#31774262C211yesmaximal, characteristic, complemented
4#31774222C211yesmaximal, characteristic, complemented
5#31774211C211yesmaximal, characteristic, complemented
6#31774205C211yesmaximal, characteristic, complemented
7#31774150C211yesmaximal, characteristic, complemented
8#31774133C211yesmaximal, characteristic, complemented
9#31774093C211yesmaximal, characteristic, complemented
10#31774044C211yesmaximal, characteristic, complemented
11#31774044C211yesmaximal, characteristic, complemented
12#31773999C211yesmaximal, characteristic, complemented
13#31773899C211yesmaximal, characteristic, complemented
14#31773894C211yesmaximal, characteristic, complemented
15#435×C271C211yesmaximal, characteristic, complemented
16C2×#16864654C2211yescharacteristic
17C2×#16864654C2211yescharacteristic
18C2×#16864643C2211yescharacteristic
19C2×D2168C2211yescharacteristic
20C2×D2168C2211yescharacteristic
21#22576157C2211yescharacteristic
22#22576156—21no—
23#22576155—21no—
24#22576152C2211yescharacteristic
25#22576142—21no—
26#22576134C2211yescharacteristic
27#22576134C2211yescharacteristic
28#22576134C2211yescharacteristic
29#22576134C2211yescharacteristic
30#22576133—21no—
31#22576133—21no—
32#22576132—21no—
33C4×Dic542C2211yescharacteristic
34C4×D1084C2211yescharacteristic
35#22576122—21no—
36(C22⋊D271)⋊C4—21no—
37#22576119C2211yescharacteristic
38C2×C4⋊Dic271C2211yescharacteristic
39#22576094C2211yescharacteristic
40#22576094C2211yescharacteristic
41#22576092C2211yescharacteristic
42#22576085C2211yescharacteristic
43#22576085C2211yescharacteristic
44#22576085C2211yescharacteristic
45#22576082C2211yescharacteristic
46#22576082C2211yescharacteristic
47#22576082C2211yescharacteristic
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—22no—
61#16864654—41no—
62#16864654—41no—
63C2×Dic542C2311yescharacteristic
64C2×D1084—21no—
65C2×D1084—21no—
66C2×D1084C2311yescharacteristic
67C2×D1084C2311yescharacteristic
68C2×D1084C2311yescharacteristic
69C2×C22⋊D271—21no—
70C2×C22⋊D271—21no—
71C2×C22⋊D271—21no—
72C2×C22⋊D271—21no—
73C2×C22⋊D271—21no—
74C2×C22⋊D271—21no—
75C22×Dic271—21no—
76C2×C4×D271—21no—
77C2×C4×D271—21no—
78C2×C4×D271—21no—
79#16864643—22no—
80D2168—41no—
81D2168—41no—
82C4⋊Dic271—21no—
83C4⋊Dic271C2311yescharacteristic
84C4⋊Dic271C2311yescharacteristic
85C4⋊Dic271C2311yescharacteristic
86C4⋊Dic271C2311yescharacteristic
87Dic271⋊C4—21no—
88Dic271⋊C4—21no—
89Dic271⋊C4—21no—
90C22⋊Dic271—21no—
91(C2×D271)⋊C4—21no—
92(C2×D271)⋊C4—21no—
93(C2×D271)⋊C4—21no—
94(C2×D271)⋊C4—21no—
95(C2×D271)⋊C4—21no—
96C4×Dic271—21no—
97C4×Dic271—21no—
98C2×D4×C271D411yescharacteristic
99C22×C4×C271C2311yescharacteristic
100C22×C4×C271C2311yescharacteristic
101M16×C271—41no—
102C2×C8×C271—41no—
103C2×C8×C271C2311yescharacteristic
104C2×C8×C271C2311yescharacteristic
105C2×C8×C271C2311yescharacteristic
106C2×C8×C271C2311yescharacteristic
107C4⋊C4×C271D411yescharacteristic
108C22⋊C4×C271D411yescharacteristic
109C22⋊C4×C271D411yescharacteristic
110C42×C271C2311yescharacteristic
111C22×D271—21no—
112C22×D271—21no—
113C22×D271—21no—
114Dic542—21no—
115Dic542#4112yes—
116D1084—21no—
117D1084—21no—
118D1084—21no—
119D1084—21no—
120D1084—21no—
121D1084—21no—
122D1084—42no—
123D1084—81no—
124C22⋊D271—42no—
125C22⋊D271—42no—
126C22⋊D271—42no—
127C22⋊D271—81no—
128C22⋊D271—81no—
129C22⋊D271—81no—
130C2×Dic271—21no—
131C2×Dic271—21no—
132C2×Dic271—21no—
133C2×Dic271—21no—
134C2×Dic271—21no—
135C2×Dic271—81no—
136C4×D271—42no—
137C4×D271—42no—
138C4×D271—81no—
139C23×C271C2×D411yescharacteristic
140C23×C271C2×D411yescharacteristic
141D4×C271—41no—
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×C271—21no—
161C22×C271C22×D411yescharacteristic
162C2×D271—41no—
163C2×D271—41no—
164C2×D271—41no—
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×C271C2×#4111yescharacteristic
176C4×C271H(5,𝔽2)11yescharacteristic
177Dic271—22no—
178Dic271—41no—
179Dic271—41no—
180Dic271—41no—
181Dic271—41no—
182C2×C271—41no—
183C2×C271—41no—
184C2×C271#54611yescharacteristic
185C2×C271#57511yescharacteristic
186C2×C271#57611yescharacteristic
187D271—81no—
188D271—81no—
189D271—81no—
190C271#330911yescharacteristic, complemented, Sylow
191#3309—2711nomaximal, Sylow
192#553—2711no—
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#435D27111yescharacteristic, complemented
205#417—2711no—
206#416—2711no—
207C2×#41—2711no—
208C2×#41—2711no—
209C2×SD16—2711no—
210C2×D8—2711no—
211C2×D8—2711no—
212C2×M16C2×D27111yescharacteristic
213C22×C8C2×D27111yescharacteristic
214#127—2711no—
215#127—5421no—
216#126—5421no—
217#125—2711no—
218#123—5421no—
219#121—2711no—
220#121—2711no—
221#121—2711no—
222#121—2711no—
223#121—5421no—
224#121—5421no—
225#121—5421no—
226C4×Q8—2711no—
227C4×D4—2711no—
228C4×D4—5421no—
229C4×D4—5421no—
230C4×D4C2×D27111yescharacteristic
231#117—2711no—
232C2×C4⋊C4—2711no—
233#107—2711no—
234#107—2711no—
235#106—2711no—
236C4⋊C8C2×D27111yescharacteristic
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⋊C8C2×D27111yescharacteristic
248C22⋊C8C2×D27111yescharacteristic
249#97C2×D27111yescharacteristic
250#41—5422no—
251#41—5422no—
252#41—10841no—
253#41—10841no—
254C2×Q8—2711no—
255C2×D4—2711no—
256C2×D4—2711no—
257C2×D4—2711no—
258C2×D4—5421no—
259C2×D4—5421no—
260C2×D4—5421no—
261C2×D4—5421no—
262C2×D4—5421no—
263C2×D4—5421no—
264C2×D4—5421no—
265C2×D4—5421no—
266C2×D4D108411yescharacteristic
267C22×C4—5421no—
268C22×C4—5421no—
269C22×C4—5421no—
270C22×C4—5421no—
271C22×C4C22×D27111yescharacteristic
272C22×C4C22×D27111yescharacteristic
273SD16—5422no—
274D8—10841no—
275D8—10841no—
276M16—41no—
277C2×C8—41no—
278C2×C8C22×D27111yescharacteristic
279C2×C8C22×D27111yescharacteristic
280C2×C8C22×D27111yescharacteristic
281C2×C8C22×D27111yescharacteristic
282C4⋊C4—2711no—
283C4⋊C4—2711no—
284C4⋊C4—2711no—
285C4⋊C4—2711no—
286C4⋊C4—5421no—
287C4⋊C4—5421no—
288C4⋊C4—5421no—
289C4⋊C4—5421no—
290C4⋊C4D108411yescharacteristic
291C22⋊C4—5421no—
292C22⋊C4—5421no—
293C22⋊C4—5421no—
294C22⋊C4—5421no—
295C22⋊C4—5421no—
296C22⋊C4—5421no—
297C22⋊C4D108411yescharacteristic
298C22⋊C4D108411yescharacteristic
299C42—5421no—
300C42—5421no—
301C42C22×D27111yescharacteristic
302C23—5421no—
303C23—5421no—
304C23—5421no—
305C23C2×D108411yescharacteristic
306C23C2×D108411yescharacteristic
307Q8—2712no—
308Q8—5421no—
309D4—41no—
310D4—5421no—
311D4—5421no—
312D4—5421no—
313D4—5421no—
314D4—5421no—
315D4—5421no—
316D4—10842no—
317D4—10842no—
318D4—10842no—
319D4—10842no—
320D4—21681no—
321D4—21681no—
322D4—21681no—
323D4—21681no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—5421no—
329C2×C4—5421no—
330C2×C4—5421no—
331C2×C4—5421no—
332C2×C4—5421no—
333C2×C4—10842no—
334C2×C4—10842no—
335C2×C4—21681no—
336C2×C4—21681no—
337C2×C4C2×D108411yescharacteristic
338C2×C4C2×D108411yescharacteristic
339C2×C4C2×D108411yescharacteristic
340C2×C4C2×D108411yescharacteristic
341C2×C4C23×D27111yescharacteristic
342C8—21no—
343C8—21no—
344C8—21no—
345C8—21no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—10841no—
353C22—10841no—
354C22—10841no—
355C22—10841no—
356C22—10841no—
357C22—10841no—
358C22—10841no—
359C22—10841no—
360C22—10841no—
361C22C22×D108411yescharacteristic
362C4—21no—
363C4—21no—
364C4—21no—
365C4—21no—
366C4—5422no—
367C4—10841no—
368C4—10841no—
369C4—10841no—
370C4—10841no—
371C4#41×D27111yescharacteristic
372C4#2257620511yescharacteristic
373C2—41no—
374C2—41no—
375C2—21681no—
376C2—21681no—
377C2—21681no—
378C2#3177454211yescharacteristic
379C2#3177469711yescharacteristic
380C2#3177470211yescharacteristic
subgroupG/H
centerC22C22×D1084
commutator, cosocleC2×C4×C271C24
FrattiniC2×C4C23×D271
Fitting#435×C271C2
socleC22×C271C22×D4
hypercenter#435D271
hypocenterC271#3309
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. #31774593C2semidirect
2. #31774568C2semidirect
3. #31774262C2semidirect
4. #31774222C2semidirect
5. #31774211C2semidirect
6. #31774205C2semidirect
7. #31774150C2semidirect
8. #31774133C2semidirect
9. #31774093C2semidirect
10. #31774044C2semidirect
11. #31774044C2semidirect
12. #31773999C2semidirect
13. #31773899C2semidirect
14. #31773894C2semidirect
15. #435×C271C2semidirect
190. C271#3309semidirect
204. #435D271semidirect

Maximal subgroups

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

subgroupindex
#317745932
#317745682
#317742622
#317742222
#317742112
#317742052
#317741502
#317741332
#317740932
#317740442
#317739992
#317738992
#317738942
#435×C2712
#3309271