Finite Group Databasebeta

← #46846957

Subgroups — #46846957

Order 34688.

408 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31774444C211yesmaximal, characteristic, complemented
2#31774429C211yesmaximal, characteristic, complemented
3#31774305C211yesmaximal, characteristic, complemented
4#31774285C211yesmaximal, characteristic, complemented
5#31774260C211yesmaximal, characteristic, complemented
6#31774255C211yesmaximal, characteristic, complemented
7#31774149C211yesmaximal, characteristic, complemented
8#31774147C211yesmaximal, characteristic, complemented
9#31774144C211yesmaximal, characteristic, complemented
10#31774142C211yesmaximal, characteristic, complemented
11C4×#16864643C211yesmaximal, characteristic, complemented
12C4×#16864642C211yesmaximal, characteristic, complemented
13C4×#16864639C211yesmaximal, characteristic, complemented
14C4×#16864637C211yesmaximal, characteristic, complemented
15C4×D8×C271C211yesmaximal, characteristic, complemented
16C2×#16864654—21no—
17C2×#16864643C2211yescharacteristic
18C2×#16864642C2211yescharacteristic
19C2×#16864639C2211yescharacteristic
20C2×#16864637C2211yescharacteristic
21C2×#16864637C2211yescharacteristic
22#22576159C2211yescharacteristic
23#22576156C2211yescharacteristic
24#22576153—21no—
25#22576151C2211yescharacteristic
26#22576147C2211yescharacteristic
27#22576146—21no—
28#22576142—21no—
29#22576140C2211yescharacteristic
30#22576135C2211yescharacteristic
31#22576133—21no—
32#22576131C2211yescharacteristic
33#22576131C2211yescharacteristic
34C4×Dic542C2211yescharacteristic
35C4×D1084C2211yescharacteristic
36C4×C22⋊D271—21no—
37C4×C22⋊D271—21no—
38#22576119—21no—
39C42×D271C2211yescharacteristic
40#22576093C2211yescharacteristic
41#22576092C2211yescharacteristic
42#22576091C2211yescharacteristic
43#22576085C2211yescharacteristic
44#22576083C2211yescharacteristic
45#22576082C2211yescharacteristic
46#22576081C2211yescharacteristic
47#22576081C2211yescharacteristic
48#22576080C2211yescharacteristic
49#22576070C2211yescharacteristic
50#22576070C2211yescharacteristic
51C4×C271⋊C8C2211yescharacteristic
52C2×D8×C271C2211yescharacteristic
53C4×D4×C271C2211yescharacteristic
54C4×D4×C271C2211yescharacteristic
55#107×C271C2211yescharacteristic
56#102×C271C2211yescharacteristic
57#102×C271C2211yescharacteristic
58C4×C8×C271C2211yescharacteristic
59#16864654—44no—
60C2×Dic542—21no—
61C2×Dic542C2311yescharacteristic
62C2×D1084—21no—
63C2×D1084C2311yescharacteristic
64C2×C22⋊D271—21no—
65C2×C22⋊D271—21no—
66C2×C22⋊D271—21no—
67C2×C22⋊D271—21no—
68C2×C4×D271—21no—
69C2×C4×D271D411yescharacteristic
70C2×C4×D271D411yescharacteristic
71C2×C4×D271C2311yescharacteristic
72#16864643—22no—
73#16864642—22no—
74#16864639—22no—
75#16864637—22no—
76#16864637—22no—
77C2×C271⋊C8C2311yescharacteristic
78C2×C271⋊C8C2311yescharacteristic
79C4⋊Dic271—21no—
80C4⋊Dic271—21no—
81C4⋊Dic271C2311yescharacteristic
82C4⋊Dic271C2311yescharacteristic
83Dic271⋊C4—21no—
84Dic271⋊C4—21no—
85Dic271⋊C4—21no—
86C22⋊Dic271—21no—
87C22⋊Dic271—21no—
88C22⋊Dic271—21no—
89C22⋊Dic271—21no—
90(C2×D271)⋊C4—21no—
91(C2×D271)⋊C4—21no—
92(C2×D271)⋊C4—21no—
93C4×Dic271—21no—
94C4×Dic271D411yescharacteristic
95C4×Dic271D411yescharacteristic
96C4×Dic271C2311yescharacteristic
97C2×D4×C271C2311yescharacteristic
98C2×D4×C271C2311yescharacteristic
99C22×C4×C271—21no—
100C22×C4×C271—21no—
101D8×C271—22no—
102C2×C8×C271C2311yescharacteristic
103C2×C8×C271C2311yescharacteristic
104C4⋊C4×C271C2311yescharacteristic
105C4⋊C4×C271C2311yescharacteristic
106C22⋊C4×C271—21no—
107C22⋊C4×C271—21no—
108C42×C271C2311yescharacteristic
109C22×D271—21no—
110C22×D271C2×D411yescharacteristic
111Dic542—21no—
112Dic542—21no—
113Dic542—42no—
114D1084—21no—
115D1084—21no—
116D1084—42no—
117C22⋊D271—42no—
118C22⋊D271—42no—
119C22⋊D271—42no—
120C22⋊D271—42no—
121C2×Dic271—21no—
122C2×Dic271—21no—
123C2×Dic271—21no—
124C2×Dic271C2×D411yescharacteristic
125C2×Dic271C2×D411yescharacteristic
126C2×Dic271C2×D411yescharacteristic
127C4×D271—22no—
128C4×D271—21no—
129C4×D271—21no—
130C4×D271—41no—
131C4×D271—42no—
132C271⋊C8—21no—
133C271⋊C8#4112yescomplemented
134C23×C271—21no—
135C23×C271—21no—
136D4×C271—21no—
137D4×C271—21no—
138D4×C271—21no—
139D4×C271—21no—
140C2×C4×C271—21no—
141C2×C4×C271—21no—
142C2×C4×C271—42no—
143C2×C4×C271—42no—
144C2×C4×C271C2×D411yescharacteristic
145C2×C4×C271C2×D411yescharacteristic
146C2×C4×C271C2411yescharacteristic
147C8×C271—21no—
148C8×C271#4112yescomplemented
149C22×C271—41no—
150C22×C271—41no—
151C22×C271—41no—
152C22×C271—41no—
153C22×C271—41no—
154C22×C271—41no—
155C22×C271C22×D411yescharacteristic
156C2×D271—21no—
157C2×D271—21no—
158C2×D271—21no—
159C2×D271—41no—
160C2×D271—41no—
161C2×D271—41no—
162C4×C271—21no—
163C4×C271—41no—
164C4×C271—41no—
165C4×C271AGL(1,ℤ/8)12yes—
166C4×C271C2×#4111yescharacteristic
167C4×C271C2×#4111yescharacteristic
168Dic271—21no—
169Dic271—21no—
170Dic271—21no—
171Dic271—41no—
172Dic271—41no—
173Dic271—41no—
174C2×C271—81no—
175C2×C271—81no—
176C2×C271#53211yescharacteristic
177C2×C271C2×AGL(1,ℤ/8)11yescharacteristic
178C2×C271#57511yescharacteristic
179D271—41no—
180D271—81no—
181C271#317111yescharacteristic, complemented, Sylow
182#3171—2711nomaximal, Sylow
183#532—2711no—
184#529—2711no—
185#501—2711no—
186#496—2711no—
187#490—2711no—
188#489—2711no—
189#469—2711no—
190#469—2711no—
191#468—2711no—
192#468—2711no—
193C4×SD16—2711no—
194C4×SD16—2711no—
195C4×D8—2711no—
196C4×D8D27111yescharacteristic, complemented
197C4×M16—2711no—
198C2×#41—5421no—
199C2×SD16—2711no—
200C2×SD16—2711no—
201C2×D8—2711no—
202C2×D8C2×D27111yescharacteristic
203C2×M16—2711no—
204C2×M16—2711no—
205C4⋊Q8—2711no—
206#127—2711no—
207#126—5421no—
208#125—2711no—
209#124—2711no—
210#124—5421no—
211#123—5421no—
212C22⋊Q8—2711no—
213#121—2711no—
214#121—2711no—
215#121—2711no—
216#121—5421no—
217C4×Q8—2711no—
218C4×D4—2711no—
219C4×D4—5421no—
220C4×D4—5421no—
221C4×D4C2×D27111yescharacteristic
222C4×D4C2×D27111yescharacteristic
223#117—5421no—
224C2×C42—2711no—
225#107—2711no—
226#107C2×D27111yescharacteristic
227#106—2711no—
228#106—2711no—
229#103—2711no—
230#103—2711no—
231#102—2711no—
232#102—2711no—
233#102—2711no—
234#102—2711no—
235#102C2×D27111yescharacteristic
236#102C2×D27111yescharacteristic
237#97—2711no—
238#97—2711no—
239C4×C8—2711no—
240C4×C8C2×D27111yescharacteristic
241#41—10844no—
242C2×Q8—2711no—
243C2×Q8—5421no—
244C2×D4—2711no—
245C2×D4—5421no—
246C2×D4—5421no—
247C2×D4—5421no—
248C2×D4—5421no—
249C2×D4—5421no—
250C2×D4C22×D27111yescharacteristic
251C2×D4C22×D27111yescharacteristic
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—2711no—
255C22×C4—2711no—
256C22×C4—2711no—
257C22×C4—5421no—
258SD16—5422no—
259SD16—5422no—
260D8—22no—
261D8—5422no—
262M16—5422no—
263M16—5422no—
264C2×C8—2711no—
265C2×C8—2711no—
266C2×C8C22×D27111yescharacteristic
267C2×C8C22×D27111yescharacteristic
268C4⋊C4—2711no—
269C4⋊C4—2711no—
270C4⋊C4—5421no—
271C4⋊C4—5421no—
272C4⋊C4—5421no—
273C4⋊C4—5421no—
274C4⋊C4—5421no—
275C4⋊C4C22×D27111yescharacteristic
276C4⋊C4C22×D27111yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—5421no—
280C22⋊C4—5421no—
281C22⋊C4—5421no—
282C22⋊C4—5421no—
283C22⋊C4—5421no—
284C22⋊C4—5421no—
285C22⋊C4—5421no—
286C42—2711no—
287C42—2711no—
288C42—2711no—
289C42—5421no—
290C42C22×D27111yescharacteristic
291C23—21no—
292C23—21no—
293C23—2711no—
294C23—5421no—
295Q8—5421no—
296Q8—5421no—
297Q8—10842no—
298D4—21no—
299D4—21no—
300D4—21no—
301D4—21no—
302D4—5421no—
303D4—5421no—
304D4—10842no—
305D4—10842no—
306D4—10842no—
307D4—10842no—
308D4—10842no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—2711no—
314C2×C4—2711no—
315C2×C4—2711no—
316C2×C4—5422no—
317C2×C4—5421no—
318C2×C4—5421no—
319C2×C4—5421no—
320C2×C4—5421no—
321C2×C4—5421no—
322C2×C4—10841no—
323C2×C4—10842no—
324C2×C4D4×D27111yescharacteristic
325C2×C4D4×D27111yescharacteristic
326C2×C4C23×D27111yescharacteristic
327C8—21no—
328C8—2712no—
329C8—5421no—
330C8#1686465412yescomplemented
331C22—41no—
332C22—41no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—5421no—
338C22—5421no—
339C22—5421no—
340C22—10841no—
341C22—10841no—
342C22—10841no—
343C22C2×D4×D27111yescharacteristic
344C4—21no—
345C4—41no—
346C4—41no—
347C4—5421no—
348C4—5421no—
349C4—5421no—
350C4—10841no—
351C4—10841no—
352C4—10841no—
353C4#2257618412yes—
354C4#41×D27111yescharacteristic
355C4C2×#1686465411yescharacteristic
356C2—81no—
357C2—81no—
358C2—10841no—
359C2—21681no—
360C2#3177444411yescharacteristic
361C2C2×#2257618411yescharacteristic
362C2#3177469411yescharacteristic
subgroupG/H
centerC2×C4D4×D271
commutator, cosocleC2×C4×C271C24
FrattiniC2×C4C23×D271
FittingC4×D8×C271C2
socleC22×C271C22×D4
hypercenterC4×D8D271
hypocenterC271#3171
LCSG ▷ C2×C4×C271 ▷ C2×C271 ▷ C271
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. #31774444C2semidirect
2. #31774429C2semidirect
3. #31774305C2semidirect
4. #31774285C2semidirect
5. #31774260C2semidirect
6. #31774255C2semidirect
7. #31774149C2semidirect
8. #31774147C2semidirect
9. #31774144C2semidirect
10. #31774142C2semidirect
11. C4×#16864643C2semidirect
12. C4×#16864642C2semidirect
13. C4×#16864639C2semidirect
14. C4×#16864637C2semidirect
15. C4×D8×C271C2semidirect
133. C271⋊C8#41semidirect
148. C8×C271#41semidirect
181. C271#3171semidirect
196. C4×D8D271semidirect
330. C8#16864654semidirect

Maximal subgroups

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

subgroupindex
#317744442
#317744292
#317743052
#317742852
#317742602
#317742552
#317741492
#317741472
#317741442
#317741422
C4×#168646432
C4×#168646422
C4×#168646392
C4×#168646372
C4×D8×C2712
#3171271