Finite Group Databasebeta

← #46846643

Subgroups — #46846643

Order 34688.

384 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31774518C211yesmaximal, characteristic, complemented
2#31774377C211yesmaximal, characteristic, complemented
3#31774228C211yesmaximal, characteristic, complemented
4#31774216C211yesmaximal, characteristic, complemented
5#31774188C211yesmaximal, characteristic, complemented
6#31774183C211yesmaximal, characteristic, complemented
7#31774120C211yesmaximal, characteristic, complemented
8#31774113C211yesmaximal, characteristic, complemented
9#31774061C211yesmaximal, characteristic, complemented
10#31774044C211yesmaximal, characteristic
11#31774010C211yesmaximal, characteristic, complemented
12#31774005C211yesmaximal, characteristic, complemented
13C4×#16864643C211yesmaximal, characteristic, complemented
14C4×#16864643C211yesmaximal, characteristic, complemented
15#433×C271C211yesmaximal, characteristic, complemented
16C2×#16864654C2211yescharacteristic
17C2×Dic1084C2211yescharacteristic
18C2×#16864643C2211yescharacteristic
19C2×#16864643C2211yescharacteristic
20C2×D2168C2211yescharacteristic
21#22576160C2211yescharacteristic
22#22576155—21no—
23#22576148C2211yescharacteristic
24#22576146—21no—
25#22576142—21no—
26#22576139C2211yescharacteristic
27#22576138—21no—
28#22576134C2211yescharacteristic
29C4×Dic542C2211yescharacteristic
30C4×Dic542C2211yescharacteristic
31C4×Dic542C2211yescharacteristic
32C4×D1084C2211yescharacteristic
33C4×D1084C2211yescharacteristic
34C4×D1084C2211yescharacteristic
35(C22⋊D271)⋊C4—21no—
36(C22⋊D271)⋊C4—21no—
37#22576118—21no—
38C2×C4⋊Dic271C2211yescharacteristic
39C4⋊C4×D271—21no—
40#22576092C2211yescharacteristic
41#22576092C2211yescharacteristic
42#22576092C2211yescharacteristic
43#22576092C2211yescharacteristic
44#22576085C2211yescharacteristic
45#22576085C2211yescharacteristic
46#22576085C2211yescharacteristic
47#22576085C2211yescharacteristic
48#22576082C2211yescharacteristic
49#22576082C2211yescharacteristic
50#22576082C2211yescharacteristic
51#22576082C2211yescharacteristic
52#117×C271C2211yescharacteristic
53C4⋊C8×C271C2211yescharacteristic
54C4⋊C8×C271C2211yescharacteristic
55C22⋊C8×C271C2211yescharacteristic
56C22⋊C8×C271C2211yescharacteristic
57#97×C271C2211yescharacteristic
58C4×C8×C271C2211yescharacteristic
59#16864654—22no—
60#16864654—22no—
61C2×Dic542—21no—
62C2×Dic542C2311yescharacteristic
63C2×Dic542C2311yescharacteristic
64C2×D1084C2311yescharacteristic
65C2×D1084C2311yescharacteristic
66C2×C22⋊D271—21no—
67C2×C22⋊D271—21no—
68C22×Dic271—21no—
69C2×C4×D271—21no—
70C2×C4×D271—21no—
71C2×C4×D271—21no—
72C2×C4×D271—21no—
73Dic1084—22no—
74#16864643—22no—
75#16864643—22no—
76D2168—22no—
77C4⋊Dic271—21no—
78C4⋊Dic271—21no—
79C4⋊Dic271C2311yescharacteristic
80C4⋊Dic271C2311yescharacteristic
81C4⋊Dic271C2311yescharacteristic
82C4⋊Dic271C2311yescharacteristic
83Dic271⋊C4—21no—
84Dic271⋊C4—21no—
85Dic271⋊C4—21no—
86Dic271⋊C4—21no—
87C22⋊Dic271—21no—
88(C2×D271)⋊C4—21no—
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—
94C4×Dic271—21no—
95C4×Dic271—21no—
96C4×Dic271—21no—
97C22×C4×C271C2311yescharacteristic
98C2×C8×C271C2311yescharacteristic
99C2×C8×C271C2311yescharacteristic
100C2×C8×C271C2311yescharacteristic
101C2×C8×C271C2311yescharacteristic
102C4⋊C4×C271D411yescharacteristic
103C4⋊C4×C271D411yescharacteristic
104C22⋊C4×C271D411yescharacteristic
105C22⋊C4×C271D411yescharacteristic
106C42×C271C2311yescharacteristic
107C42×C271C2311yescharacteristic
108C22×D271—21no—
109C22×D271—21no—
110Dic542—21no—
111Dic542—21no—
112Dic542—21no—
113Dic542—81no—
114Dic542#4112yes—
115D1084—21no—
116D1084—21no—
117D1084—21no—
118D1084#4112yes—
119C22⋊D271—24no—
120C22⋊D271—81no—
121C2×Dic271—21no—
122C2×Dic271—21no—
123C2×Dic271—21no—
124C2×Dic271—21no—
125C2×Dic271—21no—
126C2×Dic271—21no—
127C2×Dic271—81no—
128C4×D271—24no—
129C4×D271—81no—
130C4×D271—81no—
131C4×D271—81no—
132C23×C271C2×D411yescharacteristic
133C2×C4×C271—21no—
134C2×C4×C271—21no—
135C2×C4×C271C2×D411yescharacteristic
136C2×C4×C271C2×D411yescharacteristic
137C2×C4×C271C2×D411yescharacteristic
138C2×C4×C271C2×D411yescharacteristic
139C2×C4×C271C2×D411yescharacteristic
140C2×C4×C271C2411yescharacteristic
141C8×C271—21no—
142C8×C271—21no—
143C8×C271—21no—
144C8×C271—21no—
145C22×C271—21no—
146C22×C271—21no—
147C22×C271—21no—
148C22×C271C22×D411yescharacteristic
149C2×D271—22no—
150C2×D271—41no—
151C2×D271—41no—
152C2×D271—41no—
153C2×D271—41no—
154C2×D271—41no—
155C4×C271—21no—
156C4×C271—21no—
157C4×C271—21no—
158C4×C271—21no—
159C4×C271—21no—
160C4×C271C2×#4111yescharacteristic
161C4×C271C2×#4111yescharacteristic
162Dic271—22no—
163Dic271—41no—
164Dic271—41no—
165Dic271—41no—
166Dic271—41no—
167Dic271—41no—
168C2×C271—41no—
169C2×C271#52511yescharacteristic
170C2×C271#57711yescharacteristic
171C2×C271#57711yescharacteristic
172D271—42no—
173D271—81no—
174C271#312511yescharacteristic, complemented, Sylow
175#3125—2711nomaximal, Sylow
176#542—2711no—
177#520—2711no—
178#483—2711no—
179#481—2711no—
180#476—2711no—
181#475—2711no—
182#464—2711no—
183#463—2711no—
184#452—2711no—
185#449—2711no—
186#442—2711no—
187#441—2711no—
188C4×SD16—2711no—
189C4×SD16—2711no—
190#433D27111yescharacteristic, complemented
191C2×#41—2711no—
192C2×Q16—2711no—
193C2×SD16—2711no—
194C2×SD16—2711no—
195C2×D8—2711no—
196C4⋊Q8—2711no—
197#126—5421no—
198#124—2711no—
199#124—5421no—
200#123—5421no—
201C22⋊Q8—2711no—
202C22⋊Q8—5421no—
203#121—2711no—
204C4×Q8—2711no—
205C4×Q8—2711no—
206C4×Q8—2711no—
207C4×D4—2711no—
208C4×D4—2711no—
209C4×D4—2711no—
210C4×D4—5421no—
211C4×D4—5421no—
212#117—5421no—
213#117C2×D27111yescharacteristic
214C2×C4⋊C4—2711no—
215C2×C4⋊C4—5421no—
216#106—2711no—
217#106—2711no—
218#106—2711no—
219#106—2711no—
220C4⋊C8C2×D27111yescharacteristic
221C4⋊C8C2×D27111yescharacteristic
222#103—2711no—
223#103—2711no—
224#103—2711no—
225#103—2711no—
226#102—2711no—
227#102—2711no—
228#102—2711no—
229#102—2711no—
230C22⋊C8C2×D27111yescharacteristic
231C22⋊C8C2×D27111yescharacteristic
232#97C2×D27111yescharacteristic
233C4×C8C2×D27111yescharacteristic
234#41—5422no—
235#41—5422no—
236C2×Q8—2711no—
237C2×Q8—2711no—
238C2×Q8—5421no—
239C2×D4—2711no—
240C2×D4—2711no—
241C2×D4—5421no—
242C2×D4—5421no—
243C22×C4—5421no—
244C22×C4—5421no—
245C22×C4—5421no—
246C22×C4—5421no—
247C22×C4—5421no—
248C22×C4C22×D27111yescharacteristic
249Q16—5422no—
250SD16—5422no—
251SD16—5422no—
252D8—5422no—
253C2×C8C22×D27111yescharacteristic
254C2×C8C22×D27111yescharacteristic
255C2×C8C22×D27111yescharacteristic
256C2×C8C22×D27111yescharacteristic
257C4⋊C4—2711no—
258C4⋊C4—2711no—
259C4⋊C4—2711no—
260C4⋊C4—2711no—
261C4⋊C4—5421no—
262C4⋊C4—5421no—
263C4⋊C4—5421no—
264C4⋊C4—5421no—
265C4⋊C4—5421no—
266C4⋊C4—5421no—
267C4⋊C4D108411yescharacteristic
268C4⋊C4D108411yescharacteristic
269C22⋊C4—5421no—
270C22⋊C4—5421no—
271C22⋊C4—5421no—
272C22⋊C4—5421no—
273C22⋊C4—5421no—
274C22⋊C4—5421no—
275C22⋊C4—5421no—
276C22⋊C4D108411yescharacteristic
277C22⋊C4D108411yescharacteristic
278C42—5421no—
279C42—5421no—
280C42—5421no—
281C42C22×D27111yescharacteristic
282C42C22×D27111yescharacteristic
283C23—5421no—
284C23—5421no—
285C23C2×D108411yescharacteristic
286Q8—2712no—
287Q8—5421no—
288Q8—5421no—
289Q8—5421no—
290Q8—21681no—
291D4—2712no—
292D4—5424no—
293D4—5421no—
294D4—5421no—
295D4—5421no—
296D4—21681no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—5424no—
300C2×C4—5421no—
301C2×C4—5421no—
302C2×C4—5421no—
303C2×C4—5421no—
304C2×C4—5421no—
305C2×C4—5421no—
306C2×C4—21681no—
307C2×C4—21681no—
308C2×C4—21681no—
309C2×C4—21681no—
310C2×C4C2×D108411yescharacteristic
311C2×C4C2×D108411yescharacteristic
312C2×C4C2×D108411yescharacteristic
313C2×C4C2×D108411yescharacteristic
314C2×C4C2×D108411yescharacteristic
315C2×C4C23×D27111yescharacteristic
316C8—21no—
317C8—21no—
318C8—21no—
319C8—21no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—5422no—
324C22—10841no—
325C22—10841no—
326C22—10841no—
327C22—10841no—
328C22—10841no—
329C22C22×D108411yescharacteristic
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—21no—
335C4—5422no—
336C4—10841no—
337C4—10841no—
338C4—10841no—
339C4—10841no—
340C4—10841no—
341C4#41×D27111yescharacteristic
342C4#41×D27111yescharacteristic
343C2—41no—
344C2—10842no—
345C2—21681no—
346C2#3177440911yescharacteristic
347C2#3177470911yescharacteristic
348C2#3177470911yescharacteristic
subgroupG/H
centerC22C22×D1084
commutator, cosocleC2×C4×C271C24
FrattiniC2×C4C23×D271
Fitting#433×C271C2
socleC22×C271C22×D4
prime radical#31774044C2
hypercenter#433D271
hypocenterC271#3125
LCSG ▷ C2×C4×C271 ▷ C2×C271 ▷ C271
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #31774518C2semidirect
2. #31774377C2semidirect
3. #31774228C2semidirect
4. #31774216C2semidirect
5. #31774188C2semidirect
6. #31774183C2semidirect
7. #31774120C2semidirect
8. #31774113C2semidirect
9. #31774061C2semidirect
11. #31774010C2semidirect
12. #31774005C2semidirect
13. C4×#16864643C2semidirect
14. C4×#16864643C2semidirect
15. #433×C271C2semidirect
174. C271#3125semidirect
190. #433D271semidirect

Maximal subgroups

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

subgroupindex
#317745182
#317743772
#317742282
#317742162
#317741882
#317741832
#317741202
#317741132
#317740612
#317740442
#317740102
#317740052
C4×#168646432
#433×C2712
#3125271