Finite Group Databasebeta

← #464×D271 #46845804

Subgroups — #464×D271 #46845804

Order 34688.

500 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q16×D271C211yesmaximal, characteristic, complemented
2C2×SD16×D271C211yesmaximal, characteristic
3#124×D271C211yesmaximal, characteristic
4C4×Q8×D271C211yesmaximal, characteristic, complemented
5#31774122C211yesmaximal, characteristic, complemented
6#31774121C211yesmaximal, characteristic, complemented
7#31774120C211yesmaximal, characteristic, complemented
8#31774119C211yesmaximal, characteristic, complemented
9#31774118C211yesmaximal, characteristic, complemented
10#31774117C211yesmaximal, characteristic, complemented
11#31774116C211yesmaximal, characteristic, complemented
12C4⋊C8×D271C211yesmaximal, characteristic, complemented
13#103×D271C211yesmaximal, characteristic, complemented
14#102×D271C211yesmaximal, characteristic
15#464×C271C211yesmaximal, characteristic, complemented
16C2×Q8×D271C2211yescharacteristic
17C2×Q8×D271C2211yescharacteristic
18C2×D4×D271C2211yescharacteristic
19C2×Dic1084C2211yescharacteristic, complemented
20C2×#16864644C2211yescharacteristic, complemented
21C2×#16864644C2211yescharacteristic, complemented
22Q16×D271—24no—
23C2×#16864643C2211yescharacteristic
24C2×#16864642C2211yescharacteristic
25C2×#16864641C2211yescharacteristic
26SD16×D271—24no—
27C2×C8×D271C2211yescharacteristic
28C2×C8×D271C2211yescharacteristic
29#22576149C2211yescharacteristic
30#22576148C2211yescharacteristic
31#22576147C2211yescharacteristic
32#22576146—21no—
33#22576146—21no—
34Q8×Dic271C2211yescharacteristic, complemented
35C4×Dic542—21no—
36C4×Dic542C2211yescharacteristic, complemented
37#22576125—21no—
38#22576125C2211yescharacteristic, complemented
39C4⋊C4×D271—21no—
40C4⋊C4×D271C2211yescharacteristic
41C22⋊C4×D271—21no—
42C22⋊C4×D271—21no—
43C42×D271—21no—
44C42×D271C2211yescharacteristic
45C4⋊(C271⋊C8)C2211yescharacteristic, complemented
46Dic271⋊C8C2211yescharacteristic, complemented
47Dic271⋊C8C2211yescharacteristic, complemented
48#22576085C2211yescharacteristic, complemented
49#22576084C2211yescharacteristic, complemented
50#22576083C2211yescharacteristic, complemented
51#22576082C2211yescharacteristic
52#22576081C2211yescharacteristic
53#22576080C2211yescharacteristic
54C2×Q16×C271C2211yescharacteristic, complemented
55C2×SD16×C271C2211yescharacteristic
56#124×C271C2211yescharacteristic
57C4×Q8×C271C2211yescharacteristic, complemented
58C4⋊C8×C271C2211yescharacteristic, complemented
59#103×C271C2211yescharacteristic, complemented
60#102×C271C2211yescharacteristic
61C23×D271—21no—
62C2×Dic542—21no—
63C2×Dic542—21no—
64C2×Dic542C2311yescharacteristic
65C2×Dic542C2311yescharacteristic
66Q8×D271—22no—
67Q8×D271—22no—
68Q8×D271—22no—
69Q8×D271D414yes—
70C2×D1084C2311yescharacteristic
71C2×C22⋊D271—21no—
72D4×D271—22no—
73D4×D271—22no—
74C2×C4×D271—21no—
75C2×C4×D271—21no—
76C2×C4×D271—21no—
77C2×C4×D271D411yescharacteristic
78C2×C4×D271D411yescharacteristic
79C2×C4×D271C2311yescharacteristic
80Dic1084—22no—
81#16864644—22no—
82#16864644—22no—
83#16864643—22no—
84#16864642—22no—
85#16864641—22no—
86C2×C271⋊C8C2311yescharacteristic
87C2×C271⋊C8C2311yescharacteristic
88C8×D271—22no—
89C8×D271—22no—
90C4⋊Dic271—21no—
91C4⋊Dic271C2311yescharacteristic
92Dic271⋊C4—21no—
93Dic271⋊C4—21no—
94Dic271⋊C4—21no—
95C22⋊Dic271—21no—
96C22⋊Dic271—21no—
97(C2×D271)⋊C4—21no—
98(C2×D271)⋊C4—21no—
99(C2×D271)⋊C4—21no—
100(C2×D271)⋊C4—21no—
101C4×Dic271—21no—
102C4×Dic271—21no—
103C4×Dic271—21no—
104C4×Dic271D411yescharacteristic
105C4×Dic271D411yescharacteristic
106C4×Dic271C2311yescharacteristic
107C2×Q8×C271C2311yescharacteristic
108C2×Q8×C271C2311yescharacteristic
109C2×D4×C271C2311yescharacteristic
110Q16×C271—22no—
111SD16×C271—22no—
112C2×C8×C271C2311yescharacteristic
113C2×C8×C271C2311yescharacteristic
114C4⋊C4×C271—21no—
115C4⋊C4×C271C2311yescharacteristic
116C22⋊C4×C271—21no—
117C22⋊C4×C271—21no—
118C42×C271—21no—
119C42×C271C2311yescharacteristic
120C22×D271—21no—
121C22×D271—42no—
122C22×D271—42no—
123C22×D271—42no—
124C22×D271C2×D411yescharacteristic
125Dic542—21no—
126Dic542—24no—
127Dic542—21no—
128Dic542—21no—
129Dic542—42no—
130Dic542C2×D412yes—
131D1084—21no—
132D1084—21no—
133C22⋊D271—42no—
134C2×Dic271—21no—
135C2×Dic271—21no—
136C2×Dic271—21no—
137C2×Dic271C2×D411yescharacteristic
138C2×Dic271C2×D411yescharacteristic
139C2×Dic271C2×D411yescharacteristic
140C4×D271—24no—
141C4×D271—22no—
142C4×D271—22no—
143C4×D271—42no—
144C4×D271—42no—
145C4×D271C2×D412yes—
146C4×D271#4112yes—
147C271⋊C8—21no—
148C271⋊C8—21no—
149C23×C271—21no—
150Q8×C271—21no—
151Q8×C271—21no—
152Q8×C271—21no—
153Q8×C271C2×D412yes—
154D4×C271—21no—
155D4×C271—21no—
156C2×C4×C271—21no—
157C2×C4×C271—21no—
158C2×C4×C271—21no—
159C2×C4×C271C2×D411yescharacteristic
160C2×C4×C271C2×D411yescharacteristic
161C2×C4×C271C2411yescharacteristic
162C8×C271—21no—
163C8×C271—21no—
164C22×C271—41no—
165C22×C271—41no—
166C22×C271—41no—
167C22×C271C22×D411yescharacteristic
168C2×D271—41no—
169C2×D271—41no—
170C2×D271—41no—
171C2×D271—84no—
172C2×D271#12112yes—
173C2×D271#13512yes—
174C2×D271#13712yes—
175C4×C271—22no—
176C4×C271—21no—
177C4×C271—21no—
178C4×C271—41no—
179C4×C271—41no—
180C4×C271C22×D411yescharacteristic
181C4×C271C2×#4111yescharacteristic
182Dic271—22no—
183Dic271—21no—
184Dic271—21no—
185Dic271—41no—
186Dic271—41no—
187Dic271#12112yes—
188C2×C271—81no—
189C2×C271C2×#12111yescharacteristic
190C2×C271C2×#13511yescharacteristic
191C2×C271C2×#13711yescharacteristic
192D271—81no—
193D271#46414yesdirect product factor
194C271C2×#46411yescharacteristic, complemented, Sylow
195C2×#464—2711nomaximal, Sylow
196C22×Q16—2711no—
197C22×SD16—2711no—
198C2×#124—2711no—
199C2×C4×Q8—2711no—
200#464—2711no—
201#464—2711no—
202#464—2711no—
203#464—2711no—
204#464—2711no—
205#464—2711no—
206#464—2711no—
207#464D27111yescharacteristic, direct product factor
208C2×C4⋊C8—2711no—
209C2×#103—2711no—
210C2×#102—2711no—
211C22×Q8—2711no—
212C22×Q8—2711no—
213C22×D4—2711no—
214C2×Q16—2711no—
215C2×Q16—2711no—
216C2×Q16—2711no—
217C2×Q16—5424no—
218C2×Q16C2×D27111yescharacteristic, complemented
219C2×SD16—2711no—
220C2×SD16—2711no—
221C2×SD16—2711no—
222C2×SD16—5424no—
223C2×SD16C2×D27111yescharacteristic
224C22×C8—2711no—
225C22×C8—2711no—
226#124—2711no—
227#124—2711no—
228#124—2711no—
229#124—5421no—
230#124—5421no—
231#124C2×D27111yescharacteristic
232C4×Q8—2711no—
233C4×Q8—2711no—
234C4×Q8—2711no—
235C4×Q8—5421no—
236C4×Q8—5421no—
237C4×Q8C2×D27111yescharacteristic, complemented
238C2×C4⋊C4—2711no—
239C2×C4⋊C4—5421no—
240C2×C22⋊C4—5421no—
241C2×C22⋊C4—5421no—
242C2×C42—2711no—
243C2×C42—5421no—
244C4⋊C8—2711no—
245C4⋊C8—2711no—
246C4⋊C8—2711no—
247C4⋊C8C2×D27111yescharacteristic, complemented
248#103—2711no—
249#103—2711no—
250#103—2711no—
251#103C2×D27111yescharacteristic, complemented
252#102—2711no—
253#102—2711no—
254#102—2711no—
255#102C2×D27111yescharacteristic
256C24—5421no—
257C2×Q8—2714no—
258C2×Q8—2711no—
259C2×Q8—2711no—
260C2×Q8—5421no—
261C2×Q8—5421no—
262C2×Q8—5422no—
263C2×Q8—5422no—
264C2×Q8—5422no—
265C2×Q8C22×D27111yescharacteristic
266C2×Q8C22×D27111yescharacteristic
267C2×D4—2711no—
268C2×D4—5422no—
269C2×D4—5422no—
270C2×D4—5421no—
271C2×D4C22×D27111yescharacteristic
272C22×C4—2711no—
273C22×C4—2711no—
274C22×C4—2711no—
275C22×C4—5421no—
276C22×C4—5421no—
277C22×C4—5421no—
278Q16—22no—
279Q16—5422no—
280Q16—5422no—
281Q16—5422no—
282SD16—22no—
283SD16—5422no—
284SD16—5422no—
285SD16—5422no—
286C2×C8—2711no—
287C2×C8—2711no—
288C2×C8—5422no—
289C2×C8—5422no—
290C2×C8C22×D27111yescharacteristic
291C2×C8C22×D27111yescharacteristic
292C4⋊C4—21no—
293C4⋊C4—2711no—
294C4⋊C4—5421no—
295C4⋊C4—5421no—
296C4⋊C4—5421no—
297C4⋊C4—5421no—
298C4⋊C4C22×D27111yescharacteristic
299C22⋊C4—21no—
300C22⋊C4—21no—
301C22⋊C4—5421no—
302C22⋊C4—5421no—
303C22⋊C4—5421no—
304C22⋊C4—5421no—
305C22⋊C4—5421no—
306C22⋊C4—5421no—
307C42—21no—
308C42—2711no—
309C42—2711no—
310C42—2711no—
311C42—5421no—
312C42—5421no—
313C42—5421no—
314C42C22×D27111yescharacteristic
315C23—21no—
316C23—2711no—
317C23—5421no—
318C23—10842no—
319C23—10842no—
320C23—10842no—
321Q8—21no—
322Q8—21no—
323Q8—21no—
324Q8—2712no—
325Q8—5424no—
326Q8—5421no—
327Q8—5421no—
328Q8—5421no—
329Q8—10842no—
330Q8D4×D27112yes—
331D4—21no—
332D4—21no—
333D4—5421no—
334D4—5421no—
335D4—10842no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—2711no—
340C2×C4—2712no—
341C2×C4—2712no—
342C2×C4—2711no—
343C2×C4—2711no—
344C2×C4—5422no—
345C2×C4—5422no—
346C2×C4—5424no—
347C2×C4—5421no—
348C2×C4—5421no—
349C2×C4—5421no—
350C2×C4—10842no—
351C2×C4—10842no—
352C2×C4D4×D27111yescharacteristic
353C2×C4D4×D27111yescharacteristic
354C2×C4C23×D27111yescharacteristic
355C8—21no—
356C8—21no—
357C8—5421no—
358C8—5421no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22—2712no—
363C22—2712no—
364C22—2712no—
365C22—10841no—
366C22—10841no—
367C22—10841no—
368C22—21684no—
369C22C2×D4×D27111yescharacteristic
370C4—22no—
371C4—21no—
372C4—21no—
373C4—41no—
374C4—41no—
375C4—2712no—
376C4—5422no—
377C4—5421no—
378C4—5421no—
379C4—10841no—
380C4—10841no—
381C4C2×D4×D27111yescharacteristic
382C4#41×D27111yescharacteristic
383C2—81no—
384C2—2714no—
385C2—21681no—
386C2#121×D27111yescharacteristic
387C2#135×D27111yescharacteristic
388C2#137×D27111yescharacteristic
subgroupG/H
centerC22C2×D4×D271
commutator, cosocleC2×C4×C271C24
FrattiniC2×C4C23×D271
Fitting#464×C271C2
socleC22×C271C22×D4
prime radicalC2×D4×D271C22
hypercenter#464D271
hypocenterC271C2×#464
LCSG ▷ C2×C4×C271 ▷ C2×C271 ▷ C271
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

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

NH ≅ G/Ntype
1. C2×Q16×D271C2semidirect
4. C4×Q8×D271C2semidirect
5. #31774122C2semidirect
6. #31774121C2semidirect
7. #31774120C2semidirect
8. #31774119C2semidirect
9. #31774118C2semidirect
10. #31774117C2semidirect
11. #31774116C2semidirect
12. C4⋊C8×D271C2semidirect
13. #103×D271C2semidirect
15. #464×C271C2semidirect
19. C2×Dic1084C22semidirect
20. C2×#16864644C22semidirect
21. C2×#16864644C22semidirect
34. Q8×Dic271C22semidirect
36. C4×Dic542C22semidirect
38. #22576125C22semidirect
45. C4⋊(C271⋊C8)C22semidirect
46. Dic271⋊C8C22semidirect
47. Dic271⋊C8C22semidirect
48. #22576085C22semidirect
49. #22576084C22semidirect
50. #22576083C22semidirect
54. C2×Q16×C271C22semidirect
57. C4×Q8×C271C22semidirect
58. C4⋊C8×C271C22semidirect
59. #103×C271C22semidirect
193. D271#464direct (N × H)
194. C271C2×#464semidirect
207. #464D271direct (N × H)
218. C2×Q16C2×D271semidirect
237. C4×Q8C2×D271semidirect
247. C4⋊C8C2×D271semidirect
251. #103C2×D271semidirect

Maximal subgroups

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

subgroupindex
C2×Q16×D2712
C2×SD16×D2712
#124×D2712
C4×Q8×D2712
#317741222
#317741212
#317741202
#317741192
#317741182
#317741172
#317741162
C4⋊C8×D2712
#103×D2712
#102×D2712
#464×C2712
C2×#464271