Finite Group Databasebeta

← C4×#22576135 #46838879

Subgroups — C4×#22576135 #46838879

Order 34688.

824 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22576135C211yesmaximal, characteristic
2C2×C4×D1084C211yesmaximal, characteristic, complemented
3C2×C4×D1084C212yesmaximal, complemented
4C2×C42×D271C211yesmaximal, characteristic, complemented
5#31773798C211yesmaximal, characteristic, complemented
6#31773796C211yesmaximal, characteristic, complemented
7#31773789C212yesmaximal, complemented
8#31773775C212yesmaximal, complemented
9#31773754C211yesmaximal, characteristic, complemented
10C4×(C2×D271)⋊C4C212yesmaximal, complemented
11C4×C4⋊C4×C271C211yesmaximal, characteristic, complemented
12C22×D1084C2212yes—
13C22×D1084C2211yescharacteristic
14C22×C4×D271C2212yes—
15C22×C4×D271C2211yescharacteristic
16C22×C4×D271C2211yescharacteristic
17C22×C4×D271C2211yescharacteristic
18#22576135C418yesdirect product factor
19C4×D1084—28no—
20C4×D1084—24no—
21C2×C4⋊Dic271C2211yescharacteristic
22C2×C4⋊Dic271C2212yes—
23C2×(C2×D271)⋊C4C2212yes—
24C2×(C2×D271)⋊C4C2212yes—
25C2×(C2×D271)⋊C4C2212yes—
26C2×(C2×D271)⋊C4C2212yes—
27C2×(C2×D271)⋊C4C2212yes—
28C2×C4×Dic271C2211yescharacteristic
29C2×C4×Dic271C2211yescharacteristic
30C2×C4×Dic271C2211yescharacteristic
31C42×D271—24no—
32C271⋊#95C2212yes—
33C271⋊#95C2212yes—
34C2×C4⋊C4×C271C2211yescharacteristic
35C2×C4⋊C4×C271C2211yescharacteristic
36C2×C42×C271C2212yes—
37C2×C42×C271C2211yescharacteristic
38#95×C271C2212yes—
39C23×D271C2312yes—
40C23×D271C2311yescharacteristic
41C2×D1084—24no—
42C2×D1084—24no—
43C2×D1084—22no—
44C2×D1084—22no—
45C2×D1084C2×C418yescomplemented
46C2×D1084C2×C414yescomplemented
47C22×Dic271C2312yes—
48C22×Dic271C2311yescharacteristic
49C22×Dic271C2311yescharacteristic
50C22×Dic271C2311yescharacteristic
51C2×C4×D271—22no—
52C2×C4×D271—22no—
53C2×C4×D271—22no—
54C2×C4×D271—22no—
55C2×C4×D271—22no—
56C2×C4×D271—24no—
57C2×C4×D271—24no—
58C2×C4×D271—22no—
59C2×C4×D271—22no—
60C2×C4×D271—24no—
61C2×C4×D271C2×C414yescomplemented
62C2×C4×D271D414yescomplemented
63C4⋊Dic271—24no—
64C4⋊Dic271—22no—
65(C2×D271)⋊C4—24no—
66(C2×D271)⋊C4—24no—
67(C2×D271)⋊C4—24no—
68(C2×D271)⋊C4—24no—
69(C2×D271)⋊C4C2×C418yescomplemented
70C4×Dic271—22no—
71C4×Dic271—22no—
72C4×Dic271—22no—
73C22×C4×C271C2312yes—
74C22×C4×C271C2312yes—
75C22×C4×C271C2311yescharacteristic
76C22×C4×C271C2311yescharacteristic
77C22×C4×C271C2311yescharacteristic
78C4⋊C4×C271—22no—
79C4⋊C4×C271C2×C414yescomplemented
80C42×C271—24no—
81C42×C271D414yescomplemented
82C22×D271—21no—
83C22×D271—21no—
84C22×D271—21no—
85C22×D271—21no—
86C22×D271—22no—
87C22×D271—22no—
88C22×D271—22no—
89C22×D271—22no—
90C22×D271—22no—
91C22×D271—22no—
92C22×D271C22×C414yes—
93C22×D271C22×C412yes—
94C22×D271C2×D412yes—
95C22×D271#4112yes—
96D1084—216no—
97D1084—28no—
98C2×Dic271—21no—
99C2×Dic271—21no—
100C2×Dic271—21no—
101C2×Dic271—21no—
102C2×Dic271—21no—
103C2×Dic271—21no—
104C2×Dic271—22no—
105C2×Dic271—22no—
106C2×Dic271—22no—
107C2×Dic271C22×C412yes—
108C2×Dic271C2×D412yes—
109C2×Dic271#4112yes—
110C4×D271—28no—
111C4×D271—28no—
112C4×D271—28no—
113C4×D271—48no—
114C23×C271C2411yescharacteristic
115C2×C4×C271—22no—
116C2×C4×C271—21no—
117C2×C4×C271—21no—
118C2×C4×C271—22no—
119C2×C4×C271—22no—
120C2×C4×C271—22no—
121C2×C4×C271—22no—
122C2×C4×C271C22×C414yes—
123C2×C4×C271C22×C412yes—
124C2×C4×C271C2×D412yes—
125C2×C4×C271C2×D412yes—
126C2×C4×C271C2×D412yes—
127C2×C4×C271C2×D412yes—
128C2×C4×C271#4112yes—
129C2×C4×C271#4112yes—
130C22×C271C23×C411yescharacteristic
131C22×C271C22×D411yescharacteristic
132C22×C271C22×D411yescharacteristic
133C22×C271C2×#4111yescharacteristic
134C22×C271C2×#4111yescharacteristic
135C22×C271C2×#4111yescharacteristic
136C22×C271C2×#4111yescharacteristic
137C2×D271—22no—
138C2×D271—22no—
139C2×D271—22no—
140C2×D271—22no—
141C2×D271—22no—
142C2×D271—22no—
143C2×D271—24no—
144C2×D271—24no—
145C2×D271—24no—
146C2×D271—42no—
147C2×D271—42no—
148C2×D271—42no—
149C2×D271—42no—
150C2×D271C4×D414yescomplemented
151C4×C271—24no—
152C4×C271—22no—
153C4×C271—42no—
154C4×C271C4×D414yescomplemented
155C4×C271#12114yescomplemented
156Dic271—22no—
157Dic271—22no—
158Dic271—22no—
159Dic271—42no—
160C2×C271C2×C4×D411yescharacteristic
161C2×C271C2×C4×D411yescharacteristic
162C2×C271C4×#4111yescharacteristic
163C2×C271C2×#12111yescharacteristic
164C2×C271#52511yescharacteristic
165C2×C271#52911yescharacteristic
166C2×C271#53211yescharacteristic
167D271—24no—
168D271—44no—
169C271C4×#12111yescharacteristic, complemented, Sylow
170C4×#121—2711nomaximal, Sylow
171C2×#121—2711no—
172C2×C4×D4—2712no—
173C2×C4×D4—2711no—
174C22×C42—2711no—
175#390—2711no—
176#389—2711no—
177#388—2712no—
178#386—2712no—
179#380—2711no—
180C4×C4⋊C4D27111yescharacteristic, complemented
181C4×C22⋊C4—2712no—
182C22×D4—2712no—
183C22×D4—2711no—
184C23×C4—2711no—
185C23×C4—2711no—
186C23×C4—2711no—
187C23×C4—2712no—
188#121—2718no—
189C4×D4—5428no—
190C4×D4—5424no—
191C2×C4⋊C4—2711no—
192C2×C4⋊C4—2712no—
193C2×C4⋊C4C2×D27111yescharacteristic
194C2×C4⋊C4C2×D27111yescharacteristic
195C2×C22⋊C4—2712no—
196C2×C22⋊C4—2712no—
197C2×C22⋊C4—2712no—
198C2×C22⋊C4—2712no—
199C2×C22⋊C4—2712no—
200C2×C42—2711no—
201C2×C42—2711no—
202C2×C42—2711no—
203C2×C42—5424no—
204C2×C42C2×D27112yes—
205C2×C42C2×D27111yescharacteristic
206#95—2712no—
207#95—2712no—
208#95C2×D27112yes—
209C24—2711no—
210C24—2712no—
211C2×D4—2718no—
212C2×D4—2714no—
213C2×D4—5424no—
214C2×D4—5424no—
215C2×D4—5422no—
216C2×D4—5422no—
217C22×C4—2711no—
218C22×C4—2711no—
219C22×C4—2711no—
220C22×C4—2714no—
221C22×C4—2714no—
222C22×C4—2712no—
223C22×C4—5422no—
224C22×C4—5422no—
225C22×C4—5422no—
226C22×C4—5422no—
227C22×C4—5422no—
228C22×C4—5422no—
229C22×C4—5422no—
230C22×C4—5424no—
231C22×C4—5424no—
232C22×C4—5424no—
233C22×C4C22×D27112yes—
234C22×C4C22×D27112yes—
235C22×C4C22×D27111yescharacteristic
236C22×C4C22×D27111yescharacteristic
237C22×C4C22×D27111yescharacteristic
238C4⋊C4—22no—
239C4⋊C4—5424no—
240C4⋊C4—5422no—
241C4⋊C4C4×D27114yescomplemented
242C22⋊C4—2718no—
243C22⋊C4—5424no—
244C22⋊C4—5424no—
245C22⋊C4—5424no—
246C22⋊C4—5424no—
247C42—24no—
248C42—5422no—
249C42—5422no—
250C42—5422no—
251C42D108414yescomplemented
252C23—2712no—
253C23—2712no—
254C23—2712no—
255C23—2714no—
256C23—5421no—
257C23—5421no—
258C23—5421no—
259C23—5421no—
260C23—5422no—
261C23—5422no—
262C23—5422no—
263C23—5422no—
264C23—5422no—
265C23—5422no—
266C23C23×D27111yescharacteristic
267D4—54216no—
268D4—5428no—
269C2×C4—22no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—22no—
273C2×C4—22no—
274C2×C4—22no—
275C2×C4—22no—
276C2×C4—2712no—
277C2×C4—2712no—
278C2×C4—2712no—
279C2×C4—5428no—
280C2×C4—5421no—
281C2×C4—5421no—
282C2×C4—5421no—
283C2×C4—5421no—
284C2×C4—5421no—
285C2×C4—5421no—
286C2×C4—5428no—
287C2×C4—5428no—
288C2×C4—5422no—
289C2×C4—5422no—
290C2×C4—5422no—
291C2×C4—10848no—
292C2×C4C2×C4×D27114yes—
293C2×C4C2×C4×D27112yes—
294C2×C4D4×D27112yes—
295C2×C4C2×D108412yes—
296C2×C4C2×D108412yes—
297C2×C4C2×D108412yes—
298C2×C4#1686465412yes—
299C2×C4#1686465512yes—
300C22—2714no—
301C22—5422no—
302C22—5422no—
303C22—5422no—
304C22—5422no—
305C22—5422no—
306C22—5422no—
307C22—5424no—
308C22—5424no—
309C22—5424no—
310C22—10842no—
311C22—10842no—
312C22—10842no—
313C22—10842no—
314C22C22×C4×D27111yescharacteristic
315C22C2×D4×D27111yescharacteristic
316C22C22×D108411yescharacteristic
317C22#41×D27111yescharacteristic
318C22#41×D27111yescharacteristic
319C22C2×#1686465411yescharacteristic
320C22C2×#1686465511yescharacteristic
321C4—24no—
322C4—22no—
323C4—42no—
324C4—5422no—
325C4—5422no—
326C4—5422no—
327C4—10842no—
328C4C4×D108414yescomplemented
329C4#2257613514yesdirect product factor
330C2—5424no—
331C2—10844no—
332C2C4×D4×D27111yescharacteristic
333C2C2×C4×D108411yescharacteristic
334C2C4×#1686465511yescharacteristic
335C2C2×#2257613511yescharacteristic
336C2#3177440911yescharacteristic
337C2#3177443411yescharacteristic
338C2#3177444411yescharacteristic
subgroupG/H
centerC22×C4C22×D271
commutatorC22×C271C23×C4
FrattiniC23C23×D271
FittingC4×C4⋊C4×C271C2
socle, cosocleC23×C271C24
prime radicalC2×#22576135C2
hypercenterC4×C4⋊C4D271
hypocenterC271C4×#121
LCSG ▷ C22×C271 ▷ C271
UCSC1 ◁ C22×C4 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×D1084C2semidirect
3. C2×C4×D1084C2semidirect
4. C2×C42×D271C2semidirect
5. #31773798C2semidirect
6. #31773796C2semidirect
7. #31773789C2semidirect
8. #31773775C2semidirect
9. #31773754C2semidirect
10. C4×(C2×D271)⋊C4C2semidirect
11. C4×C4⋊C4×C271C2semidirect
18. #22576135C4direct (N × H)
45. C2×D1084C2×C4semidirect
46. C2×D1084C2×C4semidirect
61. C2×C4×D271C2×C4semidirect
62. C2×C4×D271D4semidirect
69. (C2×D271)⋊C4C2×C4semidirect
79. C4⋊C4×C271C2×C4semidirect
81. C42×C271D4semidirect
150. C2×D271C4×D4semidirect
154. C4×C271C4×D4semidirect
155. C4×C271#121semidirect
169. C271C4×#121semidirect
180. C4×C4⋊C4D271semidirect
241. C4⋊C4C4×D271semidirect
251. C42D1084semidirect
328. C4C4×D1084semidirect
329. C4#22576135direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#225761352
C2×C4×D10842
C2×C42×D2712
#317737982
#317737962
#317737892
#317737752
#317737542
C4×(C2×D271)⋊C42
C4×C4⋊C4×C2712
C4×#121271