Finite Group Databasebeta

← C4×#10622539 #14751935

Subgroups — C4×#10622539 #14751935

Order 2816.

1206 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622539C212yesmaximal
2#13068469C212yesmaximal, complemented
3C4×C4⋊(C11⋊C8)C212yesmaximal, complemented
4#13068378C212yesmaximal
5C4×C22⋊(C11⋊C8)C212yesmaximal
6#13068365C212yesmaximal, complemented
7C4×#66867C212yesmaximal, complemented
8C2×C43×C11C211yesmaximal, characteristic
9C22×C42×C11C412yes—
10C22×C42×C11C412yes—
11C22×C42×C11C2211yescharacteristic
12C22×C42×C11C2211yescharacteristic
13C22×C42×C11C2211yescharacteristic
14C43×C11C412yes—
15C43×C11C412yes—
16C43×C11C2211yescharacteristic
17C43×C11C2211yescharacteristic
18C43×C11C2211yescharacteristic
19C43×C11C2211yescharacteristic
20C2×C22⋊(C11⋊C8)C2214yes—
21#10622539C4116yesdirect product factor
22C2×C4⋊(C11⋊C8)C2214yes—
23C2×#66867C2214yes—
24C2×#66867C2214yes—
25C2×C4×C11⋊C8C2214yes—
26#10622162C2214yes—
27#10622162C2214yes—
28C23×C4×C11C2×C412yes—
29C23×C4×C11C2×C411yescharacteristic
30C23×C4×C11C2×C411yescharacteristic
31C23×C4×C11C2×C412yes—
32C23×C4×C11C2311yescharacteristic
33C2×C42×C11—28no—
34C2×C42×C11—28no—
35C2×C42×C11—24no—
36C2×C42×C11—24no—
37C2×C42×C11C2×C418yes—
38C2×C42×C11C2×C412yes—
39C2×C42×C11C2×C412yes—
40C2×C42×C11C2×C412yes—
41C2×C42×C11C2×C412yes—
42C2×C42×C11C2×C412yes—
43C2×C42×C11C2×C412yes—
44C2×C42×C11C2×C412yes—
45C2×C42×C11C2×C412yes—
46C2×C42×C11C2×C412yes—
47C2×C42×C11C2×C411yescharacteristic
48C2×C42×C11C2×C411yescharacteristic
49C2×C42×C11C2×C412yes—
50C2×C42×C11C2311yescharacteristic
51C2×C42×C11C2311yescharacteristic
52C2×C42×C11C2311yescharacteristic
53C2×C42×C11C2311yescharacteristic
54C2×C42×C11C2311yescharacteristic
55C2×C42×C11C2311yescharacteristic
56C22×C11⋊C8C2318yes—
57C22⋊(C11⋊C8)C2×C4116yes—
58C4⋊(C11⋊C8)C2×C4116yescomplemented
59#66867—28no—
60#66867C2×C4116yescomplemented
61C4×C11⋊C8—28no—
62C4×#432—111nomaximal, Sylow
63C24×C11C22×C411yescharacteristic
64C22×C4×C11—24no—
65C22×C4×C11—24no—
66C22×C4×C11—24no—
67C22×C4×C11—24no—
68C22×C4×C11—24no—
69C22×C4×C11—24no—
70C22×C4×C11—24no—
71C22×C4×C11—22no—
72C22×C4×C11—22no—
73C22×C4×C11C4214yes—
74C22×C4×C11C4214yes—
75C22×C4×C11M1618yes—
76C22×C4×C11C22×C411yescharacteristic
77C22×C4×C11C22×C411yescharacteristic
78C22×C4×C11C22×C411yescharacteristic
79C22×C4×C11C22×C411yescharacteristic
80C22×C4×C11C22×C414yes—
81C22×C4×C11C22×C412yes—
82C22×C4×C11C22×C412yes—
83C22×C4×C11C22×C412yes—
84C22×C4×C11C22×C411yescharacteristic
85C22×C4×C11C22×C412yes—
86C22×C4×C11C2411yescharacteristic
87C42×C11—24no—
88C42×C11—24no—
89C42×C11—24no—
90C42×C11—24no—
91C42×C11—24no—
92C42×C11—24no—
93C42×C11—24no—
94C42×C11—24no—
95C42×C11—24no—
96C42×C11—22no—
97C42×C11—22no—
98C42×C11C4214yes—
99C42×C11C4214yes—
100C42×C11M1618yes—
101C42×C11C22×C414yes—
102C42×C11C22×C414yes—
103C42×C11#4114yes—
104C42×C11#4114yes—
105C2×C11⋊C8—28no—
106C2×C11⋊C8—28no—
107C2×C11⋊C8C22×C4116yes—
108C2×#432—112no—
109C2×C43D1111yescharacteristic
110#1767—112no—
111C4×C4⋊C8—112no—
112#1749—112no—
113C4×C22⋊C8—112no—
114#1745—112no—
115C4×#97—112no—
116C23×C11—21no—
117C23×C11—21no—
118C23×C11—22no—
119C23×C11C2×C4212yes—
120C23×C11C2×M1614yes—
121C23×C11C23×C411yescharacteristic
122C2×C4×C11—216no—
123C2×C4×C11—22no—
124C2×C4×C11—22no—
125C2×C4×C11—21no—
126C2×C4×C11—21no—
127C2×C4×C11—22no—
128C2×C4×C11—22no—
129C2×C4×C11—22no—
130C2×C4×C11—22no—
131C2×C4×C11—22no—
132C2×C4×C11—22no—
133C2×C4×C11—22no—
134C2×C4×C11—28no—
135C2×C4×C11—28no—
136C2×C4×C11—28no—
137C2×C4×C11—216no—
138C2×C4×C11C2×C4212yes—
139C2×C4×C11C2×C4212yes—
140C2×C4×C11C2×C4212yes—
141C2×C4×C11C2×C4212yes—
142C2×C4×C11C2×C4212yes—
143C2×C4×C11#11714yes—
144C2×C4×C11#11714yes—
145C2×C4×C11C2×M1614yes—
146C2×C4×C11C2×M1614yes—
147C2×C4×C11C2×M1614yes—
148C2×C4×C11C2×M1614yes—
149C2×C4×C11C2×M1614yes—
150C2×C4×C11C23×C412yes—
151C2×C4×C11C2×#4112yes—
152C2×C4×C11C2×#4112yes—
153C11⋊C8—216no—
154C22×C42Dic1112yes—
155C22×C42Dic1112yes—
156C22×C42C2×D1111yescharacteristic
157C22×C42C2×D1111yescharacteristic
158C22×C42C2×D1111yescharacteristic
159#432—1116no—
160C2×C4⋊C8—114no—
161C2×C22⋊C8—114no—
162C2×#97—114no—
163C2×#97—114no—
164C2×C4×C8—114no—
165C43Dic1112yes—
166C43Dic1112yes—
167C43C2×D1111yescharacteristic
168C43C2×D1111yescharacteristic
169C43C2×D1111yescharacteristic
170C43C2×D1111yescharacteristic
171#336—114no—
172#336—114no—
173C22×C11—22no—
174C22×C11—24no—
175C22×C11—24no—
176C22×C11—22no—
177C22×C11C4×M1614yes—
178C22×C11C22×C4211yescharacteristic
179C22×C11C2×#11711yescharacteristic
180C22×C11C2×#11711yescharacteristic
181C22×C11C22×M1612yes—
182C22×C11C22×M1612yes—
183C4×C11—22no—
184C4×C11—22no—
185C4×C11—22no—
186C4×C11—24no—
187C4×C11—24no—
188C4×C11—24no—
189C4×C11—22no—
190C4×C11C4×M1614yes—
191C4×C11#43218yescomplemented
192C4×C11C4×#4114yes—
193C23×C4C2×Dic1112yes—
194C23×C4C2×Dic1112yes—
195C23×C4C2×Dic1111yescharacteristic
196C23×C4C2×Dic1111yescharacteristic
197C23×C4C22×D1111yescharacteristic
198C22×C8—118no—
199C2×C42—28no—
200C2×C42—28no—
201C2×C42—24no—
202C2×C42—24no—
203C2×C42C4×D1118yes—
204C2×C42C2×Dic1112yes—
205C2×C42C2×Dic1112yes—
206C2×C42C2×Dic1112yes—
207C2×C42C2×Dic1112yes—
208C2×C42C2×Dic1112yes—
209C2×C42C2×Dic1112yes—
210C2×C42C2×Dic1112yes—
211C2×C42C2×Dic1112yes—
212C2×C42C2×Dic1112yes—
213C2×C42C2×Dic1112yes—
214C2×C42C2×Dic1111yescharacteristic
215C2×C42C2×Dic1111yescharacteristic
216C2×C42C22×D1111yescharacteristic
217C2×C42C22×D1111yescharacteristic
218C2×C42C22×D1111yescharacteristic
219C2×C42C22×D1111yescharacteristic
220C2×C42C22×D1111yescharacteristic
221C2×C42C22×D1111yescharacteristic
222C4⋊C8—1116no—
223C22⋊C8—1116no—
224#97—1116no—
225#97—228no—
226C4×C8—228no—
227C2×C11—24no—
228C2×C11C4×#11711yescharacteristic
229C2×C11C2×C4×M1611yescharacteristic
230C2×C11C2×C4×M1611yescharacteristic
231C2×C11C2×#43212yes—
232C2×C11#292012yes—
233C24C22×Dic1111yescharacteristic
234C22×C4—24no—
235C22×C4—24no—
236C22×C4—24no—
237C22×C4—24no—
238C22×C4—24no—
239C22×C4—24no—
240C22×C4—24no—
241C22×C4—22no—
242C22×C4—22no—
243C22×C4#431818yes—
244C22×C4C4×Dic1114yes—
245C22×C4C4×Dic1114yes—
246C22×C4C2×C4×D1114yes—
247C22×C4C22×Dic1112yes—
248C22×C4C22×Dic1112yes—
249C22×C4C22×Dic1111yescharacteristic
250C22×C4C22×Dic1111yescharacteristic
251C22×C4C22×Dic1111yescharacteristic
252C22×C4C22×Dic1111yescharacteristic
253C22×C4C22×Dic1112yes—
254C22×C4C22×Dic1111yescharacteristic
255C22×C4C22×Dic1112yes—
256C22×C4C23×D1111yescharacteristic
257C2×C8—1116no—
258C2×C8—228no—
259C2×C8—228no—
260C42—24no—
261C42—24no—
262C42—24no—
263C42—24no—
264C42—24no—
265C42—24no—
266C42—24no—
267C42—24no—
268C42—24no—
269C42—22no—
270C42—22no—
271C42#431818yes—
272C42C4×Dic1114yes—
273C42C4×Dic1114yes—
274C42C2×C4×D1114yes—
275C42C2×C4×D1114yes—
276C42#433914yes—
277C42#433914yes—
278C11C4×#43211yescharacteristic, complemented, Sylow
279C23—22no—
280C23—21no—
281C23—21no—
282C23C2×#431814yes—
283C23C2×C4×Dic1112yes—
284C23C23×Dic1111yescharacteristic
285C2×C4—216no—
286C2×C4—28no—
287C2×C4—22no—
288C2×C4—22no—
289C2×C4—22no—
290C2×C4—22no—
291C2×C4—22no—
292C2×C4—22no—
293C2×C4—22no—
294C2×C4—22no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—22no—
298C2×C4—28no—
299C2×C4—28no—
300C2×C4—216no—
301C2×C4C2×#431814yes—
302C2×C4C2×#431814yes—
303C2×C4C2×#431814yes—
304C2×C4C2×#431814yes—
305C2×C4C2×#431814yes—
306C2×C4C2×C4×Dic1112yes—
307C2×C4C2×C4×Dic1112yes—
308C2×C4C2×C4×Dic1112yes—
309C2×C4C2×C4×Dic1112yes—
310C2×C4C2×C4×Dic1112yes—
311C2×C4#6697914yes—
312C2×C4#6697914yes—
313C2×C4C22×C4×D1112yes—
314C2×C4C2×#433912yes—
315C2×C4C2×#433912yes—
316C8—2216no—
317C22—24no—
318C22—22no—
319C22—22no—
320C22—24no—
321C22C4×#431814yes—
322C22C22×#431812yes—
323C22C22×#431812yes—
324C22C22×C4×Dic1111yescharacteristic
325C22C2×#6697911yescharacteristic
326C22C2×#6697911yescharacteristic
327C4—24no—
328C4—24no—
329C4—22no—
330C4—22no—
331C4—22no—
332C4—22no—
333C4—24no—
334C4C4×#431814yes—
335C4#1062253918yesdirect product factor
336C4C4×#433914yes—
337C2—24no—
338C2C4×#6697911yescharacteristic
339C2C2×C4×#431811yescharacteristic
340C2C2×C4×#431811yescharacteristic
341C2C2×#1062253912yes—
342C2#1307724912yes—
subgroupG/H
centerC2×C42C22×D11
commutatorC22×C11C22×C42
FrattiniC22×C4C23×D11
FittingC2×C43×C11C2
socleC23×C11C23×C4
prime radicalC24×C11C22×C4
cosocleC22×C4×C11C24
hypercenterC2×C43D11
hypocenterC11C4×#432
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C42 ◁ C2×C43

Complements

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

NH ≅ G/Ntype
2. #13068469C2semidirect
3. C4×C4⋊(C11⋊C8)C2semidirect
6. #13068365C2semidirect
7. C4×#66867C2semidirect
21. #10622539C4direct (N × H)
58. C4⋊(C11⋊C8)C2×C4semidirect
60. #66867C2×C4semidirect
191. C4×C11#432semidirect
278. C11C4×#432semidirect
335. C4#10622539direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106225392
#130684692
C4×C4⋊(C11⋊C8)2
#130683782
C4×C22⋊(C11⋊C8)2
#130683652
C4×#668672
C2×C43×C112
C4×#43211