Finite Group Databasebeta

← C2×C11×#2853 #14613811

Subgroups — C2×C11×#2853 #14613811

Order 2816.

3354 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
1C22×C11×#123C211yesmaximal, characteristic
2C23×C42×C11C211yesmaximal, characteristic, complemented
3C11×#2853C2116yesmaximal, direct product factor
4C2×C11×#388C214yesmaximal, complemented
5C2×C11×#387C214yesmaximal, complemented
6C2×C11×#386C212yesmaximal
7C2×C11×#385C212yesmaximal, complemented
8C2×C11×#381C211yesmaximal, characteristic, complemented
9C23×D4×C11C2211yescharacteristic
10C24×C4×C11C2212yes—
11C24×C4×C11C2211yescharacteristic
12C2×C11×#123—28no—
13C2×C11×#123C2218yes—
14C22×C11×C4⋊C4C2212yes—
15C22×C11×C4⋊C4C2214yes—
16C22×C11×C22⋊C4C2211yescharacteristic
17C22×C11×C22⋊C4C2212yes—
18C22×C11×C22⋊C4C2212yes—
19C22×C11×C22⋊C4C2214yes—
20C22×C42×C11—28no—
21C22×C42×C11C2214yes—
22C22×C42×C11C2218yescomplemented
23C11×#388C22132yescomplemented
24C11×#387C22132yescomplemented
25C11×#386C22116yes—
26C11×#385C22116yescomplemented
27C11×#381C2218yescomplemented
28C2×C11×#95C2214yes—
29C2×C11×#95C2214yes—
30C2×C11×#95C2214yes—
31C25×C11C2311yescharacteristic
32C25×C11C2311yescharacteristic
33C22×D4×C11—24no—
34C22×D4×C11—28no—
35C22×D4×C11C2314yes—
36C23×C4×C11—28no—
37C23×C4×C11—28no—
38C23×C4×C11—216no—
39C23×C4×C11D418yes—
40C23×C4×C11C2318yes—
41C23×C4×C11C2314yes—
42C23×C4×C11C2312yes—
43C23×C4×C11C2311yescharacteristic
44C23×C4×C11C2314yes—
45C23×C4×C11C2312yes—
46C23×C4×C11C2314yes—
47C11×#123—232no—
48C2×C11×C4⋊C4—28no—
49C2×C11×C4⋊C4—216no—
50C2×C11×C4⋊C4C23116yes—
51C2×C11×C4⋊C4C2318yes—
52C2×C11×C22⋊C4—24no—
53C2×C11×C22⋊C4—28no—
54C2×C11×C22⋊C4—28no—
55C2×C11×C22⋊C4—216no—
56C2×C11×C22⋊C4C2318yes—
57C2×C11×C22⋊C4C2314yes—
58C2×C11×C22⋊C4C23116yes—
59C2×C11×C22⋊C4C2318yes—
60C2×C42×C11—216no—
61C2×C42×C11—232no—
62C2×C42×C11C23116yes—
63C11×#95C23116yes—
64C11×#95C23116yes—
65C11×#95C23116yes—
66C2×#2853C1111yesmaximal, characteristic, direct product factor, Sylow
67C24×C11—28no—
68C24×C11—22no—
69C24×C11—28no—
70C24×C11—24no—
71C24×C11C2×D414yes—
72C24×C11#4118yes—
73C24×C11C2412yes—
74C24×C11C2412yes—
75C24×C11C2411yescharacteristic
76C2×D4×C11—28no—
77C2×D4×C11—216no—
78C2×D4×C11—416no—
79C22×C4×C11—264no—
80C22×C4×C11—232no—
81C22×C4×C11—216no—
82C22×C4×C11—28no—
83C22×C4×C11—216no—
84C22×C4×C11—28no—
85C22×C4×C11—28no—
86C22×C4×C11—232no—
87C22×C4×C11—24no—
88C22×C4×C11—22no—
89C22×C4×C11—28no—
90C22×C4×C11—28no—
91C22×C4×C11—28no—
92C22×C4×C11—28no—
93C22×C4×C11—24no—
94C22×C4×C11C2×D418yes—
95C22×C4×C11C2×D4116yes—
96C22×C4×C11#41116yes—
97C22×C4×C11C2418yes—
98C22×C4×C11C2412yes—
99C22×C4×C11C2414yes—
100C22×C4×C11C2414yes—
101C22×C4×C11C2418yes—
102C11×C4⋊C4—216no—
103C11×C4⋊C4—232no—
104C11×C22⋊C4—28no—
105C11×C22⋊C4—216no—
106C11×C22⋊C4—216no—
107C11×C22⋊C4—232no—
108C42×C11—232no—
109C22×#123C2×C1111yescharacteristic
110C23×C42C2×C1111yescharacteristic, complemented
111#2853C2×C11116yesdirect product factor
112C2×#388C2×C1114yescomplemented
113C2×#387C2×C1114yescomplemented
114C2×#386C2×C1112yes—
115C2×#385C2×C1112yescomplemented
116C2×#381C2×C1111yescharacteristic, complemented
117C23×C11—216no—
118C23×C11—232no—
119C23×C11—28no—
120C23×C11—22no—
121C23×C11—28no—
122C23×C11—24no—
123C23×C11—44no—
124C23×C11—48no—
125C23×C11—416no—
126C23×C11#123116yes—
127C23×C11C22×D414yes—
128C23×C11C22×D412yes—
129C23×C11C2×#4118yes—
130C23×C11C2×#4114yes—
131C23×C11C2×#4118yes—
132C23×C11C2511yescharacteristic
133D4×C11—416no—
134C2×C4×C11—264no—
135C2×C4×C11—232no—
136C2×C4×C11—216no—
137C2×C4×C11—232no—
138C2×C4×C11—28no—
139C2×C4×C11—28no—
140C2×C4×C11—28no—
141C2×C4×C11—24no—
142C2×C4×C11—22no—
143C2×C4×C11—28no—
144C2×C4×C11—28no—
145C2×C4×C11—28no—
146C2×C4×C11—28no—
147C2×C4×C11—24no—
148C2×C4×C11—44no—
149C2×C4×C11—48no—
150C2×C4×C11—416no—
151C2×C4×C11C22×D418yes—
152C2×C4×C11C2×#41116yes—
153C23×D4C22×C1111yescharacteristic
154C24×C4C22×C1112yes—
155C24×C4C22×C1111yescharacteristic
156C2×#123—28no—
157C2×#123C22×C1118yes—
158C22×C4⋊C4C22×C1112yes—
159C22×C4⋊C4C22×C1114yes—
160C22×C22⋊C4C22×C1111yescharacteristic
161C22×C22⋊C4C22×C1112yes—
162C22×C22⋊C4C22×C1112yes—
163C22×C22⋊C4C22×C1114yes—
164C22×C42—28no—
165C22×C42C22×C1114yes—
166C22×C42C22×C1118yescomplemented
167#388C22×C11132yescomplemented
168#387C22×C11132yescomplemented
169#386C22×C11116yes—
170#385C22×C11116yescomplemented
171#381C22×C1118yescomplemented
172C2×#95C22×C1114yes—
173C2×#95C22×C1114yes—
174C2×#95C22×C1114yes—
175C22×C11—232no—
176C22×C11—28no—
177C22×C11—216no—
178C22×C11—42no—
179C22×C11—44no—
180C22×C11—48no—
181C22×C11—88no—
182C22×C11C2×#12318yes—
183C22×C11C2×#12314yes—
184C22×C11#52518yes—
185C22×C11#529116yes—
186C22×C11C23×D411yescharacteristic
187C22×C11C22×#4112yes—
188C22×C11C22×#4114yes—
189C4×C11—28no—
190C4×C11—216no—
191C4×C11—42no—
192C4×C11—44no—
193C4×C11—48no—
194C25C23×C1111yescharacteristic
195C25C23×C1111yescharacteristic
196C22×D4—24no—
197C22×D4—28no—
198C22×D4C23×C1114yes—
199C23×C4—28no—
200C23×C4—28no—
201C23×C4—216no—
202C23×C4D4×C1118yes—
203C23×C4C23×C1112yes—
204C23×C4C23×C1114yes—
205C23×C4C23×C1111yescharacteristic
206C23×C4C23×C1118yes—
207C23×C4C23×C1112yes—
208C23×C4C23×C1114yes—
209C23×C4C23×C1114yes—
210#123—232no—
211C2×C4⋊C4—28no—
212C2×C4⋊C4—216no—
213C2×C4⋊C4C23×C1118yes—
214C2×C4⋊C4C23×C11116yes—
215C2×C22⋊C4—24no—
216C2×C22⋊C4—28no—
217C2×C22⋊C4—28no—
218C2×C22⋊C4—216no—
219C2×C22⋊C4C23×C1114yes—
220C2×C22⋊C4C23×C1118yes—
221C2×C22⋊C4C23×C1118yes—
222C2×C22⋊C4C23×C11116yes—
223C2×C42—216no—
224C2×C42—232no—
225C2×C42C23×C11116yes—
226#95C23×C11116yes—
227#95C23×C11116yes—
228#95C23×C11116yes—
229C2×C11—28no—
230C2×C11—82no—
231C2×C11#285318yesdirect product factor
232C2×C11C22×#12311yescharacteristic
233C2×C11C2×#52512yes—
234C2×C11C2×#52914yes—
235C24—28no—
236C24—22no—
237C24—28no—
238C24—24no—
239C24C2×D4×C1114yes—
240C24C11×#4118yes—
241C24C24×C1112yes—
242C24C24×C1112yes—
243C24C24×C1111yescharacteristic
244C2×D4—28no—
245C2×D4—216no—
246C2×D4—416no—
247C22×C4—264no—
248C22×C4—232no—
249C22×C4—216no—
250C22×C4—28no—
251C22×C4—216no—
252C22×C4—28no—
253C22×C4—28no—
254C22×C4—232no—
255C22×C4—24no—
256C22×C4—22no—
257C22×C4—28no—
258C22×C4—28no—
259C22×C4—28no—
260C22×C4—28no—
261C22×C4—24no—
262C22×C4C2×D4×C1118yes—
263C22×C4C2×D4×C11116yes—
264C22×C4C11×#41116yes—
265C22×C4C24×C1118yes—
266C22×C4C24×C1112yes—
267C22×C4C24×C1114yes—
268C22×C4C24×C1114yes—
269C22×C4C24×C1118yes—
270C4⋊C4—216no—
271C4⋊C4—232no—
272C22⋊C4—28no—
273C22⋊C4—216no—
274C22⋊C4—216no—
275C22⋊C4—232no—
276C42—232no—
277C11C2×#285311yescharacteristic, direct product factor, Sylow
278C23—216no—
279C23—232no—
280C23—28no—
281C23—22no—
282C23—28no—
283C23—24no—
284C23—44no—
285C23—48no—
286C23—416no—
287C23C11×#123116yes—
288C23C22×D4×C1114yes—
289C23C22×D4×C1112yes—
290C23C2×C11×#4118yes—
291C23C2×C11×#4114yes—
292C23C2×C11×#4118yes—
293C23C25×C1111yescharacteristic
294D4—416no—
295C2×C4—264no—
296C2×C4—232no—
297C2×C4—216no—
298C2×C4—232no—
299C2×C4—28no—
300C2×C4—28no—
301C2×C4—28no—
302C2×C4—24no—
303C2×C4—22no—
304C2×C4—28no—
305C2×C4—28no—
306C2×C4—28no—
307C2×C4—28no—
308C2×C4—24no—
309C2×C4—44no—
310C2×C4—48no—
311C2×C4—416no—
312C2×C4C22×D4×C1118yes—
313C2×C4C2×C11×#41116yes—
314C22—28no—
315C22—216no—
316C22—232no—
317C22—42no—
318C22—44no—
319C22—48no—
320C22—88no—
321C22C2×C11×#12318yes—
322C22C2×C11×#12314yes—
323C22C11×#52518yes—
324C22C11×#529116yes—
325C22C23×D4×C1111yescharacteristic
326C22C22×C11×#4112yes—
327C22C22×C11×#4114yes—
328C4—28no—
329C4—216no—
330C4—42no—
331C4—44no—
332C4—48no—
333C2—28no—
334C2—82no—
335C2C11×#285318yesdirect product factor
336C2C22×C11×#12311yescharacteristic
337C2C2×C11×#52512yes—
338C2C2×C11×#52914yes—
subgroupG/H
center, socleC24×C11C24
commutator, Frattini, cosocleC23C25×C11
prime radicalC23×D4×C11C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C23×C42×C11C2semidirect
3. C11×#2853C2direct (N × H)
4. C2×C11×#388C2semidirect
5. C2×C11×#387C2semidirect
7. C2×C11×#385C2semidirect
8. C2×C11×#381C2semidirect
22. C22×C42×C11C22semidirect
23. C11×#388C22semidirect
24. C11×#387C22semidirect
26. C11×#385C22semidirect
27. C11×#381C22semidirect
66. C2×#2853C11direct (N × H)
110. C23×C42C2×C11semidirect
111. #2853C2×C11direct (N × H)
112. C2×#388C2×C11semidirect
113. C2×#387C2×C11semidirect
115. C2×#385C2×C11semidirect
116. C2×#381C2×C11semidirect
166. C22×C42C22×C11semidirect
167. #388C22×C11semidirect
168. #387C22×C11semidirect
170. #385C22×C11semidirect
171. #381C22×C11semidirect
231. C2×C11#2853direct (N × H)
277. C11C2×#2853direct (N × H)
335. C2C11×#2853direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C11×#1232
C23×C42×C112
C11×#28532
C2×C11×#3882
C2×C11×#3872
C2×C11×#3862
C2×C11×#3852
C2×C11×#3812
C2×#285311