Finite Group Databasebeta

← C2×C11×#2135 #14610561

Subgroups — C2×C11×#2135 #14610561

Order 2816.

1198 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#536C211yesmaximal, characteristic
2C2×C11×#413C212yesmaximal
3C11×#2135C218yesmaximal, direct product factor
4C2×C11×#356C214yesmaximal, complemented
5C22×C11×#41C2211yescharacteristic
6C23×Q8×C11C411yescharacteristic
7C22×C11×M16—22no—
8C11×#536—24no—
9C11×#536C414yes—
10C11×#536C2214yes—
11C2×C11×C4⋊Q8C2212yes—
12C2×C11×#124C412yes—
13C2×C11×#123—22no—
14C2×C11×C22⋊Q8—22no—
15C2×C11×#117C411yescharacteristic
16C11×#413—24no—
17C11×#413C2218yes—
18C2×C11×#101C2214yes—
19C2×C11×#100—22no—
20C11×#356C22116yescomplemented
21C2×C11×#41—42no—
22C2×C11×#41—42no—
23C2×C11×#41C2×C412yes—
24C2×C11×#41D414yes—
25C2×C11×#41C2312yes—
26C22×Q8×C11—22no—
27C22×Q8×C11—21no—
28C22×Q8×C11—42no—
29C22×Q8×C11—42no—
30C22×Q8×C11C2×C412yes—
31C22×Q8×C11C2×C414yes—
32C22×Q8×C11C2311yescharacteristic
33C22×D4×C11C2×C411yescharacteristic
34C22×D4×C11D412yes—
35C23×C4×C11—21no—
36C23×C4×C11C2×C411yescharacteristic
37C23×C4×C11D412yes—
38C2×C11×M16—24no—
39C2×C11×M16—28no—
40C2×C11×M16—42no—
41C2×C11×M16—44no—
42C22×C8×C11—42no—
43C11×C4⋊Q8—24no—
44C11×C4⋊Q8C2×C414yes—
45C11×C4⋊Q8C2314yes—
46C11×#124—24no—
47C11×#124C2×C418yes—
48C11×#123—28no—
49C11×#123—28no—
50C11×C22⋊Q8—28no—
51C11×C22⋊Q8—28no—
52C11×#117—22no—
53C11×#117C2×C414yes—
54C2×C11×C4⋊C4—21no—
55C2×C11×C4⋊C4—24no—
56C2×C11×C22⋊C4—21no—
57C2×C11×C22⋊C4—24no—
58C2×C42×C11C2×C412yes—
59C11×#101—24no—
60C11×#101C2318yes—
61C11×#100—28no—
62C2×#2135C1111yesmaximal, characteristic, direct product factor, Sylow
63C24×C11C22⋊C412yes—
64C24×C11C22⋊C411yescharacteristic
65C11×#41—44no—
66C11×#41—44no—
67C11×#41—44no—
68C11×#41—44no—
69C2×Q8×C11—24no—
70C2×Q8×C11—22no—
71C2×Q8×C11—41no—
72C2×Q8×C11—41no—
73C2×Q8×C11—48no—
74C2×Q8×C11—48no—
75C2×Q8×C11—42no—
76C2×Q8×C11—42no—
77C2×Q8×C11—42no—
78C2×Q8×C11—42no—
79C2×Q8×C11C22×C414yes—
80C2×Q8×C11C22×C411yescharacteristic
81C2×Q8×C11C2×D412yes—
82C2×Q8×C11C2411yescharacteristic
83C2×D4×C11—41no—
84C2×D4×C11—41no—
85C2×D4×C11—42no—
86C2×D4×C11—42no—
87C2×D4×C11C22⋊C414yes—
88C2×D4×C11C22⋊C412yes—
89C2×D4×C11C22×C412yes—
90C2×D4×C11C2×D414yes—
91C22×C4×C11—22no—
92C22×C4×C11—24no—
93C22×C4×C11—22no—
94C22×C4×C11—22no—
95C22×C4×C11—22no—
96C22×C4×C11—22no—
97C22×C4×C11—22no—
98C22×C4×C11—24no—
99C22×C4×C11—42no—
100C22×C4×C11—42no—
101C22×C4×C11C22⋊C412yes—
102C22×C4×C11C22⋊C414yes—
103C22×C4×C11C22⋊C411yescharacteristic
104C22×C4×C11C22×C411yescharacteristic
105C22×C4×C11C22×C412yes—
106C22×C4×C11C2×D412yes—
107C22×C4×C11C2×D414yes—
108C11×M16—28no—
109C11×M16—44no—
110C11×M16—48no—
111C2×C8×C11—44no—
112C2×C8×C11—48no—
113C11×C4⋊C4—24no—
114C11×C4⋊C4—28no—
115C11×C4⋊C4—28no—
116C11×C22⋊C4—24no—
117C11×C22⋊C4—216no—
118C42×C11—22no—
119C42×C11C22×C414yes—
120C2×#536C2×C1111yescharacteristic
121C2×#413C2×C1112yes—
122#2135C2×C1118yesdirect product factor
123C2×#356C2×C1114yescomplemented
124C23×C11—21no—
125C23×C11—21no—
126C23×C11—22no—
127C23×C11—22no—
128C23×C11—42no—
129C23×C11—44no—
130C23×C11C2×C22⋊C411yescharacteristic
131C23×C11C2×C22⋊C414yes—
132C23×C11C2×C22⋊C412yes—
133Q8×C11—41no—
134Q8×C11—42no—
135Q8×C11—41no—
136Q8×C11—44no—
137Q8×C11—44no—
138Q8×C11—48no—
139D4×C11—44no—
140D4×C11—42no—
141D4×C11—42no—
142D4×C11—44no—
143C2×C4×C11—22no—
144C2×C4×C11—21no—
145C2×C4×C11—22no—
146C2×C4×C11—21no—
147C2×C4×C11—24no—
148C2×C4×C11—24no—
149C2×C4×C11—24no—
150C2×C4×C11—24no—
151C2×C4×C11—24no—
152C2×C4×C11—24no—
153C2×C4×C11—24no—
154C2×C4×C11—24no—
155C2×C4×C11—44no—
156C2×C4×C11—48no—
157C2×C4×C11—42no—
158C2×C4×C11—42no—
159C2×C4×C11#9912yes—
160C2×C4×C11#9912yes—
161C2×C4×C11C2×C22⋊C411yescharacteristic
162C2×C4×C11C2×C22⋊C412yes—
163C2×C4×C11C2×C22⋊C412yes—
164C2×C4×C11C23×C411yescharacteristic
165C2×C4×C11C22×D412yes—
166C8×C11—48no—
167C22×#41C22×C1111yescharacteristic
168C23×Q8C4×C1111yescharacteristic
169C22×M16—22no—
170#536—24no—
171#536C4×C1114yes—
172#536C22×C1114yes—
173C2×C4⋊Q8C22×C1112yes—
174C2×#124C4×C1112yes—
175C2×#123—22no—
176C2×C22⋊Q8—22no—
177C2×#117C4×C1111yescharacteristic
178#413—24no—
179#413C22×C1118yes—
180C2×#101C22×C1114yes—
181C2×#100—22no—
182#356C22×C11116yescomplemented
183C22×C11—22no—
184C22×C11—22no—
185C22×C11—24no—
186C22×C11—42no—
187C22×C11—44no—
188C22×C11—42no—
189C22×C11—42no—
190C22×C11—44no—
191C22×C11—82no—
192C22×C11C2×#9911yescharacteristic
193C22×C11C2×#9911yescharacteristic
194C22×C11C22×C22⋊C411yescharacteristic
195C4×C11—22no—
196C4×C11—21no—
197C4×C11—21no—
198C4×C11—22no—
199C4×C11—44no—
200C4×C11—44no—
201C4×C11C2×#9914yes—
202C2×#41—42no—
203C2×#41—42no—
204C2×#41C2×C4×C1112yes—
205C2×#41D4×C1114yes—
206C2×#41C23×C1112yes—
207C22×Q8—21no—
208C22×Q8—22no—
209C22×Q8—42no—
210C22×Q8—42no—
211C22×Q8C2×C4×C1112yes—
212C22×Q8C2×C4×C1114yes—
213C22×Q8C23×C1111yescharacteristic
214C22×D4C2×C4×C1111yescharacteristic
215C22×D4D4×C1112yes—
216C23×C4—21no—
217C23×C4C2×C4×C1111yescharacteristic
218C23×C4D4×C1112yes—
219C2×M16—24no—
220C2×M16—28no—
221C2×M16—42no—
222C2×M16—44no—
223C22×C8—42no—
224C4⋊Q8—24no—
225C4⋊Q8C2×C4×C1114yes—
226C4⋊Q8C23×C1114yes—
227#124—24no—
228#124C2×C4×C1118yes—
229#123—28no—
230#123—28no—
231C22⋊Q8—28no—
232C22⋊Q8—28no—
233#117—22no—
234#117C2×C4×C1114yes—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—24no—
237C2×C22⋊C4—21no—
238C2×C22⋊C4—24no—
239C2×C42C2×C4×C1112yes—
240#101—24no—
241#101C23×C1118yes—
242#100—28no—
243C2×C11—21no—
244C2×C11—21no—
245C2×C11—42no—
246C2×C11—44no—
247C2×C11#213512yesdirect product factor
248C2×C11C22×#9911yescharacteristic
249C24C11×C22⋊C412yes—
250C24C11×C22⋊C411yescharacteristic
251#41—44no—
252#41—44no—
253#41—44no—
254#41—44no—
255C2×Q8—24no—
256C2×Q8—22no—
257C2×Q8—41no—
258C2×Q8—41no—
259C2×Q8—48no—
260C2×Q8—48no—
261C2×Q8—42no—
262C2×Q8—42no—
263C2×Q8—42no—
264C2×Q8—42no—
265C2×Q8C22×C4×C1114yes—
266C2×Q8C22×C4×C1111yescharacteristic
267C2×Q8C2×D4×C1112yes—
268C2×Q8C24×C1111yescharacteristic
269C2×D4—41no—
270C2×D4—41no—
271C2×D4—42no—
272C2×D4—42no—
273C2×D4C11×C22⋊C414yes—
274C2×D4C11×C22⋊C412yes—
275C2×D4C22×C4×C1112yes—
276C2×D4C2×D4×C1114yes—
277C22×C4—22no—
278C22×C4—22no—
279C22×C4—24no—
280C22×C4—22no—
281C22×C4—22no—
282C22×C4—22no—
283C22×C4—22no—
284C22×C4—24no—
285C22×C4—42no—
286C22×C4—42no—
287C22×C4C11×C22⋊C412yes—
288C22×C4C11×C22⋊C414yes—
289C22×C4C11×C22⋊C411yescharacteristic
290C22×C4C22×C4×C1111yescharacteristic
291C22×C4C22×C4×C1112yes—
292C22×C4C2×D4×C1112yes—
293C22×C4C2×D4×C1114yes—
294M16—28no—
295M16—44no—
296M16—48no—
297C2×C8—44no—
298C2×C8—48no—
299C4⋊C4—24no—
300C4⋊C4—28no—
301C4⋊C4—28no—
302C22⋊C4—24no—
303C22⋊C4—216no—
304C42—22no—
305C42C22×C4×C1114yes—
306C11C2×#213511yescharacteristic, direct product factor, Sylow
307C23—21no—
308C23—21no—
309C23—22no—
310C23—22no—
311C23—42no—
312C23—44no—
313C23C2×C11×C22⋊C411yescharacteristic
314C23C2×C11×C22⋊C414yes—
315C23C2×C11×C22⋊C412yes—
316Q8—41no—
317Q8—42no—
318Q8—41no—
319Q8—44no—
320Q8—44no—
321Q8—48no—
322D4—42no—
323D4—44no—
324D4—42no—
325D4—44no—
326C2×C4—22no—
327C2×C4—22no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—24no—
331C2×C4—24no—
332C2×C4—24no—
333C2×C4—24no—
334C2×C4—24no—
335C2×C4—24no—
336C2×C4—24no—
337C2×C4—24no—
338C2×C4—44no—
339C2×C4—48no—
340C2×C4—42no—
341C2×C4—42no—
342C2×C4C11×#9912yes—
343C2×C4C11×#9912yes—
344C2×C4C2×C11×C22⋊C411yescharacteristic
345C2×C4C2×C11×C22⋊C412yes—
346C2×C4C2×C11×C22⋊C412yes—
347C2×C4C23×C4×C1111yescharacteristic
348C2×C4C22×D4×C1112yes—
349C8—48no—
350C22—22no—
351C22—22no—
352C22—24no—
353C22—42no—
354C22—44no—
355C22—42no—
356C22—42no—
357C22—44no—
358C22—82no—
359C22C2×C11×#9911yescharacteristic
360C22C2×C11×#9911yescharacteristic
361C22C22×C11×C22⋊C411yescharacteristic
362C4—22no—
363C4—21no—
364C4—22no—
365C4—21no—
366C4—44no—
367C4—44no—
368C4C2×C11×#9914yes—
369C2—21no—
370C2—21no—
371C2—42no—
372C2—44no—
373C2C11×#213512yesdirect product factor
374C2C22×C11×#9911yescharacteristic
subgroupG/H
center, socleC22×C11C2×#99
commutatorC2×C4C23×C4×C11
Frattini, cosocleC2×Q8C24×C11
prime radicalC22×C11×#41C22
LCSG ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C22×C4×C11 ◁ C22×C11×#41 ◁ G

Complements

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

NH ≅ G/Ntype
3. C11×#2135C2direct (N × H)
4. C2×C11×#356C2semidirect
20. C11×#356C22semidirect
62. C2×#2135C11direct (N × H)
122. #2135C2×C11direct (N × H)
123. C2×#356C2×C11semidirect
182. #356C22×C11semidirect
247. C2×C11#2135direct (N × H)
306. C11C2×#2135direct (N × H)
373. C2C11×#2135direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5362
C2×C11×#4132
C11×#21352
C2×C11×#3562
C2×#213511