Finite Group Databasebeta

← C11×#19213 #14596406

Subgroups — C11×#19213 #14596406

Order 2816.

594 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3229C211yesmaximal, characteristic
2C11×#3209C211yesmaximal, characteristic
3C2×C11×#487C211yesmaximal, characteristic
4C11×#2960C211yesmaximal, characteristic
5C11×#1700C214yesmaximal, complemented
6C11×#1680C214yesmaximal, complemented
7C11×#1564C211yesmaximal, characteristic
8C11×#1549C211yesmaximal, characteristic
9C11×#1546C211yesmaximal, characteristic
10C11×#533C2211yescharacteristic
11C2×C11×C4⋊Q8C2211yescharacteristic
12C2×C11×C4⋊Q8C2211yescharacteristic
13C11×#498—21no—
14C11×#494—21no—
15C11×#487—21no—
16C11×#487—21no—
17C11×#487—21no—
18C11×#487—21no—
19C11×#487C2212yes—
20C11×#487C2212yes—
21C11×#483—22no—
22C11×#475C2214yes—
23C11×#462C2214yes—
24C11×#451—22no—
25C11×#446—21no—
26C11×#446C2212yes—
27C8×Q8×C11—21no—
28C8×Q8×C11C2212yes—
29C11×#431C2211yescharacteristic
30C11×#431C2211yescharacteristic
31C11×#424—21no—
32C11×#423C2211yescharacteristic
33C2×C11×#103—21no—
34C2×C11×#103—21no—
35C11×#405—21no—
36C2×C4×C8×C11C2211yescharacteristic
37C11×#335C2212yes—
38C11×#334C2212yes—
39C11×#332C2214yes—
40C11×#332C2214yes—
41C22×Q8×C11—21no—
42C22×Q8×C11—21no—
43C2×C11×Q16—24no—
44C2×C11×M16—21no—
45C22×C8×C11D411yescharacteristic
46C22×C8×C11D411yescharacteristic
47C11×C4⋊Q8—21no—
48C11×C4⋊Q8—21no—
49C11×C4⋊Q8—21no—
50C11×C4⋊Q8—21no—
51C11×C4⋊Q8—21no—
52C11×C4⋊Q8—21no—
53C11×C4⋊Q8D411yescharacteristic
54C11×C4⋊Q8D411yescharacteristic
55C11×C4⋊Q8C2312yes—
56C11×C4⋊Q8C2312yes—
57C11×#125—21no—
58C11×C22⋊Q8—21no—
59C11×C22⋊Q8D412yes—
60C4×Q8×C11—21no—
61C4×Q8×C11C2312yes—
62C11×#117—21no—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4—21no—
67C2×C42×C11C2311yescharacteristic
68C11×#106—24no—
69C11×C4⋊C8—22no—
70C11×C4⋊C8—22no—
71C11×C4⋊C8—21no—
72C11×C4⋊C8C2312yes—
73C11×C4⋊C8C2312yes—
74C11×C4⋊C8C2312yes—
75C11×#103—24no—
76C11×#103—22no—
77C11×#103—22no—
78C11×#103—22no—
79C11×#103—22no—
80C11×#103—24no—
81C11×C22⋊C8—21no—
82C11×C22⋊C8—21no—
83C11×#97—22no—
84C4×C8×C11—22no—
85C4×C8×C11—21no—
86C4×C8×C11—21no—
87C4×C8×C11D411yescharacteristic
88C4×C8×C11D411yescharacteristic
89C4×C8×C11C2311yescharacteristic
90C4×C8×C11C2311yescharacteristic
91#19213C1111yesmaximal, characteristic, direct product factor, Sylow
92C2×Q8×C11—21no—
93C2×Q8×C11—22no—
94C2×Q8×C11—22no—
95C2×Q8×C11—41no—
96C2×Q8×C11—41no—
97C2×Q8×C11—42no—
98C2×Q8×C11—42no—
99C2×Q8×C11—82no—
100C2×Q8×C11C2×D412yes—
101C22×C4×C11—41no—
102C22×C4×C11—41no—
103C22×C4×C11C2×D411yescharacteristic
104C22×C4×C11C2×D411yescharacteristic
105C22×C4×C11#4111yescharacteristic
106C11×Q16—84no—
107C11×M16—42no—
108C2×C8×C11—22no—
109C2×C8×C11—22no—
110C2×C8×C11—22no—
111C2×C8×C11—22no—
112C2×C8×C11—22no—
113C2×C8×C11C2×D411yescharacteristic
114C2×C8×C11C2×D411yescharacteristic
115C2×C8×C11C2×D411yescharacteristic
116C2×C8×C11C2×D411yescharacteristic
117C11×C4⋊C4—21no—
118C11×C4⋊C4—21no—
119C11×C4⋊C4—21no—
120C11×C4⋊C4—22no—
121C11×C4⋊C4—22no—
122C11×C4⋊C4—22no—
123C11×C4⋊C4—22no—
124C11×C4⋊C4—22no—
125C11×C4⋊C4—22no—
126C11×C4⋊C4—41no—
127C11×C4⋊C4—41no—
128C11×C4⋊C4—41no—
129C11×C4⋊C4—41no—
130C11×C4⋊C4C2×D412yes—
131C11×C22⋊C4—22no—
132C42×C11—22no—
133C42×C11C2×D411yescharacteristic
134C42×C11C2×D411yescharacteristic
135C42×C11#4111yescharacteristic
136C42×C11C2411yescharacteristic
137#3229C2×C1111yescharacteristic
138#3209C2×C1111yescharacteristic
139C2×#487C2×C1111yescharacteristic
140#2960C2×C1111yescharacteristic
141#1700C2×C1114yescomplemented
142#1680C2×C1114yescomplemented
143#1564C2×C1111yescharacteristic
144#1549C2×C1111yescharacteristic
145#1546C2×C1111yescharacteristic
146C23×C11#12111yescharacteristic
147Q8×C11—24no—
148Q8×C11—42no—
149Q8×C11—42no—
150Q8×C11—42no—
151Q8×C11—44no—
152Q8×C11—82no—
153Q8×C11—82no—
154C2×C4×C11—22no—
155C2×C4×C11—22no—
156C2×C4×C11—22no—
157C2×C4×C11—22no—
158C2×C4×C11—42no—
159C2×C4×C11—42no—
160C2×C4×C11—82no—
161C2×C4×C11—82no—
162C2×C4×C11#12111yescharacteristic
163C2×C4×C11#12111yescharacteristic
164C2×C4×C11#12111yescharacteristic
165C2×C4×C11#13512yes—
166C2×C4×C11#13712yes—
167C2×C4×C11C22×D411yescharacteristic
168C2×C4×C11C22×D411yescharacteristic
169C2×C4×C11C2×#4111yescharacteristic
170C8×C11—21no—
171C8×C11—21no—
172C8×C11—21no—
173C8×C11—21no—
174C8×C11—42no—
175C8×C11—42no—
176C8×C11—42no—
177#533C22×C1111yescharacteristic
178C2×C4⋊Q8C22×C1111yescharacteristic
179C2×C4⋊Q8C22×C1111yescharacteristic
180#498—21no—
181#494—21no—
182#487—21no—
183#487—21no—
184#487—21no—
185#487—21no—
186#487C22×C1112yes—
187#487C22×C1112yes—
188#483—22no—
189#475C22×C1114yes—
190#462C22×C1114yes—
191#451—22no—
192#446—21no—
193#446C22×C1112yes—
194C8×Q8—21no—
195C8×Q8C22×C1112yes—
196#431C22×C1111yescharacteristic
197#431C22×C1111yescharacteristic
198#424—21no—
199#423C22×C1111yescharacteristic
200C2×#103—21no—
201C2×#103—21no—
202#405—21no—
203C2×C4×C8C22×C1111yescharacteristic
204#335C22×C1112yes—
205#334C22×C1112yes—
206#332C22×C1114yes—
207#332C22×C1114yes—
208C22×C11—21no—
209C22×C11—21no—
210C22×C11#46412yes—
211C22×C11C2×#12111yescharacteristic
212C4×C11—21no—
213C4×C11—21no—
214C4×C11—42no—
215C4×C11—42no—
216C4×C11—82no—
217C4×C11—82no—
218C4×C11#46412yes—
219C4×C11#47312yes—
220C4×C11C2×#13511yescharacteristic
221C4×C11C2×#13711yescharacteristic
222C4×C11#57712yes—
223C22×Q8—21no—
224C22×Q8—21no—
225C2×Q16—24no—
226C2×M16—21no—
227C22×C8D4×C1111yescharacteristic
228C22×C8D4×C1111yescharacteristic
229C4⋊Q8—21no—
230C4⋊Q8—21no—
231C4⋊Q8—21no—
232C4⋊Q8—21no—
233C4⋊Q8—21no—
234C4⋊Q8—21no—
235C4⋊Q8D4×C1111yescharacteristic
236C4⋊Q8D4×C1111yescharacteristic
237C4⋊Q8C23×C1112yes—
238C4⋊Q8C23×C1112yes—
239#125—21no—
240C22⋊Q8—21no—
241C22⋊Q8D4×C1112yes—
242C4×Q8—21no—
243C4×Q8C23×C1112yes—
244#117—21no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—21no—
249C2×C42C23×C1111yescharacteristic
250#106—24no—
251C4⋊C8—22no—
252C4⋊C8—22no—
253C4⋊C8—21no—
254C4⋊C8C23×C1112yes—
255C4⋊C8C23×C1112yes—
256C4⋊C8C23×C1112yes—
257#103—24no—
258#103—22no—
259#103—22no—
260#103—22no—
261#103—22no—
262#103—24no—
263C22⋊C8—21no—
264C22⋊C8—21no—
265#97—22no—
266C4×C8—22no—
267C4×C8—21no—
268C4×C8—21no—
269C4×C8D4×C1111yescharacteristic
270C4×C8D4×C1111yescharacteristic
271C4×C8C23×C1111yescharacteristic
272C4×C8C23×C1111yescharacteristic
273C2×C11—22no—
274C2×C11C2×#46411yescharacteristic
275C2×C11#305711yescharacteristic
276C2×C11C2×#47311yescharacteristic
277C2×Q8—21no—
278C2×Q8—22no—
279C2×Q8—22no—
280C2×Q8—41no—
281C2×Q8—41no—
282C2×Q8—42no—
283C2×Q8—42no—
284C2×Q8—82no—
285C2×Q8C2×D4×C1112yes—
286C22×C4—41no—
287C22×C4—41no—
288C22×C4C2×D4×C1111yescharacteristic
289C22×C4C2×D4×C1111yescharacteristic
290C22×C4C11×#4111yescharacteristic
291Q16—84no—
292M16—42no—
293C2×C8—22no—
294C2×C8—22no—
295C2×C8—22no—
296C2×C8—22no—
297C2×C8—22no—
298C2×C8C2×D4×C1111yescharacteristic
299C2×C8C2×D4×C1111yescharacteristic
300C2×C8C2×D4×C1111yescharacteristic
301C2×C8C2×D4×C1111yescharacteristic
302C4⋊C4—21no—
303C4⋊C4—21no—
304C4⋊C4—21no—
305C4⋊C4—22no—
306C4⋊C4—22no—
307C4⋊C4—22no—
308C4⋊C4—22no—
309C4⋊C4—22no—
310C4⋊C4—22no—
311C4⋊C4—41no—
312C4⋊C4—41no—
313C4⋊C4—41no—
314C4⋊C4—41no—
315C4⋊C4C2×D4×C1112yes—
316C22⋊C4—22no—
317C42—22no—
318C42C2×D4×C1111yescharacteristic
319C42C2×D4×C1111yescharacteristic
320C42C11×#4111yescharacteristic
321C42C24×C1111yescharacteristic
322C11#1921311yescharacteristic, direct product factor, Sylow
323C23C11×#12111yescharacteristic
324Q8—24no—
325Q8—42no—
326Q8—42no—
327Q8—42no—
328Q8—44no—
329Q8—82no—
330Q8—82no—
331C2×C4—22no—
332C2×C4—22no—
333C2×C4—22no—
334C2×C4—22no—
335C2×C4—42no—
336C2×C4—42no—
337C2×C4—82no—
338C2×C4—82no—
339C2×C4C11×#12111yescharacteristic
340C2×C4C11×#12111yescharacteristic
341C2×C4C11×#12111yescharacteristic
342C2×C4C11×#13512yes—
343C2×C4C11×#13712yes—
344C2×C4C22×D4×C1111yescharacteristic
345C2×C4C22×D4×C1111yescharacteristic
346C2×C4C2×C11×#4111yescharacteristic
347C8—21no—
348C8—21no—
349C8—21no—
350C8—21no—
351C8—42no—
352C8—42no—
353C8—42no—
354C22—21no—
355C22—21no—
356C22C11×#46412yes—
357C22C2×C11×#12111yescharacteristic
358C4—21no—
359C4—21no—
360C4—42no—
361C4—42no—
362C4—82no—
363C4—82no—
364C4C11×#46412yes—
365C4C11×#47312yes—
366C4C2×C11×#13511yescharacteristic
367C4C2×C11×#13711yescharacteristic
368C4C11×#57712yes—
369C2—22no—
370C2C2×C11×#46411yescharacteristic
371C2C11×#305711yescharacteristic
372C2C2×C11×#47311yescharacteristic
subgroupG/H
center, socleC22×C11C2×#121
commutator, Frattini, cosocleC42C24×C11
prime radicalC23×C11#121
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
5. C11×#1700C2semidirect
6. C11×#1680C2semidirect
91. #19213C11direct (N × H)
141. #1700C2×C11semidirect
142. #1680C2×C11semidirect
322. C11#19213direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#32292
C11×#32092
C2×C11×#4872
C11×#29602
C11×#17002
C11×#16802
C11×#15642
C11×#15492
C11×#15462
#1921311