Finite Group Databasebeta

← C11×#19207 #14596400

Subgroups — C11×#19207 #14596400

Order 2816.

594 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3230C211yesmaximal, characteristic
2C11×#3209C211yesmaximal, characteristic
3C2×C11×#498C211yesmaximal, characteristic
4C11×#2960C211yesmaximal, characteristic
5C11×#1692C214yesmaximal, complemented
6C11×#1672C214yesmaximal, complemented
7C11×#1564C211yesmaximal, characteristic
8C11×#1549C211yesmaximal, characteristic
9C11×#1548C211yesmaximal, characteristic
10C11×#533C2211yescharacteristic
11C2×C11×C4⋊Q8C2211yescharacteristic
12C2×C11×C4⋊Q8C2211yescharacteristic
13C11×#500—21no—
14C11×#498—21no—
15C11×#498—21no—
16C11×#498C2212yes—
17C11×#498C2212yes—
18C11×#494—21no—
19C11×#487—21no—
20C11×#487—21no—
21C11×#484—22no—
22C11×#477C2214yes—
23C11×#462C2214yes—
24C11×#451—22no—
25C11×#446—21no—
26C11×#446C2212yes—
27C8×Q8×C11—21no—
28C8×Q8×C11C2212yes—
29C11×#431C2211yescharacteristic
30C11×#431C2211yescharacteristic
31C2×C11×#106—21no—
32C2×C11×#106—21no—
33C11×#424—21no—
34C11×#423C2211yescharacteristic
35C11×#405—21no—
36C2×C4×C8×C11C2211yescharacteristic
37C11×#335C2212yes—
38C11×#334C2212yes—
39C11×#333C2214yes—
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×#107—24no—
69C11×#106—22no—
70C11×#106—22no—
71C11×#106—22no—
72C11×#106—22no—
73C11×C4⋊C8—22no—
74C11×C4⋊C8—22no—
75C11×C4⋊C8—21no—
76C11×C4⋊C8C2312yes—
77C11×C4⋊C8C2312yes—
78C11×C4⋊C8C2312yes—
79C11×#103—24no—
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#19207C1111yesmaximal, 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—82no—
98C2×Q8×C11—82no—
99C2×Q8×C11C2×D412yes—
100C22×C4×C11—41no—
101C22×C4×C11—41no—
102C22×C4×C11C2×D411yescharacteristic
103C22×C4×C11C2×D411yescharacteristic
104C22×C4×C11#4111yescharacteristic
105C11×Q16—84no—
106C11×M16—42no—
107C2×C8×C11—22no—
108C2×C8×C11—22no—
109C2×C8×C11—22no—
110C2×C8×C11—22no—
111C2×C8×C11Q1614yescomplemented
112C2×C8×C11C2×D411yescharacteristic
113C2×C8×C11C2×D411yescharacteristic
114C2×C8×C11C2×D411yescharacteristic
115C2×C8×C11C2×D411yescharacteristic
116C11×C4⋊C4—21no—
117C11×C4⋊C4—21no—
118C11×C4⋊C4—21no—
119C11×C4⋊C4—22no—
120C11×C4⋊C4—22no—
121C11×C4⋊C4—22no—
122C11×C4⋊C4—22no—
123C11×C4⋊C4—22no—
124C11×C4⋊C4—22no—
125C11×C4⋊C4—41no—
126C11×C4⋊C4—41no—
127C11×C4⋊C4—41no—
128C11×C4⋊C4—41no—
129C11×C4⋊C4C2×D412yes—
130C11×C22⋊C4—22no—
131C42×C11—22no—
132C42×C11C2×D411yescharacteristic
133C42×C11C2×D411yescharacteristic
134C42×C11#4111yescharacteristic
135C42×C11C2411yescharacteristic
136#3230C2×C1111yescharacteristic
137#3209C2×C1111yescharacteristic
138C2×#498C2×C1111yescharacteristic
139#2960C2×C1111yescharacteristic
140#1692C2×C1114yescomplemented
141#1672C2×C1114yescomplemented
142#1564C2×C1111yescharacteristic
143#1549C2×C1111yescharacteristic
144#1548C2×C1111yescharacteristic
145C23×C11#12111yescharacteristic
146Q8×C11—24no—
147Q8×C11—42no—
148Q8×C11—44no—
149Q8×C11—82no—
150Q8×C11—82no—
151Q8×C11—82no—
152C2×C4×C11—22no—
153C2×C4×C11—22no—
154C2×C4×C11—22no—
155C2×C4×C11—22no—
156C2×C4×C11—42no—
157C2×C4×C11—42no—
158C2×C4×C11—82no—
159C2×C4×C11—82no—
160C2×C4×C11#12111yescharacteristic
161C2×C4×C11#12111yescharacteristic
162C2×C4×C11#12111yescharacteristic
163C2×C4×C11C2×Q1612yes—
164C2×C4×C11#13712yes—
165C2×C4×C11C22×D411yescharacteristic
166C2×C4×C11C22×D411yescharacteristic
167C2×C4×C11C2×#4111yescharacteristic
168C8×C11—21no—
169C8×C11—21no—
170C8×C11—42no—
171C8×C11—42no—
172C8×C11—42no—
173C8×C11C2×Q1612yes—
174C8×C11C2×Q1612yes—
175#533C22×C1111yescharacteristic
176C2×C4⋊Q8C22×C1111yescharacteristic
177C2×C4⋊Q8C22×C1111yescharacteristic
178#500—21no—
179#498—21no—
180#498—21no—
181#498C22×C1112yes—
182#498C22×C1112yes—
183#494—21no—
184#487—21no—
185#487—21no—
186#484—22no—
187#477C22×C1114yes—
188#462C22×C1114yes—
189#451—22no—
190#446—21no—
191#446C22×C1112yes—
192C8×Q8—21no—
193C8×Q8C22×C1112yes—
194#431C22×C1111yescharacteristic
195#431C22×C1111yescharacteristic
196C2×#106—21no—
197C2×#106—21no—
198#424—21no—
199#423C22×C1111yescharacteristic
200#405—21no—
201C2×C4×C8C22×C1111yescharacteristic
202#335C22×C1112yes—
203#334C22×C1112yes—
204#333C22×C1114yes—
205#332C22×C1114yes—
206C22×C11—21no—
207C22×C11—21no—
208C22×C11#46212yes—
209C22×C11C2×#12111yescharacteristic
210C4×C11—21no—
211C4×C11—21no—
212C4×C11—42no—
213C4×C11—42no—
214C4×C11—82no—
215C4×C11—82no—
216C4×C11#46212yes—
217C4×C11#47112yes—
218C4×C11C22×Q1611yescharacteristic
219C4×C11C2×#13711yescharacteristic
220C4×C11#57712yes—
221C22×Q8—21no—
222C22×Q8—21no—
223C2×Q16—24no—
224C2×M16—21no—
225C22×C8D4×C1111yescharacteristic
226C22×C8D4×C1111yescharacteristic
227C4⋊Q8—21no—
228C4⋊Q8—21no—
229C4⋊Q8—21no—
230C4⋊Q8—21no—
231C4⋊Q8—21no—
232C4⋊Q8—21no—
233C4⋊Q8D4×C1111yescharacteristic
234C4⋊Q8D4×C1111yescharacteristic
235C4⋊Q8C23×C1112yes—
236C4⋊Q8C23×C1112yes—
237#125—21no—
238C22⋊Q8—21no—
239C22⋊Q8D4×C1112yes—
240C4×Q8—21no—
241C4×Q8C23×C1112yes—
242#117—21no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—21no—
247C2×C42C23×C1111yescharacteristic
248#107—24no—
249#106—22no—
250#106—22no—
251#106—22no—
252#106—22no—
253C4⋊C8—22no—
254C4⋊C8—22no—
255C4⋊C8—21no—
256C4⋊C8C23×C1112yes—
257C4⋊C8C23×C1112yes—
258C4⋊C8C23×C1112yes—
259#103—24no—
260#103—24no—
261C22⋊C8—21no—
262C22⋊C8—21no—
263#97—22no—
264C4×C8—22no—
265C4×C8—21no—
266C4×C8—21no—
267C4×C8D4×C1111yescharacteristic
268C4×C8D4×C1111yescharacteristic
269C4×C8C23×C1111yescharacteristic
270C4×C8C23×C1111yescharacteristic
271C2×C11—22no—
272C2×C11C2×#46211yescharacteristic
273C2×C11#305711yescharacteristic
274C2×C11C2×#47111yescharacteristic
275C2×Q8—21no—
276C2×Q8—22no—
277C2×Q8—22no—
278C2×Q8—41no—
279C2×Q8—41no—
280C2×Q8—82no—
281C2×Q8—82no—
282C2×Q8C2×D4×C1112yes—
283C22×C4—41no—
284C22×C4—41no—
285C22×C4C2×D4×C1111yescharacteristic
286C22×C4C2×D4×C1111yescharacteristic
287C22×C4C11×#4111yescharacteristic
288Q16—84no—
289M16—42no—
290C2×C8—22no—
291C2×C8—22no—
292C2×C8—22no—
293C2×C8—22no—
294C2×C8C11×Q1614yescomplemented
295C2×C8C2×D4×C1111yescharacteristic
296C2×C8C2×D4×C1111yescharacteristic
297C2×C8C2×D4×C1111yescharacteristic
298C2×C8C2×D4×C1111yescharacteristic
299C4⋊C4—21no—
300C4⋊C4—21no—
301C4⋊C4—21no—
302C4⋊C4—22no—
303C4⋊C4—22no—
304C4⋊C4—22no—
305C4⋊C4—22no—
306C4⋊C4—22no—
307C4⋊C4—22no—
308C4⋊C4—41no—
309C4⋊C4—41no—
310C4⋊C4—41no—
311C4⋊C4—41no—
312C4⋊C4C2×D4×C1112yes—
313C22⋊C4—22no—
314C42—22no—
315C42C2×D4×C1111yescharacteristic
316C42C2×D4×C1111yescharacteristic
317C42C11×#4111yescharacteristic
318C42C24×C1111yescharacteristic
319C11#1920711yescharacteristic, direct product factor, Sylow
320C23C11×#12111yescharacteristic
321Q8—24no—
322Q8—42no—
323Q8—44no—
324Q8—82no—
325Q8—82no—
326Q8—82no—
327C2×C4—22no—
328C2×C4—22no—
329C2×C4—22no—
330C2×C4—22no—
331C2×C4—42no—
332C2×C4—42no—
333C2×C4—82no—
334C2×C4—82no—
335C2×C4C11×#12111yescharacteristic
336C2×C4C11×#12111yescharacteristic
337C2×C4C11×#12111yescharacteristic
338C2×C4C2×C11×Q1612yes—
339C2×C4C11×#13712yes—
340C2×C4C22×D4×C1111yescharacteristic
341C2×C4C22×D4×C1111yescharacteristic
342C2×C4C2×C11×#4111yescharacteristic
343C8—21no—
344C8—21no—
345C8—42no—
346C8—42no—
347C8—42no—
348C8C2×C11×Q1612yes—
349C8C2×C11×Q1612yes—
350C22—21no—
351C22—21no—
352C22C11×#46212yes—
353C22C2×C11×#12111yescharacteristic
354C4—21no—
355C4—21no—
356C4—42no—
357C4—42no—
358C4—82no—
359C4—82no—
360C4C11×#46212yes—
361C4C11×#47112yes—
362C4C22×C11×Q1611yescharacteristic
363C4C2×C11×#13711yescharacteristic
364C4C11×#57712yes—
365C2—22no—
366C2C2×C11×#46211yescharacteristic
367C2C11×#305711yescharacteristic
368C2C2×C11×#47111yescharacteristic
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×#1692C2semidirect
6. C11×#1672C2semidirect
91. #19207C11direct (N × H)
111. C2×C8×C11Q16semidirect
140. #1692C2×C11semidirect
141. #1672C2×C11semidirect
294. C2×C8C11×Q16semidirect
319. C11#19207direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#32302
C11×#32092
C2×C11×#4982
C11×#29602
C11×#16922
C11×#16722
C11×#15642
C11×#15492
C11×#15482
#1920711