Finite Group Databasebeta

← C11×#11226 #14588419

Subgroups — C11×#11226 #14588419

Order 2816.

882 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2296C211yesmaximal, characteristic
2C2×C4×C11×C4⋊C4C211yesmaximal, characteristic
3C2×C11×#339C212yesmaximal
4C2×C11×#339C212yesmaximal
5C11×#1728C211yesmaximal, characteristic
6C22×C11×M16C2212yes—
7C2×C11×#117C2211yescharacteristic
8C2×C11×#117C2211yescharacteristic
9C22×C11×C4⋊C4—21no—
10C22×C42×C11C2212yes—
11C22×C42×C11C2211yescharacteristic
12C11×#389C412yescomplemented
13C11×#389C412yescomplemented
14C11×#385—21no—
15C11×#385—21no—
16C4×C11×C4⋊C4—24no—
17C4×C11×C4⋊C4—22no—
18C2×C11×#95—21no—
19C11×#339—24no—
20C11×#339—24no—
21C11×#336—22no—
22C23×C4×C11—22no—
23C23×C4×C11D411yescharacteristic
24C23×C4×C11D411yescharacteristic
25C23×C4×C11C2311yescharacteristic
26C2×C11×M16—22no—
27C2×C11×M16—22no—
28C2×C11×M16—22no—
29C2×C11×M16—22no—
30C2×C11×M16—22no—
31C2×C11×M16Q814yes—
32C22×C8×C11—22no—
33C11×#117—21no—
34C11×#117—21no—
35C11×#117—22no—
36C11×#117—22no—
37C11×#117D412yes—
38C11×#117Q812yes—
39C2×C11×C4⋊C4—28no—
40C2×C11×C4⋊C4—24no—
41C2×C11×C4⋊C4—22no—
42C2×C11×C4⋊C4—22no—
43C2×C11×C4⋊C4C2×C411yescharacteristic
44C2×C11×C4⋊C4C2×C411yescharacteristic
45C2×C11×C4⋊C4C2×C412yes—
46C2×C11×C22⋊C4—21no—
47C2×C11×C22⋊C4—21no—
48C2×C42×C11—22no—
49C2×C42×C11—21no—
50C2×C42×C11—22no—
51C2×C42×C11—22no—
52C2×C42×C11—22no—
53C2×C42×C11—22no—
54C2×C42×C11—22no—
55C2×C42×C11—22no—
56C2×C42×C11—21no—
57C2×C42×C11C2×C412yes—
58C2×C42×C11D414yes—
59C2×C42×C11D412yes—
60C11×#95—24no—
61C11×#95—22no—
62C11×#95—22no—
63#11226C1111yesmaximal, characteristic, direct product factor, Sylow
64C24×C11C2×D411yescharacteristic
65C22×C4×C11—21no—
66C22×C4×C11—21no—
67C22×C4×C11—24no—
68C22×C4×C11—28no—
69C22×C4×C11—22no—
70C22×C4×C11—21no—
71C22×C4×C11—24no—
72C22×C4×C11—21no—
73C22×C4×C11—21no—
74C22×C4×C11—21no—
75C22×C4×C11—42no—
76C22×C4×C11—44no—
77C22×C4×C11—42no—
78C22×C4×C11—42no—
79C22×C4×C11C22⋊C412yes—
80C22×C4×C11C22⋊C412yes—
81C22×C4×C11C22×C411yescharacteristic
82C22×C4×C11C2×D411yescharacteristic
83C22×C4×C11C2×D412yes—
84C22×C4×C11C2×D411yescharacteristic
85C22×C4×C11C2×Q811yescharacteristic
86C22×C4×C11C2×Q812yes—
87C22×C4×C11#4111yescharacteristic
88C22×C4×C11#4111yescharacteristic
89C22×C4×C11#4112yes—
90C22×C4×C11#4112yes—
91C11×M16—24no—
92C11×M16—24no—
93C11×M16—42no—
94C11×M16—42no—
95C2×C8×C11—24no—
96C2×C8×C11—42no—
97C2×C8×C11—42no—
98C11×C4⋊C4—216no—
99C11×C4⋊C4—22no—
100C11×C4⋊C4—22no—
101C11×C4⋊C4—22no—
102C11×C4⋊C4—44no—
103C11×C4⋊C4—44no—
104C11×C4⋊C4C4⋊C414yescomplemented
105C11×C22⋊C4—22no—
106C11×C22⋊C4—22no—
107C11×C22⋊C4—41no—
108C11×C22⋊C4—41no—
109C42×C11—24no—
110C42×C11—24no—
111C42×C11—22no—
112C42×C11—22no—
113C42×C11—24no—
114C42×C11—24no—
115C42×C11—42no—
116C42×C11—42no—
117C42×C11—42no—
118#2296C2×C1111yescharacteristic
119C2×C4×C4⋊C4C2×C1111yescharacteristic
120C2×#339C2×C1112yes—
121C2×#339C2×C1112yes—
122#1728C2×C1111yescharacteristic
123C23×C11—22no—
124C23×C11—22no—
125C23×C11C2×C22⋊C411yescharacteristic
126C23×C11#12011yescharacteristic
127C23×C11#12111yescharacteristic
128C23×C11C22⋊Q811yescharacteristic
129C23×C11#12311yescharacteristic
130C23×C11#12411yescharacteristic
131C23×C11C4⋊Q811yescharacteristic
132C2×C4×C11—24no—
133C2×C4×C11—24no—
134C2×C4×C11—22no—
135C2×C4×C11—22no—
136C2×C4×C11—28no—
137C2×C4×C11—24no—
138C2×C4×C11—22no—
139C2×C4×C11—22no—
140C2×C4×C11—22no—
141C2×C4×C11—48no—
142C2×C4×C11—44no—
143C2×C4×C11—48no—
144C2×C4×C11—42no—
145C2×C4×C11—42no—
146C2×C4×C11—44no—
147C2×C4×C11—42no—
148C2×C4×C11—42no—
149C2×C4×C11—41no—
150C2×C4×C11—41no—
151C2×C4×C11—42no—
152C2×C4×C11—42no—
153C2×C4×C11#10414yes—
154C2×C4×C11C2×C4⋊C411yescharacteristic
155C2×C4×C11#11711yescharacteristic
156C2×C4×C11C4×D412yes—
157C2×C4×C11C4×Q812yes—
158C2×C4×C11#12112yes—
159C2×C4×C11#12111yescharacteristic
160C2×C4×C11#12112yes—
161C2×C4×C11C22⋊Q812yes—
162C2×C4×C11C22⋊Q812yes—
163C2×C4×C11C22⋊Q812yes—
164C2×C4×C11C22⋊Q811yescharacteristic
165C2×C4×C11#12312yes—
166C2×C4×C11#12512yes—
167C2×C4×C11#12512yes—
168C2×C4×C11#12612yes—
169C2×C4×C11C4⋊Q812yes—
170C8×C11—44no—
171C22×M16C22×C1112yes—
172C2×#117C22×C1111yescharacteristic
173C2×#117C22×C1111yescharacteristic
174C22×C4⋊C4—21no—
175C22×C42C22×C1112yes—
176C22×C42C22×C1111yescharacteristic
177#389C4×C1112yescomplemented
178#389C4×C1112yescomplemented
179#385—21no—
180#385—21no—
181C4×C4⋊C4—24no—
182C4×C4⋊C4—22no—
183C2×#95—21no—
184#339—24no—
185#339—24no—
186#336—22no—
187C22×C11—22no—
188C22×C11—22no—
189C22×C11—21no—
190C22×C11—21no—
191C22×C11—21no—
192C22×C11—21no—
193C22×C11—22no—
194C22×C11—22no—
195C22×C11#38011yescharacteristic
196C22×C11#38611yescharacteristic
197C22×C11#39111yescharacteristic
198C22×C11#39411yescharacteristic
199C22×C11#39511yescharacteristic
200C22×C11#39811yescharacteristic
201C22×C11#40011yescharacteristic
202C22×C11C2×#10412yes—
203C22×C11#42112yes—
204C4×C11—24no—
205C4×C11—48no—
206C4×C11—44no—
207C4×C11—42no—
208C4×C11—81no—
209C4×C11—81no—
210C4×C11#38712yes—
211C4×C11#38912yes—
212C4×C11#39612yes—
213C4×C11#39812yes—
214C23×C4—22no—
215C23×C4D4×C1111yescharacteristic
216C23×C4D4×C1111yescharacteristic
217C23×C4C23×C1111yescharacteristic
218C2×M16—22no—
219C2×M16—22no—
220C2×M16—22no—
221C2×M16—22no—
222C2×M16—22no—
223C2×M16Q8×C1114yes—
224C22×C8—22no—
225#117—21no—
226#117—21no—
227#117—22no—
228#117—22no—
229#117D4×C1112yes—
230#117Q8×C1112yes—
231C2×C4⋊C4—24no—
232C2×C4⋊C4—28no—
233C2×C4⋊C4—22no—
234C2×C4⋊C4—22no—
235C2×C4⋊C4C2×C4×C1111yescharacteristic
236C2×C4⋊C4C2×C4×C1111yescharacteristic
237C2×C4⋊C4C2×C4×C1112yes—
238C2×C22⋊C4—21no—
239C2×C22⋊C4—21no—
240C2×C42—21no—
241C2×C42—22no—
242C2×C42—22no—
243C2×C42—22no—
244C2×C42—22no—
245C2×C42—22no—
246C2×C42—22no—
247C2×C42—21no—
248C2×C42—22no—
249C2×C42C2×C4×C1112yes—
250C2×C42D4×C1114yes—
251C2×C42D4×C1112yes—
252#95—24no—
253#95—22no—
254#95—22no—
255C2×C11—21no—
256C2×C11—21no—
257C2×C11—21no—
258C2×C11—21no—
259C2×C11#144111yescharacteristic
260C2×C11#180612yes—
261C2×C11#189611yescharacteristic
262C2×C11#189711yescharacteristic
263C2×C11#198612yes—
264C24C2×D4×C1111yescharacteristic
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—24no—
268C22×C4—28no—
269C22×C4—22no—
270C22×C4—21no—
271C22×C4—24no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—42no—
276C22×C4—44no—
277C22×C4—42no—
278C22×C4—42no—
279C22×C4C11×C22⋊C412yes—
280C22×C4C11×C22⋊C412yes—
281C22×C4C22×C4×C1111yescharacteristic
282C22×C4C2×D4×C1111yescharacteristic
283C22×C4C2×D4×C1112yes—
284C22×C4C2×D4×C1111yescharacteristic
285C22×C4C2×Q8×C1111yescharacteristic
286C22×C4C2×Q8×C1112yes—
287C22×C4C11×#4111yescharacteristic
288C22×C4C11×#4111yescharacteristic
289C22×C4C11×#4112yes—
290C22×C4C11×#4112yes—
291M16—24no—
292M16—24no—
293M16—42no—
294M16—42no—
295C2×C8—24no—
296C2×C8—42no—
297C2×C8—42no—
298C4⋊C4—216no—
299C4⋊C4—22no—
300C4⋊C4—22no—
301C4⋊C4—22no—
302C4⋊C4—44no—
303C4⋊C4—44no—
304C4⋊C4C11×C4⋊C414yescomplemented
305C22⋊C4—22no—
306C22⋊C4—22no—
307C22⋊C4—41no—
308C22⋊C4—41no—
309C42—24no—
310C42—24no—
311C42—22no—
312C42—22no—
313C42—24no—
314C42—24no—
315C42—42no—
316C42—42no—
317C42—42no—
318C11#1122611yescharacteristic, direct product factor, Sylow
319C23—22no—
320C23—22no—
321C23C2×C11×C22⋊C411yescharacteristic
322C23C11×#12011yescharacteristic
323C23C11×#12111yescharacteristic
324C23C11×C22⋊Q811yescharacteristic
325C23C11×#12311yescharacteristic
326C23C11×#12411yescharacteristic
327C23C11×C4⋊Q811yescharacteristic
328C2×C4—24no—
329C2×C4—24no—
330C2×C4—22no—
331C2×C4—22no—
332C2×C4—28no—
333C2×C4—24no—
334C2×C4—22no—
335C2×C4—22no—
336C2×C4—22no—
337C2×C4—44no—
338C2×C4—48no—
339C2×C4—48no—
340C2×C4—42no—
341C2×C4—42no—
342C2×C4—44no—
343C2×C4—42no—
344C2×C4—42no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—42no—
348C2×C4—42no—
349C2×C4C11×#10414yes—
350C2×C4C2×C11×C4⋊C411yescharacteristic
351C2×C4C11×#11711yescharacteristic
352C2×C4C4×D4×C1112yes—
353C2×C4C4×Q8×C1112yes—
354C2×C4C11×#12112yes—
355C2×C4C11×#12111yescharacteristic
356C2×C4C11×#12112yes—
357C2×C4C11×C22⋊Q812yes—
358C2×C4C11×C22⋊Q812yes—
359C2×C4C11×C22⋊Q812yes—
360C2×C4C11×C22⋊Q811yescharacteristic
361C2×C4C11×#12312yes—
362C2×C4C11×#12512yes—
363C2×C4C11×#12512yes—
364C2×C4C11×#12612yes—
365C2×C4C11×C4⋊Q812yes—
366C8—44no—
367C22—21no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—22no—
372C22—22no—
373C22—22no—
374C22—22no—
375C22C11×#38011yescharacteristic
376C22C11×#38611yescharacteristic
377C22C11×#39111yescharacteristic
378C22C11×#39411yescharacteristic
379C22C11×#39511yescharacteristic
380C22C11×#39811yescharacteristic
381C22C11×#40011yescharacteristic
382C22C2×C11×#10412yes—
383C22C11×#42112yes—
384C4—24no—
385C4—48no—
386C4—42no—
387C4—44no—
388C4—81no—
389C4—81no—
390C4C11×#38712yes—
391C4C11×#38912yes—
392C4C11×#39612yes—
393C4C11×#39812yes—
394C2—21no—
395C2—21no—
396C2—21no—
397C2—21no—
398C2C11×#144111yescharacteristic
399C2C11×#180612yes—
400C2C11×#189611yescharacteristic
401C2C11×#189711yescharacteristic
402C2C11×#198612yes—
subgroupG/H
centerC22×C4×C11C2×D4
commutatorC22×C4C22×C4×C11
Frattini, cosocleC23×C4C23×C11
socleC23×C11C2×C22⋊C4
prime radicalC24×C11C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4×C11 ◁ C22×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
12. C11×#389C4semidirect
13. C11×#389C4semidirect
63. #11226C11direct (N × H)
104. C11×C4⋊C4C4⋊C4semidirect
177. #389C4×C11semidirect
178. #389C4×C11semidirect
304. C4⋊C4C11×C4⋊C4semidirect
318. C11#11226direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#22962
C2×C4×C11×C4⋊C42
C2×C11×#3392
C11×#17282
#1122611