Finite Group Databasebeta

← C11×#7599 #14584792

Subgroups — C11×#7599 #14584792

Order 2816.

588 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C11×#121C211yesmaximal, characteristic
2C11×#1817C211yesmaximal, characteristic, complemented
3C11×#1797C211yesmaximal, characteristic, complemented
4C11×#1271C212yesmaximal, complemented
5C11×#1270C212yesmaximal, complemented
6C2×C11×#121C411yescharacteristic
7C2×C4×D4×C11—21no—
8C2×C4×D4×C11C411yescharacteristic
9C22×C42×C11C2211yescharacteristic
10C2×C11×C4⋊C8—21no—
11C2×C11×C22⋊C8—21no—
12C2×C11×C22⋊C8—21no—
13C11×#390C2211yescharacteristic
14C11×#389C2211yescharacteristic
15C11×#388—21no—
16C11×#386—21no—
17C11×#380C411yescharacteristic
18C4×C11×C4⋊C4C411yescharacteristic
19C4×C11×C22⋊C4—21no—
20C11×#336—21no—
21C11×#336C2212yes—
22C11×#336C2212yes—
23C22×D4×C11—21no—
24C22×D4×C11C2×C411yescharacteristic
25C23×C4×C11—21no—
26C23×C4×C11C2×C411yescharacteristic
27C23×C4×C11D411yescharacteristic
28C23×C4×C11D411yescharacteristic
29C22×C8×C11—22no—
30C22×C8×C11—22no—
31C11×#121—22no—
32C11×#121C814yescomplemented
33C4×D4×C11—42no—
34C4×D4×C11—44no—
35C2×C11×C4⋊C4—21no—
36C2×C11×C4⋊C4C2×C411yescharacteristic
37C2×C11×C4⋊C4C2×C411yescharacteristic
38C2×C11×C4⋊C4C2×C411yescharacteristic
39C2×C11×C22⋊C4—21no—
40C2×C11×C22⋊C4—21no—
41C2×C11×C22⋊C4—21no—
42C2×C11×C22⋊C4—21no—
43C2×C11×C22⋊C4—21no—
44C2×C42×C11—21no—
45C2×C42×C11—42no—
46C2×C42×C11C2×C411yescharacteristic
47C2×C42×C11D411yescharacteristic
48C2×C42×C11D411yescharacteristic
49C2×C42×C11C2311yescharacteristic
50C11×C4⋊C8—42no—
51C11×C22⋊C8—42no—
52C11×C22⋊C8—42no—
53C11×#95—21no—
54C11×#95—21no—
55C11×#95—21no—
56#7599C1111yesmaximal, characteristic, direct product factor, Sylow
57C24×C11—21no—
58C24×C11C22⋊C411yescharacteristic
59C2×D4×C11—24no—
60C2×D4×C11—21no—
61C2×D4×C11—41no—
62C2×D4×C11—41no—
63C2×D4×C11—42no—
64C2×D4×C11—42no—
65C2×D4×C11C2×C812yes—
66C22×C4×C11—21no—
67C22×C4×C11—22no—
68C22×C4×C11—21no—
69C22×C4×C11—22no—
70C22×C4×C11—21no—
71C22×C4×C11—21no—
72C22×C4×C11—21no—
73C22×C4×C11—41no—
74C22×C4×C11—41no—
75C22×C4×C11—41no—
76C22×C4×C11—41no—
77C22×C4×C11—41no—
78C22×C4×C11—42no—
79C22×C4×C11—42no—
80C22×C4×C11—42no—
81C22×C4×C11C22⋊C411yescharacteristic
82C22×C4×C11C22⋊C411yescharacteristic
83C22×C4×C11C22⋊C411yescharacteristic
84C22×C4×C11C2×C812yes—
85C22×C4×C11M1612yes—
86C22×C4×C11C22×C411yescharacteristic
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11C2×D411yescharacteristic
89C2×C8×C11—42no—
90C2×C8×C11—42no—
91C2×C8×C11—42no—
92C2×C8×C11—42no—
93C2×C8×C11—42no—
94C2×C8×C11—42no—
95C11×C4⋊C4—21no—
96C11×C4⋊C4—41no—
97C11×C4⋊C4—41no—
98C11×C4⋊C4—42no—
99C11×C4⋊C4C2×C812yes—
100C11×C22⋊C4—24no—
101C11×C22⋊C4—42no—
102C11×C22⋊C4—42no—
103C11×C22⋊C4—41no—
104C11×C22⋊C4—42no—
105C11×C22⋊C4—41no—
106C42×C11—22no—
107C42×C11—22no—
108C42×C11—41no—
109C42×C11—41no—
110C42×C11—42no—
111C4×#121C2×C1111yescharacteristic
112#1817C2×C1111yescharacteristic, complemented
113#1797C2×C1111yescharacteristic, complemented
114#1271C2×C1112yescomplemented
115#1270C2×C1112yescomplemented
116C23×C11—21no—
117C23×C11—21no—
118C23×C11—21no—
119C23×C11—21no—
120C23×C11—21no—
121C23×C11—21no—
122C23×C11—22no—
123C23×C11—41no—
124C23×C11—41no—
125C23×C11—41no—
126C23×C11—41no—
127C23×C11—41no—
128C23×C11—41no—
129C23×C11C22⋊C812yes—
130C23×C11C2×C22⋊C411yescharacteristic
131D4×C11—42no—
132D4×C11—42no—
133D4×C11—48no—
134C2×C4×C11—21no—
135C2×C4×C11—21no—
136C2×C4×C11—21no—
137C2×C4×C11—21no—
138C2×C4×C11—21no—
139C2×C4×C11—21no—
140C2×C4×C11—21no—
141C2×C4×C11—21no—
142C2×C4×C11—21no—
143C2×C4×C11—21no—
144C2×C4×C11—22no—
145C2×C4×C11—21no—
146C2×C4×C11—21no—
147C2×C4×C11—21no—
148C2×C4×C11—42no—
149C2×C4×C11—42no—
150C2×C4×C11—44no—
151C2×C4×C11—42no—
152C2×C4×C11—42no—
153C2×C4×C11—41no—
154C2×C4×C11—41no—
155C2×C4×C11—41no—
156C2×C4×C11—41no—
157C2×C4×C11—41no—
158C2×C4×C11—41no—
159C2×C4×C11—41no—
160C2×C4×C11—41no—
161C2×C4×C11—84no—
162C2×C4×C11C22⋊C812yes—
163C2×C4×C11#9912yes—
164C2×C4×C11C22×C811yescharacteristic
165C2×C4×C11C2×M1611yescharacteristic
166C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
167C2×C4×C11AGL(1,ℤ/8)12yes—
168C2×C4×C11#13711yescharacteristic
169C8×C11—82no—
170C8×C11—82no—
171C2×#121C4×C1111yescharacteristic
172C2×C4×D4—21no—
173C2×C4×D4C4×C1111yescharacteristic
174C22×C42C22×C1111yescharacteristic
175C2×C4⋊C8—21no—
176C2×C22⋊C8—21no—
177C2×C22⋊C8—21no—
178#390C22×C1111yescharacteristic
179#389C22×C1111yescharacteristic
180#388—21no—
181#386—21no—
182#380C4×C1111yescharacteristic
183C4×C4⋊C4C4×C1111yescharacteristic
184C4×C22⋊C4—21no—
185#336—21no—
186#336C22×C1112yes—
187#336C22×C1112yes—
188C22×C11—22no—
189C22×C11—22no—
190C22×C11—22no—
191C22×C11—41no—
192C22×C11—41no—
193C22×C11—41no—
194C22×C11—41no—
195C22×C11—42no—
196C22×C11—42no—
197C22×C11—42no—
198C22×C11—81no—
199C22×C11—81no—
200C22×C11—81no—
201C22×C11—81no—
202C22×C11C2×C22⋊C811yescharacteristic
203C22×C11C2×#9911yescharacteristic
204C22×C11#41311yescharacteristic
205C22×C11#41711yescharacteristic
206C22×C11#41811yescharacteristic
207C22×C11#42111yescharacteristic
208C22×C11#42111yescharacteristic
209C4×C11—22no—
210C4×C11—21no—
211C4×C11—21no—
212C4×C11—22no—
213C4×C11—22no—
214C4×C11—21no—
215C4×C11—21no—
216C4×C11—42no—
217C4×C11—41no—
218C4×C11—81no—
219C4×C11—81no—
220C22×D4—21no—
221C22×D4C2×C4×C1111yescharacteristic
222C23×C4—21no—
223C23×C4C2×C4×C1111yescharacteristic
224C23×C4D4×C1111yescharacteristic
225C23×C4D4×C1111yescharacteristic
226C22×C8—22no—
227C22×C8—22no—
228#121—22no—
229#121C8×C1114yescomplemented
230C4×D4—42no—
231C4×D4—44no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4C2×C4×C1111yescharacteristic
234C2×C4⋊C4C2×C4×C1111yescharacteristic
235C2×C4⋊C4C2×C4×C1111yescharacteristic
236C2×C22⋊C4—21no—
237C2×C22⋊C4—21no—
238C2×C22⋊C4—21no—
239C2×C22⋊C4—21no—
240C2×C22⋊C4—21no—
241C2×C42—21no—
242C2×C42—42no—
243C2×C42C2×C4×C1111yescharacteristic
244C2×C42D4×C1111yescharacteristic
245C2×C42D4×C1111yescharacteristic
246C2×C42C23×C1111yescharacteristic
247C4⋊C8—42no—
248C22⋊C8—42no—
249C22⋊C8—42no—
250#95—21no—
251#95—21no—
252#95—21no—
253C2×C11—42no—
254C2×C11—82no—
255C2×C11#145911yescharacteristic
256C2×C11#147711yescharacteristic
257C2×C11#147811yescharacteristic
258C2×C11#151011yescharacteristic
259C2×C11#151311yescharacteristic
260C2×C11#153511yescharacteristic
261C2×C11#155711yescharacteristic
262C24—21no—
263C24C11×C22⋊C411yescharacteristic
264C2×D4—24no—
265C2×D4—21no—
266C2×D4—41no—
267C2×D4—41no—
268C2×D4—42no—
269C2×D4—42no—
270C2×D4C2×C8×C1112yes—
271C22×C4—21no—
272C22×C4—22no—
273C22×C4—21no—
274C22×C4—22no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—41no—
279C22×C4—41no—
280C22×C4—41no—
281C22×C4—41no—
282C22×C4—41no—
283C22×C4—42no—
284C22×C4—42no—
285C22×C4—42no—
286C22×C4C11×C22⋊C411yescharacteristic
287C22×C4C11×C22⋊C411yescharacteristic
288C22×C4C11×C22⋊C411yescharacteristic
289C22×C4C2×C8×C1112yes—
290C22×C4C11×M1612yes—
291C22×C4C22×C4×C1111yescharacteristic
292C22×C4C2×D4×C1111yescharacteristic
293C22×C4C2×D4×C1111yescharacteristic
294C2×C8—42no—
295C2×C8—42no—
296C2×C8—42no—
297C2×C8—42no—
298C2×C8—42no—
299C2×C8—42no—
300C4⋊C4—21no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C4⋊C4—42no—
304C4⋊C4C2×C8×C1112yes—
305C22⋊C4—24no—
306C22⋊C4—42no—
307C22⋊C4—42no—
308C22⋊C4—42no—
309C22⋊C4—41no—
310C22⋊C4—41no—
311C42—22no—
312C42—22no—
313C42—41no—
314C42—41no—
315C42—42no—
316C11#759911yescharacteristic, direct product factor, Sylow
317C23—21no—
318C23—21no—
319C23—21no—
320C23—21no—
321C23—21no—
322C23—21no—
323C23—22no—
324C23—41no—
325C23—41no—
326C23—41no—
327C23—41no—
328C23—41no—
329C23—41no—
330C23C11×C22⋊C812yes—
331C23C2×C11×C22⋊C411yescharacteristic
332D4—42no—
333D4—42no—
334D4—48no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—22no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—42no—
350C2×C4—42no—
351C2×C4—44no—
352C2×C4—42no—
353C2×C4—42no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—84no—
363C2×C4C11×C22⋊C812yes—
364C2×C4C11×#9912yes—
365C2×C4C22×C8×C1111yescharacteristic
366C2×C4C2×C11×M1611yescharacteristic
367C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
368C2×C4C11×AGL(1,ℤ/8)12yes—
369C2×C4C11×#13711yescharacteristic
370C8—82no—
371C8—82no—
372C22—22no—
373C22—22no—
374C22—22no—
375C22—41no—
376C22—41no—
377C22—41no—
378C22—41no—
379C22—42no—
380C22—42no—
381C22—42no—
382C22—81no—
383C22—81no—
384C22—81no—
385C22—81no—
386C22C2×C11×C22⋊C811yescharacteristic
387C22C2×C11×#9911yescharacteristic
388C22C11×#41311yescharacteristic
389C22C11×#41711yescharacteristic
390C22C11×#41811yescharacteristic
391C22C11×#42111yescharacteristic
392C22C11×#42111yescharacteristic
393C4—22no—
394C4—21no—
395C4—21no—
396C4—22no—
397C4—22no—
398C4—21no—
399C4—21no—
400C4—42no—
401C4—41no—
402C4—81no—
403C4—81no—
404C2—42no—
405C2—82no—
406C2C11×#145911yescharacteristic
407C2C11×#147711yescharacteristic
408C2C11×#147811yescharacteristic
409C2C11×#151011yescharacteristic
410C2C11×#151311yescharacteristic
411C2C11×#153511yescharacteristic
412C2C11×#155711yescharacteristic
subgroupG/H
center, socleC23×C11C2×C22⋊C4
commutatorC2×C4C22×C8×C11
Frattini, cosocleC2×C42C23×C11
prime radicalC2×C11×#121C4
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C11 ◁ C22×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#1817C2semidirect
3. C11×#1797C2semidirect
4. C11×#1271C2semidirect
5. C11×#1270C2semidirect
32. C11×#121C8semidirect
56. #7599C11direct (N × H)
112. #1817C2×C11semidirect
113. #1797C2×C11semidirect
114. #1271C2×C11semidirect
115. #1270C2×C11semidirect
229. #121C8×C11semidirect
316. C11#7599direct (N × H)

Maximal subgroups

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

subgroupindex
C4×C11×#1212
C11×#18172
C11×#17972
C11×#12712
C11×#12702
#759911