Finite Group Databasebeta

← C11×#9086 #14586279

Subgroups — C11×#9086 #14586279

Order 2816.

604 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#432C211yesmaximal, characteristic
2C2×C11×#387C211yesmaximal, characteristic
3C11×#1817C211yesmaximal, characteristic
4C2×C11×#324C212yesmaximal
5C11×#1280C212yesmaximal
6C22×C11×C4⋊C4C411yescharacteristic
7C22×C11×C4⋊C4C2211yescharacteristic
8C22×C42×C11C2211yescharacteristic
9C11×#432—24no—
10C2×C11×C4⋊C8—21no—
11C2×C11×C22⋊C8C2212yes—
12C2×C11×C22⋊C8C2212yes—
13C2×C11×#97—21no—
14C11×#387—21no—
15C11×#387—21no—
16C11×#387—21no—
17C11×#387—21no—
18C2×C11×#95C411yescharacteristic
19C2×C11×#95C411yescharacteristic
20C2×C11×#95C411yescharacteristic
21C2×C11×#95C2211yescharacteristic
22C11×#336—21no—
23C11×#336—21no—
24C11×#324—24no—
25C23×C4×C11C2×C411yescharacteristic
26C23×C4×C11C2×C411yescharacteristic
27C23×C4×C11C2×C411yescharacteristic
28C23×C4×C11C2×C411yescharacteristic
29C23×C4×C11C2×C411yescharacteristic
30C23×C4×C11C2×C411yescharacteristic
31C23×C4×C11C2311yescharacteristic
32C22×C8×C11—22no—
33C22×C8×C11—22no—
34C2×C11×C4⋊C4—21no—
35C2×C11×C4⋊C4—21no—
36C2×C11×C4⋊C4—22no—
37C2×C11×C4⋊C4—22no—
38C2×C11×C4⋊C4—22no—
39C2×C11×C4⋊C4—21no—
40C2×C11×C4⋊C4—21no—
41C2×C11×C4⋊C4—22no—
42C2×C42×C11—22no—
43C2×C42×C11—22no—
44C2×C42×C11D411yescharacteristic
45C2×C42×C11D411yescharacteristic
46C2×C42×C11D411yescharacteristic
47C2×C42×C11D411yescharacteristic
48C11×C4⋊C8—24no—
49C11×C22⋊C8—22no—
50C11×C22⋊C8—22no—
51C11×C22⋊C8—22no—
52C11×C22⋊C8D414yes—
53C11×#97—24no—
54C11×#95—21no—
55C11×#95—21no—
56C11×#95—21no—
57C11×#95—21no—
58C11×#95—21no—
59C11×#95—21no—
60C11×#95—21no—
61C11×#95—21no—
62#9086C1111yesmaximal, characteristic, direct product factor, Sylow
63C24×C11C22×C411yescharacteristic
64C22×C4×C11—21no—
65C22×C4×C11—21no—
66C22×C4×C11—22no—
67C22×C4×C11—22no—
68C22×C4×C11—22no—
69C22×C4×C11—21no—
70C22×C4×C11—21no—
71C22×C4×C11—21no—
72C22×C4×C11—21no—
73C22×C4×C11—22no—
74C22×C4×C11—22no—
75C22×C4×C11—22no—
76C22×C4×C11—21no—
77C22×C4×C11—21no—
78C22×C4×C11—22no—
79C22×C4×C11—22no—
80C22×C4×C11—41no—
81C22×C4×C11—41no—
82C22×C4×C11—41no—
83C22×C4×C11—41no—
84C22×C4×C11—41no—
85C22×C4×C11—41no—
86C22×C4×C11—41no—
87C22×C4×C11—41no—
88C22×C4×C11—41no—
89C22×C4×C11C22⋊C411yescharacteristic
90C22×C4×C11C22⋊C411yescharacteristic
91C22×C4×C11C22⋊C411yescharacteristic
92C22×C4×C11C22⋊C411yescharacteristic
93C22×C4×C11M1612yes—
94C22×C4×C11M1612yes—
95C22×C4×C11C2×D411yescharacteristic
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11C2×D412yes—
98C22×C4×C11#4112yes—
99C2×C8×C11—24no—
100C2×C8×C11—42no—
101C2×C8×C11—42no—
102C2×C8×C11—42no—
103C2×C8×C11—42no—
104C2×C8×C11—42no—
105C11×C4⋊C4—24no—
106C11×C4⋊C4—24no—
107C11×C4⋊C4—41no—
108C11×C4⋊C4—42no—
109C11×C4⋊C4—41no—
110C42×C11—21no—
111C42×C11—21no—
112C42×C11—22no—
113C42×C11—22no—
114C42×C11—21no—
115C42×C11—21no—
116C2×#432C2×C1111yescharacteristic
117C2×#387C2×C1111yescharacteristic
118#1817C2×C1111yescharacteristic
119C2×#324C2×C1112yes—
120#1280C2×C1112yes—
121C23×C11—21no—
122C23×C11—21no—
123C23×C11—21no—
124C23×C11—21no—
125C23×C11C2×C22⋊C411yescharacteristic
126C23×C11C4×D412yes—
127C23×C11C2×M1611yescharacteristic
128C23×C11C2×M1611yescharacteristic
129C23×C11#13112yes—
130C2×C4×C11—21no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11—21no—
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—22no—
142C2×C4×C11—22no—
143C2×C4×C11—21no—
144C2×C4×C11—21no—
145C2×C4×C11—21no—
146C2×C4×C11—21no—
147C2×C4×C11—24no—
148C2×C4×C11—42no—
149C2×C4×C11—42no—
150C2×C4×C11—44no—
151C2×C4×C11—42no—
152C2×C4×C11—41no—
153C2×C4×C11—41no—
154C2×C4×C11—41no—
155C2×C4×C11—41no—
156C2×C4×C11—42no—
157C2×C4×C11—42no—
158C2×C4×C11—42no—
159C2×C4×C11—42no—
160C2×C4×C11—41no—
161C2×C4×C11—41no—
162C2×C4×C11—41no—
163C2×C4×C11—41no—
164C2×C4×C11—41no—
165C2×C4×C11—41no—
166C2×C4×C11—82no—
167C2×C4×C11—82no—
168C2×C4×C11#10112yes—
169C2×C4×C11#12011yescharacteristic
170C2×C4×C11#12112yes—
171C2×C4×C11#12311yescharacteristic
172C8×C11—44no—
173C8×C11—82no—
174C22×C4⋊C4C4×C1111yescharacteristic
175C22×C4⋊C4C22×C1111yescharacteristic
176C22×C42C22×C1111yescharacteristic
177#432—24no—
178C2×C4⋊C8—21no—
179C2×C22⋊C8C22×C1112yes—
180C2×C22⋊C8C22×C1112yes—
181C2×#97—21no—
182#387—21no—
183#387—21no—
184#387—21no—
185#387—21no—
186C2×#95C4×C1111yescharacteristic
187C2×#95C4×C1111yescharacteristic
188C2×#95C4×C1111yescharacteristic
189C2×#95C22×C1111yescharacteristic
190#336—21no—
191#336—21no—
192#324—24no—
193C22×C11—22no—
194C22×C11—22no—
195C22×C11—21no—
196C22×C11—21no—
197C22×C11—21no—
198C22×C11—21no—
199C22×C11—22no—
200C22×C11—22no—
201C22×C11#38611yescharacteristic
202C22×C11#40711yescharacteristic
203C22×C11#40811yescharacteristic
204C22×C11#41011yescharacteristic
205C22×C11#41011yescharacteristic
206C22×C11C2×#10111yescharacteristic
207C22×C11#41311yescharacteristic
208C22×C11#43512yes—
209C22×C11#43612yes—
210C4×C11—21no—
211C4×C11—22no—
212C4×C11—21no—
213C4×C11—22no—
214C4×C11—41no—
215C4×C11—41no—
216C4×C11—42no—
217C4×C11—41no—
218C4×C11—42no—
219C4×C11—81no—
220C4×C11—81no—
221C23×C4C2×C4×C1111yescharacteristic
222C23×C4C2×C4×C1111yescharacteristic
223C23×C4C2×C4×C1111yescharacteristic
224C23×C4C2×C4×C1111yescharacteristic
225C23×C4C2×C4×C1111yescharacteristic
226C23×C4C2×C4×C1111yescharacteristic
227C23×C4C23×C1111yescharacteristic
228C22×C8—22no—
229C22×C8—22no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—22no—
233C2×C4⋊C4—22no—
234C2×C4⋊C4—22no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—22no—
238C2×C42—22no—
239C2×C42—22no—
240C2×C42D4×C1111yescharacteristic
241C2×C42D4×C1111yescharacteristic
242C2×C42D4×C1111yescharacteristic
243C2×C42D4×C1111yescharacteristic
244C4⋊C8—24no—
245C22⋊C8—22no—
246C22⋊C8—22no—
247C22⋊C8—22no—
248C22⋊C8D4×C1114yes—
249#97—24no—
250#95—21no—
251#95—21no—
252#95—21no—
253#95—21no—
254#95—21no—
255#95—21no—
256#95—21no—
257#95—21no—
258C2×C11—22no—
259C2×C11—22no—
260C2×C11#146411yescharacteristic
261C2×C11#146711yescharacteristic
262C2×C11#147011yescharacteristic
263C2×C11#147311yescharacteristic
264C2×C11#187011yescharacteristic
265C2×C11#189911yescharacteristic
266C2×C11#190111yescharacteristic
267C24C22×C4×C1111yescharacteristic
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—22no—
271C22×C4—22no—
272C22×C4—22no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—22no—
278C22×C4—22no—
279C22×C4—22no—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—22no—
283C22×C4—22no—
284C22×C4—41no—
285C22×C4—41no—
286C22×C4—41no—
287C22×C4—41no—
288C22×C4—41no—
289C22×C4—41no—
290C22×C4—41no—
291C22×C4—41no—
292C22×C4—41no—
293C22×C4C11×C22⋊C411yescharacteristic
294C22×C4C11×C22⋊C411yescharacteristic
295C22×C4C11×C22⋊C411yescharacteristic
296C22×C4C11×C22⋊C411yescharacteristic
297C22×C4C11×M1612yes—
298C22×C4C11×M1612yes—
299C22×C4C2×D4×C1111yescharacteristic
300C22×C4C2×D4×C1111yescharacteristic
301C22×C4C2×D4×C1112yes—
302C22×C4C11×#4112yes—
303C2×C8—24no—
304C2×C8—42no—
305C2×C8—42no—
306C2×C8—42no—
307C2×C8—42no—
308C2×C8—42no—
309C4⋊C4—24no—
310C4⋊C4—24no—
311C4⋊C4—41no—
312C4⋊C4—42no—
313C4⋊C4—41no—
314C42—21no—
315C42—21no—
316C42—22no—
317C42—22no—
318C42—21no—
319C42—21no—
320C11#908611yescharacteristic, direct product factor, Sylow
321C23—21no—
322C23—21no—
323C23—21no—
324C23—21no—
325C23C2×C11×C22⋊C411yescharacteristic
326C23C4×D4×C1112yes—
327C23C2×C11×M1611yescharacteristic
328C23C2×C11×M1611yescharacteristic
329C23C11×#13112yes—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—22no—
342C2×C4—22no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—24no—
348C2×C4—42no—
349C2×C4—42no—
350C2×C4—44no—
351C2×C4—42no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—42no—
357C2×C4—42no—
358C2×C4—42no—
359C2×C4—42no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—82no—
367C2×C4—82no—
368C2×C4C11×#10112yes—
369C2×C4C11×#12011yescharacteristic
370C2×C4C11×#12112yes—
371C2×C4C11×#12311yescharacteristic
372C8—44no—
373C8—82no—
374C22—22no—
375C22—22no—
376C22—21no—
377C22—21no—
378C22—21no—
379C22—21no—
380C22—22no—
381C22—22no—
382C22C11×#38611yescharacteristic
383C22C11×#40711yescharacteristic
384C22C11×#40811yescharacteristic
385C22C11×#41011yescharacteristic
386C22C11×#41011yescharacteristic
387C22C2×C11×#10111yescharacteristic
388C22C11×#41311yescharacteristic
389C22C11×#43512yes—
390C22C11×#43612yes—
391C4—21no—
392C4—22no—
393C4—21no—
394C4—22no—
395C4—41no—
396C4—41no—
397C4—42no—
398C4—41no—
399C4—42no—
400C4—81no—
401C4—81no—
402C2—22no—
403C2—22no—
404C2C11×#146411yescharacteristic
405C2C11×#146711yescharacteristic
406C2C11×#147011yescharacteristic
407C2C11×#147311yescharacteristic
408C2C11×#187011yescharacteristic
409C2C11×#189911yescharacteristic
410C2C11×#190111yescharacteristic
subgroupG/H
center, socleC23×C11C2×C22⋊C4
commutatorC24C22×C4×C11
Frattini, cosocleC23×C4C23×C11
prime radicalC24×C11C22×C4
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C22×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
62. #9086C11direct (N × H)
320. C11#9086direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4322
C2×C11×#3872
C11×#18172
C2×C11×#3242
C11×#12802
#908611