Finite Group Databasebeta

← C11×#9272 #14586465

Subgroups — C11×#9272 #14586465

Order 2816.

428 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3229C211yesmaximal, characteristic
2C11×#2962C211yesmaximal, characteristic
3C11×#1966C211yesmaximal, characteristic
4C11×#1550C211yesmaximal, characteristic
5C2×C11×#332C211yesmaximal, characteristic
6C11×#1301C211yesmaximal, characteristic
7C11×#1283C211yesmaximal, characteristic
8C11×#533C2211yescharacteristic
9C2×C11×C4⋊Q8C2211yescharacteristic
10C11×#498—21no—
11C11×#487—21no—
12C11×#483C414yes—
13C11×#475—22no—
14C11×#446—22no—
15C11×#446—21no—
16C8×Q8×C11—21no—
17C11×#431C2211yescharacteristic
18C11×#424—21no—
19C11×#423C2211yescharacteristic
20C2×C11×C4⋊C8C2211yescharacteristic
21C2×C11×C4⋊C8C2211yescharacteristic
22C2×C11×#101—21no—
23C2×C11×#101—21no—
24C11×#405—21no—
25C4×C11×M16C2211yescharacteristic
26C11×#333—21no—
27C11×#332—21no—
28C11×#332—21no—
29C11×#332—21no—
30C22×Q8×C11—21no—
31C2×C11×M16—21no—
32C2×C11×M16D411yescharacteristic
33C2×C11×M16D411yescharacteristic
34C22×C8×C11—21no—
35C22×C8×C11—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8—21no—
38C11×C4⋊Q8—21no—
39C11×C4⋊Q8—21no—
40C11×C4⋊Q8D411yescharacteristic
41C11×C4⋊Q8D411yescharacteristic
42C11×#125—21no—
43C11×C22⋊Q8—21no—
44C11×C22⋊Q8C2×C412yes—
45C4×Q8×C11—21no—
46C4×Q8×C11D412yes—
47C11×#117—21no—
48C2×C11×C4⋊C4—21no—
49C2×C11×C4⋊C4C2×C412yes—
50C2×C42×C11C2311yescharacteristic
51C11×#106—24no—
52C11×C4⋊C8—22no—
53C11×C4⋊C8—22no—
54C11×C4⋊C8—21no—
55C11×C4⋊C8—21no—
56C11×C4⋊C8—21no—
57C11×C4⋊C8—21no—
58C11×C4⋊C8—21no—
59C11×C4⋊C8—21no—
60C11×C4⋊C8D411yescharacteristic
61C11×C4⋊C8D411yescharacteristic
62C11×#103—24no—
63C11×#101—42no—
64C11×#101—42no—
65C11×C22⋊C8C2×C412yes—
66C11×#97—22no—
67C11×#97—21no—
68C4×C8×C11—22no—
69C4×C8×C11—21no—
70C4×C8×C11—21no—
71#9272C1111yesmaximal, characteristic, direct product factor, Sylow
72C2×Q8×C11—21no—
73C2×Q8×C11—41no—
74C2×Q8×C11—41no—
75C2×Q8×C11—41no—
76C2×Q8×C11—41no—
77C2×Q8×C11—41no—
78C2×Q8×C11—41no—
79C2×Q8×C11C22⋊C412yes—
80C22×C4×C11—22no—
81C22×C4×C11C22×C411yescharacteristic
82C22×C4×C11C2×D411yescharacteristic
83C22×C4×C11#4111yescharacteristic
84C11×M16—21no—
85C11×M16—21no—
86C11×M16—21no—
87C11×M16—41no—
88C11×M16—41no—
89C11×M16SD1612yes—
90C2×C8×C11—22no—
91C2×C8×C11—21no—
92C2×C8×C11—21no—
93C2×C8×C11—21no—
94C2×C8×C11—21no—
95C2×C8×C11—41no—
96C2×C8×C11—41no—
97C2×C8×C11—41no—
98C2×C8×C11—41no—
99C2×C8×C11—81no—
100C11×C4⋊C4—22no—
101C11×C4⋊C4—21no—
102C11×C4⋊C4—21no—
103C11×C4⋊C4—21no—
104C11×C4⋊C4—22no—
105C11×C4⋊C4—22no—
106C11×C4⋊C4—22no—
107C11×C4⋊C4—41no—
108C11×C4⋊C4—41no—
109C11×C4⋊C4C22⋊C412yes—
110C11×C22⋊C4—22no—
111C42×C11—22no—
112C42×C11C2×D411yescharacteristic
113C42×C11C2×D411yescharacteristic
114C42×C11C2×D411yescharacteristic
115C42×C11#4111yescharacteristic
116#3229C2×C1111yescharacteristic
117#2962C2×C1111yescharacteristic
118#1966C2×C1111yescharacteristic
119#1550C2×C1111yescharacteristic
120C2×#332C2×C1111yescharacteristic
121#1301C2×C1111yescharacteristic
122#1283C2×C1111yescharacteristic
123C23×C11C4×D411yescharacteristic
124Q8×C11—42no—
125Q8×C11—41no—
126Q8×C11—41no—
127Q8×C11—81no—
128Q8×C11—81no—
129Q8×C11—81no—
130Q8×C11—81no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11—22no—
134C2×C4×C11—22no—
135C2×C4×C11—41no—
136C2×C4×C11—42no—
137C2×C4×C11—42no—
138C2×C4×C11—42no—
139C2×C4×C11C2×C22⋊C411yescharacteristic
140C2×C4×C11C4×D411yescharacteristic
141C2×C4×C11#12011yescharacteristic
142C2×C4×C11#12111yescharacteristic
143C2×C4×C11#12111yescharacteristic
144C2×C4×C11#12311yescharacteristic
145C2×C4×C11C2×SD1611yescharacteristic
146C2×C4×C11#13511yescharacteristic
147C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
148C2×C4×C11#13711yescharacteristic
149C8×C11—22no—
150C8×C11—42no—
151C8×C11—41no—
152C8×C11—41no—
153C8×C11—41no—
154C8×C11—81no—
155C8×C11—81no—
156#533C22×C1111yescharacteristic
157C2×C4⋊Q8C22×C1111yescharacteristic
158#498—21no—
159#487—21no—
160#483C4×C1114yes—
161#475—22no—
162#446—22no—
163#446—21no—
164C8×Q8—21no—
165#431C22×C1111yescharacteristic
166#424—21no—
167#423C22×C1111yescharacteristic
168C2×C4⋊C8C22×C1111yescharacteristic
169C2×C4⋊C8C22×C1111yescharacteristic
170C2×#101—21no—
171C2×#101—21no—
172#405—21no—
173C4×M16C22×C1111yescharacteristic
174#333—21no—
175#332—21no—
176#332—21no—
177#332—21no—
178C22×C11—21no—
179C22×C11—21no—
180C22×C11#38611yescharacteristic
181C22×C11C4×SD1611yescharacteristic
182C22×C11#44011yescharacteristic
183C4×C11—21no—
184C4×C11—21no—
185C4×C11—21no—
186C4×C11—42no—
187C4×C11—42no—
188C4×C11—82no—
189C4×C11#44811yescharacteristic
190C4×C11#44911yescharacteristic
191C4×C11#46011yescharacteristic
192C4×C11#46411yescharacteristic
193C4×C11#47111yescharacteristic
194C4×C11#47311yescharacteristic
195C22×Q8—21no—
196C2×M16—21no—
197C2×M16D4×C1111yescharacteristic
198C2×M16D4×C1111yescharacteristic
199C22×C8—21no—
200C22×C8—21no—
201C4⋊Q8—21no—
202C4⋊Q8—21no—
203C4⋊Q8—21no—
204C4⋊Q8—21no—
205C4⋊Q8D4×C1111yescharacteristic
206C4⋊Q8D4×C1111yescharacteristic
207#125—21no—
208C22⋊Q8—21no—
209C22⋊Q8C2×C4×C1112yes—
210C4×Q8—21no—
211C4×Q8D4×C1112yes—
212#117—21no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4C2×C4×C1112yes—
215C2×C42C23×C1111yescharacteristic
216#106—24no—
217C4⋊C8—22no—
218C4⋊C8—22no—
219C4⋊C8—21no—
220C4⋊C8—21no—
221C4⋊C8—21no—
222C4⋊C8—21no—
223C4⋊C8—21no—
224C4⋊C8—21no—
225C4⋊C8D4×C1111yescharacteristic
226C4⋊C8D4×C1111yescharacteristic
227#103—24no—
228#101—42no—
229#101—42no—
230C22⋊C8C2×C4×C1112yes—
231#97—22no—
232#97—21no—
233C4×C8—22no—
234C4×C8—21no—
235C4×C8—21no—
236C2×C11—21no—
237C2×C11—21no—
238C2×C11#188011yescharacteristic
239C2×C11#190811yescharacteristic
240C2×C11#191511yescharacteristic
241C2×Q8—21no—
242C2×Q8—41no—
243C2×Q8—41no—
244C2×Q8—41no—
245C2×Q8—41no—
246C2×Q8—41no—
247C2×Q8—41no—
248C2×Q8C11×C22⋊C412yes—
249C22×C4—22no—
250C22×C4C22×C4×C1111yescharacteristic
251C22×C4C2×D4×C1111yescharacteristic
252C22×C4C11×#4111yescharacteristic
253M16—21no—
254M16—21no—
255M16—21no—
256M16—41no—
257M16—41no—
258M16C11×SD1612yes—
259C2×C8—21no—
260C2×C8—22no—
261C2×C8—21no—
262C2×C8—21no—
263C2×C8—21no—
264C2×C8—41no—
265C2×C8—41no—
266C2×C8—41no—
267C2×C8—41no—
268C2×C8—81no—
269C4⋊C4—22no—
270C4⋊C4—21no—
271C4⋊C4—21no—
272C4⋊C4—21no—
273C4⋊C4—22no—
274C4⋊C4—22no—
275C4⋊C4—22no—
276C4⋊C4—41no—
277C4⋊C4—41no—
278C4⋊C4C11×C22⋊C412yes—
279C22⋊C4—22no—
280C42—22no—
281C42C2×D4×C1111yescharacteristic
282C42C2×D4×C1111yescharacteristic
283C42C2×D4×C1111yescharacteristic
284C42C11×#4111yescharacteristic
285C11#927211yescharacteristic, direct product factor, Sylow
286C23C4×D4×C1111yescharacteristic
287Q8—42no—
288Q8—41no—
289Q8—41no—
290Q8—81no—
291Q8—81no—
292Q8—81no—
293Q8—81no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—41no—
299C2×C4—42no—
300C2×C4—42no—
301C2×C4—42no—
302C2×C4C2×C11×C22⋊C411yescharacteristic
303C2×C4C4×D4×C1111yescharacteristic
304C2×C4C11×#12011yescharacteristic
305C2×C4C11×#12111yescharacteristic
306C2×C4C11×#12111yescharacteristic
307C2×C4C11×#12311yescharacteristic
308C2×C4C2×C11×SD1611yescharacteristic
309C2×C4C11×#13511yescharacteristic
310C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
311C2×C4C11×#13711yescharacteristic
312C8—22no—
313C8—42no—
314C8—41no—
315C8—41no—
316C8—41no—
317C8—81no—
318C8—81no—
319C22—21no—
320C22—21no—
321C22C11×#38611yescharacteristic
322C22C4×C11×SD1611yescharacteristic
323C22C11×#44011yescharacteristic
324C4—21no—
325C4—21no—
326C4—21no—
327C4—42no—
328C4—42no—
329C4—82no—
330C4C11×#44811yescharacteristic
331C4C11×#44911yescharacteristic
332C4C11×#46011yescharacteristic
333C4C11×#46411yescharacteristic
334C4C11×#47111yescharacteristic
335C4C11×#47311yescharacteristic
336C2—21no—
337C2—21no—
338C2C11×#188011yescharacteristic
339C2C11×#190811yescharacteristic
340C2C11×#191511yescharacteristic
subgroupG/H
center, socleC22×C11#386
commutatorC22×C4C22×C4×C11
Frattini, cosocleC2×C42C23×C11
prime radicalC23×C11C4×D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
71. #9272C11direct (N × H)
285. C11#9272direct (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×#29622
C11×#19662
C11×#15502
C2×C11×#3322
C11×#13012
C11×#12832
#927211