Finite Group Databasebeta

← C11×#7820 #14585013

Subgroups — C11×#7820 #14585013

Order 2816.

396 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 94 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2808C211yesmaximal, characteristic
2C11×#2093C211yesmaximal, characteristic
3C11×#2084C211yesmaximal, characteristic, complemented
4C11×#2072C211yesmaximal, characteristic, complemented
5C11×#1272C211yesmaximal, characteristic, complemented
6C11×#1271C211yesmaximal, characteristic, complemented
7C11×#1270C211yesmaximal, characteristic
8C2×C11×#107—21no—
9C2×C11×#106—21no—
10C2×C11×#103—21no—
11C2×C11×#102—21no—
12C11×#397—21no—
13C11×#394—21no—
14C11×#393—21no—
15C11×#391C2211yescharacteristic
16C11×#390C2211yescharacteristic
17C11×#389C2211yescharacteristic
18C11×#388—21no—
19C11×#388—21no—
20C11×#387—21no—
21C11×#384C2211yescharacteristic
22C11×#340—21no—
23C11×#340—21no—
24C11×#336C2211yescharacteristic
25C11×#336C2211yescharacteristic
26C11×#336C2211yescharacteristic
27C22×Q8×C11D411yescharacteristic
28C22×D4×C11D411yescharacteristic
29C22×C8×C11—21no—
30C22×C8×C11—21no—
31C22×C8×C11—21no—
32C2×C11×C4⋊C4—21no—
33C2×C11×C4⋊C4—21no—
34C2×C11×C4⋊C4—21no—
35C2×C11×C4⋊C4—21no—
36C2×C11×C4⋊C4D411yescharacteristic
37C2×C11×C4⋊C4D411yescharacteristic
38C2×C11×C4⋊C4D411yescharacteristic
39C2×C11×C4⋊C4D411yescharacteristic
40C2×C11×C22⋊C4—21no—
41C2×C11×C22⋊C4—21no—
42C2×C11×C22⋊C4—21no—
43C2×C11×C22⋊C4—21no—
44C2×C11×C22⋊C4—21no—
45C2×C11×C22⋊C4—21no—
46C2×C42×C11—21no—
47C2×C42×C11C2311yescharacteristic
48C11×#107—42no—
49C11×#106—42no—
50C11×#103—42no—
51C11×#102—42no—
52C11×#95—21no—
53C11×#95—21no—
54C11×#95—21no—
55C11×#95—21no—
56C11×#95—21no—
57C11×#95—21no—
58#7820C1111yesmaximal, characteristic, direct product factor, Sylow
59C24×C11—21no—
60C2×Q8×C11—21no—
61C2×Q8×C11—21no—
62C2×Q8×C11—41no—
63C2×Q8×C11—41no—
64C2×D4×C11—21no—
65C2×D4×C11—21no—
66C2×D4×C11—41no—
67C2×D4×C11—41no—
68C22×C4×C11—21no—
69C22×C4×C11—21no—
70C22×C4×C11—21no—
71C22×C4×C11—21no—
72C22×C4×C11—21no—
73C22×C4×C11—41no—
74C22×C4×C11C2×D411yescharacteristic
75C22×C4×C11C2×D411yescharacteristic
76C22×C4×C11C2×D411yescharacteristic
77C2×C8×C11—22no—
78C2×C8×C11—22no—
79C2×C8×C11—41no—
80C2×C8×C11—41no—
81C2×C8×C11—41no—
82C2×C8×C11—41no—
83C2×C8×C11—41no—
84C2×C8×C11—41no—
85C2×C8×C11—41no—
86C11×C4⋊C4—21no—
87C11×C4⋊C4—21no—
88C11×C4⋊C4—41no—
89C11×C4⋊C4—41no—
90C11×C4⋊C4—41no—
91C11×C4⋊C4—41no—
92C11×C4⋊C4—41no—
93C11×C4⋊C4—41no—
94C11×C4⋊C4—41no—
95C11×C4⋊C4—41no—
96C11×C4⋊C4—41no—
97C11×C4⋊C4—41no—
98C11×C4⋊C4—41no—
99C11×C22⋊C4—41no—
100C11×C22⋊C4—41no—
101C11×C22⋊C4—41no—
102C11×C22⋊C4—41no—
103C11×C22⋊C4—81no—
104C11×C22⋊C4—81no—
105C11×C22⋊C4—81no—
106C11×C22⋊C4—81no—
107C42×C11—41no—
108C42×C11—81no—
109#2808C2×C1111yescharacteristic
110#2093C2×C1111yescharacteristic
111#2084C2×C1111yescharacteristic, complemented
112#2072C2×C1111yescharacteristic, complemented
113#1272C2×C1111yescharacteristic, complemented
114#1271C2×C1111yescharacteristic, complemented
115#1270C2×C1111yescharacteristic
116C23×C11—41no—
117C23×C11—41no—
118C23×C11—41no—
119C23×C11—41no—
120C23×C11—41no—
121C23×C11—41no—
122C23×C11—41no—
123C23×C11#12011yescharacteristic
124Q8×C11—42no—
125Q8×C11—81no—
126D4×C11—42no—
127D4×C11—81no—
128C2×C4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11—21no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11—21no—
134C2×C4×C11—41no—
135C2×C4×C11—41no—
136C2×C4×C11—41no—
137C2×C4×C11—41no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11—41no—
142C2×C4×C11—41no—
143C2×C4×C11—41no—
144C2×C4×C11—41no—
145C2×C4×C11—41no—
146C2×C4×C11—41no—
147C2×C4×C11—41no—
148C2×C4×C11—41no—
149C2×C4×C11—81no—
150C2×C4×C11—81no—
151C2×C4×C11—81no—
152C2×C4×C11#13511yescharacteristic
153C2×C4×C11#13511yescharacteristic
154C2×C4×C11#13511yescharacteristic
155C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
156C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
157C2×C4×C11#13711yescharacteristic
158C8×C11—42no—
159C8×C11—42no—
160C8×C11—81no—
161C2×#107—21no—
162C2×#106—21no—
163C2×#103—21no—
164C2×#102—21no—
165#397—21no—
166#394—21no—
167#393—21no—
168#391C22×C1111yescharacteristic
169#390C22×C1111yescharacteristic
170#389C22×C1111yescharacteristic
171#388—21no—
172#388—21no—
173#387—21no—
174#384C22×C1111yescharacteristic
175#340—21no—
176#340—21no—
177#336C22×C1111yescharacteristic
178#336C22×C1111yescharacteristic
179#336C22×C1111yescharacteristic
180C22×C11—81no—
181C22×C11—81no—
182C22×C11—81no—
183C22×C11—81no—
184C22×C11—81no—
185C22×C11—81no—
186C22×C11—81no—
187C22×C11#44911yescharacteristic
188C22×C11#44911yescharacteristic
189C22×C11#45211yescharacteristic
190C22×C11#45311yescharacteristic
191C22×C11#45511yescharacteristic
192C22×C11#45611yescharacteristic
193C22×C11#45811yescharacteristic
194C4×C11—21no—
195C4×C11—21no—
196C4×C11—21no—
197C4×C11—21no—
198C4×C11—21no—
199C4×C11—21no—
200C4×C11—81no—
201C4×C11—81no—
202C4×C11—81no—
203C4×C11—81no—
204C4×C11—81no—
205C4×C11—161no—
206C22×Q8D4×C1111yescharacteristic
207C22×D4D4×C1111yescharacteristic
208C22×C8—21no—
209C22×C8—21no—
210C22×C8—21no—
211C2×C4⋊C4—21no—
212C2×C4⋊C4—21no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4D4×C1111yescharacteristic
216C2×C4⋊C4D4×C1111yescharacteristic
217C2×C4⋊C4D4×C1111yescharacteristic
218C2×C4⋊C4D4×C1111yescharacteristic
219C2×C22⋊C4—21no—
220C2×C22⋊C4—21no—
221C2×C22⋊C4—21no—
222C2×C22⋊C4—21no—
223C2×C22⋊C4—21no—
224C2×C22⋊C4—21no—
225C2×C42—21no—
226C2×C42C23×C1111yescharacteristic
227#107—42no—
228#106—42no—
229#103—42no—
230#102—42no—
231#95—21no—
232#95—21no—
233#95—21no—
234#95—21no—
235#95—21no—
236#95—21no—
237C2×C11—161no—
238C2×C11#160911yescharacteristic
239C2×C11#161211yescharacteristic
240C2×C11#161811yescharacteristic
241C2×C11#162011yescharacteristic
242C2×C11#164611yescharacteristic
243C2×C11#165211yescharacteristic
244C2×C11#166111yescharacteristic
245C24—21no—
246C2×Q8—21no—
247C2×Q8—21no—
248C2×Q8—41no—
249C2×Q8—41no—
250C2×D4—21no—
251C2×D4—21no—
252C2×D4—41no—
253C2×D4—41no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—41no—
260C22×C4C2×D4×C1111yescharacteristic
261C22×C4C2×D4×C1111yescharacteristic
262C22×C4C2×D4×C1111yescharacteristic
263C2×C8—22no—
264C2×C8—22no—
265C2×C8—41no—
266C2×C8—41no—
267C2×C8—41no—
268C2×C8—41no—
269C2×C8—41no—
270C2×C8—41no—
271C2×C8—41no—
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4—41no—
275C4⋊C4—41no—
276C4⋊C4—41no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C4⋊C4—41no—
282C4⋊C4—41no—
283C4⋊C4—41no—
284C4⋊C4—41no—
285C22⋊C4—41no—
286C22⋊C4—41no—
287C22⋊C4—41no—
288C22⋊C4—41no—
289C22⋊C4—81no—
290C22⋊C4—81no—
291C22⋊C4—81no—
292C22⋊C4—81no—
293C42—41no—
294C42—81no—
295C11#782011yescharacteristic, direct product factor, Sylow
296C23—41no—
297C23—41no—
298C23—41no—
299C23—41no—
300C23—41no—
301C23—41no—
302C23—41no—
303C23C11×#12011yescharacteristic
304Q8—42no—
305Q8—81no—
306D4—42no—
307D4—81no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—81no—
330C2×C4—81no—
331C2×C4—81no—
332C2×C4C11×#13511yescharacteristic
333C2×C4C11×#13511yescharacteristic
334C2×C4C11×#13511yescharacteristic
335C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
336C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
337C2×C4C11×#13711yescharacteristic
338C8—42no—
339C8—42no—
340C8—81no—
341C22—81no—
342C22—81no—
343C22—81no—
344C22—81no—
345C22—81no—
346C22—81no—
347C22—81no—
348C22C11×#44911yescharacteristic
349C22C11×#44911yescharacteristic
350C22C11×#45211yescharacteristic
351C22C11×#45311yescharacteristic
352C22C11×#45511yescharacteristic
353C22C11×#45611yescharacteristic
354C22C11×#45811yescharacteristic
355C4—21no—
356C4—21no—
357C4—21no—
358C4—21no—
359C4—21no—
360C4—21no—
361C4—81no—
362C4—81no—
363C4—81no—
364C4—81no—
365C4—81no—
366C4—161no—
367C2—161no—
368C2C11×#160911yescharacteristic
369C2C11×#161211yescharacteristic
370C2C11×#161811yescharacteristic
371C2C11×#162011yescharacteristic
372C2C11×#164611yescharacteristic
373C2C11×#165211yescharacteristic
374C2C11×#166111yescharacteristic
subgroupG/H
center, socleC23×C11#120
commutator, Frattini, cosocleC2×C42C23×C11
prime radicalC22×D4×C11D4
LCSG ▷ C2×C42 ▷ C23 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
3. C11×#2084C2semidirect
4. C11×#2072C2semidirect
5. C11×#1272C2semidirect
6. C11×#1271C2semidirect
58. #7820C11direct (N × H)
111. #2084C2×C11semidirect
112. #2072C2×C11semidirect
113. #1272C2×C11semidirect
114. #1271C2×C11semidirect
295. C11#7820direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#28082
C11×#20932
C11×#20842
C11×#20722
C11×#12722
C11×#12712
C11×#12702
#782011