Finite Group Databasebeta

← C11×#12231 #14589424

Subgroups — C11×#12231 #14589424

Order 2816.

412 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 70 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×#2826C211yesmaximal, characteristic
2C11×#2062C211yesmaximal, characteristic, complemented
3C11×#1614C211yesmaximal, characteristic, complemented
4C11×#1596C211yesmaximal, characteristic
5C11×#1352C211yesmaximal, characteristic, complemented
6C11×#1343C211yesmaximal, characteristic
7C11×#1326C211yesmaximal, characteristic, complemented
8C11×#543C2211yescharacteristic
9C11×#484—21no—
10C11×#450—21no—
11C11×#400—21no—
12C11×#399C2211yescharacteristic
13C11×#397—21no—
14C11×#396—21no—
15C11×#394—21no—
16C11×#394—21no—
17C11×#392C2211yescharacteristic
18C11×#386—21no—
19C11×#385—21no—
20C11×#385C2211yescharacteristic
21C11×#342—21no—
22C11×#342C2211yescharacteristic
23C11×#328—21no—
24C11×#328—21no—
25C11×#323C2211yescharacteristic
26C11×#323C2211yescharacteristic
27C22×D4×C11—21no—
28C22×D4×C11D411yescharacteristic
29C23×C4×C11D411yescharacteristic
30C2×C11×SD16—41no—
31C11×C22⋊Q8—21no—
32C11×C22⋊Q8—21no—
33C11×C22⋊Q8—41no—
34C11×C22⋊Q8—41no—
35C2×C11×C4⋊C4—21no—
36C2×C11×C4⋊C4—21no—
37C2×C11×C4⋊C4—21no—
38C2×C11×C4⋊C4—41no—
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×C11×C22⋊C4—21no—
47C2×C11×C22⋊C4—21no—
48C2×C11×C22⋊C4D411yescharacteristic
49C2×C11×C22⋊C4C2311yescharacteristic
50C11×#107—41no—
51C11×#103—41no—
52C11×#102—41no—
53C11×C22⋊C8—21no—
54C11×C22⋊C8—21no—
55C11×#95—21no—
56C11×#95—21no—
57C11×#95—21no—
58C11×#95—21no—
59C11×#95—41no—
60C11×#95D411yescharacteristic
61C11×#95D411yescharacteristic
62#12231C1111yesmaximal, characteristic, direct product factor, Sylow
63C24×C11—21no—
64C24×C11C2×D411yescharacteristic
65C2×Q8×C11—21no—
66C2×Q8×C11—21no—
67C2×D4×C11—41no—
68C2×D4×C11—41no—
69C2×D4×C11—41no—
70C2×D4×C11—81no—
71C2×D4×C11—81no—
72C2×D4×C11—81no—
73C22×C4×C11—21no—
74C22×C4×C11—21no—
75C22×C4×C11—21no—
76C22×C4×C11—21no—
77C22×C4×C11—21no—
78C22×C4×C11—21no—
79C22×C4×C11—21no—
80C22×C4×C11—41no—
81C22×C4×C11—41no—
82C22×C4×C11—81no—
83C22×C4×C11C2×D411yescharacteristic
84C22×C4×C11C2×D411yescharacteristic
85C11×SD16—82no—
86C2×C8×C11—41no—
87C2×C8×C11—41no—
88C11×C4⋊C4—21no—
89C11×C4⋊C4—21no—
90C11×C4⋊C4—41no—
91C11×C4⋊C4—41no—
92C11×C4⋊C4—41no—
93C11×C4⋊C4—81no—
94C11×C4⋊C4—81no—
95C11×C4⋊C4—81no—
96C11×C4⋊C4—82no—
97C11×C22⋊C4—22no—
98C11×C22⋊C4—21no—
99C11×C22⋊C4—21no—
100C11×C22⋊C4—41no—
101C11×C22⋊C4—41no—
102C11×C22⋊C4—41no—
103C11×C22⋊C4—41no—
104C11×C22⋊C4—81no—
105C11×C22⋊C4—81no—
106C11×C22⋊C4—81no—
107C11×C22⋊C4—81no—
108C11×C22⋊C4—81no—
109C11×C22⋊C4—81no—
110#2826C2×C1111yescharacteristic
111#2062C2×C1111yescharacteristic, complemented
112#1614C2×C1111yescharacteristic, complemented
113#1596C2×C1111yescharacteristic
114#1352C2×C1111yescharacteristic, complemented
115#1343C2×C1111yescharacteristic
116#1326C2×C1111yescharacteristic, complemented
117C23×C11—21no—
118C23×C11—21no—
119C23×C11—41no—
120C23×C11—41no—
121C23×C11—41no—
122C23×C11—41no—
123C23×C11—41no—
124C23×C11—41no—
125C23×C11—41no—
126C23×C11—41no—
127C23×C11—41no—
128C23×C11#12011yescharacteristic
129C23×C11#13511yescharacteristic
130C23×C11#13711yescharacteristic
131Q8×C11—81no—
132Q8×C11—81no—
133D4×C11—42no—
134D4×C11—81no—
135D4×C11—82no—
136D4×C11—82no—
137C2×C4×C11—21no—
138C2×C4×C11—21no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11—42no—
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—41no—
150C2×C4×C11—41no—
151C2×C4×C11—41no—
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—81no—
161C2×C4×C11—81no—
162C2×C4×C11—81no—
163C2×C4×C11—81no—
164C2×C4×C11—81no—
165C8×C11—81no—
166C8×C11—81no—
167#543C22×C1111yescharacteristic
168#484—21no—
169#450—21no—
170#400—21no—
171#399C22×C1111yescharacteristic
172#397—21no—
173#396—21no—
174#394—21no—
175#394—21no—
176#392C22×C1111yescharacteristic
177#386—21no—
178#385—21no—
179#385C22×C1111yescharacteristic
180#342—21no—
181#342C22×C1111yescharacteristic
182#328—21no—
183#328—21no—
184#323C22×C1111yescharacteristic
185#323C22×C1111yescharacteristic
186C22×C11—21no—
187C22×C11—21no—
188C22×C11—21no—
189C22×C11—21no—
190C22×C11—41no—
191C22×C11—41no—
192C22×C11—41no—
193C22×C11—41no—
194C22×C11—81no—
195C22×C11—81no—
196C22×C11—81no—
197C22×C11—81no—
198C22×C11—81no—
199C22×C11—81no—
200C22×C11—81no—
201C22×C11—81no—
202C22×C11#45211yescharacteristic
203C22×C11#45611yescharacteristic
204C22×C11B(4,𝔽2)11yescharacteristic
205C4×C11—41no—
206C4×C11—41no—
207C4×C11—81no—
208C4×C11—81no—
209C4×C11—81no—
210C4×C11—82no—
211C4×C11—81no—
212C4×C11—81no—
213C4×C11—81no—
214C4×C11—81no—
215C22×D4—21no—
216C22×D4D4×C1111yescharacteristic
217C23×C4D4×C1111yescharacteristic
218C2×SD16—41no—
219C22⋊Q8—21no—
220C22⋊Q8—21no—
221C22⋊Q8—41no—
222C22⋊Q8—41no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—41no—
227C2×C4⋊C4D4×C1111yescharacteristic
228C2×C22⋊C4—21no—
229C2×C22⋊C4—21no—
230C2×C22⋊C4—21no—
231C2×C22⋊C4—21no—
232C2×C22⋊C4—21no—
233C2×C22⋊C4—21no—
234C2×C22⋊C4—21no—
235C2×C22⋊C4—21no—
236C2×C22⋊C4D4×C1111yescharacteristic
237C2×C22⋊C4C23×C1111yescharacteristic
238#107—41no—
239#103—41no—
240#102—41no—
241C22⋊C8—21no—
242C22⋊C8—21no—
243#95—21no—
244#95—21no—
245#95—21no—
246#95—21no—
247#95—41no—
248#95D4×C1111yescharacteristic
249#95D4×C1111yescharacteristic
250C2×C11—21no—
251C2×C11—21no—
252C2×C11—41no—
253C2×C11—41no—
254C2×C11—161no—
255C2×C11#160311yescharacteristic
256C2×C11#220011yescharacteristic
257C2×C11#220011yescharacteristic
258C24—21no—
259C24C2×D4×C1111yescharacteristic
260C2×Q8—21no—
261C2×Q8—21no—
262C2×D4—41no—
263C2×D4—41no—
264C2×D4—41no—
265C2×D4—81no—
266C2×D4—81no—
267C2×D4—81no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—41no—
276C22×C4—41no—
277C22×C4—81no—
278C22×C4C2×D4×C1111yescharacteristic
279C22×C4C2×D4×C1111yescharacteristic
280SD16—82no—
281C2×C8—41no—
282C2×C8—41no—
283C4⋊C4—21no—
284C4⋊C4—21no—
285C4⋊C4—41no—
286C4⋊C4—41no—
287C4⋊C4—41no—
288C4⋊C4—81no—
289C4⋊C4—81no—
290C4⋊C4—81no—
291C4⋊C4—82no—
292C22⋊C4—22no—
293C22⋊C4—21no—
294C22⋊C4—21no—
295C22⋊C4—41no—
296C22⋊C4—41no—
297C22⋊C4—41no—
298C22⋊C4—41no—
299C22⋊C4—81no—
300C22⋊C4—81no—
301C22⋊C4—81no—
302C22⋊C4—81no—
303C22⋊C4—81no—
304C22⋊C4—81no—
305C11#1223111yescharacteristic, direct product factor, Sylow
306C23—21no—
307C23—21no—
308C23—41no—
309C23—41no—
310C23—41no—
311C23—41no—
312C23—41no—
313C23—41no—
314C23—41no—
315C23—41no—
316C23—41no—
317C23C11×#12011yescharacteristic
318C23C11×#13511yescharacteristic
319C23C11×#13711yescharacteristic
320Q8—81no—
321Q8—81no—
322D4—42no—
323D4—81no—
324D4—82no—
325D4—82no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—42no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—42no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—81no—
350C2×C4—81no—
351C2×C4—81no—
352C2×C4—81no—
353C2×C4—81no—
354C8—81no—
355C8—81no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—81no—
365C22—81no—
366C22—81no—
367C22—81no—
368C22—81no—
369C22—81no—
370C22—81no—
371C22—81no—
372C22C11×#45211yescharacteristic
373C22C11×#45611yescharacteristic
374C22C11×B(4,𝔽2)11yescharacteristic
375C4—41no—
376C4—41no—
377C4—81no—
378C4—81no—
379C4—81no—
380C4—82no—
381C4—81no—
382C4—81no—
383C4—81no—
384C4—81no—
385C2—21no—
386C2—21no—
387C2—41no—
388C2—41no—
389C2—161no—
390C2C11×#160311yescharacteristic
391C2C11×#220011yescharacteristic
392C2C11×#220011yescharacteristic
subgroupG/H
center, socleC22×C11B(4,𝔽2)
commutator, Frattini, cosocleC2×C22⋊C4C23×C11
prime radicalC11×#392C22
LCSG ▷ C2×C22⋊C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C11 ◁ C2×C11×C22⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#2062C2semidirect
3. C11×#1614C2semidirect
5. C11×#1352C2semidirect
7. C11×#1326C2semidirect
62. #12231C11direct (N × H)
111. #2062C2×C11semidirect
112. #1614C2×C11semidirect
114. #1352C2×C11semidirect
116. #1326C2×C11semidirect
305. C11#12231direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#28262
C11×#20622
C11×#16142
C11×#15962
C11×#13522
C11×#13432
C11×#13262
#1223111