Finite Group Databasebeta

← C11×#12243 #14589436

Subgroups — C11×#12243 #14589436

Order 2816.

464 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 464 conjugacy classes of subgroups — too many to draw. Only its 74 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×#2693C211yesmaximal, characteristic
2C11×#2062C211yesmaximal, characteristic, complemented
3C11×#1608C211yesmaximal, characteristic, complemented
4C11×#1596C211yesmaximal, characteristic
5C11×#1344C211yesmaximal, characteristic, complemented
6C11×#1343C211yesmaximal, characteristic
7C11×#1326C211yesmaximal, characteristic, complemented
8C11×#543C2211yescharacteristic
9C2×C11×#123—21no—
10C11×#483—21no—
11C11×#450—21no—
12C11×#400—21no—
13C11×#397C2211yescharacteristic
14C11×#396—21no—
15C11×#392C2211yescharacteristic
16C11×#386—21no—
17C11×#386—21no—
18C11×#385—21no—
19C11×#385C2211yescharacteristic
20C11×#380—21no—
21C11×#342—21no—
22C11×#342C2211yescharacteristic
23C11×#328—21no—
24C11×#328—21no—
25C11×#323C2211yescharacteristic
26C11×#323C2211yescharacteristic
27C22×D4×C11—21no—
28C22×D4×C11D411yescharacteristic
29C23×C4×C11—21no—
30C23×C4×C11D411yescharacteristic
31C2×C11×SD16—41no—
32C11×#123—42no—
33C11×#123—42no—
34C11×C22⋊Q8—21no—
35C11×C22⋊Q8—21no—
36C11×C22⋊Q8—41no—
37C11×C22⋊Q8—41no—
38C2×C11×C4⋊C4—21no—
39C2×C11×C4⋊C4—21no—
40C2×C11×C4⋊C4—21no—
41C2×C11×C4⋊C4—41no—
42C2×C11×C4⋊C4D411yescharacteristic
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⋊C4—21no—
49C2×C11×C22⋊C4—21no—
50C2×C11×C22⋊C4D411yescharacteristic
51C2×C11×C22⋊C4C2311yescharacteristic
52C11×#106—41no—
53C11×#103—41no—
54C11×#102—41no—
55C11×C22⋊C8—21no—
56C11×C22⋊C8—21no—
57C11×#95—21no—
58C11×#95—21no—
59C11×#95—21no—
60C11×#95—21no—
61C11×#95—41no—
62C11×#95D411yescharacteristic
63C11×#95D411yescharacteristic
64#12243C1111yesmaximal, characteristic, direct product factor, Sylow
65C24×C11—21no—
66C24×C11C2×D411yescharacteristic
67C2×Q8×C11—21no—
68C2×Q8×C11—21no—
69C2×D4×C11—41no—
70C2×D4×C11—42no—
71C2×D4×C11—42no—
72C2×D4×C11—41no—
73C2×D4×C11—41no—
74C2×D4×C11—81no—
75C22×C4×C11—21no—
76C22×C4×C11—21no—
77C22×C4×C11—21no—
78C22×C4×C11—21no—
79C22×C4×C11—21no—
80C22×C4×C11—21no—
81C22×C4×C11—21no—
82C22×C4×C11—42no—
83C22×C4×C11—41no—
84C22×C4×C11—41no—
85C22×C4×C11—42no—
86C22×C4×C11—81no—
87C22×C4×C11—81no—
88C22×C4×C11C2×D411yescharacteristic
89C22×C4×C11C2×D411yescharacteristic
90C11×SD16—82no—
91C2×C8×C11—41no—
92C2×C8×C11—41no—
93C11×C4⋊C4—21no—
94C11×C4⋊C4—21no—
95C11×C4⋊C4—42no—
96C11×C4⋊C4—42no—
97C11×C4⋊C4—41no—
98C11×C4⋊C4—41no—
99C11×C4⋊C4—41no—
100C11×C4⋊C4—81no—
101C11×C4⋊C4—82no—
102C11×C22⋊C4—21no—
103C11×C22⋊C4—22no—
104C11×C22⋊C4—41no—
105C11×C22⋊C4—42no—
106C11×C22⋊C4—41no—
107C11×C22⋊C4—41no—
108C11×C22⋊C4—41no—
109C11×C22⋊C4—41no—
110C11×C22⋊C4—41no—
111C11×C22⋊C4—81no—
112C11×C22⋊C4—81no—
113C11×C22⋊C4—81no—
114C11×C22⋊C4SD1612yescomplemented
115#2693C2×C1111yescharacteristic
116#2062C2×C1111yescharacteristic, complemented
117#1608C2×C1111yescharacteristic, complemented
118#1596C2×C1111yescharacteristic
119#1344C2×C1111yescharacteristic, complemented
120#1343C2×C1111yescharacteristic
121#1326C2×C1111yescharacteristic, complemented
122C23×C11—21no—
123C23×C11—21no—
124C23×C11—22no—
125C23×C11—41no—
126C23×C11—41no—
127C23×C11—41no—
128C23×C11—41no—
129C23×C11—41no—
130C23×C11—41no—
131C23×C11—41no—
132C23×C11—41no—
133C23×C11#12011yescharacteristic
134C23×C11C2×SD1611yescharacteristic
135C23×C11AGL(1,ℤ/8)11yescharacteristic
136Q8×C11—81no—
137Q8×C11—81no—
138D4×C11—42no—
139D4×C11—81no—
140D4×C11—82no—
141D4×C11—82no—
142C2×C4×C11—22no—
143C2×C4×C11—21no—
144C2×C4×C11—21no—
145C2×C4×C11—41no—
146C2×C4×C11—41no—
147C2×C4×C11—41no—
148C2×C4×C11—41no—
149C2×C4×C11—42no—
150C2×C4×C11—41no—
151C2×C4×C11—41no—
152C2×C4×C11—41no—
153C2×C4×C11—41no—
154C2×C4×C11—41no—
155C2×C4×C11—41no—
156C2×C4×C11—42no—
157C2×C4×C11—41no—
158C2×C4×C11—41no—
159C2×C4×C11—41no—
160C2×C4×C11—41no—
161C2×C4×C11—41no—
162C2×C4×C11—41no—
163C2×C4×C11—41no—
164C2×C4×C11—41no—
165C2×C4×C11—84no—
166C2×C4×C11—81no—
167C2×C4×C11—81no—
168C2×C4×C11—81no—
169C2×C4×C11—81no—
170C2×C4×C11—81no—
171C8×C11—81no—
172C8×C11—81no—
173#543C22×C1111yescharacteristic
174C2×#123—21no—
175#483—21no—
176#450—21no—
177#400—21no—
178#397C22×C1111yescharacteristic
179#396—21no—
180#392C22×C1111yescharacteristic
181#386—21no—
182#386—21no—
183#385—21no—
184#385C22×C1111yescharacteristic
185#380—21no—
186#342—21no—
187#342C22×C1111yescharacteristic
188#328—21no—
189#328—21no—
190#323C22×C1111yescharacteristic
191#323C22×C1111yescharacteristic
192C22×C11—21no—
193C22×C11—21no—
194C22×C11—21no—
195C22×C11—21no—
196C22×C11—41no—
197C22×C11—41no—
198C22×C11—42no—
199C22×C11—42no—
200C22×C11—41no—
201C22×C11—41no—
202C22×C11—42no—
203C22×C11—81no—
204C22×C11—81no—
205C22×C11—81no—
206C22×C11—81no—
207C22×C11—81no—
208C22×C11#45011yescharacteristic
209C22×C11#45611yescharacteristic
210C22×C11B(4,𝔽2)11yescharacteristic
211C4×C11—42no—
212C4×C11—41no—
213C4×C11—41no—
214C4×C11—81no—
215C4×C11—81no—
216C4×C11—82no—
217C4×C11—81no—
218C4×C11—81no—
219C4×C11—81no—
220C4×C11—81no—
221C22×D4—21no—
222C22×D4D4×C1111yescharacteristic
223C23×C4—21no—
224C23×C4D4×C1111yescharacteristic
225C2×SD16—41no—
226#123—42no—
227#123—42no—
228C22⋊Q8—21no—
229C22⋊Q8—21no—
230C22⋊Q8—41no—
231C22⋊Q8—41no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—41no—
236C2×C4⋊C4D4×C1111yescharacteristic
237C2×C22⋊C4—21no—
238C2×C22⋊C4—21no—
239C2×C22⋊C4—21no—
240C2×C22⋊C4—21no—
241C2×C22⋊C4—21no—
242C2×C22⋊C4—21no—
243C2×C22⋊C4—21no—
244C2×C22⋊C4D4×C1111yescharacteristic
245C2×C22⋊C4C23×C1111yescharacteristic
246#106—41no—
247#103—41no—
248#102—41no—
249C22⋊C8—21no—
250C22⋊C8—21no—
251#95—21no—
252#95—21no—
253#95—21no—
254#95—21no—
255#95—41no—
256#95D4×C1111yescharacteristic
257#95D4×C1111yescharacteristic
258C2×C11—21no—
259C2×C11—21no—
260C2×C11—41no—
261C2×C11—41no—
262C2×C11—82no—
263C2×C11#160411yescharacteristic
264C2×C11#219711yescharacteristic
265C2×C11#220011yescharacteristic
266C24—21no—
267C24C2×D4×C1111yescharacteristic
268C2×Q8—21no—
269C2×Q8—21no—
270C2×D4—41no—
271C2×D4—42no—
272C2×D4—42no—
273C2×D4—41no—
274C2×D4—41no—
275C2×D4—81no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—21no—
283C22×C4—42no—
284C22×C4—41no—
285C22×C4—41no—
286C22×C4—42no—
287C22×C4—81no—
288C22×C4—81no—
289C22×C4C2×D4×C1111yescharacteristic
290C22×C4C2×D4×C1111yescharacteristic
291SD16—82no—
292C2×C8—41no—
293C2×C8—41no—
294C4⋊C4—21no—
295C4⋊C4—21no—
296C4⋊C4—41no—
297C4⋊C4—42no—
298C4⋊C4—42no—
299C4⋊C4—41no—
300C4⋊C4—41no—
301C4⋊C4—81no—
302C4⋊C4—82no—
303C22⋊C4—21no—
304C22⋊C4—22no—
305C22⋊C4—41no—
306C22⋊C4—42no—
307C22⋊C4—41no—
308C22⋊C4—41no—
309C22⋊C4—41no—
310C22⋊C4—41no—
311C22⋊C4—41no—
312C22⋊C4—81no—
313C22⋊C4—81no—
314C22⋊C4—81no—
315C22⋊C4C11×SD1612yescomplemented
316C11#1224311yescharacteristic, direct product factor, Sylow
317C23—21no—
318C23—21no—
319C23—22no—
320C23—41no—
321C23—41no—
322C23—41no—
323C23—41no—
324C23—41no—
325C23—41no—
326C23—41no—
327C23—41no—
328C23C11×#12011yescharacteristic
329C23C2×C11×SD1611yescharacteristic
330C23C11×AGL(1,ℤ/8)11yescharacteristic
331Q8—81no—
332Q8—81no—
333D4—42no—
334D4—81no—
335D4—82no—
336D4—82no—
337C2×C4—22no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—42no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—42no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—84no—
361C2×C4—81no—
362C2×C4—81no—
363C2×C4—81no—
364C2×C4—81no—
365C2×C4—81no—
366C8—81no—
367C8—81no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—41no—
373C22—41no—
374C22—42no—
375C22—42no—
376C22—41no—
377C22—41no—
378C22—42no—
379C22—81no—
380C22—81no—
381C22—81no—
382C22—81no—
383C22—81no—
384C22C11×#45011yescharacteristic
385C22C11×#45611yescharacteristic
386C22C11×B(4,𝔽2)11yescharacteristic
387C4—42no—
388C4—41no—
389C4—41no—
390C4—81no—
391C4—81no—
392C4—82no—
393C4—81no—
394C4—81no—
395C4—81no—
396C4—81no—
397C2—21no—
398C2—21no—
399C2—41no—
400C2—41no—
401C2—82no—
402C2C11×#160411yescharacteristic
403C2C11×#219711yescharacteristic
404C2C11×#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×#1608C2semidirect
5. C11×#1344C2semidirect
7. C11×#1326C2semidirect
64. #12243C11direct (N × H)
114. C11×C22⋊C4SD16semidirect
116. #2062C2×C11semidirect
117. #1608C2×C11semidirect
119. #1344C2×C11semidirect
121. #1326C2×C11semidirect
315. C22⋊C4C11×SD16semidirect
316. C11#12243direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#26932
C11×#20622
C11×#16082
C11×#15962
C11×#13442
C11×#13432
C11×#13262
#1224311