Finite Group Databasebeta

← C11×#12195 #14589388

Subgroups — C11×#12195 #14589388

Order 2816.

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

normal subgroups only

This group has 458 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×#2572C211yesmaximal, characteristic, complemented
2C11×#2007C211yesmaximal, characteristic, complemented
3C11×#1616C211yesmaximal, characteristic, complemented
4C11×#1598C211yesmaximal, characteristic
5C11×#1353C211yesmaximal, characteristic, complemented
6C11×#1345C211yesmaximal, characteristic, complemented
7C11×#1319C211yesmaximal, characteristic, complemented
8C2×C11×#137—21no—
9C11×#537C2211yescharacteristic
10C11×#481—21no—
11C11×#447—21no—
12C2×C11×#104—21no—
13C11×#400C2211yescharacteristic
14C11×#394C2211yescharacteristic
15C11×#393—21no—
16C11×#391C2211yescharacteristic
17C11×#388—21no—
18C11×#386—21no—
19C11×#383—21no—
20C11×#381—21no—
21C4×C11×C22⋊C4—21no—
22C11×#343C2211yescharacteristic
23C11×#327—21no—
24C11×#327—21no—
25C11×#324C2211yescharacteristic
26C11×#324C2211yescharacteristic
27C2×C11×#41—21no—
28C22×Q8×C11D411yescharacteristic
29C22×D4×C11D411yescharacteristic
30C23×C4×C11—21no—
31C11×#137—42no—
32C11×#137—42no—
33C2×C11×Q16—41no—
34C2×C11×SD16—41no—
35C2×C11×D8—41no—
36C2×C11×M16—21no—
37C11×C22⋊Q8—41no—
38C11×#121—21no—
39C11×#121—21no—
40C11×#121—41no—
41C2×C11×C4⋊C4D411yescharacteristic
42C2×C11×C4⋊C4C2311yescharacteristic
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×C42×C11—21no—
49C2×C42×C11D411yescharacteristic
50C11×#106—41no—
51C11×#104—42no—
52C11×#102—41no—
53C11×#102—41no—
54C11×C22⋊C8—21no—
55C11×C22⋊C8—21no—
56C11×#95—21no—
57C11×#95—21no—
58C11×#95—21no—
59C11×#95—21no—
60C11×#95—21no—
61C11×#95—21no—
62C11×#95—21no—
63C11×#95D411yescharacteristic
64C11×#95D411yescharacteristic
65#12195C1111yesmaximal, characteristic, direct product factor, Sylow
66C24×C11—21no—
67C11×#41—41no—
68C11×#41—41no—
69C11×#41—41no—
70C11×#41—41no—
71C2×Q8×C11—21no—
72C2×Q8×C11—21no—
73C2×Q8×C11—21no—
74C2×Q8×C11—41no—
75C2×Q8×C11—41no—
76C2×D4×C11—21no—
77C2×D4×C11—21no—
78C2×D4×C11—21no—
79C2×D4×C11—41no—
80C2×D4×C11—42no—
81C2×D4×C11—41no—
82C22×C4×C11—21no—
83C22×C4×C11—21no—
84C22×C4×C11—21no—
85C22×C4×C11—21no—
86C22×C4×C11—21no—
87C22×C4×C11—41no—
88C22×C4×C11—42no—
89C22×C4×C11—42no—
90C22×C4×C11—81no—
91C22×C4×C11C2×D411yescharacteristic
92C22×C4×C11C2×D411yescharacteristic
93C22×C4×C11C2×D411yescharacteristic
94C11×Q16—44no—
95C11×SD16—44no—
96C11×D8—82no—
97C11×M16—22no—
98C11×M16—41no—
99C2×C8×C11—41no—
100C2×C8×C11—41no—
101C2×C8×C11—41no—
102C11×C4⋊C4—21no—
103C11×C4⋊C4—21no—
104C11×C4⋊C4—41no—
105C11×C4⋊C4—41no—
106C11×C22⋊C4—42no—
107C11×C22⋊C4—41no—
108C11×C22⋊C4—41no—
109C11×C22⋊C4—42no—
110C11×C22⋊C4—41no—
111C11×C22⋊C4—41no—
112C11×C22⋊C4—81no—
113C11×C22⋊C4—81no—
114C42×C11—42no—
115C42×C11—41no—
116#2572C2×C1111yescharacteristic, complemented
117#2007C2×C1111yescharacteristic, complemented
118#1616C2×C1111yescharacteristic, complemented
119#1598C2×C1111yescharacteristic
120#1353C2×C1111yescharacteristic, complemented
121#1345C2×C1111yescharacteristic, complemented
122#1319C2×C1111yescharacteristic, complemented
123C23×C11—22no—
124C23×C11—41no—
125C23×C11—41no—
126C23×C11—41no—
127C23×C11—41no—
128C23×C11—41no—
129C23×C11—41no—
130C23×C11—41no—
131C23×C11#12011yescharacteristic
132Q8×C11—42no—
133Q8×C11—41no—
134Q8×C11—41no—
135Q8×C11—81no—
136D4×C11—41no—
137D4×C11—41no—
138D4×C11—42no—
139D4×C11—81no—
140D4×C11—81no—
141D4×C11—81no—
142D4×C11—81no—
143D4×C11—81no—
144C2×C4×C11—21no—
145C2×C4×C11—21no—
146C2×C4×C11—22no—
147C2×C4×C11—21no—
148C2×C4×C11—21no—
149C2×C4×C11—41no—
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—41no—
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—41no—
166C2×C4×C11—81no—
167C2×C4×C11—81no—
168C2×C4×C11—84no—
169C2×C4×C11#13511yescharacteristic
170C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
171C8×C11—42no—
172C8×C11—81no—
173C8×C11—81no—
174C2×#137—21no—
175#537C22×C1111yescharacteristic
176#481—21no—
177#447—21no—
178C2×#104—21no—
179#400C22×C1111yescharacteristic
180#394C22×C1111yescharacteristic
181#393—21no—
182#391C22×C1111yescharacteristic
183#388—21no—
184#386—21no—
185#383—21no—
186#381—21no—
187C4×C22⋊C4—21no—
188#343C22×C1111yescharacteristic
189#327—21no—
190#327—21no—
191#324C22×C1111yescharacteristic
192#324C22×C1111yescharacteristic
193C22×C11—21no—
194C22×C11—21no—
195C22×C11—42no—
196C22×C11—42no—
197C22×C11—42no—
198C22×C11—81no—
199C22×C11—81no—
200C22×C11—81no—
201C22×C11—81no—
202C22×C11—81no—
203C22×C11—81no—
204C22×C11—81no—
205C22×C11#44911yescharacteristic
206C22×C11#45311yescharacteristic
207C22×C11B(4,𝔽2)11yescharacteristic
208C4×C11—21no—
209C4×C11—21no—
210C4×C11—42no—
211C4×C11—41no—
212C4×C11—41no—
213C4×C11—81no—
214C4×C11—81no—
215C4×C11—81no—
216C4×C11—81no—
217C4×C11—81no—
218C2×#41—21no—
219C22×Q8D4×C1111yescharacteristic
220C22×D4D4×C1111yescharacteristic
221C23×C4—21no—
222#137—42no—
223#137—42no—
224C2×Q16—41no—
225C2×SD16—41no—
226C2×D8—41no—
227C2×M16—21no—
228C22⋊Q8—41no—
229#121—21no—
230#121—21no—
231#121—41no—
232C2×C4⋊C4D4×C1111yescharacteristic
233C2×C4⋊C4C23×C1111yescharacteristic
234C2×C22⋊C4—21no—
235C2×C22⋊C4—21no—
236C2×C22⋊C4—21no—
237C2×C22⋊C4—21no—
238C2×C22⋊C4—21no—
239C2×C42—21no—
240C2×C42D4×C1111yescharacteristic
241#106—41no—
242#104—42no—
243#102—41no—
244#102—41no—
245C22⋊C8—21no—
246C22⋊C8—21no—
247#95—21no—
248#95—21no—
249#95—21no—
250#95—21no—
251#95—21no—
252#95—21no—
253#95—21no—
254#95D4×C1111yescharacteristic
255#95D4×C1111yescharacteristic
256C2×C11—21no—
257C2×C11—21no—
258C2×C11—82no—
259C2×C11—161no—
260C2×C11#160011yescharacteristic
261C2×C11#219711yescharacteristic
262C2×C11#220411yescharacteristic
263C24—21no—
264#41—41no—
265#41—41no—
266#41—41no—
267#41—41no—
268C2×Q8—21no—
269C2×Q8—21no—
270C2×Q8—21no—
271C2×Q8—41no—
272C2×Q8—41no—
273C2×D4—21no—
274C2×D4—21no—
275C2×D4—21no—
276C2×D4—41no—
277C2×D4—42no—
278C2×D4—41no—
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—21no—
283C22×C4—21no—
284C22×C4—41no—
285C22×C4—42no—
286C22×C4—42no—
287C22×C4—81no—
288C22×C4C2×D4×C1111yescharacteristic
289C22×C4C2×D4×C1111yescharacteristic
290C22×C4C2×D4×C1111yescharacteristic
291Q16—44no—
292SD16—44no—
293D8—82no—
294M16—22no—
295M16—41no—
296C2×C8—41no—
297C2×C8—41no—
298C2×C8—41no—
299C4⋊C4—21no—
300C4⋊C4—21no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C22⋊C4—42no—
304C22⋊C4—41no—
305C22⋊C4—41no—
306C22⋊C4—42no—
307C22⋊C4—41no—
308C22⋊C4—41no—
309C22⋊C4—81no—
310C22⋊C4—81no—
311C42—41no—
312C42—42no—
313C11#1219511yescharacteristic, direct product factor, Sylow
314C23—22no—
315C23—41no—
316C23—41no—
317C23—41no—
318C23—41no—
319C23—41no—
320C23—41no—
321C23—41no—
322C23C11×#12011yescharacteristic
323Q8—42no—
324Q8—41no—
325Q8—41no—
326Q8—81no—
327D4—41no—
328D4—41no—
329D4—42no—
330D4—81no—
331D4—81no—
332D4—81no—
333D4—81no—
334D4—81no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—22no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—81no—
358C2×C4—81no—
359C2×C4—84no—
360C2×C4C11×#13511yescharacteristic
361C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
362C8—42no—
363C8—81no—
364C8—81no—
365C22—21no—
366C22—21no—
367C22—42no—
368C22—42no—
369C22—42no—
370C22—81no—
371C22—81no—
372C22—81no—
373C22—81no—
374C22—81no—
375C22—81no—
376C22—81no—
377C22C11×#44911yescharacteristic
378C22C11×#45311yescharacteristic
379C22C11×B(4,𝔽2)11yescharacteristic
380C4—21no—
381C4—21no—
382C4—42no—
383C4—41no—
384C4—41no—
385C4—81no—
386C4—81no—
387C4—81no—
388C4—81no—
389C4—81no—
390C2—21no—
391C2—21no—
392C2—82no—
393C2—161no—
394C2C11×#160011yescharacteristic
395C2C11×#219711yescharacteristic
396C2C11×#220411yescharacteristic
subgroupG/H
center, socleC22×C11B(4,𝔽2)
commutator, Frattini, cosocleC2×C4⋊C4C23×C11
prime radicalC11×#1598C2
LCSG ▷ C2×C4⋊C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C11 ◁ C2×C11×C4⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#2572C2semidirect
2. C11×#2007C2semidirect
3. C11×#1616C2semidirect
5. C11×#1353C2semidirect
6. C11×#1345C2semidirect
7. C11×#1319C2semidirect
65. #12195C11direct (N × H)
116. #2572C2×C11semidirect
117. #2007C2×C11semidirect
118. #1616C2×C11semidirect
120. #1353C2×C11semidirect
121. #1345C2×C11semidirect
122. #1319C2×C11semidirect
313. C11#12195direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#25722
C11×#20072
C11×#16162
C11×#15982
C11×#13532
C11×#13452
C11×#13192
#1219511