Finite Group Databasebeta

← C11×#12199 #14589392

Subgroups — C11×#12199 #14589392

Order 2816.

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

normal subgroups only

This group has 434 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×#2832C211yesmaximal, characteristic, complemented
2C11×#2007C211yesmaximal, characteristic, complemented
3C11×#1604C211yesmaximal, characteristic, complemented
4C11×#1598C211yesmaximal, characteristic
5C11×#1354C211yesmaximal, characteristic, complemented
6C11×#1345C211yesmaximal, characteristic, complemented
7C11×#1319C211yesmaximal, characteristic, complemented
8C2×C11×#137—21no—
9C11×#537C2211yescharacteristic
10C11×#448—21no—
11C11×#447—21no—
12C2×C11×#104—21no—
13C11×#400—21no—
14C11×#397—21no—
15C11×#395C2211yescharacteristic
16C11×#394—21no—
17C11×#394C2211yescharacteristic
18C11×#393—21no—
19C11×#393—21no—
20C11×#391C2211yescharacteristic
21C11×#388—21no—
22C11×#343C2211yescharacteristic
23C11×#327—21no—
24C11×#327—21no—
25C11×#324C2211yescharacteristic
26C11×#324C2211yescharacteristic
27C2×C11×#41—21no—
28C22×Q8×C11D411yescharacteristic
29C22×Q8×C11D411yescharacteristic
30C22×D4×C11D411yescharacteristic
31C11×#137—42no—
32C11×#137—42no—
33C2×C11×Q16—41no—
34C2×C11×SD16—41no—
35C2×C11×SD16—41no—
36C2×C11×D8—41no—
37C2×C11×M16—21no—
38C11×C22⋊Q8—41no—
39C11×#121—21no—
40C11×#121—21no—
41C11×#121—41no—
42C2×C11×C4⋊C4—21no—
43C2×C11×C4⋊C4—21no—
44C2×C11×C4⋊C4C2311yescharacteristic
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⋊C4—21no—
51C2×C42×C11D411yescharacteristic
52C11×#104—42no—
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—21no—
62C11×#95—21no—
63C11×#95D411yescharacteristic
64C11×#95D411yescharacteristic
65#12199C1111yesmaximal, 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×Q8×C11—41no—
77C2×Q8×C11—81no—
78C2×D4×C11—21no—
79C2×D4×C11—21no—
80C2×D4×C11—21no—
81C2×D4×C11—41no—
82C2×D4×C11—41no—
83C2×D4×C11—81no—
84C22×C4×C11—21no—
85C22×C4×C11—21no—
86C22×C4×C11—21no—
87C22×C4×C11—21no—
88C22×C4×C11—21no—
89C22×C4×C11—41no—
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11C2×D411yescharacteristic
92C22×C4×C11C2×D411yescharacteristic
93C11×Q16—44no—
94C11×SD16—44no—
95C11×SD16—82no—
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—81no—
106C11×C4⋊C4—81no—
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⋊C4—81no—
115C11×C22⋊C4—81no—
116C42×C11—41no—
117#2832C2×C1111yescharacteristic, complemented
118#2007C2×C1111yescharacteristic, complemented
119#1604C2×C1111yescharacteristic, complemented
120#1598C2×C1111yescharacteristic
121#1354C2×C1111yescharacteristic, complemented
122#1345C2×C1111yescharacteristic, complemented
123#1319C2×C1111yescharacteristic, complemented
124C23×C11—41no—
125C23×C11—41no—
126C23×C11—41no—
127C23×C11—41no—
128C23×C11—41no—
129C23×C11—41no—
130C23×C11—41no—
131C23×C11—41no—
132C23×C11#12011yescharacteristic
133Q8×C11—42no—
134Q8×C11—41no—
135Q8×C11—41no—
136Q8×C11—42no—
137Q8×C11—81no—
138Q8×C11—81no—
139D4×C11—41no—
140D4×C11—41no—
141D4×C11—42no—
142D4×C11—81no—
143D4×C11—81no—
144D4×C11—81no—
145D4×C11—81no—
146D4×C11—81no—
147C2×C4×C11—21no—
148C2×C4×C11—21no—
149C2×C4×C11—21no—
150C2×C4×C11—21no—
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—41no—
167C2×C4×C11—41no—
168C2×C4×C11—41no—
169C2×C4×C11—81no—
170C2×C4×C11—81no—
171C2×C4×C11#13511yescharacteristic
172C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
173C8×C11—42no—
174C8×C11—81no—
175C8×C11—81no—
176C2×#137—21no—
177#537C22×C1111yescharacteristic
178#448—21no—
179#447—21no—
180C2×#104—21no—
181#400—21no—
182#397—21no—
183#395C22×C1111yescharacteristic
184#394—21no—
185#394C22×C1111yescharacteristic
186#393—21no—
187#393—21no—
188#391C22×C1111yescharacteristic
189#388—21no—
190#343C22×C1111yescharacteristic
191#327—21no—
192#327—21no—
193#324C22×C1111yescharacteristic
194#324C22×C1111yescharacteristic
195C22×C11—21no—
196C22×C11—21no—
197C22×C11—81no—
198C22×C11—81no—
199C22×C11—81no—
200C22×C11—81no—
201C22×C11—81no—
202C22×C11—81no—
203C22×C11—81no—
204C22×C11—81no—
205C22×C11—81no—
206C22×C11—81no—
207C22×C11#44911yescharacteristic
208C22×C11#45311yescharacteristic
209C22×C11B(4,𝔽2)11yescharacteristic
210C4×C11—21no—
211C4×C11—21no—
212C4×C11—41no—
213C4×C11—41no—
214C4×C11—81no—
215C4×C11—81no—
216C4×C11—81no—
217C4×C11—81no—
218C4×C11—81no—
219C4×C11—81no—
220C2×#41—21no—
221C22×Q8D4×C1111yescharacteristic
222C22×Q8D4×C1111yescharacteristic
223C22×D4D4×C1111yescharacteristic
224#137—42no—
225#137—42no—
226C2×Q16—41no—
227C2×SD16—41no—
228C2×SD16—41no—
229C2×D8—41no—
230C2×M16—21no—
231C22⋊Q8—41no—
232#121—21no—
233#121—21no—
234#121—41no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4C23×C1111yescharacteristic
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×C42D4×C1111yescharacteristic
245#104—42no—
246#103—41no—
247#102—41no—
248C22⋊C8—21no—
249C22⋊C8—21no—
250#95—21no—
251#95—21no—
252#95—21no—
253#95—21no—
254#95—21no—
255#95—21no—
256#95D4×C1111yescharacteristic
257#95D4×C1111yescharacteristic
258C2×C11—21no—
259C2×C11—21no—
260C2×C11—161no—
261C2×C11—161no—
262C2×C11#160011yescharacteristic
263C2×C11#219911yescharacteristic
264C2×C11#220311yescharacteristic
265C24—21no—
266#41—41no—
267#41—41no—
268#41—41no—
269#41—41no—
270C2×Q8—21no—
271C2×Q8—21no—
272C2×Q8—21no—
273C2×Q8—41no—
274C2×Q8—41no—
275C2×Q8—41no—
276C2×Q8—81no—
277C2×D4—21no—
278C2×D4—21no—
279C2×D4—21no—
280C2×D4—41no—
281C2×D4—41no—
282C2×D4—81no—
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—21no—
286C22×C4—21no—
287C22×C4—21no—
288C22×C4—41no—
289C22×C4C2×D4×C1111yescharacteristic
290C22×C4C2×D4×C1111yescharacteristic
291C22×C4C2×D4×C1111yescharacteristic
292Q16—44no—
293SD16—44no—
294SD16—82no—
295D8—82no—
296M16—22no—
297M16—41no—
298C2×C8—41no—
299C2×C8—41no—
300C2×C8—41no—
301C4⋊C4—21no—
302C4⋊C4—21no—
303C4⋊C4—41no—
304C4⋊C4—81no—
305C4⋊C4—81no—
306C22⋊C4—41no—
307C22⋊C4—41no—
308C22⋊C4—41no—
309C22⋊C4—41no—
310C22⋊C4—81no—
311C22⋊C4—81no—
312C22⋊C4—81no—
313C22⋊C4—81no—
314C22⋊C4—81no—
315C42—41no—
316C11#1219911yescharacteristic, direct product factor, Sylow
317C23—41no—
318C23—41no—
319C23—41no—
320C23—41no—
321C23—41no—
322C23—41no—
323C23—41no—
324C23—41no—
325C23C11×#12011yescharacteristic
326Q8—42no—
327Q8—41no—
328Q8—41no—
329Q8—42no—
330Q8—81no—
331Q8—81no—
332D4—41no—
333D4—41no—
334D4—42no—
335D4—81no—
336D4—81no—
337D4—81no—
338D4—81no—
339D4—81no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
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—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—81no—
363C2×C4—81no—
364C2×C4C11×#13511yescharacteristic
365C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
366C8—42no—
367C8—81no—
368C8—81no—
369C22—21no—
370C22—21no—
371C22—81no—
372C22—81no—
373C22—81no—
374C22—81no—
375C22—81no—
376C22—81no—
377C22—81no—
378C22—81no—
379C22—81no—
380C22—81no—
381C22C11×#44911yescharacteristic
382C22C11×#45311yescharacteristic
383C22C11×B(4,𝔽2)11yescharacteristic
384C4—21no—
385C4—21no—
386C4—41no—
387C4—41no—
388C4—81no—
389C4—81no—
390C4—81no—
391C4—81no—
392C4—81no—
393C4—81no—
394C2—21no—
395C2—21no—
396C2—161no—
397C2—161no—
398C2C11×#160011yescharacteristic
399C2C11×#219911yescharacteristic
400C2C11×#220311yescharacteristic
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×#2832C2semidirect
2. C11×#2007C2semidirect
3. C11×#1604C2semidirect
5. C11×#1354C2semidirect
6. C11×#1345C2semidirect
7. C11×#1319C2semidirect
65. #12199C11direct (N × H)
117. #2832C2×C11semidirect
118. #2007C2×C11semidirect
119. #1604C2×C11semidirect
121. #1354C2×C11semidirect
122. #1345C2×C11semidirect
123. #1319C2×C11semidirect
316. C11#12199direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#28322
C11×#20072
C11×#16042
C11×#15982
C11×#13542
C11×#13452
C11×#13192
#1219911