Finite Group Databasebeta

← C11×#12133 #14589326

Subgroups — C11×#12133 #14589326

Order 2816.

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

normal subgroups only

This group has 554 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×#2463C211yesmaximal, characteristic, complemented
2C11×#2044C211yesmaximal, characteristic, complemented
3C11×#1601C211yesmaximal, characteristic, complemented
4C11×#1595C211yesmaximal, characteristic
5C11×#1351C211yesmaximal, characteristic, complemented
6C11×#1343C211yesmaximal, characteristic, complemented
7C11×#1326C211yesmaximal, characteristic, complemented
8C11×#534C2211yescharacteristic
9C2×C11×C22⋊Q8—21no—
10C2×C4×D4×C11—21no—
11C11×#448—21no—
12C11×#447—21no—
13C2×C11×#99—21no—
14C11×#394—21no—
15C11×#393C2211yescharacteristic
16C11×#392C2211yescharacteristic
17C11×#388—21no—
18C11×#387—21no—
19C11×#386—21no—
20C11×#386—21no—
21C11×#385C2211yescharacteristic
22C11×#342C2211yescharacteristic
23C11×#327—21no—
24C11×#327—21no—
25C11×#323C2211yescharacteristic
26C11×#323C2211yescharacteristic
27C22×Q8×C11D411yescharacteristic
28C22×D4×C11—21no—
29C22×D4×C11—21no—
30C22×D4×C11D411yescharacteristic
31C23×C4×C11—21no—
32C23×C4×C11D411yescharacteristic
33C2×C11×SD16—41no—
34C2×C11×D8—41no—
35C11×#123—41no—
36C11×C22⋊Q8—44no—
37C11×#121—21no—
38C11×#121—21no—
39C11×#120—41no—
40C4×D4×C11—44no—
41C2×C11×C4⋊C4—21no—
42C2×C11×C4⋊C4—21no—
43C2×C11×C4⋊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⋊C4—41no—
51C2×C11×C22⋊C4D411yescharacteristic
52C2×C11×C22⋊C4C2311yescharacteristic
53C2×C42×C11—21no—
54C11×#103—41no—
55C11×#102—41no—
56C11×#99—42no—
57C11×C22⋊C8—21no—
58C11×C22⋊C8—21no—
59C11×#95—21no—
60C11×#95—21no—
61C11×#95—21no—
62C11×#95—41no—
63C11×#95D411yescharacteristic
64C11×#95D411yescharacteristic
65#12133C1111yesmaximal, characteristic, direct product factor, Sylow
66C24×C11—21no—
67C24×C11—21no—
68C24×C11C2×D411yescharacteristic
69C2×Q8×C11—42no—
70C2×Q8×C11—41no—
71C2×D4×C11—21no—
72C2×D4×C11—21no—
73C2×D4×C11—42no—
74C2×D4×C11—41no—
75C2×D4×C11—42no—
76C2×D4×C11—41no—
77C2×D4×C11—41no—
78C2×D4×C11—42no—
79C2×D4×C11—41no—
80C2×D4×C11—41no—
81C2×D4×C11—41no—
82C2×D4×C11—41no—
83C2×D4×C11—41no—
84C2×D4×C11—41no—
85C22×C4×C11—21no—
86C22×C4×C11—21no—
87C22×C4×C11—21no—
88C22×C4×C11—21no—
89C22×C4×C11—21no—
90C22×C4×C11—21no—
91C22×C4×C11—42no—
92C22×C4×C11—42no—
93C22×C4×C11—42no—
94C22×C4×C11—41no—
95C22×C4×C11—41no—
96C22×C4×C11—81no—
97C22×C4×C11C2×D411yescharacteristic
98C22×C4×C11C2×D411yescharacteristic
99C11×SD16—82no—
100C11×D8—82no—
101C2×C8×C11—41no—
102C2×C8×C11—41no—
103C11×C4⋊C4—24no—
104C11×C4⋊C4—21no—
105C11×C4⋊C4—21no—
106C11×C4⋊C4—42no—
107C11×C4⋊C4—42no—
108C11×C22⋊C4—21no—
109C11×C22⋊C4—21no—
110C11×C22⋊C4—41no—
111C11×C22⋊C4—42no—
112C11×C22⋊C4—42no—
113C11×C22⋊C4—42no—
114C11×C22⋊C4—42no—
115C11×C22⋊C4—41no—
116C11×C22⋊C4—41no—
117C11×C22⋊C4—42no—
118C11×C22⋊C4—41no—
119C11×C22⋊C4—41no—
120C11×C22⋊C4—82no—
121C42×C11—42no—
122#2463C2×C1111yescharacteristic, complemented
123#2044C2×C1111yescharacteristic, complemented
124#1601C2×C1111yescharacteristic, complemented
125#1595C2×C1111yescharacteristic
126#1351C2×C1111yescharacteristic, complemented
127#1343C2×C1111yescharacteristic, complemented
128#1326C2×C1111yescharacteristic, complemented
129C23×C11—21no—
130C23×C11—21no—
131C23×C11—22no—
132C23×C11—41no—
133C23×C11—41no—
134C23×C11—41no—
135C23×C11—41no—
136C23×C11—41no—
137C23×C11—41no—
138C23×C11—41no—
139C23×C11—41no—
140C23×C11—41no—
141C23×C11—41no—
142C23×C11—41no—
143C23×C11—81no—
144C23×C11—81no—
145C23×C11#12011yescharacteristic
146C23×C11#13511yescharacteristic
147C23×C11AGL(1,ℤ/8)11yescharacteristic
148Q8×C11—42no—
149Q8×C11—81no—
150D4×C11—42no—
151D4×C11—44no—
152D4×C11—44no—
153D4×C11—81no—
154D4×C11—81no—
155D4×C11—81no—
156D4×C11—81no—
157D4×C11—81no—
158D4×C11—81no—
159D4×C11—81no—
160C2×C4×C11—22no—
161C2×C4×C11—22no—
162C2×C4×C11—22no—
163C2×C4×C11—21no—
164C2×C4×C11—21no—
165C2×C4×C11—41no—
166C2×C4×C11—41no—
167C2×C4×C11—41no—
168C2×C4×C11—41no—
169C2×C4×C11—41no—
170C2×C4×C11—41no—
171C2×C4×C11—41no—
172C2×C4×C11—41no—
173C2×C4×C11—42no—
174C2×C4×C11—41no—
175C2×C4×C11—41no—
176C2×C4×C11—41no—
177C2×C4×C11—41no—
178C2×C4×C11—41no—
179C2×C4×C11—41no—
180C2×C4×C11—41no—
181C2×C4×C11—41no—
182C2×C4×C11—41no—
183C2×C4×C11—81no—
184C2×C4×C11—84no—
185C2×C4×C11—81no—
186C2×C4×C11—81no—
187C2×C4×C11—81no—
188C8×C11—81no—
189C8×C11—81no—
190#534C22×C1111yescharacteristic
191C2×C22⋊Q8—21no—
192C2×C4×D4—21no—
193#448—21no—
194#447—21no—
195C2×#99—21no—
196#394—21no—
197#393C22×C1111yescharacteristic
198#392C22×C1111yescharacteristic
199#388—21no—
200#387—21no—
201#386—21no—
202#386—21no—
203#385C22×C1111yescharacteristic
204#342C22×C1111yescharacteristic
205#327—21no—
206#327—21no—
207#323C22×C1111yescharacteristic
208#323C22×C1111yescharacteristic
209C22×C11—21no—
210C22×C11—21no—
211C22×C11—21no—
212C22×C11—21no—
213C22×C11—41no—
214C22×C11—41no—
215C22×C11—42no—
216C22×C11—42no—
217C22×C11—41no—
218C22×C11—41no—
219C22×C11—42no—
220C22×C11—81no—
221C22×C11—81no—
222C22×C11—81no—
223C22×C11—82no—
224C22×C11—81no—
225C22×C11—81no—
226C22×C11—81no—
227C22×C11—81no—
228C22×C11—81no—
229C22×C11—161no—
230C22×C11#44911yescharacteristic
231C22×C11#45411yescharacteristic
232C22×C11B(4,𝔽2)11yescharacteristic
233C4×C11—42no—
234C4×C11—42no—
235C4×C11—42no—
236C4×C11—41no—
237C4×C11—41no—
238C4×C11—81no—
239C4×C11—81no—
240C4×C11—81no—
241C4×C11—161no—
242C22×Q8D4×C1111yescharacteristic
243C22×D4—21no—
244C22×D4—21no—
245C22×D4D4×C1111yescharacteristic
246C23×C4—21no—
247C23×C4D4×C1111yescharacteristic
248C2×SD16—41no—
249C2×D8—41no—
250#123—41no—
251C22⋊Q8—44no—
252#121—21no—
253#121—21no—
254#120—41no—
255C4×D4—44no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—21no—
259C2×C22⋊C4—21no—
260C2×C22⋊C4—21no—
261C2×C22⋊C4—21no—
262C2×C22⋊C4—21no—
263C2×C22⋊C4—21no—
264C2×C22⋊C4—21no—
265C2×C22⋊C4—41no—
266C2×C22⋊C4D4×C1111yescharacteristic
267C2×C22⋊C4C23×C1111yescharacteristic
268C2×C42—21no—
269#103—41no—
270#102—41no—
271#99—42no—
272C22⋊C8—21no—
273C22⋊C8—21no—
274#95—21no—
275#95—21no—
276#95—21no—
277#95—41no—
278#95D4×C1111yescharacteristic
279#95D4×C1111yescharacteristic
280C2×C11—21no—
281C2×C11—21no—
282C2×C11—41no—
283C2×C11—41no—
284C2×C11—82no—
285C2×C11—161no—
286C2×C11#159711yescharacteristic
287C2×C11#219611yescharacteristic
288C2×C11#219711yescharacteristic
289C24—21no—
290C24—21no—
291C24C2×D4×C1111yescharacteristic
292C2×Q8—42no—
293C2×Q8—41no—
294C2×D4—21no—
295C2×D4—21no—
296C2×D4—42no—
297C2×D4—41no—
298C2×D4—42no—
299C2×D4—41no—
300C2×D4—41no—
301C2×D4—42no—
302C2×D4—41no—
303C2×D4—41no—
304C2×D4—41no—
305C2×D4—41no—
306C2×D4—41no—
307C2×D4—41no—
308C22×C4—21no—
309C22×C4—21no—
310C22×C4—21no—
311C22×C4—21no—
312C22×C4—21no—
313C22×C4—21no—
314C22×C4—42no—
315C22×C4—42no—
316C22×C4—42no—
317C22×C4—41no—
318C22×C4—41no—
319C22×C4—81no—
320C22×C4C2×D4×C1111yescharacteristic
321C22×C4C2×D4×C1111yescharacteristic
322SD16—82no—
323D8—82no—
324C2×C8—41no—
325C2×C8—41no—
326C4⋊C4—24no—
327C4⋊C4—21no—
328C4⋊C4—21no—
329C4⋊C4—42no—
330C4⋊C4—42no—
331C22⋊C4—21no—
332C22⋊C4—21no—
333C22⋊C4—41no—
334C22⋊C4—42no—
335C22⋊C4—42no—
336C22⋊C4—42no—
337C22⋊C4—42no—
338C22⋊C4—41no—
339C22⋊C4—41no—
340C22⋊C4—42no—
341C22⋊C4—41no—
342C22⋊C4—41no—
343C22⋊C4—82no—
344C42—42no—
345C11#1213311yescharacteristic, direct product factor, Sylow
346C23—21no—
347C23—21no—
348C23—22no—
349C23—41no—
350C23—41no—
351C23—41no—
352C23—41no—
353C23—41no—
354C23—41no—
355C23—41no—
356C23—41no—
357C23—41no—
358C23—41no—
359C23—41no—
360C23—81no—
361C23—81no—
362C23C11×#12011yescharacteristic
363C23C11×#13511yescharacteristic
364C23C11×AGL(1,ℤ/8)11yescharacteristic
365Q8—42no—
366Q8—81no—
367D4—42no—
368D4—44no—
369D4—44no—
370D4—81no—
371D4—81no—
372D4—81no—
373D4—81no—
374D4—81no—
375D4—81no—
376D4—81no—
377C2×C4—22no—
378C2×C4—22no—
379C2×C4—22no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—42no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—81no—
401C2×C4—84no—
402C2×C4—81no—
403C2×C4—81no—
404C2×C4—81no—
405C8—81no—
406C8—81no—
407C22—21no—
408C22—21no—
409C22—21no—
410C22—21no—
411C22—41no—
412C22—41no—
413C22—42no—
414C22—42no—
415C22—41no—
416C22—41no—
417C22—42no—
418C22—81no—
419C22—81no—
420C22—81no—
421C22—82no—
422C22—81no—
423C22—81no—
424C22—81no—
425C22—81no—
426C22—81no—
427C22—161no—
428C22C11×#44911yescharacteristic
429C22C11×#45411yescharacteristic
430C22C11×B(4,𝔽2)11yescharacteristic
431C4—42no—
432C4—41no—
433C4—42no—
434C4—42no—
435C4—41no—
436C4—81no—
437C4—81no—
438C4—81no—
439C4—161no—
440C2—21no—
441C2—21no—
442C2—41no—
443C2—41no—
444C2—82no—
445C2—161no—
446C2C11×#159711yescharacteristic
447C2C11×#219611yescharacteristic
448C2C11×#219711yescharacteristic
subgroupG/H
center, socleC22×C11B(4,𝔽2)
commutator, Frattini, cosocleC2×C22⋊C4C23×C11
prime radicalC11×#1595C2
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
1. C11×#2463C2semidirect
2. C11×#2044C2semidirect
3. C11×#1601C2semidirect
5. C11×#1351C2semidirect
6. C11×#1343C2semidirect
7. C11×#1326C2semidirect
65. #12133C11direct (N × H)
122. #2463C2×C11semidirect
123. #2044C2×C11semidirect
124. #1601C2×C11semidirect
126. #1351C2×C11semidirect
127. #1343C2×C11semidirect
128. #1326C2×C11semidirect
345. C11#12133direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#24632
C11×#20442
C11×#16012
C11×#15952
C11×#13512
C11×#13432
C11×#13262
#1213311