Finite Group Databasebeta

← C11×#12136 #14589329

Subgroups — C11×#12136 #14589329

Order 2816.

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

normal subgroups only

This group has 456 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×#2824C211yesmaximal, 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
9C11×#448—21no—
10C11×#447—21no—
11C2×C11×#99—21no—
12C11×#400—21no—
13C11×#397—21no—
14C11×#394—21no—
15C11×#394—21no—
16C11×#393—21no—
17C11×#393C2211yescharacteristic
18C11×#392C2211yescharacteristic
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×C11D411yescharacteristic
32C2×C11×SD16—41no—
33C2×C11×D8—41no—
34C11×#123—41no—
35C11×#121—21no—
36C11×#121—21no—
37C11×#120—41no—
38C2×C11×C4⋊C4—21no—
39C2×C11×C4⋊C4—21no—
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—41no—
48C2×C11×C22⋊C4D411yescharacteristic
49C2×C11×C22⋊C4C2311yescharacteristic
50C11×#103—41no—
51C11×#102—41no—
52C11×#99—42no—
53C11×C22⋊C8—21no—
54C11×C22⋊C8—21no—
55C11×#95—21no—
56C11×#95—21no—
57C11×#95—21no—
58C11×#95—21no—
59C11×#95—21no—
60C11×#95—41no—
61C11×#95D411yescharacteristic
62C11×#95D411yescharacteristic
63#12136C1111yesmaximal, characteristic, direct product factor, Sylow
64C24×C11—21no—
65C24×C11—21no—
66C24×C11C2×D411yescharacteristic
67C2×Q8×C11—41no—
68C2×Q8×C11—81no—
69C2×D4×C11—21no—
70C2×D4×C11—21no—
71C2×D4×C11—41no—
72C2×D4×C11—41no—
73C2×D4×C11—41no—
74C2×D4×C11—41no—
75C2×D4×C11—41no—
76C2×D4×C11—41no—
77C2×D4×C11—41no—
78C2×D4×C11—41no—
79C2×D4×C11—41no—
80C2×D4×C11—81no—
81C2×D4×C11—81no—
82C2×D4×C11—81no—
83C22×C4×C11—21no—
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×C11—41no—
91C22×C4×C11—81no—
92C22×C4×C11C2×D411yescharacteristic
93C22×C4×C11C2×D411yescharacteristic
94C11×SD16—82no—
95C11×D8—82no—
96C2×C8×C11—41no—
97C2×C8×C11—41no—
98C11×C4⋊C4—21no—
99C11×C4⋊C4—21no—
100C11×C4⋊C4—81no—
101C11×C4⋊C4—81no—
102C11×C22⋊C4—21no—
103C11×C22⋊C4—21no—
104C11×C22⋊C4—41no—
105C11×C22⋊C4—41no—
106C11×C22⋊C4—41no—
107C11×C22⋊C4—41no—
108C11×C22⋊C4—41no—
109C11×C22⋊C4—81no—
110C11×C22⋊C4—81no—
111C11×C22⋊C4—81no—
112C11×C22⋊C4—81no—
113C11×C22⋊C4—81no—
114C11×C22⋊C4—81no—
115C11×C22⋊C4—82no—
116#2824C2×C1111yescharacteristic, complemented
117#2044C2×C1111yescharacteristic, complemented
118#1601C2×C1111yescharacteristic, complemented
119#1595C2×C1111yescharacteristic
120#1351C2×C1111yescharacteristic, complemented
121#1343C2×C1111yescharacteristic, complemented
122#1326C2×C1111yescharacteristic, complemented
123C23×C11—21no—
124C23×C11—21no—
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—41no—
134C23×C11—41no—
135C23×C11—41no—
136C23×C11—41no—
137C23×C11—81no—
138C23×C11—81no—
139C23×C11#12011yescharacteristic
140C23×C11#13511yescharacteristic
141C23×C11AGL(1,ℤ/8)11yescharacteristic
142Q8×C11—42no—
143Q8×C11—81no—
144D4×C11—42no—
145D4×C11—81no—
146D4×C11—81no—
147D4×C11—81no—
148D4×C11—81no—
149D4×C11—81no—
150D4×C11—82no—
151D4×C11—82no—
152D4×C11—81no—
153D4×C11—81no—
154C2×C4×C11—21no—
155C2×C4×C11—21no—
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—41no—
170C2×C4×C11—42no—
171C2×C4×C11—41no—
172C2×C4×C11—41no—
173C2×C4×C11—41no—
174C2×C4×C11—41no—
175C2×C4×C11—41no—
176C2×C4×C11—41no—
177C2×C4×C11—81no—
178C2×C4×C11—81no—
179C2×C4×C11—81no—
180C2×C4×C11—81no—
181C8×C11—81no—
182C8×C11—81no—
183#534C22×C1111yescharacteristic
184#448—21no—
185#447—21no—
186C2×#99—21no—
187#400—21no—
188#397—21no—
189#394—21no—
190#394—21no—
191#393—21no—
192#393C22×C1111yescharacteristic
193#392C22×C1111yescharacteristic
194#386—21no—
195#386—21no—
196#385C22×C1111yescharacteristic
197#342C22×C1111yescharacteristic
198#327—21no—
199#327—21no—
200#323C22×C1111yescharacteristic
201#323C22×C1111yescharacteristic
202C22×C11—21no—
203C22×C11—21no—
204C22×C11—21no—
205C22×C11—21no—
206C22×C11—41no—
207C22×C11—41no—
208C22×C11—41no—
209C22×C11—41no—
210C22×C11—81no—
211C22×C11—81no—
212C22×C11—81no—
213C22×C11—81no—
214C22×C11—81no—
215C22×C11—82no—
216C22×C11—81no—
217C22×C11—81no—
218C22×C11—81no—
219C22×C11—81no—
220C22×C11—81no—
221C22×C11—81no—
222C22×C11—161no—
223C22×C11#44911yescharacteristic
224C22×C11#45411yescharacteristic
225C22×C11B(4,𝔽2)11yescharacteristic
226C4×C11—41no—
227C4×C11—41no—
228C4×C11—81no—
229C4×C11—81no—
230C4×C11—81no—
231C4×C11—81no—
232C4×C11—81no—
233C4×C11—81no—
234C4×C11—161no—
235C22×Q8D4×C1111yescharacteristic
236C22×D4—21no—
237C22×D4—21no—
238C22×D4D4×C1111yescharacteristic
239C23×C4D4×C1111yescharacteristic
240C2×SD16—41no—
241C2×D8—41no—
242#123—41no—
243#121—21no—
244#121—21no—
245#120—41no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—21no—
248C2×C22⋊C4—21no—
249C2×C22⋊C4—21no—
250C2×C22⋊C4—21no—
251C2×C22⋊C4—21no—
252C2×C22⋊C4—21no—
253C2×C22⋊C4—21no—
254C2×C22⋊C4—21no—
255C2×C22⋊C4—41no—
256C2×C22⋊C4D4×C1111yescharacteristic
257C2×C22⋊C4C23×C1111yescharacteristic
258#103—41no—
259#102—41no—
260#99—42no—
261C22⋊C8—21no—
262C22⋊C8—21no—
263#95—21no—
264#95—21no—
265#95—21no—
266#95—21no—
267#95—21no—
268#95—41no—
269#95D4×C1111yescharacteristic
270#95D4×C1111yescharacteristic
271C2×C11—21no—
272C2×C11—21no—
273C2×C11—41no—
274C2×C11—41no—
275C2×C11—161no—
276C2×C11—161no—
277C2×C11#159711yescharacteristic
278C2×C11#219911yescharacteristic
279C2×C11#220011yescharacteristic
280C24—21no—
281C24—21no—
282C24C2×D4×C1111yescharacteristic
283C2×Q8—41no—
284C2×Q8—81no—
285C2×D4—21no—
286C2×D4—21no—
287C2×D4—41no—
288C2×D4—41no—
289C2×D4—41no—
290C2×D4—41no—
291C2×D4—41no—
292C2×D4—41no—
293C2×D4—41no—
294C2×D4—41no—
295C2×D4—41no—
296C2×D4—81no—
297C2×D4—81no—
298C2×D4—81no—
299C22×C4—21no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—21no—
304C22×C4—21no—
305C22×C4—41no—
306C22×C4—41no—
307C22×C4—81no—
308C22×C4C2×D4×C1111yescharacteristic
309C22×C4C2×D4×C1111yescharacteristic
310SD16—82no—
311D8—82no—
312C2×C8—41no—
313C2×C8—41no—
314C4⋊C4—21no—
315C4⋊C4—21no—
316C4⋊C4—81no—
317C4⋊C4—81no—
318C22⋊C4—21no—
319C22⋊C4—21no—
320C22⋊C4—41no—
321C22⋊C4—41no—
322C22⋊C4—41no—
323C22⋊C4—41no—
324C22⋊C4—41no—
325C22⋊C4—81no—
326C22⋊C4—81no—
327C22⋊C4—81no—
328C22⋊C4—81no—
329C22⋊C4—81no—
330C22⋊C4—81no—
331C22⋊C4—82no—
332C11#1213611yescharacteristic, direct product factor, Sylow
333C23—21no—
334C23—21no—
335C23—41no—
336C23—41no—
337C23—41no—
338C23—41no—
339C23—41no—
340C23—41no—
341C23—41no—
342C23—41no—
343C23—41no—
344C23—41no—
345C23—41no—
346C23—41no—
347C23—81no—
348C23—81no—
349C23C11×#12011yescharacteristic
350C23C11×#13511yescharacteristic
351C23C11×AGL(1,ℤ/8)11yescharacteristic
352Q8—42no—
353Q8—81no—
354D4—42no—
355D4—81no—
356D4—81no—
357D4—81no—
358D4—81no—
359D4—81no—
360D4—82no—
361D4—82no—
362D4—81no—
363D4—81no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—42no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—81no—
388C2×C4—81no—
389C2×C4—81no—
390C2×C4—81no—
391C8—81no—
392C8—81no—
393C22—21no—
394C22—21no—
395C22—21no—
396C22—21no—
397C22—41no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—81no—
402C22—81no—
403C22—81no—
404C22—81no—
405C22—81no—
406C22—82no—
407C22—81no—
408C22—81no—
409C22—81no—
410C22—81no—
411C22—81no—
412C22—81no—
413C22—161no—
414C22C11×#44911yescharacteristic
415C22C11×#45411yescharacteristic
416C22C11×B(4,𝔽2)11yescharacteristic
417C4—41no—
418C4—41no—
419C4—81no—
420C4—81no—
421C4—81no—
422C4—81no—
423C4—81no—
424C4—81no—
425C4—161no—
426C2—21no—
427C2—21no—
428C2—41no—
429C2—41no—
430C2—161no—
431C2—161no—
432C2C11×#159711yescharacteristic
433C2C11×#219911yescharacteristic
434C2C11×#220011yescharacteristic
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×#2824C2semidirect
2. C11×#2044C2semidirect
3. C11×#1601C2semidirect
5. C11×#1351C2semidirect
6. C11×#1343C2semidirect
7. C11×#1326C2semidirect
63. #12136C11direct (N × H)
116. #2824C2×C11semidirect
117. #2044C2×C11semidirect
118. #1601C2×C11semidirect
120. #1351C2×C11semidirect
121. #1343C2×C11semidirect
122. #1326C2×C11semidirect
332. C11#12136direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#28242
C11×#20442
C11×#16012
C11×#15952
C11×#13512
C11×#13432
C11×#13262
#1213611