Finite Group Databasebeta

← C11×#12266 #14589459

Subgroups — C11×#12266 #14589459

Order 2816.

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

normal subgroups only

This group has 592 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×#2670C211yesmaximal, characteristic
2C11×#2029C211yesmaximal, characteristic, complemented
3C11×#1602C211yesmaximal, characteristic, complemented
4C11×#1596C211yesmaximal, characteristic, complemented
5C11×#1351C211yesmaximal, characteristic, complemented
6C11×#1343C211yesmaximal, characteristic, complemented
7C11×#1316C211yesmaximal, characteristic, complemented
8C11×#543C2211yescharacteristic
9C2×C11×#124—21no—
10C2×C11×#120—21no—
11C11×#451—21no—
12C11×#450—21no—
13C11×#394—21no—
14C11×#393C2211yescharacteristic
15C11×#392—21no—
16C11×#392C2211yescharacteristic
17C11×#390—21no—
18C11×#388—21no—
19C11×#379—21no—
20C11×#379C2211yescharacteristic
21C11×#342—21no—
22C11×#342C2211yescharacteristic
23C11×#328—21no—
24C11×#328—21no—
25C11×#323C2211yescharacteristic
26C11×#323C2211yescharacteristic
27C25×C11D411yescharacteristic
28C22×Q8×C11D411yescharacteristic
29C22×D4×C11—21no—
30C22×D4×C11—21no—
31C22×D4×C11—21no—
32C22×D4×C11D411yescharacteristic
33C2×C11×Q16—41no—
34C2×C11×SD16—41no—
35C11×#124—44no—
36C11×C22⋊Q8—21no—
37C11×C22⋊Q8—21no—
38C11×C22⋊Q8—41no—
39C11×C22⋊Q8—41no—
40C11×#120—44no—
41C2×C11×C4⋊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—21no—
48C2×C11×C22⋊C4—21no—
49C2×C11×C22⋊C4—21no—
50C2×C11×C22⋊C4—21no—
51C2×C11×C22⋊C4—21no—
52C2×C11×C22⋊C4—41no—
53C2×C11×C22⋊C4—41no—
54C2×C11×C22⋊C4D411yescharacteristic
55C2×C11×C22⋊C4C2311yescharacteristic
56C2×C42×C11—21no—
57C11×#103—41no—
58C11×#102—41no—
59C11×C22⋊C8—21no—
60C11×C22⋊C8—21no—
61C11×#95—21no—
62C11×#95D411yescharacteristic
63C11×#95D411yescharacteristic
64#12266C1111yesmaximal, characteristic, direct product factor, Sylow
65C24×C11—21no—
66C24×C11—21no—
67C24×C11—21no—
68C24×C11—21no—
69C24×C11—41no—
70C24×C11—42no—
71C24×C11—41no—
72C24×C11—81no—
73C24×C11C2×D411yescharacteristic
74C2×Q8×C11—21no—
75C2×Q8×C11—21no—
76C2×Q8×C11—42no—
77C2×Q8×C11—41no—
78C2×D4×C11—41no—
79C2×D4×C11—42no—
80C2×D4×C11—42no—
81C2×D4×C11—42no—
82C2×D4×C11—42no—
83C2×D4×C11—41no—
84C2×D4×C11—41no—
85C2×D4×C11—81no—
86C2×D4×C11—81no—
87C2×D4×C11—81no—
88C2×D4×C11—81no—
89C2×D4×C11—81no—
90C22×C4×C11—21no—
91C22×C4×C11—21no—
92C22×C4×C11—21no—
93C22×C4×C11—21no—
94C22×C4×C11—21no—
95C22×C4×C11—21no—
96C22×C4×C11—41no—
97C22×C4×C11C2×D411yescharacteristic
98C22×C4×C11C2×D411yescharacteristic
99C11×Q16—82no—
100C11×SD16—82no—
101C2×C8×C11—41no—
102C2×C8×C11—41no—
103C11×C4⋊C4—21no—
104C11×C4⋊C4—21no—
105C11×C4⋊C4—41no—
106C11×C4⋊C4—41no—
107C11×C4⋊C4—81no—
108C11×C22⋊C4—24no—
109C11×C22⋊C4—41no—
110C11×C22⋊C4—42no—
111C11×C22⋊C4—42no—
112C11×C22⋊C4—42no—
113C11×C22⋊C4—42no—
114C11×C22⋊C4—41no—
115C11×C22⋊C4—42no—
116C11×C22⋊C4—41no—
117C11×C22⋊C4—41no—
118C11×C22⋊C4—41no—
119C11×C22⋊C4—41no—
120C11×C22⋊C4—81no—
121C11×C22⋊C4—81no—
122C11×C22⋊C4—82no—
123C11×C22⋊C4—82no—
124C42×C11—42no—
125#2670C2×C1111yescharacteristic
126#2029C2×C1111yescharacteristic, complemented
127#1602C2×C1111yescharacteristic, complemented
128#1596C2×C1111yescharacteristic, complemented
129#1351C2×C1111yescharacteristic, complemented
130#1343C2×C1111yescharacteristic, complemented
131#1316C2×C1111yescharacteristic, complemented
132C23×C11—21no—
133C23×C11—21no—
134C23×C11—22no—
135C23×C11—41no—
136C23×C11—41no—
137C23×C11—41no—
138C23×C11—41no—
139C23×C11—41no—
140C23×C11—42no—
141C23×C11—41no—
142C23×C11—41no—
143C23×C11—41no—
144C23×C11—41no—
145C23×C11—42no—
146C23×C11—42no—
147C23×C11—41no—
148C23×C11—41no—
149C23×C11—41no—
150C23×C11—41no—
151C23×C11—41no—
152C23×C11—41no—
153C23×C11—81no—
154C23×C11—82no—
155C23×C11—81no—
156C23×C11—82no—
157C23×C11—84no—
158C23×C11—81no—
159C23×C11#12011yescharacteristic
160C23×C11#13511yescharacteristic
161C23×C11#13711yescharacteristic
162Q8×C11—42no—
163Q8×C11—81no—
164Q8×C11—81no—
165Q8×C11—81no—
166D4×C11—42no—
167D4×C11—82no—
168D4×C11—82no—
169D4×C11—84no—
170D4×C11—81no—
171D4×C11—84no—
172C2×C4×C11—22no—
173C2×C4×C11—22no—
174C2×C4×C11—21no—
175C2×C4×C11—21no—
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—41no—
184C2×C4×C11—41no—
185C2×C4×C11—41no—
186C2×C4×C11—41no—
187C2×C4×C11—41no—
188C2×C4×C11—41no—
189C2×C4×C11—41no—
190C2×C4×C11—81no—
191C2×C4×C11—81no—
192C2×C4×C11—81no—
193C2×C4×C11—81no—
194C2×C4×C11—81no—
195C8×C11—81no—
196C8×C11—81no—
197#543C22×C1111yescharacteristic
198C2×#124—21no—
199C2×#120—21no—
200#451—21no—
201#450—21no—
202#394—21no—
203#393C22×C1111yescharacteristic
204#392—21no—
205#392C22×C1111yescharacteristic
206#390—21no—
207#388—21no—
208#379—21no—
209#379C22×C1111yescharacteristic
210#342—21no—
211#342C22×C1111yescharacteristic
212#328—21no—
213#328—21no—
214#323C22×C1111yescharacteristic
215#323C22×C1111yescharacteristic
216C22×C11—21no—
217C22×C11—21no—
218C22×C11—21no—
219C22×C11—21no—
220C22×C11—41no—
221C22×C11—41no—
222C22×C11—42no—
223C22×C11—42no—
224C22×C11—41no—
225C22×C11—41no—
226C22×C11—44no—
227C22×C11—42no—
228C22×C11—81no—
229C22×C11—81no—
230C22×C11—81no—
231C22×C11—81no—
232C22×C11—81no—
233C22×C11—81no—
234C22×C11—81no—
235C22×C11—82no—
236C22×C11—82no—
237C22×C11—82no—
238C22×C11—81no—
239C22×C11—81no—
240C22×C11—81no—
241C22×C11—81no—
242C22×C11—81no—
243C22×C11#45211yescharacteristic
244C22×C11#45511yescharacteristic
245C22×C11B(4,𝔽2)11yescharacteristic
246C4×C11—42no—
247C4×C11—42no—
248C4×C11—41no—
249C4×C11—41no—
250C4×C11—81no—
251C4×C11—81no—
252C4×C11—81no—
253C4×C11—81no—
254C4×C11—161no—
255C25D4×C1111yescharacteristic
256C22×Q8D4×C1111yescharacteristic
257C22×D4—21no—
258C22×D4—21no—
259C22×D4—21no—
260C22×D4D4×C1111yescharacteristic
261C2×Q16—41no—
262C2×SD16—41no—
263#124—44no—
264C22⋊Q8—21no—
265C22⋊Q8—21no—
266C22⋊Q8—41no—
267C22⋊Q8—41no—
268#120—44no—
269C2×C4⋊C4—21no—
270C2×C22⋊C4—21no—
271C2×C22⋊C4—21no—
272C2×C22⋊C4—21no—
273C2×C22⋊C4—21no—
274C2×C22⋊C4—21no—
275C2×C22⋊C4—21no—
276C2×C22⋊C4—21no—
277C2×C22⋊C4—21no—
278C2×C22⋊C4—21no—
279C2×C22⋊C4—21no—
280C2×C22⋊C4—41no—
281C2×C22⋊C4—41no—
282C2×C22⋊C4D4×C1111yescharacteristic
283C2×C22⋊C4C23×C1111yescharacteristic
284C2×C42—21no—
285#103—41no—
286#102—41no—
287C22⋊C8—21no—
288C22⋊C8—21no—
289#95—21no—
290#95D4×C1111yescharacteristic
291#95D4×C1111yescharacteristic
292C2×C11—21no—
293C2×C11—21no—
294C2×C11—41no—
295C2×C11—41no—
296C2×C11—82no—
297C2×C11—161no—
298C2×C11#160611yescharacteristic
299C2×C11#219611yescharacteristic
300C2×C11#219911yescharacteristic
301C24—21no—
302C24—21no—
303C24—21no—
304C24—21no—
305C24—41no—
306C24—42no—
307C24—41no—
308C24—81no—
309C24C2×D4×C1111yescharacteristic
310C2×Q8—21no—
311C2×Q8—21no—
312C2×Q8—42no—
313C2×Q8—41no—
314C2×D4—41no—
315C2×D4—42no—
316C2×D4—42no—
317C2×D4—42no—
318C2×D4—42no—
319C2×D4—41no—
320C2×D4—41no—
321C2×D4—81no—
322C2×D4—81no—
323C2×D4—81no—
324C2×D4—81no—
325C2×D4—81no—
326C22×C4—21no—
327C22×C4—21no—
328C22×C4—21no—
329C22×C4—21no—
330C22×C4—21no—
331C22×C4—21no—
332C22×C4—41no—
333C22×C4C2×D4×C1111yescharacteristic
334C22×C4C2×D4×C1111yescharacteristic
335Q16—82no—
336SD16—82no—
337C2×C8—41no—
338C2×C8—41no—
339C4⋊C4—21no—
340C4⋊C4—21no—
341C4⋊C4—41no—
342C4⋊C4—41no—
343C4⋊C4—81no—
344C22⋊C4—24no—
345C22⋊C4—41no—
346C22⋊C4—42no—
347C22⋊C4—42no—
348C22⋊C4—42no—
349C22⋊C4—42no—
350C22⋊C4—41no—
351C22⋊C4—42no—
352C22⋊C4—41no—
353C22⋊C4—41no—
354C22⋊C4—41no—
355C22⋊C4—41no—
356C22⋊C4—81no—
357C22⋊C4—81no—
358C22⋊C4—82no—
359C22⋊C4—82no—
360C42—42no—
361C11#1226611yescharacteristic, direct product factor, Sylow
362C23—21no—
363C23—21no—
364C23—22no—
365C23—41no—
366C23—41no—
367C23—41no—
368C23—41no—
369C23—41no—
370C23—42no—
371C23—41no—
372C23—41no—
373C23—41no—
374C23—41no—
375C23—42no—
376C23—42no—
377C23—41no—
378C23—41no—
379C23—41no—
380C23—41no—
381C23—41no—
382C23—41no—
383C23—81no—
384C23—82no—
385C23—81no—
386C23—82no—
387C23—84no—
388C23—81no—
389C23C11×#12011yescharacteristic
390C23C11×#13511yescharacteristic
391C23C11×#13711yescharacteristic
392Q8—42no—
393Q8—81no—
394Q8—81no—
395Q8—81no—
396D4—42no—
397D4—82no—
398D4—82no—
399D4—84no—
400D4—81no—
401D4—84no—
402C2×C4—22no—
403C2×C4—22no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—81no—
421C2×C4—81no—
422C2×C4—81no—
423C2×C4—81no—
424C2×C4—81no—
425C8—81no—
426C8—81no—
427C22—21no—
428C22—21no—
429C22—21no—
430C22—21no—
431C22—41no—
432C22—41no—
433C22—42no—
434C22—42no—
435C22—41no—
436C22—41no—
437C22—44no—
438C22—42no—
439C22—81no—
440C22—81no—
441C22—81no—
442C22—81no—
443C22—81no—
444C22—81no—
445C22—81no—
446C22—82no—
447C22—82no—
448C22—82no—
449C22—81no—
450C22—81no—
451C22—81no—
452C22—81no—
453C22—81no—
454C22C11×#45211yescharacteristic
455C22C11×#45511yescharacteristic
456C22C11×B(4,𝔽2)11yescharacteristic
457C4—42no—
458C4—41no—
459C4—42no—
460C4—41no—
461C4—81no—
462C4—81no—
463C4—81no—
464C4—81no—
465C4—161no—
466C2—21no—
467C2—21no—
468C2—41no—
469C2—41no—
470C2—82no—
471C2—161no—
472C2C11×#160611yescharacteristic
473C2C11×#219611yescharacteristic
474C2C11×#219911yescharacteristic
subgroupG/H
center, socleC22×C11B(4,𝔽2)
commutator, Frattini, cosocleC2×C22⋊C4C23×C11
prime radicalC11×#2670C2
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×#2029C2semidirect
3. C11×#1602C2semidirect
4. C11×#1596C2semidirect
5. C11×#1351C2semidirect
6. C11×#1343C2semidirect
7. C11×#1316C2semidirect
64. #12266C11direct (N × H)
126. #2029C2×C11semidirect
127. #1602C2×C11semidirect
128. #1596C2×C11semidirect
129. #1351C2×C11semidirect
130. #1343C2×C11semidirect
131. #1316C2×C11semidirect
361. C11#12266direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#26702
C11×#20292
C11×#16022
C11×#15962
C11×#13512
C11×#13432
C11×#13162
#1226611