Finite Group Databasebeta

← C11×#32700 #14609893

Subgroups — C11×#32700 #14609893

Order 2816.

778 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2104C212yesmaximal, complemented
2C11×#2032C212yesmaximal, complemented
3C11×#2029C211yesmaximal, characteristic, complemented
4C11×#2021C211yesmaximal, characteristic
5C11×#1913C212yesmaximal, complemented
6C11×#1898C212yesmaximal, complemented
7C11×#1889C212yesmaximal, complemented
8C11×#1828C212yesmaximal, complemented
9C11×#1819C211yesmaximal, characteristic, complemented
10C11×#543C2211yescharacteristic
11C11×#534C2211yescharacteristic
12C2×C11×#120C2212yes—
13C11×#518C2212yes—
14C22×C11×C22⋊C4C2211yescharacteristic
15C2×C11×#99C2212yes—
16C2×C11×#99C2212yes—
17C2×C11×#99C2212yes—
18C2×C11×#99C2212yes—
19C11×#379C2211yescharacteristic
20C11×#379C2212yes—
21C11×#379C2211yescharacteristic
22C11×#342C2212yes—
23C11×#342C2212yes—
24C11×#342C2212yes—
25C11×#342C2212yes—
26C11×#342C2212yes—
27C11×#342C2212yes—
28C11×#342C2211yescharacteristic
29C11×#342C2211yescharacteristic
30C11×#342C2212yes—
31C25×C11C2311yescharacteristic
32C22×D4×C11—22no—
33C22×D4×C11C2312yes—
34C23×C4×C11—21no—
35C11×#123—22no—
36C11×C22⋊Q8—42no—
37C11×C22⋊Q8—41no—
38C11×#121—41no—
39C11×#120—22no—
40C11×#120—22no—
41C11×#120—22no—
42C11×#120—42no—
43C4×D4×C11—42no—
44C4×D4×C11—42no—
45C11×#117—22no—
46C2×C11×C22⋊C4—22no—
47C2×C11×C22⋊C4—21no—
48C2×C11×C22⋊C4—22no—
49C2×C11×C22⋊C4—41no—
50C2×C11×C22⋊C4—41no—
51C2×C11×C22⋊C4—41no—
52C2×C11×C22⋊C4—42no—
53C2×C11×C22⋊C4—41no—
54C2×C11×C22⋊C4C2311yescharacteristic
55C2×C11×C22⋊C4C2312yes—
56C2×C11×C22⋊C4C2312yes—
57C2×C11×C22⋊C4C2312yes—
58C2×C11×C22⋊C4C2312yes—
59C2×C11×C22⋊C4C2312yes—
60C2×C11×C22⋊C4C2311yescharacteristic
61C11×#99—42no—
62C11×#99—42no—
63C11×#99—42no—
64C11×#99—42no—
65#32700C1111yesmaximal, characteristic, direct product factor, Sylow
66C24×C11—22no—
67C24×C11—21no—
68C24×C11—21no—
69C24×C11—22no—
70C24×C11—82no—
71C24×C11#4111yescharacteristic
72C24×C11#4111yescharacteristic
73C24×C11#4112yes—
74C24×C11C2411yescharacteristic
75C2×Q8×C11—41no—
76C2×D4×C11—22no—
77C2×D4×C11—22no—
78C2×D4×C11—22no—
79C2×D4×C11—22no—
80C2×D4×C11—22no—
81C2×D4×C11—22no—
82C2×D4×C11—42no—
83C2×D4×C11—42no—
84C2×D4×C11—41no—
85C2×D4×C11—84no—
86C22×C4×C11—22no—
87C22×C4×C11—22no—
88C22×C4×C11—22no—
89C22×C4×C11—22no—
90C22×C4×C11—21no—
91C22×C4×C11—22no—
92C22×C4×C11—21no—
93C22×C4×C11—41no—
94C22×C4×C11—41no—
95C22×C4×C11—42no—
96C22×C4×C11—82no—
97C22×C4×C11#4112yes—
98C11×C4⋊C4—41no—
99C11×C4⋊C4—42no—
100C11×C4⋊C4—43no—
101C11×C22⋊C4—22no—
102C11×C22⋊C4—22no—
103C11×C22⋊C4—22no—
104C11×C22⋊C4—22no—
105C11×C22⋊C4—22no—
106C11×C22⋊C4—22no—
107C11×C22⋊C4—22no—
108C11×C22⋊C4—22no—
109C11×C22⋊C4—22no—
110C11×C22⋊C4—22no—
111C11×C22⋊C4—22no—
112C11×C22⋊C4—22no—
113C11×C22⋊C4—42no—
114C11×C22⋊C4—42no—
115C11×C22⋊C4—42no—
116C11×C22⋊C4—42no—
117C11×C22⋊C4—42no—
118C11×C22⋊C4—82no—
119C11×C22⋊C4—84no—
120C11×C22⋊C4—82no—
121C42×C11—42no—
122#2104C2×C1112yescomplemented
123#2032C2×C1112yescomplemented
124#2029C2×C1111yescharacteristic, complemented
125#2021C2×C1111yescharacteristic
126#1913C2×C1112yescomplemented
127#1898C2×C1112yescomplemented
128#1889C2×C1112yescomplemented
129#1828C2×C1112yescomplemented
130#1819C2×C1111yescharacteristic, complemented
131C23×C11—21no—
132C23×C11—22no—
133C23×C11—21no—
134C23×C11—22no—
135C23×C11—22no—
136C23×C11—22no—
137C23×C11—22no—
138C23×C11—42no—
139C23×C11—42no—
140C23×C11—42no—
141C23×C11—44no—
142C23×C11—44no—
143C23×C11—42no—
144C23×C11—41no—
145C23×C11—41no—
146C23×C11—81no—
147C23×C11—81no—
148C23×C11—81no—
149C23×C11—81no—
150C23×C11—82no—
151C23×C11—82no—
152C23×C11—82no—
153C23×C11C2×#4112yes—
154C23×C11C2×#4111yescharacteristic
155C23×C11H(5,𝔽2)11yescharacteristic
156C23×C11H(5,𝔽2)12yes—
157C23×C11H(5,𝔽2)11yescharacteristic
158Q8×C11—161no—
159D4×C11—42no—
160D4×C11—42no—
161D4×C11—42no—
162D4×C11—42no—
163D4×C11—84no—
164D4×C11—84no—
165D4×C11—161no—
166C2×C4×C11—22no—
167C2×C4×C11—22no—
168C2×C4×C11—22no—
169C2×C4×C11—42no—
170C2×C4×C11—42no—
171C2×C4×C11—42no—
172C2×C4×C11—41no—
173C2×C4×C11—42no—
174C2×C4×C11—42no—
175C2×C4×C11—41no—
176C2×C4×C11—82no—
177C2×C4×C11—82no—
178C2×C4×C11—82no—
179C2×C4×C11—82no—
180C2×C4×C11—81no—
181C2×C4×C11—81no—
182C2×C4×C11—82no—
183C2×C4×C11—82no—
184C2×C4×C11—82no—
185C2×C4×C11—162no—
186#543C22×C1111yescharacteristic
187#534C22×C1111yescharacteristic
188C2×#120C22×C1112yes—
189#518C22×C1112yes—
190C22×C22⋊C4C22×C1111yescharacteristic
191C2×#99C22×C1112yes—
192C2×#99C22×C1112yes—
193C2×#99C22×C1112yes—
194C2×#99C22×C1112yes—
195#379C22×C1111yescharacteristic
196#379C22×C1111yescharacteristic
197#379C22×C1112yes—
198#342C22×C1112yes—
199#342C22×C1112yes—
200#342C22×C1111yescharacteristic
201#342C22×C1112yes—
202#342C22×C1112yes—
203#342C22×C1111yescharacteristic
204#342C22×C1112yes—
205#342C22×C1112yes—
206#342C22×C1112yes—
207C22×C11—22no—
208C22×C11—24no—
209C22×C11—41no—
210C22×C11—41no—
211C22×C11—42no—
212C22×C11—41no—
213C22×C11—42no—
214C22×C11—41no—
215C22×C11—42no—
216C22×C11—42no—
217C22×C11—41no—
218C22×C11—41no—
219C22×C11—42no—
220C22×C11—41no—
221C22×C11—42no—
222C22×C11—41no—
223C22×C11—82no—
224C22×C11—84no—
225C22×C11—82no—
226C22×C11—82no—
227C22×C11—82no—
228C22×C11—82no—
229C22×C11#53812yes—
230C22×C11#53811yescharacteristic
231C22×C11#55111yescharacteristic
232C22×C11#55112yes—
233C22×C11#56011yescharacteristic
234C4×C11—42no—
235C4×C11—82no—
236C4×C11—82no—
237C4×C11—82no—
238C4×C11—82no—
239C4×C11—81no—
240C4×C11—81no—
241C4×C11—82no—
242C25C23×C1111yescharacteristic
243C22×D4—22no—
244C22×D4C23×C1112yes—
245C23×C4—21no—
246#123—22no—
247C22⋊Q8—42no—
248C22⋊Q8—41no—
249#121—41no—
250#120—22no—
251#120—22no—
252#120—22no—
253#120—42no—
254C4×D4—42no—
255C4×D4—42no—
256#117—22no—
257C2×C22⋊C4—22no—
258C2×C22⋊C4—21no—
259C2×C22⋊C4—22no—
260C2×C22⋊C4—41no—
261C2×C22⋊C4—41no—
262C2×C22⋊C4—41no—
263C2×C22⋊C4—42no—
264C2×C22⋊C4—41no—
265C2×C22⋊C4C23×C1112yes—
266C2×C22⋊C4C23×C1112yes—
267C2×C22⋊C4C23×C1112yes—
268C2×C22⋊C4C23×C1112yes—
269C2×C22⋊C4C23×C1111yescharacteristic
270C2×C22⋊C4C23×C1111yescharacteristic
271C2×C22⋊C4C23×C1112yes—
272#99—42no—
273#99—42no—
274#99—42no—
275#99—42no—
276C2×C11—21no—
277C2×C11—21no—
278C2×C11—22no—
279C2×C11—22no—
280C2×C11—21no—
281C2×C11—42no—
282C2×C11—81no—
283C2×C11—82no—
284C2×C11#276011yescharacteristic
285C24—22no—
286C24—21no—
287C24—21no—
288C24—22no—
289C24—82no—
290C24C11×#4111yescharacteristic
291C24C11×#4111yescharacteristic
292C24C11×#4112yes—
293C24C24×C1111yescharacteristic
294C2×Q8—41no—
295C2×D4—22no—
296C2×D4—22no—
297C2×D4—22no—
298C2×D4—22no—
299C2×D4—22no—
300C2×D4—22no—
301C2×D4—42no—
302C2×D4—42no—
303C2×D4—41no—
304C2×D4—84no—
305C22×C4—22no—
306C22×C4—22no—
307C22×C4—22no—
308C22×C4—22no—
309C22×C4—21no—
310C22×C4—22no—
311C22×C4—21no—
312C22×C4—41no—
313C22×C4—41no—
314C22×C4—42no—
315C22×C4—82no—
316C22×C4C11×#4112yes—
317C4⋊C4—41no—
318C4⋊C4—42no—
319C4⋊C4—43no—
320C22⋊C4—22no—
321C22⋊C4—22no—
322C22⋊C4—22no—
323C22⋊C4—22no—
324C22⋊C4—22no—
325C22⋊C4—22no—
326C22⋊C4—22no—
327C22⋊C4—22no—
328C22⋊C4—22no—
329C22⋊C4—22no—
330C22⋊C4—22no—
331C22⋊C4—22no—
332C22⋊C4—42no—
333C22⋊C4—42no—
334C22⋊C4—42no—
335C22⋊C4—42no—
336C22⋊C4—42no—
337C22⋊C4—82no—
338C22⋊C4—84no—
339C22⋊C4—82no—
340C42—42no—
341C11#3270011yescharacteristic, direct product factor, Sylow
342C23—21no—
343C23—22no—
344C23—21no—
345C23—22no—
346C23—22no—
347C23—22no—
348C23—22no—
349C23—42no—
350C23—42no—
351C23—42no—
352C23—44no—
353C23—44no—
354C23—42no—
355C23—41no—
356C23—41no—
357C23—81no—
358C23—81no—
359C23—81no—
360C23—81no—
361C23—82no—
362C23—82no—
363C23—82no—
364C23C2×C11×#4112yes—
365C23C2×C11×#4111yescharacteristic
366C23C11×H(5,𝔽2)11yescharacteristic
367C23C11×H(5,𝔽2)12yes—
368C23C11×H(5,𝔽2)11yescharacteristic
369Q8—161no—
370D4—42no—
371D4—42no—
372D4—42no—
373D4—42no—
374D4—84no—
375D4—84no—
376D4—161no—
377C2×C4—22no—
378C2×C4—22no—
379C2×C4—22no—
380C2×C4—42no—
381C2×C4—42no—
382C2×C4—42no—
383C2×C4—41no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—41no—
387C2×C4—82no—
388C2×C4—82no—
389C2×C4—82no—
390C2×C4—82no—
391C2×C4—81no—
392C2×C4—81no—
393C2×C4—82no—
394C2×C4—82no—
395C2×C4—82no—
396C2×C4—162no—
397C22—22no—
398C22—24no—
399C22—41no—
400C22—41no—
401C22—42no—
402C22—41no—
403C22—42no—
404C22—41no—
405C22—42no—
406C22—42no—
407C22—41no—
408C22—41no—
409C22—42no—
410C22—41no—
411C22—42no—
412C22—41no—
413C22—82no—
414C22—84no—
415C22—82no—
416C22—82no—
417C22—82no—
418C22—82no—
419C22C11×#53812yes—
420C22C11×#53811yescharacteristic
421C22C11×#55111yescharacteristic
422C22C11×#55112yes—
423C22C11×#56011yescharacteristic
424C4—42no—
425C4—82no—
426C4—82no—
427C4—82no—
428C4—82no—
429C4—81no—
430C4—81no—
431C4—82no—
432C2—21no—
433C2—21no—
434C2—22no—
435C2—22no—
436C2—21no—
437C2—42no—
438C2—81no—
439C2—82no—
440C2C11×#276011yescharacteristic
subgroupG/H
center, socleC2×C11#2760
commutator, Frattini, cosocleC24C24×C11
prime radicalC11×#2021C2
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C2×C11 ◁ C24×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#2104C2semidirect
2. C11×#2032C2semidirect
3. C11×#2029C2semidirect
5. C11×#1913C2semidirect
6. C11×#1898C2semidirect
7. C11×#1889C2semidirect
8. C11×#1828C2semidirect
9. C11×#1819C2semidirect
65. #32700C11direct (N × H)
122. #2104C2×C11semidirect
123. #2032C2×C11semidirect
124. #2029C2×C11semidirect
126. #1913C2×C11semidirect
127. #1898C2×C11semidirect
128. #1889C2×C11semidirect
129. #1828C2×C11semidirect
130. #1819C2×C11semidirect
341. C11#32700direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#21042
C11×#20322
C11×#20292
C11×#20212
C11×#19132
C11×#18982
C11×#18892
C11×#18282
C11×#18192
#3270011