Finite Group Databasebeta

← C11×#13305 #14590498

Subgroups — C11×#13305 #14590498

Order 2816.

618 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×SD32C211yesmaximal, characteristic, complemented
2C2×C11×#467C211yesmaximal, characteristic, complemented
3C2×C11×#466C211yesmaximal, characteristic
4C2×C11×#358C211yesmaximal, characteristic, complemented
5C2×C11×#357C211yesmaximal, characteristic, complemented
6C2×C11×C22⋊C16C211yesmaximal, characteristic, complemented
7C11×#1380C211yesmaximal, characteristic, complemented
8C22×C11×Q16C2211yescharacteristic
9C22×C11×D8C2211yescharacteristic
10C23×C8×C11C2211yescharacteristic
11C2×C11×C22⋊Q8—21no—
12C2×C11×#121—21no—
13C2×C11×SD32—22no—
14C2×C11×SD32—22no—
15C2×C11×SD32—22no—
16C22×C11×C16C2211yescharacteristic
17C22×C11×C16C2211yescharacteristic
18C11×#467—22no—
19C11×#467—22no—
20C11×#466—22no—
21C11×#466—22no—
22C2×C11×#107C2211yescharacteristic
23C2×C11×#107C2211yescharacteristic
24C2×C11×#103—21no—
25C2×C11×#102—21no—
26C11×#358—22no—
27C11×#357—22no—
28C11×C22⋊C16—22no—
29C22×Q8×C11—21no—
30C22×D4×C11—21no—
31C22×D4×C11—41no—
32C23×C4×C11D411yescharacteristic
33C2×C11×Q16—21no—
34C2×C11×Q16—21no—
35C2×C11×Q16—21no—
36C2×C11×Q16—21no—
37C2×C11×Q16—21no—
38C2×C11×Q16D412yescomplemented
39C2×C11×D8—21no—
40C2×C11×D8—21no—
41C2×C11×D8—21no—
42C2×C11×D8—21no—
43C2×C11×D8—21no—
44C2×C11×D8D412yes—
45C22×C8×C11—21no—
46C22×C8×C11—21no—
47C22×C8×C11—21no—
48C22×C8×C11—21no—
49C22×C8×C11—21no—
50C22×C8×C11—21no—
51C22×C8×C11D411yescharacteristic
52C22×C8×C11C2311yescharacteristic
53C11×C22⋊Q8—24no—
54C11×C22⋊Q8—42no—
55C11×#121—24no—
56C11×#121—42no—
57C2×C11×C4⋊C4—21no—
58C2×C11×C4⋊C4—21no—
59C2×C11×C4⋊C4—41no—
60C2×C11×C22⋊C4—41no—
61C2×C11×C22⋊C4—41no—
62C11×SD32—28no—
63C2×C11×C16—21no—
64C2×C11×C16—21no—
65C2×C11×C16—21no—
66C2×C11×C16—21no—
67C2×C11×C16—21no—
68C2×C11×C16D412yescomplemented
69C11×#107—21no—
70C11×#107—21no—
71C11×#107D412yes—
72C11×#107D412yescomplemented
73C11×#103—24no—
74C11×#102—24no—
75#13305C1111yesmaximal, characteristic, direct product factor, Sylow
76C24×C11—41no—
77C24×C11D811yescharacteristic
78C2×Q8×C11—22no—
79C2×Q8×C11—41no—
80C2×Q8×C11—41no—
81C2×Q8×C11—41no—
82C2×Q8×C11—41no—
83C2×Q8×C11—41no—
84C2×D4×C11—22no—
85C2×D4×C11—44no—
86C2×D4×C11—41no—
87C2×D4×C11—41no—
88C2×D4×C11—41no—
89C2×D4×C11—41no—
90C2×D4×C11—41no—
91C2×D4×C11—82no—
92C2×D4×C11—82no—
93C22×C4×C11—21no—
94C22×C4×C11—21no—
95C22×C4×C11—21no—
96C22×C4×C11—21no—
97C22×C4×C11—21no—
98C22×C4×C11—21no—
99C22×C4×C11—41no—
100C22×C4×C11—41no—
101C22×C4×C11—41no—
102C22×C4×C11D811yescharacteristic
103C22×C4×C11C2×D411yescharacteristic
104C11×Q16—22no—
105C11×Q16—22no—
106C11×Q16—41no—
107C11×Q16—41no—
108C11×D8—22no—
109C11×D8—22no—
110C11×D8—41no—
111C11×D8—41no—
112C2×C8×C11—21no—
113C2×C8×C11—21no—
114C2×C8×C11—21no—
115C2×C8×C11—41no—
116C2×C8×C11—41no—
117C2×C8×C11—41no—
118C2×C8×C11—41no—
119C2×C8×C11C2×D411yescharacteristic
120C2×C8×C11C2×D411yescharacteristic
121C2×C8×C11C2×D411yescharacteristic
122C2×C8×C11C2×D411yescharacteristic
123C2×C8×C11C2×D411yescharacteristic
124C2×C8×C11#4111yescharacteristic
125C11×C4⋊C4—22no—
126C11×C4⋊C4—22no—
127C11×C4⋊C4—44no—
128C11×C4⋊C4—41no—
129C11×C4⋊C4—41no—
130C11×C22⋊C4—44no—
131C11×C22⋊C4—44no—
132C11×C16—22no—
133C11×C16—41no—
134C22×SD32C2×C1111yescharacteristic, complemented
135C2×#467C2×C1111yescharacteristic, complemented
136C2×#466C2×C1111yescharacteristic
137C2×#358C2×C1111yescharacteristic, complemented
138C2×#357C2×C1111yescharacteristic, complemented
139C2×C22⋊C16C2×C1111yescharacteristic, complemented
140#1380C2×C1111yescharacteristic, complemented
141C23×C11—21no—
142C23×C11—21no—
143C23×C11—21no—
144C23×C11—21no—
145C23×C11—21no—
146C23×C11—21no—
147C23×C11—42no—
148C23×C11—81no—
149C23×C11—81no—
150C23×C11—81no—
151C23×C11—81no—
152C23×C11—81no—
153C23×C11—81no—
154C23×C11SD3212yescomplemented
155C23×C11C2×D811yescharacteristic
156Q8×C11—42no—
157Q8×C11—42no—
158Q8×C11—81no—
159Q8×C11—81no—
160D4×C11—42no—
161D4×C11—42no—
162D4×C11—88no—
163D4×C11—81no—
164D4×C11—81no—
165C2×C4×C11—21no—
166C2×C4×C11—21no—
167C2×C4×C11—21no—
168C2×C4×C11—41no—
169C2×C4×C11—41no—
170C2×C4×C11—41no—
171C2×C4×C11—41no—
172C2×C4×C11—42no—
173C2×C4×C11—42no—
174C2×C4×C11—42no—
175C2×C4×C11—81no—
176C2×C4×C11—81no—
177C2×C4×C11—81no—
178C2×C4×C11—81no—
179C2×C4×C11—81no—
180C2×C4×C11—81no—
181C2×C4×C11#12011yescharacteristic
182C2×C4×C11#12011yescharacteristic
183C2×C4×C11#12111yescharacteristic
184C2×C4×C11#13511yescharacteristic
185C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
186C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
187C8×C11—41no—
188C8×C11#12011yescharacteristic
189C8×C11#12111yescharacteristic
190C8×C11#12111yescharacteristic
191C8×C11#12711yescharacteristic
192C22×Q16C22×C1111yescharacteristic
193C22×D8C22×C1111yescharacteristic
194C23×C8C22×C1111yescharacteristic
195C2×C22⋊Q8—21no—
196C2×#121—21no—
197C2×SD32—22no—
198C2×SD32—22no—
199C2×SD32—22no—
200C22×C16C22×C1111yescharacteristic
201C22×C16C22×C1111yescharacteristic
202#467—22no—
203#467—22no—
204#466—22no—
205#466—22no—
206C2×#107C22×C1111yescharacteristic
207C2×#107C22×C1111yescharacteristic
208C2×#103—21no—
209C2×#102—21no—
210#358—22no—
211#357—22no—
212C22⋊C16—22no—
213C22×C11—22no—
214C22×C11—22no—
215C22×C11—22no—
216C22×C11—41no—
217C22×C11—41no—
218C22×C11—41no—
219C22×C11—41no—
220C22×C11—82no—
221C22×C11—82no—
222C22×C11—82no—
223C22×C11—161no—
224C22×C11—161no—
225C22×C11—161no—
226C22×C11—161no—
227C22×C11#44711yescharacteristic
228C22×C11#44711yescharacteristic
229C22×C11#46611yescharacteristic
230C22×C11C2×SD3211yescharacteristic
231C22×C11#50811yescharacteristic
232C22×C11#50911yescharacteristic
233C22×C11#51011yescharacteristic
234C4×C11—41no—
235C4×C11—82no—
236C4×C11—82no—
237C4×C11—82no—
238C4×C11#39211yescharacteristic
239C4×C11#44911yescharacteristic
240C4×C11#44911yescharacteristic
241C4×C11#46911yescharacteristic
242C22×Q8—21no—
243C22×D4—21no—
244C22×D4—41no—
245C23×C4D4×C1111yescharacteristic
246C2×Q16—21no—
247C2×Q16—21no—
248C2×Q16—21no—
249C2×Q16—21no—
250C2×Q16—21no—
251C2×Q16D4×C1112yescomplemented
252C2×D8—21no—
253C2×D8—21no—
254C2×D8—21no—
255C2×D8—21no—
256C2×D8—21no—
257C2×D8D4×C1112yes—
258C22×C8—21no—
259C22×C8—21no—
260C22×C8—21no—
261C22×C8—21no—
262C22×C8—21no—
263C22×C8—21no—
264C22×C8D4×C1111yescharacteristic
265C22×C8C23×C1111yescharacteristic
266C22⋊Q8—24no—
267C22⋊Q8—42no—
268#121—24no—
269#121—42no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—41no—
273C2×C22⋊C4—41no—
274C2×C22⋊C4—41no—
275SD32—28no—
276C2×C16—21no—
277C2×C16—21no—
278C2×C16—21no—
279C2×C16—21no—
280C2×C16—21no—
281C2×C16D4×C1112yescomplemented
282#107—21no—
283#107—21no—
284#107D4×C1112yes—
285#107D4×C1112yescomplemented
286#103—24no—
287#102—24no—
288C2×C11—42no—
289C2×C11—162no—
290C2×C11#199911yescharacteristic
291C2×C11#218511yescharacteristic
292C2×C11#218611yescharacteristic
293C2×C11#218711yescharacteristic
294C2×C11#218911yescharacteristic
295C2×C11#221711yescharacteristic
296C2×C11#222011yescharacteristic
297C24—41no—
298C24C11×D811yescharacteristic
299C2×Q8—22no—
300C2×Q8—41no—
301C2×Q8—41no—
302C2×Q8—41no—
303C2×Q8—41no—
304C2×Q8—41no—
305C2×D4—22no—
306C2×D4—44no—
307C2×D4—41no—
308C2×D4—41no—
309C2×D4—41no—
310C2×D4—41no—
311C2×D4—41no—
312C2×D4—82no—
313C2×D4—82no—
314C22×C4—21no—
315C22×C4—21no—
316C22×C4—21no—
317C22×C4—21no—
318C22×C4—21no—
319C22×C4—21no—
320C22×C4—41no—
321C22×C4—41no—
322C22×C4—41no—
323C22×C4C11×D811yescharacteristic
324C22×C4C2×D4×C1111yescharacteristic
325Q16—22no—
326Q16—22no—
327Q16—41no—
328Q16—41no—
329D8—22no—
330D8—22no—
331D8—41no—
332D8—41no—
333C2×C8—21no—
334C2×C8—21no—
335C2×C8—21no—
336C2×C8—41no—
337C2×C8—41no—
338C2×C8—41no—
339C2×C8—41no—
340C2×C8C2×D4×C1111yescharacteristic
341C2×C8C2×D4×C1111yescharacteristic
342C2×C8C2×D4×C1111yescharacteristic
343C2×C8C2×D4×C1111yescharacteristic
344C2×C8C2×D4×C1111yescharacteristic
345C2×C8C11×#4111yescharacteristic
346C4⋊C4—22no—
347C4⋊C4—22no—
348C4⋊C4—44no—
349C4⋊C4—41no—
350C4⋊C4—41no—
351C22⋊C4—44no—
352C22⋊C4—44no—
353C16—22no—
354C16—41no—
355C11#1330511yescharacteristic, direct product factor, Sylow
356C23—21no—
357C23—21no—
358C23—21no—
359C23—21no—
360C23—21no—
361C23—21no—
362C23—42no—
363C23—81no—
364C23—81no—
365C23—81no—
366C23—81no—
367C23—81no—
368C23—81no—
369C23C11×SD3212yescomplemented
370C23C2×C11×D811yescharacteristic
371Q8—42no—
372Q8—42no—
373Q8—81no—
374Q8—81no—
375D4—42no—
376D4—42no—
377D4—88no—
378D4—81no—
379D4—81no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—42no—
388C2×C4—42no—
389C2×C4—42no—
390C2×C4—81no—
391C2×C4—81no—
392C2×C4—81no—
393C2×C4—81no—
394C2×C4—81no—
395C2×C4—81no—
396C2×C4C11×#12011yescharacteristic
397C2×C4C11×#12011yescharacteristic
398C2×C4C11×#12111yescharacteristic
399C2×C4C11×#13511yescharacteristic
400C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
401C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
402C8—41no—
403C8C11×#12011yescharacteristic
404C8C11×#12111yescharacteristic
405C8C11×#12111yescharacteristic
406C8C11×#12711yescharacteristic
407C22—22no—
408C22—22no—
409C22—22no—
410C22—41no—
411C22—41no—
412C22—41no—
413C22—41no—
414C22—82no—
415C22—82no—
416C22—82no—
417C22—161no—
418C22—161no—
419C22—161no—
420C22—161no—
421C22C11×#44711yescharacteristic
422C22C11×#44711yescharacteristic
423C22C11×#46611yescharacteristic
424C22C2×C11×SD3211yescharacteristic
425C22C11×#50811yescharacteristic
426C22C11×#50911yescharacteristic
427C22C11×#51011yescharacteristic
428C4—41no—
429C4—82no—
430C4—82no—
431C4—82no—
432C4C11×#39211yescharacteristic
433C4C11×#44911yescharacteristic
434C4C11×#44911yescharacteristic
435C4C11×#46911yescharacteristic
436C2—42no—
437C2—162no—
438C2C11×#199911yescharacteristic
439C2C11×#218511yescharacteristic
440C2C11×#218611yescharacteristic
441C2C11×#218711yescharacteristic
442C2C11×#218911yescharacteristic
443C2C11×#221711yescharacteristic
444C2C11×#222011yescharacteristic
subgroupG/H
center, socleC23×C11C2×D8
commutator, Frattini, cosocleC22×C8C23×C11
prime radicalC2×C11×#466C2
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C23×C4×C11 ◁ C23×C8×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C11×SD32C2semidirect
2. C2×C11×#467C2semidirect
4. C2×C11×#358C2semidirect
5. C2×C11×#357C2semidirect
6. C2×C11×C22⋊C16C2semidirect
7. C11×#1380C2semidirect
38. C2×C11×Q16D4semidirect
68. C2×C11×C16D4semidirect
72. C11×#107D4semidirect
75. #13305C11direct (N × H)
134. C22×SD32C2×C11semidirect
135. C2×#467C2×C11semidirect
137. C2×#358C2×C11semidirect
138. C2×#357C2×C11semidirect
139. C2×C22⋊C16C2×C11semidirect
140. #1380C2×C11semidirect
154. C23×C11SD32semidirect
251. C2×Q16D4×C11semidirect
281. C2×C16D4×C11semidirect
285. #107D4×C11semidirect
355. C11#13305direct (N × H)
369. C23C11×SD32semidirect

Maximal subgroups

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

subgroupindex
C22×C11×SD322
C2×C11×#4672
C2×C11×#4662
C2×C11×#3582
C2×C11×#3572
C2×C11×C22⋊C162
C11×#13802
#1330511