Finite Group Databasebeta

← C11×#32970 #14610163

Subgroups — C11×#32970 #14610163

Order 2816.

1194 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C11×2−1+4C211yesmaximal, characteristic
2C11×#3079C212yesmaximal, complemented
3C11×#2568C211yesmaximal, characteristic, complemented
4C11×#1860C214yesmaximal, complemented
5C11×#1857C212yesmaximal, complemented
6C11×#1806C212yesmaximal, complemented
7C11×#1801C211yesmaximal, characteristic, complemented
8C11×#1793C212yesmaximal
9C2×C11×2−1+4C2211yescharacteristic
10C2×C11×C4⋊Q8C2211yescharacteristic
11C11×#520—22no—
12C11×#520—22no—
13C11×#520C2212yes—
14C11×#519—22no—
15C11×#519C2211yescharacteristic
16C4×C11×#41—22no—
17C4×C11×#41—22no—
18C4×C11×#41C2212yes—
19C2×C4×Q8×C11—22no—
20C2×C4×Q8×C11C2211yescharacteristic
21C11×#477—22no—
22C11×#476—22no—
23C11×#475—22no—
24C11×#474—22no—
25C11×#428C2214yes—
26C11×#423C2212yes—
27C2×C11×#104C2214yes—
28C11×#417C2214yes—
29C2×C11×#101C2212yes—
30C11×#400—22no—
31C11×#391—22no—
32C11×#391C2212yes—
33C11×#382C2212yes—
34C4×C11×C4⋊C4C2211yescharacteristic
35C11×#343C2212yes—
36C11×#339C2214yes—
37C11×2−1+4—24no—
38C11×2−1+4—22no—
39C11×2−1+4Q814yescomplemented
40C2×C11×#41—22no—
41C2×C11×#41—22no—
42C2×C11×#41C2312yes—
43C22×Q8×C11—22no—
44C22×Q8×C11—21no—
45C22×Q8×C11C2311yescharacteristic
46C2×C11×M16C2314yes—
47C11×C4⋊Q8—22no—
48C11×C4⋊Q8—22no—
49C4×Q8×C11—22no—
50C4×Q8×C11—24no—
51C4×Q8×C11—22no—
52C4×Q8×C11—22no—
53C4×Q8×C11—22no—
54C4×Q8×C11—22no—
55C4×Q8×C11—22no—
56C4×Q8×C11—22no—
57C4×Q8×C11D412yes—
58C4×Q8×C11D412yes—
59C4×D4×C11—22no—
60C4×D4×C11—24no—
61C4×D4×C11—22no—
62C4×D4×C11—22no—
63C4×D4×C11—22no—
64C4×D4×C11—24no—
65C4×D4×C11—22no—
66C4×D4×C11D412yes—
67C4×D4×C11D412yes—
68C11×#117—24no—
69C11×#117—24no—
70C11×#117—22no—
71C11×#117—22no—
72C11×#117—22no—
73C11×#117C2312yes—
74C2×C11×C4⋊C4—24no—
75C2×C11×C4⋊C4—22no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4D412yes—
79C2×C11×C4⋊C4C2312yes—
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C42×C11—24no—
82C2×C42×C11—22no—
83C2×C42×C11D412yes—
84C2×C42×C11C2312yes—
85C2×C42×C11C2311yescharacteristic
86C11×#107—24no—
87C11×#106—24no—
88C11×C4⋊C8—22no—
89C11×C4⋊C8—22no—
90C11×#104—28no—
91C11×#103—24no—
92C11×#102—24no—
93C11×#101—24no—
94C11×#95—21no—
95C11×#95—24no—
96C11×#95—24no—
97#32970C1111yesmaximal, characteristic, direct product factor, Sylow
98C11×#41—28no—
99C11×#41—28no—
100C11×#41—28no—
101C11×#41—28no—
102C11×#41—22no—
103C11×#41—22no—
104C11×#41C2×Q814yes—
105C11×#41#4114yes—
106C2×Q8×C11—22no—
107C2×Q8×C11—28no—
108C2×Q8×C11—28no—
109C2×Q8×C11—22no—
110C2×Q8×C11—22no—
111C2×Q8×C11—44no—
112C2×Q8×C11—41no—
113C2×Q8×C11—41no—
114C2×Q8×C11C2×D412yes—
115C2×Q8×C11C2×Q812yes—
116C2×Q8×C11#4112yes—
117C2×D4×C11—22no—
118C2×D4×C11—22no—
119C2×D4×C11C2×D412yes—
120C22×C4×C11—24no—
121C22×C4×C11—22no—
122C22×C4×C11—24no—
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11—22no—
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11C2×D412yes—
129C22×C4×C11C2×D412yes—
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11C2411yescharacteristic
132C11×M16—24no—
133C11×M16—24no—
134C2×C8×C11—24no—
135C11×C4⋊C4—24no—
136C11×C4⋊C4—22no—
137C11×C4⋊C4—22no—
138C11×C4⋊C4—22no—
139C11×C4⋊C4—24no—
140C11×C4⋊C4—22no—
141C11×C4⋊C4—22no—
142C11×C4⋊C4—24no—
143C11×C4⋊C4—42no—
144C11×C4⋊C4—42no—
145C11×C4⋊C4C2×D412yes—
146C11×C4⋊C4C2×D412yes—
147C11×C22⋊C4—24no—
148C11×C22⋊C4—22no—
149C11×C22⋊C4—22no—
150C11×C22⋊C4—22no—
151C42×C11—24no—
152C42×C11—24no—
153C42×C11—22no—
154C42×C11—22no—
155C42×C11—22no—
156C42×C11—22no—
157C42×C11—22no—
158C42×C11—24no—
159C42×C11C2×D412yes—
160C42×C11C2×D412yes—
161C4×2−1+4C2×C1111yescharacteristic
162#3079C2×C1112yescomplemented
163#2568C2×C1111yescharacteristic, complemented
164#1860C2×C1114yescomplemented
165#1857C2×C1112yescomplemented
166#1806C2×C1112yescomplemented
167#1801C2×C1111yescharacteristic, complemented
168#1793C2×C1112yes—
169C23×C11—22no—
170C23×C11C22×D411yescharacteristic
171Q8×C11—28no—
172Q8×C11—24no—
173Q8×C11—22no—
174Q8×C11—24no—
175Q8×C11—82no—
176Q8×C11—82no—
177Q8×C11C22⋊Q814yes—
178D4×C11—28no—
179D4×C11—24no—
180D4×C11—24no—
181D4×C11—22no—
182D4×C11C22⋊Q814yes—
183C2×C4×C11—216no—
184C2×C4×C11—22no—
185C2×C4×C11—22no—
186C2×C4×C11—22no—
187C2×C4×C11—24no—
188C2×C4×C11—24no—
189C2×C4×C11—22no—
190C2×C4×C11—22no—
191C2×C4×C11—22no—
192C2×C4×C11—22no—
193C2×C4×C11—41no—
194C2×C4×C11—44no—
195C2×C4×C11—42no—
196C2×C4×C11—42no—
197C2×C4×C11—42no—
198C2×C4×C11—44no—
199C2×C4×C11—42no—
200C2×C4×C11—42no—
201C2×C4×C11—82no—
202C2×C4×C11—84no—
203C2×C4×C11#12011yescharacteristic
204C2×C4×C11#12012yes—
205C2×C4×C11#12011yescharacteristic
206C2×C4×C11C22⋊Q814yes—
207C2×C4×C11C22×D412yes—
208C2×C4×C11C22×Q811yescharacteristic
209C2×C4×C11C2×#4112yes—
210C2×C4×C11C2×#4111yescharacteristic
211C8×C11—44no—
212C2×2−1+4C22×C1111yescharacteristic
213C2×C4⋊Q8C22×C1111yescharacteristic
214#520—22no—
215#520—22no—
216#520C22×C1112yes—
217#519—22no—
218#519C22×C1111yescharacteristic
219C4×#41—22no—
220C4×#41—22no—
221C4×#41C22×C1112yes—
222C2×C4×Q8—22no—
223C2×C4×Q8C22×C1111yescharacteristic
224#477—22no—
225#476—22no—
226#475—22no—
227#474—22no—
228#428C22×C1114yes—
229#423C22×C1112yes—
230C2×#104C22×C1114yes—
231#417C22×C1114yes—
232C2×#101C22×C1112yes—
233#400—22no—
234#391—22no—
235#391C22×C1112yes—
236#382C22×C1112yes—
237C4×C4⋊C4C22×C1111yescharacteristic
238#343C22×C1112yes—
239#339C22×C1114yes—
240C22×C11—21no—
241C22×C11—21no—
242C22×C11—24no—
243C22×C11—42no—
244C22×C11—42no—
245C22×C11C2×#12011yescharacteristic
246C22×C11C2×C22⋊Q811yescharacteristic
247C22×C11#52511yescharacteristic
248C4×C11—24no—
249C4×C11—24no—
250C4×C11—21no—
251C4×C11—22no—
252C4×C11—42no—
253C4×C11—42no—
254C4×C11—42no—
255C4×C11—82no—
256C4×C11—82no—
257C4×C11#45412yes—
258C4×C11C2×C22⋊Q812yes—
259C4×C11#52512yes—
2602−1+4—24no—
2612−1+4—22no—
2622−1+4Q8×C1114yescomplemented
263C2×#41—22no—
264C2×#41—22no—
265C2×#41C23×C1112yes—
266C22×Q8—22no—
267C22×Q8—21no—
268C22×Q8C23×C1111yescharacteristic
269C2×M16C23×C1114yes—
270C4⋊Q8—22no—
271C4⋊Q8—22no—
272C4×Q8—22no—
273C4×Q8—24no—
274C4×Q8—22no—
275C4×Q8—22no—
276C4×Q8—22no—
277C4×Q8—22no—
278C4×Q8—22no—
279C4×Q8—22no—
280C4×Q8D4×C1112yes—
281C4×Q8D4×C1112yes—
282C4×D4—22no—
283C4×D4—24no—
284C4×D4—22no—
285C4×D4—22no—
286C4×D4—22no—
287C4×D4—24no—
288C4×D4—22no—
289C4×D4D4×C1112yes—
290C4×D4D4×C1112yes—
291#117—24no—
292#117—24no—
293#117—22no—
294#117—22no—
295#117—22no—
296#117C23×C1112yes—
297C2×C4⋊C4—24no—
298C2×C4⋊C4—22no—
299C2×C4⋊C4—21no—
300C2×C4⋊C4—21no—
301C2×C4⋊C4D4×C1112yes—
302C2×C4⋊C4C23×C1112yes—
303C2×C4⋊C4C23×C1111yescharacteristic
304C2×C42—24no—
305C2×C42—22no—
306C2×C42D4×C1112yes—
307C2×C42C23×C1112yes—
308C2×C42C23×C1111yescharacteristic
309#107—24no—
310#106—24no—
311C4⋊C8—22no—
312C4⋊C8—22no—
313#104—28no—
314#103—24no—
315#102—24no—
316#101—24no—
317#95—21no—
318#95—24no—
319#95—24no—
320C2×C11—21no—
321C2×C11—21no—
322C2×C11—44no—
323C2×C11#284811yescharacteristic
324C2×C11C2×#45411yescharacteristic
325C2×C11#302211yescharacteristic
326#41—28no—
327#41—28no—
328#41—28no—
329#41—28no—
330#41—22no—
331#41—22no—
332#41C2×Q8×C1114yes—
333#41C11×#4114yes—
334C2×Q8—22no—
335C2×Q8—28no—
336C2×Q8—28no—
337C2×Q8—22no—
338C2×Q8—22no—
339C2×Q8—44no—
340C2×Q8—41no—
341C2×Q8—41no—
342C2×Q8C2×D4×C1112yes—
343C2×Q8C2×Q8×C1112yes—
344C2×Q8C11×#4112yes—
345C2×D4—22no—
346C2×D4—22no—
347C2×D4C2×D4×C1112yes—
348C22×C4—24no—
349C22×C4—22no—
350C22×C4—24no—
351C22×C4—22no—
352C22×C4—22no—
353C22×C4—22no—
354C22×C4—22no—
355C22×C4C2×D4×C1111yescharacteristic
356C22×C4C2×D4×C1112yes—
357C22×C4C2×D4×C1112yes—
358C22×C4C2×D4×C1111yescharacteristic
359C22×C4C24×C1111yescharacteristic
360M16—24no—
361M16—24no—
362C2×C8—24no—
363C4⋊C4—24no—
364C4⋊C4—22no—
365C4⋊C4—22no—
366C4⋊C4—22no—
367C4⋊C4—24no—
368C4⋊C4—22no—
369C4⋊C4—22no—
370C4⋊C4—24no—
371C4⋊C4—42no—
372C4⋊C4—42no—
373C4⋊C4C2×D4×C1112yes—
374C4⋊C4C2×D4×C1112yes—
375C22⋊C4—24no—
376C22⋊C4—22no—
377C22⋊C4—22no—
378C22⋊C4—22no—
379C42—24no—
380C42—24no—
381C42—22no—
382C42—22no—
383C42—22no—
384C42—22no—
385C42—22no—
386C42—24no—
387C42C2×D4×C1112yes—
388C42C2×D4×C1112yes—
389C11#3297011yescharacteristic, direct product factor, Sylow
390C23—22no—
391C23C22×D4×C1111yescharacteristic
392Q8—28no—
393Q8—24no—
394Q8—22no—
395Q8—24no—
396Q8—82no—
397Q8—82no—
398Q8C11×C22⋊Q814yes—
399D4—28no—
400D4—24no—
401D4—24no—
402D4—22no—
403D4C11×C22⋊Q814yes—
404C2×C4—216no—
405C2×C4—22no—
406C2×C4—22no—
407C2×C4—22no—
408C2×C4—24no—
409C2×C4—24no—
410C2×C4—22no—
411C2×C4—22no—
412C2×C4—22no—
413C2×C4—22no—
414C2×C4—41no—
415C2×C4—44no—
416C2×C4—42no—
417C2×C4—42no—
418C2×C4—42no—
419C2×C4—44no—
420C2×C4—42no—
421C2×C4—42no—
422C2×C4—82no—
423C2×C4—84no—
424C2×C4C11×#12011yescharacteristic
425C2×C4C11×#12012yes—
426C2×C4C11×#12011yescharacteristic
427C2×C4C11×C22⋊Q814yes—
428C2×C4C22×D4×C1112yes—
429C2×C4C22×Q8×C1111yescharacteristic
430C2×C4C2×C11×#4112yes—
431C2×C4C2×C11×#4111yescharacteristic
432C8—44no—
433C22—21no—
434C22—21no—
435C22—24no—
436C22—42no—
437C22—42no—
438C22C2×C11×#12011yescharacteristic
439C22C2×C11×C22⋊Q811yescharacteristic
440C22C11×#52511yescharacteristic
441C4—21no—
442C4—22no—
443C4—24no—
444C4—24no—
445C4—42no—
446C4—42no—
447C4—42no—
448C4—82no—
449C4—82no—
450C4C11×#45412yes—
451C4C2×C11×C22⋊Q812yes—
452C4C11×#52512yes—
453C2—21no—
454C2—21no—
455C2—44no—
456C2C11×#284811yescharacteristic
457C2C2×C11×#45411yescharacteristic
458C2C11×#302211yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×2−1+4C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#3079C2semidirect
3. C11×#2568C2semidirect
4. C11×#1860C2semidirect
5. C11×#1857C2semidirect
6. C11×#1806C2semidirect
7. C11×#1801C2semidirect
39. C11×2−1+4Q8semidirect
97. #32970C11direct (N × H)
162. #3079C2×C11semidirect
163. #2568C2×C11semidirect
164. #1860C2×C11semidirect
165. #1857C2×C11semidirect
166. #1806C2×C11semidirect
167. #1801C2×C11semidirect
262. 2−1+4Q8×C11semidirect
389. C11#32970direct (N × H)

Maximal subgroups

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

subgroupindex
C4×C11×2−1+42
C11×#30792
C11×#25682
C11×#18602
C11×#18572
C11×#18062
C11×#18012
C11×#17932
#3297011