Finite Group Databasebeta

← C11×#23512 #14600705

Subgroups — C11×#23512 #14600705

Order 2816.

1414 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#536C211yesmaximal, characteristic
2C2×C11×#417C211yesmaximal, characteristic
3C2×C11×#419C211yesmaximal, characteristic, complemented
4C2×C11×#416C211yesmaximal, characteristic
5C22×C11×#103C211yesmaximal, characteristic, complemented
6C11×#2316C211yesmaximal, characteristic, complemented
7C11×#2043C214yesmaximal, complemented
8C11×#2042C214yesmaximal, complemented
9C11×#1729C211yesmaximal, characteristic, complemented
10C22×C11×#41C2211yescharacteristic
11C23×Q8×C11C2211yescharacteristic
12C22×C11×M16C2211yescharacteristic
13C23×C8×C11C2211yescharacteristic
14C11×#536—24no—
15C11×#536—24no—
16C2×C11×C4⋊Q8C2212yes—
17C2×C11×#124C2212yes—
18C2×C11×#123—22no—
19C2×C11×C22⋊Q8—22no—
20C2×C11×#117C2211yescharacteristic
21C2×C11×#117C2211yescharacteristic
22C22×C11×C4⋊C4C2211yescharacteristic
23C11×#419—24no—
24C11×#417—24no—
25C11×#416—24no—
26C2×C11×#103—24no—
27C2×C11×#103C2214yes—
28C2×C11×#103C2212yes—
29C2×C11×#103C2214yes—
30C2×C11×#103C2212yes—
31C2×C11×#102C2212yes—
32C2×C11×#102C2212yes—
33C11×#389—22no—
34C11×#389C2214yes—
35C11×#380—22no—
36C11×#336C2214yes—
37C2×C11×#41—22no—
38C2×C11×#41—22no—
39C2×C11×#41—22no—
40C2×C11×#41—22no—
41C2×C11×#41—22no—
42C2×C11×#41D414yes—
43C22×Q8×C11—21no—
44C22×Q8×C11—22no—
45C22×Q8×C11—22no—
46C22×Q8×C11—22no—
47C22×Q8×C11—22no—
48C22×Q8×C11—22no—
49C22×Q8×C11D414yes—
50C22×Q8×C11C2312yes—
51C22×Q8×C11C2311yescharacteristic
52C22×D4×C11—21no—
53C22×D4×C11C2311yescharacteristic
54C23×C4×C11—21no—
55C23×C4×C11—21no—
56C23×C4×C11—21no—
57C23×C4×C11C2311yescharacteristic
58C2×C11×M16—22no—
59C2×C11×M16—22no—
60C2×C11×M16—22no—
61C22×C8×C11—22no—
62C22×C8×C11—22no—
63C22×C8×C11—22no—
64C22×C8×C11C2312yes—
65C22×C8×C11C2312yes—
66C11×C4⋊Q8—24no—
67C11×C4⋊Q8—24no—
68C11×#124—24no—
69C11×#124—24no—
70C11×#123—216no—
71C11×C22⋊Q8—216no—
72C11×#117—22no—
73C11×#117—22no—
74C11×#117—22no—
75C11×#117—22no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4—24no—
78C2×C11×C4⋊C4—22no—
79C2×C11×C4⋊C4—24no—
80C2×C11×C4⋊C4D412yes—
81C2×C11×C4⋊C4D414yes—
82C2×C11×C4⋊C4C2312yes—
83C2×C11×C4⋊C4C2312yes—
84C2×C11×C22⋊C4—24no—
85C2×C11×C22⋊C4—21no—
86C2×C11×C22⋊C4D412yes—
87C2×C42×C11—21no—
88C2×C42×C11C2312yes—
89C11×#103—24no—
90C11×#103—28no—
91C11×#103—28no—
92C11×#103—24no—
93C11×#102—24no—
94C11×#102—24no—
95C11×#95—24no—
96#23512C1111yesmaximal, characteristic, direct product factor, Sylow
97C24×C11—21no—
98C24×C11C2×D411yescharacteristic
99C11×#41—28no—
100C11×#41—28no—
101C11×#41—44no—
102C11×#41—44no—
103C2×Q8×C11—24no—
104C2×Q8×C11—22no—
105C2×Q8×C11—21no—
106C2×Q8×C11—28no—
107C2×Q8×C11—28no—
108C2×Q8×C11—22no—
109C2×Q8×C11—21no—
110C2×Q8×C11—22no—
111C2×Q8×C11—22no—
112C2×Q8×C11—22no—
113C2×Q8×C11—21no—
114C2×Q8×C11—21no—
115C2×Q8×C11—21no—
116C2×Q8×C11—42no—
117C2×Q8×C11—44no—
118C2×Q8×C11—44no—
119C2×Q8×C11—42no—
120C2×Q8×C11C2×D414yes—
121C2×Q8×C11C2×D412yes—
122C2×D4×C11—24no—
123C2×D4×C11—21no—
124C2×D4×C11—21no—
125C2×D4×C11—21no—
126C2×D4×C11—21no—
127C2×D4×C11—21no—
128C2×D4×C11—42no—
129C2×D4×C11—42no—
130C2×D4×C11C2×D412yes—
131C22×C4×C11—24no—
132C22×C4×C11—22no—
133C22×C4×C11—22no—
134C22×C4×C11—21no—
135C22×C4×C11—24no—
136C22×C4×C11—24no—
137C22×C4×C11—22no—
138C22×C4×C11—42no—
139C22×C4×C11—42no—
140C22×C4×C11—42no—
141C22×C4×C11—42no—
142C22×C4×C11—82no—
143C22×C4×C11C2×D414yes—
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D412yes—
146C22×C4×C11C2×D412yes—
147C22×C4×C11C2×D412yes—
148C22×C4×C11#4112yes—
149C22×C4×C11#4112yes—
150C22×C4×C11#4112yes—
151C22×C4×C11C2411yescharacteristic
152C11×M16—44no—
153C2×C8×C11—22no—
154C2×C8×C11—22no—
155C2×C8×C11—22no—
156C2×C8×C11—22no—
157C2×C8×C11—22no—
158C2×C8×C11—22no—
159C2×C8×C11—44no—
160C11×C4⋊C4—216no—
161C11×C4⋊C4—24no—
162C11×C4⋊C4—24no—
163C11×C4⋊C4—22no—
164C11×C4⋊C4—22no—
165C11×C4⋊C4—22no—
166C11×C4⋊C4—84no—
167C11×C4⋊C4C2×D414yes—
168C11×C22⋊C4—216no—
169C11×C22⋊C4—24no—
170C11×C22⋊C4—42no—
171C42×C11—22no—
172C42×C11—22no—
173C42×C11—42no—
174C2×#536C2×C1111yescharacteristic
175C2×#417C2×C1111yescharacteristic
176C2×#419C2×C1111yescharacteristic, complemented
177C2×#416C2×C1111yescharacteristic
178C22×#103C2×C1111yescharacteristic, complemented
179#2316C2×C1111yescharacteristic, complemented
180#2043C2×C1114yescomplemented
181#2042C2×C1114yescomplemented
182#1729C2×C1111yescharacteristic, complemented
183C23×C11—22no—
184C23×C11—22no—
185C23×C11—22no—
186C23×C11—41no—
187C23×C11—41no—
188C23×C11—42no—
189C23×C11—42no—
190C23×C11#12012yes—
191C23×C11#12112yes—
192C23×C11#12412yes—
193C23×C11C22×D411yescharacteristic
194Q8×C11—24no—
195Q8×C11—22no—
196Q8×C11—24no—
197Q8×C11—22no—
198Q8×C11—42no—
199Q8×C11—41no—
200Q8×C11—42no—
201Q8×C11—41no—
202Q8×C11—48no—
203D4×C11—22no—
204D4×C11—22no—
205D4×C11—48no—
206D4×C11—41no—
207D4×C11—41no—
208C2×C4×C11—24no—
209C2×C4×C11—24no—
210C2×C4×C11—22no—
211C2×C4×C11—24no—
212C2×C4×C11—24no—
213C2×C4×C11—24no—
214C2×C4×C11—41no—
215C2×C4×C11—42no—
216C2×C4×C11—41no—
217C2×C4×C11—42no—
218C2×C4×C11—44no—
219C2×C4×C11—48no—
220C2×C4×C11—48no—
221C2×C4×C11—42no—
222C2×C4×C11—42no—
223C2×C4×C11—42no—
224C2×C4×C11—84no—
225C2×C4×C11#12012yes—
226C2×C4×C11#12114yes—
227C2×C4×C11#12114yes—
228C2×C4×C11#12112yes—
229C2×C4×C11#12314yes—
230C2×C4×C11#12314yes—
231C2×C4×C11#12412yes—
232C2×C4×C11C22×D411yescharacteristic
233C2×C4×C11C22×D411yescharacteristic
234C2×C4×C11C22×D411yescharacteristic
235C2×C4×C11C2×#4111yescharacteristic
236C2×C4×C11C2×#4111yescharacteristic
237C2×C4×C11C2×#4111yescharacteristic
238C8×C11—42no—
239C8×C11—42no—
240C22×#41C22×C1111yescharacteristic
241C23×Q8C22×C1111yescharacteristic
242C22×M16C22×C1111yescharacteristic
243C23×C8C22×C1111yescharacteristic
244#536—24no—
245#536—24no—
246C2×C4⋊Q8C22×C1112yes—
247C2×#124C22×C1112yes—
248C2×#123—22no—
249C2×C22⋊Q8—22no—
250C2×#117C22×C1111yescharacteristic
251C2×#117C22×C1111yescharacteristic
252C22×C4⋊C4C22×C1111yescharacteristic
253#419—24no—
254#417—24no—
255#416—24no—
256C2×#103—24no—
257C2×#103C22×C1114yes—
258C2×#103C22×C1112yes—
259C2×#103C22×C1114yes—
260C2×#103C22×C1112yes—
261C2×#102C22×C1112yes—
262C2×#102C22×C1112yes—
263#389—22no—
264#389C22×C1114yes—
265#380—22no—
266#336C22×C1114yes—
267C22×C11—24no—
268C22×C11—24no—
269C22×C11—22no—
270C22×C11—22no—
271C22×C11—42no—
272C22×C11—44no—
273C22×C11—82no—
274C22×C11—81no—
275C22×C11—81no—
276C22×C11#39414yes—
277C22×C11C2×#12011yescharacteristic
278C22×C11C2×#12111yescharacteristic
279C22×C11C2×#12411yescharacteristic
280C22×C11#57712yes—
281C22×C11#57812yes—
282C4×C11—42no—
283C4×C11—44no—
284C4×C11—44no—
285C4×C11—44no—
286C4×C11—82no—
287C4×C11#39414yes—
288C4×C11C2×#12111yescharacteristic
289C4×C11C2×#12111yescharacteristic
290C4×C11C2×#12311yescharacteristic
291C4×C11C2×#12311yescharacteristic
292C2×#41—22no—
293C2×#41—22no—
294C2×#41—22no—
295C2×#41—22no—
296C2×#41—22no—
297C2×#41D4×C1114yes—
298C22×Q8—21no—
299C22×Q8—22no—
300C22×Q8—22no—
301C22×Q8—22no—
302C22×Q8—22no—
303C22×Q8—22no—
304C22×Q8D4×C1114yes—
305C22×Q8C23×C1112yes—
306C22×Q8C23×C1111yescharacteristic
307C22×D4—21no—
308C22×D4C23×C1111yescharacteristic
309C23×C4—21no—
310C23×C4—21no—
311C23×C4—21no—
312C23×C4C23×C1111yescharacteristic
313C2×M16—22no—
314C2×M16—22no—
315C2×M16—22no—
316C22×C8—22no—
317C22×C8—22no—
318C22×C8—22no—
319C22×C8C23×C1112yes—
320C22×C8C23×C1112yes—
321C4⋊Q8—24no—
322C4⋊Q8—24no—
323#124—24no—
324#124—24no—
325#123—216no—
326C22⋊Q8—216no—
327#117—22no—
328#117—22no—
329#117—22no—
330#117—22no—
331C2×C4⋊C4—21no—
332C2×C4⋊C4—24no—
333C2×C4⋊C4—22no—
334C2×C4⋊C4—24no—
335C2×C4⋊C4D4×C1112yes—
336C2×C4⋊C4D4×C1114yes—
337C2×C4⋊C4C23×C1112yes—
338C2×C4⋊C4C23×C1112yes—
339C2×C22⋊C4—24no—
340C2×C22⋊C4—21no—
341C2×C22⋊C4D4×C1112yes—
342C2×C42—21no—
343C2×C42C23×C1112yes—
344#103—24no—
345#103—28no—
346#103—28no—
347#103—24no—
348#102—24no—
349#102—24no—
350#95—24no—
351C2×C11—24no—
352C2×C11—82no—
353C2×C11C2×#39411yescharacteristic
354C2×C11#301312yes—
355C2×C11#304211yescharacteristic
356C2×C11#304411yescharacteristic
357C2×C11#313712yes—
358C24—21no—
359C24C2×D4×C1111yescharacteristic
360#41—28no—
361#41—28no—
362#41—44no—
363#41—44no—
364C2×Q8—24no—
365C2×Q8—22no—
366C2×Q8—21no—
367C2×Q8—28no—
368C2×Q8—28no—
369C2×Q8—22no—
370C2×Q8—21no—
371C2×Q8—22no—
372C2×Q8—22no—
373C2×Q8—22no—
374C2×Q8—21no—
375C2×Q8—21no—
376C2×Q8—21no—
377C2×Q8—42no—
378C2×Q8—44no—
379C2×Q8—44no—
380C2×Q8—42no—
381C2×Q8C2×D4×C1114yes—
382C2×Q8C2×D4×C1112yes—
383C2×D4—24no—
384C2×D4—21no—
385C2×D4—21no—
386C2×D4—21no—
387C2×D4—21no—
388C2×D4—21no—
389C2×D4—42no—
390C2×D4—42no—
391C2×D4C2×D4×C1112yes—
392C22×C4—24no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—21no—
396C22×C4—24no—
397C22×C4—24no—
398C22×C4—22no—
399C22×C4—42no—
400C22×C4—42no—
401C22×C4—42no—
402C22×C4—42no—
403C22×C4—82no—
404C22×C4C2×D4×C1114yes—
405C22×C4C2×D4×C1111yescharacteristic
406C22×C4C2×D4×C1112yes—
407C22×C4C2×D4×C1112yes—
408C22×C4C2×D4×C1112yes—
409C22×C4C11×#4112yes—
410C22×C4C11×#4112yes—
411C22×C4C11×#4112yes—
412C22×C4C24×C1111yescharacteristic
413M16—44no—
414C2×C8—22no—
415C2×C8—22no—
416C2×C8—22no—
417C2×C8—22no—
418C2×C8—22no—
419C2×C8—22no—
420C2×C8—44no—
421C4⋊C4—216no—
422C4⋊C4—24no—
423C4⋊C4—24no—
424C4⋊C4—22no—
425C4⋊C4—22no—
426C4⋊C4—22no—
427C4⋊C4—84no—
428C4⋊C4C2×D4×C1114yes—
429C22⋊C4—216no—
430C22⋊C4—24no—
431C22⋊C4—42no—
432C42—22no—
433C42—22no—
434C42—42no—
435C11#2351211yescharacteristic, direct product factor, Sylow
436C23—22no—
437C23—22no—
438C23—22no—
439C23—41no—
440C23—41no—
441C23—42no—
442C23—42no—
443C23C11×#12012yes—
444C23C11×#12112yes—
445C23C11×#12412yes—
446C23C22×D4×C1111yescharacteristic
447Q8—24no—
448Q8—22no—
449Q8—24no—
450Q8—22no—
451Q8—42no—
452Q8—41no—
453Q8—42no—
454Q8—41no—
455Q8—48no—
456D4—22no—
457D4—22no—
458D4—48no—
459D4—41no—
460D4—41no—
461C2×C4—24no—
462C2×C4—24no—
463C2×C4—22no—
464C2×C4—24no—
465C2×C4—24no—
466C2×C4—24no—
467C2×C4—41no—
468C2×C4—42no—
469C2×C4—41no—
470C2×C4—42no—
471C2×C4—48no—
472C2×C4—44no—
473C2×C4—48no—
474C2×C4—42no—
475C2×C4—42no—
476C2×C4—42no—
477C2×C4—84no—
478C2×C4C11×#12012yes—
479C2×C4C11×#12114yes—
480C2×C4C11×#12114yes—
481C2×C4C11×#12112yes—
482C2×C4C11×#12314yes—
483C2×C4C11×#12314yes—
484C2×C4C11×#12412yes—
485C2×C4C22×D4×C1111yescharacteristic
486C2×C4C22×D4×C1111yescharacteristic
487C2×C4C22×D4×C1111yescharacteristic
488C2×C4C2×C11×#4111yescharacteristic
489C2×C4C2×C11×#4111yescharacteristic
490C2×C4C2×C11×#4111yescharacteristic
491C8—42no—
492C8—42no—
493C22—24no—
494C22—22no—
495C22—22no—
496C22—24no—
497C22—42no—
498C22—44no—
499C22—81no—
500C22—81no—
501C22—82no—
502C22C11×#39414yes—
503C22C2×C11×#12011yescharacteristic
504C22C2×C11×#12111yescharacteristic
505C22C2×C11×#12411yescharacteristic
506C22C11×#57712yes—
507C22C11×#57812yes—
508C4—42no—
509C4—44no—
510C4—44no—
511C4—44no—
512C4—82no—
513C4C11×#39414yes—
514C4C2×C11×#12111yescharacteristic
515C4C2×C11×#12111yescharacteristic
516C4C2×C11×#12311yescharacteristic
517C4C2×C11×#12311yescharacteristic
518C2—24no—
519C2—82no—
520C2C2×C11×#39411yescharacteristic
521C2C11×#301312yes—
522C2C11×#304211yescharacteristic
523C2C11×#304411yescharacteristic
524C2C11×#313712yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC22×C11×#41C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C11×#117 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C11×#419C2semidirect
5. C22×C11×#103C2semidirect
6. C11×#2316C2semidirect
7. C11×#2043C2semidirect
8. C11×#2042C2semidirect
9. C11×#1729C2semidirect
96. #23512C11direct (N × H)
176. C2×#419C2×C11semidirect
178. C22×#103C2×C11semidirect
179. #2316C2×C11semidirect
180. #2043C2×C11semidirect
181. #2042C2×C11semidirect
182. #1729C2×C11semidirect
435. C11#23512direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5362
C2×C11×#4172
C2×C11×#4192
C2×C11×#4162
C22×C11×#1032
C11×#23162
C11×#20432
C11×#20422
C11×#17292
#2351211