Finite Group Databasebeta

← C11×#19416 #14596609

Subgroups — C11×#19416 #14596609

Order 2816.

694 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3226C211yesmaximal, characteristic, complemented
2C11×#3039C211yesmaximal, characteristic, complemented
3C11×#3035C211yesmaximal, characteristic
4C11×#2988C211yesmaximal, characteristic, complemented
5C11×#1682C212yesmaximal, complemented
6C11×#1681C212yesmaximal, complemented
7C11×#1674C212yesmaximal, complemented
8C11×#1673C212yesmaximal, complemented
9C11×#1571C211yesmaximal, characteristic, complemented
10C11×#1547C211yesmaximal, characteristic, complemented
11C2×C11×#332C211yesmaximal, characteristic, complemented
12C2×C11×#137—21no—
13C2×C11×#135—21no—
14C11×#532C2211yescharacteristic
15C2×C11×C4⋊Q8C2211yescharacteristic
16C4×C11×#41C2211yescharacteristic
17C11×#500C2212yes—
18C11×#486C2212yes—
19C11×#480—22no—
20C11×#474—21no—
21C11×#474—21no—
22C11×#464—21no—
23C11×#463—21no—
24C11×#462—21no—
25C11×#462C2211yescharacteristic
26C11×#462C2212yes—
27C11×#461—21no—
28C11×#461C2211yescharacteristic
29C11×#461C2212yes—
30C11×#460C2211yescharacteristic
31C11×#459C2211yescharacteristic
32C8×Q8×C11C2212yes—
33C8×D4×C11—22no—
34C8×D4×C11C2212yes—
35C11×#431—21no—
36C11×#431C2211yescharacteristic
37C11×#423C2211yescharacteristic
38C2×C11×C4⋊C8—21no—
39C2×C11×C4⋊C8C2211yescharacteristic
40C2×C11×C4⋊C8C2211yescharacteristic
41C11×#419—21no—
42C11×#416—21no—
43C11×#335C2212yes—
44C11×#335C2212yes—
45C11×#332C2212yes—
46C11×#332C2212yes—
47C11×#332C2212yes—
48C11×#331C2212yes—
49C2×C11×#41—21no—
50C2×C11×#41D411yescharacteristic
51C22×Q8×C11—21no—
52C11×#137—44no—
53C11×#135—44no—
54C2×C11×Q16—21no—
55C2×C11×Q16—22no—
56C2×C11×SD16—21no—
57C2×C11×SD16—21no—
58C2×C11×SD16—22no—
59C2×C11×D8—21no—
60C2×C11×M16—21no—
61C22×C8×C11—21no—
62C22×C8×C11—21no—
63C22×C8×C11—22no—
64C11×C4⋊Q8—21no—
65C11×C4⋊Q8—21no—
66C11×C4⋊Q8—21no—
67C11×C4⋊Q8C2311yescharacteristic
68C11×C4⋊Q8C2312yes—
69C11×#127C2311yescharacteristic
70C11×#124—21no—
71C11×#121—21no—
72C11×#121—21no—
73C4×Q8×C11D411yescharacteristic
74C4×Q8×C11C2311yescharacteristic
75C4×D4×C11—21no—
76C4×D4×C11—21no—
77C4×D4×C11—21no—
78C4×D4×C11—21no—
79C4×D4×C11D411yescharacteristic
80C4×D4×C11C2311yescharacteristic
81C11×#117—21no—
82C11×#117D411yescharacteristic
83C2×C11×C4⋊C4—21no—
84C2×C11×C4⋊C4—21no—
85C2×C42×C11—21no—
86C2×C42×C11C2311yescharacteristic
87C11×#107—22no—
88C11×#107—22no—
89C11×C4⋊C8—22no—
90C11×C4⋊C8—21no—
91C11×C4⋊C8—21no—
92C11×C4⋊C8—21no—
93C11×C4⋊C8D411yescharacteristic
94C11×C4⋊C8D411yescharacteristic
95C11×C4⋊C8C2312yes—
96C11×C4⋊C8C2312yes—
97C11×C4⋊C8C2311yescharacteristic
98C11×C4⋊C8C2311yescharacteristic
99C11×#103—21no—
100C11×#103—21no—
101C11×#103—22no—
102C11×#103—22no—
103C11×#102—22no—
104C11×#102—22no—
105C11×#102—21no—
106C11×#102—21no—
107C11×C22⋊C8—22no—
108C11×C22⋊C8D412yes—
109C4×C8×C11—22no—
110C4×C8×C11C2312yes—
111#19416C1111yesmaximal, characteristic, direct product factor, Sylow
112C11×#41—22no—
113C11×#41—42no—
114C11×#41—42no—
115C11×#41D814yes—
116C2×Q8×C11—21no—
117C2×Q8×C11—22no—
118C2×Q8×C11—41no—
119C2×Q8×C11—42no—
120C2×Q8×C11—42no—
121C2×Q8×C11C2×D411yescharacteristic
122C2×D4×C11—21no—
123C2×D4×C11—21no—
124C2×D4×C11—21no—
125C2×D4×C11—21no—
126C2×D4×C11—41no—
127C2×D4×C11C2×D411yescharacteristic
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11—41no—
132C22×C4×C11—41no—
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11#4111yescharacteristic
136C11×Q16—42no—
137C11×Q16—44no—
138C11×SD16—42no—
139C11×SD16—42no—
140C11×SD16—44no—
141C11×D8—42no—
142C11×M16—42no—
143C2×C8×C11—22no—
144C2×C8×C11—21no—
145C2×C8×C11—21no—
146C2×C8×C11—22no—
147C2×C8×C11—42no—
148C2×C8×C11—81no—
149C2×C8×C11—82no—
150C2×C8×C11C2×D412yes—
151C2×C8×C11C2×D412yes—
152C11×C4⋊C4—21no—
153C11×C4⋊C4—21no—
154C11×C4⋊C4—22no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—22no—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—41no—
159C11×C4⋊C4—41no—
160C11×C4⋊C4C2×D411yescharacteristic
161C11×C4⋊C4C2×D411yescharacteristic
162C11×C22⋊C4—21no—
163C11×C22⋊C4—21no—
164C11×C22⋊C4—21no—
165C11×C22⋊C4—41no—
166C11×C22⋊C4—41no—
167C42×C11—21no—
168C42×C11—21no—
169C42×C11—21no—
170C42×C11C2×D411yescharacteristic
171C42×C11C2×D411yescharacteristic
172C42×C11#4111yescharacteristic
173C42×C11C2411yescharacteristic
174#3226C2×C1111yescharacteristic, complemented
175#3039C2×C1111yescharacteristic, complemented
176#3035C2×C1111yescharacteristic
177#2988C2×C1111yescharacteristic, complemented
178#1682C2×C1112yescomplemented
179#1681C2×C1112yescomplemented
180#1674C2×C1112yescomplemented
181#1673C2×C1112yescomplemented
182#1571C2×C1111yescharacteristic, complemented
183#1547C2×C1111yescharacteristic, complemented
184C2×#332C2×C1111yescharacteristic, complemented
185C23×C11—21no—
186C23×C11—41no—
187C23×C11#12111yescharacteristic
188Q8×C11—21no—
189Q8×C11—42no—
190Q8×C11—41no—
191Q8×C11—42no—
192Q8×C11—41no—
193Q8×C11—82no—
194Q8×C11C2×D812yes—
195D4×C11—24no—
196D4×C11—21no—
197D4×C11—41no—
198D4×C11—41no—
199D4×C11—41no—
200D4×C11—41no—
201D4×C11—81no—
202D4×C11—82no—
203D4×C11C2×D812yes—
204C2×C4×C11—21no—
205C2×C4×C11—21no—
206C2×C4×C11—21no—
207C2×C4×C11—24no—
208C2×C4×C11—21no—
209C2×C4×C11—21no—
210C2×C4×C11—41no—
211C2×C4×C11—41no—
212C2×C4×C11—41no—
213C2×C4×C11—41no—
214C2×C4×C11—42no—
215C2×C4×C11—81no—
216C2×C4×C11—82no—
217C2×C4×C11—82no—
218C2×C4×C11#12111yescharacteristic
219C2×C4×C11#12111yescharacteristic
220C2×C4×C11#12111yescharacteristic
221C2×C4×C11C2×D812yes—
222C2×C4×C11#13512yes—
223C2×C4×C11C22×D411yescharacteristic
224C2×C4×C11C22×D411yescharacteristic
225C2×C4×C11C2×#4111yescharacteristic
226C8×C11—22no—
227C8×C11—22no—
228C8×C11—41no—
229C8×C11—41no—
230C8×C11—42no—
231C8×C11—42no—
232C2×#137—21no—
233C2×#135—21no—
234#532C22×C1111yescharacteristic
235C2×C4⋊Q8C22×C1111yescharacteristic
236C4×#41C22×C1111yescharacteristic
237#500C22×C1112yes—
238#486C22×C1112yes—
239#480—22no—
240#474—21no—
241#474—21no—
242#464—21no—
243#463—21no—
244#462—21no—
245#462C22×C1111yescharacteristic
246#462C22×C1112yes—
247#461—21no—
248#461C22×C1111yescharacteristic
249#461C22×C1112yes—
250#460C22×C1111yescharacteristic
251#459C22×C1111yescharacteristic
252C8×Q8C22×C1112yes—
253C8×D4—22no—
254C8×D4C22×C1112yes—
255#431—21no—
256#431C22×C1111yescharacteristic
257#423C22×C1111yescharacteristic
258C2×C4⋊C8—21no—
259C2×C4⋊C8C22×C1111yescharacteristic
260C2×C4⋊C8C22×C1111yescharacteristic
261#419—21no—
262#416—21no—
263#335C22×C1112yes—
264#335C22×C1112yes—
265#332C22×C1112yes—
266#332C22×C1112yes—
267#332C22×C1112yes—
268#331C22×C1112yes—
269C22×C11—21no—
270C22×C11—21no—
271C22×C11—22no—
272C22×C11—41no—
273C22×C11—41no—
274C22×C11—81no—
275C22×C11—81no—
276C22×C11—81no—
277C22×C11#46612yes—
278C22×C11C2×#12111yescharacteristic
279C4×C11—21no—
280C4×C11—22no—
281C4×C11—21no—
282C4×C11—21no—
283C4×C11—41no—
284C4×C11—41no—
285C4×C11—81no—
286C4×C11—82no—
287C4×C11#46612yes—
288C4×C11C22×D811yescharacteristic
289C4×C11C2×#13511yescharacteristic
290C4×C11#57711yescharacteristic
291C4×C11#57811yescharacteristic
292C2×#41—21no—
293C2×#41D4×C1111yescharacteristic
294C22×Q8—21no—
295#137—44no—
296#135—44no—
297C2×Q16—21no—
298C2×Q16—22no—
299C2×SD16—21no—
300C2×SD16—21no—
301C2×SD16—22no—
302C2×D8—21no—
303C2×M16—21no—
304C22×C8—21no—
305C22×C8—21no—
306C22×C8—22no—
307C4⋊Q8—21no—
308C4⋊Q8—21no—
309C4⋊Q8—21no—
310C4⋊Q8C23×C1112yes—
311C4⋊Q8C23×C1111yescharacteristic
312#127C23×C1111yescharacteristic
313#124—21no—
314#121—21no—
315#121—21no—
316C4×Q8D4×C1111yescharacteristic
317C4×Q8C23×C1111yescharacteristic
318C4×D4—21no—
319C4×D4—21no—
320C4×D4—21no—
321C4×D4—21no—
322C4×D4D4×C1111yescharacteristic
323C4×D4C23×C1111yescharacteristic
324#117—21no—
325#117D4×C1111yescharacteristic
326C2×C4⋊C4—21no—
327C2×C4⋊C4—21no—
328C2×C42—21no—
329C2×C42C23×C1111yescharacteristic
330#107—22no—
331#107—22no—
332C4⋊C8—22no—
333C4⋊C8—21no—
334C4⋊C8—21no—
335C4⋊C8—21no—
336C4⋊C8D4×C1111yescharacteristic
337C4⋊C8D4×C1111yescharacteristic
338C4⋊C8C23×C1112yes—
339C4⋊C8C23×C1112yes—
340C4⋊C8C23×C1111yescharacteristic
341C4⋊C8C23×C1111yescharacteristic
342#103—21no—
343#103—21no—
344#103—22no—
345#103—22no—
346#102—22no—
347#102—22no—
348#102—21no—
349#102—21no—
350C22⋊C8—22no—
351C22⋊C8D4×C1112yes—
352C4×C8—22no—
353C4×C8C23×C1112yes—
354C2×C11—22no—
355C2×C11—42no—
356C2×C11—161no—
357C2×C11#304611yescharacteristic
358C2×C11C2×#46611yescharacteristic
359C2×C11#306911yescharacteristic
360#41—22no—
361#41—42no—
362#41—42no—
363#41C11×D814yes—
364C2×Q8—21no—
365C2×Q8—22no—
366C2×Q8—41no—
367C2×Q8—42no—
368C2×Q8—42no—
369C2×Q8C2×D4×C1111yescharacteristic
370C2×D4—21no—
371C2×D4—21no—
372C2×D4—21no—
373C2×D4—21no—
374C2×D4—41no—
375C2×D4C2×D4×C1111yescharacteristic
376C22×C4—21no—
377C22×C4—21no—
378C22×C4—21no—
379C22×C4—41no—
380C22×C4—41no—
381C22×C4C2×D4×C1111yescharacteristic
382C22×C4C2×D4×C1111yescharacteristic
383C22×C4C11×#4111yescharacteristic
384Q16—42no—
385Q16—44no—
386SD16—42no—
387SD16—42no—
388SD16—44no—
389D8—42no—
390M16—42no—
391C2×C8—22no—
392C2×C8—21no—
393C2×C8—21no—
394C2×C8—22no—
395C2×C8—42no—
396C2×C8—82no—
397C2×C8—81no—
398C2×C8C2×D4×C1112yes—
399C2×C8C2×D4×C1112yes—
400C4⋊C4—21no—
401C4⋊C4—21no—
402C4⋊C4—22no—
403C4⋊C4—21no—
404C4⋊C4—22no—
405C4⋊C4—21no—
406C4⋊C4—41no—
407C4⋊C4—41no—
408C4⋊C4C2×D4×C1111yescharacteristic
409C4⋊C4C2×D4×C1111yescharacteristic
410C22⋊C4—21no—
411C22⋊C4—21no—
412C22⋊C4—21no—
413C22⋊C4—41no—
414C22⋊C4—41no—
415C42—21no—
416C42—21no—
417C42—21no—
418C42C2×D4×C1111yescharacteristic
419C42C2×D4×C1111yescharacteristic
420C42C11×#4111yescharacteristic
421C42C24×C1111yescharacteristic
422C11#1941611yescharacteristic, direct product factor, Sylow
423C23—21no—
424C23—41no—
425C23C11×#12111yescharacteristic
426Q8—21no—
427Q8—42no—
428Q8—41no—
429Q8—42no—
430Q8—41no—
431Q8—82no—
432Q8C2×C11×D812yes—
433D4—24no—
434D4—21no—
435D4—41no—
436D4—41no—
437D4—41no—
438D4—41no—
439D4—81no—
440D4—82no—
441D4C2×C11×D812yes—
442C2×C4—21no—
443C2×C4—21no—
444C2×C4—21no—
445C2×C4—24no—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—41no—
449C2×C4—41no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—42no—
453C2×C4—81no—
454C2×C4—82no—
455C2×C4—82no—
456C2×C4C11×#12111yescharacteristic
457C2×C4C11×#12111yescharacteristic
458C2×C4C11×#12111yescharacteristic
459C2×C4C2×C11×D812yes—
460C2×C4C11×#13512yes—
461C2×C4C22×D4×C1111yescharacteristic
462C2×C4C22×D4×C1111yescharacteristic
463C2×C4C2×C11×#4111yescharacteristic
464C8—22no—
465C8—22no—
466C8—41no—
467C8—41no—
468C8—42no—
469C8—42no—
470C22—21no—
471C22—21no—
472C22—22no—
473C22—41no—
474C22—41no—
475C22—81no—
476C22—81no—
477C22—81no—
478C22C11×#46612yes—
479C22C2×C11×#12111yescharacteristic
480C4—21no—
481C4—22no—
482C4—21no—
483C4—21no—
484C4—41no—
485C4—41no—
486C4—81no—
487C4—82no—
488C4C11×#46612yes—
489C4C22×C11×D811yescharacteristic
490C4C2×C11×#13511yescharacteristic
491C4C11×#57711yescharacteristic
492C4C11×#57811yescharacteristic
493C2—22no—
494C2—42no—
495C2—161no—
496C2C11×#304611yescharacteristic
497C2C2×C11×#46611yescharacteristic
498C2C11×#306911yescharacteristic
subgroupG/H
center, socleC22×C11C2×#121
commutator, Frattini, cosocleC42C24×C11
prime radicalC11×#3035C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3226C2semidirect
2. C11×#3039C2semidirect
4. C11×#2988C2semidirect
5. C11×#1682C2semidirect
6. C11×#1681C2semidirect
7. C11×#1674C2semidirect
8. C11×#1673C2semidirect
9. C11×#1571C2semidirect
10. C11×#1547C2semidirect
11. C2×C11×#332C2semidirect
111. #19416C11direct (N × H)
174. #3226C2×C11semidirect
175. #3039C2×C11semidirect
177. #2988C2×C11semidirect
178. #1682C2×C11semidirect
179. #1681C2×C11semidirect
180. #1674C2×C11semidirect
181. #1673C2×C11semidirect
182. #1571C2×C11semidirect
183. #1547C2×C11semidirect
184. C2×#332C2×C11semidirect
422. C11#19416direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#32262
C11×#30392
C11×#30352
C11×#29882
C11×#16822
C11×#16812
C11×#16742
C11×#16732
C11×#15712
C11×#15472
C2×C11×#3322
#1941611