Finite Group Databasebeta

← C2×C11×#1931 #14598267

Subgroups — C2×C11×#1931 #14598267

Order 2816.

1154 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#428C211yesmaximal, characteristic, complemented
2C2×C11×#418C211yesmaximal, characteristic
3C22×C11×#102C211yesmaximal, characteristic
4C22×C11×#100C211yesmaximal, characteristic
5C2×C11×#405C211yesmaximal, characteristic, complemented
6C11×#1931C218yesmaximal, direct product factor
7C2×C11×#343C211yesmaximal, characteristic, complemented
8C2×C11×#341C211yesmaximal, characteristic, complemented
9C23×D4×C11C2211yescharacteristic
10C22×C11×M16C2211yescharacteristic
11C22×C11×M16C2211yescharacteristic
12C22×C11×M16C2211yescharacteristic
13C23×C8×C11C2211yescharacteristic
14C2×C11×#117C2211yescharacteristic
15C22×C11×C4⋊C4C2211yescharacteristic
16C11×#428—22no—
17C11×#428C2214yescomplemented
18C2×C11×#107—21no—
19C2×C11×#106—21no—
20C11×#418—22no—
21C11×#418C2214yes—
22C2×C11×#102—21no—
23C2×C11×#102—21no—
24C2×C11×#102—22no—
25C2×C11×#102—21no—
26C2×C11×#102—21no—
27C2×C11×#102C2214yes—
28C2×C11×#100C418yescomplemented
29C2×C11×#100C2214yes—
30C11×#405—22no—
31C11×#405C2214yescomplemented
32C2×C11×#97—21no—
33C2×C4×C8×C11—21no—
34C11×#343C2214yescomplemented
35C11×#341C2214yescomplemented
36C25×C11—21no—
37C22×D4×C11—21no—
38C22×D4×C11—21no—
39C22×D4×C11—21no—
40C22×D4×C11—21no—
41C22×D4×C11—22no—
42C22×D4×C11—22no—
43C22×D4×C11—21no—
44C22×D4×C11—22no—
45C22×D4×C11C2×C414yes—
46C22×D4×C11C2312yes—
47C23×C4×C11—21no—
48C23×C4×C11C2311yescharacteristic
49C2×C11×M16—21no—
50C2×C11×M16—21no—
51C2×C11×M16—22no—
52C2×C11×M16—22no—
53C2×C11×M16—21no—
54C2×C11×M16—22no—
55C2×C11×M16—22no—
56C2×C11×M16C2×C414yes—
57C2×C11×M16C2×C414yes—
58C2×C11×M16C2312yes—
59C2×C11×M16C2312yes—
60C2×C11×M16C2312yes—
61C22×C8×C11—21no—
62C22×C8×C11—21no—
63C22×C8×C11—22no—
64C22×C8×C11—22no—
65C22×C8×C11—21no—
66C22×C8×C11D411yescharacteristic
67C22×C8×C11D411yescharacteristic
68C22×C8×C11D412yes—
69C22×C8×C11C2312yes—
70C11×#117—21no—
71C11×#117—21no—
72C11×#117D412yes—
73C11×#117C2312yes—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4D411yescharacteristic
80C2×C11×C4⋊C4D411yescharacteristic
81C2×C11×C4⋊C4C2312yes—
82C2×C11×C22⋊C4—21no—
83C2×C42×C11—21no—
84C11×#107—24no—
85C11×#106—24no—
86C11×#102—24no—
87C11×#102—24no—
88C11×#102—24no—
89C11×#102—24no—
90C11×#100C2×C4116yescomplemented
91C11×#97—24no—
92C4×C8×C11—24no—
93C2×#1931C1111yesmaximal, characteristic, direct product factor, Sylow
94C24×C11—24no—
95C24×C11—22no—
96C24×C11—41no—
97C24×C11—41no—
98C24×C11—42no—
99C24×C11—82no—
100C24×C11—82no—
101C24×C11#4111yescharacteristic
102C2×D4×C11—24no—
103C2×D4×C11—24no—
104C2×D4×C11—24no—
105C2×D4×C11—24no—
106C2×D4×C11—24no—
107C2×D4×C11—22no—
108C2×D4×C11—22no—
109C2×D4×C11—22no—
110C2×D4×C11—22no—
111C2×D4×C11—22no—
112C2×D4×C11—41no—
113C2×D4×C11—41no—
114C2×D4×C11—42no—
115C2×D4×C11—42no—
116C2×D4×C11—42no—
117C2×D4×C11—42no—
118C2×D4×C11—42no—
119C2×D4×C11C22×C414yes—
120C22×C4×C11—21no—
121C22×C4×C11—21no—
122C22×C4×C11—22no—
123C22×C4×C11—41no—
124C22×C4×C11—41no—
125C22×C4×C11—82no—
126C22×C4×C11C22×C412yes—
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11C2×D411yescharacteristic
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11#4111yescharacteristic
132C22×C4×C11#4112yes—
133C22×C4×C11#4112yes—
134C22×C4×C11#4112yes—
135C22×C4×C11C2411yescharacteristic
136C11×M16—24no—
137C11×M16—24no—
138C11×M16—22no—
139C11×M16—22no—
140C11×M16—22no—
141C11×M16—22no—
142C11×M16—42no—
143C11×M16C22×C414yes—
144C11×M16C22×C414yes—
145C2×C8×C11—24no—
146C2×C8×C11—24no—
147C2×C8×C11—22no—
148C2×C8×C11—22no—
149C2×C8×C11—24no—
150C2×C8×C11—22no—
151C2×C8×C11—22no—
152C2×C8×C11—22no—
153C2×C8×C11—22no—
154C2×C8×C11—22no—
155C2×C8×C11—42no—
156C2×C8×C11C2×D412yes—
157C2×C8×C11C2×D412yes—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—22no—
161C11×C4⋊C4—22no—
162C11×C4⋊C4—41no—
163C11×C4⋊C4—41no—
164C11×C4⋊C4C2×D412yes—
165C11×C4⋊C4C2×D412yes—
166C11×C22⋊C4—22no—
167C11×C22⋊C4—22no—
168C42×C11—22no—
169C42×C11—22no—
170C2×#428C2×C1111yescharacteristic, complemented
171C2×#418C2×C1111yescharacteristic
172C22×#102C2×C1111yescharacteristic
173C22×#100C2×C1111yescharacteristic
174C2×#405C2×C1111yescharacteristic, complemented
175#1931C2×C1118yesdirect product factor
176C2×#343C2×C1111yescharacteristic, complemented
177C2×#341C2×C1111yescharacteristic, complemented
178C23×C11—22no—
179C23×C11—22no—
180C23×C11—24no—
181C23×C11—42no—
182C23×C11—42no—
183C23×C11—44no—
184C23×C11—44no—
185C23×C11—88no—
186C23×C11—82no—
187C23×C11—82no—
188C23×C11—88no—
189C23×C11—82no—
190C23×C11—82no—
191C23×C11—82no—
192C23×C11—82no—
193C23×C11#11712yes—
194C23×C11#12111yescharacteristic
195C23×C11#12111yescharacteristic
196C23×C11#12612yes—
197C23×C11C2×#4111yescharacteristic
198D4×C11—24no—
199D4×C11—24no—
200D4×C11—42no—
201D4×C11—42no—
202D4×C11—44no—
203D4×C11—44no—
204C2×C4×C11—22no—
205C2×C4×C11—22no—
206C2×C4×C11—42no—
207C2×C4×C11—42no—
208C2×C4×C11—42no—
209C2×C4×C11—82no—
210C2×C4×C11—82no—
211C2×C4×C11—82no—
212C2×C4×C11#11712yes—
213C2×C4×C11C4×D412yes—
214C2×C4×C11C4×D412yes—
215C2×C4×C11C4×D412yes—
216C2×C4×C11C4×D412yes—
217C2×C4×C11#12111yescharacteristic
218C2×C4×C11#12111yescharacteristic
219C2×C4×C11#12312yes—
220C2×C4×C11#12312yes—
221C2×C4×C11#12412yes—
222C2×C4×C11#12412yes—
223C2×C4×C11#12612yes—
224C2×C4×C11C23×C411yescharacteristic
225C2×C4×C11C22×D411yescharacteristic
226C2×C4×C11C22×D411yescharacteristic
227C2×C4×C11C2×#4111yescharacteristic
228C2×C4×C11C2×#4111yescharacteristic
229C2×C4×C11C2×#4111yescharacteristic
230C8×C11—24no—
231C8×C11—24no—
232C8×C11—22no—
233C8×C11—22no—
234C8×C11—42no—
235C23×D4C22×C1111yescharacteristic
236C22×M16C22×C1111yescharacteristic
237C22×M16C22×C1111yescharacteristic
238C22×M16C22×C1111yescharacteristic
239C23×C8C22×C1111yescharacteristic
240C2×#117C22×C1111yescharacteristic
241C22×C4⋊C4C22×C1111yescharacteristic
242#428—22no—
243#428C22×C1114yescomplemented
244C2×#107—21no—
245C2×#106—21no—
246#418—22no—
247#418C22×C1114yes—
248C2×#102—21no—
249C2×#102—21no—
250C2×#102—22no—
251C2×#102—21no—
252C2×#102—21no—
253C2×#102C22×C1114yes—
254C2×#100C4×C1118yescomplemented
255C2×#100C22×C1114yes—
256#405—22no—
257#405C22×C1114yescomplemented
258C2×#97—21no—
259C2×C4×C8—21no—
260#343C22×C1114yescomplemented
261#341C22×C1114yescomplemented
262C22×C11—24no—
263C22×C11—24no—
264C22×C11—21no—
265C22×C11—21no—
266C22×C11—21no—
267C22×C11—21no—
268C22×C11—44no—
269C22×C11—84no—
270C22×C11—84no—
271C22×C11—88no—
272C22×C11—88no—
273C22×C11—82no—
274C22×C11—82no—
275C22×C11#38812yes—
276C22×C11#38812yes—
277C22×C11#47112yes—
278C22×C11#47212yes—
279C22×C11C2×#11711yescharacteristic
280C22×C11C2×#12111yescharacteristic
281C22×C11C2×#12611yescharacteristic
282C4×C11—42no—
283C4×C11—42no—
284C4×C11—82no—
285C4×C11#38812yes—
286C4×C11#38812yes—
287C4×C11C2×C4×D411yescharacteristic
288C4×C11C2×C4×D411yescharacteristic
289C4×C11C2×#12311yescharacteristic
290C4×C11C2×#12411yescharacteristic
291C25—21no—
292C22×D4—21no—
293C22×D4—21no—
294C22×D4—21no—
295C22×D4—21no—
296C22×D4—22no—
297C22×D4—22no—
298C22×D4—21no—
299C22×D4—22no—
300C22×D4C2×C4×C1114yes—
301C22×D4C23×C1112yes—
302C23×C4—21no—
303C23×C4C23×C1111yescharacteristic
304C2×M16—21no—
305C2×M16—21no—
306C2×M16—22no—
307C2×M16—22no—
308C2×M16—21no—
309C2×M16—22no—
310C2×M16—22no—
311C2×M16C2×C4×C1114yes—
312C2×M16C2×C4×C1114yes—
313C2×M16C23×C1112yes—
314C2×M16C23×C1112yes—
315C2×M16C23×C1112yes—
316C22×C8—21no—
317C22×C8—21no—
318C22×C8—22no—
319C22×C8—22no—
320C22×C8—21no—
321C22×C8D4×C1111yescharacteristic
322C22×C8D4×C1111yescharacteristic
323C22×C8D4×C1112yes—
324C22×C8C23×C1112yes—
325#117—21no—
326#117—21no—
327#117D4×C1112yes—
328#117C23×C1112yes—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—21no—
331C2×C4⋊C4—21no—
332C2×C4⋊C4—21no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4D4×C1111yescharacteristic
335C2×C4⋊C4D4×C1111yescharacteristic
336C2×C4⋊C4C23×C1112yes—
337C2×C22⋊C4—21no—
338C2×C42—21no—
339#107—24no—
340#106—24no—
341#102—24no—
342#102—24no—
343#102—24no—
344#102—24no—
345#100C2×C4×C11116yescomplemented
346#97—24no—
347C4×C8—24no—
348C2×C11—21no—
349C2×C11—21no—
350C2×C11—22no—
351C2×C11—84no—
352C2×C11#193114yesdirect product factor
353C2×C11C2×#38811yescharacteristic
354C2×C11C2×#47111yescharacteristic
355C2×C11C2×#47211yescharacteristic
356C24—24no—
357C24—22no—
358C24—41no—
359C24—41no—
360C24—42no—
361C24—82no—
362C24—82no—
363C24C11×#4111yescharacteristic
364C2×D4—24no—
365C2×D4—24no—
366C2×D4—24no—
367C2×D4—24no—
368C2×D4—24no—
369C2×D4—22no—
370C2×D4—22no—
371C2×D4—22no—
372C2×D4—22no—
373C2×D4—22no—
374C2×D4—41no—
375C2×D4—41no—
376C2×D4—42no—
377C2×D4—42no—
378C2×D4—42no—
379C2×D4—42no—
380C2×D4—42no—
381C2×D4C22×C4×C1114yes—
382C22×C4—21no—
383C22×C4—21no—
384C22×C4—22no—
385C22×C4—41no—
386C22×C4—41no—
387C22×C4—82no—
388C22×C4C22×C4×C1112yes—
389C22×C4C2×D4×C1111yescharacteristic
390C22×C4C2×D4×C1111yescharacteristic
391C22×C4C2×D4×C1111yescharacteristic
392C22×C4C2×D4×C1111yescharacteristic
393C22×C4C11×#4111yescharacteristic
394C22×C4C11×#4112yes—
395C22×C4C11×#4112yes—
396C22×C4C11×#4112yes—
397C22×C4C24×C1111yescharacteristic
398M16—24no—
399M16—24no—
400M16—22no—
401M16—22no—
402M16—22no—
403M16—22no—
404M16—42no—
405M16C22×C4×C1114yes—
406M16C22×C4×C1114yes—
407C2×C8—24no—
408C2×C8—24no—
409C2×C8—22no—
410C2×C8—22no—
411C2×C8—24no—
412C2×C8—22no—
413C2×C8—22no—
414C2×C8—22no—
415C2×C8—22no—
416C2×C8—22no—
417C2×C8—42no—
418C2×C8C2×D4×C1112yes—
419C2×C8C2×D4×C1112yes—
420C4⋊C4—21no—
421C4⋊C4—21no—
422C4⋊C4—22no—
423C4⋊C4—22no—
424C4⋊C4—41no—
425C4⋊C4—41no—
426C4⋊C4C2×D4×C1112yes—
427C4⋊C4C2×D4×C1112yes—
428C22⋊C4—22no—
429C22⋊C4—22no—
430C42—22no—
431C42—22no—
432C11C2×#193111yescharacteristic, direct product factor, Sylow
433C23—22no—
434C23—22no—
435C23—24no—
436C23—42no—
437C23—44no—
438C23—44no—
439C23—42no—
440C23—88no—
441C23—82no—
442C23—82no—
443C23—88no—
444C23—82no—
445C23—82no—
446C23—82no—
447C23—82no—
448C23C11×#11712yes—
449C23C11×#12111yescharacteristic
450C23C11×#12111yescharacteristic
451C23C11×#12612yes—
452C23C2×C11×#4111yescharacteristic
453D4—24no—
454D4—24no—
455D4—42no—
456D4—44no—
457D4—44no—
458D4—42no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—42no—
462C2×C4—42no—
463C2×C4—42no—
464C2×C4—82no—
465C2×C4—82no—
466C2×C4—82no—
467C2×C4C11×#11712yes—
468C2×C4C4×D4×C1112yes—
469C2×C4C4×D4×C1112yes—
470C2×C4C4×D4×C1112yes—
471C2×C4C4×D4×C1112yes—
472C2×C4C11×#12111yescharacteristic
473C2×C4C11×#12111yescharacteristic
474C2×C4C11×#12312yes—
475C2×C4C11×#12312yes—
476C2×C4C11×#12412yes—
477C2×C4C11×#12412yes—
478C2×C4C11×#12612yes—
479C2×C4C23×C4×C1111yescharacteristic
480C2×C4C22×D4×C1111yescharacteristic
481C2×C4C22×D4×C1111yescharacteristic
482C2×C4C2×C11×#4111yescharacteristic
483C2×C4C2×C11×#4111yescharacteristic
484C2×C4C2×C11×#4111yescharacteristic
485C8—24no—
486C8—24no—
487C8—22no—
488C8—22no—
489C8—42no—
490C22—24no—
491C22—24no—
492C22—21no—
493C22—21no—
494C22—21no—
495C22—21no—
496C22—44no—
497C22—84no—
498C22—88no—
499C22—84no—
500C22—88no—
501C22—82no—
502C22—82no—
503C22C11×#38812yes—
504C22C11×#38812yes—
505C22C11×#47112yes—
506C22C11×#47212yes—
507C22C2×C11×#11711yescharacteristic
508C22C2×C11×#12111yescharacteristic
509C22C2×C11×#12611yescharacteristic
510C4—42no—
511C4—42no—
512C4—82no—
513C4C11×#38812yes—
514C4C11×#38812yes—
515C4C2×C4×D4×C1111yescharacteristic
516C4C2×C4×D4×C1111yescharacteristic
517C4C2×C11×#12311yescharacteristic
518C4C2×C11×#12411yescharacteristic
519C2—21no—
520C2—22no—
521C2—21no—
522C2—84no—
523C2C11×#193114yesdirect product factor
524C2C2×C11×#38811yescharacteristic
525C2C2×C11×#47111yescharacteristic
526C2C2×C11×#47211yescharacteristic
subgroupG/H
center, socleC23×C11#121
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC23×D4×C11C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#428C2semidirect
5. C2×C11×#405C2semidirect
6. C11×#1931C2direct (N × H)
7. C2×C11×#343C2semidirect
8. C2×C11×#341C2semidirect
17. C11×#428C22semidirect
28. C2×C11×#100C4semidirect
31. C11×#405C22semidirect
34. C11×#343C22semidirect
35. C11×#341C22semidirect
90. C11×#100C2×C4semidirect
93. C2×#1931C11direct (N × H)
170. C2×#428C2×C11semidirect
174. C2×#405C2×C11semidirect
175. #1931C2×C11direct (N × H)
176. C2×#343C2×C11semidirect
177. C2×#341C2×C11semidirect
243. #428C22×C11semidirect
254. C2×#100C4×C11semidirect
257. #405C22×C11semidirect
260. #343C22×C11semidirect
261. #341C22×C11semidirect
345. #100C2×C4×C11semidirect
352. C2×C11#1931direct (N × H)
432. C11C2×#1931direct (N × H)
523. C2C11×#1931direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4282
C2×C11×#4182
C22×C11×#1022
C22×C11×#1002
C2×C11×#4052
C11×#19312
C2×C11×#3432
C2×C11×#3412
C2×#193111