Finite Group Databasebeta

← C2×C11×#3357 #14638443

Subgroups — C2×C11×#3357 #14638443

Order 2816.

1930 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#555C211yesmaximal, characteristic
2C2×C11×#554C211yesmaximal, characteristic, complemented
3C11×#3357C2116yesmaximal, direct product factor
4C2×C11×#500C211yesmaximal, characteristic, complemented
5C2×C11×#485C212yesmaximal, complemented
6C2×C11×#480C212yesmaximal, complemented
7C2×C11×#477C211yesmaximal, characteristic, complemented
8C2×C11×#476C211yesmaximal, characteristic, complemented
9C2×C11×#468C212yesmaximal, complemented
10C2×C4×C11×SD16C211yesmaximal, characteristic, complemented
11C2×C11×#436C211yesmaximal, characteristic, complemented
12C2×C11×#428C212yesmaximal, complemented
13C22×C11×SD16C2211yescharacteristic
14C22×C11×M16C2212yes—
15C11×#555—24no—
16C11×#555C2218yes—
17C11×#554—24no—
18C11×#554C2218yescomplemented
19C2×C11×C4⋊Q8C2211yescharacteristic
20C2×C11×C4⋊Q8C2211yescharacteristic
21C2×C11×#125—21no—
22C2×C11×#124—22no—
23C2×C11×C22⋊Q8—22no—
24C2×C11×C22⋊Q8C2212yes—
25C2×C11×#121—21no—
26C2×C11×#121C2212yes—
27C2×C4×Q8×C11C2211yescharacteristic
28C2×C4×D4×C11—21no—
29C2×C4×D4×C11C2211yescharacteristic
30C2×C4×D4×C11C2211yescharacteristic
31C2×C11×#117—21no—
32C2×C11×#117C2212yes—
33C22×C11×C4⋊C4C2212yes—
34C11×#500C2218yescomplemented
35C11×#485C22116yescomplemented
36C11×#480C22116yescomplemented
37C11×#477C2218yescomplemented
38C11×#476C2218yescomplemented
39C11×#468C22116yescomplemented
40C4×C11×SD16C2218yescomplemented
41C11×#436C2218yescomplemented
42C11×#428C22116yescomplemented
43C2×C11×#107C2212yes—
44C2×C11×#107C2212yes—
45C2×C11×#107C2212yes—
46C2×C11×#106C2211yescharacteristic
47C2×C11×#106C2212yes—
48C2×C11×C4⋊C8C2211yescharacteristic
49C2×C11×#103C2211yescharacteristic
50C2×C11×#103C2212yes—
51C2×C11×#102C2211yescharacteristic
52C2×C11×#102C2212yes—
53C2×C11×C22⋊C8C2212yes—
54C2×C4×C8×C11C2211yescharacteristic
55C22×Q8×C11—21no—
56C22×Q8×C11—21no—
57C22×Q8×C11C2311yescharacteristic
58C22×D4×C11—22no—
59C22×D4×C11D411yescharacteristic
60C22×D4×C11C2311yescharacteristic
61C23×C4×C11—22no—
62C23×C4×C11—21no—
63C23×C4×C11C2312yes—
64C2×C11×SD16—24no—
65C2×C11×SD16C2314yes—
66C2×C11×M16—28no—
67C2×C11×M16C2318yes—
68C22×C8×C11C2311yescharacteristic
69C22×C8×C11C2312yes—
70C22×C8×C11C2311yescharacteristic
71C11×C4⋊Q8—22no—
72C11×C4⋊Q8—22no—
73C11×C4⋊Q8C2314yes—
74C11×C4⋊Q8C2314yes—
75C11×#125—28no—
76C11×#124—216no—
77C11×C22⋊Q8—24no—
78C11×C22⋊Q8—216no—
79C11×C22⋊Q8C2318yes—
80C11×#121—28no—
81C11×#121—24no—
82C11×#121C2318yes—
83C4×Q8×C11—22no—
84C4×Q8×C11C2314yes—
85C4×D4×C11—28no—
86C4×D4×C11—22no—
87C4×D4×C11D414yes—
88C4×D4×C11C2314yes—
89C4×D4×C11C2314yes—
90C11×#117—24no—
91C11×#117—28no—
92C11×#117C2318yes—
93C2×C11×C4⋊C4—22no—
94C2×C11×C4⋊C4—24no—
95C2×C11×C4⋊C4—21no—
96C2×C11×C4⋊C4—21no—
97C2×C11×C4⋊C4—21no—
98C2×C11×C4⋊C4—22no—
99C2×C11×C4⋊C4D411yescharacteristic
100C2×C11×C4⋊C4C2311yescharacteristic
101C2×C11×C4⋊C4C2312yes—
102C2×C11×C4⋊C4C2318yes—
103C2×C11×C4⋊C4C2311yescharacteristic
104C2×C11×C4⋊C4C2312yes—
105C2×C11×C22⋊C4—22no—
106C2×C11×C22⋊C4—22no—
107C2×C11×C22⋊C4—22no—
108C2×C11×C22⋊C4—21no—
109C2×C11×C22⋊C4D412yes—
110C2×C42×C11—22no—
111C2×C42×C11—21no—
112C2×C42×C11C2311yescharacteristic
113C11×#107C2318yes—
114C11×#107C2318yes—
115C11×#107C2318yes—
116C11×#106C2314yes—
117C11×#106C2318yes—
118C11×C4⋊C8C2314yes—
119C11×#103C2314yes—
120C11×#103C2318yes—
121C11×#102C2314yes—
122C11×#102C2318yes—
123C11×C22⋊C8C2318yes—
124C4×C8×C11C2314yes—
125C2×#3357C1111yesmaximal, characteristic, direct product factor, Sylow
126C24×C11—21no—
127C24×C11C2×D412yes—
128C2×Q8×C11—21no—
129C2×Q8×C11—24no—
130C2×Q8×C11—24no—
131C2×Q8×C11—22no—
132C2×Q8×C11—22no—
133C2×Q8×C11—82no—
134C2×Q8×C11—82no—
135C2×Q8×C11C2412yes—
136C2×D4×C11—28no—
137C2×D4×C11—24no—
138C2×D4×C11—21no—
139C2×D4×C11—22no—
140C2×D4×C11—22no—
141C2×D4×C11—84no—
142C2×D4×C11C2×D414yes—
143C2×D4×C11C2412yes—
144C22×C4×C11—24no—
145C22×C4×C11—24no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—22no—
149C22×C4×C11—21no—
150C22×C4×C11—22no—
151C22×C4×C11—28no—
152C22×C4×C11—24no—
153C22×C4×C11—44no—
154C22×C4×C11—84no—
155C22×C4×C11C2×D414yes—
156C22×C4×C11C2×D412yes—
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2×D411yescharacteristic
159C22×C4×C11C2414yes—
160C22×C4×C11C2411yescharacteristic
161C11×SD16—28no—
162C11×M16—216no—
163C2×C8×C11—24no—
164C2×C8×C11—22no—
165C2×C8×C11#4114yes—
166C2×C8×C11C2412yes—
167C2×C8×C11C2414yes—
168C2×C8×C11C2412yes—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—28no—
171C11×C4⋊C4—22no—
172C11×C4⋊C4—24no—
173C11×C4⋊C4—24no—
174C11×C4⋊C4—24no—
175C11×C4⋊C4—28no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—22no—
178C11×C4⋊C4C2×D414yes—
179C11×C4⋊C4C2412yes—
180C11×C4⋊C4C2414yes—
181C11×C4⋊C4C2412yes—
182C11×C4⋊C4C2414yes—
183C11×C22⋊C4—28no—
184C11×C22⋊C4—28no—
185C11×C22⋊C4—28no—
186C11×C22⋊C4—24no—
187C11×C22⋊C4C2×D418yes—
188C42×C11—28no—
189C42×C11—24no—
190C42×C11C2×D412yes—
191C42×C11C2412yes—
192C2×#555C2×C1111yescharacteristic
193C2×#554C2×C1111yescharacteristic, complemented
194#3357C2×C11116yesdirect product factor
195C2×#500C2×C1111yescharacteristic, complemented
196C2×#485C2×C1112yescomplemented
197C2×#480C2×C1112yescomplemented
198C2×#477C2×C1111yescharacteristic, complemented
199C2×#476C2×C1111yescharacteristic, complemented
200C2×#468C2×C1112yescomplemented
201C2×C4×SD16C2×C1111yescharacteristic, complemented
202C2×#436C2×C1111yescharacteristic, complemented
203C2×#428C2×C1112yescomplemented
204C23×C11—24no—
205C23×C11—24no—
206C23×C11—24no—
207C23×C11—22no—
208C23×C11—42no—
209C23×C11—42no—
210C23×C11—42no—
211C23×C11C22×D414yes—
212C23×C11C22×D411yescharacteristic
213Q8×C11—22no—
214Q8×C11—22no—
215Q8×C11—42no—
216Q8×C11—84no—
217Q8×C11—84no—
218D4×C11—28no—
219D4×C11—22no—
220D4×C11—22no—
221D4×C11—42no—
222D4×C11—88no—
223C2×C4×C11—24no—
224C2×C4×C11—22no—
225C2×C4×C11—28no—
226C2×C4×C11—24no—
227C2×C4×C11—24no—
228C2×C4×C11—22no—
229C2×C4×C11—22no—
230C2×C4×C11—24no—
231C2×C4×C11—22no—
232C2×C4×C11—24no—
233C2×C4×C11—42no—
234C2×C4×C11—42no—
235C2×C4×C11—42no—
236C2×C4×C11—44no—
237C2×C4×C11—44no—
238C2×C4×C11—48no—
239C2×C4×C11—88no—
240C2×C4×C11#13714yes—
241C2×C4×C11C22×D414yes—
242C2×C4×C11C22×D412yes—
243C2×C4×C11C22×D411yescharacteristic
244C2×C4×C11C22×D412yes—
245C2×C4×C11C2×#4112yes—
246C2×C4×C112−1+412yes—
247C2×C4×C11C2511yescharacteristic
248C8×C11—24no—
249C8×C11—22no—
250C8×C11C2×#4114yes—
251C22×SD16C22×C1111yescharacteristic
252C22×M16C22×C1112yes—
253#555—24no—
254#555C22×C1118yes—
255#554—24no—
256#554C22×C1118yescomplemented
257C2×C4⋊Q8C22×C1111yescharacteristic
258C2×C4⋊Q8C22×C1111yescharacteristic
259C2×#125—21no—
260C2×#124—22no—
261C2×C22⋊Q8—22no—
262C2×C22⋊Q8C22×C1112yes—
263C2×#121—21no—
264C2×#121C22×C1112yes—
265C2×C4×Q8C22×C1111yescharacteristic
266C2×C4×D4—21no—
267C2×C4×D4C22×C1111yescharacteristic
268C2×C4×D4C22×C1111yescharacteristic
269C2×#117—21no—
270C2×#117C22×C1112yes—
271C22×C4⋊C4C22×C1112yes—
272#500C22×C1118yescomplemented
273#485C22×C11116yescomplemented
274#480C22×C11116yescomplemented
275#477C22×C1118yescomplemented
276#476C22×C1118yescomplemented
277#468C22×C11116yescomplemented
278C4×SD16C22×C1118yescomplemented
279#436C22×C1118yescomplemented
280#428C22×C11116yescomplemented
281C2×#107C22×C1112yes—
282C2×#107C22×C1112yes—
283C2×#107C22×C1112yes—
284C2×#106C22×C1112yes—
285C2×#106C22×C1111yescharacteristic
286C2×C4⋊C8C22×C1111yescharacteristic
287C2×#103C22×C1112yes—
288C2×#103C22×C1111yescharacteristic
289C2×#102C22×C1111yescharacteristic
290C2×#102C22×C1112yes—
291C2×C22⋊C8C22×C1112yes—
292C2×C4×C8C22×C1111yescharacteristic
293C22×C11—24no—
294C22×C11—24no—
295C22×C11—24no—
296C22×C11—48no—
297C22×C11—42no—
298C22×C11—42no—
299C22×C11—42no—
300C22×C11—84no—
301C22×C11#54712yes—
302C22×C11C2×#13712yes—
303C22×C11#57612yes—
304C22×C11C23×D411yescharacteristic
305C4×C11—24no—
306C4×C11—22no—
307C4×C11—42no—
308C4×C11—42no—
309C4×C11—42no—
310C4×C11—44no—
311C4×C11—44no—
312C4×C11#54712yes—
313C4×C11C2×#13714yes—
314C4×C11C22×#4111yescharacteristic
315C4×C11C2×2−1+411yescharacteristic
316C22×Q8—21no—
317C22×Q8—21no—
318C22×Q8C23×C1111yescharacteristic
319C22×D4—22no—
320C22×D4D4×C1111yescharacteristic
321C22×D4C23×C1111yescharacteristic
322C23×C4—22no—
323C23×C4—21no—
324C23×C4C23×C1112yes—
325C2×SD16—24no—
326C2×SD16C23×C1114yes—
327C2×M16—28no—
328C2×M16C23×C1118yes—
329C22×C8C23×C1112yes—
330C22×C8C23×C1111yescharacteristic
331C22×C8C23×C1111yescharacteristic
332C4⋊Q8—22no—
333C4⋊Q8—22no—
334C4⋊Q8C23×C1114yes—
335C4⋊Q8C23×C1114yes—
336#125—28no—
337#124—216no—
338C22⋊Q8—24no—
339C22⋊Q8—216no—
340C22⋊Q8C23×C1118yes—
341#121—28no—
342#121—24no—
343#121C23×C1118yes—
344C4×Q8—22no—
345C4×Q8C23×C1114yes—
346C4×D4—28no—
347C4×D4—22no—
348C4×D4D4×C1114yes—
349C4×D4C23×C1114yes—
350C4×D4C23×C1114yes—
351#117—24no—
352#117—28no—
353#117C23×C1118yes—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—24no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4D4×C1111yescharacteristic
361C2×C4⋊C4C23×C1111yescharacteristic
362C2×C4⋊C4C23×C1112yes—
363C2×C4⋊C4C23×C1118yes—
364C2×C4⋊C4C23×C1111yescharacteristic
365C2×C4⋊C4C23×C1112yes—
366C2×C22⋊C4—22no—
367C2×C22⋊C4—22no—
368C2×C22⋊C4—22no—
369C2×C22⋊C4—21no—
370C2×C22⋊C4D4×C1112yes—
371C2×C42—22no—
372C2×C42—21no—
373C2×C42C23×C1111yescharacteristic
374#107C23×C1118yes—
375#107C23×C1118yes—
376#107C23×C1118yes—
377#106C23×C1114yes—
378#106C23×C1118yes—
379C4⋊C8C23×C1114yes—
380#103C23×C1114yes—
381#103C23×C1118yes—
382#102C23×C1114yes—
383#102C23×C1118yes—
384C22⋊C8C23×C1118yes—
385C4×C8C23×C1114yes—
386C2×C11—44no—
387C2×C11—82no—
388C2×C11#335714yesdirect product factor
389C2×C11C2×#54711yescharacteristic
390C2×C11C22×#13711yescharacteristic
391C2×C11C2×#57611yescharacteristic
392C24—21no—
393C24C2×D4×C1112yes—
394C2×Q8—21no—
395C2×Q8—24no—
396C2×Q8—24no—
397C2×Q8—22no—
398C2×Q8—22no—
399C2×Q8—82no—
400C2×Q8—82no—
401C2×Q8C24×C1112yes—
402C2×D4—28no—
403C2×D4—24no—
404C2×D4—21no—
405C2×D4—22no—
406C2×D4—22no—
407C2×D4—84no—
408C2×D4C2×D4×C1114yes—
409C2×D4C24×C1112yes—
410C22×C4—24no—
411C22×C4—24no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—22no—
415C22×C4—21no—
416C22×C4—22no—
417C22×C4—28no—
418C22×C4—24no—
419C22×C4—44no—
420C22×C4—84no—
421C22×C4C2×D4×C1112yes—
422C22×C4C2×D4×C1111yescharacteristic
423C22×C4C2×D4×C1114yes—
424C22×C4C2×D4×C1111yescharacteristic
425C22×C4C24×C1114yes—
426C22×C4C24×C1111yescharacteristic
427SD16—28no—
428M16—216no—
429C2×C8—24no—
430C2×C8—22no—
431C2×C8C11×#4114yes—
432C2×C8C24×C1112yes—
433C2×C8C24×C1114yes—
434C2×C8C24×C1112yes—
435C4⋊C4—21no—
436C4⋊C4—28no—
437C4⋊C4—22no—
438C4⋊C4—24no—
439C4⋊C4—24no—
440C4⋊C4—24no—
441C4⋊C4—28no—
442C4⋊C4—21no—
443C4⋊C4—22no—
444C4⋊C4C2×D4×C1114yes—
445C4⋊C4C24×C1112yes—
446C4⋊C4C24×C1114yes—
447C4⋊C4C24×C1112yes—
448C4⋊C4C24×C1114yes—
449C22⋊C4—28no—
450C22⋊C4—28no—
451C22⋊C4—28no—
452C22⋊C4—24no—
453C22⋊C4C2×D4×C1118yes—
454C42—28no—
455C42—24no—
456C42C2×D4×C1112yes—
457C42C24×C1112yes—
458C11C2×#335711yescharacteristic, direct product factor, Sylow
459C23—24no—
460C23—24no—
461C23—24no—
462C23—22no—
463C23—42no—
464C23—42no—
465C23—42no—
466C23C22×D4×C1114yes—
467C23C22×D4×C1111yescharacteristic
468Q8—22no—
469Q8—22no—
470Q8—42no—
471Q8—84no—
472Q8—84no—
473D4—28no—
474D4—22no—
475D4—22no—
476D4—42no—
477D4—88no—
478C2×C4—24no—
479C2×C4—22no—
480C2×C4—28no—
481C2×C4—24no—
482C2×C4—24no—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—24no—
486C2×C4—22no—
487C2×C4—24no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—44no—
492C2×C4—44no—
493C2×C4—48no—
494C2×C4—88no—
495C2×C4C11×#13714yes—
496C2×C4C22×D4×C1114yes—
497C2×C4C22×D4×C1112yes—
498C2×C4C22×D4×C1111yescharacteristic
499C2×C4C22×D4×C1112yes—
500C2×C4C2×C11×#4112yes—
501C2×C4C11×2−1+412yes—
502C2×C4C25×C1111yescharacteristic
503C8—24no—
504C8—22no—
505C8C2×C11×#4114yes—
506C22—24no—
507C22—24no—
508C22—24no—
509C22—48no—
510C22—42no—
511C22—42no—
512C22—42no—
513C22—84no—
514C22C11×#54712yes—
515C22C2×C11×#13712yes—
516C22C11×#57612yes—
517C22C23×D4×C1111yescharacteristic
518C4—24no—
519C4—22no—
520C4—42no—
521C4—42no—
522C4—42no—
523C4—44no—
524C4—44no—
525C4C11×#54712yes—
526C4C2×C11×#13714yes—
527C4C22×C11×#4111yescharacteristic
528C4C2×C11×2−1+411yescharacteristic
529C2—44no—
530C2—82no—
531C2C11×#335714yesdirect product factor
532C2C2×C11×#54711yescharacteristic
533C2C22×C11×#13711yescharacteristic
534C2C2×C11×#57611yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC2×C4C25×C11
prime radicalC2×C11×#555C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C4×D4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#554C2semidirect
3. C11×#3357C2direct (N × H)
4. C2×C11×#500C2semidirect
5. C2×C11×#485C2semidirect
6. C2×C11×#480C2semidirect
7. C2×C11×#477C2semidirect
8. C2×C11×#476C2semidirect
9. C2×C11×#468C2semidirect
10. C2×C4×C11×SD16C2semidirect
11. C2×C11×#436C2semidirect
12. C2×C11×#428C2semidirect
18. C11×#554C22semidirect
34. C11×#500C22semidirect
35. C11×#485C22semidirect
36. C11×#480C22semidirect
37. C11×#477C22semidirect
38. C11×#476C22semidirect
39. C11×#468C22semidirect
40. C4×C11×SD16C22semidirect
41. C11×#436C22semidirect
42. C11×#428C22semidirect
125. C2×#3357C11direct (N × H)
193. C2×#554C2×C11semidirect
194. #3357C2×C11direct (N × H)
195. C2×#500C2×C11semidirect
196. C2×#485C2×C11semidirect
197. C2×#480C2×C11semidirect
198. C2×#477C2×C11semidirect
199. C2×#476C2×C11semidirect
200. C2×#468C2×C11semidirect
201. C2×C4×SD16C2×C11semidirect
202. C2×#436C2×C11semidirect
203. C2×#428C2×C11semidirect
256. #554C22×C11semidirect
272. #500C22×C11semidirect
273. #485C22×C11semidirect
274. #480C22×C11semidirect
275. #477C22×C11semidirect
276. #476C22×C11semidirect
277. #468C22×C11semidirect
278. C4×SD16C22×C11semidirect
279. #436C22×C11semidirect
280. #428C22×C11semidirect
388. C2×C11#3357direct (N × H)
458. C11C2×#3357direct (N × H)
531. C2C11×#3357direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5552
C2×C11×#5542
C11×#33572
C2×C11×#5002
C2×C11×#4852
C2×C11×#4802
C2×C11×#4772
C2×C11×#4762
C2×C11×#4682
C2×C4×C11×SD162
C2×C11×#4362
C2×C11×#4282
C2×#335711