Finite Group Databasebeta

← C11×#27098 #14604291

Subgroups — C11×#27098 #14604291

Order 2816.

728 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2496C211yesmaximal, characteristic
2C11×#2360C211yesmaximal, characteristic
3C11×#2088C211yesmaximal, characteristic, complemented
4C11×#2084C211yesmaximal, characteristic, complemented
5C11×#2035C211yesmaximal, characteristic
6C11×#2035C211yesmaximal, characteristic
7C11×#1933C211yesmaximal, characteristic, complemented
8C11×#1927C211yesmaximal, characteristic, complemented
9C11×#1923C211yesmaximal, characteristic
10C11×#1919C211yesmaximal, characteristic, complemented
11C11×#1865C211yesmaximal, characteristic, complemented
12C11×#1853C211yesmaximal, characteristic
13C11×#1824C211yesmaximal, characteristic
14C11×#1803C211yesmaximal, characteristic, complemented
15C4×C11×#106C211yesmaximal, characteristic, complemented
16C2×C11×#126—21no—
17C2×C11×C22⋊Q8C2211yescharacteristic
18C2×C4×Q8×C11C2211yescharacteristic
19C22×C11×C4⋊C4C2211yescharacteristic
20C2×C11×#106C2211yescharacteristic
21C2×C11×#106C2211yescharacteristic
22C2×C11×#106C2211yescharacteristic
23C2×C11×#106C2211yescharacteristic
24C2×C11×C4⋊C8C2211yescharacteristic
25C2×C11×#103C2211yescharacteristic
26C2×C11×#103C2211yescharacteristic
27C2×C11×#103C2211yescharacteristic
28C2×C11×#103C2211yescharacteristic
29C2×C11×C22⋊C8C2211yescharacteristic
30C2×C11×C22⋊C8C2211yescharacteristic
31C2×C4×C8×C11C2211yescharacteristic
32C11×#400—21no—
33C11×#397—21no—
34C11×#391C2211yescharacteristic
35C11×#389—21no—
36C11×#389C2211yescharacteristic
37C11×#389C2211yescharacteristic
38C11×#389C2211yescharacteristic
39C11×#387—21no—
40C11×#387—21no—
41C11×#385—21no—
42C11×#384C2211yescharacteristic
43C11×#380C2211yescharacteristic
44C11×#380C2211yescharacteristic
45C4×C11×C4⋊C4C2211yescharacteristic
46C4×C11×C4⋊C4C2211yescharacteristic
47C4×C11×C22⋊C4—21no—
48C4×C11×C22⋊C4C2211yescharacteristic
49C11×#340C2211yescharacteristic
50C11×#340C2211yescharacteristic
51C11×#340C2211yescharacteristic
52C11×#340C2211yescharacteristic
53C11×#340C2211yescharacteristic
54C11×#340C2211yescharacteristic
55C11×#340C2211yescharacteristic
56C11×#340C2211yescharacteristic
57C11×#336C2211yescharacteristic
58C11×#336C2211yescharacteristic
59C22×Q8×C11C2311yescharacteristic
60C23×C4×C11—21no—
61C23×C4×C11C2311yescharacteristic
62C22×C8×C11C2311yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C11×#126—44no—
67C11×C22⋊Q8—22no—
68C11×C22⋊Q8—22no—
69C4×Q8×C11—22no—
70C4×Q8×C11—41no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—22no—
73C2×C11×C4⋊C4—21no—
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⋊C4—21no—
80C2×C11×C4⋊C4—41no—
81C2×C11×C4⋊C4C2311yescharacteristic
82C2×C11×C4⋊C4C2311yescharacteristic
83C2×C11×C4⋊C4C2311yescharacteristic
84C2×C11×C4⋊C4C2311yescharacteristic
85C2×C11×C4⋊C4C2311yescharacteristic
86C2×C11×C4⋊C4C2311yescharacteristic
87C2×C11×C4⋊C4C2311yescharacteristic
88C2×C11×C22⋊C4—21no—
89C2×C11×C22⋊C4—21no—
90C2×C11×C22⋊C4—21no—
91C2×C11×C22⋊C4D411yescharacteristic
92C2×C11×C22⋊C4D411yescharacteristic
93C2×C42×C11—21no—
94C2×C42×C11—21no—
95C2×C42×C11—21no—
96C2×C42×C11C2311yescharacteristic
97C2×C42×C11C2311yescharacteristic
98C11×#106—22no—
99C11×#106—22no—
100C11×#106—22no—
101C11×#106—41no—
102C11×C4⋊C8—41no—
103C11×#103—22no—
104C11×#103—22no—
105C11×#103—22no—
106C11×#103—41no—
107C11×C22⋊C8—22no—
108C11×C22⋊C8—41no—
109C4×C8×C11—22no—
110C11×#95—21no—
111C11×#95—21no—
112C11×#95—21no—
113C11×#95—21no—
114C11×#95—21no—
115C11×#95—21no—
116C11×#95—21no—
117C11×#95—21no—
118C11×#95—21no—
119C11×#95D411yescharacteristic
120C11×#95D411yescharacteristic
121#27098C1111yesmaximal, characteristic, direct product factor, Sylow
122C24×C11C2×D411yescharacteristic
123C2×Q8×C11—21no—
124C2×Q8×C11—21no—
125C2×Q8×C11—21no—
126C2×Q8×C11—21no—
127C2×Q8×C11—21no—
128C2×Q8×C11#4112yes—
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—42no—
144C22×C4×C11—42no—
145C22×C4×C11—81no—
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2411yescharacteristic
152C2×C8×C11—21no—
153C2×C8×C11—21no—
154C2×C8×C11—21no—
155C2×C8×C11—21no—
156C2×C8×C11—21no—
157C2×C8×C11—21no—
158C2×C8×C11—21no—
159C2×C8×C11—21no—
160C2×C8×C11—21no—
161C2×C8×C11—21no—
162C2×C8×C11—21no—
163C2×C8×C11#4112yes—
164C11×C4⋊C4—24no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—42no—
178C11×C4⋊C4—42no—
179C11×C4⋊C4—42no—
180C11×C4⋊C4—42no—
181C11×C4⋊C4—42no—
182C11×C4⋊C4—42no—
183C11×C4⋊C4—81no—
184C11×C4⋊C4#4112yes—
185C11×C4⋊C4#4112yes—
186C11×C22⋊C4—24no—
187C11×C22⋊C4—41no—
188C11×C22⋊C4—42no—
189C11×C22⋊C4—42no—
190C11×C22⋊C4SD1614yes—
191C42×C11—21no—
192C42×C11—21no—
193C42×C11—21no—
194C42×C11—21no—
195C42×C11—42no—
196C42×C11—42no—
197C42×C11—81no—
198#2496C2×C1111yescharacteristic
199#2360C2×C1111yescharacteristic
200#2088C2×C1111yescharacteristic, complemented
201#2084C2×C1111yescharacteristic, complemented
202#2035C2×C1111yescharacteristic
203#2035C2×C1111yescharacteristic
204#1933C2×C1111yescharacteristic, complemented
205#1927C2×C1111yescharacteristic, complemented
206#1923C2×C1111yescharacteristic
207#1919C2×C1111yescharacteristic, complemented
208#1865C2×C1111yescharacteristic, complemented
209#1853C2×C1111yescharacteristic
210#1824C2×C1111yescharacteristic
211#1803C2×C1111yescharacteristic, complemented
212C4×#106C2×C1111yescharacteristic, complemented
213C23×C11—21no—
214C23×C11—21no—
215C23×C11—21no—
216C23×C11—21no—
217C23×C11—21no—
218C23×C11—21no—
219C23×C11C2×SD1612yes—
220C23×C11C22×D411yescharacteristic
221Q8×C11—22no—
222Q8×C11—22no—
223Q8×C11—41no—
224Q8×C11—41no—
225C2×C4×C11—21no—
226C2×C4×C11—21no—
227C2×C4×C11—21no—
228C2×C4×C11—21no—
229C2×C4×C11—22no—
230C2×C4×C11—22no—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—22no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11—41no—
266C2×C4×C11—84no—
267C2×C4×C11C2×SD1612yes—
268C2×C4×C11C2×SD1612yes—
269C2×C4×C11C2×#4111yescharacteristic
270C2×C4×C11C2×#4111yescharacteristic
271C2×C4×C11C2×#4111yescharacteristic
272C2×C4×C11C2×#4111yescharacteristic
273C2×C4×C11H(5,𝔽2)11yescharacteristic
274C2×C4×C112−1+411yescharacteristic
275C8×C11—22no—
276C8×C11—41no—
277C8×C11—41no—
278C8×C11—41no—
279C2×#126—21no—
280C2×C22⋊Q8C22×C1111yescharacteristic
281C2×C4×Q8C22×C1111yescharacteristic
282C22×C4⋊C4C22×C1111yescharacteristic
283C2×#106C22×C1111yescharacteristic
284C2×#106C22×C1111yescharacteristic
285C2×#106C22×C1111yescharacteristic
286C2×#106C22×C1111yescharacteristic
287C2×C4⋊C8C22×C1111yescharacteristic
288C2×#103C22×C1111yescharacteristic
289C2×#103C22×C1111yescharacteristic
290C2×#103C22×C1111yescharacteristic
291C2×#103C22×C1111yescharacteristic
292C2×C22⋊C8C22×C1111yescharacteristic
293C2×C22⋊C8C22×C1111yescharacteristic
294C2×C4×C8C22×C1111yescharacteristic
295#400—21no—
296#397—21no—
297#391C22×C1111yescharacteristic
298#389—21no—
299#389C22×C1111yescharacteristic
300#389C22×C1111yescharacteristic
301#389C22×C1111yescharacteristic
302#387—21no—
303#387—21no—
304#385—21no—
305#384C22×C1111yescharacteristic
306#380C22×C1111yescharacteristic
307#380C22×C1111yescharacteristic
308C4×C4⋊C4C22×C1111yescharacteristic
309C4×C4⋊C4C22×C1111yescharacteristic
310C4×C22⋊C4—21no—
311C4×C22⋊C4C22×C1111yescharacteristic
312#340C22×C1111yescharacteristic
313#340C22×C1111yescharacteristic
314#340C22×C1111yescharacteristic
315#340C22×C1111yescharacteristic
316#340C22×C1111yescharacteristic
317#340C22×C1111yescharacteristic
318#340C22×C1111yescharacteristic
319#340C22×C1111yescharacteristic
320#336C22×C1111yescharacteristic
321#336C22×C1111yescharacteristic
322C22×C11—22no—
323C22×C11—22no—
324C22×C11—22no—
325C22×C11—41no—
326C22×C11—41no—
327C22×C11—41no—
328C22×C11—41no—
329C22×C11#52511yescharacteristic
330C22×C11#54611yescharacteristic
331C22×C11#54711yescharacteristic
332C22×C11C22×SD1611yescharacteristic
333C22×C11#57511yescharacteristic
334C22×C11#57711yescharacteristic
335C22×C11#57811yescharacteristic
336C4×C11—22no—
337C4×C11—22no—
338C4×C11—41no—
339C4×C11—42no—
340C4×C11—41no—
341C4×C11—42no—
342C4×C11—41no—
343C4×C11—42no—
344C4×C11—81no—
345C4×C11—81no—
346C4×C11—81no—
347C4×C11—81no—
348C4×C11—81no—
349C4×C11#52911yescharacteristic
350C4×C11#54211yescharacteristic
351C4×C11#55211yescharacteristic
352C4×C11#55311yescharacteristic
353C22×Q8C23×C1111yescharacteristic
354C23×C4—21no—
355C23×C4C23×C1111yescharacteristic
356C22×C8C23×C1111yescharacteristic
357C22×C8C23×C1111yescharacteristic
358C22×C8C23×C1111yescharacteristic
359C22×C8C23×C1111yescharacteristic
360#126—44no—
361C22⋊Q8—22no—
362C22⋊Q8—22no—
363C4×Q8—22no—
364C4×Q8—41no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—41no—
375C2×C4⋊C4C23×C1111yescharacteristic
376C2×C4⋊C4C23×C1111yescharacteristic
377C2×C4⋊C4C23×C1111yescharacteristic
378C2×C4⋊C4C23×C1111yescharacteristic
379C2×C4⋊C4C23×C1111yescharacteristic
380C2×C4⋊C4C23×C1111yescharacteristic
381C2×C4⋊C4C23×C1111yescharacteristic
382C2×C22⋊C4—21no—
383C2×C22⋊C4—21no—
384C2×C22⋊C4—21no—
385C2×C22⋊C4D4×C1111yescharacteristic
386C2×C22⋊C4D4×C1111yescharacteristic
387C2×C42—21no—
388C2×C42—21no—
389C2×C42—21no—
390C2×C42C23×C1111yescharacteristic
391C2×C42C23×C1111yescharacteristic
392#106—22no—
393#106—22no—
394#106—22no—
395#106—41no—
396C4⋊C8—41no—
397#103—22no—
398#103—22no—
399#103—22no—
400#103—41no—
401C22⋊C8—22no—
402C22⋊C8—41no—
403C4×C8—22no—
404#95—21no—
405#95—21no—
406#95—21no—
407#95—21no—
408#95—21no—
409#95—21no—
410#95—21no—
411#95—21no—
412#95—21no—
413#95D4×C1111yescharacteristic
414#95D4×C1111yescharacteristic
415C2×C11—42no—
416C2×C11#246811yescharacteristic
417C2×C11#310311yescharacteristic
418C2×C11#312011yescharacteristic
419C2×C11#329811yescharacteristic
420C2×C11#332311yescharacteristic
421C2×C11#333511yescharacteristic
422C2×C11#334911yescharacteristic
423C24C2×D4×C1111yescharacteristic
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8—21no—
428C2×Q8—21no—
429C2×Q8C11×#4112yes—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—42no—
445C22×C4—42no—
446C22×C4—81no—
447C22×C4C2×D4×C1111yescharacteristic
448C22×C4C2×D4×C1111yescharacteristic
449C22×C4C2×D4×C1111yescharacteristic
450C22×C4C2×D4×C1111yescharacteristic
451C22×C4C2×D4×C1111yescharacteristic
452C22×C4C24×C1111yescharacteristic
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8C11×#4112yes—
465C4⋊C4—24no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—42no—
479C4⋊C4—42no—
480C4⋊C4—42no—
481C4⋊C4—42no—
482C4⋊C4—42no—
483C4⋊C4—42no—
484C4⋊C4—81no—
485C4⋊C4C11×#4112yes—
486C4⋊C4C11×#4112yes—
487C22⋊C4—24no—
488C22⋊C4—41no—
489C22⋊C4—42no—
490C22⋊C4—42no—
491C22⋊C4C11×SD1614yes—
492C42—21no—
493C42—21no—
494C42—21no—
495C42—21no—
496C42—42no—
497C42—42no—
498C42—81no—
499C11#2709811yescharacteristic, direct product factor, Sylow
500C23—21no—
501C23—21no—
502C23—21no—
503C23—21no—
504C23—21no—
505C23—21no—
506C23C2×C11×SD1612yes—
507C23C22×D4×C1111yescharacteristic
508Q8—22no—
509Q8—22no—
510Q8—41no—
511Q8—41no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—22no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—84no—
554C2×C4C2×C11×SD1612yes—
555C2×C4C2×C11×SD1612yes—
556C2×C4C2×C11×#4111yescharacteristic
557C2×C4C2×C11×#4111yescharacteristic
558C2×C4C2×C11×#4111yescharacteristic
559C2×C4C2×C11×#4111yescharacteristic
560C2×C4C11×H(5,𝔽2)11yescharacteristic
561C2×C4C11×2−1+411yescharacteristic
562C8—22no—
563C8—41no—
564C8—41no—
565C8—41no—
566C22—22no—
567C22—22no—
568C22—22no—
569C22—41no—
570C22—41no—
571C22—41no—
572C22—41no—
573C22C11×#52511yescharacteristic
574C22C11×#54611yescharacteristic
575C22C11×#54711yescharacteristic
576C22C22×C11×SD1611yescharacteristic
577C22C11×#57511yescharacteristic
578C22C11×#57711yescharacteristic
579C22C11×#57811yescharacteristic
580C4—22no—
581C4—22no—
582C4—41no—
583C4—42no—
584C4—41no—
585C4—42no—
586C4—41no—
587C4—42no—
588C4—81no—
589C4—81no—
590C4—81no—
591C4—81no—
592C4—81no—
593C4C11×#52911yescharacteristic
594C4C11×#54211yescharacteristic
595C4C11×#55211yescharacteristic
596C4C11×#55311yescharacteristic
597C2—42no—
598C2C11×#246811yescharacteristic
599C2C11×#310311yescharacteristic
600C2C11×#312011yescharacteristic
601C2C11×#329811yescharacteristic
602C2C11×#332311yescharacteristic
603C2C11×#333511yescharacteristic
604C2C11×#334911yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC24×C11C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C4×C11×C22⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
3. C11×#2088C2semidirect
4. C11×#2084C2semidirect
7. C11×#1933C2semidirect
8. C11×#1927C2semidirect
10. C11×#1919C2semidirect
11. C11×#1865C2semidirect
14. C11×#1803C2semidirect
15. C4×C11×#106C2semidirect
121. #27098C11direct (N × H)
200. #2088C2×C11semidirect
201. #2084C2×C11semidirect
204. #1933C2×C11semidirect
205. #1927C2×C11semidirect
207. #1919C2×C11semidirect
208. #1865C2×C11semidirect
211. #1803C2×C11semidirect
212. C4×#106C2×C11semidirect
499. C11#27098direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#24962
C11×#23602
C11×#20882
C11×#20842
C11×#20352
C11×#19332
C11×#19272
C11×#19232
C11×#19192
C11×#18652
C11×#18532
C11×#18242
C11×#18032
C4×C11×#1062
#2709811