Finite Group Databasebeta

← C11×#24861 #14602054

Subgroups — C11×#24861 #14602054

Order 2816.

1238 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#480C211yesmaximal, characteristic, complemented
2C22×C11×#102C211yesmaximal, characteristic, complemented
3C11×#2408C211yesmaximal, characteristic
4D4×C11×C4⋊C4C211yesmaximal, characteristic, complemented
5C11×#2093C211yesmaximal, characteristic, complemented
6C11×#2071C211yesmaximal, characteristic, complemented
7C11×#2033C211yesmaximal, characteristic, complemented
8C11×#2033C211yesmaximal, characteristic, complemented
9C11×#1925C211yesmaximal, characteristic, complemented
10C11×#1925C211yesmaximal, characteristic, complemented
11C11×#1874C211yesmaximal, characteristic, complemented
12C11×#1869C211yesmaximal, characteristic, complemented
13C11×#1852C211yesmaximal, characteristic, complemented
14C11×#1808C211yesmaximal, characteristic, complemented
15C11×#1786C211yesmaximal, characteristic, complemented
16C23×D4×C11C2211yescharacteristic
17C23×C8×C11C2211yescharacteristic
18C2×C11×#121C2211yescharacteristic
19C2×C11×#121C2211yescharacteristic
20C2×C11×#120—21no—
21C2×C4×D4×C11—21no—
22C2×C4×D4×C11C2211yescharacteristic
23C22×C11×C4⋊C4C2211yescharacteristic
24C22×C11×C4⋊C4C2211yescharacteristic, complemented
25C11×#480—24no—
26C2×C11×#107C2211yescharacteristic, complemented
27C2×C11×#107C2211yescharacteristic, complemented
28C2×C11×#107C2211yescharacteristic, complemented
29C2×C11×#107C2211yescharacteristic, complemented
30C2×C11×#102—24no—
31C2×C11×#102C2211yescharacteristic
32C2×C11×#102C2211yescharacteristic
33C2×C11×#102C2211yescharacteristic
34C2×C11×#102C2211yescharacteristic
35C2×C11×#102C2211yescharacteristic
36C2×C11×#102C2211yescharacteristic
37C2×C11×#102C2211yescharacteristic
38C2×C11×#102C2211yescharacteristic
39C2×C11×C22⋊C8C2211yescharacteristic
40C2×C11×C22⋊C8C2211yescharacteristic, complemented
41C2×C11×C22⋊C8C2211yescharacteristic, complemented
42C11×#394—21no—
43C11×#392—21no—
44C11×#390C2211yescharacteristic
45C11×#390C2211yescharacteristic
46C11×#389—21no—
47C11×#385—21no—
48C11×#385—21no—
49C11×#384C2211yescharacteristic, complemented
50C11×#380C2211yescharacteristic
51C11×#380C2211yescharacteristic
52C11×#380C2211yescharacteristic, complemented
53C11×#379—21no—
54C4×C11×C4⋊C4C2211yescharacteristic, complemented
55C11×#340C2211yescharacteristic, complemented
56C11×#340C2211yescharacteristic, complemented
57C11×#340C2211yescharacteristic, complemented
58C11×#340C2211yescharacteristic, complemented
59C11×#336C2211yescharacteristic, complemented
60C11×#336C2211yescharacteristic, complemented
61C25×C11—21no—
62C22×D4×C11—22no—
63C22×D4×C11—22no—
64C22×D4×C11—21no—
65C22×D4×C11—21no—
66C22×D4×C11—21no—
67C22×D4×C11—22no—
68C22×D4×C11—22no—
69C22×D4×C11—41no—
70C22×D4×C11—41no—
71C22×D4×C11D411yescharacteristic
72C22×D4×C11C2311yescharacteristic
73C22×D4×C11C2311yescharacteristic
74C23×C4×C11—21no—
75C23×C4×C11—21no—
76C23×C4×C11C2311yescharacteristic
77C23×C4×C11C2311yescharacteristic
78C22×C8×C11—22no—
79C22×C8×C11—22no—
80C22×C8×C11—41no—
81C22×C8×C11C2311yescharacteristic
82C22×C8×C11C2311yescharacteristic
83C22×C8×C11C2311yescharacteristic
84C22×C8×C11C2311yescharacteristic
85C11×#121—22no—
86C11×#121—22no—
87C11×#121—41no—
88C11×#121—41no—
89C11×#120—44no—
90C4×D4×C11—22no—
91C4×D4×C11—22no—
92C4×D4×C11—44no—
93C2×C11×C4⋊C4—22no—
94C2×C11×C4⋊C4—22no—
95C2×C11×C4⋊C4—21no—
96C2×C11×C4⋊C4—21no—
97C2×C11×C4⋊C4—21no—
98C2×C11×C4⋊C4—21no—
99C2×C11×C4⋊C4—41no—
100C2×C11×C4⋊C4—41no—
101C2×C11×C4⋊C4D411yescharacteristic
102C2×C11×C4⋊C4C2311yescharacteristic
103C2×C11×C4⋊C4C2311yescharacteristic
104C2×C11×C4⋊C4C2311yescharacteristic
105C2×C11×C4⋊C4C2311yescharacteristic
106C2×C11×C4⋊C4C2311yescharacteristic
107C2×C11×C4⋊C4C2311yescharacteristic
108C2×C11×C22⋊C4—21no—
109C2×C11×C22⋊C4—21no—
110C2×C11×C22⋊C4—21no—
111C2×C11×C22⋊C4—21no—
112C2×C11×C22⋊C4—21no—
113C2×C11×C22⋊C4—21no—
114C2×C11×C22⋊C4—21no—
115C2×C11×C22⋊C4—21no—
116C2×C11×C22⋊C4—21no—
117C2×C11×C22⋊C4D411yescharacteristic
118C2×C11×C22⋊C4D411yescharacteristic
119C2×C42×C11—21no—
120C2×C42×C11C2311yescharacteristic
121C11×#107—22no—
122C11×#107—22no—
123C11×#107—41no—
124C11×#107—41no—
125C11×#102—22no—
126C11×#102—22no—
127C11×#102—22no—
128C11×#102—22no—
129C11×#102—22no—
130C11×#102—41no—
131C11×#102—41no—
132C11×#102D414yescomplemented
133C11×C22⋊C8—22no—
134C11×C22⋊C8—22no—
135C11×C22⋊C8—41no—
136C11×#95—21no—
137C11×#95—21no—
138C11×#95—21no—
139C11×#95—21no—
140#24861C1111yesmaximal, characteristic, direct product factor, Sylow
141C24×C11—21no—
142C24×C11—21no—
143C24×C11—42no—
144C24×C11—42no—
145C24×C11—42no—
146C24×C11—42no—
147C24×C11—42no—
148C24×C11—81no—
149C24×C11—81no—
150C24×C11C2×D411yescharacteristic
151C24×C11C2×D411yescharacteristic
152C2×D4×C11—22no—
153C2×D4×C11—22no—
154C2×D4×C11—28no—
155C2×D4×C11—21no—
156C2×D4×C11—21no—
157C2×D4×C11—21no—
158C2×D4×C11—21no—
159C2×D4×C11—21no—
160C2×D4×C11—21no—
161C2×D4×C11—21no—
162C2×D4×C11—21no—
163C2×D4×C11—21no—
164C2×D4×C11—21no—
165C2×D4×C11—44no—
166C2×D4×C11—44no—
167C2×D4×C11—42no—
168C2×D4×C11—42no—
169C2×D4×C11—44no—
170C2×D4×C11—42no—
171C2×D4×C11—42no—
172C2×D4×C11—42no—
173C2×D4×C11—42no—
174C2×D4×C11—42no—
175C2×D4×C11—81no—
176C2×D4×C11—81no—
177C2×D4×C11D814yes—
178C2×D4×C11C2×D412yes—
179C2×D4×C11#4112yes—
180C22×C4×C11—21no—
181C22×C4×C11—21no—
182C22×C4×C11—21no—
183C22×C4×C11—21no—
184C22×C4×C11—21no—
185C22×C4×C11—21no—
186C22×C4×C11—21no—
187C22×C4×C11—21no—
188C22×C4×C11—21no—
189C22×C4×C11—21no—
190C22×C4×C11—21no—
191C22×C4×C11—21no—
192C22×C4×C11—21no—
193C22×C4×C11—21no—
194C22×C4×C11—21no—
195C22×C4×C11—21no—
196C22×C4×C11—42no—
197C22×C4×C11—42no—
198C22×C4×C11—42no—
199C22×C4×C11—42no—
200C22×C4×C11—81no—
201C22×C4×C11—81no—
202C22×C4×C11C2×D411yescharacteristic
203C22×C4×C11C2×D411yescharacteristic
204C22×C4×C11C2×D411yescharacteristic
205C22×C4×C11C2×D411yescharacteristic
206C22×C4×C11#4112yes—
207C22×C4×C11#4112yes—
208C22×C4×C11C2411yescharacteristic
209C2×C8×C11—21no—
210C2×C8×C11—21no—
211C2×C8×C11—21no—
212C2×C8×C11—21no—
213C2×C8×C11—21no—
214C2×C8×C11—21no—
215C2×C8×C11—21no—
216C2×C8×C11—21no—
217C2×C8×C11—21no—
218C2×C8×C11—21no—
219C2×C8×C11—21no—
220C2×C8×C11—44no—
221C2×C8×C11C2×D412yes—
222C11×C4⋊C4—22no—
223C11×C4⋊C4—21no—
224C11×C4⋊C4—21no—
225C11×C4⋊C4—21no—
226C11×C4⋊C4—21no—
227C11×C4⋊C4—21no—
228C11×C4⋊C4—21no—
229C11×C4⋊C4—21no—
230C11×C4⋊C4—21no—
231C11×C4⋊C4—21no—
232C11×C4⋊C4—21no—
233C11×C4⋊C4—21no—
234C11×C4⋊C4—42no—
235C11×C4⋊C4—42no—
236C11×C4⋊C4—42no—
237C11×C4⋊C4—81no—
238C11×C4⋊C4C2×D412yes—
239C11×C22⋊C4—22no—
240C11×C22⋊C4—22no—
241C11×C22⋊C4—42no—
242C11×C22⋊C4—42no—
243C11×C22⋊C4—42no—
244C11×C22⋊C4—42no—
245C11×C22⋊C4—42no—
246C11×C22⋊C4—42no—
247C11×C22⋊C4—42no—
248C11×C22⋊C4—81no—
249C11×C22⋊C4—81no—
250C42×C11—21no—
251C42×C11—21no—
252C42×C11—42no—
253C2×#480C2×C1111yescharacteristic, complemented
254C22×#102C2×C1111yescharacteristic, complemented
255#2408C2×C1111yescharacteristic
256D4×C4⋊C4C2×C1111yescharacteristic, complemented
257#2093C2×C1111yescharacteristic, complemented
258#2071C2×C1111yescharacteristic, complemented
259#2033C2×C1111yescharacteristic, complemented
260#2033C2×C1111yescharacteristic, complemented
261#1925C2×C1111yescharacteristic, complemented
262#1925C2×C1111yescharacteristic, complemented
263#1874C2×C1111yescharacteristic, complemented
264#1869C2×C1111yescharacteristic, complemented
265#1852C2×C1111yescharacteristic, complemented
266#1808C2×C1111yescharacteristic, complemented
267#1786C2×C1111yescharacteristic, complemented
268C23×C11—21no—
269C23×C11—21no—
270C23×C11—21no—
271C23×C11—21no—
272C23×C11—21no—
273C23×C11—21no—
274C23×C11—21no—
275C23×C11—21no—
276C23×C11—21no—
277C23×C11—21no—
278C23×C11—22no—
279C23×C11—22no—
280C23×C11—48no—
281C23×C11—41no—
282C23×C11—41no—
283C23×C11—41no—
284C23×C11—41no—
285C23×C11—41no—
286C23×C11—41no—
287C23×C11—41no—
288C23×C11—41no—
289C23×C11—41no—
290C23×C11—41no—
291C23×C11—41no—
292C23×C11—41no—
293C23×C11—84no—
294C23×C11—84no—
295C23×C11—84no—
296C23×C11—84no—
297C23×C11—84no—
298C23×C11—84no—
299C23×C11#12312yes—
300C23×C11C2×D812yes—
301C23×C11C2×D812yes—
302C23×C11#13712yes—
303C23×C11C22×D411yescharacteristic
304D4×C11—28no—
305D4×C11—22no—
306D4×C11—22no—
307D4×C11—22no—
308D4×C11—22no—
309D4×C11—48no—
310D4×C11—41no—
311D4×C11—41no—
312D4×C11—41no—
313D4×C11—41no—
314D4×C11—84no—
315D4×C11—84no—
316C2×C4×C11—21no—
317C2×C4×C11—21no—
318C2×C4×C11—21no—
319C2×C4×C11—21no—
320C2×C4×C11—22no—
321C2×C4×C11—22no—
322C2×C4×C11—22no—
323C2×C4×C11—22no—
324C2×C4×C11—21no—
325C2×C4×C11—21no—
326C2×C4×C11—21no—
327C2×C4×C11—22no—
328C2×C4×C11—21no—
329C2×C4×C11—21no—
330C2×C4×C11—21no—
331C2×C4×C11—41no—
332C2×C4×C11—41no—
333C2×C4×C11—41no—
334C2×C4×C11—41no—
335C2×C4×C11—41no—
336C2×C4×C11—41no—
337C2×C4×C11—41no—
338C2×C4×C11—41no—
339C2×C4×C11—41no—
340C2×C4×C11—41no—
341C2×C4×C11—41no—
342C2×C4×C11—41no—
343C2×C4×C11—41no—
344C2×C4×C11—41no—
345C2×C4×C11—41no—
346C2×C4×C11—41no—
347C2×C4×C11—41no—
348C2×C4×C11—41no—
349C2×C4×C11—41no—
350C2×C4×C11—41no—
351C2×C4×C11—41no—
352C2×C4×C11—84no—
353C2×C4×C11—84no—
354C2×C4×C11#12312yes—
355C2×C4×C11C2×D812yes—
356C2×C4×C11C22×D411yescharacteristic
357C2×C4×C11C2×#4111yescharacteristic
358C2×C4×C11C2×#4111yescharacteristic
359C2×C4×C11C2×#4111yescharacteristic
360C2×C4×C11H(5,𝔽2)11yescharacteristic
361C2×C4×C11H(5,𝔽2)11yescharacteristic
362C8×C11—22no—
363C8×C11—41no—
364C8×C11—41no—
365C8×C11—41no—
366C23×D4C22×C1111yescharacteristic
367C23×C8C22×C1111yescharacteristic
368C2×#121C22×C1111yescharacteristic
369C2×#121C22×C1111yescharacteristic
370C2×#120—21no—
371C2×C4×D4—21no—
372C2×C4×D4C22×C1111yescharacteristic
373C22×C4⋊C4C22×C1111yescharacteristic
374C22×C4⋊C4C22×C1111yescharacteristic, complemented
375#480—24no—
376C2×#107C22×C1111yescharacteristic, complemented
377C2×#107C22×C1111yescharacteristic, complemented
378C2×#107C22×C1111yescharacteristic, complemented
379C2×#107C22×C1111yescharacteristic, complemented
380C2×#102—24no—
381C2×#102C22×C1111yescharacteristic
382C2×#102C22×C1111yescharacteristic
383C2×#102C22×C1111yescharacteristic
384C2×#102C22×C1111yescharacteristic
385C2×#102C22×C1111yescharacteristic
386C2×#102C22×C1111yescharacteristic
387C2×#102C22×C1111yescharacteristic
388C2×#102C22×C1111yescharacteristic
389C2×C22⋊C8C22×C1111yescharacteristic
390C2×C22⋊C8C22×C1111yescharacteristic, complemented
391C2×C22⋊C8C22×C1111yescharacteristic, complemented
392#394—21no—
393#392—21no—
394#390C22×C1111yescharacteristic
395#390C22×C1111yescharacteristic
396#389—21no—
397#385—21no—
398#385—21no—
399#384C22×C1111yescharacteristic, complemented
400#380C22×C1111yescharacteristic
401#380C22×C1111yescharacteristic
402#380C22×C1111yescharacteristic, complemented
403#379—21no—
404C4×C4⋊C4C22×C1111yescharacteristic, complemented
405#340C22×C1111yescharacteristic, complemented
406#340C22×C1111yescharacteristic, complemented
407#340C22×C1111yescharacteristic, complemented
408#340C22×C1111yescharacteristic, complemented
409#336C22×C1111yescharacteristic, complemented
410#336C22×C1111yescharacteristic, complemented
411C22×C11—22no—
412C22×C11—22no—
413C22×C11—22no—
414C22×C11—22no—
415C22×C11—22no—
416C22×C11—22no—
417C22×C11—22no—
418C22×C11—22no—
419C22×C11—22no—
420C22×C11—41no—
421C22×C11—41no—
422C22×C11—41no—
423C22×C11—41no—
424C22×C11—42no—
425C22×C11—42no—
426C22×C11—42no—
427C22×C11—42no—
428C22×C11—42no—
429C22×C11—42no—
430C22×C11—816no—
431C22×C11—81no—
432C22×C11—81no—
433C22×C11—81no—
434C22×C11—81no—
435C22×C11—81no—
436C22×C11—81no—
437C22×C11—81no—
438C22×C11—81no—
439C22×C11#48014yescomplemented
440C22×C11C2×#12311yescharacteristic
441C22×C11D4211yescharacteristic
442C22×C11#54611yescharacteristic
443C22×C11C22×D811yescharacteristic
444C22×C11C2×#13711yescharacteristic
445C22×C11#57611yescharacteristic
446C22×C11#57711yescharacteristic
447C4×C11—22no—
448C4×C11—22no—
449C4×C11—41no—
450C4×C11—41no—
451C4×C11—42no—
452C4×C11—81no—
453C4×C11—81no—
454C4×C11—81no—
455C4×C11—81no—
456C4×C11—81no—
457C4×C11#52511yescharacteristic
458C4×C11#53811yescharacteristic
459C4×C11#54611yescharacteristic
460C4×C11#55111yescharacteristic
461C25—21no—
462C22×D4—22no—
463C22×D4—22no—
464C22×D4—21no—
465C22×D4—21no—
466C22×D4—21no—
467C22×D4—22no—
468C22×D4—22no—
469C22×D4—41no—
470C22×D4—41no—
471C22×D4D4×C1111yescharacteristic
472C22×D4C23×C1111yescharacteristic
473C22×D4C23×C1111yescharacteristic
474C23×C4—21no—
475C23×C4—21no—
476C23×C4C23×C1111yescharacteristic
477C23×C4C23×C1111yescharacteristic
478C22×C8—22no—
479C22×C8—22no—
480C22×C8—41no—
481C22×C8C23×C1111yescharacteristic
482C22×C8C23×C1111yescharacteristic
483C22×C8C23×C1111yescharacteristic
484C22×C8C23×C1111yescharacteristic
485#121—22no—
486#121—22no—
487#121—41no—
488#121—41no—
489#120—44no—
490C4×D4—22no—
491C4×D4—22no—
492C4×D4—44no—
493C2×C4⋊C4—22no—
494C2×C4⋊C4—22no—
495C2×C4⋊C4—21no—
496C2×C4⋊C4—21no—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—41no—
500C2×C4⋊C4—41no—
501C2×C4⋊C4D4×C1111yescharacteristic
502C2×C4⋊C4C23×C1111yescharacteristic
503C2×C4⋊C4C23×C1111yescharacteristic
504C2×C4⋊C4C23×C1111yescharacteristic
505C2×C4⋊C4C23×C1111yescharacteristic
506C2×C4⋊C4C23×C1111yescharacteristic
507C2×C4⋊C4C23×C1111yescharacteristic
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4D4×C1111yescharacteristic
518C2×C22⋊C4D4×C1111yescharacteristic
519C2×C42—21no—
520C2×C42C23×C1111yescharacteristic
521#107—22no—
522#107—22no—
523#107—41no—
524#107—41no—
525#102—22no—
526#102—22no—
527#102—22no—
528#102—22no—
529#102—22no—
530#102—41no—
531#102—41no—
532#102D4×C1114yescomplemented
533C22⋊C8—22no—
534C22⋊C8—22no—
535C22⋊C8—41no—
536#95—21no—
537#95—21no—
538#95—21no—
539#95—21no—
540C2×C11—24no—
541C2×C11—42no—
542C2×C11—82no—
543C2×C11—82no—
544C2×C11#241811yescharacteristic
545C2×C11C2×#48011yescharacteristic
546C2×C11#309611yescharacteristic
547C2×C11#326611yescharacteristic
548C2×C11D4×D811yescharacteristic
549C2×C11#329411yescharacteristic
550C2×C11#331411yescharacteristic
551C24—21no—
552C24—21no—
553C24—42no—
554C24—42no—
555C24—42no—
556C24—42no—
557C24—42no—
558C24—81no—
559C24—81no—
560C24C2×D4×C1111yescharacteristic
561C24C2×D4×C1111yescharacteristic
562C2×D4—22no—
563C2×D4—22no—
564C2×D4—28no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—44no—
576C2×D4—44no—
577C2×D4—42no—
578C2×D4—42no—
579C2×D4—44no—
580C2×D4—42no—
581C2×D4—42no—
582C2×D4—42no—
583C2×D4—42no—
584C2×D4—42no—
585C2×D4—81no—
586C2×D4—81no—
587C2×D4C11×D814yes—
588C2×D4C2×D4×C1112yes—
589C2×D4C11×#4112yes—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—42no—
607C22×C4—42no—
608C22×C4—42no—
609C22×C4—42no—
610C22×C4—81no—
611C22×C4—81no—
612C22×C4C2×D4×C1111yescharacteristic
613C22×C4C2×D4×C1111yescharacteristic
614C22×C4C2×D4×C1111yescharacteristic
615C22×C4C2×D4×C1111yescharacteristic
616C22×C4C11×#4112yes—
617C22×C4C11×#4112yes—
618C22×C4C24×C1111yescharacteristic
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—44no—
631C2×C8C2×D4×C1112yes—
632C4⋊C4—22no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—42no—
645C4⋊C4—42no—
646C4⋊C4—42no—
647C4⋊C4—81no—
648C4⋊C4C2×D4×C1112yes—
649C22⋊C4—22no—
650C22⋊C4—22no—
651C22⋊C4—42no—
652C22⋊C4—42no—
653C22⋊C4—42no—
654C22⋊C4—42no—
655C22⋊C4—42no—
656C22⋊C4—42no—
657C22⋊C4—42no—
658C22⋊C4—81no—
659C22⋊C4—81no—
660C42—21no—
661C42—21no—
662C42—42no—
663C11#2486111yescharacteristic, direct product factor, Sylow
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—22no—
675C23—22no—
676C23—48no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—84no—
690C23—84no—
691C23—84no—
692C23—84no—
693C23—84no—
694C23—84no—
695C23C11×#12312yes—
696C23C2×C11×D812yes—
697C23C2×C11×D812yes—
698C23C11×#13712yes—
699C23C22×D4×C1111yescharacteristic
700D4—28no—
701D4—22no—
702D4—22no—
703D4—22no—
704D4—22no—
705D4—48no—
706D4—41no—
707D4—41no—
708D4—41no—
709D4—41no—
710D4—84no—
711D4—84no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—22no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—84no—
749C2×C4—84no—
750C2×C4C11×#12312yes—
751C2×C4C2×C11×D812yes—
752C2×C4C22×D4×C1111yescharacteristic
753C2×C4C2×C11×#4111yescharacteristic
754C2×C4C2×C11×#4111yescharacteristic
755C2×C4C2×C11×#4111yescharacteristic
756C2×C4C11×H(5,𝔽2)11yescharacteristic
757C2×C4C11×H(5,𝔽2)11yescharacteristic
758C8—22no—
759C8—41no—
760C8—41no—
761C8—41no—
762C22—22no—
763C22—22no—
764C22—22no—
765C22—22no—
766C22—22no—
767C22—22no—
768C22—22no—
769C22—22no—
770C22—22no—
771C22—41no—
772C22—41no—
773C22—41no—
774C22—41no—
775C22—42no—
776C22—42no—
777C22—42no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—816no—
782C22—81no—
783C22—81no—
784C22—81no—
785C22—81no—
786C22—81no—
787C22—81no—
788C22—81no—
789C22—81no—
790C22C11×#48014yescomplemented
791C22C2×C11×#12311yescharacteristic
792C22D42×C1111yescharacteristic
793C22C11×#54611yescharacteristic
794C22C22×C11×D811yescharacteristic
795C22C2×C11×#13711yescharacteristic
796C22C11×#57611yescharacteristic
797C22C11×#57711yescharacteristic
798C4—22no—
799C4—22no—
800C4—41no—
801C4—42no—
802C4—41no—
803C4—81no—
804C4—81no—
805C4—81no—
806C4—81no—
807C4—81no—
808C4C11×#52511yescharacteristic
809C4C11×#53811yescharacteristic
810C4C11×#54611yescharacteristic
811C4C11×#55111yescharacteristic
812C2—24no—
813C2—42no—
814C2—82no—
815C2—82no—
816C2C11×#241811yescharacteristic
817C2C2×C11×#48011yescharacteristic
818C2C11×#309611yescharacteristic
819C2C11×#326611yescharacteristic
820C2D4×C11×D811yescharacteristic
821C2C11×#329411yescharacteristic
822C2C11×#331411yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#2408C2
LCSG ▷ C22×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
1. C2×C11×#480C2semidirect
2. C22×C11×#102C2semidirect
4. D4×C11×C4⋊C4C2semidirect
5. C11×#2093C2semidirect
6. C11×#2071C2semidirect
7. C11×#2033C2semidirect
8. C11×#2033C2semidirect
9. C11×#1925C2semidirect
10. C11×#1925C2semidirect
11. C11×#1874C2semidirect
12. C11×#1869C2semidirect
13. C11×#1852C2semidirect
14. C11×#1808C2semidirect
15. C11×#1786C2semidirect
24. C22×C11×C4⋊C4C22semidirect
26. C2×C11×#107C22semidirect
27. C2×C11×#107C22semidirect
28. C2×C11×#107C22semidirect
29. C2×C11×#107C22semidirect
40. C2×C11×C22⋊C8C22semidirect
41. C2×C11×C22⋊C8C22semidirect
49. C11×#384C22semidirect
52. C11×#380C22semidirect
54. C4×C11×C4⋊C4C22semidirect
55. C11×#340C22semidirect
56. C11×#340C22semidirect
57. C11×#340C22semidirect
58. C11×#340C22semidirect
59. C11×#336C22semidirect
60. C11×#336C22semidirect
132. C11×#102D4semidirect
140. #24861C11direct (N × H)
253. C2×#480C2×C11semidirect
254. C22×#102C2×C11semidirect
256. D4×C4⋊C4C2×C11semidirect
257. #2093C2×C11semidirect
258. #2071C2×C11semidirect
259. #2033C2×C11semidirect
260. #2033C2×C11semidirect
261. #1925C2×C11semidirect
262. #1925C2×C11semidirect
263. #1874C2×C11semidirect
264. #1869C2×C11semidirect
265. #1852C2×C11semidirect
266. #1808C2×C11semidirect
267. #1786C2×C11semidirect
374. C22×C4⋊C4C22×C11semidirect
376. C2×#107C22×C11semidirect
377. C2×#107C22×C11semidirect
378. C2×#107C22×C11semidirect
379. C2×#107C22×C11semidirect
390. C2×C22⋊C8C22×C11semidirect
391. C2×C22⋊C8C22×C11semidirect
399. #384C22×C11semidirect
402. #380C22×C11semidirect
404. C4×C4⋊C4C22×C11semidirect
405. #340C22×C11semidirect
406. #340C22×C11semidirect
407. #340C22×C11semidirect
408. #340C22×C11semidirect
409. #336C22×C11semidirect
410. #336C22×C11semidirect
439. C22×C11#480semidirect
532. #102D4×C11semidirect
663. C11#24861direct (N × H)
790. C22C11×#480semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#4802
C22×C11×#1022
C11×#24082
D4×C11×C4⋊C42
C11×#20932
C11×#20712
C11×#20332
C11×#19252
C11×#18742
C11×#18692
C11×#18522
C11×#18082
C11×#17862
#2486111