Finite Group Databasebeta

← C11×#24047 #14601240

Subgroups — C11×#24047 #14601240

Order 2816.

1310 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×#548C211yesmaximal, characteristic
2C2×C11×#482C211yesmaximal, characteristic, complemented
3C2×C11×#419C211yesmaximal, characteristic, complemented
4C11×#2485C211yesmaximal, characteristic, complemented
5C11×#2042C211yesmaximal, characteristic, complemented
6C11×#2042C211yesmaximal, characteristic, complemented
7C11×#2036C211yesmaximal, characteristic, complemented
8C11×#2035C211yesmaximal, characteristic, complemented
9C11×#1895C211yesmaximal, characteristic, complemented
10C11×#1870C211yesmaximal, characteristic, complemented
11C11×#1865C211yesmaximal, characteristic, complemented
12C11×#1863C211yesmaximal, characteristic, complemented
13C11×#1788C211yesmaximal, characteristic, complemented
14C11×#1788C211yesmaximal, characteristic, complemented
15C11×#1787C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic
17C23×Q8×C11C2211yescharacteristic
18C22×C11×M16C2211yescharacteristic
19C11×#548—24no—
20C11×#548—24no—
21C2×C11×#124—21no—
22C2×C11×#124C2211yescharacteristic
23C2×C11×C22⋊Q8—21no—
24C2×C11×C22⋊Q8C2211yescharacteristic
25C2×C11×#121—21no—
26C2×C11×#121C2211yescharacteristic
27C2×C4×Q8×C11C2211yescharacteristic
28C2×C4×D4×C11—21no—
29C2×C4×D4×C11C2211yescharacteristic
30C2×C11×#117C2211yescharacteristic
31C11×#482—24no—
32C2×C11×#107C2211yescharacteristic
33C2×C11×#106C2211yescharacteristic
34C11×#419—24no—
35C2×C11×#103C2211yescharacteristic
36C2×C11×#103C2211yescharacteristic
37C2×C11×#103C2211yescharacteristic
38C2×C11×#103C2211yescharacteristic
39C2×C11×#103C2211yescharacteristic
40C2×C11×#103C2211yescharacteristic
41C2×C11×#103C2211yescharacteristic
42C2×C11×#103C2211yescharacteristic
43C2×C11×#102C2211yescharacteristic
44C2×C11×#102C2211yescharacteristic
45C2×C11×#102C2211yescharacteristic
46C2×C11×#102C2211yescharacteristic
47C2×C11×C22⋊C8C2211yescharacteristic
48C2×C11×C22⋊C8C2211yescharacteristic
49C2×C11×C22⋊C8C2211yescharacteristic
50C11×#397—21no—
51C11×#394—21no—
52C11×#389C2211yescharacteristic
53C11×#389C2211yescharacteristic
54C11×#388—21no—
55C11×#387—21no—
56C11×#380C2211yescharacteristic
57C11×#380C2211yescharacteristic
58C11×#380C2211yescharacteristic
59C11×#340C2211yescharacteristic
60C11×#340C2211yescharacteristic
61C11×#336C2211yescharacteristic
62C11×#336C2211yescharacteristic
63C2×C11×#41—22no—
64C2×C11×#41—22no—
65C2×C11×#41—22no—
66C2×C11×#41—22no—
67C2×C11×#41—41no—
68C2×C11×#41—41no—
69C22×Q8×C11—21no—
70C22×Q8×C11—22no—
71C22×Q8×C11—22no—
72C22×Q8×C11—22no—
73C22×Q8×C11—41no—
74C22×Q8×C11—41no—
75C22×Q8×C11D414yes—
76C22×Q8×C11C2311yescharacteristic
77C22×Q8×C11C2311yescharacteristic
78C22×D4×C11—21no—
79C22×D4×C11—21no—
80C22×D4×C11D411yescharacteristic
81C22×D4×C11C2311yescharacteristic
82C23×C4×C11—21no—
83C23×C4×C11—21no—
84C23×C4×C11C2311yescharacteristic
85C23×C4×C11C2311yescharacteristic
86C2×C11×M16—22no—
87C2×C11×M16—41no—
88C2×C11×M16—41no—
89C22×C8×C11C2311yescharacteristic
90C22×C8×C11C2311yescharacteristic
91C22×C8×C11C2311yescharacteristic
92C22×C8×C11C2311yescharacteristic
93C11×#124—28no—
94C11×#124—22no—
95C11×#124—22no—
96C11×C22⋊Q8—28no—
97C11×C22⋊Q8—22no—
98C11×C22⋊Q8—22no—
99C11×#121—28no—
100C11×#121—22no—
101C11×#121D414yes—
102C4×Q8×C11—22no—
103C4×Q8×C11—22no—
104C4×D4×C11—28no—
105C4×D4×C11—22no—
106C4×D4×C11—22no—
107C11×#117—22no—
108C11×#117—22no—
109C2×C11×C4⋊C4—21no—
110C2×C11×C4⋊C4—21no—
111C2×C11×C4⋊C4—21no—
112C2×C11×C4⋊C4—21no—
113C2×C11×C4⋊C4D411yescharacteristic
114C2×C11×C4⋊C4C2311yescharacteristic
115C2×C11×C4⋊C4C2311yescharacteristic
116C2×C11×C4⋊C4C2311yescharacteristic
117C2×C11×C4⋊C4C2311yescharacteristic
118C2×C11×C4⋊C4C2311yescharacteristic
119C2×C11×C22⋊C4—21no—
120C2×C11×C22⋊C4—21no—
121C2×C11×C22⋊C4—21no—
122C2×C11×C22⋊C4—21no—
123C2×C11×C22⋊C4—21no—
124C2×C11×C22⋊C4—21no—
125C2×C11×C22⋊C4—21no—
126C2×C11×C22⋊C4—21no—
127C2×C11×C22⋊C4D411yescharacteristic
128C2×C11×C22⋊C4D411yescharacteristic
129C2×C42×C11—21no—
130C2×C42×C11—21no—
131C2×C42×C11C2311yescharacteristic
132C11×#107—22no—
133C11×#106—22no—
134C11×#103—22no—
135C11×#103—22no—
136C11×#103—22no—
137C11×#103—22no—
138C11×#103—22no—
139C11×#103—22no—
140C11×#103—41no—
141C11×#103—41no—
142C11×#102—22no—
143C11×#102—22no—
144C11×#102—41no—
145C11×#102—41no—
146C11×C22⋊C8—22no—
147C11×C22⋊C8—41no—
148C11×C22⋊C8—41no—
149C11×#95—21no—
150C11×#95—21no—
151C11×#95—21no—
152C11×#95—21no—
153C11×#95—21no—
154#24047C1111yesmaximal, characteristic, direct product factor, Sylow
155C24×C11—21no—
156C24×C11C2×D411yescharacteristic
157C24×C11C2×D411yescharacteristic
158C11×#41—44no—
159C11×#41—44no—
160C11×#41—44no—
161C11×#41—44no—
162C2×Q8×C11—24no—
163C2×Q8×C11—21no—
164C2×Q8×C11—21no—
165C2×Q8×C11—21no—
166C2×Q8×C11—21no—
167C2×Q8×C11—28no—
168C2×Q8×C11—21no—
169C2×Q8×C11—21no—
170C2×Q8×C11—21no—
171C2×Q8×C11—21no—
172C2×Q8×C11—42no—
173C2×Q8×C11—42no—
174C2×Q8×C11—44no—
175C2×Q8×C11—44no—
176C2×Q8×C11—44no—
177C2×Q8×C11C2×D412yes—
178C2×Q8×C11C2×D412yes—
179C2×Q8×C11#4112yes—
180C2×Q8×C11#4112yes—
181C2×D4×C11—24no—
182C2×D4×C11—22no—
183C2×D4×C11—24no—
184C2×D4×C11—21no—
185C2×D4×C11—21no—
186C2×D4×C11—21no—
187C2×D4×C11—21no—
188C2×D4×C11—21no—
189C2×D4×C11—41no—
190C2×D4×C11—41no—
191C2×D4×C11—42no—
192C2×D4×C11—42no—
193C2×D4×C11—42no—
194C2×D4×C11—42no—
195C2×D4×C11C2×D412yes—
196C22×C4×C11—21no—
197C22×C4×C11—21no—
198C22×C4×C11—21no—
199C22×C4×C11—21no—
200C22×C4×C11—21no—
201C22×C4×C11—24no—
202C22×C4×C11—24no—
203C22×C4×C11—21no—
204C22×C4×C11—21no—
205C22×C4×C11—21no—
206C22×C4×C11—21no—
207C22×C4×C11—21no—
208C22×C4×C11—21no—
209C22×C4×C11—21no—
210C22×C4×C11—21no—
211C22×C4×C11—21no—
212C22×C4×C11—21no—
213C22×C4×C11—21no—
214C22×C4×C11—21no—
215C22×C4×C11—42no—
216C22×C4×C11—42no—
217C22×C4×C11—42no—
218C22×C4×C11—42no—
219C22×C4×C11C2×D411yescharacteristic
220C22×C4×C11C2×D411yescharacteristic
221C22×C4×C11C2×D411yescharacteristic
222C22×C4×C11C2×D411yescharacteristic
223C22×C4×C11C2×D412yes—
224C22×C4×C11C2×D412yes—
225C22×C4×C11C2411yescharacteristic
226C11×M16—44no—
227C2×C8×C11—21no—
228C2×C8×C11—21no—
229C2×C8×C11—21no—
230C2×C8×C11—21no—
231C2×C8×C11—21no—
232C2×C8×C11—21no—
233C2×C8×C11—21no—
234C2×C8×C11—21no—
235C2×C8×C11—21no—
236C2×C8×C11—21no—
237C2×C8×C11—21no—
238C2×C8×C11—21no—
239C11×C4⋊C4—24no—
240C11×C4⋊C4—24no—
241C11×C4⋊C4—22no—
242C11×C4⋊C4—21no—
243C11×C4⋊C4—21no—
244C11×C4⋊C4—21no—
245C11×C4⋊C4—21no—
246C11×C4⋊C4—21no—
247C11×C4⋊C4—21no—
248C11×C4⋊C4—21no—
249C11×C4⋊C4—21no—
250C11×C4⋊C4—21no—
251C11×C4⋊C4—42no—
252C11×C4⋊C4—81no—
253C11×C4⋊C4C2×D412yes—
254C11×C22⋊C4—24no—
255C11×C22⋊C4—24no—
256C11×C22⋊C4—24no—
257C11×C22⋊C4—22no—
258C11×C22⋊C4—24no—
259C11×C22⋊C4—22no—
260C11×C22⋊C4—42no—
261C11×C22⋊C4—42no—
262C11×C22⋊C4—81no—
263C11×C22⋊C4—81no—
264C42×C11—24no—
265C42×C11—21no—
266C42×C11—21no—
267C42×C11—42no—
268C2×#548C2×C1111yescharacteristic
269C2×#482C2×C1111yescharacteristic, complemented
270C2×#419C2×C1111yescharacteristic, complemented
271#2485C2×C1111yescharacteristic, complemented
272#2042C2×C1111yescharacteristic, complemented
273#2042C2×C1111yescharacteristic, complemented
274#2036C2×C1111yescharacteristic, complemented
275#2035C2×C1111yescharacteristic, complemented
276#1895C2×C1111yescharacteristic, complemented
277#1870C2×C1111yescharacteristic, complemented
278#1865C2×C1111yescharacteristic, complemented
279#1863C2×C1111yescharacteristic, complemented
280#1788C2×C1111yescharacteristic, complemented
281#1788C2×C1111yescharacteristic, complemented
282#1787C2×C1111yescharacteristic, complemented
283C23×C11—21no—
284C23×C11—21no—
285C23×C11—21no—
286C23×C11—21no—
287C23×C11—21no—
288C23×C11—21no—
289C23×C11—21no—
290C23×C11—22no—
291C23×C11—21no—
292C23×C11—21no—
293C23×C11—21no—
294C23×C11—21no—
295C23×C11—21no—
296C23×C11—21no—
297C23×C11—41no—
298C23×C11—41no—
299C23×C11—41no—
300C23×C11—41no—
301C23×C11—41no—
302C23×C11—41no—
303C23×C11#12012yes—
304C23×C11C22×D411yescharacteristic
305Q8×C11—22no—
306Q8×C11—22no—
307Q8×C11—22no—
308Q8×C11—22no—
309Q8×C11—22no—
310Q8×C11—48no—
311Q8×C11—41no—
312Q8×C11—41no—
313Q8×C11#12314yes—
314D4×C11—22no—
315D4×C11—22no—
316D4×C11—48no—
317D4×C11—44no—
318D4×C11—48no—
319D4×C11—41no—
320D4×C11—41no—
321C2×C4×C11—22no—
322C2×C4×C11—21no—
323C2×C4×C11—21no—
324C2×C4×C11—22no—
325C2×C4×C11—22no—
326C2×C4×C11—22no—
327C2×C4×C11—22no—
328C2×C4×C11—22no—
329C2×C4×C11—22no—
330C2×C4×C11—21no—
331C2×C4×C11—21no—
332C2×C4×C11—22no—
333C2×C4×C11—22no—
334C2×C4×C11—21no—
335C2×C4×C11—21no—
336C2×C4×C11—21no—
337C2×C4×C11—21no—
338C2×C4×C11—21no—
339C2×C4×C11—21no—
340C2×C4×C11—21no—
341C2×C4×C11—48no—
342C2×C4×C11—48no—
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—41no—
353C2×C4×C11—41no—
354C2×C4×C11—41no—
355C2×C4×C11—41no—
356C2×C4×C11—41no—
357C2×C4×C11—41no—
358C2×C4×C11—41no—
359C2×C4×C11—41no—
360C2×C4×C11—41no—
361C2×C4×C11—41no—
362C2×C4×C11—41no—
363C2×C4×C11#12012yes—
364C2×C4×C11C22×D411yescharacteristic
365C2×C4×C11C22×D411yescharacteristic
366C2×C4×C11C2×#4111yescharacteristic
367C2×C4×C11C2×#4111yescharacteristic
368C2×C4×C11H(5,𝔽2)11yescharacteristic
369C2×C4×C11H(5,𝔽2)11yescharacteristic
370C8×C11—41no—
371C8×C11—41no—
372C8×C11—41no—
373C8×C11—41no—
374C22×#41C22×C1111yescharacteristic
375C23×Q8C22×C1111yescharacteristic
376C22×M16C22×C1111yescharacteristic
377#548—24no—
378#548—24no—
379C2×#124—21no—
380C2×#124C22×C1111yescharacteristic
381C2×C22⋊Q8—21no—
382C2×C22⋊Q8C22×C1111yescharacteristic
383C2×#121—21no—
384C2×#121C22×C1111yescharacteristic
385C2×C4×Q8C22×C1111yescharacteristic
386C2×C4×D4—21no—
387C2×C4×D4C22×C1111yescharacteristic
388C2×#117C22×C1111yescharacteristic
389#482—24no—
390C2×#107C22×C1111yescharacteristic
391C2×#106C22×C1111yescharacteristic
392#419—24no—
393C2×#103C22×C1111yescharacteristic
394C2×#103C22×C1111yescharacteristic
395C2×#103C22×C1111yescharacteristic
396C2×#103C22×C1111yescharacteristic
397C2×#103C22×C1111yescharacteristic
398C2×#103C22×C1111yescharacteristic
399C2×#103C22×C1111yescharacteristic
400C2×#103C22×C1111yescharacteristic
401C2×#102C22×C1111yescharacteristic
402C2×#102C22×C1111yescharacteristic
403C2×#102C22×C1111yescharacteristic
404C2×#102C22×C1111yescharacteristic
405C2×C22⋊C8C22×C1111yescharacteristic
406C2×C22⋊C8C22×C1111yescharacteristic
407C2×C22⋊C8C22×C1111yescharacteristic
408#397—21no—
409#394—21no—
410#389C22×C1111yescharacteristic
411#389C22×C1111yescharacteristic
412#388—21no—
413#387—21no—
414#380C22×C1111yescharacteristic
415#380C22×C1111yescharacteristic
416#380C22×C1111yescharacteristic
417#340C22×C1111yescharacteristic
418#340C22×C1111yescharacteristic
419#336C22×C1111yescharacteristic
420#336C22×C1111yescharacteristic
421C22×C11—22no—
422C22×C11—22no—
423C22×C11—22no—
424C22×C11—41no—
425C22×C11—41no—
426C22×C11—41no—
427C22×C11—41no—
428C22×C11—42no—
429C22×C11—41no—
430C22×C11—41no—
431C22×C11—42no—
432C22×C11—41no—
433C22×C11—42no—
434C22×C11—41no—
435C22×C11—41no—
436C22×C11—41no—
437C22×C11—41no—
438C22×C11—81no—
439C22×C11—81no—
440C22×C11—81no—
441C22×C11—81no—
442C22×C11C2×#12011yescharacteristic
443C22×C11#54611yescharacteristic
444C22×C11#54611yescharacteristic
445C22×C11#57511yescharacteristic
446C22×C11#57511yescharacteristic
447C22×C11#57711yescharacteristic
448C22×C11#57811yescharacteristic
449C4×C11—22no—
450C4×C11—24no—
451C4×C11—41no—
452C4×C11—42no—
453C4×C11—41no—
454C4×C11—42no—
455C4×C11—41no—
456C4×C11—81no—
457C4×C11—81no—
458C4×C11—81no—
459C4×C11—81no—
460C4×C11C2×#12311yescharacteristic
461C4×C11#53411yescharacteristic
462C4×C11#54611yescharacteristic
463C4×C11#54611yescharacteristic
464C2×#41—22no—
465C2×#41—22no—
466C2×#41—22no—
467C2×#41—22no—
468C2×#41—41no—
469C2×#41—41no—
470C22×Q8—21no—
471C22×Q8—22no—
472C22×Q8—22no—
473C22×Q8—22no—
474C22×Q8—41no—
475C22×Q8—41no—
476C22×Q8D4×C1114yes—
477C22×Q8C23×C1111yescharacteristic
478C22×Q8C23×C1111yescharacteristic
479C22×D4—21no—
480C22×D4—21no—
481C22×D4D4×C1111yescharacteristic
482C22×D4C23×C1111yescharacteristic
483C23×C4—21no—
484C23×C4—21no—
485C23×C4C23×C1111yescharacteristic
486C23×C4C23×C1111yescharacteristic
487C2×M16—22no—
488C2×M16—41no—
489C2×M16—41no—
490C22×C8C23×C1111yescharacteristic
491C22×C8C23×C1111yescharacteristic
492C22×C8C23×C1111yescharacteristic
493C22×C8C23×C1111yescharacteristic
494#124—28no—
495#124—22no—
496#124—22no—
497C22⋊Q8—28no—
498C22⋊Q8—22no—
499C22⋊Q8—22no—
500#121—28no—
501#121—22no—
502#121D4×C1114yes—
503C4×Q8—22no—
504C4×Q8—22no—
505C4×D4—28no—
506C4×D4—22no—
507C4×D4—22no—
508#117—22no—
509#117—22no—
510C2×C4⋊C4—21no—
511C2×C4⋊C4—21no—
512C2×C4⋊C4—21no—
513C2×C4⋊C4—21no—
514C2×C4⋊C4D4×C1111yescharacteristic
515C2×C4⋊C4C23×C1111yescharacteristic
516C2×C4⋊C4C23×C1111yescharacteristic
517C2×C4⋊C4C23×C1111yescharacteristic
518C2×C4⋊C4C23×C1111yescharacteristic
519C2×C4⋊C4C23×C1111yescharacteristic
520C2×C22⋊C4—21no—
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—21no—
524C2×C22⋊C4—21no—
525C2×C22⋊C4—21no—
526C2×C22⋊C4—21no—
527C2×C22⋊C4—21no—
528C2×C22⋊C4D4×C1111yescharacteristic
529C2×C22⋊C4D4×C1111yescharacteristic
530C2×C42—21no—
531C2×C42—21no—
532C2×C42C23×C1111yescharacteristic
533#107—22no—
534#106—22no—
535#103—22no—
536#103—22no—
537#103—22no—
538#103—22no—
539#103—22no—
540#103—22no—
541#103—41no—
542#103—41no—
543#102—22no—
544#102—22no—
545#102—41no—
546#102—41no—
547C22⋊C8—22no—
548C22⋊C8—41no—
549C22⋊C8—41no—
550#95—21no—
551#95—21no—
552#95—21no—
553#95—21no—
554#95—21no—
555C2×C11—42no—
556C2×C11—81no—
557C2×C11—82no—
558C2×C11#240511yescharacteristic
559C2×C11#300511yescharacteristic
560C2×C11#301311yescharacteristic
561C2×C11#331311yescharacteristic
562C2×C11#332111yescharacteristic
563C2×C11#332611yescharacteristic
564C2×C11#332711yescharacteristic
565C24—21no—
566C24C2×D4×C1111yescharacteristic
567C24C2×D4×C1111yescharacteristic
568#41—44no—
569#41—44no—
570#41—44no—
571#41—44no—
572C2×Q8—24no—
573C2×Q8—21no—
574C2×Q8—21no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8—28no—
578C2×Q8—21no—
579C2×Q8—21no—
580C2×Q8—21no—
581C2×Q8—21no—
582C2×Q8—42no—
583C2×Q8—42no—
584C2×Q8—44no—
585C2×Q8—44no—
586C2×Q8—44no—
587C2×Q8C2×D4×C1112yes—
588C2×Q8C2×D4×C1112yes—
589C2×Q8C11×#4112yes—
590C2×Q8C11×#4112yes—
591C2×D4—24no—
592C2×D4—22no—
593C2×D4—24no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—41no—
600C2×D4—41no—
601C2×D4—42no—
602C2×D4—42no—
603C2×D4—42no—
604C2×D4—42no—
605C2×D4C2×D4×C1112yes—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—24no—
612C22×C4—24no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—42no—
626C22×C4—42no—
627C22×C4—42no—
628C22×C4—42no—
629C22×C4C2×D4×C1111yescharacteristic
630C22×C4C2×D4×C1111yescharacteristic
631C22×C4C2×D4×C1111yescharacteristic
632C22×C4C2×D4×C1111yescharacteristic
633C22×C4C2×D4×C1112yes—
634C22×C4C2×D4×C1112yes—
635C22×C4C24×C1111yescharacteristic
636M16—44no—
637C2×C8—21no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—21no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—21no—
648C2×C8—21no—
649C4⋊C4—24no—
650C4⋊C4—24no—
651C4⋊C4—22no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—42no—
662C4⋊C4—81no—
663C4⋊C4C2×D4×C1112yes—
664C22⋊C4—24no—
665C22⋊C4—24no—
666C22⋊C4—24no—
667C22⋊C4—22no—
668C22⋊C4—24no—
669C22⋊C4—22no—
670C22⋊C4—42no—
671C22⋊C4—42no—
672C22⋊C4—81no—
673C22⋊C4—81no—
674C42—24no—
675C42—21no—
676C42—21no—
677C42—42no—
678C11#2404711yescharacteristic, direct product factor, Sylow
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—22no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—41no—
694C23—41no—
695C23—41no—
696C23—41no—
697C23—41no—
698C23—41no—
699C23C11×#12012yes—
700C23C22×D4×C1111yescharacteristic
701Q8—22no—
702Q8—22no—
703Q8—22no—
704Q8—22no—
705Q8—22no—
706Q8—48no—
707Q8—41no—
708Q8—41no—
709Q8C11×#12314yes—
710D4—22no—
711D4—22no—
712D4—48no—
713D4—44no—
714D4—48no—
715D4—41no—
716D4—41no—
717C2×C4—22no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—48no—
738C2×C4—48no—
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—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4C11×#12012yes—
760C2×C4C22×D4×C1111yescharacteristic
761C2×C4C22×D4×C1111yescharacteristic
762C2×C4C2×C11×#4111yescharacteristic
763C2×C4C2×C11×#4111yescharacteristic
764C2×C4C11×H(5,𝔽2)11yescharacteristic
765C2×C4C11×H(5,𝔽2)11yescharacteristic
766C8—41no—
767C8—41no—
768C8—41no—
769C8—41no—
770C22—22no—
771C22—22no—
772C22—22no—
773C22—41no—
774C22—41no—
775C22—41no—
776C22—41no—
777C22—42no—
778C22—41no—
779C22—41no—
780C22—42no—
781C22—41no—
782C22—42no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—41no—
787C22—81no—
788C22—81no—
789C22—81no—
790C22—81no—
791C22C2×C11×#12011yescharacteristic
792C22C11×#54611yescharacteristic
793C22C11×#54611yescharacteristic
794C22C11×#57511yescharacteristic
795C22C11×#57511yescharacteristic
796C22C11×#57711yescharacteristic
797C22C11×#57811yescharacteristic
798C4—22no—
799C4—24no—
800C4—41no—
801C4—42no—
802C4—41no—
803C4—42no—
804C4—41no—
805C4—81no—
806C4—81no—
807C4—81no—
808C4—81no—
809C4C2×C11×#12311yescharacteristic
810C4C11×#53411yescharacteristic
811C4C11×#54611yescharacteristic
812C4C11×#54611yescharacteristic
813C2—42no—
814C2—81no—
815C2—82no—
816C2C11×#240511yescharacteristic
817C2C11×#300511yescharacteristic
818C2C11×#301311yescharacteristic
819C2C11×#331311yescharacteristic
820C2C11×#332111yescharacteristic
821C2C11×#332611yescharacteristic
822C2C11×#332711yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#548C2
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
2. C2×C11×#482C2semidirect
3. C2×C11×#419C2semidirect
4. C11×#2485C2semidirect
5. C11×#2042C2semidirect
6. C11×#2042C2semidirect
7. C11×#2036C2semidirect
8. C11×#2035C2semidirect
9. C11×#1895C2semidirect
10. C11×#1870C2semidirect
11. C11×#1865C2semidirect
12. C11×#1863C2semidirect
13. C11×#1788C2semidirect
14. C11×#1788C2semidirect
15. C11×#1787C2semidirect
154. #24047C11direct (N × H)
269. C2×#482C2×C11semidirect
270. C2×#419C2×C11semidirect
271. #2485C2×C11semidirect
272. #2042C2×C11semidirect
273. #2042C2×C11semidirect
274. #2036C2×C11semidirect
275. #2035C2×C11semidirect
276. #1895C2×C11semidirect
277. #1870C2×C11semidirect
278. #1865C2×C11semidirect
279. #1863C2×C11semidirect
280. #1788C2×C11semidirect
281. #1788C2×C11semidirect
282. #1787C2×C11semidirect
678. C11#24047direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5482
C2×C11×#4822
C2×C11×#4192
C11×#24852
C11×#20422
C11×#20362
C11×#20352
C11×#18952
C11×#18702
C11×#18652
C11×#18632
C11×#17882
C11×#17872
#2404711