Finite Group Databasebeta

← C11×#23938 #14601131

Subgroups — C11×#23938 #14601131

Order 2816.

1308 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×#529C211yesmaximal, characteristic, complemented
2C2×C11×#452C211yesmaximal, characteristic, complemented
3C2×C11×#449C211yesmaximal, characteristic
4C11×#2297C211yesmaximal, characteristic, complemented
5C11×#2026C211yesmaximal, characteristic, complemented
6C11×#2025C211yesmaximal, characteristic, complemented
7C11×#2015C211yesmaximal, characteristic, complemented
8C11×#2012C211yesmaximal, characteristic, complemented
9C11×#1880C211yesmaximal, characteristic, complemented
10C11×#1879C211yesmaximal, characteristic, complemented
11C11×#1878C211yesmaximal, characteristic, complemented
12C11×#1877C211yesmaximal, characteristic, complemented
13C11×#1875C211yesmaximal, characteristic, complemented
14C11×#1873C211yesmaximal, characteristic, complemented
15C11×#1817C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic
17C22×C11×Q16C2211yescharacteristic
18C22×C11×SD16C2211yescharacteristic
19C22×C11×SD16C2211yescharacteristic
20C22×C11×D8C2211yescharacteristic
21C11×#529—24no—
22C11×#529—24no—
23C2×C11×#126—21no—
24C2×C11×#125C2211yescharacteristic
25C2×C11×#124C2211yescharacteristic
26C2×C11×#123—21no—
27C2×C11×C22⋊Q8C2211yescharacteristic
28C2×C11×#121C2211yescharacteristic
29C2×C4×Q8×C11C2211yescharacteristic
30C2×C4×D4×C11—21no—
31C2×C4×D4×C11C2211yescharacteristic
32C2×C11×#117—21no—
33C2×C11×#117C2211yescharacteristic
34C22×C42×C11C2211yescharacteristic
35C11×#452—24no—
36C11×#449—24no—
37C2×C11×#103C2211yescharacteristic
38C2×C11×#103C2211yescharacteristic
39C2×C11×#103C2211yescharacteristic
40C2×C11×#103C2211yescharacteristic
41C2×C11×#102C2211yescharacteristic
42C2×C11×#102C2211yescharacteristic
43C2×C11×#102C2211yescharacteristic
44C2×C11×#102C2211yescharacteristic
45C2×C11×C22⋊C8C2211yescharacteristic
46C2×C11×C22⋊C8C2211yescharacteristic
47C11×#391C2211yescharacteristic
48C11×#391C2211yescharacteristic
49C11×#390C2211yescharacteristic
50C11×#390C2211yescharacteristic
51C11×#386—21no—
52C11×#386—21no—
53C4×C11×C22⋊C4—21no—
54C4×C11×C22⋊C4—21no—
55C11×#340C2211yescharacteristic
56C11×#340C2211yescharacteristic
57C11×#340C2211yescharacteristic
58C11×#340C2211yescharacteristic
59C11×#336C2211yescharacteristic
60C11×#336C2211yescharacteristic
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×C11C2311yescharacteristic
70C22×Q8×C11C2311yescharacteristic
71C22×D4×C11—21no—
72C22×D4×C11—21no—
73C22×D4×C11C2311yescharacteristic
74C22×D4×C11C2311yescharacteristic
75C23×C4×C11—21no—
76C23×C4×C11—21no—
77C23×C4×C11D411yescharacteristic
78C23×C4×C11D411yescharacteristic
79C23×C4×C11C2311yescharacteristic
80C2×C11×Q16—22no—
81C2×C11×Q16—22no—
82C2×C11×Q16—41no—
83C2×C11×SD16—22no—
84C2×C11×SD16—22no—
85C2×C11×SD16—22no—
86C2×C11×SD16—22no—
87C2×C11×SD16—41no—
88C2×C11×SD16—41no—
89C2×C11×D8—22no—
90C2×C11×D8—22no—
91C2×C11×D8—41no—
92C22×C8×C11C2311yescharacteristic
93C22×C8×C11C2311yescharacteristic
94C22×C8×C11C2311yescharacteristic
95C22×C8×C11C2311yescharacteristic
96C11×#126—28no—
97C11×#125—22no—
98C11×#125—22no—
99C11×#124—22no—
100C11×#124—22no—
101C11×#123—28no—
102C11×C22⋊Q8—22no—
103C11×C22⋊Q8D414yes—
104C11×#121—22no—
105C11×#121D414yes—
106C4×Q8×C11—22no—
107C4×Q8×C11—22no—
108C4×D4×C11—28no—
109C4×D4×C11—22no—
110C4×D4×C11—22no—
111C11×#117—28no—
112C11×#117—41no—
113C11×#117—41no—
114C2×C11×C4⋊C4—21no—
115C2×C11×C4⋊C4—21no—
116C2×C11×C4⋊C4—21no—
117C2×C11×C4⋊C4—21no—
118C2×C11×C4⋊C4C2311yescharacteristic
119C2×C11×C4⋊C4C2311yescharacteristic
120C2×C11×C4⋊C4C2311yescharacteristic
121C2×C11×C4⋊C4C2311yescharacteristic
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⋊C4—21no—
128C2×C11×C22⋊C4—21no—
129C2×C11×C22⋊C4—21no—
130C2×C11×C22⋊C4—21no—
131C2×C11×C22⋊C4—21no—
132C2×C42×C11—22no—
133C2×C42×C11—22no—
134C2×C42×C11—21no—
135C2×C42×C11—21no—
136C2×C42×C11D411yescharacteristic
137C2×C42×C11D411yescharacteristic
138C2×C42×C11C2311yescharacteristic
139C2×C42×C11C2311yescharacteristic
140C11×#103—22no—
141C11×#103—22no—
142C11×#103—41no—
143C11×#103—41no—
144C11×#102—22no—
145C11×#102—22no—
146C11×#102—41no—
147C11×#102—41no—
148C11×C22⋊C8—22no—
149C11×C22⋊C8—22no—
150C11×#95—21no—
151C11×#95—21no—
152C11×#95—21no—
153C11×#95—21no—
154#23938C1111yesmaximal, characteristic, direct product factor, Sylow
155C24×C11—21no—
156C24×C11—21no—
157C24×C11C2×D411yescharacteristic
158C11×#41—44no—
159C11×#41—44no—
160C11×#41—44no—
161C11×#41—44no—
162C2×Q8×C11—21no—
163C2×Q8×C11—21no—
164C2×Q8×C11—21no—
165C2×Q8×C11—21no—
166C2×Q8×C11—21no—
167C2×Q8×C11—21no—
168C2×Q8×C11—21no—
169C2×Q8×C11—21no—
170C2×Q8×C11—21no—
171C2×Q8×C11—21no—
172C2×Q8×C11C2×D412yes—
173C2×Q8×C11#4112yes—
174C2×D4×C11—24no—
175C2×D4×C11—24no—
176C2×D4×C11—21no—
177C2×D4×C11—21no—
178C2×D4×C11—21no—
179C2×D4×C11—21no—
180C2×D4×C11—21no—
181C2×D4×C11—21no—
182C2×D4×C11—21no—
183C2×D4×C11—21no—
184C2×D4×C11—21no—
185C2×D4×C11—21no—
186C2×D4×C11—42no—
187C2×D4×C11—42no—
188C2×D4×C11—42no—
189C2×D4×C11—42no—
190C2×D4×C11C2×D412yes—
191C2×D4×C11#4112yes—
192C22×C4×C11—21no—
193C22×C4×C11—21no—
194C22×C4×C11—21no—
195C22×C4×C11—21no—
196C22×C4×C11—24no—
197C22×C4×C11—24no—
198C22×C4×C11—22no—
199C22×C4×C11—22no—
200C22×C4×C11—21no—
201C22×C4×C11—21no—
202C22×C4×C11—21no—
203C22×C4×C11—21no—
204C22×C4×C11—22no—
205C22×C4×C11—21no—
206C22×C4×C11—21no—
207C22×C4×C11—41no—
208C22×C4×C11—41no—
209C22×C4×C11—41no—
210C22×C4×C11—42no—
211C22×C4×C11—42no—
212C22×C4×C11—42no—
213C22×C4×C11—42no—
214C22×C4×C11C2×D411yescharacteristic
215C22×C4×C11C2×D411yescharacteristic
216C22×C4×C11C2×D411yescharacteristic
217C22×C4×C11C2×D411yescharacteristic
218C22×C4×C11C2×D412yes—
219C22×C4×C11C2×D412yes—
220C22×C4×C11C2×D411yescharacteristic
221C22×C4×C11C2411yescharacteristic
222C11×Q16—44no—
223C11×SD16—44no—
224C11×SD16—44no—
225C11×D8—44no—
226C2×C8×C11—21no—
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—
238C11×C4⋊C4—24no—
239C11×C4⋊C4—24no—
240C11×C4⋊C4—24no—
241C11×C4⋊C4—24no—
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⋊C4C2×D412yes—
249C11×C4⋊C4C2×D412yes—
250C11×C22⋊C4—24no—
251C11×C22⋊C4—24no—
252C11×C22⋊C4—24no—
253C11×C22⋊C4—24no—
254C11×C22⋊C4—24no—
255C11×C22⋊C4—42no—
256C11×C22⋊C4—42no—
257C11×C22⋊C4—42no—
258C11×C22⋊C4—42no—
259C11×C22⋊C4—42no—
260C42×C11—24no—
261C42×C11—22no—
262C42×C11—22no—
263C42×C11—21no—
264C42×C11—21no—
265C42×C11—21no—
266C42×C11—21no—
267C42×C11—42no—
268C2×#529C2×C1111yescharacteristic, complemented
269C2×#452C2×C1111yescharacteristic, complemented
270C2×#449C2×C1111yescharacteristic
271#2297C2×C1111yescharacteristic, complemented
272#2026C2×C1111yescharacteristic, complemented
273#2025C2×C1111yescharacteristic, complemented
274#2015C2×C1111yescharacteristic, complemented
275#2012C2×C1111yescharacteristic, complemented
276#1880C2×C1111yescharacteristic, complemented
277#1879C2×C1111yescharacteristic, complemented
278#1878C2×C1111yescharacteristic, complemented
279#1877C2×C1111yescharacteristic, complemented
280#1875C2×C1111yescharacteristic, complemented
281#1873C2×C1111yescharacteristic, complemented
282#1817C2×C1111yescharacteristic, complemented
283C23×C11—21no—
284C23×C11—21no—
285C23×C11—21no—
286C23×C11—21no—
287C23×C11—21no—
288C23×C11—21no—
289C23×C11—22no—
290C23×C11—22no—
291C23×C11—41no—
292C23×C11—41no—
293C23×C11—41no—
294C23×C11—41no—
295C23×C11—41no—
296C23×C11—41no—
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—41no—
310Q8×C11—41no—
311Q8×C11—41no—
312Q8×C11—41no—
313D4×C11—22no—
314D4×C11—22no—
315D4×C11—22no—
316D4×C11—22no—
317D4×C11—48no—
318D4×C11—48no—
319D4×C11—41no—
320D4×C11—41no—
321D4×C11—41no—
322D4×C11—41no—
323C2×C4×C11—21no—
324C2×C4×C11—21no—
325C2×C4×C11—21no—
326C2×C4×C11—21no—
327C2×C4×C11—22no—
328C2×C4×C11—22no—
329C2×C4×C11—22no—
330C2×C4×C11—22no—
331C2×C4×C11—21no—
332C2×C4×C11—21no—
333C2×C4×C11—21no—
334C2×C4×C11—22no—
335C2×C4×C11—22no—
336C2×C4×C11—22no—
337C2×C4×C11—22no—
338C2×C4×C11—21no—
339C2×C4×C11—21no—
340C2×C4×C11—21no—
341C2×C4×C11—21no—
342C2×C4×C11—21no—
343C2×C4×C11—21no—
344C2×C4×C11—44no—
345C2×C4×C11—48no—
346C2×C4×C11—48no—
347C2×C4×C11—44no—
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#12012yes—
363C2×C4×C11#13512yes—
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
375C22×Q16C22×C1111yescharacteristic
376C22×SD16C22×C1111yescharacteristic
377C22×SD16C22×C1111yescharacteristic
378C22×D8C22×C1111yescharacteristic
379#529—24no—
380#529—24no—
381C2×#126—21no—
382C2×#125C22×C1111yescharacteristic
383C2×#124C22×C1111yescharacteristic
384C2×#123—21no—
385C2×C22⋊Q8C22×C1111yescharacteristic
386C2×#121C22×C1111yescharacteristic
387C2×C4×Q8C22×C1111yescharacteristic
388C2×C4×D4—21no—
389C2×C4×D4C22×C1111yescharacteristic
390C2×#117—21no—
391C2×#117C22×C1111yescharacteristic
392C22×C42C22×C1111yescharacteristic
393#452—24no—
394#449—24no—
395C2×#103C22×C1111yescharacteristic
396C2×#103C22×C1111yescharacteristic
397C2×#103C22×C1111yescharacteristic
398C2×#103C22×C1111yescharacteristic
399C2×#102C22×C1111yescharacteristic
400C2×#102C22×C1111yescharacteristic
401C2×#102C22×C1111yescharacteristic
402C2×#102C22×C1111yescharacteristic
403C2×C22⋊C8C22×C1111yescharacteristic
404C2×C22⋊C8C22×C1111yescharacteristic
405#391C22×C1111yescharacteristic
406#391C22×C1111yescharacteristic
407#390C22×C1111yescharacteristic
408#390C22×C1111yescharacteristic
409#386—21no—
410#386—21no—
411C4×C22⋊C4—21no—
412C4×C22⋊C4—21no—
413#340C22×C1111yescharacteristic
414#340C22×C1111yescharacteristic
415#340C22×C1111yescharacteristic
416#340C22×C1111yescharacteristic
417#336C22×C1111yescharacteristic
418#336C22×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—42no—
430C22×C11—42no—
431C22×C11—42no—
432C22×C11—42no—
433C22×C11—42no—
434C22×C11—81no—
435C22×C11—81no—
436C22×C11—81no—
437C22×C11—81no—
438C22×C11—81no—
439C22×C11—81no—
440C22×C11—81no—
441C22×C11—81no—
442C22×C11C2×#12011yescharacteristic
443C22×C11#52511yescharacteristic
444C22×C11#53511yescharacteristic
445C22×C11C2×#13511yescharacteristic
446C22×C11#57511yescharacteristic
447C22×C11#57511yescharacteristic
448C22×C11#57511yescharacteristic
449C4×C11—22no—
450C4×C11—22no—
451C4×C11—42no—
452C4×C11—42no—
453C4×C11—41no—
454C4×C11—42no—
455C4×C11—41no—
456C4×C11—41no—
457C4×C11—42no—
458C4×C11—81no—
459C4×C11—81no—
460C4×C11#54611yescharacteristic
461C4×C11#54611yescharacteristic
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×Q8C23×C1111yescharacteristic
471C22×Q8C23×C1111yescharacteristic
472C22×D4—21no—
473C22×D4—21no—
474C22×D4C23×C1111yescharacteristic
475C22×D4C23×C1111yescharacteristic
476C23×C4—21no—
477C23×C4—21no—
478C23×C4D4×C1111yescharacteristic
479C23×C4D4×C1111yescharacteristic
480C23×C4C23×C1111yescharacteristic
481C2×Q16—22no—
482C2×Q16—22no—
483C2×Q16—41no—
484C2×SD16—22no—
485C2×SD16—22no—
486C2×SD16—22no—
487C2×SD16—22no—
488C2×SD16—41no—
489C2×SD16—41no—
490C2×D8—22no—
491C2×D8—22no—
492C2×D8—41no—
493C22×C8C23×C1111yescharacteristic
494C22×C8C23×C1111yescharacteristic
495C22×C8C23×C1111yescharacteristic
496C22×C8C23×C1111yescharacteristic
497#126—28no—
498#125—22no—
499#125—22no—
500#124—22no—
501#124—22no—
502#123—28no—
503C22⋊Q8—22no—
504C22⋊Q8D4×C1114yes—
505#121—22no—
506#121D4×C1114yes—
507C4×Q8—22no—
508C4×Q8—22no—
509C4×D4—28no—
510C4×D4—22no—
511C4×D4—22no—
512#117—28no—
513#117—41no—
514#117—41no—
515C2×C4⋊C4—21no—
516C2×C4⋊C4—21no—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4C23×C1111yescharacteristic
520C2×C4⋊C4C23×C1111yescharacteristic
521C2×C4⋊C4C23×C1111yescharacteristic
522C2×C4⋊C4C23×C1111yescharacteristic
523C2×C22⋊C4—21no—
524C2×C22⋊C4—21no—
525C2×C22⋊C4—21no—
526C2×C22⋊C4—21no—
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—21no—
533C2×C42—21no—
534C2×C42—22no—
535C2×C42—22no—
536C2×C42—21no—
537C2×C42D4×C1111yescharacteristic
538C2×C42D4×C1111yescharacteristic
539C2×C42C23×C1111yescharacteristic
540C2×C42C23×C1111yescharacteristic
541#103—22no—
542#103—22no—
543#103—41no—
544#103—41no—
545#102—22no—
546#102—22no—
547#102—41no—
548#102—41no—
549C22⋊C8—22no—
550C22⋊C8—22no—
551#95—21no—
552#95—21no—
553#95—21no—
554#95—21no—
555C2×C11—42no—
556C2×C11—82no—
557C2×C11—82no—
558C2×C11#240411yescharacteristic
559C2×C11#300211yescharacteristic
560C2×C11#300511yescharacteristic
561C2×C11#310211yescharacteristic
562C2×C11#311111yescharacteristic
563C2×C11#321211yescharacteristic
564C2×C11#321911yescharacteristic
565C24—21no—
566C24—21no—
567C24C2×D4×C1111yescharacteristic
568#41—44no—
569#41—44no—
570#41—44no—
571#41—44no—
572C2×Q8—21no—
573C2×Q8—21no—
574C2×Q8—21no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8—21no—
579C2×Q8—21no—
580C2×Q8—21no—
581C2×Q8—21no—
582C2×Q8C2×D4×C1112yes—
583C2×Q8C11×#4112yes—
584C2×D4—24no—
585C2×D4—24no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—42no—
597C2×D4—42no—
598C2×D4—42no—
599C2×D4—42no—
600C2×D4C2×D4×C1112yes—
601C2×D4C11×#4112yes—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—24no—
607C22×C4—24no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—22no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—41no—
618C22×C4—41no—
619C22×C4—41no—
620C22×C4—42no—
621C22×C4—42no—
622C22×C4—42no—
623C22×C4—42no—
624C22×C4C2×D4×C1111yescharacteristic
625C22×C4C2×D4×C1111yescharacteristic
626C22×C4C2×D4×C1111yescharacteristic
627C22×C4C2×D4×C1111yescharacteristic
628C22×C4C2×D4×C1112yes—
629C22×C4C2×D4×C1112yes—
630C22×C4C2×D4×C1111yescharacteristic
631C22×C4C24×C1111yescharacteristic
632Q16—44no—
633SD16—44no—
634SD16—44no—
635D8—44no—
636C2×C8—21no—
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—
648C4⋊C4—24no—
649C4⋊C4—24no—
650C4⋊C4—24no—
651C4⋊C4—24no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4C2×D4×C1112yes—
659C4⋊C4C2×D4×C1112yes—
660C22⋊C4—24no—
661C22⋊C4—24no—
662C22⋊C4—24no—
663C22⋊C4—24no—
664C22⋊C4—24no—
665C22⋊C4—42no—
666C22⋊C4—42no—
667C22⋊C4—42no—
668C22⋊C4—42no—
669C22⋊C4—42no—
670C42—24no—
671C42—22no—
672C42—22no—
673C42—21no—
674C42—21no—
675C42—21no—
676C42—21no—
677C42—42no—
678C11#2393811yescharacteristic, direct product factor, Sylow
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—22no—
686C23—22no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—41no—
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—41no—
706Q8—41no—
707Q8—41no—
708Q8—41no—
709D4—22no—
710D4—22no—
711D4—22no—
712D4—22no—
713D4—48no—
714D4—48no—
715D4—41no—
716D4—41no—
717D4—41no—
718D4—41no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—44no—
741C2×C4—48no—
742C2×C4—48no—
743C2×C4—44no—
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×C4C11×#12012yes—
759C2×C4C11×#13512yes—
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—42no—
779C22—42no—
780C22—42no—
781C22—42no—
782C22—42no—
783C22—81no—
784C22—81no—
785C22—81no—
786C22—81no—
787C22—81no—
788C22—81no—
789C22—81no—
790C22—81no—
791C22C2×C11×#12011yescharacteristic
792C22C11×#52511yescharacteristic
793C22C11×#53511yescharacteristic
794C22C2×C11×#13511yescharacteristic
795C22C11×#57511yescharacteristic
796C22C11×#57511yescharacteristic
797C22C11×#57511yescharacteristic
798C4—22no—
799C4—22no—
800C4—42no—
801C4—42no—
802C4—41no—
803C4—42no—
804C4—41no—
805C4—41no—
806C4—42no—
807C4—81no—
808C4—81no—
809C4C11×#54611yescharacteristic
810C4C11×#54611yescharacteristic
811C4C11×#54611yescharacteristic
812C4C11×#54611yescharacteristic
813C2—42no—
814C2—82no—
815C2—82no—
816C2C11×#240411yescharacteristic
817C2C11×#300211yescharacteristic
818C2C11×#300511yescharacteristic
819C2C11×#310211yescharacteristic
820C2C11×#311111yescharacteristic
821C2C11×#321211yescharacteristic
822C2C11×#321911yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#449C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C22×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#529C2semidirect
2. C2×C11×#452C2semidirect
4. C11×#2297C2semidirect
5. C11×#2026C2semidirect
6. C11×#2025C2semidirect
7. C11×#2015C2semidirect
8. C11×#2012C2semidirect
9. C11×#1880C2semidirect
10. C11×#1879C2semidirect
11. C11×#1878C2semidirect
12. C11×#1877C2semidirect
13. C11×#1875C2semidirect
14. C11×#1873C2semidirect
15. C11×#1817C2semidirect
154. #23938C11direct (N × H)
268. C2×#529C2×C11semidirect
269. C2×#452C2×C11semidirect
271. #2297C2×C11semidirect
272. #2026C2×C11semidirect
273. #2025C2×C11semidirect
274. #2015C2×C11semidirect
275. #2012C2×C11semidirect
276. #1880C2×C11semidirect
277. #1879C2×C11semidirect
278. #1878C2×C11semidirect
279. #1877C2×C11semidirect
280. #1875C2×C11semidirect
281. #1873C2×C11semidirect
282. #1817C2×C11semidirect
678. C11#23938direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5292
C2×C11×#4522
C2×C11×#4492
C11×#22972
C11×#20262
C11×#20252
C11×#20152
C11×#20122
C11×#18802
C11×#18792
C11×#18782
C11×#18772
C11×#18752
C11×#18732
C11×#18172
#2393811