Finite Group Databasebeta

← C11×#24136 #14601329

Subgroups — C11×#24136 #14601329

Order 2816.

1238 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#553C211yesmaximal, characteristic, complemented
2C2×C11×#478C211yesmaximal, characteristic, complemented
3C2×C11×#442C211yesmaximal, characteristic, complemented
4C11×#2537C211yesmaximal, characteristic, complemented
5C11×#2034C211yesmaximal, characteristic, complemented
6C11×#2033C211yesmaximal, characteristic, complemented
7C11×#1999C211yesmaximal, characteristic, complemented
8C11×#1999C211yesmaximal, characteristic, complemented
9C11×#1992C211yesmaximal, characteristic, complemented
10C11×#1955C211yesmaximal, characteristic, complemented
11C11×#1875C211yesmaximal, characteristic, complemented
12C11×#1874C211yesmaximal, characteristic, complemented
13C11×#1854C211yesmaximal, characteristic, complemented
14C11×#1853C211yesmaximal, characteristic, complemented
15C11×#1802C211yesmaximal, characteristic, complemented
16C22×C11×D8C2211yescharacteristic
17C11×#553—24no—
18C11×#553—24no—
19C2×C11×#126—21no—
20C2×C11×#125C2211yescharacteristic
21C2×C11×#123—21no—
22C2×C11×#121—21no—
23C2×C11×#121—21no—
24C2×C11×#121C2211yescharacteristic
25C2×C11×#121C2211yescharacteristic
26C2×C11×#121C2211yescharacteristic
27C2×C11×#121C2211yescharacteristic
28C2×C4×D4×C11—21no—
29C2×C4×D4×C11C2211yescharacteristic
30C2×C4×D4×C11C2211yescharacteristic
31C2×C4×D4×C11C2211yescharacteristic
32C2×C11×#117C2211yescharacteristic
33C22×C11×C4⋊C4C2211yescharacteristic
34C11×#478—24no—
35C11×#442—24no—
36C2×C11×#107C2211yescharacteristic
37C2×C11×#106C2211yescharacteristic
38C2×C11×#106C2211yescharacteristic
39C2×C11×C4⋊C8C2211yescharacteristic
40C2×C11×#102C2211yescharacteristic
41C2×C11×#102C2211yescharacteristic
42C2×C11×#102C2211yescharacteristic
43C2×C11×#102C2211yescharacteristic
44C2×C11×#102C2211yescharacteristic
45C2×C11×#102C2211yescharacteristic
46C2×C11×C22⋊C8C2211yescharacteristic
47C2×C11×C22⋊C8C2211yescharacteristic
48C2×C11×C22⋊C8C2211yescharacteristic
49C2×C11×C22⋊C8C2211yescharacteristic
50C2×C11×#97C2211yescharacteristic
51C11×#394—21no—
52C11×#394—21no—
53C11×#384C2211yescharacteristic
54C11×#380—21no—
55C11×#380C2211yescharacteristic
56C11×#380C2211yescharacteristic
57C11×#340C2211yescharacteristic
58C11×#340C2211yescharacteristic
59C11×#340C2211yescharacteristic
60C11×#340C2211yescharacteristic
61C11×#340C2211yescharacteristic
62C11×#340C2211yescharacteristic
63C22×D4×C11—21no—
64C22×D4×C11—21no—
65C22×D4×C11—21no—
66C22×D4×C11—21no—
67C22×D4×C11D411yescharacteristic
68C22×D4×C11C2311yescharacteristic
69C22×D4×C11C2311yescharacteristic
70C23×C4×C11—21no—
71C23×C4×C11—21no—
72C23×C4×C11—21no—
73C23×C4×C11C2311yescharacteristic
74C23×C4×C11C2311yescharacteristic
75C2×C11×D8—22no—
76C2×C11×D8—22no—
77C2×C11×D8—22no—
78C22×C8×C11C2311yescharacteristic
79C22×C8×C11C2311yescharacteristic
80C22×C8×C11C2311yescharacteristic
81C22×C8×C11C2311yescharacteristic
82C11×#126—28no—
83C11×#125—22no—
84C11×#125D414yescomplemented
85C11×#123—28no—
86C11×#121—28no—
87C11×#121—22no—
88C11×#121—22no—
89C11×#121—22no—
90C11×#121—22no—
91C11×#121—22no—
92C11×#121—22no—
93C11×#121—41no—
94C11×#121—41no—
95C11×#121—44no—
96C4×D4×C11—28no—
97C4×D4×C11—22no—
98C4×D4×C11—22no—
99C4×D4×C11—22no—
100C4×D4×C11—22no—
101C4×D4×C11—22no—
102C4×D4×C11D414yescomplemented
103C11×#117—22no—
104C11×#117—22no—
105C2×C11×C4⋊C4—21no—
106C2×C11×C4⋊C4—21no—
107C2×C11×C4⋊C4—21no—
108C2×C11×C4⋊C4—22no—
109C2×C11×C4⋊C4—22no—
110C2×C11×C4⋊C4—21no—
111C2×C11×C4⋊C4—21no—
112C2×C11×C4⋊C4D411yescharacteristic
113C2×C11×C4⋊C4C2311yescharacteristic
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⋊C4—21no—
128C2×C11×C22⋊C4D411yescharacteristic
129C2×C11×C22⋊C4D411yescharacteristic
130C2×C42×C11—21no—
131C2×C42×C11C2311yescharacteristic
132C11×#107—22no—
133C11×#106—22no—
134C11×#106—22no—
135C11×C4⋊C8—22no—
136C11×#102—22no—
137C11×#102—22no—
138C11×#102—22no—
139C11×#102—22no—
140C11×#102—41no—
141C11×#102—41no—
142C11×C22⋊C8—22no—
143C11×C22⋊C8—22no—
144C11×C22⋊C8—41no—
145C11×C22⋊C8—41no—
146C11×#97—22no—
147C11×#95—21no—
148C11×#95—21no—
149#24136C1111yesmaximal, characteristic, direct product factor, Sylow
150C24×C11—21no—
151C24×C11—21no—
152C24×C11C2×D411yescharacteristic
153C24×C11C2×D411yescharacteristic
154C2×D4×C11—24no—
155C2×D4×C11—22no—
156C2×D4×C11—24no—
157C2×D4×C11—22no—
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—21no—
166C2×D4×C11—21no—
167C2×D4×C11—21no—
168C2×D4×C11—41no—
169C2×D4×C11—42no—
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×C11—81no—
178C2×D4×C11—81no—
179C2×D4×C11C2×D412yes—
180C2×D4×C11#4112yes—
181C22×C4×C11—21no—
182C22×C4×C11—21no—
183C22×C4×C11—21no—
184C22×C4×C11—24no—
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—21no—
197C22×C4×C11—24no—
198C22×C4×C11—21no—
199C22×C4×C11—21no—
200C22×C4×C11—21no—
201C22×C4×C11—42no—
202C22×C4×C11—42no—
203C22×C4×C11—42no—
204C22×C4×C11—81no—
205C22×C4×C11—81no—
206C22×C4×C11—81no—
207C22×C4×C11—81no—
208C22×C4×C11C2×D411yescharacteristic
209C22×C4×C11C2×D411yescharacteristic
210C22×C4×C11C2×D411yescharacteristic
211C22×C4×C11C2×D411yescharacteristic
212C22×C4×C11C2411yescharacteristic
213C11×D8—28no—
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—21no—
221C2×C8×C11—21no—
222C2×C8×C11—21no—
223C2×C8×C11—21no—
224C2×C8×C11—21no—
225C2×C8×C11#4112yes—
226C11×C4⋊C4—24no—
227C11×C4⋊C4—24no—
228C11×C4⋊C4—24no—
229C11×C4⋊C4—22no—
230C11×C4⋊C4—21no—
231C11×C4⋊C4—21no—
232C11×C4⋊C4—21no—
233C11×C4⋊C4—21no—
234C11×C4⋊C4—21no—
235C11×C4⋊C4—21no—
236C11×C4⋊C4—21no—
237C11×C4⋊C4—21no—
238C11×C4⋊C4—21no—
239C11×C4⋊C4—42no—
240C11×C4⋊C4—81no—
241C11×C4⋊C4C2×D412yes—
242C11×C4⋊C4C2×D412yes—
243C11×C4⋊C4C2×D412yes—
244C11×C22⋊C4—24no—
245C11×C22⋊C4—24no—
246C11×C22⋊C4—24no—
247C11×C22⋊C4—24no—
248C11×C22⋊C4—22no—
249C11×C22⋊C4—22no—
250C11×C22⋊C4—42no—
251C11×C22⋊C4—42no—
252C11×C22⋊C4—42no—
253C11×C22⋊C4—42no—
254C11×C22⋊C4—42no—
255C42×C11—24no—
256C42×C11C2×D412yes—
257C42×C11C2×D412yes—
258C2×#553C2×C1111yescharacteristic, complemented
259C2×#478C2×C1111yescharacteristic, complemented
260C2×#442C2×C1111yescharacteristic, complemented
261#2537C2×C1111yescharacteristic, complemented
262#2034C2×C1111yescharacteristic, complemented
263#2033C2×C1111yescharacteristic, complemented
264#1999C2×C1111yescharacteristic, complemented
265#1999C2×C1111yescharacteristic, complemented
266#1992C2×C1111yescharacteristic, complemented
267#1955C2×C1111yescharacteristic, complemented
268#1875C2×C1111yescharacteristic, complemented
269#1874C2×C1111yescharacteristic, complemented
270#1854C2×C1111yescharacteristic, complemented
271#1853C2×C1111yescharacteristic, complemented
272#1802C2×C1111yescharacteristic, complemented
273C23×C11—21no—
274C23×C11—21no—
275C23×C11—21no—
276C23×C11—21no—
277C23×C11—21no—
278C23×C11—21no—
279C23×C11—21no—
280C23×C11—22no—
281C23×C11—22no—
282C23×C11—21no—
283C23×C11—21no—
284C23×C11—21no—
285C23×C11—21no—
286C23×C11—21no—
287C23×C11—21no—
288C23×C11—41no—
289C23×C11—41no—
290C23×C11—41no—
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×C11AGL(1,ℤ/8)12yes—
301C23×C11C22×D411yescharacteristic
302D4×C11—22no—
303D4×C11—22no—
304D4×C11—22no—
305D4×C11—22no—
306D4×C11—44no—
307D4×C11—48no—
308D4×C11—41no—
309D4×C11—41no—
310D4×C11—41no—
311D4×C11—41no—
312D4×C11—84no—
313D4×C11—84no—
314D4×C11—84no—
315C2×C4×C11—21no—
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—21no—
323C2×C4×C11—22no—
324C2×C4×C11—21no—
325C2×C4×C11—21no—
326C2×C4×C11—21no—
327C2×C4×C11—21no—
328C2×C4×C11—41no—
329C2×C4×C11—41no—
330C2×C4×C11—41no—
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—84no—
352C2×C4×C11—84no—
353C2×C4×C11—84no—
354C2×C4×C11#12012yes—
355C2×C4×C11#12012yes—
356C2×C4×C11C22×D411yescharacteristic
357C2×C4×C11C22×D411yescharacteristic
358C2×C4×C11C2×#4111yescharacteristic
359C2×C4×C11C2×#4111yescharacteristic
360C2×C4×C11H(5,𝔽2)11yescharacteristic
361C2×C4×C112−1+411yescharacteristic
362C8×C11—22no—
363C8×C11—41no—
364C8×C11—41no—
365C8×C11—41no—
366C22×D8C22×C1111yescharacteristic
367#553—24no—
368#553—24no—
369C2×#126—21no—
370C2×#125C22×C1111yescharacteristic
371C2×#123—21no—
372C2×#121—21no—
373C2×#121—21no—
374C2×#121C22×C1111yescharacteristic
375C2×#121C22×C1111yescharacteristic
376C2×#121C22×C1111yescharacteristic
377C2×#121C22×C1111yescharacteristic
378C2×C4×D4—21no—
379C2×C4×D4C22×C1111yescharacteristic
380C2×C4×D4C22×C1111yescharacteristic
381C2×C4×D4C22×C1111yescharacteristic
382C2×#117C22×C1111yescharacteristic
383C22×C4⋊C4C22×C1111yescharacteristic
384#478—24no—
385#442—24no—
386C2×#107C22×C1111yescharacteristic
387C2×#106C22×C1111yescharacteristic
388C2×#106C22×C1111yescharacteristic
389C2×C4⋊C8C22×C1111yescharacteristic
390C2×#102C22×C1111yescharacteristic
391C2×#102C22×C1111yescharacteristic
392C2×#102C22×C1111yescharacteristic
393C2×#102C22×C1111yescharacteristic
394C2×#102C22×C1111yescharacteristic
395C2×#102C22×C1111yescharacteristic
396C2×C22⋊C8C22×C1111yescharacteristic
397C2×C22⋊C8C22×C1111yescharacteristic
398C2×C22⋊C8C22×C1111yescharacteristic
399C2×C22⋊C8C22×C1111yescharacteristic
400C2×#97C22×C1111yescharacteristic
401#394—21no—
402#394—21no—
403#384C22×C1111yescharacteristic
404#380—21no—
405#380C22×C1111yescharacteristic
406#380C22×C1111yescharacteristic
407#340C22×C1111yescharacteristic
408#340C22×C1111yescharacteristic
409#340C22×C1111yescharacteristic
410#340C22×C1111yescharacteristic
411#340C22×C1111yescharacteristic
412#340C22×C1111yescharacteristic
413C22×C11—22no—
414C22×C11—22no—
415C22×C11—22no—
416C22×C11—41no—
417C22×C11—41no—
418C22×C11—41no—
419C22×C11—41no—
420C22×C11—41no—
421C22×C11—41no—
422C22×C11—41no—
423C22×C11—42no—
424C22×C11—42no—
425C22×C11—41no—
426C22×C11—42no—
427C22×C11—42no—
428C22×C11—41no—
429C22×C11—41no—
430C22×C11—42no—
431C22×C11—41no—
432C22×C11—42no—
433C22×C11—81no—
434C22×C11—81no—
435C22×C11—81no—
436C22×C11—81no—
437C22×C11—81no—
438C22×C11—81no—
439C22×C11—81no—
440C22×C11—81no—
441C22×C11C2×#12011yescharacteristic
442C22×C11#54611yescharacteristic
443C22×C11#54711yescharacteristic
444C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
445C22×C11#57511yescharacteristic
446C22×C11#57611yescharacteristic
447C22×C11#57711yescharacteristic
448C4×C11—22no—
449C4×C11—22no—
450C4×C11—41no—
451C4×C11—41no—
452C4×C11—42no—
453C4×C11—42no—
454C4×C11—42no—
455C4×C11—81no—
456C4×C11—81no—
457C4×C11—81no—
458C4×C11#52511yescharacteristic
459C4×C11#53711yescharacteristic
460C4×C11#54811yescharacteristic
461C4×C11#55011yescharacteristic
462C22×D4—21no—
463C22×D4—21no—
464C22×D4—21no—
465C22×D4—21no—
466C22×D4D4×C1111yescharacteristic
467C22×D4C23×C1111yescharacteristic
468C22×D4C23×C1111yescharacteristic
469C23×C4—21no—
470C23×C4—21no—
471C23×C4—21no—
472C23×C4C23×C1111yescharacteristic
473C23×C4C23×C1111yescharacteristic
474C2×D8—22no—
475C2×D8—22no—
476C2×D8—22no—
477C22×C8C23×C1111yescharacteristic
478C22×C8C23×C1111yescharacteristic
479C22×C8C23×C1111yescharacteristic
480C22×C8C23×C1111yescharacteristic
481#126—28no—
482#125—22no—
483#125D4×C1114yescomplemented
484#123—28no—
485#121—28no—
486#121—22no—
487#121—22no—
488#121—22no—
489#121—22no—
490#121—22no—
491#121—22no—
492#121—41no—
493#121—41no—
494#121—44no—
495C4×D4—28no—
496C4×D4—22no—
497C4×D4—22no—
498C4×D4—22no—
499C4×D4—22no—
500C4×D4—22no—
501C4×D4D4×C1114yescomplemented
502#117—22no—
503#117—22no—
504C2×C4⋊C4—21no—
505C2×C4⋊C4—21no—
506C2×C4⋊C4—21no—
507C2×C4⋊C4—22no—
508C2×C4⋊C4—22no—
509C2×C4⋊C4—21no—
510C2×C4⋊C4—21no—
511C2×C4⋊C4D4×C1111yescharacteristic
512C2×C4⋊C4C23×C1111yescharacteristic
513C2×C4⋊C4C23×C1111yescharacteristic
514C2×C4⋊C4C23×C1111yescharacteristic
515C2×C4⋊C4C23×C1111yescharacteristic
516C2×C4⋊C4C23×C1111yescharacteristic
517C2×C4⋊C4C23×C1111yescharacteristic
518C2×C22⋊C4—21no—
519C2×C22⋊C4—21no—
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⋊C4D4×C1111yescharacteristic
528C2×C22⋊C4D4×C1111yescharacteristic
529C2×C42—21no—
530C2×C42C23×C1111yescharacteristic
531#107—22no—
532#106—22no—
533#106—22no—
534C4⋊C8—22no—
535#102—22no—
536#102—22no—
537#102—22no—
538#102—22no—
539#102—41no—
540#102—41no—
541C22⋊C8—22no—
542C22⋊C8—22no—
543C22⋊C8—41no—
544C22⋊C8—41no—
545#97—22no—
546#95—21no—
547#95—21no—
548C2×C11—42no—
549C2×C11—81no—
550C2×C11—82no—
551C2×C11—82no—
552C2×C11#240711yescharacteristic
553C2×C11#300611yescharacteristic
554C2×C11#301211yescharacteristic
555C2×C11#330711yescharacteristic
556C2×C11#331811yescharacteristic
557C2×C11#334511yescharacteristic
558C2×C11#334711yescharacteristic
559C24—21no—
560C24—21no—
561C24C2×D4×C1111yescharacteristic
562C24C2×D4×C1111yescharacteristic
563C2×D4—24no—
564C2×D4—22no—
565C2×D4—24no—
566C2×D4—22no—
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—21no—
576C2×D4—21no—
577C2×D4—41no—
578C2×D4—42no—
579C2×D4—42no—
580C2×D4—42no—
581C2×D4—42no—
582C2×D4—42no—
583C2×D4—42no—
584C2×D4—81no—
585C2×D4—81no—
586C2×D4—81no—
587C2×D4—81no—
588C2×D4C2×D4×C1112yes—
589C2×D4C11×#4112yes—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—24no—
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—24no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—42no—
611C22×C4—42no—
612C22×C4—42no—
613C22×C4—81no—
614C22×C4—81no—
615C22×C4—81no—
616C22×C4—81no—
617C22×C4C2×D4×C1111yescharacteristic
618C22×C4C2×D4×C1111yescharacteristic
619C22×C4C2×D4×C1111yescharacteristic
620C22×C4C2×D4×C1111yescharacteristic
621C22×C4C24×C1111yescharacteristic
622D8—28no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8C11×#4112yes—
635C4⋊C4—24no—
636C4⋊C4—24no—
637C4⋊C4—24no—
638C4⋊C4—22no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—42no—
649C4⋊C4—81no—
650C4⋊C4C2×D4×C1112yes—
651C4⋊C4C2×D4×C1112yes—
652C4⋊C4C2×D4×C1112yes—
653C22⋊C4—24no—
654C22⋊C4—24no—
655C22⋊C4—24no—
656C22⋊C4—24no—
657C22⋊C4—22no—
658C22⋊C4—22no—
659C22⋊C4—42no—
660C22⋊C4—42no—
661C22⋊C4—42no—
662C22⋊C4—42no—
663C22⋊C4—42no—
664C42—24no—
665C42C2×D4×C1112yes—
666C42C2×D4×C1112yes—
667C11#2413611yescharacteristic, direct product factor, Sylow
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—22no—
676C23—22no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23C11×AGL(1,ℤ/8)12yes—
696C23C22×D4×C1111yescharacteristic
697D4—22no—
698D4—22no—
699D4—22no—
700D4—22no—
701D4—44no—
702D4—48no—
703D4—41no—
704D4—41no—
705D4—41no—
706D4—41no—
707D4—84no—
708D4—84no—
709D4—84no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—21no—
718C2×C4—22no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
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—84no—
747C2×C4—84no—
748C2×C4—84no—
749C2×C4C11×#12012yes—
750C2×C4C11×#12012yes—
751C2×C4C22×D4×C1111yescharacteristic
752C2×C4C22×D4×C1111yescharacteristic
753C2×C4C2×C11×#4111yescharacteristic
754C2×C4C2×C11×#4111yescharacteristic
755C2×C4C11×H(5,𝔽2)11yescharacteristic
756C2×C4C11×2−1+411yescharacteristic
757C8—22no—
758C8—41no—
759C8—41no—
760C8—41no—
761C22—22no—
762C22—22no—
763C22—22no—
764C22—41no—
765C22—41no—
766C22—41no—
767C22—41no—
768C22—41no—
769C22—42no—
770C22—42no—
771C22—41no—
772C22—42no—
773C22—42no—
774C22—41no—
775C22—41no—
776C22—42no—
777C22—41no—
778C22—42no—
779C22—41no—
780C22—41no—
781C22—81no—
782C22—81no—
783C22—81no—
784C22—81no—
785C22—81no—
786C22—81no—
787C22—81no—
788C22—81no—
789C22C2×C11×#12011yescharacteristic
790C22C11×#54611yescharacteristic
791C22C11×#54711yescharacteristic
792C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
793C22C11×#57511yescharacteristic
794C22C11×#57611yescharacteristic
795C22C11×#57711yescharacteristic
796C4—22no—
797C4—22no—
798C4—41no—
799C4—41no—
800C4—42no—
801C4—42no—
802C4—42no—
803C4—81no—
804C4—81no—
805C4—81no—
806C4C11×#52511yescharacteristic
807C4C11×#53711yescharacteristic
808C4C11×#54811yescharacteristic
809C4C11×#55011yescharacteristic
810C2—42no—
811C2—81no—
812C2—82no—
813C2—82no—
814C2C11×#240711yescharacteristic
815C2C11×#300611yescharacteristic
816C2C11×#301211yescharacteristic
817C2C11×#330711yescharacteristic
818C2C11×#331811yescharacteristic
819C2C11×#334511yescharacteristic
820C2C11×#334711yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
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×#553C2semidirect
2. C2×C11×#478C2semidirect
3. C2×C11×#442C2semidirect
4. C11×#2537C2semidirect
5. C11×#2034C2semidirect
6. C11×#2033C2semidirect
7. C11×#1999C2semidirect
8. C11×#1999C2semidirect
9. C11×#1992C2semidirect
10. C11×#1955C2semidirect
11. C11×#1875C2semidirect
12. C11×#1874C2semidirect
13. C11×#1854C2semidirect
14. C11×#1853C2semidirect
15. C11×#1802C2semidirect
84. C11×#125D4semidirect
102. C4×D4×C11D4semidirect
149. #24136C11direct (N × H)
258. C2×#553C2×C11semidirect
259. C2×#478C2×C11semidirect
260. C2×#442C2×C11semidirect
261. #2537C2×C11semidirect
262. #2034C2×C11semidirect
263. #2033C2×C11semidirect
264. #1999C2×C11semidirect
265. #1999C2×C11semidirect
266. #1992C2×C11semidirect
267. #1955C2×C11semidirect
268. #1875C2×C11semidirect
269. #1874C2×C11semidirect
270. #1854C2×C11semidirect
271. #1853C2×C11semidirect
272. #1802C2×C11semidirect
483. #125D4×C11semidirect
501. C4×D4D4×C11semidirect
667. C11#24136direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5532
C2×C11×#4782
C2×C11×#4422
C11×#25372
C11×#20342
C11×#20332
C11×#19992
C11×#19922
C11×#19552
C11×#18752
C11×#18742
C11×#18542
C11×#18532
C11×#18022
#2413611