Finite Group Databasebeta

← C11×#24124 #14601317

Subgroups — C11×#24124 #14601317

Order 2816.

1216 conjugacy classes of subgroups.

The subgroup lattice has 816 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×C4×C11×D8C211yesmaximal, characteristic, complemented
4C11×#2535C211yesmaximal, characteristic, complemented
5C11×#2034C211yesmaximal, characteristic, complemented
6C11×#2033C211yesmaximal, characteristic, complemented
7C11×#1999C211yesmaximal, characteristic, complemented
8C11×#1999C211yesmaximal, characteristic, complemented
9C11×#1991C211yesmaximal, characteristic, complemented
10C11×#1954C211yesmaximal, characteristic, complemented
11C11×#1875C211yesmaximal, characteristic, complemented
12C11×#1874C211yesmaximal, characteristic, complemented
13C11×#1854C211yesmaximal, characteristic, complemented
14C11×#1852C211yesmaximal, characteristic, complemented
15C11×#1804C211yesmaximal, 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×#121C2211yescharacteristic
24C2×C11×#121C2211yescharacteristic
25C2×C11×#121C2211yescharacteristic
26C2×C11×#121C2211yescharacteristic
27C2×C4×D4×C11—21no—
28C2×C4×D4×C11C2211yescharacteristic
29C2×C4×D4×C11C2211yescharacteristic
30C2×C4×D4×C11C2211yescharacteristic
31C2×C11×#117C2211yescharacteristic
32C22×C11×C4⋊C4C2211yescharacteristic
33C11×#478—24no—
34C4×C11×D8—24no—
35C2×C11×#107C2211yescharacteristic
36C2×C11×#107C2211yescharacteristic
37C2×C11×#106C2211yescharacteristic
38C2×C11×C4⋊C8C2211yescharacteristic
39C2×C11×#102C2211yescharacteristic
40C2×C11×#102C2211yescharacteristic
41C2×C11×#102C2211yescharacteristic
42C2×C11×#102C2211yescharacteristic
43C2×C11×#102C2211yescharacteristic
44C2×C11×#102C2211yescharacteristic
45C2×C11×C22⋊C8C2211yescharacteristic
46C2×C11×C22⋊C8C2211yescharacteristic
47C2×C11×C22⋊C8C2211yescharacteristic
48C2×C11×C22⋊C8C2211yescharacteristic
49C2×C4×C8×C11C2211yescharacteristic
50C11×#397—21no—
51C11×#392—21no—
52C11×#386—21no—
53C11×#386—21no—
54C11×#382C2211yescharacteristic
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—
95C4×D4×C11—28no—
96C4×D4×C11—22no—
97C4×D4×C11—22no—
98C4×D4×C11—22no—
99C4×D4×C11—22no—
100C4×D4×C11—22no—
101C4×D4×C11D414yescomplemented
102C11×#117—22no—
103C11×#117—22no—
104C2×C11×C4⋊C4—21no—
105C2×C11×C4⋊C4—21no—
106C2×C11×C4⋊C4—21no—
107C2×C11×C4⋊C4—22no—
108C2×C11×C4⋊C4—22no—
109C2×C11×C4⋊C4D411yescharacteristic
110C2×C11×C4⋊C4C2311yescharacteristic
111C2×C11×C4⋊C4C2311yescharacteristic
112C2×C11×C4⋊C4C2311yescharacteristic
113C2×C11×C4⋊C4C2311yescharacteristic
114C2×C11×C4⋊C4C2311yescharacteristic
115C2×C11×C4⋊C4C2311yescharacteristic
116C2×C11×C22⋊C4—21no—
117C2×C11×C22⋊C4—21no—
118C2×C11×C22⋊C4—21no—
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⋊C4D411yescharacteristic
126C2×C11×C22⋊C4D411yescharacteristic
127C2×C42×C11—21no—
128C2×C42×C11C2311yescharacteristic
129C11×#107—22no—
130C11×#107—22no—
131C11×#106—22no—
132C11×C4⋊C8—22no—
133C11×#102—22no—
134C11×#102—22no—
135C11×#102—22no—
136C11×#102—22no—
137C11×#102—41no—
138C11×#102—41no—
139C11×C22⋊C8—22no—
140C11×C22⋊C8—22no—
141C11×C22⋊C8—41no—
142C11×C22⋊C8—41no—
143C4×C8×C11—22no—
144C11×#95—21no—
145C11×#95—21no—
146C11×#95—21no—
147C11×#95—21no—
148#24124C1111yesmaximal, characteristic, direct product factor, Sylow
149C24×C11—21no—
150C24×C11—21no—
151C24×C11C2×D411yescharacteristic
152C24×C11C2×D411yescharacteristic
153C2×D4×C11—24no—
154C2×D4×C11—22no—
155C2×D4×C11—24no—
156C2×D4×C11—22no—
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—21no—
166C2×D4×C11—21no—
167C2×D4×C11—41no—
168C2×D4×C11—42no—
169C2×D4×C11—42no—
170C2×D4×C11—42no—
171C2×D4×C11—42no—
172C2×D4×C11—42no—
173C2×D4×C11—42no—
174C2×D4×C11—81no—
175C2×D4×C11—81no—
176C2×D4×C11—81no—
177C2×D4×C11—81no—
178C2×D4×C11C2×D412yes—
179C2×D4×C11#4112yes—
180C22×C4×C11—21no—
181C22×C4×C11—21no—
182C22×C4×C11—21no—
183C22×C4×C11—24no—
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—24no—
197C22×C4×C11—21no—
198C22×C4×C11—21no—
199C22×C4×C11—21no—
200C22×C4×C11—42no—
201C22×C4×C11—81no—
202C22×C4×C11—81no—
203C22×C4×C11—81no—
204C22×C4×C11—81no—
205C22×C4×C11—81no—
206C22×C4×C11—81no—
207C22×C4×C11C2×D411yescharacteristic
208C22×C4×C11C2×D411yescharacteristic
209C22×C4×C11C2×D411yescharacteristic
210C22×C4×C11C2×D411yescharacteristic
211C22×C4×C11C2411yescharacteristic
212C11×D8—28no—
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—21no—
221C2×C8×C11—21no—
222C2×C8×C11—21no—
223C2×C8×C11—21no—
224C2×C8×C11#4112yes—
225C11×C4⋊C4—24no—
226C11×C4⋊C4—24no—
227C11×C4⋊C4—24no—
228C11×C4⋊C4—22no—
229C11×C4⋊C4—21no—
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⋊C4C2×D412yes—
239C11×C4⋊C4C2×D412yes—
240C11×C4⋊C4C2×D412yes—
241C11×C22⋊C4—24no—
242C11×C22⋊C4—24no—
243C11×C22⋊C4—24no—
244C11×C22⋊C4—24no—
245C11×C22⋊C4—22no—
246C11×C22⋊C4—22no—
247C11×C22⋊C4—42no—
248C11×C22⋊C4—42no—
249C11×C22⋊C4—42no—
250C11×C22⋊C4—81no—
251C11×C22⋊C4—81no—
252C42×C11—24no—
253C42×C11C2×D412yes—
254C42×C11C2×D412yes—
255C2×#553C2×C1111yescharacteristic, complemented
256C2×#478C2×C1111yescharacteristic, complemented
257C2×C4×D8C2×C1111yescharacteristic, complemented
258#2535C2×C1111yescharacteristic, complemented
259#2034C2×C1111yescharacteristic, complemented
260#2033C2×C1111yescharacteristic, complemented
261#1999C2×C1111yescharacteristic, complemented
262#1999C2×C1111yescharacteristic, complemented
263#1991C2×C1111yescharacteristic, complemented
264#1954C2×C1111yescharacteristic, complemented
265#1875C2×C1111yescharacteristic, complemented
266#1874C2×C1111yescharacteristic, complemented
267#1854C2×C1111yescharacteristic, complemented
268#1852C2×C1111yescharacteristic, complemented
269#1804C2×C1111yescharacteristic, complemented
270C23×C11—21no—
271C23×C11—21no—
272C23×C11—21no—
273C23×C11—21no—
274C23×C11—21no—
275C23×C11—21no—
276C23×C11—21no—
277C23×C11—22no—
278C23×C11—22no—
279C23×C11—21no—
280C23×C11—21no—
281C23×C11—21no—
282C23×C11—21no—
283C23×C11—21no—
284C23×C11—21no—
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—41no—
294C23×C11—41no—
295C23×C11—41no—
296C23×C11—41no—
297C23×C11#13512yes—
298C23×C11C22×D411yescharacteristic
299D4×C11—22no—
300D4×C11—22no—
301D4×C11—22no—
302D4×C11—22no—
303D4×C11—44no—
304D4×C11—48no—
305D4×C11—41no—
306D4×C11—41no—
307D4×C11—41no—
308D4×C11—41no—
309D4×C11—84no—
310D4×C11—84no—
311D4×C11—84no—
312C2×C4×C11—21no—
313C2×C4×C11—21no—
314C2×C4×C11—21no—
315C2×C4×C11—21no—
316C2×C4×C11—21no—
317C2×C4×C11—22no—
318C2×C4×C11—22no—
319C2×C4×C11—21no—
320C2×C4×C11—22no—
321C2×C4×C11—21no—
322C2×C4×C11—21no—
323C2×C4×C11—21no—
324C2×C4×C11—21no—
325C2×C4×C11—41no—
326C2×C4×C11—41no—
327C2×C4×C11—41no—
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—84no—
349C2×C4×C11—84no—
350C2×C4×C11—84no—
351C2×C4×C11#12012yes—
352C2×C4×C11#12012yes—
353C2×C4×C11C22×D411yescharacteristic
354C2×C4×C11C22×D411yescharacteristic
355C2×C4×C11C2×#4111yescharacteristic
356C2×C4×C11C2×#4111yescharacteristic
357C2×C4×C11H(5,𝔽2)11yescharacteristic
358C2×C4×C112−1+411yescharacteristic
359C8×C11—22no—
360C8×C11—41no—
361C8×C11—41no—
362C8×C11—41no—
363C22×D8C22×C1111yescharacteristic
364#553—24no—
365#553—24no—
366C2×#126—21no—
367C2×#125C22×C1111yescharacteristic
368C2×#123—21no—
369C2×#121—21no—
370C2×#121C22×C1111yescharacteristic
371C2×#121C22×C1111yescharacteristic
372C2×#121C22×C1111yescharacteristic
373C2×#121C22×C1111yescharacteristic
374C2×C4×D4—21no—
375C2×C4×D4C22×C1111yescharacteristic
376C2×C4×D4C22×C1111yescharacteristic
377C2×C4×D4C22×C1111yescharacteristic
378C2×#117C22×C1111yescharacteristic
379C22×C4⋊C4C22×C1111yescharacteristic
380#478—24no—
381C4×D8—24no—
382C2×#107C22×C1111yescharacteristic
383C2×#107C22×C1111yescharacteristic
384C2×#106C22×C1111yescharacteristic
385C2×C4⋊C8C22×C1111yescharacteristic
386C2×#102C22×C1111yescharacteristic
387C2×#102C22×C1111yescharacteristic
388C2×#102C22×C1111yescharacteristic
389C2×#102C22×C1111yescharacteristic
390C2×#102C22×C1111yescharacteristic
391C2×#102C22×C1111yescharacteristic
392C2×C22⋊C8C22×C1111yescharacteristic
393C2×C22⋊C8C22×C1111yescharacteristic
394C2×C22⋊C8C22×C1111yescharacteristic
395C2×C22⋊C8C22×C1111yescharacteristic
396C2×C4×C8C22×C1111yescharacteristic
397#397—21no—
398#392—21no—
399#386—21no—
400#386—21no—
401#382C22×C1111yescharacteristic
402#380C22×C1111yescharacteristic
403#380C22×C1111yescharacteristic
404#340C22×C1111yescharacteristic
405#340C22×C1111yescharacteristic
406#340C22×C1111yescharacteristic
407#340C22×C1111yescharacteristic
408#340C22×C1111yescharacteristic
409#340C22×C1111yescharacteristic
410C22×C11—22no—
411C22×C11—22no—
412C22×C11—22no—
413C22×C11—41no—
414C22×C11—41no—
415C22×C11—41no—
416C22×C11—41no—
417C22×C11—41no—
418C22×C11—41no—
419C22×C11—41no—
420C22×C11—42no—
421C22×C11—42no—
422C22×C11—41no—
423C22×C11—42no—
424C22×C11—42no—
425C22×C11—41no—
426C22×C11—42no—
427C22×C11—41no—
428C22×C11—41no—
429C22×C11—42no—
430C22×C11—81no—
431C22×C11—81no—
432C22×C11—81no—
433C22×C11—81no—
434C22×C11—81no—
435C22×C11—81no—
436C22×C11—81no—
437C22×C11—81no—
438C22×C11C2×#12011yescharacteristic
439C22×C11#54611yescharacteristic
440C22×C11#54711yescharacteristic
441C22×C11C2×#13511yescharacteristic
442C22×C11#57511yescharacteristic
443C22×C11#57611yescharacteristic
444C22×C11#57611yescharacteristic
445C4×C11—22no—
446C4×C11—22no—
447C4×C11—41no—
448C4×C11—41no—
449C4×C11—42no—
450C4×C11—42no—
451C4×C11—42no—
452C4×C11—81no—
453C4×C11—81no—
454C4×C11—81no—
455C4×C11#52511yescharacteristic
456C4×C11#53711yescharacteristic
457C4×C11#54811yescharacteristic
458C4×C11#55011yescharacteristic
459C22×D4—21no—
460C22×D4—21no—
461C22×D4—21no—
462C22×D4—21no—
463C22×D4D4×C1111yescharacteristic
464C22×D4C23×C1111yescharacteristic
465C22×D4C23×C1111yescharacteristic
466C23×C4—21no—
467C23×C4—21no—
468C23×C4—21no—
469C23×C4C23×C1111yescharacteristic
470C23×C4C23×C1111yescharacteristic
471C2×D8—22no—
472C2×D8—22no—
473C2×D8—22no—
474C22×C8C23×C1111yescharacteristic
475C22×C8C23×C1111yescharacteristic
476C22×C8C23×C1111yescharacteristic
477C22×C8C23×C1111yescharacteristic
478#126—28no—
479#125—22no—
480#125D4×C1114yescomplemented
481#123—28no—
482#121—28no—
483#121—22no—
484#121—22no—
485#121—22no—
486#121—22no—
487#121—22no—
488#121—22no—
489#121—41no—
490#121—41no—
491C4×D4—28no—
492C4×D4—22no—
493C4×D4—22no—
494C4×D4—22no—
495C4×D4—22no—
496C4×D4—22no—
497C4×D4D4×C1114yescomplemented
498#117—22no—
499#117—22no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—21no—
502C2×C4⋊C4—21no—
503C2×C4⋊C4—22no—
504C2×C4⋊C4—22no—
505C2×C4⋊C4D4×C1111yescharacteristic
506C2×C4⋊C4C23×C1111yescharacteristic
507C2×C4⋊C4C23×C1111yescharacteristic
508C2×C4⋊C4C23×C1111yescharacteristic
509C2×C4⋊C4C23×C1111yescharacteristic
510C2×C4⋊C4C23×C1111yescharacteristic
511C2×C4⋊C4C23×C1111yescharacteristic
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C22⋊C4—21no—
519C2×C22⋊C4—21no—
520C2×C22⋊C4—21no—
521C2×C22⋊C4D4×C1111yescharacteristic
522C2×C22⋊C4D4×C1111yescharacteristic
523C2×C42—21no—
524C2×C42C23×C1111yescharacteristic
525#107—22no—
526#107—22no—
527#106—22no—
528C4⋊C8—22no—
529#102—22no—
530#102—22no—
531#102—22no—
532#102—22no—
533#102—41no—
534#102—41no—
535C22⋊C8—22no—
536C22⋊C8—22no—
537C22⋊C8—41no—
538C22⋊C8—41no—
539C4×C8—22no—
540#95—21no—
541#95—21no—
542#95—21no—
543#95—21no—
544C2×C11—42no—
545C2×C11—81no—
546C2×C11—82no—
547C2×C11—82no—
548C2×C11#240711yescharacteristic
549C2×C11#300211yescharacteristic
550C2×C11#300811yescharacteristic
551C2×C11#329711yescharacteristic
552C2×C11#332211yescharacteristic
553C2×C11#333911yescharacteristic
554C2×C11#335511yescharacteristic
555C24—21no—
556C24—21no—
557C24C2×D4×C1111yescharacteristic
558C24C2×D4×C1111yescharacteristic
559C2×D4—24no—
560C2×D4—22no—
561C2×D4—24no—
562C2×D4—22no—
563C2×D4—21no—
564C2×D4—21no—
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—41no—
574C2×D4—42no—
575C2×D4—42no—
576C2×D4—42no—
577C2×D4—42no—
578C2×D4—42no—
579C2×D4—42no—
580C2×D4—81no—
581C2×D4—81no—
582C2×D4—81no—
583C2×D4—81no—
584C2×D4C2×D4×C1112yes—
585C2×D4C11×#4112yes—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—24no—
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—24no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—42no—
607C22×C4—81no—
608C22×C4—81no—
609C22×C4—81no—
610C22×C4—81no—
611C22×C4—81no—
612C22×C4—81no—
613C22×C4C2×D4×C1111yescharacteristic
614C22×C4C2×D4×C1111yescharacteristic
615C22×C4C2×D4×C1111yescharacteristic
616C22×C4C2×D4×C1111yescharacteristic
617C22×C4C24×C1111yescharacteristic
618D8—28no—
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×C8C11×#4112yes—
631C4⋊C4—24no—
632C4⋊C4—24no—
633C4⋊C4—24no—
634C4⋊C4—22no—
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⋊C4C2×D4×C1112yes—
645C4⋊C4C2×D4×C1112yes—
646C4⋊C4C2×D4×C1112yes—
647C22⋊C4—24no—
648C22⋊C4—24no—
649C22⋊C4—24no—
650C22⋊C4—24no—
651C22⋊C4—22no—
652C22⋊C4—22no—
653C22⋊C4—42no—
654C22⋊C4—42no—
655C22⋊C4—42no—
656C22⋊C4—81no—
657C22⋊C4—81no—
658C42—24no—
659C42C2×D4×C1112yes—
660C42C2×D4×C1112yes—
661C11#2412411yescharacteristic, direct product factor, Sylow
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—22no—
670C23—22no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23C11×#13512yes—
690C23C22×D4×C1111yescharacteristic
691D4—22no—
692D4—22no—
693D4—22no—
694D4—22no—
695D4—44no—
696D4—48no—
697D4—41no—
698D4—41no—
699D4—41no—
700D4—41no—
701D4—84no—
702D4—84no—
703D4—84no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—21no—
712C2×C4—22no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
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—84no—
741C2×C4—84no—
742C2×C4—84no—
743C2×C4C11×#12012yes—
744C2×C4C11×#12012yes—
745C2×C4C22×D4×C1111yescharacteristic
746C2×C4C22×D4×C1111yescharacteristic
747C2×C4C2×C11×#4111yescharacteristic
748C2×C4C2×C11×#4111yescharacteristic
749C2×C4C11×H(5,𝔽2)11yescharacteristic
750C2×C4C11×2−1+411yescharacteristic
751C8—22no—
752C8—41no—
753C8—41no—
754C8—41no—
755C22—22no—
756C22—22no—
757C22—22no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—42no—
764C22—42no—
765C22—41no—
766C22—42no—
767C22—42no—
768C22—41no—
769C22—42no—
770C22—41no—
771C22—41no—
772C22—42no—
773C22—41no—
774C22—41no—
775C22—81no—
776C22—81no—
777C22—81no—
778C22—81no—
779C22—81no—
780C22—81no—
781C22—81no—
782C22—81no—
783C22C2×C11×#12011yescharacteristic
784C22C11×#54611yescharacteristic
785C22C11×#54711yescharacteristic
786C22C2×C11×#13511yescharacteristic
787C22C11×#57511yescharacteristic
788C22C11×#57611yescharacteristic
789C22C11×#57611yescharacteristic
790C4—22no—
791C4—22no—
792C4—41no—
793C4—41no—
794C4—42no—
795C4—42no—
796C4—42no—
797C4—81no—
798C4—81no—
799C4—81no—
800C4C11×#52511yescharacteristic
801C4C11×#53711yescharacteristic
802C4C11×#54811yescharacteristic
803C4C11×#55011yescharacteristic
804C2—42no—
805C2—81no—
806C2—82no—
807C2—82no—
808C2C11×#240711yescharacteristic
809C2C11×#300211yescharacteristic
810C2C11×#300811yescharacteristic
811C2C11×#329711yescharacteristic
812C2C11×#332211yescharacteristic
813C2C11×#333911yescharacteristic
814C2C11×#335511yescharacteristic
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×C4×C11×D8C2semidirect
4. C11×#2535C2semidirect
5. C11×#2034C2semidirect
6. C11×#2033C2semidirect
7. C11×#1999C2semidirect
8. C11×#1999C2semidirect
9. C11×#1991C2semidirect
10. C11×#1954C2semidirect
11. C11×#1875C2semidirect
12. C11×#1874C2semidirect
13. C11×#1854C2semidirect
14. C11×#1852C2semidirect
15. C11×#1804C2semidirect
84. C11×#125D4semidirect
101. C4×D4×C11D4semidirect
148. #24124C11direct (N × H)
255. C2×#553C2×C11semidirect
256. C2×#478C2×C11semidirect
257. C2×C4×D8C2×C11semidirect
258. #2535C2×C11semidirect
259. #2034C2×C11semidirect
260. #2033C2×C11semidirect
261. #1999C2×C11semidirect
262. #1999C2×C11semidirect
263. #1991C2×C11semidirect
264. #1954C2×C11semidirect
265. #1875C2×C11semidirect
266. #1874C2×C11semidirect
267. #1854C2×C11semidirect
268. #1852C2×C11semidirect
269. #1804C2×C11semidirect
480. #125D4×C11semidirect
497. C4×D4D4×C11semidirect
661. C11#24124direct (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×C4×C11×D82
C11×#25352
C11×#20342
C11×#20332
C11×#19992
C11×#19912
C11×#19542
C11×#18752
C11×#18742
C11×#18542
C11×#18522
C11×#18042
#2412411