Finite Group Databasebeta

← C11×#24443 #14601636

Subgroups — C11×#24443 #14601636

Order 2816.

1510 conjugacy classes of subgroups.

The subgroup lattice has 918 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#550C211yesmaximal, characteristic
2C2×C11×#468C211yesmaximal, characteristic, complemented
3C2×C11×#452C211yesmaximal, characteristic, complemented
4C2×C11×#452C211yesmaximal, characteristic, complemented
5C2×C11×#417C211yesmaximal, characteristic, complemented
6C11×#2417C211yesmaximal, characteristic, complemented
7C11×#2041C211yesmaximal, characteristic, complemented
8C11×#2033C211yesmaximal, characteristic, complemented
9C11×#2014C211yesmaximal, characteristic, complemented
10C11×#2000C211yesmaximal, characteristic, complemented
11C11×#1878C211yesmaximal, characteristic, complemented
12C11×#1874C211yesmaximal, characteristic, complemented
13C11×#1870C211yesmaximal, characteristic, complemented
14C11×#1863C211yesmaximal, characteristic, complemented
15C11×#1788C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic
17C22×C11×#41C2211yescharacteristic
18C22×C11×Q16C2211yescharacteristic
19C22×C11×SD16C2211yescharacteristic
20C22×C11×SD16C2211yescharacteristic
21C22×C11×M16C2211yescharacteristic
22C11×#550—24no—
23C11×#550—24no—
24C2×C11×#127—21no—
25C2×C11×#127C2211yescharacteristic
26C2×C11×C22⋊Q8C2211yescharacteristic
27C2×C11×C22⋊Q8C2211yescharacteristic
28C2×C11×#121—21no—
29C2×C11×#121—21no—
30C2×C11×#121C2211yescharacteristic
31C2×C11×#121C2211yescharacteristic
32C2×C4×Q8×C11C2211yescharacteristic
33C2×C4×D4×C11—21no—
34C2×C4×D4×C11C2211yescharacteristic
35C22×C11×C4⋊C4C2211yescharacteristic
36C11×#468—24no—
37C11×#452—24no—
38C11×#452—24no—
39C2×C11×#107C2211yescharacteristic
40C11×#417—24no—
41C2×C11×#103C2211yescharacteristic
42C2×C11×#103C2211yescharacteristic
43C2×C11×#103C2211yescharacteristic
44C2×C11×#103C2211yescharacteristic
45C2×C11×#102C2211yescharacteristic
46C2×C11×#102C2211yescharacteristic
47C2×C11×#102C2211yescharacteristic
48C2×C11×#102C2211yescharacteristic
49C2×C11×#102C2211yescharacteristic
50C2×C11×#102C2211yescharacteristic
51C2×C11×C22⋊C8C2211yescharacteristic
52C2×C11×C22⋊C8C2211yescharacteristic
53C2×C11×C22⋊C8C2211yescharacteristic
54C11×#398—21no—
55C11×#396—21no—
56C11×#391C2211yescharacteristic
57C11×#389C2211yescharacteristic
58C11×#386—21no—
59C11×#380—21no—
60C11×#380C2211yescharacteristic
61C11×#340C2211yescharacteristic
62C11×#340C2211yescharacteristic
63C11×#336C2211yescharacteristic
64C11×#336C2211yescharacteristic
65C2×C11×#41—22no—
66C2×C11×#41—22no—
67C2×C11×#41—22no—
68C2×C11×#41—22no—
69C2×C11×#41—22no—
70C2×C11×#41—22no—
71C2×C11×#41—22no—
72C2×C11×#41—41no—
73C2×C11×#41—41no—
74C2×C11×#41—41no—
75C2×C11×#41—41no—
76C2×C11×#41D414yes—
77C22×Q8×C11C2311yescharacteristic
78C22×Q8×C11C2311yescharacteristic
79C22×D4×C11—21no—
80C22×D4×C11—21no—
81C22×D4×C11—21no—
82C22×D4×C11—21no—
83C22×D4×C11—21no—
84C22×D4×C11—21no—
85C22×D4×C11D411yescharacteristic
86C22×D4×C11C2311yescharacteristic
87C22×D4×C11C2311yescharacteristic
88C23×C4×C11—21no—
89C23×C4×C11—21no—
90C23×C4×C11—21no—
91C23×C4×C11C2311yescharacteristic
92C23×C4×C11C2311yescharacteristic
93C2×C11×Q16—22no—
94C2×C11×Q16—22no—
95C2×C11×Q16—22no—
96C2×C11×SD16—22no—
97C2×C11×SD16—22no—
98C2×C11×SD16—22no—
99C2×C11×SD16—41no—
100C2×C11×SD16—41no—
101C2×C11×SD16—41no—
102C2×C11×M16—22no—
103C2×C11×M16—22no—
104C2×C11×M16—41no—
105C22×C8×C11C2311yescharacteristic
106C22×C8×C11C2311yescharacteristic
107C22×C8×C11C2311yescharacteristic
108C22×C8×C11C2311yescharacteristic
109C11×#127—28no—
110C11×#127—22no—
111C11×#127—22no—
112C11×C22⋊Q8—22no—
113C11×C22⋊Q8—22no—
114C11×C22⋊Q8—22no—
115C11×C22⋊Q8—41no—
116C11×#121—28no—
117C11×#121—28no—
118C11×#121—22no—
119C11×#121—22no—
120C11×#121—22no—
121C11×#121D414yes—
122C4×Q8×C11—22no—
123C4×Q8×C11—22no—
124C4×D4×C11—28no—
125C4×D4×C11—22no—
126C4×D4×C11—22no—
127C2×C11×C4⋊C4—21no—
128C2×C11×C4⋊C4—22no—
129C2×C11×C4⋊C4—21no—
130C2×C11×C4⋊C4—21no—
131C2×C11×C4⋊C4—21no—
132C2×C11×C4⋊C4—21no—
133C2×C11×C4⋊C4—41no—
134C2×C11×C4⋊C4D411yescharacteristic
135C2×C11×C4⋊C4C2311yescharacteristic
136C2×C11×C4⋊C4C2311yescharacteristic
137C2×C11×C4⋊C4C2311yescharacteristic
138C2×C11×C4⋊C4C2311yescharacteristic
139C2×C11×C22⋊C4—21no—
140C2×C11×C22⋊C4—21no—
141C2×C11×C22⋊C4—21no—
142C2×C11×C22⋊C4—21no—
143C2×C11×C22⋊C4—21no—
144C2×C11×C22⋊C4D411yescharacteristic
145C2×C11×C22⋊C4D411yescharacteristic
146C2×C42×C11—21no—
147C2×C42×C11C2311yescharacteristic
148C11×#107—22no—
149C11×#103—22no—
150C11×#103—22no—
151C11×#103—22no—
152C11×#103D414yescomplemented
153C11×#102—22no—
154C11×#102—22no—
155C11×#102—22no—
156C11×#102—22no—
157C11×#102—22no—
158C11×#102—41no—
159C11×C22⋊C8—22no—
160C11×C22⋊C8—22no—
161C11×C22⋊C8—41no—
162C11×#95—21no—
163C11×#95—21no—
164C11×#95—21no—
165C11×#95—21no—
166#24443C1111yesmaximal, characteristic, direct product factor, Sylow
167C24×C11—21no—
168C24×C11—21no—
169C24×C11C2×D411yescharacteristic
170C24×C11C2×D411yescharacteristic
171C11×#41—28no—
172C11×#41—44no—
173C11×#41—44no—
174C11×#41—44no—
175C11×#41—44no—
176C11×#41—44no—
177C11×#41—44no—
178C11×#41—44no—
179C2×Q8×C11—21no—
180C2×Q8×C11—21no—
181C2×Q8×C11—21no—
182C2×Q8×C11—21no—
183C2×Q8×C11—21no—
184C2×Q8×C11—21no—
185C2×Q8×C11—21no—
186C2×Q8×C11—21no—
187C2×Q8×C11—21no—
188C2×Q8×C11C2×D412yes—
189C2×Q8×C11C2×D412yes—
190C2×Q8×C11#4112yes—
191C2×D4×C11—24no—
192C2×D4×C11—24no—
193C2×D4×C11—22no—
194C2×D4×C11—24no—
195C2×D4×C11—24no—
196C2×D4×C11—24no—
197C2×D4×C11—24no—
198C2×D4×C11—22no—
199C2×D4×C11—21no—
200C2×D4×C11—21no—
201C2×D4×C11—21no—
202C2×D4×C11—21no—
203C2×D4×C11—21no—
204C2×D4×C11—21no—
205C2×D4×C11—21no—
206C2×D4×C11—21no—
207C2×D4×C11—21no—
208C2×D4×C11—21no—
209C2×D4×C11—41no—
210C2×D4×C11—42no—
211C2×D4×C11—42no—
212C2×D4×C11—42no—
213C2×D4×C11—42no—
214C2×D4×C11—42no—
215C2×D4×C11—42no—
216C2×D4×C11—81no—
217C2×D4×C11—81no—
218C2×D4×C11—81no—
219C2×D4×C11—81no—
220C2×D4×C11—81no—
221C2×D4×C11—81no—
222C2×D4×C11C2×D412yes—
223C2×D4×C11C2×D412yes—
224C22×C4×C11—21no—
225C22×C4×C11—21no—
226C22×C4×C11—21no—
227C22×C4×C11—21no—
228C22×C4×C11—21no—
229C22×C4×C11—24no—
230C22×C4×C11—21no—
231C22×C4×C11—21no—
232C22×C4×C11—24no—
233C22×C4×C11—21no—
234C22×C4×C11—21no—
235C22×C4×C11—21no—
236C22×C4×C11—21no—
237C22×C4×C11—21no—
238C22×C4×C11—21no—
239C22×C4×C11—21no—
240C22×C4×C11—21no—
241C22×C4×C11—21no—
242C22×C4×C11—42no—
243C22×C4×C11—42no—
244C22×C4×C11—42no—
245C22×C4×C11—42no—
246C22×C4×C11—42no—
247C22×C4×C11—42no—
248C22×C4×C11—81no—
249C22×C4×C11C2×D411yescharacteristic
250C22×C4×C11C2×D411yescharacteristic
251C22×C4×C11C2×D411yescharacteristic
252C22×C4×C11C2×D412yes—
253C22×C4×C11C2×D412yes—
254C22×C4×C11C2×D411yescharacteristic
255C22×C4×C11C2411yescharacteristic
256C11×Q16—44no—
257C11×SD16—44no—
258C11×SD16—44no—
259C11×M16—44no—
260C2×C8×C11—21no—
261C2×C8×C11—21no—
262C2×C8×C11—21no—
263C2×C8×C11—21no—
264C2×C8×C11—21no—
265C2×C8×C11—21no—
266C2×C8×C11—21no—
267C2×C8×C11—21no—
268C2×C8×C11—21no—
269C2×C8×C11—21no—
270C2×C8×C11—21no—
271C2×C8×C11C2×D412yes—
272C11×C4⋊C4—24no—
273C11×C4⋊C4—22no—
274C11×C4⋊C4—21no—
275C11×C4⋊C4—21no—
276C11×C4⋊C4—21no—
277C11×C4⋊C4—21no—
278C11×C4⋊C4—21no—
279C11×C4⋊C4—21no—
280C11×C4⋊C4—42no—
281C11×C4⋊C4—42no—
282C11×C4⋊C4—42no—
283C11×C4⋊C4—81no—
284C11×C4⋊C4C2×D412yes—
285C11×C4⋊C4C2×D412yes—
286C11×C22⋊C4—24no—
287C11×C22⋊C4—22no—
288C11×C22⋊C4—24no—
289C11×C22⋊C4—22no—
290C11×C22⋊C4—42no—
291C11×C22⋊C4—42no—
292C11×C22⋊C4—81no—
293C42×C11—24no—
294C42×C11—21no—
295C42×C11—21no—
296C2×#550C2×C1111yescharacteristic
297C2×#468C2×C1111yescharacteristic, complemented
298C2×#452C2×C1111yescharacteristic, complemented
299C2×#452C2×C1111yescharacteristic, complemented
300C2×#417C2×C1111yescharacteristic, complemented
301#2417C2×C1111yescharacteristic, complemented
302#2041C2×C1111yescharacteristic, complemented
303#2033C2×C1111yescharacteristic, complemented
304#2014C2×C1111yescharacteristic, complemented
305#2000C2×C1111yescharacteristic, complemented
306#1878C2×C1111yescharacteristic, complemented
307#1874C2×C1111yescharacteristic, complemented
308#1870C2×C1111yescharacteristic, complemented
309#1863C2×C1111yescharacteristic, complemented
310#1788C2×C1111yescharacteristic, complemented
311C23×C11—21no—
312C23×C11—21no—
313C23×C11—21no—
314C23×C11—21no—
315C23×C11—21no—
316C23×C11—21no—
317C23×C11—21no—
318C23×C11—22no—
319C23×C11—22no—
320C23×C11—21no—
321C23×C11—21no—
322C23×C11—21no—
323C23×C11—21no—
324C23×C11—21no—
325C23×C11—21no—
326C23×C11—41no—
327C23×C11—41no—
328C23×C11—41no—
329C23×C11—41no—
330C23×C11—41no—
331C23×C11—41no—
332C23×C11—41no—
333C23×C11—41no—
334C23×C11—41no—
335C23×C11—41no—
336C23×C11—41no—
337C23×C11—41no—
338C23×C11#12012yes—
339C23×C11C22×D411yescharacteristic
340Q8×C11—22no—
341Q8×C11—22no—
342Q8×C11—22no—
343Q8×C11—41no—
344Q8×C11—41no—
345Q8×C11—41no—
346Q8×C11—41no—
347Q8×C11#12114yes—
348D4×C11—22no—
349D4×C11—22no—
350D4×C11—22no—
351D4×C11—22no—
352D4×C11—44no—
353D4×C11—48no—
354D4×C11—48no—
355D4×C11—48no—
356D4×C11—41no—
357D4×C11—41no—
358D4×C11—41no—
359D4×C11—41no—
360D4×C11—84no—
361D4×C11—84no—
362D4×C11—84no—
363C2×C4×C11—21no—
364C2×C4×C11—22no—
365C2×C4×C11—21no—
366C2×C4×C11—22no—
367C2×C4×C11—21no—
368C2×C4×C11—22no—
369C2×C4×C11—21no—
370C2×C4×C11—22no—
371C2×C4×C11—22no—
372C2×C4×C11—22no—
373C2×C4×C11—22no—
374C2×C4×C11—21no—
375C2×C4×C11—22no—
376C2×C4×C11—21no—
377C2×C4×C11—22no—
378C2×C4×C11—21no—
379C2×C4×C11—21no—
380C2×C4×C11—21no—
381C2×C4×C11—21no—
382C2×C4×C11—48no—
383C2×C4×C11—48no—
384C2×C4×C11—41no—
385C2×C4×C11—41no—
386C2×C4×C11—41no—
387C2×C4×C11—41no—
388C2×C4×C11—41no—
389C2×C4×C11—41no—
390C2×C4×C11—41no—
391C2×C4×C11—41no—
392C2×C4×C11—41no—
393C2×C4×C11—41no—
394C2×C4×C11—41no—
395C2×C4×C11—41no—
396C2×C4×C11—41no—
397C2×C4×C11—41no—
398C2×C4×C11—41no—
399C2×C4×C11—41no—
400C2×C4×C11—41no—
401C2×C4×C11—84no—
402C2×C4×C11#12012yes—
403C2×C4×C11#13712yes—
404C2×C4×C11C22×D411yescharacteristic
405C2×C4×C11C22×D411yescharacteristic
406C2×C4×C11C22×D411yescharacteristic
407C2×C4×C11C2×#4111yescharacteristic
408C2×C4×C11H(5,𝔽2)11yescharacteristic
409C2×C4×C11H(5,𝔽2)11yescharacteristic
410C8×C11—22no—
411C8×C11—41no—
412C8×C11—41no—
413C8×C11—41no—
414C22×#41C22×C1111yescharacteristic
415C22×#41C22×C1111yescharacteristic
416C22×Q16C22×C1111yescharacteristic
417C22×SD16C22×C1111yescharacteristic
418C22×SD16C22×C1111yescharacteristic
419C22×M16C22×C1111yescharacteristic
420#550—24no—
421#550—24no—
422C2×#127—21no—
423C2×#127C22×C1111yescharacteristic
424C2×C22⋊Q8C22×C1111yescharacteristic
425C2×C22⋊Q8C22×C1111yescharacteristic
426C2×#121—21no—
427C2×#121—21no—
428C2×#121C22×C1111yescharacteristic
429C2×#121C22×C1111yescharacteristic
430C2×C4×Q8C22×C1111yescharacteristic
431C2×C4×D4—21no—
432C2×C4×D4C22×C1111yescharacteristic
433C22×C4⋊C4C22×C1111yescharacteristic
434#468—24no—
435#452—24no—
436#452—24no—
437C2×#107C22×C1111yescharacteristic
438#417—24no—
439C2×#103C22×C1111yescharacteristic
440C2×#103C22×C1111yescharacteristic
441C2×#103C22×C1111yescharacteristic
442C2×#103C22×C1111yescharacteristic
443C2×#102C22×C1111yescharacteristic
444C2×#102C22×C1111yescharacteristic
445C2×#102C22×C1111yescharacteristic
446C2×#102C22×C1111yescharacteristic
447C2×#102C22×C1111yescharacteristic
448C2×#102C22×C1111yescharacteristic
449C2×C22⋊C8C22×C1111yescharacteristic
450C2×C22⋊C8C22×C1111yescharacteristic
451C2×C22⋊C8C22×C1111yescharacteristic
452#398—21no—
453#396—21no—
454#391C22×C1111yescharacteristic
455#389C22×C1111yescharacteristic
456#386—21no—
457#380—21no—
458#380C22×C1111yescharacteristic
459#340C22×C1111yescharacteristic
460#340C22×C1111yescharacteristic
461#336C22×C1111yescharacteristic
462#336C22×C1111yescharacteristic
463C22×C11—22no—
464C22×C11—22no—
465C22×C11—22no—
466C22×C11—41no—
467C22×C11—41no—
468C22×C11—41no—
469C22×C11—41no—
470C22×C11—41no—
471C22×C11—42no—
472C22×C11—42no—
473C22×C11—41no—
474C22×C11—41no—
475C22×C11—42no—
476C22×C11—42no—
477C22×C11—41no—
478C22×C11—42no—
479C22×C11—42no—
480C22×C11—41no—
481C22×C11—41no—
482C22×C11—41no—
483C22×C11—81no—
484C22×C11—81no—
485C22×C11—81no—
486C22×C11—81no—
487C22×C11—81no—
488C22×C11—81no—
489C22×C11—81no—
490C22×C11—81no—
491C22×C11C2×#12011yescharacteristic
492C22×C11D4211yescharacteristic
493C22×C11#54611yescharacteristic
494C22×C11C2×#13711yescharacteristic
495C22×C11#57511yescharacteristic
496C22×C11#57611yescharacteristic
497C22×C11#57711yescharacteristic
498C4×C11—22no—
499C4×C11—24no—
500C4×C11—22no—
501C4×C11—41no—
502C4×C11—41no—
503C4×C11—42no—
504C4×C11—42no—
505C4×C11—81no—
506C4×C11—81no—
507C4×C11—81no—
508C4×C11C2×#12111yescharacteristic
509C4×C11#53411yescharacteristic
510C4×C11D4211yescharacteristic
511C4×C11#54611yescharacteristic
512C2×#41—22no—
513C2×#41—22no—
514C2×#41—22no—
515C2×#41—22no—
516C2×#41—22no—
517C2×#41—22no—
518C2×#41—22no—
519C2×#41—41no—
520C2×#41—41no—
521C2×#41—41no—
522C2×#41—41no—
523C2×#41D4×C1114yes—
524C22×Q8C23×C1111yescharacteristic
525C22×Q8C23×C1111yescharacteristic
526C22×D4—21no—
527C22×D4—21no—
528C22×D4—21no—
529C22×D4—21no—
530C22×D4—21no—
531C22×D4—21no—
532C22×D4D4×C1111yescharacteristic
533C22×D4C23×C1111yescharacteristic
534C22×D4C23×C1111yescharacteristic
535C23×C4—21no—
536C23×C4—21no—
537C23×C4—21no—
538C23×C4C23×C1111yescharacteristic
539C23×C4C23×C1111yescharacteristic
540C2×Q16—22no—
541C2×Q16—22no—
542C2×Q16—22no—
543C2×SD16—22no—
544C2×SD16—22no—
545C2×SD16—22no—
546C2×SD16—41no—
547C2×SD16—41no—
548C2×SD16—41no—
549C2×M16—22no—
550C2×M16—22no—
551C2×M16—41no—
552C22×C8C23×C1111yescharacteristic
553C22×C8C23×C1111yescharacteristic
554C22×C8C23×C1111yescharacteristic
555C22×C8C23×C1111yescharacteristic
556#127—28no—
557#127—22no—
558#127—22no—
559C22⋊Q8—22no—
560C22⋊Q8—22no—
561C22⋊Q8—22no—
562C22⋊Q8—41no—
563#121—28no—
564#121—28no—
565#121—22no—
566#121—22no—
567#121—22no—
568#121D4×C1114yes—
569C4×Q8—22no—
570C4×Q8—22no—
571C4×D4—28no—
572C4×D4—22no—
573C4×D4—22no—
574C2×C4⋊C4—21no—
575C2×C4⋊C4—22no—
576C2×C4⋊C4—21no—
577C2×C4⋊C4—21no—
578C2×C4⋊C4—21no—
579C2×C4⋊C4—21no—
580C2×C4⋊C4—41no—
581C2×C4⋊C4D4×C1111yescharacteristic
582C2×C4⋊C4C23×C1111yescharacteristic
583C2×C4⋊C4C23×C1111yescharacteristic
584C2×C4⋊C4C23×C1111yescharacteristic
585C2×C4⋊C4C23×C1111yescharacteristic
586C2×C22⋊C4—21no—
587C2×C22⋊C4—21no—
588C2×C22⋊C4—21no—
589C2×C22⋊C4—21no—
590C2×C22⋊C4—21no—
591C2×C22⋊C4D4×C1111yescharacteristic
592C2×C22⋊C4D4×C1111yescharacteristic
593C2×C42—21no—
594C2×C42C23×C1111yescharacteristic
595#107—22no—
596#103—22no—
597#103—22no—
598#103—22no—
599#103D4×C1114yescomplemented
600#102—22no—
601#102—22no—
602#102—22no—
603#102—22no—
604#102—22no—
605#102—41no—
606C22⋊C8—22no—
607C22⋊C8—22no—
608C22⋊C8—41no—
609#95—21no—
610#95—21no—
611#95—21no—
612#95—21no—
613C2×C11—42no—
614C2×C11—81no—
615C2×C11—82no—
616C2×C11—82no—
617C2×C11#241011yescharacteristic
618C2×C11#300711yescharacteristic
619C2×C11#301211yescharacteristic
620C2×C11#326811yescharacteristic
621C2×C11#327811yescharacteristic
622C2×C11#331711yescharacteristic
623C2×C11#333311yescharacteristic
624C24—21no—
625C24—21no—
626C24C2×D4×C1111yescharacteristic
627C24C2×D4×C1111yescharacteristic
628#41—28no—
629#41—44no—
630#41—44no—
631#41—44no—
632#41—44no—
633#41—44no—
634#41—44no—
635#41—44no—
636C2×Q8—21no—
637C2×Q8—21no—
638C2×Q8—21no—
639C2×Q8—21no—
640C2×Q8—21no—
641C2×Q8—21no—
642C2×Q8—21no—
643C2×Q8—21no—
644C2×Q8—21no—
645C2×Q8C2×D4×C1112yes—
646C2×Q8C2×D4×C1112yes—
647C2×Q8C11×#4112yes—
648C2×D4—24no—
649C2×D4—24no—
650C2×D4—22no—
651C2×D4—24no—
652C2×D4—24no—
653C2×D4—24no—
654C2×D4—24no—
655C2×D4—22no—
656C2×D4—21no—
657C2×D4—21no—
658C2×D4—21no—
659C2×D4—21no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—41no—
667C2×D4—42no—
668C2×D4—42no—
669C2×D4—42no—
670C2×D4—42no—
671C2×D4—42no—
672C2×D4—42no—
673C2×D4—81no—
674C2×D4—81no—
675C2×D4—81no—
676C2×D4—81no—
677C2×D4—81no—
678C2×D4—81no—
679C2×D4C2×D4×C1112yes—
680C2×D4C2×D4×C1112yes—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—24no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—24no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—42no—
700C22×C4—42no—
701C22×C4—42no—
702C22×C4—42no—
703C22×C4—42no—
704C22×C4—42no—
705C22×C4—81no—
706C22×C4C2×D4×C1111yescharacteristic
707C22×C4C2×D4×C1111yescharacteristic
708C22×C4C2×D4×C1111yescharacteristic
709C22×C4C2×D4×C1112yes—
710C22×C4C2×D4×C1112yes—
711C22×C4C2×D4×C1111yescharacteristic
712C22×C4C24×C1111yescharacteristic
713Q16—44no—
714SD16—44no—
715SD16—44no—
716M16—44no—
717C2×C8—21no—
718C2×C8—21no—
719C2×C8—21no—
720C2×C8—21no—
721C2×C8—21no—
722C2×C8—21no—
723C2×C8—21no—
724C2×C8—21no—
725C2×C8—21no—
726C2×C8—21no—
727C2×C8—21no—
728C2×C8C2×D4×C1112yes—
729C4⋊C4—24no—
730C4⋊C4—22no—
731C4⋊C4—21no—
732C4⋊C4—21no—
733C4⋊C4—21no—
734C4⋊C4—21no—
735C4⋊C4—21no—
736C4⋊C4—21no—
737C4⋊C4—42no—
738C4⋊C4—42no—
739C4⋊C4—42no—
740C4⋊C4—81no—
741C4⋊C4C2×D4×C1112yes—
742C4⋊C4C2×D4×C1112yes—
743C22⋊C4—24no—
744C22⋊C4—22no—
745C22⋊C4—24no—
746C22⋊C4—22no—
747C22⋊C4—42no—
748C22⋊C4—42no—
749C22⋊C4—81no—
750C42—24no—
751C42—21no—
752C42—21no—
753C11#2444311yescharacteristic, direct product factor, Sylow
754C23—21no—
755C23—21no—
756C23—21no—
757C23—21no—
758C23—21no—
759C23—21no—
760C23—21no—
761C23—22no—
762C23—22no—
763C23—21no—
764C23—21no—
765C23—21no—
766C23—21no—
767C23—21no—
768C23—21no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23C11×#12012yes—
782C23C22×D4×C1111yescharacteristic
783Q8—22no—
784Q8—22no—
785Q8—22no—
786Q8—41no—
787Q8—41no—
788Q8—41no—
789Q8—41no—
790Q8C11×#12114yes—
791D4—22no—
792D4—22no—
793D4—22no—
794D4—22no—
795D4—44no—
796D4—48no—
797D4—48no—
798D4—48no—
799D4—41no—
800D4—41no—
801D4—41no—
802D4—41no—
803D4—84no—
804D4—84no—
805D4—84no—
806C2×C4—21no—
807C2×C4—22no—
808C2×C4—21no—
809C2×C4—22no—
810C2×C4—21no—
811C2×C4—22no—
812C2×C4—21no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—21no—
818C2×C4—22no—
819C2×C4—21no—
820C2×C4—22no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—21no—
825C2×C4—48no—
826C2×C4—48no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—84no—
845C2×C4C11×#12012yes—
846C2×C4C11×#13712yes—
847C2×C4C22×D4×C1111yescharacteristic
848C2×C4C22×D4×C1111yescharacteristic
849C2×C4C22×D4×C1111yescharacteristic
850C2×C4C2×C11×#4111yescharacteristic
851C2×C4C11×H(5,𝔽2)11yescharacteristic
852C2×C4C11×H(5,𝔽2)11yescharacteristic
853C8—22no—
854C8—41no—
855C8—41no—
856C8—41no—
857C22—22no—
858C22—22no—
859C22—22no—
860C22—41no—
861C22—41no—
862C22—41no—
863C22—41no—
864C22—42no—
865C22—42no—
866C22—41no—
867C22—41no—
868C22—42no—
869C22—42no—
870C22—41no—
871C22—42no—
872C22—42no—
873C22—41no—
874C22—41no—
875C22—41no—
876C22—41no—
877C22—81no—
878C22—81no—
879C22—81no—
880C22—81no—
881C22—81no—
882C22—81no—
883C22—81no—
884C22—81no—
885C22C2×C11×#12011yescharacteristic
886C22D42×C1111yescharacteristic
887C22C11×#54611yescharacteristic
888C22C2×C11×#13711yescharacteristic
889C22C11×#57511yescharacteristic
890C22C11×#57611yescharacteristic
891C22C11×#57711yescharacteristic
892C4—22no—
893C4—24no—
894C4—22no—
895C4—41no—
896C4—41no—
897C4—42no—
898C4—42no—
899C4—81no—
900C4—81no—
901C4—81no—
902C4C2×C11×#12111yescharacteristic
903C4C11×#53411yescharacteristic
904C4D42×C1111yescharacteristic
905C4C11×#54611yescharacteristic
906C2—42no—
907C2—81no—
908C2—82no—
909C2—82no—
910C2C11×#241011yescharacteristic
911C2C11×#300711yescharacteristic
912C2C11×#301211yescharacteristic
913C2C11×#326811yescharacteristic
914C2C11×#327811yescharacteristic
915C2C11×#331711yescharacteristic
916C2C11×#333311yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#550C2
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×#468C2semidirect
3. C2×C11×#452C2semidirect
4. C2×C11×#452C2semidirect
5. C2×C11×#417C2semidirect
6. C11×#2417C2semidirect
7. C11×#2041C2semidirect
8. C11×#2033C2semidirect
9. C11×#2014C2semidirect
10. C11×#2000C2semidirect
11. C11×#1878C2semidirect
12. C11×#1874C2semidirect
13. C11×#1870C2semidirect
14. C11×#1863C2semidirect
15. C11×#1788C2semidirect
152. C11×#103D4semidirect
166. #24443C11direct (N × H)
297. C2×#468C2×C11semidirect
298. C2×#452C2×C11semidirect
299. C2×#452C2×C11semidirect
300. C2×#417C2×C11semidirect
301. #2417C2×C11semidirect
302. #2041C2×C11semidirect
303. #2033C2×C11semidirect
304. #2014C2×C11semidirect
305. #2000C2×C11semidirect
306. #1878C2×C11semidirect
307. #1874C2×C11semidirect
308. #1870C2×C11semidirect
309. #1863C2×C11semidirect
310. #1788C2×C11semidirect
599. #103D4×C11semidirect
753. C11#24443direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5502
C2×C11×#4682
C2×C11×#4522
C2×C11×#4172
C11×#24172
C11×#20412
C11×#20332
C11×#20142
C11×#20002
C11×#18782
C11×#18742
C11×#18702
C11×#18632
C11×#17882
#2444311