Finite Group Databasebeta

← C11×#24634 #14601827

Subgroups — C11×#24634 #14601827

Order 2816.

952 conjugacy classes of subgroups.

The subgroup lattice has 746 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#463C211yesmaximal, characteristic, complemented
2C2×C4×C11×D8C211yesmaximal, characteristic, complemented
3C11×#2544C211yesmaximal, characteristic, complemented
4C11×#2357C211yesmaximal, characteristic, complemented
5C11×#2055C211yesmaximal, characteristic, complemented
6C11×#2054C211yesmaximal, characteristic, complemented
7C11×#2012C211yesmaximal, characteristic, complemented
8C11×#2011C211yesmaximal, characteristic
9C11×#1983C211yesmaximal, characteristic, complemented
10C11×#1982C211yesmaximal, characteristic, complemented
11C11×#1958C211yesmaximal, characteristic, complemented
12C11×#1939C211yesmaximal, characteristic, complemented
13C11×#1928C211yesmaximal, characteristic, complemented
14C11×#1925C211yesmaximal, characteristic, complemented
15C11×#1804C211yesmaximal, characteristic, complemented
16C22×C11×SD16C2211yescharacteristic
17C22×C11×D8C2211yescharacteristic
18C22×C11×D8C2211yescharacteristic
19C2×C11×#127C2211yescharacteristic
20C2×C11×#124C2211yescharacteristic
21C2×C11×#124C2211yescharacteristic
22C2×C4×D4×C11C2211yescharacteristic
23C2×C4×D4×C11C2211yescharacteristic
24C11×#463—24no—
25C4×C11×D8—24no—
26C2×C11×#107C2211yescharacteristic
27C2×C11×C4⋊C8C2211yescharacteristic
28C2×C11×C4⋊C8C2211yescharacteristic
29C2×C11×C4⋊C8C2211yescharacteristic
30C2×C11×#103C2211yescharacteristic
31C2×C11×#103C2211yescharacteristic
32C2×C11×#103C2211yescharacteristic
33C2×C11×#102C2211yescharacteristic
34C2×C11×#102C2211yescharacteristic
35C2×C11×#102C2211yescharacteristic
36C2×C11×#102C2211yescharacteristic
37C2×C11×#102C2211yescharacteristic
38C2×C11×#102C2211yescharacteristic
39C2×C11×#102C2211yescharacteristic
40C2×C4×C8×C11C2211yescharacteristic
41C11×#394—21no—
42C11×#394—21no—
43C11×#391C2211yescharacteristic
44C11×#390C2211yescharacteristic
45C11×#390C2211yescharacteristic
46C11×#390C2211yescharacteristic
47C11×#388—21no—
48C11×#388—21no—
49C11×#386—21no—
50C11×#386—21no—
51C11×#382C2211yescharacteristic
52C11×#381—21no—
53C4×C11×C4⋊C4C2211yescharacteristic
54C4×C11×C4⋊C4C2211yescharacteristic
55C4×C11×C4⋊C4C2211yescharacteristic
56C4×C11×C22⋊C4—21no—
57C11×#340C2211yescharacteristic
58C11×#340C2211yescharacteristic
59C11×#336C2211yescharacteristic
60C11×#336C2211yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C22×D4×C11—21no—
63C22×D4×C11—21no—
64C22×D4×C11C2311yescharacteristic
65C22×D4×C11C2311yescharacteristic
66C22×D4×C11C2311yescharacteristic
67C23×C4×C11—21no—
68C23×C4×C11—21no—
69C2×C11×SD16—22no—
70C2×C11×SD16—41no—
71C2×C11×SD16—41no—
72C2×C11×D8—22no—
73C2×C11×D8—22no—
74C2×C11×D8—22no—
75C2×C11×D8—22no—
76C2×C11×D8—41no—
77C2×C11×D8—41no—
78C22×C8×C11C2311yescharacteristic
79C22×C8×C11C2311yescharacteristic
80C22×C8×C11C2311yescharacteristic
81C22×C8×C11C2311yescharacteristic
82C11×#127—22no—
83C11×#127—41no—
84C11×#124—22no—
85C11×#124—22no—
86C11×#124—22no—
87C11×#124—41no—
88C4×D4×C11—22no—
89C4×D4×C11—22no—
90C4×D4×C11—22no—
91C4×D4×C11D414yescomplemented
92C2×C11×C4⋊C4D411yescharacteristic
93C2×C11×C4⋊C4D411yescharacteristic
94C2×C11×C4⋊C4C2311yescharacteristic
95C2×C11×C4⋊C4C2311yescharacteristic
96C2×C11×C4⋊C4C2311yescharacteristic
97C2×C11×C4⋊C4C2311yescharacteristic
98C2×C11×C22⋊C4—21no—
99C2×C11×C22⋊C4—21no—
100C2×C11×C22⋊C4—21no—
101C2×C11×C22⋊C4—21no—
102C2×C11×C22⋊C4—21no—
103C2×C11×C22⋊C4—21no—
104C2×C11×C22⋊C4—21no—
105C2×C11×C22⋊C4—21no—
106C2×C11×C22⋊C4—21no—
107C2×C11×C22⋊C4—21no—
108C2×C11×C22⋊C4—21no—
109C2×C11×C22⋊C4—21no—
110C2×C42×C11—21no—
111C2×C42×C11—21no—
112C2×C42×C11C2311yescharacteristic
113C2×C42×C11C2311yescharacteristic
114C2×C42×C11C2311yescharacteristic
115C11×#107—22no—
116C11×C4⋊C8—22no—
117C11×C4⋊C8—41no—
118C11×C4⋊C8—41no—
119C11×#103—22no—
120C11×#103—22no—
121C11×#103—41no—
122C11×#102—22no—
123C11×#102—22no—
124C11×#102—22no—
125C11×#102—22no—
126C11×#102—41no—
127C11×#102—41no—
128C11×#102—41no—
129C4×C8×C11—22no—
130C11×#95—21no—
131C11×#95—21no—
132C11×#95—21no—
133C11×#95—21no—
134C11×#95—21no—
135C11×#95—21no—
136C11×#95D411yescharacteristic
137C11×#95D411yescharacteristic
138#24634C1111yesmaximal, characteristic, direct product factor, Sylow
139C24×C11—21no—
140C24×C11—21no—
141C24×C11—21no—
142C2×Q8×C11—21no—
143C2×Q8×C11—21no—
144C2×Q8×C11—21no—
145C2×Q8×C11—21no—
146C2×Q8×C11—21no—
147C2×Q8×C11—21no—
148C2×D4×C11—21no—
149C2×D4×C11—21no—
150C2×D4×C11—21no—
151C2×D4×C11—21no—
152C2×D4×C11—21no—
153C2×D4×C11—21no—
154C2×D4×C11—21no—
155C2×D4×C11—21no—
156C2×D4×C11—21no—
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—42no—
165C2×D4×C11—42no—
166C2×D4×C11—42no—
167C2×D4×C11—42no—
168C2×D4×C11—81no—
169C2×D4×C11—81no—
170C2×D4×C11C2×D412yes—
171C2×D4×C11#4112yes—
172C22×C4×C11—21no—
173C22×C4×C11—24no—
174C22×C4×C11—21no—
175C22×C4×C11—21no—
176C22×C4×C11—21no—
177C22×C4×C11—21no—
178C22×C4×C11—42no—
179C22×C4×C11—81no—
180C22×C4×C11—81no—
181C22×C4×C11—81no—
182C22×C4×C11—81no—
183C22×C4×C11C2×D411yescharacteristic
184C22×C4×C11C2×D411yescharacteristic
185C22×C4×C11C2×D411yescharacteristic
186C22×C4×C11C2×D411yescharacteristic
187C22×C4×C11C2×D411yescharacteristic
188C22×C4×C11C2×D411yescharacteristic
189C22×C4×C11C2411yescharacteristic
190C11×SD16—44no—
191C11×D8—28no—
192C11×D8—44no—
193C2×C8×C11—21no—
194C2×C8×C11—21no—
195C2×C8×C11—21no—
196C2×C8×C11—21no—
197C2×C8×C11—21no—
198C2×C8×C11—21no—
199C2×C8×C11—21no—
200C2×C8×C11—21no—
201C2×C8×C11—21no—
202C2×C8×C11—21no—
203C2×C8×C11—21no—
204C2×C8×C11#4112yes—
205C11×C4⋊C4—22no—
206C11×C4⋊C4—21no—
207C11×C4⋊C4—21no—
208C11×C4⋊C4—21no—
209C11×C4⋊C4—21no—
210C11×C4⋊C4—21no—
211C11×C4⋊C4—21no—
212C11×C4⋊C4—21no—
213C11×C4⋊C4—41no—
214C11×C4⋊C4C2×D412yes—
215C11×C22⋊C4—24no—
216C11×C22⋊C4—42no—
217C11×C22⋊C4—42no—
218C11×C22⋊C4—42no—
219C11×C22⋊C4—42no—
220C11×C22⋊C4—42no—
221C11×C22⋊C4—42no—
222C11×C22⋊C4—42no—
223C11×C22⋊C4—81no—
224C11×C22⋊C4—81no—
225C11×C22⋊C4—81no—
226C11×C22⋊C4—81no—
227C42×C11—21no—
228C42×C11—21no—
229C42×C11—21no—
230C42×C11—21no—
231C42×C11—81no—
232C42×C11—81no—
233C42×C11C2×D412yes—
234C42×C11#4112yes—
235C2×#463C2×C1111yescharacteristic, complemented
236C2×C4×D8C2×C1111yescharacteristic, complemented
237#2544C2×C1111yescharacteristic, complemented
238#2357C2×C1111yescharacteristic, complemented
239#2055C2×C1111yescharacteristic, complemented
240#2054C2×C1111yescharacteristic, complemented
241#2012C2×C1111yescharacteristic, complemented
242#2011C2×C1111yescharacteristic
243#1983C2×C1111yescharacteristic, complemented
244#1982C2×C1111yescharacteristic, complemented
245#1958C2×C1111yescharacteristic, complemented
246#1939C2×C1111yescharacteristic, complemented
247#1928C2×C1111yescharacteristic, complemented
248#1925C2×C1111yescharacteristic, complemented
249#1804C2×C1111yescharacteristic, complemented
250C23×C11—22no—
251C23×C11—22no—
252C23×C11—41no—
253C23×C11—41no—
254C23×C11—41no—
255C23×C11—41no—
256C23×C11—41no—
257C23×C11—41no—
258C23×C11—41no—
259C23×C11—41no—
260C23×C11—41no—
261C23×C11—41no—
262C23×C11—41no—
263C23×C11—41no—
264C23×C11—41no—
265C23×C11—41no—
266C23×C11—41no—
267C23×C11—41no—
268C23×C11—41no—
269C23×C11—41no—
270C23×C11—41no—
271C23×C11C22×D411yescharacteristic
272Q8×C11—41no—
273Q8×C11—41no—
274Q8×C11—41no—
275Q8×C11—41no—
276D4×C11—22no—
277D4×C11—22no—
278D4×C11—22no—
279D4×C11—22no—
280D4×C11—41no—
281D4×C11—41no—
282D4×C11—41no—
283D4×C11—41no—
284D4×C11—41no—
285D4×C11—41no—
286D4×C11—41no—
287D4×C11—41no—
288D4×C11—84no—
289D4×C11—84no—
290C2×C4×C11—21no—
291C2×C4×C11—21no—
292C2×C4×C11—21no—
293C2×C4×C11—21no—
294C2×C4×C11—21no—
295C2×C4×C11—21no—
296C2×C4×C11—22no—
297C2×C4×C11—21no—
298C2×C4×C11—21no—
299C2×C4×C11—21no—
300C2×C4×C11—21no—
301C2×C4×C11—21no—
302C2×C4×C11—21no—
303C2×C4×C11—21no—
304C2×C4×C11—21no—
305C2×C4×C11—21no—
306C2×C4×C11—41no—
307C2×C4×C11—41no—
308C2×C4×C11—41no—
309C2×C4×C11—41no—
310C2×C4×C11—41no—
311C2×C4×C11—41no—
312C2×C4×C11—41no—
313C2×C4×C11—41no—
314C2×C4×C11—41no—
315C2×C4×C11—41no—
316C2×C4×C11—41no—
317C2×C4×C11—41no—
318C2×C4×C11—41no—
319C2×C4×C11—41no—
320C2×C4×C11—84no—
321C2×C4×C11—84no—
322C2×C4×C11#12112yes—
323C2×C4×C11#12112yes—
324C2×C4×C11#13512yes—
325C2×C4×C11C22×D411yescharacteristic
326C2×C4×C11C2×#4111yescharacteristic
327C2×C4×C11C2×#4111yescharacteristic
328C2×C4×C11C2×#4111yescharacteristic
329C2×C4×C11H(5,𝔽2)11yescharacteristic
330C2×C4×C11H(5,𝔽2)11yescharacteristic
331C8×C11—22no—
332C8×C11—41no—
333C8×C11—41no—
334C8×C11—41no—
335C22×SD16C22×C1111yescharacteristic
336C22×D8C22×C1111yescharacteristic
337C22×D8C22×C1111yescharacteristic
338C2×#127C22×C1111yescharacteristic
339C2×#124C22×C1111yescharacteristic
340C2×#124C22×C1111yescharacteristic
341C2×C4×D4C22×C1111yescharacteristic
342C2×C4×D4C22×C1111yescharacteristic
343#463—24no—
344C4×D8—24no—
345C2×#107C22×C1111yescharacteristic
346C2×C4⋊C8C22×C1111yescharacteristic
347C2×C4⋊C8C22×C1111yescharacteristic
348C2×C4⋊C8C22×C1111yescharacteristic
349C2×#103C22×C1111yescharacteristic
350C2×#103C22×C1111yescharacteristic
351C2×#103C22×C1111yescharacteristic
352C2×#102C22×C1111yescharacteristic
353C2×#102C22×C1111yescharacteristic
354C2×#102C22×C1111yescharacteristic
355C2×#102C22×C1111yescharacteristic
356C2×#102C22×C1111yescharacteristic
357C2×#102C22×C1111yescharacteristic
358C2×#102C22×C1111yescharacteristic
359C2×C4×C8C22×C1111yescharacteristic
360#394—21no—
361#394—21no—
362#391C22×C1111yescharacteristic
363#390C22×C1111yescharacteristic
364#390C22×C1111yescharacteristic
365#390C22×C1111yescharacteristic
366#388—21no—
367#388—21no—
368#386—21no—
369#386—21no—
370#382C22×C1111yescharacteristic
371#381—21no—
372C4×C4⋊C4C22×C1111yescharacteristic
373C4×C4⋊C4C22×C1111yescharacteristic
374C4×C4⋊C4C22×C1111yescharacteristic
375C4×C22⋊C4—21no—
376#340C22×C1111yescharacteristic
377#340C22×C1111yescharacteristic
378#336C22×C1111yescharacteristic
379#336C22×C1111yescharacteristic
380C22×C11—42no—
381C22×C11—42no—
382C22×C11—42no—
383C22×C11—42no—
384C22×C11—42no—
385C22×C11—42no—
386C22×C11—81no—
387C22×C11—81no—
388C22×C11—81no—
389C22×C11—81no—
390C22×C11—81no—
391C22×C11—81no—
392C22×C11—81no—
393C22×C11—81no—
394C22×C11—81no—
395C22×C11—81no—
396C22×C11—81no—
397C22×C11—81no—
398C22×C11—81no—
399C22×C11—81no—
400C22×C11—81no—
401C22×C11C2×#12111yescharacteristic
402C22×C11#54611yescharacteristic
403C22×C11#55011yescharacteristic
404C22×C11C2×#13511yescharacteristic
405C22×C11#57511yescharacteristic
406C22×C11#57611yescharacteristic
407C22×C11#57611yescharacteristic
408C4×C11—22no—
409C4×C11—22no—
410C4×C11—22no—
411C4×C11—42no—
412C4×C11—41no—
413C4×C11—41no—
414C4×C11—41no—
415C4×C11—81no—
416C4×C11—81no—
417C4×C11—81no—
418C4×C11—81no—
419C4×C11#52511yescharacteristic
420C4×C11#53511yescharacteristic
421C4×C11#55311yescharacteristic
422C4×C11#55511yescharacteristic
423C22×Q8C23×C1111yescharacteristic
424C22×D4—21no—
425C22×D4—21no—
426C22×D4C23×C1111yescharacteristic
427C22×D4C23×C1111yescharacteristic
428C22×D4C23×C1111yescharacteristic
429C23×C4—21no—
430C23×C4—21no—
431C2×SD16—22no—
432C2×SD16—41no—
433C2×SD16—41no—
434C2×D8—22no—
435C2×D8—22no—
436C2×D8—22no—
437C2×D8—22no—
438C2×D8—41no—
439C2×D8—41no—
440C22×C8C23×C1111yescharacteristic
441C22×C8C23×C1111yescharacteristic
442C22×C8C23×C1111yescharacteristic
443C22×C8C23×C1111yescharacteristic
444#127—22no—
445#127—41no—
446#124—22no—
447#124—22no—
448#124—22no—
449#124—41no—
450C4×D4—22no—
451C4×D4—22no—
452C4×D4—22no—
453C4×D4D4×C1114yescomplemented
454C2×C4⋊C4D4×C1111yescharacteristic
455C2×C4⋊C4D4×C1111yescharacteristic
456C2×C4⋊C4C23×C1111yescharacteristic
457C2×C4⋊C4C23×C1111yescharacteristic
458C2×C4⋊C4C23×C1111yescharacteristic
459C2×C4⋊C4C23×C1111yescharacteristic
460C2×C22⋊C4—21no—
461C2×C22⋊C4—21no—
462C2×C22⋊C4—21no—
463C2×C22⋊C4—21no—
464C2×C22⋊C4—21no—
465C2×C22⋊C4—21no—
466C2×C22⋊C4—21no—
467C2×C22⋊C4—21no—
468C2×C22⋊C4—21no—
469C2×C22⋊C4—21no—
470C2×C22⋊C4—21no—
471C2×C22⋊C4—21no—
472C2×C42—21no—
473C2×C42—21no—
474C2×C42C23×C1111yescharacteristic
475C2×C42C23×C1111yescharacteristic
476C2×C42C23×C1111yescharacteristic
477#107—22no—
478C4⋊C8—22no—
479C4⋊C8—41no—
480C4⋊C8—41no—
481#103—22no—
482#103—22no—
483#103—41no—
484#102—22no—
485#102—22no—
486#102—22no—
487#102—22no—
488#102—41no—
489#102—41no—
490#102—41no—
491C4×C8—22no—
492#95—21no—
493#95—21no—
494#95—21no—
495#95—21no—
496#95—21no—
497#95—21no—
498#95D4×C1111yescharacteristic
499#95D4×C1111yescharacteristic
500C2×C11—82no—
501C2×C11—82no—
502C2×C11—161no—
503C2×C11#241411yescharacteristic
504C2×C11#303511yescharacteristic
505C2×C11#304111yescharacteristic
506C2×C11#329711yescharacteristic
507C2×C11#332211yescharacteristic
508C2×C11#339611yescharacteristic
509C2×C11#340311yescharacteristic
510C24—21no—
511C24—21no—
512C24—21no—
513C2×Q8—21no—
514C2×Q8—21no—
515C2×Q8—21no—
516C2×Q8—21no—
517C2×Q8—21no—
518C2×Q8—21no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—21no—
526C2×D4—21no—
527C2×D4—21no—
528C2×D4—21no—
529C2×D4—21no—
530C2×D4—21no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—21no—
534C2×D4—21no—
535C2×D4—42no—
536C2×D4—42no—
537C2×D4—42no—
538C2×D4—42no—
539C2×D4—81no—
540C2×D4—81no—
541C2×D4C2×D4×C1112yes—
542C2×D4C11×#4112yes—
543C22×C4—21no—
544C22×C4—24no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—42no—
550C22×C4—81no—
551C22×C4—81no—
552C22×C4—81no—
553C22×C4—81no—
554C22×C4C2×D4×C1111yescharacteristic
555C22×C4C2×D4×C1111yescharacteristic
556C22×C4C2×D4×C1111yescharacteristic
557C22×C4C2×D4×C1111yescharacteristic
558C22×C4C2×D4×C1111yescharacteristic
559C22×C4C2×D4×C1111yescharacteristic
560C22×C4C24×C1111yescharacteristic
561SD16—44no—
562D8—28no—
563D8—44no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8C11×#4112yes—
576C4⋊C4—22no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—41no—
585C4⋊C4C2×D4×C1112yes—
586C22⋊C4—24no—
587C22⋊C4—42no—
588C22⋊C4—42no—
589C22⋊C4—42no—
590C22⋊C4—42no—
591C22⋊C4—42no—
592C22⋊C4—42no—
593C22⋊C4—42no—
594C22⋊C4—81no—
595C22⋊C4—81no—
596C22⋊C4—81no—
597C22⋊C4—81no—
598C42—21no—
599C42—21no—
600C42—21no—
601C42—21no—
602C42—81no—
603C42—81no—
604C42C2×D4×C1112yes—
605C42C11×#4112yes—
606C11#2463411yescharacteristic, direct product factor, Sylow
607C23—22no—
608C23—22no—
609C23—41no—
610C23—41no—
611C23—41no—
612C23—41no—
613C23—41no—
614C23—41no—
615C23—41no—
616C23—41no—
617C23—41no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—41no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23C22×D4×C1111yescharacteristic
629Q8—41no—
630Q8—41no—
631Q8—41no—
632Q8—41no—
633D4—22no—
634D4—22no—
635D4—22no—
636D4—22no—
637D4—41no—
638D4—41no—
639D4—41no—
640D4—41no—
641D4—41no—
642D4—41no—
643D4—41no—
644D4—41no—
645D4—84no—
646D4—84no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—22no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—84no—
678C2×C4—84no—
679C2×C4C11×#12112yes—
680C2×C4C11×#12112yes—
681C2×C4C11×#13512yes—
682C2×C4C22×D4×C1111yescharacteristic
683C2×C4C2×C11×#4111yescharacteristic
684C2×C4C2×C11×#4111yescharacteristic
685C2×C4C2×C11×#4111yescharacteristic
686C2×C4C11×H(5,𝔽2)11yescharacteristic
687C2×C4C11×H(5,𝔽2)11yescharacteristic
688C8—22no—
689C8—41no—
690C8—41no—
691C8—41no—
692C22—42no—
693C22—42no—
694C22—42no—
695C22—42no—
696C22—42no—
697C22—42no—
698C22—81no—
699C22—81no—
700C22—81no—
701C22—81no—
702C22—81no—
703C22—81no—
704C22—81no—
705C22—81no—
706C22—81no—
707C22—81no—
708C22—81no—
709C22—81no—
710C22—81no—
711C22—81no—
712C22—81no—
713C22C2×C11×#12111yescharacteristic
714C22C11×#54611yescharacteristic
715C22C11×#55011yescharacteristic
716C22C2×C11×#13511yescharacteristic
717C22C11×#57511yescharacteristic
718C22C11×#57611yescharacteristic
719C22C11×#57611yescharacteristic
720C4—22no—
721C4—22no—
722C4—22no—
723C4—42no—
724C4—41no—
725C4—41no—
726C4—41no—
727C4—81no—
728C4—81no—
729C4—81no—
730C4—81no—
731C4C11×#52511yescharacteristic
732C4C11×#53511yescharacteristic
733C4C11×#55311yescharacteristic
734C4C11×#55511yescharacteristic
735C2—82no—
736C2—82no—
737C2—161no—
738C2C11×#241411yescharacteristic
739C2C11×#303511yescharacteristic
740C2C11×#304111yescharacteristic
741C2C11×#329711yescharacteristic
742C2C11×#332211yescharacteristic
743C2C11×#339611yescharacteristic
744C2C11×#340311yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#2011C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C4×C11×C4⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#463C2semidirect
2. C2×C4×C11×D8C2semidirect
3. C11×#2544C2semidirect
4. C11×#2357C2semidirect
5. C11×#2055C2semidirect
6. C11×#2054C2semidirect
7. C11×#2012C2semidirect
9. C11×#1983C2semidirect
10. C11×#1982C2semidirect
11. C11×#1958C2semidirect
12. C11×#1939C2semidirect
13. C11×#1928C2semidirect
14. C11×#1925C2semidirect
15. C11×#1804C2semidirect
91. C4×D4×C11D4semidirect
138. #24634C11direct (N × H)
235. C2×#463C2×C11semidirect
236. C2×C4×D8C2×C11semidirect
237. #2544C2×C11semidirect
238. #2357C2×C11semidirect
239. #2055C2×C11semidirect
240. #2054C2×C11semidirect
241. #2012C2×C11semidirect
243. #1983C2×C11semidirect
244. #1982C2×C11semidirect
245. #1958C2×C11semidirect
246. #1939C2×C11semidirect
247. #1928C2×C11semidirect
248. #1925C2×C11semidirect
249. #1804C2×C11semidirect
453. C4×D4D4×C11semidirect
606. C11#24634direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4632
C2×C4×C11×D82
C11×#25442
C11×#23572
C11×#20552
C11×#20542
C11×#20122
C11×#20112
C11×#19832
C11×#19822
C11×#19582
C11×#19392
C11×#19282
C11×#19252
C11×#18042
#2463411