Finite Group Databasebeta

← C11×#24765 #14601958

Subgroups — C11×#24765 #14601958

Order 2816.

946 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#468C211yesmaximal, characteristic
2C2×C11×#467C211yesmaximal, characteristic, complemented
3C2×C11×#464C211yesmaximal, characteristic, complemented
4C2×C11×#424C211yesmaximal, characteristic, complemented
5C11×#2620C211yesmaximal, characteristic
6C11×#2323C211yesmaximal, characteristic, complemented
7C11×#2068C211yesmaximal, characteristic, complemented
8C11×#2067C211yesmaximal, characteristic, complemented
9C11×#2056C211yesmaximal, characteristic, complemented
10C11×#2055C211yesmaximal, characteristic, complemented
11C11×#1983C211yesmaximal, characteristic, complemented
12C11×#1947C211yesmaximal, characteristic, complemented
13C11×#1894C211yesmaximal, characteristic, complemented
14C11×#1893C211yesmaximal, characteristic
15C11×#1803C211yesmaximal, characteristic, complemented
16C22×C11×Q16C2211yescharacteristic
17C22×C11×SD16C2211yescharacteristic
18C22×C11×M16C2211yescharacteristic
19C23×C8×C11C2211yescharacteristic
20C2×C11×#124C2211yescharacteristic
21C2×C11×C22⋊Q8C2211yescharacteristic
22C2×C11×C22⋊Q8C2211yescharacteristic
23C2×C11×#121C2211yescharacteristic
24C2×C4×Q8×C11C2211yescharacteristic
25C2×C11×#117C2211yescharacteristic
26C11×#468—24no—
27C11×#467—24no—
28C11×#464—24no—
29C2×C11×#107C2211yescharacteristic
30C2×C11×#107C2211yescharacteristic
31C11×#424—24no—
32C2×C11×C4⋊C8C2211yescharacteristic
33C2×C11×C4⋊C8C2211yescharacteristic
34C2×C11×C4⋊C8C2211yescharacteristic
35C2×C11×C4⋊C8C2211yescharacteristic
36C2×C11×#103C2211yescharacteristic
37C2×C11×#103C2211yescharacteristic
38C2×C11×#103C2211yescharacteristic
39C2×C11×#103C2211yescharacteristic
40C2×C11×#103C2211yescharacteristic
41C2×C11×#102C2211yescharacteristic
42C2×C11×#102C2211yescharacteristic
43C2×C11×#102C2211yescharacteristic
44C11×#396—21no—
45C11×#396—21no—
46C11×#394—21no—
47C11×#394—21no—
48C11×#391C2211yescharacteristic
49C11×#391C2211yescharacteristic
50C11×#390C2211yescharacteristic
51C11×#389—21no—
52C11×#389C2211yescharacteristic
53C11×#388—21no—
54C11×#388—21no—
55C11×#387—21no—
56C11×#384C2211yescharacteristic
57C11×#380C2211yescharacteristic
58C4×C11×C4⋊C4C2211yescharacteristic
59C11×#340C2211yescharacteristic
60C11×#340C2211yescharacteristic
61C11×#340C2211yescharacteristic
62C11×#340C2211yescharacteristic
63C22×Q8×C11C2311yescharacteristic
64C22×Q8×C11C2311yescharacteristic
65C22×D4×C11—21no—
66C22×D4×C11C2311yescharacteristic
67C23×C4×C11C2311yescharacteristic
68C2×C11×Q16—22no—
69C2×C11×Q16—22no—
70C2×C11×Q16—41no—
71C2×C11×SD16—22no—
72C2×C11×SD16—22no—
73C2×C11×SD16—41no—
74C2×C11×M16—22no—
75C2×C11×M16—22no—
76C2×C11×M16—41no—
77C22×C8×C11—22no—
78C22×C8×C11—22no—
79C22×C8×C11—41no—
80C22×C8×C11C2311yescharacteristic
81C22×C8×C11C2311yescharacteristic
82C22×C8×C11C2311yescharacteristic
83C22×C8×C11C2311yescharacteristic
84C11×#124—22no—
85C11×#124—22no—
86C11×C22⋊Q8—22no—
87C11×C22⋊Q8—22no—
88C11×C22⋊Q8—22no—
89C11×C22⋊Q8D414yes—
90C11×#121—22no—
91C11×#121—22no—
92C4×Q8×C11—22no—
93C4×Q8×C11—22no—
94C11×#117—22no—
95C11×#117—22no—
96C2×C11×C4⋊C4—21no—
97C2×C11×C4⋊C4—21no—
98C2×C11×C4⋊C4—21no—
99C2×C11×C4⋊C4—21no—
100C2×C11×C4⋊C4—21no—
101C2×C11×C4⋊C4—21no—
102C2×C11×C4⋊C4D411yescharacteristic
103C2×C11×C4⋊C4D411yescharacteristic
104C2×C11×C4⋊C4C2311yescharacteristic
105C2×C11×C4⋊C4C2311yescharacteristic
106C2×C11×C4⋊C4C2311yescharacteristic
107C2×C11×C4⋊C4C2311yescharacteristic
108C2×C11×C4⋊C4C2311yescharacteristic
109C2×C11×C22⋊C4—21no—
110C2×C11×C22⋊C4—21no—
111C2×C11×C22⋊C4—21no—
112C2×C11×C22⋊C4—21no—
113C2×C11×C22⋊C4—21no—
114C2×C11×C22⋊C4—21no—
115C2×C11×C22⋊C4—21no—
116C2×C11×C22⋊C4—21no—
117C2×C11×C22⋊C4D411yescharacteristic
118C2×C11×C22⋊C4D411yescharacteristic
119C2×C42×C11—21no—
120C2×C42×C11—21no—
121C2×C42×C11C2311yescharacteristic
122C2×C42×C11C2311yescharacteristic
123C11×#107—22no—
124C11×#107—22no—
125C11×C4⋊C8—22no—
126C11×C4⋊C8—22no—
127C11×C4⋊C8—22no—
128C11×C4⋊C8D414yescomplemented
129C11×#103—22no—
130C11×#103—22no—
131C11×#103—22no—
132C11×#103—22no—
133C11×#103—41no—
134C11×#102—22no—
135C11×#102—22no—
136C11×#102—41no—
137C11×#95—21no—
138C11×#95—21no—
139C11×#95—21no—
140C11×#95—21no—
141C11×#95—21no—
142C11×#95—21no—
143C11×#95—21no—
144#24765C1111yesmaximal, characteristic, direct product factor, Sylow
145C24×C11—21no—
146C24×C11C2×D411yescharacteristic
147C2×Q8×C11—21no—
148C2×Q8×C11—21no—
149C2×Q8×C11—21no—
150C2×Q8×C11—21no—
151C2×Q8×C11—21no—
152C2×Q8×C11—21no—
153C2×Q8×C11—21no—
154C2×Q8×C11—21no—
155C2×Q8×C11—21no—
156C2×Q8×C11—21no—
157C2×Q8×C11—21no—
158C2×Q8×C11C2×D412yes—
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—42no—
166C2×D4×C11—81no—
167C2×D4×C11—81no—
168C22×C4×C11—21no—
169C22×C4×C11—21no—
170C22×C4×C11—21no—
171C22×C4×C11—21no—
172C22×C4×C11—21no—
173C22×C4×C11—21no—
174C22×C4×C11—21no—
175C22×C4×C11—21no—
176C22×C4×C11—21no—
177C22×C4×C11—21no—
178C22×C4×C11—21no—
179C22×C4×C11C2×D411yescharacteristic
180C22×C4×C11C2×D411yescharacteristic
181C22×C4×C11C2×D411yescharacteristic
182C22×C4×C11C2×D411yescharacteristic
183C22×C4×C11C2×D411yescharacteristic
184C22×C4×C11C2×D412yes—
185C22×C4×C11#4112yes—
186C22×C4×C11C2411yescharacteristic
187C11×Q16—44no—
188C11×SD16—44no—
189C11×M16—44no—
190C2×C8×C11—21no—
191C2×C8×C11—21no—
192C2×C8×C11—21no—
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—44no—
201C2×C8×C11C2×D412yes—
202C2×C8×C11C2×D412yes—
203C11×C4⋊C4—24no—
204C11×C4⋊C4—22no—
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—21no—
214C11×C4⋊C4—21no—
215C11×C4⋊C4—42no—
216C11×C4⋊C4—42no—
217C11×C4⋊C4—81no—
218C11×C4⋊C4—81no—
219C11×C4⋊C4—81no—
220C11×C4⋊C4C2×D412yes—
221C11×C22⋊C4—24no—
222C11×C22⋊C4—22no—
223C11×C22⋊C4—22no—
224C11×C22⋊C4—42no—
225C11×C22⋊C4—42no—
226C11×C22⋊C4—42no—
227C11×C22⋊C4—42no—
228C11×C22⋊C4—81no—
229C11×C22⋊C4—81no—
230C11×C22⋊C4—81no—
231C42×C11—21no—
232C42×C11—21no—
233C42×C11—42no—
234C42×C11—81no—
235C42×C11C2×D412yes—
236C42×C11#4112yes—
237C2×#468C2×C1111yescharacteristic
238C2×#467C2×C1111yescharacteristic, complemented
239C2×#464C2×C1111yescharacteristic, complemented
240C2×#424C2×C1111yescharacteristic, complemented
241#2620C2×C1111yescharacteristic
242#2323C2×C1111yescharacteristic, complemented
243#2068C2×C1111yescharacteristic, complemented
244#2067C2×C1111yescharacteristic, complemented
245#2056C2×C1111yescharacteristic, complemented
246#2055C2×C1111yescharacteristic, complemented
247#1983C2×C1111yescharacteristic, complemented
248#1947C2×C1111yescharacteristic, complemented
249#1894C2×C1111yescharacteristic, complemented
250#1893C2×C1111yescharacteristic
251#1803C2×C1111yescharacteristic, complemented
252C23×C11—21no—
253C23×C11—21no—
254C23×C11—21no—
255C23×C11—21no—
256C23×C11—21no—
257C23×C11—21no—
258C23×C11—41no—
259C23×C11—41no—
260C23×C11—41no—
261C23×C11—41no—
262C23×C11—41no—
263C23×C11—41no—
264C23×C11—41no—
265C23×C11#12112yes—
266C23×C11C22×D411yescharacteristic
267Q8×C11—22no—
268Q8×C11—22no—
269Q8×C11—41no—
270Q8×C11—41no—
271Q8×C11—41no—
272Q8×C11—41no—
273Q8×C11—41no—
274Q8×C11—41no—
275D4×C11—41no—
276D4×C11—41no—
277D4×C11—41no—
278D4×C11—41no—
279D4×C11—84no—
280C2×C4×C11—21no—
281C2×C4×C11—21no—
282C2×C4×C11—21no—
283C2×C4×C11—21no—
284C2×C4×C11—21no—
285C2×C4×C11—21no—
286C2×C4×C11—22no—
287C2×C4×C11—22no—
288C2×C4×C11—22no—
289C2×C4×C11—22no—
290C2×C4×C11—21no—
291C2×C4×C11—21no—
292C2×C4×C11—22no—
293C2×C4×C11—22no—
294C2×C4×C11—21no—
295C2×C4×C11—21no—
296C2×C4×C11—21no—
297C2×C4×C11—21no—
298C2×C4×C11—41no—
299C2×C4×C11—41no—
300C2×C4×C11—41no—
301C2×C4×C11—41no—
302C2×C4×C11—41no—
303C2×C4×C11—41no—
304C2×C4×C11—41no—
305C2×C4×C11—41no—
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#12112yes—
318C2×C4×C11#12112yes—
319C2×C4×C11#12112yes—
320C2×C4×C11C22×D411yescharacteristic
321C2×C4×C11C22×D411yescharacteristic
322C2×C4×C11C2×#4111yescharacteristic
323C2×C4×C11C2×#4111yescharacteristic
324C2×C4×C11H(5,𝔽2)11yescharacteristic
325C2×C4×C112−1+411yescharacteristic
326C8×C11—22no—
327C8×C11—22no—
328C8×C11—41no—
329C8×C11—41no—
330C22×Q16C22×C1111yescharacteristic
331C22×SD16C22×C1111yescharacteristic
332C22×M16C22×C1111yescharacteristic
333C23×C8C22×C1111yescharacteristic
334C2×#124C22×C1111yescharacteristic
335C2×C22⋊Q8C22×C1111yescharacteristic
336C2×C22⋊Q8C22×C1111yescharacteristic
337C2×#121C22×C1111yescharacteristic
338C2×C4×Q8C22×C1111yescharacteristic
339C2×#117C22×C1111yescharacteristic
340#468—24no—
341#467—24no—
342#464—24no—
343C2×#107C22×C1111yescharacteristic
344C2×#107C22×C1111yescharacteristic
345#424—24no—
346C2×C4⋊C8C22×C1111yescharacteristic
347C2×C4⋊C8C22×C1111yescharacteristic
348C2×C4⋊C8C22×C1111yescharacteristic
349C2×C4⋊C8C22×C1111yescharacteristic
350C2×#103C22×C1111yescharacteristic
351C2×#103C22×C1111yescharacteristic
352C2×#103C22×C1111yescharacteristic
353C2×#103C22×C1111yescharacteristic
354C2×#103C22×C1111yescharacteristic
355C2×#102C22×C1111yescharacteristic
356C2×#102C22×C1111yescharacteristic
357C2×#102C22×C1111yescharacteristic
358#396—21no—
359#396—21no—
360#394—21no—
361#394—21no—
362#391C22×C1111yescharacteristic
363#391C22×C1111yescharacteristic
364#390C22×C1111yescharacteristic
365#389—21no—
366#389C22×C1111yescharacteristic
367#388—21no—
368#388—21no—
369#387—21no—
370#384C22×C1111yescharacteristic
371#380C22×C1111yescharacteristic
372C4×C4⋊C4C22×C1111yescharacteristic
373#340C22×C1111yescharacteristic
374#340C22×C1111yescharacteristic
375#340C22×C1111yescharacteristic
376#340C22×C1111yescharacteristic
377C22×C11—22no—
378C22×C11—22no—
379C22×C11—22no—
380C22×C11—41no—
381C22×C11—41no—
382C22×C11—41no—
383C22×C11—41no—
384C22×C11—81no—
385C22×C11—81no—
386C22×C11—81no—
387C22×C11—81no—
388C22×C11—81no—
389C22×C11—81no—
390C22×C11—81no—
391C22×C11C2×#12111yescharacteristic
392C22×C11C2×#12111yescharacteristic
393C22×C11#53711yescharacteristic
394C22×C11#57611yescharacteristic
395C22×C11#57711yescharacteristic
396C22×C11#57811yescharacteristic
397C22×C11#57811yescharacteristic
398C4×C11—22no—
399C4×C11—22no—
400C4×C11—22no—
401C4×C11—42no—
402C4×C11—42no—
403C4×C11—41no—
404C4×C11—41no—
405C4×C11—81no—
406C4×C11—81no—
407C4×C11—81no—
408C4×C11—81no—
409C4×C11—81no—
410C4×C11D4211yescharacteristic
411C4×C11#54711yescharacteristic
412C4×C11#54811yescharacteristic
413C4×C11#55311yescharacteristic
414C22×Q8C23×C1111yescharacteristic
415C22×Q8C23×C1111yescharacteristic
416C22×D4—21no—
417C22×D4C23×C1111yescharacteristic
418C23×C4C23×C1111yescharacteristic
419C2×Q16—22no—
420C2×Q16—22no—
421C2×Q16—41no—
422C2×SD16—22no—
423C2×SD16—22no—
424C2×SD16—41no—
425C2×M16—22no—
426C2×M16—22no—
427C2×M16—41no—
428C22×C8—22no—
429C22×C8—22no—
430C22×C8—41no—
431C22×C8C23×C1111yescharacteristic
432C22×C8C23×C1111yescharacteristic
433C22×C8C23×C1111yescharacteristic
434C22×C8C23×C1111yescharacteristic
435#124—22no—
436#124—22no—
437C22⋊Q8—22no—
438C22⋊Q8—22no—
439C22⋊Q8—22no—
440C22⋊Q8D4×C1114yes—
441#121—22no—
442#121—22no—
443C4×Q8—22no—
444C4×Q8—22no—
445#117—22no—
446#117—22no—
447C2×C4⋊C4—21no—
448C2×C4⋊C4—21no—
449C2×C4⋊C4—21no—
450C2×C4⋊C4—21no—
451C2×C4⋊C4—21no—
452C2×C4⋊C4—21no—
453C2×C4⋊C4D4×C1111yescharacteristic
454C2×C4⋊C4D4×C1111yescharacteristic
455C2×C4⋊C4C23×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⋊C4D4×C1111yescharacteristic
469C2×C22⋊C4D4×C1111yescharacteristic
470C2×C42—21no—
471C2×C42—21no—
472C2×C42C23×C1111yescharacteristic
473C2×C42C23×C1111yescharacteristic
474#107—22no—
475#107—22no—
476C4⋊C8—22no—
477C4⋊C8—22no—
478C4⋊C8—22no—
479C4⋊C8D4×C1114yescomplemented
480#103—22no—
481#103—22no—
482#103—22no—
483#103—22no—
484#103—41no—
485#102—22no—
486#102—22no—
487#102—41no—
488#95—21no—
489#95—21no—
490#95—21no—
491#95—21no—
492#95—21no—
493#95—21no—
494#95—21no—
495C2×C11—42no—
496C2×C11—161no—
497C2×C11#241611yescharacteristic
498C2×C11#304411yescharacteristic
499C2×C11#304511yescharacteristic
500C2×C11#306111yescharacteristic
501C2×C11#306311yescharacteristic
502C2×C11#325811yescharacteristic
503C2×C11#326211yescharacteristic
504C24—21no—
505C24C2×D4×C1111yescharacteristic
506C2×Q8—21no—
507C2×Q8—21no—
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—21no—
511C2×Q8—21no—
512C2×Q8—21no—
513C2×Q8—21no—
514C2×Q8—21no—
515C2×Q8—21no—
516C2×Q8—21no—
517C2×Q8C2×D4×C1112yes—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—42no—
525C2×D4—81no—
526C2×D4—81no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4C2×D4×C1111yescharacteristic
539C22×C4C2×D4×C1111yescharacteristic
540C22×C4C2×D4×C1111yescharacteristic
541C22×C4C2×D4×C1111yescharacteristic
542C22×C4C2×D4×C1111yescharacteristic
543C22×C4C2×D4×C1112yes—
544C22×C4C11×#4112yes—
545C22×C4C24×C1111yescharacteristic
546Q16—44no—
547SD16—44no—
548M16—44no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—44no—
560C2×C8C2×D4×C1112yes—
561C2×C8C2×D4×C1112yes—
562C4⋊C4—24no—
563C4⋊C4—22no—
564C4⋊C4—22no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—42no—
575C4⋊C4—42no—
576C4⋊C4—81no—
577C4⋊C4—81no—
578C4⋊C4—81no—
579C4⋊C4C2×D4×C1112yes—
580C22⋊C4—24no—
581C22⋊C4—22no—
582C22⋊C4—22no—
583C22⋊C4—42no—
584C22⋊C4—42no—
585C22⋊C4—42no—
586C22⋊C4—42no—
587C22⋊C4—81no—
588C22⋊C4—81no—
589C22⋊C4—81no—
590C42—21no—
591C42—21no—
592C42—42no—
593C42—81no—
594C42C2×D4×C1112yes—
595C42C11×#4112yes—
596C11#2476511yescharacteristic, direct product factor, Sylow
597C23—21no—
598C23—21no—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—41no—
604C23—41no—
605C23—41no—
606C23—41no—
607C23—41no—
608C23—41no—
609C23—41no—
610C23C11×#12112yes—
611C23C22×D4×C1111yescharacteristic
612Q8—22no—
613Q8—22no—
614Q8—41no—
615Q8—41no—
616Q8—41no—
617Q8—41no—
618Q8—41no—
619Q8—41no—
620D4—41no—
621D4—41no—
622D4—41no—
623D4—41no—
624D4—84no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4C11×#12112yes—
663C2×C4C11×#12112yes—
664C2×C4C11×#12112yes—
665C2×C4C22×D4×C1111yescharacteristic
666C2×C4C22×D4×C1111yescharacteristic
667C2×C4C2×C11×#4111yescharacteristic
668C2×C4C2×C11×#4111yescharacteristic
669C2×C4C11×H(5,𝔽2)11yescharacteristic
670C2×C4C11×2−1+411yescharacteristic
671C8—22no—
672C8—22no—
673C8—41no—
674C8—41no—
675C22—22no—
676C22—22no—
677C22—22no—
678C22—41no—
679C22—41no—
680C22—41no—
681C22—41no—
682C22—81no—
683C22—81no—
684C22—81no—
685C22—81no—
686C22—81no—
687C22—81no—
688C22—81no—
689C22C2×C11×#12111yescharacteristic
690C22C2×C11×#12111yescharacteristic
691C22C11×#53711yescharacteristic
692C22C11×#57611yescharacteristic
693C22C11×#57711yescharacteristic
694C22C11×#57811yescharacteristic
695C22C11×#57811yescharacteristic
696C4—22no—
697C4—22no—
698C4—22no—
699C4—42no—
700C4—42no—
701C4—41no—
702C4—41no—
703C4—81no—
704C4—81no—
705C4—81no—
706C4—81no—
707C4—81no—
708C4D42×C1111yescharacteristic
709C4C11×#54711yescharacteristic
710C4C11×#54811yescharacteristic
711C4C11×#55311yescharacteristic
712C2—42no—
713C2—161no—
714C2C11×#241611yescharacteristic
715C2C11×#304411yescharacteristic
716C2C11×#304511yescharacteristic
717C2C11×#306111yescharacteristic
718C2C11×#306311yescharacteristic
719C2C11×#325811yescharacteristic
720C2C11×#326211yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#121C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C11×#117 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#467C2semidirect
3. C2×C11×#464C2semidirect
4. C2×C11×#424C2semidirect
6. C11×#2323C2semidirect
7. C11×#2068C2semidirect
8. C11×#2067C2semidirect
9. C11×#2056C2semidirect
10. C11×#2055C2semidirect
11. C11×#1983C2semidirect
12. C11×#1947C2semidirect
13. C11×#1894C2semidirect
15. C11×#1803C2semidirect
128. C11×C4⋊C8D4semidirect
144. #24765C11direct (N × H)
238. C2×#467C2×C11semidirect
239. C2×#464C2×C11semidirect
240. C2×#424C2×C11semidirect
242. #2323C2×C11semidirect
243. #2068C2×C11semidirect
244. #2067C2×C11semidirect
245. #2056C2×C11semidirect
246. #2055C2×C11semidirect
247. #1983C2×C11semidirect
248. #1947C2×C11semidirect
249. #1894C2×C11semidirect
251. #1803C2×C11semidirect
479. C4⋊C8D4×C11semidirect
596. C11#24765direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4682
C2×C11×#4672
C2×C11×#4642
C2×C11×#4242
C11×#26202
C11×#23232
C11×#20682
C11×#20672
C11×#20562
C11×#20552
C11×#19832
C11×#19472
C11×#18942
C11×#18932
C11×#18032
#2476511