Finite Group Databasebeta

← C11×#24516 #14601709

Subgroups — C11×#24516 #14601709

Order 2816.

1056 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#450C211yesmaximal, characteristic
2C2×C11×#433C211yesmaximal, characteristic, complemented
3C11×#2625C211yesmaximal, characteristic, complemented
4C11×#2309C211yesmaximal, characteristic
5C11×#2067C211yesmaximal, characteristic, complemented
6C11×#2065C211yesmaximal, characteristic, complemented
7C11×#2055C211yesmaximal, characteristic, complemented
8C11×#2055C211yesmaximal, characteristic, complemented
9C11×#1973C211yesmaximal, characteristic, complemented
10C11×#1968C211yesmaximal, characteristic, complemented
11C11×#1936C211yesmaximal, characteristic, complemented
12C11×#1934C211yesmaximal, characteristic, complemented
13C11×#1873C211yesmaximal, characteristic, complemented
14C11×#1854C211yesmaximal, characteristic, complemented
15C11×#1786C211yesmaximal, characteristic
16C23×D4×C11C2211yescharacteristic
17C22×C11×SD16C2211yescharacteristic
18C22×C11×SD16C2211yescharacteristic
19C2×C11×C22⋊Q8C2211yescharacteristic
20C2×C11×#117C2211yescharacteristic
21C2×C11×#117C2211yescharacteristic
22C11×#450—24no—
23C11×#433—24no—
24C2×C11×#107C2211yescharacteristic, complemented
25C2×C11×#106C2211yescharacteristic, complemented
26C2×C11×C4⋊C8C2211yescharacteristic, complemented
27C2×C11×C4⋊C8C2211yescharacteristic, complemented
28C2×C11×#103C2211yescharacteristic, complemented
29C2×C11×#103C2211yescharacteristic, complemented
30C2×C11×#102C2211yescharacteristic
31C2×C11×#102C2211yescharacteristic
32C2×C11×#102C2211yescharacteristic
33C2×C11×#102C2211yescharacteristic
34C2×C11×#102C2211yescharacteristic
35C2×C11×#102C2211yescharacteristic
36C2×C11×C22⋊C8C2211yescharacteristic
37C2×C11×C22⋊C8C2211yescharacteristic
38C2×C11×#97C2211yescharacteristic, complemented
39C2×C4×C8×C11C2211yescharacteristic, complemented
40C11×#400—21no—
41C11×#398—21no—
42C11×#397—21no—
43C11×#397—21no—
44C11×#391C2211yescharacteristic, complemented
45C11×#391C2211yescharacteristic, complemented
46C11×#390—21no—
47C11×#390—21no—
48C11×#390C2211yescharacteristic
49C11×#390C2211yescharacteristic
50C11×#390C2211yescharacteristic
51C11×#390C2211yescharacteristic
52C11×#389C2211yescharacteristic, complemented
53C11×#389C2211yescharacteristic, complemented
54C11×#380C2211yescharacteristic
55C11×#379—21no—
56C11×#379—21no—
57C11×#340C2211yescharacteristic, complemented
58C11×#340C2211yescharacteristic, complemented
59C11×#340C2211yescharacteristic, complemented
60C11×#340C2211yescharacteristic, complemented
61C25×C11—21no—
62C22×Q8×C11C2311yescharacteristic
63C22×D4×C11—22no—
64C22×D4×C11—22no—
65C22×D4×C11—21no—
66C22×D4×C11—22no—
67C22×D4×C11—22no—
68C22×D4×C11—41no—
69C22×D4×C11—41no—
70C22×D4×C11C2311yescharacteristic
71C22×D4×C11C2311yescharacteristic
72C23×C4×C11C2311yescharacteristic
73C2×C11×SD16—22no—
74C2×C11×SD16—22no—
75C2×C11×SD16—22no—
76C2×C11×SD16—22no—
77C2×C11×SD16—41no—
78C2×C11×SD16—41no—
79C22×C8×C11C2311yescharacteristic
80C22×C8×C11C2311yescharacteristic
81C22×C8×C11C2311yescharacteristic
82C22×C8×C11C2311yescharacteristic
83C11×C22⋊Q8—22no—
84C11×C22⋊Q8—22no—
85C11×#117—22no—
86C11×#117—22no—
87C11×#117—41no—
88C11×#117—41no—
89C2×C11×C4⋊C4—21no—
90C2×C11×C4⋊C4—21no—
91C2×C11×C4⋊C4—21no—
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×C4⋊C4C2311yescharacteristic
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×C11×C22⋊C4D411yescharacteristic
111C2×C11×C22⋊C4D411yescharacteristic
112C2×C42×C11—21no—
113C2×C42×C11C2311yescharacteristic
114C2×C42×C11C2311yescharacteristic
115C11×#107—41no—
116C11×#106—41no—
117C11×C4⋊C8—22no—
118C11×C4⋊C8—22no—
119C11×#103—41no—
120C11×#103—41no—
121C11×#102—22no—
122C11×#102—22no—
123C11×#102—22no—
124C11×#102—22no—
125C11×#102—41no—
126C11×#102—41no—
127C11×C22⋊C8—22no—
128C11×C22⋊C8D414yes—
129C11×#97—22no—
130C4×C8×C11—22no—
131C11×#95—21no—
132C11×#95—21no—
133C11×#95—21no—
134C11×#95—21no—
135C11×#95—21no—
136C11×#95—21no—
137C11×#95—21no—
138#24516C1111yesmaximal, characteristic, direct product factor, Sylow
139C24×C11—24no—
140C24×C11—21no—
141C24×C11—21no—
142C24×C11—42no—
143C24×C11—42no—
144C24×C11—81no—
145C24×C11—81no—
146C24×C11—81no—
147C24×C11—81no—
148C24×C11C2×D411yescharacteristic
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×D4×C11—24no—
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—21no—
165C2×D4×C11—21no—
166C2×D4×C11—44no—
167C2×D4×C11—44no—
168C2×D4×C11—44no—
169C2×D4×C11—44no—
170C2×D4×C11—42no—
171C2×D4×C11—42no—
172C2×D4×C11#4112yes—
173C2×D4×C11#4112yes—
174C22×C4×C11—21no—
175C22×C4×C11—21no—
176C22×C4×C11—21no—
177C22×C4×C11—21no—
178C22×C4×C11—21no—
179C22×C4×C11—21no—
180C22×C4×C11—21no—
181C22×C4×C11—21no—
182C22×C4×C11—21no—
183C22×C4×C11—21no—
184C22×C4×C11C2×D411yescharacteristic
185C22×C4×C11C2×D411yescharacteristic
186C22×C4×C11C2×D411yescharacteristic
187C22×C4×C11C2×D411yescharacteristic
188C22×C4×C11C2×D411yescharacteristic
189C22×C4×C11C2×D412yes—
190C22×C4×C11#4112yes—
191C22×C4×C11C2411yescharacteristic
192C11×SD16—44no—
193C11×SD16—44no—
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×C11C2×D412yes—
205C2×C8×C11C2×D412yes—
206C11×C4⋊C4—22no—
207C11×C4⋊C4—22no—
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—21no—
216C11×C4⋊C4—21no—
217C11×C4⋊C4—21no—
218C11×C4⋊C4—42no—
219C11×C4⋊C4—81no—
220C11×C4⋊C4—81no—
221C11×C22⋊C4—22no—
222C11×C22⋊C4—22no—
223C11×C22⋊C4—42no—
224C11×C22⋊C4—42no—
225C11×C22⋊C4—81no—
226C11×C22⋊C4—81no—
227C11×C22⋊C4—81no—
228C11×C22⋊C4—81no—
229C11×C22⋊C4—81no—
230C11×C22⋊C4—81no—
231C11×C22⋊C4—81no—
232C11×C22⋊C4—81no—
233C11×C22⋊C4—81no—
234C42×C11—21no—
235C42×C11—21no—
236C42×C11—21no—
237C42×C11—21no—
238C42×C11—42no—
239C2×#450C2×C1111yescharacteristic
240C2×#433C2×C1111yescharacteristic, complemented
241#2625C2×C1111yescharacteristic, complemented
242#2309C2×C1111yescharacteristic
243#2067C2×C1111yescharacteristic, complemented
244#2065C2×C1111yescharacteristic, complemented
245#2055C2×C1111yescharacteristic, complemented
246#2055C2×C1111yescharacteristic, complemented
247#1973C2×C1111yescharacteristic, complemented
248#1968C2×C1111yescharacteristic, complemented
249#1936C2×C1111yescharacteristic, complemented
250#1934C2×C1111yescharacteristic, complemented
251#1873C2×C1111yescharacteristic, complemented
252#1854C2×C1111yescharacteristic, complemented
253#1786C2×C1111yescharacteristic
254C23×C11—21no—
255C23×C11—21no—
256C23×C11—21no—
257C23×C11—21no—
258C23×C11—21no—
259C23×C11—21no—
260C23×C11—22no—
261C23×C11—22no—
262C23×C11—48no—
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×C11—41no—
272C23×C11—41no—
273C23×C11—41no—
274C23×C11—41no—
275C23×C11—84no—
276C23×C11—84no—
277C23×C11—84no—
278C23×C11—84no—
279C23×C11—84no—
280C23×C11—84no—
281C23×C11#12112yes—
282C23×C11C22×D411yescharacteristic
283Q8×C11—41no—
284Q8×C11—41no—
285Q8×C11—41no—
286Q8×C11—41no—
287D4×C11—22no—
288D4×C11—22no—
289D4×C11—22no—
290D4×C11—22no—
291D4×C11—48no—
292D4×C11—41no—
293D4×C11—41no—
294D4×C11—41no—
295D4×C11—41no—
296C2×C4×C11—21no—
297C2×C4×C11—21no—
298C2×C4×C11—22no—
299C2×C4×C11—22no—
300C2×C4×C11—22no—
301C2×C4×C11—22no—
302C2×C4×C11—21no—
303C2×C4×C11—21no—
304C2×C4×C11—21no—
305C2×C4×C11—21no—
306C2×C4×C11—21no—
307C2×C4×C11—21no—
308C2×C4×C11—21no—
309C2×C4×C11—21no—
310C2×C4×C11—21no—
311C2×C4×C11—21no—
312C2×C4×C11—21no—
313C2×C4×C11—21no—
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—41no—
321C2×C4×C11—41no—
322C2×C4×C11—41no—
323C2×C4×C11—41no—
324C2×C4×C11—41no—
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#12112yes—
333C2×C4×C11C22×D411yescharacteristic
334C2×C4×C11C2×#4111yescharacteristic
335C2×C4×C11C2×#4111yescharacteristic
336C2×C4×C11C2×#4111yescharacteristic
337C2×C4×C11H(5,𝔽2)11yescharacteristic
338C2×C4×C11H(5,𝔽2)11yescharacteristic
339C8×C11—22no—
340C8×C11—22no—
341C8×C11—41no—
342C8×C11—41no—
343C23×D4C22×C1111yescharacteristic
344C22×SD16C22×C1111yescharacteristic
345C22×SD16C22×C1111yescharacteristic
346C2×C22⋊Q8C22×C1111yescharacteristic
347C2×#117C22×C1111yescharacteristic
348C2×#117C22×C1111yescharacteristic
349#450—24no—
350#433—24no—
351C2×#107C22×C1111yescharacteristic, complemented
352C2×#106C22×C1111yescharacteristic, complemented
353C2×C4⋊C8C22×C1111yescharacteristic, complemented
354C2×C4⋊C8C22×C1111yescharacteristic, complemented
355C2×#103C22×C1111yescharacteristic, complemented
356C2×#103C22×C1111yescharacteristic, complemented
357C2×#102C22×C1111yescharacteristic
358C2×#102C22×C1111yescharacteristic
359C2×#102C22×C1111yescharacteristic
360C2×#102C22×C1111yescharacteristic
361C2×#102C22×C1111yescharacteristic
362C2×#102C22×C1111yescharacteristic
363C2×C22⋊C8C22×C1111yescharacteristic
364C2×C22⋊C8C22×C1111yescharacteristic
365C2×#97C22×C1111yescharacteristic, complemented
366C2×C4×C8C22×C1111yescharacteristic, complemented
367#400—21no—
368#398—21no—
369#397—21no—
370#397—21no—
371#391C22×C1111yescharacteristic, complemented
372#391C22×C1111yescharacteristic, complemented
373#390—21no—
374#390—21no—
375#390C22×C1111yescharacteristic
376#390C22×C1111yescharacteristic
377#390C22×C1111yescharacteristic
378#390C22×C1111yescharacteristic
379#389C22×C1111yescharacteristic, complemented
380#389C22×C1111yescharacteristic, complemented
381#380C22×C1111yescharacteristic
382#379—21no—
383#379—21no—
384#340C22×C1111yescharacteristic, complemented
385#340C22×C1111yescharacteristic, complemented
386#340C22×C1111yescharacteristic, complemented
387#340C22×C1111yescharacteristic, complemented
388C22×C11—22no—
389C22×C11—22no—
390C22×C11—22no—
391C22×C11—41no—
392C22×C11—41no—
393C22×C11—41no—
394C22×C11—41no—
395C22×C11—42no—
396C22×C11—42no—
397C22×C11—42no—
398C22×C11—42no—
399C22×C11—42no—
400C22×C11—42no—
401C22×C11—816no—
402C22×C11—81no—
403C22×C11—81no—
404C22×C11—81no—
405C22×C11—81no—
406C22×C11—81no—
407C22×C11—81no—
408C22×C11—81no—
409C22×C11—81no—
410C22×C11C2×#12111yescharacteristic
411C22×C11#52511yescharacteristic
412C22×C11#53511yescharacteristic
413C22×C11#57611yescharacteristic
414C22×C11#57711yescharacteristic
415C22×C11#57711yescharacteristic
416C22×C11#57711yescharacteristic
417C4×C11—22no—
418C4×C11—41no—
419C4×C11—41no—
420C4×C11—41no—
421C4×C11—41no—
422C4×C11—81no—
423C4×C11—81no—
424C4×C11—81no—
425C4×C11—81no—
426C4×C11—81no—
427C4×C11—81no—
428C4×C11#54611yescharacteristic
429C4×C11#54611yescharacteristic
430C4×C11#55111yescharacteristic
431C4×C11#55111yescharacteristic
432C25—21no—
433C22×Q8C23×C1111yescharacteristic
434C22×D4—22no—
435C22×D4—22no—
436C22×D4—21no—
437C22×D4—22no—
438C22×D4—22no—
439C22×D4—41no—
440C22×D4—41no—
441C22×D4C23×C1111yescharacteristic
442C22×D4C23×C1111yescharacteristic
443C23×C4C23×C1111yescharacteristic
444C2×SD16—22no—
445C2×SD16—22no—
446C2×SD16—22no—
447C2×SD16—22no—
448C2×SD16—41no—
449C2×SD16—41no—
450C22×C8C23×C1111yescharacteristic
451C22×C8C23×C1111yescharacteristic
452C22×C8C23×C1111yescharacteristic
453C22×C8C23×C1111yescharacteristic
454C22⋊Q8—22no—
455C22⋊Q8—22no—
456#117—22no—
457#117—22no—
458#117—41no—
459#117—41no—
460C2×C4⋊C4—21no—
461C2×C4⋊C4—21no—
462C2×C4⋊C4—21no—
463C2×C4⋊C4D4×C1111yescharacteristic
464C2×C4⋊C4D4×C1111yescharacteristic
465C2×C4⋊C4C23×C1111yescharacteristic
466C2×C4⋊C4C23×C1111yescharacteristic
467C2×C4⋊C4C23×C1111yescharacteristic
468C2×C4⋊C4C23×C1111yescharacteristic
469C2×C4⋊C4C23×C1111yescharacteristic
470C2×C22⋊C4—21no—
471C2×C22⋊C4—21no—
472C2×C22⋊C4—21no—
473C2×C22⋊C4—21no—
474C2×C22⋊C4—21no—
475C2×C22⋊C4—21no—
476C2×C22⋊C4—21no—
477C2×C22⋊C4—21no—
478C2×C22⋊C4—21no—
479C2×C22⋊C4—21no—
480C2×C22⋊C4—21no—
481C2×C22⋊C4D4×C1111yescharacteristic
482C2×C22⋊C4D4×C1111yescharacteristic
483C2×C42—21no—
484C2×C42C23×C1111yescharacteristic
485C2×C42C23×C1111yescharacteristic
486#107—41no—
487#106—41no—
488C4⋊C8—22no—
489C4⋊C8—22no—
490#103—41no—
491#103—41no—
492#102—22no—
493#102—22no—
494#102—22no—
495#102—22no—
496#102—41no—
497#102—41no—
498C22⋊C8—22no—
499C22⋊C8D4×C1114yes—
500#97—22no—
501C4×C8—22no—
502#95—21no—
503#95—21no—
504#95—21no—
505#95—21no—
506#95—21no—
507#95—21no—
508#95—21no—
509C2×C11—42no—
510C2×C11—82no—
511C2×C11—82no—
512C2×C11#241111yescharacteristic
513C2×C11#305711yescharacteristic
514C2×C11#306211yescharacteristic
515C2×C11#311811yescharacteristic
516C2×C11#312311yescharacteristic
517C2×C11#322211yescharacteristic
518C2×C11#322411yescharacteristic
519C24—24no—
520C24—21no—
521C24—21no—
522C24—42no—
523C24—42no—
524C24—81no—
525C24—81no—
526C24—81no—
527C24—81no—
528C24C2×D4×C1111yescharacteristic
529C2×Q8—21no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—21no—
533C2×Q8—21no—
534C2×Q8—21no—
535C2×D4—24no—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—44no—
547C2×D4—44no—
548C2×D4—44no—
549C2×D4—44no—
550C2×D4—42no—
551C2×D4—42no—
552C2×D4C11×#4112yes—
553C2×D4C11×#4112yes—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4C2×D4×C1111yescharacteristic
565C22×C4C2×D4×C1111yescharacteristic
566C22×C4C2×D4×C1111yescharacteristic
567C22×C4C2×D4×C1111yescharacteristic
568C22×C4C2×D4×C1111yescharacteristic
569C22×C4C2×D4×C1112yes—
570C22×C4C11×#4112yes—
571C22×C4C24×C1111yescharacteristic
572SD16—44no—
573SD16—44no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8C2×D4×C1112yes—
585C2×C8C2×D4×C1112yes—
586C4⋊C4—22no—
587C4⋊C4—22no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—42no—
599C4⋊C4—81no—
600C4⋊C4—81no—
601C22⋊C4—22no—
602C22⋊C4—22no—
603C22⋊C4—42no—
604C22⋊C4—42no—
605C22⋊C4—81no—
606C22⋊C4—81no—
607C22⋊C4—81no—
608C22⋊C4—81no—
609C22⋊C4—81no—
610C22⋊C4—81no—
611C22⋊C4—81no—
612C22⋊C4—81no—
613C22⋊C4—81no—
614C42—21no—
615C42—21no—
616C42—21no—
617C42—21no—
618C42—42no—
619C11#2451611yescharacteristic, direct product factor, Sylow
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—22no—
627C23—22no—
628C23—48no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—84no—
642C23—84no—
643C23—84no—
644C23—84no—
645C23—84no—
646C23—84no—
647C23C11×#12112yes—
648C23C22×D4×C1111yescharacteristic
649Q8—41no—
650Q8—41no—
651Q8—41no—
652Q8—41no—
653D4—22no—
654D4—22no—
655D4—22no—
656D4—22no—
657D4—48no—
658D4—41no—
659D4—41no—
660D4—41no—
661D4—41no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4C11×#12112yes—
699C2×C4C22×D4×C1111yescharacteristic
700C2×C4C2×C11×#4111yescharacteristic
701C2×C4C2×C11×#4111yescharacteristic
702C2×C4C2×C11×#4111yescharacteristic
703C2×C4C11×H(5,𝔽2)11yescharacteristic
704C2×C4C11×H(5,𝔽2)11yescharacteristic
705C8—22no—
706C8—22no—
707C8—41no—
708C8—41no—
709C22—22no—
710C22—22no—
711C22—22no—
712C22—41no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—42no—
717C22—42no—
718C22—42no—
719C22—42no—
720C22—42no—
721C22—42no—
722C22—816no—
723C22—81no—
724C22—81no—
725C22—81no—
726C22—81no—
727C22—81no—
728C22—81no—
729C22—81no—
730C22—81no—
731C22C2×C11×#12111yescharacteristic
732C22C11×#52511yescharacteristic
733C22C11×#53511yescharacteristic
734C22C11×#57611yescharacteristic
735C22C11×#57711yescharacteristic
736C22C11×#57711yescharacteristic
737C22C11×#57711yescharacteristic
738C4—22no—
739C4—41no—
740C4—41no—
741C4—41no—
742C4—41no—
743C4—81no—
744C4—81no—
745C4—81no—
746C4—81no—
747C4—81no—
748C4—81no—
749C4C11×#54611yescharacteristic
750C4C11×#54611yescharacteristic
751C4C11×#55111yescharacteristic
752C4C11×#55111yescharacteristic
753C2—42no—
754C2—82no—
755C2—82no—
756C2C11×#241111yescharacteristic
757C2C11×#305711yescharacteristic
758C2C11×#306211yescharacteristic
759C2C11×#311811yescharacteristic
760C2C11×#312311yescharacteristic
761C2C11×#322211yescharacteristic
762C2C11×#322411yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC23×D4×C11C22
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×#433C2semidirect
3. C11×#2625C2semidirect
5. C11×#2067C2semidirect
6. C11×#2065C2semidirect
7. C11×#2055C2semidirect
8. C11×#2055C2semidirect
9. C11×#1973C2semidirect
10. C11×#1968C2semidirect
11. C11×#1936C2semidirect
12. C11×#1934C2semidirect
13. C11×#1873C2semidirect
14. C11×#1854C2semidirect
24. C2×C11×#107C22semidirect
25. C2×C11×#106C22semidirect
26. C2×C11×C4⋊C8C22semidirect
27. C2×C11×C4⋊C8C22semidirect
28. C2×C11×#103C22semidirect
29. C2×C11×#103C22semidirect
38. C2×C11×#97C22semidirect
39. C2×C4×C8×C11C22semidirect
44. C11×#391C22semidirect
45. C11×#391C22semidirect
52. C11×#389C22semidirect
53. C11×#389C22semidirect
57. C11×#340C22semidirect
58. C11×#340C22semidirect
59. C11×#340C22semidirect
60. C11×#340C22semidirect
138. #24516C11direct (N × H)
240. C2×#433C2×C11semidirect
241. #2625C2×C11semidirect
243. #2067C2×C11semidirect
244. #2065C2×C11semidirect
245. #2055C2×C11semidirect
246. #2055C2×C11semidirect
247. #1973C2×C11semidirect
248. #1968C2×C11semidirect
249. #1936C2×C11semidirect
250. #1934C2×C11semidirect
251. #1873C2×C11semidirect
252. #1854C2×C11semidirect
351. C2×#107C22×C11semidirect
352. C2×#106C22×C11semidirect
353. C2×C4⋊C8C22×C11semidirect
354. C2×C4⋊C8C22×C11semidirect
355. C2×#103C22×C11semidirect
356. C2×#103C22×C11semidirect
365. C2×#97C22×C11semidirect
366. C2×C4×C8C22×C11semidirect
371. #391C22×C11semidirect
372. #391C22×C11semidirect
379. #389C22×C11semidirect
380. #389C22×C11semidirect
384. #340C22×C11semidirect
385. #340C22×C11semidirect
386. #340C22×C11semidirect
387. #340C22×C11semidirect
619. C11#24516direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4502
C2×C11×#4332
C11×#26252
C11×#23092
C11×#20672
C11×#20652
C11×#20552
C11×#19732
C11×#19682
C11×#19362
C11×#19342
C11×#18732
C11×#18542
C11×#17862
#2451611