Finite Group Databasebeta

← C11×#24564 #14601757

Subgroups — C11×#24564 #14601757

Order 2816.

982 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#484C211yesmaximal, characteristic, complemented
2C2×C11×#408C211yesmaximal, characteristic
3C11×#2616C211yesmaximal, characteristic
4C11×#2311C211yesmaximal, characteristic
5C11×#2076C211yesmaximal, characteristic, complemented
6C11×#2075C211yesmaximal, characteristic, complemented
7C11×#2036C211yesmaximal, characteristic, complemented
8C11×#2035C211yesmaximal, characteristic, complemented
9C11×#1894C211yesmaximal, characteristic, complemented
10C11×#1892C211yesmaximal, characteristic, complemented
11C11×#1873C211yesmaximal, characteristic, complemented
12C11×#1854C211yesmaximal, characteristic, complemented
13C11×#1823C211yesmaximal, characteristic, complemented
14C11×#1809C211yesmaximal, characteristic, complemented
15C11×#1808C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic
17C22×C11×M16C2211yescharacteristic
18C23×C8×C11C2211yescharacteristic
19C2×C11×C22⋊Q8C2211yescharacteristic
20C2×C11×C22⋊Q8C2211yescharacteristic
21C2×C11×C22⋊Q8C2211yescharacteristic
22C2×C11×#117C2211yescharacteristic
23C22×C11×C4⋊C4C2211yescharacteristic
24C11×#484—24no—
25C2×C11×#107C2211yescharacteristic
26C2×C11×#107C2211yescharacteristic
27C2×C11×#107C2211yescharacteristic
28C2×C11×#106C2211yescharacteristic
29C2×C11×#103C2211yescharacteristic
30C2×C11×#103C2211yescharacteristic
31C2×C11×#103C2211yescharacteristic
32C2×C11×#103C2211yescharacteristic
33C11×#408—24no—
34C2×C11×C22⋊C8C2211yescharacteristic
35C2×C11×C22⋊C8C2211yescharacteristic
36C2×C11×C22⋊C8C2211yescharacteristic
37C2×C11×C22⋊C8C2211yescharacteristic
38C11×#395—21no—
39C11×#394—21no—
40C11×#394—21no—
41C11×#394—21no—
42C11×#391—21no—
43C11×#390—21no—
44C11×#386—21no—
45C11×#386—21no—
46C11×#380C2211yescharacteristic
47C11×#380C2211yescharacteristic
48C11×#380C2211yescharacteristic
49C11×#380C2211yescharacteristic
50C11×#380C2211yescharacteristic
51C11×#380C2211yescharacteristic
52C11×#380C2211yescharacteristic
53C11×#340C2211yescharacteristic
54C11×#340C2211yescharacteristic
55C11×#340C2211yescharacteristic
56C11×#340C2211yescharacteristic
57C11×#340C2211yescharacteristic
58C11×#340C2211yescharacteristic
59C11×#340C2211yescharacteristic
60C11×#340C2211yescharacteristic
61C2×C11×#41—22no—
62C2×C11×#41—22no—
63C2×C11×#41—22no—
64C2×C11×#41—22no—
65C2×C11×#41—41no—
66C2×C11×#41—41no—
67C22×Q8×C11D411yescharacteristic
68C22×Q8×C11C2311yescharacteristic
69C22×D4×C11D411yescharacteristic
70C22×D4×C11D411yescharacteristic
71C22×D4×C11D411yescharacteristic
72C23×C4×C11—21no—
73C23×C4×C11C2311yescharacteristic
74C23×C4×C11C2311yescharacteristic
75C23×C4×C11C2311yescharacteristic
76C2×C11×M16—22no—
77C2×C11×M16—22no—
78C2×C11×M16—41no—
79C22×C8×C11—22no—
80C22×C8×C11—22no—
81C22×C8×C11—41no—
82C22×C8×C11C2311yescharacteristic
83C22×C8×C11C2311yescharacteristic
84C22×C8×C11C2311yescharacteristic
85C22×C8×C11C2311yescharacteristic
86C11×C22⋊Q8—22no—
87C11×C22⋊Q8—22no—
88C11×C22⋊Q8—22no—
89C11×C22⋊Q8—22no—
90C11×C22⋊Q8—41no—
91C11×C22⋊Q8—41no—
92C11×#117—41no—
93C11×#117—41no—
94C2×C11×C4⋊C4—22no—
95C2×C11×C4⋊C4—22no—
96C2×C11×C4⋊C4—21no—
97C2×C11×C4⋊C4—21no—
98C2×C11×C4⋊C4—21no—
99C2×C11×C4⋊C4—21no—
100C2×C11×C4⋊C4C2311yescharacteristic
101C2×C11×C4⋊C4C2311yescharacteristic
102C2×C11×C4⋊C4C2311yescharacteristic
103C2×C11×C4⋊C4C2311yescharacteristic
104C2×C11×C4⋊C4C2311yescharacteristic
105C2×C11×C4⋊C4C2311yescharacteristic
106C2×C11×C4⋊C4C2311yescharacteristic
107C2×C11×C22⋊C4—21no—
108C2×C11×C22⋊C4—21no—
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⋊C4—21no—
118C2×C42×C11—21no—
119C11×#107—22no—
120C11×#107—22no—
121C11×#107—41no—
122C11×#106—41no—
123C11×#103—22no—
124C11×#103—22no—
125C11×#103—41no—
126C11×#103—41no—
127C11×C22⋊C8—22no—
128C11×C22⋊C8—22no—
129C11×C22⋊C8—22no—
130C11×C22⋊C8D414yes—
131C11×#95—21no—
132C11×#95—21no—
133C11×#95—21no—
134C11×#95—21no—
135C11×#95—21no—
136C11×#95—21no—
137C11×#95—21no—
138#24564C1111yesmaximal, characteristic, direct product factor, Sylow
139C24×C11C2×D411yescharacteristic
140C24×C11C2×D411yescharacteristic
141C24×C11C2×D411yescharacteristic
142C11×#41—44no—
143C11×#41—44no—
144C11×#41—44no—
145C11×#41—44no—
146C2×Q8×C11—22no—
147C2×Q8×C11—22no—
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—41no—
155C2×D4×C11—22no—
156C2×D4×C11—22no—
157C2×D4×C11—22no—
158C2×D4×C11—22no—
159C2×D4×C11—22no—
160C2×D4×C11—22no—
161C2×D4×C11—41no—
162C2×D4×C11—41no—
163C2×D4×C11—41no—
164C22×C4×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11—21no—
167C22×C4×C11—21no—
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×C11—21no—
180C22×C4×C11—21no—
181C22×C4×C11—21no—
182C22×C4×C11—21no—
183C22×C4×C11—21no—
184C22×C4×C11—21no—
185C22×C4×C11—21no—
186C22×C4×C11—42no—
187C22×C4×C11—81no—
188C22×C4×C11—81no—
189C22×C4×C11C2×D411yescharacteristic
190C22×C4×C11C2×D411yescharacteristic
191C22×C4×C11C2×D412yes—
192C22×C4×C11C2×D411yescharacteristic
193C22×C4×C11#4112yes—
194C22×C4×C11#4112yes—
195C22×C4×C11#4112yes—
196C22×C4×C11C2411yescharacteristic
197C11×M16—44no—
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—21no—
205C2×C8×C11—21no—
206C2×C8×C11—21no—
207C2×C8×C11—21no—
208C2×C8×C11—44no—
209C2×C8×C11C2×D412yes—
210C2×C8×C11C2×D412yes—
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—21no—
219C11×C4⋊C4—21no—
220C11×C4⋊C4—21no—
221C11×C4⋊C4—21no—
222C11×C4⋊C4—21no—
223C11×C4⋊C4—21no—
224C11×C4⋊C4—21no—
225C11×C4⋊C4—42no—
226C11×C4⋊C4—42no—
227C11×C4⋊C4—42no—
228C11×C4⋊C4—42no—
229C11×C22⋊C4—42no—
230C11×C22⋊C4—42no—
231C11×C22⋊C4—42no—
232C11×C22⋊C4—42no—
233C11×C22⋊C4—81no—
234C11×C22⋊C4—81no—
235C11×C22⋊C4—81no—
236C11×C22⋊C4—81no—
237C11×C22⋊C4—81no—
238C11×C22⋊C4—81no—
239C11×C22⋊C4—81no—
240C42×C11—42no—
241C2×#484C2×C1111yescharacteristic, complemented
242C2×#408C2×C1111yescharacteristic
243#2616C2×C1111yescharacteristic
244#2311C2×C1111yescharacteristic
245#2076C2×C1111yescharacteristic, complemented
246#2075C2×C1111yescharacteristic, complemented
247#2036C2×C1111yescharacteristic, complemented
248#2035C2×C1111yescharacteristic, complemented
249#1894C2×C1111yescharacteristic, complemented
250#1892C2×C1111yescharacteristic, complemented
251#1873C2×C1111yescharacteristic, complemented
252#1854C2×C1111yescharacteristic, complemented
253#1823C2×C1111yescharacteristic, complemented
254#1809C2×C1111yescharacteristic, complemented
255#1808C2×C1111yescharacteristic, complemented
256C23×C11—21no—
257C23×C11—21no—
258C23×C11—21no—
259C23×C11—21no—
260C23×C11—21no—
261C23×C11—21no—
262C23×C11—21no—
263C23×C11—21no—
264C23×C11—21no—
265C23×C11—21no—
266C23×C11—21no—
267C23×C11—21no—
268C23×C11—21no—
269C23×C11—21no—
270C23×C11—21no—
271C23×C11—21no—
272C23×C11—21no—
273C23×C11—21no—
274C23×C11—21no—
275C23×C11#12112yes—
276C23×C11#12312yes—
277C23×C11C22×D411yescharacteristic
278Q8×C11—44no—
279Q8×C11—41no—
280Q8×C11—41no—
281Q8×C11—41no—
282Q8×C11—41no—
283D4×C11—44no—
284D4×C11—44no—
285D4×C11—44no—
286C2×C4×C11—21no—
287C2×C4×C11—21no—
288C2×C4×C11—21no—
289C2×C4×C11—21no—
290C2×C4×C11—22no—
291C2×C4×C11—22no—
292C2×C4×C11—22no—
293C2×C4×C11—22no—
294C2×C4×C11—22no—
295C2×C4×C11—22no—
296C2×C4×C11—22no—
297C2×C4×C11—22no—
298C2×C4×C11—21no—
299C2×C4×C11—21no—
300C2×C4×C11—21no—
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—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—84no—
330C2×C4×C11#12112yes—
331C2×C4×C11#12312yes—
332C2×C4×C11C22×D411yescharacteristic
333C2×C4×C11C2×#4111yescharacteristic
334C2×C4×C11C2×#4111yescharacteristic
335C2×C4×C11C2×#4111yescharacteristic
336C2×C4×C11H(5,𝔽2)11yescharacteristic
337C2×C4×C11H(5,𝔽2)11yescharacteristic
338C8×C11—22no—
339C8×C11—22no—
340C8×C11—41no—
341C8×C11—41no—
342C22×#41C22×C1111yescharacteristic
343C22×M16C22×C1111yescharacteristic
344C23×C8C22×C1111yescharacteristic
345C2×C22⋊Q8C22×C1111yescharacteristic
346C2×C22⋊Q8C22×C1111yescharacteristic
347C2×C22⋊Q8C22×C1111yescharacteristic
348C2×#117C22×C1111yescharacteristic
349C22×C4⋊C4C22×C1111yescharacteristic
350#484—24no—
351C2×#107C22×C1111yescharacteristic
352C2×#107C22×C1111yescharacteristic
353C2×#107C22×C1111yescharacteristic
354C2×#106C22×C1111yescharacteristic
355C2×#103C22×C1111yescharacteristic
356C2×#103C22×C1111yescharacteristic
357C2×#103C22×C1111yescharacteristic
358C2×#103C22×C1111yescharacteristic
359#408—24no—
360C2×C22⋊C8C22×C1111yescharacteristic
361C2×C22⋊C8C22×C1111yescharacteristic
362C2×C22⋊C8C22×C1111yescharacteristic
363C2×C22⋊C8C22×C1111yescharacteristic
364#395—21no—
365#394—21no—
366#394—21no—
367#394—21no—
368#391—21no—
369#390—21no—
370#386—21no—
371#386—21no—
372#380C22×C1111yescharacteristic
373#380C22×C1111yescharacteristic
374#380C22×C1111yescharacteristic
375#380C22×C1111yescharacteristic
376#380C22×C1111yescharacteristic
377#380C22×C1111yescharacteristic
378#380C22×C1111yescharacteristic
379#340C22×C1111yescharacteristic
380#340C22×C1111yescharacteristic
381#340C22×C1111yescharacteristic
382#340C22×C1111yescharacteristic
383#340C22×C1111yescharacteristic
384#340C22×C1111yescharacteristic
385#340C22×C1111yescharacteristic
386#340C22×C1111yescharacteristic
387C22×C11—22no—
388C22×C11—22no—
389C22×C11—22no—
390C22×C11—22no—
391C22×C11—22no—
392C22×C11—22no—
393C22×C11—41no—
394C22×C11—41no—
395C22×C11—41no—
396C22×C11—41no—
397C22×C11—41no—
398C22×C11—41no—
399C22×C11—41no—
400C22×C11—41no—
401C22×C11—41no—
402C22×C11—41no—
403C22×C11—41no—
404C22×C11—41no—
405C22×C11—41no—
406C22×C11—41no—
407C22×C11—41no—
408C22×C11C2×#12111yescharacteristic
409C22×C11C2×#12311yescharacteristic
410C22×C11#53411yescharacteristic
411C22×C11#57611yescharacteristic
412C22×C11#57711yescharacteristic
413C22×C11#57811yescharacteristic
414C22×C11#57811yescharacteristic
415C4×C11—22no—
416C4×C11—22no—
417C4×C11—41no—
418C4×C11—81no—
419C4×C11—81no—
420C4×C11—81no—
421C4×C11—81no—
422C4×C11—81no—
423C4×C11—81no—
424C4×C11—81no—
425C4×C11—81no—
426C4×C11#54611yescharacteristic
427C4×C11#54611yescharacteristic
428C4×C11#55111yescharacteristic
429C4×C11#55111yescharacteristic
430C2×#41—22no—
431C2×#41—22no—
432C2×#41—22no—
433C2×#41—22no—
434C2×#41—41no—
435C2×#41—41no—
436C22×Q8D4×C1111yescharacteristic
437C22×Q8C23×C1111yescharacteristic
438C22×D4D4×C1111yescharacteristic
439C22×D4D4×C1111yescharacteristic
440C22×D4D4×C1111yescharacteristic
441C23×C4—21no—
442C23×C4C23×C1111yescharacteristic
443C23×C4C23×C1111yescharacteristic
444C23×C4C23×C1111yescharacteristic
445C2×M16—22no—
446C2×M16—22no—
447C2×M16—41no—
448C22×C8—22no—
449C22×C8—22no—
450C22×C8—41no—
451C22×C8C23×C1111yescharacteristic
452C22×C8C23×C1111yescharacteristic
453C22×C8C23×C1111yescharacteristic
454C22×C8C23×C1111yescharacteristic
455C22⋊Q8—22no—
456C22⋊Q8—22no—
457C22⋊Q8—22no—
458C22⋊Q8—22no—
459C22⋊Q8—41no—
460C22⋊Q8—41no—
461#117—41no—
462#117—41no—
463C2×C4⋊C4—22no—
464C2×C4⋊C4—22no—
465C2×C4⋊C4—21no—
466C2×C4⋊C4—21no—
467C2×C4⋊C4—21no—
468C2×C4⋊C4—21no—
469C2×C4⋊C4C23×C1111yescharacteristic
470C2×C4⋊C4C23×C1111yescharacteristic
471C2×C4⋊C4C23×C1111yescharacteristic
472C2×C4⋊C4C23×C1111yescharacteristic
473C2×C4⋊C4C23×C1111yescharacteristic
474C2×C4⋊C4C23×C1111yescharacteristic
475C2×C4⋊C4C23×C1111yescharacteristic
476C2×C22⋊C4—21no—
477C2×C22⋊C4—21no—
478C2×C22⋊C4—21no—
479C2×C22⋊C4—21no—
480C2×C22⋊C4—21no—
481C2×C22⋊C4—21no—
482C2×C22⋊C4—21no—
483C2×C22⋊C4—21no—
484C2×C22⋊C4—21no—
485C2×C22⋊C4—21no—
486C2×C22⋊C4—21no—
487C2×C42—21no—
488#107—22no—
489#107—22no—
490#107—41no—
491#106—41no—
492#103—22no—
493#103—22no—
494#103—41no—
495#103—41no—
496C22⋊C8—22no—
497C22⋊C8—22no—
498C22⋊C8—22no—
499C22⋊C8D4×C1114yes—
500#95—21no—
501#95—21no—
502#95—21no—
503#95—21no—
504#95—21no—
505#95—21no—
506#95—21no—
507C2×C11—42no—
508C2×C11—42no—
509C2×C11—81no—
510C2×C11#241211yescharacteristic
511C2×C11#305911yescharacteristic
512C2×C11#306211yescharacteristic
513C2×C11#309711yescharacteristic
514C2×C11#309811yescharacteristic
515C2×C11#320111yescharacteristic
516C2×C11#320311yescharacteristic
517C24C2×D4×C1111yescharacteristic
518C24C2×D4×C1111yescharacteristic
519C24C2×D4×C1111yescharacteristic
520#41—44no—
521#41—44no—
522#41—44no—
523#41—44no—
524C2×Q8—22no—
525C2×Q8—22no—
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8—21no—
529C2×Q8—21no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—41no—
533C2×D4—22no—
534C2×D4—22no—
535C2×D4—22no—
536C2×D4—22no—
537C2×D4—22no—
538C2×D4—22no—
539C2×D4—41no—
540C2×D4—41no—
541C2×D4—41no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
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×C4—42no—
565C22×C4—81no—
566C22×C4—81no—
567C22×C4C2×D4×C1111yescharacteristic
568C22×C4C2×D4×C1111yescharacteristic
569C22×C4C2×D4×C1112yes—
570C22×C4C2×D4×C1111yescharacteristic
571C22×C4C11×#4112yes—
572C22×C4C11×#4112yes—
573C22×C4C11×#4112yes—
574C22×C4C24×C1111yescharacteristic
575M16—44no—
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×C8—21no—
585C2×C8—21no—
586C2×C8—44no—
587C2×C8C2×D4×C1112yes—
588C2×C8C2×D4×C1112yes—
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—21no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—42no—
604C4⋊C4—42no—
605C4⋊C4—42no—
606C4⋊C4—42no—
607C22⋊C4—42no—
608C22⋊C4—42no—
609C22⋊C4—42no—
610C22⋊C4—42no—
611C22⋊C4—81no—
612C22⋊C4—81no—
613C22⋊C4—81no—
614C22⋊C4—81no—
615C22⋊C4—81no—
616C22⋊C4—81no—
617C22⋊C4—81no—
618C42—42no—
619C11#2456411yescharacteristic, direct product factor, Sylow
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23C11×#12112yes—
640C23C11×#12312yes—
641C23C22×D4×C1111yescharacteristic
642Q8—44no—
643Q8—41no—
644Q8—41no—
645Q8—41no—
646Q8—41no—
647D4—44no—
648D4—44no—
649D4—44no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
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—41no—
678C2×C4—41no—
679C2×C4—41no—
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—84no—
694C2×C4C11×#12112yes—
695C2×C4C11×#12312yes—
696C2×C4C22×D4×C1111yescharacteristic
697C2×C4C2×C11×#4111yescharacteristic
698C2×C4C2×C11×#4111yescharacteristic
699C2×C4C2×C11×#4111yescharacteristic
700C2×C4C11×H(5,𝔽2)11yescharacteristic
701C2×C4C11×H(5,𝔽2)11yescharacteristic
702C8—22no—
703C8—22no—
704C8—41no—
705C8—41no—
706C22—22no—
707C22—22no—
708C22—22no—
709C22—22no—
710C22—22no—
711C22—22no—
712C22—41no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22—41no—
721C22—41no—
722C22—41no—
723C22—41no—
724C22—41no—
725C22—41no—
726C22—41no—
727C22C2×C11×#12111yescharacteristic
728C22C2×C11×#12311yescharacteristic
729C22C11×#53411yescharacteristic
730C22C11×#57611yescharacteristic
731C22C11×#57711yescharacteristic
732C22C11×#57811yescharacteristic
733C22C11×#57811yescharacteristic
734C4—22no—
735C4—22no—
736C4—41no—
737C4—81no—
738C4—81no—
739C4—81no—
740C4—81no—
741C4—81no—
742C4—81no—
743C4—81no—
744C4—81no—
745C4C11×#54611yescharacteristic
746C4C11×#54611yescharacteristic
747C4C11×#55111yescharacteristic
748C4C11×#55111yescharacteristic
749C2—42no—
750C2—42no—
751C2—81no—
752C2C11×#241211yescharacteristic
753C2C11×#305911yescharacteristic
754C2C11×#306211yescharacteristic
755C2C11×#309711yescharacteristic
756C2C11×#309811yescharacteristic
757C2C11×#320111yescharacteristic
758C2C11×#320311yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC22×C11×#41C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C22×C11×#41 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#484C2semidirect
5. C11×#2076C2semidirect
6. C11×#2075C2semidirect
7. C11×#2036C2semidirect
8. C11×#2035C2semidirect
9. C11×#1894C2semidirect
10. C11×#1892C2semidirect
11. C11×#1873C2semidirect
12. C11×#1854C2semidirect
13. C11×#1823C2semidirect
14. C11×#1809C2semidirect
15. C11×#1808C2semidirect
138. #24564C11direct (N × H)
241. C2×#484C2×C11semidirect
245. #2076C2×C11semidirect
246. #2075C2×C11semidirect
247. #2036C2×C11semidirect
248. #2035C2×C11semidirect
249. #1894C2×C11semidirect
250. #1892C2×C11semidirect
251. #1873C2×C11semidirect
252. #1854C2×C11semidirect
253. #1823C2×C11semidirect
254. #1809C2×C11semidirect
255. #1808C2×C11semidirect
619. C11#24564direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4842
C2×C11×#4082
C11×#26162
C11×#23112
C11×#20762
C11×#20752
C11×#20362
C11×#20352
C11×#18942
C11×#18922
C11×#18732
C11×#18542
C11×#18232
C11×#18092
C11×#18082
#2456411