Finite Group Databasebeta

← C11×#24518 #14601711

Subgroups — C11×#24518 #14601711

Order 2816.

938 conjugacy classes of subgroups.

The subgroup lattice has 718 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#448C211yesmaximal, characteristic
2C2×C11×#433C211yesmaximal, characteristic, complemented
3C11×#2624C211yesmaximal, characteristic
4C11×#2310C211yesmaximal, characteristic, complemented
5C11×#2068C211yesmaximal, characteristic, complemented
6C11×#2066C211yesmaximal, characteristic, complemented
7C11×#2055C211yesmaximal, characteristic, complemented
8C11×#2055C211yesmaximal, characteristic, complemented
9C11×#1973C211yesmaximal, characteristic, complemented
10C11×#1968C211yesmaximal, characteristic, complemented
11C11×#1935C211yesmaximal, characteristic, complemented
12C11×#1933C211yesmaximal, characteristic, complemented
13C11×#1875C211yesmaximal, characteristic
14C11×#1854C211yesmaximal, characteristic, complemented
15C11×#1787C211yesmaximal, characteristic, complemented
16C23×Q8×C11C2211yescharacteristic
17C22×C11×SD16C2211yescharacteristic
18C22×C11×SD16C2211yescharacteristic
19C2×C11×#121C2211yescharacteristic
20C2×C11×#117C2211yescharacteristic
21C2×C11×#117C2211yescharacteristic
22C11×#448—24no—
23C11×#433—24no—
24C2×C11×#107C2211yescharacteristic
25C2×C11×#106C2211yescharacteristic
26C2×C11×C4⋊C8C2211yescharacteristic
27C2×C11×C4⋊C8C2211yescharacteristic
28C2×C11×#103C2211yescharacteristic
29C2×C11×#103C2211yescharacteristic
30C2×C11×#103C2211yescharacteristic
31C2×C11×#103C2211yescharacteristic
32C2×C11×#103C2211yescharacteristic
33C2×C11×#103C2211yescharacteristic
34C2×C11×#102C2211yescharacteristic
35C2×C11×#102C2211yescharacteristic
36C2×C11×C22⋊C8C2211yescharacteristic
37C2×C11×C22⋊C8C2211yescharacteristic
38C2×C11×#97C2211yescharacteristic
39C2×C4×C8×C11C2211yescharacteristic
40C11×#399—21no—
41C11×#397—21no—
42C11×#394—21no—
43C11×#394—21no—
44C11×#391—21no—
45C11×#391—21no—
46C11×#391C2211yescharacteristic
47C11×#391C2211yescharacteristic
48C11×#391C2211yescharacteristic
49C11×#391C2211yescharacteristic
50C11×#390C2211yescharacteristic
51C11×#390C2211yescharacteristic
52C11×#389C2211yescharacteristic
53C11×#389C2211yescharacteristic
54C11×#381—21no—
55C11×#381—21no—
56C11×#380C2211yescharacteristic
57C11×#340C2211yescharacteristic
58C11×#340C2211yescharacteristic
59C11×#340C2211yescharacteristic
60C11×#340C2211yescharacteristic
61C22×Q8×C11—22no—
62C22×Q8×C11—22no—
63C22×Q8×C11—21no—
64C22×Q8×C11—22no—
65C22×Q8×C11—22no—
66C22×Q8×C11—41no—
67C22×Q8×C11—41no—
68C22×Q8×C11C2311yescharacteristic
69C22×Q8×C11C2311yescharacteristic
70C22×D4×C11—21no—
71C22×D4×C11C2311yescharacteristic
72C23×C4×C11—21no—
73C23×C4×C11C2311yescharacteristic
74C2×C11×SD16—22no—
75C2×C11×SD16—22no—
76C2×C11×SD16—22no—
77C2×C11×SD16—22no—
78C2×C11×SD16—41no—
79C2×C11×SD16—41no—
80C22×C8×C11C2311yescharacteristic
81C22×C8×C11C2311yescharacteristic
82C22×C8×C11C2311yescharacteristic
83C22×C8×C11C2311yescharacteristic
84C11×#121—22no—
85C11×#121—22no—
86C11×#117—22no—
87C11×#117—22no—
88C11×#117—41no—
89C11×#117—41no—
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⋊C4D411yescharacteristic
107C2×C11×C22⋊C4D411yescharacteristic
108C2×C42×C11—21no—
109C2×C42×C11C2311yescharacteristic
110C2×C42×C11C2311yescharacteristic
111C11×#107—41no—
112C11×#106—41no—
113C11×C4⋊C8—22no—
114C11×C4⋊C8—22no—
115C11×#103—22no—
116C11×#103—22no—
117C11×#103—22no—
118C11×#103—22no—
119C11×#103—41no—
120C11×#103—41no—
121C11×#102—41no—
122C11×#102—41no—
123C11×C22⋊C8—22no—
124C11×C22⋊C8D414yes—
125C11×#97—22no—
126C4×C8×C11—22no—
127C11×#95—21no—
128C11×#95—21no—
129C11×#95—21no—
130C11×#95—21no—
131C11×#95—21no—
132C11×#95—21no—
133C11×#95—21no—
134C11×#95—21no—
135C11×#95—21no—
136C11×#95—21no—
137C11×#95—21no—
138#24518C1111yesmaximal, characteristic, direct product factor, Sylow
139C24×C11—21no—
140C24×C11C2×D411yescharacteristic
141C2×Q8×C11—24no—
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×Q8×C11—21no—
149C2×Q8×C11—21no—
150C2×Q8×C11—21no—
151C2×Q8×C11—21no—
152C2×Q8×C11—44no—
153C2×Q8×C11—44no—
154C2×Q8×C11—44no—
155C2×Q8×C11—44no—
156C2×Q8×C11—42no—
157C2×Q8×C11—42no—
158C2×Q8×C11#4112yes—
159C2×Q8×C11#4112yes—
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—42no—
167C2×D4×C11—81no—
168C2×D4×C11—81no—
169C22×C4×C11—21no—
170C22×C4×C11—21no—
171C22×C4×C11—21no—
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—21no—
179C22×C4×C11—21no—
180C22×C4×C11—21no—
181C22×C4×C11—42no—
182C22×C4×C11—42no—
183C22×C4×C11C2×D411yescharacteristic
184C22×C4×C11C2×D411yescharacteristic
185C22×C4×C11C2×D411yescharacteristic
186C22×C4×C11C2×D411yescharacteristic
187C22×C4×C11C2×D411yescharacteristic
188C22×C4×C11C2×D412yes—
189C22×C4×C11#4112yes—
190C22×C4×C11C2411yescharacteristic
191C11×SD16—44no—
192C11×SD16—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×C11C2×D412yes—
204C2×C8×C11C2×D412yes—
205C11×C4⋊C4—22no—
206C11×C4⋊C4—22no—
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—21no—
216C11×C4⋊C4—21no—
217C11×C4⋊C4—81no—
218C11×C4⋊C4—81no—
219C11×C22⋊C4—22no—
220C11×C22⋊C4—22no—
221C11×C22⋊C4—42no—
222C11×C22⋊C4—42no—
223C11×C22⋊C4—81no—
224C11×C22⋊C4—81no—
225C11×C22⋊C4—81no—
226C11×C22⋊C4—81no—
227C11×C22⋊C4—81no—
228C42×C11—21no—
229C42×C11—21no—
230C42×C11—21no—
231C42×C11—21no—
232C42×C11—42no—
233C2×#448C2×C1111yescharacteristic
234C2×#433C2×C1111yescharacteristic, complemented
235#2624C2×C1111yescharacteristic
236#2310C2×C1111yescharacteristic, complemented
237#2068C2×C1111yescharacteristic, complemented
238#2066C2×C1111yescharacteristic, complemented
239#2055C2×C1111yescharacteristic, complemented
240#2055C2×C1111yescharacteristic, complemented
241#1973C2×C1111yescharacteristic, complemented
242#1968C2×C1111yescharacteristic, complemented
243#1935C2×C1111yescharacteristic, complemented
244#1933C2×C1111yescharacteristic, complemented
245#1875C2×C1111yescharacteristic
246#1854C2×C1111yescharacteristic, complemented
247#1787C2×C1111yescharacteristic, complemented
248C23×C11—21no—
249C23×C11—21no—
250C23×C11—21no—
251C23×C11—21no—
252C23×C11—21no—
253C23×C11—21no—
254C23×C11—41no—
255C23×C11—41no—
256C23×C11—41no—
257C23×C11—41no—
258C23×C11—41no—
259C23×C11—41no—
260C23×C11—41no—
261C23×C11#12112yes—
262C23×C11C22×D411yescharacteristic
263Q8×C11—22no—
264Q8×C11—22no—
265Q8×C11—22no—
266Q8×C11—22no—
267Q8×C11—48no—
268Q8×C11—41no—
269Q8×C11—41no—
270Q8×C11—41no—
271Q8×C11—41no—
272D4×C11—41no—
273D4×C11—41no—
274D4×C11—41no—
275D4×C11—41no—
276D4×C11—84no—
277C2×C4×C11—21no—
278C2×C4×C11—21no—
279C2×C4×C11—22no—
280C2×C4×C11—22no—
281C2×C4×C11—22no—
282C2×C4×C11—22no—
283C2×C4×C11—21no—
284C2×C4×C11—21no—
285C2×C4×C11—21no—
286C2×C4×C11—21no—
287C2×C4×C11—22no—
288C2×C4×C11—22no—
289C2×C4×C11—21no—
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—21no—
297C2×C4×C11—48no—
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×C11C22×D411yescharacteristic
319C2×C4×C11C2×#4111yescharacteristic
320C2×C4×C11C2×#4111yescharacteristic
321C2×C4×C11C2×#4111yescharacteristic
322C2×C4×C11H(5,𝔽2)11yescharacteristic
323C2×C4×C11H(5,𝔽2)11yescharacteristic
324C8×C11—22no—
325C8×C11—22no—
326C8×C11—41no—
327C8×C11—41no—
328C23×Q8C22×C1111yescharacteristic
329C22×SD16C22×C1111yescharacteristic
330C22×SD16C22×C1111yescharacteristic
331C2×#121C22×C1111yescharacteristic
332C2×#117C22×C1111yescharacteristic
333C2×#117C22×C1111yescharacteristic
334#448—24no—
335#433—24no—
336C2×#107C22×C1111yescharacteristic
337C2×#106C22×C1111yescharacteristic
338C2×C4⋊C8C22×C1111yescharacteristic
339C2×C4⋊C8C22×C1111yescharacteristic
340C2×#103C22×C1111yescharacteristic
341C2×#103C22×C1111yescharacteristic
342C2×#103C22×C1111yescharacteristic
343C2×#103C22×C1111yescharacteristic
344C2×#103C22×C1111yescharacteristic
345C2×#103C22×C1111yescharacteristic
346C2×#102C22×C1111yescharacteristic
347C2×#102C22×C1111yescharacteristic
348C2×C22⋊C8C22×C1111yescharacteristic
349C2×C22⋊C8C22×C1111yescharacteristic
350C2×#97C22×C1111yescharacteristic
351C2×C4×C8C22×C1111yescharacteristic
352#399—21no—
353#397—21no—
354#394—21no—
355#394—21no—
356#391—21no—
357#391—21no—
358#391C22×C1111yescharacteristic
359#391C22×C1111yescharacteristic
360#391C22×C1111yescharacteristic
361#391C22×C1111yescharacteristic
362#390C22×C1111yescharacteristic
363#390C22×C1111yescharacteristic
364#389C22×C1111yescharacteristic
365#389C22×C1111yescharacteristic
366#381—21no—
367#381—21no—
368#380C22×C1111yescharacteristic
369#340C22×C1111yescharacteristic
370#340C22×C1111yescharacteristic
371#340C22×C1111yescharacteristic
372#340C22×C1111yescharacteristic
373C22×C11—22no—
374C22×C11—22no—
375C22×C11—22no—
376C22×C11—41no—
377C22×C11—41no—
378C22×C11—41no—
379C22×C11—41no—
380C22×C11—81no—
381C22×C11—81no—
382C22×C11—81no—
383C22×C11—81no—
384C22×C11—81no—
385C22×C11—81no—
386C22×C11—81no—
387C22×C11C2×#12111yescharacteristic
388C22×C11#52511yescharacteristic
389C22×C11#53511yescharacteristic
390C22×C11#57711yescharacteristic
391C22×C11#57711yescharacteristic
392C22×C11#57711yescharacteristic
393C22×C11#57811yescharacteristic
394C4×C11—22no—
395C4×C11—42no—
396C4×C11—42no—
397C4×C11—41no—
398C4×C11—41no—
399C4×C11—41no—
400C4×C11—41no—
401C4×C11—81no—
402C4×C11—81no—
403C4×C11—81no—
404C4×C11—81no—
405C4×C11—81no—
406C4×C11#54611yescharacteristic
407C4×C11#54611yescharacteristic
408C4×C11#55111yescharacteristic
409C4×C11#55111yescharacteristic
410C22×Q8—22no—
411C22×Q8—22no—
412C22×Q8—21no—
413C22×Q8—22no—
414C22×Q8—22no—
415C22×Q8—41no—
416C22×Q8—41no—
417C22×Q8C23×C1111yescharacteristic
418C22×Q8C23×C1111yescharacteristic
419C22×D4—21no—
420C22×D4C23×C1111yescharacteristic
421C23×C4—21no—
422C23×C4C23×C1111yescharacteristic
423C2×SD16—22no—
424C2×SD16—22no—
425C2×SD16—22no—
426C2×SD16—22no—
427C2×SD16—41no—
428C2×SD16—41no—
429C22×C8C23×C1111yescharacteristic
430C22×C8C23×C1111yescharacteristic
431C22×C8C23×C1111yescharacteristic
432C22×C8C23×C1111yescharacteristic
433#121—22no—
434#121—22no—
435#117—22no—
436#117—22no—
437#117—41no—
438#117—41no—
439C2×C4⋊C4—21no—
440C2×C4⋊C4—21no—
441C2×C4⋊C4D4×C1111yescharacteristic
442C2×C4⋊C4D4×C1111yescharacteristic
443C2×C4⋊C4C23×C1111yescharacteristic
444C2×C4⋊C4C23×C1111yescharacteristic
445C2×C4⋊C4C23×C1111yescharacteristic
446C2×C4⋊C4C23×C1111yescharacteristic
447C2×C4⋊C4C23×C1111yescharacteristic
448C2×C22⋊C4—21no—
449C2×C22⋊C4—21no—
450C2×C22⋊C4—21no—
451C2×C22⋊C4—21no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—21no—
455C2×C22⋊C4D4×C1111yescharacteristic
456C2×C22⋊C4D4×C1111yescharacteristic
457C2×C42—21no—
458C2×C42C23×C1111yescharacteristic
459C2×C42C23×C1111yescharacteristic
460#107—41no—
461#106—41no—
462C4⋊C8—22no—
463C4⋊C8—22no—
464#103—22no—
465#103—22no—
466#103—22no—
467#103—22no—
468#103—41no—
469#103—41no—
470#102—41no—
471#102—41no—
472C22⋊C8—22no—
473C22⋊C8D4×C1114yes—
474#97—22no—
475C4×C8—22no—
476#95—21no—
477#95—21no—
478#95—21no—
479#95—21no—
480#95—21no—
481#95—21no—
482#95—21no—
483#95—21no—
484#95—21no—
485#95—21no—
486#95—21no—
487C2×C11—42no—
488C2×C11—161no—
489C2×C11#241111yescharacteristic
490C2×C11#305711yescharacteristic
491C2×C11#306311yescharacteristic
492C2×C11#312111yescharacteristic
493C2×C11#312611yescharacteristic
494C2×C11#322111yescharacteristic
495C2×C11#322511yescharacteristic
496C24—21no—
497C24C2×D4×C1111yescharacteristic
498C2×Q8—24no—
499C2×Q8—21no—
500C2×Q8—21no—
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8—21no—
504C2×Q8—21no—
505C2×Q8—21no—
506C2×Q8—21no—
507C2×Q8—21no—
508C2×Q8—21no—
509C2×Q8—44no—
510C2×Q8—44no—
511C2×Q8—44no—
512C2×Q8—44no—
513C2×Q8—42no—
514C2×Q8—42no—
515C2×Q8C11×#4112yes—
516C2×Q8C11×#4112yes—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—42no—
524C2×D4—81no—
525C2×D4—81no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—24no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—42no—
539C22×C4—42no—
540C22×C4C2×D4×C1111yescharacteristic
541C22×C4C2×D4×C1111yescharacteristic
542C22×C4C2×D4×C1111yescharacteristic
543C22×C4C2×D4×C1111yescharacteristic
544C22×C4C2×D4×C1111yescharacteristic
545C22×C4C2×D4×C1112yes—
546C22×C4C11×#4112yes—
547C22×C4C24×C1111yescharacteristic
548SD16—44no—
549SD16—44no—
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—21no—
560C2×C8C2×D4×C1112yes—
561C2×C8C2×D4×C1112yes—
562C4⋊C4—22no—
563C4⋊C4—22no—
564C4⋊C4—21no—
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—81no—
575C4⋊C4—81no—
576C22⋊C4—22no—
577C22⋊C4—22no—
578C22⋊C4—42no—
579C22⋊C4—42no—
580C22⋊C4—81no—
581C22⋊C4—81no—
582C22⋊C4—81no—
583C22⋊C4—81no—
584C22⋊C4—81no—
585C42—21no—
586C42—21no—
587C42—21no—
588C42—21no—
589C42—42no—
590C11#2451811yescharacteristic, direct product factor, Sylow
591C23—21no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23—41no—
601C23—41no—
602C23—41no—
603C23—41no—
604C23C11×#12112yes—
605C23C22×D4×C1111yescharacteristic
606Q8—22no—
607Q8—22no—
608Q8—22no—
609Q8—22no—
610Q8—48no—
611Q8—41no—
612Q8—41no—
613Q8—41no—
614Q8—41no—
615D4—41no—
616D4—41no—
617D4—41no—
618D4—41no—
619D4—84no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—48no—
641C2×C4—41no—
642C2×C4—41no—
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×C4C11×#12112yes—
661C2×C4C22×D4×C1111yescharacteristic
662C2×C4C2×C11×#4111yescharacteristic
663C2×C4C2×C11×#4111yescharacteristic
664C2×C4C2×C11×#4111yescharacteristic
665C2×C4C11×H(5,𝔽2)11yescharacteristic
666C2×C4C11×H(5,𝔽2)11yescharacteristic
667C8—22no—
668C8—22no—
669C8—41no—
670C8—41no—
671C22—22no—
672C22—22no—
673C22—22no—
674C22—41no—
675C22—41no—
676C22—41no—
677C22—41no—
678C22—81no—
679C22—81no—
680C22—81no—
681C22—81no—
682C22—81no—
683C22—81no—
684C22—81no—
685C22C2×C11×#12111yescharacteristic
686C22C11×#52511yescharacteristic
687C22C11×#53511yescharacteristic
688C22C11×#57711yescharacteristic
689C22C11×#57711yescharacteristic
690C22C11×#57711yescharacteristic
691C22C11×#57811yescharacteristic
692C4—22no—
693C4—42no—
694C4—42no—
695C4—41no—
696C4—41no—
697C4—41no—
698C4—41no—
699C4—81no—
700C4—81no—
701C4—81no—
702C4—81no—
703C4—81no—
704C4C11×#54611yescharacteristic
705C4C11×#54611yescharacteristic
706C4C11×#55111yescharacteristic
707C4C11×#55111yescharacteristic
708C2—42no—
709C2—161no—
710C2C11×#241111yescharacteristic
711C2C11×#305711yescharacteristic
712C2C11×#306311yescharacteristic
713C2C11×#312111yescharacteristic
714C2C11×#312611yescharacteristic
715C2C11×#322111yescharacteristic
716C2C11×#322511yescharacteristic
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×#433C2semidirect
4. C11×#2310C2semidirect
5. C11×#2068C2semidirect
6. C11×#2066C2semidirect
7. C11×#2055C2semidirect
8. C11×#2055C2semidirect
9. C11×#1973C2semidirect
10. C11×#1968C2semidirect
11. C11×#1935C2semidirect
12. C11×#1933C2semidirect
14. C11×#1854C2semidirect
15. C11×#1787C2semidirect
138. #24518C11direct (N × H)
234. C2×#433C2×C11semidirect
236. #2310C2×C11semidirect
237. #2068C2×C11semidirect
238. #2066C2×C11semidirect
239. #2055C2×C11semidirect
240. #2055C2×C11semidirect
241. #1973C2×C11semidirect
242. #1968C2×C11semidirect
243. #1935C2×C11semidirect
244. #1933C2×C11semidirect
246. #1854C2×C11semidirect
247. #1787C2×C11semidirect
590. C11#24518direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4482
C2×C11×#4332
C11×#26242
C11×#23102
C11×#20682
C11×#20662
C11×#20552
C11×#19732
C11×#19682
C11×#19352
C11×#19332
C11×#18752
C11×#18542
C11×#17872
#2451811