Finite Group Databasebeta

← C11×#24898 #14602091

Subgroups — C11×#24898 #14602091

Order 2816.

1016 conjugacy classes of subgroups.

The subgroup lattice has 730 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#448C211yesmaximal, characteristic
2C2×C4×C11×SD16C211yesmaximal, characteristic, complemented
3C11×#2422C211yesmaximal, characteristic
4Q8×C11×C22⋊C4C211yesmaximal, characteristic, complemented
5C11×#2096C211yesmaximal, characteristic, complemented
6C11×#2077C211yesmaximal, characteristic, complemented
7C11×#2055C211yesmaximal, characteristic, complemented
8C11×#2034C211yesmaximal, characteristic
9C11×#1933C211yesmaximal, characteristic, complemented
10C11×#1923C211yesmaximal, characteristic, complemented
11C11×#1880C211yesmaximal, characteristic, complemented
12C11×#1877C211yesmaximal, characteristic, complemented
13C11×#1865C211yesmaximal, characteristic, complemented
14C11×#1803C211yesmaximal, characteristic, complemented
15C11×#1787C211yesmaximal, characteristic, complemented
16C23×Q8×C11C2211yescharacteristic
17C22×C11×SD16C2211yescharacteristic
18C22×C11×SD16C2211yescharacteristic
19C2×C11×#123—21no—
20C2×C11×#121C2211yescharacteristic
21C2×C4×Q8×C11C2211yescharacteristic
22C2×C4×Q8×C11C2211yescharacteristic
23C2×C4×D4×C11C2211yescharacteristic
24C11×#448—24no—
25C4×C11×SD16—24no—
26C2×C11×#106C2211yescharacteristic
27C2×C11×#106C2211yescharacteristic
28C2×C11×C4⋊C8C2211yescharacteristic
29C2×C11×#103C2211yescharacteristic
30C2×C11×#103C2211yescharacteristic
31C2×C11×#103C2211yescharacteristic
32C2×C11×#103C2211yescharacteristic
33C2×C11×#103C2211yescharacteristic
34C2×C11×#103C2211yescharacteristic
35C2×C11×#102C2211yescharacteristic
36C2×C11×#102C2211yescharacteristic
37C2×C11×C22⋊C8C2211yescharacteristic
38C2×C11×C22⋊C8C2211yescharacteristic
39C2×C4×C8×C11C2211yescharacteristic
40C11×#397—21no—
41C11×#394—21no—
42C11×#391—21no—
43C11×#391—21no—
44C11×#391C2211yescharacteristic
45C11×#391C2211yescharacteristic
46C11×#390C2211yescharacteristic
47C11×#389C2211yescharacteristic
48C11×#385—21no—
49C11×#384C2211yescharacteristic
50C11×#380—21no—
51C11×#380C2211yescharacteristic
52C11×#380C2211yescharacteristic
53C4×C11×C22⋊C4—21no—
54C4×C11×C22⋊C4C2211yescharacteristic
55C11×#340C2211yescharacteristic
56C11×#340C2211yescharacteristic
57C11×#340C2211yescharacteristic
58C11×#340C2211yescharacteristic
59C11×#336C2211yescharacteristic
60C11×#336C2211yescharacteristic
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×C11—21no—
74C23×C4×C11C2311yescharacteristic
75C2×C11×SD16—22no—
76C2×C11×SD16—22no—
77C2×C11×SD16—22no—
78C2×C11×SD16—22no—
79C2×C11×SD16—41no—
80C2×C11×SD16D414yes—
81C22×C8×C11C2311yescharacteristic
82C22×C8×C11C2311yescharacteristic
83C22×C8×C11C2311yescharacteristic
84C22×C8×C11C2311yescharacteristic
85C11×#123—44no—
86C11×#121—22no—
87C11×#121—41no—
88C4×Q8×C11—22no—
89C4×Q8×C11—22no—
90C4×Q8×C11—41no—
91C4×Q8×C11—41no—
92C4×D4×C11—22no—
93C4×D4×C11—41no—
94C2×C11×C4⋊C4—21no—
95C2×C11×C4⋊C4—21no—
96C2×C11×C4⋊C4—21no—
97C2×C11×C4⋊C4—21no—
98C2×C11×C4⋊C4—21no—
99C2×C11×C4⋊C4C2311yescharacteristic
100C2×C11×C4⋊C4C2311yescharacteristic
101C2×C11×C4⋊C4C2311yescharacteristic
102C2×C11×C4⋊C4C2311yescharacteristic
103C2×C11×C4⋊C4C2311yescharacteristic
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×C11—21no—
114C2×C42×C11C2311yescharacteristic
115C2×C42×C11C2311yescharacteristic
116C11×#106—22no—
117C11×#106—41no—
118C11×C4⋊C8—41no—
119C11×#103—22no—
120C11×#103—22no—
121C11×#103—22no—
122C11×#103—22no—
123C11×#103—22no—
124C11×#103—41no—
125C11×#102—22no—
126C11×#102—41no—
127C11×C22⋊C8—22no—
128C11×C22⋊C8—41no—
129C4×C8×C11—22no—
130C11×#95—21no—
131C11×#95—21no—
132C11×#95—21no—
133C11×#95—21no—
134C11×#95—21no—
135C11×#95—21no—
136C11×#95—21no—
137C11×#95D411yescharacteristic
138C11×#95D411yescharacteristic
139#24898C1111yesmaximal, characteristic, direct product factor, Sylow
140C24×C11—21no—
141C24×C11C2×D411yescharacteristic
142C2×Q8×C11—24no—
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—42no—
152C2×Q8×C11—42no—
153C2×Q8×C11—44no—
154C2×Q8×C11—44no—
155C2×Q8×C11—44no—
156C2×Q8×C11—44no—
157C2×Q8×C11C2×D412yes—
158C2×Q8×C11#4112yes—
159C2×Q8×C11#4112yes—
160C2×Q8×C11#4112yes—
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—42no—
168C2×D4×C11—81no—
169C2×D4×C11C2×D412yes—
170C22×C4×C11—21no—
171C22×C4×C11—24no—
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—42no—
185C22×C4×C11—42no—
186C22×C4×C11—42no—
187C22×C4×C11—42no—
188C22×C4×C11—81no—
189C22×C4×C11C2×D411yescharacteristic
190C22×C4×C11C2×D411yescharacteristic
191C22×C4×C11C2×D411yescharacteristic
192C22×C4×C11C2×D411yescharacteristic
193C22×C4×C11C2×D411yescharacteristic
194C22×C4×C11C2411yescharacteristic
195C11×SD16—28no—
196C11×SD16—44no—
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—21no—
205C2×C8×C11—21no—
206C2×C8×C11—21no—
207C2×C8×C11—21no—
208C2×C8×C11C2×D412yes—
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—21no—
219C11×C4⋊C4—42no—
220C11×C4⋊C4—42no—
221C11×C4⋊C4—42no—
222C11×C4⋊C4—42no—
223C11×C4⋊C4—81no—
224C11×C22⋊C4—41no—
225C11×C22⋊C4—42no—
226C11×C22⋊C4—42no—
227C11×C22⋊C4—42no—
228C11×C22⋊C4—42no—
229C11×C22⋊C4—42no—
230C11×C22⋊C4—42no—
231C11×C22⋊C4SD1614yescomplemented
232C42×C11—21no—
233C42×C11—21no—
234C42×C11—21no—
235C42×C11—21no—
236C42×C11—42no—
237C42×C11—42no—
238C2×#448C2×C1111yescharacteristic
239C2×C4×SD16C2×C1111yescharacteristic, complemented
240#2422C2×C1111yescharacteristic
241Q8×C22⋊C4C2×C1111yescharacteristic, complemented
242#2096C2×C1111yescharacteristic, complemented
243#2077C2×C1111yescharacteristic, complemented
244#2055C2×C1111yescharacteristic, complemented
245#2034C2×C1111yescharacteristic
246#1933C2×C1111yescharacteristic, complemented
247#1923C2×C1111yescharacteristic, complemented
248#1880C2×C1111yescharacteristic, complemented
249#1877C2×C1111yescharacteristic, complemented
250#1865C2×C1111yescharacteristic, complemented
251#1803C2×C1111yescharacteristic, complemented
252#1787C2×C1111yescharacteristic, complemented
253C23×C11—21no—
254C23×C11—21no—
255C23×C11—21no—
256C23×C11—21no—
257C23×C11—21no—
258C23×C11—21no—
259C23×C11—22no—
260C23×C11—41no—
261C23×C11—41no—
262C23×C11—41no—
263C23×C11—41no—
264C23×C11—41no—
265C23×C11—41no—
266C23×C11C2×SD1612yes—
267C23×C11C22×D411yescharacteristic
268Q8×C11—22no—
269Q8×C11—22no—
270Q8×C11—22no—
271Q8×C11—22no—
272Q8×C11—22no—
273Q8×C11—48no—
274Q8×C11—41no—
275Q8×C11—41no—
276Q8×C11#12314yescomplemented
277D4×C11—22no—
278D4×C11—22no—
279D4×C11—41no—
280D4×C11—41no—
281D4×C11—84no—
282C2×C4×C11—22no—
283C2×C4×C11—21no—
284C2×C4×C11—22no—
285C2×C4×C11—21no—
286C2×C4×C11—22no—
287C2×C4×C11—21no—
288C2×C4×C11—21no—
289C2×C4×C11—22no—
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—21no—
298C2×C4×C11—21no—
299C2×C4×C11—48no—
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—41no—
318C2×C4×C11—41no—
319C2×C4×C11—41no—
320C2×C4×C11—41no—
321C2×C4×C11—84no—
322C2×C4×C11C2×SD1612yes—
323C2×C4×C11C2×SD1612yes—
324C2×C4×C11C22×D411yescharacteristic
325C2×C4×C11C2×#4111yescharacteristic
326C2×C4×C11C2×#4111yescharacteristic
327C2×C4×C11C2×#4111yescharacteristic
328C2×C4×C11H(5,𝔽2)11yescharacteristic
329C2×C4×C11H(5,𝔽2)11yescharacteristic
330C8×C11—22no—
331C8×C11—41no—
332C8×C11—41no—
333C8×C11—41no—
334C23×Q8C22×C1111yescharacteristic
335C22×SD16C22×C1111yescharacteristic
336C22×SD16C22×C1111yescharacteristic
337C2×#123—21no—
338C2×#121C22×C1111yescharacteristic
339C2×C4×Q8C22×C1111yescharacteristic
340C2×C4×Q8C22×C1111yescharacteristic
341C2×C4×D4C22×C1111yescharacteristic
342#448—24no—
343C4×SD16—24no—
344C2×#106C22×C1111yescharacteristic
345C2×#106C22×C1111yescharacteristic
346C2×C4⋊C8C22×C1111yescharacteristic
347C2×#103C22×C1111yescharacteristic
348C2×#103C22×C1111yescharacteristic
349C2×#103C22×C1111yescharacteristic
350C2×#103C22×C1111yescharacteristic
351C2×#103C22×C1111yescharacteristic
352C2×#103C22×C1111yescharacteristic
353C2×#102C22×C1111yescharacteristic
354C2×#102C22×C1111yescharacteristic
355C2×C22⋊C8C22×C1111yescharacteristic
356C2×C22⋊C8C22×C1111yescharacteristic
357C2×C4×C8C22×C1111yescharacteristic
358#397—21no—
359#394—21no—
360#391—21no—
361#391—21no—
362#391C22×C1111yescharacteristic
363#391C22×C1111yescharacteristic
364#390C22×C1111yescharacteristic
365#389C22×C1111yescharacteristic
366#385—21no—
367#384C22×C1111yescharacteristic
368#380—21no—
369#380C22×C1111yescharacteristic
370#380C22×C1111yescharacteristic
371C4×C22⋊C4—21no—
372C4×C22⋊C4C22×C1111yescharacteristic
373#340C22×C1111yescharacteristic
374#340C22×C1111yescharacteristic
375#340C22×C1111yescharacteristic
376#340C22×C1111yescharacteristic
377#336C22×C1111yescharacteristic
378#336C22×C1111yescharacteristic
379C22×C11—22no—
380C22×C11—22no—
381C22×C11—22no—
382C22×C11—41no—
383C22×C11—41no—
384C22×C11—41no—
385C22×C11—41no—
386C22×C11—42no—
387C22×C11—42no—
388C22×C11—42no—
389C22×C11—81no—
390C22×C11—81no—
391C22×C11—81no—
392C22×C11—81no—
393C22×C11#52511yescharacteristic
394C22×C11D4211yescharacteristic
395C22×C11#54611yescharacteristic
396C22×C11C22×SD1611yescharacteristic
397C22×C11#57511yescharacteristic
398C22×C11#57711yescharacteristic
399C22×C11#57811yescharacteristic
400C4×C11—24no—
401C4×C11—22no—
402C4×C11—22no—
403C4×C11—41no—
404C4×C11—42no—
405C4×C11—41no—
406C4×C11—41no—
407C4×C11—81no—
408C4×C11—81no—
409C4×C11—81no—
410C4×C11—81no—
411C4×C11—81no—
412C4×C11C2×#12311yescharacteristic
413C4×C11#53811yescharacteristic
414C4×C11#54611yescharacteristic
415C4×C11#55111yescharacteristic
416C22×Q8—22no—
417C22×Q8—22no—
418C22×Q8—21no—
419C22×Q8—22no—
420C22×Q8—22no—
421C22×Q8—41no—
422C22×Q8—41no—
423C22×Q8C23×C1111yescharacteristic
424C22×Q8C23×C1111yescharacteristic
425C22×D4—21no—
426C22×D4C23×C1111yescharacteristic
427C23×C4—21no—
428C23×C4—21no—
429C23×C4C23×C1111yescharacteristic
430C2×SD16—22no—
431C2×SD16—22no—
432C2×SD16—22no—
433C2×SD16—22no—
434C2×SD16—41no—
435C2×SD16D4×C1114yes—
436C22×C8C23×C1111yescharacteristic
437C22×C8C23×C1111yescharacteristic
438C22×C8C23×C1111yescharacteristic
439C22×C8C23×C1111yescharacteristic
440#123—44no—
441#121—22no—
442#121—41no—
443C4×Q8—22no—
444C4×Q8—22no—
445C4×Q8—41no—
446C4×Q8—41no—
447C4×D4—22no—
448C4×D4—41no—
449C2×C4⋊C4—21no—
450C2×C4⋊C4—21no—
451C2×C4⋊C4—21no—
452C2×C4⋊C4—21no—
453C2×C4⋊C4—21no—
454C2×C4⋊C4C23×C1111yescharacteristic
455C2×C4⋊C4C23×C1111yescharacteristic
456C2×C4⋊C4C23×C1111yescharacteristic
457C2×C4⋊C4C23×C1111yescharacteristic
458C2×C4⋊C4C23×C1111yescharacteristic
459C2×C22⋊C4—21no—
460C2×C22⋊C4—21no—
461C2×C22⋊C4—21no—
462C2×C22⋊C4—21no—
463C2×C22⋊C4—21no—
464C2×C22⋊C4—21no—
465C2×C22⋊C4D4×C1111yescharacteristic
466C2×C22⋊C4D4×C1111yescharacteristic
467C2×C42—21no—
468C2×C42—21no—
469C2×C42C23×C1111yescharacteristic
470C2×C42C23×C1111yescharacteristic
471#106—22no—
472#106—41no—
473C4⋊C8—41no—
474#103—22no—
475#103—22no—
476#103—22no—
477#103—22no—
478#103—22no—
479#103—41no—
480#102—22no—
481#102—41no—
482C22⋊C8—22no—
483C22⋊C8—41no—
484C4×C8—22no—
485#95—21no—
486#95—21no—
487#95—21no—
488#95—21no—
489#95—21no—
490#95—21no—
491#95—21no—
492#95D4×C1111yescharacteristic
493#95D4×C1111yescharacteristic
494C2×C11—42no—
495C2×C11—82no—
496C2×C11#241811yescharacteristic
497C2×C11#310311yescharacteristic
498C2×C11#312111yescharacteristic
499C2×C11#326911yescharacteristic
500C2×C11D4×SD1611yescharacteristic
501C2×C11#329811yescharacteristic
502C2×C11#332611yescharacteristic
503C24—21no—
504C24C2×D4×C1111yescharacteristic
505C2×Q8—24no—
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—42no—
515C2×Q8—42no—
516C2×Q8—44no—
517C2×Q8—44no—
518C2×Q8—44no—
519C2×Q8—44no—
520C2×Q8C2×D4×C1112yes—
521C2×Q8C11×#4112yes—
522C2×Q8C11×#4112yes—
523C2×Q8C11×#4112yes—
524C2×D4—21no—
525C2×D4—21no—
526C2×D4—21no—
527C2×D4—21no—
528C2×D4—21no—
529C2×D4—42no—
530C2×D4—42no—
531C2×D4—81no—
532C2×D4C2×D4×C1112yes—
533C22×C4—21no—
534C22×C4—24no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—42no—
548C22×C4—42no—
549C22×C4—42no—
550C22×C4—42no—
551C22×C4—81no—
552C22×C4C2×D4×C1111yescharacteristic
553C22×C4C2×D4×C1111yescharacteristic
554C22×C4C2×D4×C1111yescharacteristic
555C22×C4C2×D4×C1111yescharacteristic
556C22×C4C2×D4×C1111yescharacteristic
557C22×C4C24×C1111yescharacteristic
558SD16—28no—
559SD16—44no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8C2×D4×C1112yes—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—42no—
583C4⋊C4—42no—
584C4⋊C4—42no—
585C4⋊C4—42no—
586C4⋊C4—81no—
587C22⋊C4—41no—
588C22⋊C4—42no—
589C22⋊C4—42no—
590C22⋊C4—42no—
591C22⋊C4—42no—
592C22⋊C4—42no—
593C22⋊C4—42no—
594C22⋊C4C11×SD1614yescomplemented
595C42—21no—
596C42—21no—
597C42—21no—
598C42—21no—
599C42—42no—
600C42—42no—
601C11#2489811yescharacteristic, direct product factor, Sylow
602C23—21no—
603C23—21no—
604C23—21no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23—22no—
609C23—41no—
610C23—41no—
611C23—41no—
612C23—41no—
613C23—41no—
614C23—41no—
615C23C2×C11×SD1612yes—
616C23C22×D4×C1111yescharacteristic
617Q8—22no—
618Q8—22no—
619Q8—22no—
620Q8—22no—
621Q8—22no—
622Q8—48no—
623Q8—41no—
624Q8—41no—
625Q8C11×#12314yescomplemented
626D4—22no—
627D4—22no—
628D4—41no—
629D4—41no—
630D4—84no—
631C2×C4—22no—
632C2×C4—21no—
633C2×C4—22no—
634C2×C4—21no—
635C2×C4—22no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—22no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—48no—
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×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—84no—
671C2×C4C2×C11×SD1612yes—
672C2×C4C2×C11×SD1612yes—
673C2×C4C22×D4×C1111yescharacteristic
674C2×C4C2×C11×#4111yescharacteristic
675C2×C4C2×C11×#4111yescharacteristic
676C2×C4C2×C11×#4111yescharacteristic
677C2×C4C11×H(5,𝔽2)11yescharacteristic
678C2×C4C11×H(5,𝔽2)11yescharacteristic
679C8—22no—
680C8—41no—
681C8—41no—
682C8—41no—
683C22—22no—
684C22—22no—
685C22—22no—
686C22—41no—
687C22—41no—
688C22—41no—
689C22—41no—
690C22—42no—
691C22—42no—
692C22—42no—
693C22—81no—
694C22—81no—
695C22—81no—
696C22—81no—
697C22C11×#52511yescharacteristic
698C22D42×C1111yescharacteristic
699C22C11×#54611yescharacteristic
700C22C22×C11×SD1611yescharacteristic
701C22C11×#57511yescharacteristic
702C22C11×#57711yescharacteristic
703C22C11×#57811yescharacteristic
704C4—24no—
705C4—22no—
706C4—22no—
707C4—41no—
708C4—42no—
709C4—41no—
710C4—41no—
711C4—81no—
712C4—81no—
713C4—81no—
714C4—81no—
715C4—81no—
716C4C2×C11×#12311yescharacteristic
717C4C11×#53811yescharacteristic
718C4C11×#54611yescharacteristic
719C4C11×#55111yescharacteristic
720C2—42no—
721C2—82no—
722C2C11×#241811yescharacteristic
723C2C11×#310311yescharacteristic
724C2C11×#312111yescharacteristic
725C2C11×#326911yescharacteristic
726C2D4×C11×SD1611yescharacteristic
727C2C11×#329811yescharacteristic
728C2C11×#332611yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#121C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C4×C11×C22⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C4×C11×SD16C2semidirect
4. Q8×C11×C22⋊C4C2semidirect
5. C11×#2096C2semidirect
6. C11×#2077C2semidirect
7. C11×#2055C2semidirect
9. C11×#1933C2semidirect
10. C11×#1923C2semidirect
11. C11×#1880C2semidirect
12. C11×#1877C2semidirect
13. C11×#1865C2semidirect
14. C11×#1803C2semidirect
15. C11×#1787C2semidirect
139. #24898C11direct (N × H)
231. C11×C22⋊C4SD16semidirect
239. C2×C4×SD16C2×C11semidirect
241. Q8×C22⋊C4C2×C11semidirect
242. #2096C2×C11semidirect
243. #2077C2×C11semidirect
244. #2055C2×C11semidirect
246. #1933C2×C11semidirect
247. #1923C2×C11semidirect
248. #1880C2×C11semidirect
249. #1877C2×C11semidirect
250. #1865C2×C11semidirect
251. #1803C2×C11semidirect
252. #1787C2×C11semidirect
276. Q8×C11#123semidirect
594. C22⋊C4C11×SD16semidirect
601. C11#24898direct (N × H)
625. Q8C11×#123semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#4482
C2×C4×C11×SD162
C11×#24222
Q8×C11×C22⋊C42
C11×#20962
C11×#20772
C11×#20552
C11×#20342
C11×#19332
C11×#19232
C11×#18802
C11×#18772
C11×#18652
C11×#18032
C11×#17872
#2489811