Finite Group Databasebeta

← C11×#11067 #14588260

Subgroups — C11×#11067 #14588260

Order 2816.

1066 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×#103C211yesmaximal, characteristic
2C22×C11×#103C211yesmaximal, characteristic
3C2×C11×#391C211yesmaximal, characteristic
4C2×C11×#389C211yesmaximal, characteristic
5C2×C11×#340C211yesmaximal, characteristic
6C2×C11×#340C211yesmaximal, characteristic
7C2×C11×#336C211yesmaximal, characteristic
8C23×Q8×C11C2211yescharacteristic
9C23×C8×C11C2211yescharacteristic
10C23×C8×C11C2211yescharacteristic
11C22×C11×C4⋊C4—21no—
12C22×C11×C4⋊C4C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×C11×C4⋊C4C2211yescharacteristic
15C22×C42×C11C2211yescharacteristic
16C2×C11×#103—22no—
17C2×C11×#103—22no—
18C2×C11×#103—22no—
19C2×C11×#103—22no—
20C2×C11×#103—22no—
21C2×C11×#103C414yescomplemented
22C11×#391—22no—
23C11×#391—22no—
24C11×#389—22no—
25C11×#389—22no—
26C2×C11×#95—21no—
27C2×C11×#95—21no—
28C2×C11×#95—21no—
29C11×#340—22no—
30C11×#340—22no—
31C11×#336—22no—
32C22×Q8×C11—21no—
33C22×Q8×C11—21no—
34C22×Q8×C11—21no—
35C22×Q8×C11—21no—
36C22×Q8×C11—21no—
37C22×Q8×C11—21no—
38C22×Q8×C11—21no—
39C22×Q8×C11—21no—
40C22×Q8×C11—21no—
41C22×Q8×C11—21no—
42C22×Q8×C11—21no—
43C22×Q8×C11C2×C412yes—
44C22×Q8×C11D412yes—
45C22×Q8×C11Q812yes—
46C23×C4×C11—21no—
47C23×C4×C11—21no—
48C23×C4×C11—21no—
49C23×C4×C11—21no—
50C23×C4×C11D411yescharacteristic
51C23×C4×C11D411yescharacteristic
52C23×C4×C11C2311yescharacteristic
53C22×C8×C11—21no—
54C22×C8×C11—21no—
55C22×C8×C11—21no—
56C22×C8×C11—21no—
57C22×C8×C11—21no—
58C22×C8×C11—21no—
59C22×C8×C11—21no—
60C22×C8×C11—21no—
61C22×C8×C11—21no—
62C22×C8×C11—21no—
63C22×C8×C11—21no—
64C22×C8×C11—21no—
65C22×C8×C11C2×C412yes—
66C22×C8×C11D412yes—
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4—24no—
79C2×C11×C4⋊C4—21no—
80C2×C11×C4⋊C4—21no—
81C2×C11×C4⋊C4—42no—
82C2×C11×C4⋊C4—42no—
83C2×C11×C4⋊C4C2×C412yes—
84C2×C11×C4⋊C4D412yes—
85C2×C11×C4⋊C4D412yes—
86C2×C11×C4⋊C4D412yes—
87C2×C11×C4⋊C4D412yes—
88C2×C42×C11—21no—
89C2×C42×C11—21no—
90C2×C42×C11—21no—
91C2×C42×C11—21no—
92C2×C42×C11—21no—
93C2×C42×C11—21no—
94C11×#103—28no—
95C11×#103—28no—
96C11×#95—24no—
97C11×#95—24no—
98C11×#95—24no—
99#11067C1111yesmaximal, characteristic, direct product factor, Sylow
100C24×C11C2×D411yescharacteristic
101C2×Q8×C11—22no—
102C2×Q8×C11—22no—
103C2×Q8×C11—22no—
104C2×Q8×C11—22no—
105C2×Q8×C11—22no—
106C2×Q8×C11—22no—
107C2×Q8×C11—22no—
108C2×Q8×C11—22no—
109C2×Q8×C11—22no—
110C2×Q8×C11—22no—
111C2×Q8×C11—22no—
112C2×Q8×C11—22no—
113C2×Q8×C11—22no—
114C2×Q8×C11—22no—
115C2×Q8×C11—22no—
116C2×Q8×C11—41no—
117C2×Q8×C11—41no—
118C2×Q8×C11—41no—
119C2×Q8×C11—41no—
120C2×Q8×C11—41no—
121C2×Q8×C11—41no—
122C2×Q8×C11—41no—
123C2×Q8×C11—41no—
124C2×Q8×C11—41no—
125C2×Q8×C11—41no—
126C2×Q8×C11—41no—
127C2×Q8×C11—41no—
128C2×Q8×C11C4⋊C414yescomplemented
129C22×C4×C11—22no—
130C22×C4×C11—22no—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—22no—
135C22×C4×C11—22no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—22no—
140C22×C4×C11—22no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—22no—
148C22×C4×C11—22no—
149C22×C4×C11—41no—
150C22×C4×C11—41no—
151C22×C4×C11—41no—
152C22×C4×C11—41no—
153C22×C4×C11—41no—
154C22×C4×C11—41no—
155C22×C4×C11—41no—
156C22×C4×C11—41no—
157C22×C4×C11—41no—
158C22×C4×C11—41no—
159C22×C4×C11—41no—
160C22×C4×C11—41no—
161C22×C4×C11—41no—
162C22×C4×C11—41no—
163C22×C4×C11—41no—
164C22×C4×C11—41no—
165C22×C4×C11—41no—
166C22×C4×C11—41no—
167C22×C4×C11—41no—
168C22×C4×C11—41no—
169C22×C4×C11SD1612yes—
170C22×C4×C11Q1612yes—
171C22×C4×C11C22×C411yescharacteristic
172C22×C4×C11C2×D411yescharacteristic
173C22×C4×C11C2×D411yescharacteristic
174C22×C4×C11C2×D411yescharacteristic
175C22×C4×C11C2×D411yescharacteristic
176C22×C4×C11C2×D411yescharacteristic
177C22×C4×C11C2×D411yescharacteristic
178C22×C4×C11C2×Q811yescharacteristic
179C22×C4×C11#4111yescharacteristic
180C22×C4×C11#4111yescharacteristic
181C22×C4×C11#4111yescharacteristic
182C22×C4×C11#4111yescharacteristic
183C22×C4×C11#4111yescharacteristic
184C22×C4×C11#4111yescharacteristic
185C2×C8×C11—22no—
186C2×C8×C11—22no—
187C2×C8×C11—22no—
188C2×C8×C11—22no—
189C2×C8×C11—22no—
190C2×C8×C11—22no—
191C2×C8×C11—41no—
192C2×C8×C11—41no—
193C2×C8×C11—41no—
194C2×C8×C11—41no—
195C2×C8×C11—41no—
196C2×C8×C11—41no—
197C2×C8×C11—41no—
198C2×C8×C11—41no—
199C11×C4⋊C4—22no—
200C11×C4⋊C4—22no—
201C11×C4⋊C4—22no—
202C11×C4⋊C4—22no—
203C11×C4⋊C4—22no—
204C11×C4⋊C4—22no—
205C11×C4⋊C4—22no—
206C11×C4⋊C4—48no—
207C11×C4⋊C4—41no—
208C11×C4⋊C4—41no—
209C11×C4⋊C4—41no—
210C11×C4⋊C4—41no—
211C11×C4⋊C4C22⋊C414yes—
212C42×C11—41no—
213C42×C11—41no—
214C42×C11—41no—
215C42×C11—41no—
216C22×#103C2×C1111yescharacteristic
217C22×#103C2×C1111yescharacteristic
218C2×#391C2×C1111yescharacteristic
219C2×#389C2×C1111yescharacteristic
220C2×#340C2×C1111yescharacteristic
221C2×#340C2×C1111yescharacteristic
222C2×#336C2×C1111yescharacteristic
223C23×C11C4×D411yescharacteristic
224C23×C11#12011yescharacteristic
225C23×C11#12011yescharacteristic
226C23×C11#12111yescharacteristic
227C23×C11#12111yescharacteristic
228C23×C11C22⋊Q811yescharacteristic
229C23×C11#12411yescharacteristic
230C23×C11C2×SD1611yescharacteristic
231C23×C11C2×Q1611yescharacteristic
232C23×C11#13511yescharacteristic
233C23×C11#13511yescharacteristic
234C23×C11AGL(1,ℤ/8)11yescharacteristic
235C23×C11#13711yescharacteristic
236C23×C11#13711yescharacteristic
237C23×C11#13711yescharacteristic
238Q8×C11—24no—
239Q8×C11—24no—
240Q8×C11—42no—
241Q8×C11—42no—
242Q8×C11—42no—
243Q8×C11—42no—
244Q8×C11—42no—
245Q8×C11—42no—
246C2×C4×C11—24no—
247C2×C4×C11—24no—
248C2×C4×C11—22no—
249C2×C4×C11—22no—
250C2×C4×C11—22no—
251C2×C4×C11—22no—
252C2×C4×C11—22no—
253C2×C4×C11—22no—
254C2×C4×C11—42no—
255C2×C4×C11—42no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11—42no—
259C2×C4×C11—42no—
260C2×C4×C11—42no—
261C2×C4×C11—42no—
262C2×C4×C11—42no—
263C2×C4×C11—42no—
264C2×C4×C11—41no—
265C2×C4×C11—42no—
266C2×C4×C11—41no—
267C2×C4×C11—41no—
268C2×C4×C11—41no—
269C2×C4×C11—42no—
270C2×C4×C11—42no—
271C2×C4×C11—42no—
272C2×C4×C11—41no—
273C2×C4×C11—41no—
274C2×C4×C11—42no—
275C2×C4×C11—42no—
276C2×C4×C11—42no—
277C2×C4×C11—42no—
278C2×C4×C11—42no—
279C2×C4×C11—42no—
280C2×C4×C11—81no—
281C2×C4×C11—81no—
282C2×C4×C11—81no—
283C2×C4×C11—81no—
284C2×C4×C11—81no—
285C2×C4×C11—81no—
286C2×C4×C11—81no—
287C2×C4×C11—81no—
288C2×C4×C11C2×C22⋊C411yescharacteristic
289C2×C4×C11C2×C4⋊C411yescharacteristic
290C2×C4×C11#11711yescharacteristic
291C2×C4×C11C4×D411yescharacteristic
292C2×C4×C11C4×D411yescharacteristic
293C2×C4×C11C4×D411yescharacteristic
294C2×C4×C11#12011yescharacteristic
295C2×C4×C11#12111yescharacteristic
296C2×C4×C11#12111yescharacteristic
297C2×C4×C11#12111yescharacteristic
298C2×C4×C11#12111yescharacteristic
299C2×C4×C11#12111yescharacteristic
300C2×C4×C11#12111yescharacteristic
301C2×C4×C11C22⋊Q811yescharacteristic
302C2×C4×C11C22⋊Q811yescharacteristic
303C2×C4×C11C22⋊Q811yescharacteristic
304C2×C4×C11C22⋊Q811yescharacteristic
305C2×C4×C11C22⋊Q811yescharacteristic
306C2×C4×C11#12311yescharacteristic
307C2×C4×C11#12311yescharacteristic
308C2×C4×C11#12311yescharacteristic
309C2×C4×C11#12311yescharacteristic
310C2×C4×C11#12311yescharacteristic
311C2×C4×C11#12411yescharacteristic
312C2×C4×C11#12411yescharacteristic
313C2×C4×C11#12611yescharacteristic
314C2×C4×C11#12611yescharacteristic
315C2×C4×C11#12711yescharacteristic
316C8×C11—42no—
317C8×C11—42no—
318C23×Q8C22×C1111yescharacteristic
319C23×C8C22×C1111yescharacteristic
320C23×C8C22×C1111yescharacteristic
321C22×C4⋊C4—21no—
322C22×C4⋊C4C22×C1111yescharacteristic
323C22×C4⋊C4C22×C1111yescharacteristic
324C22×C4⋊C4C22×C1111yescharacteristic
325C22×C42C22×C1111yescharacteristic
326C2×#103—22no—
327C2×#103—22no—
328C2×#103—22no—
329C2×#103—22no—
330C2×#103—22no—
331C2×#103C4×C1114yescomplemented
332#391—22no—
333#391—22no—
334#389—22no—
335#389—22no—
336C2×#95—21no—
337C2×#95—21no—
338C2×#95—21no—
339#340—22no—
340#340—22no—
341#336—22no—
342C22×C11#38511yescharacteristic
343C22×C11#38611yescharacteristic
344C22×C11#38811yescharacteristic
345C22×C11#39211yescharacteristic
346C22×C11#39311yescharacteristic
347C22×C11#39411yescharacteristic
348C22×C11#39611yescharacteristic
349C22×C11C4×SD1611yescharacteristic
350C22×C11C4×Q1611yescharacteristic
351C22×C11#44011yescharacteristic
352C22×C11#44111yescharacteristic
353C22×C11#44811yescharacteristic
354C22×C11#44911yescharacteristic
355C22×C11#45011yescharacteristic
356C22×C11#45111yescharacteristic
357C22×C11#45111yescharacteristic
358C22×C11#45211yescharacteristic
359C22×C11#45211yescharacteristic
360C22×C11#45211yescharacteristic
361C22×C11#46111yescharacteristic
362C22×C11#46211yescharacteristic
363C22×C11#46311yescharacteristic
364C22×C11#46411yescharacteristic
365C22×C11#46511yescharacteristic
366C22×C11#46711yescharacteristic
367C22×C11#46811yescharacteristic
368C22×C11#47011yescharacteristic
369C22×C11#47511yescharacteristic
370C22×C11#47711yescharacteristic
371C22×C11#47911yescharacteristic
372C22×C11#47911yescharacteristic
373C22×C11#48711yescharacteristic
374C22×C11#48811yescharacteristic
375C22×C11#48911yescharacteristic
376C22×C11#49111yescharacteristic
377C4×C11—44no—
378C4×C11—44no—
379C4×C11—42no—
380C4×C11—42no—
381C4×C11—82no—
382C4×C11—82no—
383C4×C11#38011yescharacteristic
384C4×C11#38511yescharacteristic
385C4×C11#38811yescharacteristic
386C4×C11#39011yescharacteristic
387C4×C11#39411yescharacteristic
388C4×C11#39611yescharacteristic
389C4×C11#39711yescharacteristic
390C4×C11#39911yescharacteristic
391C22×Q8—21no—
392C22×Q8—21no—
393C22×Q8—21no—
394C22×Q8—21no—
395C22×Q8—21no—
396C22×Q8—21no—
397C22×Q8—21no—
398C22×Q8—21no—
399C22×Q8—21no—
400C22×Q8—21no—
401C22×Q8—21no—
402C22×Q8C2×C4×C1112yes—
403C22×Q8D4×C1112yes—
404C22×Q8Q8×C1112yes—
405C23×C4—21no—
406C23×C4—21no—
407C23×C4—21no—
408C23×C4—21no—
409C23×C4D4×C1111yescharacteristic
410C23×C4D4×C1111yescharacteristic
411C23×C4C23×C1111yescharacteristic
412C22×C8—21no—
413C22×C8—21no—
414C22×C8—21no—
415C22×C8—21no—
416C22×C8—21no—
417C22×C8—21no—
418C22×C8—21no—
419C22×C8—21no—
420C22×C8—21no—
421C22×C8—21no—
422C22×C8—21no—
423C22×C8—21no—
424C22×C8C2×C4×C1112yes—
425C22×C8D4×C1112yes—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—21no—
433C2×C4⋊C4—21no—
434C2×C4⋊C4—21no—
435C2×C4⋊C4—21no—
436C2×C4⋊C4—21no—
437C2×C4⋊C4—24no—
438C2×C4⋊C4—21no—
439C2×C4⋊C4—21no—
440C2×C4⋊C4—42no—
441C2×C4⋊C4—42no—
442C2×C4⋊C4C2×C4×C1112yes—
443C2×C4⋊C4D4×C1112yes—
444C2×C4⋊C4D4×C1112yes—
445C2×C4⋊C4D4×C1112yes—
446C2×C4⋊C4D4×C1112yes—
447C2×C42—21no—
448C2×C42—21no—
449C2×C42—21no—
450C2×C42—21no—
451C2×C42—21no—
452C2×C42—21no—
453#103—28no—
454#103—28no—
455#95—24no—
456#95—24no—
457#95—24no—
458C2×C11#143911yescharacteristic
459C2×C11#186311yescharacteristic
460C2×C11#186511yescharacteristic
461C2×C11#187711yescharacteristic
462C2×C11#187811yescharacteristic
463C2×C11#193311yescharacteristic
464C2×C11#193511yescharacteristic
465C2×C11#200011yescharacteristic
466C2×C11#200111yescharacteristic
467C2×C11#202411yescharacteristic
468C2×C11#202611yescharacteristic
469C2×C11#204211yescharacteristic
470C2×C11#204311yescharacteristic
471C2×C11#206611yescharacteristic
472C2×C11#206811yescharacteristic
473C24C2×D4×C1111yescharacteristic
474C2×Q8—22no—
475C2×Q8—22no—
476C2×Q8—22no—
477C2×Q8—22no—
478C2×Q8—22no—
479C2×Q8—22no—
480C2×Q8—22no—
481C2×Q8—22no—
482C2×Q8—22no—
483C2×Q8—22no—
484C2×Q8—22no—
485C2×Q8—22no—
486C2×Q8—22no—
487C2×Q8—22no—
488C2×Q8—22no—
489C2×Q8—41no—
490C2×Q8—41no—
491C2×Q8—41no—
492C2×Q8—41no—
493C2×Q8—41no—
494C2×Q8—41no—
495C2×Q8—41no—
496C2×Q8—41no—
497C2×Q8—41no—
498C2×Q8—41no—
499C2×Q8—41no—
500C2×Q8—41no—
501C2×Q8C11×C4⋊C414yescomplemented
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—41no—
523C22×C4—41no—
524C22×C4—41no—
525C22×C4—41no—
526C22×C4—41no—
527C22×C4—41no—
528C22×C4—41no—
529C22×C4—41no—
530C22×C4—41no—
531C22×C4—41no—
532C22×C4—41no—
533C22×C4—41no—
534C22×C4—41no—
535C22×C4—41no—
536C22×C4—41no—
537C22×C4—41no—
538C22×C4—41no—
539C22×C4—41no—
540C22×C4—41no—
541C22×C4—41no—
542C22×C4C11×SD1612yes—
543C22×C4C11×Q1612yes—
544C22×C4C22×C4×C1111yescharacteristic
545C22×C4C2×D4×C1111yescharacteristic
546C22×C4C2×D4×C1111yescharacteristic
547C22×C4C2×D4×C1111yescharacteristic
548C22×C4C2×D4×C1111yescharacteristic
549C22×C4C2×D4×C1111yescharacteristic
550C22×C4C2×D4×C1111yescharacteristic
551C22×C4C2×Q8×C1111yescharacteristic
552C22×C4C11×#4111yescharacteristic
553C22×C4C11×#4111yescharacteristic
554C22×C4C11×#4111yescharacteristic
555C22×C4C11×#4111yescharacteristic
556C22×C4C11×#4111yescharacteristic
557C22×C4C11×#4111yescharacteristic
558C2×C8—22no—
559C2×C8—22no—
560C2×C8—22no—
561C2×C8—22no—
562C2×C8—22no—
563C2×C8—22no—
564C2×C8—41no—
565C2×C8—41no—
566C2×C8—41no—
567C2×C8—41no—
568C2×C8—41no—
569C2×C8—41no—
570C2×C8—41no—
571C2×C8—41no—
572C4⋊C4—22no—
573C4⋊C4—22no—
574C4⋊C4—22no—
575C4⋊C4—22no—
576C4⋊C4—22no—
577C4⋊C4—22no—
578C4⋊C4—22no—
579C4⋊C4—48no—
580C4⋊C4—41no—
581C4⋊C4—41no—
582C4⋊C4—41no—
583C4⋊C4—41no—
584C4⋊C4C11×C22⋊C414yes—
585C42—41no—
586C42—41no—
587C42—41no—
588C42—41no—
589C11#1106711yescharacteristic, direct product factor, Sylow
590C23C4×D4×C1111yescharacteristic
591C23C11×#12011yescharacteristic
592C23C11×#12011yescharacteristic
593C23C11×#12111yescharacteristic
594C23C11×#12111yescharacteristic
595C23C11×C22⋊Q811yescharacteristic
596C23C11×#12411yescharacteristic
597C23C2×C11×SD1611yescharacteristic
598C23C2×C11×Q1611yescharacteristic
599C23C11×#13511yescharacteristic
600C23C11×#13511yescharacteristic
601C23C11×AGL(1,ℤ/8)11yescharacteristic
602C23C11×#13711yescharacteristic
603C23C11×#13711yescharacteristic
604C23C11×#13711yescharacteristic
605Q8—24no—
606Q8—24no—
607Q8—42no—
608Q8—42no—
609Q8—42no—
610Q8—42no—
611Q8—42no—
612Q8—42no—
613C2×C4—24no—
614C2×C4—24no—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—42no—
622C2×C4—42no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—42no—
626C2×C4—42no—
627C2×C4—42no—
628C2×C4—42no—
629C2×C4—42no—
630C2×C4—42no—
631C2×C4—41no—
632C2×C4—42no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—42no—
637C2×C4—42no—
638C2×C4—42no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—42no—
642C2×C4—42no—
643C2×C4—42no—
644C2×C4—42no—
645C2×C4—42no—
646C2×C4—42no—
647C2×C4—81no—
648C2×C4—81no—
649C2×C4—81no—
650C2×C4—81no—
651C2×C4—81no—
652C2×C4—81no—
653C2×C4—81no—
654C2×C4—81no—
655C2×C4C2×C11×C22⋊C411yescharacteristic
656C2×C4C2×C11×C4⋊C411yescharacteristic
657C2×C4C11×#11711yescharacteristic
658C2×C4C4×D4×C1111yescharacteristic
659C2×C4C4×D4×C1111yescharacteristic
660C2×C4C4×D4×C1111yescharacteristic
661C2×C4C11×#12011yescharacteristic
662C2×C4C11×#12111yescharacteristic
663C2×C4C11×#12111yescharacteristic
664C2×C4C11×#12111yescharacteristic
665C2×C4C11×#12111yescharacteristic
666C2×C4C11×#12111yescharacteristic
667C2×C4C11×#12111yescharacteristic
668C2×C4C11×C22⋊Q811yescharacteristic
669C2×C4C11×C22⋊Q811yescharacteristic
670C2×C4C11×C22⋊Q811yescharacteristic
671C2×C4C11×C22⋊Q811yescharacteristic
672C2×C4C11×C22⋊Q811yescharacteristic
673C2×C4C11×#12311yescharacteristic
674C2×C4C11×#12311yescharacteristic
675C2×C4C11×#12311yescharacteristic
676C2×C4C11×#12311yescharacteristic
677C2×C4C11×#12311yescharacteristic
678C2×C4C11×#12411yescharacteristic
679C2×C4C11×#12411yescharacteristic
680C2×C4C11×#12611yescharacteristic
681C2×C4C11×#12611yescharacteristic
682C2×C4C11×#12711yescharacteristic
683C8—42no—
684C8—42no—
685C22C11×#38511yescharacteristic
686C22C11×#38611yescharacteristic
687C22C11×#38811yescharacteristic
688C22C11×#39211yescharacteristic
689C22C11×#39311yescharacteristic
690C22C11×#39411yescharacteristic
691C22C11×#39611yescharacteristic
692C22C4×C11×SD1611yescharacteristic
693C22C4×C11×Q1611yescharacteristic
694C22C11×#44011yescharacteristic
695C22C11×#44111yescharacteristic
696C22C11×#44811yescharacteristic
697C22C11×#44911yescharacteristic
698C22C11×#45011yescharacteristic
699C22C11×#45111yescharacteristic
700C22C11×#45111yescharacteristic
701C22C11×#45211yescharacteristic
702C22C11×#45211yescharacteristic
703C22C11×#45211yescharacteristic
704C22C11×#46111yescharacteristic
705C22C11×#46211yescharacteristic
706C22C11×#46311yescharacteristic
707C22C11×#46411yescharacteristic
708C22C11×#46511yescharacteristic
709C22C11×#46711yescharacteristic
710C22C11×#46811yescharacteristic
711C22C11×#47011yescharacteristic
712C22C11×#47511yescharacteristic
713C22C11×#47711yescharacteristic
714C22C11×#47911yescharacteristic
715C22C11×#47911yescharacteristic
716C22C11×#48711yescharacteristic
717C22C11×#48811yescharacteristic
718C22C11×#48911yescharacteristic
719C22C11×#49111yescharacteristic
720C4—44no—
721C4—44no—
722C4—42no—
723C4—42no—
724C4—82no—
725C4—82no—
726C4C11×#38011yescharacteristic
727C4C11×#38511yescharacteristic
728C4C11×#38811yescharacteristic
729C4C11×#39011yescharacteristic
730C4C11×#39411yescharacteristic
731C4C11×#39611yescharacteristic
732C4C11×#39711yescharacteristic
733C4C11×#39911yescharacteristic
734C2C11×#143911yescharacteristic
735C2C11×#186311yescharacteristic
736C2C11×#186511yescharacteristic
737C2C11×#187711yescharacteristic
738C2C11×#187811yescharacteristic
739C2C11×#193311yescharacteristic
740C2C11×#193511yescharacteristic
741C2C11×#200011yescharacteristic
742C2C11×#200111yescharacteristic
743C2C11×#202411yescharacteristic
744C2C11×#202611yescharacteristic
745C2C11×#204211yescharacteristic
746C2C11×#204311yescharacteristic
747C2C11×#206611yescharacteristic
748C2C11×#206811yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C11C2×D4
commutatorC22×C4C22×C4×C11
Frattini, cosocleC23×C4C23×C11
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24×C11 ◁ C22×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
21. C2×C11×#103C4semidirect
99. #11067C11direct (N × H)
128. C2×Q8×C11C4⋊C4semidirect
331. C2×#103C4×C11semidirect
501. C2×Q8C11×C4⋊C4semidirect
589. C11#11067direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C11×#1032
C2×C11×#3912
C2×C11×#3892
C2×C11×#3402
C2×C11×#3362
#1106711