Finite Group Databasebeta

← C11×#24017 #14601210

Subgroups — C11×#24017 #14601210

Order 2816.

1340 conjugacy classes of subgroups.

The subgroup lattice has 870 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#537C211yesmaximal, characteristic
2C2×C11×#485C211yesmaximal, characteristic, complemented
3C2×C11×#482C211yesmaximal, characteristic, complemented
4C11×#2311C211yesmaximal, characteristic, complemented
5C11×#2036C211yesmaximal, characteristic, complemented
6C11×#2035C211yesmaximal, characteristic, complemented
7C11×#2034C211yesmaximal, characteristic, complemented
8C11×#2033C211yesmaximal, characteristic, complemented
9C11×#1874C211yesmaximal, characteristic, complemented
10C11×#1872C211yesmaximal, characteristic, complemented
11C11×#1853C211yesmaximal, characteristic, complemented
12C11×#1852C211yesmaximal, characteristic, complemented
13C11×#1788C211yesmaximal, characteristic, complemented
14C11×#1788C211yesmaximal, characteristic, complemented
15C11×#1780C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic
17C22×C11×#41C2211yescharacteristic
18C11×#537—24no—
19C11×#537—24no—
20C2×C11×C22⋊Q8—21no—
21C2×C11×C22⋊Q8C2211yescharacteristic
22C2×C11×C22⋊Q8C2211yescharacteristic
23C2×C11×#121—21no—
24C2×C11×#121—21no—
25C2×C11×#121—21no—
26C2×C11×#121C2211yescharacteristic
27C2×C11×#121C2211yescharacteristic
28C2×C11×#117C2211yescharacteristic
29C22×C11×C4⋊C4C2211yescharacteristic
30C22×C11×C4⋊C4C2211yescharacteristic
31C11×#485—24no—
32C11×#482—24no—
33C2×C11×#107C2211yescharacteristic
34C2×C11×#107C2211yescharacteristic
35C2×C11×#106C2211yescharacteristic
36C2×C11×#106C2211yescharacteristic
37C2×C11×#103C2211yescharacteristic
38C2×C11×#103C2211yescharacteristic
39C2×C11×#103C2211yescharacteristic
40C2×C11×#103C2211yescharacteristic
41C2×C11×#102C2211yescharacteristic
42C2×C11×#102C2211yescharacteristic
43C2×C11×#102C2211yescharacteristic
44C2×C11×#102C2211yescharacteristic
45C2×C11×C22⋊C8C2211yescharacteristic
46C2×C11×C22⋊C8C2211yescharacteristic
47C2×C11×C22⋊C8C2211yescharacteristic
48C2×C11×C22⋊C8C2211yescharacteristic
49C2×C11×C22⋊C8C2211yescharacteristic
50C2×C11×C22⋊C8C2211yescharacteristic
51C11×#391—21no—
52C11×#390—21no—
53C11×#386—21no—
54C11×#386—21no—
55C11×#380C2211yescharacteristic
56C11×#380C2211yescharacteristic
57C11×#380C2211yescharacteristic
58C11×#380C2211yescharacteristic
59C11×#340C2211yescharacteristic
60C11×#340C2211yescharacteristic
61C11×#340C2211yescharacteristic
62C11×#340C2211yescharacteristic
63C2×C11×#41—22no—
64C2×C11×#41—22no—
65C2×C11×#41—22no—
66C2×C11×#41—22no—
67C2×C11×#41—22no—
68C2×C11×#41—22no—
69C2×C11×#41—22no—
70C2×C11×#41—22no—
71C2×C11×#41—41no—
72C2×C11×#41—41no—
73C2×C11×#41—41no—
74C2×C11×#41—41no—
75C22×Q8×C11D411yescharacteristic
76C22×Q8×C11C2311yescharacteristic
77C22×D4×C11—21no—
78C22×D4×C11—21no—
79C22×D4×C11—21no—
80C22×D4×C11D411yescharacteristic
81C22×D4×C11D411yescharacteristic
82C22×D4×C11D411yescharacteristic
83C22×D4×C11C2311yescharacteristic
84C23×C4×C11—21no—
85C23×C4×C11—21no—
86C23×C4×C11—21no—
87C23×C4×C11C2311yescharacteristic
88C23×C4×C11C2311yescharacteristic
89C23×C4×C11C2311yescharacteristic
90C22×C8×C11C2311yescharacteristic
91C22×C8×C11C2311yescharacteristic
92C22×C8×C11C2311yescharacteristic
93C22×C8×C11C2311yescharacteristic
94C11×C22⋊Q8—28no—
95C11×C22⋊Q8—22no—
96C11×C22⋊Q8—22no—
97C11×C22⋊Q8—22no—
98C11×C22⋊Q8D414yes—
99C11×#121—28no—
100C11×#121—28no—
101C11×#121—28no—
102C11×#121—22no—
103C11×#121—22no—
104C11×#121—22no—
105C11×#121D414yes—
106C11×#117—22no—
107C11×#117—22no—
108C2×C11×C4⋊C4—21no—
109C2×C11×C4⋊C4—21no—
110C2×C11×C4⋊C4—21no—
111C2×C11×C4⋊C4—22no—
112C2×C11×C4⋊C4—22no—
113C2×C11×C4⋊C4—21no—
114C2×C11×C4⋊C4—41no—
115C2×C11×C4⋊C4—41no—
116C2×C11×C4⋊C4C2311yescharacteristic
117C2×C11×C4⋊C4C2311yescharacteristic
118C2×C11×C4⋊C4C2311yescharacteristic
119C2×C11×C4⋊C4C2311yescharacteristic
120C2×C11×C4⋊C4C2311yescharacteristic
121C2×C11×C4⋊C4C2311yescharacteristic
122C2×C11×C22⋊C4—21no—
123C2×C11×C22⋊C4—21no—
124C2×C11×C22⋊C4—21no—
125C2×C11×C22⋊C4—21no—
126C2×C11×C22⋊C4—21no—
127C2×C11×C22⋊C4—21no—
128C2×C11×C22⋊C4—21no—
129C2×C11×C22⋊C4—21no—
130C2×C11×C22⋊C4—21no—
131C2×C42×C11—21no—
132C11×#107—22no—
133C11×#107—22no—
134C11×#106—22no—
135C11×#106—22no—
136C11×#103—22no—
137C11×#103—22no—
138C11×#103—41no—
139C11×#103—41no—
140C11×#102—22no—
141C11×#102—22no—
142C11×#102—41no—
143C11×#102—41no—
144C11×C22⋊C8—22no—
145C11×C22⋊C8—22no—
146C11×C22⋊C8—22no—
147C11×C22⋊C8—22no—
148C11×C22⋊C8—41no—
149C11×C22⋊C8—41no—
150C11×#95—21no—
151C11×#95—21no—
152C11×#95—21no—
153C11×#95—21no—
154#24017C1111yesmaximal, characteristic, direct product factor, Sylow
155C24×C11—21no—
156C24×C11C2×D411yescharacteristic
157C24×C11C2×D411yescharacteristic
158C24×C11C2×D411yescharacteristic
159C11×#41—44no—
160C11×#41—44no—
161C11×#41—44no—
162C11×#41—44no—
163C11×#41—44no—
164C11×#41—44no—
165C11×#41—44no—
166C11×#41—44no—
167C2×Q8×C11—22no—
168C2×Q8×C11—22no—
169C2×Q8×C11—21no—
170C2×Q8×C11—21no—
171C2×Q8×C11—21no—
172C2×Q8×C11—21no—
173C2×Q8×C11—21no—
174C2×Q8×C11—41no—
175C2×Q8×C11C2×D412yes—
176C2×D4×C11—24no—
177C2×D4×C11—22no—
178C2×D4×C11—22no—
179C2×D4×C11—22no—
180C2×D4×C11—22no—
181C2×D4×C11—24no—
182C2×D4×C11—24no—
183C2×D4×C11—22no—
184C2×D4×C11—22no—
185C2×D4×C11—21no—
186C2×D4×C11—21no—
187C2×D4×C11—21no—
188C2×D4×C11—21no—
189C2×D4×C11—21no—
190C2×D4×C11—41no—
191C2×D4×C11—41no—
192C2×D4×C11—41no—
193C2×D4×C11—42no—
194C2×D4×C11—42no—
195C2×D4×C11—81no—
196C2×D4×C11—81no—
197C2×D4×C11—81no—
198C2×D4×C11—81no—
199C2×D4×C11C2×D412yes—
200C22×C4×C11—21no—
201C22×C4×C11—21no—
202C22×C4×C11—21no—
203C22×C4×C11—21no—
204C22×C4×C11—21no—
205C22×C4×C11—21no—
206C22×C4×C11—21no—
207C22×C4×C11—21no—
208C22×C4×C11—24no—
209C22×C4×C11—21no—
210C22×C4×C11—21no—
211C22×C4×C11—21no—
212C22×C4×C11—24no—
213C22×C4×C11—21no—
214C22×C4×C11—21no—
215C22×C4×C11—21no—
216C22×C4×C11—21no—
217C22×C4×C11—21no—
218C22×C4×C11—21no—
219C22×C4×C11—21no—
220C22×C4×C11—21no—
221C22×C4×C11—21no—
222C22×C4×C11—21no—
223C22×C4×C11—42no—
224C22×C4×C11—42no—
225C22×C4×C11—42no—
226C22×C4×C11—81no—
227C22×C4×C11—81no—
228C22×C4×C11—81no—
229C22×C4×C11—81no—
230C22×C4×C11C2×D411yescharacteristic
231C22×C4×C11C2×D411yescharacteristic
232C22×C4×C11C2×D412yes—
233C22×C4×C11C2×D412yes—
234C22×C4×C11C2×D411yescharacteristic
235C22×C4×C11#4112yes—
236C22×C4×C11#4112yes—
237C22×C4×C11C2411yescharacteristic
238C2×C8×C11—21no—
239C2×C8×C11—21no—
240C2×C8×C11—21no—
241C2×C8×C11—21no—
242C2×C8×C11—21no—
243C2×C8×C11—21no—
244C2×C8×C11—21no—
245C2×C8×C11—21no—
246C2×C8×C11—21no—
247C2×C8×C11—21no—
248C2×C8×C11—21no—
249C2×C8×C11—21no—
250C11×C4⋊C4—24no—
251C11×C4⋊C4—24no—
252C11×C4⋊C4—24no—
253C11×C4⋊C4—21no—
254C11×C4⋊C4—21no—
255C11×C4⋊C4—21no—
256C11×C4⋊C4—21no—
257C11×C4⋊C4—21no—
258C11×C4⋊C4—21no—
259C11×C4⋊C4—21no—
260C11×C4⋊C4—21no—
261C11×C4⋊C4—21no—
262C11×C4⋊C4—21no—
263C11×C4⋊C4—42no—
264C11×C4⋊C4C2×D412yes—
265C11×C4⋊C4C2×D412yes—
266C11×C22⋊C4—24no—
267C11×C22⋊C4—24no—
268C11×C22⋊C4—24no—
269C11×C22⋊C4—24no—
270C11×C22⋊C4—42no—
271C11×C22⋊C4—81no—
272C11×C22⋊C4—81no—
273C11×C22⋊C4—81no—
274C11×C22⋊C4—81no—
275C42×C11—42no—
276C2×#537C2×C1111yescharacteristic
277C2×#485C2×C1111yescharacteristic, complemented
278C2×#482C2×C1111yescharacteristic, complemented
279#2311C2×C1111yescharacteristic, complemented
280#2036C2×C1111yescharacteristic, complemented
281#2035C2×C1111yescharacteristic, complemented
282#2034C2×C1111yescharacteristic, complemented
283#2033C2×C1111yescharacteristic, complemented
284#1874C2×C1111yescharacteristic, complemented
285#1872C2×C1111yescharacteristic, complemented
286#1853C2×C1111yescharacteristic, complemented
287#1852C2×C1111yescharacteristic, complemented
288#1788C2×C1111yescharacteristic, complemented
289#1788C2×C1111yescharacteristic, complemented
290#1780C2×C1111yescharacteristic, complemented
291C23×C11—21no—
292C23×C11—21no—
293C23×C11—21no—
294C23×C11—21no—
295C23×C11—21no—
296C23×C11—21no—
297C23×C11—21no—
298C23×C11—21no—
299C23×C11—21no—
300C23×C11—21no—
301C23×C11—21no—
302C23×C11—21no—
303C23×C11—21no—
304C23×C11—22no—
305C23×C11—21no—
306C23×C11—21no—
307C23×C11—21no—
308C23×C11—21no—
309C23×C11—21no—
310C23×C11—21no—
311C23×C11—41no—
312C23×C11—41no—
313C23×C11—41no—
314C23×C11—41no—
315C23×C11—41no—
316C23×C11—41no—
317C23×C11#12012yes—
318C23×C11#12312yes—
319C23×C11C22×D411yescharacteristic
320Q8×C11—22no—
321Q8×C11—22no—
322Q8×C11—44no—
323Q8×C11—41no—
324Q8×C11—41no—
325D4×C11—22no—
326D4×C11—22no—
327D4×C11—44no—
328D4×C11—44no—
329D4×C11—44no—
330D4×C11—48no—
331D4×C11—41no—
332D4×C11—41no—
333D4×C11—84no—
334D4×C11—84no—
335C2×C4×C11—21no—
336C2×C4×C11—21no—
337C2×C4×C11—21no—
338C2×C4×C11—21no—
339C2×C4×C11—22no—
340C2×C4×C11—22no—
341C2×C4×C11—22no—
342C2×C4×C11—22no—
343C2×C4×C11—22no—
344C2×C4×C11—22no—
345C2×C4×C11—22no—
346C2×C4×C11—22no—
347C2×C4×C11—22no—
348C2×C4×C11—22no—
349C2×C4×C11—22no—
350C2×C4×C11—21no—
351C2×C4×C11—21no—
352C2×C4×C11—21no—
353C2×C4×C11—48no—
354C2×C4×C11—41no—
355C2×C4×C11—41no—
356C2×C4×C11—41no—
357C2×C4×C11—41no—
358C2×C4×C11—41no—
359C2×C4×C11—41no—
360C2×C4×C11—41no—
361C2×C4×C11—41no—
362C2×C4×C11—41no—
363C2×C4×C11—41no—
364C2×C4×C11—41no—
365C2×C4×C11—41no—
366C2×C4×C11—41no—
367C2×C4×C11—41no—
368C2×C4×C11—41no—
369C2×C4×C11—41no—
370C2×C4×C11—41no—
371C2×C4×C11—41no—
372C2×C4×C11—41no—
373C2×C4×C11—41no—
374C2×C4×C11—41no—
375C2×C4×C11—41no—
376C2×C4×C11—84no—
377C2×C4×C11—84no—
378C2×C4×C11#12012yes—
379C2×C4×C11#12312yes—
380C2×C4×C11C22×D411yescharacteristic
381C2×C4×C11C22×D411yescharacteristic
382C2×C4×C11C2×#4111yescharacteristic
383C2×C4×C11C2×#4111yescharacteristic
384C2×C4×C11H(5,𝔽2)11yescharacteristic
385C2×C4×C11H(5,𝔽2)11yescharacteristic
386C8×C11—41no—
387C8×C11—41no—
388C8×C11—41no—
389C8×C11—41no—
390C22×#41C22×C1111yescharacteristic
391C22×#41C22×C1111yescharacteristic
392#537—24no—
393#537—24no—
394C2×C22⋊Q8—21no—
395C2×C22⋊Q8C22×C1111yescharacteristic
396C2×C22⋊Q8C22×C1111yescharacteristic
397C2×#121—21no—
398C2×#121—21no—
399C2×#121—21no—
400C2×#121C22×C1111yescharacteristic
401C2×#121C22×C1111yescharacteristic
402C2×#117C22×C1111yescharacteristic
403C22×C4⋊C4C22×C1111yescharacteristic
404C22×C4⋊C4C22×C1111yescharacteristic
405#485—24no—
406#482—24no—
407C2×#107C22×C1111yescharacteristic
408C2×#107C22×C1111yescharacteristic
409C2×#106C22×C1111yescharacteristic
410C2×#106C22×C1111yescharacteristic
411C2×#103C22×C1111yescharacteristic
412C2×#103C22×C1111yescharacteristic
413C2×#103C22×C1111yescharacteristic
414C2×#103C22×C1111yescharacteristic
415C2×#102C22×C1111yescharacteristic
416C2×#102C22×C1111yescharacteristic
417C2×#102C22×C1111yescharacteristic
418C2×#102C22×C1111yescharacteristic
419C2×C22⋊C8C22×C1111yescharacteristic
420C2×C22⋊C8C22×C1111yescharacteristic
421C2×C22⋊C8C22×C1111yescharacteristic
422C2×C22⋊C8C22×C1111yescharacteristic
423C2×C22⋊C8C22×C1111yescharacteristic
424C2×C22⋊C8C22×C1111yescharacteristic
425#391—21no—
426#390—21no—
427#386—21no—
428#386—21no—
429#380C22×C1111yescharacteristic
430#380C22×C1111yescharacteristic
431#380C22×C1111yescharacteristic
432#380C22×C1111yescharacteristic
433#340C22×C1111yescharacteristic
434#340C22×C1111yescharacteristic
435#340C22×C1111yescharacteristic
436#340C22×C1111yescharacteristic
437C22×C11—22no—
438C22×C11—22no—
439C22×C11—22no—
440C22×C11—22no—
441C22×C11—22no—
442C22×C11—22no—
443C22×C11—41no—
444C22×C11—41no—
445C22×C11—41no—
446C22×C11—41no—
447C22×C11—41no—
448C22×C11—41no—
449C22×C11—41no—
450C22×C11—41no—
451C22×C11—41no—
452C22×C11—41no—
453C22×C11—42no—
454C22×C11—41no—
455C22×C11—41no—
456C22×C11—41no—
457C22×C11—41no—
458C22×C11—42no—
459C22×C11—41no—
460C22×C11—42no—
461C22×C11—81no—
462C22×C11—81no—
463C22×C11—81no—
464C22×C11—81no—
465C22×C11C2×#12011yescharacteristic
466C22×C11C2×#12311yescharacteristic
467C22×C11#53411yescharacteristic
468C22×C11#57611yescharacteristic
469C22×C11#57711yescharacteristic
470C22×C11#57711yescharacteristic
471C22×C11#57811yescharacteristic
472C4×C11—22no—
473C4×C11—22no—
474C4×C11—41no—
475C4×C11—42no—
476C4×C11—42no—
477C4×C11—42no—
478C4×C11—81no—
479C4×C11—81no—
480C4×C11—81no—
481C4×C11—81no—
482C4×C11#54611yescharacteristic
483C4×C11#54611yescharacteristic
484C4×C11#54611yescharacteristic
485C4×C11#54611yescharacteristic
486C2×#41—22no—
487C2×#41—22no—
488C2×#41—22no—
489C2×#41—22no—
490C2×#41—22no—
491C2×#41—22no—
492C2×#41—22no—
493C2×#41—22no—
494C2×#41—41no—
495C2×#41—41no—
496C2×#41—41no—
497C2×#41—41no—
498C22×Q8D4×C1111yescharacteristic
499C22×Q8C23×C1111yescharacteristic
500C22×D4—21no—
501C22×D4—21no—
502C22×D4—21no—
503C22×D4D4×C1111yescharacteristic
504C22×D4D4×C1111yescharacteristic
505C22×D4D4×C1111yescharacteristic
506C22×D4C23×C1111yescharacteristic
507C23×C4—21no—
508C23×C4—21no—
509C23×C4—21no—
510C23×C4C23×C1111yescharacteristic
511C23×C4C23×C1111yescharacteristic
512C23×C4C23×C1111yescharacteristic
513C22×C8C23×C1111yescharacteristic
514C22×C8C23×C1111yescharacteristic
515C22×C8C23×C1111yescharacteristic
516C22×C8C23×C1111yescharacteristic
517C22⋊Q8—28no—
518C22⋊Q8—22no—
519C22⋊Q8—22no—
520C22⋊Q8—22no—
521C22⋊Q8D4×C1114yes—
522#121—28no—
523#121—28no—
524#121—28no—
525#121—22no—
526#121—22no—
527#121—22no—
528#121D4×C1114yes—
529#117—22no—
530#117—22no—
531C2×C4⋊C4—21no—
532C2×C4⋊C4—21no—
533C2×C4⋊C4—21no—
534C2×C4⋊C4—22no—
535C2×C4⋊C4—22no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4—41no—
538C2×C4⋊C4—41no—
539C2×C4⋊C4C23×C1111yescharacteristic
540C2×C4⋊C4C23×C1111yescharacteristic
541C2×C4⋊C4C23×C1111yescharacteristic
542C2×C4⋊C4C23×C1111yescharacteristic
543C2×C4⋊C4C23×C1111yescharacteristic
544C2×C4⋊C4C23×C1111yescharacteristic
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—21no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—21no—
554C2×C42—21no—
555#107—22no—
556#107—22no—
557#106—22no—
558#106—22no—
559#103—22no—
560#103—22no—
561#103—41no—
562#103—41no—
563#102—22no—
564#102—22no—
565#102—41no—
566#102—41no—
567C22⋊C8—22no—
568C22⋊C8—22no—
569C22⋊C8—22no—
570C22⋊C8—22no—
571C22⋊C8—41no—
572C22⋊C8—41no—
573#95—21no—
574#95—21no—
575#95—21no—
576#95—21no—
577C2×C11—42no—
578C2×C11—42no—
579C2×C11—81no—
580C2×C11—82no—
581C2×C11#240511yescharacteristic
582C2×C11#301211yescharacteristic
583C2×C11#301311yescharacteristic
584C2×C11#309811yescharacteristic
585C2×C11#309911yescharacteristic
586C2×C11#319811yescharacteristic
587C2×C11#320111yescharacteristic
588C24—21no—
589C24C2×D4×C1111yescharacteristic
590C24C2×D4×C1111yescharacteristic
591C24C2×D4×C1111yescharacteristic
592#41—44no—
593#41—44no—
594#41—44no—
595#41—44no—
596#41—44no—
597#41—44no—
598#41—44no—
599#41—44no—
600C2×Q8—22no—
601C2×Q8—22no—
602C2×Q8—21no—
603C2×Q8—21no—
604C2×Q8—21no—
605C2×Q8—21no—
606C2×Q8—21no—
607C2×Q8—41no—
608C2×Q8C2×D4×C1112yes—
609C2×D4—24no—
610C2×D4—22no—
611C2×D4—22no—
612C2×D4—22no—
613C2×D4—22no—
614C2×D4—24no—
615C2×D4—24no—
616C2×D4—22no—
617C2×D4—22no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—41no—
624C2×D4—41no—
625C2×D4—41no—
626C2×D4—42no—
627C2×D4—42no—
628C2×D4—81no—
629C2×D4—81no—
630C2×D4—81no—
631C2×D4—81no—
632C2×D4C2×D4×C1112yes—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—24no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—24no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—42no—
657C22×C4—42no—
658C22×C4—42no—
659C22×C4—81no—
660C22×C4—81no—
661C22×C4—81no—
662C22×C4—81no—
663C22×C4C2×D4×C1111yescharacteristic
664C22×C4C2×D4×C1111yescharacteristic
665C22×C4C2×D4×C1112yes—
666C22×C4C2×D4×C1112yes—
667C22×C4C2×D4×C1111yescharacteristic
668C22×C4C11×#4112yes—
669C22×C4C11×#4112yes—
670C22×C4C24×C1111yescharacteristic
671C2×C8—21no—
672C2×C8—21no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—21no—
680C2×C8—21no—
681C2×C8—21no—
682C2×C8—21no—
683C4⋊C4—24no—
684C4⋊C4—24no—
685C4⋊C4—24no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—21no—
692C4⋊C4—21no—
693C4⋊C4—21no—
694C4⋊C4—21no—
695C4⋊C4—21no—
696C4⋊C4—42no—
697C4⋊C4C2×D4×C1112yes—
698C4⋊C4C2×D4×C1112yes—
699C22⋊C4—24no—
700C22⋊C4—24no—
701C22⋊C4—24no—
702C22⋊C4—24no—
703C22⋊C4—42no—
704C22⋊C4—81no—
705C22⋊C4—81no—
706C22⋊C4—81no—
707C22⋊C4—81no—
708C42—42no—
709C11#2401711yescharacteristic, direct product factor, Sylow
710C23—21no—
711C23—21no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—22no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23C11×#12012yes—
737C23C11×#12312yes—
738C23C22×D4×C1111yescharacteristic
739Q8—22no—
740Q8—22no—
741Q8—44no—
742Q8—41no—
743Q8—41no—
744D4—22no—
745D4—22no—
746D4—44no—
747D4—44no—
748D4—44no—
749D4—48no—
750D4—41no—
751D4—41no—
752D4—84no—
753D4—84no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—48no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—84no—
796C2×C4—84no—
797C2×C4C11×#12012yes—
798C2×C4C11×#12312yes—
799C2×C4C22×D4×C1111yescharacteristic
800C2×C4C22×D4×C1111yescharacteristic
801C2×C4C2×C11×#4111yescharacteristic
802C2×C4C2×C11×#4111yescharacteristic
803C2×C4C11×H(5,𝔽2)11yescharacteristic
804C2×C4C11×H(5,𝔽2)11yescharacteristic
805C8—41no—
806C8—41no—
807C8—41no—
808C8—41no—
809C22—22no—
810C22—22no—
811C22—22no—
812C22—22no—
813C22—22no—
814C22—22no—
815C22—41no—
816C22—41no—
817C22—41no—
818C22—41no—
819C22—41no—
820C22—41no—
821C22—41no—
822C22—41no—
823C22—42no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—42no—
829C22—41no—
830C22—42no—
831C22—41no—
832C22—41no—
833C22—81no—
834C22—81no—
835C22—81no—
836C22—81no—
837C22C2×C11×#12011yescharacteristic
838C22C2×C11×#12311yescharacteristic
839C22C11×#53411yescharacteristic
840C22C11×#57611yescharacteristic
841C22C11×#57711yescharacteristic
842C22C11×#57711yescharacteristic
843C22C11×#57811yescharacteristic
844C4—22no—
845C4—22no—
846C4—41no—
847C4—42no—
848C4—42no—
849C4—42no—
850C4—81no—
851C4—81no—
852C4—81no—
853C4—81no—
854C4C11×#54611yescharacteristic
855C4C11×#54611yescharacteristic
856C4C11×#54611yescharacteristic
857C4C11×#54611yescharacteristic
858C2—42no—
859C2—42no—
860C2—81no—
861C2—82no—
862C2C11×#240511yescharacteristic
863C2C11×#301211yescharacteristic
864C2C11×#301311yescharacteristic
865C2C11×#309811yescharacteristic
866C2C11×#309911yescharacteristic
867C2C11×#319811yescharacteristic
868C2C11×#320111yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#537C2
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
2. C2×C11×#485C2semidirect
3. C2×C11×#482C2semidirect
4. C11×#2311C2semidirect
5. C11×#2036C2semidirect
6. C11×#2035C2semidirect
7. C11×#2034C2semidirect
8. C11×#2033C2semidirect
9. C11×#1874C2semidirect
10. C11×#1872C2semidirect
11. C11×#1853C2semidirect
12. C11×#1852C2semidirect
13. C11×#1788C2semidirect
14. C11×#1788C2semidirect
15. C11×#1780C2semidirect
154. #24017C11direct (N × H)
277. C2×#485C2×C11semidirect
278. C2×#482C2×C11semidirect
279. #2311C2×C11semidirect
280. #2036C2×C11semidirect
281. #2035C2×C11semidirect
282. #2034C2×C11semidirect
283. #2033C2×C11semidirect
284. #1874C2×C11semidirect
285. #1872C2×C11semidirect
286. #1853C2×C11semidirect
287. #1852C2×C11semidirect
288. #1788C2×C11semidirect
289. #1788C2×C11semidirect
290. #1780C2×C11semidirect
709. C11#24017direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5372
C2×C11×#4852
C2×C11×#4822
C11×#23112
C11×#20362
C11×#20352
C11×#20342
C11×#20332
C11×#18742
C11×#18722
C11×#18532
C11×#18522
C11×#17882
C11×#17802
#2401711