Finite Group Databasebeta

← C11×#24139 #14601332

Subgroups — C11×#24139 #14601332

Order 2816.

1090 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#552C211yesmaximal, characteristic
2C2×C11×#479C211yesmaximal, characteristic, complemented
3C2×C11×#441C211yesmaximal, characteristic, complemented
4C11×#2538C211yesmaximal, characteristic
5C11×#2036C211yesmaximal, characteristic, complemented
6C11×#2035C211yesmaximal, characteristic, complemented
7C11×#2001C211yesmaximal, characteristic, complemented
8C11×#2001C211yesmaximal, characteristic, complemented
9C11×#1992C211yesmaximal, characteristic, complemented
10C11×#1955C211yesmaximal, characteristic
11C11×#1873C211yesmaximal, characteristic, complemented
12C11×#1872C211yesmaximal, characteristic, complemented
13C11×#1854C211yesmaximal, characteristic, complemented
14C11×#1853C211yesmaximal, characteristic, complemented
15C11×#1803C211yesmaximal, characteristic, complemented
16C22×C11×Q16C2211yescharacteristic
17C11×#552—24no—
18C11×#552—24no—
19C2×C11×#126—21no—
20C2×C11×#125—21no—
21C2×C11×#125C2211yescharacteristic
22C2×C11×#123—21no—
23C2×C11×C22⋊Q8C2211yescharacteristic
24C2×C11×C22⋊Q8C2211yescharacteristic
25C2×C11×C22⋊Q8C2211yescharacteristic
26C2×C11×C22⋊Q8C2211yescharacteristic
27C2×C4×Q8×C11C2211yescharacteristic
28C2×C4×Q8×C11C2211yescharacteristic
29C2×C4×D4×C11C2211yescharacteristic
30C2×C11×#117—21no—
31C2×C11×#117C2211yescharacteristic
32C22×C11×C4⋊C4C2211yescharacteristic
33C11×#479—24no—
34C11×#441—24no—
35C2×C11×#107C2211yescharacteristic
36C2×C11×#106C2211yescharacteristic
37C2×C11×#106C2211yescharacteristic
38C2×C11×C4⋊C8C2211yescharacteristic
39C2×C11×#103C2211yescharacteristic
40C2×C11×#103C2211yescharacteristic
41C2×C11×#103C2211yescharacteristic
42C2×C11×#103C2211yescharacteristic
43C2×C11×#103C2211yescharacteristic
44C2×C11×#103C2211yescharacteristic
45C2×C11×C22⋊C8C2211yescharacteristic
46C2×C11×C22⋊C8C2211yescharacteristic
47C2×C11×C22⋊C8C2211yescharacteristic
48C2×C11×C22⋊C8C2211yescharacteristic
49C2×C11×#97C2211yescharacteristic
50C11×#396—21no—
51C11×#396—21no—
52C11×#390—21no—
53C11×#389—21no—
54C11×#384C2211yescharacteristic
55C11×#380C2211yescharacteristic
56C11×#380C2211yescharacteristic
57C11×#340C2211yescharacteristic
58C11×#340C2211yescharacteristic
59C11×#340C2211yescharacteristic
60C11×#340C2211yescharacteristic
61C11×#340C2211yescharacteristic
62C11×#340C2211yescharacteristic
63C22×Q8×C11C2311yescharacteristic
64C22×Q8×C11C2311yescharacteristic
65C22×D4×C11D411yescharacteristic
66C23×C4×C11—21no—
67C23×C4×C11C2311yescharacteristic
68C23×C4×C11C2311yescharacteristic
69C2×C11×Q16—22no—
70C2×C11×Q16—22no—
71C2×C11×Q16—22no—
72C22×C8×C11C2311yescharacteristic
73C22×C8×C11C2311yescharacteristic
74C22×C8×C11C2311yescharacteristic
75C22×C8×C11C2311yescharacteristic
76C11×#126—28no—
77C11×#125—28no—
78C11×#125—22no—
79C11×#125D414yes—
80C11×#123—28no—
81C11×C22⋊Q8—22no—
82C11×C22⋊Q8—22no—
83C11×C22⋊Q8—22no—
84C11×C22⋊Q8—22no—
85C11×C22⋊Q8—22no—
86C11×C22⋊Q8—22no—
87C11×C22⋊Q8—41no—
88C11×C22⋊Q8—41no—
89C4×Q8×C11—22no—
90C4×Q8×C11—22no—
91C4×Q8×C11—22no—
92C4×Q8×C11D414yes—
93C4×D4×C11—22no—
94C4×D4×C11—22no—
95C11×#117—28no—
96C11×#117—22no—
97C11×#117—22no—
98C2×C11×C4⋊C4—21no—
99C2×C11×C4⋊C4—21no—
100C2×C11×C4⋊C4—21no—
101C2×C11×C4⋊C4—21no—
102C2×C11×C4⋊C4—21no—
103C2×C11×C4⋊C4—21no—
104C2×C11×C4⋊C4—22no—
105C2×C11×C4⋊C4—22no—
106C2×C11×C4⋊C4—21no—
107C2×C11×C4⋊C4—21no—
108C2×C11×C4⋊C4—21no—
109C2×C11×C4⋊C4—21no—
110C2×C11×C4⋊C4—21no—
111C2×C11×C4⋊C4D411yescharacteristic
112C2×C11×C4⋊C4C2311yescharacteristic
113C2×C11×C4⋊C4C2311yescharacteristic
114C2×C11×C4⋊C4C2311yescharacteristic
115C2×C11×C4⋊C4C2311yescharacteristic
116C2×C11×C4⋊C4C2311yescharacteristic
117C2×C11×C4⋊C4C2311yescharacteristic
118C2×C11×C22⋊C4—21no—
119C2×C11×C22⋊C4—21no—
120C2×C11×C22⋊C4—21no—
121C2×C11×C22⋊C4—21no—
122C2×C11×C22⋊C4—21no—
123C2×C11×C22⋊C4—21no—
124C2×C11×C22⋊C4—21no—
125C2×C11×C22⋊C4D411yescharacteristic
126C2×C11×C22⋊C4D411yescharacteristic
127C2×C42×C11—21no—
128C2×C42×C11—21no—
129C2×C42×C11—21no—
130C2×C42×C11C2311yescharacteristic
131C11×#107—22no—
132C11×#106—22no—
133C11×#106—22no—
134C11×C4⋊C8—22no—
135C11×#103—22no—
136C11×#103—22no—
137C11×#103—22no—
138C11×#103—22no—
139C11×#103—41no—
140C11×#103—41no—
141C11×C22⋊C8—22no—
142C11×C22⋊C8—22no—
143C11×C22⋊C8—41no—
144C11×C22⋊C8—41no—
145C11×#97—22no—
146C11×#95—21no—
147C11×#95—21no—
148#24139C1111yesmaximal, characteristic, direct product factor, Sylow
149C24×C11C2×D411yescharacteristic
150C24×C11C2×D411yescharacteristic
151C2×Q8×C11—21no—
152C2×Q8×C11—21no—
153C2×Q8×C11—21no—
154C2×Q8×C11—21no—
155C2×Q8×C11—21no—
156C2×Q8×C11—21no—
157C2×Q8×C11—21no—
158C2×Q8×C11—21no—
159C2×Q8×C11—21no—
160C2×Q8×C11—21no—
161C2×Q8×C11C2×D412yes—
162C2×Q8×C11#4112yes—
163C2×D4×C11—22no—
164C2×D4×C11—22no—
165C2×D4×C11—41no—
166C22×C4×C11—24no—
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—21no—
187C22×C4×C11—42no—
188C22×C4×C11—42no—
189C22×C4×C11C2×D411yescharacteristic
190C22×C4×C11C2×D411yescharacteristic
191C22×C4×C11C2×D411yescharacteristic
192C22×C4×C11C2×D411yescharacteristic
193C22×C4×C11C2411yescharacteristic
194C11×Q16—28no—
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×C11—21no—
204C2×C8×C11—21no—
205C2×C8×C11—21no—
206C2×C8×C11#4112yes—
207C11×C4⋊C4—24no—
208C11×C4⋊C4—24no—
209C11×C4⋊C4—24no—
210C11×C4⋊C4—24no—
211C11×C4⋊C4—24no—
212C11×C4⋊C4—24no—
213C11×C4⋊C4—22no—
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—42no—
224C11×C4⋊C4—42no—
225C11×C4⋊C4—42no—
226C11×C4⋊C4—42no—
227C11×C4⋊C4—81no—
228C11×C4⋊C4C2×D412yes—
229C11×C4⋊C4C2×D412yes—
230C11×C4⋊C4C2×D412yes—
231C11×C22⋊C4—24no—
232C11×C22⋊C4—24no—
233C11×C22⋊C4—24no—
234C11×C22⋊C4—22no—
235C11×C22⋊C4—22no—
236C11×C22⋊C4—42no—
237C11×C22⋊C4—42no—
238C11×C22⋊C4—81no—
239C11×C22⋊C4—81no—
240C42×C11—24no—
241C42×C11—24no—
242C42×C11—42no—
243C42×C11C2×D412yes—
244C42×C11C2×D412yes—
245C2×#552C2×C1111yescharacteristic
246C2×#479C2×C1111yescharacteristic, complemented
247C2×#441C2×C1111yescharacteristic, complemented
248#2538C2×C1111yescharacteristic
249#2036C2×C1111yescharacteristic, complemented
250#2035C2×C1111yescharacteristic, complemented
251#2001C2×C1111yescharacteristic, complemented
252#2001C2×C1111yescharacteristic, complemented
253#1992C2×C1111yescharacteristic, complemented
254#1955C2×C1111yescharacteristic
255#1873C2×C1111yescharacteristic, complemented
256#1872C2×C1111yescharacteristic, complemented
257#1854C2×C1111yescharacteristic, complemented
258#1853C2×C1111yescharacteristic, complemented
259#1803C2×C1111yescharacteristic, complemented
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#13712yes—
274C23×C11C22×D411yescharacteristic
275Q8×C11—22no—
276Q8×C11—22no—
277Q8×C11—22no—
278Q8×C11—22no—
279Q8×C11—41no—
280Q8×C11—41no—
281Q8×C11—41no—
282Q8×C11—41no—
283D4×C11—44no—
284C2×C4×C11—21no—
285C2×C4×C11—21no—
286C2×C4×C11—21no—
287C2×C4×C11—21no—
288C2×C4×C11—21no—
289C2×C4×C11—22no—
290C2×C4×C11—22no—
291C2×C4×C11—22no—
292C2×C4×C11—21no—
293C2×C4×C11—22no—
294C2×C4×C11—22no—
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—41no—
322C2×C4×C11—41no—
323C2×C4×C11—41no—
324C2×C4×C11—41no—
325C2×C4×C11—41no—
326C2×C4×C11—41no—
327C2×C4×C11#12012yes—
328C2×C4×C11#12012yes—
329C2×C4×C11C22×D411yescharacteristic
330C2×C4×C11C22×D411yescharacteristic
331C2×C4×C11C2×#4111yescharacteristic
332C2×C4×C11C2×#4111yescharacteristic
333C2×C4×C11H(5,𝔽2)11yescharacteristic
334C2×C4×C112−1+411yescharacteristic
335C8×C11—22no—
336C8×C11—41no—
337C8×C11—41no—
338C8×C11—41no—
339C22×Q16C22×C1111yescharacteristic
340#552—24no—
341#552—24no—
342C2×#126—21no—
343C2×#125—21no—
344C2×#125C22×C1111yescharacteristic
345C2×#123—21no—
346C2×C22⋊Q8C22×C1111yescharacteristic
347C2×C22⋊Q8C22×C1111yescharacteristic
348C2×C22⋊Q8C22×C1111yescharacteristic
349C2×C22⋊Q8C22×C1111yescharacteristic
350C2×C4×Q8C22×C1111yescharacteristic
351C2×C4×Q8C22×C1111yescharacteristic
352C2×C4×D4C22×C1111yescharacteristic
353C2×#117—21no—
354C2×#117C22×C1111yescharacteristic
355C22×C4⋊C4C22×C1111yescharacteristic
356#479—24no—
357#441—24no—
358C2×#107C22×C1111yescharacteristic
359C2×#106C22×C1111yescharacteristic
360C2×#106C22×C1111yescharacteristic
361C2×C4⋊C8C22×C1111yescharacteristic
362C2×#103C22×C1111yescharacteristic
363C2×#103C22×C1111yescharacteristic
364C2×#103C22×C1111yescharacteristic
365C2×#103C22×C1111yescharacteristic
366C2×#103C22×C1111yescharacteristic
367C2×#103C22×C1111yescharacteristic
368C2×C22⋊C8C22×C1111yescharacteristic
369C2×C22⋊C8C22×C1111yescharacteristic
370C2×C22⋊C8C22×C1111yescharacteristic
371C2×C22⋊C8C22×C1111yescharacteristic
372C2×#97C22×C1111yescharacteristic
373#396—21no—
374#396—21no—
375#390—21no—
376#389—21no—
377#384C22×C1111yescharacteristic
378#380C22×C1111yescharacteristic
379#380C22×C1111yescharacteristic
380#340C22×C1111yescharacteristic
381#340C22×C1111yescharacteristic
382#340C22×C1111yescharacteristic
383#340C22×C1111yescharacteristic
384#340C22×C1111yescharacteristic
385#340C22×C1111yescharacteristic
386C22×C11—22no—
387C22×C11—22no—
388C22×C11—22no—
389C22×C11—41no—
390C22×C11—41no—
391C22×C11—41no—
392C22×C11—41no—
393C22×C11—41no—
394C22×C11—41no—
395C22×C11—41no—
396C22×C11—41no—
397C22×C11—41no—
398C22×C11—41no—
399C22×C11—41no—
400C22×C11C2×#12011yescharacteristic
401C22×C11#54611yescharacteristic
402C22×C11#54711yescharacteristic
403C22×C11C2×#13711yescharacteristic
404C22×C11#57511yescharacteristic
405C22×C11#57711yescharacteristic
406C22×C11#57811yescharacteristic
407C4×C11—22no—
408C4×C11—22no—
409C4×C11—41no—
410C4×C11—41no—
411C4×C11—42no—
412C4×C11—42no—
413C4×C11—42no—
414C4×C11—42no—
415C4×C11—42no—
416C4×C11—81no—
417C4×C11—81no—
418C4×C11—81no—
419C4×C11#52511yescharacteristic
420C4×C11#53711yescharacteristic
421C4×C11#54811yescharacteristic
422C4×C11#55011yescharacteristic
423C22×Q8C23×C1111yescharacteristic
424C22×Q8C23×C1111yescharacteristic
425C22×D4D4×C1111yescharacteristic
426C23×C4—21no—
427C23×C4C23×C1111yescharacteristic
428C23×C4C23×C1111yescharacteristic
429C2×Q16—22no—
430C2×Q16—22no—
431C2×Q16—22no—
432C22×C8C23×C1111yescharacteristic
433C22×C8C23×C1111yescharacteristic
434C22×C8C23×C1111yescharacteristic
435C22×C8C23×C1111yescharacteristic
436#126—28no—
437#125—28no—
438#125—22no—
439#125D4×C1114yes—
440#123—28no—
441C22⋊Q8—22no—
442C22⋊Q8—22no—
443C22⋊Q8—22no—
444C22⋊Q8—22no—
445C22⋊Q8—22no—
446C22⋊Q8—22no—
447C22⋊Q8—41no—
448C22⋊Q8—41no—
449C4×Q8—22no—
450C4×Q8—22no—
451C4×Q8—22no—
452C4×Q8D4×C1114yes—
453C4×D4—22no—
454C4×D4—22no—
455#117—28no—
456#117—22no—
457#117—22no—
458C2×C4⋊C4—21no—
459C2×C4⋊C4—21no—
460C2×C4⋊C4—21no—
461C2×C4⋊C4—21no—
462C2×C4⋊C4—21no—
463C2×C4⋊C4—21no—
464C2×C4⋊C4—22no—
465C2×C4⋊C4—22no—
466C2×C4⋊C4—21no—
467C2×C4⋊C4—21no—
468C2×C4⋊C4—21no—
469C2×C4⋊C4—21no—
470C2×C4⋊C4—21no—
471C2×C4⋊C4D4×C1111yescharacteristic
472C2×C4⋊C4C23×C1111yescharacteristic
473C2×C4⋊C4C23×C1111yescharacteristic
474C2×C4⋊C4C23×C1111yescharacteristic
475C2×C4⋊C4C23×C1111yescharacteristic
476C2×C4⋊C4C23×C1111yescharacteristic
477C2×C4⋊C4C23×C1111yescharacteristic
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⋊C4D4×C1111yescharacteristic
486C2×C22⋊C4D4×C1111yescharacteristic
487C2×C42—21no—
488C2×C42—21no—
489C2×C42—21no—
490C2×C42C23×C1111yescharacteristic
491#107—22no—
492#106—22no—
493#106—22no—
494C4⋊C8—22no—
495#103—22no—
496#103—22no—
497#103—22no—
498#103—22no—
499#103—41no—
500#103—41no—
501C22⋊C8—22no—
502C22⋊C8—22no—
503C22⋊C8—41no—
504C22⋊C8—41no—
505#97—22no—
506#95—21no—
507#95—21no—
508C2×C11—42no—
509C2×C11—81no—
510C2×C11#240711yescharacteristic
511C2×C11#300711yescharacteristic
512C2×C11#301311yescharacteristic
513C2×C11#331211yescharacteristic
514C2×C11#331711yescharacteristic
515C2×C11#334411yescharacteristic
516C2×C11#334911yescharacteristic
517C24C2×D4×C1111yescharacteristic
518C24C2×D4×C1111yescharacteristic
519C2×Q8—21no—
520C2×Q8—21no—
521C2×Q8—21no—
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8—21no—
529C2×Q8C2×D4×C1112yes—
530C2×Q8C11×#4112yes—
531C2×D4—22no—
532C2×D4—22no—
533C2×D4—41no—
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—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—42no—
556C22×C4—42no—
557C22×C4C2×D4×C1111yescharacteristic
558C22×C4C2×D4×C1111yescharacteristic
559C22×C4C2×D4×C1111yescharacteristic
560C22×C4C2×D4×C1111yescharacteristic
561C22×C4C24×C1111yescharacteristic
562Q16—28no—
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×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8C11×#4112yes—
575C4⋊C4—24no—
576C4⋊C4—24no—
577C4⋊C4—24no—
578C4⋊C4—24no—
579C4⋊C4—24no—
580C4⋊C4—24no—
581C4⋊C4—22no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—42no—
592C4⋊C4—42no—
593C4⋊C4—42no—
594C4⋊C4—42no—
595C4⋊C4—81no—
596C4⋊C4C2×D4×C1112yes—
597C4⋊C4C2×D4×C1112yes—
598C4⋊C4C2×D4×C1112yes—
599C22⋊C4—24no—
600C22⋊C4—24no—
601C22⋊C4—24no—
602C22⋊C4—22no—
603C22⋊C4—22no—
604C22⋊C4—42no—
605C22⋊C4—42no—
606C22⋊C4—81no—
607C22⋊C4—81no—
608C42—24no—
609C42—24no—
610C42—42no—
611C42C2×D4×C1112yes—
612C42C2×D4×C1112yes—
613C11#2413911yescharacteristic, direct product factor, Sylow
614C23—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23C11×#13712yes—
628C23C22×D4×C1111yescharacteristic
629Q8—22no—
630Q8—22no—
631Q8—22no—
632Q8—22no—
633Q8—41no—
634Q8—41no—
635Q8—41no—
636Q8—41no—
637D4—44no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—21no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—48no—
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—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×C4C11×#12012yes—
682C2×C4C11×#12012yes—
683C2×C4C22×D4×C1111yescharacteristic
684C2×C4C22×D4×C1111yescharacteristic
685C2×C4C2×C11×#4111yescharacteristic
686C2×C4C2×C11×#4111yescharacteristic
687C2×C4C11×H(5,𝔽2)11yescharacteristic
688C2×C4C11×2−1+411yescharacteristic
689C8—22no—
690C8—41no—
691C8—41no—
692C8—41no—
693C22—22no—
694C22—22no—
695C22—22no—
696C22—41no—
697C22—41no—
698C22—41no—
699C22—41no—
700C22—41no—
701C22—41no—
702C22—41no—
703C22—41no—
704C22—41no—
705C22—41no—
706C22—41no—
707C22C2×C11×#12011yescharacteristic
708C22C11×#54611yescharacteristic
709C22C11×#54711yescharacteristic
710C22C2×C11×#13711yescharacteristic
711C22C11×#57511yescharacteristic
712C22C11×#57711yescharacteristic
713C22C11×#57811yescharacteristic
714C4—22no—
715C4—22no—
716C4—41no—
717C4—41no—
718C4—42no—
719C4—42no—
720C4—42no—
721C4—42no—
722C4—42no—
723C4—81no—
724C4—81no—
725C4—81no—
726C4C11×#52511yescharacteristic
727C4C11×#53711yescharacteristic
728C4C11×#54811yescharacteristic
729C4C11×#55011yescharacteristic
730C2—42no—
731C2—81no—
732C2C11×#240711yescharacteristic
733C2C11×#300711yescharacteristic
734C2C11×#301311yescharacteristic
735C2C11×#331211yescharacteristic
736C2C11×#331711yescharacteristic
737C2C11×#334411yescharacteristic
738C2C11×#334911yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC22×D4×C11D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C4×D4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#479C2semidirect
3. C2×C11×#441C2semidirect
5. C11×#2036C2semidirect
6. C11×#2035C2semidirect
7. C11×#2001C2semidirect
8. C11×#2001C2semidirect
9. C11×#1992C2semidirect
11. C11×#1873C2semidirect
12. C11×#1872C2semidirect
13. C11×#1854C2semidirect
14. C11×#1853C2semidirect
15. C11×#1803C2semidirect
148. #24139C11direct (N × H)
246. C2×#479C2×C11semidirect
247. C2×#441C2×C11semidirect
249. #2036C2×C11semidirect
250. #2035C2×C11semidirect
251. #2001C2×C11semidirect
252. #2001C2×C11semidirect
253. #1992C2×C11semidirect
255. #1873C2×C11semidirect
256. #1872C2×C11semidirect
257. #1854C2×C11semidirect
258. #1853C2×C11semidirect
259. #1803C2×C11semidirect
613. C11#24139direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5522
C2×C11×#4792
C2×C11×#4412
C11×#25382
C11×#20362
C11×#20352
C11×#20012
C11×#19922
C11×#19552
C11×#18732
C11×#18722
C11×#18542
C11×#18532
C11×#18032
#2413911