Finite Group Databasebeta

← C11×#26174 #14603367

Subgroups — C11×#26174 #14603367

Order 2816.

1016 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#459C211yesmaximal, characteristic
2C2×C11×#442C211yesmaximal, characteristic, complemented
3C11×#2445C211yesmaximal, characteristic, complemented
4D4×C11×C4⋊C4C211yesmaximal, characteristic, complemented
5C11×#2094C211yesmaximal, characteristic, complemented
6C11×#2088C211yesmaximal, characteristic, complemented
7C11×#2071C211yesmaximal, characteristic, complemented
8C11×#2041C211yesmaximal, characteristic, complemented
9C11×#1936C211yesmaximal, characteristic, complemented
10C11×#1917C211yesmaximal, characteristic, complemented
11C11×#1879C211yesmaximal, characteristic, complemented
12C11×#1879C211yesmaximal, characteristic, complemented
13C11×#1879C211yesmaximal, characteristic, complemented
14C11×#1864C211yesmaximal, characteristic, complemented
15C11×#1864C211yesmaximal, characteristic, complemented
16C22×C11×D8C2211yescharacteristic
17C22×C11×D8C2211yescharacteristic
18C2×C11×#127C2211yescharacteristic
19C2×C11×#123—21no—
20C2×C4×D4×C11C2211yescharacteristic
21C2×C4×D4×C11C2211yescharacteristic
22C2×C4×D4×C11C2211yescharacteristic
23C2×C4×D4×C11C2211yescharacteristic
24C22×C11×C4⋊C4—21no—
25C11×#459—24no—
26C11×#442—24no—
27C2×C11×#106C2211yescharacteristic
28C2×C11×#106C2211yescharacteristic
29C2×C11×C4⋊C8C2211yescharacteristic
30C2×C11×#102C2211yescharacteristic
31C2×C11×#102C2211yescharacteristic
32C2×C11×#102C2211yescharacteristic
33C2×C11×#102C2211yescharacteristic
34C2×C11×#102C2211yescharacteristic
35C2×C11×#102C2211yescharacteristic
36C2×C11×#102C2211yescharacteristic
37C2×C11×#102C2211yescharacteristic
38C2×C11×#97C2211yescharacteristic
39C11×#394—21no—
40C11×#394—21no—
41C11×#390C2211yescharacteristic
42C11×#390C2211yescharacteristic
43C11×#390C2211yescharacteristic
44C11×#389C2211yescharacteristic
45C11×#389C2211yescharacteristic
46C11×#389C2211yescharacteristic
47C11×#386—21no—
48C11×#385—21no—
49C11×#385—21no—
50C11×#384C2211yescharacteristic
51C11×#380—21no—
52C4×C11×C4⋊C4C2211yescharacteristic
53C11×#340C2211yescharacteristic
54C11×#340C2211yescharacteristic
55C11×#340C2211yescharacteristic
56C11×#340C2211yescharacteristic
57C11×#336C2211yescharacteristic
58C11×#336C2211yescharacteristic
59C11×#336C2211yescharacteristic
60C11×#336C2211yescharacteristic
61C22×D4×C11—21no—
62C22×D4×C11—21no—
63C22×D4×C11C2311yescharacteristic
64C22×D4×C11C2311yescharacteristic
65C22×D4×C11C2311yescharacteristic
66C23×C4×C11—21no—
67C23×C4×C11—21no—
68C23×C4×C11—21no—
69C23×C4×C11—21no—
70C2×C11×D8—22no—
71C2×C11×D8—22no—
72C2×C11×D8—22no—
73C2×C11×D8—22no—
74C2×C11×D8—22no—
75C2×C11×D8D414yes—
76C22×C8×C11C2311yescharacteristic
77C22×C8×C11C2311yescharacteristic
78C22×C8×C11C2311yescharacteristic
79C22×C8×C11C2311yescharacteristic
80C11×#127—22no—
81C11×#127—41no—
82C11×#123—44no—
83C4×D4×C11—22no—
84C4×D4×C11—22no—
85C4×D4×C11—22no—
86C4×D4×C11—22no—
87C4×D4×C11—22no—
88C4×D4×C11—41no—
89C4×D4×C11—41no—
90C4×D4×C11—41no—
91C2×C11×C4⋊C4—21no—
92C2×C11×C4⋊C4—21no—
93C2×C11×C4⋊C4—21no—
94C2×C11×C4⋊C4—21no—
95C2×C11×C4⋊C4—21no—
96C2×C11×C4⋊C4—44no—
97C2×C11×C4⋊C4D411yescharacteristic
98C2×C11×C4⋊C4D411yescharacteristic
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⋊C4—21no—
111C2×C11×C22⋊C4—21no—
112C2×C11×C22⋊C4—21no—
113C2×C11×C22⋊C4—21no—
114C2×C42×C11C2311yescharacteristic
115C2×C42×C11C2311yescharacteristic
116C2×C42×C11C2311yescharacteristic
117C11×#106—22no—
118C11×#106—41no—
119C11×C4⋊C8—22no—
120C11×#102—22no—
121C11×#102—22no—
122C11×#102—22no—
123C11×#102—22no—
124C11×#102—22no—
125C11×#102—22no—
126C11×#102—22no—
127C11×#102—41no—
128C11×#97—22no—
129C11×#95—21no—
130C11×#95—21no—
131C11×#95—21no—
132C11×#95D411yescharacteristic
133C11×#95D411yescharacteristic
134#26174C1111yesmaximal, characteristic, direct product factor, Sylow
135C24×C11—21no—
136C24×C11—21no—
137C24×C11—21no—
138C2×D4×C11—21no—
139C2×D4×C11—21no—
140C2×D4×C11—21no—
141C2×D4×C11—21no—
142C2×D4×C11—21no—
143C2×D4×C11—21no—
144C2×D4×C11—21no—
145C2×D4×C11—21no—
146C2×D4×C11—21no—
147C2×D4×C11—21no—
148C2×D4×C11—21no—
149C2×D4×C11—21no—
150C2×D4×C11—21no—
151C2×D4×C11—21no—
152C2×D4×C11—42no—
153C2×D4×C11—42no—
154C2×D4×C11—42no—
155C2×D4×C11—42no—
156C2×D4×C11—81no—
157C2×D4×C11—81no—
158C2×D4×C11C2×D412yes—
159C2×D4×C11C2×D412yes—
160C2×D4×C11#4112yes—
161C2×D4×C11#4112yes—
162C22×C4×C11—24no—
163C22×C4×C11—21no—
164C22×C4×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11—21no—
167C22×C4×C11—21no—
168C22×C4×C11—42no—
169C22×C4×C11—42no—
170C22×C4×C11—42no—
171C22×C4×C11—42no—
172C22×C4×C11—42no—
173C22×C4×C11—42no—
174C22×C4×C11—42no—
175C22×C4×C11—42no—
176C22×C4×C11—81no—
177C22×C4×C11—81no—
178C22×C4×C11—81no—
179C22×C4×C11C2×D411yescharacteristic
180C22×C4×C11C2×D411yescharacteristic
181C22×C4×C11C2×D411yescharacteristic
182C22×C4×C11C2×D411yescharacteristic
183C22×C4×C11C2×D411yescharacteristic
184C22×C4×C11C2×D411yescharacteristic
185C22×C4×C11C2411yescharacteristic
186C11×D8—28no—
187C11×D8—44no—
188C2×C8×C11—21no—
189C2×C8×C11—21no—
190C2×C8×C11—21no—
191C2×C8×C11—21no—
192C2×C8×C11—21no—
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×C11C2×D412yes—
200C11×C4⋊C4—22no—
201C11×C4⋊C4—22no—
202C11×C4⋊C4—21no—
203C11×C4⋊C4—21no—
204C11×C4⋊C4—21no—
205C11×C4⋊C4—21no—
206C11×C4⋊C4—21no—
207C11×C4⋊C4—21no—
208C11×C4⋊C4—21no—
209C11×C4⋊C4—21no—
210C11×C4⋊C4—21no—
211C11×C4⋊C4—42no—
212C11×C4⋊C4—42no—
213C11×C4⋊C4—42no—
214C11×C4⋊C4—42no—
215C11×C4⋊C4—81no—
216C11×C4⋊C4#4112yes—
217C11×C22⋊C4—24no—
218C11×C22⋊C4—42no—
219C11×C22⋊C4—42no—
220C11×C22⋊C4—42no—
221C11×C22⋊C4—42no—
222C11×C22⋊C4—42no—
223C11×C22⋊C4—42no—
224C11×C22⋊C4—81no—
225C11×C22⋊C4—81no—
226C11×C22⋊C4—81no—
227C42×C11—21no—
228C42×C11—21no—
229C42×C11—21no—
230C42×C11—21no—
231C42×C11—21no—
232C42×C11—21no—
233C2×#459C2×C1111yescharacteristic
234C2×#442C2×C1111yescharacteristic, complemented
235#2445C2×C1111yescharacteristic, complemented
236D4×C4⋊C4C2×C1111yescharacteristic, complemented
237#2094C2×C1111yescharacteristic, complemented
238#2088C2×C1111yescharacteristic, complemented
239#2071C2×C1111yescharacteristic, complemented
240#2041C2×C1111yescharacteristic, complemented
241#1936C2×C1111yescharacteristic, complemented
242#1917C2×C1111yescharacteristic, complemented
243#1879C2×C1111yescharacteristic, complemented
244#1879C2×C1111yescharacteristic, complemented
245#1879C2×C1111yescharacteristic, complemented
246#1864C2×C1111yescharacteristic, complemented
247#1864C2×C1111yescharacteristic, complemented
248C23×C11—22no—
249C23×C11—22no—
250C23×C11—22no—
251C23×C11—22no—
252C23×C11—41no—
253C23×C11—41no—
254C23×C11—41no—
255C23×C11—41no—
256C23×C11—41no—
257C23×C11—41no—
258C23×C11—41no—
259C23×C11—41no—
260C23×C11—41no—
261C23×C11—41no—
262C23×C11—41no—
263C23×C11—41no—
264C23×C11—41no—
265C23×C11—41no—
266C23×C11—41no—
267C23×C11—41no—
268C23×C11—41no—
269C23×C11C22×D411yescharacteristic
270D4×C11—22no—
271D4×C11—22no—
272D4×C11—22no—
273D4×C11—22no—
274D4×C11—22no—
275D4×C11—41no—
276D4×C11—41no—
277D4×C11—41no—
278D4×C11—41no—
279D4×C11—41no—
280D4×C11—41no—
281D4×C11—84no—
282D4×C11—84no—
283D4×C11#12314yescomplemented
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—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—21no—
300C2×C4×C11—21no—
301C2×C4×C11—48no—
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—84no—
317C2×C4×C11—84no—
318C2×C4×C11—84no—
319C2×C4×C11AGL(1,ℤ/8)12yes—
320C2×C4×C11AGL(1,ℤ/8)12yes—
321C2×C4×C11C22×D411yescharacteristic
322C2×C4×C11C2×#4111yescharacteristic
323C2×C4×C11C2×#4111yescharacteristic
324C2×C4×C11C2×#4111yescharacteristic
325C2×C4×C11H(5,𝔽2)11yescharacteristic
326C2×C4×C112−1+411yescharacteristic
327C8×C11—22no—
328C8×C11—41no—
329C8×C11—41no—
330C8×C11—41no—
331C22×D8C22×C1111yescharacteristic
332C22×D8C22×C1111yescharacteristic
333C2×#127C22×C1111yescharacteristic
334C2×#123—21no—
335C2×C4×D4C22×C1111yescharacteristic
336C2×C4×D4C22×C1111yescharacteristic
337C2×C4×D4C22×C1111yescharacteristic
338C2×C4×D4C22×C1111yescharacteristic
339C22×C4⋊C4—21no—
340#459—24no—
341#442—24no—
342C2×#106C22×C1111yescharacteristic
343C2×#106C22×C1111yescharacteristic
344C2×C4⋊C8C22×C1111yescharacteristic
345C2×#102C22×C1111yescharacteristic
346C2×#102C22×C1111yescharacteristic
347C2×#102C22×C1111yescharacteristic
348C2×#102C22×C1111yescharacteristic
349C2×#102C22×C1111yescharacteristic
350C2×#102C22×C1111yescharacteristic
351C2×#102C22×C1111yescharacteristic
352C2×#102C22×C1111yescharacteristic
353C2×#97C22×C1111yescharacteristic
354#394—21no—
355#394—21no—
356#390C22×C1111yescharacteristic
357#390C22×C1111yescharacteristic
358#390C22×C1111yescharacteristic
359#389C22×C1111yescharacteristic
360#389C22×C1111yescharacteristic
361#389C22×C1111yescharacteristic
362#386—21no—
363#385—21no—
364#385—21no—
365#384C22×C1111yescharacteristic
366#380—21no—
367C4×C4⋊C4C22×C1111yescharacteristic
368#340C22×C1111yescharacteristic
369#340C22×C1111yescharacteristic
370#340C22×C1111yescharacteristic
371#340C22×C1111yescharacteristic
372#336C22×C1111yescharacteristic
373#336C22×C1111yescharacteristic
374#336C22×C1111yescharacteristic
375#336C22×C1111yescharacteristic
376C22×C11—24no—
377C22×C11—42no—
378C22×C11—42no—
379C22×C11—42no—
380C22×C11—42no—
381C22×C11—42no—
382C22×C11—42no—
383C22×C11—42no—
384C22×C11—42no—
385C22×C11—42no—
386C22×C11—81no—
387C22×C11—81no—
388C22×C11—81no—
389C22×C11—81no—
390C22×C11—81no—
391C22×C11—81no—
392C22×C11—81no—
393C22×C11—81no—
394C22×C11—81no—
395C22×C11—81no—
396C22×C11—81no—
397C22×C11#52511yescharacteristic
398C22×C11D4211yescharacteristic
399C22×C11#54811yescharacteristic
400C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
401C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
402C22×C11#57611yescharacteristic
403C22×C11#57711yescharacteristic
404C4×C11—22no—
405C4×C11—22no—
406C4×C11—42no—
407C4×C11—41no—
408C4×C11—41no—
409C4×C11—41no—
410C4×C11—41no—
411C4×C11—81no—
412C4×C11—81no—
413C4×C11—81no—
414C4×C11—81no—
415C4×C11C2×#12311yescharacteristic
416C4×C11#53911yescharacteristic
417C4×C11#54711yescharacteristic
418C4×C11#55311yescharacteristic
419C22×D4—21no—
420C22×D4—21no—
421C22×D4C23×C1111yescharacteristic
422C22×D4C23×C1111yescharacteristic
423C22×D4C23×C1111yescharacteristic
424C23×C4—21no—
425C23×C4—21no—
426C23×C4—21no—
427C23×C4—21no—
428C2×D8—22no—
429C2×D8—22no—
430C2×D8—22no—
431C2×D8—22no—
432C2×D8—22no—
433C2×D8D4×C1114yes—
434C22×C8C23×C1111yescharacteristic
435C22×C8C23×C1111yescharacteristic
436C22×C8C23×C1111yescharacteristic
437C22×C8C23×C1111yescharacteristic
438#127—22no—
439#127—41no—
440#123—44no—
441C4×D4—22no—
442C4×D4—22no—
443C4×D4—22no—
444C4×D4—22no—
445C4×D4—22no—
446C4×D4—41no—
447C4×D4—41no—
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⋊C4—44no—
455C2×C4⋊C4D4×C1111yescharacteristic
456C2×C4⋊C4D4×C1111yescharacteristic
457C2×C4⋊C4C23×C1111yescharacteristic
458C2×C4⋊C4C23×C1111yescharacteristic
459C2×C4⋊C4C23×C1111yescharacteristic
460C2×C4⋊C4C23×C1111yescharacteristic
461C2×C4⋊C4C23×C1111yescharacteristic
462C2×C22⋊C4—21no—
463C2×C22⋊C4—21no—
464C2×C22⋊C4—21no—
465C2×C22⋊C4—21no—
466C2×C22⋊C4—21no—
467C2×C22⋊C4—21no—
468C2×C22⋊C4—21no—
469C2×C22⋊C4—21no—
470C2×C22⋊C4—21no—
471C2×C22⋊C4—21no—
472C2×C42C23×C1111yescharacteristic
473C2×C42C23×C1111yescharacteristic
474C2×C42C23×C1111yescharacteristic
475#106—22no—
476#106—41no—
477C4⋊C8—22no—
478#102—22no—
479#102—22no—
480#102—22no—
481#102—22no—
482#102—22no—
483#102—22no—
484#102—22no—
485#102—41no—
486#97—22no—
487#95—21no—
488#95—21no—
489#95—21no—
490#95D4×C1111yescharacteristic
491#95D4×C1111yescharacteristic
492C2×C11—44no—
493C2×C11—82no—
494C2×C11—161no—
495C2×C11#244311yescharacteristic
496C2×C11#310911yescharacteristic
497C2×C11#311911yescharacteristic
498C2×C11#326411yescharacteristic
499C2×C11#327211yescharacteristic
500C2×C11#336611yescharacteristic
501C2×C11#337311yescharacteristic
502C24—21no—
503C24—21no—
504C24—21no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—21no—
514C2×D4—21no—
515C2×D4—21no—
516C2×D4—21no—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—42no—
520C2×D4—42no—
521C2×D4—42no—
522C2×D4—42no—
523C2×D4—81no—
524C2×D4—81no—
525C2×D4C2×D4×C1112yes—
526C2×D4C2×D4×C1112yes—
527C2×D4C11×#4112yes—
528C2×D4C11×#4112yes—
529C22×C4—24no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—42no—
536C22×C4—42no—
537C22×C4—42no—
538C22×C4—42no—
539C22×C4—42no—
540C22×C4—42no—
541C22×C4—42no—
542C22×C4—42no—
543C22×C4—81no—
544C22×C4—81no—
545C22×C4—81no—
546C22×C4C2×D4×C1111yescharacteristic
547C22×C4C2×D4×C1111yescharacteristic
548C22×C4C2×D4×C1111yescharacteristic
549C22×C4C2×D4×C1111yescharacteristic
550C22×C4C2×D4×C1111yescharacteristic
551C22×C4C2×D4×C1111yescharacteristic
552C22×C4C24×C1111yescharacteristic
553D8—28no—
554D8—44no—
555C2×C8—21no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8C2×D4×C1112yes—
567C4⋊C4—22no—
568C4⋊C4—22no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—42no—
579C4⋊C4—42no—
580C4⋊C4—42no—
581C4⋊C4—42no—
582C4⋊C4—81no—
583C4⋊C4C11×#4112yes—
584C22⋊C4—24no—
585C22⋊C4—42no—
586C22⋊C4—42no—
587C22⋊C4—42no—
588C22⋊C4—42no—
589C22⋊C4—42no—
590C22⋊C4—42no—
591C22⋊C4—81no—
592C22⋊C4—81no—
593C22⋊C4—81no—
594C42—21no—
595C42—21no—
596C42—21no—
597C42—21no—
598C42—21no—
599C42—21no—
600C11#2617411yescharacteristic, direct product factor, Sylow
601C23—22no—
602C23—22no—
603C23—22no—
604C23—22no—
605C23—41no—
606C23—41no—
607C23—41no—
608C23—41no—
609C23—41no—
610C23—41no—
611C23—41no—
612C23—41no—
613C23—41no—
614C23—41no—
615C23—41no—
616C23—41no—
617C23—41no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23—41no—
622C23C22×D4×C1111yescharacteristic
623D4—22no—
624D4—22no—
625D4—22no—
626D4—22no—
627D4—22no—
628D4—41no—
629D4—41no—
630D4—41no—
631D4—41no—
632D4—41no—
633D4—41no—
634D4—84no—
635D4—84no—
636D4C11×#12314yescomplemented
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—22no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—48no—
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—84no—
670C2×C4—84no—
671C2×C4—84no—
672C2×C4C11×AGL(1,ℤ/8)12yes—
673C2×C4C11×AGL(1,ℤ/8)12yes—
674C2×C4C22×D4×C1111yescharacteristic
675C2×C4C2×C11×#4111yescharacteristic
676C2×C4C2×C11×#4111yescharacteristic
677C2×C4C2×C11×#4111yescharacteristic
678C2×C4C11×H(5,𝔽2)11yescharacteristic
679C2×C4C11×2−1+411yescharacteristic
680C8—22no—
681C8—41no—
682C8—41no—
683C8—41no—
684C22—24no—
685C22—42no—
686C22—42no—
687C22—42no—
688C22—42no—
689C22—42no—
690C22—42no—
691C22—42no—
692C22—42no—
693C22—42no—
694C22—81no—
695C22—81no—
696C22—81no—
697C22—81no—
698C22—81no—
699C22—81no—
700C22—81no—
701C22—81no—
702C22—81no—
703C22—81no—
704C22—81no—
705C22C11×#52511yescharacteristic
706C22D42×C1111yescharacteristic
707C22C11×#54811yescharacteristic
708C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
709C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
710C22C11×#57611yescharacteristic
711C22C11×#57711yescharacteristic
712C4—22no—
713C4—22no—
714C4—41no—
715C4—41no—
716C4—41no—
717C4—42no—
718C4—41no—
719C4—81no—
720C4—81no—
721C4—81no—
722C4—81no—
723C4C2×C11×#12311yescharacteristic
724C4C11×#53911yescharacteristic
725C4C11×#54711yescharacteristic
726C4C11×#55311yescharacteristic
727C2—44no—
728C2—82no—
729C2—161no—
730C2C11×#244311yescharacteristic
731C2C11×#310911yescharacteristic
732C2C11×#311911yescharacteristic
733C2C11×#326411yescharacteristic
734C2C11×#327211yescharacteristic
735C2C11×#336611yescharacteristic
736C2C11×#337311yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#459C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C4×C11×C4⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#442C2semidirect
3. C11×#2445C2semidirect
4. D4×C11×C4⋊C4C2semidirect
5. C11×#2094C2semidirect
6. C11×#2088C2semidirect
7. C11×#2071C2semidirect
8. C11×#2041C2semidirect
9. C11×#1936C2semidirect
10. C11×#1917C2semidirect
11. C11×#1879C2semidirect
12. C11×#1879C2semidirect
13. C11×#1879C2semidirect
14. C11×#1864C2semidirect
15. C11×#1864C2semidirect
134. #26174C11direct (N × H)
234. C2×#442C2×C11semidirect
235. #2445C2×C11semidirect
236. D4×C4⋊C4C2×C11semidirect
237. #2094C2×C11semidirect
238. #2088C2×C11semidirect
239. #2071C2×C11semidirect
240. #2041C2×C11semidirect
241. #1936C2×C11semidirect
242. #1917C2×C11semidirect
243. #1879C2×C11semidirect
244. #1879C2×C11semidirect
245. #1879C2×C11semidirect
246. #1864C2×C11semidirect
247. #1864C2×C11semidirect
283. D4×C11#123semidirect
600. C11#26174direct (N × H)
636. D4C11×#123semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#4592
C2×C11×#4422
C11×#24452
D4×C11×C4⋊C42
C11×#20942
C11×#20882
C11×#20712
C11×#20412
C11×#19362
C11×#19172
C11×#18792
C11×#18642
#2617411