Finite Group Databasebeta

← C11×#24539 #14601732

Subgroups — C11×#24539 #14601732

Order 2816.

1198 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#447C211yesmaximal, characteristic
2C2×C11×#418C211yesmaximal, characteristic, complemented
3C11×#2500C211yesmaximal, characteristic, complemented
4D4×C11×C22⋊C4C211yesmaximal, characteristic, complemented
5C11×#2073C211yesmaximal, characteristic, complemented
6C11×#2071C211yesmaximal, characteristic, complemented
7C11×#2054C211yesmaximal, characteristic, complemented
8C11×#2054C211yesmaximal, characteristic, complemented
9C11×#1895C211yesmaximal, characteristic, complemented
10C11×#1879C211yesmaximal, characteristic, complemented
11C11×#1879C211yesmaximal, characteristic, complemented
12C11×#1851C211yesmaximal, characteristic, complemented
13C11×#1825C211yesmaximal, characteristic, complemented
14C11×#1804C211yesmaximal, characteristic, complemented
15C11×#1802C211yesmaximal, characteristic, complemented
16C23×D4×C11C2211yescharacteristic
17C22×C11×D8C2211yescharacteristic
18C22×C11×D8C2211yescharacteristic
19C22×C11×M16C2211yescharacteristic
20C2×C11×#121C2211yescharacteristic
21C2×C4×D4×C11C2211yescharacteristic
22C2×C4×D4×C11C2211yescharacteristic
23C2×C11×#117C2211yescharacteristic
24C22×C11×C22⋊C4—21no—
25C11×#447—24no—
26C2×C11×C4⋊C8C2211yescharacteristic, complemented
27C2×C11×C4⋊C8C2211yescharacteristic, complemented
28C11×#418—24no—
29C2×C11×#102C2211yescharacteristic
30C2×C11×#102C2211yescharacteristic
31C2×C11×#102C2211yescharacteristic
32C2×C11×#102C2211yescharacteristic
33C2×C11×#102C2211yescharacteristic
34C2×C11×#102C2211yescharacteristic
35C2×C11×#102C2211yescharacteristic, complemented
36C2×C11×#102C2211yescharacteristic, complemented
37C2×C11×C22⋊C8C2211yescharacteristic
38C11×#394—21no—
39C11×#394—21no—
40C11×#390C2211yescharacteristic
41C11×#390C2211yescharacteristic
42C11×#390C2211yescharacteristic, complemented
43C11×#390C2211yescharacteristic, complemented
44C11×#388—21no—
45C11×#388—21no—
46C11×#386—21no—
47C11×#386—21no—
48C11×#384C2211yescharacteristic, complemented
49C11×#382C2211yescharacteristic, complemented
50C11×#380C2211yescharacteristic
51C11×#379—21no—
52C4×C11×C22⋊C4C2211yescharacteristic
53C11×#340C2211yescharacteristic, complemented
54C11×#340C2211yescharacteristic, complemented
55C11×#340C2211yescharacteristic, complemented
56C11×#340C2211yescharacteristic, complemented
57C11×#340C2211yescharacteristic, complemented
58C11×#340C2211yescharacteristic, complemented
59C11×#336C2211yescharacteristic, complemented
60C11×#336C2211yescharacteristic, complemented
61C25×C11—21no—
62C22×D4×C11—22no—
63C22×D4×C11—22no—
64C22×D4×C11—21no—
65C22×D4×C11—21no—
66C22×D4×C11—22no—
67C22×D4×C11—41no—
68C22×D4×C11—41no—
69C22×D4×C11D414yes—
70C22×D4×C11C2311yescharacteristic
71C22×D4×C11C2311yescharacteristic
72C22×D4×C11C2311yescharacteristic
73C23×C4×C11—21no—
74C23×C4×C11—21no—
75C23×C4×C11C2311yescharacteristic
76C2×C11×D8—22no—
77C2×C11×D8—22no—
78C2×C11×D8—22no—
79C2×C11×D8—22no—
80C2×C11×D8—41no—
81C2×C11×D8—41no—
82C2×C11×M16—22no—
83C2×C11×M16—41no—
84C2×C11×M16—41no—
85C22×C8×C11C2311yescharacteristic
86C22×C8×C11C2311yescharacteristic
87C22×C8×C11C2311yescharacteristic
88C22×C8×C11C2311yescharacteristic
89C11×#121—22no—
90C11×#121—22no—
91C4×D4×C11—22no—
92C4×D4×C11—22no—
93C4×D4×C11—41no—
94C4×D4×C11—41no—
95C11×#117—22no—
96C11×#117—22no—
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⋊C4—21no—
111C2×C11×C22⋊C4—21no—
112C2×C11×C22⋊C4—21no—
113C2×C11×C22⋊C4—21no—
114C2×C11×C22⋊C4—21no—
115C2×C11×C22⋊C4—21no—
116C2×C11×C22⋊C4—21no—
117C2×C11×C22⋊C4—44no—
118C2×C11×C22⋊C4D411yescharacteristic
119C2×C11×C22⋊C4D411yescharacteristic
120C2×C42×C11—21no—
121C2×C42×C11C2311yescharacteristic
122C2×C42×C11C2311yescharacteristic
123C11×C4⋊C8—41no—
124C11×C4⋊C8—41no—
125C11×#102—22no—
126C11×#102—22no—
127C11×#102—22no—
128C11×#102—22no—
129C11×#102—22no—
130C11×#102—22no—
131C11×#102—41no—
132C11×#102—41no—
133C11×C22⋊C8—22no—
134C11×#95—21no—
135C11×#95—21no—
136C11×#95—21no—
137C11×#95D411yescharacteristic
138C11×#95D411yescharacteristic
139#24539C1111yesmaximal, characteristic, direct product factor, Sylow
140C24×C11—21no—
141C24×C11—21no—
142C24×C11—24no—
143C24×C11—21no—
144C24×C11—42no—
145C24×C11—42no—
146C24×C11—42no—
147C24×C11—42no—
148C24×C11—81no—
149C24×C11—81no—
150C24×C11C2×D411yescharacteristic
151C2×D4×C11—28no—
152C2×D4×C11—24no—
153C2×D4×C11—21no—
154C2×D4×C11—21no—
155C2×D4×C11—21no—
156C2×D4×C11—21no—
157C2×D4×C11—21no—
158C2×D4×C11—21no—
159C2×D4×C11—21no—
160C2×D4×C11—21no—
161C2×D4×C11—21no—
162C2×D4×C11—21no—
163C2×D4×C11—21no—
164C2×D4×C11—21no—
165C2×D4×C11—21no—
166C2×D4×C11—21no—
167C2×D4×C11—44no—
168C2×D4×C11—44no—
169C2×D4×C11—44no—
170C2×D4×C11—42no—
171C2×D4×C11—42no—
172C2×D4×C11—42no—
173C2×D4×C11—81no—
174C2×D4×C11—81no—
175C2×D4×C11C2×D412yes—
176C2×D4×C11C2×D412yes—
177C2×D4×C11#4112yes—
178C2×D4×C11#4112yes—
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—21no—
188C22×C4×C11—42no—
189C22×C4×C11—42no—
190C22×C4×C11—42no—
191C22×C4×C11—42no—
192C22×C4×C11—81no—
193C22×C4×C11—81no—
194C22×C4×C11C2×D411yescharacteristic
195C22×C4×C11C2×D411yescharacteristic
196C22×C4×C11C2×D411yescharacteristic
197C22×C4×C11C2×D411yescharacteristic
198C22×C4×C11C2×D412yes—
199C22×C4×C11C2×D411yescharacteristic
200C22×C4×C11#4112yes—
201C22×C4×C11C2411yescharacteristic
202C11×D8—44no—
203C11×D8—44no—
204C11×M16—44no—
205C2×C8×C11—21no—
206C2×C8×C11—21no—
207C2×C8×C11—21no—
208C2×C8×C11—21no—
209C2×C8×C11—21no—
210C2×C8×C11—21no—
211C2×C8×C11—21no—
212C2×C8×C11—21no—
213C2×C8×C11—21no—
214C2×C8×C11—21no—
215C2×C8×C11—21no—
216C2×C8×C11—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—21no—
224C11×C4⋊C4—21no—
225C11×C4⋊C4—21no—
226C11×C4⋊C4—21no—
227C11×C4⋊C4—81no—
228C11×C4⋊C4—81no—
229C11×C22⋊C4—22no—
230C11×C22⋊C4—41no—
231C11×C22⋊C4—42no—
232C11×C22⋊C4—42no—
233C11×C22⋊C4—42no—
234C11×C22⋊C4—42no—
235C11×C22⋊C4—42no—
236C11×C22⋊C4—42no—
237C11×C22⋊C4—42no—
238C11×C22⋊C4—42no—
239C11×C22⋊C4—42no—
240C11×C22⋊C4—81no—
241C11×C22⋊C4—81no—
242C11×C22⋊C4—81no—
243C11×C22⋊C4—81no—
244C42×C11—21no—
245C42×C11—21no—
246C42×C11—21no—
247C42×C11—21no—
248C42×C11—42no—
249C2×#447C2×C1111yescharacteristic
250C2×#418C2×C1111yescharacteristic, complemented
251#2500C2×C1111yescharacteristic, complemented
252D4×C22⋊C4C2×C1111yescharacteristic, complemented
253#2073C2×C1111yescharacteristic, complemented
254#2071C2×C1111yescharacteristic, complemented
255#2054C2×C1111yescharacteristic, complemented
256#2054C2×C1111yescharacteristic, complemented
257#1895C2×C1111yescharacteristic, complemented
258#1879C2×C1111yescharacteristic, complemented
259#1879C2×C1111yescharacteristic, complemented
260#1851C2×C1111yescharacteristic, complemented
261#1825C2×C1111yescharacteristic, complemented
262#1804C2×C1111yescharacteristic, complemented
263#1802C2×C1111yescharacteristic, complemented
264C23×C11—22no—
265C23×C11—22no—
266C23×C11—22no—
267C23×C11—21no—
268C23×C11—21no—
269C23×C11—21no—
270C23×C11—21no—
271C23×C11—21no—
272C23×C11—21no—
273C23×C11—22no—
274C23×C11—48no—
275C23×C11—48no—
276C23×C11—41no—
277C23×C11—41no—
278C23×C11—41no—
279C23×C11—41no—
280C23×C11—41no—
281C23×C11—41no—
282C23×C11—41no—
283C23×C11—41no—
284C23×C11—41no—
285C23×C11—41no—
286C23×C11—41no—
287C23×C11—41no—
288C23×C11—41no—
289C23×C11—41no—
290C23×C11—41no—
291C23×C11—41no—
292C23×C11—41no—
293C23×C11—84no—
294C23×C11—84no—
295C23×C11—84no—
296C23×C11—84no—
297C23×C11—84no—
298C23×C11#12112yes—
299C23×C11C22×D411yescharacteristic
300D4×C11—22no—
301D4×C11—22no—
302D4×C11—22no—
303D4×C11—22no—
304D4×C11—22no—
305D4×C11—48no—
306D4×C11—41no—
307D4×C11—41no—
308D4×C11—41no—
309D4×C11—41no—
310D4×C11—41no—
311D4×C11—41no—
312D4×C11—84no—
313D4×C11#12314yes—
314C2×C4×C11—21no—
315C2×C4×C11—21no—
316C2×C4×C11—21no—
317C2×C4×C11—21no—
318C2×C4×C11—22no—
319C2×C4×C11—22no—
320C2×C4×C11—22no—
321C2×C4×C11—22no—
322C2×C4×C11—21no—
323C2×C4×C11—21no—
324C2×C4×C11—21no—
325C2×C4×C11—21no—
326C2×C4×C11—21no—
327C2×C4×C11—21no—
328C2×C4×C11—21no—
329C2×C4×C11—21no—
330C2×C4×C11—21no—
331C2×C4×C11—41no—
332C2×C4×C11—41no—
333C2×C4×C11—41no—
334C2×C4×C11—41no—
335C2×C4×C11—41no—
336C2×C4×C11—41no—
337C2×C4×C11—41no—
338C2×C4×C11—41no—
339C2×C4×C11—41no—
340C2×C4×C11—41no—
341C2×C4×C11—41no—
342C2×C4×C11—41no—
343C2×C4×C11—41no—
344C2×C4×C11—41no—
345C2×C4×C11—41no—
346C2×C4×C11—84no—
347C2×C4×C11—84no—
348C2×C4×C11#12112yes—
349C2×C4×C11AGL(1,ℤ/8)12yes—
350C2×C4×C11C22×D411yescharacteristic
351C2×C4×C11C2×#4111yescharacteristic
352C2×C4×C11C2×#4111yescharacteristic
353C2×C4×C11C2×#4111yescharacteristic
354C2×C4×C11H(5,𝔽2)11yescharacteristic
355C2×C4×C11H(5,𝔽2)11yescharacteristic
356C8×C11—41no—
357C8×C11—41no—
358C8×C11—41no—
359C8×C11—41no—
360C23×D4C22×C1111yescharacteristic
361C22×D8C22×C1111yescharacteristic
362C22×D8C22×C1111yescharacteristic
363C22×M16C22×C1111yescharacteristic
364C2×#121C22×C1111yescharacteristic
365C2×C4×D4C22×C1111yescharacteristic
366C2×C4×D4C22×C1111yescharacteristic
367C2×#117C22×C1111yescharacteristic
368C22×C22⋊C4—21no—
369#447—24no—
370C2×C4⋊C8C22×C1111yescharacteristic, complemented
371C2×C4⋊C8C22×C1111yescharacteristic, complemented
372#418—24no—
373C2×#102C22×C1111yescharacteristic
374C2×#102C22×C1111yescharacteristic
375C2×#102C22×C1111yescharacteristic
376C2×#102C22×C1111yescharacteristic
377C2×#102C22×C1111yescharacteristic
378C2×#102C22×C1111yescharacteristic
379C2×#102C22×C1111yescharacteristic, complemented
380C2×#102C22×C1111yescharacteristic, complemented
381C2×C22⋊C8C22×C1111yescharacteristic
382#394—21no—
383#394—21no—
384#390C22×C1111yescharacteristic
385#390C22×C1111yescharacteristic
386#390C22×C1111yescharacteristic, complemented
387#390C22×C1111yescharacteristic, complemented
388#388—21no—
389#388—21no—
390#386—21no—
391#386—21no—
392#384C22×C1111yescharacteristic, complemented
393#382C22×C1111yescharacteristic, complemented
394#380C22×C1111yescharacteristic
395#379—21no—
396C4×C22⋊C4C22×C1111yescharacteristic
397#340C22×C1111yescharacteristic, complemented
398#340C22×C1111yescharacteristic, complemented
399#340C22×C1111yescharacteristic, complemented
400#340C22×C1111yescharacteristic, complemented
401#340C22×C1111yescharacteristic, complemented
402#340C22×C1111yescharacteristic, complemented
403#336C22×C1111yescharacteristic, complemented
404#336C22×C1111yescharacteristic, complemented
405C22×C11—22no—
406C22×C11—24no—
407C22×C11—22no—
408C22×C11—22no—
409C22×C11—42no—
410C22×C11—42no—
411C22×C11—42no—
412C22×C11—41no—
413C22×C11—41no—
414C22×C11—42no—
415C22×C11—41no—
416C22×C11—42no—
417C22×C11—42no—
418C22×C11—41no—
419C22×C11—42no—
420C22×C11—42no—
421C22×C11—42no—
422C22×C11—816no—
423C22×C11—81no—
424C22×C11—81no—
425C22×C11—81no—
426C22×C11—81no—
427C22×C11—81no—
428C22×C11—81no—
429C22×C11—81no—
430C22×C11—81no—
431C22×C11—81no—
432C22×C11—81no—
433C22×C11—81no—
434C22×C11C2×#12111yescharacteristic
435C22×C11#54611yescharacteristic
436C22×C11#54611yescharacteristic
437C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
438C22×C11#57511yescharacteristic
439C22×C11#57611yescharacteristic
440C22×C11#57611yescharacteristic
441C4×C11—22no—
442C4×C11—22no—
443C4×C11—41no—
444C4×C11—41no—
445C4×C11—41no—
446C4×C11—81no—
447C4×C11—81no—
448C4×C11—81no—
449C4×C11—81no—
450C4×C11—81no—
451C4×C11C2×#12311yescharacteristic
452C4×C11#53411yescharacteristic
453C4×C11#55111yescharacteristic
454C4×C11#55111yescharacteristic
455C25—21no—
456C22×D4—22no—
457C22×D4—22no—
458C22×D4—21no—
459C22×D4—21no—
460C22×D4—22no—
461C22×D4—41no—
462C22×D4—41no—
463C22×D4D4×C1114yes—
464C22×D4C23×C1111yescharacteristic
465C22×D4C23×C1111yescharacteristic
466C22×D4C23×C1111yescharacteristic
467C23×C4—21no—
468C23×C4—21no—
469C23×C4C23×C1111yescharacteristic
470C2×D8—22no—
471C2×D8—22no—
472C2×D8—22no—
473C2×D8—22no—
474C2×D8—41no—
475C2×D8—41no—
476C2×M16—22no—
477C2×M16—41no—
478C2×M16—41no—
479C22×C8C23×C1111yescharacteristic
480C22×C8C23×C1111yescharacteristic
481C22×C8C23×C1111yescharacteristic
482C22×C8C23×C1111yescharacteristic
483#121—22no—
484#121—22no—
485C4×D4—22no—
486C4×D4—22no—
487C4×D4—41no—
488C4×D4—41no—
489#117—22no—
490#117—22no—
491C2×C4⋊C4—21no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4C23×C1111yescharacteristic
494C2×C4⋊C4C23×C1111yescharacteristic
495C2×C4⋊C4C23×C1111yescharacteristic
496C2×C4⋊C4C23×C1111yescharacteristic
497C2×C4⋊C4C23×C1111yescharacteristic
498C2×C22⋊C4—21no—
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—21no—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4—21no—
506C2×C22⋊C4—21no—
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—44no—
512C2×C22⋊C4D4×C1111yescharacteristic
513C2×C22⋊C4D4×C1111yescharacteristic
514C2×C42—21no—
515C2×C42C23×C1111yescharacteristic
516C2×C42C23×C1111yescharacteristic
517C4⋊C8—41no—
518C4⋊C8—41no—
519#102—22no—
520#102—22no—
521#102—22no—
522#102—22no—
523#102—22no—
524#102—22no—
525#102—41no—
526#102—41no—
527C22⋊C8—22no—
528#95—21no—
529#95—21no—
530#95—21no—
531#95D4×C1111yescharacteristic
532#95D4×C1111yescharacteristic
533C2×C11—42no—
534C2×C11—44no—
535C2×C11—82no—
536C2×C11—161no—
537C2×C11#241211yescharacteristic
538C2×C11#303611yescharacteristic
539C2×C11#304111yescharacteristic
540C2×C11#331811yescharacteristic
541C2×C11#331911yescharacteristic
542C2×C11#332211yescharacteristic
543C2×C11#332511yescharacteristic
544C24—21no—
545C24—21no—
546C24—24no—
547C24—21no—
548C24—42no—
549C24—42no—
550C24—42no—
551C24—42no—
552C24—81no—
553C24—81no—
554C24C2×D4×C1111yescharacteristic
555C2×D4—28no—
556C2×D4—24no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—44no—
572C2×D4—44no—
573C2×D4—44no—
574C2×D4—42no—
575C2×D4—42no—
576C2×D4—42no—
577C2×D4—81no—
578C2×D4—81no—
579C2×D4C2×D4×C1112yes—
580C2×D4C2×D4×C1112yes—
581C2×D4C11×#4112yes—
582C2×D4C11×#4112yes—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—42no—
593C22×C4—42no—
594C22×C4—42no—
595C22×C4—42no—
596C22×C4—81no—
597C22×C4—81no—
598C22×C4C2×D4×C1111yescharacteristic
599C22×C4C2×D4×C1111yescharacteristic
600C22×C4C2×D4×C1111yescharacteristic
601C22×C4C2×D4×C1111yescharacteristic
602C22×C4C2×D4×C1112yes—
603C22×C4C2×D4×C1111yescharacteristic
604C22×C4C11×#4112yes—
605C22×C4C24×C1111yescharacteristic
606D8—44no—
607D8—44no—
608M16—44no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—21no—
619C2×C8—21no—
620C2×C8—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—81no—
632C4⋊C4—81no—
633C22⋊C4—22no—
634C22⋊C4—41no—
635C22⋊C4—42no—
636C22⋊C4—42no—
637C22⋊C4—42no—
638C22⋊C4—42no—
639C22⋊C4—42no—
640C22⋊C4—42no—
641C22⋊C4—42no—
642C22⋊C4—42no—
643C22⋊C4—42no—
644C22⋊C4—81no—
645C22⋊C4—81no—
646C22⋊C4—81no—
647C22⋊C4—81no—
648C42—21no—
649C42—21no—
650C42—21no—
651C42—21no—
652C42—42no—
653C11#2453911yescharacteristic, direct product factor, Sylow
654C23—22no—
655C23—22no—
656C23—22no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—22no—
664C23—48no—
665C23—48no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—84no—
684C23—84no—
685C23—84no—
686C23—84no—
687C23—84no—
688C23C11×#12112yes—
689C23C22×D4×C1111yescharacteristic
690D4—22no—
691D4—22no—
692D4—22no—
693D4—22no—
694D4—22no—
695D4—48no—
696D4—41no—
697D4—41no—
698D4—41no—
699D4—41no—
700D4—41no—
701D4—41no—
702D4—84no—
703D4C11×#12314yes—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—84no—
737C2×C4—84no—
738C2×C4C11×#12112yes—
739C2×C4C11×AGL(1,ℤ/8)12yes—
740C2×C4C22×D4×C1111yescharacteristic
741C2×C4C2×C11×#4111yescharacteristic
742C2×C4C2×C11×#4111yescharacteristic
743C2×C4C2×C11×#4111yescharacteristic
744C2×C4C11×H(5,𝔽2)11yescharacteristic
745C2×C4C11×H(5,𝔽2)11yescharacteristic
746C8—41no—
747C8—41no—
748C8—41no—
749C8—41no—
750C22—22no—
751C22—24no—
752C22—22no—
753C22—22no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—41no—
758C22—41no—
759C22—42no—
760C22—41no—
761C22—42no—
762C22—42no—
763C22—41no—
764C22—42no—
765C22—42no—
766C22—42no—
767C22—816no—
768C22—81no—
769C22—81no—
770C22—81no—
771C22—81no—
772C22—81no—
773C22—81no—
774C22—81no—
775C22—81no—
776C22—81no—
777C22—81no—
778C22—81no—
779C22C2×C11×#12111yescharacteristic
780C22C11×#54611yescharacteristic
781C22C11×#54611yescharacteristic
782C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
783C22C11×#57511yescharacteristic
784C22C11×#57611yescharacteristic
785C22C11×#57611yescharacteristic
786C4—22no—
787C4—22no—
788C4—41no—
789C4—41no—
790C4—41no—
791C4—81no—
792C4—81no—
793C4—81no—
794C4—81no—
795C4—81no—
796C4C2×C11×#12311yescharacteristic
797C4C11×#53411yescharacteristic
798C4C11×#55111yescharacteristic
799C4C11×#55111yescharacteristic
800C2—42no—
801C2—44no—
802C2—82no—
803C2—161no—
804C2C11×#241211yescharacteristic
805C2C11×#303611yescharacteristic
806C2C11×#304111yescharacteristic
807C2C11×#331811yescharacteristic
808C2C11×#331911yescharacteristic
809C2C11×#332211yescharacteristic
810C2C11×#332511yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#447C2
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×C11×#418C2semidirect
3. C11×#2500C2semidirect
4. D4×C11×C22⋊C4C2semidirect
5. C11×#2073C2semidirect
6. C11×#2071C2semidirect
7. C11×#2054C2semidirect
8. C11×#2054C2semidirect
9. C11×#1895C2semidirect
10. C11×#1879C2semidirect
11. C11×#1879C2semidirect
12. C11×#1851C2semidirect
13. C11×#1825C2semidirect
14. C11×#1804C2semidirect
15. C11×#1802C2semidirect
26. C2×C11×C4⋊C8C22semidirect
27. C2×C11×C4⋊C8C22semidirect
35. C2×C11×#102C22semidirect
36. C2×C11×#102C22semidirect
42. C11×#390C22semidirect
43. C11×#390C22semidirect
48. C11×#384C22semidirect
49. C11×#382C22semidirect
53. C11×#340C22semidirect
54. C11×#340C22semidirect
55. C11×#340C22semidirect
56. C11×#340C22semidirect
57. C11×#340C22semidirect
58. C11×#340C22semidirect
59. C11×#336C22semidirect
60. C11×#336C22semidirect
139. #24539C11direct (N × H)
250. C2×#418C2×C11semidirect
251. #2500C2×C11semidirect
252. D4×C22⋊C4C2×C11semidirect
253. #2073C2×C11semidirect
254. #2071C2×C11semidirect
255. #2054C2×C11semidirect
256. #2054C2×C11semidirect
257. #1895C2×C11semidirect
258. #1879C2×C11semidirect
259. #1879C2×C11semidirect
260. #1851C2×C11semidirect
261. #1825C2×C11semidirect
262. #1804C2×C11semidirect
263. #1802C2×C11semidirect
370. C2×C4⋊C8C22×C11semidirect
371. C2×C4⋊C8C22×C11semidirect
379. C2×#102C22×C11semidirect
380. C2×#102C22×C11semidirect
386. #390C22×C11semidirect
387. #390C22×C11semidirect
392. #384C22×C11semidirect
393. #382C22×C11semidirect
397. #340C22×C11semidirect
398. #340C22×C11semidirect
399. #340C22×C11semidirect
400. #340C22×C11semidirect
401. #340C22×C11semidirect
402. #340C22×C11semidirect
403. #336C22×C11semidirect
404. #336C22×C11semidirect
653. C11#24539direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4472
C2×C11×#4182
C11×#25002
D4×C11×C22⋊C42
C11×#20732
C11×#20712
C11×#20542
C11×#18952
C11×#18792
C11×#18512
C11×#18252
C11×#18042
C11×#18022
#2453911