Finite Group Databasebeta

← C11×#22445 #14599638

Subgroups — C11×#22445 #14599638

Order 2816.

1406 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×#137C211yesmaximal, characteristic
2C2×C11×#441C211yesmaximal, characteristic, complemented
3C2×C4×C11×Q16C211yesmaximal, characteristic, complemented
4C11×#2341C211yesmaximal, characteristic
5Q8×C11×C22⋊C4C211yesmaximal, characteristic, complemented
6C11×#1973C211yesmaximal, characteristic, complemented
7C11×#1968C211yesmaximal, characteristic, complemented
8C11×#1880C211yesmaximal, characteristic, complemented
9C11×#1880C211yesmaximal, characteristic, complemented
10C11×#1878C211yesmaximal, characteristic, complemented
11C11×#1878C211yesmaximal, characteristic, complemented
12C11×#1809C211yesmaximal, characteristic, complemented
13C11×#1788C211yesmaximal, characteristic
14C11×#1787C211yesmaximal, characteristic, complemented
15C11×#1753C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic
17C23×Q8×C11C2211yescharacteristic
18C2×C11×#137—24no—
19C2×C11×#137—24no—
20C2×C11×#137C418yescomplemented
21C22×C11×Q16C2211yescharacteristic
22C22×C11×Q16C2211yescharacteristic
23C22×C11×SD16C2211yescharacteristic
24C22×C11×SD16C2211yescharacteristic
25C22×C11×M16C2211yescharacteristic
26C2×C4×Q8×C11C2211yescharacteristic
27C2×C4×Q8×C11C2211yescharacteristic
28C2×C4×Q8×C11C2211yescharacteristic
29C2×C4×Q8×C11C2211yescharacteristic
30C11×#441—24no—
31C4×C11×Q16—24no—
32C2×C11×#107C2211yescharacteristic
33C2×C11×#106C2211yescharacteristic
34C2×C11×#103C2211yescharacteristic
35C2×C11×#103C2211yescharacteristic
36C2×C11×#103C2211yescharacteristic
37C2×C11×#103C2211yescharacteristic
38C2×C11×#103C2211yescharacteristic
39C2×C11×#103C2211yescharacteristic
40C2×C11×#102C2211yescharacteristic
41C2×C11×#102C2211yescharacteristic
42C2×C11×C22⋊C8C2211yescharacteristic
43C2×C11×#97C2211yescharacteristic
44C2×C4×C8×C11C2211yescharacteristic
45C11×#391—21no—
46C11×#391—21no—
47C11×#391C2211yescharacteristic
48C11×#391C2211yescharacteristic
49C11×#390—21no—
50C11×#390—21no—
51C11×#390C2211yescharacteristic
52C11×#390C2211yescharacteristic
53C11×#380—21no—
54C11×#380—21no—
55C11×#380C2211yescharacteristic
56C11×#380C2211yescharacteristic
57C4×C11×C22⋊C4—21no—
58C4×C11×C22⋊C4—21no—
59C4×C11×C22⋊C4C2211yescharacteristic
60C11×#340C2211yescharacteristic
61C11×#340C2211yescharacteristic
62C11×#336C2211yescharacteristic
63C11×#336C2211yescharacteristic
64C2×C11×#41—22no—
65C2×C11×#41—22no—
66C2×C11×#41—22no—
67C2×C11×#41—41no—
68C2×C11×#41—41no—
69C2×C11×#41C2×C414yes—
70C22×Q8×C11—21no—
71C22×Q8×C11—22no—
72C22×Q8×C11—22no—
73C22×Q8×C11—22no—
74C22×Q8×C11—41no—
75C22×Q8×C11—41no—
76C22×Q8×C11C2×C414yes—
77C22×Q8×C11C2311yescharacteristic
78C22×Q8×C11C2311yescharacteristic
79C22×Q8×C11C2311yescharacteristic
80C22×D4×C11—21no—
81C22×D4×C11C2311yescharacteristic
82C23×C4×C11—21no—
83C23×C4×C11—21no—
84C23×C4×C11C2311yescharacteristic
85C11×#137—232no—
86C2×C11×Q16—22no—
87C2×C11×Q16—22no—
88C2×C11×Q16C2×C414yes—
89C2×C11×Q16C2×C414yes—
90C2×C11×Q16D414yes—
91C2×C11×Q16D414yes—
92C2×C11×SD16—22no—
93C2×C11×SD16—22no—
94C2×C11×SD16—22no—
95C2×C11×SD16—22no—
96C2×C11×SD16C2×C414yes—
97C2×C11×SD16C2×C414yes—
98C2×C11×M16—22no—
99C2×C11×M16—22no—
100C2×C11×M16C2×C414yes—
101C22×C8×C11C2311yescharacteristic
102C22×C8×C11C2311yescharacteristic
103C22×C8×C11C2311yescharacteristic
104C22×C8×C11C2311yescharacteristic
105C4×Q8×C11—22no—
106C4×Q8×C11—22no—
107C4×Q8×C11—22no—
108C4×Q8×C11—22no—
109C4×Q8×C11—41no—
110C4×Q8×C11—41no—
111C4×Q8×C11—41no—
112C4×Q8×C11—41no—
113C2×C11×C4⋊C4—21no—
114C2×C11×C4⋊C4—21no—
115C2×C11×C4⋊C4—21no—
116C2×C11×C4⋊C4—21no—
117C2×C11×C4⋊C4C2311yescharacteristic
118C2×C11×C4⋊C4C2311yescharacteristic
119C2×C11×C4⋊C4C2311yescharacteristic
120C2×C11×C4⋊C4C2311yescharacteristic
121C2×C11×C22⋊C4—21no—
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⋊C4D411yescharacteristic
128C2×C11×C22⋊C4D411yescharacteristic
129C2×C42×C11—21no—
130C2×C42×C11—21no—
131C2×C42×C11—21no—
132C2×C42×C11—21no—
133C2×C42×C11C2311yescharacteristic
134C2×C42×C11C2311yescharacteristic
135C11×#107—22no—
136C11×#106—22no—
137C11×#103—22no—
138C11×#103—22no—
139C11×#103—22no—
140C11×#103—22no—
141C11×#103—41no—
142C11×#103—41no—
143C11×#102—41no—
144C11×#102—41no—
145C11×C22⋊C8—22no—
146C11×#97—22no—
147C4×C8×C11—22no—
148C11×#95—21no—
149C11×#95—21no—
150C11×#95—21no—
151C11×#95—21no—
152C11×#95—21no—
153C11×#95—21no—
154C11×#95D411yescharacteristic
155C11×#95D411yescharacteristic
156#22445C1111yesmaximal, characteristic, direct product factor, Sylow
157C24×C11—21no—
158C24×C11C2×D411yescharacteristic
159C11×#41—28no—
160C11×#41—44no—
161C11×#41—44no—
162C11×#41—44no—
163C2×Q8×C11—24no—
164C2×Q8×C11—21no—
165C2×Q8×C11—21no—
166C2×Q8×C11—21no—
167C2×Q8×C11—21no—
168C2×Q8×C11—21no—
169C2×Q8×C11—21no—
170C2×Q8×C11—21no—
171C2×Q8×C11—28no—
172C2×Q8×C11—21no—
173C2×Q8×C11—21no—
174C2×Q8×C11—21no—
175C2×Q8×C11—21no—
176C2×Q8×C11—42no—
177C2×Q8×C11—42no—
178C2×Q8×C11—44no—
179C2×Q8×C11—44no—
180C2×Q8×C11—44no—
181C2×Q8×C11C22×C412yes—
182C2×Q8×C11C22×C412yes—
183C2×Q8×C11C22×C412yes—
184C2×Q8×C11C2×D412yes—
185C2×Q8×C11C2×D412yes—
186C2×Q8×C11C2×D412yes—
187C2×Q8×C11C2×D412yes—
188C2×D4×C11—24no—
189C2×D4×C11—21no—
190C2×D4×C11—21no—
191C2×D4×C11—21no—
192C2×D4×C11—21no—
193C2×D4×C11—21no—
194C2×D4×C11—42no—
195C2×D4×C11—42no—
196C2×D4×C11C22×C412yes—
197C22×C4×C11—21no—
198C22×C4×C11—21no—
199C22×C4×C11—21no—
200C22×C4×C11—21no—
201C22×C4×C11—21no—
202C22×C4×C11—21no—
203C22×C4×C11—24no—
204C22×C4×C11—21no—
205C22×C4×C11—24no—
206C22×C4×C11—21no—
207C22×C4×C11—21no—
208C22×C4×C11—21no—
209C22×C4×C11—21no—
210C22×C4×C11—42no—
211C22×C4×C11—42no—
212C22×C4×C11—42no—
213C22×C4×C11—42no—
214C22×C4×C11C22×C412yes—
215C22×C4×C11C2×D411yescharacteristic
216C22×C4×C11C2×D411yescharacteristic
217C22×C4×C11C2×D411yescharacteristic
218C22×C4×C11C2×D411yescharacteristic
219C22×C4×C11C2×D411yescharacteristic
220C22×C4×C11#4112yes—
221C22×C4×C11C2411yescharacteristic
222C11×Q16—28no—
223C11×Q16C22⋊C4116yescomplemented
224C11×SD16—28no—
225C11×SD16—28no—
226C11×M16—28no—
227C2×C8×C11—21no—
228C2×C8×C11—21no—
229C2×C8×C11—21no—
230C2×C8×C11—21no—
231C2×C8×C11—21no—
232C2×C8×C11—21no—
233C2×C8×C11—21no—
234C2×C8×C11—21no—
235C2×C8×C11C22×C412yes—
236C2×C8×C11C22×C412yes—
237C2×C8×C11C2×D412yes—
238C2×C8×C11C2×D412yes—
239C11×C4⋊C4—21no—
240C11×C4⋊C4—21no—
241C11×C4⋊C4—21no—
242C11×C4⋊C4—21no—
243C11×C4⋊C4—21no—
244C11×C4⋊C4—21no—
245C11×C4⋊C4—21no—
246C11×C4⋊C4—21no—
247C11×C4⋊C4—42no—
248C11×C4⋊C4—42no—
249C11×C4⋊C4—42no—
250C11×C4⋊C4—42no—
251C11×C22⋊C4—22no—
252C11×C22⋊C4—41no—
253C11×C22⋊C4—42no—
254C11×C22⋊C4—42no—
255C11×C22⋊C4—42no—
256C11×C22⋊C4—81no—
257C11×C22⋊C4—81no—
258C11×C22⋊C4—81no—
259C42×C11—21no—
260C42×C11—21no—
261C42×C11—21no—
262C42×C11—21no—
263C42×C11—42no—
264C42×C11—42no—
265C42×C11—42no—
266C42×C11—42no—
267C22×#137C2×C1111yescharacteristic
268C2×#441C2×C1111yescharacteristic, complemented
269C2×C4×Q16C2×C1111yescharacteristic, complemented
270#2341C2×C1111yescharacteristic
271Q8×C22⋊C4C2×C1111yescharacteristic, complemented
272#1973C2×C1111yescharacteristic, complemented
273#1968C2×C1111yescharacteristic, complemented
274#1880C2×C1111yescharacteristic, complemented
275#1880C2×C1111yescharacteristic, complemented
276#1878C2×C1111yescharacteristic, complemented
277#1878C2×C1111yescharacteristic, complemented
278#1809C2×C1111yescharacteristic, complemented
279#1788C2×C1111yescharacteristic
280#1787C2×C1111yescharacteristic, complemented
281#1753C2×C1111yescharacteristic, complemented
282C23×C11—21no—
283C23×C11—21no—
284C23×C11—21no—
285C23×C11—21no—
286C23×C11—21no—
287C23×C11—21no—
288C23×C11—22no—
289C23×C11—41no—
290C23×C11—41no—
291C23×C11—41no—
292C23×C11—41no—
293C23×C11—41no—
294C23×C11—41no—
295C23×C11C4×D412yes—
296C23×C11C22×D411yescharacteristic
297Q8×C11—22no—
298Q8×C11—22no—
299Q8×C11—22no—
300Q8×C11—22no—
301Q8×C11—22no—
302Q8×C11—22no—
303Q8×C11—22no—
304Q8×C11—22no—
305Q8×C11—48no—
306Q8×C11—41no—
307Q8×C11—41no—
308Q8×C11C2×C22⋊C414yes—
309Q8×C11C2×C22⋊C414yes—
310D4×C11—22no—
311D4×C11—22no—
312D4×C11—48no—
313D4×C11—41no—
314D4×C11—41no—
315C2×C4×C11—22no—
316C2×C4×C11—22no—
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—22no—
326C2×C4×C11—22no—
327C2×C4×C11—22no—
328C2×C4×C11—22no—
329C2×C4×C11—22no—
330C2×C4×C11—21no—
331C2×C4×C11—21no—
332C2×C4×C11—21no—
333C2×C4×C11—21no—
334C2×C4×C11—21no—
335C2×C4×C11—21no—
336C2×C4×C11—21no—
337C2×C4×C11—21no—
338C2×C4×C11—21no—
339C2×C4×C11—48no—
340C2×C4×C11—48no—
341C2×C4×C11—41no—
342C2×C4×C11—41no—
343C2×C4×C11—41no—
344C2×C4×C11—41no—
345C2×C4×C11—41no—
346C2×C4×C11—41no—
347C2×C4×C11—41no—
348C2×C4×C11—41no—
349C2×C4×C11—41no—
350C2×C4×C11—41no—
351C2×C4×C11—41no—
352C2×C4×C11—41no—
353C2×C4×C11—41no—
354C2×C4×C11—41no—
355C2×C4×C11C4×D412yes—
356C2×C4×C11#13712yescomplemented
357C2×C4×C11C23×C411yescharacteristic
358C2×C4×C11C22×D411yescharacteristic
359C2×C4×C11C22×D411yescharacteristic
360C2×C4×C11C2×#4111yescharacteristic
361C2×C4×C11H(5,𝔽2)11yescharacteristic
362C2×C4×C11H(5,𝔽2)11yescharacteristic
363C8×C11—22no—
364C8×C11—41no—
365C8×C11—41no—
366C8×C11C2×C22⋊C414yes—
367C22×#41C22×C1111yescharacteristic
368C23×Q8C22×C1111yescharacteristic
369C2×#137—24no—
370C2×#137—24no—
371C2×#137C4×C1118yescomplemented
372C22×Q16C22×C1111yescharacteristic
373C22×Q16C22×C1111yescharacteristic
374C22×SD16C22×C1111yescharacteristic
375C22×SD16C22×C1111yescharacteristic
376C22×M16C22×C1111yescharacteristic
377C2×C4×Q8C22×C1111yescharacteristic
378C2×C4×Q8C22×C1111yescharacteristic
379C2×C4×Q8C22×C1111yescharacteristic
380C2×C4×Q8C22×C1111yescharacteristic
381#441—24no—
382C4×Q16—24no—
383C2×#107C22×C1111yescharacteristic
384C2×#106C22×C1111yescharacteristic
385C2×#103C22×C1111yescharacteristic
386C2×#103C22×C1111yescharacteristic
387C2×#103C22×C1111yescharacteristic
388C2×#103C22×C1111yescharacteristic
389C2×#103C22×C1111yescharacteristic
390C2×#103C22×C1111yescharacteristic
391C2×#102C22×C1111yescharacteristic
392C2×#102C22×C1111yescharacteristic
393C2×C22⋊C8C22×C1111yescharacteristic
394C2×#97C22×C1111yescharacteristic
395C2×C4×C8C22×C1111yescharacteristic
396#391—21no—
397#391—21no—
398#391C22×C1111yescharacteristic
399#391C22×C1111yescharacteristic
400#390—21no—
401#390—21no—
402#390C22×C1111yescharacteristic
403#390C22×C1111yescharacteristic
404#380—21no—
405#380—21no—
406#380C22×C1111yescharacteristic
407#380C22×C1111yescharacteristic
408C4×C22⋊C4—21no—
409C4×C22⋊C4—21no—
410C4×C22⋊C4C22×C1111yescharacteristic
411#340C22×C1111yescharacteristic
412#340C22×C1111yescharacteristic
413#336C22×C1111yescharacteristic
414#336C22×C1111yescharacteristic
415C22×C11—22no—
416C22×C11—22no—
417C22×C11—22no—
418C22×C11—41no—
419C22×C11—41no—
420C22×C11—41no—
421C22×C11—41no—
422C22×C11—42no—
423C22×C11—42no—
424C22×C11—42no—
425C22×C11—81no—
426C22×C11—81no—
427C22×C11—81no—
428C22×C11—81no—
429C22×C11C2×C4×D411yescharacteristic
430C22×C11D4211yescharacteristic
431C22×C11D4211yescharacteristic
432C22×C11C2×#13711yescharacteristic
433C22×C11#57511yescharacteristic
434C22×C11#57711yescharacteristic
435C22×C11#57811yescharacteristic
436C4×C11—22no—
437C4×C11—24no—
438C4×C11—24no—
439C4×C11—22no—
440C4×C11—42no—
441C4×C11—41no—
442C4×C11—41no—
443C4×C11—41no—
444C4×C11—81no—
445C4×C11—81no—
446C4×C11—81no—
447C4×C11—81no—
448C4×C11C22×C22⋊C411yescharacteristic
449C4×C11#51811yescharacteristic
450C4×C11#54611yescharacteristic
451C4×C11#54611yescharacteristic
452C2×#41—22no—
453C2×#41—22no—
454C2×#41—22no—
455C2×#41—41no—
456C2×#41—41no—
457C2×#41C2×C4×C1114yes—
458C22×Q8—21no—
459C22×Q8—22no—
460C22×Q8—22no—
461C22×Q8—22no—
462C22×Q8—41no—
463C22×Q8—41no—
464C22×Q8C2×C4×C1114yes—
465C22×Q8C23×C1111yescharacteristic
466C22×Q8C23×C1111yescharacteristic
467C22×Q8C23×C1111yescharacteristic
468C22×D4—21no—
469C22×D4C23×C1111yescharacteristic
470C23×C4—21no—
471C23×C4—21no—
472C23×C4C23×C1111yescharacteristic
473#137—232no—
474C2×Q16—22no—
475C2×Q16—22no—
476C2×Q16C2×C4×C1114yes—
477C2×Q16C2×C4×C1114yes—
478C2×Q16D4×C1114yes—
479C2×Q16D4×C1114yes—
480C2×SD16—22no—
481C2×SD16—22no—
482C2×SD16—22no—
483C2×SD16—22no—
484C2×SD16C2×C4×C1114yes—
485C2×SD16C2×C4×C1114yes—
486C2×M16—22no—
487C2×M16—22no—
488C2×M16C2×C4×C1114yes—
489C22×C8C23×C1111yescharacteristic
490C22×C8C23×C1111yescharacteristic
491C22×C8C23×C1111yescharacteristic
492C22×C8C23×C1111yescharacteristic
493C4×Q8—22no—
494C4×Q8—22no—
495C4×Q8—22no—
496C4×Q8—22no—
497C4×Q8—41no—
498C4×Q8—41no—
499C4×Q8—41no—
500C4×Q8—41no—
501C2×C4⋊C4—21no—
502C2×C4⋊C4—21no—
503C2×C4⋊C4—21no—
504C2×C4⋊C4—21no—
505C2×C4⋊C4C23×C1111yescharacteristic
506C2×C4⋊C4C23×C1111yescharacteristic
507C2×C4⋊C4C23×C1111yescharacteristic
508C2×C4⋊C4C23×C1111yescharacteristic
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4D4×C1111yescharacteristic
516C2×C22⋊C4D4×C1111yescharacteristic
517C2×C42—21no—
518C2×C42—21no—
519C2×C42—21no—
520C2×C42—21no—
521C2×C42C23×C1111yescharacteristic
522C2×C42C23×C1111yescharacteristic
523#107—22no—
524#106—22no—
525#103—22no—
526#103—22no—
527#103—22no—
528#103—22no—
529#103—41no—
530#103—41no—
531#102—41no—
532#102—41no—
533C22⋊C8—22no—
534#97—22no—
535C4×C8—22no—
536#95—21no—
537#95—21no—
538#95—21no—
539#95—21no—
540#95—21no—
541#95—21no—
542#95D4×C1111yescharacteristic
543#95D4×C1111yescharacteristic
544C2×C11—42no—
545C2×C11—82no—
546C2×C11D4×C22⋊C411yescharacteristic
547C2×C11C4×#13711yescharacteristic
548C2×C11#294711yescharacteristic
549C2×C11#327011yescharacteristic
550C2×C11#327111yescharacteristic
551C2×C11#327711yescharacteristic
552C2×C11#327811yescharacteristic
553C24—21no—
554C24C2×D4×C1111yescharacteristic
555#41—28no—
556#41—44no—
557#41—44no—
558#41—44no—
559C2×Q8—24no—
560C2×Q8—21no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8—21no—
564C2×Q8—21no—
565C2×Q8—21no—
566C2×Q8—21no—
567C2×Q8—28no—
568C2×Q8—21no—
569C2×Q8—21no—
570C2×Q8—21no—
571C2×Q8—21no—
572C2×Q8—42no—
573C2×Q8—42no—
574C2×Q8—44no—
575C2×Q8—44no—
576C2×Q8—44no—
577C2×Q8C22×C4×C1112yes—
578C2×Q8C22×C4×C1112yes—
579C2×Q8C22×C4×C1112yes—
580C2×Q8C2×D4×C1112yes—
581C2×Q8C2×D4×C1112yes—
582C2×Q8C2×D4×C1112yes—
583C2×Q8C2×D4×C1112yes—
584C2×D4—24no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—42no—
591C2×D4—42no—
592C2×D4C22×C4×C1112yes—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—24no—
600C22×C4—21no—
601C22×C4—24no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—42no—
607C22×C4—42no—
608C22×C4—42no—
609C22×C4—42no—
610C22×C4C22×C4×C1112yes—
611C22×C4C2×D4×C1111yescharacteristic
612C22×C4C2×D4×C1111yescharacteristic
613C22×C4C2×D4×C1111yescharacteristic
614C22×C4C2×D4×C1111yescharacteristic
615C22×C4C2×D4×C1111yescharacteristic
616C22×C4C11×#4112yes—
617C22×C4C24×C1111yescharacteristic
618Q16—28no—
619Q16C11×C22⋊C4116yescomplemented
620SD16—28no—
621SD16—28no—
622M16—28no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8C22×C4×C1112yes—
632C2×C8C22×C4×C1112yes—
633C2×C8C2×D4×C1112yes—
634C2×C8C2×D4×C1112yes—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—42no—
644C4⋊C4—42no—
645C4⋊C4—42no—
646C4⋊C4—42no—
647C22⋊C4—22no—
648C22⋊C4—41no—
649C22⋊C4—42no—
650C22⋊C4—42no—
651C22⋊C4—42no—
652C22⋊C4—81no—
653C22⋊C4—81no—
654C22⋊C4—81no—
655C42—21no—
656C42—21no—
657C42—21no—
658C42—21no—
659C42—42no—
660C42—42no—
661C42—42no—
662C42—42no—
663C11#2244511yescharacteristic, direct product factor, Sylow
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—22no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23C4×D4×C1112yes—
678C23C22×D4×C1111yescharacteristic
679Q8—22no—
680Q8—22no—
681Q8—22no—
682Q8—22no—
683Q8—22no—
684Q8—22no—
685Q8—22no—
686Q8—22no—
687Q8—48no—
688Q8—41no—
689Q8—41no—
690Q8C2×C11×C22⋊C414yes—
691Q8C2×C11×C22⋊C414yes—
692D4—22no—
693D4—22no—
694D4—48no—
695D4—41no—
696D4—41no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—21no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—22no—
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—48no—
722C2×C4—48no—
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—41no—
737C2×C4C4×D4×C1112yes—
738C2×C4C11×#13712yescomplemented
739C2×C4C23×C4×C1111yescharacteristic
740C2×C4C22×D4×C1111yescharacteristic
741C2×C4C22×D4×C1111yescharacteristic
742C2×C4C2×C11×#4111yescharacteristic
743C2×C4C11×H(5,𝔽2)11yescharacteristic
744C2×C4C11×H(5,𝔽2)11yescharacteristic
745C8—22no—
746C8—41no—
747C8—41no—
748C8C2×C11×C22⋊C414yes—
749C22—22no—
750C22—22no—
751C22—22no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—42no—
757C22—42no—
758C22—42no—
759C22—81no—
760C22—81no—
761C22—81no—
762C22—81no—
763C22C2×C4×D4×C1111yescharacteristic
764C22D42×C1111yescharacteristic
765C22D42×C1111yescharacteristic
766C22C2×C11×#13711yescharacteristic
767C22C11×#57511yescharacteristic
768C22C11×#57711yescharacteristic
769C22C11×#57811yescharacteristic
770C4—22no—
771C4—22no—
772C4—24no—
773C4—24no—
774C4—41no—
775C4—41no—
776C4—41no—
777C4—42no—
778C4—81no—
779C4—81no—
780C4—81no—
781C4—81no—
782C4C22×C11×C22⋊C411yescharacteristic
783C4C11×#51811yescharacteristic
784C4C11×#54611yescharacteristic
785C4C11×#54611yescharacteristic
786C2—42no—
787C2—82no—
788C2D4×C11×C22⋊C411yescharacteristic
789C2C4×C11×#13711yescharacteristic
790C2C11×#294711yescharacteristic
791C2C11×#327011yescharacteristic
792C2C11×#327111yescharacteristic
793C2C11×#327711yescharacteristic
794C2C11×#327811yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC22×C11×#41C22
LCSG ▷ C2×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×#441C2semidirect
3. C2×C4×C11×Q16C2semidirect
5. Q8×C11×C22⋊C4C2semidirect
6. C11×#1973C2semidirect
7. C11×#1968C2semidirect
8. C11×#1880C2semidirect
9. C11×#1880C2semidirect
10. C11×#1878C2semidirect
11. C11×#1878C2semidirect
12. C11×#1809C2semidirect
14. C11×#1787C2semidirect
15. C11×#1753C2semidirect
20. C2×C11×#137C4semidirect
156. #22445C11direct (N × H)
223. C11×Q16C22⋊C4semidirect
268. C2×#441C2×C11semidirect
269. C2×C4×Q16C2×C11semidirect
271. Q8×C22⋊C4C2×C11semidirect
272. #1973C2×C11semidirect
273. #1968C2×C11semidirect
274. #1880C2×C11semidirect
275. #1880C2×C11semidirect
276. #1878C2×C11semidirect
277. #1878C2×C11semidirect
278. #1809C2×C11semidirect
280. #1787C2×C11semidirect
281. #1753C2×C11semidirect
356. C2×C4×C11#137semidirect
371. C2×#137C4×C11semidirect
619. Q16C11×C22⋊C4semidirect
663. C11#22445direct (N × H)
738. C2×C4C11×#137semidirect

Maximal subgroups

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

subgroupindex
C22×C11×#1372
C2×C11×#4412
C2×C4×C11×Q162
C11×#23412
Q8×C11×C22⋊C42
C11×#19732
C11×#19682
C11×#18802
C11×#18782
C11×#18092
C11×#17882
C11×#17872
C11×#17532
#2244511