Finite Group Databasebeta

← C11×#24445 #14601638

Subgroups — C11×#24445 #14601638

Order 2816.

1454 conjugacy classes of subgroups.

The subgroup lattice has 882 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×Q8×C11C211yesmaximal, characteristic, complemented
2C2×C11×#468C211yesmaximal, characteristic, complemented
3C2×C11×#448C211yesmaximal, characteristic, complemented
4C2×C11×#448C211yesmaximal, characteristic, complemented
5C2×C11×#419C211yesmaximal, characteristic, complemented
6C11×#2414C211yesmaximal, characteristic
7C11×#2043C211yesmaximal, characteristic, complemented
8C11×#2036C211yesmaximal, characteristic, complemented
9C11×#2013C211yesmaximal, characteristic, complemented
10C11×#2000C211yesmaximal, characteristic, complemented
11C11×#1880C211yesmaximal, characteristic, complemented
12C11×#1873C211yesmaximal, characteristic, complemented
13C11×#1870C211yesmaximal, characteristic, complemented
14C11×#1863C211yesmaximal, characteristic, complemented
15C11×#1787C211yesmaximal, characteristic, complemented
16C23×Q8×C11C2211yescharacteristic
17C23×Q8×C11C2211yescharacteristic
18C22×C11×SD16C2211yescharacteristic
19C22×C11×SD16C2211yescharacteristic
20C22×C11×SD16C2211yescharacteristic
21C22×C11×M16C2211yescharacteristic
22D4×Q8×C11—24no—
23D4×Q8×C11—24no—
24C2×C11×C4⋊Q8—21no—
25C2×C11×C4⋊Q8C2211yescharacteristic
26C2×C11×C22⋊Q8—21no—
27C2×C11×C22⋊Q8—21no—
28C2×C11×C22⋊Q8C2211yescharacteristic
29C2×C11×C22⋊Q8C2211yescharacteristic
30C2×C11×#121C2211yescharacteristic
31C2×C11×#121C2211yescharacteristic
32C2×C4×Q8×C11C2211yescharacteristic
33C2×C4×D4×C11—21no—
34C2×C4×D4×C11C2211yescharacteristic
35C2×C11×#117C2211yescharacteristic
36C11×#468—24no—
37C11×#448—24no—
38C11×#448—24no—
39C2×C11×#107C2211yescharacteristic
40C11×#419—24no—
41C2×C11×#103C2211yescharacteristic
42C2×C11×#103C2211yescharacteristic
43C2×C11×#103C2211yescharacteristic
44C2×C11×#103C2211yescharacteristic
45C2×C11×#103C2211yescharacteristic
46C2×C11×#103C2211yescharacteristic
47C2×C11×#103C2211yescharacteristic
48C2×C11×#103C2211yescharacteristic
49C2×C11×#103C2211yescharacteristic
50C2×C11×#102C2211yescharacteristic
51C2×C11×C22⋊C8C2211yescharacteristic
52C2×C11×C22⋊C8C2211yescharacteristic
53C2×C11×C22⋊C8C2211yescharacteristic
54C11×#394—21no—
55C11×#392—21no—
56C11×#390—21no—
57C11×#390C2211yescharacteristic
58C11×#389C2211yescharacteristic
59C11×#388—21no—
60C11×#380C2211yescharacteristic
61C11×#340C2211yescharacteristic
62C11×#340C2211yescharacteristic
63C11×#336C2211yescharacteristic
64C11×#336C2211yescharacteristic
65C22×Q8×C11—22no—
66C22×Q8×C11—22no—
67C22×Q8×C11—21no—
68C22×Q8×C11—21no—
69C22×Q8×C11—22no—
70C22×Q8×C11—22no—
71C22×Q8×C11—22no—
72C22×Q8×C11—22no—
73C22×Q8×C11—22no—
74C22×Q8×C11—41no—
75C22×Q8×C11—41no—
76C22×Q8×C11—41no—
77C22×Q8×C11—41no—
78C22×Q8×C11D414yescomplemented
79C22×Q8×C11C2311yescharacteristic
80C22×Q8×C11C2311yescharacteristic
81C22×Q8×C11C2311yescharacteristic
82C22×D4×C11—21no—
83C22×D4×C11—21no—
84C22×D4×C11D411yescharacteristic
85C22×D4×C11C2311yescharacteristic
86C23×C4×C11—21no—
87C23×C4×C11—21no—
88C23×C4×C11C2311yescharacteristic
89C23×C4×C11C2311yescharacteristic
90C2×C11×SD16—22no—
91C2×C11×SD16—22no—
92C2×C11×SD16—22no—
93C2×C11×SD16—22no—
94C2×C11×SD16—22no—
95C2×C11×SD16—22no—
96C2×C11×SD16—41no—
97C2×C11×SD16—41no—
98C2×C11×SD16—41no—
99C2×C11×M16—22no—
100C2×C11×M16—22no—
101C2×C11×M16—41no—
102C22×C8×C11C2311yescharacteristic
103C22×C8×C11C2311yescharacteristic
104C22×C8×C11C2311yescharacteristic
105C22×C8×C11C2311yescharacteristic
106C11×C4⋊Q8—28no—
107C11×C4⋊Q8—22no—
108C11×C4⋊Q8—22no—
109C11×C22⋊Q8—28no—
110C11×C22⋊Q8—28no—
111C11×C22⋊Q8—22no—
112C11×C22⋊Q8—22no—
113C11×C22⋊Q8—22no—
114C11×C22⋊Q8D414yescomplemented
115C11×#121—22no—
116C11×#121—22no—
117C11×#121—22no—
118C11×#121—41no—
119C4×Q8×C11—22no—
120C4×Q8×C11—22no—
121C4×D4×C11—28no—
122C4×D4×C11—22no—
123C4×D4×C11—22no—
124C11×#117—22no—
125C11×#117—41no—
126C2×C11×C4⋊C4—21no—
127C2×C11×C4⋊C4—21no—
128C2×C11×C4⋊C4—21no—
129C2×C11×C4⋊C4—21no—
130C2×C11×C4⋊C4—21no—
131C2×C11×C4⋊C4—21no—
132C2×C11×C4⋊C4D411yescharacteristic
133C2×C11×C4⋊C4C2311yescharacteristic
134C2×C11×C4⋊C4C2311yescharacteristic
135C2×C11×C4⋊C4C2311yescharacteristic
136C2×C11×C4⋊C4C2311yescharacteristic
137C2×C11×C22⋊C4—21no—
138C2×C11×C22⋊C4—21no—
139C2×C11×C22⋊C4—21no—
140C2×C11×C22⋊C4—21no—
141C2×C11×C22⋊C4—21no—
142C2×C11×C22⋊C4—21no—
143C2×C11×C22⋊C4—21no—
144C2×C11×C22⋊C4—21no—
145C2×C11×C22⋊C4D411yescharacteristic
146C2×C11×C22⋊C4D411yescharacteristic
147C2×C42×C11—21no—
148C2×C42×C11—21no—
149C2×C42×C11C2311yescharacteristic
150C11×#107—22no—
151C11×#103—22no—
152C11×#103—22no—
153C11×#103—22no—
154C11×#103—22no—
155C11×#103—22no—
156C11×#103—22no—
157C11×#103—22no—
158C11×#103—41no—
159C11×#103D414yescomplemented
160C11×#102—22no—
161C11×C22⋊C8—22no—
162C11×C22⋊C8—22no—
163C11×C22⋊C8—41no—
164C11×#95—21no—
165C11×#95—21no—
166#24445C1111yesmaximal, characteristic, direct product factor, Sylow
167C24×C11—21no—
168C24×C11C2×D411yescharacteristic
169C24×C11C2×D411yescharacteristic
170C2×Q8×C11—24no—
171C2×Q8×C11—24no—
172C2×Q8×C11—21no—
173C2×Q8×C11—21no—
174C2×Q8×C11—21no—
175C2×Q8×C11—21no—
176C2×Q8×C11—21no—
177C2×Q8×C11—28no—
178C2×Q8×C11—21no—
179C2×Q8×C11—21no—
180C2×Q8×C11—21no—
181C2×Q8×C11—21no—
182C2×Q8×C11—21no—
183C2×Q8×C11—21no—
184C2×Q8×C11—21no—
185C2×Q8×C11—21no—
186C2×Q8×C11—42no—
187C2×Q8×C11—42no—
188C2×Q8×C11—42no—
189C2×Q8×C11—42no—
190C2×Q8×C11—44no—
191C2×Q8×C11—44no—
192C2×Q8×C11—44no—
193C2×Q8×C11—44no—
194C2×Q8×C11—44no—
195C2×Q8×C11—44no—
196C2×Q8×C11—44no—
197C2×Q8×C11C2×D412yes—
198C2×Q8×C11C2×D412yes—
199C2×Q8×C11C2×D412yes—
200C2×Q8×C11C2×D412yes—
201C2×Q8×C11#4112yes—
202C2×D4×C11—22no—
203C2×D4×C11—22no—
204C2×D4×C11—22no—
205C2×D4×C11—21no—
206C2×D4×C11—21no—
207C2×D4×C11—21no—
208C2×D4×C11—21no—
209C2×D4×C11—21no—
210C2×D4×C11—21no—
211C2×D4×C11—42no—
212C2×D4×C11—42no—
213C2×D4×C11—42no—
214C2×D4×C11—81no—
215C2×D4×C11—81no—
216C2×D4×C11—81no—
217C22×C4×C11—21no—
218C22×C4×C11—21no—
219C22×C4×C11—21no—
220C22×C4×C11—21no—
221C22×C4×C11—21no—
222C22×C4×C11—24no—
223C22×C4×C11—24no—
224C22×C4×C11—21no—
225C22×C4×C11—21no—
226C22×C4×C11—21no—
227C22×C4×C11—21no—
228C22×C4×C11—21no—
229C22×C4×C11—21no—
230C22×C4×C11—21no—
231C22×C4×C11—21no—
232C22×C4×C11—21no—
233C22×C4×C11—21no—
234C22×C4×C11—21no—
235C22×C4×C11—21no—
236C22×C4×C11—42no—
237C22×C4×C11—42no—
238C22×C4×C11—42no—
239C22×C4×C11—42no—
240C22×C4×C11C2×D411yescharacteristic
241C22×C4×C11C2×D411yescharacteristic
242C22×C4×C11C2×D411yescharacteristic
243C22×C4×C11C2×D412yes—
244C22×C4×C11C2×D412yes—
245C22×C4×C11C2×D411yescharacteristic
246C22×C4×C11C2411yescharacteristic
247C11×SD16—44no—
248C11×SD16—44no—
249C11×SD16—44no—
250C11×M16—44no—
251C2×C8×C11—21no—
252C2×C8×C11—21no—
253C2×C8×C11—21no—
254C2×C8×C11—21no—
255C2×C8×C11—21no—
256C2×C8×C11—21no—
257C2×C8×C11—21no—
258C2×C8×C11—21no—
259C2×C8×C11—21no—
260C2×C8×C11—21no—
261C2×C8×C11—21no—
262C2×C8×C11C2×D412yes—
263C11×C4⋊C4—24no—
264C11×C4⋊C4—24no—
265C11×C4⋊C4—24no—
266C11×C4⋊C4—24no—
267C11×C4⋊C4—24no—
268C11×C4⋊C4—22no—
269C11×C4⋊C4—21no—
270C11×C4⋊C4—21no—
271C11×C4⋊C4—21no—
272C11×C4⋊C4—21no—
273C11×C4⋊C4—21no—
274C11×C4⋊C4—21no—
275C11×C4⋊C4—81no—
276C11×C4⋊C4C2×D412yes—
277C11×C4⋊C4C2×D412yes—
278C11×C22⋊C4—24no—
279C11×C22⋊C4—24no—
280C11×C22⋊C4—22no—
281C11×C22⋊C4—22no—
282C11×C22⋊C4—42no—
283C11×C22⋊C4—42no—
284C11×C22⋊C4—42no—
285C11×C22⋊C4—42no—
286C11×C22⋊C4—81no—
287C11×C22⋊C4—81no—
288C42×C11—24no—
289C42×C11—21no—
290C42×C11—21no—
291C42×C11—42no—
292C2×D4×Q8C2×C1111yescharacteristic, complemented
293C2×#468C2×C1111yescharacteristic, complemented
294C2×#448C2×C1111yescharacteristic, complemented
295C2×#448C2×C1111yescharacteristic, complemented
296C2×#419C2×C1111yescharacteristic, complemented
297#2414C2×C1111yescharacteristic
298#2043C2×C1111yescharacteristic, complemented
299#2036C2×C1111yescharacteristic, complemented
300#2013C2×C1111yescharacteristic, complemented
301#2000C2×C1111yescharacteristic, complemented
302#1880C2×C1111yescharacteristic, complemented
303#1873C2×C1111yescharacteristic, complemented
304#1870C2×C1111yescharacteristic, complemented
305#1863C2×C1111yescharacteristic, complemented
306#1787C2×C1111yescharacteristic, complemented
307C23×C11—21no—
308C23×C11—21no—
309C23×C11—21no—
310C23×C11—21no—
311C23×C11—21no—
312C23×C11—21no—
313C23×C11—21no—
314C23×C11—21no—
315C23×C11—21no—
316C23×C11—21no—
317C23×C11—21no—
318C23×C11—21no—
319C23×C11—41no—
320C23×C11—41no—
321C23×C11—41no—
322C23×C11—41no—
323C23×C11—41no—
324C23×C11—41no—
325C23×C11—41no—
326C23×C11#12012yes—
327C23×C11#13712yes—
328C23×C11C22×D411yescharacteristic
329Q8×C11—22no—
330Q8×C11—22no—
331Q8×C11—22no—
332Q8×C11—22no—
333Q8×C11—22no—
334Q8×C11—22no—
335Q8×C11—22no—
336Q8×C11—48no—
337Q8×C11—48no—
338Q8×C11—41no—
339Q8×C11—41no—
340Q8×C11—41no—
341Q8×C11—41no—
342Q8×C11#12114yes—
343D4×C11—28no—
344D4×C11—41no—
345D4×C11—41no—
346D4×C11—41no—
347D4×C11—41no—
348D4×C11—84no—
349D4×C11—84no—
350C2×C4×C11—21no—
351C2×C4×C11—22no—
352C2×C4×C11—21no—
353C2×C4×C11—22no—
354C2×C4×C11—21no—
355C2×C4×C11—22no—
356C2×C4×C11—21no—
357C2×C4×C11—22no—
358C2×C4×C11—22no—
359C2×C4×C11—22no—
360C2×C4×C11—22no—
361C2×C4×C11—21no—
362C2×C4×C11—22no—
363C2×C4×C11—22no—
364C2×C4×C11—22no—
365C2×C4×C11—21no—
366C2×C4×C11—22no—
367C2×C4×C11—21no—
368C2×C4×C11—21no—
369C2×C4×C11—21no—
370C2×C4×C11—21no—
371C2×C4×C11—48no—
372C2×C4×C11—48no—
373C2×C4×C11—41no—
374C2×C4×C11—41no—
375C2×C4×C11—41no—
376C2×C4×C11—41no—
377C2×C4×C11—41no—
378C2×C4×C11—41no—
379C2×C4×C11—41no—
380C2×C4×C11—41no—
381C2×C4×C11—41no—
382C2×C4×C11—41no—
383C2×C4×C11—41no—
384C2×C4×C11—41no—
385C2×C4×C11—41no—
386C2×C4×C11—41no—
387C2×C4×C11—41no—
388C2×C4×C11—41no—
389C2×C4×C11—41no—
390C2×C4×C11—41no—
391C2×C4×C11#12012yes—
392C2×C4×C11#13712yes—
393C2×C4×C11C22×D411yescharacteristic
394C2×C4×C11C22×D411yescharacteristic
395C2×C4×C11C22×D411yescharacteristic
396C2×C4×C11C2×#4111yescharacteristic
397C2×C4×C11H(5,𝔽2)11yescharacteristic
398C2×C4×C11H(5,𝔽2)11yescharacteristic
399C8×C11—22no—
400C8×C11—41no—
401C8×C11—41no—
402C8×C11—41no—
403C23×Q8C22×C1111yescharacteristic
404C23×Q8C22×C1111yescharacteristic
405C22×SD16C22×C1111yescharacteristic
406C22×SD16C22×C1111yescharacteristic
407C22×SD16C22×C1111yescharacteristic
408C22×M16C22×C1111yescharacteristic
409D4×Q8—24no—
410D4×Q8—24no—
411C2×C4⋊Q8—21no—
412C2×C4⋊Q8C22×C1111yescharacteristic
413C2×C22⋊Q8—21no—
414C2×C22⋊Q8—21no—
415C2×C22⋊Q8C22×C1111yescharacteristic
416C2×C22⋊Q8C22×C1111yescharacteristic
417C2×#121C22×C1111yescharacteristic
418C2×#121C22×C1111yescharacteristic
419C2×C4×Q8C22×C1111yescharacteristic
420C2×C4×D4—21no—
421C2×C4×D4C22×C1111yescharacteristic
422C2×#117C22×C1111yescharacteristic
423#468—24no—
424#448—24no—
425#448—24no—
426C2×#107C22×C1111yescharacteristic
427#419—24no—
428C2×#103C22×C1111yescharacteristic
429C2×#103C22×C1111yescharacteristic
430C2×#103C22×C1111yescharacteristic
431C2×#103C22×C1111yescharacteristic
432C2×#103C22×C1111yescharacteristic
433C2×#103C22×C1111yescharacteristic
434C2×#103C22×C1111yescharacteristic
435C2×#103C22×C1111yescharacteristic
436C2×#103C22×C1111yescharacteristic
437C2×#102C22×C1111yescharacteristic
438C2×C22⋊C8C22×C1111yescharacteristic
439C2×C22⋊C8C22×C1111yescharacteristic
440C2×C22⋊C8C22×C1111yescharacteristic
441#394—21no—
442#392—21no—
443#390—21no—
444#390C22×C1111yescharacteristic
445#389C22×C1111yescharacteristic
446#388—21no—
447#380C22×C1111yescharacteristic
448#340C22×C1111yescharacteristic
449#340C22×C1111yescharacteristic
450#336C22×C1111yescharacteristic
451#336C22×C1111yescharacteristic
452C22×C11—22no—
453C22×C11—22no—
454C22×C11—22no—
455C22×C11—22no—
456C22×C11—22no—
457C22×C11—22no—
458C22×C11—41no—
459C22×C11—41no—
460C22×C11—41no—
461C22×C11—41no—
462C22×C11—41no—
463C22×C11—41no—
464C22×C11—41no—
465C22×C11—41no—
466C22×C11—81no—
467C22×C11—81no—
468C22×C11—81no—
469C22×C11—81no—
470C22×C11—81no—
471C22×C11—81no—
472C22×C11—81no—
473C22×C11C2×#12011yescharacteristic
474C22×C11D4211yescharacteristic
475C22×C11#54611yescharacteristic
476C22×C11C2×#13711yescharacteristic
477C22×C11C2×#13711yescharacteristic
478C22×C11#57711yescharacteristic
479C22×C11#57711yescharacteristic
480C4×C11—22no—
481C4×C11—24no—
482C4×C11—22no—
483C4×C11—41no—
484C4×C11—42no—
485C4×C11—42no—
486C4×C11—41no—
487C4×C11—42no—
488C4×C11—42no—
489C4×C11—81no—
490C4×C11—81no—
491C4×C11C2×#12111yescharacteristic
492C4×C11#53411yescharacteristic
493C4×C11D4211yescharacteristic
494C4×C11#54611yescharacteristic
495C22×Q8—22no—
496C22×Q8—22no—
497C22×Q8—21no—
498C22×Q8—21no—
499C22×Q8—22no—
500C22×Q8—22no—
501C22×Q8—22no—
502C22×Q8—22no—
503C22×Q8—22no—
504C22×Q8—41no—
505C22×Q8—41no—
506C22×Q8—41no—
507C22×Q8—41no—
508C22×Q8D4×C1114yescomplemented
509C22×Q8C23×C1111yescharacteristic
510C22×Q8C23×C1111yescharacteristic
511C22×Q8C23×C1111yescharacteristic
512C22×D4—21no—
513C22×D4—21no—
514C22×D4D4×C1111yescharacteristic
515C22×D4C23×C1111yescharacteristic
516C23×C4—21no—
517C23×C4—21no—
518C23×C4C23×C1111yescharacteristic
519C23×C4C23×C1111yescharacteristic
520C2×SD16—22no—
521C2×SD16—22no—
522C2×SD16—22no—
523C2×SD16—22no—
524C2×SD16—22no—
525C2×SD16—22no—
526C2×SD16—41no—
527C2×SD16—41no—
528C2×SD16—41no—
529C2×M16—22no—
530C2×M16—22no—
531C2×M16—41no—
532C22×C8C23×C1111yescharacteristic
533C22×C8C23×C1111yescharacteristic
534C22×C8C23×C1111yescharacteristic
535C22×C8C23×C1111yescharacteristic
536C4⋊Q8—28no—
537C4⋊Q8—22no—
538C4⋊Q8—22no—
539C22⋊Q8—28no—
540C22⋊Q8—28no—
541C22⋊Q8—22no—
542C22⋊Q8—22no—
543C22⋊Q8—22no—
544C22⋊Q8D4×C1114yescomplemented
545#121—22no—
546#121—22no—
547#121—22no—
548#121—41no—
549C4×Q8—22no—
550C4×Q8—22no—
551C4×D4—28no—
552C4×D4—22no—
553C4×D4—22no—
554#117—22no—
555#117—41no—
556C2×C4⋊C4—21no—
557C2×C4⋊C4—21no—
558C2×C4⋊C4—21no—
559C2×C4⋊C4—21no—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—21no—
562C2×C4⋊C4D4×C1111yescharacteristic
563C2×C4⋊C4C23×C1111yescharacteristic
564C2×C4⋊C4C23×C1111yescharacteristic
565C2×C4⋊C4C23×C1111yescharacteristic
566C2×C4⋊C4C23×C1111yescharacteristic
567C2×C22⋊C4—21no—
568C2×C22⋊C4—21no—
569C2×C22⋊C4—21no—
570C2×C22⋊C4—21no—
571C2×C22⋊C4—21no—
572C2×C22⋊C4—21no—
573C2×C22⋊C4—21no—
574C2×C22⋊C4—21no—
575C2×C22⋊C4D4×C1111yescharacteristic
576C2×C22⋊C4D4×C1111yescharacteristic
577C2×C42—21no—
578C2×C42—21no—
579C2×C42C23×C1111yescharacteristic
580#107—22no—
581#103—22no—
582#103—22no—
583#103—22no—
584#103—22no—
585#103—22no—
586#103—22no—
587#103—22no—
588#103—41no—
589#103D4×C1114yescomplemented
590#102—22no—
591C22⋊C8—22no—
592C22⋊C8—22no—
593C22⋊C8—41no—
594#95—21no—
595#95—21no—
596C2×C11—42no—
597C2×C11—42no—
598C2×C11—161no—
599C2×C11#241011yescharacteristic
600C2×C11#300411yescharacteristic
601C2×C11#301011yescharacteristic
602C2×C11#326611yescharacteristic
603C2×C11#327811yescharacteristic
604C2×C11#332011yescharacteristic
605C2×C11#332911yescharacteristic
606C24—21no—
607C24C2×D4×C1111yescharacteristic
608C24C2×D4×C1111yescharacteristic
609C2×Q8—24no—
610C2×Q8—24no—
611C2×Q8—21no—
612C2×Q8—21no—
613C2×Q8—21no—
614C2×Q8—21no—
615C2×Q8—21no—
616C2×Q8—28no—
617C2×Q8—21no—
618C2×Q8—21no—
619C2×Q8—21no—
620C2×Q8—21no—
621C2×Q8—21no—
622C2×Q8—21no—
623C2×Q8—21no—
624C2×Q8—21no—
625C2×Q8—42no—
626C2×Q8—42no—
627C2×Q8—42no—
628C2×Q8—42no—
629C2×Q8—44no—
630C2×Q8—44no—
631C2×Q8—44no—
632C2×Q8—44no—
633C2×Q8—44no—
634C2×Q8—44no—
635C2×Q8—44no—
636C2×Q8C2×D4×C1112yes—
637C2×Q8C2×D4×C1112yes—
638C2×Q8C2×D4×C1112yes—
639C2×Q8C2×D4×C1112yes—
640C2×Q8C11×#4112yes—
641C2×D4—22no—
642C2×D4—22no—
643C2×D4—22no—
644C2×D4—21no—
645C2×D4—21no—
646C2×D4—21no—
647C2×D4—21no—
648C2×D4—21no—
649C2×D4—21no—
650C2×D4—42no—
651C2×D4—42no—
652C2×D4—42no—
653C2×D4—81no—
654C2×D4—81no—
655C2×D4—81no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—24no—
662C22×C4—24no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—42no—
676C22×C4—42no—
677C22×C4—42no—
678C22×C4—42no—
679C22×C4C2×D4×C1111yescharacteristic
680C22×C4C2×D4×C1111yescharacteristic
681C22×C4C2×D4×C1111yescharacteristic
682C22×C4C2×D4×C1112yes—
683C22×C4C2×D4×C1112yes—
684C22×C4C2×D4×C1111yescharacteristic
685C22×C4C24×C1111yescharacteristic
686SD16—44no—
687SD16—44no—
688SD16—44no—
689M16—44no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—21no—
694C2×C8—21no—
695C2×C8—21no—
696C2×C8—21no—
697C2×C8—21no—
698C2×C8—21no—
699C2×C8—21no—
700C2×C8—21no—
701C2×C8C2×D4×C1112yes—
702C4⋊C4—24no—
703C4⋊C4—24no—
704C4⋊C4—24no—
705C4⋊C4—24no—
706C4⋊C4—24no—
707C4⋊C4—22no—
708C4⋊C4—21no—
709C4⋊C4—21no—
710C4⋊C4—21no—
711C4⋊C4—21no—
712C4⋊C4—21no—
713C4⋊C4—21no—
714C4⋊C4—81no—
715C4⋊C4C2×D4×C1112yes—
716C4⋊C4C2×D4×C1112yes—
717C22⋊C4—24no—
718C22⋊C4—24no—
719C22⋊C4—22no—
720C22⋊C4—22no—
721C22⋊C4—42no—
722C22⋊C4—42no—
723C22⋊C4—42no—
724C22⋊C4—42no—
725C22⋊C4—81no—
726C22⋊C4—81no—
727C42—24no—
728C42—21no—
729C42—21no—
730C42—42no—
731C11#2444511yescharacteristic, direct product factor, Sylow
732C23—21no—
733C23—21no—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—21no—
738C23—21no—
739C23—21no—
740C23—21no—
741C23—21no—
742C23—21no—
743C23—21no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23C11×#12012yes—
752C23C11×#13712yes—
753C23C22×D4×C1111yescharacteristic
754Q8—22no—
755Q8—22no—
756Q8—22no—
757Q8—22no—
758Q8—22no—
759Q8—22no—
760Q8—22no—
761Q8—48no—
762Q8—48no—
763Q8—41no—
764Q8—41no—
765Q8—41no—
766Q8—41no—
767Q8C11×#12114yes—
768D4—28no—
769D4—41no—
770D4—41no—
771D4—41no—
772D4—41no—
773D4—84no—
774D4—84no—
775C2×C4—21no—
776C2×C4—22no—
777C2×C4—21no—
778C2×C4—22no—
779C2×C4—21no—
780C2×C4—22no—
781C2×C4—21no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—21no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—21no—
791C2×C4—22no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—48no—
797C2×C4—48no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4C11×#12012yes—
817C2×C4C11×#13712yes—
818C2×C4C22×D4×C1111yescharacteristic
819C2×C4C22×D4×C1111yescharacteristic
820C2×C4C22×D4×C1111yescharacteristic
821C2×C4C2×C11×#4111yescharacteristic
822C2×C4C11×H(5,𝔽2)11yescharacteristic
823C2×C4C11×H(5,𝔽2)11yescharacteristic
824C8—22no—
825C8—41no—
826C8—41no—
827C8—41no—
828C22—22no—
829C22—22no—
830C22—22no—
831C22—22no—
832C22—22no—
833C22—22no—
834C22—41no—
835C22—41no—
836C22—41no—
837C22—41no—
838C22—41no—
839C22—41no—
840C22—41no—
841C22—41no—
842C22—81no—
843C22—81no—
844C22—81no—
845C22—81no—
846C22—81no—
847C22—81no—
848C22—81no—
849C22C2×C11×#12011yescharacteristic
850C22D42×C1111yescharacteristic
851C22C11×#54611yescharacteristic
852C22C2×C11×#13711yescharacteristic
853C22C2×C11×#13711yescharacteristic
854C22C11×#57711yescharacteristic
855C22C11×#57711yescharacteristic
856C4—22no—
857C4—24no—
858C4—22no—
859C4—41no—
860C4—42no—
861C4—42no—
862C4—41no—
863C4—42no—
864C4—42no—
865C4—81no—
866C4—81no—
867C4C2×C11×#12111yescharacteristic
868C4C11×#53411yescharacteristic
869C4D42×C1111yescharacteristic
870C4C11×#54611yescharacteristic
871C2—42no—
872C2—42no—
873C2—161no—
874C2C11×#241011yescharacteristic
875C2C11×#300411yescharacteristic
876C2C11×#301011yescharacteristic
877C2C11×#326611yescharacteristic
878C2C11×#327811yescharacteristic
879C2C11×#332011yescharacteristic
880C2C11×#332911yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#2414C2
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
1. C2×D4×Q8×C11C2semidirect
2. C2×C11×#468C2semidirect
3. C2×C11×#448C2semidirect
4. C2×C11×#448C2semidirect
5. C2×C11×#419C2semidirect
7. C11×#2043C2semidirect
8. C11×#2036C2semidirect
9. C11×#2013C2semidirect
10. C11×#2000C2semidirect
11. C11×#1880C2semidirect
12. C11×#1873C2semidirect
13. C11×#1870C2semidirect
14. C11×#1863C2semidirect
15. C11×#1787C2semidirect
78. C22×Q8×C11D4semidirect
114. C11×C22⋊Q8D4semidirect
159. C11×#103D4semidirect
166. #24445C11direct (N × H)
292. C2×D4×Q8C2×C11semidirect
293. C2×#468C2×C11semidirect
294. C2×#448C2×C11semidirect
295. C2×#448C2×C11semidirect
296. C2×#419C2×C11semidirect
298. #2043C2×C11semidirect
299. #2036C2×C11semidirect
300. #2013C2×C11semidirect
301. #2000C2×C11semidirect
302. #1880C2×C11semidirect
303. #1873C2×C11semidirect
304. #1870C2×C11semidirect
305. #1863C2×C11semidirect
306. #1787C2×C11semidirect
508. C22×Q8D4×C11semidirect
544. C22⋊Q8D4×C11semidirect
589. #103D4×C11semidirect
731. C11#24445direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D4×Q8×C112
C2×C11×#4682
C2×C11×#4482
C2×C11×#4192
C11×#24142
C11×#20432
C11×#20362
C11×#20132
C11×#20002
C11×#18802
C11×#18732
C11×#18702
C11×#18632
C11×#17872
#2444511