Finite Group Databasebeta

← C11×#23972 #14601165

Subgroups — C11×#23972 #14601165

Order 2816.

1516 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#547C211yesmaximal, characteristic, complemented
2C2×C11×#449C211yesmaximal, characteristic, complemented
3C2×C11×#417C211yesmaximal, characteristic, complemented
4C11×#2407C211yesmaximal, characteristic, complemented
5C11×#2024C211yesmaximal, characteristic, complemented
6C11×#2023C211yesmaximal, characteristic, complemented
7C11×#2000C211yesmaximal, characteristic, complemented
8C11×#1999C211yesmaximal, characteristic, complemented
9C11×#1895C211yesmaximal, characteristic, complemented
10C11×#1879C211yesmaximal, characteristic, complemented
11C11×#1877C211yesmaximal, characteristic, complemented
12C11×#1874C211yesmaximal, characteristic, complemented
13C11×#1872C211yesmaximal, characteristic, complemented
14C11×#1870C211yesmaximal, characteristic, complemented
15C11×#1824C211yesmaximal, characteristic, complemented
16C22×C11×#41—21no—
17C22×C11×#41C2211yescharacteristic
18C22×C11×SD16C2211yescharacteristic
19C22×C11×D8C2211yescharacteristic
20C22×C11×M16C2211yescharacteristic
21C11×#547—24no—
22C11×#547—24no—
23C2×C11×C4⋊Q8C2211yescharacteristic
24C2×C11×#123—21no—
25C2×C11×#123—21no—
26C2×C11×C22⋊Q8—21no—
27C2×C11×C22⋊Q8C2211yescharacteristic
28C2×C11×#121C2211yescharacteristic
29C2×C11×#121C2211yescharacteristic
30C2×C11×#121C2211yescharacteristic
31C2×C4×D4×C11C2211yescharacteristic
32C2×C4×D4×C11C2211yescharacteristic
33C22×C11×C4⋊C4C2211yescharacteristic
34C22×C11×C4⋊C4C2211yescharacteristic
35C11×#449—24no—
36C11×#417—24no—
37C2×C11×#103C2211yescharacteristic
38C2×C11×#103C2211yescharacteristic
39C2×C11×#103C2211yescharacteristic
40C2×C11×#102C2211yescharacteristic
41C2×C11×#102C2211yescharacteristic
42C2×C11×#102C2211yescharacteristic
43C2×C11×#102C2211yescharacteristic
44C2×C11×#102C2211yescharacteristic
45C2×C11×C22⋊C8C2211yescharacteristic
46C2×C11×C22⋊C8C2211yescharacteristic
47C2×C11×C22⋊C8C2211yescharacteristic
48C11×#394—21no—
49C11×#392—21no—
50C11×#391C2211yescharacteristic
51C11×#390C2211yescharacteristic
52C11×#386—21no—
53C11×#385—21no—
54C11×#380C2211yescharacteristic
55C11×#340C2211yescharacteristic
56C11×#340C2211yescharacteristic
57C11×#340C2211yescharacteristic
58C11×#340C2211yescharacteristic
59C11×#340C2211yescharacteristic
60C11×#340C2211yescharacteristic
61C11×#336C2211yescharacteristic
62C11×#336C2211yescharacteristic
63C2×C11×#41—28no—
64C2×C11×#41—22no—
65C2×C11×#41—22no—
66C2×C11×#41—22no—
67C2×C11×#41—22no—
68C2×C11×#41—41no—
69C2×C11×#41—41no—
70C2×C11×#41—44no—
71C2×C11×#41—44no—
72C22×Q8×C11—21no—
73C22×Q8×C11C2311yescharacteristic
74C22×D4×C11—21no—
75C22×D4×C11—21no—
76C22×D4×C11—21no—
77C22×D4×C11—21no—
78C22×D4×C11D411yescharacteristic
79C22×D4×C11C2311yescharacteristic
80C22×D4×C11C2311yescharacteristic
81C23×C4×C11—21no—
82C23×C4×C11—21no—
83C23×C4×C11—21no—
84C23×C4×C11—21no—
85C23×C4×C11C2311yescharacteristic
86C23×C4×C11C2311yescharacteristic
87C2×C11×SD16—22no—
88C2×C11×SD16—22no—
89C2×C11×SD16—41no—
90C2×C11×D8—22no—
91C2×C11×D8—22no—
92C2×C11×D8—41no—
93C2×C11×M16—22no—
94C2×C11×M16—41no—
95C2×C11×M16—41no—
96C22×C8×C11C2311yescharacteristic
97C22×C8×C11C2311yescharacteristic
98C22×C8×C11C2311yescharacteristic
99C22×C8×C11C2311yescharacteristic
100C11×C4⋊Q8—22no—
101C11×C4⋊Q8—22no—
102C11×#123—28no—
103C11×#123—28no—
104C11×C22⋊Q8—28no—
105C11×C22⋊Q8—22no—
106C11×C22⋊Q8—41no—
107C11×#121—22no—
108C11×#121—22no—
109C11×#121—22no—
110C11×#121—22no—
111C11×#121—41no—
112C11×#121D414yescomplemented
113C4×D4×C11—22no—
114C4×D4×C11—22no—
115C4×D4×C11—22no—
116C4×D4×C11—22no—
117C2×C11×C4⋊C4—21no—
118C2×C11×C4⋊C4—21no—
119C2×C11×C4⋊C4—22no—
120C2×C11×C4⋊C4—21no—
121C2×C11×C4⋊C4—22no—
122C2×C11×C4⋊C4—22no—
123C2×C11×C4⋊C4—21no—
124C2×C11×C4⋊C4D411yescharacteristic
125C2×C11×C4⋊C4D414yescomplemented
126C2×C11×C4⋊C4C2311yescharacteristic
127C2×C11×C4⋊C4C2311yescharacteristic
128C2×C11×C4⋊C4C2311yescharacteristic
129C2×C11×C4⋊C4C2311yescharacteristic
130C2×C11×C4⋊C4C2311yescharacteristic
131C2×C11×C22⋊C4—21no—
132C2×C11×C22⋊C4—21no—
133C2×C11×C22⋊C4—21no—
134C2×C11×C22⋊C4—21no—
135C2×C11×C22⋊C4—21no—
136C2×C11×C22⋊C4—21no—
137C2×C11×C22⋊C4—21no—
138C2×C11×C22⋊C4—21no—
139C2×C11×C22⋊C4D411yescharacteristic
140C2×C11×C22⋊C4D411yescharacteristic
141C2×C42×C11C2311yescharacteristic
142C11×#103—22no—
143C11×#103—22no—
144C11×#103—22no—
145C11×#102—22no—
146C11×#102—22no—
147C11×#102—22no—
148C11×#102—41no—
149C11×#102—41no—
150C11×C22⋊C8—22no—
151C11×C22⋊C8—41no—
152C11×C22⋊C8—41no—
153C11×#95—21no—
154C11×#95—21no—
155C11×#95—21no—
156#23972C1111yesmaximal, characteristic, direct product factor, Sylow
157C24×C11—21no—
158C24×C11—21no—
159C24×C11C2×D411yescharacteristic
160C24×C11C2×D411yescharacteristic
161C11×#41—28no—
162C11×#41—44no—
163C11×#41—44no—
164C11×#41—44no—
165C11×#41—432no—
166C2×Q8×C11—24no—
167C2×Q8×C11—21no—
168C2×Q8×C11—21no—
169C2×Q8×C11—21no—
170C2×Q8×C11—21no—
171C2×Q8×C11—21no—
172C2×Q8×C11—42no—
173C2×Q8×C11—42no—
174C2×Q8×C11#4112yescomplemented
175C2×D4×C11—22no—
176C2×D4×C11—22no—
177C2×D4×C11—24no—
178C2×D4×C11—24no—
179C2×D4×C11—22no—
180C2×D4×C11—21no—
181C2×D4×C11—21no—
182C2×D4×C11—21no—
183C2×D4×C11—21no—
184C2×D4×C11—21no—
185C2×D4×C11—21no—
186C2×D4×C11—21no—
187C2×D4×C11—21no—
188C2×D4×C11—21no—
189C2×D4×C11—21no—
190C2×D4×C11—42no—
191C2×D4×C11—42no—
192C2×D4×C11—42no—
193C2×D4×C11—42no—
194C2×D4×C11—42no—
195C2×D4×C11—42no—
196C2×D4×C11—42no—
197C2×D4×C11—42no—
198C2×D4×C11—42no—
199C2×D4×C11—81no—
200C2×D4×C11C2×D412yes—
201C2×D4×C11#4112yescomplemented
202C22×C4×C11—21no—
203C22×C4×C11—21no—
204C22×C4×C11—21no—
205C22×C4×C11—21no—
206C22×C4×C11—24no—
207C22×C4×C11—24no—
208C22×C4×C11—24no—
209C22×C4×C11—21no—
210C22×C4×C11—21no—
211C22×C4×C11—21no—
212C22×C4×C11—21no—
213C22×C4×C11—21no—
214C22×C4×C11—21no—
215C22×C4×C11—21no—
216C22×C4×C11—21no—
217C22×C4×C11—21no—
218C22×C4×C11—21no—
219C22×C4×C11—21no—
220C22×C4×C11—21no—
221C22×C4×C11—42no—
222C22×C4×C11—42no—
223C22×C4×C11—42no—
224C22×C4×C11—42no—
225C22×C4×C11—42no—
226C22×C4×C11—42no—
227C22×C4×C11—42no—
228C22×C4×C11—42no—
229C22×C4×C11—42no—
230C22×C4×C11C2×D411yescharacteristic
231C22×C4×C11C2×D411yescharacteristic
232C22×C4×C11C2×D411yescharacteristic
233C22×C4×C11C2×D412yes—
234C22×C4×C11C2×D412yes—
235C22×C4×C11C2×D411yescharacteristic
236C22×C4×C11C2411yescharacteristic
237C11×SD16—44no—
238C11×D8—44no—
239C11×M16—44no—
240C2×C8×C11—21no—
241C2×C8×C11—21no—
242C2×C8×C11—21no—
243C2×C8×C11—21no—
244C2×C8×C11—21no—
245C2×C8×C11—21no—
246C2×C8×C11—21no—
247C2×C8×C11—21no—
248C2×C8×C11—21no—
249C2×C8×C11—21no—
250C2×C8×C11—21no—
251C2×C8×C11—21no—
252C11×C4⋊C4—24no—
253C11×C4⋊C4—24no—
254C11×C4⋊C4—24no—
255C11×C4⋊C4—22no—
256C11×C4⋊C4—21no—
257C11×C4⋊C4—21no—
258C11×C4⋊C4—21no—
259C11×C4⋊C4—21no—
260C11×C4⋊C4—21no—
261C11×C4⋊C4—21no—
262C11×C4⋊C4—21no—
263C11×C4⋊C4—42no—
264C11×C4⋊C4C2×D412yes—
265C11×C4⋊C4C2×D412yes—
266C11×C4⋊C4C2×D412yes—
267C11×C22⋊C4—24no—
268C11×C22⋊C4—24no—
269C11×C22⋊C4—22no—
270C11×C22⋊C4—24no—
271C11×C22⋊C4—22no—
272C11×C22⋊C4—42no—
273C11×C22⋊C4—42no—
274C11×C22⋊C4—42no—
275C11×C22⋊C4—81no—
276C11×C22⋊C4—81no—
277C42×C11—21no—
278C42×C11—21no—
279C2×#547C2×C1111yescharacteristic, complemented
280C2×#449C2×C1111yescharacteristic, complemented
281C2×#417C2×C1111yescharacteristic, complemented
282#2407C2×C1111yescharacteristic, complemented
283#2024C2×C1111yescharacteristic, complemented
284#2023C2×C1111yescharacteristic, complemented
285#2000C2×C1111yescharacteristic, complemented
286#1999C2×C1111yescharacteristic, complemented
287#1895C2×C1111yescharacteristic, complemented
288#1879C2×C1111yescharacteristic, complemented
289#1877C2×C1111yescharacteristic, complemented
290#1874C2×C1111yescharacteristic, complemented
291#1872C2×C1111yescharacteristic, complemented
292#1870C2×C1111yescharacteristic, complemented
293#1824C2×C1111yescharacteristic, complemented
294C23×C11—21no—
295C23×C11—21no—
296C23×C11—21no—
297C23×C11—21no—
298C23×C11—21no—
299C23×C11—21no—
300C23×C11—21no—
301C23×C11—21no—
302C23×C11—21no—
303C23×C11—21no—
304C23×C11—21no—
305C23×C11—21no—
306C23×C11—22no—
307C23×C11—22no—
308C23×C11—41no—
309C23×C11—41no—
310C23×C11—41no—
311C23×C11—41no—
312C23×C11—41no—
313C23×C11—41no—
314C23×C11—41no—
315C23×C11—41no—
316C23×C11—41no—
317C23×C11—41no—
318C23×C11—41no—
319C23×C11—41no—
320C23×C11#12012yes—
321C23×C11AGL(1,ℤ/8)12yes—
322C23×C11C22×D411yescharacteristic
323Q8×C11—22no—
324Q8×C11—22no—
325Q8×C11—48no—
326Q8×C11—41no—
327Q8×C11—41no—
328D4×C11—28no—
329D4×C11—22no—
330D4×C11—22no—
331D4×C11—22no—
332D4×C11—22no—
333D4×C11—48no—
334D4×C11—48no—
335D4×C11—48no—
336D4×C11—41no—
337D4×C11—41no—
338D4×C11—41no—
339D4×C11—41no—
340D4×C11—84no—
341C2×C4×C11—21no—
342C2×C4×C11—21no—
343C2×C4×C11—21no—
344C2×C4×C11—21no—
345C2×C4×C11—22no—
346C2×C4×C11—22no—
347C2×C4×C11—22no—
348C2×C4×C11—22no—
349C2×C4×C11—21no—
350C2×C4×C11—21no—
351C2×C4×C11—22no—
352C2×C4×C11—22no—
353C2×C4×C11—22no—
354C2×C4×C11—21no—
355C2×C4×C11—22no—
356C2×C4×C11—21no—
357C2×C4×C11—21no—
358C2×C4×C11—21no—
359C2×C4×C11—48no—
360C2×C4×C11—48no—
361C2×C4×C11—48no—
362C2×C4×C11—48no—
363C2×C4×C11—41no—
364C2×C4×C11—41no—
365C2×C4×C11—41no—
366C2×C4×C11—41no—
367C2×C4×C11—41no—
368C2×C4×C11—41no—
369C2×C4×C11—41no—
370C2×C4×C11—41no—
371C2×C4×C11—41no—
372C2×C4×C11—41no—
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#12012yes—
382C2×C4×C11AGL(1,ℤ/8)12yes—
383C2×C4×C11C22×D411yescharacteristic
384C2×C4×C11C22×D411yescharacteristic
385C2×C4×C11C2×#4111yescharacteristic
386C2×C4×C11C2×#4111yescharacteristic
387C2×C4×C11H(5,𝔽2)11yescharacteristic
388C2×C4×C11H(5,𝔽2)11yescharacteristic
389C8×C11—41no—
390C8×C11—41no—
391C8×C11—41no—
392C8×C11—41no—
393C22×#41—21no—
394C22×#41C22×C1111yescharacteristic
395C22×SD16C22×C1111yescharacteristic
396C22×D8C22×C1111yescharacteristic
397C22×M16C22×C1111yescharacteristic
398#547—24no—
399#547—24no—
400C2×C4⋊Q8C22×C1111yescharacteristic
401C2×#123—21no—
402C2×#123—21no—
403C2×C22⋊Q8—21no—
404C2×C22⋊Q8C22×C1111yescharacteristic
405C2×#121C22×C1111yescharacteristic
406C2×#121C22×C1111yescharacteristic
407C2×#121C22×C1111yescharacteristic
408C2×C4×D4C22×C1111yescharacteristic
409C2×C4×D4C22×C1111yescharacteristic
410C22×C4⋊C4C22×C1111yescharacteristic
411C22×C4⋊C4C22×C1111yescharacteristic
412#449—24no—
413#417—24no—
414C2×#103C22×C1111yescharacteristic
415C2×#103C22×C1111yescharacteristic
416C2×#103C22×C1111yescharacteristic
417C2×#102C22×C1111yescharacteristic
418C2×#102C22×C1111yescharacteristic
419C2×#102C22×C1111yescharacteristic
420C2×#102C22×C1111yescharacteristic
421C2×#102C22×C1111yescharacteristic
422C2×C22⋊C8C22×C1111yescharacteristic
423C2×C22⋊C8C22×C1111yescharacteristic
424C2×C22⋊C8C22×C1111yescharacteristic
425#394—21no—
426#392—21no—
427#391C22×C1111yescharacteristic
428#390C22×C1111yescharacteristic
429#386—21no—
430#385—21no—
431#380C22×C1111yescharacteristic
432#340C22×C1111yescharacteristic
433#340C22×C1111yescharacteristic
434#340C22×C1111yescharacteristic
435#340C22×C1111yescharacteristic
436#340C22×C1111yescharacteristic
437#340C22×C1111yescharacteristic
438#336C22×C1111yescharacteristic
439#336C22×C1111yescharacteristic
440C22×C11—22no—
441C22×C11—22no—
442C22×C11—22no—
443C22×C11—22no—
444C22×C11—22no—
445C22×C11—22no—
446C22×C11—41no—
447C22×C11—41no—
448C22×C11—41no—
449C22×C11—41no—
450C22×C11—41no—
451C22×C11—41no—
452C22×C11—41no—
453C22×C11—41no—
454C22×C11—42no—
455C22×C11—42no—
456C22×C11—42no—
457C22×C11—42no—
458C22×C11—42no—
459C22×C11—42no—
460C22×C11—81no—
461C22×C11—81no—
462C22×C11—81no—
463C22×C11—81no—
464C22×C11—81no—
465C22×C11—81no—
466C22×C11—81no—
467C22×C11—81no—
468C22×C11C2×#12011yescharacteristic
469C22×C11#54611yescharacteristic
470C22×C11#54611yescharacteristic
471C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
472C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
473C22×C11#57711yescharacteristic
474C22×C11#57811yescharacteristic
475C4×C11—22no—
476C4×C11—22no—
477C4×C11—41no—
478C4×C11—42no—
479C4×C11—42no—
480C4×C11—42no—
481C4×C11—42no—
482C4×C11—41no—
483C4×C11—81no—
484C4×C11—81no—
485C4×C11#52511yescharacteristic
486C4×C11#53511yescharacteristic
487C4×C11#54611yescharacteristic
488C4×C11#54611yescharacteristic
489C2×#41—28no—
490C2×#41—22no—
491C2×#41—22no—
492C2×#41—22no—
493C2×#41—22no—
494C2×#41—41no—
495C2×#41—41no—
496C2×#41—44no—
497C2×#41—44no—
498C22×Q8—21no—
499C22×Q8C23×C1111yescharacteristic
500C22×D4—21no—
501C22×D4—21no—
502C22×D4—21no—
503C22×D4—21no—
504C22×D4D4×C1111yescharacteristic
505C22×D4C23×C1111yescharacteristic
506C22×D4C23×C1111yescharacteristic
507C23×C4—21no—
508C23×C4—21no—
509C23×C4—21no—
510C23×C4—21no—
511C23×C4C23×C1111yescharacteristic
512C23×C4C23×C1111yescharacteristic
513C2×SD16—22no—
514C2×SD16—22no—
515C2×SD16—41no—
516C2×D8—22no—
517C2×D8—22no—
518C2×D8—41no—
519C2×M16—22no—
520C2×M16—41no—
521C2×M16—41no—
522C22×C8C23×C1111yescharacteristic
523C22×C8C23×C1111yescharacteristic
524C22×C8C23×C1111yescharacteristic
525C22×C8C23×C1111yescharacteristic
526C4⋊Q8—22no—
527C4⋊Q8—22no—
528#123—28no—
529#123—28no—
530C22⋊Q8—28no—
531C22⋊Q8—22no—
532C22⋊Q8—41no—
533#121—22no—
534#121—22no—
535#121—22no—
536#121—22no—
537#121—41no—
538#121D4×C1114yescomplemented
539C4×D4—22no—
540C4×D4—22no—
541C4×D4—22no—
542C4×D4—22no—
543C2×C4⋊C4—21no—
544C2×C4⋊C4—21no—
545C2×C4⋊C4—22no—
546C2×C4⋊C4—21no—
547C2×C4⋊C4—22no—
548C2×C4⋊C4—22no—
549C2×C4⋊C4—21no—
550C2×C4⋊C4D4×C1111yescharacteristic
551C2×C4⋊C4D4×C1114yescomplemented
552C2×C4⋊C4C23×C1111yescharacteristic
553C2×C4⋊C4C23×C1111yescharacteristic
554C2×C4⋊C4C23×C1111yescharacteristic
555C2×C4⋊C4C23×C1111yescharacteristic
556C2×C4⋊C4C23×C1111yescharacteristic
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—21no—
561C2×C22⋊C4—21no—
562C2×C22⋊C4—21no—
563C2×C22⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C22⋊C4D4×C1111yescharacteristic
566C2×C22⋊C4D4×C1111yescharacteristic
567C2×C42C23×C1111yescharacteristic
568#103—22no—
569#103—22no—
570#103—22no—
571#102—22no—
572#102—22no—
573#102—22no—
574#102—41no—
575#102—41no—
576C22⋊C8—22no—
577C22⋊C8—41no—
578C22⋊C8—41no—
579#95—21no—
580#95—21no—
581#95—21no—
582C2×C11—42no—
583C2×C11—42no—
584C2×C11—82no—
585C2×C11—82no—
586C2×C11#240411yescharacteristic
587C2×C11#300311yescharacteristic
588C2×C11#301311yescharacteristic
589C2×C11#330611yescharacteristic
590C2×C11#330811yescharacteristic
591C2×C11#333011yescharacteristic
592C2×C11#333211yescharacteristic
593C24—21no—
594C24—21no—
595C24C2×D4×C1111yescharacteristic
596C24C2×D4×C1111yescharacteristic
597#41—28no—
598#41—44no—
599#41—44no—
600#41—44no—
601#41—432no—
602C2×Q8—24no—
603C2×Q8—21no—
604C2×Q8—21no—
605C2×Q8—21no—
606C2×Q8—21no—
607C2×Q8—21no—
608C2×Q8—42no—
609C2×Q8—42no—
610C2×Q8C11×#4112yescomplemented
611C2×D4—22no—
612C2×D4—22no—
613C2×D4—24no—
614C2×D4—24no—
615C2×D4—22no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—42no—
627C2×D4—42no—
628C2×D4—42no—
629C2×D4—42no—
630C2×D4—42no—
631C2×D4—42no—
632C2×D4—42no—
633C2×D4—42no—
634C2×D4—42no—
635C2×D4—81no—
636C2×D4C2×D4×C1112yes—
637C2×D4C11×#4112yescomplemented
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—24no—
643C22×C4—24no—
644C22×C4—24no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—42no—
658C22×C4—42no—
659C22×C4—42no—
660C22×C4—42no—
661C22×C4—42no—
662C22×C4—42no—
663C22×C4—42no—
664C22×C4—42no—
665C22×C4—42no—
666C22×C4C2×D4×C1111yescharacteristic
667C22×C4C2×D4×C1111yescharacteristic
668C22×C4C2×D4×C1111yescharacteristic
669C22×C4C2×D4×C1112yes—
670C22×C4C2×D4×C1112yes—
671C22×C4C2×D4×C1111yescharacteristic
672C22×C4C24×C1111yescharacteristic
673SD16—44no—
674D8—44no—
675M16—44no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—21no—
680C2×C8—21no—
681C2×C8—21no—
682C2×C8—21no—
683C2×C8—21no—
684C2×C8—21no—
685C2×C8—21no—
686C2×C8—21no—
687C2×C8—21no—
688C4⋊C4—24no—
689C4⋊C4—24no—
690C4⋊C4—24no—
691C4⋊C4—22no—
692C4⋊C4—21no—
693C4⋊C4—21no—
694C4⋊C4—21no—
695C4⋊C4—21no—
696C4⋊C4—21no—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4—42no—
700C4⋊C4C2×D4×C1112yes—
701C4⋊C4C2×D4×C1112yes—
702C4⋊C4C2×D4×C1112yes—
703C22⋊C4—24no—
704C22⋊C4—24no—
705C22⋊C4—22no—
706C22⋊C4—24no—
707C22⋊C4—22no—
708C22⋊C4—42no—
709C22⋊C4—42no—
710C22⋊C4—42no—
711C22⋊C4—81no—
712C22⋊C4—81no—
713C42—21no—
714C42—21no—
715C11#2397211yescharacteristic, direct product factor, Sylow
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—22no—
729C23—22no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23C11×#12012yes—
743C23C11×AGL(1,ℤ/8)12yes—
744C23C22×D4×C1111yescharacteristic
745Q8—22no—
746Q8—22no—
747Q8—48no—
748Q8—41no—
749Q8—41no—
750D4—28no—
751D4—22no—
752D4—22no—
753D4—22no—
754D4—22no—
755D4—48no—
756D4—48no—
757D4—48no—
758D4—41no—
759D4—41no—
760D4—41no—
761D4—41no—
762D4—84no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—21no—
777C2×C4—22no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—48no—
782C2×C4—48no—
783C2×C4—48no—
784C2×C4—48no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4C11×#12012yes—
804C2×C4C11×AGL(1,ℤ/8)12yes—
805C2×C4C22×D4×C1111yescharacteristic
806C2×C4C22×D4×C1111yescharacteristic
807C2×C4C2×C11×#4111yescharacteristic
808C2×C4C2×C11×#4111yescharacteristic
809C2×C4C11×H(5,𝔽2)11yescharacteristic
810C2×C4C11×H(5,𝔽2)11yescharacteristic
811C8—41no—
812C8—41no—
813C8—41no—
814C8—41no—
815C22—22no—
816C22—22no—
817C22—22no—
818C22—22no—
819C22—22no—
820C22—22no—
821C22—41no—
822C22—41no—
823C22—41no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—42no—
830C22—42no—
831C22—42no—
832C22—42no—
833C22—42no—
834C22—42no—
835C22—81no—
836C22—81no—
837C22—81no—
838C22—81no—
839C22—81no—
840C22—81no—
841C22—81no—
842C22—81no—
843C22C2×C11×#12011yescharacteristic
844C22C11×#54611yescharacteristic
845C22C11×#54611yescharacteristic
846C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
847C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
848C22C11×#57711yescharacteristic
849C22C11×#57811yescharacteristic
850C4—22no—
851C4—22no—
852C4—41no—
853C4—42no—
854C4—42no—
855C4—42no—
856C4—42no—
857C4—41no—
858C4—81no—
859C4—81no—
860C4C11×#52511yescharacteristic
861C4C11×#53511yescharacteristic
862C4C11×#54611yescharacteristic
863C4C11×#54611yescharacteristic
864C2—42no—
865C2—42no—
866C2—82no—
867C2—82no—
868C2C11×#240411yescharacteristic
869C2C11×#300311yescharacteristic
870C2C11×#301311yescharacteristic
871C2C11×#330611yescharacteristic
872C2C11×#330811yescharacteristic
873C2C11×#333011yescharacteristic
874C2C11×#333211yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
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×C11×#547C2semidirect
2. C2×C11×#449C2semidirect
3. C2×C11×#417C2semidirect
4. C11×#2407C2semidirect
5. C11×#2024C2semidirect
6. C11×#2023C2semidirect
7. C11×#2000C2semidirect
8. C11×#1999C2semidirect
9. C11×#1895C2semidirect
10. C11×#1879C2semidirect
11. C11×#1877C2semidirect
12. C11×#1874C2semidirect
13. C11×#1872C2semidirect
14. C11×#1870C2semidirect
15. C11×#1824C2semidirect
112. C11×#121D4semidirect
125. C2×C11×C4⋊C4D4semidirect
156. #23972C11direct (N × H)
174. C2×Q8×C11#41semidirect
201. C2×D4×C11#41semidirect
279. C2×#547C2×C11semidirect
280. C2×#449C2×C11semidirect
281. C2×#417C2×C11semidirect
282. #2407C2×C11semidirect
283. #2024C2×C11semidirect
284. #2023C2×C11semidirect
285. #2000C2×C11semidirect
286. #1999C2×C11semidirect
287. #1895C2×C11semidirect
288. #1879C2×C11semidirect
289. #1877C2×C11semidirect
290. #1874C2×C11semidirect
291. #1872C2×C11semidirect
292. #1870C2×C11semidirect
293. #1824C2×C11semidirect
538. #121D4×C11semidirect
551. C2×C4⋊C4D4×C11semidirect
610. C2×Q8C11×#41semidirect
637. C2×D4C11×#41semidirect
715. C11#23972direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5472
C2×C11×#4492
C2×C11×#4172
C11×#24072
C11×#20242
C11×#20232
C11×#20002
C11×#19992
C11×#18952
C11×#18792
C11×#18772
C11×#18742
C11×#18722
C11×#18702
C11×#18242
#2397211