Finite Group Databasebeta

← C11×#23879 #14601072

Subgroups — C11×#23879 #14601072

Order 2816.

1840 conjugacy classes of subgroups.

The subgroup lattice has 900 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×AGL(1,ℤ/8)C211yesmaximal, characteristic, complemented
2C11×#3489C211yesmaximal, characteristic, complemented
3C2×C11×#454C212yesmaximal, complemented
4C11×#3003C211yesmaximal, characteristic, complemented
5C11×#2435C211yesmaximal, characteristic, complemented
6C11×#2006C212yesmaximal, complemented
7C11×#2003C212yesmaximal, complemented
8C11×#1901C211yesmaximal, characteristic, complemented
9C11×#1883C212yesmaximal, complemented
10C11×#1871C211yesmaximal, characteristic, complemented
11C11×#1789C211yesmaximal, characteristic, complemented
12C2×C11×2−1+4C2211yescharacteristic, complemented
13C22×C11×#41C2211yescharacteristic
14C23×D4×C11C2211yescharacteristic
15C2×C11×AGL(1,ℤ/8)—21no—
16C2×C11×AGL(1,ℤ/8)—21no—
17C2×C11×AGL(1,ℤ/8)—28no—
18C2×C11×AGL(1,ℤ/8)C2212yes—
19C2×C11×AGL(1,ℤ/8)C2212yes—
20C2×C11×AGL(1,ℤ/8)C2212yescomplemented
21C22×C11×SD16—21no—
22C22×C11×D8—21no—
23C22×C11×M16C2211yescharacteristic
24D4×Q8×C11—21no—
25C11×#548—21no—
26C11×#547—21no—
27C11×#547—22no—
28C11×#546—21no—
29C11×#546—22no—
30C11×#537—21no—
31C11×#537C2211yescharacteristic, complemented
32C11×#536—21no—
33C11×#536C2211yescharacteristic, complemented
34C2×C11×#124C2212yescomplemented
35C11×#525—21no—
36C11×#525C2211yescharacteristic
37C2×C11×C22⋊Q8—21no—
38C2×C11×C22⋊Q8C2211yescharacteristic
39C11×#520C2211yescharacteristic, complemented
40C11×#454—28no—
41C11×#450—21no—
42C11×#450—21no—
43C11×#447—21no—
44C11×#447—21no—
45C2×C11×#104C2212yescomplemented
46C2×C11×#104C2212yescomplemented
47C2×C11×#104C2212yescomplemented
48C11×#418C2212yescomplemented
49C2×C11×#101C2212yescomplemented
50C11×#407C2211yescharacteristic
51C11×#394—22no—
52C11×#390C2212yescomplemented
53C11×#379—22no—
54C4×C11×C22⋊C4C2211yescharacteristic
55C11×#343C2212yescomplemented
56C11×#339C2212yescomplemented
57C25×C11—21no—
58C11×2−1+4—24no—
59C11×2−1+4—42no—
60C2×C11×#41—21no—
61C2×C11×#41—21no—
62C2×C11×#41—21no—
63C2×C11×#41—22no—
64C2×C11×#41—21no—
65C2×C11×#41—24no—
66C2×C11×#41—42no—
67C2×C11×#41D411yescharacteristic
68C2×C11×#41D411yescharacteristic
69C2×C11×#41C2311yescharacteristic
70C2×C11×#41C2311yescharacteristic
71C2×C11×#41C2311yescharacteristic
72C22×Q8×C11—21no—
73C22×Q8×C11—21no—
74C22×Q8×C11D411yescharacteristic
75C22×Q8×C11C2311yescharacteristic
76C22×D4×C11—24no—
77C22×D4×C11—21no—
78C22×D4×C11—21no—
79C22×D4×C11—21no—
80C22×D4×C11—21no—
81C22×D4×C11—21no—
82C22×D4×C11—21no—
83C22×D4×C11—42no—
84C22×D4×C11D411yescharacteristic
85C22×D4×C11C2312yes—
86C23×C4×C11—21no—
87C23×C4×C11C2311yescharacteristic
88C11×AGL(1,ℤ/8)—28no—
89C11×AGL(1,ℤ/8)—28no—
90C11×AGL(1,ℤ/8)—24no—
91C11×AGL(1,ℤ/8)—24no—
92C11×AGL(1,ℤ/8)—24no—
93C11×AGL(1,ℤ/8)—24no—
94C11×AGL(1,ℤ/8)—42no—
95C11×AGL(1,ℤ/8)D418yescomplemented
96C2×C11×SD16—28no—
97C2×C11×SD16—22no—
98C2×C11×SD16—22no—
99C2×C11×SD16—22no—
100C2×C11×D8—28no—
101C2×C11×D8—22no—
102C2×C11×D8—22no—
103C2×C11×D8—22no—
104C2×C11×M16—21no—
105C2×C11×M16—24no—
106C2×C11×M16C2312yes—
107C2×C11×M16C2312yes—
108C22×C8×C11—21no—
109C11×C4⋊Q8—22no—
110C11×C4⋊Q8—21no—
111C11×#124—22no—
112C11×#124—21no—
113C11×#124—24no—
114C11×#124—42no—
115C11×#123—22no—
116C11×#123—22no—
117C11×#123—22no—
118C11×#123—21no—
119C11×#123—22no—
120C11×C22⋊Q8—22no—
121C11×C22⋊Q8—22no—
122C11×C22⋊Q8—22no—
123C11×C22⋊Q8—21no—
124C11×C22⋊Q8—21no—
125C11×C22⋊Q8—21no—
126C11×C22⋊Q8—21no—
127C11×C22⋊Q8—21no—
128C11×C22⋊Q8—21no—
129C11×C22⋊Q8—21no—
130C11×C22⋊Q8—21no—
131C11×C22⋊Q8D411yescharacteristic
132C11×C22⋊Q8D411yescharacteristic
133C11×#121—22no—
134C11×#121—22no—
135C11×#121—22no—
136C11×#121—21no—
137C11×#121—21no—
138C11×#121—22no—
139C11×#121D411yescharacteristic
140C11×#121D411yescharacteristic
141C11×#120—22no—
142C11×#120—21no—
143C4×Q8×C11—21no—
144C4×D4×C11—22no—
145C4×D4×C11—22no—
146C4×D4×C11—21no—
147C4×D4×C11—22no—
148C4×D4×C11—21no—
149C4×D4×C11—21no—
150C11×#117—21no—
151C11×#117C2311yescharacteristic
152C2×C11×C4⋊C4—22no—
153C2×C11×C4⋊C4—21no—
154C2×C11×C4⋊C4D412yes—
155C2×C11×C4⋊C4C2311yescharacteristic
156C2×C11×C22⋊C4—22no—
157C2×C11×C22⋊C4—21no—
158C2×C11×C22⋊C4—24no—
159C2×C11×C22⋊C4—24no—
160C2×C11×C22⋊C4D412yes—
161C2×C42×C11C2312yes—
162C11×#104—24no—
163C11×#104—24no—
164C11×#104—42no—
165C11×#102—22no—
166C11×#102—22no—
167C11×#101—24no—
168C11×C22⋊C8—21no—
169C11×C22⋊C8—21no—
170C11×#95—21no—
171#23879C1111yesmaximal, characteristic, direct product factor, Sylow
172C24×C11—22no—
173C24×C11—21no—
174C24×C11—44no—
175C24×C11—44no—
176C24×C11—41no—
177C24×C11—41no—
178C24×C11—82no—
179C24×C11C2×D411yescharacteristic
180C11×#41—22no—
181C11×#41—22no—
182C11×#41—22no—
183C11×#41—22no—
184C11×#41—22no—
185C11×#41—22no—
186C11×#41—22no—
187C11×#41—44no—
188C11×#41—41no—
189C11×#41—41no—
190C11×#41—44no—
191C11×#41—44no—
192C11×#41—48no—
193C11×#41—42no—
194C11×#41—42no—
195C11×#41C2×D414yes—
196C2×Q8×C11—22no—
197C2×Q8×C11—21no—
198C2×Q8×C11—22no—
199C2×Q8×C11—21no—
200C2×Q8×C11—21no—
201C2×Q8×C11—22no—
202C2×Q8×C11—22no—
203C2×Q8×C11—41no—
204C2×Q8×C11—44no—
205C2×Q8×C11—42no—
206C2×Q8×C11—42no—
207C2×Q8×C11C2×D411yescharacteristic
208C2×Q8×C11C2×D411yescharacteristic
209C2×Q8×C11C2×D411yescharacteristic
210C2×D4×C11—21no—
211C2×D4×C11—24no—
212C2×D4×C11—24no—
213C2×D4×C11—22no—
214C2×D4×C11—22no—
215C2×D4×C11—21no—
216C2×D4×C11—21no—
217C2×D4×C11—21no—
218C2×D4×C11—21no—
219C2×D4×C11—21no—
220C2×D4×C11—22no—
221C2×D4×C11—21no—
222C2×D4×C11—21no—
223C2×D4×C11—22no—
224C2×D4×C11—22no—
225C2×D4×C11—22no—
226C2×D4×C11—22no—
227C2×D4×C11—22no—
228C2×D4×C11—41no—
229C2×D4×C11—44no—
230C2×D4×C11—44no—
231C2×D4×C11—44no—
232C2×D4×C11—42no—
233C2×D4×C11—42no—
234C2×D4×C11—44no—
235C2×D4×C11—41no—
236C2×D4×C11—41no—
237C2×D4×C11C2×D411yescharacteristic
238C2×D4×C11C2×D411yescharacteristic
239C2×D4×C11C2×D414yes—
240C2×D4×C11C2×D411yescharacteristic
241C22×C4×C11—21no—
242C22×C4×C11—22no—
243C22×C4×C11—22no—
244C22×C4×C11—22no—
245C22×C4×C11—22no—
246C22×C4×C11—21no—
247C22×C4×C11—22no—
248C22×C4×C11—21no—
249C22×C4×C11—21no—
250C22×C4×C11—21no—
251C22×C4×C11—21no—
252C22×C4×C11—22no—
253C22×C4×C11—44no—
254C22×C4×C11C2×D412yes—
255C22×C4×C11C2×D411yescharacteristic
256C22×C4×C11C2×D411yescharacteristic
257C22×C4×C11C2×D411yescharacteristic
258C22×C4×C11C2×D411yescharacteristic
259C22×C4×C11C2×D411yescharacteristic
260C22×C4×C11C2×D412yes—
261C22×C4×C11C2411yescharacteristic
262C11×SD16—28no—
263C11×SD16—28no—
264C11×SD16—44no—
265C11×D8—28no—
266C11×D8—28no—
267C11×D8—44no—
268C11×M16—24no—
269C11×M16—22no—
270C11×M16—22no—
271C11×M16—22no—
272C11×M16C2×D414yes—
273C2×C8×C11—24no—
274C2×C8×C11—22no—
275C2×C8×C11—22no—
276C11×C4⋊C4—22no—
277C11×C4⋊C4—22no—
278C11×C4⋊C4—22no—
279C11×C4⋊C4—22no—
280C11×C4⋊C4—21no—
281C11×C4⋊C4—22no—
282C11×C4⋊C4—22no—
283C11×C4⋊C4—21no—
284C11×C4⋊C4—21no—
285C11×C4⋊C4—21no—
286C11×C4⋊C4C2×D411yescharacteristic
287C11×C4⋊C4C2×D411yescharacteristic
288C11×C22⋊C4—22no—
289C11×C22⋊C4—22no—
290C11×C22⋊C4—22no—
291C11×C22⋊C4—22no—
292C11×C22⋊C4—22no—
293C11×C22⋊C4—21no—
294C11×C22⋊C4—22no—
295C11×C22⋊C4—22no—
296C11×C22⋊C4—21no—
297C11×C22⋊C4—21no—
298C11×C22⋊C4—21no—
299C11×C22⋊C4—21no—
300C11×C22⋊C4—48no—
301C11×C22⋊C4—42no—
302C11×C22⋊C4—84no—
303C42×C11—22no—
304C42×C11—21no—
305C42×C11—22no—
306C42×C11—22no—
307C22×AGL(1,ℤ/8)C2×C1111yescharacteristic, complemented
308#3489C2×C1111yescharacteristic, complemented
309C2×#454C2×C1112yescomplemented
310#3003C2×C1111yescharacteristic, complemented
311#2435C2×C1111yescharacteristic, complemented
312#2006C2×C1112yescomplemented
313#2003C2×C1112yescomplemented
314#1901C2×C1111yescharacteristic, complemented
315#1883C2×C1112yescomplemented
316#1871C2×C1111yescharacteristic, complemented
317#1789C2×C1111yescharacteristic, complemented
318C23×C11—21no—
319C23×C11—22no—
320C23×C11—22no—
321C23×C11—21no—
322C23×C11—21no—
323C23×C11—24no—
324C23×C11—41no—
325C23×C11—42no—
326C23×C11—44no—
327C23×C11—44no—
328C23×C11—44no—
329C23×C11—44no—
330C23×C11—42no—
331C23×C11—42no—
332C23×C11—42no—
333C23×C11—81no—
334C23×C11—82no—
335C23×C11—82no—
336C23×C11—82no—
337C23×C11—816no—
338C23×C11—82no—
339C23×C11#12011yescharacteristic
340C23×C11#12011yescharacteristic
341C23×C11C22×D411yescharacteristic
342Q8×C11—21no—
343Q8×C11—21no—
344Q8×C11—21no—
345Q8×C11—22no—
346Q8×C11—42no—
347Q8×C11—44no—
348Q8×C11—41no—
349Q8×C11—41no—
350Q8×C11—42no—
351Q8×C11#12012yes—
352D4×C11—24no—
353D4×C11—21no—
354D4×C11—24no—
355D4×C11—21no—
356D4×C11—21no—
357D4×C11—22no—
358D4×C11—24no—
359D4×C11—42no—
360D4×C11—42no—
361D4×C11—44no—
362D4×C11—44no—
363D4×C11—42no—
364D4×C11—44no—
365D4×C11—42no—
366D4×C11—42no—
367D4×C11—42no—
368D4×C11—42no—
369D4×C11—42no—
370D4×C11—81no—
371D4×C11—82no—
372D4×C11#12012yes—
373C2×C4×C11—21no—
374C2×C4×C11—22no—
375C2×C4×C11—21no—
376C2×C4×C11—21no—
377C2×C4×C11—21no—
378C2×C4×C11—21no—
379C2×C4×C11—22no—
380C2×C4×C11—22no—
381C2×C4×C11—24no—
382C2×C4×C11—21no—
383C2×C4×C11—22no—
384C2×C4×C11—21no—
385C2×C4×C11—21no—
386C2×C4×C11—22no—
387C2×C4×C11—21no—
388C2×C4×C11—24no—
389C2×C4×C11—42no—
390C2×C4×C11—42no—
391C2×C4×C11—42no—
392C2×C4×C11—44no—
393C2×C4×C11—44no—
394C2×C4×C11—41no—
395C2×C4×C11—41no—
396C2×C4×C11—42no—
397C2×C4×C11—42no—
398C2×C4×C11—42no—
399C2×C4×C11—42no—
400C2×C4×C11—42no—
401C2×C4×C11—82no—
402C2×C4×C11#12011yescharacteristic
403C2×C4×C11#12011yescharacteristic
404C2×C4×C11C22×D411yescharacteristic
405C2×C4×C11C22×D412yes—
406C2×C4×C11C22×D411yescharacteristic
407C2×C4×C11H(5,𝔽2)12yes—
408C8×C11—24no—
409C8×C11—42no—
410C2×2−1+4C22×C1111yescharacteristic, complemented
411C22×#41C22×C1111yescharacteristic
412C23×D4C22×C1111yescharacteristic
413C2×AGL(1,ℤ/8)—21no—
414C2×AGL(1,ℤ/8)—21no—
415C2×AGL(1,ℤ/8)—28no—
416C2×AGL(1,ℤ/8)C22×C1112yes—
417C2×AGL(1,ℤ/8)C22×C1112yes—
418C2×AGL(1,ℤ/8)C22×C1112yescomplemented
419C22×SD16—21no—
420C22×D8—21no—
421C22×M16C22×C1111yescharacteristic
422D4×Q8—21no—
423#548—21no—
424#547—21no—
425#547—22no—
426#546—21no—
427#546—22no—
428#537—21no—
429#537C22×C1111yescharacteristic, complemented
430#536—21no—
431#536C22×C1111yescharacteristic, complemented
432C2×#124C22×C1112yescomplemented
433#525—21no—
434#525C22×C1111yescharacteristic
435C2×C22⋊Q8—21no—
436C2×C22⋊Q8C22×C1111yescharacteristic
437#520C22×C1111yescharacteristic, complemented
438#454—28no—
439#450—21no—
440#450—21no—
441#447—21no—
442#447—21no—
443C2×#104C22×C1112yescomplemented
444C2×#104C22×C1112yescomplemented
445C2×#104C22×C1112yescomplemented
446#418C22×C1112yescomplemented
447C2×#101C22×C1112yescomplemented
448#407C22×C1111yescharacteristic
449#394—22no—
450#390C22×C1112yescomplemented
451#379—22no—
452C4×C22⋊C4C22×C1111yescharacteristic
453#343C22×C1112yescomplemented
454#339C22×C1112yescomplemented
455C22×C11—21no—
456C22×C11—21no—
457C22×C11—21no—
458C22×C11—21no—
459C22×C11—21no—
460C22×C11—22no—
461C22×C11—21no—
462C22×C11—21no—
463C22×C11—44no—
464C22×C11—48no—
465C22×C11—41no—
466C22×C11—41no—
467C22×C11—41no—
468C22×C11—41no—
469C22×C11—44no—
470C22×C11—41no—
471C22×C11—41no—
472C22×C11—41no—
473C22×C11—41no—
474C22×C11—84no—
475C22×C11—84no—
476C22×C11—88no—
477C22×C11—88no—
478C22×C11—82no—
479C22×C11—82no—
480C22×C11#45412yescomplemented
481C22×C11C2×#12011yescharacteristic
482C22×C11D4212yes—
483C4×C11—21no—
484C4×C11—21no—
485C4×C11—22no—
486C4×C11—42no—
487C4×C11—41no—
488C4×C11—41no—
489C4×C11—41no—
490C4×C11—42no—
491C4×C11—41no—
492C4×C11—82no—
493C4×C11C2×#12011yescharacteristic
494C4×C11#53411yescharacteristic
495C4×C11D4212yes—
496C25—21no—
4972−1+4—24no—
4982−1+4—42no—
499C2×#41—21no—
500C2×#41—21no—
501C2×#41—21no—
502C2×#41—22no—
503C2×#41—21no—
504C2×#41—24no—
505C2×#41—42no—
506C2×#41D4×C1111yescharacteristic
507C2×#41D4×C1111yescharacteristic
508C2×#41C23×C1111yescharacteristic
509C2×#41C23×C1111yescharacteristic
510C2×#41C23×C1111yescharacteristic
511C22×Q8—21no—
512C22×Q8—21no—
513C22×Q8D4×C1111yescharacteristic
514C22×Q8C23×C1111yescharacteristic
515C22×D4—24no—
516C22×D4—21no—
517C22×D4—21no—
518C22×D4—21no—
519C22×D4—21no—
520C22×D4—21no—
521C22×D4—21no—
522C22×D4—42no—
523C22×D4D4×C1111yescharacteristic
524C22×D4C23×C1112yes—
525C23×C4—21no—
526C23×C4C23×C1111yescharacteristic
527AGL(1,ℤ/8)—28no—
528AGL(1,ℤ/8)—28no—
529AGL(1,ℤ/8)—24no—
530AGL(1,ℤ/8)—24no—
531AGL(1,ℤ/8)—24no—
532AGL(1,ℤ/8)—24no—
533AGL(1,ℤ/8)—42no—
534AGL(1,ℤ/8)D4×C1118yescomplemented
535C2×SD16—28no—
536C2×SD16—22no—
537C2×SD16—22no—
538C2×SD16—22no—
539C2×D8—28no—
540C2×D8—22no—
541C2×D8—22no—
542C2×D8—22no—
543C2×M16—21no—
544C2×M16—24no—
545C2×M16C23×C1112yes—
546C2×M16C23×C1112yes—
547C22×C8—21no—
548C4⋊Q8—22no—
549C4⋊Q8—21no—
550#124—22no—
551#124—21no—
552#124—24no—
553#124—42no—
554#123—22no—
555#123—22no—
556#123—22no—
557#123—21no—
558#123—22no—
559C22⋊Q8—22no—
560C22⋊Q8—22no—
561C22⋊Q8—22no—
562C22⋊Q8—21no—
563C22⋊Q8—21no—
564C22⋊Q8—21no—
565C22⋊Q8—21no—
566C22⋊Q8—21no—
567C22⋊Q8—21no—
568C22⋊Q8—21no—
569C22⋊Q8—21no—
570C22⋊Q8D4×C1111yescharacteristic
571C22⋊Q8D4×C1111yescharacteristic
572#121—22no—
573#121—22no—
574#121—22no—
575#121—21no—
576#121—21no—
577#121—22no—
578#121D4×C1111yescharacteristic
579#121D4×C1111yescharacteristic
580#120—22no—
581#120—21no—
582C4×Q8—21no—
583C4×D4—22no—
584C4×D4—22no—
585C4×D4—21no—
586C4×D4—22no—
587C4×D4—21no—
588C4×D4—21no—
589#117—21no—
590#117C23×C1111yescharacteristic
591C2×C4⋊C4—22no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4D4×C1112yes—
594C2×C4⋊C4C23×C1111yescharacteristic
595C2×C22⋊C4—22no—
596C2×C22⋊C4—21no—
597C2×C22⋊C4—24no—
598C2×C22⋊C4—24no—
599C2×C22⋊C4D4×C1112yes—
600C2×C42C23×C1112yes—
601#104—24no—
602#104—24no—
603#104—42no—
604#102—22no—
605#102—22no—
606#101—24no—
607C22⋊C8—21no—
608C22⋊C8—21no—
609#95—21no—
610C2×C11—22no—
611C2×C11—22no—
612C2×C11—41no—
613C2×C11—42no—
614C2×C11—81no—
615C2×C11—81no—
616C2×C11—84no—
617C2×C11#240311yescharacteristic
618C2×C11C2×#45411yescharacteristic
619C2×C11#302111yescharacteristic
620C24—22no—
621C24—21no—
622C24—44no—
623C24—44no—
624C24—41no—
625C24—41no—
626C24—82no—
627C24C2×D4×C1111yescharacteristic
628#41—22no—
629#41—22no—
630#41—22no—
631#41—22no—
632#41—22no—
633#41—22no—
634#41—22no—
635#41—44no—
636#41—41no—
637#41—41no—
638#41—44no—
639#41—44no—
640#41—48no—
641#41—42no—
642#41—42no—
643#41C2×D4×C1114yes—
644C2×Q8—22no—
645C2×Q8—21no—
646C2×Q8—22no—
647C2×Q8—21no—
648C2×Q8—21no—
649C2×Q8—22no—
650C2×Q8—22no—
651C2×Q8—41no—
652C2×Q8—44no—
653C2×Q8—42no—
654C2×Q8—42no—
655C2×Q8C2×D4×C1111yescharacteristic
656C2×Q8C2×D4×C1111yescharacteristic
657C2×Q8C2×D4×C1111yescharacteristic
658C2×D4—21no—
659C2×D4—24no—
660C2×D4—24no—
661C2×D4—22no—
662C2×D4—22no—
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—21no—
668C2×D4—22no—
669C2×D4—21no—
670C2×D4—21no—
671C2×D4—22no—
672C2×D4—22no—
673C2×D4—22no—
674C2×D4—22no—
675C2×D4—22no—
676C2×D4—41no—
677C2×D4—44no—
678C2×D4—44no—
679C2×D4—44no—
680C2×D4—42no—
681C2×D4—42no—
682C2×D4—44no—
683C2×D4—41no—
684C2×D4—41no—
685C2×D4C2×D4×C1111yescharacteristic
686C2×D4C2×D4×C1111yescharacteristic
687C2×D4C2×D4×C1114yes—
688C2×D4C2×D4×C1111yescharacteristic
689C22×C4—21no—
690C22×C4—22no—
691C22×C4—22no—
692C22×C4—22no—
693C22×C4—22no—
694C22×C4—21no—
695C22×C4—22no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—22no—
701C22×C4—44no—
702C22×C4C2×D4×C1112yes—
703C22×C4C2×D4×C1111yescharacteristic
704C22×C4C2×D4×C1111yescharacteristic
705C22×C4C2×D4×C1111yescharacteristic
706C22×C4C2×D4×C1111yescharacteristic
707C22×C4C2×D4×C1111yescharacteristic
708C22×C4C2×D4×C1112yes—
709C22×C4C24×C1111yescharacteristic
710SD16—28no—
711SD16—28no—
712SD16—44no—
713D8—28no—
714D8—28no—
715D8—44no—
716M16—24no—
717M16—22no—
718M16—22no—
719M16—22no—
720M16C2×D4×C1114yes—
721C2×C8—24no—
722C2×C8—22no—
723C2×C8—22no—
724C4⋊C4—22no—
725C4⋊C4—22no—
726C4⋊C4—22no—
727C4⋊C4—22no—
728C4⋊C4—21no—
729C4⋊C4—22no—
730C4⋊C4—22no—
731C4⋊C4—21no—
732C4⋊C4—21no—
733C4⋊C4—21no—
734C4⋊C4C2×D4×C1111yescharacteristic
735C4⋊C4C2×D4×C1111yescharacteristic
736C22⋊C4—22no—
737C22⋊C4—22no—
738C22⋊C4—22no—
739C22⋊C4—22no—
740C22⋊C4—22no—
741C22⋊C4—21no—
742C22⋊C4—22no—
743C22⋊C4—22no—
744C22⋊C4—21no—
745C22⋊C4—21no—
746C22⋊C4—21no—
747C22⋊C4—21no—
748C22⋊C4—48no—
749C22⋊C4—42no—
750C22⋊C4—84no—
751C42—22no—
752C42—21no—
753C42—22no—
754C42—22no—
755C11#2387911yescharacteristic, direct product factor, Sylow
756C23—21no—
757C23—22no—
758C23—22no—
759C23—21no—
760C23—21no—
761C23—24no—
762C23—41no—
763C23—42no—
764C23—44no—
765C23—44no—
766C23—44no—
767C23—44no—
768C23—42no—
769C23—42no—
770C23—42no—
771C23—81no—
772C23—82no—
773C23—82no—
774C23—82no—
775C23—816no—
776C23—82no—
777C23C11×#12011yescharacteristic
778C23C11×#12011yescharacteristic
779C23C22×D4×C1111yescharacteristic
780Q8—21no—
781Q8—21no—
782Q8—21no—
783Q8—22no—
784Q8—42no—
785Q8—44no—
786Q8—41no—
787Q8—41no—
788Q8—42no—
789Q8C11×#12012yes—
790D4—24no—
791D4—21no—
792D4—24no—
793D4—21no—
794D4—21no—
795D4—22no—
796D4—24no—
797D4—42no—
798D4—42no—
799D4—44no—
800D4—44no—
801D4—42no—
802D4—44no—
803D4—42no—
804D4—42no—
805D4—42no—
806D4—42no—
807D4—42no—
808D4—81no—
809D4—82no—
810D4C11×#12012yes—
811C2×C4—21no—
812C2×C4—22no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—24no—
820C2×C4—21no—
821C2×C4—22no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—22no—
825C2×C4—21no—
826C2×C4—24no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—42no—
830C2×C4—44no—
831C2×C4—44no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—42no—
835C2×C4—42no—
836C2×C4—42no—
837C2×C4—42no—
838C2×C4—42no—
839C2×C4—82no—
840C2×C4C11×#12011yescharacteristic
841C2×C4C11×#12011yescharacteristic
842C2×C4C22×D4×C1111yescharacteristic
843C2×C4C22×D4×C1112yes—
844C2×C4C22×D4×C1111yescharacteristic
845C2×C4C11×H(5,𝔽2)12yes—
846C8—24no—
847C8—42no—
848C22—21no—
849C22—21no—
850C22—21no—
851C22—21no—
852C22—21no—
853C22—22no—
854C22—21no—
855C22—21no—
856C22—44no—
857C22—48no—
858C22—41no—
859C22—41no—
860C22—41no—
861C22—41no—
862C22—44no—
863C22—41no—
864C22—41no—
865C22—41no—
866C22—41no—
867C22—84no—
868C22—84no—
869C22—88no—
870C22—88no—
871C22—82no—
872C22—82no—
873C22C11×#45412yescomplemented
874C22C2×C11×#12011yescharacteristic
875C22D42×C1112yes—
876C4—21no—
877C4—21no—
878C4—22no—
879C4—42no—
880C4—41no—
881C4—41no—
882C4—41no—
883C4—42no—
884C4—41no—
885C4—82no—
886C4C2×C11×#12011yescharacteristic
887C4C11×#53411yescharacteristic
888C4D42×C1112yes—
889C2—22no—
890C2—22no—
891C2—41no—
892C2—42no—
893C2—84no—
894C2—81no—
895C2—81no—
896C2C11×#240311yescharacteristic
897C2C2×C11×#45411yescharacteristic
898C2C11×#302111yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C11×AGL(1,ℤ/8)C2semidirect
2. C11×#3489C2semidirect
3. C2×C11×#454C2semidirect
4. C11×#3003C2semidirect
5. C11×#2435C2semidirect
6. C11×#2006C2semidirect
7. C11×#2003C2semidirect
8. C11×#1901C2semidirect
9. C11×#1883C2semidirect
10. C11×#1871C2semidirect
11. C11×#1789C2semidirect
12. C2×C11×2−1+4C22semidirect
20. C2×C11×AGL(1,ℤ/8)C22semidirect
31. C11×#537C22semidirect
33. C11×#536C22semidirect
34. C2×C11×#124C22semidirect
39. C11×#520C22semidirect
45. C2×C11×#104C22semidirect
46. C2×C11×#104C22semidirect
47. C2×C11×#104C22semidirect
48. C11×#418C22semidirect
49. C2×C11×#101C22semidirect
52. C11×#390C22semidirect
55. C11×#343C22semidirect
56. C11×#339C22semidirect
95. C11×AGL(1,ℤ/8)D4semidirect
171. #23879C11direct (N × H)
307. C22×AGL(1,ℤ/8)C2×C11semidirect
308. #3489C2×C11semidirect
309. C2×#454C2×C11semidirect
310. #3003C2×C11semidirect
311. #2435C2×C11semidirect
312. #2006C2×C11semidirect
313. #2003C2×C11semidirect
314. #1901C2×C11semidirect
315. #1883C2×C11semidirect
316. #1871C2×C11semidirect
317. #1789C2×C11semidirect
410. C2×2−1+4C22×C11semidirect
418. C2×AGL(1,ℤ/8)C22×C11semidirect
429. #537C22×C11semidirect
431. #536C22×C11semidirect
432. C2×#124C22×C11semidirect
437. #520C22×C11semidirect
443. C2×#104C22×C11semidirect
444. C2×#104C22×C11semidirect
445. C2×#104C22×C11semidirect
446. #418C22×C11semidirect
447. C2×#101C22×C11semidirect
450. #390C22×C11semidirect
453. #343C22×C11semidirect
454. #339C22×C11semidirect
480. C22×C11#454semidirect
534. AGL(1,ℤ/8)D4×C11semidirect
755. C11#23879direct (N × H)
873. C22C11×#454semidirect

Maximal subgroups

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

subgroupindex
C22×C11×AGL(1,ℤ/8)2
C11×#34892
C2×C11×#4542
C11×#30032
C11×#24352
C11×#20062
C11×#20032
C11×#19012
C11×#18832
C11×#18712
C11×#17892
#2387911