Finite Group Databasebeta

← C11×#25192 #14602385

Subgroups — C11×#25192 #14602385

Order 2816.

1054 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3062C211yesmaximal, characteristic, complemented
2C11×#3045C211yesmaximal, characteristic, complemented
3C2×C11×#453C211yesmaximal, characteristic, complemented
4C11×#3012C211yesmaximal, characteristic, complemented
5C2×C11×#444C211yesmaximal, characteristic, complemented
6C11×#2897C211yesmaximal, characteristic, complemented
7C11×#2063C211yesmaximal, characteristic, complemented
8C11×#2051C211yesmaximal, characteristic, complemented
9C11×#2040C211yesmaximal, characteristic, complemented
10C11×#2002C211yesmaximal, characteristic, complemented
11C11×#1961C211yesmaximal, characteristic, complemented
12C11×#1938C211yesmaximal, characteristic, complemented
13C11×#1907C211yesmaximal, characteristic, complemented
14C11×#1907C211yesmaximal, characteristic, complemented
15C11×#1860C211yesmaximal, characteristic, complemented
16C2×C11×H(5,𝔽2)C2211yescharacteristic
17C2×C11×AGL(1,ℤ/8)C2211yescharacteristic
18C2×C11×AGL(1,ℤ/8)C2211yescharacteristic
19C2×C11×AGL(1,ℤ/8)C2211yescharacteristic
20C2×C11×#135C2211yescharacteristic
21C2×C11×#131C2211yescharacteristic
22C2×C11×#131C2211yescharacteristic, complemented
23C11×#537C2211yescharacteristic
24C11×#535C2211yescharacteristic, complemented
25C2×C11×#127C2211yescharacteristic
26C11×#520C2211yescharacteristic
27C11×#469—21no—
28C11×#468—21no—
29C11×#466—21no—
30C11×#465—21no—
31C11×#464—21no—
32C11×#463—21no—
33C11×#460—21no—
34C11×#459—21no—
35C11×#453—24no—
36C11×#452—21no—
37C11×#450—21no—
38C11×#449—21no—
39C11×#447—21no—
40C11×#444—24no—
41C2×C11×#108C2211yescharacteristic, complemented
42C11×#428C2211yescharacteristic, complemented
43C11×#424C2211yescharacteristic, complemented
44C2×C11×#104C2211yescharacteristic
45C2×C11×#104C2211yescharacteristic
46C2×C11×#104C2211yescharacteristic, complemented
47C11×#418—21no—
48C11×#418C2211yescharacteristic
49C11×#417—21no—
50C11×#417C2211yescharacteristic
51C11×#417C2211yescharacteristic
52C11×#417C2211yescharacteristic, complemented
53C11×#416—21no—
54C11×#416C2211yescharacteristic
55C2×C11×#102—21no—
56C2×C11×#102C2211yescharacteristic
57C2×C11×#102C2211yescharacteristic
58C2×C11×#102C2211yescharacteristic, complemented
59C2×C11×#102C2211yescharacteristic, complemented
60C2×C11×#100C2211yescharacteristic
61C2×C11×#100C2211yescharacteristic, complemented
62C11×#408C2211yescharacteristic
63C2×C11×#97C2211yescharacteristic, complemented
64C11×#382C2211yescharacteristic, complemented
65C11×#343C2211yescharacteristic, complemented
66C11×#343C2211yescharacteristic, complemented
67C11×#341C2211yescharacteristic, complemented
68C11×#339C2211yescharacteristic, complemented
69C11×H(5,𝔽2)—22no—
70C11×H(5,𝔽2)—22no—
71C11×H(5,𝔽2)—22no—
72C11×H(5,𝔽2)—41no—
73C2×C11×#41—21no—
74C2×C11×#41—21no—
75C2×C11×#41C2311yescharacteristic
76C2×C11×#41C2311yescharacteristic
77C2×C11×#41C2311yescharacteristic
78C22×D4×C11—21no—
79C22×D4×C11—21no—
80C22×D4×C11—41no—
81C22×D4×C11—41no—
82C22×D4×C11C2311yescharacteristic
83C22×D4×C11C2311yescharacteristic
84C11×AGL(1,ℤ/8)—22no—
85C11×AGL(1,ℤ/8)—22no—
86C11×AGL(1,ℤ/8)—22no—
87C11×AGL(1,ℤ/8)—22no—
88C11×AGL(1,ℤ/8)—41no—
89C11×AGL(1,ℤ/8)—41no—
90C11×#135—22no—
91C11×#135—22no—
92C2×C11×Q16D411yescharacteristic, complemented
93C2×C11×SD16—21no—
94C2×C11×SD16—21no—
95C2×C11×SD16—21no—
96C2×C11×SD16D411yescharacteristic, complemented
97C2×C11×SD16D411yescharacteristic, complemented
98C2×C11×D8—21no—
99C2×C11×D8—21no—
100C2×C11×D8—21no—
101C2×C11×D8D411yescharacteristic, complemented
102C11×#131—22no—
103C11×#131—22no—
104C11×#131—41no—
105C11×#131—41no—
106C2×C11×M16—21no—
107C2×C11×M16—21no—
108C2×C11×M16C2311yescharacteristic
109C2×C11×M16C2311yescharacteristic
110C2×C11×M16C2311yescharacteristic
111C2×C11×M16C2311yescharacteristic
112C22×C8×C11—21no—
113C22×C8×C11—21no—
114C22×C8×C11C2311yescharacteristic
115C22×C8×C11C2311yescharacteristic
116C11×#127—21no—
117C11×#127—22no—
118C11×#127—22no—
119C11×#124—21no—
120C11×C22⋊Q8—21no—
121C11×C22⋊Q8—21no—
122C11×#121—21no—
123C11×#121—21no—
124C11×#121—21no—
125C11×#121—21no—
126C11×#121—41no—
127C11×#120—41no—
128C4×Q8×C11—21no—
129C4×D4×C11—21no—
130C4×D4×C11—41no—
131C11×#117—21no—
132C11×#117C2311yescharacteristic
133C2×C11×C4⋊C4—21no—
134C2×C11×C4⋊C4C2311yescharacteristic
135C2×C11×C4⋊C4C2311yescharacteristic
136C2×C42×C11C2311yescharacteristic
137C11×#108—22no—
138C11×#107—21no—
139C11×#106—21no—
140C11×C4⋊C8—21no—
141C11×C4⋊C8—21no—
142C11×#104—22no—
143C11×#104—22no—
144C11×#104D414yescomplemented
145C11×#103—21no—
146C11×#103—21no—
147C11×#103—21no—
148C11×#103D411yescharacteristic, complemented
149C11×#103D411yescharacteristic, complemented
150C11×#102—21no—
151C11×#102—21no—
152C11×#102—21no—
153C11×#102—21no—
154C11×#102—21no—
155C11×#102—21no—
156C11×#102—21no—
157C11×#102—21no—
158C11×#102—21no—
159C11×#102—21no—
160C11×#102—21no—
161C11×#102—21no—
162C11×#102—21no—
163C11×#102D411yescharacteristic, complemented
164C11×#102D411yescharacteristic, complemented
165C11×#100—22no—
166C11×#100—41no—
167C11×C22⋊C8—21no—
168C11×C22⋊C8—21no—
169C11×#97—22no—
170C11×#95—41no—
171#25192C1111yesmaximal, characteristic, direct product factor, Sylow
172C24×C11—21no—
173C24×C11—21no—
174C24×C11—41no—
175C11×#41—21no—
176C11×#41—21no—
177C11×#41—24no—
178C11×#41—21no—
179C11×#41—21no—
180C11×#41—21no—
181C11×#41—21no—
182C11×#41—21no—
183C11×#41—21no—
184C11×#41—21no—
185C11×#41—21no—
186C11×#41—42no—
187C11×#41—42no—
188C11×#41—42no—
189C11×#41C2×D412yes—
190C11×#41#4112yes—
191C2×Q8×C11C2×D411yescharacteristic
192C2×Q8×C11C2×D411yescharacteristic
193C2×Q8×C11C2×D411yescharacteristic
194C2×D4×C11—21no—
195C2×D4×C11—24no—
196C2×D4×C11—21no—
197C2×D4×C11—21no—
198C2×D4×C11—21no—
199C2×D4×C11—21no—
200C2×D4×C11—21no—
201C2×D4×C11—21no—
202C2×D4×C11—21no—
203C2×D4×C11—21no—
204C2×D4×C11—21no—
205C2×D4×C11—21no—
206C2×D4×C11—21no—
207C2×D4×C11—21no—
208C2×D4×C11—21no—
209C2×D4×C11—42no—
210C2×D4×C11—41no—
211C2×D4×C11—41no—
212C2×D4×C11—44no—
213C2×D4×C11—41no—
214C2×D4×C11—41no—
215C2×D4×C11—42no—
216C2×D4×C11—44no—
217C2×D4×C11—44no—
218C2×D4×C11—42no—
219C2×D4×C11—41no—
220C2×D4×C11—82no—
221C2×D4×C11—82no—
222C2×D4×C11C2×D411yescharacteristic
223C2×D4×C11C2×D411yescharacteristic
224C2×D4×C11C2×D411yescharacteristic
225C2×D4×C11#4112yes—
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—41no—
233C22×C4×C11—41no—
234C22×C4×C11C2411yescharacteristic
235C11×Q16—22no—
236C11×SD16—22no—
237C11×SD16—22no—
238C11×SD16—42no—
239C11×SD16—42no—
240C11×SD16—42no—
241C11×D8—22no—
242C11×D8—42no—
243C11×D8—42no—
244C11×D8—42no—
245C11×M16—21no—
246C11×M16—21no—
247C11×M16—21no—
248C11×M16—21no—
249C11×M16—21no—
250C11×M16—21no—
251C11×M16—21no—
252C11×M16—42no—
253C11×M16—42no—
254C11×M16C2×D412yes—
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×C11—21no—
263C2×C8×C11—42no—
264C2×C8×C11—42no—
265C2×C8×C11C2×D411yescharacteristic
266C2×C8×C11C2×D411yescharacteristic
267C2×C8×C11C2×D411yescharacteristic
268C2×C8×C11C2×D411yescharacteristic
269C11×C4⋊C4—21no—
270C11×C4⋊C4—21no—
271C11×C4⋊C4—21no—
272C11×C4⋊C4—21no—
273C11×C4⋊C4—41no—
274C11×C4⋊C4—41no—
275C11×C4⋊C4C2×D411yescharacteristic
276C11×C4⋊C4C2×D411yescharacteristic
277C11×C22⋊C4—21no—
278C11×C22⋊C4—41no—
279C11×C22⋊C4—41no—
280C11×C22⋊C4—41no—
281C11×C22⋊C4—41no—
282C11×C22⋊C4—41no—
283C42×C11—21no—
284C42×C11—21no—
285C42×C11—41no—
286C42×C11C2×D412yes—
287#3062C2×C1111yescharacteristic, complemented
288#3045C2×C1111yescharacteristic, complemented
289C2×#453C2×C1111yescharacteristic, complemented
290#3012C2×C1111yescharacteristic, complemented
291C2×#444C2×C1111yescharacteristic, complemented
292#2897C2×C1111yescharacteristic, complemented
293#2063C2×C1111yescharacteristic, complemented
294#2051C2×C1111yescharacteristic, complemented
295#2040C2×C1111yescharacteristic, complemented
296#2002C2×C1111yescharacteristic, complemented
297#1961C2×C1111yescharacteristic, complemented
298#1938C2×C1111yescharacteristic, complemented
299#1907C2×C1111yescharacteristic, complemented
300#1907C2×C1111yescharacteristic, complemented
301#1860C2×C1111yescharacteristic, complemented
302C23×C11—21no—
303C23×C11—21no—
304C23×C11—21no—
305C23×C11—22no—
306C23×C11—44no—
307C23×C11—41no—
308C23×C11—41no—
309C23×C11—41no—
310C23×C11—41no—
311C23×C11—41no—
312C23×C11—81no—
313C23×C11—81no—
314C23×C11—81no—
315C23×C11—81no—
316C23×C11—161no—
317C23×C11—161no—
318C23×C11H(5,𝔽2)11yescharacteristic
319Q8×C11—21no—
320Q8×C11—21no—
321Q8×C11—21no—
322Q8×C11—21no—
323Q8×C11—21no—
324Q8×C11#12112yes—
325D4×C11—22no—
326D4×C11—22no—
327D4×C11—21no—
328D4×C11—21no—
329D4×C11—22no—
330D4×C11—21no—
331D4×C11—21no—
332D4×C11—21no—
333D4×C11—22no—
334D4×C11—44no—
335D4×C11—44no—
336D4×C11—41no—
337D4×C11—41no—
338D4×C11—41no—
339D4×C11—41no—
340D4×C11—41no—
341D4×C11—41no—
342D4×C11—41no—
343D4×C11—41no—
344D4×C11—41no—
345D4×C11—41no—
346D4×C11—88no—
347D4×C11—161no—
348D4×C11—161no—
349D4×C11—161no—
350D4×C11#12112yes—
351C2×C4×C11—21no—
352C2×C4×C11—22no—
353C2×C4×C11—22no—
354C2×C4×C11—21no—
355C2×C4×C11—21no—
356C2×C4×C11—21no—
357C2×C4×C11—21no—
358C2×C4×C11—22no—
359C2×C4×C11—44no—
360C2×C4×C11—41no—
361C2×C4×C11—41no—
362C2×C4×C11—41no—
363C2×C4×C11—41no—
364C2×C4×C11—41no—
365C2×C4×C11—41no—
366C2×C4×C11—41no—
367C2×C4×C11—41no—
368C2×C4×C11—81no—
369C2×C4×C11—81no—
370C2×C4×C11—161no—
371C2×C4×C11C22×D411yescharacteristic
372C2×C4×C11C22×D411yescharacteristic
373C2×C4×C11C22×D411yescharacteristic
374C2×C4×C11C2×#4111yescharacteristic
375C2×C4×C11C2×#4111yescharacteristic
376C2×C4×C11H(5,𝔽2)11yescharacteristic
377C8×C11—21no—
378C8×C11—21no—
379C8×C11—21no—
380C8×C11—21no—
381C8×C11—22no—
382C8×C11—41no—
383C8×C11—41no—
384C8×C11—41no—
385C2×H(5,𝔽2)C22×C1111yescharacteristic
386C2×AGL(1,ℤ/8)C22×C1111yescharacteristic
387C2×AGL(1,ℤ/8)C22×C1111yescharacteristic
388C2×AGL(1,ℤ/8)C22×C1111yescharacteristic
389C2×#135C22×C1111yescharacteristic
390C2×#131C22×C1111yescharacteristic
391C2×#131C22×C1111yescharacteristic, complemented
392#537C22×C1111yescharacteristic
393#535C22×C1111yescharacteristic, complemented
394C2×#127C22×C1111yescharacteristic
395#520C22×C1111yescharacteristic
396#469—21no—
397#468—21no—
398#466—21no—
399#465—21no—
400#464—21no—
401#463—21no—
402#460—21no—
403#459—21no—
404#453—24no—
405#452—21no—
406#450—21no—
407#449—21no—
408#447—21no—
409#444—24no—
410C2×#108C22×C1111yescharacteristic, complemented
411#428C22×C1111yescharacteristic, complemented
412#424C22×C1111yescharacteristic, complemented
413C2×#104C22×C1111yescharacteristic
414C2×#104C22×C1111yescharacteristic
415C2×#104C22×C1111yescharacteristic, complemented
416#418—21no—
417#418C22×C1111yescharacteristic
418#417—21no—
419#417C22×C1111yescharacteristic
420#417C22×C1111yescharacteristic
421#417C22×C1111yescharacteristic, complemented
422#416—21no—
423#416C22×C1111yescharacteristic
424C2×#102—21no—
425C2×#102C22×C1111yescharacteristic
426C2×#102C22×C1111yescharacteristic
427C2×#102C22×C1111yescharacteristic, complemented
428C2×#102C22×C1111yescharacteristic, complemented
429C2×#100C22×C1111yescharacteristic
430C2×#100C22×C1111yescharacteristic, complemented
431#408C22×C1111yescharacteristic
432C2×#97C22×C1111yescharacteristic, complemented
433#382C22×C1111yescharacteristic, complemented
434#343C22×C1111yescharacteristic, complemented
435#343C22×C1111yescharacteristic, complemented
436#341C22×C1111yescharacteristic, complemented
437#339C22×C1111yescharacteristic, complemented
438C22×C11—21no—
439C22×C11—21no—
440C22×C11—22no—
441C22×C11—41no—
442C22×C11—41no—
443C22×C11—41no—
444C22×C11—42no—
445C22×C11—41no—
446C22×C11—41no—
447C22×C11—41no—
448C22×C11—41no—
449C22×C11—41no—
450C22×C11—82no—
451C22×C11—82no—
452C22×C11—81no—
453C22×C11—81no—
454C22×C11—81no—
455C22×C11—81no—
456C22×C11—81no—
457C22×C11—161no—
458C22×C11—161no—
459C22×C11—164no—
460C22×C11#53811yescharacteristic
461C22×C11D4211yescharacteristic
462C22×C11#54611yescharacteristic
463C4×C11—22no—
464C4×C11—42no—
465C4×C11—41no—
466C4×C11—41no—
467C4×C11—41no—
468C4×C11—41no—
469C4×C11—81no—
470C4×C11—81no—
471C4×C11C2×#12111yescharacteristic
472C4×C11#52511yescharacteristic
473C4×C11D4211yescharacteristic
474C4×C11#54611yescharacteristic
475H(5,𝔽2)—22no—
476H(5,𝔽2)—22no—
477H(5,𝔽2)—22no—
478H(5,𝔽2)—41no—
479C2×#41—21no—
480C2×#41—21no—
481C2×#41C23×C1111yescharacteristic
482C2×#41C23×C1111yescharacteristic
483C2×#41C23×C1111yescharacteristic
484C22×D4—21no—
485C22×D4—21no—
486C22×D4—41no—
487C22×D4—41no—
488C22×D4C23×C1111yescharacteristic
489C22×D4C23×C1111yescharacteristic
490AGL(1,ℤ/8)—22no—
491AGL(1,ℤ/8)—22no—
492AGL(1,ℤ/8)—22no—
493AGL(1,ℤ/8)—22no—
494AGL(1,ℤ/8)—41no—
495AGL(1,ℤ/8)—41no—
496#135—22no—
497#135—22no—
498C2×Q16D4×C1111yescharacteristic, complemented
499C2×SD16—21no—
500C2×SD16—21no—
501C2×SD16—21no—
502C2×SD16D4×C1111yescharacteristic, complemented
503C2×SD16D4×C1111yescharacteristic, complemented
504C2×D8—21no—
505C2×D8—21no—
506C2×D8—21no—
507C2×D8D4×C1111yescharacteristic, complemented
508#131—22no—
509#131—22no—
510#131—41no—
511#131—41no—
512C2×M16—21no—
513C2×M16—21no—
514C2×M16C23×C1111yescharacteristic
515C2×M16C23×C1111yescharacteristic
516C2×M16C23×C1111yescharacteristic
517C2×M16C23×C1111yescharacteristic
518C22×C8—21no—
519C22×C8—21no—
520C22×C8C23×C1111yescharacteristic
521C22×C8C23×C1111yescharacteristic
522#127—21no—
523#127—22no—
524#127—22no—
525#124—21no—
526C22⋊Q8—21no—
527C22⋊Q8—21no—
528#121—21no—
529#121—21no—
530#121—21no—
531#121—21no—
532#121—41no—
533#120—41no—
534C4×Q8—21no—
535C4×D4—21no—
536C4×D4—41no—
537#117—21no—
538#117C23×C1111yescharacteristic
539C2×C4⋊C4—21no—
540C2×C4⋊C4C23×C1111yescharacteristic
541C2×C4⋊C4C23×C1111yescharacteristic
542C2×C42C23×C1111yescharacteristic
543#108—22no—
544#107—21no—
545#106—21no—
546C4⋊C8—21no—
547C4⋊C8—21no—
548#104—22no—
549#104—22no—
550#104D4×C1114yescomplemented
551#103—21no—
552#103—21no—
553#103—21no—
554#103D4×C1111yescharacteristic, complemented
555#103D4×C1111yescharacteristic, complemented
556#102—21no—
557#102—21no—
558#102—21no—
559#102—21no—
560#102—21no—
561#102—21no—
562#102—21no—
563#102—21no—
564#102—21no—
565#102—21no—
566#102—21no—
567#102—21no—
568#102—21no—
569#102D4×C1111yescharacteristic, complemented
570#102D4×C1111yescharacteristic, complemented
571#100—22no—
572#100—41no—
573C22⋊C8—21no—
574C22⋊C8—21no—
575#97—22no—
576#95—41no—
577C2×C11—21no—
578C2×C11—21no—
579C2×C11—42no—
580C2×C11—81no—
581C2×C11—81no—
582C2×C11—82no—
583C2×C11—161no—
584C2×C11#242411yescharacteristic
585C2×C11#328811yescharacteristic
586C2×C11#328811yescharacteristic
587C24—21no—
588C24—21no—
589C24—41no—
590#41—21no—
591#41—21no—
592#41—24no—
593#41—21no—
594#41—21no—
595#41—21no—
596#41—21no—
597#41—21no—
598#41—21no—
599#41—21no—
600#41—21no—
601#41—42no—
602#41—42no—
603#41—42no—
604#41C2×D4×C1112yes—
605#41C11×#4112yes—
606C2×Q8C2×D4×C1111yescharacteristic
607C2×Q8C2×D4×C1111yescharacteristic
608C2×Q8C2×D4×C1111yescharacteristic
609C2×D4—21no—
610C2×D4—24no—
611C2×D4—21no—
612C2×D4—21no—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—21no—
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—42no—
625C2×D4—41no—
626C2×D4—41no—
627C2×D4—44no—
628C2×D4—41no—
629C2×D4—41no—
630C2×D4—42no—
631C2×D4—44no—
632C2×D4—44no—
633C2×D4—42no—
634C2×D4—41no—
635C2×D4—82no—
636C2×D4—82no—
637C2×D4C2×D4×C1111yescharacteristic
638C2×D4C2×D4×C1111yescharacteristic
639C2×D4C2×D4×C1111yescharacteristic
640C2×D4C11×#4112yes—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—41no—
648C22×C4—41no—
649C22×C4C24×C1111yescharacteristic
650Q16—22no—
651SD16—22no—
652SD16—22no—
653SD16—42no—
654SD16—42no—
655SD16—42no—
656D8—22no—
657D8—42no—
658D8—42no—
659D8—42no—
660M16—21no—
661M16—21no—
662M16—21no—
663M16—21no—
664M16—21no—
665M16—21no—
666M16—21no—
667M16—42no—
668M16—42no—
669M16C2×D4×C1112yes—
670C2×C8—21no—
671C2×C8—21no—
672C2×C8—21no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—42no—
679C2×C8—42no—
680C2×C8C2×D4×C1111yescharacteristic
681C2×C8C2×D4×C1111yescharacteristic
682C2×C8C2×D4×C1111yescharacteristic
683C2×C8C2×D4×C1111yescharacteristic
684C4⋊C4—21no—
685C4⋊C4—21no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—41no—
689C4⋊C4—41no—
690C4⋊C4C2×D4×C1111yescharacteristic
691C4⋊C4C2×D4×C1111yescharacteristic
692C22⋊C4—21no—
693C22⋊C4—41no—
694C22⋊C4—41no—
695C22⋊C4—41no—
696C22⋊C4—41no—
697C22⋊C4—41no—
698C42—21no—
699C42—21no—
700C42—41no—
701C42C2×D4×C1112yes—
702C11#2519211yescharacteristic, direct product factor, Sylow
703C23—21no—
704C23—21no—
705C23—21no—
706C23—22no—
707C23—44no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—81no—
714C23—81no—
715C23—81no—
716C23—81no—
717C23—161no—
718C23—161no—
719C23C11×H(5,𝔽2)11yescharacteristic
720Q8—21no—
721Q8—21no—
722Q8—21no—
723Q8—21no—
724Q8—21no—
725Q8C11×#12112yes—
726D4—22no—
727D4—22no—
728D4—21no—
729D4—21no—
730D4—22no—
731D4—21no—
732D4—21no—
733D4—21no—
734D4—22no—
735D4—44no—
736D4—44no—
737D4—41no—
738D4—41no—
739D4—41no—
740D4—41no—
741D4—41no—
742D4—41no—
743D4—41no—
744D4—41no—
745D4—41no—
746D4—41no—
747D4—88no—
748D4—161no—
749D4—161no—
750D4—161no—
751D4C11×#12112yes—
752C2×C4—21no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—22no—
760C2×C4—44no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—81no—
770C2×C4—81no—
771C2×C4—161no—
772C2×C4C22×D4×C1111yescharacteristic
773C2×C4C22×D4×C1111yescharacteristic
774C2×C4C22×D4×C1111yescharacteristic
775C2×C4C2×C11×#4111yescharacteristic
776C2×C4C2×C11×#4111yescharacteristic
777C2×C4C11×H(5,𝔽2)11yescharacteristic
778C8—21no—
779C8—21no—
780C8—21no—
781C8—21no—
782C8—22no—
783C8—41no—
784C8—41no—
785C8—41no—
786C22—21no—
787C22—21no—
788C22—22no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—42no—
793C22—41no—
794C22—41no—
795C22—41no—
796C22—41no—
797C22—41no—
798C22—82no—
799C22—82no—
800C22—81no—
801C22—81no—
802C22—81no—
803C22—81no—
804C22—81no—
805C22—161no—
806C22—161no—
807C22—164no—
808C22C11×#53811yescharacteristic
809C22D42×C1111yescharacteristic
810C22C11×#54611yescharacteristic
811C4—22no—
812C4—42no—
813C4—41no—
814C4—41no—
815C4—41no—
816C4—41no—
817C4—81no—
818C4—81no—
819C4C2×C11×#12111yescharacteristic
820C4C11×#52511yescharacteristic
821C4D42×C1111yescharacteristic
822C4C11×#54611yescharacteristic
823C2—21no—
824C2—21no—
825C2—42no—
826C2—81no—
827C2—81no—
828C2—82no—
829C2—161no—
830C2C11×#242411yescharacteristic
831C2C11×#328811yescharacteristic
832C2C11×#328811yescharacteristic
subgroupG/H
center, socleC22×C11D42
commutator, Frattini, cosocleC22×C4C24×C11
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C22×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3062C2semidirect
2. C11×#3045C2semidirect
3. C2×C11×#453C2semidirect
4. C11×#3012C2semidirect
5. C2×C11×#444C2semidirect
6. C11×#2897C2semidirect
7. C11×#2063C2semidirect
8. C11×#2051C2semidirect
9. C11×#2040C2semidirect
10. C11×#2002C2semidirect
11. C11×#1961C2semidirect
12. C11×#1938C2semidirect
13. C11×#1907C2semidirect
14. C11×#1907C2semidirect
15. C11×#1860C2semidirect
22. C2×C11×#131C22semidirect
24. C11×#535C22semidirect
41. C2×C11×#108C22semidirect
42. C11×#428C22semidirect
43. C11×#424C22semidirect
46. C2×C11×#104C22semidirect
52. C11×#417C22semidirect
58. C2×C11×#102C22semidirect
59. C2×C11×#102C22semidirect
61. C2×C11×#100C22semidirect
63. C2×C11×#97C22semidirect
64. C11×#382C22semidirect
65. C11×#343C22semidirect
66. C11×#343C22semidirect
67. C11×#341C22semidirect
68. C11×#339C22semidirect
92. C2×C11×Q16D4semidirect
96. C2×C11×SD16D4semidirect
97. C2×C11×SD16D4semidirect
101. C2×C11×D8D4semidirect
144. C11×#104D4semidirect
148. C11×#103D4semidirect
149. C11×#103D4semidirect
163. C11×#102D4semidirect
164. C11×#102D4semidirect
171. #25192C11direct (N × H)
287. #3062C2×C11semidirect
288. #3045C2×C11semidirect
289. C2×#453C2×C11semidirect
290. #3012C2×C11semidirect
291. C2×#444C2×C11semidirect
292. #2897C2×C11semidirect
293. #2063C2×C11semidirect
294. #2051C2×C11semidirect
295. #2040C2×C11semidirect
296. #2002C2×C11semidirect
297. #1961C2×C11semidirect
298. #1938C2×C11semidirect
299. #1907C2×C11semidirect
300. #1907C2×C11semidirect
301. #1860C2×C11semidirect
391. C2×#131C22×C11semidirect
393. #535C22×C11semidirect
410. C2×#108C22×C11semidirect
411. #428C22×C11semidirect
412. #424C22×C11semidirect
415. C2×#104C22×C11semidirect
421. #417C22×C11semidirect
427. C2×#102C22×C11semidirect
428. C2×#102C22×C11semidirect
430. C2×#100C22×C11semidirect
432. C2×#97C22×C11semidirect
433. #382C22×C11semidirect
434. #343C22×C11semidirect
435. #343C22×C11semidirect
436. #341C22×C11semidirect
437. #339C22×C11semidirect
498. C2×Q16D4×C11semidirect
502. C2×SD16D4×C11semidirect
503. C2×SD16D4×C11semidirect
507. C2×D8D4×C11semidirect
550. #104D4×C11semidirect
554. #103D4×C11semidirect
555. #103D4×C11semidirect
569. #102D4×C11semidirect
570. #102D4×C11semidirect
702. C11#25192direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#30622
C11×#30452
C2×C11×#4532
C11×#30122
C2×C11×#4442
C11×#28972
C11×#20632
C11×#20512
C11×#20402
C11×#20022
C11×#19612
C11×#19382
C11×#19072
C11×#18602
#2519211