Finite Group Databasebeta

← C4×C11×#577 #14637365

Subgroups — C4×C11×#577 #14637365

Order 2816.

2742 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#577C211yesmaximal, characteristic
2C4×C11×2−1+4C211yesmaximal, characteristic, complemented
3C4×C11×H(5,𝔽2)C211yesmaximal, characteristic, complemented
4C11×#2952C213yesmaximal, complemented
5C11×#2949C213yesmaximal, complemented
6C11×#2947C213yesmaximal, complemented
7C11×#2946C213yesmaximal, complemented
8C4×C11×#137C213yesmaximal, complemented
9C4×C11×AGL(1,ℤ/8)C213yesmaximal, complemented
10C4×C11×#135C213yesmaximal, complemented
11C2×C4×C11×SD16C213yesmaximal, complemented
12C11×#2912C211yesmaximal, characteristic, complemented
13C11×#2898C211yesmaximal, characteristic, complemented
14C11×#2897C211yesmaximal, characteristic, complemented
15C4×C11×#131C211yesmaximal, characteristic, complemented
16C2×C11×2−1+4C2211yescharacteristic
17C2×C11×H(5,𝔽2)C2211yescharacteristic
18C11×#577C4116yesdirect product factor
19C2×C11×#137C2213yes—
20C2×C11×AGL(1,ℤ/8)C2213yes—
21C2×C11×#135C2213yes—
22C22×C11×SD16C2213yes—
23C2×C11×#131C2211yescharacteristic
24C2×C11×#131C2211yescharacteristic
25C11×#520—21no—
26C11×#520—23no—
27C11×#520C2213yes—
28C11×#520C2211yescharacteristic
29C11×#520C2211yescharacteristic
30C11×#520C2213yescomplemented
31C11×#519—21no—
32C11×#519C2213yescomplemented
33C11×#518—23no—
34C11×#518C2213yes—
35C4×C11×#41—21no—
36C4×C11×#41—23no—
37C4×C11×#41C2213yes—
38C4×C11×#41C2211yescharacteristic
39C4×C11×#41C2213yescomplemented
40C2×C4×Q8×C11—21no—
41C2×C4×Q8×C11C2213yescomplemented
42C2×C4×D4×C11—23no—
43C2×C4×D4×C11C2213yes—
44C11×#442C2216yescomplemented
45C11×#441C2216yescomplemented
46C11×#440C2216yescomplemented
47C11×#440C2216yescomplemented
48C4×C11×Q16C2213yescomplemented
49C4×C11×Q16C2213yescomplemented
50C4×C11×SD16C2213yescomplemented
51C4×C11×SD16C2216yescomplemented
52C4×C11×SD16C2216yescomplemented
53C4×C11×SD16C2216yescomplemented
54C4×C11×SD16C2211yescharacteristic, complemented
55C4×C11×SD16C2213yescomplemented
56C4×C11×SD16C2213yescomplemented
57C4×C11×D8C2213yescomplemented
58C4×C11×D8C2213yescomplemented
59C11×#428C2213yescomplemented
60C11×#428C2213yescomplemented
61C11×#427C2213yescomplemented
62C2×C11×#106C2213yescomplemented
63C11×#419C2213yescomplemented
64C11×#418C2213yes—
65C11×#417C2213yes—
66C11×#417C2213yescomplemented
67C11×#416C2213yes—
68C11×#416C2213yescomplemented
69C2×C11×#103C2213yescomplemented
70C2×C11×#102C2213yes—
71C11×#405C2213yescomplemented
72C11×#405C2213yescomplemented
73C4×C11×M16C2213yescomplemented
74C2×C4×C8×C11C2213yescomplemented
75C11×2−1+4—24no—
76C11×2−1+4C2×C418yescomplemented
77C11×H(5,𝔽2)—24no—
78C11×H(5,𝔽2)C2×C418yescomplemented
79C2×C11×#41—21no—
80C2×C11×#41—23no—
81C2×C11×#41C2313yes—
82C2×C11×#41C2313yes—
83C2×C11×#41C2311yescharacteristic
84C22×Q8×C11—21no—
85C22×Q8×C11C2313yes—
86C22×D4×C11—23no—
87C22×D4×C11C2313yes—
88C23×C4×C11—23no—
89C11×#137C2×C4124yescomplemented
90C11×AGL(1,ℤ/8)C2×C4124yescomplemented
91C11×#135C2×C4124yescomplemented
92C2×C11×Q16C2313yes—
93C2×C11×SD16C2×C4124yescomplemented
94C2×C11×SD16C2313yes—
95C2×C11×SD16C2316yes—
96C2×C11×SD16C2311yescharacteristic
97C2×C11×D8C2313yes—
98C11×#131—24no—
99C11×#131C2×C418yescomplemented
100C2×C11×M16C2313yes—
101C2×C11×M16C2313yes—
102C22×C8×C11C2313yes—
103C22×C8×C11C2313yes—
104C4×Q8×C11—21no—
105C4×Q8×C11—21no—
106C4×Q8×C11—23no—
107C4×Q8×C11—23no—
108C4×Q8×C11—23no—
109C4×Q8×C11—23no—
110C4×Q8×C11D411yescharacteristic
111C4×Q8×C11D411yescharacteristic
112C4×Q8×C11C2313yes—
113C4×Q8×C11C2316yes—
114C4×Q8×C11C2311yescharacteristic
115C4×Q8×C11C2313yes—
116C4×Q8×C11C2313yes—
117C4×D4×C11—23no—
118C4×D4×C11—23no—
119C4×D4×C11—23no—
120C4×D4×C11—23no—
121C4×D4×C11—23no—
122C4×D4×C11—23no—
123C4×D4×C11—23no—
124C4×D4×C11—23no—
125C4×D4×C11—26no—
126C4×D4×C11—26no—
127C4×D4×C11—23no—
128C4×D4×C11—23no—
129C4×D4×C11D413yes—
130C4×D4×C11D413yes—
131C4×D4×C11C2313yes—
132C4×D4×C11C2316yes—
133C4×D4×C11C2313yes—
134C4×D4×C11C2311yescharacteristic
135C4×D4×C11C2313yes—
136C11×#117—23no—
137C11×#117—23no—
138C11×#117—26no—
139C11×#117—23no—
140C11×#117—23no—
141C11×#117C2313yes—
142C11×#117C2313yes—
143C11×#117C2313yes—
144C2×C11×C4⋊C4—23no—
145C2×C11×C4⋊C4—23no—
146C2×C11×C4⋊C4—23no—
147C2×C11×C4⋊C4C2313yes—
148C2×C11×C4⋊C4C2313yes—
149C2×C11×C22⋊C4—23no—
150C2×C11×C22⋊C4—26no—
151C2×C42×C11—23no—
152C2×C42×C11—23no—
153C2×C42×C11—23no—
154C2×C42×C11C2313yes—
155C11×#107C2313yes—
156C11×#107C2313yes—
157C11×#106C2313yes—
158C11×#106C2316yes—
159C11×#106C2311yescharacteristic
160C11×#103C2313yes—
161C11×#103C2316yes—
162C11×#103C2311yescharacteristic
163C11×#103C2313yes—
164C11×#103C2313yes—
165C11×#102C2313yes—
166C11×#102C2316yes—
167C11×#102C2313yes—
168C11×#102C2311yescharacteristic
169C11×#102C2313yes—
170C11×#97C2316yes—
171C4×C8×C11C2311yescharacteristic
172C4×C8×C11C2313yes—
173C4×C8×C11C2313yes—
174C4×C8×C11C2313yes—
175C4×#577C1111yesmaximal, characteristic, direct product factor, Sylow
176C24×C11—23no—
177C11×#41—28no—
178C11×#41—224no—
179C11×#41—26no—
180C11×#41—26no—
181C11×#41C22×C4112yes—
182C11×#41C22×C414yes—
183C11×#41C22×C4112yescomplemented
184C11×#41#4114yes—
185C2×Q8×C11—28no—
186C2×Q8×C11—23no—
187C2×Q8×C11—26no—
188C2×Q8×C11C22×C4112yescomplemented
189C2×Q8×C11C2×D411yescharacteristic
190C2×Q8×C11C2413yes—
191C2×Q8×C11C2411yescharacteristic
192C2×D4×C11—23no—
193C2×D4×C11—23no—
194C2×D4×C11—224no—
195C2×D4×C11—23no—
196C2×D4×C11—26no—
197C2×D4×C11C22×C4112yes—
198C2×D4×C11C2×D413yes—
199C2×D4×C11C2411yescharacteristic
200C2×D4×C11C2413yes—
201C22×C4×C11—23no—
202C22×C4×C11—23no—
203C22×C4×C11—23no—
204C22×C4×C11—23no—
205C22×C4×C11—23no—
206C22×C4×C11—21no—
207C22×C4×C11—23no—
208C22×C4×C11—23no—
209C22×C4×C11—23no—
210C22×C4×C11—26no—
211C22×C4×C11—86no—
212C22×C4×C11C2×D413yes—
213C22×C4×C11C2×D413yes—
214C22×C4×C11C2413yes—
215C11×Q16C22×C4112yescomplemented
216C11×SD16C22×C4112yescomplemented
217C11×SD16C22×C4124yescomplemented
218C11×SD16C22×C414yescomplemented
219C11×D8C22×C4112yescomplemented
220C11×M16—26no—
221C11×M16C22×C4112yescomplemented
222C2×C8×C11—26no—
223C2×C8×C11C22×C4112yescomplemented
224C2×C8×C11C2411yescharacteristic
225C2×C8×C11C2413yes—
226C2×C8×C11C2411yescharacteristic
227C2×C8×C11C2413yes—
228C11×C4⋊C4—23no—
229C11×C4⋊C4—26no—
230C11×C4⋊C4—23no—
231C11×C4⋊C4—23no—
232C11×C4⋊C4—23no—
233C11×C4⋊C4—21no—
234C11×C4⋊C4—23no—
235C11×C4⋊C4C2×D413yes—
236C11×C4⋊C4C2×D413yes—
237C11×C4⋊C4C2413yes—
238C11×C4⋊C4C2411yescharacteristic
239C11×C4⋊C4C2413yes—
240C11×C4⋊C4C2411yescharacteristic
241C11×C22⋊C4—23no—
242C11×C22⋊C4—23no—
243C11×C22⋊C4—23no—
244C11×C22⋊C4—26no—
245C11×C22⋊C4—23no—
246C11×C22⋊C4—21no—
247C11×C22⋊C4—23no—
248C11×C22⋊C4C2×D416yes—
249C42×C11—23no—
250C42×C11—23no—
251C42×C11—26no—
252C42×C11—23no—
253C42×C11—23no—
254C42×C11—21no—
255C42×C11—23no—
256C42×C11C2×D413yes—
257C42×C11C2×D413yes—
258C42×C11C2413yes—
259C42×C11C2411yescharacteristic
260C2×#577C2×C1111yescharacteristic
261C4×2−1+4C2×C1111yescharacteristic, complemented
262C4×H(5,𝔽2)C2×C1111yescharacteristic, complemented
263#2952C2×C1113yescomplemented
264#2949C2×C1113yescomplemented
265#2947C2×C1113yescomplemented
266#2946C2×C1113yescomplemented
267C4×#137C2×C1113yescomplemented
268C4×AGL(1,ℤ/8)C2×C1113yescomplemented
269C4×#135C2×C1113yescomplemented
270C2×C4×SD16C2×C1113yescomplemented
271#2912C2×C1111yescharacteristic, complemented
272#2898C2×C1111yescharacteristic, complemented
273#2897C2×C1111yescharacteristic, complemented
274C4×#131C2×C1111yescharacteristic, complemented
275C23×C11—21no—
276C23×C11—23no—
277C23×C11—212no—
278C23×C11—83no—
279C23×C11—83no—
280C23×C11C22×D413yes—
281Q8×C11—212no—
282Q8×C11—23no—
283Q8×C11—21no—
284Q8×C11C4×D414yes—
285Q8×C11C23×C416yes—
286Q8×C11C23×C412yes—
287D4×C11—212no—
288D4×C11—212no—
289D4×C11—212no—
290D4×C11—23no—
291D4×C11—21no—
292D4×C11C4×D4112yes—
293D4×C11C23×C412yes—
294D4×C11C23×C416yes—
295C2×C4×C11—212no—
296C2×C4×C11—21no—
297C2×C4×C11—23no—
298C2×C4×C11—212no—
299C2×C4×C11—212no—
300C2×C4×C11—26no—
301C2×C4×C11—21no—
302C2×C4×C11—21no—
303C2×C4×C11—23no—
304C2×C4×C11—23no—
305C2×C4×C11—43no—
306C2×C4×C11—42no—
307C2×C4×C11—46no—
308C2×C4×C11—83no—
309C2×C4×C11—83no—
310C2×C4×C11—86no—
311C2×C4×C11—83no—
312C2×C4×C11—83no—
313C2×C4×C11C23×C416yes—
314C2×C4×C11C22×D413yes—
315C2×C4×C11C22×D413yes—
316C2×C4×C11C22×D411yescharacteristic
317C2×C4×C11C22×D413yes—
318C2×C4×C11C22×D411yescharacteristic
319C2×C4×C11C2×#4116yes—
320C2×C4×C11C2511yescharacteristic
321C8×C11—21no—
322C8×C11—23no—
323C8×C11C23×C412yes—
324C8×C11C23×C416yes—
325C2×2−1+4C22×C1111yescharacteristic
326C2×H(5,𝔽2)C22×C1111yescharacteristic
327#577C4×C11116yesdirect product factor
328C2×#137C22×C1113yes—
329C2×AGL(1,ℤ/8)C22×C1113yes—
330C2×#135C22×C1113yes—
331C22×SD16C22×C1113yes—
332C2×#131C22×C1111yescharacteristic
333C2×#131C22×C1111yescharacteristic
334#520—21no—
335#520—23no—
336#520C22×C1113yes—
337#520C22×C1111yescharacteristic
338#520C22×C1111yescharacteristic
339#520C22×C1113yescomplemented
340#519—21no—
341#519C22×C1113yescomplemented
342#518—23no—
343#518C22×C1113yes—
344C4×#41—21no—
345C4×#41—23no—
346C4×#41C22×C1113yes—
347C4×#41C22×C1111yescharacteristic
348C4×#41C22×C1113yescomplemented
349C2×C4×Q8—21no—
350C2×C4×Q8C22×C1113yescomplemented
351C2×C4×D4—23no—
352C2×C4×D4C22×C1113yes—
353#442C22×C1116yescomplemented
354#441C22×C1116yescomplemented
355#440C22×C1116yescomplemented
356#440C22×C1116yescomplemented
357C4×Q16C22×C1113yescomplemented
358C4×Q16C22×C1113yescomplemented
359C4×SD16C22×C1113yescomplemented
360C4×SD16C22×C1116yescomplemented
361C4×SD16C22×C1116yescomplemented
362C4×SD16C22×C1116yescomplemented
363C4×SD16C22×C1111yescharacteristic, complemented
364C4×SD16C22×C1113yescomplemented
365C4×SD16C22×C1113yescomplemented
366C4×D8C22×C1113yescomplemented
367C4×D8C22×C1113yescomplemented
368#428C22×C1113yescomplemented
369#428C22×C1113yescomplemented
370#427C22×C1113yescomplemented
371C2×#106C22×C1113yescomplemented
372#419C22×C1113yescomplemented
373#418C22×C1113yes—
374#417C22×C1113yes—
375#417C22×C1113yescomplemented
376#416C22×C1113yes—
377#416C22×C1113yescomplemented
378C2×#103C22×C1113yescomplemented
379C2×#102C22×C1113yes—
380#405C22×C1113yescomplemented
381#405C22×C1113yescomplemented
382C4×M16C22×C1113yescomplemented
383C2×C4×C8C22×C1113yescomplemented
384C22×C11—23no—
385C22×C11—23no—
386C22×C11—22no—
387C22×C11—26no—
388C22×C11—41no—
389C22×C11—43no—
390C22×C11—43no—
391C22×C11—41no—
392C22×C11—812no—
393C22×C11C2×C4×D416yes—
394C22×C11C23×D411yescharacteristic
395C4×C11—21no—
396C4×C11—23no—
397C4×C11—22no—
398C4×C11—26no—
399C4×C11—23no—
400C4×C11—41no—
401C4×C11—43no—
402C4×C11—41no—
403C4×C11—43no—
404C4×C11C2×C4×D416yes—
405C4×C11#57712yesdirect product factor
406C4×C11C24×C411yescharacteristic
407C4×C11C22×#4111yescharacteristic
4082−1+4—24no—
4092−1+4C2×C4×C1118yescomplemented
410H(5,𝔽2)—24no—
411H(5,𝔽2)C2×C4×C1118yescomplemented
412C2×#41—21no—
413C2×#41—23no—
414C2×#41C23×C1113yes—
415C2×#41C23×C1113yes—
416C2×#41C23×C1111yescharacteristic
417C22×Q8—21no—
418C22×Q8C23×C1113yes—
419C22×D4—23no—
420C22×D4C23×C1113yes—
421C23×C4—23no—
422#137C2×C4×C11124yescomplemented
423AGL(1,ℤ/8)C2×C4×C11124yescomplemented
424#135C2×C4×C11124yescomplemented
425C2×Q16C23×C1113yes—
426C2×SD16C2×C4×C11124yescomplemented
427C2×SD16C23×C1113yes—
428C2×SD16C23×C1116yes—
429C2×SD16C23×C1111yescharacteristic
430C2×D8C23×C1113yes—
431#131—24no—
432#131C2×C4×C1118yescomplemented
433C2×M16C23×C1113yes—
434C2×M16C23×C1113yes—
435C22×C8C23×C1113yes—
436C22×C8C23×C1113yes—
437C4×Q8—21no—
438C4×Q8—21no—
439C4×Q8—23no—
440C4×Q8—23no—
441C4×Q8—23no—
442C4×Q8—23no—
443C4×Q8D4×C1111yescharacteristic
444C4×Q8D4×C1111yescharacteristic
445C4×Q8C23×C1113yes—
446C4×Q8C23×C1116yes—
447C4×Q8C23×C1111yescharacteristic
448C4×Q8C23×C1113yes—
449C4×Q8C23×C1113yes—
450C4×D4—23no—
451C4×D4—23no—
452C4×D4—23no—
453C4×D4—23no—
454C4×D4—23no—
455C4×D4—23no—
456C4×D4—23no—
457C4×D4—23no—
458C4×D4—26no—
459C4×D4—26no—
460C4×D4—23no—
461C4×D4—23no—
462C4×D4D4×C1113yes—
463C4×D4D4×C1113yes—
464C4×D4C23×C1113yes—
465C4×D4C23×C1116yes—
466C4×D4C23×C1113yes—
467C4×D4C23×C1111yescharacteristic
468C4×D4C23×C1113yes—
469#117—23no—
470#117—23no—
471#117—26no—
472#117—23no—
473#117—23no—
474#117C23×C1113yes—
475#117C23×C1113yes—
476#117C23×C1113yes—
477C2×C4⋊C4—23no—
478C2×C4⋊C4—23no—
479C2×C4⋊C4—23no—
480C2×C4⋊C4C23×C1113yes—
481C2×C4⋊C4C23×C1113yes—
482C2×C22⋊C4—23no—
483C2×C22⋊C4—26no—
484C2×C42—23no—
485C2×C42—23no—
486C2×C42—23no—
487C2×C42C23×C1113yes—
488#107C23×C1113yes—
489#107C23×C1113yes—
490#106C23×C1113yes—
491#106C23×C1116yes—
492#106C23×C1111yescharacteristic
493#103C23×C1113yes—
494#103C23×C1116yes—
495#103C23×C1111yescharacteristic
496#103C23×C1113yes—
497#103C23×C1113yes—
498#102C23×C1113yes—
499#102C23×C1116yes—
500#102C23×C1113yes—
501#102C23×C1111yescharacteristic
502#102C23×C1113yes—
503#97C23×C1116yes—
504C4×C8C23×C1111yescharacteristic
505C4×C8C23×C1113yes—
506C4×C8C23×C1113yes—
507C4×C8C23×C1113yes—
508C2×C11—26no—
509C2×C11—42no—
510C2×C11—46no—
511C2×C11C22×C4×D411yescharacteristic
512C2×C11C2×#57711yescharacteristic
513C2×C11#358411yescharacteristic
514C24—23no—
515#41—28no—
516#41—224no—
517#41—26no—
518#41—26no—
519#41C22×C4×C11112yes—
520#41C22×C4×C1114yes—
521#41C22×C4×C11112yescomplemented
522#41C11×#4114yes—
523C2×Q8—28no—
524C2×Q8—23no—
525C2×Q8—26no—
526C2×Q8C22×C4×C11112yescomplemented
527C2×Q8C2×D4×C1111yescharacteristic
528C2×Q8C24×C1113yes—
529C2×Q8C24×C1111yescharacteristic
530C2×D4—23no—
531C2×D4—23no—
532C2×D4—224no—
533C2×D4—23no—
534C2×D4—26no—
535C2×D4C22×C4×C11112yes—
536C2×D4C2×D4×C1113yes—
537C2×D4C24×C1111yescharacteristic
538C2×D4C24×C1113yes—
539C22×C4—23no—
540C22×C4—23no—
541C22×C4—23no—
542C22×C4—23no—
543C22×C4—23no—
544C22×C4—21no—
545C22×C4—23no—
546C22×C4—23no—
547C22×C4—23no—
548C22×C4—26no—
549C22×C4—86no—
550C22×C4C2×D4×C1113yes—
551C22×C4C2×D4×C1113yes—
552C22×C4C24×C1113yes—
553Q16C22×C4×C11112yescomplemented
554SD16C22×C4×C11112yescomplemented
555SD16C22×C4×C11124yescomplemented
556SD16C22×C4×C1114yescomplemented
557D8C22×C4×C11112yescomplemented
558M16—26no—
559M16C22×C4×C11112yescomplemented
560C2×C8—26no—
561C2×C8C22×C4×C11112yescomplemented
562C2×C8C24×C1111yescharacteristic
563C2×C8C24×C1113yes—
564C2×C8C24×C1111yescharacteristic
565C2×C8C24×C1113yes—
566C4⋊C4—23no—
567C4⋊C4—26no—
568C4⋊C4—23no—
569C4⋊C4—23no—
570C4⋊C4—23no—
571C4⋊C4—21no—
572C4⋊C4—23no—
573C4⋊C4C2×D4×C1113yes—
574C4⋊C4C2×D4×C1113yes—
575C4⋊C4C24×C1113yes—
576C4⋊C4C24×C1111yescharacteristic
577C4⋊C4C24×C1113yes—
578C4⋊C4C24×C1111yescharacteristic
579C22⋊C4—23no—
580C22⋊C4—23no—
581C22⋊C4—23no—
582C22⋊C4—26no—
583C22⋊C4—23no—
584C22⋊C4—21no—
585C22⋊C4—23no—
586C22⋊C4C2×D4×C1116yes—
587C42—21no—
588C42—23no—
589C42—23no—
590C42—23no—
591C42—26no—
592C42—23no—
593C42—23no—
594C42C2×D4×C1113yes—
595C42C2×D4×C1113yes—
596C42C24×C1111yescharacteristic
597C42C24×C1113yes—
598C11C4×#57711yescharacteristic, direct product factor, Sylow
599C23—21no—
600C23—23no—
601C23—212no—
602C23—83no—
603C23—83no—
604C23C22×D4×C1113yes—
605Q8—212no—
606Q8—23no—
607Q8—21no—
608Q8C4×D4×C1114yes—
609Q8C23×C4×C1116yes—
610Q8C23×C4×C1112yes—
611D4—212no—
612D4—212no—
613D4—212no—
614D4—23no—
615D4—21no—
616D4C4×D4×C11112yes—
617D4C23×C4×C1112yes—
618D4C23×C4×C1116yes—
619C2×C4—212no—
620C2×C4—21no—
621C2×C4—23no—
622C2×C4—212no—
623C2×C4—212no—
624C2×C4—26no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—23no—
628C2×C4—23no—
629C2×C4—43no—
630C2×C4—42no—
631C2×C4—46no—
632C2×C4—83no—
633C2×C4—83no—
634C2×C4—86no—
635C2×C4—83no—
636C2×C4—83no—
637C2×C4C23×C4×C1116yes—
638C2×C4C22×D4×C1113yes—
639C2×C4C22×D4×C1113yes—
640C2×C4C22×D4×C1111yescharacteristic
641C2×C4C22×D4×C1113yes—
642C2×C4C22×D4×C1111yescharacteristic
643C2×C4C2×C11×#4116yes—
644C2×C4C25×C1111yescharacteristic
645C8—21no—
646C8—23no—
647C8C23×C4×C1112yes—
648C8C23×C4×C1116yes—
649C22—23no—
650C22—23no—
651C22—22no—
652C22—26no—
653C22—43no—
654C22—41no—
655C22—41no—
656C22—43no—
657C22—812no—
658C22C2×C4×D4×C1116yes—
659C22C23×D4×C1111yescharacteristic
660C4—22no—
661C4—26no—
662C4—23no—
663C4—21no—
664C4—23no—
665C4—43no—
666C4—41no—
667C4—41no—
668C4—43no—
669C4C2×C4×D4×C1116yes—
670C4C11×#57712yesdirect product factor
671C4C24×C4×C1111yescharacteristic
672C4C22×C11×#4111yescharacteristic
673C2—26no—
674C2—46no—
675C2—42no—
676C2C22×C4×D4×C1111yescharacteristic
677C2C2×C11×#57711yescharacteristic
678C2C11×#358411yescharacteristic
subgroupG/H
centerC2×C4×C11C22×D4
commutatorC4C24×C4×C11
Frattini, cosocleC2×C4C25×C11
socleC22×C11C23×D4
prime radicalC2×C11×#577C2
LCSG ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C11 ◁ C4×C11×#41 ◁ G

Complements

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

NH ≅ G/Ntype
2. C4×C11×2−1+4C2semidirect
3. C4×C11×H(5,𝔽2)C2semidirect
4. C11×#2952C2semidirect
5. C11×#2949C2semidirect
6. C11×#2947C2semidirect
7. C11×#2946C2semidirect
8. C4×C11×#137C2semidirect
9. C4×C11×AGL(1,ℤ/8)C2semidirect
10. C4×C11×#135C2semidirect
11. C2×C4×C11×SD16C2semidirect
12. C11×#2912C2semidirect
13. C11×#2898C2semidirect
14. C11×#2897C2semidirect
15. C4×C11×#131C2semidirect
18. C11×#577C4direct (N × H)
30. C11×#520C22semidirect
32. C11×#519C22semidirect
39. C4×C11×#41C22semidirect
41. C2×C4×Q8×C11C22semidirect
44. C11×#442C22semidirect
45. C11×#441C22semidirect
46. C11×#440C22semidirect
47. C11×#440C22semidirect
48. C4×C11×Q16C22semidirect
49. C4×C11×Q16C22semidirect
50. C4×C11×SD16C22semidirect
51. C4×C11×SD16C22semidirect
52. C4×C11×SD16C22semidirect
53. C4×C11×SD16C22semidirect
54. C4×C11×SD16C22semidirect
55. C4×C11×SD16C22semidirect
56. C4×C11×SD16C22semidirect
57. C4×C11×D8C22semidirect
58. C4×C11×D8C22semidirect
59. C11×#428C22semidirect
60. C11×#428C22semidirect
61. C11×#427C22semidirect
62. C2×C11×#106C22semidirect
63. C11×#419C22semidirect
66. C11×#417C22semidirect
68. C11×#416C22semidirect
69. C2×C11×#103C22semidirect
71. C11×#405C22semidirect
72. C11×#405C22semidirect
73. C4×C11×M16C22semidirect
74. C2×C4×C8×C11C22semidirect
76. C11×2−1+4C2×C4semidirect
78. C11×H(5,𝔽2)C2×C4semidirect
89. C11×#137C2×C4semidirect
90. C11×AGL(1,ℤ/8)C2×C4semidirect
91. C11×#135C2×C4semidirect
93. C2×C11×SD16C2×C4semidirect
99. C11×#131C2×C4semidirect
175. C4×#577C11direct (N × H)
183. C11×#41C22×C4semidirect
188. C2×Q8×C11C22×C4semidirect
215. C11×Q16C22×C4semidirect
216. C11×SD16C22×C4semidirect
217. C11×SD16C22×C4semidirect
218. C11×SD16C22×C4semidirect
219. C11×D8C22×C4semidirect
221. C11×M16C22×C4semidirect
223. C2×C8×C11C22×C4semidirect
261. C4×2−1+4C2×C11semidirect
262. C4×H(5,𝔽2)C2×C11semidirect
263. #2952C2×C11semidirect
264. #2949C2×C11semidirect
265. #2947C2×C11semidirect
266. #2946C2×C11semidirect
267. C4×#137C2×C11semidirect
268. C4×AGL(1,ℤ/8)C2×C11semidirect
269. C4×#135C2×C11semidirect
270. C2×C4×SD16C2×C11semidirect
271. #2912C2×C11semidirect
272. #2898C2×C11semidirect
273. #2897C2×C11semidirect
274. C4×#131C2×C11semidirect
327. #577C4×C11direct (N × H)
339. #520C22×C11semidirect
341. #519C22×C11semidirect
348. C4×#41C22×C11semidirect
350. C2×C4×Q8C22×C11semidirect
353. #442C22×C11semidirect
354. #441C22×C11semidirect
355. #440C22×C11semidirect
356. #440C22×C11semidirect
357. C4×Q16C22×C11semidirect
358. C4×Q16C22×C11semidirect
359. C4×SD16C22×C11semidirect
360. C4×SD16C22×C11semidirect
361. C4×SD16C22×C11semidirect
362. C4×SD16C22×C11semidirect
363. C4×SD16C22×C11semidirect
364. C4×SD16C22×C11semidirect
365. C4×SD16C22×C11semidirect
366. C4×D8C22×C11semidirect
367. C4×D8C22×C11semidirect
368. #428C22×C11semidirect
369. #428C22×C11semidirect
370. #427C22×C11semidirect
371. C2×#106C22×C11semidirect
372. #419C22×C11semidirect
375. #417C22×C11semidirect
377. #416C22×C11semidirect
378. C2×#103C22×C11semidirect
380. #405C22×C11semidirect
381. #405C22×C11semidirect
382. C4×M16C22×C11semidirect
383. C2×C4×C8C22×C11semidirect
405. C4×C11#577direct (N × H)
409. 2−1+4C2×C4×C11semidirect
411. H(5,𝔽2)C2×C4×C11semidirect
422. #137C2×C4×C11semidirect
423. AGL(1,ℤ/8)C2×C4×C11semidirect
424. #135C2×C4×C11semidirect
426. C2×SD16C2×C4×C11semidirect
432. #131C2×C4×C11semidirect
521. #41C22×C4×C11semidirect
526. C2×Q8C22×C4×C11semidirect
553. Q16C22×C4×C11semidirect
554. SD16C22×C4×C11semidirect
555. SD16C22×C4×C11semidirect
556. SD16C22×C4×C11semidirect
557. D8C22×C4×C11semidirect
559. M16C22×C4×C11semidirect
561. C2×C8C22×C4×C11semidirect
598. C11C4×#577direct (N × H)
670. C4C11×#577direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5772
C4×C11×2−1+42
C4×C11×H(5,𝔽2)2
C11×#29522
C11×#29492
C11×#29472
C11×#29462
C4×C11×#1372
C4×C11×AGL(1,ℤ/8)2
C4×C11×#1352
C2×C4×C11×SD162
C11×#29122
C11×#28982
C11×#28972
C4×C11×#1312
C4×#57711