Finite Group Databasebeta

← C2×C11×#1903 #14598187

Subgroups — C2×C11×#1903 #14598187

Order 2816.

1782 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×AGL(1,ℤ/8)C211yesmaximal, characteristic
2C2×C11×#568C211yesmaximal, characteristic, complemented
3C2×C11×#421C211yesmaximal, characteristic, complemented
4C2×C11×#418C211yesmaximal, characteristic, complemented
5C22×C11×#100C211yesmaximal, characteristic, complemented
6C11×#1903C218yesmaximal, direct product factor
7C2×C11×#344C211yesmaximal, characteristic, complemented
8C2×C11×#338C211yesmaximal, characteristic, complemented
9C22×C11×#41C2211yescharacteristic
10C23×D4×C11C2211yescharacteristic
11C2×C11×AGL(1,ℤ/8)—22no—
12C2×C11×AGL(1,ℤ/8)—22no—
13C2×C11×AGL(1,ℤ/8)—22no—
14C2×C11×AGL(1,ℤ/8)—22no—
15C2×C11×AGL(1,ℤ/8)C414yescomplemented
16C2×C11×AGL(1,ℤ/8)C2214yes—
17C22×C11×SD16C412yescomplemented
18C22×C11×D8C412yescomplemented
19C11×#568—22no—
20C11×#568—22no—
21C11×#568—22no—
22C11×#568C2214yescomplemented
23C2×C11×#131—22no—
24C2×C11×#131—22no—
25C22×C11×M16—22no—
26C22×C11×M16C2211yescharacteristic
27C22×C11×M16C2211yescharacteristic
28C22×C11×M16C2211yescharacteristic
29C22×C11×M16C2211yescharacteristic
30C2×C11×#117C2211yescharacteristic
31C11×#421—22no—
32C11×#421C2214yescomplemented
33C2×C11×#104—22no—
34C11×#418—22no—
35C11×#418C2214yescomplemented
36C2×C11×#102—22no—
37C2×C11×#100—22no—
38C2×C11×#100—22no—
39C2×C11×#100C2214yescomplemented
40C11×#344C2214yescomplemented
41C11×#338C2214yescomplemented
42C25×C11—21no—
43C2×C11×#41—21no—
44C2×C11×#41—21no—
45C2×C11×#41—21no—
46C2×C11×#41—21no—
47C2×C11×#41—21no—
48C2×C11×#41—21no—
49C2×C11×#41C2×C412yes—
50C2×C11×#41D412yes—
51C2×C11×#41D412yes—
52C2×C11×#41D412yes—
53C2×C11×#41D412yes—
54C2×C11×#41C2312yes—
55C22×Q8×C11C2×C411yescharacteristic
56C22×D4×C11—21no—
57C22×D4×C11—21no—
58C22×D4×C11—21no—
59C22×D4×C11—21no—
60C22×D4×C11—21no—
61C22×D4×C11—21no—
62C22×D4×C11—21no—
63C22×D4×C11—21no—
64C22×D4×C11—21no—
65C22×D4×C11—21no—
66C22×D4×C11—21no—
67C22×D4×C11—21no—
68C22×D4×C11C2×C412yes—
69C22×D4×C11C2×C412yes—
70C22×D4×C11C2×C411yescharacteristic
71C22×D4×C11C2312yes—
72C23×C4×C11—21no—
73C23×C4×C11C2311yescharacteristic
74C11×AGL(1,ℤ/8)—28no—
75C11×AGL(1,ℤ/8)—28no—
76C11×AGL(1,ℤ/8)—28no—
77C11×AGL(1,ℤ/8)—28no—
78C2×C11×SD16—24no—
79C2×C11×SD16—24no—
80C2×C11×SD16C2×C418yescomplemented
81C2×C11×D8—24no—
82C2×C11×D8—24no—
83C2×C11×D8C2×C418yescomplemented
84C11×#131—28no—
85C11×#131—28no—
86C11×#131—28no—
87C11×#131—28no—
88C2×C11×M16—24no—
89C2×C11×M16—28no—
90C2×C11×M16—21no—
91C2×C11×M16—21no—
92C2×C11×M16—21no—
93C2×C11×M16—21no—
94C2×C11×M16—21no—
95C2×C11×M16—21no—
96C2×C11×M16—21no—
97C2×C11×M16—21no—
98C2×C11×M16—21no—
99C2×C11×M16—21no—
100C2×C11×M16—21no—
101C2×C11×M16—28no—
102C2×C11×M16—21no—
103C2×C11×M16—21no—
104C2×C11×M16—21no—
105C2×C11×M16—21no—
106C2×C11×M16—21no—
107C2×C11×M16C2×C412yes—
108C2×C11×M16D412yes—
109C2×C11×M16D412yes—
110C2×C11×M16D412yes—
111C2×C11×M16C2312yes—
112C2×C11×M16C2312yes—
113C2×C11×M16C2312yes—
114C2×C11×M16C2312yes—
115C22×C8×C11—24no—
116C22×C8×C11—21no—
117C22×C8×C11—21no—
118C22×C8×C11C2×C412yes—
119C22×C8×C11D412yes—
120C11×#117—21no—
121C11×#117—21no—
122C11×#117—21no—
123C11×#117C2312yes—
124C2×C11×C4⋊C4—21no—
125C2×C11×C22⋊C4—21no—
126C2×C42×C11—21no—
127C11×#104—28no—
128C11×#102—28no—
129C11×#100—28no—
130C2×#1903C1111yesmaximal, characteristic, direct product factor, Sylow
131C24×C11—21no—
132C24×C11—22no—
133C24×C11—22no—
134C24×C11—22no—
135C24×C11—41no—
136C24×C11—41no—
137C24×C11—41no—
138C24×C11—41no—
139C24×C11—84no—
140C24×C11#4111yescharacteristic
141C11×#41—22no—
142C11×#41—22no—
143C11×#41—22no—
144C11×#41—22no—
145C11×#41—22no—
146C11×#41—22no—
147C11×#41—22no—
148C11×#41—22no—
149C11×#41—22no—
150C11×#41—22no—
151C11×#41—22no—
152C11×#41—22no—
153C11×#41C22⋊C414yes—
154C11×#41C22⋊C414yes—
155C11×#41C2×D414yes—
156C11×#41C2×D414yes—
157C2×Q8×C11—21no—
158C2×Q8×C11—21no—
159C2×Q8×C11—21no—
160C2×Q8×C11C22⋊C412yes—
161C2×Q8×C11C22⋊C412yes—
162C2×Q8×C11C22×C412yes—
163C2×D4×C11—22no—
164C2×D4×C11—22no—
165C2×D4×C11—22no—
166C2×D4×C11—22no—
167C2×D4×C11—22no—
168C2×D4×C11—22no—
169C2×D4×C11—22no—
170C2×D4×C11—22no—
171C2×D4×C11—22no—
172C2×D4×C11—22no—
173C2×D4×C11—21no—
174C2×D4×C11—21no—
175C2×D4×C11—21no—
176C2×D4×C11—22no—
177C2×D4×C11—22no—
178C2×D4×C11—22no—
179C2×D4×C11—22no—
180C2×D4×C11—22no—
181C2×D4×C11—22no—
182C2×D4×C11—22no—
183C2×D4×C11—22no—
184C2×D4×C11—22no—
185C2×D4×C11—22no—
186C2×D4×C11—22no—
187C2×D4×C11—41no—
188C2×D4×C11—41no—
189C2×D4×C11—41no—
190C2×D4×C11—41no—
191C2×D4×C11—41no—
192C2×D4×C11—41no—
193C2×D4×C11—41no—
194C2×D4×C11—41no—
195C2×D4×C11—41no—
196C2×D4×C11—41no—
197C2×D4×C11—41no—
198C2×D4×C11—41no—
199C2×D4×C11C22⋊C412yes—
200C2×D4×C11C22⋊C412yes—
201C2×D4×C11C22×C414yes—
202C2×D4×C11C22×C412yes—
203C22×C4×C11—21no—
204C22×C4×C11—22no—
205C22×C4×C11—22no—
206C22×C4×C11—22no—
207C22×C4×C11—22no—
208C22×C4×C11—22no—
209C22×C4×C11—22no—
210C22×C4×C11—41no—
211C22×C4×C11C22×C411yescharacteristic
212C22×C4×C11C22×C411yescharacteristic
213C22×C4×C11C2×D411yescharacteristic
214C22×C4×C11C2×D411yescharacteristic
215C22×C4×C11C2×D411yescharacteristic
216C22×C4×C11C2×D411yescharacteristic
217C22×C4×C11C2×D411yescharacteristic
218C22×C4×C11C2×D411yescharacteristic
219C22×C4×C11C2×D411yescharacteristic
220C22×C4×C11C2×D411yescharacteristic
221C22×C4×C11#4111yescharacteristic
222C22×C4×C11#4111yescharacteristic
223C22×C4×C11#4111yescharacteristic
224C22×C4×C11C2411yescharacteristic
225C11×SD16—216no—
226C11×D8—216no—
227C11×M16—216no—
228C11×M16—22no—
229C11×M16—22no—
230C11×M16—22no—
231C11×M16—22no—
232C11×M16—22no—
233C11×M16—22no—
234C11×M16—22no—
235C11×M16—22no—
236C11×M16—22no—
237C11×M16—22no—
238C11×M16—22no—
239C11×M16—22no—
240C11×M16—22no—
241C11×M16—41no—
242C11×M16—41no—
243C11×M16C2×D414yes—
244C2×C8×C11—216no—
245C2×C8×C11—22no—
246C2×C8×C11—22no—
247C2×C8×C11—22no—
248C2×C8×C11—22no—
249C2×C8×C11—22no—
250C2×C8×C11—22no—
251C2×C8×C11—22no—
252C2×C8×C11—22no—
253C2×C8×C11—41no—
254C2×C8×C11—41no—
255C2×C8×C11C22×C414yes—
256C2×C8×C11C2×D414yes—
257C11×C4⋊C4—22no—
258C11×C4⋊C4—41no—
259C11×C22⋊C4—22no—
260C11×C22⋊C4—41no—
261C42×C11—22no—
262C42×C11—41no—
263C22×AGL(1,ℤ/8)C2×C1111yescharacteristic
264C2×#568C2×C1111yescharacteristic, complemented
265C2×#421C2×C1111yescharacteristic, complemented
266C2×#418C2×C1111yescharacteristic, complemented
267C22×#100C2×C1111yescharacteristic, complemented
268#1903C2×C1118yesdirect product factor
269C2×#344C2×C1111yescharacteristic, complemented
270C2×#338C2×C1111yescharacteristic, complemented
271C23×C11—22no—
272C23×C11—22no—
273C23×C11—22no—
274C23×C11—24no—
275C23×C11—42no—
276C23×C11—42no—
277C23×C11—42no—
278C23×C11—42no—
279C23×C11—42no—
280C23×C11—42no—
281C23×C11—42no—
282C23×C11—82no—
283C23×C11—84no—
284C23×C11—84no—
285C23×C11—84no—
286C23×C11—84no—
287C23×C11—84no—
288C23×C11—84no—
289C23×C11—84no—
290C23×C11C4×D411yescharacteristic
291C23×C11C4×D411yescharacteristic
292C23×C11#12111yescharacteristic
293C23×C11#12111yescharacteristic
294C23×C11#12311yescharacteristic
295C23×C11#12311yescharacteristic
296C23×C11C2×#4111yescharacteristic
297Q8×C11—22no—
298Q8×C11—22no—
299Q8×C11—22no—
300Q8×C11C2×C22⋊C414yes—
301D4×C11—24no—
302D4×C11—24no—
303D4×C11—24no—
304D4×C11—24no—
305D4×C11—24no—
306D4×C11—22no—
307D4×C11—24no—
308D4×C11—22no—
309D4×C11—22no—
310D4×C11—42no—
311D4×C11—42no—
312D4×C11—42no—
313D4×C11—42no—
314D4×C11—42no—
315D4×C11—42no—
316D4×C11C2×C22⋊C414yes—
317C2×C4×C11—22no—
318C2×C4×C11—22no—
319C2×C4×C11—22no—
320C2×C4×C11—24no—
321C2×C4×C11—24no—
322C2×C4×C11—24no—
323C2×C4×C11—24no—
324C2×C4×C11—42no—
325C2×C4×C11—82no—
326C2×C4×C11C2×C22⋊C411yescharacteristic
327C2×C4×C11C2×C22⋊C411yescharacteristic
328C2×C4×C11C2×C22⋊C411yescharacteristic
329C2×C4×C11C2×C22⋊C411yescharacteristic
330C2×C4×C11C4×D411yescharacteristic
331C2×C4×C11C4×D411yescharacteristic
332C2×C4×C11C4×D411yescharacteristic
333C2×C4×C11C4×D411yescharacteristic
334C2×C4×C11C4×D411yescharacteristic
335C2×C4×C11C4×D411yescharacteristic
336C2×C4×C11#12011yescharacteristic
337C2×C4×C11#12011yescharacteristic
338C2×C4×C11#12011yescharacteristic
339C2×C4×C11#12011yescharacteristic
340C2×C4×C11#12111yescharacteristic
341C2×C4×C11#12111yescharacteristic
342C2×C4×C11#12111yescharacteristic
343C2×C4×C11#12111yescharacteristic
344C2×C4×C11#12111yescharacteristic
345C2×C4×C11#12111yescharacteristic
346C2×C4×C11#12311yescharacteristic
347C2×C4×C11#12311yescharacteristic
348C2×C4×C11C23×C411yescharacteristic
349C2×C4×C11C22×D411yescharacteristic
350C2×C4×C11C22×D411yescharacteristic
351C2×C4×C11C22×D411yescharacteristic
352C2×C4×C11C22×D411yescharacteristic
353C2×C4×C11C2×#4111yescharacteristic
354C8×C11—24no—
355C8×C11—24no—
356C8×C11—24no—
357C8×C11—42no—
358C22×#41C22×C1111yescharacteristic
359C23×D4C22×C1111yescharacteristic
360C2×AGL(1,ℤ/8)—22no—
361C2×AGL(1,ℤ/8)—22no—
362C2×AGL(1,ℤ/8)—22no—
363C2×AGL(1,ℤ/8)—22no—
364C2×AGL(1,ℤ/8)C4×C1114yescomplemented
365C2×AGL(1,ℤ/8)C22×C1114yes—
366C22×SD16C4×C1112yescomplemented
367C22×D8C4×C1112yescomplemented
368#568—22no—
369#568—22no—
370#568—22no—
371#568C22×C1114yescomplemented
372C2×#131—22no—
373C2×#131—22no—
374C22×M16—22no—
375C22×M16C22×C1111yescharacteristic
376C22×M16C22×C1111yescharacteristic
377C22×M16C22×C1111yescharacteristic
378C22×M16C22×C1111yescharacteristic
379C2×#117C22×C1111yescharacteristic
380#421—22no—
381#421C22×C1114yescomplemented
382C2×#104—22no—
383#418—22no—
384#418C22×C1114yescomplemented
385C2×#102—22no—
386C2×#100—22no—
387C2×#100—22no—
388C2×#100C22×C1114yescomplemented
389#344C22×C1114yescomplemented
390#338C22×C1114yescomplemented
391C22×C11—22no—
392C22×C11—22no—
393C22×C11—22no—
394C22×C11—24no—
395C22×C11—41no—
396C22×C11—41no—
397C22×C11—41no—
398C22×C11—41no—
399C22×C11—44no—
400C22×C11—44no—
401C22×C11—82no—
402C22×C11—82no—
403C22×C11—84no—
404C22×C11—84no—
405C22×C11—84no—
406C22×C11—84no—
407C22×C11—84no—
408C22×C11—84no—
409C22×C11—84no—
410C22×C11#38611yescharacteristic
411C22×C11#38611yescharacteristic
412C22×C11#38611yescharacteristic
413C22×C11#38611yescharacteristic
414C22×C11C2×C4×D411yescharacteristic
415C22×C11C2×#12111yescharacteristic
416C22×C11C2×#12311yescharacteristic
417C4×C11—24no—
418C4×C11—82no—
419C4×C11#38611yescharacteristic
420C4×C11#38611yescharacteristic
421C4×C11#38611yescharacteristic
422C4×C11#38611yescharacteristic
423C4×C11C22×C22⋊C411yescharacteristic
424C4×C11C2×C4×D411yescharacteristic
425C4×C11C2×#12011yescharacteristic
426C4×C11C2×#12111yescharacteristic
427C25—21no—
428C2×#41—21no—
429C2×#41—21no—
430C2×#41—21no—
431C2×#41—21no—
432C2×#41—21no—
433C2×#41—21no—
434C2×#41C2×C4×C1112yes—
435C2×#41D4×C1112yes—
436C2×#41D4×C1112yes—
437C2×#41D4×C1112yes—
438C2×#41D4×C1112yes—
439C2×#41C23×C1112yes—
440C22×Q8C2×C4×C1111yescharacteristic
441C22×D4—21no—
442C22×D4—21no—
443C22×D4—21no—
444C22×D4—21no—
445C22×D4—21no—
446C22×D4—21no—
447C22×D4—21no—
448C22×D4—21no—
449C22×D4—21no—
450C22×D4—21no—
451C22×D4—21no—
452C22×D4—21no—
453C22×D4C2×C4×C1112yes—
454C22×D4C2×C4×C1112yes—
455C22×D4C2×C4×C1111yescharacteristic
456C22×D4C23×C1112yes—
457C23×C4—21no—
458C23×C4C23×C1111yescharacteristic
459AGL(1,ℤ/8)—28no—
460AGL(1,ℤ/8)—28no—
461AGL(1,ℤ/8)—28no—
462AGL(1,ℤ/8)—28no—
463C2×SD16—24no—
464C2×SD16—24no—
465C2×SD16C2×C4×C1118yescomplemented
466C2×D8—24no—
467C2×D8—24no—
468C2×D8C2×C4×C1118yescomplemented
469#131—28no—
470#131—28no—
471#131—28no—
472#131—28no—
473C2×M16—24no—
474C2×M16—28no—
475C2×M16—21no—
476C2×M16—21no—
477C2×M16—21no—
478C2×M16—21no—
479C2×M16—21no—
480C2×M16—21no—
481C2×M16—21no—
482C2×M16—21no—
483C2×M16—21no—
484C2×M16—21no—
485C2×M16—21no—
486C2×M16—28no—
487C2×M16—21no—
488C2×M16—21no—
489C2×M16—21no—
490C2×M16—21no—
491C2×M16—21no—
492C2×M16C2×C4×C1112yes—
493C2×M16D4×C1112yes—
494C2×M16D4×C1112yes—
495C2×M16D4×C1112yes—
496C2×M16C23×C1112yes—
497C2×M16C23×C1112yes—
498C2×M16C23×C1112yes—
499C2×M16C23×C1112yes—
500C22×C8—24no—
501C22×C8—21no—
502C22×C8—21no—
503C22×C8C2×C4×C1112yes—
504C22×C8D4×C1112yes—
505#117—21no—
506#117—21no—
507#117—21no—
508#117C23×C1112yes—
509C2×C4⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C42—21no—
512#104—28no—
513#102—28no—
514#100—28no—
515C2×C11—21no—
516C2×C11—21no—
517C2×C11—21no—
518C2×C11—21no—
519C2×C11—21no—
520C2×C11—21no—
521C2×C11—44no—
522C2×C11—84no—
523C2×C11#190312yesdirect product factor
524C2×C11C2×#38611yescharacteristic
525C24—21no—
526C24—22no—
527C24—22no—
528C24—22no—
529C24—41no—
530C24—41no—
531C24—41no—
532C24—41no—
533C24—84no—
534C24C11×#4111yescharacteristic
535#41—22no—
536#41—22no—
537#41—22no—
538#41—22no—
539#41—22no—
540#41—22no—
541#41—22no—
542#41—22no—
543#41—22no—
544#41—22no—
545#41—22no—
546#41—22no—
547#41C11×C22⋊C414yes—
548#41C11×C22⋊C414yes—
549#41C2×D4×C1114yes—
550#41C2×D4×C1114yes—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8—21no—
554C2×Q8C11×C22⋊C412yes—
555C2×Q8C11×C22⋊C412yes—
556C2×Q8C22×C4×C1112yes—
557C2×D4—22no—
558C2×D4—22no—
559C2×D4—22no—
560C2×D4—22no—
561C2×D4—22no—
562C2×D4—22no—
563C2×D4—22no—
564C2×D4—22no—
565C2×D4—22no—
566C2×D4—22no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—22no—
571C2×D4—22no—
572C2×D4—22no—
573C2×D4—22no—
574C2×D4—22no—
575C2×D4—22no—
576C2×D4—22no—
577C2×D4—22no—
578C2×D4—22no—
579C2×D4—22no—
580C2×D4—22no—
581C2×D4—41no—
582C2×D4—41no—
583C2×D4—41no—
584C2×D4—41no—
585C2×D4—41no—
586C2×D4—41no—
587C2×D4—41no—
588C2×D4—41no—
589C2×D4—41no—
590C2×D4—41no—
591C2×D4—41no—
592C2×D4—41no—
593C2×D4C11×C22⋊C412yes—
594C2×D4C11×C22⋊C412yes—
595C2×D4C22×C4×C1114yes—
596C2×D4C22×C4×C1112yes—
597C22×C4—21no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—41no—
605C22×C4C22×C4×C1111yescharacteristic
606C22×C4C22×C4×C1111yescharacteristic
607C22×C4C2×D4×C1111yescharacteristic
608C22×C4C2×D4×C1111yescharacteristic
609C22×C4C2×D4×C1111yescharacteristic
610C22×C4C2×D4×C1111yescharacteristic
611C22×C4C2×D4×C1111yescharacteristic
612C22×C4C2×D4×C1111yescharacteristic
613C22×C4C2×D4×C1111yescharacteristic
614C22×C4C2×D4×C1111yescharacteristic
615C22×C4C11×#4111yescharacteristic
616C22×C4C11×#4111yescharacteristic
617C22×C4C11×#4111yescharacteristic
618C22×C4C24×C1111yescharacteristic
619SD16—216no—
620D8—216no—
621M16—216no—
622M16—22no—
623M16—22no—
624M16—22no—
625M16—22no—
626M16—22no—
627M16—22no—
628M16—22no—
629M16—22no—
630M16—22no—
631M16—22no—
632M16—22no—
633M16—22no—
634M16—22no—
635M16—41no—
636M16—41no—
637M16C2×D4×C1114yes—
638C2×C8—216no—
639C2×C8—22no—
640C2×C8—22no—
641C2×C8—22no—
642C2×C8—22no—
643C2×C8—22no—
644C2×C8—22no—
645C2×C8—22no—
646C2×C8—22no—
647C2×C8—41no—
648C2×C8—41no—
649C2×C8C22×C4×C1114yes—
650C2×C8C2×D4×C1114yes—
651C4⋊C4—22no—
652C4⋊C4—41no—
653C22⋊C4—22no—
654C22⋊C4—41no—
655C42—22no—
656C42—41no—
657C11C2×#190311yescharacteristic, direct product factor, Sylow
658C23—22no—
659C23—22no—
660C23—22no—
661C23—24no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—82no—
670C23—84no—
671C23—84no—
672C23—84no—
673C23—84no—
674C23—84no—
675C23—84no—
676C23—84no—
677C23C4×D4×C1111yescharacteristic
678C23C4×D4×C1111yescharacteristic
679C23C11×#12111yescharacteristic
680C23C11×#12111yescharacteristic
681C23C11×#12311yescharacteristic
682C23C11×#12311yescharacteristic
683C23C2×C11×#4111yescharacteristic
684Q8—22no—
685Q8—22no—
686Q8—22no—
687Q8C2×C11×C22⋊C414yes—
688D4—24no—
689D4—24no—
690D4—24no—
691D4—24no—
692D4—24no—
693D4—22no—
694D4—24no—
695D4—22no—
696D4—22no—
697D4—42no—
698D4—42no—
699D4—42no—
700D4—42no—
701D4—42no—
702D4—42no—
703D4C2×C11×C22⋊C414yes—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—42no—
712C2×C4—82no—
713C2×C4C2×C11×C22⋊C411yescharacteristic
714C2×C4C2×C11×C22⋊C411yescharacteristic
715C2×C4C2×C11×C22⋊C411yescharacteristic
716C2×C4C2×C11×C22⋊C411yescharacteristic
717C2×C4C4×D4×C1111yescharacteristic
718C2×C4C4×D4×C1111yescharacteristic
719C2×C4C4×D4×C1111yescharacteristic
720C2×C4C4×D4×C1111yescharacteristic
721C2×C4C4×D4×C1111yescharacteristic
722C2×C4C4×D4×C1111yescharacteristic
723C2×C4C11×#12011yescharacteristic
724C2×C4C11×#12011yescharacteristic
725C2×C4C11×#12011yescharacteristic
726C2×C4C11×#12011yescharacteristic
727C2×C4C11×#12111yescharacteristic
728C2×C4C11×#12111yescharacteristic
729C2×C4C11×#12111yescharacteristic
730C2×C4C11×#12111yescharacteristic
731C2×C4C11×#12111yescharacteristic
732C2×C4C11×#12111yescharacteristic
733C2×C4C11×#12311yescharacteristic
734C2×C4C11×#12311yescharacteristic
735C2×C4C23×C4×C1111yescharacteristic
736C2×C4C22×D4×C1111yescharacteristic
737C2×C4C22×D4×C1111yescharacteristic
738C2×C4C22×D4×C1111yescharacteristic
739C2×C4C22×D4×C1111yescharacteristic
740C2×C4C2×C11×#4111yescharacteristic
741C8—24no—
742C8—24no—
743C8—24no—
744C8—42no—
745C22—22no—
746C22—22no—
747C22—22no—
748C22—24no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—44no—
754C22—44no—
755C22—82no—
756C22—82no—
757C22—84no—
758C22—84no—
759C22—84no—
760C22—84no—
761C22—84no—
762C22—84no—
763C22—84no—
764C22C11×#38611yescharacteristic
765C22C11×#38611yescharacteristic
766C22C11×#38611yescharacteristic
767C22C11×#38611yescharacteristic
768C22C2×C4×D4×C1111yescharacteristic
769C22C2×C11×#12111yescharacteristic
770C22C2×C11×#12311yescharacteristic
771C4—24no—
772C4—82no—
773C4C11×#38611yescharacteristic
774C4C11×#38611yescharacteristic
775C4C11×#38611yescharacteristic
776C4C11×#38611yescharacteristic
777C4C22×C11×C22⋊C411yescharacteristic
778C4C2×C4×D4×C1111yescharacteristic
779C4C2×C11×#12011yescharacteristic
780C4C2×C11×#12111yescharacteristic
781C2—21no—
782C2—21no—
783C2—21no—
784C2—21no—
785C2—21no—
786C2—21no—
787C2—44no—
788C2—84no—
789C2C11×#190312yesdirect product factor
790C2C2×C11×#38611yescharacteristic
subgroupG/H
center, socleC22×C11#386
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC22×C11×AGL(1,ℤ/8)C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#568C2semidirect
3. C2×C11×#421C2semidirect
4. C2×C11×#418C2semidirect
5. C22×C11×#100C2semidirect
6. C11×#1903C2direct (N × H)
7. C2×C11×#344C2semidirect
8. C2×C11×#338C2semidirect
15. C2×C11×AGL(1,ℤ/8)C4semidirect
17. C22×C11×SD16C4semidirect
18. C22×C11×D8C4semidirect
22. C11×#568C22semidirect
32. C11×#421C22semidirect
35. C11×#418C22semidirect
39. C2×C11×#100C22semidirect
40. C11×#344C22semidirect
41. C11×#338C22semidirect
80. C2×C11×SD16C2×C4semidirect
83. C2×C11×D8C2×C4semidirect
130. C2×#1903C11direct (N × H)
264. C2×#568C2×C11semidirect
265. C2×#421C2×C11semidirect
266. C2×#418C2×C11semidirect
267. C22×#100C2×C11semidirect
268. #1903C2×C11direct (N × H)
269. C2×#344C2×C11semidirect
270. C2×#338C2×C11semidirect
364. C2×AGL(1,ℤ/8)C4×C11semidirect
366. C22×SD16C4×C11semidirect
367. C22×D8C4×C11semidirect
371. #568C22×C11semidirect
381. #421C22×C11semidirect
384. #418C22×C11semidirect
388. C2×#100C22×C11semidirect
389. #344C22×C11semidirect
390. #338C22×C11semidirect
465. C2×SD16C2×C4×C11semidirect
468. C2×D8C2×C4×C11semidirect
523. C2×C11#1903direct (N × H)
657. C11C2×#1903direct (N × H)
789. C2C11×#1903direct (N × H)

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
C2×C11×#5682
C2×C11×#4212
C2×C11×#4182
C22×C11×#1002
C11×#19032
C2×C11×#3442
C2×C11×#3382
C2×#190311