Finite Group Databasebeta

← C2×C11×#2416 #14611865

Subgroups — C2×C11×#2416 #14611865

Order 2816.

4782 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×#121C211yesmaximal, characteristic, complemented
2C22×C11×#121C212yesmaximal, complemented
3C22×C11×#121C211yesmaximal, characteristic, complemented
4C22×C4×D4×C11C211yesmaximal, characteristic, complemented
5C23×C11×C4⋊C4C211yesmaximal, characteristic, complemented
6C11×#2416C2116yesmaximal, direct product factor
7C2×C11×#396C212yesmaximal, complemented
8C2×C11×#394C212yesmaximal, complemented
9C2×C11×#390C211yesmaximal, characteristic, complemented
10C2×C11×#389C211yesmaximal, characteristic, complemented
11C2×C11×#386C212yesmaximal, complemented
12C2×C11×#380C211yesmaximal, characteristic, complemented
13C23×D4×C11C2212yes—
14C23×D4×C11C2211yescharacteristic
15C23×D4×C11C2212yes—
16C23×D4×C11C2211yescharacteristic
17C24×C4×C11C2211yescharacteristic
18C24×C4×C11C2212yes—
19C24×C4×C11C2211yescharacteristic
20C2×C11×#121—216no—
21C2×C11×#121—28no—
22C2×C11×#121—28no—
23C2×C11×#121C22116yescomplemented
24C2×C11×#121C2218yescomplemented
25C2×C11×#121C2218yescomplemented
26C2×C4×D4×C11—28no—
27C2×C4×D4×C11C2218yescomplemented
28C22×C11×C4⋊C4—28no—
29C22×C11×C4⋊C4C2212yes—
30C22×C11×C4⋊C4C2211yescharacteristic
31C22×C11×C4⋊C4C2212yes—
32C22×C11×C4⋊C4C2211yescharacteristic
33C22×C11×C4⋊C4C2211yescharacteristic
34C22×C11×C4⋊C4C2211yescharacteristic
35C22×C11×C4⋊C4C2218yescomplemented
36C22×C11×C22⋊C4C2211yescharacteristic
37C22×C11×C22⋊C4C2212yes—
38C22×C11×C22⋊C4C2212yes—
39C22×C11×C22⋊C4C2212yes—
40C22×C11×C22⋊C4C2212yes—
41C22×C11×C22⋊C4C2211yescharacteristic
42C22×C11×C22⋊C4C2212yes—
43C22×C42×C11C2211yescharacteristic
44C11×#396C22116yescomplemented
45C11×#394C22116yescomplemented
46C11×#390C2218yescomplemented
47C11×#389C2218yescomplemented
48C11×#386C22116yescomplemented
49C11×#380C2218yescomplemented
50C2×C11×#95C2212yes—
51C2×C11×#95C2212yes—
52C25×C11C2312yes—
53C25×C11C2311yescharacteristic
54C25×C11C2311yescharacteristic
55C22×D4×C11—24no—
56C22×D4×C11—24no—
57C22×D4×C11—28no—
58C22×D4×C11—28no—
59C22×D4×C11—28no—
60C22×D4×C11—28no—
61C22×D4×C11—28no—
62C22×D4×C11—24no—
63C22×D4×C11—24no—
64C22×D4×C11—24no—
65C22×D4×C11—44no—
66C22×D4×C11D418yescomplemented
67C22×D4×C11C2318yes—
68C22×D4×C11C2314yes—
69C22×D4×C11C2318yes—
70C22×D4×C11C2314yes—
71C23×C4×C11—24no—
72C23×C4×C11—24no—
73C23×C4×C11—28no—
74C23×C4×C11—28no—
75C23×C4×C11—24no—
76C23×C4×C11—24no—
77C23×C4×C11—24no—
78C23×C4×C11—44no—
79C23×C4×C11D418yescomplemented
80C23×C4×C11C2314yes—
81C23×C4×C11C2311yescharacteristic
82C23×C4×C11C2311yescharacteristic
83C23×C4×C11C2312yes—
84C23×C4×C11C2312yes—
85C23×C4×C11C2318yes—
86C23×C4×C11C2311yescharacteristic
87C23×C4×C11C2311yescharacteristic
88C23×C4×C11C2312yes—
89C23×C4×C11C2314yes—
90C23×C4×C11C2311yescharacteristic
91C11×#121—264no—
92C11×#121—232no—
93C11×#121—232no—
94C4×D4×C11—232no—
95C2×C11×C4⋊C4—28no—
96C2×C11×C4⋊C4—24no—
97C2×C11×C4⋊C4—24no—
98C2×C11×C4⋊C4—28no—
99C2×C11×C4⋊C4—24no—
100C2×C11×C4⋊C4—232no—
101C2×C11×C4⋊C4D418yescomplemented
102C2×C11×C4⋊C4C2314yes—
103C2×C11×C4⋊C4C2318yes—
104C2×C11×C4⋊C4C2314yes—
105C2×C11×C4⋊C4C2314yes—
106C2×C11×C4⋊C4C2318yes—
107C2×C11×C4⋊C4C2314yes—
108C2×C11×C22⋊C4—24no—
109C2×C11×C22⋊C4—28no—
110C2×C11×C22⋊C4—24no—
111C2×C11×C22⋊C4—28no—
112C2×C11×C22⋊C4—28no—
113C2×C11×C22⋊C4—28no—
114C2×C11×C22⋊C4—44no—
115C2×C11×C22⋊C4C2314yes—
116C2×C11×C22⋊C4C2314yes—
117C2×C11×C22⋊C4C2318yes—
118C2×C11×C22⋊C4C2318yes—
119C2×C11×C22⋊C4C2318yes—
120C2×C11×C22⋊C4C2318yes—
121C2×C11×C22⋊C4C2318yes—
122C2×C42×C11—24no—
123C2×C42×C11C2314yes—
124C11×#95C2318yes—
125C11×#95C2318yes—
126C2×#2416C1111yesmaximal, characteristic, direct product factor, Sylow
127C24×C11—22no—
128C24×C11—22no—
129C24×C11—22no—
130C24×C11—22no—
131C24×C11—22no—
132C24×C11—22no—
133C24×C11—22no—
134C24×C11—22no—
135C24×C11—22no—
136C24×C11—22no—
137C24×C11—24no—
138C24×C11—24no—
139C24×C11—24no—
140C24×C11—24no—
141C24×C11—24no—
142C24×C11—24no—
143C24×C11—24no—
144C24×C11C2×D414yes—
145C24×C11C2×D414yes—
146C24×C11C2×D414yes—
147C24×C11#4114yes—
148C24×C11C2414yes—
149C24×C11C2412yes—
150C24×C11C2412yes—
151C24×C11C2411yescharacteristic
152C2×D4×C11—232no—
153C2×D4×C11—28no—
154C2×D4×C11—28no—
155C2×D4×C11—216no—
156C2×D4×C11—216no—
157C2×D4×C11—216no—
158C2×D4×C11—216no—
159C2×D4×C11—216no—
160C2×D4×C11—28no—
161C2×D4×C11—28no—
162C2×D4×C11—28no—
163C2×D4×C11—48no—
164C2×D4×C11—432no—
165C2×D4×C11—432no—
166C2×D4×C11—416no—
167C2×D4×C11C2×D4116yescomplemented
168C22×C4×C11—22no—
169C22×C4×C11—22no—
170C22×C4×C11—24no—
171C22×C4×C11—22no—
172C22×C4×C11—22no—
173C22×C4×C11—24no—
174C22×C4×C11—232no—
175C22×C4×C11—28no—
176C22×C4×C11—28no—
177C22×C4×C11—22no—
178C22×C4×C11—22no—
179C22×C4×C11—24no—
180C22×C4×C11—22no—
181C22×C4×C11—24no—
182C22×C4×C11—24no—
183C22×C4×C11—24no—
184C22×C4×C11—216no—
185C22×C4×C11—22no—
186C22×C4×C11—24no—
187C22×C4×C11—22no—
188C22×C4×C11—24no—
189C22×C4×C11—22no—
190C22×C4×C11—216no—
191C22×C4×C11—28no—
192C22×C4×C11—28no—
193C22×C4×C11—28no—
194C22×C4×C11—48no—
195C22×C4×C11—432no—
196C22×C4×C11—416no—
197C22×C4×C11C2×D414yes—
198C22×C4×C11C2×D414yes—
199C22×C4×C11C2×D418yes—
200C22×C4×C11C2×D414yes—
201C22×C4×C11C2×D414yes—
202C22×C4×C11C2×D4116yescomplemented
203C22×C4×C11#4114yes—
204C22×C4×C11C2412yes—
205C22×C4×C11C2412yes—
206C22×C4×C11C2414yes—
207C22×C4×C11C2414yes—
208C22×C4×C11C2414yes—
209C22×C4×C11C2412yes—
210C22×C4×C11C2412yes—
211C22×C4×C11C2412yes—
212C11×C4⋊C4—216no—
213C11×C4⋊C4—28no—
214C11×C4⋊C4—28no—
215C11×C4⋊C4—216no—
216C11×C4⋊C4—28no—
217C11×C4⋊C4C2×D4116yescomplemented
218C11×C22⋊C4—28no—
219C11×C22⋊C4—216no—
220C11×C22⋊C4—28no—
221C11×C22⋊C4—216no—
222C11×C22⋊C4—216no—
223C11×C22⋊C4—216no—
224C11×C22⋊C4—48no—
225C42×C11—28no—
226C22×#121C2×C1111yescharacteristic, complemented
227C22×#121C2×C1112yescomplemented
228C22×#121C2×C1111yescharacteristic, complemented
229C22×C4×D4C2×C1111yescharacteristic, complemented
230C23×C4⋊C4C2×C1111yescharacteristic, complemented
231#2416C2×C11116yesdirect product factor
232C2×#396C2×C1112yescomplemented
233C2×#394C2×C1112yescomplemented
234C2×#390C2×C1111yescharacteristic, complemented
235C2×#389C2×C1111yescharacteristic, complemented
236C2×#386C2×C1112yescomplemented
237C2×#380C2×C1111yescharacteristic, complemented
238C23×C11—28no—
239C23×C11—28no—
240C23×C11—28no—
241C23×C11—28no—
242C23×C11—28no—
243C23×C11—28no—
244C23×C11—22no—
245C23×C11—22no—
246C23×C11—22no—
247C23×C11—22no—
248C23×C11—28no—
249C23×C11—28no—
250C23×C11—28no—
251C23×C11—22no—
252C23×C11—22no—
253C23×C11—22no—
254C23×C11—22no—
255C23×C11—22no—
256C23×C11—22no—
257C23×C11—24no—
258C23×C11—24no—
259C23×C11—24no—
260C23×C11—24no—
261C23×C11—24no—
262C23×C11—24no—
263C23×C11—24no—
264C23×C11—44no—
265C23×C11—44no—
266C23×C11—44no—
267C23×C11—44no—
268C23×C11—48no—
269C23×C11—48no—
270C23×C11—48no—
271C23×C11—48no—
272C23×C11—48no—
273C23×C11—48no—
274C23×C11—48no—
275C23×C11#121116yescomplemented
276C23×C11C22×D414yes—
277C23×C11C22×D414yes—
278C23×C11C22×D414yes—
279C23×C11C22×D412yes—
280C23×C11C22×D412yes—
281C23×C11C22×D412yes—
282C23×C11C2×#4114yes—
283C23×C11C2×#4112yes—
284C23×C11C2×#4112yes—
285C23×C11H(5,𝔽2)12yes—
286C23×C112−1+412yes—
287C23×C11C2511yescharacteristic
288D4×C11—232no—
289D4×C11—432no—
290D4×C11—432no—
291D4×C11—416no—
292C2×C4×C11—28no—
293C2×C4×C11—28no—
294C2×C4×C11—216no—
295C2×C4×C11—22no—
296C2×C4×C11—22no—
297C2×C4×C11—24no—
298C2×C4×C11—22no—
299C2×C4×C11—22no—
300C2×C4×C11—24no—
301C2×C4×C11—232no—
302C2×C4×C11—22no—
303C2×C4×C11—22no—
304C2×C4×C11—24no—
305C2×C4×C11—22no—
306C2×C4×C11—24no—
307C2×C4×C11—24no—
308C2×C4×C11—24no—
309C2×C4×C11—22no—
310C2×C4×C11—24no—
311C2×C4×C11—22no—
312C2×C4×C11—24no—
313C2×C4×C11—22no—
314C2×C4×C11—432no—
315C2×C4×C11—44no—
316C2×C4×C11—48no—
317C2×C4×C11—44no—
318C2×C4×C11—48no—
319C2×C4×C11—416no—
320C2×C4×C11#121116yescomplemented
321C2×C4×C11C22×D414yes—
322C2×C4×C11C22×D414yes—
323C2×C4×C11C22×D418yes—
324C2×C4×C11C22×D414yes—
325C2×C4×C11C22×D414yes—
326C2×C4×C11C2×#4114yes—
327C23×D4C22×C1112yes—
328C23×D4C22×C1111yescharacteristic
329C23×D4C22×C1112yes—
330C23×D4C22×C1111yescharacteristic
331C24×C4C22×C1111yescharacteristic
332C24×C4C22×C1112yes—
333C24×C4C22×C1111yescharacteristic
334C2×#121—216no—
335C2×#121—28no—
336C2×#121—28no—
337C2×#121C22×C11116yescomplemented
338C2×#121C22×C1118yescomplemented
339C2×#121C22×C1118yescomplemented
340C2×C4×D4—28no—
341C2×C4×D4C22×C1118yescomplemented
342C22×C4⋊C4—28no—
343C22×C4⋊C4C22×C1112yes—
344C22×C4⋊C4C22×C1111yescharacteristic
345C22×C4⋊C4C22×C1112yes—
346C22×C4⋊C4C22×C1111yescharacteristic
347C22×C4⋊C4C22×C1111yescharacteristic
348C22×C4⋊C4C22×C1111yescharacteristic
349C22×C4⋊C4C22×C1118yescomplemented
350C22×C22⋊C4C22×C1111yescharacteristic
351C22×C22⋊C4C22×C1112yes—
352C22×C22⋊C4C22×C1112yes—
353C22×C22⋊C4C22×C1112yes—
354C22×C22⋊C4C22×C1112yes—
355C22×C22⋊C4C22×C1111yescharacteristic
356C22×C22⋊C4C22×C1112yes—
357C22×C42C22×C1111yescharacteristic
358#396C22×C11116yescomplemented
359#394C22×C11116yescomplemented
360#390C22×C1118yescomplemented
361#389C22×C1118yescomplemented
362#386C22×C11116yescomplemented
363#380C22×C1118yescomplemented
364C2×#95C22×C1112yes—
365C2×#95C22×C1112yes—
366C22×C11—24no—
367C22×C11—232no—
368C22×C11—24no—
369C22×C11—24no—
370C22×C11—24no—
371C22×C11—24no—
372C22×C11—24no—
373C22×C11—24no—
374C22×C11—24no—
375C22×C11—24no—
376C22×C11—42no—
377C22×C11—416no—
378C22×C11—42no—
379C22×C11—42no—
380C22×C11—42no—
381C22×C11—44no—
382C22×C11—44no—
383C22×C11—44no—
384C22×C11—44no—
385C22×C11—44no—
386C22×C11—44no—
387C22×C11—44no—
388C22×C11—816no—
389C22×C11C2×#12114yes—
390C22×C11C2×#12114yes—
391C22×C11C2×#12118yescomplemented
392C22×C11#53714yes—
393C22×C11D4214yes—
394C22×C11#54714yes—
395C22×C11#54814yes—
396C22×C11#55314yes—
397C22×C11C23×D411yescharacteristic
398C22×C11C23×D411yescharacteristic
399C22×C11C23×D411yescharacteristic
400C22×C11C22×#4111yescharacteristic
401C22×C11C22×#4111yescharacteristic
402C22×C11C2×H(5,𝔽2)11yescharacteristic
403C22×C11C2×2−1+411yescharacteristic
404C4×C11—24no—
405C4×C11—24no—
406C4×C11—28no—
407C4×C11—42no—
408C4×C11—44no—
409C4×C11—42no—
410C4×C11—44no—
411C4×C11C2×#12118yescomplemented
412C25C23×C1112yes—
413C25C23×C1111yescharacteristic
414C25C23×C1111yescharacteristic
415C22×D4—24no—
416C22×D4—24no—
417C22×D4—28no—
418C22×D4—28no—
419C22×D4—28no—
420C22×D4—28no—
421C22×D4—28no—
422C22×D4—24no—
423C22×D4—24no—
424C22×D4—24no—
425C22×D4—44no—
426C22×D4D4×C1118yescomplemented
427C22×D4C23×C1118yes—
428C22×D4C23×C1114yes—
429C22×D4C23×C1118yes—
430C22×D4C23×C1114yes—
431C23×C4—24no—
432C23×C4—24no—
433C23×C4—28no—
434C23×C4—28no—
435C23×C4—24no—
436C23×C4—24no—
437C23×C4—24no—
438C23×C4—44no—
439C23×C4D4×C1118yescomplemented
440C23×C4C23×C1111yescharacteristic
441C23×C4C23×C1112yes—
442C23×C4C23×C1111yescharacteristic
443C23×C4C23×C1112yes—
444C23×C4C23×C1114yes—
445C23×C4C23×C1118yes—
446C23×C4C23×C1111yescharacteristic
447C23×C4C23×C1111yescharacteristic
448C23×C4C23×C1112yes—
449C23×C4C23×C1114yes—
450C23×C4C23×C1111yescharacteristic
451#121—264no—
452#121—232no—
453#121—232no—
454C4×D4—232no—
455C2×C4⋊C4—28no—
456C2×C4⋊C4—24no—
457C2×C4⋊C4—24no—
458C2×C4⋊C4—28no—
459C2×C4⋊C4—24no—
460C2×C4⋊C4—232no—
461C2×C4⋊C4D4×C1118yescomplemented
462C2×C4⋊C4C23×C1114yes—
463C2×C4⋊C4C23×C1118yes—
464C2×C4⋊C4C23×C1114yes—
465C2×C4⋊C4C23×C1114yes—
466C2×C4⋊C4C23×C1118yes—
467C2×C4⋊C4C23×C1114yes—
468C2×C22⋊C4—24no—
469C2×C22⋊C4—28no—
470C2×C22⋊C4—24no—
471C2×C22⋊C4—28no—
472C2×C22⋊C4—28no—
473C2×C22⋊C4—28no—
474C2×C22⋊C4—44no—
475C2×C22⋊C4C23×C1114yes—
476C2×C22⋊C4C23×C1114yes—
477C2×C22⋊C4C23×C1118yes—
478C2×C22⋊C4C23×C1118yes—
479C2×C22⋊C4C23×C1118yes—
480C2×C22⋊C4C23×C1118yes—
481C2×C22⋊C4C23×C1118yes—
482C2×C42—24no—
483C2×C42C23×C1114yes—
484#95C23×C1118yes—
485#95C23×C1118yes—
486C2×C11—28no—
487C2×C11—44no—
488C2×C11—84no—
489C2×C11#241618yesdirect product factor
490C2×C11C22×#12111yescharacteristic
491C2×C11C22×#12111yescharacteristic
492C2×C11C2×#53711yescharacteristic
493C2×C11C2×D4211yescharacteristic
494C2×C11C2×#54711yescharacteristic
495C2×C11C2×#54811yescharacteristic
496C2×C11C2×#55311yescharacteristic
497C24—22no—
498C24—22no—
499C24—22no—
500C24—22no—
501C24—22no—
502C24—22no—
503C24—22no—
504C24—22no—
505C24—22no—
506C24—22no—
507C24—24no—
508C24—24no—
509C24—24no—
510C24—24no—
511C24—24no—
512C24—24no—
513C24—24no—
514C24C2×D4×C1114yes—
515C24C2×D4×C1114yes—
516C24C2×D4×C1114yes—
517C24C11×#4114yes—
518C24C24×C1114yes—
519C24C24×C1112yes—
520C24C24×C1112yes—
521C24C24×C1111yescharacteristic
522C2×D4—232no—
523C2×D4—28no—
524C2×D4—28no—
525C2×D4—216no—
526C2×D4—216no—
527C2×D4—216no—
528C2×D4—216no—
529C2×D4—216no—
530C2×D4—28no—
531C2×D4—28no—
532C2×D4—28no—
533C2×D4—48no—
534C2×D4—432no—
535C2×D4—432no—
536C2×D4—416no—
537C2×D4C2×D4×C11116yescomplemented
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—24no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—24no—
544C22×C4—232no—
545C22×C4—28no—
546C22×C4—28no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—24no—
550C22×C4—22no—
551C22×C4—24no—
552C22×C4—24no—
553C22×C4—24no—
554C22×C4—216no—
555C22×C4—22no—
556C22×C4—24no—
557C22×C4—22no—
558C22×C4—24no—
559C22×C4—22no—
560C22×C4—216no—
561C22×C4—28no—
562C22×C4—28no—
563C22×C4—28no—
564C22×C4—48no—
565C22×C4—432no—
566C22×C4—416no—
567C22×C4C2×D4×C1114yes—
568C22×C4C2×D4×C1114yes—
569C22×C4C2×D4×C1118yes—
570C22×C4C2×D4×C1114yes—
571C22×C4C2×D4×C1114yes—
572C22×C4C2×D4×C11116yescomplemented
573C22×C4C11×#4114yes—
574C22×C4C24×C1112yes—
575C22×C4C24×C1112yes—
576C22×C4C24×C1114yes—
577C22×C4C24×C1114yes—
578C22×C4C24×C1114yes—
579C22×C4C24×C1112yes—
580C22×C4C24×C1112yes—
581C22×C4C24×C1112yes—
582C4⋊C4—216no—
583C4⋊C4—28no—
584C4⋊C4—28no—
585C4⋊C4—216no—
586C4⋊C4—28no—
587C4⋊C4C2×D4×C11116yescomplemented
588C22⋊C4—28no—
589C22⋊C4—216no—
590C22⋊C4—28no—
591C22⋊C4—216no—
592C22⋊C4—216no—
593C22⋊C4—216no—
594C22⋊C4—48no—
595C42—28no—
596C11C2×#241611yescharacteristic, direct product factor, Sylow
597C23—28no—
598C23—28no—
599C23—28no—
600C23—28no—
601C23—28no—
602C23—28no—
603C23—22no—
604C23—22no—
605C23—22no—
606C23—22no—
607C23—28no—
608C23—28no—
609C23—28no—
610C23—22no—
611C23—22no—
612C23—22no—
613C23—22no—
614C23—22no—
615C23—22no—
616C23—24no—
617C23—24no—
618C23—24no—
619C23—24no—
620C23—24no—
621C23—24no—
622C23—24no—
623C23—44no—
624C23—44no—
625C23—44no—
626C23—44no—
627C23—48no—
628C23—48no—
629C23—48no—
630C23—48no—
631C23—48no—
632C23—48no—
633C23—48no—
634C23C11×#121116yescomplemented
635C23C22×D4×C1114yes—
636C23C22×D4×C1114yes—
637C23C22×D4×C1114yes—
638C23C22×D4×C1112yes—
639C23C22×D4×C1112yes—
640C23C22×D4×C1112yes—
641C23C2×C11×#4114yes—
642C23C2×C11×#4112yes—
643C23C2×C11×#4112yes—
644C23C11×H(5,𝔽2)12yes—
645C23C11×2−1+412yes—
646C23C25×C1111yescharacteristic
647D4—232no—
648D4—432no—
649D4—432no—
650D4—416no—
651C2×C4—28no—
652C2×C4—28no—
653C2×C4—216no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—24no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—24no—
660C2×C4—232no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—24no—
664C2×C4—22no—
665C2×C4—24no—
666C2×C4—24no—
667C2×C4—24no—
668C2×C4—22no—
669C2×C4—24no—
670C2×C4—22no—
671C2×C4—24no—
672C2×C4—22no—
673C2×C4—432no—
674C2×C4—44no—
675C2×C4—48no—
676C2×C4—44no—
677C2×C4—48no—
678C2×C4—416no—
679C2×C4C11×#121116yescomplemented
680C2×C4C22×D4×C1114yes—
681C2×C4C22×D4×C1114yes—
682C2×C4C22×D4×C1118yes—
683C2×C4C22×D4×C1114yes—
684C2×C4C22×D4×C1114yes—
685C2×C4C2×C11×#4114yes—
686C22—24no—
687C22—232no—
688C22—24no—
689C22—24no—
690C22—24no—
691C22—24no—
692C22—24no—
693C22—24no—
694C22—24no—
695C22—24no—
696C22—42no—
697C22—416no—
698C22—42no—
699C22—42no—
700C22—42no—
701C22—44no—
702C22—44no—
703C22—44no—
704C22—44no—
705C22—44no—
706C22—44no—
707C22—44no—
708C22—816no—
709C22C2×C11×#12114yes—
710C22C2×C11×#12114yes—
711C22C2×C11×#12118yescomplemented
712C22C11×#53714yes—
713C22D42×C1114yes—
714C22C11×#54714yes—
715C22C11×#54814yes—
716C22C11×#55314yes—
717C22C23×D4×C1111yescharacteristic
718C22C23×D4×C1111yescharacteristic
719C22C23×D4×C1111yescharacteristic
720C22C22×C11×#4111yescharacteristic
721C22C22×C11×#4111yescharacteristic
722C22C2×C11×H(5,𝔽2)11yescharacteristic
723C22C2×C11×2−1+411yescharacteristic
724C4—24no—
725C4—24no—
726C4—28no—
727C4—42no—
728C4—44no—
729C4—42no—
730C4—44no—
731C4C2×C11×#12118yescomplemented
732C2—28no—
733C2—44no—
734C2—84no—
735C2C11×#241618yesdirect product factor
736C2C22×C11×#12111yescharacteristic
737C2C22×C11×#12111yescharacteristic
738C2C2×C11×#53711yescharacteristic
739C2C2×D42×C1111yescharacteristic
740C2C2×C11×#54711yescharacteristic
741C2C2×C11×#54811yescharacteristic
742C2C2×C11×#55311yescharacteristic
subgroupG/H
center, socleC24×C11C24
commutator, Frattini, cosocleC23C25×C11
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C11×#121C2semidirect
2. C22×C11×#121C2semidirect
3. C22×C11×#121C2semidirect
4. C22×C4×D4×C11C2semidirect
5. C23×C11×C4⋊C4C2semidirect
6. C11×#2416C2direct (N × H)
7. C2×C11×#396C2semidirect
8. C2×C11×#394C2semidirect
9. C2×C11×#390C2semidirect
10. C2×C11×#389C2semidirect
11. C2×C11×#386C2semidirect
12. C2×C11×#380C2semidirect
23. C2×C11×#121C22semidirect
24. C2×C11×#121C22semidirect
25. C2×C11×#121C22semidirect
27. C2×C4×D4×C11C22semidirect
35. C22×C11×C4⋊C4C22semidirect
44. C11×#396C22semidirect
45. C11×#394C22semidirect
46. C11×#390C22semidirect
47. C11×#389C22semidirect
48. C11×#386C22semidirect
49. C11×#380C22semidirect
66. C22×D4×C11D4semidirect
79. C23×C4×C11D4semidirect
101. C2×C11×C4⋊C4D4semidirect
126. C2×#2416C11direct (N × H)
167. C2×D4×C11C2×D4semidirect
202. C22×C4×C11C2×D4semidirect
217. C11×C4⋊C4C2×D4semidirect
226. C22×#121C2×C11semidirect
227. C22×#121C2×C11semidirect
228. C22×#121C2×C11semidirect
229. C22×C4×D4C2×C11semidirect
230. C23×C4⋊C4C2×C11semidirect
231. #2416C2×C11direct (N × H)
232. C2×#396C2×C11semidirect
233. C2×#394C2×C11semidirect
234. C2×#390C2×C11semidirect
235. C2×#389C2×C11semidirect
236. C2×#386C2×C11semidirect
237. C2×#380C2×C11semidirect
275. C23×C11#121semidirect
320. C2×C4×C11#121semidirect
337. C2×#121C22×C11semidirect
338. C2×#121C22×C11semidirect
339. C2×#121C22×C11semidirect
341. C2×C4×D4C22×C11semidirect
349. C22×C4⋊C4C22×C11semidirect
358. #396C22×C11semidirect
359. #394C22×C11semidirect
360. #390C22×C11semidirect
361. #389C22×C11semidirect
362. #386C22×C11semidirect
363. #380C22×C11semidirect
391. C22×C11C2×#121semidirect
411. C4×C11C2×#121semidirect
426. C22×D4D4×C11semidirect
439. C23×C4D4×C11semidirect
461. C2×C4⋊C4D4×C11semidirect
489. C2×C11#2416direct (N × H)
537. C2×D4C2×D4×C11semidirect
572. C22×C4C2×D4×C11semidirect
587. C4⋊C4C2×D4×C11semidirect
596. C11C2×#2416direct (N × H)
634. C23C11×#121semidirect
679. C2×C4C11×#121semidirect
711. C22C2×C11×#121semidirect
731. C4C2×C11×#121semidirect
735. C2C11×#2416direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C11×#1212
C22×C4×D4×C112
C23×C11×C4⋊C42
C11×#24162
C2×C11×#3962
C2×C11×#3942
C2×C11×#3902
C2×C11×#3892
C2×C11×#3862
C2×C11×#3802
C2×#241611