Finite Group Databasebeta

← C11×#13814 #14591007

Subgroups — C11×#13814 #14591007

Order 2816.

2298 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#385C212yesmaximal
2C2×C4×C11×C4⋊C4C211yesmaximal, characteristic, complemented
3C2×C4×C11×C22⋊C4C212yesmaximal
4C2×C4×C11×C22⋊C4C211yesmaximal, characteristic
5C22×C11×#95C211yesmaximal, characteristic
6C11×#1436C212yesmaximal, complemented
7C11×#1436C212yesmaximal, complemented
8C11×C4⋊#95C211yesmaximal, characteristic, complemented
9C11×#1434C211yesmaximal, characteristic, complemented
10C11×C22⋊#95C211yesmaximal, characteristic
11C4×C11×#95C211yesmaximal, characteristic, complemented
12C24×C4×C11C2211yescharacteristic
13C24×C4×C11C2212yes—
14C22×C11×C4⋊C4C2212yes—
15C22×C11×C4⋊C4C2212yes—
16C22×C11×C22⋊C4C2212yes—
17C22×C11×C22⋊C4C2211yescharacteristic
18C22×C11×C22⋊C4C2211yescharacteristic
19C22×C42×C11C2212yes—
20C22×C42×C11C2212yes—
21C22×C42×C11C2211yescharacteristic
22C22×C42×C11C2211yescharacteristic
23C11×#385C4116yescomplemented
24C4×C11×C4⋊C4—24no—
25C4×C11×C22⋊C4—28no—
26C4×C11×C22⋊C4C418yescomplemented
27C2×C11×#95—24no—
28C2×C11×#95C2211yescharacteristic
29C2×C11×#95C2211yescharacteristic
30C2×C11×#95C2211yescharacteristic
31C2×C11×#95C2212yes—
32C2×C11×#95C2212yes—
33C2×C11×#95C2212yes—
34C2×C11×#95C2212yes—
35C2×C11×#95C2212yes—
36C2×C11×#95C2212yes—
37C2×C11×#95C2211yescharacteristic
38C2×C11×#95C2211yescharacteristic
39C2×C11×#95C2211yescharacteristic
40C25×C11C2311yescharacteristic
41C23×C4×C11—24no—
42C23×C4×C11—24no—
43C23×C4×C11—24no—
44C23×C4×C11—22no—
45C23×C4×C11—24no—
46C23×C4×C11—22no—
47C23×C4×C11—24no—
48C23×C4×C11—42no—
49C23×C4×C11—42no—
50C23×C4×C11—42no—
51C23×C4×C11C2×C414yes—
52C23×C4×C11C2×C418yes—
53C23×C4×C11C2312yes—
54C23×C4×C11C2312yes—
55C23×C4×C11C2311yescharacteristic
56C23×C4×C11C2312yes—
57C23×C4×C11C2311yescharacteristic
58C23×C4×C11C2311yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2312yes—
63C2×C11×C4⋊C4—24no—
64C2×C11×C4⋊C4—24no—
65C2×C11×C4⋊C4—42no—
66C2×C11×C4⋊C4—42no—
67C2×C11×C4⋊C4C2×C418yescomplemented
68C2×C11×C4⋊C4C2×C418yescomplemented
69C2×C11×C22⋊C4—24no—
70C2×C11×C22⋊C4—24no—
71C2×C11×C22⋊C4C2×C418yes—
72C2×C11×C22⋊C4C2×C414yes—
73C2×C11×C22⋊C4C2×C418yes—
74C2×C11×C22⋊C4C2×C414yes—
75C2×C11×C22⋊C4D414yes—
76C2×C11×C22⋊C4Q814yes—
77C2×C42×C11—22no—
78C2×C42×C11—22no—
79C2×C42×C11—24no—
80C2×C42×C11—24no—
81C2×C42×C11—24no—
82C2×C42×C11—24no—
83C2×C42×C11—42no—
84C2×C42×C11—42no—
85C2×C42×C11—42no—
86C2×C42×C11C2×C414yescomplemented
87C2×C42×C11C2×C414yescomplemented
88C11×#95—22no—
89C11×#95—24no—
90C11×#95—24no—
91C11×#95—24no—
92C11×#95—22no—
93C11×#95—22no—
94C11×#95—42no—
95C11×#95C2×C414yescomplemented
96C11×#95C2×C414yescomplemented
97C11×#95C2×C418yescomplemented
98C11×#95C2×C418yescomplemented
99C11×#95D414yes—
100#13814C1111yesmaximal, characteristic, direct product factor, Sylow
101C24×C11—21no—
102C24×C11—22no—
103C24×C11—21no—
104C24×C11—21no—
105C24×C11—22no—
106C24×C11—21no—
107C24×C11C22×C412yes—
108C24×C11C22×C414yes—
109C24×C11C2×D412yes—
110C24×C11C2×Q812yes—
111C24×C11#4114yes—
112C24×C11C2411yescharacteristic
113C22×C4×C11—21no—
114C22×C4×C11—22no—
115C22×C4×C11—21no—
116C22×C4×C11—21no—
117C22×C4×C11—21no—
118C22×C4×C11—22no—
119C22×C4×C11—22no—
120C22×C4×C11—22no—
121C22×C4×C11—22no—
122C22×C4×C11—22no—
123C22×C4×C11—21no—
124C22×C4×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11—22no—
127C22×C4×C11—22no—
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11—28no—
132C22×C4×C11—216no—
133C22×C4×C11—22no—
134C22×C4×C11—22no—
135C22×C4×C11—21no—
136C22×C4×C11—22no—
137C22×C4×C11—22no—
138C22×C4×C11—22no—
139C22×C4×C11—22no—
140C22×C4×C11—22no—
141C22×C4×C11—22no—
142C22×C4×C11—22no—
143C22×C4×C11—22no—
144C22×C4×C11—22no—
145C22×C4×C11—22no—
146C22×C4×C11—22no—
147C22×C4×C11—21no—
148C22×C4×C11—22no—
149C22×C4×C11—22no—
150C22×C4×C11—22no—
151C22×C4×C11—22no—
152C22×C4×C11—22no—
153C22×C4×C11—22no—
154C22×C4×C11—22no—
155C22×C4×C11—28no—
156C22×C4×C11—216no—
157C22×C4×C11—44no—
158C22×C4×C11—48no—
159C22×C4×C11—48no—
160C22×C4×C11—48no—
161C22×C4×C11—48no—
162C22×C4×C11—48no—
163C22×C4×C11—48no—
164C22×C4×C11—48no—
165C22×C4×C11C22×C414yes—
166C22×C4×C11C22×C412yes—
167C22×C4×C11C22×C414yes—
168C22×C4×C11C22×C414yes—
169C22×C4×C11C22×C412yes—
170C22×C4×C11C22×C412yes—
171C22×C4×C11C22×C414yes—
172C22×C4×C11C22×C414yes—
173C22×C4×C11C22×C412yes—
174C22×C4×C11C22×C412yes—
175C22×C4×C11C22×C414yes—
176C22×C4×C11C22×C412yes—
177C22×C4×C11C2×D412yes—
178C22×C4×C11C2×D412yes—
179C22×C4×C11C2×D412yes—
180C22×C4×C11C2×D414yes—
181C22×C4×C11C2×Q812yes—
182C22×C4×C11C2×Q812yes—
183C22×C4×C11#4112yes—
184C22×C4×C11#4114yes—
185C11×C4⋊C4—216no—
186C11×C4⋊C4—48no—
187C11×C22⋊C4—216no—
188C11×C22⋊C4C42116yescomplemented
189C11×C22⋊C4C4⋊C4116yescomplemented
190C42×C11—28no—
191C42×C11—44no—
192C42×C11—48no—
193C42×C11—48no—
194C2×#385C2×C1112yes—
195C2×C4×C4⋊C4C2×C1111yescharacteristic, complemented
196C2×C4×C22⋊C4C2×C1112yes—
197C2×C4×C22⋊C4C2×C1111yescharacteristic
198C22×#95C2×C1111yescharacteristic
199#1436C2×C1112yescomplemented
200#1436C2×C1112yescomplemented
201C4⋊#95C2×C1111yescharacteristic, complemented
202#1434C2×C1111yescharacteristic, complemented
203C22⋊#95C2×C1111yescharacteristic
204C4×#95C2×C1111yescharacteristic, complemented
205C23×C11—22no—
206C23×C11—24no—
207C23×C11—22no—
208C23×C11—24no—
209C23×C11—22no—
210C23×C11—24no—
211C23×C11—22no—
212C23×C11—24no—
213C23×C11—22no—
214C23×C11—24no—
215C23×C11—24no—
216C23×C11—22no—
217C23×C11—22no—
218C23×C11—24no—
219C23×C11—24no—
220C23×C11—24no—
221C23×C11—22no—
222C23×C11—24no—
223C23×C11C2×C4214yes—
224C23×C11C2×C4⋊C414yes—
225C23×C11#11714yes—
226C23×C11C4×D418yes—
227C23×C11C4×Q818yes—
228C23×C11C23×C411yescharacteristic
229C23×C11C23×C412yes—
230C23×C11C22×D411yescharacteristic
231C23×C11C22×D411yescharacteristic
232C23×C11C22×Q811yescharacteristic
233C23×C11C2×#4112yes—
234C23×C11C2×#4112yes—
235C23×C11C2×#4111yescharacteristic
236C23×C11H(5,𝔽2)11yescharacteristic
237C23×C11H(5,𝔽2)12yes—
238C23×C112−1+411yescharacteristic
239C2×C4×C11—22no—
240C2×C4×C11—22no—
241C2×C4×C11—22no—
242C2×C4×C11—24no—
243C2×C4×C11—24no—
244C2×C4×C11—22no—
245C2×C4×C11—22no—
246C2×C4×C11—24no—
247C2×C4×C11—22no—
248C2×C4×C11—22no—
249C2×C4×C11—22no—
250C2×C4×C11—24no—
251C2×C4×C11—24no—
252C2×C4×C11—22no—
253C2×C4×C11—22no—
254C2×C4×C11—24no—
255C2×C4×C11—22no—
256C2×C4×C11—24no—
257C2×C4×C11—24no—
258C2×C4×C11—24no—
259C2×C4×C11—24no—
260C2×C4×C11—24no—
261C2×C4×C11—22no—
262C2×C4×C11—22no—
263C2×C4×C11—24no—
264C2×C4×C11—24no—
265C2×C4×C11—22no—
266C2×C4×C11—24no—
267C2×C4×C11—22no—
268C2×C4×C11—24no—
269C2×C4×C11—24no—
270C2×C4×C11—24no—
271C2×C4×C11—22no—
272C2×C4×C11—24no—
273C2×C4×C11—24no—
274C2×C4×C11—24no—
275C2×C4×C11—24no—
276C2×C4×C11—24no—
277C2×C4×C11—22no—
278C2×C4×C11—24no—
279C2×C4×C11—416no—
280C2×C4×C11—432no—
281C2×C4×C11—42no—
282C2×C4×C11—42no—
283C2×C4×C11—42no—
284C2×C4×C11—42no—
285C2×C4×C11—42no—
286C2×C4×C11—42no—
287C2×C4×C11—42no—
288C2×C4×C11—42no—
289C2×C4×C11—42no—
290C2×C4×C11—42no—
291C2×C4×C11—42no—
292C2×C4×C11—42no—
293C2×C4×C11—42no—
294C2×C4×C11—42no—
295C2×C4×C11C2×C4214yes—
296C2×C4×C11C2×C4214yes—
297C2×C4×C11C2×C4⋊C414yes—
298C2×C4×C11C2×C4⋊C414yes—
299C2×C4×C11C4×D414yes—
300C2×C4×C11C4×D418yes—
301C24×C4C22×C1111yescharacteristic
302C24×C4C22×C1112yes—
303C22×C4⋊C4C22×C1112yes—
304C22×C4⋊C4C22×C1112yes—
305C22×C22⋊C4C22×C1112yes—
306C22×C22⋊C4C22×C1111yescharacteristic
307C22×C22⋊C4C22×C1111yescharacteristic
308C22×C42C22×C1112yes—
309C22×C42C22×C1112yes—
310C22×C42C22×C1111yescharacteristic
311C22×C42C22×C1111yescharacteristic
312#385C4×C11116yescomplemented
313C4×C4⋊C4—24no—
314C4×C22⋊C4—28no—
315C4×C22⋊C4C4×C1118yescomplemented
316C2×#95—24no—
317C2×#95C22×C1111yescharacteristic
318C2×#95C22×C1111yescharacteristic
319C2×#95C22×C1111yescharacteristic
320C2×#95C22×C1112yes—
321C2×#95C22×C1112yes—
322C2×#95C22×C1112yes—
323C2×#95C22×C1112yes—
324C2×#95C22×C1112yes—
325C2×#95C22×C1112yes—
326C2×#95C22×C1111yescharacteristic
327C2×#95C22×C1111yescharacteristic
328C2×#95C22×C1111yescharacteristic
329C22×C11—24no—
330C22×C11—24no—
331C22×C11—24no—
332C22×C11—24no—
333C22×C11—28no—
334C22×C11—28no—
335C22×C11—28no—
336C22×C11—28no—
337C22×C11—24no—
338C22×C11—24no—
339C22×C11C4×C4⋊C418yescomplemented
340C22×C11C22×C4211yescharacteristic
341C22×C11C22×C4⋊C411yescharacteristic
342C22×C11C2×#11711yescharacteristic
343C22×C11C2×C4×D411yescharacteristic
344C22×C11C2×C4×D412yes—
345C22×C11C2×C4×D412yes—
346C22×C11C2×C4×Q812yes—
347C22×C11C4×#4111yescharacteristic
348C22×C11C4×#4112yes—
349C22×C11#51811yescharacteristic
350C22×C11#51812yes—
351C22×C11#52011yescharacteristic
352C22×C11#52012yes—
353C22×C11D4211yescharacteristic
354C22×C11#54612yes—
355C22×C11#54612yes—
356C22×C11#54711yescharacteristic
357C22×C11D4×Q811yescharacteristic
358C22×C11#55112yes—
359C22×C11#55112yes—
360C22×C11#55212yes—
361C22×C11#55411yescharacteristic
362C22×C11#55412yes—
363C4×C11—24no—
364C4×C11—24no—
365C4×C11—24no—
366C4×C11—28no—
367C4×C11—24no—
368C4×C11—24no—
369C4×C11—42no—
370C4×C11—44no—
371C4×C11—44no—
372C4×C11—44no—
373C25C23×C1111yescharacteristic
374C23×C4—24no—
375C23×C4—24no—
376C23×C4—24no—
377C23×C4—22no—
378C23×C4—24no—
379C23×C4—22no—
380C23×C4—24no—
381C23×C4—42no—
382C23×C4—42no—
383C23×C4—42no—
384C23×C4C2×C4×C1114yes—
385C23×C4C2×C4×C1118yes—
386C23×C4C23×C1112yes—
387C23×C4C23×C1112yes—
388C23×C4C23×C1112yes—
389C23×C4C23×C1111yescharacteristic
390C23×C4C23×C1111yescharacteristic
391C23×C4C23×C1111yescharacteristic
392C23×C4C23×C1111yescharacteristic
393C23×C4C23×C1111yescharacteristic
394C23×C4C23×C1112yes—
395C23×C4C23×C1111yescharacteristic
396C2×C4⋊C4—24no—
397C2×C4⋊C4—24no—
398C2×C4⋊C4—42no—
399C2×C4⋊C4—42no—
400C2×C4⋊C4C2×C4×C1118yescomplemented
401C2×C4⋊C4C2×C4×C1118yescomplemented
402C2×C22⋊C4—24no—
403C2×C22⋊C4—24no—
404C2×C22⋊C4C2×C4×C1118yes—
405C2×C22⋊C4C2×C4×C1114yes—
406C2×C22⋊C4C2×C4×C1118yes—
407C2×C22⋊C4C2×C4×C1114yes—
408C2×C22⋊C4D4×C1114yes—
409C2×C22⋊C4Q8×C1114yes—
410C2×C42—22no—
411C2×C42—22no—
412C2×C42—24no—
413C2×C42—24no—
414C2×C42—24no—
415C2×C42—24no—
416C2×C42—42no—
417C2×C42—42no—
418C2×C42—42no—
419C2×C42C2×C4×C1114yescomplemented
420C2×C42C2×C4×C1114yescomplemented
421#95—22no—
422#95—24no—
423#95—24no—
424#95—24no—
425#95—22no—
426#95—22no—
427#95—42no—
428#95C2×C4×C1114yescomplemented
429#95C2×C4×C1114yescomplemented
430#95C2×C4×C1118yescomplemented
431#95C2×C4×C1118yescomplemented
432#95D4×C1114yes—
433C2×C11—28no—
434C2×C11C2×C4×C4⋊C411yescharacteristic
435C2×C11C42×D411yescharacteristic
436C2×C11#227511yescharacteristic
437C2×C11#234211yescharacteristic
438C2×C11#234311yescharacteristic
439C2×C11D4×C4⋊C411yescharacteristic
440C2×C11#234911yescharacteristic
441C2×C11#235812yes—
442C2×C11#235912yes—
443C2×C11#236012yes—
444C2×C11#236812yes—
445C24—21no—
446C24—22no—
447C24—21no—
448C24—21no—
449C24—22no—
450C24—21no—
451C24C22×C4×C1112yes—
452C24C22×C4×C1114yes—
453C24C2×D4×C1112yes—
454C24C2×Q8×C1112yes—
455C24C11×#4114yes—
456C24C24×C1111yescharacteristic
457C22×C4—21no—
458C22×C4—22no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—21no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—28no—
476C22×C4—216no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—21no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—21no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—28no—
500C22×C4—216no—
501C22×C4—44no—
502C22×C4—48no—
503C22×C4—48no—
504C22×C4—48no—
505C22×C4—48no—
506C22×C4—48no—
507C22×C4—48no—
508C22×C4—48no—
509C22×C4C22×C4×C1114yes—
510C22×C4C22×C4×C1112yes—
511C22×C4C22×C4×C1114yes—
512C22×C4C22×C4×C1114yes—
513C22×C4C22×C4×C1112yes—
514C22×C4C22×C4×C1112yes—
515C22×C4C22×C4×C1114yes—
516C22×C4C22×C4×C1114yes—
517C22×C4C22×C4×C1112yes—
518C22×C4C22×C4×C1112yes—
519C22×C4C22×C4×C1114yes—
520C22×C4C22×C4×C1112yes—
521C22×C4C2×D4×C1112yes—
522C22×C4C2×D4×C1112yes—
523C22×C4C2×D4×C1112yes—
524C22×C4C2×D4×C1114yes—
525C22×C4C2×Q8×C1112yes—
526C22×C4C2×Q8×C1112yes—
527C22×C4C11×#4112yes—
528C22×C4C11×#4114yes—
529C4⋊C4—216no—
530C4⋊C4—48no—
531C22⋊C4—216no—
532C22⋊C4C42×C11116yescomplemented
533C22⋊C4C11×C4⋊C4116yescomplemented
534C42—28no—
535C42—44no—
536C42—48no—
537C42—48no—
538C11#1381411yescharacteristic, direct product factor, Sylow
539C23—22no—
540C23—24no—
541C23—22no—
542C23—24no—
543C23—22no—
544C23—24no—
545C23—22no—
546C23—24no—
547C23—22no—
548C23—24no—
549C23—24no—
550C23—22no—
551C23—22no—
552C23—24no—
553C23—24no—
554C23—24no—
555C23—22no—
556C23—24no—
557C23C2×C42×C1114yes—
558C23C2×C11×C4⋊C414yes—
559C23C11×#11714yes—
560C23C4×D4×C1118yes—
561C23C4×Q8×C1118yes—
562C23C23×C4×C1111yescharacteristic
563C23C23×C4×C1112yes—
564C23C22×D4×C1111yescharacteristic
565C23C22×D4×C1111yescharacteristic
566C23C22×Q8×C1111yescharacteristic
567C23C2×C11×#4112yes—
568C23C2×C11×#4112yes—
569C23C2×C11×#4111yescharacteristic
570C23C11×H(5,𝔽2)11yescharacteristic
571C23C11×H(5,𝔽2)12yes—
572C23C11×2−1+411yescharacteristic
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—24no—
577C2×C4—24no—
578C2×C4—22no—
579C2×C4—24no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—24no—
585C2×C4—24no—
586C2×C4—22no—
587C2×C4—24no—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—24no—
591C2×C4—24no—
592C2×C4—24no—
593C2×C4—24no—
594C2×C4—24no—
595C2×C4—22no—
596C2×C4—22no—
597C2×C4—24no—
598C2×C4—24no—
599C2×C4—22no—
600C2×C4—24no—
601C2×C4—22no—
602C2×C4—24no—
603C2×C4—24no—
604C2×C4—24no—
605C2×C4—22no—
606C2×C4—24no—
607C2×C4—24no—
608C2×C4—24no—
609C2×C4—24no—
610C2×C4—24no—
611C2×C4—22no—
612C2×C4—24no—
613C2×C4—416no—
614C2×C4—432no—
615C2×C4—42no—
616C2×C4—42no—
617C2×C4—42no—
618C2×C4—42no—
619C2×C4—42no—
620C2×C4—42no—
621C2×C4—42no—
622C2×C4—42no—
623C2×C4—42no—
624C2×C4—42no—
625C2×C4—42no—
626C2×C4—42no—
627C2×C4—42no—
628C2×C4—42no—
629C2×C4C2×C42×C1114yes—
630C2×C4C2×C42×C1114yes—
631C2×C4C2×C11×C4⋊C414yes—
632C2×C4C2×C11×C4⋊C414yes—
633C2×C4C4×D4×C1114yes—
634C2×C4C4×D4×C1118yes—
635C22—24no—
636C22—24no—
637C22—24no—
638C22—24no—
639C22—24no—
640C22—24no—
641C22—28no—
642C22—28no—
643C22—28no—
644C22—28no—
645C22C4×C11×C4⋊C418yescomplemented
646C22C22×C42×C1111yescharacteristic
647C22C22×C11×C4⋊C411yescharacteristic
648C22C2×C11×#11711yescharacteristic
649C22C2×C4×D4×C1112yes—
650C22C2×C4×D4×C1111yescharacteristic
651C22C2×C4×D4×C1112yes—
652C22C2×C4×Q8×C1112yes—
653C22C4×C11×#4111yescharacteristic
654C22C4×C11×#4112yes—
655C22C11×#51811yescharacteristic
656C22C11×#51812yes—
657C22C11×#52011yescharacteristic
658C22C11×#52012yes—
659C22D42×C1111yescharacteristic
660C22C11×#54612yes—
661C22C11×#54612yes—
662C22C11×#54711yescharacteristic
663C22D4×Q8×C1111yescharacteristic
664C22C11×#55112yes—
665C22C11×#55112yes—
666C22C11×#55212yes—
667C22C11×#55411yescharacteristic
668C22C11×#55412yes—
669C4—24no—
670C4—24no—
671C4—24no—
672C4—24no—
673C4—24no—
674C4—28no—
675C4—42no—
676C4—44no—
677C4—44no—
678C4—44no—
679C2—28no—
680C2C2×C4×C11×C4⋊C411yescharacteristic
681C2C42×D4×C1111yescharacteristic
682C2C11×#227511yescharacteristic
683C2C11×#234211yescharacteristic
684C2C11×#234311yescharacteristic
685C2D4×C11×C4⋊C411yescharacteristic
686C2C11×#234911yescharacteristic
687C2C11×#235812yes—
688C2C11×#235912yes—
689C2C11×#236012yes—
690C2C11×#236812yes—
subgroupG/H
center, socleC24×C11C24
commutatorC22C22×C42×C11
Frattini, cosocleC24C24×C11
prime radicalC25×C11C23
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C24×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C4×C11×C4⋊C4C2semidirect
6. C11×#1436C2semidirect
7. C11×#1436C2semidirect
8. C11×C4⋊#95C2semidirect
9. C11×#1434C2semidirect
11. C4×C11×#95C2semidirect
23. C11×#385C4semidirect
26. C4×C11×C22⋊C4C4semidirect
67. C2×C11×C4⋊C4C2×C4semidirect
68. C2×C11×C4⋊C4C2×C4semidirect
86. C2×C42×C11C2×C4semidirect
87. C2×C42×C11C2×C4semidirect
95. C11×#95C2×C4semidirect
96. C11×#95C2×C4semidirect
97. C11×#95C2×C4semidirect
98. C11×#95C2×C4semidirect
100. #13814C11direct (N × H)
188. C11×C22⋊C4C42semidirect
189. C11×C22⋊C4C4⋊C4semidirect
195. C2×C4×C4⋊C4C2×C11semidirect
199. #1436C2×C11semidirect
200. #1436C2×C11semidirect
201. C4⋊#95C2×C11semidirect
202. #1434C2×C11semidirect
204. C4×#95C2×C11semidirect
312. #385C4×C11semidirect
315. C4×C22⋊C4C4×C11semidirect
339. C22×C11C4×C4⋊C4semidirect
400. C2×C4⋊C4C2×C4×C11semidirect
401. C2×C4⋊C4C2×C4×C11semidirect
419. C2×C42C2×C4×C11semidirect
420. C2×C42C2×C4×C11semidirect
428. #95C2×C4×C11semidirect
429. #95C2×C4×C11semidirect
430. #95C2×C4×C11semidirect
431. #95C2×C4×C11semidirect
532. C22⋊C4C42×C11semidirect
533. C22⋊C4C11×C4⋊C4semidirect
538. C11#13814direct (N × H)
645. C22C4×C11×C4⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#3852
C2×C4×C11×C4⋊C42
C2×C4×C11×C22⋊C42
C22×C11×#952
C11×#14362
C11×C4⋊#952
C11×#14342
C11×C22⋊#952
C4×C11×#952
#1381411