Finite Group Databasebeta

← C11×#23922 #14601115

Subgroups — C11×#23922 #14601115

Order 2816.

1928 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#525C211yesmaximal, characteristic
2C22×C11×C22⋊Q8C211yesmaximal, characteristic, complemented
3C2×C11×#452C212yesmaximal, complemented
4C2×C11×#451C211yesmaximal, characteristic, complemented
5C2×C11×#448C211yesmaximal, characteristic, complemented
6C11×#2001C212yesmaximal, complemented
7C11×#2000C212yesmaximal, complemented
8C11×#1874C211yesmaximal, characteristic, complemented
9C11×#1873C212yesmaximal, complemented
10C11×#1872C211yesmaximal, characteristic, complemented
11C11×#1779C211yesmaximal, characteristic, complemented
12C22×C11×#41C2211yescharacteristic
13C23×Q8×C11C2211yescharacteristic
14C24×C4×C11C2211yescharacteristic
15C22×C11×Q16C2212yescomplemented
16C22×C11×SD16C2212yescomplemented
17C11×#525—24no—
18C11×#525—24no—
19C2×C11×#123—21no—
20C2×C11×C22⋊Q8—21no—
21C2×C11×C22⋊Q8—21no—
22C2×C11×C22⋊Q8—28no—
23C2×C11×C22⋊Q8C2212yes—
24C2×C11×C22⋊Q8C2211yescharacteristic
25C2×C11×C22⋊Q8C2211yescharacteristic
26C2×C11×C22⋊Q8C2212yes—
27C2×C11×#121C2211yescharacteristic
28C2×C11×#121C2211yescharacteristic
29C2×C11×#120—21no—
30C2×C4×D4×C11—21no—
31C2×C4×D4×C11—21no—
32C2×C11×#117C2211yescharacteristic
33C22×C11×C4⋊C4—21no—
34C22×C11×C4⋊C4C2211yescharacteristic
35C22×C11×C22⋊C4—21no—
36C11×#452—28no—
37C11×#451—24no—
38C11×#448—24no—
39C2×C11×#103C2212yescomplemented
40C2×C11×#103C2212yescomplemented
41C2×C11×#103C2212yescomplemented
42C2×C11×#102C2212yescomplemented
43C2×C11×C22⋊C8C2211yescharacteristic
44C2×C11×C22⋊C8C2212yes—
45C2×C11×C22⋊C8C2211yescharacteristic
46C2×C11×C22⋊C8C2212yes—
47C11×#340C2212yescomplemented
48C11×#340C2212yescomplemented
49C25×C11D411yescharacteristic
50C2×C11×#41—22no—
51C2×C11×#41—22no—
52C2×C11×#41—24no—
53C2×C11×#41—42no—
54C22×Q8×C11—24no—
55C22×Q8×C11—21no—
56C22×Q8×C11—22no—
57C22×Q8×C11—22no—
58C22×Q8×C11—42no—
59C22×Q8×C11C2312yes—
60C22×Q8×C11C2311yescharacteristic
61C22×D4×C11—21no—
62C22×D4×C11—21no—
63C22×D4×C11—21no—
64C22×D4×C11C2311yescharacteristic
65C23×C4×C11—21no—
66C23×C4×C11—21no—
67C23×C4×C11—21no—
68C23×C4×C11—24no—
69C23×C4×C11—22no—
70C23×C4×C11—22no—
71C23×C4×C11—42no—
72C23×C4×C11D411yescharacteristic
73C23×C4×C11D411yescharacteristic
74C23×C4×C11D411yescharacteristic
75C23×C4×C11C2311yescharacteristic
76C23×C4×C11C2311yescharacteristic
77C23×C4×C11C2311yescharacteristic
78C2×C11×Q16—24no—
79C2×C11×Q16—24no—
80C2×C11×Q16—42no—
81C2×C11×SD16—24no—
82C2×C11×SD16—24no—
83C2×C11×SD16—42no—
84C22×C8×C11C2312yes—
85C22×C8×C11C2312yes—
86C11×#123—28no—
87C11×C22⋊Q8—28no—
88C11×C22⋊Q8—28no—
89C11×C22⋊Q8—24no—
90C11×C22⋊Q8—22no—
91C11×C22⋊Q8—24no—
92C11×C22⋊Q8—22no—
93C11×C22⋊Q8—24no—
94C11×C22⋊Q8—22no—
95C11×C22⋊Q8D414yes—
96C11×C22⋊Q8D418yescomplemented
97C11×#121—22no—
98C11×#121—22no—
99C11×#121—22no—
100C11×#121D414yes—
101C11×#120—28no—
102C4×D4×C11—28no—
103C4×D4×C11—28no—
104C11×#117—22no—
105C11×#117—22no—
106C2×C11×C4⋊C4—28no—
107C2×C11×C4⋊C4—22no—
108C2×C11×C4⋊C4—22no—
109C2×C11×C4⋊C4—21no—
110C2×C11×C4⋊C4—21no—
111C2×C11×C4⋊C4—21no—
112C2×C11×C4⋊C4—24no—
113C2×C11×C4⋊C4C2312yes—
114C2×C11×C4⋊C4C2311yescharacteristic
115C2×C11×C4⋊C4C2311yescharacteristic
116C2×C11×C22⋊C4—28no—
117C2×C11×C22⋊C4—22no—
118C2×C11×C22⋊C4—22no—
119C2×C11×C22⋊C4—21no—
120C2×C11×C22⋊C4—21no—
121C2×C11×C22⋊C4—21no—
122C2×C11×C22⋊C4—21no—
123C2×C11×C22⋊C4—21no—
124C2×C42×C11—21no—
125C11×#103—24no—
126C11×#103—24no—
127C11×#103—24no—
128C11×#102—24no—
129C11×C22⋊C8—22no—
130C11×C22⋊C8—22no—
131C11×C22⋊C8—24no—
132C11×C22⋊C8—42no—
133#23922C1111yesmaximal, characteristic, direct product factor, Sylow
134C24×C11—22no—
135C24×C11—22no—
136C24×C11—22no—
137C24×C11—22no—
138C24×C11—22no—
139C24×C11—21no—
140C24×C11—41no—
141C24×C11—41no—
142C24×C11C2×D411yescharacteristic
143C24×C11C2×D411yescharacteristic
144C24×C11C2×D411yescharacteristic
145C11×#41—48no—
146C11×#41—48no—
147C2×Q8×C11—24no—
148C2×Q8×C11—22no—
149C2×Q8×C11—21no—
150C2×Q8×C11—22no—
151C2×Q8×C11—22no—
152C2×Q8×C11—22no—
153C2×Q8×C11—22no—
154C2×Q8×C11—22no—
155C2×Q8×C11—22no—
156C2×Q8×C11—48no—
157C2×Q8×C11—48no—
158C2×Q8×C11—42no—
159C2×Q8×C11—42no—
160C2×Q8×C11C2×D412yes—
161C2×Q8×C11C2×D414yes—
162C2×D4×C11—24no—
163C2×D4×C11—24no—
164C2×D4×C11—24no—
165C2×D4×C11—22no—
166C2×D4×C11—21no—
167C2×D4×C11—22no—
168C2×D4×C11—42no—
169C2×D4×C11—42no—
170C2×D4×C11—42no—
171C2×D4×C11—42no—
172C2×D4×C11—42no—
173C2×D4×C11—42no—
174C2×D4×C11C2×D412yes—
175C22×C4×C11—22no—
176C22×C4×C11—21no—
177C22×C4×C11—21no—
178C22×C4×C11—22no—
179C22×C4×C11—22no—
180C22×C4×C11—24no—
181C22×C4×C11—24no—
182C22×C4×C11—24no—
183C22×C4×C11—22no—
184C22×C4×C11—22no—
185C22×C4×C11—21no—
186C22×C4×C11—21no—
187C22×C4×C11—22no—
188C22×C4×C11—21no—
189C22×C4×C11—22no—
190C22×C4×C11—22no—
191C22×C4×C11—22no—
192C22×C4×C11—22no—
193C22×C4×C11—22no—
194C22×C4×C11—21no—
195C22×C4×C11—21no—
196C22×C4×C11—22no—
197C22×C4×C11—22no—
198C22×C4×C11—41no—
199C22×C4×C11—41no—
200C22×C4×C11—41no—
201C22×C4×C11—48no—
202C22×C4×C11—48no—
203C22×C4×C11—42no—
204C22×C4×C11—42no—
205C22×C4×C11—42no—
206C22×C4×C11—42no—
207C22×C4×C11—42no—
208C22×C4×C11—42no—
209C22×C4×C11C2×D411yescharacteristic
210C22×C4×C11C2×D411yescharacteristic
211C22×C4×C11C2×D411yescharacteristic
212C22×C4×C11C2×D412yes—
213C22×C4×C11C2×D412yes—
214C22×C4×C11C2×D414yes—
215C22×C4×C11C2411yescharacteristic
216C11×Q16—48no—
217C11×SD16—48no—
218C2×C8×C11—22no—
219C2×C8×C11—22no—
220C2×C8×C11—22no—
221C2×C8×C11—22no—
222C2×C8×C11—22no—
223C2×C8×C11—22no—
224C11×C4⋊C4—24no—
225C11×C4⋊C4—28no—
226C11×C4⋊C4—24no—
227C11×C4⋊C4—28no—
228C11×C4⋊C4—24no—
229C11×C4⋊C4—22no—
230C11×C4⋊C4—21no—
231C11×C4⋊C4—21no—
232C11×C4⋊C4C2×D414yes—
233C11×C4⋊C4C2×D412yes—
234C11×C4⋊C4C2×D412yes—
235C11×C22⋊C4—28no—
236C11×C22⋊C4—24no—
237C11×C22⋊C4—24no—
238C11×C22⋊C4—24no—
239C11×C22⋊C4—28no—
240C11×C22⋊C4—24no—
241C11×C22⋊C4—24no—
242C42×C11—24no—
243C2×#525C2×C1111yescharacteristic
244C22×C22⋊Q8C2×C1111yescharacteristic, complemented
245C2×#452C2×C1112yescomplemented
246C2×#451C2×C1111yescharacteristic, complemented
247C2×#448C2×C1111yescharacteristic, complemented
248#2001C2×C1112yescomplemented
249#2000C2×C1112yescomplemented
250#1874C2×C1111yescharacteristic, complemented
251#1873C2×C1112yescomplemented
252#1872C2×C1111yescharacteristic, complemented
253#1779C2×C1111yescharacteristic, complemented
254C23×C11—21no—
255C23×C11—21no—
256C23×C11—21no—
257C23×C11—21no—
258C23×C11—28no—
259C23×C11—21no—
260C23×C11—21no—
261C23×C11—21no—
262C23×C11—21no—
263C23×C11—21no—
264C23×C11—21no—
265C23×C11—21no—
266C23×C11—21no—
267C23×C11—21no—
268C23×C11—21no—
269C23×C11—21no—
270C23×C11—21no—
271C23×C11—22no—
272C23×C11—44no—
273C23×C11—44no—
274C23×C11—44no—
275C23×C11—44no—
276C23×C11—44no—
277C23×C11—44no—
278C23×C11—41no—
279C23×C11—41no—
280C23×C11—41no—
281C23×C11—41no—
282C23×C11—41no—
283C23×C11—41no—
284C23×C11#12012yes—
285C23×C11#12012yes—
286C23×C11#13512yes—
287C23×C11#13712yes—
288C23×C11#13712yes—
289C23×C11C22×D411yescharacteristic
290Q8×C11—24no—
291Q8×C11—24no—
292Q8×C11—24no—
293Q8×C11—48no—
294Q8×C11—42no—
295Q8×C11—42no—
296Q8×C11—42no—
297D4×C11—24no—
298D4×C11—48no—
299D4×C11—48no—
300D4×C11—48no—
301D4×C11—42no—
302C2×C4×C11—21no—
303C2×C4×C11—21no—
304C2×C4×C11—21no—
305C2×C4×C11—21no—
306C2×C4×C11—24no—
307C2×C4×C11—24no—
308C2×C4×C11—24no—
309C2×C4×C11—24no—
310C2×C4×C11—22no—
311C2×C4×C11—22no—
312C2×C4×C11—24no—
313C2×C4×C11—21no—
314C2×C4×C11—22no—
315C2×C4×C11—24no—
316C2×C4×C11—21no—
317C2×C4×C11—21no—
318C2×C4×C11—44no—
319C2×C4×C11—44no—
320C2×C4×C11—44no—
321C2×C4×C11—48no—
322C2×C4×C11—48no—
323C2×C4×C11—48no—
324C2×C4×C11—41no—
325C2×C4×C11—42no—
326C2×C4×C11—41no—
327C2×C4×C11—42no—
328C2×C4×C11—42no—
329C2×C4×C11—41no—
330C2×C4×C11—41no—
331C2×C4×C11—41no—
332C2×C4×C11—42no—
333C2×C4×C11—41no—
334C2×C4×C11—42no—
335C2×C4×C11—42no—
336C2×C4×C11#12012yes—
337C2×C4×C11#12012yes—
338C2×C4×C11C22×D412yes—
339C2×C4×C11C22×D411yescharacteristic
340C2×C4×C11C22×D411yescharacteristic
341C2×C4×C11H(5,𝔽2)12yes—
342C8×C11—42no—
343C8×C11—42no—
344C22×#41C22×C1111yescharacteristic
345C23×Q8C22×C1111yescharacteristic
346C24×C4C22×C1111yescharacteristic
347C22×Q16C22×C1112yescomplemented
348C22×SD16C22×C1112yescomplemented
349#525—24no—
350#525—24no—
351C2×#123—21no—
352C2×C22⋊Q8—21no—
353C2×C22⋊Q8—21no—
354C2×C22⋊Q8—28no—
355C2×C22⋊Q8C22×C1112yes—
356C2×C22⋊Q8C22×C1111yescharacteristic
357C2×C22⋊Q8C22×C1111yescharacteristic
358C2×C22⋊Q8C22×C1112yes—
359C2×#121C22×C1111yescharacteristic
360C2×#121C22×C1111yescharacteristic
361C2×#120—21no—
362C2×C4×D4—21no—
363C2×C4×D4—21no—
364C2×#117C22×C1111yescharacteristic
365C22×C4⋊C4—21no—
366C22×C4⋊C4C22×C1111yescharacteristic
367C22×C22⋊C4—21no—
368#452—28no—
369#451—24no—
370#448—24no—
371C2×#103C22×C1112yescomplemented
372C2×#103C22×C1112yescomplemented
373C2×#103C22×C1112yescomplemented
374C2×#102C22×C1112yescomplemented
375C2×C22⋊C8C22×C1111yescharacteristic
376C2×C22⋊C8C22×C1112yes—
377C2×C22⋊C8C22×C1111yescharacteristic
378C2×C22⋊C8C22×C1112yes—
379#340C22×C1112yescomplemented
380#340C22×C1112yescomplemented
381C22×C11—22no—
382C22×C11—22no—
383C22×C11—22no—
384C22×C11—22no—
385C22×C11—22no—
386C22×C11—22no—
387C22×C11—22no—
388C22×C11—22no—
389C22×C11—22no—
390C22×C11—22no—
391C22×C11—22no—
392C22×C11—22no—
393C22×C11—416no—
394C22×C11—41no—
395C22×C11—41no—
396C22×C11—41no—
397C22×C11—41no—
398C22×C11—41no—
399C22×C11—41no—
400C22×C11—41no—
401C22×C11—41no—
402C22×C11—42no—
403C22×C11—42no—
404C22×C11—42no—
405C22×C11—81no—
406C22×C11—81no—
407C22×C11—81no—
408C22×C11—81no—
409C22×C11#45214yescomplemented
410C22×C11C2×#12011yescharacteristic
411C22×C11C2×#12011yescharacteristic
412C22×C11#53411yescharacteristic
413C22×C11C2×#13511yescharacteristic
414C22×C11C2×#13711yescharacteristic
415C22×C11C2×#13711yescharacteristic
416C22×C11#57511yescharacteristic
417C4×C11—22no—
418C4×C11—22no—
419C4×C11—41no—
420C4×C11—42no—
421C4×C11—44no—
422C4×C11—42no—
423C4×C11—44no—
424C4×C11—42no—
425C4×C11D4212yes—
426C4×C11D4212yes—
427C25D4×C1111yescharacteristic
428C2×#41—22no—
429C2×#41—22no—
430C2×#41—24no—
431C2×#41—42no—
432C22×Q8—24no—
433C22×Q8—21no—
434C22×Q8—22no—
435C22×Q8—22no—
436C22×Q8—42no—
437C22×Q8C23×C1112yes—
438C22×Q8C23×C1111yescharacteristic
439C22×D4—21no—
440C22×D4—21no—
441C22×D4—21no—
442C22×D4C23×C1111yescharacteristic
443C23×C4—21no—
444C23×C4—21no—
445C23×C4—21no—
446C23×C4—24no—
447C23×C4—22no—
448C23×C4—22no—
449C23×C4—42no—
450C23×C4D4×C1111yescharacteristic
451C23×C4D4×C1111yescharacteristic
452C23×C4D4×C1111yescharacteristic
453C23×C4C23×C1111yescharacteristic
454C23×C4C23×C1111yescharacteristic
455C23×C4C23×C1111yescharacteristic
456C2×Q16—24no—
457C2×Q16—24no—
458C2×Q16—42no—
459C2×SD16—24no—
460C2×SD16—24no—
461C2×SD16—42no—
462C22×C8C23×C1112yes—
463C22×C8C23×C1112yes—
464#123—28no—
465C22⋊Q8—28no—
466C22⋊Q8—28no—
467C22⋊Q8—24no—
468C22⋊Q8—22no—
469C22⋊Q8—24no—
470C22⋊Q8—22no—
471C22⋊Q8—24no—
472C22⋊Q8—22no—
473C22⋊Q8D4×C1114yes—
474C22⋊Q8D4×C1118yescomplemented
475#121—22no—
476#121—22no—
477#121—22no—
478#121D4×C1114yes—
479#120—28no—
480C4×D4—28no—
481C4×D4—28no—
482#117—22no—
483#117—22no—
484C2×C4⋊C4—28no—
485C2×C4⋊C4—22no—
486C2×C4⋊C4—22no—
487C2×C4⋊C4—21no—
488C2×C4⋊C4—21no—
489C2×C4⋊C4—21no—
490C2×C4⋊C4—24no—
491C2×C4⋊C4C23×C1112yes—
492C2×C4⋊C4C23×C1111yescharacteristic
493C2×C4⋊C4C23×C1111yescharacteristic
494C2×C22⋊C4—28no—
495C2×C22⋊C4—22no—
496C2×C22⋊C4—22no—
497C2×C22⋊C4—21no—
498C2×C22⋊C4—21no—
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—21no—
502C2×C42—21no—
503#103—24no—
504#103—24no—
505#103—24no—
506#102—24no—
507C22⋊C8—22no—
508C22⋊C8—22no—
509C22⋊C8—24no—
510C22⋊C8—42no—
511C2×C11—24no—
512C2×C11—42no—
513C2×C11—42no—
514C2×C11—82no—
515C2×C11#240311yescharacteristic
516C2×C11C2×#45211yescharacteristic
517C2×C11#300211yescharacteristic
518C2×C11#300411yescharacteristic
519C2×C11#300711yescharacteristic
520C2×C11#319011yescharacteristic
521C2×C11#319611yescharacteristic
522C24—22no—
523C24—22no—
524C24—22no—
525C24—22no—
526C24—22no—
527C24—21no—
528C24—41no—
529C24—41no—
530C24C2×D4×C1111yescharacteristic
531C24C2×D4×C1111yescharacteristic
532C24C2×D4×C1111yescharacteristic
533#41—48no—
534#41—48no—
535C2×Q8—24no—
536C2×Q8—22no—
537C2×Q8—21no—
538C2×Q8—22no—
539C2×Q8—22no—
540C2×Q8—22no—
541C2×Q8—22no—
542C2×Q8—22no—
543C2×Q8—22no—
544C2×Q8—48no—
545C2×Q8—48no—
546C2×Q8—42no—
547C2×Q8—42no—
548C2×Q8C2×D4×C1112yes—
549C2×Q8C2×D4×C1114yes—
550C2×D4—24no—
551C2×D4—24no—
552C2×D4—24no—
553C2×D4—22no—
554C2×D4—21no—
555C2×D4—22no—
556C2×D4—42no—
557C2×D4—42no—
558C2×D4—42no—
559C2×D4—42no—
560C2×D4—42no—
561C2×D4—42no—
562C2×D4C2×D4×C1112yes—
563C22×C4—22no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—24no—
569C22×C4—24no—
570C22×C4—24no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—22no—
576C22×C4—21no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—41no—
587C22×C4—41no—
588C22×C4—41no—
589C22×C4—48no—
590C22×C4—48no—
591C22×C4—42no—
592C22×C4—42no—
593C22×C4—42no—
594C22×C4—42no—
595C22×C4—42no—
596C22×C4—42no—
597C22×C4C2×D4×C1111yescharacteristic
598C22×C4C2×D4×C1111yescharacteristic
599C22×C4C2×D4×C1111yescharacteristic
600C22×C4C2×D4×C1112yes—
601C22×C4C2×D4×C1112yes—
602C22×C4C2×D4×C1114yes—
603C22×C4C24×C1111yescharacteristic
604Q16—48no—
605SD16—48no—
606C2×C8—22no—
607C2×C8—22no—
608C2×C8—22no—
609C2×C8—22no—
610C2×C8—22no—
611C2×C8—22no—
612C4⋊C4—24no—
613C4⋊C4—28no—
614C4⋊C4—24no—
615C4⋊C4—28no—
616C4⋊C4—24no—
617C4⋊C4—22no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4C2×D4×C1114yes—
621C4⋊C4C2×D4×C1112yes—
622C4⋊C4C2×D4×C1112yes—
623C22⋊C4—28no—
624C22⋊C4—24no—
625C22⋊C4—24no—
626C22⋊C4—24no—
627C22⋊C4—28no—
628C22⋊C4—24no—
629C22⋊C4—24no—
630C42—24no—
631C11#2392211yescharacteristic, direct product factor, Sylow
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—28no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—22no—
650C23—44no—
651C23—44no—
652C23—44no—
653C23—44no—
654C23—44no—
655C23—44no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23C11×#12012yes—
663C23C11×#12012yes—
664C23C11×#13512yes—
665C23C11×#13712yes—
666C23C11×#13712yes—
667C23C22×D4×C1111yescharacteristic
668Q8—24no—
669Q8—24no—
670Q8—24no—
671Q8—48no—
672Q8—42no—
673Q8—42no—
674Q8—42no—
675D4—24no—
676D4—48no—
677D4—48no—
678D4—48no—
679D4—42no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—24no—
685C2×C4—24no—
686C2×C4—24no—
687C2×C4—24no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—24no—
691C2×C4—21no—
692C2×C4—22no—
693C2×C4—24no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—44no—
697C2×C4—44no—
698C2×C4—44no—
699C2×C4—48no—
700C2×C4—48no—
701C2×C4—48no—
702C2×C4—41no—
703C2×C4—42no—
704C2×C4—41no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—42no—
711C2×C4—41no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4C11×#12012yes—
715C2×C4C11×#12012yes—
716C2×C4C22×D4×C1112yes—
717C2×C4C22×D4×C1111yescharacteristic
718C2×C4C22×D4×C1111yescharacteristic
719C2×C4C11×H(5,𝔽2)12yes—
720C8—42no—
721C8—42no—
722C22—22no—
723C22—22no—
724C22—22no—
725C22—22no—
726C22—22no—
727C22—22no—
728C22—22no—
729C22—22no—
730C22—22no—
731C22—22no—
732C22—22no—
733C22—22no—
734C22—416no—
735C22—41no—
736C22—41no—
737C22—41no—
738C22—41no—
739C22—41no—
740C22—41no—
741C22—41no—
742C22—41no—
743C22—42no—
744C22—42no—
745C22—42no—
746C22—81no—
747C22—81no—
748C22—81no—
749C22—81no—
750C22C11×#45214yescomplemented
751C22C2×C11×#12011yescharacteristic
752C22C2×C11×#12011yescharacteristic
753C22C11×#53411yescharacteristic
754C22C2×C11×#13511yescharacteristic
755C22C2×C11×#13711yescharacteristic
756C22C2×C11×#13711yescharacteristic
757C22C11×#57511yescharacteristic
758C4—22no—
759C4—22no—
760C4—41no—
761C4—42no—
762C4—44no—
763C4—42no—
764C4—44no—
765C4—42no—
766C4D42×C1112yes—
767C4D42×C1112yes—
768C2—24no—
769C2—42no—
770C2—42no—
771C2—82no—
772C2C11×#240311yescharacteristic
773C2C2×C11×#45211yescharacteristic
774C2C11×#300211yescharacteristic
775C2C11×#300411yescharacteristic
776C2C11×#300711yescharacteristic
777C2C11×#319011yescharacteristic
778C2C11×#319611yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#525C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C24×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×C11×C22⋊Q8C2semidirect
3. C2×C11×#452C2semidirect
4. C2×C11×#451C2semidirect
5. C2×C11×#448C2semidirect
6. C11×#2001C2semidirect
7. C11×#2000C2semidirect
8. C11×#1874C2semidirect
9. C11×#1873C2semidirect
10. C11×#1872C2semidirect
11. C11×#1779C2semidirect
15. C22×C11×Q16C22semidirect
16. C22×C11×SD16C22semidirect
39. C2×C11×#103C22semidirect
40. C2×C11×#103C22semidirect
41. C2×C11×#103C22semidirect
42. C2×C11×#102C22semidirect
47. C11×#340C22semidirect
48. C11×#340C22semidirect
96. C11×C22⋊Q8D4semidirect
133. #23922C11direct (N × H)
244. C22×C22⋊Q8C2×C11semidirect
245. C2×#452C2×C11semidirect
246. C2×#451C2×C11semidirect
247. C2×#448C2×C11semidirect
248. #2001C2×C11semidirect
249. #2000C2×C11semidirect
250. #1874C2×C11semidirect
251. #1873C2×C11semidirect
252. #1872C2×C11semidirect
253. #1779C2×C11semidirect
347. C22×Q16C22×C11semidirect
348. C22×SD16C22×C11semidirect
371. C2×#103C22×C11semidirect
372. C2×#103C22×C11semidirect
373. C2×#103C22×C11semidirect
374. C2×#102C22×C11semidirect
379. #340C22×C11semidirect
380. #340C22×C11semidirect
409. C22×C11#452semidirect
474. C22⋊Q8D4×C11semidirect
631. C11#23922direct (N × H)
750. C22C11×#452semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#5252
C22×C11×C22⋊Q82
C2×C11×#4522
C2×C11×#4512
C2×C11×#4482
C11×#20012
C11×#20002
C11×#18742
C11×#18732
C11×#18722
C11×#17792
#2392211