Finite Group Databasebeta

← C11×#24364 #14601557

Subgroups — C11×#24364 #14601557

Order 2816.

1512 conjugacy classes of subgroups.

The subgroup lattice has 902 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×#135C211yesmaximal, characteristic, complemented
2C2×C11×#463C211yesmaximal, characteristic, complemented
3C2×C11×#459C211yesmaximal, characteristic, complemented
4C2×C11×#449C211yesmaximal, characteristic, complemented
5C11×#2431C211yesmaximal, characteristic, complemented
6C11×#2339C211yesmaximal, characteristic, complemented
7C11×#2056C211yesmaximal, characteristic, complemented
8C11×#2055C211yesmaximal, characteristic, complemented
9C11×#2015C211yesmaximal, characteristic, complemented
10C11×#2014C211yesmaximal, characteristic, complemented
11C11×#1893C211yesmaximal, characteristic, complemented
12C11×#1879C211yesmaximal, characteristic, complemented
13C11×#1877C211yesmaximal, characteristic, complemented
14C11×#1850C211yesmaximal, characteristic, complemented
15C11×#1788C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic
17C22×C11×#41C2211yescharacteristic
18C2×C11×#135—24no—
19C2×C11×#135—24no—
20C2×C11×#135—24no—
21C22×C11×Q16C2211yescharacteristic
22C22×C11×SD16C2211yescharacteristic
23C22×C11×SD16C2211yescharacteristic
24C22×C11×SD16C2211yescharacteristic
25C22×C11×D8C2211yescharacteristic
26C22×C11×D8C2211yescharacteristic
27C23×C8×C11C2211yescharacteristic
28C2×C11×#127C2211yescharacteristic
29C2×C11×#124C2211yescharacteristic
30C2×C11×#121C2211yescharacteristic
31C2×C4×D4×C11C2211yescharacteristic
32C2×C4×D4×C11C2211yescharacteristic
33C11×#463—24no—
34C11×#459—24no—
35C11×#449—24no—
36C2×C11×C4⋊C8C2211yescharacteristic
37C2×C11×C4⋊C8C2211yescharacteristic
38C2×C11×#103C2211yescharacteristic
39C2×C11×#103C2211yescharacteristic
40C2×C11×#103C2211yescharacteristic
41C2×C11×#102C2211yescharacteristic
42C2×C11×#102C2211yescharacteristic
43C2×C11×#102C2211yescharacteristic
44C2×C11×#102C2211yescharacteristic
45C2×C11×#102C2211yescharacteristic
46C2×C11×C22⋊C8C2211yescharacteristic
47C11×#392—21no—
48C11×#392—21no—
49C11×#391C2211yescharacteristic
50C11×#391C2211yescharacteristic
51C11×#391C2211yescharacteristic
52C11×#390C2211yescharacteristic
53C11×#386—21no—
54C11×#386—21no—
55C11×#386—21no—
56C11×#386—21no—
57C11×#381—21no—
58C11×#380C2211yescharacteristic
59C4×C11×C22⋊C4C2211yescharacteristic
60C2×C11×#95—21no—
61C11×#340C2211yescharacteristic
62C11×#340C2211yescharacteristic
63C11×#336C2211yescharacteristic
64C11×#336C2211yescharacteristic
65C2×C11×#41—22no—
66C2×C11×#41—22no—
67C2×C11×#41—22no—
68C2×C11×#41—22no—
69C2×C11×#41—22no—
70C2×C11×#41—22no—
71C2×C11×#41—22no—
72C2×C11×#41—41no—
73C2×C11×#41—41no—
74C2×C11×#41—41no—
75C2×C11×#41—41no—
76C2×C11×#41D414yescomplemented
77C22×Q8×C11C2311yescharacteristic
78C22×Q8×C11C2311yescharacteristic
79C22×D4×C11—21no—
80C22×D4×C11—21no—
81C22×D4×C11—21no—
82C22×D4×C11—21no—
83C22×D4×C11—21no—
84C22×D4×C11C2311yescharacteristic
85C22×D4×C11C2311yescharacteristic
86C22×D4×C11C2311yescharacteristic
87C23×C4×C11—21no—
88C23×C4×C11—21no—
89C23×C4×C11—21no—
90C23×C4×C11—21no—
91C23×C4×C11C2311yescharacteristic
92C11×#135—232no—
93C2×C11×Q16—22no—
94C2×C11×Q16—22no—
95C2×C11×Q16—22no—
96C2×C11×SD16—22no—
97C2×C11×SD16—22no—
98C2×C11×SD16—22no—
99C2×C11×SD16—22no—
100C2×C11×SD16—22no—
101C2×C11×SD16—22no—
102C2×C11×SD16—41no—
103C2×C11×SD16—41no—
104C2×C11×SD16D414yescomplemented
105C2×C11×D8—22no—
106C2×C11×D8—22no—
107C2×C11×D8—22no—
108C2×C11×D8—22no—
109C2×C11×D8—22no—
110C2×C11×D8D414yescomplemented
111C22×C8×C11—22no—
112C22×C8×C11—22no—
113C22×C8×C11—22no—
114C22×C8×C11C2311yescharacteristic
115C22×C8×C11C2311yescharacteristic
116C22×C8×C11C2311yescharacteristic
117C22×C8×C11C2311yescharacteristic
118C11×#127—22no—
119C11×#127—41no—
120C11×#124—22no—
121C11×#124—41no—
122C11×#121—22no—
123C11×#121—22no—
124C4×D4×C11—22no—
125C4×D4×C11—22no—
126C4×D4×C11—41no—
127C4×D4×C11—41no—
128C2×C11×C4⋊C4C2311yescharacteristic
129C2×C11×C4⋊C4C2311yescharacteristic
130C2×C11×C4⋊C4C2311yescharacteristic
131C2×C11×C22⋊C4—21no—
132C2×C11×C22⋊C4—21no—
133C2×C11×C22⋊C4—21no—
134C2×C11×C22⋊C4—21no—
135C2×C11×C22⋊C4—21no—
136C2×C11×C22⋊C4—21no—
137C2×C11×C22⋊C4—21no—
138C2×C11×C22⋊C4—21no—
139C2×C11×C22⋊C4D411yescharacteristic
140C2×C11×C22⋊C4D411yescharacteristic
141C2×C42×C11C2311yescharacteristic
142C2×C42×C11C2311yescharacteristic
143C11×C4⋊C8—22no—
144C11×C4⋊C8—22no—
145C11×#103—22no—
146C11×#103—22no—
147C11×#103—41no—
148C11×#102—22no—
149C11×#102—22no—
150C11×#102—22no—
151C11×#102—22no—
152C11×#102—41no—
153C11×C22⋊C8—22no—
154C11×#95—21no—
155C11×#95—21no—
156C11×#95—21no—
157C11×#95—21no—
158C11×#95—21no—
159C11×#95—21no—
160C11×#95—21no—
161C11×#95D411yescharacteristic
162C11×#95D411yescharacteristic
163#24364C1111yesmaximal, characteristic, direct product factor, Sylow
164C24×C11—21no—
165C24×C11—21no—
166C24×C11—21no—
167C24×C11C2×D411yescharacteristic
168C11×#41—28no—
169C11×#41—28no—
170C11×#41—44no—
171C11×#41—44no—
172C11×#41—44no—
173C11×#41—44no—
174C11×#41—44no—
175C11×#41—44no—
176C2×Q8×C11—21no—
177C2×Q8×C11—21no—
178C2×Q8×C11—21no—
179C2×Q8×C11—21no—
180C2×Q8×C11—21no—
181C2×Q8×C11—21no—
182C2×Q8×C11—21no—
183C2×Q8×C11—21no—
184C2×Q8×C11—21no—
185C2×Q8×C11—21no—
186C2×Q8×C11C2×D412yes—
187C2×Q8×C11C2×D412yes—
188C2×D4×C11—24no—
189C2×D4×C11—21no—
190C2×D4×C11—21no—
191C2×D4×C11—21no—
192C2×D4×C11—21no—
193C2×D4×C11—21no—
194C2×D4×C11—21no—
195C2×D4×C11—21no—
196C2×D4×C11—21no—
197C2×D4×C11—21no—
198C2×D4×C11—21no—
199C2×D4×C11—21no—
200C2×D4×C11—21no—
201C2×D4×C11—21no—
202C2×D4×C11—21no—
203C2×D4×C11—42no—
204C2×D4×C11—42no—
205C2×D4×C11—42no—
206C2×D4×C11—42no—
207C2×D4×C11—42no—
208C2×D4×C11—42no—
209C2×D4×C11—42no—
210C2×D4×C11—42no—
211C2×D4×C11—42no—
212C2×D4×C11—42no—
213C2×D4×C11—81no—
214C2×D4×C11—81no—
215C2×D4×C11—81no—
216C2×D4×C11—81no—
217C2×D4×C11C2×D412yes—
218C2×D4×C11C2×D412yes—
219C2×D4×C11C2×D412yes—
220C2×D4×C11C2×D412yes—
221C22×C4×C11—21no—
222C22×C4×C11—21no—
223C22×C4×C11—21no—
224C22×C4×C11—21no—
225C22×C4×C11—21no—
226C22×C4×C11—21no—
227C22×C4×C11—24no—
228C22×C4×C11—21no—
229C22×C4×C11—21no—
230C22×C4×C11—21no—
231C22×C4×C11—42no—
232C22×C4×C11—42no—
233C22×C4×C11—42no—
234C22×C4×C11—42no—
235C22×C4×C11—42no—
236C22×C4×C11—42no—
237C22×C4×C11—42no—
238C22×C4×C11—42no—
239C22×C4×C11—42no—
240C22×C4×C11—81no—
241C22×C4×C11—81no—
242C22×C4×C11C2×D411yescharacteristic
243C22×C4×C11C2×D411yescharacteristic
244C22×C4×C11C2×D411yescharacteristic
245C22×C4×C11C2×D411yescharacteristic
246C22×C4×C11C2×D412yes—
247C22×C4×C11C2×D411yescharacteristic
248C22×C4×C11#4112yes—
249C22×C4×C11C2411yescharacteristic
250C11×Q16—28no—
251C11×SD16—28no—
252C11×SD16—28no—
253C11×SD16—44no—
254C11×D8—28no—
255C11×D8—44no—
256C2×C8×C11—28no—
257C2×C8×C11—21no—
258C2×C8×C11—21no—
259C2×C8×C11—21no—
260C2×C8×C11—21no—
261C2×C8×C11—21no—
262C2×C8×C11—21no—
263C2×C8×C11—21no—
264C2×C8×C11—21no—
265C2×C8×C11—21no—
266C2×C8×C11—21no—
267C2×C8×C11C2×D412yes—
268C2×C8×C11C2×D412yes—
269C11×C4⋊C4—21no—
270C11×C4⋊C4—21no—
271C11×C4⋊C4—21no—
272C11×C4⋊C4—21no—
273C11×C4⋊C4—21no—
274C11×C4⋊C4—21no—
275C11×C22⋊C4—22no—
276C11×C22⋊C4—41no—
277C11×C22⋊C4—42no—
278C11×C22⋊C4—42no—
279C11×C22⋊C4—42no—
280C11×C22⋊C4—42no—
281C11×C22⋊C4—42no—
282C11×C22⋊C4—81no—
283C11×C22⋊C4—81no—
284C11×C22⋊C4—81no—
285C42×C11—21no—
286C42×C11—21no—
287C42×C11—21no—
288C42×C11—21no—
289C22×#135C2×C1111yescharacteristic, complemented
290C2×#463C2×C1111yescharacteristic, complemented
291C2×#459C2×C1111yescharacteristic, complemented
292C2×#449C2×C1111yescharacteristic, complemented
293#2431C2×C1111yescharacteristic, complemented
294#2339C2×C1111yescharacteristic, complemented
295#2056C2×C1111yescharacteristic, complemented
296#2055C2×C1111yescharacteristic, complemented
297#2015C2×C1111yescharacteristic, complemented
298#2014C2×C1111yescharacteristic, complemented
299#1893C2×C1111yescharacteristic, complemented
300#1879C2×C1111yescharacteristic, complemented
301#1877C2×C1111yescharacteristic, complemented
302#1850C2×C1111yescharacteristic, complemented
303#1788C2×C1111yescharacteristic, complemented
304C23×C11—22no—
305C23×C11—22no—
306C23×C11—22no—
307C23×C11—21no—
308C23×C11—21no—
309C23×C11—21no—
310C23×C11—21no—
311C23×C11—21no—
312C23×C11—21no—
313C23×C11—22no—
314C23×C11—41no—
315C23×C11—41no—
316C23×C11—41no—
317C23×C11—41no—
318C23×C11—41no—
319C23×C11—41no—
320C23×C11—41no—
321C23×C11—41no—
322C23×C11—41no—
323C23×C11—41no—
324C23×C11—41no—
325C23×C11—41no—
326C23×C11—41no—
327C23×C11—41no—
328C23×C11—41no—
329C23×C11—41no—
330C23×C11—41no—
331C23×C11#12112yes—
332C23×C11C22×D411yescharacteristic
333Q8×C11—22no—
334Q8×C11—22no—
335Q8×C11—22no—
336Q8×C11—22no—
337Q8×C11—41no—
338Q8×C11—41no—
339Q8×C11—41no—
340Q8×C11—41no—
341D4×C11—22no—
342D4×C11—22no—
343D4×C11—22no—
344D4×C11—22no—
345D4×C11—22no—
346D4×C11—48no—
347D4×C11—48no—
348D4×C11—41no—
349D4×C11—41no—
350D4×C11—41no—
351D4×C11—41no—
352D4×C11—41no—
353D4×C11—41no—
354D4×C11—84no—
355D4×C11—84no—
356D4×C11—84no—
357D4×C11#12014yes—
358C2×C4×C11—21no—
359C2×C4×C11—21no—
360C2×C4×C11—21no—
361C2×C4×C11—21no—
362C2×C4×C11—22no—
363C2×C4×C11—22no—
364C2×C4×C11—22no—
365C2×C4×C11—22no—
366C2×C4×C11—22no—
367C2×C4×C11—21no—
368C2×C4×C11—21no—
369C2×C4×C11—21no—
370C2×C4×C11—22no—
371C2×C4×C11—21no—
372C2×C4×C11—21no—
373C2×C4×C11—21no—
374C2×C4×C11—21no—
375C2×C4×C11—21no—
376C2×C4×C11—21no—
377C2×C4×C11—48no—
378C2×C4×C11—48no—
379C2×C4×C11—41no—
380C2×C4×C11—41no—
381C2×C4×C11—41no—
382C2×C4×C11—41no—
383C2×C4×C11—41no—
384C2×C4×C11—41no—
385C2×C4×C11—41no—
386C2×C4×C11—41no—
387C2×C4×C11—41no—
388C2×C4×C11—41no—
389C2×C4×C11—41no—
390C2×C4×C11—41no—
391C2×C4×C11—41no—
392C2×C4×C11—84no—
393C2×C4×C11—84no—
394C2×C4×C11#12112yes—
395C2×C4×C11#13512yescomplemented
396C2×C4×C11C22×D411yescharacteristic
397C2×C4×C11C22×D411yescharacteristic
398C2×C4×C11C22×D411yescharacteristic
399C2×C4×C11C2×#4111yescharacteristic
400C2×C4×C11H(5,𝔽2)11yescharacteristic
401C2×C4×C11H(5,𝔽2)11yescharacteristic
402C8×C11—22no—
403C8×C11—22no—
404C8×C11—41no—
405C8×C11—41no—
406C22×#41C22×C1111yescharacteristic
407C22×#41C22×C1111yescharacteristic
408C2×#135—24no—
409C2×#135—24no—
410C2×#135—24no—
411C22×Q16C22×C1111yescharacteristic
412C22×SD16C22×C1111yescharacteristic
413C22×SD16C22×C1111yescharacteristic
414C22×SD16C22×C1111yescharacteristic
415C22×D8C22×C1111yescharacteristic
416C22×D8C22×C1111yescharacteristic
417C23×C8C22×C1111yescharacteristic
418C2×#127C22×C1111yescharacteristic
419C2×#124C22×C1111yescharacteristic
420C2×#121C22×C1111yescharacteristic
421C2×C4×D4C22×C1111yescharacteristic
422C2×C4×D4C22×C1111yescharacteristic
423#463—24no—
424#459—24no—
425#449—24no—
426C2×C4⋊C8C22×C1111yescharacteristic
427C2×C4⋊C8C22×C1111yescharacteristic
428C2×#103C22×C1111yescharacteristic
429C2×#103C22×C1111yescharacteristic
430C2×#103C22×C1111yescharacteristic
431C2×#102C22×C1111yescharacteristic
432C2×#102C22×C1111yescharacteristic
433C2×#102C22×C1111yescharacteristic
434C2×#102C22×C1111yescharacteristic
435C2×#102C22×C1111yescharacteristic
436C2×C22⋊C8C22×C1111yescharacteristic
437#392—21no—
438#392—21no—
439#391C22×C1111yescharacteristic
440#391C22×C1111yescharacteristic
441#391C22×C1111yescharacteristic
442#390C22×C1111yescharacteristic
443#386—21no—
444#386—21no—
445#386—21no—
446#386—21no—
447#381—21no—
448#380C22×C1111yescharacteristic
449C4×C22⋊C4C22×C1111yescharacteristic
450C2×#95—21no—
451#340C22×C1111yescharacteristic
452#340C22×C1111yescharacteristic
453#336C22×C1111yescharacteristic
454#336C22×C1111yescharacteristic
455C22×C11—22no—
456C22×C11—24no—
457C22×C11—22no—
458C22×C11—22no—
459C22×C11—41no—
460C22×C11—42no—
461C22×C11—42no—
462C22×C11—41no—
463C22×C11—42no—
464C22×C11—41no—
465C22×C11—41no—
466C22×C11—42no—
467C22×C11—42no—
468C22×C11—42no—
469C22×C11—42no—
470C22×C11—42no—
471C22×C11—42no—
472C22×C11—81no—
473C22×C11—81no—
474C22×C11—81no—
475C22×C11—81no—
476C22×C11—81no—
477C22×C11—81no—
478C22×C11—81no—
479C22×C11—81no—
480C22×C11—81no—
481C22×C11—81no—
482C22×C11—81no—
483C22×C11C2×#12111yescharacteristic
484C22×C11D4211yescharacteristic
485C22×C11D4211yescharacteristic
486C22×C11C2×#13511yescharacteristic
487C22×C11#57511yescharacteristic
488C22×C11#57611yescharacteristic
489C22×C11#57711yescharacteristic
490C4×C11—22no—
491C4×C11—22no—
492C4×C11—42no—
493C4×C11—42no—
494C4×C11—41no—
495C4×C11—41no—
496C4×C11—41no—
497C4×C11—81no—
498C4×C11—81no—
499C4×C11—81no—
500C4×C11C2×#12011yescharacteristic
501C4×C11#53411yescharacteristic
502C4×C11#54611yescharacteristic
503C4×C11#54611yescharacteristic
504C2×#41—22no—
505C2×#41—22no—
506C2×#41—22no—
507C2×#41—22no—
508C2×#41—22no—
509C2×#41—22no—
510C2×#41—22no—
511C2×#41—41no—
512C2×#41—41no—
513C2×#41—41no—
514C2×#41—41no—
515C2×#41D4×C1114yescomplemented
516C22×Q8C23×C1111yescharacteristic
517C22×Q8C23×C1111yescharacteristic
518C22×D4—21no—
519C22×D4—21no—
520C22×D4—21no—
521C22×D4—21no—
522C22×D4—21no—
523C22×D4C23×C1111yescharacteristic
524C22×D4C23×C1111yescharacteristic
525C22×D4C23×C1111yescharacteristic
526C23×C4—21no—
527C23×C4—21no—
528C23×C4—21no—
529C23×C4—21no—
530C23×C4C23×C1111yescharacteristic
531#135—232no—
532C2×Q16—22no—
533C2×Q16—22no—
534C2×Q16—22no—
535C2×SD16—22no—
536C2×SD16—22no—
537C2×SD16—22no—
538C2×SD16—22no—
539C2×SD16—22no—
540C2×SD16—22no—
541C2×SD16—41no—
542C2×SD16—41no—
543C2×SD16D4×C1114yescomplemented
544C2×D8—22no—
545C2×D8—22no—
546C2×D8—22no—
547C2×D8—22no—
548C2×D8—22no—
549C2×D8D4×C1114yescomplemented
550C22×C8—22no—
551C22×C8—22no—
552C22×C8—22no—
553C22×C8C23×C1111yescharacteristic
554C22×C8C23×C1111yescharacteristic
555C22×C8C23×C1111yescharacteristic
556C22×C8C23×C1111yescharacteristic
557#127—22no—
558#127—41no—
559#124—22no—
560#124—41no—
561#121—22no—
562#121—22no—
563C4×D4—22no—
564C4×D4—22no—
565C4×D4—41no—
566C4×D4—41no—
567C2×C4⋊C4C23×C1111yescharacteristic
568C2×C4⋊C4C23×C1111yescharacteristic
569C2×C4⋊C4C23×C1111yescharacteristic
570C2×C22⋊C4—21no—
571C2×C22⋊C4—21no—
572C2×C22⋊C4—21no—
573C2×C22⋊C4—21no—
574C2×C22⋊C4—21no—
575C2×C22⋊C4—21no—
576C2×C22⋊C4—21no—
577C2×C22⋊C4—21no—
578C2×C22⋊C4D4×C1111yescharacteristic
579C2×C22⋊C4D4×C1111yescharacteristic
580C2×C42C23×C1111yescharacteristic
581C2×C42C23×C1111yescharacteristic
582C4⋊C8—22no—
583C4⋊C8—22no—
584#103—22no—
585#103—22no—
586#103—41no—
587#102—22no—
588#102—22no—
589#102—22no—
590#102—22no—
591#102—41no—
592C22⋊C8—22no—
593#95—21no—
594#95—21no—
595#95—21no—
596#95—21no—
597#95—21no—
598#95—21no—
599#95—21no—
600#95D4×C1111yescharacteristic
601#95D4×C1111yescharacteristic
602C2×C11—42no—
603C2×C11—44no—
604C2×C11—82no—
605C2×C11—161no—
606C2×C11#241011yescharacteristic
607C2×C11#303511yescharacteristic
608C2×C11#304511yescharacteristic
609C2×C11#326711yescharacteristic
610C2×C11#326811yescharacteristic
611C2×C11#328011yescharacteristic
612C2×C11#328411yescharacteristic
613C24—21no—
614C24—21no—
615C24—21no—
616C24C2×D4×C1111yescharacteristic
617#41—28no—
618#41—28no—
619#41—44no—
620#41—44no—
621#41—44no—
622#41—44no—
623#41—44no—
624#41—44no—
625C2×Q8—21no—
626C2×Q8—21no—
627C2×Q8—21no—
628C2×Q8—21no—
629C2×Q8—21no—
630C2×Q8—21no—
631C2×Q8—21no—
632C2×Q8—21no—
633C2×Q8—21no—
634C2×Q8—21no—
635C2×Q8C2×D4×C1112yes—
636C2×Q8C2×D4×C1112yes—
637C2×D4—24no—
638C2×D4—21no—
639C2×D4—21no—
640C2×D4—21no—
641C2×D4—21no—
642C2×D4—21no—
643C2×D4—21no—
644C2×D4—21no—
645C2×D4—21no—
646C2×D4—21no—
647C2×D4—21no—
648C2×D4—21no—
649C2×D4—21no—
650C2×D4—21no—
651C2×D4—21no—
652C2×D4—42no—
653C2×D4—42no—
654C2×D4—42no—
655C2×D4—42no—
656C2×D4—42no—
657C2×D4—42no—
658C2×D4—42no—
659C2×D4—42no—
660C2×D4—42no—
661C2×D4—42no—
662C2×D4—81no—
663C2×D4—81no—
664C2×D4—81no—
665C2×D4—81no—
666C2×D4C2×D4×C1112yes—
667C2×D4C2×D4×C1112yes—
668C2×D4C2×D4×C1112yes—
669C2×D4C2×D4×C1112yes—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—24no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—42no—
681C22×C4—42no—
682C22×C4—42no—
683C22×C4—42no—
684C22×C4—42no—
685C22×C4—42no—
686C22×C4—42no—
687C22×C4—42no—
688C22×C4—42no—
689C22×C4—81no—
690C22×C4—81no—
691C22×C4C2×D4×C1111yescharacteristic
692C22×C4C2×D4×C1111yescharacteristic
693C22×C4C2×D4×C1111yescharacteristic
694C22×C4C2×D4×C1111yescharacteristic
695C22×C4C2×D4×C1112yes—
696C22×C4C2×D4×C1111yescharacteristic
697C22×C4C11×#4112yes—
698C22×C4C24×C1111yescharacteristic
699Q16—28no—
700SD16—28no—
701SD16—28no—
702SD16—44no—
703D8—28no—
704D8—44no—
705C2×C8—28no—
706C2×C8—21no—
707C2×C8—21no—
708C2×C8—21no—
709C2×C8—21no—
710C2×C8—21no—
711C2×C8—21no—
712C2×C8—21no—
713C2×C8—21no—
714C2×C8—21no—
715C2×C8—21no—
716C2×C8C2×D4×C1112yes—
717C2×C8C2×D4×C1112yes—
718C4⋊C4—21no—
719C4⋊C4—21no—
720C4⋊C4—21no—
721C4⋊C4—21no—
722C4⋊C4—21no—
723C4⋊C4—21no—
724C22⋊C4—22no—
725C22⋊C4—41no—
726C22⋊C4—42no—
727C22⋊C4—42no—
728C22⋊C4—42no—
729C22⋊C4—42no—
730C22⋊C4—42no—
731C22⋊C4—81no—
732C22⋊C4—81no—
733C22⋊C4—81no—
734C42—21no—
735C42—21no—
736C42—21no—
737C42—21no—
738C11#2436411yescharacteristic, direct product factor, Sylow
739C23—22no—
740C23—22no—
741C23—22no—
742C23—21no—
743C23—21no—
744C23—21no—
745C23—21no—
746C23—21no—
747C23—21no—
748C23—22no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23—41no—
754C23—41no—
755C23—41no—
756C23—41no—
757C23—41no—
758C23—41no—
759C23—41no—
760C23—41no—
761C23—41no—
762C23—41no—
763C23—41no—
764C23—41no—
765C23—41no—
766C23C11×#12112yes—
767C23C22×D4×C1111yescharacteristic
768Q8—22no—
769Q8—22no—
770Q8—22no—
771Q8—22no—
772Q8—41no—
773Q8—41no—
774Q8—41no—
775Q8—41no—
776D4—22no—
777D4—22no—
778D4—22no—
779D4—22no—
780D4—22no—
781D4—48no—
782D4—48no—
783D4—41no—
784D4—41no—
785D4—41no—
786D4—41no—
787D4—41no—
788D4—41no—
789D4—84no—
790D4—84no—
791D4—84no—
792D4C11×#12014yes—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—22no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—48no—
813C2×C4—48no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—84no—
828C2×C4—84no—
829C2×C4C11×#12112yes—
830C2×C4C11×#13512yescomplemented
831C2×C4C22×D4×C1111yescharacteristic
832C2×C4C22×D4×C1111yescharacteristic
833C2×C4C22×D4×C1111yescharacteristic
834C2×C4C2×C11×#4111yescharacteristic
835C2×C4C11×H(5,𝔽2)11yescharacteristic
836C2×C4C11×H(5,𝔽2)11yescharacteristic
837C8—22no—
838C8—22no—
839C8—41no—
840C8—41no—
841C22—22no—
842C22—24no—
843C22—22no—
844C22—22no—
845C22—41no—
846C22—42no—
847C22—42no—
848C22—41no—
849C22—42no—
850C22—41no—
851C22—41no—
852C22—42no—
853C22—42no—
854C22—42no—
855C22—42no—
856C22—42no—
857C22—42no—
858C22—81no—
859C22—81no—
860C22—81no—
861C22—81no—
862C22—81no—
863C22—81no—
864C22—81no—
865C22—81no—
866C22—81no—
867C22—81no—
868C22—81no—
869C22C2×C11×#12111yescharacteristic
870C22D42×C1111yescharacteristic
871C22D42×C1111yescharacteristic
872C22C2×C11×#13511yescharacteristic
873C22C11×#57511yescharacteristic
874C22C11×#57611yescharacteristic
875C22C11×#57711yescharacteristic
876C4—22no—
877C4—22no—
878C4—42no—
879C4—42no—
880C4—41no—
881C4—41no—
882C4—41no—
883C4—81no—
884C4—81no—
885C4—81no—
886C4C2×C11×#12011yescharacteristic
887C4C11×#53411yescharacteristic
888C4C11×#54611yescharacteristic
889C4C11×#54611yescharacteristic
890C2—42no—
891C2—44no—
892C2—82no—
893C2—161no—
894C2C11×#241011yescharacteristic
895C2C11×#303511yescharacteristic
896C2C11×#304511yescharacteristic
897C2C11×#326711yescharacteristic
898C2C11×#326811yescharacteristic
899C2C11×#328011yescharacteristic
900C2C11×#328411yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C4×C11×C22⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C11×#135C2semidirect
2. C2×C11×#463C2semidirect
3. C2×C11×#459C2semidirect
4. C2×C11×#449C2semidirect
5. C11×#2431C2semidirect
6. C11×#2339C2semidirect
7. C11×#2056C2semidirect
8. C11×#2055C2semidirect
9. C11×#2015C2semidirect
10. C11×#2014C2semidirect
11. C11×#1893C2semidirect
12. C11×#1879C2semidirect
13. C11×#1877C2semidirect
14. C11×#1850C2semidirect
15. C11×#1788C2semidirect
76. C2×C11×#41D4semidirect
104. C2×C11×SD16D4semidirect
110. C2×C11×D8D4semidirect
163. #24364C11direct (N × H)
289. C22×#135C2×C11semidirect
290. C2×#463C2×C11semidirect
291. C2×#459C2×C11semidirect
292. C2×#449C2×C11semidirect
293. #2431C2×C11semidirect
294. #2339C2×C11semidirect
295. #2056C2×C11semidirect
296. #2055C2×C11semidirect
297. #2015C2×C11semidirect
298. #2014C2×C11semidirect
299. #1893C2×C11semidirect
300. #1879C2×C11semidirect
301. #1877C2×C11semidirect
302. #1850C2×C11semidirect
303. #1788C2×C11semidirect
395. C2×C4×C11#135semidirect
515. C2×#41D4×C11semidirect
543. C2×SD16D4×C11semidirect
549. C2×D8D4×C11semidirect
738. C11#24364direct (N × H)
830. C2×C4C11×#135semidirect

Maximal subgroups

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

subgroupindex
C22×C11×#1352
C2×C11×#4632
C2×C11×#4592
C2×C11×#4492
C11×#24312
C11×#23392
C11×#20562
C11×#20552
C11×#20152
C11×#20142
C11×#18932
C11×#18792
C11×#18772
C11×#18502
C11×#17882
#2436411