Finite Group Databasebeta

← C11×#23857 #14601050

Subgroups — C11×#23857 #14601050

Order 2816.

1852 conjugacy classes of subgroups.

The subgroup lattice has 1010 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×#135C211yesmaximal, characteristic, complemented
2C2×C11×#550C211yesmaximal, characteristic, complemented
3C2×C11×#452C211yesmaximal, characteristic, complemented
4C2×C11×#449C211yesmaximal, characteristic, complemented
5C2×C11×#449C211yesmaximal, characteristic, complemented
6C11×#2407C211yesmaximal, characteristic, complemented
7C11×#2014C211yesmaximal, characteristic, complemented
8C11×#2011C211yesmaximal, characteristic, complemented
9C11×#2000C211yesmaximal, characteristic, complemented
10C11×#1999C211yesmaximal, characteristic, complemented
11C11×#1893C211yesmaximal, characteristic, complemented
12C11×#1880C211yesmaximal, characteristic, complemented
13C11×#1878C211yesmaximal, characteristic, complemented
14C11×#1869C211yesmaximal, characteristic, complemented
15C11×#1788C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic
17C22×C11×#41C2211yescharacteristic
18C22×C11×#41C2211yescharacteristic
19C2×C11×#135—24no—
20C2×C11×#135—24no—
21C2×C11×#135—24no—
22C22×C11×Q16C2211yescharacteristic
23C22×C11×SD16C2211yescharacteristic
24C22×C11×SD16C2211yescharacteristic
25C22×C11×SD16C2211yescharacteristic
26C22×C11×D8C2211yescharacteristic
27C22×C11×D8C2211yescharacteristic
28C23×C8×C11C2211yescharacteristic
29C11×#550—24no—
30C11×#550—24no—
31C2×C11×#127—21no—
32C2×C11×#127C2211yescharacteristic
33C2×C11×C22⋊Q8C2211yescharacteristic
34C2×C11×#121—21no—
35C2×C11×#121—21no—
36C2×C11×#121C2211yescharacteristic
37C2×C11×#121C2211yescharacteristic
38C2×C11×#121C2211yescharacteristic
39C2×C4×Q8×C11C2211yescharacteristic
40C2×C4×D4×C11—21no—
41C2×C4×D4×C11C2211yescharacteristic
42C11×#452—24no—
43C11×#449—24no—
44C11×#449—24no—
45C2×C11×#103C2211yescharacteristic
46C2×C11×#103C2211yescharacteristic
47C2×C11×#103C2211yescharacteristic
48C2×C11×#102C2211yescharacteristic
49C2×C11×#102C2211yescharacteristic
50C2×C11×#102C2211yescharacteristic
51C2×C11×#102C2211yescharacteristic
52C2×C11×#102C2211yescharacteristic
53C2×C11×C22⋊C8C2211yescharacteristic
54C2×C11×C22⋊C8C2211yescharacteristic
55C2×C11×C22⋊C8C2211yescharacteristic
56C11×#394—21no—
57C11×#392—21no—
58C11×#391C2211yescharacteristic
59C11×#390C2211yescharacteristic
60C11×#386—21no—
61C11×#385—21no—
62C11×#380C2211yescharacteristic
63C11×#340C2211yescharacteristic
64C11×#340C2211yescharacteristic
65C11×#336C2211yescharacteristic
66C11×#336C2211yescharacteristic
67C2×C11×#41—22no—
68C2×C11×#41—22no—
69C2×C11×#41—22no—
70C2×C11×#41—22no—
71C2×C11×#41—22no—
72C2×C11×#41—22no—
73C2×C11×#41—22no—
74C2×C11×#41—22no—
75C2×C11×#41—22no—
76C2×C11×#41—22no—
77C2×C11×#41—22no—
78C2×C11×#41—41no—
79C2×C11×#41—41no—
80C2×C11×#41—41no—
81C2×C11×#41—41no—
82C2×C11×#41—41no—
83C2×C11×#41—41no—
84C2×C11×#41D414yescomplemented
85C22×Q8×C11C2311yescharacteristic
86C22×Q8×C11C2311yescharacteristic
87C22×D4×C11—21no—
88C22×D4×C11—21no—
89C22×D4×C11—21no—
90C22×D4×C11—21no—
91C22×D4×C11—21no—
92C22×D4×C11—21no—
93C22×D4×C11—21no—
94C22×D4×C11—21no—
95C22×D4×C11D411yescharacteristic
96C22×D4×C11C2311yescharacteristic
97C22×D4×C11C2311yescharacteristic
98C22×D4×C11C2311yescharacteristic
99C23×C4×C11—21no—
100C23×C4×C11—21no—
101C23×C4×C11—21no—
102C23×C4×C11C2311yescharacteristic
103C23×C4×C11C2311yescharacteristic
104C11×#135—232no—
105C2×C11×Q16—22no—
106C2×C11×Q16—22no—
107C2×C11×Q16D414yescomplemented
108C2×C11×SD16—22no—
109C2×C11×SD16—22no—
110C2×C11×SD16—22no—
111C2×C11×SD16—22no—
112C2×C11×SD16—22no—
113C2×C11×SD16—22no—
114C2×C11×SD16—22no—
115C2×C11×SD16—41no—
116C2×C11×SD16D414yescomplemented
117C2×C11×D8—22no—
118C2×C11×D8—22no—
119C2×C11×D8—22no—
120C2×C11×D8—22no—
121C2×C11×D8—22no—
122C2×C11×D8—41no—
123C22×C8×C11—22no—
124C22×C8×C11—22no—
125C22×C8×C11—22no—
126C22×C8×C11C2311yescharacteristic
127C22×C8×C11C2311yescharacteristic
128C22×C8×C11C2311yescharacteristic
129C22×C8×C11C2311yescharacteristic
130C11×#127—28no—
131C11×#127—22no—
132C11×#127—22no—
133C11×C22⋊Q8—22no—
134C11×C22⋊Q8—41no—
135C11×#121—28no—
136C11×#121—28no—
137C11×#121—22no—
138C11×#121—22no—
139C11×#121—22no—
140C11×#121—22no—
141C11×#121—41no—
142C11×#121D414yescomplemented
143C4×Q8×C11—22no—
144C4×Q8×C11—22no—
145C4×D4×C11—28no—
146C4×D4×C11—22no—
147C4×D4×C11—22no—
148C2×C11×C4⋊C4—21no—
149C2×C11×C4⋊C4—21no—
150C2×C11×C4⋊C4D411yescharacteristic
151C2×C11×C4⋊C4C2311yescharacteristic
152C2×C11×C4⋊C4C2311yescharacteristic
153C2×C11×C4⋊C4C2311yescharacteristic
154C2×C11×C22⋊C4—21no—
155C2×C11×C22⋊C4—21no—
156C2×C11×C22⋊C4—21no—
157C2×C11×C22⋊C4—21no—
158C2×C11×C22⋊C4—21no—
159C2×C11×C22⋊C4—21no—
160C2×C11×C22⋊C4—21no—
161C2×C11×C22⋊C4D411yescharacteristic
162C2×C11×C22⋊C4D411yescharacteristic
163C2×C42×C11—21no—
164C2×C42×C11C2311yescharacteristic
165C11×#103—22no—
166C11×#103—22no—
167C11×#103—22no—
168C11×#102—22no—
169C11×#102—22no—
170C11×#102—22no—
171C11×#102—41no—
172C11×#102—41no—
173C11×C22⋊C8—22no—
174C11×C22⋊C8—22no—
175C11×C22⋊C8—22no—
176C11×#95—21no—
177C11×#95—21no—
178C11×#95—21no—
179#23857C1111yesmaximal, characteristic, direct product factor, Sylow
180C24×C11—21no—
181C24×C11—21no—
182C24×C11—21no—
183C24×C11C2×D411yescharacteristic
184C24×C11C2×D411yescharacteristic
185C11×#41—28no—
186C11×#41—28no—
187C11×#41—44no—
188C11×#41—44no—
189C11×#41—44no—
190C11×#41—44no—
191C11×#41—44no—
192C11×#41—44no—
193C11×#41—44no—
194C11×#41—44no—
195C11×#41—44no—
196C11×#41—44no—
197C2×Q8×C11—21no—
198C2×Q8×C11—21no—
199C2×Q8×C11—21no—
200C2×Q8×C11—21no—
201C2×Q8×C11—21no—
202C2×Q8×C11—21no—
203C2×Q8×C11—21no—
204C2×Q8×C11—21no—
205C2×Q8×C11C2×D412yes—
206C2×Q8×C11C2×D412yes—
207C2×Q8×C11C2×D412yes—
208C2×Q8×C11C2×D412yes—
209C2×D4×C11—24no—
210C2×D4×C11—24no—
211C2×D4×C11—22no—
212C2×D4×C11—24no—
213C2×D4×C11—24no—
214C2×D4×C11—24no—
215C2×D4×C11—24no—
216C2×D4×C11—22no—
217C2×D4×C11—21no—
218C2×D4×C11—21no—
219C2×D4×C11—21no—
220C2×D4×C11—21no—
221C2×D4×C11—21no—
222C2×D4×C11—21no—
223C2×D4×C11—21no—
224C2×D4×C11—21no—
225C2×D4×C11—21no—
226C2×D4×C11—21no—
227C2×D4×C11—21no—
228C2×D4×C11—21no—
229C2×D4×C11—21no—
230C2×D4×C11—21no—
231C2×D4×C11—21no—
232C2×D4×C11—41no—
233C2×D4×C11—42no—
234C2×D4×C11—42no—
235C2×D4×C11—42no—
236C2×D4×C11—42no—
237C2×D4×C11—42no—
238C2×D4×C11—42no—
239C2×D4×C11—42no—
240C2×D4×C11—42no—
241C2×D4×C11—42no—
242C2×D4×C11—42no—
243C2×D4×C11—42no—
244C2×D4×C11—81no—
245C2×D4×C11—81no—
246C2×D4×C11—81no—
247C2×D4×C11—81no—
248C2×D4×C11—81no—
249C2×D4×C11—81no—
250C2×D4×C11—81no—
251C2×D4×C11C2×D412yes—
252C2×D4×C11C2×D412yes—
253C2×D4×C11C2×D412yes—
254C22×C4×C11—21no—
255C22×C4×C11—21no—
256C22×C4×C11—21no—
257C22×C4×C11—21no—
258C22×C4×C11—21no—
259C22×C4×C11—24no—
260C22×C4×C11—21no—
261C22×C4×C11—21no—
262C22×C4×C11—24no—
263C22×C4×C11—21no—
264C22×C4×C11—21no—
265C22×C4×C11—21no—
266C22×C4×C11—21no—
267C22×C4×C11—21no—
268C22×C4×C11—21no—
269C22×C4×C11—21no—
270C22×C4×C11—21no—
271C22×C4×C11—42no—
272C22×C4×C11—42no—
273C22×C4×C11—42no—
274C22×C4×C11—42no—
275C22×C4×C11—42no—
276C22×C4×C11—42no—
277C22×C4×C11—42no—
278C22×C4×C11C2×D411yescharacteristic
279C22×C4×C11C2×D411yescharacteristic
280C22×C4×C11C2×D411yescharacteristic
281C22×C4×C11C2×D412yes—
282C22×C4×C11C2×D412yes—
283C22×C4×C11C2×D411yescharacteristic
284C22×C4×C11C2411yescharacteristic
285C11×Q16—28no—
286C11×SD16—28no—
287C11×SD16—28no—
288C11×SD16—44no—
289C11×D8—28no—
290C11×D8—44no—
291C2×C8×C11—28no—
292C2×C8×C11—21no—
293C2×C8×C11—21no—
294C2×C8×C11—21no—
295C2×C8×C11—21no—
296C2×C8×C11—21no—
297C2×C8×C11—21no—
298C2×C8×C11—21no—
299C2×C8×C11—21no—
300C2×C8×C11—21no—
301C2×C8×C11—21no—
302C2×C8×C11C2×D412yes—
303C2×C8×C11C2×D412yes—
304C11×C4⋊C4—24no—
305C11×C4⋊C4—22no—
306C11×C4⋊C4—21no—
307C11×C4⋊C4—21no—
308C11×C4⋊C4—21no—
309C11×C4⋊C4—21no—
310C11×C4⋊C4—21no—
311C11×C4⋊C4—42no—
312C11×C4⋊C4C2×D412yes—
313C11×C22⋊C4—24no—
314C11×C22⋊C4—22no—
315C11×C22⋊C4—24no—
316C11×C22⋊C4—22no—
317C11×C22⋊C4—42no—
318C11×C22⋊C4—42no—
319C11×C22⋊C4—42no—
320C11×C22⋊C4—81no—
321C11×C22⋊C4—81no—
322C42×C11—24no—
323C42×C11—21no—
324C42×C11—21no—
325C22×#135C2×C1111yescharacteristic, complemented
326C2×#550C2×C1111yescharacteristic, complemented
327C2×#452C2×C1111yescharacteristic, complemented
328C2×#449C2×C1111yescharacteristic, complemented
329C2×#449C2×C1111yescharacteristic, complemented
330#2407C2×C1111yescharacteristic, complemented
331#2014C2×C1111yescharacteristic, complemented
332#2011C2×C1111yescharacteristic, complemented
333#2000C2×C1111yescharacteristic, complemented
334#1999C2×C1111yescharacteristic, complemented
335#1893C2×C1111yescharacteristic, complemented
336#1880C2×C1111yescharacteristic, complemented
337#1878C2×C1111yescharacteristic, complemented
338#1869C2×C1111yescharacteristic, complemented
339#1788C2×C1111yescharacteristic, complemented
340C23×C11—21no—
341C23×C11—21no—
342C23×C11—21no—
343C23×C11—21no—
344C23×C11—21no—
345C23×C11—21no—
346C23×C11—21no—
347C23×C11—22no—
348C23×C11—22no—
349C23×C11—21no—
350C23×C11—22no—
351C23×C11—21no—
352C23×C11—21no—
353C23×C11—21no—
354C23×C11—21no—
355C23×C11—21no—
356C23×C11—41no—
357C23×C11—41no—
358C23×C11—41no—
359C23×C11—41no—
360C23×C11—41no—
361C23×C11—41no—
362C23×C11—41no—
363C23×C11—41no—
364C23×C11—41no—
365C23×C11—41no—
366C23×C11—41no—
367C23×C11—41no—
368C23×C11—41no—
369C23×C11—41no—
370C23×C11—41no—
371C23×C11—41no—
372C23×C11—41no—
373C23×C11—41no—
374C23×C11#12012yes—
375C23×C11C22×D411yescharacteristic
376Q8×C11—22no—
377Q8×C11—22no—
378Q8×C11—22no—
379Q8×C11—22no—
380Q8×C11—22no—
381Q8×C11—41no—
382Q8×C11—41no—
383Q8×C11#12014yes—
384D4×C11—22no—
385D4×C11—22no—
386D4×C11—22no—
387D4×C11—22no—
388D4×C11—22no—
389D4×C11—22no—
390D4×C11—44no—
391D4×C11—48no—
392D4×C11—48no—
393D4×C11—48no—
394D4×C11—48no—
395D4×C11—41no—
396D4×C11—41no—
397D4×C11—41no—
398D4×C11—41no—
399D4×C11—41no—
400D4×C11—41no—
401D4×C11—84no—
402D4×C11—84no—
403D4×C11—84no—
404D4×C11—84no—
405C2×C4×C11—21no—
406C2×C4×C11—22no—
407C2×C4×C11—21no—
408C2×C4×C11—21no—
409C2×C4×C11—22no—
410C2×C4×C11—22no—
411C2×C4×C11—21no—
412C2×C4×C11—22no—
413C2×C4×C11—22no—
414C2×C4×C11—22no—
415C2×C4×C11—22no—
416C2×C4×C11—21no—
417C2×C4×C11—22no—
418C2×C4×C11—21no—
419C2×C4×C11—21no—
420C2×C4×C11—22no—
421C2×C4×C11—21no—
422C2×C4×C11—21no—
423C2×C4×C11—21no—
424C2×C4×C11—48no—
425C2×C4×C11—48no—
426C2×C4×C11—48no—
427C2×C4×C11—41no—
428C2×C4×C11—41no—
429C2×C4×C11—41no—
430C2×C4×C11—41no—
431C2×C4×C11—41no—
432C2×C4×C11—41no—
433C2×C4×C11—41no—
434C2×C4×C11—41no—
435C2×C4×C11—41no—
436C2×C4×C11—41no—
437C2×C4×C11—41no—
438C2×C4×C11—41no—
439C2×C4×C11—41no—
440C2×C4×C11—41no—
441C2×C4×C11#12012yes—
442C2×C4×C11#13512yescomplemented
443C2×C4×C11C22×D411yescharacteristic
444C2×C4×C11C22×D411yescharacteristic
445C2×C4×C11C22×D411yescharacteristic
446C2×C4×C11C22×D411yescharacteristic
447C2×C4×C11H(5,𝔽2)11yescharacteristic
448C2×C4×C11H(5,𝔽2)11yescharacteristic
449C8×C11—22no—
450C8×C11—22no—
451C8×C11—41no—
452C8×C11—41no—
453C22×#41C22×C1111yescharacteristic
454C22×#41C22×C1111yescharacteristic
455C22×#41C22×C1111yescharacteristic
456C2×#135—24no—
457C2×#135—24no—
458C2×#135—24no—
459C22×Q16C22×C1111yescharacteristic
460C22×SD16C22×C1111yescharacteristic
461C22×SD16C22×C1111yescharacteristic
462C22×SD16C22×C1111yescharacteristic
463C22×D8C22×C1111yescharacteristic
464C22×D8C22×C1111yescharacteristic
465C23×C8C22×C1111yescharacteristic
466#550—24no—
467#550—24no—
468C2×#127—21no—
469C2×#127C22×C1111yescharacteristic
470C2×C22⋊Q8C22×C1111yescharacteristic
471C2×#121—21no—
472C2×#121—21no—
473C2×#121C22×C1111yescharacteristic
474C2×#121C22×C1111yescharacteristic
475C2×#121C22×C1111yescharacteristic
476C2×C4×Q8C22×C1111yescharacteristic
477C2×C4×D4—21no—
478C2×C4×D4C22×C1111yescharacteristic
479#452—24no—
480#449—24no—
481#449—24no—
482C2×#103C22×C1111yescharacteristic
483C2×#103C22×C1111yescharacteristic
484C2×#103C22×C1111yescharacteristic
485C2×#102C22×C1111yescharacteristic
486C2×#102C22×C1111yescharacteristic
487C2×#102C22×C1111yescharacteristic
488C2×#102C22×C1111yescharacteristic
489C2×#102C22×C1111yescharacteristic
490C2×C22⋊C8C22×C1111yescharacteristic
491C2×C22⋊C8C22×C1111yescharacteristic
492C2×C22⋊C8C22×C1111yescharacteristic
493#394—21no—
494#392—21no—
495#391C22×C1111yescharacteristic
496#390C22×C1111yescharacteristic
497#386—21no—
498#385—21no—
499#380C22×C1111yescharacteristic
500#340C22×C1111yescharacteristic
501#340C22×C1111yescharacteristic
502#336C22×C1111yescharacteristic
503#336C22×C1111yescharacteristic
504C22×C11—22no—
505C22×C11—22no—
506C22×C11—22no—
507C22×C11—41no—
508C22×C11—41no—
509C22×C11—41no—
510C22×C11—41no—
511C22×C11—42no—
512C22×C11—42no—
513C22×C11—42no—
514C22×C11—41no—
515C22×C11—41no—
516C22×C11—42no—
517C22×C11—42no—
518C22×C11—41no—
519C22×C11—42no—
520C22×C11—42no—
521C22×C11—41no—
522C22×C11—42no—
523C22×C11—41no—
524C22×C11—41no—
525C22×C11—42no—
526C22×C11—41no—
527C22×C11—81no—
528C22×C11—81no—
529C22×C11—81no—
530C22×C11—81no—
531C22×C11—81no—
532C22×C11—81no—
533C22×C11—81no—
534C22×C11—81no—
535C22×C11—81no—
536C22×C11—81no—
537C22×C11—81no—
538C22×C11—81no—
539C22×C11C2×#12011yescharacteristic
540C22×C11D4211yescharacteristic
541C22×C11D4211yescharacteristic
542C22×C11C2×#13511yescharacteristic
543C22×C11#57511yescharacteristic
544C22×C11#57611yescharacteristic
545C22×C11#57711yescharacteristic
546C4×C11—22no—
547C4×C11—24no—
548C4×C11—22no—
549C4×C11—41no—
550C4×C11—42no—
551C4×C11—41no—
552C4×C11—42no—
553C4×C11—81no—
554C4×C11—81no—
555C4×C11C2×#12011yescharacteristic
556C4×C11#53411yescharacteristic
557C4×C11D4211yescharacteristic
558C4×C11D4211yescharacteristic
559C2×#41—22no—
560C2×#41—22no—
561C2×#41—22no—
562C2×#41—22no—
563C2×#41—22no—
564C2×#41—22no—
565C2×#41—22no—
566C2×#41—22no—
567C2×#41—22no—
568C2×#41—22no—
569C2×#41—22no—
570C2×#41—41no—
571C2×#41—41no—
572C2×#41—41no—
573C2×#41—41no—
574C2×#41—41no—
575C2×#41—41no—
576C2×#41D4×C1114yescomplemented
577C22×Q8C23×C1111yescharacteristic
578C22×Q8C23×C1111yescharacteristic
579C22×D4—21no—
580C22×D4—21no—
581C22×D4—21no—
582C22×D4—21no—
583C22×D4—21no—
584C22×D4—21no—
585C22×D4—21no—
586C22×D4—21no—
587C22×D4D4×C1111yescharacteristic
588C22×D4C23×C1111yescharacteristic
589C22×D4C23×C1111yescharacteristic
590C22×D4C23×C1111yescharacteristic
591C23×C4—21no—
592C23×C4—21no—
593C23×C4—21no—
594C23×C4C23×C1111yescharacteristic
595C23×C4C23×C1111yescharacteristic
596#135—232no—
597C2×Q16—22no—
598C2×Q16—22no—
599C2×Q16D4×C1114yescomplemented
600C2×SD16—22no—
601C2×SD16—22no—
602C2×SD16—22no—
603C2×SD16—22no—
604C2×SD16—22no—
605C2×SD16—22no—
606C2×SD16—22no—
607C2×SD16—41no—
608C2×SD16D4×C1114yescomplemented
609C2×D8—22no—
610C2×D8—22no—
611C2×D8—22no—
612C2×D8—22no—
613C2×D8—22no—
614C2×D8—41no—
615C22×C8—22no—
616C22×C8—22no—
617C22×C8—22no—
618C22×C8C23×C1111yescharacteristic
619C22×C8C23×C1111yescharacteristic
620C22×C8C23×C1111yescharacteristic
621C22×C8C23×C1111yescharacteristic
622#127—28no—
623#127—22no—
624#127—22no—
625C22⋊Q8—22no—
626C22⋊Q8—41no—
627#121—28no—
628#121—28no—
629#121—22no—
630#121—22no—
631#121—22no—
632#121—22no—
633#121—41no—
634#121D4×C1114yescomplemented
635C4×Q8—22no—
636C4×Q8—22no—
637C4×D4—28no—
638C4×D4—22no—
639C4×D4—22no—
640C2×C4⋊C4—21no—
641C2×C4⋊C4—21no—
642C2×C4⋊C4D4×C1111yescharacteristic
643C2×C4⋊C4C23×C1111yescharacteristic
644C2×C4⋊C4C23×C1111yescharacteristic
645C2×C4⋊C4C23×C1111yescharacteristic
646C2×C22⋊C4—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—21no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4D4×C1111yescharacteristic
654C2×C22⋊C4D4×C1111yescharacteristic
655C2×C42—21no—
656C2×C42C23×C1111yescharacteristic
657#103—22no—
658#103—22no—
659#103—22no—
660#102—22no—
661#102—22no—
662#102—22no—
663#102—41no—
664#102—41no—
665C22⋊C8—22no—
666C22⋊C8—22no—
667C22⋊C8—22no—
668#95—21no—
669#95—21no—
670#95—21no—
671C2×C11—42no—
672C2×C11—81no—
673C2×C11—82no—
674C2×C11—82no—
675C2×C11—82no—
676C2×C11#240311yescharacteristic
677C2×C11#300211yescharacteristic
678C2×C11#301211yescharacteristic
679C2×C11#326811yescharacteristic
680C2×C11#327111yescharacteristic
681C2×C11#328411yescharacteristic
682C2×C11#328711yescharacteristic
683C24—21no—
684C24—21no—
685C24—21no—
686C24C2×D4×C1111yescharacteristic
687C24C2×D4×C1111yescharacteristic
688#41—28no—
689#41—28no—
690#41—44no—
691#41—44no—
692#41—44no—
693#41—44no—
694#41—44no—
695#41—44no—
696#41—44no—
697#41—44no—
698#41—44no—
699#41—44no—
700C2×Q8—21no—
701C2×Q8—21no—
702C2×Q8—21no—
703C2×Q8—21no—
704C2×Q8—21no—
705C2×Q8—21no—
706C2×Q8—21no—
707C2×Q8—21no—
708C2×Q8C2×D4×C1112yes—
709C2×Q8C2×D4×C1112yes—
710C2×Q8C2×D4×C1112yes—
711C2×Q8C2×D4×C1112yes—
712C2×D4—24no—
713C2×D4—24no—
714C2×D4—22no—
715C2×D4—24no—
716C2×D4—24no—
717C2×D4—24no—
718C2×D4—24no—
719C2×D4—22no—
720C2×D4—21no—
721C2×D4—21no—
722C2×D4—21no—
723C2×D4—21no—
724C2×D4—21no—
725C2×D4—21no—
726C2×D4—21no—
727C2×D4—21no—
728C2×D4—21no—
729C2×D4—21no—
730C2×D4—21no—
731C2×D4—21no—
732C2×D4—21no—
733C2×D4—21no—
734C2×D4—21no—
735C2×D4—41no—
736C2×D4—42no—
737C2×D4—42no—
738C2×D4—42no—
739C2×D4—42no—
740C2×D4—42no—
741C2×D4—42no—
742C2×D4—42no—
743C2×D4—42no—
744C2×D4—42no—
745C2×D4—42no—
746C2×D4—42no—
747C2×D4—81no—
748C2×D4—81no—
749C2×D4—81no—
750C2×D4—81no—
751C2×D4—81no—
752C2×D4—81no—
753C2×D4—81no—
754C2×D4C2×D4×C1112yes—
755C2×D4C2×D4×C1112yes—
756C2×D4C2×D4×C1112yes—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—24no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—24no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—42no—
775C22×C4—42no—
776C22×C4—42no—
777C22×C4—42no—
778C22×C4—42no—
779C22×C4—42no—
780C22×C4—42no—
781C22×C4C2×D4×C1111yescharacteristic
782C22×C4C2×D4×C1111yescharacteristic
783C22×C4C2×D4×C1111yescharacteristic
784C22×C4C2×D4×C1112yes—
785C22×C4C2×D4×C1112yes—
786C22×C4C2×D4×C1111yescharacteristic
787C22×C4C24×C1111yescharacteristic
788Q16—28no—
789SD16—28no—
790SD16—28no—
791SD16—44no—
792D8—28no—
793D8—44no—
794C2×C8—28no—
795C2×C8—21no—
796C2×C8—21no—
797C2×C8—21no—
798C2×C8—21no—
799C2×C8—21no—
800C2×C8—21no—
801C2×C8—21no—
802C2×C8—21no—
803C2×C8—21no—
804C2×C8—21no—
805C2×C8C2×D4×C1112yes—
806C2×C8C2×D4×C1112yes—
807C4⋊C4—24no—
808C4⋊C4—22no—
809C4⋊C4—21no—
810C4⋊C4—21no—
811C4⋊C4—21no—
812C4⋊C4—21no—
813C4⋊C4—21no—
814C4⋊C4—42no—
815C4⋊C4C2×D4×C1112yes—
816C22⋊C4—24no—
817C22⋊C4—22no—
818C22⋊C4—24no—
819C22⋊C4—22no—
820C22⋊C4—42no—
821C22⋊C4—42no—
822C22⋊C4—42no—
823C22⋊C4—81no—
824C22⋊C4—81no—
825C42—24no—
826C42—21no—
827C42—21no—
828C11#2385711yescharacteristic, direct product factor, Sylow
829C23—21no—
830C23—21no—
831C23—21no—
832C23—21no—
833C23—21no—
834C23—21no—
835C23—21no—
836C23—22no—
837C23—22no—
838C23—21no—
839C23—22no—
840C23—21no—
841C23—21no—
842C23—21no—
843C23—21no—
844C23—21no—
845C23—41no—
846C23—41no—
847C23—41no—
848C23—41no—
849C23—41no—
850C23—41no—
851C23—41no—
852C23—41no—
853C23—41no—
854C23—41no—
855C23—41no—
856C23—41no—
857C23—41no—
858C23—41no—
859C23—41no—
860C23—41no—
861C23—41no—
862C23—41no—
863C23C11×#12012yes—
864C23C22×D4×C1111yescharacteristic
865Q8—22no—
866Q8—22no—
867Q8—22no—
868Q8—22no—
869Q8—22no—
870Q8—41no—
871Q8—41no—
872Q8C11×#12014yes—
873D4—22no—
874D4—22no—
875D4—22no—
876D4—22no—
877D4—22no—
878D4—22no—
879D4—44no—
880D4—48no—
881D4—48no—
882D4—48no—
883D4—48no—
884D4—41no—
885D4—41no—
886D4—41no—
887D4—41no—
888D4—41no—
889D4—41no—
890D4—84no—
891D4—84no—
892D4—84no—
893D4—84no—
894C2×C4—21no—
895C2×C4—22no—
896C2×C4—21no—
897C2×C4—21no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—21no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—21no—
906C2×C4—22no—
907C2×C4—21no—
908C2×C4—21no—
909C2×C4—22no—
910C2×C4—21no—
911C2×C4—21no—
912C2×C4—21no—
913C2×C4—48no—
914C2×C4—48no—
915C2×C4—48no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4C11×#12012yes—
931C2×C4C11×#13512yescomplemented
932C2×C4C22×D4×C1111yescharacteristic
933C2×C4C22×D4×C1111yescharacteristic
934C2×C4C22×D4×C1111yescharacteristic
935C2×C4C22×D4×C1111yescharacteristic
936C2×C4C11×H(5,𝔽2)11yescharacteristic
937C2×C4C11×H(5,𝔽2)11yescharacteristic
938C8—22no—
939C8—22no—
940C8—41no—
941C8—41no—
942C22—22no—
943C22—22no—
944C22—22no—
945C22—41no—
946C22—41no—
947C22—41no—
948C22—41no—
949C22—42no—
950C22—42no—
951C22—42no—
952C22—41no—
953C22—41no—
954C22—42no—
955C22—42no—
956C22—41no—
957C22—42no—
958C22—42no—
959C22—41no—
960C22—42no—
961C22—41no—
962C22—41no—
963C22—42no—
964C22—41no—
965C22—81no—
966C22—81no—
967C22—81no—
968C22—81no—
969C22—81no—
970C22—81no—
971C22—81no—
972C22—81no—
973C22—81no—
974C22—81no—
975C22—81no—
976C22—81no—
977C22C2×C11×#12011yescharacteristic
978C22D42×C1111yescharacteristic
979C22D42×C1111yescharacteristic
980C22C2×C11×#13511yescharacteristic
981C22C11×#57511yescharacteristic
982C22C11×#57611yescharacteristic
983C22C11×#57711yescharacteristic
984C4—22no—
985C4—24no—
986C4—22no—
987C4—41no—
988C4—42no—
989C4—41no—
990C4—42no—
991C4—81no—
992C4—81no—
993C4C2×C11×#12011yescharacteristic
994C4C11×#53411yescharacteristic
995C4D42×C1111yescharacteristic
996C4D42×C1111yescharacteristic
997C2—42no—
998C2—81no—
999C2—82no—
1000C2—82no—
1001C2—82no—
1002C2C11×#240311yescharacteristic
1003C2C11×#300211yescharacteristic
1004C2C11×#301211yescharacteristic
1005C2C11×#326811yescharacteristic
1006C2C11×#327111yescharacteristic
1007C2C11×#328411yescharacteristic
1008C2C11×#328711yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C4×D4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C11×#135C2semidirect
2. C2×C11×#550C2semidirect
3. C2×C11×#452C2semidirect
4. C2×C11×#449C2semidirect
5. C2×C11×#449C2semidirect
6. C11×#2407C2semidirect
7. C11×#2014C2semidirect
8. C11×#2011C2semidirect
9. C11×#2000C2semidirect
10. C11×#1999C2semidirect
11. C11×#1893C2semidirect
12. C11×#1880C2semidirect
13. C11×#1878C2semidirect
14. C11×#1869C2semidirect
15. C11×#1788C2semidirect
84. C2×C11×#41D4semidirect
107. C2×C11×Q16D4semidirect
116. C2×C11×SD16D4semidirect
142. C11×#121D4semidirect
179. #23857C11direct (N × H)
325. C22×#135C2×C11semidirect
326. C2×#550C2×C11semidirect
327. C2×#452C2×C11semidirect
328. C2×#449C2×C11semidirect
329. C2×#449C2×C11semidirect
330. #2407C2×C11semidirect
331. #2014C2×C11semidirect
332. #2011C2×C11semidirect
333. #2000C2×C11semidirect
334. #1999C2×C11semidirect
335. #1893C2×C11semidirect
336. #1880C2×C11semidirect
337. #1878C2×C11semidirect
338. #1869C2×C11semidirect
339. #1788C2×C11semidirect
442. C2×C4×C11#135semidirect
576. C2×#41D4×C11semidirect
599. C2×Q16D4×C11semidirect
608. C2×SD16D4×C11semidirect
634. #121D4×C11semidirect
828. C11#23857direct (N × H)
931. 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×#5502
C2×C11×#4522
C2×C11×#4492
C11×#24072
C11×#20142
C11×#20112
C11×#20002
C11×#19992
C11×#18932
C11×#18802
C11×#18782
C11×#18692
C11×#17882
#2385711