Finite Group Databasebeta

← C11×#61457 #14638650

Subgroups — C11×#61457 #14638650

Order 2816.

1814 conjugacy classes of subgroups.

The subgroup lattice has 1116 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3482C211yesmaximal, characteristic
2Q8×C11×#41C211yesmaximal, characteristic, complemented
3C11×#3398C211yesmaximal, characteristic, complemented
4C11×#3387C211yesmaximal, characteristic, complemented
5C11×#3374C211yesmaximal, characteristic, complemented
6C11×#3369C211yesmaximal, characteristic, complemented
7C11×#3344C212yesmaximal, complemented
8C11×#3335C211yesmaximal, characteristic, complemented
9C11×#3316C212yesmaximal, complemented
10C11×#3312C212yesmaximal, complemented
11C11×#3299C211yesmaximal, characteristic, complemented
12C11×#3298C211yesmaximal, characteristic, complemented
13D4×C11×Q16C211yesmaximal, characteristic, complemented
14C11×#3270C212yesmaximal, complemented
15C11×#3185C211yesmaximal, characteristic, complemented
16C11×#3181C212yesmaximal, complemented
17C11×#3117C212yesmaximal, complemented
18C11×#3116C211yesmaximal, characteristic, complemented
19C11×#3113C212yesmaximal, complemented
20C11×#3113C211yesmaximal, characteristic, complemented
21C11×#2970C211yesmaximal, characteristic, complemented
22C4×C11×#137C211yesmaximal, characteristic, complemented
23C2×C11×#441C212yesmaximal, complemented
24C2×C11×#137C2211yescharacteristic
25C22×C11×Q16C2212yes—
26Q82×C11C2211yescharacteristic
27C11×#557—21no—
28C11×#557C2211yescharacteristic
29C11×#557C2211yescharacteristic
30C11×#556—21no—
31C11×#556C2211yescharacteristic
32C11×#554—21no—
33C11×#554—22no—
34C11×#554C2211yescharacteristic
35C11×#554C2212yes—
36C11×#552—22no—
37C11×#552C2212yes—
38D4×Q8×C11C2212yes—
39D4×Q8×C11C2211yescharacteristic
40D4×Q8×C11C2211yescharacteristic
41C11×#548C2212yes—
42C11×#547—21no—
43C11×#547C2211yescharacteristic
44C11×#533—21no—
45C11×#533—22no—
46C11×#533—21no—
47C11×#533C2212yes—
48C11×#533C2211yescharacteristic
49C11×#533C2211yescharacteristic
50C11×#529—22no—
51C11×#529C2212yes—
52C4×C11×#41—21no—
53C4×C11×#41—21no—
54C4×C11×#41C2211yescharacteristic
55C4×C11×#41C2211yescharacteristic
56C2×C4×Q8×C11C2212yes—
57C2×C4×Q8×C11C2212yes—
58C2×C4×Q8×C11C2211yescharacteristic
59C11×#501C2212yes—
60C11×#498C2211yescharacteristic
61C11×#497C2212yes—
62C11×#494C2211yescharacteristic
63C11×#491C2212yes—
64C11×#489C2212yes—
65C11×#487C2211yescharacteristic
66C11×#487C2211yescharacteristic
67C11×#485C2212yes—
68C11×#484C2212yes—
69C11×#483C2212yes—
70C11×#483C2212yes—
71C11×#483C2212yes—
72C11×#481C2212yes—
73C11×#479C2212yes—
74C11×#479C2212yes—
75C11×#477C2211yescharacteristic
76C11×#476C2211yescharacteristic
77C11×#475C2211yescharacteristic
78C11×#475C2212yes—
79C11×#475C2211yescharacteristic
80C11×#475C2212yes—
81C11×#470C2212yes—
82C11×#470C2212yes—
83C11×#467C2212yes—
84C11×#467C2212yes—
85C11×#465C2212yes—
86C11×#465C2212yes—
87C11×#464C2212yes—
88C11×#464C2212yes—
89C11×#462C2212yes—
90C11×#462C2211yescharacteristic
91C11×#462C2211yescharacteristic
92C11×#462C2211yescharacteristic
93C11×#462C2212yes—
94C11×#461C2211yescharacteristic
95C11×#452C2212yes—
96C11×#451C2212yes—
97C11×#451C2212yes—
98C11×#451C2212yes—
99C11×#451C2212yes—
100C11×#448C2212yes—
101C11×#446C2211yescharacteristic
102C11×#446C2211yescharacteristic
103C11×#441C2212yes—
104C11×#441C2212yes—
105C11×#441C2212yes—
106C11×#441C2211yescharacteristic
107C11×#441C2212yes—
108C11×#441C2212yes—
109C11×#441C2212yes—
110C11×#441C2212yes—
111C11×#441C2212yes—
112C11×#441C2212yes—
113C11×#441C2211yescharacteristic
114C11×#440C2211yescharacteristic
115C11×#440C2212yes—
116C11×#440C2211yescharacteristic
117C4×C11×Q16C2211yescharacteristic
118C4×C11×Q16C2211yescharacteristic
119C4×C11×SD16C2211yescharacteristic
120C4×C11×SD16C2211yescharacteristic
121C11×#435C2212yes—
122C11×#435C2212yes—
123C8×D4×C11C2211yescharacteristic
124C8×D4×C11C2211yescharacteristic
125C11×#432C2211yescharacteristic
126C11×#432C2212yes—
127C11×#428C2211yescharacteristic
128C2×C11×#106C2212yes—
129C11×#419C2211yescharacteristic
130C11×#417C2211yescharacteristic
131C2×C11×#103C2212yes—
132C2×C11×#103C2212yes—
133C4×C11×M16C2211yescharacteristic
134C2×C11×#97C2212yes—
135C2×C11×#41—21no—
136C2×C11×#41D411yescharacteristic
137C2×C11×#41C2311yescharacteristic
138C22×Q8×C11C2312yes—
139C22×Q8×C11C2312yes—
140C22×Q8×C11C2311yescharacteristic
141C11×#137—24no—
142C2×C11×Q16—28no—
143C2×C11×Q16C2312yes—
144C2×C11×Q16C2312yes—
145C2×C11×Q16C2312yes—
146C2×C11×Q16C2311yescharacteristic
147C2×C11×Q16C2312yes—
148C2×C11×Q16C2312yes—
149C2×C11×Q16C2311yescharacteristic
150C2×C11×SD16C2311yescharacteristic
151C2×C11×SD16C2311yescharacteristic
152C2×C11×SD16C2312yes—
153C2×C11×M16C2311yescharacteristic
154C2×C11×M16C2311yescharacteristic
155C22×C8×C11C2312yes—
156C22×C8×C11C2312yes—
157C11×C4⋊Q8—21no—
158C11×C4⋊Q8—21no—
159C11×C4⋊Q8—22no—
160C11×C4⋊Q8—21no—
161C11×C4⋊Q8—21no—
162C11×C4⋊Q8—22no—
163C11×C4⋊Q8C2312yes—
164C11×C4⋊Q8C2311yescharacteristic
165C11×C4⋊Q8C2311yescharacteristic
166C11×C4⋊Q8C2312yes—
167C11×C4⋊Q8C2311yescharacteristic
168C11×C4⋊Q8C2311yescharacteristic
169C11×#126—22no—
170C11×#126—22no—
171C11×#126—22no—
172C11×#125—22no—
173C11×#125—22no—
174C11×#125—21no—
175C11×#125—22no—
176C11×#125—22no—
177C11×#125—21no—
178C11×#125—21no—
179C11×#125—21no—
180C11×#125—22no—
181C11×#125C2312yes—
182C11×#124—22no—
183C11×#124C2312yes—
184C11×#123—22no—
185C11×#123—22no—
186C11×#123—22no—
187C11×C22⋊Q8—21no—
188C11×C22⋊Q8—21no—
189C11×C22⋊Q8—22no—
190C11×C22⋊Q8—21no—
191C11×C22⋊Q8—21no—
192C11×C22⋊Q8—22no—
193C11×C22⋊Q8—22no—
194C11×C22⋊Q8—22no—
195C11×C22⋊Q8—22no—
196C11×C22⋊Q8—22no—
197C11×C22⋊Q8—22no—
198C11×C22⋊Q8—22no—
199C11×C22⋊Q8—22no—
200C11×C22⋊Q8C2312yes—
201C11×C22⋊Q8C2312yes—
202C11×C22⋊Q8C2312yes—
203C11×C22⋊Q8C2312yes—
204C11×C22⋊Q8C2312yes—
205C11×#121—22no—
206C11×#121C2312yes—
207C4×Q8×C11—21no—
208C4×Q8×C11—21no—
209C4×Q8×C11—21no—
210C4×Q8×C11—22no—
211C4×Q8×C11—21no—
212C4×Q8×C11—22no—
213C4×Q8×C11—22no—
214C4×Q8×C11—21no—
215C4×Q8×C11—22no—
216C4×Q8×C11—21no—
217C4×Q8×C11—21no—
218C4×Q8×C11—22no—
219C4×Q8×C11D411yescharacteristic
220C4×Q8×C11C2311yescharacteristic
221C4×Q8×C11C2311yescharacteristic
222C4×Q8×C11C2312yes—
223C4×Q8×C11C2312yes—
224C4×Q8×C11C2311yescharacteristic
225C4×Q8×C11C2312yes—
226C4×Q8×C11C2311yescharacteristic
227C4×Q8×C11C2312yes—
228C4×Q8×C11C2312yes—
229C4×Q8×C11C2311yescharacteristic
230C4×Q8×C11C2312yes—
231C4×Q8×C11C2311yescharacteristic
232C4×Q8×C11C2311yescharacteristic
233C4×D4×C11—21no—
234C4×D4×C11—22no—
235C4×D4×C11—21no—
236C4×D4×C11—22no—
237C4×D4×C11—21no—
238C4×D4×C11—22no—
239C4×D4×C11—21no—
240C4×D4×C11—21no—
241C4×D4×C11—22no—
242C4×D4×C11D411yescharacteristic
243C4×D4×C11D412yes—
244C4×D4×C11C2311yescharacteristic
245C4×D4×C11C2311yescharacteristic
246C4×D4×C11C2311yescharacteristic
247C4×D4×C11C2312yes—
248C11×#117—22no—
249C11×#117—21no—
250C11×#117—21no—
251C11×#117—21no—
252C11×#117—22no—
253C11×#117—21no—
254C11×#117—22no—
255C11×#117D412yes—
256C11×#117D411yescharacteristic
257C11×#117C2311yescharacteristic
258C2×C11×C4⋊C4—22no—
259C2×C11×C4⋊C4—22no—
260C2×C11×C4⋊C4—21no—
261C2×C11×C4⋊C4C2312yes—
262C2×C11×C4⋊C4C2312yes—
263C2×C11×C4⋊C4C2311yescharacteristic
264C2×C42×C11—22no—
265C2×C42×C11—22no—
266C2×C42×C11—21no—
267C2×C42×C11—21no—
268C2×C42×C11C2312yes—
269C2×C42×C11C2311yescharacteristic
270C11×#107C2311yescharacteristic
271C11×#107C2312yes—
272C11×#107C2311yescharacteristic
273C11×#106C2312yes—
274C11×#106C2312yes—
275C11×#106C2312yes—
276C11×#106C2311yescharacteristic
277C11×#106C2312yes—
278C11×#106C2312yes—
279C11×#106C2311yescharacteristic
280C11×C4⋊C8C2311yescharacteristic
281C11×C4⋊C8C2311yescharacteristic
282C11×C4⋊C8C2312yes—
283C11×C4⋊C8C2312yes—
284C11×#103C2312yes—
285C11×#103C2312yes—
286C11×#103C2311yescharacteristic
287C11×#103C2312yes—
288C11×#103C2312yes—
289C11×#103C2312yes—
290C11×#103C2311yescharacteristic
291C11×#103C2311yescharacteristic
292C11×#103C2312yes—
293C11×#103C2312yes—
294C11×#103C2312yes—
295C11×#103C2312yes—
296C11×#103C2311yescharacteristic
297C11×#103C2311yescharacteristic
298C11×#103C2311yescharacteristic
299C11×#103C2312yes—
300C11×#103C2312yes—
301C11×#102C2311yescharacteristic
302C11×#102C2312yes—
303C11×#102C2311yescharacteristic
304C11×C22⋊C8C2312yes—
305C11×C22⋊C8C2312yes—
306C11×C22⋊C8C2312yes—
307C11×#97C2312yes—
308C11×#97C2312yes—
309C11×#97C2311yescharacteristic
310C11×#97C2312yes—
311C11×#97C2311yescharacteristic
312C4×C8×C11C2311yescharacteristic
313C4×C8×C11C2311yescharacteristic
314#61457C1111yesmaximal, characteristic, direct product factor, Sylow
315C11×#41—24no—
316C11×#41—22no—
317C11×#41—41no—
318C11×#41—44no—
319C2×Q8×C11—22no—
320C2×Q8×C11—21no—
321C2×Q8×C11—22no—
322C2×Q8×C11—21no—
323C2×Q8×C11—22no—
324C2×Q8×C11—21no—
325C2×Q8×C11—24no—
326C2×Q8×C11—24no—
327C2×Q8×C11—22no—
328C2×Q8×C11—42no—
329C2×Q8×C11—42no—
330C2×Q8×C11—41no—
331C2×Q8×C11C2×D411yescharacteristic
332C2×Q8×C11C2412yes—
333C2×Q8×C11C2411yescharacteristic
334C2×Q8×C11C2412yes—
335C2×Q8×C11C2411yescharacteristic
336C2×Q8×C11C2411yescharacteristic
337C2×D4×C11—21no—
338C2×D4×C11—22no—
339C2×D4×C11C2×D412yes—
340C2×D4×C11C2×D411yescharacteristic
341C2×D4×C11C2411yescharacteristic
342C22×C4×C11—22no—
343C22×C4×C11—22no—
344C22×C4×C11—21no—
345C22×C4×C11—22no—
346C22×C4×C11—21no—
347C22×C4×C11—22no—
348C22×C4×C11—21no—
349C22×C4×C11—21no—
350C22×C4×C11—21no—
351C22×C4×C11C2×D412yes—
352C22×C4×C11C2×D411yescharacteristic
353C22×C4×C11C2×D412yes—
354C22×C4×C11C2×D411yescharacteristic
355C22×C4×C11C2412yes—
356C22×C4×C11C2411yescharacteristic
357C11×Q16—24no—
358C11×Q16—24no—
359C11×Q16—24no—
360C11×Q16—22no—
361C11×Q16—42no—
362C11×Q16—42no—
363C11×Q16#4114yescomplemented
364C11×SD16—22no—
365C11×SD16—22no—
366C11×SD16—42no—
367C11×M16—22no—
368C11×M16—41no—
369C2×C8×C11—24no—
370C2×C8×C11—42no—
371C2×C8×C11C2411yescharacteristic
372C2×C8×C11C2411yescharacteristic
373C2×C8×C11C2411yescharacteristic
374C2×C8×C11C2412yes—
375C2×C8×C11C2412yes—
376C2×C8×C11C2411yescharacteristic
377C11×C4⋊C4—21no—
378C11×C4⋊C4—21no—
379C11×C4⋊C4—22no—
380C11×C4⋊C4—22no—
381C11×C4⋊C4—21no—
382C11×C4⋊C4—22no—
383C11×C4⋊C4—21no—
384C11×C4⋊C4—22no—
385C11×C4⋊C4—21no—
386C11×C4⋊C4—22no—
387C11×C4⋊C4—22no—
388C11×C4⋊C4—21no—
389C11×C4⋊C4—22no—
390C11×C4⋊C4—22no—
391C11×C4⋊C4—21no—
392C11×C4⋊C4—22no—
393C11×C4⋊C4—22no—
394C11×C4⋊C4—21no—
395C11×C4⋊C4—22no—
396C11×C4⋊C4—21no—
397C11×C4⋊C4—22no—
398C11×C4⋊C4—21no—
399C11×C4⋊C4—21no—
400C11×C4⋊C4—22no—
401C11×C4⋊C4—21no—
402C11×C4⋊C4—22no—
403C11×C4⋊C4—22no—
404C11×C4⋊C4—21no—
405C11×C4⋊C4—22no—
406C11×C4⋊C4—22no—
407C11×C4⋊C4—22no—
408C11×C4⋊C4C2×D411yescharacteristic
409C11×C4⋊C4C2×D412yes—
410C11×C4⋊C4C2×D412yes—
411C11×C4⋊C4C2×D411yescharacteristic
412C11×C4⋊C4C2411yescharacteristic
413C11×C4⋊C4C2411yescharacteristic
414C11×C4⋊C4C2412yes—
415C11×C4⋊C4C2411yescharacteristic
416C11×C4⋊C4C2412yes—
417C11×C4⋊C4C2411yescharacteristic
418C11×C22⋊C4—22no—
419C11×C22⋊C4—22no—
420C11×C22⋊C4—22no—
421C11×C22⋊C4—22no—
422C11×C22⋊C4—22no—
423C11×C22⋊C4—21no—
424C11×C22⋊C4—22no—
425C11×C22⋊C4—21no—
426C11×C22⋊C4—21no—
427C11×C22⋊C4—22no—
428C11×C22⋊C4—22no—
429C11×C22⋊C4C2×D412yes—
430C11×C22⋊C4C2×D412yes—
431C11×C22⋊C4C2×D412yes—
432C42×C11—21no—
433C42×C11—21no—
434C42×C11—21no—
435C42×C11—22no—
436C42×C11—22no—
437C42×C11—21no—
438C42×C11—22no—
439C42×C11—21no—
440C42×C11—22no—
441C42×C11—22no—
442C42×C11—21no—
443C42×C11—22no—
444C42×C11—21no—
445C42×C11C2×D411yescharacteristic
446C42×C11C2×D411yescharacteristic
447C42×C11C2×D412yes—
448C42×C11C2×D412yes—
449C42×C11C2411yescharacteristic
450C42×C11C2411yescharacteristic
451C42×C11C2412yes—
452#3482C2×C1111yescharacteristic
453Q8×#41C2×C1111yescharacteristic, complemented
454#3398C2×C1111yescharacteristic, complemented
455#3387C2×C1111yescharacteristic, complemented
456#3374C2×C1111yescharacteristic, complemented
457#3369C2×C1111yescharacteristic, complemented
458#3344C2×C1112yescomplemented
459#3335C2×C1111yescharacteristic, complemented
460#3316C2×C1112yescomplemented
461#3312C2×C1112yescomplemented
462#3299C2×C1111yescharacteristic, complemented
463#3298C2×C1111yescharacteristic, complemented
464D4×Q16C2×C1111yescharacteristic, complemented
465#3270C2×C1112yescomplemented
466#3185C2×C1111yescharacteristic, complemented
467#3181C2×C1112yescomplemented
468#3117C2×C1112yescomplemented
469#3116C2×C1111yescharacteristic, complemented
470#3113C2×C1112yescomplemented
471#3113C2×C1111yescharacteristic, complemented
472#2970C2×C1111yescharacteristic, complemented
473C4×#137C2×C1111yescharacteristic, complemented
474C2×#441C2×C1112yescomplemented
475C23×C11—21no—
476C23×C11C22×D411yescharacteristic
477C23×C11C22×D412yes—
478Q8×C11—22no—
479Q8×C11—21no—
480Q8×C11—21no—
481Q8×C11—21no—
482Q8×C11—22no—
483Q8×C11—22no—
484Q8×C11—22no—
485Q8×C11—22no—
486Q8×C11—21no—
487Q8×C11—42no—
488Q8×C11—44no—
489Q8×C11—44no—
490Q8×C11—42no—
491Q8×C11—82no—
492Q8×C11—81no—
493Q8×C11C2×#4112yes—
494Q8×C11C2×#4112yes—
495D4×C11—24no—
496D4×C11—21no—
497D4×C11—21no—
498D4×C11—42no—
499D4×C11—44no—
500D4×C11#13714yescomplemented
501C2×C4×C11—24no—
502C2×C4×C11—21no—
503C2×C4×C11—21no—
504C2×C4×C11—22no—
505C2×C4×C11—22no—
506C2×C4×C11—21no—
507C2×C4×C11—22no—
508C2×C4×C11—21no—
509C2×C4×C11—21no—
510C2×C4×C11—21no—
511C2×C4×C11—21no—
512C2×C4×C11—22no—
513C2×C4×C11—21no—
514C2×C4×C11—22no—
515C2×C4×C11—22no—
516C2×C4×C11—22no—
517C2×C4×C11—21no—
518C2×C4×C11—42no—
519C2×C4×C11—41no—
520C2×C4×C11—42no—
521C2×C4×C11—44no—
522C2×C4×C11—44no—
523C2×C4×C11—42no—
524C2×C4×C11—42no—
525C2×C4×C11—44no—
526C2×C4×C11—42no—
527C2×C4×C11—82no—
528C2×C4×C11—81no—
529C2×C4×C11C22×D411yescharacteristic
530C2×C4×C11C22×D411yescharacteristic
531C2×C4×C11C22×D412yes—
532C2×C4×C11C22×D412yes—
533C2×C4×C11C22×D411yescharacteristic
534C2×C4×C11C22×D412yes—
535C2×C4×C11C22×D411yescharacteristic
536C2×C4×C11C22×D411yescharacteristic
537C2×C4×C11C2511yescharacteristic
538C8×C11—22no—
539C8×C11—21no—
540C8×C11—21no—
541C8×C11—22no—
542C8×C11—21no—
543C8×C11C2×#4112yes—
544C2×#137C22×C1111yescharacteristic
545C22×Q16C22×C1112yes—
546Q82C22×C1111yescharacteristic
547#557—21no—
548#557C22×C1111yescharacteristic
549#557C22×C1111yescharacteristic
550#556—21no—
551#556C22×C1111yescharacteristic
552#554—21no—
553#554—22no—
554#554C22×C1111yescharacteristic
555#554C22×C1112yes—
556#552—22no—
557#552C22×C1112yes—
558D4×Q8C22×C1112yes—
559D4×Q8C22×C1111yescharacteristic
560D4×Q8C22×C1111yescharacteristic
561#548C22×C1112yes—
562#547—21no—
563#547C22×C1111yescharacteristic
564#533—21no—
565#533—22no—
566#533—21no—
567#533C22×C1112yes—
568#533C22×C1111yescharacteristic
569#533C22×C1111yescharacteristic
570#529—22no—
571#529C22×C1112yes—
572C4×#41—21no—
573C4×#41—21no—
574C4×#41C22×C1111yescharacteristic
575C4×#41C22×C1111yescharacteristic
576C2×C4×Q8C22×C1112yes—
577C2×C4×Q8C22×C1111yescharacteristic
578C2×C4×Q8C22×C1112yes—
579#501C22×C1112yes—
580#498C22×C1111yescharacteristic
581#497C22×C1112yes—
582#494C22×C1111yescharacteristic
583#491C22×C1112yes—
584#489C22×C1112yes—
585#487C22×C1111yescharacteristic
586#487C22×C1111yescharacteristic
587#485C22×C1112yes—
588#484C22×C1112yes—
589#483C22×C1112yes—
590#483C22×C1112yes—
591#483C22×C1112yes—
592#481C22×C1112yes—
593#479C22×C1112yes—
594#479C22×C1112yes—
595#477C22×C1111yescharacteristic
596#476C22×C1111yescharacteristic
597#475C22×C1111yescharacteristic
598#475C22×C1112yes—
599#475C22×C1111yescharacteristic
600#475C22×C1112yes—
601#470C22×C1112yes—
602#470C22×C1112yes—
603#467C22×C1112yes—
604#467C22×C1112yes—
605#465C22×C1112yes—
606#465C22×C1112yes—
607#464C22×C1112yes—
608#464C22×C1112yes—
609#462C22×C1111yescharacteristic
610#462C22×C1112yes—
611#462C22×C1111yescharacteristic
612#462C22×C1112yes—
613#462C22×C1111yescharacteristic
614#461C22×C1111yescharacteristic
615#452C22×C1112yes—
616#451C22×C1112yes—
617#451C22×C1112yes—
618#451C22×C1112yes—
619#451C22×C1112yes—
620#448C22×C1112yes—
621#446C22×C1111yescharacteristic
622#446C22×C1111yescharacteristic
623#441C22×C1112yes—
624#441C22×C1112yes—
625#441C22×C1111yescharacteristic
626#441C22×C1112yes—
627#441C22×C1112yes—
628#441C22×C1112yes—
629#441C22×C1112yes—
630#441C22×C1112yes—
631#441C22×C1112yes—
632#441C22×C1112yes—
633#441C22×C1111yescharacteristic
634#440C22×C1112yes—
635#440C22×C1111yescharacteristic
636#440C22×C1111yescharacteristic
637C4×Q16C22×C1111yescharacteristic
638C4×Q16C22×C1111yescharacteristic
639C4×SD16C22×C1111yescharacteristic
640C4×SD16C22×C1111yescharacteristic
641#435C22×C1112yes—
642#435C22×C1112yes—
643C8×D4C22×C1111yescharacteristic
644C8×D4C22×C1111yescharacteristic
645#432C22×C1111yescharacteristic
646#432C22×C1112yes—
647#428C22×C1111yescharacteristic
648C2×#106C22×C1112yes—
649#419C22×C1111yescharacteristic
650#417C22×C1111yescharacteristic
651C2×#103C22×C1112yes—
652C2×#103C22×C1112yes—
653C4×M16C22×C1111yescharacteristic
654C2×#97C22×C1112yes—
655C22×C11—22no—
656C22×C11—22no—
657C22×C11—21no—
658C22×C11—21no—
659C22×C11—21no—
660C22×C11—41no—
661C22×C11—41no—
662C22×C11—41no—
663C22×C11C2×#13714yes—
664C22×C11C23×D411yescharacteristic
665C4×C11—21no—
666C4×C11—22no—
667C4×C11—21no—
668C4×C11—21no—
669C4×C11—22no—
670C4×C11—22no—
671C4×C11—22no—
672C4×C11—21no—
673C4×C11—22no—
674C4×C11—41no—
675C4×C11—41no—
676C4×C11—42no—
677C4×C11—41no—
678C4×C11—42no—
679C4×C11—41no—
680C4×C11—42no—
681C4×C11—41no—
682C4×C11—42no—
683C4×C11C2×#13712yes—
684C4×C11C22×#4111yescharacteristic
685C4×C11#58511yescharacteristic
686C2×#41—21no—
687C2×#41D4×C1111yescharacteristic
688C2×#41C23×C1111yescharacteristic
689C22×Q8C23×C1112yes—
690C22×Q8C23×C1112yes—
691C22×Q8C23×C1111yescharacteristic
692#137—24no—
693C2×Q16—28no—
694C2×Q16C23×C1112yes—
695C2×Q16C23×C1112yes—
696C2×Q16C23×C1112yes—
697C2×Q16C23×C1111yescharacteristic
698C2×Q16C23×C1112yes—
699C2×Q16C23×C1112yes—
700C2×Q16C23×C1111yescharacteristic
701C2×SD16C23×C1111yescharacteristic
702C2×SD16C23×C1111yescharacteristic
703C2×SD16C23×C1112yes—
704C2×M16C23×C1111yescharacteristic
705C2×M16C23×C1111yescharacteristic
706C22×C8C23×C1112yes—
707C22×C8C23×C1112yes—
708C4⋊Q8—21no—
709C4⋊Q8—21no—
710C4⋊Q8—22no—
711C4⋊Q8—21no—
712C4⋊Q8—21no—
713C4⋊Q8—22no—
714C4⋊Q8C23×C1111yescharacteristic
715C4⋊Q8C23×C1111yescharacteristic
716C4⋊Q8C23×C1112yes—
717C4⋊Q8C23×C1111yescharacteristic
718C4⋊Q8C23×C1112yes—
719C4⋊Q8C23×C1111yescharacteristic
720#126—22no—
721#126—22no—
722#126—22no—
723#125—22no—
724#125—22no—
725#125—21no—
726#125—22no—
727#125—22no—
728#125—21no—
729#125—21no—
730#125—21no—
731#125—22no—
732#125C23×C1112yes—
733#124—22no—
734#124C23×C1112yes—
735#123—22no—
736#123—22no—
737#123—22no—
738C22⋊Q8—21no—
739C22⋊Q8—21no—
740C22⋊Q8—22no—
741C22⋊Q8—21no—
742C22⋊Q8—21no—
743C22⋊Q8—22no—
744C22⋊Q8—22no—
745C22⋊Q8—22no—
746C22⋊Q8—22no—
747C22⋊Q8—22no—
748C22⋊Q8—22no—
749C22⋊Q8—22no—
750C22⋊Q8—22no—
751C22⋊Q8C23×C1112yes—
752C22⋊Q8C23×C1112yes—
753C22⋊Q8C23×C1112yes—
754C22⋊Q8C23×C1112yes—
755C22⋊Q8C23×C1112yes—
756#121—22no—
757#121C23×C1112yes—
758C4×Q8—21no—
759C4×Q8—21no—
760C4×Q8—21no—
761C4×Q8—22no—
762C4×Q8—21no—
763C4×Q8—22no—
764C4×Q8—22no—
765C4×Q8—21no—
766C4×Q8—22no—
767C4×Q8—21no—
768C4×Q8—21no—
769C4×Q8—22no—
770C4×Q8D4×C1111yescharacteristic
771C4×Q8C23×C1111yescharacteristic
772C4×Q8C23×C1111yescharacteristic
773C4×Q8C23×C1112yes—
774C4×Q8C23×C1111yescharacteristic
775C4×Q8C23×C1112yes—
776C4×Q8C23×C1112yes—
777C4×Q8C23×C1111yescharacteristic
778C4×Q8C23×C1112yes—
779C4×Q8C23×C1112yes—
780C4×Q8C23×C1111yescharacteristic
781C4×Q8C23×C1112yes—
782C4×Q8C23×C1111yescharacteristic
783C4×Q8C23×C1111yescharacteristic
784C4×D4—21no—
785C4×D4—22no—
786C4×D4—21no—
787C4×D4—22no—
788C4×D4—21no—
789C4×D4—22no—
790C4×D4—21no—
791C4×D4—21no—
792C4×D4—22no—
793C4×D4D4×C1111yescharacteristic
794C4×D4D4×C1112yes—
795C4×D4C23×C1111yescharacteristic
796C4×D4C23×C1111yescharacteristic
797C4×D4C23×C1111yescharacteristic
798C4×D4C23×C1112yes—
799#117—22no—
800#117—21no—
801#117—21no—
802#117—21no—
803#117—22no—
804#117—21no—
805#117—22no—
806#117D4×C1112yes—
807#117D4×C1111yescharacteristic
808#117C23×C1111yescharacteristic
809C2×C4⋊C4—22no—
810C2×C4⋊C4—22no—
811C2×C4⋊C4—21no—
812C2×C4⋊C4C23×C1112yes—
813C2×C4⋊C4C23×C1112yes—
814C2×C4⋊C4C23×C1111yescharacteristic
815C2×C42—22no—
816C2×C42—22no—
817C2×C42—21no—
818C2×C42—21no—
819C2×C42C23×C1112yes—
820C2×C42C23×C1111yescharacteristic
821#107C23×C1111yescharacteristic
822#107C23×C1111yescharacteristic
823#107C23×C1112yes—
824#106C23×C1111yescharacteristic
825#106C23×C1112yes—
826#106C23×C1112yes—
827#106C23×C1112yes—
828#106C23×C1111yescharacteristic
829#106C23×C1112yes—
830#106C23×C1112yes—
831C4⋊C8C23×C1111yescharacteristic
832C4⋊C8C23×C1111yescharacteristic
833C4⋊C8C23×C1112yes—
834C4⋊C8C23×C1112yes—
835#103C23×C1111yescharacteristic
836#103C23×C1111yescharacteristic
837#103C23×C1112yes—
838#103C23×C1112yes—
839#103C23×C1112yes—
840#103C23×C1112yes—
841#103C23×C1112yes—
842#103C23×C1112yes—
843#103C23×C1111yescharacteristic
844#103C23×C1111yescharacteristic
845#103C23×C1111yescharacteristic
846#103C23×C1111yescharacteristic
847#103C23×C1112yes—
848#103C23×C1112yes—
849#103C23×C1112yes—
850#103C23×C1112yes—
851#103C23×C1112yes—
852#102C23×C1111yescharacteristic
853#102C23×C1111yescharacteristic
854#102C23×C1112yes—
855C22⋊C8C23×C1112yes—
856C22⋊C8C23×C1112yes—
857C22⋊C8C23×C1112yes—
858#97C23×C1111yescharacteristic
859#97C23×C1112yes—
860#97C23×C1112yes—
861#97C23×C1112yes—
862#97C23×C1111yescharacteristic
863C4×C8C23×C1111yescharacteristic
864C4×C8C23×C1111yescharacteristic
865C2×C11—24no—
866C2×C11—41no—
867C2×C11—81no—
868C2×C11D4×#4111yescharacteristic
869C2×C11C22×#13711yescharacteristic
870C2×C11#358611yescharacteristic
871#41—24no—
872#41—22no—
873#41—41no—
874#41—44no—
875C2×Q8—22no—
876C2×Q8—21no—
877C2×Q8—22no—
878C2×Q8—21no—
879C2×Q8—22no—
880C2×Q8—21no—
881C2×Q8—24no—
882C2×Q8—24no—
883C2×Q8—22no—
884C2×Q8—42no—
885C2×Q8—42no—
886C2×Q8—41no—
887C2×Q8C2×D4×C1111yescharacteristic
888C2×Q8C24×C1112yes—
889C2×Q8C24×C1111yescharacteristic
890C2×Q8C24×C1112yes—
891C2×Q8C24×C1111yescharacteristic
892C2×Q8C24×C1111yescharacteristic
893C2×D4—21no—
894C2×D4—22no—
895C2×D4C2×D4×C1112yes—
896C2×D4C2×D4×C1111yescharacteristic
897C2×D4C24×C1111yescharacteristic
898C22×C4—22no—
899C22×C4—22no—
900C22×C4—21no—
901C22×C4—22no—
902C22×C4—21no—
903C22×C4—22no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4C2×D4×C1112yes—
908C22×C4C2×D4×C1111yescharacteristic
909C22×C4C2×D4×C1112yes—
910C22×C4C2×D4×C1111yescharacteristic
911C22×C4C24×C1112yes—
912C22×C4C24×C1111yescharacteristic
913Q16—24no—
914Q16—24no—
915Q16—22no—
916Q16—24no—
917Q16—42no—
918Q16—42no—
919Q16C11×#4114yescomplemented
920SD16—22no—
921SD16—22no—
922SD16—42no—
923M16—22no—
924M16—41no—
925C2×C8—24no—
926C2×C8—42no—
927C2×C8C24×C1111yescharacteristic
928C2×C8C24×C1111yescharacteristic
929C2×C8C24×C1111yescharacteristic
930C2×C8C24×C1112yes—
931C2×C8C24×C1112yes—
932C2×C8C24×C1111yescharacteristic
933C4⋊C4—21no—
934C4⋊C4—21no—
935C4⋊C4—22no—
936C4⋊C4—22no—
937C4⋊C4—21no—
938C4⋊C4—22no—
939C4⋊C4—21no—
940C4⋊C4—22no—
941C4⋊C4—21no—
942C4⋊C4—22no—
943C4⋊C4—22no—
944C4⋊C4—21no—
945C4⋊C4—22no—
946C4⋊C4—22no—
947C4⋊C4—21no—
948C4⋊C4—22no—
949C4⋊C4—22no—
950C4⋊C4—21no—
951C4⋊C4—22no—
952C4⋊C4—21no—
953C4⋊C4—22no—
954C4⋊C4—21no—
955C4⋊C4—21no—
956C4⋊C4—22no—
957C4⋊C4—21no—
958C4⋊C4—22no—
959C4⋊C4—22no—
960C4⋊C4—21no—
961C4⋊C4—22no—
962C4⋊C4—22no—
963C4⋊C4—22no—
964C4⋊C4C2×D4×C1111yescharacteristic
965C4⋊C4C2×D4×C1112yes—
966C4⋊C4C2×D4×C1112yes—
967C4⋊C4C2×D4×C1111yescharacteristic
968C4⋊C4C24×C1111yescharacteristic
969C4⋊C4C24×C1111yescharacteristic
970C4⋊C4C24×C1112yes—
971C4⋊C4C24×C1111yescharacteristic
972C4⋊C4C24×C1112yes—
973C4⋊C4C24×C1111yescharacteristic
974C22⋊C4—22no—
975C22⋊C4—22no—
976C22⋊C4—22no—
977C22⋊C4—22no—
978C22⋊C4—22no—
979C22⋊C4—21no—
980C22⋊C4—22no—
981C22⋊C4—21no—
982C22⋊C4—21no—
983C22⋊C4—22no—
984C22⋊C4—22no—
985C22⋊C4C2×D4×C1112yes—
986C22⋊C4C2×D4×C1112yes—
987C22⋊C4C2×D4×C1112yes—
988C42—21no—
989C42—21no—
990C42—21no—
991C42—22no—
992C42—22no—
993C42—21no—
994C42—22no—
995C42—21no—
996C42—22no—
997C42—22no—
998C42—21no—
999C42—22no—
1000C42—21no—
1001C42C2×D4×C1111yescharacteristic
1002C42C2×D4×C1111yescharacteristic
1003C42C2×D4×C1112yes—
1004C42C2×D4×C1112yes—
1005C42C24×C1111yescharacteristic
1006C42C24×C1111yescharacteristic
1007C42C24×C1112yes—
1008C11#6145711yescharacteristic, direct product factor, Sylow
1009C23—21no—
1010C23C22×D4×C1111yescharacteristic
1011C23C22×D4×C1112yes—
1012Q8—22no—
1013Q8—21no—
1014Q8—21no—
1015Q8—21no—
1016Q8—22no—
1017Q8—22no—
1018Q8—22no—
1019Q8—22no—
1020Q8—21no—
1021Q8—42no—
1022Q8—44no—
1023Q8—44no—
1024Q8—42no—
1025Q8—82no—
1026Q8—81no—
1027Q8C2×C11×#4112yes—
1028Q8C2×C11×#4112yes—
1029D4—24no—
1030D4—21no—
1031D4—21no—
1032D4—42no—
1033D4—44no—
1034D4C11×#13714yescomplemented
1035C2×C4—24no—
1036C2×C4—21no—
1037C2×C4—21no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—21no—
1041C2×C4—22no—
1042C2×C4—21no—
1043C2×C4—21no—
1044C2×C4—21no—
1045C2×C4—21no—
1046C2×C4—22no—
1047C2×C4—21no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—22no—
1051C2×C4—21no—
1052C2×C4—42no—
1053C2×C4—41no—
1054C2×C4—42no—
1055C2×C4—44no—
1056C2×C4—44no—
1057C2×C4—42no—
1058C2×C4—42no—
1059C2×C4—44no—
1060C2×C4—42no—
1061C2×C4—82no—
1062C2×C4—81no—
1063C2×C4C22×D4×C1111yescharacteristic
1064C2×C4C22×D4×C1111yescharacteristic
1065C2×C4C22×D4×C1112yes—
1066C2×C4C22×D4×C1112yes—
1067C2×C4C22×D4×C1111yescharacteristic
1068C2×C4C22×D4×C1112yes—
1069C2×C4C22×D4×C1111yescharacteristic
1070C2×C4C22×D4×C1111yescharacteristic
1071C2×C4C25×C1111yescharacteristic
1072C8—22no—
1073C8—21no—
1074C8—21no—
1075C8—22no—
1076C8—21no—
1077C8C2×C11×#4112yes—
1078C22—22no—
1079C22—22no—
1080C22—21no—
1081C22—21no—
1082C22—21no—
1083C22—41no—
1084C22—41no—
1085C22—41no—
1086C22C2×C11×#13714yes—
1087C22C23×D4×C1111yescharacteristic
1088C4—21no—
1089C4—22no—
1090C4—22no—
1091C4—22no—
1092C4—21no—
1093C4—22no—
1094C4—21no—
1095C4—22no—
1096C4—21no—
1097C4—42no—
1098C4—41no—
1099C4—42no—
1100C4—41no—
1101C4—42no—
1102C4—41no—
1103C4—41no—
1104C4—42no—
1105C4—41no—
1106C4C2×C11×#13712yes—
1107C4C22×C11×#4111yescharacteristic
1108C4C11×#58511yescharacteristic
1109C2—24no—
1110C2—41no—
1111C2—81no—
1112C2D4×C11×#4111yescharacteristic
1113C2C22×C11×#13711yescharacteristic
1114C2C11×#358611yescharacteristic
subgroupG/H
center, socleC22×C11C23×D4
commutator, Frattini, cosocleC2×C4C25×C11
prime radicalC11×#3482C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C4×C11×#41 ◁ G

Complements

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

NH ≅ G/Ntype
2. Q8×C11×#41C2semidirect
3. C11×#3398C2semidirect
4. C11×#3387C2semidirect
5. C11×#3374C2semidirect
6. C11×#3369C2semidirect
7. C11×#3344C2semidirect
8. C11×#3335C2semidirect
9. C11×#3316C2semidirect
10. C11×#3312C2semidirect
11. C11×#3299C2semidirect
12. C11×#3298C2semidirect
13. D4×C11×Q16C2semidirect
14. C11×#3270C2semidirect
15. C11×#3185C2semidirect
16. C11×#3181C2semidirect
17. C11×#3117C2semidirect
18. C11×#3116C2semidirect
19. C11×#3113C2semidirect
20. C11×#3113C2semidirect
21. C11×#2970C2semidirect
22. C4×C11×#137C2semidirect
23. C2×C11×#441C2semidirect
314. #61457C11direct (N × H)
363. C11×Q16#41semidirect
453. Q8×#41C2×C11semidirect
454. #3398C2×C11semidirect
455. #3387C2×C11semidirect
456. #3374C2×C11semidirect
457. #3369C2×C11semidirect
458. #3344C2×C11semidirect
459. #3335C2×C11semidirect
460. #3316C2×C11semidirect
461. #3312C2×C11semidirect
462. #3299C2×C11semidirect
463. #3298C2×C11semidirect
464. D4×Q16C2×C11semidirect
465. #3270C2×C11semidirect
466. #3185C2×C11semidirect
467. #3181C2×C11semidirect
468. #3117C2×C11semidirect
469. #3116C2×C11semidirect
470. #3113C2×C11semidirect
471. #3113C2×C11semidirect
472. #2970C2×C11semidirect
473. C4×#137C2×C11semidirect
474. C2×#441C2×C11semidirect
500. D4×C11#137semidirect
919. Q16C11×#41semidirect
1008. C11#61457direct (N × H)
1034. D4C11×#137semidirect

Maximal subgroups

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

subgroupindex
C11×#34822
Q8×C11×#412
C11×#33982
C11×#33872
C11×#33742
C11×#33692
C11×#33442
C11×#33352
C11×#33162
C11×#33122
C11×#32992
C11×#32982
D4×C11×Q162
C11×#32702
C11×#31852
C11×#31812
C11×#31172
C11×#31162
C11×#31132
C11×#29702
C4×C11×#1372
C2×C11×#4412
#6145711