Finite Group Databasebeta

← C11×#61499 #14638692

Subgroups — C11×#61499 #14638692

Order 2816.

1806 conjugacy classes of subgroups.

The subgroup lattice has 1118 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3523C211yesmaximal, characteristic, complemented
2C11×#3522C211yesmaximal, characteristic
3C11×#3400C211yesmaximal, characteristic, complemented
4C11×#3387C211yesmaximal, characteristic, complemented
5C11×#3365C211yesmaximal, characteristic, complemented
6C11×#3363C211yesmaximal, characteristic, complemented
7C11×#3356C211yesmaximal, characteristic, complemented
8C11×#3343C212yesmaximal, complemented
9C11×#3304C211yesmaximal, characteristic, complemented
10C11×#3300C212yesmaximal, complemented
11C11×#3299C211yesmaximal, characteristic, complemented
12C11×#3298C212yesmaximal, complemented
13C11×#3278C211yesmaximal, characteristic, complemented
14C11×#3270C212yesmaximal, complemented
15C11×#3178C212yesmaximal, complemented
16C11×#3167C211yesmaximal, characteristic, complemented
17C11×#3121C212yesmaximal, complemented
18C11×#3120C212yesmaximal, complemented
19C11×#3113C211yesmaximal, characteristic, complemented
20C11×#3112C211yesmaximal, characteristic, complemented
21C11×#2966C211yesmaximal, characteristic, complemented
22C11×#2947C212yesmaximal, complemented
23C2×C4×C11×Q16C211yesmaximal, characteristic, complemented
24C2×C11×#137C2212yes—
25C22×C11×Q16C2211yescharacteristic
26C11×#559—21no—
27C11×#559C2211yescharacteristic
28Q82×C11C2211yescharacteristic
29C11×#557—21no—
30C11×#557C2211yescharacteristic
31C11×#557C2211yescharacteristic
32C11×#556—21no—
33C11×#556C2211yescharacteristic
34C11×#554—21no—
35C11×#554C2211yescharacteristic
36C11×#552—22no—
37C11×#552C2212yes—
38C11×#550C2211yescharacteristic
39D4×Q8×C11C2212yes—
40D4×Q8×C11C2211yescharacteristic
41C11×#548C2212yes—
42C11×#547—22no—
43C11×#547C2212yes—
44C11×#542—22no—
45C11×#542C2212yes—
46C11×#541—22no—
47C11×#541C2212yes—
48C11×#533—21no—
49C11×#533C2211yescharacteristic
50C11×#532—21no—
51C11×#532C2211yescharacteristic
52C11×#529—21no—
53C11×#529—21no—
54C11×#529C2211yescharacteristic
55C11×#520C2212yes—
56C11×#519C2212yes—
57C2×C4×Q8×C11C2211yescharacteristic
58C2×C4×Q8×C11C2211yescharacteristic
59C11×#501C2212yes—
60C11×#498C2211yescharacteristic
61C11×#497C2212yes—
62C11×#492C2211yescharacteristic
63C11×#488C2212yes—
64C11×#487C2211yescharacteristic
65C11×#487C2212yes—
66C11×#486C2211yescharacteristic
67C11×#485C2212yes—
68C11×#484C2212yes—
69C11×#483C2212yes—
70C11×#483C2212yes—
71C11×#482C2212yes—
72C11×#480C2212yes—
73C11×#479C2212yes—
74C11×#478C2212yes—
75C11×#477C2211yescharacteristic
76C11×#477C2212yes—
77C11×#477C2211yescharacteristic
78C11×#475C2212yes—
79C11×#475C2211yescharacteristic
80C11×#475C2211yescharacteristic
81C11×#470C2212yes—
82C11×#468C2212yes—
83C11×#467C2212yes—
84C11×#465C2212yes—
85C11×#465C2212yes—
86C11×#465C2212yes—
87C11×#464C2212yes—
88C11×#464C2212yes—
89C11×#462C2212yes—
90C11×#462C2211yescharacteristic
91C11×#462C2211yescharacteristic
92C11×#461C2212yes—
93C11×#460C2211yescharacteristic
94C11×#460C2211yescharacteristic
95C11×#452C2212yes—
96C11×#452C2212yes—
97C11×#451C2212yes—
98C11×#451C2212yes—
99C11×#448C2212yes—
100C11×#448C2212yes—
101C11×#446C2211yescharacteristic
102C8×Q8×C11C2211yescharacteristic
103C11×#441C2212yes—
104C11×#441C2212yes—
105C11×#441C2212yes—
106C11×#440C2212yes—
107C11×#440C2212yes—
108C11×#440C2212yes—
109C4×C11×Q16C2211yescharacteristic
110C4×C11×Q16C2211yescharacteristic
111C4×C11×Q16C2211yescharacteristic
112C4×C11×Q16C2211yescharacteristic
113C4×C11×Q16C2211yescharacteristic
114C4×C11×Q16C2211yescharacteristic
115C4×C11×Q16C2211yescharacteristic
116C4×C11×Q16C2211yescharacteristic
117C4×C11×Q16C2212yes—
118C4×C11×SD16C2212yes—
119C4×C11×SD16C2212yes—
120C4×C11×SD16C2212yes—
121C11×#436C2211yescharacteristic
122C11×#435C2212yes—
123C8×D4×C11C2212yes—
124C8×D4×C11C2211yescharacteristic
125C11×#433C2212yes—
126C11×#432C2211yescharacteristic
127C11×#428C2212yes—
128C2×C11×#107C2211yescharacteristic
129C11×#416C2212yes—
130C2×C11×#103C2211yescharacteristic
131C2×C11×#103C2211yescharacteristic
132C2×C11×#103C2212yes—
133C11×#405C2212yes—
134C2×C4×C8×C11C2211yescharacteristic
135C2×C11×#41—22no—
136C2×C11×#41—21no—
137C2×C11×#41C2312yes—
138C22×Q8×C11C2311yescharacteristic
139C22×Q8×C11C2311yescharacteristic
140C22×Q8×C11C2312yes—
141C11×#137—28no—
142C2×C11×Q16—24no—
143C2×C11×Q16C2311yescharacteristic
144C2×C11×Q16C2311yescharacteristic
145C2×C11×Q16C2311yescharacteristic
146C2×C11×Q16C2312yes—
147C2×C11×Q16C2312yes—
148C2×C11×Q16C2311yescharacteristic
149C2×C11×SD16C2312yes—
150C2×C11×SD16C2312yes—
151C2×C11×SD16C2312yes—
152C2×C11×SD16C2312yes—
153C2×C11×M16C2312yes—
154C22×C8×C11C2311yescharacteristic
155C22×C8×C11C2311yescharacteristic
156C22×C8×C11C2312yes—
157C11×C4⋊Q8—21no—
158C11×C4⋊Q8—21no—
159C11×C4⋊Q8—21no—
160C11×C4⋊Q8—22no—
161C11×C4⋊Q8—22no—
162C11×C4⋊Q8C2311yescharacteristic
163C11×C4⋊Q8C2312yes—
164C11×C4⋊Q8C2311yescharacteristic
165C11×C4⋊Q8C2311yescharacteristic
166C11×C4⋊Q8C2312yes—
167C11×#127—21no—
168C11×#127C2311yescharacteristic
169C11×#126—22no—
170C11×#126—22no—
171C11×#126—22no—
172C11×#126—22no—
173C11×#126—22no—
174C11×#126D412yes—
175C11×#125—21no—
176C11×#125—21no—
177C11×#125—22no—
178C11×#125—22no—
179C11×#125—22no—
180C11×#125—22no—
181C11×#125—22no—
182C11×#125—21no—
183C11×#125D411yescharacteristic
184C11×#125C2312yes—
185C11×#124—21no—
186C11×#124—21no—
187C11×#124—22no—
188C11×#124—22no—
189C11×#124—21no—
190C11×#124D411yescharacteristic
191C11×#124C2312yes—
192C11×#123—22no—
193C11×#123—22no—
194C11×#123—22no—
195C11×#123—22no—
196C11×#123—22no—
197C11×#123D412yes—
198C11×C22⋊Q8—21no—
199C11×C22⋊Q8—22no—
200C11×C22⋊Q8—22no—
201C11×C22⋊Q8—22no—
202C11×C22⋊Q8—22no—
203C11×C22⋊Q8—22no—
204C11×C22⋊Q8—22no—
205C11×C22⋊Q8—22no—
206C11×C22⋊Q8D411yescharacteristic
207C11×C22⋊Q8C2312yes—
208C11×C22⋊Q8C2312yes—
209C11×C22⋊Q8C2312yes—
210C11×C22⋊Q8C2312yes—
211C11×#121—22no—
212C11×#121—21no—
213C11×#121—22no—
214C11×#121D411yescharacteristic
215C11×#121C2312yes—
216C11×#121C2312yes—
217C4×Q8×C11—21no—
218C4×Q8×C11—21no—
219C4×Q8×C11—22no—
220C4×Q8×C11—22no—
221C4×Q8×C11—21no—
222C4×Q8×C11—21no—
223C4×Q8×C11—21no—
224C4×Q8×C11—21no—
225C4×Q8×C11—21no—
226C4×Q8×C11—21no—
227C4×Q8×C11—21no—
228C4×Q8×C11C2311yescharacteristic
229C4×Q8×C11C2311yescharacteristic
230C4×Q8×C11C2311yescharacteristic
231C4×Q8×C11C2311yescharacteristic
232C4×Q8×C11C2311yescharacteristic
233C4×Q8×C11C2311yescharacteristic
234C4×Q8×C11C2311yescharacteristic
235C4×Q8×C11C2311yescharacteristic
236C4×Q8×C11C2312yes—
237C4×Q8×C11C2312yes—
238C4×Q8×C11C2312yes—
239C4×Q8×C11C2312yes—
240C4×Q8×C11C2311yescharacteristic
241C4×D4×C11—22no—
242C4×D4×C11—21no—
243C4×D4×C11—21no—
244C4×D4×C11—21no—
245C4×D4×C11—21no—
246C4×D4×C11—22no—
247C4×D4×C11—22no—
248C4×D4×C11—22no—
249C4×D4×C11—21no—
250C4×D4×C11C2312yes—
251C4×D4×C11C2312yes—
252C4×D4×C11C2312yes—
253C4×D4×C11C2311yescharacteristic
254C11×#117—21no—
255C11×#117—22no—
256C11×#117—22no—
257C11×#117—22no—
258C11×#117—22no—
259C11×#117C2312yes—
260C11×#117C2312yes—
261C2×C11×C4⋊C4—21no—
262C2×C11×C4⋊C4—21no—
263C2×C11×C4⋊C4—22no—
264C2×C11×C4⋊C4C2311yescharacteristic
265C2×C11×C4⋊C4C2311yescharacteristic
266C2×C11×C4⋊C4C2312yes—
267C2×C42×C11—21no—
268C2×C42×C11—21no—
269C2×C42×C11C2311yescharacteristic
270C11×#107C2311yescharacteristic
271C11×#107C2312yes—
272C11×#107C2311yescharacteristic
273C11×#107C2311yescharacteristic
274C11×#107C2311yescharacteristic
275C11×#107C2312yes—
276C11×#106C2312yes—
277C11×#106C2312yes—
278C11×#106C2312yes—
279C11×#106C2312yes—
280C11×C4⋊C8C2311yescharacteristic
281C11×C4⋊C8C2311yescharacteristic
282C11×C4⋊C8C2312yes—
283C11×C4⋊C8C2312yes—
284C11×#103C2311yescharacteristic
285C11×#103C2311yescharacteristic
286C11×#103C2312yes—
287C11×#103C2311yescharacteristic
288C11×#103C2311yescharacteristic
289C11×#103C2311yescharacteristic
290C11×#103C2311yescharacteristic
291C11×#103C2311yescharacteristic
292C11×#103C2311yescharacteristic
293C11×#103C2312yes—
294C11×#103C2312yes—
295C11×#103C2312yes—
296C11×#103C2312yes—
297C11×#103C2312yes—
298C11×#103C2312yes—
299C11×#103C2312yes—
300C11×#102C2312yes—
301C11×#102C2312yes—
302C11×#102C2312yes—
303C11×#102C2312yes—
304C11×C22⋊C8C2312yes—
305C11×C22⋊C8C2312yes—
306C11×C22⋊C8C2312yes—
307C11×#97C2312yes—
308C11×#97C2312yes—
309C4×C8×C11C2311yescharacteristic
310C4×C8×C11C2311yescharacteristic
311C4×C8×C11C2311yescharacteristic
312C4×C8×C11C2311yescharacteristic
313C4×C8×C11C2312yes—
314#61499C1111yesmaximal, characteristic, direct product factor, Sylow
315C11×#41—24no—
316C11×#41—42no—
317C11×#41—82no—
318C11×#41—84no—
319C2×Q8×C11—21no—
320C2×Q8×C11—21no—
321C2×Q8×C11—22no—
322C2×Q8×C11—21no—
323C2×Q8×C11—22no—
324C2×Q8×C11—21no—
325C2×Q8×C11—22no—
326C2×Q8×C11—22no—
327C2×Q8×C11—24no—
328C2×Q8×C11—41no—
329C2×Q8×C11—41no—
330C2×Q8×C11—42no—
331C2×Q8×C11C2×D411yescharacteristic
332C2×Q8×C11C2411yescharacteristic
333C2×Q8×C11C2412yes—
334C2×Q8×C11C2411yescharacteristic
335C2×Q8×C11C2411yescharacteristic
336C2×Q8×C11C2411yescharacteristic
337C2×D4×C11—22no—
338C2×D4×C11—22no—
339C2×D4×C11—22no—
340C2×D4×C11—21no—
341C2×D4×C11—21no—
342C2×D4×C11C2×D411yescharacteristic
343C2×D4×C11C2×D412yes—
344C2×D4×C11C2412yes—
345C22×C4×C11—21no—
346C22×C4×C11—21no—
347C22×C4×C11—21no—
348C22×C4×C11—21no—
349C22×C4×C11—22no—
350C22×C4×C11—22no—
351C22×C4×C11—22no—
352C22×C4×C11—22no—
353C22×C4×C11—22no—
354C22×C4×C11C2×D411yescharacteristic
355C22×C4×C11C2×D411yescharacteristic
356C22×C4×C11C2411yescharacteristic
357C22×C4×C11C2412yes—
358C11×Q16—22no—
359C11×Q16—22no—
360C11×Q16—22no—
361C11×Q16—24no—
362C11×Q16—42no—
363C11×Q16#4114yescomplemented
364C11×SD16—24no—
365C11×SD16—24no—
366C11×SD16—42no—
367C11×SD16—42no—
368C11×M16—24no—
369C2×C8×C11—22no—
370C2×C8×C11—41no—
371C2×C8×C11—42no—
372C2×C8×C11C2411yescharacteristic
373C2×C8×C11C2411yescharacteristic
374C2×C8×C11C2411yescharacteristic
375C2×C8×C11C2412yes—
376C2×C8×C11C2412yes—
377C2×C8×C11C2411yescharacteristic
378C11×C4⋊C4—21no—
379C11×C4⋊C4—22no—
380C11×C4⋊C4—21no—
381C11×C4⋊C4—22no—
382C11×C4⋊C4—21no—
383C11×C4⋊C4—21no—
384C11×C4⋊C4—21no—
385C11×C4⋊C4—21no—
386C11×C4⋊C4—21no—
387C11×C4⋊C4—21no—
388C11×C4⋊C4—21no—
389C11×C4⋊C4—21no—
390C11×C4⋊C4—22no—
391C11×C4⋊C4—22no—
392C11×C4⋊C4—22no—
393C11×C4⋊C4—21no—
394C11×C4⋊C4—22no—
395C11×C4⋊C4—21no—
396C11×C4⋊C4—22no—
397C11×C4⋊C4—21no—
398C11×C4⋊C4—21no—
399C11×C4⋊C4—22no—
400C11×C4⋊C4—22no—
401C11×C4⋊C4—22no—
402C11×C4⋊C4—22no—
403C11×C4⋊C4—22no—
404C11×C4⋊C4—22no—
405C11×C4⋊C4—22no—
406C11×C4⋊C4C2×D412yes—
407C11×C4⋊C4C2×D412yes—
408C11×C4⋊C4C2×D411yescharacteristic
409C11×C4⋊C4C2×D411yescharacteristic
410C11×C4⋊C4C2×D412yes—
411C11×C4⋊C4C2×D412yes—
412C11×C4⋊C4C2412yes—
413C11×C4⋊C4C2411yescharacteristic
414C11×C4⋊C4C2411yescharacteristic
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—22no—
424C11×C22⋊C4—22no—
425C11×C22⋊C4—22no—
426C11×C22⋊C4—22no—
427C11×C22⋊C4—22no—
428C11×C22⋊C4—22no—
429C11×C22⋊C4C2×D412yes—
430C11×C22⋊C4C2×D412yes—
431C11×C22⋊C4C2×D412yes—
432C11×C22⋊C4C2×D412yes—
433C11×C22⋊C4C2×D412yes—
434C42×C11—21no—
435C42×C11—21no—
436C42×C11—21no—
437C42×C11—21no—
438C42×C11—21no—
439C42×C11—21no—
440C42×C11—21no—
441C42×C11—21no—
442C42×C11—22no—
443C42×C11—22no—
444C42×C11—22no—
445C42×C11—22no—
446C42×C11—22no—
447C42×C11C2×D411yescharacteristic
448C42×C11C2×D411yescharacteristic
449C42×C11C2411yescharacteristic
450C42×C11C2411yescharacteristic
451C42×C11C2412yes—
452#3523C2×C1111yescharacteristic, complemented
453#3522C2×C1111yescharacteristic
454#3400C2×C1111yescharacteristic, complemented
455#3387C2×C1111yescharacteristic, complemented
456#3365C2×C1111yescharacteristic, complemented
457#3363C2×C1111yescharacteristic, complemented
458#3356C2×C1111yescharacteristic, complemented
459#3343C2×C1112yescomplemented
460#3304C2×C1111yescharacteristic, complemented
461#3300C2×C1112yescomplemented
462#3299C2×C1111yescharacteristic, complemented
463#3298C2×C1112yescomplemented
464#3278C2×C1111yescharacteristic, complemented
465#3270C2×C1112yescomplemented
466#3178C2×C1112yescomplemented
467#3167C2×C1111yescharacteristic, complemented
468#3121C2×C1112yescomplemented
469#3120C2×C1112yescomplemented
470#3113C2×C1111yescharacteristic, complemented
471#3112C2×C1111yescharacteristic, complemented
472#2966C2×C1111yescharacteristic, complemented
473#2947C2×C1112yescomplemented
474C2×C4×Q16C2×C1111yescharacteristic, complemented
475C23×C11—22no—
476C23×C11C22×D412yes—
477C23×C11C22×D411yescharacteristic
478Q8×C11—22no—
479Q8×C11—21no—
480Q8×C11—21no—
481Q8×C11—22no—
482Q8×C11—21no—
483Q8×C11—21no—
484Q8×C11—21no—
485Q8×C11—22no—
486Q8×C11—21no—
487Q8×C11—44no—
488Q8×C11—42no—
489Q8×C11—42no—
490Q8×C11—42no—
491Q8×C11—81no—
492Q8×C11—82no—
493Q8×C11C2×#4112yes—
494Q8×C11C2×#4112yes—
495D4×C11—24no—
496D4×C11—22no—
497D4×C11—22no—
498D4×C11—22no—
499D4×C11—44no—
500D4×C11—44no—
501D4×C11—42no—
502D4×C11—81no—
503D4×C11—82no—
504C2×C4×C11—22no—
505C2×C4×C11—21no—
506C2×C4×C11—21no—
507C2×C4×C11—22no—
508C2×C4×C11—21no—
509C2×C4×C11—22no—
510C2×C4×C11—21no—
511C2×C4×C11—22no—
512C2×C4×C11—21no—
513C2×C4×C11—22no—
514C2×C4×C11—21no—
515C2×C4×C11—21no—
516C2×C4×C11—21no—
517C2×C4×C11—22no—
518C2×C4×C11—21no—
519C2×C4×C11—21no—
520C2×C4×C11—22no—
521C2×C4×C11—44no—
522C2×C4×C11—42no—
523C2×C4×C11—42no—
524C2×C4×C11—44no—
525C2×C4×C11—42no—
526C2×C4×C11—42no—
527C2×C4×C11—82no—
528C2×C4×C11—82no—
529C2×C4×C11—82no—
530C2×C4×C11C22×D411yescharacteristic
531C2×C4×C11C22×D411yescharacteristic
532C2×C4×C11C22×D412yes—
533C2×C4×C11C22×D412yes—
534C2×C4×C11C22×D412yes—
535C2×C4×C11C22×D411yescharacteristic
536C2×C4×C11C22×D411yescharacteristic
537C2×C4×C11C22×D411yescharacteristic
538C2×C4×C11C2511yescharacteristic
539C8×C11—21no—
540C8×C11—22no—
541C8×C11—21no—
542C8×C11—21no—
543C8×C11—22no—
544C8×C11C2×#4112yes—
545C2×#137C22×C1112yes—
546C22×Q16C22×C1111yescharacteristic
547#559—21no—
548#559C22×C1111yescharacteristic
549Q82C22×C1111yescharacteristic
550#557—21no—
551#557C22×C1111yescharacteristic
552#557C22×C1111yescharacteristic
553#556—21no—
554#556C22×C1111yescharacteristic
555#554—21no—
556#554C22×C1111yescharacteristic
557#552—22no—
558#552C22×C1112yes—
559#550C22×C1111yescharacteristic
560D4×Q8C22×C1112yes—
561D4×Q8C22×C1111yescharacteristic
562#548C22×C1112yes—
563#547—22no—
564#547C22×C1112yes—
565#542—22no—
566#542C22×C1112yes—
567#541—22no—
568#541C22×C1112yes—
569#533—21no—
570#533C22×C1111yescharacteristic
571#532—21no—
572#532C22×C1111yescharacteristic
573#529—21no—
574#529—21no—
575#529C22×C1111yescharacteristic
576#520C22×C1112yes—
577#519C22×C1112yes—
578C2×C4×Q8C22×C1111yescharacteristic
579C2×C4×Q8C22×C1111yescharacteristic
580#501C22×C1112yes—
581#498C22×C1111yescharacteristic
582#497C22×C1112yes—
583#492C22×C1111yescharacteristic
584#488C22×C1112yes—
585#487C22×C1111yescharacteristic
586#487C22×C1112yes—
587#486C22×C1111yescharacteristic
588#485C22×C1112yes—
589#484C22×C1112yes—
590#483C22×C1112yes—
591#483C22×C1112yes—
592#482C22×C1112yes—
593#480C22×C1112yes—
594#479C22×C1112yes—
595#478C22×C1112yes—
596#477C22×C1112yes—
597#477C22×C1111yescharacteristic
598#477C22×C1111yescharacteristic
599#475C22×C1111yescharacteristic
600#475C22×C1111yescharacteristic
601#475C22×C1112yes—
602#470C22×C1112yes—
603#468C22×C1112yes—
604#467C22×C1112yes—
605#465C22×C1112yes—
606#465C22×C1112yes—
607#465C22×C1112yes—
608#464C22×C1112yes—
609#464C22×C1112yes—
610#462C22×C1111yescharacteristic
611#462C22×C1112yes—
612#462C22×C1111yescharacteristic
613#461C22×C1112yes—
614#460C22×C1111yescharacteristic
615#460C22×C1111yescharacteristic
616#452C22×C1112yes—
617#452C22×C1112yes—
618#451C22×C1112yes—
619#451C22×C1112yes—
620#448C22×C1112yes—
621#448C22×C1112yes—
622#446C22×C1111yescharacteristic
623C8×Q8C22×C1111yescharacteristic
624#441C22×C1112yes—
625#441C22×C1112yes—
626#441C22×C1112yes—
627#440C22×C1112yes—
628#440C22×C1112yes—
629#440C22×C1112yes—
630C4×Q16C22×C1111yescharacteristic
631C4×Q16C22×C1111yescharacteristic
632C4×Q16C22×C1112yes—
633C4×Q16C22×C1111yescharacteristic
634C4×Q16C22×C1111yescharacteristic
635C4×Q16C22×C1111yescharacteristic
636C4×Q16C22×C1111yescharacteristic
637C4×Q16C22×C1111yescharacteristic
638C4×Q16C22×C1111yescharacteristic
639C4×SD16C22×C1112yes—
640C4×SD16C22×C1112yes—
641C4×SD16C22×C1112yes—
642#436C22×C1111yescharacteristic
643#435C22×C1112yes—
644C8×D4C22×C1112yes—
645C8×D4C22×C1111yescharacteristic
646#433C22×C1112yes—
647#432C22×C1111yescharacteristic
648#428C22×C1112yes—
649C2×#107C22×C1111yescharacteristic
650#416C22×C1112yes—
651C2×#103C22×C1111yescharacteristic
652C2×#103C22×C1111yescharacteristic
653C2×#103C22×C1112yes—
654#405C22×C1112yes—
655C2×C4×C8C22×C1111yescharacteristic
656C22×C11—21no—
657C22×C11—21no—
658C22×C11—22no—
659C22×C11—22no—
660C22×C11—22no—
661C22×C11—42no—
662C22×C11—42no—
663C22×C11—42no—
664C22×C11#57712yes—
665C22×C11C23×D411yescharacteristic
666C4×C11—22no—
667C4×C11—21no—
668C4×C11—22no—
669C4×C11—22no—
670C4×C11—21no—
671C4×C11—21no—
672C4×C11—22no—
673C4×C11—21no—
674C4×C11—22no—
675C4×C11—41no—
676C4×C11—42no—
677C4×C11—41no—
678C4×C11—41no—
679C4×C11—41no—
680C4×C11—41no—
681C4×C11—41no—
682C4×C11—42no—
683C4×C11—42no—
684C4×C11#57812yes—
685C4×C11C22×#4111yescharacteristic
686C4×C11#58511yescharacteristic
687C2×#41—22no—
688C2×#41—21no—
689C2×#41C23×C1112yes—
690C22×Q8C23×C1111yescharacteristic
691C22×Q8C23×C1111yescharacteristic
692C22×Q8C23×C1112yes—
693#137—28no—
694C2×Q16—24no—
695C2×Q16C23×C1111yescharacteristic
696C2×Q16C23×C1111yescharacteristic
697C2×Q16C23×C1111yescharacteristic
698C2×Q16C23×C1112yes—
699C2×Q16C23×C1112yes—
700C2×Q16C23×C1111yescharacteristic
701C2×SD16C23×C1112yes—
702C2×SD16C23×C1112yes—
703C2×SD16C23×C1112yes—
704C2×SD16C23×C1112yes—
705C2×M16C23×C1112yes—
706C22×C8C23×C1111yescharacteristic
707C22×C8C23×C1111yescharacteristic
708C22×C8C23×C1112yes—
709C4⋊Q8—21no—
710C4⋊Q8—21no—
711C4⋊Q8—21no—
712C4⋊Q8—22no—
713C4⋊Q8—22no—
714C4⋊Q8C23×C1111yescharacteristic
715C4⋊Q8C23×C1112yes—
716C4⋊Q8C23×C1111yescharacteristic
717C4⋊Q8C23×C1111yescharacteristic
718C4⋊Q8C23×C1112yes—
719#127—21no—
720#127C23×C1111yescharacteristic
721#126—22no—
722#126—22no—
723#126—22no—
724#126—22no—
725#126—22no—
726#126D4×C1112yes—
727#125—21no—
728#125—21no—
729#125—22no—
730#125—22no—
731#125—22no—
732#125—22no—
733#125—22no—
734#125—21no—
735#125D4×C1111yescharacteristic
736#125C23×C1112yes—
737#124—21no—
738#124—21no—
739#124—22no—
740#124—22no—
741#124—21no—
742#124D4×C1111yescharacteristic
743#124C23×C1112yes—
744#123—22no—
745#123—22no—
746#123—22no—
747#123—22no—
748#123—22no—
749#123D4×C1112yes—
750C22⋊Q8—21no—
751C22⋊Q8—22no—
752C22⋊Q8—22no—
753C22⋊Q8—22no—
754C22⋊Q8—22no—
755C22⋊Q8—22no—
756C22⋊Q8—22no—
757C22⋊Q8—22no—
758C22⋊Q8D4×C1111yescharacteristic
759C22⋊Q8C23×C1112yes—
760C22⋊Q8C23×C1112yes—
761C22⋊Q8C23×C1112yes—
762C22⋊Q8C23×C1112yes—
763#121—22no—
764#121—21no—
765#121—22no—
766#121D4×C1111yescharacteristic
767#121C23×C1112yes—
768#121C23×C1112yes—
769C4×Q8—21no—
770C4×Q8—21no—
771C4×Q8—22no—
772C4×Q8—22no—
773C4×Q8—21no—
774C4×Q8—21no—
775C4×Q8—21no—
776C4×Q8—21no—
777C4×Q8—21no—
778C4×Q8—21no—
779C4×Q8—21no—
780C4×Q8C23×C1111yescharacteristic
781C4×Q8C23×C1111yescharacteristic
782C4×Q8C23×C1111yescharacteristic
783C4×Q8C23×C1111yescharacteristic
784C4×Q8C23×C1111yescharacteristic
785C4×Q8C23×C1111yescharacteristic
786C4×Q8C23×C1111yescharacteristic
787C4×Q8C23×C1111yescharacteristic
788C4×Q8C23×C1112yes—
789C4×Q8C23×C1112yes—
790C4×Q8C23×C1112yes—
791C4×Q8C23×C1112yes—
792C4×Q8C23×C1111yescharacteristic
793C4×D4—22no—
794C4×D4—21no—
795C4×D4—21no—
796C4×D4—21no—
797C4×D4—21no—
798C4×D4—22no—
799C4×D4—22no—
800C4×D4—22no—
801C4×D4—21no—
802C4×D4C23×C1112yes—
803C4×D4C23×C1112yes—
804C4×D4C23×C1112yes—
805C4×D4C23×C1111yescharacteristic
806#117—21no—
807#117—22no—
808#117—22no—
809#117—22no—
810#117—22no—
811#117C23×C1112yes—
812#117C23×C1112yes—
813C2×C4⋊C4—21no—
814C2×C4⋊C4—21no—
815C2×C4⋊C4—22no—
816C2×C4⋊C4C23×C1111yescharacteristic
817C2×C4⋊C4C23×C1111yescharacteristic
818C2×C4⋊C4C23×C1112yes—
819C2×C42—21no—
820C2×C42—21no—
821C2×C42C23×C1111yescharacteristic
822#107C23×C1111yescharacteristic
823#107C23×C1111yescharacteristic
824#107C23×C1111yescharacteristic
825#107C23×C1111yescharacteristic
826#107C23×C1112yes—
827#107C23×C1112yes—
828#106C23×C1112yes—
829#106C23×C1112yes—
830#106C23×C1112yes—
831#106C23×C1112yes—
832C4⋊C8C23×C1111yescharacteristic
833C4⋊C8C23×C1111yescharacteristic
834C4⋊C8C23×C1112yes—
835C4⋊C8C23×C1112yes—
836#103C23×C1111yescharacteristic
837#103C23×C1111yescharacteristic
838#103C23×C1112yes—
839#103C23×C1111yescharacteristic
840#103C23×C1111yescharacteristic
841#103C23×C1111yescharacteristic
842#103C23×C1111yescharacteristic
843#103C23×C1111yescharacteristic
844#103C23×C1111yescharacteristic
845#103C23×C1112yes—
846#103C23×C1112yes—
847#103C23×C1112yes—
848#103C23×C1112yes—
849#103C23×C1112yes—
850#103C23×C1112yes—
851#103C23×C1112yes—
852#102C23×C1112yes—
853#102C23×C1112yes—
854#102C23×C1112yes—
855#102C23×C1112yes—
856C22⋊C8C23×C1112yes—
857C22⋊C8C23×C1112yes—
858C22⋊C8C23×C1112yes—
859#97C23×C1112yes—
860#97C23×C1112yes—
861C4×C8C23×C1111yescharacteristic
862C4×C8C23×C1111yescharacteristic
863C4×C8C23×C1111yescharacteristic
864C4×C8C23×C1111yescharacteristic
865C4×C8C23×C1112yes—
866C2×C11—22no—
867C2×C11—42no—
868C2×C11—82no—
869C2×C11D4×#4111yescharacteristic
870C2×C11C2×#57711yescharacteristic
871C2×C11C2×#57811yescharacteristic
872#41—24no—
873#41—42no—
874#41—82no—
875#41—84no—
876C2×Q8—21no—
877C2×Q8—21no—
878C2×Q8—22no—
879C2×Q8—21no—
880C2×Q8—22no—
881C2×Q8—21no—
882C2×Q8—22no—
883C2×Q8—22no—
884C2×Q8—24no—
885C2×Q8—41no—
886C2×Q8—41no—
887C2×Q8—42no—
888C2×Q8C2×D4×C1111yescharacteristic
889C2×Q8C24×C1111yescharacteristic
890C2×Q8C24×C1112yes—
891C2×Q8C24×C1111yescharacteristic
892C2×Q8C24×C1111yescharacteristic
893C2×Q8C24×C1111yescharacteristic
894C2×D4—22no—
895C2×D4—22no—
896C2×D4—22no—
897C2×D4—21no—
898C2×D4—21no—
899C2×D4C2×D4×C1111yescharacteristic
900C2×D4C2×D4×C1112yes—
901C2×D4C24×C1112yes—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—22no—
907C22×C4—22no—
908C22×C4—22no—
909C22×C4—22no—
910C22×C4—22no—
911C22×C4C2×D4×C1111yescharacteristic
912C22×C4C2×D4×C1111yescharacteristic
913C22×C4C24×C1111yescharacteristic
914C22×C4C24×C1112yes—
915Q16—22no—
916Q16—22no—
917Q16—24no—
918Q16—22no—
919Q16—42no—
920Q16C11×#4114yescomplemented
921SD16—24no—
922SD16—24no—
923SD16—42no—
924SD16—42no—
925M16—24no—
926C2×C8—22no—
927C2×C8—41no—
928C2×C8—42no—
929C2×C8C24×C1111yescharacteristic
930C2×C8C24×C1111yescharacteristic
931C2×C8C24×C1111yescharacteristic
932C2×C8C24×C1112yes—
933C2×C8C24×C1112yes—
934C2×C8C24×C1111yescharacteristic
935C4⋊C4—21no—
936C4⋊C4—22no—
937C4⋊C4—21no—
938C4⋊C4—22no—
939C4⋊C4—21no—
940C4⋊C4—21no—
941C4⋊C4—21no—
942C4⋊C4—21no—
943C4⋊C4—21no—
944C4⋊C4—21no—
945C4⋊C4—21no—
946C4⋊C4—21no—
947C4⋊C4—22no—
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—22no—
958C4⋊C4—22no—
959C4⋊C4—22no—
960C4⋊C4—22no—
961C4⋊C4—22no—
962C4⋊C4—22no—
963C4⋊C4C2×D4×C1112yes—
964C4⋊C4C2×D4×C1112yes—
965C4⋊C4C2×D4×C1111yescharacteristic
966C4⋊C4C2×D4×C1111yescharacteristic
967C4⋊C4C2×D4×C1112yes—
968C4⋊C4C2×D4×C1112yes—
969C4⋊C4C24×C1112yes—
970C4⋊C4C24×C1111yescharacteristic
971C4⋊C4C24×C1111yescharacteristic
972C4⋊C4C24×C1111yescharacteristic
973C4⋊C4C24×C1112yes—
974C4⋊C4C24×C1111yescharacteristic
975C22⋊C4—22no—
976C22⋊C4—22no—
977C22⋊C4—22no—
978C22⋊C4—22no—
979C22⋊C4—22no—
980C22⋊C4—22no—
981C22⋊C4—22no—
982C22⋊C4—22no—
983C22⋊C4—22no—
984C22⋊C4—22no—
985C22⋊C4—22no—
986C22⋊C4C2×D4×C1112yes—
987C22⋊C4C2×D4×C1112yes—
988C22⋊C4C2×D4×C1112yes—
989C22⋊C4C2×D4×C1112yes—
990C22⋊C4C2×D4×C1112yes—
991C42—21no—
992C42—21no—
993C42—21no—
994C42—21no—
995C42—21no—
996C42—21no—
997C42—21no—
998C42—21no—
999C42—22no—
1000C42—22no—
1001C42—22no—
1002C42—22no—
1003C42—22no—
1004C42C2×D4×C1111yescharacteristic
1005C42C2×D4×C1111yescharacteristic
1006C42C24×C1111yescharacteristic
1007C42C24×C1111yescharacteristic
1008C42C24×C1112yes—
1009C11#6149911yescharacteristic, direct product factor, Sylow
1010C23—22no—
1011C23C22×D4×C1112yes—
1012C23C22×D4×C1111yescharacteristic
1013Q8—22no—
1014Q8—21no—
1015Q8—21no—
1016Q8—22no—
1017Q8—21no—
1018Q8—21no—
1019Q8—21no—
1020Q8—22no—
1021Q8—21no—
1022Q8—44no—
1023Q8—42no—
1024Q8—42no—
1025Q8—42no—
1026Q8—81no—
1027Q8—82no—
1028Q8C2×C11×#4112yes—
1029Q8C2×C11×#4112yes—
1030D4—24no—
1031D4—22no—
1032D4—22no—
1033D4—22no—
1034D4—44no—
1035D4—44no—
1036D4—42no—
1037D4—81no—
1038D4—82no—
1039C2×C4—22no—
1040C2×C4—21no—
1041C2×C4—21no—
1042C2×C4—22no—
1043C2×C4—21no—
1044C2×C4—22no—
1045C2×C4—21no—
1046C2×C4—22no—
1047C2×C4—21no—
1048C2×C4—22no—
1049C2×C4—21no—
1050C2×C4—21no—
1051C2×C4—21no—
1052C2×C4—22no—
1053C2×C4—21no—
1054C2×C4—21no—
1055C2×C4—22no—
1056C2×C4—44no—
1057C2×C4—42no—
1058C2×C4—42no—
1059C2×C4—44no—
1060C2×C4—42no—
1061C2×C4—42no—
1062C2×C4—82no—
1063C2×C4—82no—
1064C2×C4—82no—
1065C2×C4C22×D4×C1111yescharacteristic
1066C2×C4C22×D4×C1111yescharacteristic
1067C2×C4C22×D4×C1112yes—
1068C2×C4C22×D4×C1112yes—
1069C2×C4C22×D4×C1112yes—
1070C2×C4C22×D4×C1111yescharacteristic
1071C2×C4C22×D4×C1111yescharacteristic
1072C2×C4C22×D4×C1111yescharacteristic
1073C2×C4C25×C1111yescharacteristic
1074C8—21no—
1075C8—22no—
1076C8—21no—
1077C8—21no—
1078C8—22no—
1079C8C2×C11×#4112yes—
1080C22—21no—
1081C22—21no—
1082C22—22no—
1083C22—22no—
1084C22—22no—
1085C22—42no—
1086C22—42no—
1087C22—42no—
1088C22C11×#57712yes—
1089C22C23×D4×C1111yescharacteristic
1090C4—22no—
1091C4—21no—
1092C4—22no—
1093C4—22no—
1094C4—21no—
1095C4—21no—
1096C4—22no—
1097C4—21no—
1098C4—22no—
1099C4—41no—
1100C4—42no—
1101C4—41no—
1102C4—41no—
1103C4—41no—
1104C4—41no—
1105C4—41no—
1106C4—42no—
1107C4—42no—
1108C4C11×#57812yes—
1109C4C22×C11×#4111yescharacteristic
1110C4C11×#58511yescharacteristic
1111C2—22no—
1112C2—42no—
1113C2—82no—
1114C2D4×C11×#4111yescharacteristic
1115C2C2×C11×#57711yescharacteristic
1116C2C2×C11×#57811yescharacteristic
subgroupG/H
center, socleC22×C11C23×D4
commutator, Frattini, cosocleC2×C4C25×C11
prime radicalC11×#3522C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C11×#529 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3523C2semidirect
3. C11×#3400C2semidirect
4. C11×#3387C2semidirect
5. C11×#3365C2semidirect
6. C11×#3363C2semidirect
7. C11×#3356C2semidirect
8. C11×#3343C2semidirect
9. C11×#3304C2semidirect
10. C11×#3300C2semidirect
11. C11×#3299C2semidirect
12. C11×#3298C2semidirect
13. C11×#3278C2semidirect
14. C11×#3270C2semidirect
15. C11×#3178C2semidirect
16. C11×#3167C2semidirect
17. C11×#3121C2semidirect
18. C11×#3120C2semidirect
19. C11×#3113C2semidirect
20. C11×#3112C2semidirect
21. C11×#2966C2semidirect
22. C11×#2947C2semidirect
23. C2×C4×C11×Q16C2semidirect
314. #61499C11direct (N × H)
363. C11×Q16#41semidirect
452. #3523C2×C11semidirect
454. #3400C2×C11semidirect
455. #3387C2×C11semidirect
456. #3365C2×C11semidirect
457. #3363C2×C11semidirect
458. #3356C2×C11semidirect
459. #3343C2×C11semidirect
460. #3304C2×C11semidirect
461. #3300C2×C11semidirect
462. #3299C2×C11semidirect
463. #3298C2×C11semidirect
464. #3278C2×C11semidirect
465. #3270C2×C11semidirect
466. #3178C2×C11semidirect
467. #3167C2×C11semidirect
468. #3121C2×C11semidirect
469. #3120C2×C11semidirect
470. #3113C2×C11semidirect
471. #3112C2×C11semidirect
472. #2966C2×C11semidirect
473. #2947C2×C11semidirect
474. C2×C4×Q16C2×C11semidirect
920. Q16C11×#41semidirect
1009. C11#61499direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35232
C11×#35222
C11×#34002
C11×#33872
C11×#33652
C11×#33632
C11×#33562
C11×#33432
C11×#33042
C11×#33002
C11×#32992
C11×#32982
C11×#32782
C11×#32702
C11×#31782
C11×#31672
C11×#31212
C11×#31202
C11×#31132
C11×#31122
C11×#29662
C11×#29472
C2×C4×C11×Q162
#6149911