Finite Group Databasebeta

← C11×#36725 #14613918

Subgroups — C11×#36725 #14613918

Order 2816.

3282 conjugacy classes of subgroups.

The subgroup lattice has 1092 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2846C212yesmaximal, complemented
2C11×#2736C211yesmaximal, characteristic, complemented
3C11×#2735C211yesmaximal, characteristic, complemented
4C11×#2735C212yesmaximal, complemented
5C11×#2697C212yesmaximal, complemented
6C11×#2685C212yesmaximal, complemented
7C11×#2685C212yesmaximal, complemented
8C11×#2684C212yesmaximal, complemented
9C11×#2678C212yesmaximal, complemented
10C11×#2670C211yesmaximal, characteristic, complemented
11C11×#2668C211yesmaximal, characteristic, complemented
12C11×#2626C211yesmaximal, characteristic, complemented
13C11×#2617C211yesmaximal, characteristic, complemented
14C11×#2480C212yesmaximal, complemented
15C11×#2472C212yesmaximal, complemented
16C11×#2424C212yesmaximal, complemented
17C11×#2418C212yesmaximal, complemented
18C11×#2321C212yesmaximal, complemented
19C2×C11×#379C211yesmaximal, characteristic, complemented
20C26×C11C2211yescharacteristic
21C2×C11×#126C2212yescomplemented
22C2×C11×#124C2212yescomplemented
23C2×C11×#123C2212yescomplemented
24C2×C11×C22⋊Q8C2211yescharacteristic, complemented
25C2×C11×#121C2212yescomplemented
26C2×C11×#121C2211yescharacteristic, complemented
27C2×C11×#120C2212yes—
28C2×C11×#120C2212yes—
29C2×C11×#120C2212yes—
30C2×C11×#120C2212yes—
31C2×C11×#120C2212yes—
32C2×C11×#120C2212yes—
33C2×C11×#120C2212yes—
34C2×C4×D4×C11C2212yescomplemented
35C22×C11×C22⋊C4C2212yes—
36C22×C11×C22⋊C4C2212yes—
37C22×C11×C22⋊C4C2211yescharacteristic
38C22×C11×C22⋊C4C2211yescharacteristic
39C11×#399C2211yescharacteristic, complemented
40C11×#399C2212yescomplemented
41C11×#399C2211yescharacteristic, complemented
42C11×#397C2212yescomplemented
43C11×#397C2212yescomplemented
44C11×#397C2212yescomplemented
45C11×#397C2212yescomplemented
46C11×#397C2212yescomplemented
47C11×#397C2211yescharacteristic, complemented
48C11×#397C2211yescharacteristic, complemented
49C11×#396C2212yescomplemented
50C11×#396C2212yescomplemented
51C11×#396C2212yescomplemented
52C11×#396C2212yescomplemented
53C11×#394C2212yescomplemented
54C11×#394C2212yescomplemented
55C11×#394C2212yescomplemented
56C11×#394C2212yescomplemented
57C11×#394C2212yescomplemented
58C11×#394C2212yescomplemented
59C11×#394C2212yescomplemented
60C11×#394C2212yescomplemented
61C11×#393C2211yescharacteristic, complemented
62C11×#393C2211yescharacteristic, complemented
63C11×#393C2212yescomplemented
64C11×#392C2211yescharacteristic, complemented
65C11×#392C2212yescomplemented
66C11×#392C2211yescharacteristic, complemented
67C11×#390C2212yescomplemented
68C11×#390C2212yescomplemented
69C11×#390C2212yescomplemented
70C11×#390C2212yescomplemented
71C11×#388C2212yescomplemented
72C11×#388C2212yescomplemented
73C11×#388C2212yescomplemented
74C11×#388C2212yescomplemented
75C11×#388C2212yescomplemented
76C11×#388C2212yescomplemented
77C11×#388C2212yescomplemented
78C11×#388C2212yescomplemented
79C11×#388C2212yescomplemented
80C11×#388C2212yescomplemented
81C11×#388C2212yescomplemented
82C11×#388C2212yescomplemented
83C11×#386C2212yescomplemented
84C11×#386C2212yescomplemented
85C11×#386C2212yescomplemented
86C11×#386C2212yescomplemented
87C11×#386C2212yescomplemented
88C11×#386C2212yescomplemented
89C11×#385C2212yescomplemented
90C11×#385C2212yescomplemented
91C11×#380C2211yescharacteristic, complemented
92C11×#380C2211yescharacteristic, complemented
93C11×#379C2211yescharacteristic
94C11×#379C2211yescharacteristic
95C11×#379C2212yes—
96C11×#379C2212yes—
97C11×#379C2212yes—
98C11×#379C2212yes—
99C11×#379C2211yescharacteristic
100C11×#379C2212yes—
101C11×#379C2212yes—
102C11×#379C2211yescharacteristic
103C11×#379C2212yes—
104C11×#379C2212yes—
105C11×#379C2212yes—
106C4×C11×C22⋊C4C2212yescomplemented
107C25×C11—24no—
108C25×C11—44no—
109C25×C11—44no—
110C25×C11—42no—
111C25×C11—42no—
112C25×C11C2312yes—
113C25×C11C2311yescharacteristic
114C25×C11C2311yescharacteristic
115C25×C11C2312yes—
116C25×C11C2311yescharacteristic
117C22×Q8×C11C2311yescharacteristic, complemented
118C22×D4×C11C2312yes—
119C22×D4×C11C2312yes—
120C22×D4×C11C2312yes—
121C22×D4×C11C2312yes—
122C22×D4×C11C2312yes—
123C22×D4×C11C2312yes—
124C22×D4×C11C2312yes—
125C22×D4×C11C2311yescharacteristic, complemented
126C23×C4×C11C2312yes—
127C23×C4×C11C2311yescharacteristic
128C23×C4×C11C2311yescharacteristic
129C23×C4×C11C2312yescomplemented
130C11×#126—44no—
131C11×#124—44no—
132C11×#123—44no—
133C11×C22⋊Q8—42no—
134C11×#121—44no—
135C11×#121—42no—
136C11×#120—28no—
137C11×#120—44no—
138C11×#120—44no—
139C11×#120—44no—
140C11×#120—44no—
141C11×#120—44no—
142C11×#120—44no—
143C4×D4×C11—44no—
144C2×C11×C4⋊C4C2312yescomplemented
145C2×C11×C4⋊C4C2312yescomplemented
146C2×C11×C4⋊C4C2312yescomplemented
147C2×C11×C4⋊C4C2312yescomplemented
148C2×C11×C4⋊C4C2311yescharacteristic, complemented
149C2×C11×C4⋊C4C2312yescomplemented
150C2×C11×C4⋊C4C2312yescomplemented
151C2×C11×C4⋊C4C2312yescomplemented
152C2×C11×C4⋊C4C2311yescharacteristic, complemented
153C2×C11×C4⋊C4C2312yescomplemented
154C2×C11×C22⋊C4—44no—
155C2×C11×C22⋊C4—44no—
156C2×C11×C22⋊C4—42no—
157C2×C11×C22⋊C4—42no—
158C2×C11×C22⋊C4C2312yes—
159C2×C11×C22⋊C4C2312yes—
160C2×C11×C22⋊C4C2312yes—
161C2×C11×C22⋊C4C2312yes—
162C2×C11×C22⋊C4C2312yes—
163C2×C11×C22⋊C4C2312yes—
164C2×C11×C22⋊C4C2312yes—
165C2×C11×C22⋊C4C2312yes—
166C2×C11×C22⋊C4C2312yes—
167C2×C11×C22⋊C4C2312yes—
168C2×C11×C22⋊C4C2312yes—
169C2×C11×C22⋊C4C2312yes—
170C2×C11×C22⋊C4C2312yes—
171C2×C11×C22⋊C4C2311yescharacteristic
172C2×C11×C22⋊C4C2312yes—
173C2×C11×C22⋊C4C2312yes—
174C2×C11×C22⋊C4C2312yes—
175C2×C11×C22⋊C4C2311yescharacteristic
176C2×C11×C22⋊C4C2312yes—
177C2×C11×C22⋊C4C2312yes—
178C2×C11×C22⋊C4C2311yescharacteristic
179C2×C11×C22⋊C4C2311yescharacteristic
180C2×C11×C22⋊C4C2311yescharacteristic
181C2×C11×C22⋊C4C2311yescharacteristic
182C2×C11×C22⋊C4C2312yes—
183C2×C11×C22⋊C4C2312yes—
184C2×C11×C22⋊C4C2312yes—
185C2×C11×C22⋊C4C2312yes—
186C2×C11×C22⋊C4C2312yes—
187C2×C11×C22⋊C4C2312yes—
188C2×C11×C22⋊C4C2312yes—
189C2×C11×C22⋊C4C2312yes—
190C2×C11×C22⋊C4C2312yes—
191C2×C11×C22⋊C4C2312yes—
192C2×C11×C22⋊C4C2312yes—
193C2×C11×C22⋊C4C2312yes—
194C2×C11×C22⋊C4C2312yescomplemented
195C2×C11×C22⋊C4C2312yescomplemented
196C2×C11×C22⋊C4C2312yescomplemented
197C2×C11×C22⋊C4C2312yescomplemented
198C2×C11×C22⋊C4C2312yescomplemented
199C2×C11×C22⋊C4C2312yescomplemented
200C2×C42×C11C2312yescomplemented
201C2×C42×C11C2312yescomplemented
202C2×C42×C11C2312yescomplemented
203C11×#95C2312yescomplemented
204C11×#95C2312yescomplemented
205C11×#95C2311yescharacteristic, complemented
206C11×#95C2311yescharacteristic, complemented
207C11×#95C2311yescharacteristic, complemented
208C11×#95C2311yescharacteristic, complemented
209C11×#95C2312yescomplemented
210C11×#95C2312yescomplemented
211C11×#95C2312yescomplemented
212C11×#95C2312yescomplemented
213C11×#95C2312yescomplemented
214C11×#95C2312yescomplemented
215C11×#95C2312yescomplemented
216C11×#95C2312yescomplemented
217#36725C1111yesmaximal, characteristic, direct product factor, Sylow
218C24×C11—24no—
219C24×C11—24no—
220C24×C11—24no—
221C24×C11—22no—
222C24×C11—22no—
223C24×C11—22no—
224C24×C11—22no—
225C24×C11—24no—
226C24×C11—24no—
227C24×C11—24no—
228C24×C11—24no—
229C24×C11—24no—
230C24×C11—24no—
231C24×C11—24no—
232C24×C11—42no—
233C24×C11—42no—
234C24×C11—42no—
235C24×C11—42no—
236C24×C11—41no—
237C24×C11—41no—
238C24×C11—42no—
239C24×C11—42no—
240C24×C11—42no—
241C24×C11—42no—
242C24×C11—42no—
243C24×C11—41no—
244C24×C11—41no—
245C24×C11—42no—
246C24×C11—432no—
247C24×C11—416no—
248C24×C11—432no—
249C24×C11—416no—
250C24×C11—416no—
251C24×C11#4114yes—
252C24×C11C2412yes—
253C24×C11C2411yescharacteristic
254C24×C11C2411yescharacteristic
255C24×C11C2412yes—
256C24×C11C2412yes—
257C24×C11C2411yescharacteristic
258C2×Q8×C11—41no—
259C2×Q8×C11—42no—
260C2×D4×C11—24no—
261C2×D4×C11—24no—
262C2×D4×C11—24no—
263C2×D4×C11—24no—
264C2×D4×C11—24no—
265C2×D4×C11—24no—
266C2×D4×C11—24no—
267C2×D4×C11—24no—
268C2×D4×C11—24no—
269C2×D4×C11—42no—
270C2×D4×C11—42no—
271C2×D4×C11—42no—
272C2×D4×C11—42no—
273C2×D4×C11—42no—
274C2×D4×C11—42no—
275C2×D4×C11—42no—
276C2×D4×C11—42no—
277C2×D4×C11—42no—
278C2×D4×C11—42no—
279C2×D4×C11—42no—
280C2×D4×C11—42no—
281C2×D4×C11—42no—
282C2×D4×C11—41no—
283C22×C4×C11—24no—
284C22×C4×C11—22no—
285C22×C4×C11—22no—
286C22×C4×C11—42no—
287C22×C4×C11—42no—
288C22×C4×C11—42no—
289C22×C4×C11—42no—
290C22×C4×C11—42no—
291C22×C4×C11—42no—
292C22×C4×C11—42no—
293C22×C4×C11C2412yes—
294C22×C4×C11C2412yes—
295C22×C4×C11C2412yes—
296C22×C4×C11C2412yes—
297C22×C4×C11C2412yes—
298C22×C4×C11C2411yescharacteristic
299C22×C4×C11C2411yescharacteristic
300C22×C4×C11C2412yes—
301C22×C4×C11C2412yes—
302C22×C4×C11C2412yes—
303C22×C4×C11C2412yes—
304C22×C4×C11C2411yescharacteristic
305C22×C4×C11C2411yescharacteristic
306C11×C4⋊C4—42no—
307C11×C4⋊C4—42no—
308C11×C4⋊C4—41no—
309C11×C4⋊C4—41no—
310C11×C4⋊C4—42no—
311C11×C4⋊C4—42no—
312C11×C4⋊C4—42no—
313C11×C4⋊C4—42no—
314C11×C4⋊C4—42no—
315C11×C4⋊C4—42no—
316C11×C22⋊C4—24no—
317C11×C22⋊C4—24no—
318C11×C22⋊C4—24no—
319C11×C22⋊C4—24no—
320C11×C22⋊C4—24no—
321C11×C22⋊C4—24no—
322C11×C22⋊C4—24no—
323C11×C22⋊C4—24no—
324C11×C22⋊C4—24no—
325C11×C22⋊C4—24no—
326C11×C22⋊C4—24no—
327C11×C22⋊C4—24no—
328C11×C22⋊C4—24no—
329C11×C22⋊C4—42no—
330C11×C22⋊C4—42no—
331C11×C22⋊C4—41no—
332C11×C22⋊C4—42no—
333C11×C22⋊C4—42no—
334C11×C22⋊C4—42no—
335C11×C22⋊C4—41no—
336C11×C22⋊C4—41no—
337C11×C22⋊C4—41no—
338C11×C22⋊C4—41no—
339C11×C22⋊C4—41no—
340C11×C22⋊C4—42no—
341C11×C22⋊C4—42no—
342C11×C22⋊C4—42no—
343C11×C22⋊C4—42no—
344C11×C22⋊C4—42no—
345C11×C22⋊C4—42no—
346C11×C22⋊C4—42no—
347C11×C22⋊C4—42no—
348C11×C22⋊C4—42no—
349C11×C22⋊C4—42no—
350C11×C22⋊C4—42no—
351C11×C22⋊C4—42no—
352C11×C22⋊C4—42no—
353C11×C22⋊C4—42no—
354C11×C22⋊C4—42no—
355C11×C22⋊C4—42no—
356C11×C22⋊C4—42no—
357C11×C22⋊C4—42no—
358C42×C11—42no—
359C42×C11—42no—
360C42×C11—42no—
361#2846C2×C1112yescomplemented
362#2736C2×C1111yescharacteristic, complemented
363#2735C2×C1112yescomplemented
364#2735C2×C1111yescharacteristic, complemented
365#2697C2×C1112yescomplemented
366#2685C2×C1112yescomplemented
367#2685C2×C1112yescomplemented
368#2684C2×C1112yescomplemented
369#2678C2×C1112yescomplemented
370#2670C2×C1111yescharacteristic, complemented
371#2668C2×C1111yescharacteristic, complemented
372#2626C2×C1111yescharacteristic, complemented
373#2617C2×C1111yescharacteristic, complemented
374#2480C2×C1112yescomplemented
375#2472C2×C1112yescomplemented
376#2424C2×C1112yescomplemented
377#2418C2×C1112yescomplemented
378#2321C2×C1112yescomplemented
379C2×#379C2×C1111yescharacteristic, complemented
380C23×C11—22no—
381C23×C11—22no—
382C23×C11—216no—
383C23×C11—28no—
384C23×C11—22no—
385C23×C11—22no—
386C23×C11—21no—
387C23×C11—21no—
388C23×C11—21no—
389C23×C11—21no—
390C23×C11—22no—
391C23×C11—22no—
392C23×C11—22no—
393C23×C11—22no—
394C23×C11—22no—
395C23×C11—22no—
396C23×C11—22no—
397C23×C11—22no—
398C23×C11—22no—
399C23×C11—22no—
400C23×C11—22no—
401C23×C11—22no—
402C23×C11—22no—
403C23×C11—22no—
404C23×C11—22no—
405C23×C11—22no—
406C23×C11—22no—
407C23×C11—22no—
408C23×C11—22no—
409C23×C11—22no—
410C23×C11—22no—
411C23×C11—48no—
412C23×C11—48no—
413C23×C11—48no—
414C23×C11—48no—
415C23×C11—48no—
416C23×C11—48no—
417C23×C11—48no—
418C23×C11—48no—
419C23×C11—48no—
420C23×C11—48no—
421C23×C11—44no—
422C23×C11—44no—
423C23×C11—48no—
424C23×C11—48no—
425C23×C11—44no—
426C23×C11—44no—
427C23×C11—44no—
428C23×C11—44no—
429C23×C11—48no—
430C23×C11—48no—
431C23×C11—48no—
432C23×C11—48no—
433C23×C11—48no—
434C23×C11—4128no—
435C23×C11—48no—
436C23×C11—44no—
437C23×C11—44no—
438C23×C11—48no—
439C23×C11C2×#4112yes—
440C23×C11C2×#4112yes—
441C23×C11C2×#4112yes—
442C23×C11H(5,𝔽2)14yes—
443C23×C11H(5,𝔽2)14yes—
444C23×C11H(5,𝔽2)12yes—
445C23×C11H(5,𝔽2)12yes—
446C23×C11C2511yescharacteristic
447Q8×C11—82no—
448D4×C11—48no—
449D4×C11—84no—
450D4×C11—84no—
451D4×C11—84no—
452D4×C11—84no—
453D4×C11—84no—
454D4×C11—84no—
455D4×C11—82no—
456C2×C4×C11—22no—
457C2×C4×C11—22no—
458C2×C4×C11—22no—
459C2×C4×C11—22no—
460C2×C4×C11—22no—
461C2×C4×C11—22no—
462C2×C4×C11—22no—
463C2×C4×C11—22no—
464C2×C4×C11—22no—
465C2×C4×C11—22no—
466C2×C4×C11—22no—
467C2×C4×C11—22no—
468C2×C4×C11—22no—
469C2×C4×C11—22no—
470C2×C4×C11—22no—
471C2×C4×C11—22no—
472C2×C4×C11—22no—
473C2×C4×C11—22no—
474C2×C4×C11—22no—
475C2×C4×C11—22no—
476C2×C4×C11—22no—
477C2×C4×C11—22no—
478C2×C4×C11—22no—
479C2×C4×C11—22no—
480C2×C4×C11—22no—
481C2×C4×C11—22no—
482C2×C4×C11—21no—
483C2×C4×C11—22no—
484C2×C4×C11—22no—
485C2×C4×C11—22no—
486C2×C4×C11—21no—
487C2×C4×C11—22no—
488C2×C4×C11—21no—
489C2×C4×C11—21no—
490C2×C4×C11—22no—
491C2×C4×C11—84no—
492C2×C4×C11—82no—
493C2×C4×C11—82no—
494C2×C4×C11—84no—
495C26C22×C1111yescharacteristic
496C2×#126C22×C1112yescomplemented
497C2×#124C22×C1112yescomplemented
498C2×#123C22×C1112yescomplemented
499C2×C22⋊Q8C22×C1111yescharacteristic, complemented
500C2×#121C22×C1112yescomplemented
501C2×#121C22×C1111yescharacteristic, complemented
502C2×#120C22×C1112yes—
503C2×#120C22×C1112yes—
504C2×#120C22×C1112yes—
505C2×#120C22×C1112yes—
506C2×#120C22×C1112yes—
507C2×#120C22×C1112yes—
508C2×#120C22×C1112yes—
509C2×C4×D4C22×C1112yescomplemented
510C22×C22⋊C4C22×C1111yescharacteristic
511C22×C22⋊C4C22×C1111yescharacteristic
512C22×C22⋊C4C22×C1112yes—
513C22×C22⋊C4C22×C1112yes—
514#399C22×C1111yescharacteristic, complemented
515#399C22×C1111yescharacteristic, complemented
516#399C22×C1112yescomplemented
517#397C22×C1111yescharacteristic, complemented
518#397C22×C1111yescharacteristic, complemented
519#397C22×C1112yescomplemented
520#397C22×C1112yescomplemented
521#397C22×C1112yescomplemented
522#397C22×C1112yescomplemented
523#397C22×C1112yescomplemented
524#396C22×C1112yescomplemented
525#396C22×C1112yescomplemented
526#396C22×C1112yescomplemented
527#396C22×C1112yescomplemented
528#394C22×C1112yescomplemented
529#394C22×C1112yescomplemented
530#394C22×C1112yescomplemented
531#394C22×C1112yescomplemented
532#394C22×C1112yescomplemented
533#394C22×C1112yescomplemented
534#394C22×C1112yescomplemented
535#394C22×C1112yescomplemented
536#393C22×C1111yescharacteristic, complemented
537#393C22×C1111yescharacteristic, complemented
538#393C22×C1112yescomplemented
539#392C22×C1111yescharacteristic, complemented
540#392C22×C1111yescharacteristic, complemented
541#392C22×C1112yescomplemented
542#390C22×C1112yescomplemented
543#390C22×C1112yescomplemented
544#390C22×C1112yescomplemented
545#390C22×C1112yescomplemented
546#388C22×C1112yescomplemented
547#388C22×C1112yescomplemented
548#388C22×C1112yescomplemented
549#388C22×C1112yescomplemented
550#388C22×C1112yescomplemented
551#388C22×C1112yescomplemented
552#388C22×C1112yescomplemented
553#388C22×C1112yescomplemented
554#388C22×C1112yescomplemented
555#388C22×C1112yescomplemented
556#388C22×C1112yescomplemented
557#388C22×C1112yescomplemented
558#386C22×C1112yescomplemented
559#386C22×C1112yescomplemented
560#386C22×C1112yescomplemented
561#386C22×C1112yescomplemented
562#386C22×C1112yescomplemented
563#386C22×C1112yescomplemented
564#385C22×C1112yescomplemented
565#385C22×C1112yescomplemented
566#380C22×C1111yescharacteristic, complemented
567#380C22×C1111yescharacteristic, complemented
568#379C22×C1112yes—
569#379C22×C1112yes—
570#379C22×C1112yes—
571#379C22×C1112yes—
572#379C22×C1112yes—
573#379C22×C1112yes—
574#379C22×C1112yes—
575#379C22×C1111yescharacteristic
576#379C22×C1111yescharacteristic
577#379C22×C1112yes—
578#379C22×C1112yes—
579#379C22×C1111yescharacteristic
580#379C22×C1111yescharacteristic
581C4×C22⋊C4C22×C1112yescomplemented
582C22×C11—24no—
583C22×C11—24no—
584C22×C11—22no—
585C22×C11—22no—
586C22×C11—22no—
587C22×C11—22no—
588C22×C11—24no—
589C22×C11—24no—
590C22×C11—24no—
591C22×C11—24no—
592C22×C11—24no—
593C22×C11—24no—
594C22×C11—24no—
595C22×C11—24no—
596C22×C11—432no—
597C22×C11—416no—
598C22×C11—432no—
599C22×C11—416no—
600C22×C11—416no—
601C22×C11—42no—
602C22×C11—42no—
603C22×C11—42no—
604C22×C11—42no—
605C22×C11—42no—
606C22×C11—41no—
607C22×C11—41no—
608C22×C11—42no—
609C22×C11—42no—
610C22×C11—42no—
611C22×C11—42no—
612C22×C11—42no—
613C22×C11—41no—
614C22×C11—41no—
615C22×C11—42no—
616C22×C11—42no—
617C22×C11—42no—
618C22×C11—42no—
619C22×C11—42no—
620C22×C11—42no—
621C22×C11—42no—
622C22×C11#53814yes—
623C22×C11C22×#4111yescharacteristic
624C22×C11C2×H(5,𝔽2)11yescharacteristic
625C22×C11C2×H(5,𝔽2)11yescharacteristic
626C22×C11C2×H(5,𝔽2)12yes—
627C22×C11C2×H(5,𝔽2)12yes—
628C4×C11—42no—
629C4×C11—42no—
630C4×C11—42no—
631C4×C11—42no—
632C4×C11—41no—
633C4×C11—41no—
634C4×C11—42no—
635C4×C11—41no—
636C4×C11—42no—
637C4×C11—41no—
638C4×C11—42no—
639C4×C11—42no—
640C4×C11—42no—
641C25—24no—
642C25—44no—
643C25—44no—
644C25—42no—
645C25—42no—
646C25C23×C1112yes—
647C25C23×C1111yescharacteristic
648C25C23×C1111yescharacteristic
649C25C23×C1112yes—
650C25C23×C1111yescharacteristic
651C22×Q8C23×C1111yescharacteristic, complemented
652C22×D4C23×C1112yes—
653C22×D4C23×C1112yes—
654C22×D4C23×C1112yes—
655C22×D4C23×C1112yes—
656C22×D4C23×C1112yes—
657C22×D4C23×C1112yes—
658C22×D4C23×C1112yes—
659C22×D4C23×C1111yescharacteristic, complemented
660C23×C4C23×C1112yes—
661C23×C4C23×C1111yescharacteristic
662C23×C4C23×C1111yescharacteristic
663C23×C4C23×C1112yescomplemented
664#126—44no—
665#124—44no—
666#123—44no—
667C22⋊Q8—42no—
668#121—44no—
669#121—42no—
670#120—28no—
671#120—44no—
672#120—44no—
673#120—44no—
674#120—44no—
675#120—44no—
676#120—44no—
677C4×D4—44no—
678C2×C4⋊C4C23×C1112yescomplemented
679C2×C4⋊C4C23×C1112yescomplemented
680C2×C4⋊C4C23×C1111yescharacteristic, complemented
681C2×C4⋊C4C23×C1111yescharacteristic, complemented
682C2×C4⋊C4C23×C1112yescomplemented
683C2×C4⋊C4C23×C1112yescomplemented
684C2×C4⋊C4C23×C1112yescomplemented
685C2×C4⋊C4C23×C1112yescomplemented
686C2×C4⋊C4C23×C1112yescomplemented
687C2×C4⋊C4C23×C1112yescomplemented
688C2×C22⋊C4—44no—
689C2×C22⋊C4—44no—
690C2×C22⋊C4—42no—
691C2×C22⋊C4—42no—
692C2×C22⋊C4C23×C1112yes—
693C2×C22⋊C4C23×C1112yes—
694C2×C22⋊C4C23×C1112yes—
695C2×C22⋊C4C23×C1112yes—
696C2×C22⋊C4C23×C1112yes—
697C2×C22⋊C4C23×C1112yes—
698C2×C22⋊C4C23×C1112yes—
699C2×C22⋊C4C23×C1112yes—
700C2×C22⋊C4C23×C1112yes—
701C2×C22⋊C4C23×C1112yes—
702C2×C22⋊C4C23×C1112yes—
703C2×C22⋊C4C23×C1112yes—
704C2×C22⋊C4C23×C1112yes—
705C2×C22⋊C4C23×C1111yescharacteristic
706C2×C22⋊C4C23×C1112yes—
707C2×C22⋊C4C23×C1112yes—
708C2×C22⋊C4C23×C1112yes—
709C2×C22⋊C4C23×C1111yescharacteristic
710C2×C22⋊C4C23×C1112yes—
711C2×C22⋊C4C23×C1112yes—
712C2×C22⋊C4C23×C1111yescharacteristic
713C2×C22⋊C4C23×C1111yescharacteristic
714C2×C22⋊C4C23×C1111yescharacteristic
715C2×C22⋊C4C23×C1111yescharacteristic
716C2×C22⋊C4C23×C1112yes—
717C2×C22⋊C4C23×C1112yes—
718C2×C22⋊C4C23×C1112yes—
719C2×C22⋊C4C23×C1112yes—
720C2×C22⋊C4C23×C1112yes—
721C2×C22⋊C4C23×C1112yes—
722C2×C22⋊C4C23×C1112yes—
723C2×C22⋊C4C23×C1112yes—
724C2×C22⋊C4C23×C1112yes—
725C2×C22⋊C4C23×C1112yes—
726C2×C22⋊C4C23×C1112yes—
727C2×C22⋊C4C23×C1112yes—
728C2×C22⋊C4C23×C1112yescomplemented
729C2×C22⋊C4C23×C1112yescomplemented
730C2×C22⋊C4C23×C1112yescomplemented
731C2×C22⋊C4C23×C1112yescomplemented
732C2×C22⋊C4C23×C1112yescomplemented
733C2×C22⋊C4C23×C1112yescomplemented
734C2×C42C23×C1112yescomplemented
735C2×C42C23×C1112yescomplemented
736C2×C42C23×C1112yescomplemented
737#95C23×C1112yescomplemented
738#95C23×C1112yescomplemented
739#95C23×C1111yescharacteristic, complemented
740#95C23×C1111yescharacteristic, complemented
741#95C23×C1111yescharacteristic, complemented
742#95C23×C1111yescharacteristic, complemented
743#95C23×C1112yescomplemented
744#95C23×C1112yescomplemented
745#95C23×C1112yescomplemented
746#95C23×C1112yescomplemented
747#95C23×C1112yescomplemented
748#95C23×C1112yescomplemented
749#95C23×C1112yescomplemented
750#95C23×C1112yescomplemented
751C2×C11—24no—
752C2×C11—42no—
753C2×C11—42no—
754C2×C11—44no—
755C2×C11—44no—
756C2×C11—82no—
757C2×C11C2×#53811yescharacteristic
758C2×C11#349012yes—
759C2×C11#353212yes—
760C2×C11#353211yescharacteristic
761C2×C11#353211yescharacteristic
762C24—24no—
763C24—24no—
764C24—24no—
765C24—22no—
766C24—22no—
767C24—22no—
768C24—22no—
769C24—24no—
770C24—24no—
771C24—24no—
772C24—24no—
773C24—24no—
774C24—24no—
775C24—24no—
776C24—42no—
777C24—42no—
778C24—42no—
779C24—42no—
780C24—41no—
781C24—41no—
782C24—42no—
783C24—42no—
784C24—42no—
785C24—42no—
786C24—42no—
787C24—41no—
788C24—41no—
789C24—42no—
790C24—432no—
791C24—416no—
792C24—432no—
793C24—416no—
794C24—416no—
795C24C11×#4114yes—
796C24C24×C1112yes—
797C24C24×C1111yescharacteristic
798C24C24×C1111yescharacteristic
799C24C24×C1112yes—
800C24C24×C1112yes—
801C24C24×C1111yescharacteristic
802C2×Q8—41no—
803C2×Q8—42no—
804C2×D4—24no—
805C2×D4—24no—
806C2×D4—24no—
807C2×D4—24no—
808C2×D4—24no—
809C2×D4—24no—
810C2×D4—24no—
811C2×D4—24no—
812C2×D4—24no—
813C2×D4—42no—
814C2×D4—42no—
815C2×D4—42no—
816C2×D4—42no—
817C2×D4—42no—
818C2×D4—42no—
819C2×D4—42no—
820C2×D4—42no—
821C2×D4—42no—
822C2×D4—42no—
823C2×D4—42no—
824C2×D4—42no—
825C2×D4—42no—
826C2×D4—41no—
827C22×C4—24no—
828C22×C4—22no—
829C22×C4—22no—
830C22×C4—42no—
831C22×C4—42no—
832C22×C4—42no—
833C22×C4—42no—
834C22×C4—42no—
835C22×C4—42no—
836C22×C4—42no—
837C22×C4C24×C1112yes—
838C22×C4C24×C1112yes—
839C22×C4C24×C1112yes—
840C22×C4C24×C1112yes—
841C22×C4C24×C1112yes—
842C22×C4C24×C1111yescharacteristic
843C22×C4C24×C1111yescharacteristic
844C22×C4C24×C1112yes—
845C22×C4C24×C1112yes—
846C22×C4C24×C1112yes—
847C22×C4C24×C1112yes—
848C22×C4C24×C1111yescharacteristic
849C22×C4C24×C1111yescharacteristic
850C4⋊C4—42no—
851C4⋊C4—42no—
852C4⋊C4—41no—
853C4⋊C4—41no—
854C4⋊C4—42no—
855C4⋊C4—42no—
856C4⋊C4—42no—
857C4⋊C4—42no—
858C4⋊C4—42no—
859C4⋊C4—42no—
860C22⋊C4—24no—
861C22⋊C4—24no—
862C22⋊C4—24no—
863C22⋊C4—24no—
864C22⋊C4—24no—
865C22⋊C4—24no—
866C22⋊C4—24no—
867C22⋊C4—24no—
868C22⋊C4—24no—
869C22⋊C4—24no—
870C22⋊C4—24no—
871C22⋊C4—24no—
872C22⋊C4—24no—
873C22⋊C4—42no—
874C22⋊C4—42no—
875C22⋊C4—41no—
876C22⋊C4—42no—
877C22⋊C4—42no—
878C22⋊C4—42no—
879C22⋊C4—41no—
880C22⋊C4—41no—
881C22⋊C4—41no—
882C22⋊C4—41no—
883C22⋊C4—41no—
884C22⋊C4—42no—
885C22⋊C4—42no—
886C22⋊C4—42no—
887C22⋊C4—42no—
888C22⋊C4—42no—
889C22⋊C4—42no—
890C22⋊C4—42no—
891C22⋊C4—42no—
892C22⋊C4—42no—
893C22⋊C4—42no—
894C22⋊C4—42no—
895C22⋊C4—42no—
896C22⋊C4—42no—
897C22⋊C4—42no—
898C22⋊C4—42no—
899C22⋊C4—42no—
900C22⋊C4—42no—
901C22⋊C4—42no—
902C42—42no—
903C42—42no—
904C42—42no—
905C11#3672511yescharacteristic, direct product factor, Sylow
906C23—22no—
907C23—22no—
908C23—216no—
909C23—28no—
910C23—22no—
911C23—22no—
912C23—21no—
913C23—21no—
914C23—21no—
915C23—21no—
916C23—22no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
927C23—22no—
928C23—22no—
929C23—22no—
930C23—22no—
931C23—22no—
932C23—22no—
933C23—22no—
934C23—22no—
935C23—22no—
936C23—22no—
937C23—48no—
938C23—48no—
939C23—48no—
940C23—48no—
941C23—48no—
942C23—48no—
943C23—48no—
944C23—48no—
945C23—48no—
946C23—48no—
947C23—44no—
948C23—44no—
949C23—48no—
950C23—48no—
951C23—44no—
952C23—44no—
953C23—44no—
954C23—44no—
955C23—48no—
956C23—48no—
957C23—48no—
958C23—48no—
959C23—48no—
960C23—4128no—
961C23—48no—
962C23—44no—
963C23—44no—
964C23—48no—
965C23C2×C11×#4112yes—
966C23C2×C11×#4112yes—
967C23C2×C11×#4112yes—
968C23C11×H(5,𝔽2)14yes—
969C23C11×H(5,𝔽2)14yes—
970C23C11×H(5,𝔽2)12yes—
971C23C11×H(5,𝔽2)12yes—
972C23C25×C1111yescharacteristic
973Q8—82no—
974D4—48no—
975D4—84no—
976D4—84no—
977D4—84no—
978D4—84no—
979D4—84no—
980D4—84no—
981D4—82no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—21no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—21no—
1013C2×C4—22no—
1014C2×C4—21no—
1015C2×C4—21no—
1016C2×C4—22no—
1017C2×C4—84no—
1018C2×C4—82no—
1019C2×C4—82no—
1020C2×C4—84no—
1021C22—24no—
1022C22—24no—
1023C22—22no—
1024C22—22no—
1025C22—22no—
1026C22—22no—
1027C22—24no—
1028C22—24no—
1029C22—24no—
1030C22—24no—
1031C22—24no—
1032C22—24no—
1033C22—24no—
1034C22—24no—
1035C22—432no—
1036C22—416no—
1037C22—432no—
1038C22—416no—
1039C22—416no—
1040C22—42no—
1041C22—42no—
1042C22—42no—
1043C22—42no—
1044C22—42no—
1045C22—41no—
1046C22—41no—
1047C22—42no—
1048C22—42no—
1049C22—42no—
1050C22—42no—
1051C22—42no—
1052C22—41no—
1053C22—41no—
1054C22—42no—
1055C22—42no—
1056C22—42no—
1057C22—42no—
1058C22—42no—
1059C22—42no—
1060C22—42no—
1061C22C11×#53814yes—
1062C22C22×C11×#4111yescharacteristic
1063C22C2×C11×H(5,𝔽2)11yescharacteristic
1064C22C2×C11×H(5,𝔽2)11yescharacteristic
1065C22C2×C11×H(5,𝔽2)12yes—
1066C22C2×C11×H(5,𝔽2)12yes—
1067C4—42no—
1068C4—42no—
1069C4—42no—
1070C4—42no—
1071C4—41no—
1072C4—42no—
1073C4—41no—
1074C4—42no—
1075C4—41no—
1076C4—41no—
1077C4—42no—
1078C4—42no—
1079C4—42no—
1080C2—24no—
1081C2—42no—
1082C2—42no—
1083C2—44no—
1084C2—44no—
1085C2—82no—
1086C2C2×C11×#53811yescharacteristic
1087C2C11×#349012yes—
1088C2C11×#353212yes—
1089C2C11×#353211yescharacteristic
1090C2C11×#353211yescharacteristic
subgroupG/H
center, socleC23×C11C25
commutator, Frattini, cosocleC23C25×C11
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#2846C2semidirect
2. C11×#2736C2semidirect
3. C11×#2735C2semidirect
4. C11×#2735C2semidirect
5. C11×#2697C2semidirect
6. C11×#2685C2semidirect
7. C11×#2685C2semidirect
8. C11×#2684C2semidirect
9. C11×#2678C2semidirect
10. C11×#2670C2semidirect
11. C11×#2668C2semidirect
12. C11×#2626C2semidirect
13. C11×#2617C2semidirect
14. C11×#2480C2semidirect
15. C11×#2472C2semidirect
16. C11×#2424C2semidirect
17. C11×#2418C2semidirect
18. C11×#2321C2semidirect
19. C2×C11×#379C2semidirect
21. C2×C11×#126C22semidirect
22. C2×C11×#124C22semidirect
23. C2×C11×#123C22semidirect
24. C2×C11×C22⋊Q8C22semidirect
25. C2×C11×#121C22semidirect
26. C2×C11×#121C22semidirect
34. C2×C4×D4×C11C22semidirect
39. C11×#399C22semidirect
40. C11×#399C22semidirect
41. C11×#399C22semidirect
42. C11×#397C22semidirect
43. C11×#397C22semidirect
44. C11×#397C22semidirect
45. C11×#397C22semidirect
46. C11×#397C22semidirect
47. C11×#397C22semidirect
48. C11×#397C22semidirect
49. C11×#396C22semidirect
50. C11×#396C22semidirect
51. C11×#396C22semidirect
52. C11×#396C22semidirect
53. C11×#394C22semidirect
54. C11×#394C22semidirect
55. C11×#394C22semidirect
56. C11×#394C22semidirect
57. C11×#394C22semidirect
58. C11×#394C22semidirect
59. C11×#394C22semidirect
60. C11×#394C22semidirect
61. C11×#393C22semidirect
62. C11×#393C22semidirect
63. C11×#393C22semidirect
64. C11×#392C22semidirect
65. C11×#392C22semidirect
66. C11×#392C22semidirect
67. C11×#390C22semidirect
68. C11×#390C22semidirect
69. C11×#390C22semidirect
70. C11×#390C22semidirect
71. C11×#388C22semidirect
72. C11×#388C22semidirect
73. C11×#388C22semidirect
74. C11×#388C22semidirect
75. C11×#388C22semidirect
76. C11×#388C22semidirect
77. C11×#388C22semidirect
78. C11×#388C22semidirect
79. C11×#388C22semidirect
80. C11×#388C22semidirect
81. C11×#388C22semidirect
82. C11×#388C22semidirect
83. C11×#386C22semidirect
84. C11×#386C22semidirect
85. C11×#386C22semidirect
86. C11×#386C22semidirect
87. C11×#386C22semidirect
88. C11×#386C22semidirect
89. C11×#385C22semidirect
90. C11×#385C22semidirect
91. C11×#380C22semidirect
92. C11×#380C22semidirect
106. C4×C11×C22⋊C4C22semidirect
117. C22×Q8×C11C23semidirect
125. C22×D4×C11C23semidirect
129. C23×C4×C11C23semidirect
144. C2×C11×C4⋊C4C23semidirect
145. C2×C11×C4⋊C4C23semidirect
146. C2×C11×C4⋊C4C23semidirect
147. C2×C11×C4⋊C4C23semidirect
148. C2×C11×C4⋊C4C23semidirect
149. C2×C11×C4⋊C4C23semidirect
150. C2×C11×C4⋊C4C23semidirect
151. C2×C11×C4⋊C4C23semidirect
152. C2×C11×C4⋊C4C23semidirect
153. C2×C11×C4⋊C4C23semidirect
194. C2×C11×C22⋊C4C23semidirect
195. C2×C11×C22⋊C4C23semidirect
196. C2×C11×C22⋊C4C23semidirect
197. C2×C11×C22⋊C4C23semidirect
198. C2×C11×C22⋊C4C23semidirect
199. C2×C11×C22⋊C4C23semidirect
200. C2×C42×C11C23semidirect
201. C2×C42×C11C23semidirect
202. C2×C42×C11C23semidirect
203. C11×#95C23semidirect
204. C11×#95C23semidirect
205. C11×#95C23semidirect
206. C11×#95C23semidirect
207. C11×#95C23semidirect
208. C11×#95C23semidirect
209. C11×#95C23semidirect
210. C11×#95C23semidirect
211. C11×#95C23semidirect
212. C11×#95C23semidirect
213. C11×#95C23semidirect
214. C11×#95C23semidirect
215. C11×#95C23semidirect
216. C11×#95C23semidirect
217. #36725C11direct (N × H)
361. #2846C2×C11semidirect
362. #2736C2×C11semidirect
363. #2735C2×C11semidirect
364. #2735C2×C11semidirect
365. #2697C2×C11semidirect
366. #2685C2×C11semidirect
367. #2685C2×C11semidirect
368. #2684C2×C11semidirect
369. #2678C2×C11semidirect
370. #2670C2×C11semidirect
371. #2668C2×C11semidirect
372. #2626C2×C11semidirect
373. #2617C2×C11semidirect
374. #2480C2×C11semidirect
375. #2472C2×C11semidirect
376. #2424C2×C11semidirect
377. #2418C2×C11semidirect
378. #2321C2×C11semidirect
379. C2×#379C2×C11semidirect
496. C2×#126C22×C11semidirect
497. C2×#124C22×C11semidirect
498. C2×#123C22×C11semidirect
499. C2×C22⋊Q8C22×C11semidirect
500. C2×#121C22×C11semidirect
501. C2×#121C22×C11semidirect
509. C2×C4×D4C22×C11semidirect
514. #399C22×C11semidirect
515. #399C22×C11semidirect
516. #399C22×C11semidirect
517. #397C22×C11semidirect
518. #397C22×C11semidirect
519. #397C22×C11semidirect
520. #397C22×C11semidirect
521. #397C22×C11semidirect
522. #397C22×C11semidirect
523. #397C22×C11semidirect
524. #396C22×C11semidirect
525. #396C22×C11semidirect
526. #396C22×C11semidirect
527. #396C22×C11semidirect
528. #394C22×C11semidirect
529. #394C22×C11semidirect
530. #394C22×C11semidirect
531. #394C22×C11semidirect
532. #394C22×C11semidirect
533. #394C22×C11semidirect
534. #394C22×C11semidirect
535. #394C22×C11semidirect
536. #393C22×C11semidirect
537. #393C22×C11semidirect
538. #393C22×C11semidirect
539. #392C22×C11semidirect
540. #392C22×C11semidirect
541. #392C22×C11semidirect
542. #390C22×C11semidirect
543. #390C22×C11semidirect
544. #390C22×C11semidirect
545. #390C22×C11semidirect
546. #388C22×C11semidirect
547. #388C22×C11semidirect
548. #388C22×C11semidirect
549. #388C22×C11semidirect
550. #388C22×C11semidirect
551. #388C22×C11semidirect
552. #388C22×C11semidirect
553. #388C22×C11semidirect
554. #388C22×C11semidirect
555. #388C22×C11semidirect
556. #388C22×C11semidirect
557. #388C22×C11semidirect
558. #386C22×C11semidirect
559. #386C22×C11semidirect
560. #386C22×C11semidirect
561. #386C22×C11semidirect
562. #386C22×C11semidirect
563. #386C22×C11semidirect
564. #385C22×C11semidirect
565. #385C22×C11semidirect
566. #380C22×C11semidirect
567. #380C22×C11semidirect
581. C4×C22⋊C4C22×C11semidirect
651. C22×Q8C23×C11semidirect
659. C22×D4C23×C11semidirect
663. C23×C4C23×C11semidirect
678. C2×C4⋊C4C23×C11semidirect
679. C2×C4⋊C4C23×C11semidirect
680. C2×C4⋊C4C23×C11semidirect
681. C2×C4⋊C4C23×C11semidirect
682. C2×C4⋊C4C23×C11semidirect
683. C2×C4⋊C4C23×C11semidirect
684. C2×C4⋊C4C23×C11semidirect
685. C2×C4⋊C4C23×C11semidirect
686. C2×C4⋊C4C23×C11semidirect
687. C2×C4⋊C4C23×C11semidirect
728. C2×C22⋊C4C23×C11semidirect
729. C2×C22⋊C4C23×C11semidirect
730. C2×C22⋊C4C23×C11semidirect
731. C2×C22⋊C4C23×C11semidirect
732. C2×C22⋊C4C23×C11semidirect
733. C2×C22⋊C4C23×C11semidirect
734. C2×C42C23×C11semidirect
735. C2×C42C23×C11semidirect
736. C2×C42C23×C11semidirect
737. #95C23×C11semidirect
738. #95C23×C11semidirect
739. #95C23×C11semidirect
740. #95C23×C11semidirect
741. #95C23×C11semidirect
742. #95C23×C11semidirect
743. #95C23×C11semidirect
744. #95C23×C11semidirect
745. #95C23×C11semidirect
746. #95C23×C11semidirect
747. #95C23×C11semidirect
748. #95C23×C11semidirect
749. #95C23×C11semidirect
750. #95C23×C11semidirect
905. C11#36725direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#28462
C11×#27362
C11×#27352
C11×#26972
C11×#26852
C11×#26842
C11×#26782
C11×#26702
C11×#26682
C11×#26262
C11×#26172
C11×#24802
C11×#24722
C11×#24242
C11×#24182
C11×#23212
C2×C11×#3792
#3672511