Finite Group Databasebeta

← C11×#34468 #14611661

Subgroups — C11×#34468 #14611661

Order 2816.

3220 conjugacy classes of subgroups.

The subgroup lattice has 1072 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D42×C11C211yesmaximal, characteristic
2C11×#2380C211yesmaximal, characteristic, complemented
3C11×#2377C212yesmaximal, complemented
4C11×#2375C211yesmaximal, characteristic, complemented
5C11×#2364C212yesmaximal, complemented
6C11×#2358C211yesmaximal, characteristic, complemented
7C11×#2358C212yesmaximal, complemented
8C11×#2353C212yesmaximal, complemented
9D4×C11×C22⋊C4C212yesmaximal, complemented
10D4×C11×C22⋊C4C212yesmaximal, complemented
11C11×#2333C212yesmaximal, complemented
12C11×#2328C211yesmaximal, characteristic, complemented
13C11×#2325C212yesmaximal, complemented
14C11×#2321C212yesmaximal, complemented
15C11×#2321C211yesmaximal, characteristic, complemented
16C11×#2318C212yesmaximal, complemented
17C11×#2308C212yesmaximal, complemented
18C4×C11×#120C211yesmaximal, characteristic, complemented
19C2×C11×#386C212yesmaximal, complemented
20C23×D4×C11C2212yes—
21C23×D4×C11C2212yes—
22C24×C4×C11C2211yescharacteristic, complemented
23D42×C11C4116yescomplemented
24C2×C11×#127C2211yescharacteristic
25C2×C11×#121C2212yes—
26C2×C11×#121C2212yes—
27C2×C11×#120C2211yescharacteristic
28C2×C11×#120C2212yes—
29C2×C11×#120C2211yescharacteristic
30C2×C4×D4×C11C2212yes—
31C2×C4×D4×C11C2211yescharacteristic, complemented
32C2×C4×D4×C11C2212yescomplemented
33C2×C4×D4×C11C2212yescomplemented
34C2×C4×D4×C11C2212yescomplemented
35C2×C4×D4×C11C2212yescomplemented
36C2×C4×D4×C11C2211yescharacteristic, complemented
37C22×C11×C22⋊C4C2212yescomplemented
38C22×C11×C22⋊C4C2212yescomplemented
39C22×C11×C22⋊C4C2212yescomplemented
40C22×C11×C22⋊C4C2212yescomplemented
41C22×C11×C22⋊C4C2211yescharacteristic, complemented
42C11×#390C2211yescharacteristic, complemented
43C11×#390C2212yescomplemented
44C11×#390C2212yescomplemented
45C11×#390C2211yescharacteristic, complemented
46C11×#390C2212yescomplemented
47C11×#390C2212yescomplemented
48C11×#388C2212yescomplemented
49C11×#388C2212yescomplemented
50C11×#388C2212yescomplemented
51C11×#388C2212yescomplemented
52C11×#388C2212yescomplemented
53C11×#388C2212yescomplemented
54C11×#388C2212yescomplemented
55C11×#388C2212yescomplemented
56C11×#387C2212yescomplemented
57C11×#387C2212yescomplemented
58C11×#387C2212yescomplemented
59C11×#387C2212yescomplemented
60C11×#386C2212yes—
61C11×#386C2212yes—
62C11×#386C2212yes—
63C11×#386C2212yes—
64C11×#386C2212yescomplemented
65C11×#386C2211yescharacteristic, complemented
66C11×#386C2212yescomplemented
67C11×#386C2212yescomplemented
68C11×#386C2211yescharacteristic, complemented
69C11×#386C2212yescomplemented
70C11×#386C2212yescomplemented
71C11×#386C2212yescomplemented
72C11×#386C2212yescomplemented
73C11×#386C2212yescomplemented
74C11×#386C2212yescomplemented
75C11×#386C2212yescomplemented
76C11×#386C2212yescomplemented
77C11×#386C2212yescomplemented
78C11×#386C2212yescomplemented
79C11×#386C2212yescomplemented
80C11×#386C2212yescomplemented
81C11×#386C2212yescomplemented
82C11×#386C2212yescomplemented
83C11×#385C2212yescomplemented
84C11×#385C2211yescharacteristic, complemented
85C11×#385C2212yescomplemented
86C11×#385C2211yescharacteristic, complemented
87C11×#385C2212yescomplemented
88C11×#383C2212yescomplemented
89C11×#382C2211yescharacteristic, complemented
90C11×#381C2212yescomplemented
91C11×#381C2212yescomplemented
92C11×#380C2212yescomplemented
93C11×#380C2212yescomplemented
94C11×#379C2211yescharacteristic, complemented
95C11×#379C2211yescharacteristic, complemented
96C11×#379C2212yescomplemented
97C11×#379C2212yescomplemented
98C4×C11×C22⋊C4C2211yescharacteristic, complemented
99C4×C11×C22⋊C4C2212yescomplemented
100C4×C11×C22⋊C4C2212yescomplemented
101C4×C11×C22⋊C4C2212yescomplemented
102C4×C11×C22⋊C4C2211yescharacteristic, complemented
103C4×C11×C22⋊C4C2212yescomplemented
104C4×C11×C22⋊C4C2212yescomplemented
105C11×#376C2211yescharacteristic, complemented
106C2×C11×#95C2212yescomplemented
107C2×C11×#95C2212yescomplemented
108C25×C11C2311yescharacteristic
109C25×C11C2312yes—
110C25×C11C2311yescharacteristic
111C22×D4×C11—44no—
112C22×D4×C11—44no—
113C22×D4×C11—44no—
114C22×D4×C11—44no—
115C22×D4×C11C2×C4116yescomplemented
116C22×D4×C11C2×C4116yescomplemented
117C22×D4×C11C2312yes—
118C22×D4×C11C2312yes—
119C22×D4×C11C2312yes—
120C22×D4×C11C2311yescharacteristic
121C22×D4×C11C2312yes—
122C22×D4×C11C2312yes—
123C22×D4×C11C2311yescharacteristic
124C22×D4×C11C2312yes—
125C22×D4×C11C2312yes—
126C23×C4×C11—42no—
127C23×C4×C11—44no—
128C23×C4×C11C2312yes—
129C23×C4×C11C2312yes—
130C23×C4×C11C2312yes—
131C23×C4×C11C2312yes—
132C23×C4×C11C2311yescharacteristic
133C23×C4×C11C2311yescharacteristic
134C23×C4×C11C2312yes—
135C23×C4×C11C2312yes—
136C23×C4×C11C2311yescharacteristic
137C23×C4×C11C2311yescharacteristic
138C23×C4×C11C2312yes—
139C23×C4×C11C2312yes—
140C11×#127C2×C418yescomplemented
141C11×#121C2×C4116yescomplemented
142C11×#121C2×C4116yescomplemented
143C11×#120C2×C418yescomplemented
144C11×#120C2×C4116yescomplemented
145C11×#120C2×C418yescomplemented
146C4×D4×C11—42no—
147C4×D4×C11—42no—
148C4×D4×C11—44no—
149C4×D4×C11—44no—
150C4×D4×C11—44no—
151C4×D4×C11—44no—
152C4×D4×C11C2×C4116yescomplemented
153C2×C11×C4⋊C4C2312yes—
154C2×C11×C4⋊C4C2312yes—
155C2×C11×C4⋊C4C2312yes—
156C2×C11×C4⋊C4C2312yes—
157C2×C11×C4⋊C4C2311yescharacteristic
158C2×C11×C4⋊C4C2311yescharacteristic
159C2×C11×C4⋊C4C2312yes—
160C2×C11×C22⋊C4—42no—
161C2×C11×C22⋊C4—44no—
162C2×C11×C22⋊C4—44no—
163C2×C11×C22⋊C4—44no—
164C2×C11×C22⋊C4—44no—
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⋊C4C2312yes—
172C2×C11×C22⋊C4C2312yes—
173C2×C11×C22⋊C4C2312yes—
174C2×C11×C22⋊C4C2312yes—
175C2×C11×C22⋊C4C2312yes—
176C2×C11×C22⋊C4C2312yes—
177C2×C11×C22⋊C4C2312yes—
178C2×C11×C22⋊C4C2312yes—
179C2×C11×C22⋊C4C2312yes—
180C2×C11×C22⋊C4C2312yes—
181C2×C11×C22⋊C4C2312yes—
182C2×C11×C22⋊C4C2312yes—
183C2×C11×C22⋊C4C2311yescharacteristic
184C2×C11×C22⋊C4C2311yescharacteristic
185C2×C11×C22⋊C4C2311yescharacteristic
186C2×C11×C22⋊C4C2311yescharacteristic
187C2×C11×C22⋊C4C2312yes—
188C2×C11×C22⋊C4C2312yes—
189C2×C11×C22⋊C4C2312yes—
190C2×C11×C22⋊C4C2312yes—
191C2×C11×C22⋊C4C2312yes—
192C2×C11×C22⋊C4C2311yescharacteristic
193C2×C11×C22⋊C4C2311yescharacteristic
194C2×C11×C22⋊C4C2312yes—
195C2×C11×C22⋊C4C2312yes—
196C2×C42×C11C2311yescharacteristic
197C2×C42×C11C2311yescharacteristic
198C2×C42×C11C2312yes—
199C2×C42×C11C2312yes—
200C2×C42×C11C2312yes—
201C2×C42×C11C2312yes—
202C2×C42×C11C2311yescharacteristic
203C11×#95C2312yes—
204C11×#95C2312yes—
205C11×#95C2312yes—
206C11×#95C2312yes—
207C11×#95C2312yes—
208C11×#95C2312yes—
209C11×#95C2312yes—
210C11×#95C2312yes—
211C11×#95C2312yes—
212C11×#95C2312yes—
213C11×#95C2312yes—
214C11×#95C2312yes—
215C11×#95C2312yes—
216C11×#95C2312yes—
217C11×#95C2312yes—
218C11×#95C2312yes—
219C11×#95C2312yes—
220C11×#95C2312yes—
221#34468C1111yesmaximal, characteristic, direct product factor, Sylow
222C24×C11—24no—
223C24×C11—24no—
224C24×C11—24no—
225C24×C11—24no—
226C24×C11—41no—
227C24×C11—41no—
228C24×C11—42no—
229C24×C11—41no—
230C24×C11—42no—
231C24×C11—42no—
232C24×C11—42no—
233C24×C11—42no—
234C24×C11—42no—
235C24×C11—41no—
236C24×C11C22×C414yes—
237C24×C11C22×C418yes—
238C24×C11C22×C414yescomplemented
239C24×C11C2412yes—
240C24×C11C2412yes—
241C24×C11C2411yescharacteristic
242C24×C11C2411yescharacteristic
243C24×C11C2412yes—
244C2×D4×C11—24no—
245C2×D4×C11—24no—
246C2×D4×C11—24no—
247C2×D4×C11—24no—
248C2×D4×C11—24no—
249C2×D4×C11—24no—
250C2×D4×C11—41no—
251C2×D4×C11—41no—
252C2×D4×C11—42no—
253C2×D4×C11—42no—
254C2×D4×C11—42no—
255C2×D4×C11—42no—
256C2×D4×C11—42no—
257C2×D4×C11—42no—
258C2×D4×C11—42no—
259C2×D4×C11—42no—
260C2×D4×C11—41no—
261C2×D4×C11—41no—
262C2×D4×C11—432no—
263C2×D4×C11—432no—
264C2×D4×C11C22×C418yes—
265C2×D4×C11C22×C418yes—
266C2×D4×C11C22×C418yes—
267C2×D4×C11C22×C414yes—
268C2×D4×C11C22×C418yes—
269C2×D4×C11C22×C418yes—
270C2×D4×C11C22×C414yescomplemented
271C2×D4×C11C22×C418yescomplemented
272C2×D4×C11C22×C418yescomplemented
273C22×C4×C11—24no—
274C22×C4×C11—24no—
275C22×C4×C11—24no—
276C22×C4×C11—24no—
277C22×C4×C11—24no—
278C22×C4×C11—22no—
279C22×C4×C11—22no—
280C22×C4×C11—42no—
281C22×C4×C11—42no—
282C22×C4×C11—41no—
283C22×C4×C11—42no—
284C22×C4×C11—42no—
285C22×C4×C11—42no—
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—41no—
293C22×C4×C11—42no—
294C22×C4×C11—42no—
295C22×C4×C11—42no—
296C22×C4×C11—42no—
297C22×C4×C11—42no—
298C22×C4×C11—42no—
299C22×C4×C11—42no—
300C22×C4×C11—42no—
301C22×C4×C11—42no—
302C22×C4×C11—42no—
303C22×C4×C11—416no—
304C22×C4×C11C22×C418yes—
305C22×C4×C11C22×C418yescomplemented
306C22×C4×C11C2412yes—
307C22×C4×C11C2412yes—
308C22×C4×C11C2411yescharacteristic
309C22×C4×C11C2412yes—
310C22×C4×C11C2412yes—
311C22×C4×C11C2411yescharacteristic
312C22×C4×C11C2412yes—
313C22×C4×C11C2412yes—
314C22×C4×C11C2411yescharacteristic
315C22×C4×C11C2412yes—
316C22×C4×C11C2411yescharacteristic
317C22×C4×C11C2412yes—
318C22×C4×C11C2412yes—
319C22×C4×C11C2411yescharacteristic
320C11×C4⋊C4—41no—
321C11×C4⋊C4—41no—
322C11×C4⋊C4—42no—
323C11×C4⋊C4—42no—
324C11×C4⋊C4—42no—
325C11×C4⋊C4—42no—
326C11×C4⋊C4C22×C418yescomplemented
327C11×C22⋊C4—24no—
328C11×C22⋊C4—24no—
329C11×C22⋊C4—24no—
330C11×C22⋊C4—24no—
331C11×C22⋊C4—24no—
332C11×C22⋊C4—24no—
333C11×C22⋊C4—42no—
334C11×C22⋊C4—42no—
335C11×C22⋊C4—42no—
336C11×C22⋊C4—42no—
337C11×C22⋊C4—42no—
338C11×C22⋊C4—42no—
339C11×C22⋊C4—42no—
340C11×C22⋊C4—42no—
341C11×C22⋊C4—42no—
342C11×C22⋊C4—42no—
343C11×C22⋊C4—42no—
344C11×C22⋊C4—42no—
345C11×C22⋊C4—41no—
346C11×C22⋊C4—41no—
347C11×C22⋊C4—41no—
348C11×C22⋊C4—41no—
349C11×C22⋊C4—42no—
350C11×C22⋊C4—42no—
351C11×C22⋊C4—42no—
352C11×C22⋊C4—42no—
353C11×C22⋊C4C22×C418yes—
354C11×C22⋊C4C22×C414yes—
355C11×C22⋊C4C22×C418yescomplemented
356C11×C22⋊C4C22×C418yescomplemented
357C11×C22⋊C4C22×C414yescomplemented
358C42×C11—22no—
359C42×C11—41no—
360C42×C11—42no—
361C42×C11—42no—
362C42×C11—42no—
363C42×C11—42no—
364C42×C11C22×C414yescomplemented
365C2×D42C2×C1111yescharacteristic
366#2380C2×C1111yescharacteristic, complemented
367#2377C2×C1112yescomplemented
368#2375C2×C1111yescharacteristic, complemented
369#2364C2×C1112yescomplemented
370#2358C2×C1112yescomplemented
371#2358C2×C1111yescharacteristic, complemented
372#2353C2×C1112yescomplemented
373D4×C22⋊C4C2×C1112yescomplemented
374D4×C22⋊C4C2×C1112yescomplemented
375#2333C2×C1112yescomplemented
376#2328C2×C1111yescharacteristic, complemented
377#2325C2×C1112yescomplemented
378#2321C2×C1112yescomplemented
379#2321C2×C1111yescharacteristic, complemented
380#2318C2×C1112yescomplemented
381#2308C2×C1112yescomplemented
382C4×#120C2×C1111yescharacteristic, complemented
383C2×#386C2×C1112yescomplemented
384C23×C11—22no—
385C23×C11—22no—
386C23×C11—22no—
387C23×C11—22no—
388C23×C11—216no—
389C23×C11—22no—
390C23×C11—22no—
391C23×C11—22no—
392C23×C11—22no—
393C23×C11—22no—
394C23×C11—22no—
395C23×C11—21no—
396C23×C11—21no—
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—21no—
406C23×C11—21no—
407C23×C11—22no—
408C23×C11—22no—
409C23×C11—216no—
410C23×C11—44no—
411C23×C11—48no—
412C23×C11—48no—
413C23×C11—48no—
414C23×C11—44no—
415C23×C11—44no—
416C23×C11—48no—
417C23×C11—44no—
418C23×C11—84no—
419C23×C11—84no—
420C23×C11—84no—
421C23×C11—84no—
422C23×C11—82no—
423C23×C11—84no—
424C23×C11—82no—
425C23×C11C23×C412yes—
426C23×C11C23×C414yes—
427C23×C11C23×C412yes—
428C23×C11C23×C414yes—
429C23×C11C23×C414yes—
430C23×C11H(5,𝔽2)14yes—
431C23×C11H(5,𝔽2)14yes—
432C23×C11C2511yescharacteristic
433D4×C11—216no—
434D4×C11—216no—
435D4×C11—216no—
436D4×C11—48no—
437D4×C11—48no—
438D4×C11—48no—
439D4×C11—48no—
440D4×C11—44no—
441D4×C11—44no—
442C2×C4×C11—21no—
443C2×C4×C11—22no—
444C2×C4×C11—22no—
445C2×C4×C11—22no—
446C2×C4×C11—22no—
447C2×C4×C11—22no—
448C2×C4×C11—22no—
449C2×C4×C11—22no—
450C2×C4×C11—21no—
451C2×C4×C11—21no—
452C2×C4×C11—22no—
453C2×C4×C11—22no—
454C2×C4×C11—22no—
455C2×C4×C11—22no—
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—21no—
466C2×C4×C11—22no—
467C2×C4×C11—22no—
468C2×C4×C11—22no—
469C2×C4×C11—22no—
470C2×C4×C11—22no—
471C2×C4×C11—21no—
472C2×C4×C11—22no—
473C2×C4×C11—22no—
474C2×C4×C11—22no—
475C2×C4×C11—48no—
476C2×C4×C11—48no—
477C2×C4×C11—48no—
478C2×C4×C11—44no—
479C2×C4×C11—48no—
480C2×C4×C11—44no—
481C2×C4×C11—82no—
482C2×C4×C11—84no—
483C2×C4×C11—84no—
484C2×C4×C11—84no—
485C2×C4×C11—84no—
486C2×C4×C11—82no—
487C2×C4×C11C23×C412yes—
488C2×C4×C11C23×C414yes—
489C2×C4×C11C23×C414yes—
490C2×C4×C11C23×C414yes—
491C2×C4×C11H(5,𝔽2)12yes—
492C23×D4C22×C1112yes—
493C23×D4C22×C1112yes—
494C24×C4C22×C1111yescharacteristic, complemented
495D42C4×C11116yescomplemented
496C2×#127C22×C1111yescharacteristic
497C2×#121C22×C1112yes—
498C2×#121C22×C1112yes—
499C2×#120C22×C1112yes—
500C2×#120C22×C1111yescharacteristic
501C2×#120C22×C1111yescharacteristic
502C2×C4×D4C22×C1112yes—
503C2×C4×D4C22×C1111yescharacteristic, complemented
504C2×C4×D4C22×C1112yescomplemented
505C2×C4×D4C22×C1112yescomplemented
506C2×C4×D4C22×C1112yescomplemented
507C2×C4×D4C22×C1111yescharacteristic, complemented
508C2×C4×D4C22×C1112yescomplemented
509C22×C22⋊C4C22×C1112yescomplemented
510C22×C22⋊C4C22×C1112yescomplemented
511C22×C22⋊C4C22×C1111yescharacteristic, complemented
512C22×C22⋊C4C22×C1112yescomplemented
513C22×C22⋊C4C22×C1112yescomplemented
514#390C22×C1111yescharacteristic, complemented
515#390C22×C1112yescomplemented
516#390C22×C1112yescomplemented
517#390C22×C1111yescharacteristic, complemented
518#390C22×C1112yescomplemented
519#390C22×C1112yescomplemented
520#388C22×C1112yescomplemented
521#388C22×C1112yescomplemented
522#388C22×C1112yescomplemented
523#388C22×C1112yescomplemented
524#388C22×C1112yescomplemented
525#388C22×C1112yescomplemented
526#388C22×C1112yescomplemented
527#388C22×C1112yescomplemented
528#387C22×C1112yescomplemented
529#387C22×C1112yescomplemented
530#387C22×C1112yescomplemented
531#387C22×C1112yescomplemented
532#386C22×C1112yes—
533#386C22×C1112yes—
534#386C22×C1112yes—
535#386C22×C1112yes—
536#386C22×C1112yescomplemented
537#386C22×C1112yescomplemented
538#386C22×C1112yescomplemented
539#386C22×C1112yescomplemented
540#386C22×C1112yescomplemented
541#386C22×C1112yescomplemented
542#386C22×C1112yescomplemented
543#386C22×C1112yescomplemented
544#386C22×C1112yescomplemented
545#386C22×C1111yescharacteristic, complemented
546#386C22×C1112yescomplemented
547#386C22×C1112yescomplemented
548#386C22×C1112yescomplemented
549#386C22×C1112yescomplemented
550#386C22×C1112yescomplemented
551#386C22×C1112yescomplemented
552#386C22×C1112yescomplemented
553#386C22×C1111yescharacteristic, complemented
554#386C22×C1112yescomplemented
555#385C22×C1112yescomplemented
556#385C22×C1112yescomplemented
557#385C22×C1111yescharacteristic, complemented
558#385C22×C1112yescomplemented
559#385C22×C1111yescharacteristic, complemented
560#383C22×C1112yescomplemented
561#382C22×C1111yescharacteristic, complemented
562#381C22×C1112yescomplemented
563#381C22×C1112yescomplemented
564#380C22×C1112yescomplemented
565#380C22×C1112yescomplemented
566#379C22×C1111yescharacteristic, complemented
567#379C22×C1112yescomplemented
568#379C22×C1112yescomplemented
569#379C22×C1111yescharacteristic, complemented
570C4×C22⋊C4C22×C1112yescomplemented
571C4×C22⋊C4C22×C1112yescomplemented
572C4×C22⋊C4C22×C1111yescharacteristic, complemented
573C4×C22⋊C4C22×C1111yescharacteristic, complemented
574C4×C22⋊C4C22×C1112yescomplemented
575C4×C22⋊C4C22×C1112yescomplemented
576C4×C22⋊C4C22×C1112yescomplemented
577#376C22×C1111yescharacteristic, complemented
578C2×#95C22×C1112yescomplemented
579C2×#95C22×C1112yescomplemented
580C22×C11—24no—
581C22×C11—24no—
582C22×C11—24no—
583C22×C11—24no—
584C22×C11—24no—
585C22×C11—24no—
586C22×C11—24no—
587C22×C11—24no—
588C22×C11—24no—
589C22×C11—24no—
590C22×C11—24no—
591C22×C11—24no—
592C22×C11—22no—
593C22×C11—22no—
594C22×C11—24no—
595C22×C11—24no—
596C22×C11—416no—
597C22×C11—41no—
598C22×C11—41no—
599C22×C11—42no—
600C22×C11—42no—
601C22×C11—42no—
602C22×C11—42no—
603C22×C11—42no—
604C22×C11—42no—
605C22×C11—42no—
606C22×C11—42no—
607C22×C11—42no—
608C22×C11—41no—
609C22×C11—41no—
610C22×C11—42no—
611C22×C11—816no—
612C22×C11—88no—
613C22×C11#51818yes—
614C22×C11C24×C411yescharacteristic
615C22×C11C2×H(5,𝔽2)12yes—
616C22×C11C2×H(5,𝔽2)12yes—
617C22×C11C2×H(5,𝔽2)11yescharacteristic
618C22×C11#58511yescharacteristic
619C4×C11—24no—
620C4×C11—24no—
621C4×C11—24no—
622C4×C11—22no—
623C4×C11—22no—
624C4×C11—42no—
625C4×C11—41no—
626C4×C11—41no—
627C4×C11—42no—
628C4×C11—42no—
629C4×C11—42no—
630C4×C11—41no—
631C4×C11—42no—
632C4×C11—42no—
633C25C23×C1111yescharacteristic
634C25C23×C1112yes—
635C25C23×C1111yescharacteristic
636C22×D4—44no—
637C22×D4—44no—
638C22×D4—44no—
639C22×D4—44no—
640C22×D4C2×C4×C11116yescomplemented
641C22×D4C2×C4×C11116yescomplemented
642C22×D4C23×C1112yes—
643C22×D4C23×C1112yes—
644C22×D4C23×C1112yes—
645C22×D4C23×C1111yescharacteristic
646C22×D4C23×C1112yes—
647C22×D4C23×C1112yes—
648C22×D4C23×C1111yescharacteristic
649C22×D4C23×C1112yes—
650C22×D4C23×C1112yes—
651C23×C4—42no—
652C23×C4—44no—
653C23×C4C23×C1112yes—
654C23×C4C23×C1112yes—
655C23×C4C23×C1112yes—
656C23×C4C23×C1111yescharacteristic
657C23×C4C23×C1112yes—
658C23×C4C23×C1111yescharacteristic
659C23×C4C23×C1112yes—
660C23×C4C23×C1111yescharacteristic
661C23×C4C23×C1112yes—
662C23×C4C23×C1111yescharacteristic
663C23×C4C23×C1112yes—
664C23×C4C23×C1112yes—
665#127C2×C4×C1118yescomplemented
666#121C2×C4×C11116yescomplemented
667#121C2×C4×C11116yescomplemented
668#120C2×C4×C1118yescomplemented
669#120C2×C4×C11116yescomplemented
670#120C2×C4×C1118yescomplemented
671C4×D4—42no—
672C4×D4—42no—
673C4×D4—44no—
674C4×D4—44no—
675C4×D4—44no—
676C4×D4—44no—
677C4×D4C2×C4×C11116yescomplemented
678C2×C4⋊C4C23×C1112yes—
679C2×C4⋊C4C23×C1112yes—
680C2×C4⋊C4C23×C1112yes—
681C2×C4⋊C4C23×C1112yes—
682C2×C4⋊C4C23×C1111yescharacteristic
683C2×C4⋊C4C23×C1111yescharacteristic
684C2×C4⋊C4C23×C1112yes—
685C2×C22⋊C4—42no—
686C2×C22⋊C4—44no—
687C2×C22⋊C4—44no—
688C2×C22⋊C4—44no—
689C2×C22⋊C4—44no—
690C2×C22⋊C4C23×C1112yes—
691C2×C22⋊C4C23×C1112yes—
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×C1112yes—
706C2×C22⋊C4C23×C1112yes—
707C2×C22⋊C4C23×C1111yescharacteristic
708C2×C22⋊C4C23×C1111yescharacteristic
709C2×C22⋊C4C23×C1112yes—
710C2×C22⋊C4C23×C1112yes—
711C2×C22⋊C4C23×C1112yes—
712C2×C22⋊C4C23×C1112yes—
713C2×C22⋊C4C23×C1112yes—
714C2×C22⋊C4C23×C1111yescharacteristic
715C2×C22⋊C4C23×C1111yescharacteristic
716C2×C22⋊C4C23×C1112yes—
717C2×C22⋊C4C23×C1111yescharacteristic
718C2×C22⋊C4C23×C1112yes—
719C2×C22⋊C4C23×C1112yes—
720C2×C22⋊C4C23×C1111yescharacteristic
721C2×C42C23×C1111yescharacteristic
722C2×C42C23×C1112yes—
723C2×C42C23×C1112yes—
724C2×C42C23×C1112yes—
725C2×C42C23×C1112yes—
726C2×C42C23×C1111yescharacteristic
727C2×C42C23×C1111yescharacteristic
728#95C23×C1112yes—
729#95C23×C1112yes—
730#95C23×C1112yes—
731#95C23×C1112yes—
732#95C23×C1112yes—
733#95C23×C1112yes—
734#95C23×C1112yes—
735#95C23×C1112yes—
736#95C23×C1112yes—
737#95C23×C1112yes—
738#95C23×C1112yes—
739#95C23×C1112yes—
740#95C23×C1112yes—
741#95C23×C1112yes—
742#95C23×C1112yes—
743#95C23×C1112yes—
744#95C23×C1112yes—
745#95C23×C1112yes—
746C2×C11—28no—
747C2×C11—42no—
748C2×C11—42no—
749C2×C11—44no—
750C2×C11—44no—
751C2×C11C2×#51812yes—
752C2×C11C4×H(5,𝔽2)11yescharacteristic
753C2×C11#353211yescharacteristic
754C2×C11#353412yes—
755C2×C11#353711yescharacteristic
756C24—24no—
757C24—24no—
758C24—24no—
759C24—24no—
760C24—41no—
761C24—41no—
762C24—42no—
763C24—41no—
764C24—42no—
765C24—42no—
766C24—42no—
767C24—42no—
768C24—42no—
769C24—41no—
770C24C22×C4×C1114yes—
771C24C22×C4×C1118yes—
772C24C22×C4×C1114yescomplemented
773C24C24×C1112yes—
774C24C24×C1112yes—
775C24C24×C1111yescharacteristic
776C24C24×C1111yescharacteristic
777C24C24×C1112yes—
778C2×D4—24no—
779C2×D4—24no—
780C2×D4—24no—
781C2×D4—24no—
782C2×D4—24no—
783C2×D4—24no—
784C2×D4—41no—
785C2×D4—41no—
786C2×D4—42no—
787C2×D4—42no—
788C2×D4—42no—
789C2×D4—42no—
790C2×D4—42no—
791C2×D4—42no—
792C2×D4—42no—
793C2×D4—42no—
794C2×D4—41no—
795C2×D4—41no—
796C2×D4—432no—
797C2×D4—432no—
798C2×D4C22×C4×C1118yes—
799C2×D4C22×C4×C1118yes—
800C2×D4C22×C4×C1118yes—
801C2×D4C22×C4×C1114yes—
802C2×D4C22×C4×C1118yes—
803C2×D4C22×C4×C1118yes—
804C2×D4C22×C4×C1114yescomplemented
805C2×D4C22×C4×C1118yescomplemented
806C2×D4C22×C4×C1118yescomplemented
807C22×C4—24no—
808C22×C4—24no—
809C22×C4—24no—
810C22×C4—24no—
811C22×C4—24no—
812C22×C4—22no—
813C22×C4—22no—
814C22×C4—42no—
815C22×C4—42no—
816C22×C4—41no—
817C22×C4—42no—
818C22×C4—42no—
819C22×C4—42no—
820C22×C4—42no—
821C22×C4—42no—
822C22×C4—42no—
823C22×C4—42no—
824C22×C4—42no—
825C22×C4—42no—
826C22×C4—41no—
827C22×C4—42no—
828C22×C4—42no—
829C22×C4—42no—
830C22×C4—42no—
831C22×C4—42no—
832C22×C4—42no—
833C22×C4—42no—
834C22×C4—42no—
835C22×C4—42no—
836C22×C4—42no—
837C22×C4—416no—
838C22×C4C22×C4×C1118yes—
839C22×C4C22×C4×C1118yescomplemented
840C22×C4C24×C1112yes—
841C22×C4C24×C1112yes—
842C22×C4C24×C1111yescharacteristic
843C22×C4C24×C1112yes—
844C22×C4C24×C1112yes—
845C22×C4C24×C1111yescharacteristic
846C22×C4C24×C1112yes—
847C22×C4C24×C1112yes—
848C22×C4C24×C1111yescharacteristic
849C22×C4C24×C1112yes—
850C22×C4C24×C1111yescharacteristic
851C22×C4C24×C1112yes—
852C22×C4C24×C1112yes—
853C22×C4C24×C1111yescharacteristic
854C4⋊C4—41no—
855C4⋊C4—41no—
856C4⋊C4—42no—
857C4⋊C4—42no—
858C4⋊C4—42no—
859C4⋊C4—42no—
860C4⋊C4C22×C4×C1118yescomplemented
861C22⋊C4—24no—
862C22⋊C4—24no—
863C22⋊C4—24no—
864C22⋊C4—24no—
865C22⋊C4—24no—
866C22⋊C4—24no—
867C22⋊C4—42no—
868C22⋊C4—42no—
869C22⋊C4—42no—
870C22⋊C4—42no—
871C22⋊C4—42no—
872C22⋊C4—42no—
873C22⋊C4—42no—
874C22⋊C4—42no—
875C22⋊C4—42no—
876C22⋊C4—42no—
877C22⋊C4—42no—
878C22⋊C4—41no—
879C22⋊C4—41no—
880C22⋊C4—42no—
881C22⋊C4—42no—
882C22⋊C4—42no—
883C22⋊C4—42no—
884C22⋊C4—42no—
885C22⋊C4—41no—
886C22⋊C4—41no—
887C22⋊C4C22×C4×C1118yes—
888C22⋊C4C22×C4×C1114yes—
889C22⋊C4C22×C4×C1118yescomplemented
890C22⋊C4C22×C4×C1118yescomplemented
891C22⋊C4C22×C4×C1114yescomplemented
892C42—22no—
893C42—42no—
894C42—42no—
895C42—42no—
896C42—42no—
897C42—41no—
898C42C22×C4×C1114yescomplemented
899C11#3446811yescharacteristic, direct product factor, Sylow
900C23—22no—
901C23—22no—
902C23—22no—
903C23—22no—
904C23—216no—
905C23—22no—
906C23—22no—
907C23—22no—
908C23—22no—
909C23—22no—
910C23—22no—
911C23—21no—
912C23—21no—
913C23—22no—
914C23—22no—
915C23—22no—
916C23—22no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—22no—
921C23—21no—
922C23—21no—
923C23—22no—
924C23—22no—
925C23—216no—
926C23—44no—
927C23—48no—
928C23—48no—
929C23—48no—
930C23—44no—
931C23—44no—
932C23—48no—
933C23—44no—
934C23—84no—
935C23—84no—
936C23—84no—
937C23—84no—
938C23—82no—
939C23—84no—
940C23—82no—
941C23C23×C4×C1112yes—
942C23C23×C4×C1114yes—
943C23C23×C4×C1112yes—
944C23C23×C4×C1114yes—
945C23C23×C4×C1114yes—
946C23C11×H(5,𝔽2)14yes—
947C23C11×H(5,𝔽2)14yes—
948C23C25×C1111yescharacteristic
949D4—216no—
950D4—216no—
951D4—216no—
952D4—48no—
953D4—48no—
954D4—48no—
955D4—48no—
956D4—44no—
957D4—44no—
958C2×C4—21no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—21no—
967C2×C4—21no—
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—22no—
978C2×C4—22no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—21no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—21no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—48no—
992C2×C4—48no—
993C2×C4—48no—
994C2×C4—44no—
995C2×C4—48no—
996C2×C4—44no—
997C2×C4—82no—
998C2×C4—84no—
999C2×C4—84no—
1000C2×C4—84no—
1001C2×C4—84no—
1002C2×C4—82no—
1003C2×C4C23×C4×C1112yes—
1004C2×C4C23×C4×C1114yes—
1005C2×C4C23×C4×C1114yes—
1006C2×C4C23×C4×C1114yes—
1007C2×C4C11×H(5,𝔽2)12yes—
1008C22—24no—
1009C22—24no—
1010C22—24no—
1011C22—24no—
1012C22—24no—
1013C22—24no—
1014C22—24no—
1015C22—24no—
1016C22—24no—
1017C22—24no—
1018C22—24no—
1019C22—24no—
1020C22—22no—
1021C22—22no—
1022C22—24no—
1023C22—24no—
1024C22—416no—
1025C22—41no—
1026C22—41no—
1027C22—42no—
1028C22—42no—
1029C22—42no—
1030C22—42no—
1031C22—42no—
1032C22—42no—
1033C22—42no—
1034C22—42no—
1035C22—42no—
1036C22—41no—
1037C22—41no—
1038C22—42no—
1039C22—816no—
1040C22—88no—
1041C22C11×#51818yes—
1042C22C24×C4×C1111yescharacteristic
1043C22C2×C11×H(5,𝔽2)12yes—
1044C22C2×C11×H(5,𝔽2)12yes—
1045C22C2×C11×H(5,𝔽2)11yescharacteristic
1046C22C11×#58511yescharacteristic
1047C4—24no—
1048C4—24no—
1049C4—24no—
1050C4—22no—
1051C4—22no—
1052C4—42no—
1053C4—41no—
1054C4—41no—
1055C4—42no—
1056C4—42no—
1057C4—42no—
1058C4—41no—
1059C4—42no—
1060C4—42no—
1061C2—28no—
1062C2—42no—
1063C2—44no—
1064C2—42no—
1065C2—44no—
1066C2C2×C11×#51812yes—
1067C2C4×C11×H(5,𝔽2)11yescharacteristic
1068C2C11×#353211yescharacteristic
1069C2C11×#353412yes—
1070C2C11×#353711yescharacteristic
subgroupG/H
center, socleC23×C11C25
commutatorC22C24×C4×C11
Frattini, cosocleC23C25×C11
prime radicalC2×D42×C11C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#2380C2semidirect
3. C11×#2377C2semidirect
4. C11×#2375C2semidirect
5. C11×#2364C2semidirect
6. C11×#2358C2semidirect
7. C11×#2358C2semidirect
8. C11×#2353C2semidirect
9. D4×C11×C22⋊C4C2semidirect
10. D4×C11×C22⋊C4C2semidirect
11. C11×#2333C2semidirect
12. C11×#2328C2semidirect
13. C11×#2325C2semidirect
14. C11×#2321C2semidirect
15. C11×#2321C2semidirect
16. C11×#2318C2semidirect
17. C11×#2308C2semidirect
18. C4×C11×#120C2semidirect
19. C2×C11×#386C2semidirect
22. C24×C4×C11C22semidirect
23. D42×C11C4semidirect
31. C2×C4×D4×C11C22semidirect
32. C2×C4×D4×C11C22semidirect
33. C2×C4×D4×C11C22semidirect
34. C2×C4×D4×C11C22semidirect
35. C2×C4×D4×C11C22semidirect
36. C2×C4×D4×C11C22semidirect
37. C22×C11×C22⋊C4C22semidirect
38. C22×C11×C22⋊C4C22semidirect
39. C22×C11×C22⋊C4C22semidirect
40. C22×C11×C22⋊C4C22semidirect
41. C22×C11×C22⋊C4C22semidirect
42. C11×#390C22semidirect
43. C11×#390C22semidirect
44. C11×#390C22semidirect
45. C11×#390C22semidirect
46. C11×#390C22semidirect
47. C11×#390C22semidirect
48. C11×#388C22semidirect
49. C11×#388C22semidirect
50. C11×#388C22semidirect
51. C11×#388C22semidirect
52. C11×#388C22semidirect
53. C11×#388C22semidirect
54. C11×#388C22semidirect
55. C11×#388C22semidirect
56. C11×#387C22semidirect
57. C11×#387C22semidirect
58. C11×#387C22semidirect
59. C11×#387C22semidirect
64. C11×#386C22semidirect
65. C11×#386C22semidirect
66. C11×#386C22semidirect
67. C11×#386C22semidirect
68. C11×#386C22semidirect
69. C11×#386C22semidirect
70. C11×#386C22semidirect
71. C11×#386C22semidirect
72. C11×#386C22semidirect
73. C11×#386C22semidirect
74. C11×#386C22semidirect
75. C11×#386C22semidirect
76. C11×#386C22semidirect
77. C11×#386C22semidirect
78. C11×#386C22semidirect
79. C11×#386C22semidirect
80. C11×#386C22semidirect
81. C11×#386C22semidirect
82. C11×#386C22semidirect
83. C11×#385C22semidirect
84. C11×#385C22semidirect
85. C11×#385C22semidirect
86. C11×#385C22semidirect
87. C11×#385C22semidirect
88. C11×#383C22semidirect
89. C11×#382C22semidirect
90. C11×#381C22semidirect
91. C11×#381C22semidirect
92. C11×#380C22semidirect
93. C11×#380C22semidirect
94. C11×#379C22semidirect
95. C11×#379C22semidirect
96. C11×#379C22semidirect
97. C11×#379C22semidirect
98. C4×C11×C22⋊C4C22semidirect
99. C4×C11×C22⋊C4C22semidirect
100. C4×C11×C22⋊C4C22semidirect
101. C4×C11×C22⋊C4C22semidirect
102. C4×C11×C22⋊C4C22semidirect
103. C4×C11×C22⋊C4C22semidirect
104. C4×C11×C22⋊C4C22semidirect
105. C11×#376C22semidirect
106. C2×C11×#95C22semidirect
107. C2×C11×#95C22semidirect
115. C22×D4×C11C2×C4semidirect
116. C22×D4×C11C2×C4semidirect
140. C11×#127C2×C4semidirect
141. C11×#121C2×C4semidirect
142. C11×#121C2×C4semidirect
143. C11×#120C2×C4semidirect
144. C11×#120C2×C4semidirect
145. C11×#120C2×C4semidirect
152. C4×D4×C11C2×C4semidirect
221. #34468C11direct (N × H)
238. C24×C11C22×C4semidirect
270. C2×D4×C11C22×C4semidirect
271. C2×D4×C11C22×C4semidirect
272. C2×D4×C11C22×C4semidirect
305. C22×C4×C11C22×C4semidirect
326. C11×C4⋊C4C22×C4semidirect
355. C11×C22⋊C4C22×C4semidirect
356. C11×C22⋊C4C22×C4semidirect
357. C11×C22⋊C4C22×C4semidirect
364. C42×C11C22×C4semidirect
366. #2380C2×C11semidirect
367. #2377C2×C11semidirect
368. #2375C2×C11semidirect
369. #2364C2×C11semidirect
370. #2358C2×C11semidirect
371. #2358C2×C11semidirect
372. #2353C2×C11semidirect
373. D4×C22⋊C4C2×C11semidirect
374. D4×C22⋊C4C2×C11semidirect
375. #2333C2×C11semidirect
376. #2328C2×C11semidirect
377. #2325C2×C11semidirect
378. #2321C2×C11semidirect
379. #2321C2×C11semidirect
380. #2318C2×C11semidirect
381. #2308C2×C11semidirect
382. C4×#120C2×C11semidirect
383. C2×#386C2×C11semidirect
494. C24×C4C22×C11semidirect
495. D42C4×C11semidirect
503. C2×C4×D4C22×C11semidirect
504. C2×C4×D4C22×C11semidirect
505. C2×C4×D4C22×C11semidirect
506. C2×C4×D4C22×C11semidirect
507. C2×C4×D4C22×C11semidirect
508. C2×C4×D4C22×C11semidirect
509. C22×C22⋊C4C22×C11semidirect
510. C22×C22⋊C4C22×C11semidirect
511. C22×C22⋊C4C22×C11semidirect
512. C22×C22⋊C4C22×C11semidirect
513. C22×C22⋊C4C22×C11semidirect
514. #390C22×C11semidirect
515. #390C22×C11semidirect
516. #390C22×C11semidirect
517. #390C22×C11semidirect
518. #390C22×C11semidirect
519. #390C22×C11semidirect
520. #388C22×C11semidirect
521. #388C22×C11semidirect
522. #388C22×C11semidirect
523. #388C22×C11semidirect
524. #388C22×C11semidirect
525. #388C22×C11semidirect
526. #388C22×C11semidirect
527. #388C22×C11semidirect
528. #387C22×C11semidirect
529. #387C22×C11semidirect
530. #387C22×C11semidirect
531. #387C22×C11semidirect
536. #386C22×C11semidirect
537. #386C22×C11semidirect
538. #386C22×C11semidirect
539. #386C22×C11semidirect
540. #386C22×C11semidirect
541. #386C22×C11semidirect
542. #386C22×C11semidirect
543. #386C22×C11semidirect
544. #386C22×C11semidirect
545. #386C22×C11semidirect
546. #386C22×C11semidirect
547. #386C22×C11semidirect
548. #386C22×C11semidirect
549. #386C22×C11semidirect
550. #386C22×C11semidirect
551. #386C22×C11semidirect
552. #386C22×C11semidirect
553. #386C22×C11semidirect
554. #386C22×C11semidirect
555. #385C22×C11semidirect
556. #385C22×C11semidirect
557. #385C22×C11semidirect
558. #385C22×C11semidirect
559. #385C22×C11semidirect
560. #383C22×C11semidirect
561. #382C22×C11semidirect
562. #381C22×C11semidirect
563. #381C22×C11semidirect
564. #380C22×C11semidirect
565. #380C22×C11semidirect
566. #379C22×C11semidirect
567. #379C22×C11semidirect
568. #379C22×C11semidirect
569. #379C22×C11semidirect
570. C4×C22⋊C4C22×C11semidirect
571. C4×C22⋊C4C22×C11semidirect
572. C4×C22⋊C4C22×C11semidirect
573. C4×C22⋊C4C22×C11semidirect
574. C4×C22⋊C4C22×C11semidirect
575. C4×C22⋊C4C22×C11semidirect
576. C4×C22⋊C4C22×C11semidirect
577. #376C22×C11semidirect
578. C2×#95C22×C11semidirect
579. C2×#95C22×C11semidirect
640. C22×D4C2×C4×C11semidirect
641. C22×D4C2×C4×C11semidirect
665. #127C2×C4×C11semidirect
666. #121C2×C4×C11semidirect
667. #121C2×C4×C11semidirect
668. #120C2×C4×C11semidirect
669. #120C2×C4×C11semidirect
670. #120C2×C4×C11semidirect
677. C4×D4C2×C4×C11semidirect
772. C24C22×C4×C11semidirect
804. C2×D4C22×C4×C11semidirect
805. C2×D4C22×C4×C11semidirect
806. C2×D4C22×C4×C11semidirect
839. C22×C4C22×C4×C11semidirect
860. C4⋊C4C22×C4×C11semidirect
889. C22⋊C4C22×C4×C11semidirect
890. C22⋊C4C22×C4×C11semidirect
891. C22⋊C4C22×C4×C11semidirect
898. C42C22×C4×C11semidirect
899. C11#34468direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D42×C112
C11×#23802
C11×#23772
C11×#23752
C11×#23642
C11×#23582
C11×#23532
D4×C11×C22⋊C42
C11×#23332
C11×#23282
C11×#23252
C11×#23212
C11×#23182
C11×#23082
C4×C11×#1202
C2×C11×#3862
#3446811