Finite Group Databasebeta

← C11×#34483 #14611676

Subgroups — C11×#34483 #14611676

Order 2816.

2232 conjugacy classes of subgroups.

The subgroup lattice has 1032 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#553C211yesmaximal, characteristic
2C11×#2383C212yesmaximal, complemented
3C11×#2377C212yesmaximal, complemented
4C11×#2370C211yesmaximal, characteristic, complemented
5C11×#2363C211yesmaximal, characteristic, complemented
6C11×#2361C211yesmaximal, characteristic, complemented
7C11×#2359C212yesmaximal, complemented
8C11×#2354C212yesmaximal, complemented
9C11×#2352C211yesmaximal, characteristic, complemented
10C11×#2349C211yesmaximal, characteristic, complemented
11C11×#2347C211yesmaximal, characteristic, complemented
12C11×#2344C211yesmaximal, characteristic, complemented
13C11×#2335C212yesmaximal, complemented
14C11×#2334C212yesmaximal, complemented
15C11×#2324C211yesmaximal, characteristic, complemented
16C11×#2324C211yesmaximal, characteristic, complemented
17C11×#2324C212yesmaximal, complemented
18C11×#2318C212yesmaximal, complemented
19C11×#2317C211yesmaximal, characteristic, complemented
20C11×#2316C211yesmaximal, characteristic, complemented
21C4×C11×#125C211yesmaximal, characteristic, complemented
22C11×#2293C211yesmaximal, characteristic, complemented
23C11×#2293C211yesmaximal, characteristic, complemented
24C11×#553C4116yescomplemented
25C2×C11×#126C2212yes—
26C2×C11×#125C2211yescharacteristic
27C2×C11×#123C2212yes—
28C2×C11×#121C2211yescharacteristic
29C2×C11×#121C2211yescharacteristic
30C2×C11×#121C2212yes—
31C2×C4×D4×C11C2211yescharacteristic
32C2×C4×D4×C11C2211yescharacteristic
33C2×C4×D4×C11C2212yes—
34C2×C4×D4×C11C2211yescharacteristic
35C2×C4×D4×C11C2211yescharacteristic
36C2×C4×D4×C11C2212yes—
37C2×C11×#117C2211yescharacteristic
38C2×C11×#117C2211yescharacteristic
39C2×C11×#117C2212yes—
40C2×C11×#117C2211yescharacteristic
41C2×C11×#117C2212yes—
42C2×C11×#117C2211yescharacteristic
43C22×C11×C4⋊C4C2211yescharacteristic
44C22×C11×C4⋊C4C2211yescharacteristic
45C11×#390C2211yescharacteristic
46C11×#390C2211yescharacteristic
47C11×#390C2211yescharacteristic
48C11×#390C2211yescharacteristic
49C11×#390C2212yes—
50C11×#390C2212yes—
51C11×#390C2212yes—
52C11×#389C2211yescharacteristic
53C11×#389C2212yes—
54C11×#389C2212yes—
55C11×#389C2211yescharacteristic
56C11×#389C2211yescharacteristic
57C11×#389C2211yescharacteristic
58C11×#389C2211yescharacteristic
59C11×#389C2211yescharacteristic
60C11×#389C2212yes—
61C11×#389C2211yescharacteristic
62C11×#389C2211yescharacteristic
63C11×#389C2211yescharacteristic
64C11×#389C2211yescharacteristic
65C11×#388C2212yes—
66C11×#388C2212yes—
67C11×#388C2212yes—
68C11×#388C2211yescharacteristic
69C11×#388C2212yes—
70C11×#388C2211yescharacteristic
71C11×#388C2211yescharacteristic
72C11×#388C2211yescharacteristic
73C11×#388C2212yes—
74C11×#388C2212yes—
75C11×#388C2212yes—
76C11×#388C2212yes—
77C11×#388C2212yes—
78C11×#387C2212yes—
79C11×#387C2212yes—
80C11×#387C2212yes—
81C11×#387C2212yes—
82C11×#387C2212yes—
83C11×#387C2212yes—
84C11×#387C2212yes—
85C11×#386C2212yes—
86C11×#386C2212yes—
87C11×#386C2212yes—
88C11×#386C2212yes—
89C11×#386C2212yes—
90C11×#385C2212yes—
91C11×#385C2212yes—
92C11×#385C2212yes—
93C11×#385C2212yes—
94C11×#385C2212yes—
95C11×#385C2212yes—
96C11×#385C2212yes—
97C11×#384C2212yes—
98C11×#383C2212yes—
99C11×#382C2211yescharacteristic
100C11×#382C2212yes—
101C11×#381C2212yes—
102C11×#380C2212yes—
103C11×#380C2212yes—
104C11×#380C2211yescharacteristic
105C11×#380C2211yescharacteristic
106C11×#380C2212yes—
107C4×C11×C4⋊C4C2211yescharacteristic
108C4×C11×C4⋊C4C2211yescharacteristic
109C4×C11×C4⋊C4C2212yes—
110C4×C11×C4⋊C4C2211yescharacteristic
111C4×C11×C4⋊C4C2211yescharacteristic
112C4×C11×C4⋊C4C2212yes—
113C4×C11×C4⋊C4C2211yescharacteristic
114C4×C11×C4⋊C4C2211yescharacteristic
115C4×C11×C4⋊C4C2212yes—
116C4×C11×C4⋊C4C2212yes—
117C4×C11×C22⋊C4C2212yes—
118C4×C11×C22⋊C4C2211yescharacteristic
119C4×C11×C22⋊C4C2211yescharacteristic
120C4×C11×C22⋊C4C2212yes—
121C4×C11×C22⋊C4C2212yes—
122C2×C11×#95C2212yes—
123C43×C11C2211yescharacteristic
124C22×D4×C11C2311yescharacteristic
125C22×D4×C11C2312yes—
126C22×D4×C11C2311yescharacteristic
127C22×D4×C11C2312yes—
128C23×C4×C11C2311yescharacteristic
129C23×C4×C11C2311yescharacteristic
130C23×C4×C11C2312yes—
131C23×C4×C11C2312yes—
132C23×C4×C11C2312yes—
133C23×C4×C11C2312yes—
134C23×C4×C11C2312yes—
135C11×#126C2×C4116yescomplemented
136C11×#125C2×C418yescomplemented
137C11×#123C2×C4116yescomplemented
138C11×#121C2×C418yes—
139C11×#121C2×C4116yescomplemented
140C11×#121C2×C418yescomplemented
141C4×D4×C11—44no—
142C4×D4×C11—42no—
143C4×D4×C11—42no—
144C4×D4×C11C2×C4116yescomplemented
145C4×D4×C11C2×C418yescomplemented
146C4×D4×C11C2×C418yescomplemented
147C11×#117—42no—
148C11×#117—42no—
149C11×#117—44no—
150C11×#117—44no—
151C11×#117—42no—
152C11×#117C2×C418yescomplemented
153C2×C11×C4⋊C4—42no—
154C2×C11×C4⋊C4C2×C418yescomplemented
155C2×C11×C4⋊C4C2311yescharacteristic
156C2×C11×C4⋊C4C2311yescharacteristic
157C2×C11×C4⋊C4C2312yes—
158C2×C11×C4⋊C4C2311yescharacteristic
159C2×C11×C4⋊C4C2311yescharacteristic
160C2×C11×C4⋊C4C2312yes—
161C2×C11×C4⋊C4C2312yes—
162C2×C11×C4⋊C4C2312yes—
163C2×C11×C4⋊C4C2311yescharacteristic
164C2×C11×C4⋊C4C2311yescharacteristic
165C2×C11×C4⋊C4C2311yescharacteristic
166C2×C11×C4⋊C4C2311yescharacteristic
167C2×C11×C4⋊C4C2312yes—
168C2×C11×C4⋊C4C2312yes—
169C2×C11×C4⋊C4C2312yes—
170C2×C11×C4⋊C4C2312yes—
171C2×C11×C4⋊C4C2312yes—
172C2×C11×C4⋊C4C2311yescharacteristic
173C2×C11×C4⋊C4C2311yescharacteristic
174C2×C11×C4⋊C4C2311yescharacteristic
175C2×C11×C4⋊C4C2311yescharacteristic
176C2×C11×C4⋊C4C2312yes—
177C2×C11×C4⋊C4C2311yescharacteristic
178C2×C11×C4⋊C4C2312yes—
179C2×C11×C4⋊C4C2311yescharacteristic
180C2×C11×C4⋊C4C2312yes—
181C2×C11×C22⋊C4C2311yescharacteristic
182C2×C11×C22⋊C4C2312yes—
183C2×C11×C22⋊C4C2311yescharacteristic
184C2×C11×C22⋊C4C2312yes—
185C2×C11×C22⋊C4C2311yescharacteristic
186C2×C11×C22⋊C4C2311yescharacteristic
187C2×C11×C22⋊C4C2312yes—
188C2×C11×C22⋊C4C2311yescharacteristic
189C2×C11×C22⋊C4C2311yescharacteristic
190C2×C11×C22⋊C4C2312yes—
191C2×C11×C22⋊C4C2312yes—
192C2×C11×C22⋊C4C2311yescharacteristic
193C2×C11×C22⋊C4C2312yes—
194C2×C11×C22⋊C4C2312yes—
195C2×C11×C22⋊C4C2311yescharacteristic
196C2×C11×C22⋊C4C2312yes—
197C2×C11×C22⋊C4C2312yes—
198C2×C11×C22⋊C4C2312yes—
199C2×C11×C22⋊C4C2311yescharacteristic
200C2×C11×C22⋊C4C2312yes—
201C2×C11×C22⋊C4C2311yescharacteristic
202C2×C11×C22⋊C4C2312yes—
203C2×C11×C22⋊C4C2312yes—
204C2×C42×C11C2311yescharacteristic
205C2×C42×C11C2311yescharacteristic
206C2×C42×C11C2311yescharacteristic
207C2×C42×C11C2311yescharacteristic
208C2×C42×C11C2311yescharacteristic
209C2×C42×C11C2312yes—
210C2×C42×C11C2311yescharacteristic
211C2×C42×C11C2311yescharacteristic
212C2×C42×C11C2311yescharacteristic
213C2×C42×C11C2312yes—
214C2×C42×C11C2312yes—
215C2×C42×C11C2312yes—
216C2×C42×C11C2312yes—
217C2×C42×C11C2312yes—
218C2×C42×C11C2311yescharacteristic
219C2×C42×C11C2312yes—
220C11×#95C2311yescharacteristic
221C11×#95C2312yes—
222C11×#95C2312yes—
223C11×#95C2312yes—
224C11×#95C2311yescharacteristic
225C11×#95C2311yescharacteristic
226C11×#95C2312yes—
227C11×#95C2312yes—
228C11×#95C2312yes—
229C11×#95C2312yes—
230C11×#95C2311yescharacteristic
231C11×#95C2311yescharacteristic
232C11×#95C2311yescharacteristic
233C11×#95C2312yes—
234C11×#95C2312yes—
235C11×#95C2312yes—
236C11×#95C2312yes—
237C11×#95C2312yes—
238C11×#95C2312yes—
239C11×#95C2312yes—
240C11×#95C2312yes—
241C11×#95C2312yes—
242C11×#95C2312yes—
243#34483C1111yesmaximal, characteristic, direct product factor, Sylow
244C24×C11C2411yescharacteristic
245C24×C11C2412yes—
246C24×C11C2411yescharacteristic
247C2×D4×C11—22no—
248C2×D4×C11—22no—
249C2×D4×C11—42no—
250C2×D4×C11—42no—
251C2×D4×C11—41no—
252C2×D4×C11—41no—
253C2×D4×C11—42no—
254C2×D4×C11—42no—
255C2×D4×C11C22×C414yes—
256C2×D4×C11C22×C418yes—
257C2×D4×C11C22×C414yes—
258C2×D4×C11C22×C418yes—
259C22×C4×C11—22no—
260C22×C4×C11—22no—
261C22×C4×C11—22no—
262C22×C4×C11—22no—
263C22×C4×C11—42no—
264C22×C4×C11—42no—
265C22×C4×C11—42no—
266C22×C4×C11—42no—
267C22×C4×C11—42no—
268C22×C4×C11—42no—
269C22×C4×C11—42no—
270C22×C4×C11—42no—
271C22×C4×C11—42no—
272C22×C4×C11—42no—
273C22×C4×C11—42no—
274C22×C4×C11—42no—
275C22×C4×C11—42no—
276C22×C4×C11C22×C414yes—
277C22×C4×C11C22×C414yes—
278C22×C4×C11C22×C418yes—
279C22×C4×C11C22×C418yes—
280C22×C4×C11C2411yescharacteristic
281C22×C4×C11C2411yescharacteristic
282C22×C4×C11C2412yes—
283C22×C4×C11C2412yes—
284C22×C4×C11C2411yescharacteristic
285C22×C4×C11C2412yes—
286C22×C4×C11C2411yescharacteristic
287C22×C4×C11C2411yescharacteristic
288C22×C4×C11C2412yes—
289C22×C4×C11C2411yescharacteristic
290C22×C4×C11C2411yescharacteristic
291C22×C4×C11C2411yescharacteristic
292C22×C4×C11C2412yes—
293C22×C4×C11C2411yescharacteristic
294C22×C4×C11C2411yescharacteristic
295C22×C4×C11C2411yescharacteristic
296C22×C4×C11C2412yes—
297C22×C4×C11C2412yes—
298C22×C4×C11C2411yescharacteristic
299C22×C4×C11C2411yescharacteristic
300C11×C4⋊C4—22no—
301C11×C4⋊C4—22no—
302C11×C4⋊C4—24no—
303C11×C4⋊C4—22no—
304C11×C4⋊C4—22no—
305C11×C4⋊C4—42no—
306C11×C4⋊C4—41no—
307C11×C4⋊C4—41no—
308C11×C4⋊C4—42no—
309C11×C4⋊C4—42no—
310C11×C4⋊C4—42no—
311C11×C4⋊C4—42no—
312C11×C4⋊C4—41no—
313C11×C4⋊C4—41no—
314C11×C4⋊C4—42no—
315C11×C4⋊C4—42no—
316C11×C4⋊C4—41no—
317C11×C4⋊C4—41no—
318C11×C4⋊C4—42no—
319C11×C4⋊C4C22×C414yes—
320C11×C4⋊C4C22×C414yes—
321C11×C4⋊C4C22×C418yes—
322C11×C4⋊C4C22×C414yes—
323C11×C4⋊C4C22×C418yes—
324C11×C4⋊C4C22×C414yes—
325C11×C4⋊C4C22×C418yes—
326C11×C22⋊C4—22no—
327C11×C22⋊C4—24no—
328C11×C22⋊C4—22no—
329C11×C22⋊C4—42no—
330C11×C22⋊C4—42no—
331C11×C22⋊C4—41no—
332C11×C22⋊C4—42no—
333C11×C22⋊C4—41no—
334C11×C22⋊C4—41no—
335C11×C22⋊C4—41no—
336C11×C22⋊C4—41no—
337C11×C22⋊C4—41no—
338C11×C22⋊C4—42no—
339C11×C22⋊C4—42no—
340C11×C22⋊C4—42no—
341C11×C22⋊C4—42no—
342C11×C22⋊C4—42no—
343C11×C22⋊C4C22×C418yes—
344C11×C22⋊C4C22×C414yes—
345C11×C22⋊C4C22×C418yes—
346C11×C22⋊C4C22×C418yes—
347C11×C22⋊C4C22×C414yes—
348C11×C22⋊C4C22×C418yes—
349C42×C11—22no—
350C42×C11—22no—
351C42×C11—24no—
352C42×C11—22no—
353C42×C11—22no—
354C42×C11—22no—
355C42×C11—42no—
356C42×C11—41no—
357C42×C11—42no—
358C42×C11—41no—
359C42×C11—41no—
360C42×C11—42no—
361C42×C11—42no—
362C42×C11—42no—
363C42×C11C22×C418yes—
364C42×C11C22×C414yes—
365C2×#553C2×C1111yescharacteristic
366#2383C2×C1112yescomplemented
367#2377C2×C1112yescomplemented
368#2370C2×C1111yescharacteristic, complemented
369#2363C2×C1111yescharacteristic, complemented
370#2361C2×C1111yescharacteristic, complemented
371#2359C2×C1112yescomplemented
372#2354C2×C1112yescomplemented
373#2352C2×C1111yescharacteristic, complemented
374#2349C2×C1111yescharacteristic, complemented
375#2347C2×C1111yescharacteristic, complemented
376#2344C2×C1111yescharacteristic, complemented
377#2335C2×C1112yescomplemented
378#2334C2×C1112yescomplemented
379#2324C2×C1111yescharacteristic, complemented
380#2324C2×C1111yescharacteristic, complemented
381#2324C2×C1112yescomplemented
382#2318C2×C1112yescomplemented
383#2317C2×C1111yescharacteristic, complemented
384#2316C2×C1111yescharacteristic, complemented
385C4×#125C2×C1111yescharacteristic, complemented
386#2293C2×C1111yescharacteristic, complemented
387#2293C2×C1111yescharacteristic, complemented
388C23×C11—21no—
389C23×C11—22no—
390C23×C11—21no—
391C23×C11—21no—
392C23×C11—21no—
393C23×C11—22no—
394C23×C11—21no—
395C23×C11—21no—
396C23×C11—22no—
397C23×C11—21no—
398C23×C11—21no—
399C23×C11—22no—
400C23×C11—22no—
401C23×C11—21no—
402C23×C11—21no—
403C23×C11—22no—
404C23×C11—21no—
405C23×C11—21no—
406C23×C11C23×C412yes—
407C23×C11C23×C414yes—
408C23×C11C23×C412yes—
409C23×C11C2511yescharacteristic
410D4×C11—28no—
411D4×C11—48no—
412D4×C11—44no—
413D4×C11—48no—
414C2×C4×C11—21no—
415C2×C4×C11—22no—
416C2×C4×C11—21no—
417C2×C4×C11—22no—
418C2×C4×C11—21no—
419C2×C4×C11—21no—
420C2×C4×C11—21no—
421C2×C4×C11—21no—
422C2×C4×C11—21no—
423C2×C4×C11—22no—
424C2×C4×C11—21no—
425C2×C4×C11—21no—
426C2×C4×C11—21no—
427C2×C4×C11—22no—
428C2×C4×C11—22no—
429C2×C4×C11—22no—
430C2×C4×C11—28no—
431C2×C4×C11—28no—
432C2×C4×C11—21no—
433C2×C4×C11—21no—
434C2×C4×C11—21no—
435C2×C4×C11—21no—
436C2×C4×C11—21no—
437C2×C4×C11—21no—
438C2×C4×C11—22no—
439C2×C4×C11—21no—
440C2×C4×C11—21no—
441C2×C4×C11—22no—
442C2×C4×C11—22no—
443C2×C4×C11—22no—
444C2×C4×C11—22no—
445C2×C4×C11—21no—
446C2×C4×C11—22no—
447C2×C4×C11—21no—
448C2×C4×C11—22no—
449C2×C4×C11—21no—
450C2×C4×C11—21no—
451C2×C4×C11—22no—
452C2×C4×C11—21no—
453C2×C4×C11—21no—
454C2×C4×C11—22no—
455C2×C4×C11—21no—
456C2×C4×C11—21no—
457C2×C4×C11—21no—
458C2×C4×C11—22no—
459C2×C4×C11—21no—
460C2×C4×C11—21no—
461C2×C4×C11—22no—
462C2×C4×C11—21no—
463C2×C4×C11—22no—
464C2×C4×C11—21no—
465C2×C4×C11—48no—
466C2×C4×C11—48no—
467C2×C4×C11—84no—
468C2×C4×C11—84no—
469C2×C4×C11—84no—
470C2×C4×C11C23×C412yes—
471C2×C4×C11C23×C414yes—
472C2×C4×C11C23×C412yes—
473C2×C4×C11C23×C414yes—
474C2×C4×C11C23×C412yes—
475C2×C4×C11C23×C412yes—
476C2×C4×C11C23×C414yes—
477C2×C4×C11C23×C412yes—
478C2×C4×C11H(5,𝔽2)12yes—
479C2×C4×C11H(5,𝔽2)12yes—
480C2×C4×C112−1+412yes—
481#553C4×C11116yescomplemented
482C2×#126C22×C1112yes—
483C2×#125C22×C1111yescharacteristic
484C2×#123C22×C1112yes—
485C2×#121C22×C1111yescharacteristic
486C2×#121C22×C1111yescharacteristic
487C2×#121C22×C1112yes—
488C2×C4×D4C22×C1111yescharacteristic
489C2×C4×D4C22×C1111yescharacteristic
490C2×C4×D4C22×C1112yes—
491C2×C4×D4C22×C1112yes—
492C2×C4×D4C22×C1111yescharacteristic
493C2×C4×D4C22×C1111yescharacteristic
494C2×#117C22×C1111yescharacteristic
495C2×#117C22×C1111yescharacteristic
496C2×#117C22×C1111yescharacteristic
497C2×#117C22×C1112yes—
498C2×#117C22×C1112yes—
499C2×#117C22×C1111yescharacteristic
500C22×C4⋊C4C22×C1111yescharacteristic
501C22×C4⋊C4C22×C1111yescharacteristic
502#390C22×C1112yes—
503#390C22×C1111yescharacteristic
504#390C22×C1111yescharacteristic
505#390C22×C1112yes—
506#390C22×C1112yes—
507#390C22×C1111yescharacteristic
508#390C22×C1111yescharacteristic
509#389C22×C1111yescharacteristic
510#389C22×C1111yescharacteristic
511#389C22×C1111yescharacteristic
512#389C22×C1112yes—
513#389C22×C1111yescharacteristic
514#389C22×C1112yes—
515#389C22×C1111yescharacteristic
516#389C22×C1111yescharacteristic
517#389C22×C1111yescharacteristic
518#389C22×C1112yes—
519#389C22×C1111yescharacteristic
520#389C22×C1111yescharacteristic
521#389C22×C1111yescharacteristic
522#388C22×C1111yescharacteristic
523#388C22×C1112yes—
524#388C22×C1112yes—
525#388C22×C1112yes—
526#388C22×C1112yes—
527#388C22×C1112yes—
528#388C22×C1112yes—
529#388C22×C1111yescharacteristic
530#388C22×C1112yes—
531#388C22×C1112yes—
532#388C22×C1111yescharacteristic
533#388C22×C1111yescharacteristic
534#388C22×C1112yes—
535#387C22×C1112yes—
536#387C22×C1112yes—
537#387C22×C1112yes—
538#387C22×C1112yes—
539#387C22×C1112yes—
540#387C22×C1112yes—
541#387C22×C1112yes—
542#386C22×C1112yes—
543#386C22×C1112yes—
544#386C22×C1112yes—
545#386C22×C1112yes—
546#386C22×C1112yes—
547#385C22×C1112yes—
548#385C22×C1112yes—
549#385C22×C1112yes—
550#385C22×C1112yes—
551#385C22×C1112yes—
552#385C22×C1112yes—
553#385C22×C1112yes—
554#384C22×C1112yes—
555#383C22×C1112yes—
556#382C22×C1111yescharacteristic
557#382C22×C1112yes—
558#381C22×C1112yes—
559#380C22×C1112yes—
560#380C22×C1112yes—
561#380C22×C1111yescharacteristic
562#380C22×C1111yescharacteristic
563#380C22×C1112yes—
564C4×C4⋊C4C22×C1112yes—
565C4×C4⋊C4C22×C1111yescharacteristic
566C4×C4⋊C4C22×C1111yescharacteristic
567C4×C4⋊C4C22×C1112yes—
568C4×C4⋊C4C22×C1111yescharacteristic
569C4×C4⋊C4C22×C1111yescharacteristic
570C4×C4⋊C4C22×C1112yes—
571C4×C4⋊C4C22×C1112yes—
572C4×C4⋊C4C22×C1111yescharacteristic
573C4×C4⋊C4C22×C1111yescharacteristic
574C4×C22⋊C4C22×C1112yes—
575C4×C22⋊C4C22×C1112yes—
576C4×C22⋊C4C22×C1112yes—
577C4×C22⋊C4C22×C1111yescharacteristic
578C4×C22⋊C4C22×C1111yescharacteristic
579C2×#95C22×C1112yes—
580C43C22×C1111yescharacteristic
581C22×C11—22no—
582C22×C11—22no—
583C22×C11—24no—
584C22×C11—22no—
585C22×C11—22no—
586C22×C11—24no—
587C22×C11—22no—
588C22×C11—24no—
589C22×C11—22no—
590C22×C11—41no—
591C22×C11—42no—
592C22×C11—41no—
593C22×C11—42no—
594C22×C11—41no—
595C22×C11—41no—
596C22×C11—41no—
597C22×C11—42no—
598C22×C11—41no—
599C22×C11—41no—
600C22×C11—41no—
601C22×C11—42no—
602C22×C11C24×C411yescharacteristic
603C22×C11C2×H(5,𝔽2)11yescharacteristic
604C22×C11C2×H(5,𝔽2)11yescharacteristic
605C22×C11C2×2−1+411yescharacteristic
606C22×C11#58511yescharacteristic
607C22×C11#58511yescharacteristic
608C22×C11#58511yescharacteristic
609C4×C11—22no—
610C4×C11—22no—
611C4×C11—24no—
612C4×C11—22no—
613C4×C11—22no—
614C4×C11—24no—
615C4×C11—24no—
616C4×C11—22no—
617C4×C11—41no—
618C4×C11—41no—
619C4×C11—42no—
620C4×C11—41no—
621C4×C11—42no—
622C4×C11—41no—
623C4×C11—41no—
624C4×C11—42no—
625C4×C11—41no—
626C4×C11—42no—
627C4×C11—41no—
628C4×C11#52014yes—
629C22×D4C23×C1111yescharacteristic
630C22×D4C23×C1112yes—
631C22×D4C23×C1112yes—
632C22×D4C23×C1111yescharacteristic
633C23×C4C23×C1111yescharacteristic
634C23×C4C23×C1111yescharacteristic
635C23×C4C23×C1112yes—
636C23×C4C23×C1112yes—
637C23×C4C23×C1112yes—
638C23×C4C23×C1112yes—
639C23×C4C23×C1112yes—
640#126C2×C4×C11116yescomplemented
641#125C2×C4×C1118yescomplemented
642#123C2×C4×C11116yescomplemented
643#121C2×C4×C1118yes—
644#121C2×C4×C11116yescomplemented
645#121C2×C4×C1118yescomplemented
646C4×D4—44no—
647C4×D4—42no—
648C4×D4—42no—
649C4×D4C2×C4×C11116yescomplemented
650C4×D4C2×C4×C1118yescomplemented
651C4×D4C2×C4×C1118yescomplemented
652#117—42no—
653#117—42no—
654#117—44no—
655#117—44no—
656#117—42no—
657#117C2×C4×C1118yescomplemented
658C2×C4⋊C4—42no—
659C2×C4⋊C4C2×C4×C1118yescomplemented
660C2×C4⋊C4C23×C1111yescharacteristic
661C2×C4⋊C4C23×C1111yescharacteristic
662C2×C4⋊C4C23×C1112yes—
663C2×C4⋊C4C23×C1111yescharacteristic
664C2×C4⋊C4C23×C1111yescharacteristic
665C2×C4⋊C4C23×C1112yes—
666C2×C4⋊C4C23×C1112yes—
667C2×C4⋊C4C23×C1112yes—
668C2×C4⋊C4C23×C1111yescharacteristic
669C2×C4⋊C4C23×C1111yescharacteristic
670C2×C4⋊C4C23×C1111yescharacteristic
671C2×C4⋊C4C23×C1111yescharacteristic
672C2×C4⋊C4C23×C1112yes—
673C2×C4⋊C4C23×C1112yes—
674C2×C4⋊C4C23×C1112yes—
675C2×C4⋊C4C23×C1112yes—
676C2×C4⋊C4C23×C1112yes—
677C2×C4⋊C4C23×C1111yescharacteristic
678C2×C4⋊C4C23×C1111yescharacteristic
679C2×C4⋊C4C23×C1111yescharacteristic
680C2×C4⋊C4C23×C1111yescharacteristic
681C2×C4⋊C4C23×C1112yes—
682C2×C4⋊C4C23×C1111yescharacteristic
683C2×C4⋊C4C23×C1112yes—
684C2×C4⋊C4C23×C1111yescharacteristic
685C2×C4⋊C4C23×C1112yes—
686C2×C22⋊C4C23×C1111yescharacteristic
687C2×C22⋊C4C23×C1112yes—
688C2×C22⋊C4C23×C1111yescharacteristic
689C2×C22⋊C4C23×C1112yes—
690C2×C22⋊C4C23×C1111yescharacteristic
691C2×C22⋊C4C23×C1111yescharacteristic
692C2×C22⋊C4C23×C1112yes—
693C2×C22⋊C4C23×C1111yescharacteristic
694C2×C22⋊C4C23×C1111yescharacteristic
695C2×C22⋊C4C23×C1112yes—
696C2×C22⋊C4C23×C1112yes—
697C2×C22⋊C4C23×C1112yes—
698C2×C22⋊C4C23×C1112yes—
699C2×C22⋊C4C23×C1111yescharacteristic
700C2×C22⋊C4C23×C1112yes—
701C2×C22⋊C4C23×C1112yes—
702C2×C22⋊C4C23×C1111yescharacteristic
703C2×C22⋊C4C23×C1112yes—
704C2×C22⋊C4C23×C1111yescharacteristic
705C2×C22⋊C4C23×C1112yes—
706C2×C22⋊C4C23×C1112yes—
707C2×C22⋊C4C23×C1111yescharacteristic
708C2×C22⋊C4C23×C1112yes—
709C2×C42C23×C1111yescharacteristic
710C2×C42C23×C1111yescharacteristic
711C2×C42C23×C1111yescharacteristic
712C2×C42C23×C1111yescharacteristic
713C2×C42C23×C1112yes—
714C2×C42C23×C1111yescharacteristic
715C2×C42C23×C1112yes—
716C2×C42C23×C1112yes—
717C2×C42C23×C1112yes—
718C2×C42C23×C1111yescharacteristic
719C2×C42C23×C1111yescharacteristic
720C2×C42C23×C1111yescharacteristic
721C2×C42C23×C1112yes—
722C2×C42C23×C1112yes—
723C2×C42C23×C1112yes—
724C2×C42C23×C1111yescharacteristic
725#95C23×C1111yescharacteristic
726#95C23×C1112yes—
727#95C23×C1112yes—
728#95C23×C1112yes—
729#95C23×C1111yescharacteristic
730#95C23×C1111yescharacteristic
731#95C23×C1112yes—
732#95C23×C1112yes—
733#95C23×C1112yes—
734#95C23×C1112yes—
735#95C23×C1111yescharacteristic
736#95C23×C1111yescharacteristic
737#95C23×C1111yescharacteristic
738#95C23×C1112yes—
739#95C23×C1112yes—
740#95C23×C1112yes—
741#95C23×C1112yes—
742#95C23×C1112yes—
743#95C23×C1112yes—
744#95C23×C1112yes—
745#95C23×C1112yes—
746#95C23×C1112yes—
747#95C23×C1112yes—
748C2×C11—42no—
749C2×C11—42no—
750C2×C11—44no—
751C2×C11C2×#52011yescharacteristic
752C2×C11#342811yescharacteristic
753C2×C11C4×H(5,𝔽2)11yescharacteristic
754C2×C11#354611yescharacteristic
755C2×C11#355111yescharacteristic
756C2×C11#355911yescharacteristic
757C2×C11#356511yescharacteristic
758C24C24×C1111yescharacteristic
759C24C24×C1112yes—
760C24C24×C1111yescharacteristic
761C2×D4—22no—
762C2×D4—22no—
763C2×D4—42no—
764C2×D4—42no—
765C2×D4—41no—
766C2×D4—41no—
767C2×D4—42no—
768C2×D4—42no—
769C2×D4C22×C4×C1114yes—
770C2×D4C22×C4×C1118yes—
771C2×D4C22×C4×C1114yes—
772C2×D4C22×C4×C1118yes—
773C22×C4—22no—
774C22×C4—22no—
775C22×C4—22no—
776C22×C4—22no—
777C22×C4—42no—
778C22×C4—42no—
779C22×C4—42no—
780C22×C4—42no—
781C22×C4—42no—
782C22×C4—42no—
783C22×C4—42no—
784C22×C4—42no—
785C22×C4—42no—
786C22×C4—42no—
787C22×C4—42no—
788C22×C4—42no—
789C22×C4—42no—
790C22×C4C22×C4×C1114yes—
791C22×C4C22×C4×C1114yes—
792C22×C4C22×C4×C1118yes—
793C22×C4C22×C4×C1118yes—
794C22×C4C24×C1111yescharacteristic
795C22×C4C24×C1111yescharacteristic
796C22×C4C24×C1112yes—
797C22×C4C24×C1112yes—
798C22×C4C24×C1111yescharacteristic
799C22×C4C24×C1112yes—
800C22×C4C24×C1111yescharacteristic
801C22×C4C24×C1111yescharacteristic
802C22×C4C24×C1112yes—
803C22×C4C24×C1111yescharacteristic
804C22×C4C24×C1111yescharacteristic
805C22×C4C24×C1111yescharacteristic
806C22×C4C24×C1112yes—
807C22×C4C24×C1111yescharacteristic
808C22×C4C24×C1111yescharacteristic
809C22×C4C24×C1111yescharacteristic
810C22×C4C24×C1112yes—
811C22×C4C24×C1112yes—
812C22×C4C24×C1111yescharacteristic
813C22×C4C24×C1111yescharacteristic
814C4⋊C4—22no—
815C4⋊C4—22no—
816C4⋊C4—24no—
817C4⋊C4—22no—
818C4⋊C4—22no—
819C4⋊C4—42no—
820C4⋊C4—41no—
821C4⋊C4—41no—
822C4⋊C4—42no—
823C4⋊C4—42no—
824C4⋊C4—41no—
825C4⋊C4—41no—
826C4⋊C4—42no—
827C4⋊C4—41no—
828C4⋊C4—41no—
829C4⋊C4—42no—
830C4⋊C4—42no—
831C4⋊C4—42no—
832C4⋊C4—42no—
833C4⋊C4C22×C4×C1114yes—
834C4⋊C4C22×C4×C1114yes—
835C4⋊C4C22×C4×C1118yes—
836C4⋊C4C22×C4×C1114yes—
837C4⋊C4C22×C4×C1118yes—
838C4⋊C4C22×C4×C1114yes—
839C4⋊C4C22×C4×C1118yes—
840C22⋊C4—22no—
841C22⋊C4—24no—
842C22⋊C4—22no—
843C22⋊C4—41no—
844C22⋊C4—41no—
845C22⋊C4—41no—
846C22⋊C4—41no—
847C22⋊C4—42no—
848C22⋊C4—42no—
849C22⋊C4—42no—
850C22⋊C4—42no—
851C22⋊C4—42no—
852C22⋊C4—42no—
853C22⋊C4—42no—
854C22⋊C4—41no—
855C22⋊C4—42no—
856C22⋊C4—41no—
857C22⋊C4C22×C4×C1118yes—
858C22⋊C4C22×C4×C1114yes—
859C22⋊C4C22×C4×C1118yes—
860C22⋊C4C22×C4×C1118yes—
861C22⋊C4C22×C4×C1114yes—
862C22⋊C4C22×C4×C1118yes—
863C42—22no—
864C42—22no—
865C42—24no—
866C42—22no—
867C42—22no—
868C42—22no—
869C42—42no—
870C42—42no—
871C42—42no—
872C42—42no—
873C42—41no—
874C42—42no—
875C42—41no—
876C42—41no—
877C42C22×C4×C1118yes—
878C42C22×C4×C1114yes—
879C11#3448311yescharacteristic, direct product factor, Sylow
880C23—21no—
881C23—22no—
882C23—21no—
883C23—21no—
884C23—21no—
885C23—22no—
886C23—21no—
887C23—21no—
888C23—22no—
889C23—21no—
890C23—21no—
891C23—22no—
892C23—22no—
893C23—21no—
894C23—21no—
895C23—22no—
896C23—21no—
897C23—21no—
898C23C23×C4×C1112yes—
899C23C23×C4×C1114yes—
900C23C23×C4×C1112yes—
901C23C25×C1111yescharacteristic
902D4—28no—
903D4—48no—
904D4—44no—
905D4—48no—
906C2×C4—21no—
907C2×C4—22no—
908C2×C4—21no—
909C2×C4—22no—
910C2×C4—21no—
911C2×C4—21no—
912C2×C4—21no—
913C2×C4—21no—
914C2×C4—21no—
915C2×C4—22no—
916C2×C4—21no—
917C2×C4—21no—
918C2×C4—21no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—28no—
923C2×C4—28no—
924C2×C4—21no—
925C2×C4—21no—
926C2×C4—21no—
927C2×C4—21no—
928C2×C4—21no—
929C2×C4—21no—
930C2×C4—22no—
931C2×C4—21no—
932C2×C4—21no—
933C2×C4—22no—
934C2×C4—22no—
935C2×C4—22no—
936C2×C4—22no—
937C2×C4—21no—
938C2×C4—22no—
939C2×C4—21no—
940C2×C4—22no—
941C2×C4—21no—
942C2×C4—21no—
943C2×C4—22no—
944C2×C4—21no—
945C2×C4—21no—
946C2×C4—22no—
947C2×C4—21no—
948C2×C4—21no—
949C2×C4—21no—
950C2×C4—22no—
951C2×C4—21no—
952C2×C4—21no—
953C2×C4—22no—
954C2×C4—21no—
955C2×C4—22no—
956C2×C4—21no—
957C2×C4—48no—
958C2×C4—48no—
959C2×C4—84no—
960C2×C4—84no—
961C2×C4—84no—
962C2×C4C23×C4×C1112yes—
963C2×C4C23×C4×C1114yes—
964C2×C4C23×C4×C1112yes—
965C2×C4C23×C4×C1114yes—
966C2×C4C23×C4×C1112yes—
967C2×C4C23×C4×C1112yes—
968C2×C4C23×C4×C1114yes—
969C2×C4C23×C4×C1112yes—
970C2×C4C11×H(5,𝔽2)12yes—
971C2×C4C11×H(5,𝔽2)12yes—
972C2×C4C11×2−1+412yes—
973C22—22no—
974C22—22no—
975C22—24no—
976C22—22no—
977C22—22no—
978C22—24no—
979C22—22no—
980C22—24no—
981C22—22no—
982C22—41no—
983C22—42no—
984C22—41no—
985C22—42no—
986C22—41no—
987C22—41no—
988C22—41no—
989C22—42no—
990C22—41no—
991C22—41no—
992C22—41no—
993C22—42no—
994C22C24×C4×C1111yescharacteristic
995C22C2×C11×H(5,𝔽2)11yescharacteristic
996C22C2×C11×H(5,𝔽2)11yescharacteristic
997C22C2×C11×2−1+411yescharacteristic
998C22C11×#58511yescharacteristic
999C22C11×#58511yescharacteristic
1000C22C11×#58511yescharacteristic
1001C4—22no—
1002C4—22no—
1003C4—24no—
1004C4—22no—
1005C4—22no—
1006C4—24no—
1007C4—24no—
1008C4—22no—
1009C4—41no—
1010C4—42no—
1011C4—42no—
1012C4—41no—
1013C4—41no—
1014C4—41no—
1015C4—42no—
1016C4—41no—
1017C4—41no—
1018C4—42no—
1019C4—41no—
1020C4C11×#52014yes—
1021C2—42no—
1022C2—42no—
1023C2—44no—
1024C2C2×C11×#52011yescharacteristic
1025C2C11×#342811yescharacteristic
1026C2C4×C11×H(5,𝔽2)11yescharacteristic
1027C2C11×#354611yescharacteristic
1028C2C11×#355111yescharacteristic
1029C2C11×#355911yescharacteristic
1030C2C11×#356511yescharacteristic
subgroupG/H
center, socleC23×C11C25
commutatorC22C24×C4×C11
Frattini, cosocleC23C25×C11
prime radicalC2×C11×#553C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#2383C2semidirect
3. C11×#2377C2semidirect
4. C11×#2370C2semidirect
5. C11×#2363C2semidirect
6. C11×#2361C2semidirect
7. C11×#2359C2semidirect
8. C11×#2354C2semidirect
9. C11×#2352C2semidirect
10. C11×#2349C2semidirect
11. C11×#2347C2semidirect
12. C11×#2344C2semidirect
13. C11×#2335C2semidirect
14. C11×#2334C2semidirect
15. C11×#2324C2semidirect
16. C11×#2324C2semidirect
17. C11×#2324C2semidirect
18. C11×#2318C2semidirect
19. C11×#2317C2semidirect
20. C11×#2316C2semidirect
21. C4×C11×#125C2semidirect
22. C11×#2293C2semidirect
23. C11×#2293C2semidirect
24. C11×#553C4semidirect
135. C11×#126C2×C4semidirect
136. C11×#125C2×C4semidirect
137. C11×#123C2×C4semidirect
139. C11×#121C2×C4semidirect
140. C11×#121C2×C4semidirect
144. C4×D4×C11C2×C4semidirect
145. C4×D4×C11C2×C4semidirect
146. C4×D4×C11C2×C4semidirect
152. C11×#117C2×C4semidirect
154. C2×C11×C4⋊C4C2×C4semidirect
243. #34483C11direct (N × H)
366. #2383C2×C11semidirect
367. #2377C2×C11semidirect
368. #2370C2×C11semidirect
369. #2363C2×C11semidirect
370. #2361C2×C11semidirect
371. #2359C2×C11semidirect
372. #2354C2×C11semidirect
373. #2352C2×C11semidirect
374. #2349C2×C11semidirect
375. #2347C2×C11semidirect
376. #2344C2×C11semidirect
377. #2335C2×C11semidirect
378. #2334C2×C11semidirect
379. #2324C2×C11semidirect
380. #2324C2×C11semidirect
381. #2324C2×C11semidirect
382. #2318C2×C11semidirect
383. #2317C2×C11semidirect
384. #2316C2×C11semidirect
385. C4×#125C2×C11semidirect
386. #2293C2×C11semidirect
387. #2293C2×C11semidirect
481. #553C4×C11semidirect
640. #126C2×C4×C11semidirect
641. #125C2×C4×C11semidirect
642. #123C2×C4×C11semidirect
644. #121C2×C4×C11semidirect
645. #121C2×C4×C11semidirect
649. C4×D4C2×C4×C11semidirect
650. C4×D4C2×C4×C11semidirect
651. C4×D4C2×C4×C11semidirect
657. #117C2×C4×C11semidirect
659. C2×C4⋊C4C2×C4×C11semidirect
879. C11#34483direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5532
C11×#23832
C11×#23772
C11×#23702
C11×#23632
C11×#23612
C11×#23592
C11×#23542
C11×#23522
C11×#23492
C11×#23472
C11×#23442
C11×#23352
C11×#23342
C11×#23242
C11×#23182
C11×#23172
C11×#23162
C4×C11×#1252
C11×#22932
#3448311