Finite Group Databasebeta

← C11×#34914 #14612107

Subgroups — C11×#34914 #14612107

Order 2816.

2458 conjugacy classes of subgroups.

The subgroup lattice has 1068 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#529C212yesmaximal, complemented
2C11×#2560C212yesmaximal, complemented
3C11×#2559C212yesmaximal, complemented
4C11×#2558C212yesmaximal, complemented
5C11×#2557C212yesmaximal, complemented
6C11×#2512C211yesmaximal, characteristic, complemented
7C11×#2506C211yesmaximal, characteristic, complemented
8C11×#2496C211yesmaximal, characteristic, complemented
9C11×#2491C211yesmaximal, characteristic, complemented
10C11×#2452C211yesmaximal, characteristic, complemented
11C11×#2445C211yesmaximal, characteristic, complemented
12C11×#2428C211yesmaximal, characteristic
13C11×#2422C211yesmaximal, characteristic, complemented
14C11×#2398C212yesmaximal, complemented
15C11×#2392C212yesmaximal, complemented
16C4×C11×C4⋊Q8C211yesmaximal, characteristic, complemented
17C4×C11×#127C211yesmaximal, characteristic, complemented
18C4×C11×#121C211yesmaximal, characteristic, complemented
19C4×C11×#121C211yesmaximal, characteristic, complemented
20C11×#2293C211yesmaximal, characteristic, complemented
21C11×#2290C212yesmaximal, complemented
22C42×D4×C11C211yesmaximal, characteristic, complemented
23C4×C11×#117C211yesmaximal, characteristic, complemented
24C2×C11×C4⋊Q8C2211yescharacteristic
25C2×C11×#127C2211yescharacteristic
26C11×#529—216no—
27C2×C11×#126C2212yes—
28C2×C11×#126C2212yes—
29C2×C11×#125C2212yes—
30C2×C11×#124C2212yes—
31C2×C11×#123C2212yes—
32C2×C11×#123C2212yes—
33C2×C11×C22⋊Q8C2212yes—
34C2×C11×#121C2212yes—
35C2×C11×#121C2211yescharacteristic
36C2×C11×#121C2211yescharacteristic
37C2×C4×Q8×C11C2212yes—
38C2×C4×D4×C11C2212yes—
39C2×C4×D4×C11C2212yes—
40C2×C4×D4×C11C2212yes—
41C2×C4×D4×C11C2212yes—
42C2×C4×D4×C11C2211yescharacteristic
43C2×C4×D4×C11C2211yescharacteristic
44C2×C4×D4×C11C2211yescharacteristic
45C2×C4×D4×C11C2211yescharacteristic
46C2×C11×#117C2211yescharacteristic
47C2×C11×#117C2212yes—
48C2×C11×#117C2211yescharacteristic
49C22×C42×C11C2212yes—
50C22×C42×C11C2211yescharacteristic
51C11×#400C2212yes—
52C11×#400C2212yes—
53C11×#398C2212yes—
54C11×#397C2212yes—
55C11×#397C2212yes—
56C11×#397C2212yes—
57C11×#396C2212yes—
58C11×#396C2212yes—
59C11×#394C2212yes—
60C11×#394C2212yes—
61C11×#394C2212yes—
62C11×#394C2212yes—
63C11×#394C2212yes—
64C11×#393C2212yes—
65C11×#393C2212yes—
66C11×#392C2212yes—
67C11×#391C2212yes—
68C11×#390C2211yescharacteristic
69C11×#390C2211yescharacteristic
70C11×#390C2211yescharacteristic
71C11×#390C2211yescharacteristic
72C11×#390C2211yescharacteristic
73C11×#390C2211yescharacteristic
74C11×#390C2212yes—
75C11×#390C2212yes—
76C11×#389C2211yescharacteristic
77C11×#389C2211yescharacteristic
78C11×#389C2211yescharacteristic
79C11×#389C2211yescharacteristic
80C11×#389C2211yescharacteristic
81C11×#389C2211yescharacteristic
82C11×#389C2212yes—
83C11×#388C2212yes—
84C11×#388C2212yes—
85C11×#388C2212yes—
86C11×#388C2212yes—
87C11×#388C2212yes—
88C11×#388C2212yes—
89C11×#387C2212yes—
90C11×#387C2212yes—
91C11×#386C2212yes—
92C11×#386C2212yes—
93C11×#386C2212yes—
94C11×#386C2212yes—
95C11×#385C2212yes—
96C11×#385C2212yes—
97C11×#384C2211yescharacteristic
98C11×#384C2211yescharacteristic
99C11×#380C2211yescharacteristic
100C11×#380C2211yescharacteristic
101C4×C11×C4⋊C4C2212yes—
102C4×C11×C4⋊C4C2211yescharacteristic
103C4×C11×C4⋊C4C2211yescharacteristic
104C4×C11×C4⋊C4C2211yescharacteristic
105C4×C11×C4⋊C4C2211yescharacteristic
106C4×C11×C4⋊C4C2211yescharacteristic
107C4×C11×C4⋊C4C2211yescharacteristic
108C4×C11×C4⋊C4C2211yescharacteristic
109C4×C11×C4⋊C4C2211yescharacteristic
110C4×C11×C22⋊C4C2212yes—
111C4×C11×C22⋊C4C2212yes—
112C4×C11×C22⋊C4C2212yes—
113C4×C11×C22⋊C4C2212yes—
114C4×C11×C22⋊C4C2211yescharacteristic
115C4×C11×C22⋊C4C2211yescharacteristic
116C4×C11×C22⋊C4C2211yescharacteristic
117C4×C11×C22⋊C4C2211yescharacteristic
118C4×C11×C22⋊C4C2212yes—
119C4×C11×C22⋊C4C2212yes—
120C11×#376C2211yescharacteristic
121C11×#376C2211yescharacteristic
122C43×C11C2211yescharacteristic
123C43×C11C2211yescharacteristic
124C22×Q8×C11C2312yes—
125C22×D4×C11C2311yescharacteristic
126C22×D4×C11C2312yes—
127C22×D4×C11C2312yes—
128C22×D4×C11C2312yes—
129C22×D4×C11C2312yes—
130C22×D4×C11C2311yescharacteristic
131C23×C4×C11C2311yescharacteristic
132C23×C4×C11C2312yes—
133C23×C4×C11C2312yes—
134C23×C4×C11C2312yes—
135C23×C4×C11C2312yes—
136C23×C4×C11C2311yescharacteristic
137C23×C4×C11C2311yescharacteristic
138C11×C4⋊Q8—24no—
139C11×#127—24no—
140C11×#126—28no—
141C11×#126—28no—
142C11×#125—28no—
143C11×#124—28no—
144C11×#123—28no—
145C11×#123—28no—
146C11×C22⋊Q8—28no—
147C11×#121—24no—
148C11×#121—24no—
149C11×#121—28no—
150C4×Q8×C11—28no—
151C4×D4×C11—24no—
152C4×D4×C11—28no—
153C4×D4×C11—28no—
154C4×D4×C11—24no—
155C4×D4×C11—28no—
156C4×D4×C11—24no—
157C4×D4×C11—24no—
158C4×D4×C11—28no—
159C11×#117—28no—
160C11×#117—24no—
161C11×#117D418yescomplemented
162C2×C11×C4⋊C4C2311yescharacteristic
163C2×C11×C4⋊C4C2311yescharacteristic
164C2×C11×C4⋊C4C2312yes—
165C2×C11×C4⋊C4C2312yes—
166C2×C11×C4⋊C4C2311yescharacteristic
167C2×C11×C4⋊C4C2311yescharacteristic
168C2×C11×C4⋊C4C2311yescharacteristic
169C2×C11×C4⋊C4C2312yes—
170C2×C11×C4⋊C4C2312yes—
171C2×C11×C4⋊C4C2312yes—
172C2×C11×C4⋊C4C2312yes—
173C2×C11×C4⋊C4C2311yescharacteristic
174C2×C11×C4⋊C4C2311yescharacteristic
175C2×C11×C4⋊C4C2312yes—
176C2×C11×C4⋊C4C2312yes—
177C2×C11×C4⋊C4C2312yes—
178C2×C11×C4⋊C4C2312yes—
179C2×C11×C4⋊C4C2312yes—
180C2×C11×C4⋊C4C2311yescharacteristic
181C2×C11×C4⋊C4C2311yescharacteristic
182C2×C11×C4⋊C4C2311yescharacteristic
183C2×C11×C22⋊C4C2311yescharacteristic
184C2×C11×C22⋊C4C2311yescharacteristic
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⋊C4C2312yes—
195C2×C11×C22⋊C4C2312yes—
196C2×C11×C22⋊C4C2312yes—
197C2×C11×C22⋊C4C2312yes—
198C2×C11×C22⋊C4C2312yes—
199C2×C11×C22⋊C4C2312yes—
200C2×C11×C22⋊C4C2312yes—
201C2×C11×C22⋊C4C2312yes—
202C2×C11×C22⋊C4C2312yes—
203C2×C11×C22⋊C4C2312yes—
204C2×C11×C22⋊C4C2312yes—
205C2×C11×C22⋊C4C2311yescharacteristic
206C2×C11×C22⋊C4C2311yescharacteristic
207C2×C42×C11—28no—
208C2×C42×C11—24no—
209C2×C42×C11C2312yes—
210C2×C42×C11C2312yes—
211C2×C42×C11C2311yescharacteristic
212C2×C42×C11C2311yescharacteristic
213C2×C42×C11C2311yescharacteristic
214C2×C42×C11C2311yescharacteristic
215C2×C42×C11C2311yescharacteristic
216C2×C42×C11C2311yescharacteristic
217C2×C42×C11C2311yescharacteristic
218C2×C42×C11C2312yes—
219C2×C42×C11C2311yescharacteristic
220C2×C42×C11C2312yes—
221C2×C42×C11C2311yescharacteristic
222C2×C42×C11C2311yescharacteristic
223C2×C42×C11C2311yescharacteristic
224C2×C42×C11C2311yescharacteristic
225C2×C42×C11C2311yescharacteristic
226C2×C42×C11C2311yescharacteristic
227C2×C42×C11C2311yescharacteristic
228C2×C42×C11C2311yescharacteristic
229C11×#95C2311yescharacteristic
230C11×#95C2311yescharacteristic
231C11×#95C2311yescharacteristic
232C11×#95C2311yescharacteristic
233C11×#95C2311yescharacteristic
234C11×#95C2311yescharacteristic
235C11×#95C2311yescharacteristic
236C11×#95C2311yescharacteristic
237C11×#95C2312yes—
238C11×#95C2312yes—
239C11×#95C2312yes—
240C11×#95C2312yes—
241C11×#95C2312yes—
242C11×#95C2312yes—
243C11×#95C2312yes—
244C11×#95C2312yes—
245C11×#95C2312yes—
246C11×#95C2312yes—
247C11×#95C2312yes—
248C11×#95C2312yes—
249#34914C1111yesmaximal, characteristic, direct product factor, Sylow
250C24×C11C2412yes—
251C24×C11C2411yescharacteristic
252C24×C11C2412yes—
253C2×Q8×C11—24no—
254C2×Q8×C11—24no—
255C2×Q8×C11—42no—
256C2×D4×C11—24no—
257C2×D4×C11—24no—
258C2×D4×C11—24no—
259C2×D4×C11—24no—
260C2×D4×C11—24no—
261C2×D4×C11—24no—
262C2×D4×C11—22no—
263C2×D4×C11—22no—
264C2×D4×C11—24no—
265C2×D4×C11—22no—
266C2×D4×C11—24no—
267C2×D4×C11—22no—
268C2×D4×C11—22no—
269C2×D4×C11—42no—
270C2×D4×C11—42no—
271C2×D4×C11—42no—
272C2×D4×C11—42no—
273C2×D4×C11#4114yes—
274C22×C4×C11—22no—
275C22×C4×C11—22no—
276C22×C4×C11—24no—
277C22×C4×C11—24no—
278C22×C4×C11—24no—
279C22×C4×C11—24no—
280C22×C4×C11—24no—
281C22×C4×C11—22no—
282C22×C4×C11—22no—
283C22×C4×C11—24no—
284C22×C4×C11—24no—
285C22×C4×C11—24no—
286C22×C4×C11—24no—
287C22×C4×C11—24no—
288C22×C4×C11—22no—
289C22×C4×C11—22no—
290C22×C4×C11—41no—
291C22×C4×C11—41no—
292C22×C4×C11—42no—
293C22×C4×C11—42no—
294C22×C4×C11C2×D414yes—
295C22×C4×C11C2411yescharacteristic
296C22×C4×C11C2411yescharacteristic
297C22×C4×C11C2411yescharacteristic
298C22×C4×C11C2411yescharacteristic
299C22×C4×C11C2412yes—
300C22×C4×C11C2412yes—
301C22×C4×C11C2412yes—
302C22×C4×C11C2412yes—
303C22×C4×C11C2412yes—
304C22×C4×C11C2411yescharacteristic
305C22×C4×C11C2411yescharacteristic
306C22×C4×C11C2411yescharacteristic
307C22×C4×C11C2411yescharacteristic
308C22×C4×C11C2411yescharacteristic
309C22×C4×C11C2411yescharacteristic
310C22×C4×C11C2411yescharacteristic
311C22×C4×C11C2412yes—
312C22×C4×C11C2411yescharacteristic
313C22×C4×C11C2411yescharacteristic
314C22×C4×C11C2411yescharacteristic
315C11×C4⋊C4—24no—
316C11×C4⋊C4—24no—
317C11×C4⋊C4—24no—
318C11×C4⋊C4—24no—
319C11×C4⋊C4—24no—
320C11×C4⋊C4—24no—
321C11×C4⋊C4—24no—
322C11×C4⋊C4—24no—
323C11×C4⋊C4—22no—
324C11×C4⋊C4—22no—
325C11×C4⋊C4—24no—
326C11×C4⋊C4—22no—
327C11×C4⋊C4—22no—
328C11×C4⋊C4—22no—
329C11×C4⋊C4—22no—
330C11×C4⋊C4—24no—
331C11×C4⋊C4—22no—
332C11×C4⋊C4—42no—
333C11×C4⋊C4C2×D414yes—
334C11×C4⋊C4C2×D414yes—
335C11×C4⋊C4#4114yes—
336C11×C22⋊C4—24no—
337C11×C22⋊C4—24no—
338C11×C22⋊C4—24no—
339C11×C22⋊C4—24no—
340C11×C22⋊C4—24no—
341C11×C22⋊C4—24no—
342C11×C22⋊C4—24no—
343C11×C22⋊C4—24no—
344C11×C22⋊C4—24no—
345C11×C22⋊C4—24no—
346C11×C22⋊C4—22no—
347C11×C22⋊C4—22no—
348C11×C22⋊C4—24no—
349C11×C22⋊C4—24no—
350C11×C22⋊C4—24no—
351C11×C22⋊C4—24no—
352C11×C22⋊C4—24no—
353C11×C22⋊C4—24no—
354C11×C22⋊C4—42no—
355C11×C22⋊C4—42no—
356C11×C22⋊C4—42no—
357C11×C22⋊C4—42no—
358C11×C22⋊C4C2×D414yes—
359C11×C22⋊C4C2×D414yes—
360C42×C11—24no—
361C42×C11—24no—
362C42×C11—24no—
363C42×C11—24no—
364C42×C11—22no—
365C42×C11—22no—
366C42×C11—22no—
367C42×C11—22no—
368C42×C11—22no—
369C42×C11—22no—
370C42×C11—22no—
371C42×C11—22no—
372C42×C11—41no—
373C42×C11—41no—
374C42×C11—41no—
375C42×C11—41no—
376C42×C11C2×D414yes—
377C42×C11C2×D414yes—
378C42×C11#4114yes—
379C42×C11#4114yes—
380C2×#529C2×C1112yescomplemented
381#2560C2×C1112yescomplemented
382#2559C2×C1112yescomplemented
383#2558C2×C1112yescomplemented
384#2557C2×C1112yescomplemented
385#2512C2×C1111yescharacteristic, complemented
386#2506C2×C1111yescharacteristic, complemented
387#2496C2×C1111yescharacteristic, complemented
388#2491C2×C1111yescharacteristic, complemented
389#2452C2×C1111yescharacteristic, complemented
390#2445C2×C1111yescharacteristic, complemented
391#2428C2×C1111yescharacteristic
392#2422C2×C1111yescharacteristic, complemented
393#2398C2×C1112yescomplemented
394#2392C2×C1112yescomplemented
395C4×C4⋊Q8C2×C1111yescharacteristic, complemented
396C4×#127C2×C1111yescharacteristic, complemented
397C4×#121C2×C1111yescharacteristic, complemented
398C4×#121C2×C1111yescharacteristic, complemented
399#2293C2×C1111yescharacteristic, complemented
400#2290C2×C1112yescomplemented
401C42×D4C2×C1111yescharacteristic, complemented
402C4×#117C2×C1111yescharacteristic, complemented
403C23×C11—22no—
404C23×C11—21no—
405C23×C11—22no—
406C23×C11—22no—
407C23×C11—22no—
408C23×C11—21no—
409C23×C11—21no—
410C23×C11—21no—
411C23×C11—22no—
412C23×C11—22no—
413C23×C11—21no—
414C23×C11—21no—
415C23×C11—22no—
416C23×C11—22no—
417C23×C11—22no—
418C23×C11—22no—
419C23×C11—22no—
420C23×C11—22no—
421C23×C11—22no—
422C23×C11C22×D412yes—
423C23×C11C2×#4114yes—
424C23×C11C2511yescharacteristic
425Q8×C11—48no—
426D4×C11—28no—
427D4×C11—48no—
428D4×C11—48no—
429D4×C11—48no—
430D4×C11—48no—
431D4×C11—44no—
432C2×C4×C11—22no—
433C2×C4×C11—21no—
434C2×C4×C11—21no—
435C2×C4×C11—21no—
436C2×C4×C11—21no—
437C2×C4×C11—21no—
438C2×C4×C11—21no—
439C2×C4×C11—21no—
440C2×C4×C11—21no—
441C2×C4×C11—21no—
442C2×C4×C11—21no—
443C2×C4×C11—21no—
444C2×C4×C11—21no—
445C2×C4×C11—21no—
446C2×C4×C11—21no—
447C2×C4×C11—21no—
448C2×C4×C11—21no—
449C2×C4×C11—22no—
450C2×C4×C11—28no—
451C2×C4×C11—22no—
452C2×C4×C11—22no—
453C2×C4×C11—22no—
454C2×C4×C11—22no—
455C2×C4×C11—22no—
456C2×C4×C11—21no—
457C2×C4×C11—21no—
458C2×C4×C11—21no—
459C2×C4×C11—21no—
460C2×C4×C11—21no—
461C2×C4×C11—21no—
462C2×C4×C11—21no—
463C2×C4×C11—21no—
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—21no—
472C2×C4×C11—21no—
473C2×C4×C11—21no—
474C2×C4×C11—21no—
475C2×C4×C11—22no—
476C2×C4×C11—22no—
477C2×C4×C11—22no—
478C2×C4×C11—48no—
479C2×C4×C11—48no—
480C2×C4×C11—44no—
481C2×C4×C11—44no—
482C2×C4×C11—48no—
483C2×C4×C11—48no—
484C2×C4×C11C22×D412yes—
485C2×C4×C11C22×D412yes—
486C2×C4×C11C22×D412yes—
487C2×C4×C11C22×D412yes—
488C2×C4×C11C22×D412yes—
489C2×C4×C11C22×D412yes—
490C2×C4×C11C2×#4112yes—
491C2×C4×C11C2×#4112yes—
492C2×C4×C11C2×#4112yes—
493C2×C4×C11C2×#4114yes—
494C2×C4×C11C2×#4112yes—
495C2×C4×C11C2×#4112yes—
496C2×C4×C11C2×#4112yes—
497C2×C4×C11C2×#4112yes—
498C2×C4×C11C2×#4112yes—
499C2×C4⋊Q8C22×C1111yescharacteristic
500C2×#127C22×C1111yescharacteristic
501#529—216no—
502C2×#126C22×C1112yes—
503C2×#126C22×C1112yes—
504C2×#125C22×C1112yes—
505C2×#124C22×C1112yes—
506C2×#123C22×C1112yes—
507C2×#123C22×C1112yes—
508C2×C22⋊Q8C22×C1112yes—
509C2×#121C22×C1112yes—
510C2×#121C22×C1111yescharacteristic
511C2×#121C22×C1111yescharacteristic
512C2×C4×Q8C22×C1112yes—
513C2×C4×D4C22×C1112yes—
514C2×C4×D4C22×C1112yes—
515C2×C4×D4C22×C1111yescharacteristic
516C2×C4×D4C22×C1111yescharacteristic
517C2×C4×D4C22×C1112yes—
518C2×C4×D4C22×C1112yes—
519C2×C4×D4C22×C1111yescharacteristic
520C2×C4×D4C22×C1111yescharacteristic
521C2×#117C22×C1111yescharacteristic
522C2×#117C22×C1112yes—
523C2×#117C22×C1111yescharacteristic
524C22×C42C22×C1112yes—
525C22×C42C22×C1111yescharacteristic
526#400C22×C1112yes—
527#400C22×C1112yes—
528#398C22×C1112yes—
529#397C22×C1112yes—
530#397C22×C1112yes—
531#397C22×C1112yes—
532#396C22×C1112yes—
533#396C22×C1112yes—
534#394C22×C1112yes—
535#394C22×C1112yes—
536#394C22×C1112yes—
537#394C22×C1112yes—
538#394C22×C1112yes—
539#393C22×C1112yes—
540#393C22×C1112yes—
541#392C22×C1112yes—
542#391C22×C1112yes—
543#390C22×C1112yes—
544#390C22×C1111yescharacteristic
545#390C22×C1111yescharacteristic
546#390C22×C1112yes—
547#390C22×C1111yescharacteristic
548#390C22×C1111yescharacteristic
549#390C22×C1111yescharacteristic
550#390C22×C1111yescharacteristic
551#389C22×C1111yescharacteristic
552#389C22×C1111yescharacteristic
553#389C22×C1112yes—
554#389C22×C1111yescharacteristic
555#389C22×C1111yescharacteristic
556#389C22×C1111yescharacteristic
557#389C22×C1111yescharacteristic
558#388C22×C1112yes—
559#388C22×C1112yes—
560#388C22×C1112yes—
561#388C22×C1112yes—
562#388C22×C1112yes—
563#388C22×C1112yes—
564#387C22×C1112yes—
565#387C22×C1112yes—
566#386C22×C1112yes—
567#386C22×C1112yes—
568#386C22×C1112yes—
569#386C22×C1112yes—
570#385C22×C1112yes—
571#385C22×C1112yes—
572#384C22×C1111yescharacteristic
573#384C22×C1111yescharacteristic
574#380C22×C1111yescharacteristic
575#380C22×C1111yescharacteristic
576C4×C4⋊C4C22×C1111yescharacteristic
577C4×C4⋊C4C22×C1112yes—
578C4×C4⋊C4C22×C1111yescharacteristic
579C4×C4⋊C4C22×C1111yescharacteristic
580C4×C4⋊C4C22×C1111yescharacteristic
581C4×C4⋊C4C22×C1111yescharacteristic
582C4×C4⋊C4C22×C1111yescharacteristic
583C4×C4⋊C4C22×C1111yescharacteristic
584C4×C4⋊C4C22×C1111yescharacteristic
585C4×C22⋊C4C22×C1112yes—
586C4×C22⋊C4C22×C1112yes—
587C4×C22⋊C4C22×C1112yes—
588C4×C22⋊C4C22×C1112yes—
589C4×C22⋊C4C22×C1112yes—
590C4×C22⋊C4C22×C1111yescharacteristic
591C4×C22⋊C4C22×C1111yescharacteristic
592C4×C22⋊C4C22×C1111yescharacteristic
593C4×C22⋊C4C22×C1111yescharacteristic
594C4×C22⋊C4C22×C1112yes—
595#376C22×C1111yescharacteristic
596#376C22×C1111yescharacteristic
597C43C22×C1111yescharacteristic
598C43C22×C1111yescharacteristic
599C22×C11—24no—
600C22×C11—22no—
601C22×C11—24no—
602C22×C11—22no—
603C22×C11—22no—
604C22×C11—24no—
605C22×C11—41no—
606C22×C11—42no—
607C22×C11—41no—
608C22×C11—42no—
609C22×C11—42no—
610C22×C11—41no—
611C22×C11—41no—
612C22×C11—42no—
613C22×C11—42no—
614C22×C11—42no—
615C22×C11—42no—
616C22×C11—42no—
617C22×C11—42no—
618C22×C11—42no—
619C22×C11—42no—
620C22×C11C23×D411yescharacteristic
621C22×C11C22×#4111yescharacteristic
622C22×C11C22×#4111yescharacteristic
623C22×C11C22×#4111yescharacteristic
624C22×C11C22×#4111yescharacteristic
625C22×C11#58511yescharacteristic
626C22×C11#58511yescharacteristic
627C4×C11—22no—
628C4×C11—22no—
629C4×C11—22no—
630C4×C11—22no—
631C4×C11—24no—
632C4×C11—22no—
633C4×C11—22no—
634C4×C11—22no—
635C4×C11—22no—
636C4×C11—41no—
637C4×C11—42no—
638C4×C11—42no—
639C4×C11—41no—
640C4×C11—42no—
641C4×C11—42no—
642C4×C11—42no—
643C4×C11—41no—
644C4×C11—41no—
645C4×C11#52914yescomplemented
646C4×C11#53214yes—
647C22×Q8C23×C1112yes—
648C22×D4C23×C1111yescharacteristic
649C22×D4C23×C1112yes—
650C22×D4C23×C1112yes—
651C22×D4C23×C1112yes—
652C22×D4C23×C1112yes—
653C22×D4C23×C1111yescharacteristic
654C23×C4C23×C1112yes—
655C23×C4C23×C1112yes—
656C23×C4C23×C1111yescharacteristic
657C23×C4C23×C1112yes—
658C23×C4C23×C1112yes—
659C23×C4C23×C1111yescharacteristic
660C23×C4C23×C1111yescharacteristic
661C4⋊Q8—24no—
662#127—24no—
663#126—28no—
664#126—28no—
665#125—28no—
666#124—28no—
667#123—28no—
668#123—28no—
669C22⋊Q8—28no—
670#121—24no—
671#121—24no—
672#121—28no—
673C4×Q8—28no—
674C4×D4—24no—
675C4×D4—28no—
676C4×D4—28no—
677C4×D4—24no—
678C4×D4—28no—
679C4×D4—24no—
680C4×D4—24no—
681C4×D4—28no—
682#117—28no—
683#117—24no—
684#117D4×C1118yescomplemented
685C2×C4⋊C4C23×C1112yes—
686C2×C4⋊C4C23×C1112yes—
687C2×C4⋊C4C23×C1111yescharacteristic
688C2×C4⋊C4C23×C1111yescharacteristic
689C2×C4⋊C4C23×C1112yes—
690C2×C4⋊C4C23×C1112yes—
691C2×C4⋊C4C23×C1112yes—
692C2×C4⋊C4C23×C1111yescharacteristic
693C2×C4⋊C4C23×C1111yescharacteristic
694C2×C4⋊C4C23×C1111yescharacteristic
695C2×C4⋊C4C23×C1112yes—
696C2×C4⋊C4C23×C1112yes—
697C2×C4⋊C4C23×C1112yes—
698C2×C4⋊C4C23×C1112yes—
699C2×C4⋊C4C23×C1111yescharacteristic
700C2×C4⋊C4C23×C1111yescharacteristic
701C2×C4⋊C4C23×C1112yes—
702C2×C4⋊C4C23×C1112yes—
703C2×C4⋊C4C23×C1111yescharacteristic
704C2×C4⋊C4C23×C1111yescharacteristic
705C2×C4⋊C4C23×C1111yescharacteristic
706C2×C22⋊C4C23×C1112yes—
707C2×C22⋊C4C23×C1112yes—
708C2×C22⋊C4C23×C1111yescharacteristic
709C2×C22⋊C4C23×C1111yescharacteristic
710C2×C22⋊C4C23×C1112yes—
711C2×C22⋊C4C23×C1112yes—
712C2×C22⋊C4C23×C1112yes—
713C2×C22⋊C4C23×C1112yes—
714C2×C22⋊C4C23×C1112yes—
715C2×C22⋊C4C23×C1112yes—
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×C1111yescharacteristic
729C2×C22⋊C4C23×C1111yescharacteristic
730C2×C42—28no—
731C2×C42—24no—
732C2×C42C23×C1112yes—
733C2×C42C23×C1111yescharacteristic
734C2×C42C23×C1112yes—
735C2×C42C23×C1111yescharacteristic
736C2×C42C23×C1111yescharacteristic
737C2×C42C23×C1112yes—
738C2×C42C23×C1112yes—
739C2×C42C23×C1111yescharacteristic
740C2×C42C23×C1111yescharacteristic
741C2×C42C23×C1111yescharacteristic
742C2×C42C23×C1111yescharacteristic
743C2×C42C23×C1111yescharacteristic
744C2×C42C23×C1111yescharacteristic
745C2×C42C23×C1111yescharacteristic
746C2×C42C23×C1111yescharacteristic
747C2×C42C23×C1111yescharacteristic
748C2×C42C23×C1111yescharacteristic
749C2×C42C23×C1111yescharacteristic
750C2×C42C23×C1111yescharacteristic
751C2×C42C23×C1111yescharacteristic
752#95C23×C1111yescharacteristic
753#95C23×C1111yescharacteristic
754#95C23×C1111yescharacteristic
755#95C23×C1111yescharacteristic
756#95C23×C1111yescharacteristic
757#95C23×C1111yescharacteristic
758#95C23×C1111yescharacteristic
759#95C23×C1111yescharacteristic
760#95C23×C1112yes—
761#95C23×C1112yes—
762#95C23×C1112yes—
763#95C23×C1112yes—
764#95C23×C1112yes—
765#95C23×C1112yes—
766#95C23×C1112yes—
767#95C23×C1112yes—
768#95C23×C1112yes—
769#95C23×C1112yes—
770#95C23×C1112yes—
771#95C23×C1112yes—
772C2×C11—44no—
773C2×C11—42no—
774C2×C11—82no—
775C2×C11C2×#52911yescharacteristic
776C2×C11C2×#53211yescharacteristic
777C2×C11#345511yescharacteristic
778C2×C11D4×#4111yescharacteristic
779C2×C11D4×#4111yescharacteristic
780C2×C11#347511yescharacteristic
781C2×C11#348011yescharacteristic
782C24C24×C1112yes—
783C24C24×C1111yescharacteristic
784C24C24×C1112yes—
785C2×Q8—24no—
786C2×Q8—24no—
787C2×Q8—42no—
788C2×D4—24no—
789C2×D4—24no—
790C2×D4—24no—
791C2×D4—24no—
792C2×D4—24no—
793C2×D4—24no—
794C2×D4—22no—
795C2×D4—22no—
796C2×D4—24no—
797C2×D4—22no—
798C2×D4—24no—
799C2×D4—22no—
800C2×D4—22no—
801C2×D4—42no—
802C2×D4—42no—
803C2×D4—42no—
804C2×D4—42no—
805C2×D4C11×#4114yes—
806C22×C4—22no—
807C22×C4—22no—
808C22×C4—24no—
809C22×C4—24no—
810C22×C4—24no—
811C22×C4—24no—
812C22×C4—24no—
813C22×C4—22no—
814C22×C4—22no—
815C22×C4—24no—
816C22×C4—24no—
817C22×C4—24no—
818C22×C4—24no—
819C22×C4—24no—
820C22×C4—22no—
821C22×C4—22no—
822C22×C4—41no—
823C22×C4—41no—
824C22×C4—42no—
825C22×C4—42no—
826C22×C4C2×D4×C1114yes—
827C22×C4C24×C1111yescharacteristic
828C22×C4C24×C1111yescharacteristic
829C22×C4C24×C1111yescharacteristic
830C22×C4C24×C1111yescharacteristic
831C22×C4C24×C1112yes—
832C22×C4C24×C1112yes—
833C22×C4C24×C1112yes—
834C22×C4C24×C1112yes—
835C22×C4C24×C1112yes—
836C22×C4C24×C1111yescharacteristic
837C22×C4C24×C1111yescharacteristic
838C22×C4C24×C1111yescharacteristic
839C22×C4C24×C1111yescharacteristic
840C22×C4C24×C1111yescharacteristic
841C22×C4C24×C1111yescharacteristic
842C22×C4C24×C1111yescharacteristic
843C22×C4C24×C1112yes—
844C22×C4C24×C1111yescharacteristic
845C22×C4C24×C1111yescharacteristic
846C22×C4C24×C1111yescharacteristic
847C4⋊C4—24no—
848C4⋊C4—24no—
849C4⋊C4—24no—
850C4⋊C4—24no—
851C4⋊C4—24no—
852C4⋊C4—24no—
853C4⋊C4—24no—
854C4⋊C4—24no—
855C4⋊C4—22no—
856C4⋊C4—22no—
857C4⋊C4—24no—
858C4⋊C4—22no—
859C4⋊C4—22no—
860C4⋊C4—22no—
861C4⋊C4—22no—
862C4⋊C4—24no—
863C4⋊C4—22no—
864C4⋊C4—42no—
865C4⋊C4C2×D4×C1114yes—
866C4⋊C4C2×D4×C1114yes—
867C4⋊C4C11×#4114yes—
868C22⋊C4—24no—
869C22⋊C4—24no—
870C22⋊C4—24no—
871C22⋊C4—24no—
872C22⋊C4—24no—
873C22⋊C4—24no—
874C22⋊C4—24no—
875C22⋊C4—24no—
876C22⋊C4—24no—
877C22⋊C4—24no—
878C22⋊C4—22no—
879C22⋊C4—22no—
880C22⋊C4—24no—
881C22⋊C4—24no—
882C22⋊C4—24no—
883C22⋊C4—24no—
884C22⋊C4—24no—
885C22⋊C4—24no—
886C22⋊C4—42no—
887C22⋊C4—42no—
888C22⋊C4—42no—
889C22⋊C4—42no—
890C22⋊C4C2×D4×C1114yes—
891C22⋊C4C2×D4×C1114yes—
892C42—24no—
893C42—24no—
894C42—24no—
895C42—24no—
896C42—22no—
897C42—22no—
898C42—22no—
899C42—22no—
900C42—22no—
901C42—22no—
902C42—22no—
903C42—22no—
904C42—41no—
905C42—41no—
906C42—41no—
907C42—41no—
908C42C2×D4×C1114yes—
909C42C2×D4×C1114yes—
910C42C11×#4114yes—
911C42C11×#4114yes—
912C11#3491411yescharacteristic, direct product factor, Sylow
913C23—22no—
914C23—21no—
915C23—22no—
916C23—22no—
917C23—22no—
918C23—21no—
919C23—21no—
920C23—21no—
921C23—22no—
922C23—22no—
923C23—21no—
924C23—21no—
925C23—22no—
926C23—22no—
927C23—22no—
928C23—22no—
929C23—22no—
930C23—22no—
931C23—22no—
932C23C22×D4×C1112yes—
933C23C2×C11×#4114yes—
934C23C25×C1111yescharacteristic
935Q8—48no—
936D4—28no—
937D4—48no—
938D4—48no—
939D4—48no—
940D4—48no—
941D4—44no—
942C2×C4—22no—
943C2×C4—21no—
944C2×C4—21no—
945C2×C4—21no—
946C2×C4—21no—
947C2×C4—21no—
948C2×C4—21no—
949C2×C4—21no—
950C2×C4—21no—
951C2×C4—21no—
952C2×C4—21no—
953C2×C4—21no—
954C2×C4—21no—
955C2×C4—21no—
956C2×C4—21no—
957C2×C4—21no—
958C2×C4—21no—
959C2×C4—22no—
960C2×C4—28no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—21no—
967C2×C4—21no—
968C2×C4—21no—
969C2×C4—21no—
970C2×C4—21no—
971C2×C4—21no—
972C2×C4—21no—
973C2×C4—21no—
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—21no—
983C2×C4—21no—
984C2×C4—21no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—48no—
989C2×C4—48no—
990C2×C4—44no—
991C2×C4—44no—
992C2×C4—48no—
993C2×C4—48no—
994C2×C4C22×D4×C1112yes—
995C2×C4C22×D4×C1112yes—
996C2×C4C22×D4×C1112yes—
997C2×C4C22×D4×C1112yes—
998C2×C4C22×D4×C1112yes—
999C2×C4C22×D4×C1112yes—
1000C2×C4C2×C11×#4112yes—
1001C2×C4C2×C11×#4112yes—
1002C2×C4C2×C11×#4112yes—
1003C2×C4C2×C11×#4114yes—
1004C2×C4C2×C11×#4112yes—
1005C2×C4C2×C11×#4112yes—
1006C2×C4C2×C11×#4112yes—
1007C2×C4C2×C11×#4112yes—
1008C2×C4C2×C11×#4112yes—
1009C22—24no—
1010C22—22no—
1011C22—24no—
1012C22—22no—
1013C22—22no—
1014C22—24no—
1015C22—41no—
1016C22—42no—
1017C22—41no—
1018C22—42no—
1019C22—42no—
1020C22—41no—
1021C22—41no—
1022C22—42no—
1023C22—42no—
1024C22—42no—
1025C22—42no—
1026C22—42no—
1027C22—42no—
1028C22—42no—
1029C22—42no—
1030C22C23×D4×C1111yescharacteristic
1031C22C22×C11×#4111yescharacteristic
1032C22C22×C11×#4111yescharacteristic
1033C22C22×C11×#4111yescharacteristic
1034C22C22×C11×#4111yescharacteristic
1035C22C11×#58511yescharacteristic
1036C22C11×#58511yescharacteristic
1037C4—22no—
1038C4—22no—
1039C4—22no—
1040C4—22no—
1041C4—24no—
1042C4—22no—
1043C4—22no—
1044C4—22no—
1045C4—22no—
1046C4—41no—
1047C4—42no—
1048C4—42no—
1049C4—41no—
1050C4—42no—
1051C4—42no—
1052C4—42no—
1053C4—41no—
1054C4—41no—
1055C4C11×#52914yescomplemented
1056C4C11×#53214yes—
1057C2—44no—
1058C2—42no—
1059C2—82no—
1060C2C2×C11×#52911yescharacteristic
1061C2C2×C11×#53211yescharacteristic
1062C2C11×#345511yescharacteristic
1063C2D4×C11×#4111yescharacteristic
1064C2D4×C11×#4111yescharacteristic
1065C2C11×#347511yescharacteristic
1066C2C11×#348011yescharacteristic
subgroupG/H
centerC22×C4×C11C24
commutator, Frattini, cosocleC23C25×C11
socleC23×C11C25
prime radicalC11×#2428C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#529C2semidirect
2. C11×#2560C2semidirect
3. C11×#2559C2semidirect
4. C11×#2558C2semidirect
5. C11×#2557C2semidirect
6. C11×#2512C2semidirect
7. C11×#2506C2semidirect
8. C11×#2496C2semidirect
9. C11×#2491C2semidirect
10. C11×#2452C2semidirect
11. C11×#2445C2semidirect
13. C11×#2422C2semidirect
14. C11×#2398C2semidirect
15. C11×#2392C2semidirect
16. C4×C11×C4⋊Q8C2semidirect
17. C4×C11×#127C2semidirect
18. C4×C11×#121C2semidirect
19. C4×C11×#121C2semidirect
20. C11×#2293C2semidirect
21. C11×#2290C2semidirect
22. C42×D4×C11C2semidirect
23. C4×C11×#117C2semidirect
161. C11×#117D4semidirect
249. #34914C11direct (N × H)
380. C2×#529C2×C11semidirect
381. #2560C2×C11semidirect
382. #2559C2×C11semidirect
383. #2558C2×C11semidirect
384. #2557C2×C11semidirect
385. #2512C2×C11semidirect
386. #2506C2×C11semidirect
387. #2496C2×C11semidirect
388. #2491C2×C11semidirect
389. #2452C2×C11semidirect
390. #2445C2×C11semidirect
392. #2422C2×C11semidirect
393. #2398C2×C11semidirect
394. #2392C2×C11semidirect
395. C4×C4⋊Q8C2×C11semidirect
396. C4×#127C2×C11semidirect
397. C4×#121C2×C11semidirect
398. C4×#121C2×C11semidirect
399. #2293C2×C11semidirect
400. #2290C2×C11semidirect
401. C42×D4C2×C11semidirect
402. C4×#117C2×C11semidirect
645. C4×C11#529semidirect
684. #117D4×C11semidirect
912. C11#34914direct (N × H)
1055. C4C11×#529semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#5292
C11×#25602
C11×#25592
C11×#25582
C11×#25572
C11×#25122
C11×#25062
C11×#24962
C11×#24912
C11×#24522
C11×#24452
C11×#24282
C11×#24222
C11×#23982
C11×#23922
C4×C11×C4⋊Q82
C4×C11×#1272
C4×C11×#1212
C11×#22932
C11×#22902
C42×D4×C112
C4×C11×#1172
#3491411