Finite Group Databasebeta

← C11×#14052 #14591245

Subgroups — C11×#14052 #14591245

Order 2816.

2266 conjugacy classes of subgroups.

The subgroup lattice has 1082 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×C22⋊Q8C211yesmaximal, characteristic
2C2×C11×#391C211yesmaximal, characteristic, complemented
3C2×C11×#385C211yesmaximal, characteristic
4C2×C4×C11×C22⋊C4C211yesmaximal, characteristic
5C22×C11×#95C211yesmaximal, characteristic
6C11×#1446C211yesmaximal, characteristic, complemented
7C11×#1445C211yesmaximal, characteristic, complemented
8C11×#1441C211yesmaximal, characteristic, complemented
9C11×#1441C211yesmaximal, characteristic, complemented
10C11×#1436C211yesmaximal, characteristic, complemented
11C11×#1436C211yesmaximal, characteristic, complemented
12C11×C4⋊#95C211yesmaximal, characteristic, complemented
13C11×C22⋊#95C211yesmaximal, characteristic
14C11×C22⋊#95C211yesmaximal, characteristic
15C11×C22⋊#95C211yesmaximal, characteristic
16C23×Q8×C11C2211yescharacteristic
17C24×C4×C11C2211yescharacteristic
18C24×C4×C11C2211yescharacteristic
19C24×C4×C11C2211yescharacteristic
20C2×C11×C22⋊Q8—24no—
21C2×C11×C22⋊Q8—24no—
22C2×C11×C22⋊Q8C418yescomplemented
23C22×C11×C4⋊C4C2211yescharacteristic
24C22×C11×C4⋊C4C2211yescharacteristic
25C22×C11×C4⋊C4C2211yescharacteristic
26C22×C11×C4⋊C4C2211yescharacteristic
27C22×C11×C4⋊C4C2211yescharacteristic
28C22×C11×C22⋊C4C2211yescharacteristic
29C22×C11×C22⋊C4C2211yescharacteristic
30C22×C11×C22⋊C4C2211yescharacteristic
31C22×C11×C22⋊C4C2211yescharacteristic
32C22×C42×C11C2211yescharacteristic
33C22×C42×C11C2211yescharacteristic
34C11×#391—24no—
35C11×#385—24no—
36C4×C11×C22⋊C4—24no—
37C2×C11×#95—24no—
38C2×C11×#95C2211yescharacteristic
39C2×C11×#95C2211yescharacteristic
40C2×C11×#95C2211yescharacteristic
41C2×C11×#95C2211yescharacteristic
42C2×C11×#95C2211yescharacteristic
43C2×C11×#95C2211yescharacteristic
44C2×C11×#95C2211yescharacteristic
45C2×C11×#95C2211yescharacteristic
46C2×C11×#95C2211yescharacteristic
47C2×C11×#95C2211yescharacteristic
48C2×C11×#95C2211yescharacteristic
49C2×C11×#95C2211yescharacteristic
50C2×C11×#95C2211yescharacteristic
51C2×C11×#95C2211yescharacteristic
52C2×C11×#95C2211yescharacteristic
53C2×C11×#95C2211yescharacteristic
54C2×C11×#95C2211yescharacteristic
55C2×C11×#95C2211yescharacteristic
56C2×C11×#95C2211yescharacteristic
57C2×C11×#95C2211yescharacteristic
58C25×C11C2311yescharacteristic
59C22×Q8×C11—22no—
60C22×Q8×C11—22no—
61C22×Q8×C11—22no—
62C22×Q8×C11—22no—
63C22×Q8×C11—41no—
64C22×Q8×C11—41no—
65C22×Q8×C11C2×C414yescomplemented
66C23×C4×C11—22no—
67C23×C4×C11—22no—
68C23×C4×C11—22no—
69C23×C4×C11—22no—
70C23×C4×C11—22no—
71C23×C4×C11—22no—
72C23×C4×C11—22no—
73C23×C4×C11—22no—
74C23×C4×C11—22no—
75C23×C4×C11—22no—
76C23×C4×C11—22no—
77C23×C4×C11—22no—
78C23×C4×C11—22no—
79C23×C4×C11—41no—
80C23×C4×C11—41no—
81C23×C4×C11—41no—
82C23×C4×C11—41no—
83C23×C4×C11—41no—
84C23×C4×C11—41no—
85C23×C4×C11C2×C414yes—
86C23×C4×C11Q814yescomplemented
87C23×C4×C11C2311yescharacteristic
88C23×C4×C11C2311yescharacteristic
89C23×C4×C11C2311yescharacteristic
90C23×C4×C11C2311yescharacteristic
91C23×C4×C11C2311yescharacteristic
92C23×C4×C11C2311yescharacteristic
93C23×C4×C11C2311yescharacteristic
94C23×C4×C11C2311yescharacteristic
95C23×C4×C11C2311yescharacteristic
96C23×C4×C11C2311yescharacteristic
97C23×C4×C11C2311yescharacteristic
98C23×C4×C11C2311yescharacteristic
99C23×C4×C11C2311yescharacteristic
100C23×C4×C11C2311yescharacteristic
101C11×C22⋊Q8—232no—
102C2×C11×C4⋊C4—22no—
103C2×C11×C4⋊C4—22no—
104C2×C11×C4⋊C4—22no—
105C2×C11×C4⋊C4—22no—
106C2×C11×C4⋊C4—22no—
107C2×C11×C4⋊C4—22no—
108C2×C11×C4⋊C4—22no—
109C2×C11×C4⋊C4—22no—
110C2×C11×C4⋊C4—22no—
111C2×C11×C4⋊C4—22no—
112C2×C11×C4⋊C4—41no—
113C2×C11×C4⋊C4—41no—
114C2×C11×C4⋊C4C2×C414yescomplemented
115C2×C11×C4⋊C4C2×C414yescomplemented
116C2×C11×C4⋊C4C2×C414yescomplemented
117C2×C11×C22⋊C4—22no—
118C2×C11×C22⋊C4—22no—
119C2×C11×C22⋊C4—22no—
120C2×C11×C22⋊C4—22no—
121C2×C11×C22⋊C4—22no—
122C2×C11×C22⋊C4—22no—
123C2×C11×C22⋊C4—22no—
124C2×C11×C22⋊C4C2×C414yes—
125C2×C11×C22⋊C4C2×C414yes—
126C2×C11×C22⋊C4D414yes—
127C2×C11×C22⋊C4D414yes—
128C2×C11×C22⋊C4Q814yescomplemented
129C2×C42×C11—22no—
130C2×C42×C11—22no—
131C2×C42×C11—22no—
132C2×C42×C11—22no—
133C2×C42×C11—41no—
134C2×C42×C11—41no—
135C11×#95—22no—
136C11×#95—22no—
137C11×#95—22no—
138C11×#95—22no—
139C11×#95—22no—
140C11×#95—22no—
141C11×#95—22no—
142C11×#95—22no—
143C11×#95—22no—
144C11×#95—22no—
145C11×#95—22no—
146C11×#95—22no—
147C11×#95—22no—
148C11×#95—41no—
149C11×#95—41no—
150C11×#95—41no—
151C11×#95—41no—
152C11×#95—41no—
153C11×#95—41no—
154C11×#95D414yes—
155#14052C1111yesmaximal, characteristic, direct product factor, Sylow
156C24×C11—21no—
157C24×C11—21no—
158C24×C11—21no—
159C24×C11—21no—
160C24×C11—21no—
161C24×C11—21no—
162C24×C11—21no—
163C24×C11—21no—
164C24×C11C22×C412yes—
165C24×C11C2×D412yes—
166C24×C11C2×D412yes—
167C24×C11C2×Q812yes—
168C24×C11C2×Q812yes—
169C24×C11#4112yes—
170C24×C11#4112yes—
171C24×C11C2411yescharacteristic
172C2×Q8×C11—28no—
173C2×Q8×C11—28no—
174C2×Q8×C11—44no—
175C2×Q8×C11—44no—
176C2×Q8×C11—44no—
177C2×Q8×C11—44no—
178C2×Q8×C11—44no—
179C22×C4×C11—21no—
180C22×C4×C11—21no—
181C22×C4×C11—21no—
182C22×C4×C11—21no—
183C22×C4×C11—21no—
184C22×C4×C11—21no—
185C22×C4×C11—21no—
186C22×C4×C11—21no—
187C22×C4×C11—21no—
188C22×C4×C11—21no—
189C22×C4×C11—21no—
190C22×C4×C11—21no—
191C22×C4×C11—21no—
192C22×C4×C11—21no—
193C22×C4×C11—21no—
194C22×C4×C11—21no—
195C22×C4×C11—28no—
196C22×C4×C11—28no—
197C22×C4×C11—28no—
198C22×C4×C11—21no—
199C22×C4×C11—21no—
200C22×C4×C11—21no—
201C22×C4×C11—21no—
202C22×C4×C11—21no—
203C22×C4×C11—21no—
204C22×C4×C11—21no—
205C22×C4×C11—21no—
206C22×C4×C11—21no—
207C22×C4×C11—21no—
208C22×C4×C11—21no—
209C22×C4×C11—21no—
210C22×C4×C11—21no—
211C22×C4×C11—21no—
212C22×C4×C11—21no—
213C22×C4×C11—21no—
214C22×C4×C11—21no—
215C22×C4×C11—21no—
216C22×C4×C11—21no—
217C22×C4×C11—21no—
218C22×C4×C11—21no—
219C22×C4×C11—21no—
220C22×C4×C11—21no—
221C22×C4×C11—21no—
222C22×C4×C11—21no—
223C22×C4×C11—21no—
224C22×C4×C11—21no—
225C22×C4×C11—21no—
226C22×C4×C11—21no—
227C22×C4×C11—21no—
228C22×C4×C11—21no—
229C22×C4×C11—21no—
230C22×C4×C11—21no—
231C22×C4×C11—21no—
232C22×C4×C11—21no—
233C22×C4×C11—21no—
234C22×C4×C11—21no—
235C22×C4×C11—21no—
236C22×C4×C11—21no—
237C22×C4×C11—21no—
238C22×C4×C11—21no—
239C22×C4×C11—21no—
240C22×C4×C11—21no—
241C22×C4×C11—21no—
242C22×C4×C11—21no—
243C22×C4×C11—21no—
244C22×C4×C11—21no—
245C22×C4×C11—21no—
246C22×C4×C11—28no—
247C22×C4×C11—28no—
248C22×C4×C11—21no—
249C22×C4×C11—21no—
250C22×C4×C11—21no—
251C22×C4×C11—21no—
252C22×C4×C11—21no—
253C22×C4×C11—21no—
254C22×C4×C11—21no—
255C22×C4×C11—21no—
256C22×C4×C11—21no—
257C22×C4×C11—21no—
258C22×C4×C11—21no—
259C22×C4×C11—21no—
260C22×C4×C11—21no—
261C22×C4×C11—21no—
262C22×C4×C11—44no—
263C22×C4×C11—44no—
264C22×C4×C11—44no—
265C22×C4×C11—44no—
266C22×C4×C11—44no—
267C22×C4×C11—44no—
268C22×C4×C11—44no—
269C22×C4×C11—44no—
270C22×C4×C11—44no—
271C22×C4×C11—44no—
272C22×C4×C11—44no—
273C22×C4×C11—44no—
274C22×C4×C11—44no—
275C22×C4×C11—44no—
276C22×C4×C11—44no—
277C22×C4×C11—44no—
278C22×C4×C11C22×C412yes—
279C22×C4×C11C22×C412yes—
280C22×C4×C11C22×C412yes—
281C22×C4×C11C22×C412yes—
282C22×C4×C11C22×C412yes—
283C22×C4×C11C22×C412yes—
284C22×C4×C11C2×D412yes—
285C22×C4×C11C2×D412yes—
286C22×C4×C11C2×D412yes—
287C22×C4×C11C2×D412yes—
288C22×C4×C11C2×D412yes—
289C22×C4×C11C2×D412yes—
290C22×C4×C11C2×D412yes—
291C22×C4×C11C2×Q812yes—
292C22×C4×C11C2×Q812yes—
293C22×C4×C11C2×Q812yes—
294C22×C4×C11C2×Q812yes—
295C22×C4×C11#4112yes—
296C22×C4×C11#4112yes—
297C22×C4×C11#4112yes—
298C11×C4⋊C4—28no—
299C11×C4⋊C4—28no—
300C11×C4⋊C4—28no—
301C11×C4⋊C4—44no—
302C11×C4⋊C4—44no—
303C11×C22⋊C4—28no—
304C11×C22⋊C4—28no—
305C11×C22⋊C4—44no—
306C11×C22⋊C4C22⋊C4116yes—
307C42×C11—44no—
308C42×C11—44no—
309C22×C22⋊Q8C2×C1111yescharacteristic
310C2×#391C2×C1111yescharacteristic, complemented
311C2×#385C2×C1111yescharacteristic
312C2×C4×C22⋊C4C2×C1111yescharacteristic
313C22×#95C2×C1111yescharacteristic
314#1446C2×C1111yescharacteristic, complemented
315#1445C2×C1111yescharacteristic, complemented
316#1441C2×C1111yescharacteristic, complemented
317#1441C2×C1111yescharacteristic, complemented
318#1436C2×C1111yescharacteristic, complemented
319#1436C2×C1111yescharacteristic, complemented
320C4⋊#95C2×C1111yescharacteristic, complemented
321C22⋊#95C2×C1111yescharacteristic
322C22⋊#95C2×C1111yescharacteristic
323C22⋊#95C2×C1111yescharacteristic
324C23×C11—22no—
325C23×C11—22no—
326C23×C11—22no—
327C23×C11—22no—
328C23×C11—22no—
329C23×C11—22no—
330C23×C11—22no—
331C23×C11—22no—
332C23×C11—22no—
333C23×C11—22no—
334C23×C11—22no—
335C23×C11—22no—
336C23×C11—22no—
337C23×C11—22no—
338C23×C11—22no—
339C23×C11—22no—
340C23×C11—22no—
341C23×C11—22no—
342C23×C11—22no—
343C23×C11—22no—
344C23×C11—22no—
345C23×C11—22no—
346C23×C11—22no—
347C23×C11—22no—
348C23×C11—22no—
349C23×C11—22no—
350C23×C11—22no—
351C23×C11—22no—
352C23×C11C2×C22⋊C414yes—
353C23×C11C4×Q814yes—
354C23×C11C4×Q814yes—
355C23×C11C22⋊Q814yes—
356C23×C11C22⋊Q814yes—
357C23×C11#12414yes—
358C23×C11C4⋊Q814yes—
359C23×C11C23×C411yescharacteristic
360C23×C11C22×D411yescharacteristic
361C23×C11C22×D411yescharacteristic
362C23×C11C22×D411yescharacteristic
363C23×C11C22×Q811yescharacteristic
364C23×C11C22×Q811yescharacteristic
365C23×C11C2×#4111yescharacteristic
366C23×C11C2×#4111yescharacteristic
367C23×C11C2×#4111yescharacteristic
368C23×C11C2×#4111yescharacteristic
369C23×C11C2×#4111yescharacteristic
370C23×C11H(5,𝔽2)11yescharacteristic
371C23×C11H(5,𝔽2)11yescharacteristic
372C23×C11H(5,𝔽2)11yescharacteristic
373C23×C112−1+411yescharacteristic
374Q8×C11—416no—
375C2×C4×C11—22no—
376C2×C4×C11—22no—
377C2×C4×C11—22no—
378C2×C4×C11—22no—
379C2×C4×C11—22no—
380C2×C4×C11—22no—
381C2×C4×C11—22no—
382C2×C4×C11—22no—
383C2×C4×C11—22no—
384C2×C4×C11—22no—
385C2×C4×C11—22no—
386C2×C4×C11—22no—
387C2×C4×C11—22no—
388C2×C4×C11—22no—
389C2×C4×C11—22no—
390C2×C4×C11—22no—
391C2×C4×C11—22no—
392C2×C4×C11—22no—
393C2×C4×C11—22no—
394C2×C4×C11—22no—
395C2×C4×C11—22no—
396C2×C4×C11—22no—
397C2×C4×C11—22no—
398C2×C4×C11—22no—
399C2×C4×C11—22no—
400C2×C4×C11—22no—
401C2×C4×C11—22no—
402C2×C4×C11—22no—
403C2×C4×C11—22no—
404C2×C4×C11—22no—
405C2×C4×C11—22no—
406C2×C4×C11—22no—
407C2×C4×C11—22no—
408C2×C4×C11—22no—
409C2×C4×C11—22no—
410C2×C4×C11—22no—
411C2×C4×C11—22no—
412C2×C4×C11—22no—
413C2×C4×C11—22no—
414C2×C4×C11—22no—
415C2×C4×C11—22no—
416C2×C4×C11—22no—
417C2×C4×C11—22no—
418C2×C4×C11—22no—
419C2×C4×C11—22no—
420C2×C4×C11—22no—
421C2×C4×C11—22no—
422C2×C4×C11—22no—
423C2×C4×C11—416no—
424C2×C4×C11—416no—
425C2×C4×C11—416no—
426C2×C4×C11—41no—
427C2×C4×C11—41no—
428C2×C4×C11—41no—
429C2×C4×C11—41no—
430C2×C4×C11—41no—
431C2×C4×C11—41no—
432C2×C4×C11—41no—
433C2×C4×C11—41no—
434C2×C4×C11—41no—
435C2×C4×C11—41no—
436C2×C4×C11—41no—
437C2×C4×C11—41no—
438C2×C4×C11—41no—
439C2×C4×C11—41no—
440C2×C4×C11—41no—
441C2×C4×C11—41no—
442C2×C4×C11—41no—
443C2×C4×C11—41no—
444C2×C4×C11—41no—
445C2×C4×C11—41no—
446C2×C4×C11—41no—
447C2×C4×C11—41no—
448C2×C4×C11—41no—
449C2×C4×C11—41no—
450C2×C4×C11—41no—
451C2×C4×C11—41no—
452C2×C4×C11—41no—
453C2×C4×C11—41no—
454C2×C4×C11—41no—
455C2×C4×C11—41no—
456C2×C4×C11—41no—
457C2×C4×C11—41no—
458C2×C4×C11—41no—
459C2×C4×C11—41no—
460C2×C4×C11—41no—
461C2×C4×C11—41no—
462C2×C4×C11—41no—
463C2×C4×C11—41no—
464C2×C4×C11—41no—
465C2×C4×C11—41no—
466C2×C4×C11—41no—
467C2×C4×C11—41no—
468C2×C4×C11—41no—
469C2×C4×C11—41no—
470C2×C4×C11—41no—
471C2×C4×C11—41no—
472C2×C4×C11C2×C22⋊C414yes—
473C2×C4×C11C2×C22⋊C414yes—
474C2×C4×C11C4×D414yes—
475C2×C4×C11C22⋊Q814yescomplemented
476C23×Q8C22×C1111yescharacteristic
477C24×C4C22×C1111yescharacteristic
478C24×C4C22×C1111yescharacteristic
479C24×C4C22×C1111yescharacteristic
480C2×C22⋊Q8—24no—
481C2×C22⋊Q8—24no—
482C2×C22⋊Q8C4×C1118yescomplemented
483C22×C4⋊C4C22×C1111yescharacteristic
484C22×C4⋊C4C22×C1111yescharacteristic
485C22×C4⋊C4C22×C1111yescharacteristic
486C22×C4⋊C4C22×C1111yescharacteristic
487C22×C4⋊C4C22×C1111yescharacteristic
488C22×C22⋊C4C22×C1111yescharacteristic
489C22×C22⋊C4C22×C1111yescharacteristic
490C22×C22⋊C4C22×C1111yescharacteristic
491C22×C22⋊C4C22×C1111yescharacteristic
492C22×C42C22×C1111yescharacteristic
493C22×C42C22×C1111yescharacteristic
494#391—24no—
495#385—24no—
496C4×C22⋊C4—24no—
497C2×#95—24no—
498C2×#95C22×C1111yescharacteristic
499C2×#95C22×C1111yescharacteristic
500C2×#95C22×C1111yescharacteristic
501C2×#95C22×C1111yescharacteristic
502C2×#95C22×C1111yescharacteristic
503C2×#95C22×C1111yescharacteristic
504C2×#95C22×C1111yescharacteristic
505C2×#95C22×C1111yescharacteristic
506C2×#95C22×C1111yescharacteristic
507C2×#95C22×C1111yescharacteristic
508C2×#95C22×C1111yescharacteristic
509C2×#95C22×C1111yescharacteristic
510C2×#95C22×C1111yescharacteristic
511C2×#95C22×C1111yescharacteristic
512C2×#95C22×C1111yescharacteristic
513C2×#95C22×C1111yescharacteristic
514C2×#95C22×C1111yescharacteristic
515C2×#95C22×C1111yescharacteristic
516C2×#95C22×C1111yescharacteristic
517C2×#95C22×C1111yescharacteristic
518C22×C11—24no—
519C22×C11—24no—
520C22×C11—24no—
521C22×C11—24no—
522C22×C11—24no—
523C22×C11—24no—
524C22×C11—24no—
525C22×C11—24no—
526C22×C11—24no—
527C22×C11—24no—
528C22×C11—24no—
529C22×C11—24no—
530C22×C11—24no—
531C22×C11—24no—
532C22×C11#39118yescomplemented
533C22×C11C22×C22⋊C411yescharacteristic
534C22×C11C2×C4×D411yescharacteristic
535C22×C11C2×C4×Q811yescharacteristic
536C22×C11C2×C4×Q811yescharacteristic
537C22×C11C4×#4111yescharacteristic
538C22×C11#51811yescharacteristic
539C22×C11#52011yescharacteristic
540C22×C11C2×C22⋊Q811yescharacteristic
541C22×C11C2×C22⋊Q811yescharacteristic
542C22×C11C2×C22⋊Q811yescharacteristic
543C22×C11#52511yescharacteristic
544C22×C11C2×#12411yescharacteristic
545C22×C11#52911yescharacteristic
546C22×C11C2×C4⋊Q811yescharacteristic
547C22×C11#53311yescharacteristic
548C22×C11#53811yescharacteristic
549C22×C11#53911yescharacteristic
550C22×C11#54311yescharacteristic
551C22×C11#54411yescharacteristic
552C22×C11D4211yescharacteristic
553C22×C11D4211yescharacteristic
554C22×C11#54611yescharacteristic
555C22×C11#54611yescharacteristic
556C22×C11#54611yescharacteristic
557C22×C11#54611yescharacteristic
558C22×C11#54611yescharacteristic
559C22×C11#54711yescharacteristic
560C22×C11#54711yescharacteristic
561C22×C11D4×Q811yescharacteristic
562C22×C11#55111yescharacteristic
563C22×C11#55111yescharacteristic
564C22×C11#55211yescharacteristic
565C22×C11#55411yescharacteristic
566C22×C11#55411yescharacteristic
567C22×C11#55411yescharacteristic
568C4×C11—24no—
569C4×C11—24no—
570C4×C11—24no—
571C4×C11—24no—
572C4×C11—42no—
573C4×C11—42no—
574C4×C11—42no—
575C4×C11—42no—
576C4×C11—42no—
577C4×C11—42no—
578C4×C11—42no—
579C4×C11—42no—
580C4×C11—81no—
581C4×C11—81no—
582C25C23×C1111yescharacteristic
583C22×Q8—22no—
584C22×Q8—22no—
585C22×Q8—22no—
586C22×Q8—22no—
587C22×Q8—41no—
588C22×Q8—41no—
589C22×Q8C2×C4×C1114yescomplemented
590C23×C4—22no—
591C23×C4—22no—
592C23×C4—22no—
593C23×C4—22no—
594C23×C4—22no—
595C23×C4—22no—
596C23×C4—22no—
597C23×C4—22no—
598C23×C4—22no—
599C23×C4—22no—
600C23×C4—22no—
601C23×C4—22no—
602C23×C4—22no—
603C23×C4—41no—
604C23×C4—41no—
605C23×C4—41no—
606C23×C4—41no—
607C23×C4—41no—
608C23×C4—41no—
609C23×C4C2×C4×C1114yes—
610C23×C4Q8×C1114yescomplemented
611C23×C4C23×C1111yescharacteristic
612C23×C4C23×C1111yescharacteristic
613C23×C4C23×C1111yescharacteristic
614C23×C4C23×C1111yescharacteristic
615C23×C4C23×C1111yescharacteristic
616C23×C4C23×C1111yescharacteristic
617C23×C4C23×C1111yescharacteristic
618C23×C4C23×C1111yescharacteristic
619C23×C4C23×C1111yescharacteristic
620C23×C4C23×C1111yescharacteristic
621C23×C4C23×C1111yescharacteristic
622C23×C4C23×C1111yescharacteristic
623C23×C4C23×C1111yescharacteristic
624C23×C4C23×C1111yescharacteristic
625C22⋊Q8—232no—
626C2×C4⋊C4—22no—
627C2×C4⋊C4—22no—
628C2×C4⋊C4—22no—
629C2×C4⋊C4—22no—
630C2×C4⋊C4—22no—
631C2×C4⋊C4—22no—
632C2×C4⋊C4—22no—
633C2×C4⋊C4—22no—
634C2×C4⋊C4—22no—
635C2×C4⋊C4—22no—
636C2×C4⋊C4—41no—
637C2×C4⋊C4—41no—
638C2×C4⋊C4C2×C4×C1114yescomplemented
639C2×C4⋊C4C2×C4×C1114yescomplemented
640C2×C4⋊C4C2×C4×C1114yescomplemented
641C2×C22⋊C4—22no—
642C2×C22⋊C4—22no—
643C2×C22⋊C4—22no—
644C2×C22⋊C4—22no—
645C2×C22⋊C4—22no—
646C2×C22⋊C4—22no—
647C2×C22⋊C4—22no—
648C2×C22⋊C4C2×C4×C1114yes—
649C2×C22⋊C4C2×C4×C1114yes—
650C2×C22⋊C4D4×C1114yes—
651C2×C22⋊C4D4×C1114yes—
652C2×C22⋊C4Q8×C1114yescomplemented
653C2×C42—22no—
654C2×C42—22no—
655C2×C42—22no—
656C2×C42—22no—
657C2×C42—41no—
658C2×C42—41no—
659#95—22no—
660#95—22no—
661#95—22no—
662#95—22no—
663#95—22no—
664#95—22no—
665#95—22no—
666#95—22no—
667#95—22no—
668#95—22no—
669#95—22no—
670#95—22no—
671#95—22no—
672#95—41no—
673#95—41no—
674#95—41no—
675#95—41no—
676#95—41no—
677#95—41no—
678#95D4×C1114yes—
679C2×C11—28no—
680C2×C11C2×#39111yescharacteristic
681C2×C11C4×C22⋊Q811yescharacteristic
682C2×C11#232911yescharacteristic
683C2×C11D4×C22⋊C411yescharacteristic
684C2×C11#233911yescharacteristic
685C2×C11#236011yescharacteristic
686C2×C11#236811yescharacteristic
687C2×C11#243711yescharacteristic
688C2×C11#243811yescharacteristic
689C2×C11#244011yescharacteristic
690C2×C11#244911yescharacteristic
691C2×C11#245011yescharacteristic
692C2×C11#247211yescharacteristic
693C2×C11#248811yescharacteristic
694C2×C11#254911yescharacteristic
695C24—21no—
696C24—21no—
697C24—21no—
698C24—21no—
699C24—21no—
700C24—21no—
701C24—21no—
702C24—21no—
703C24C22×C4×C1112yes—
704C24C2×D4×C1112yes—
705C24C2×D4×C1112yes—
706C24C2×Q8×C1112yes—
707C24C2×Q8×C1112yes—
708C24C11×#4112yes—
709C24C11×#4112yes—
710C24C24×C1111yescharacteristic
711C2×Q8—28no—
712C2×Q8—28no—
713C2×Q8—44no—
714C2×Q8—44no—
715C2×Q8—44no—
716C2×Q8—44no—
717C2×Q8—44no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—28no—
735C22×C4—28no—
736C22×C4—28no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—28no—
786C22×C4—28no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—44no—
802C22×C4—44no—
803C22×C4—44no—
804C22×C4—44no—
805C22×C4—44no—
806C22×C4—44no—
807C22×C4—44no—
808C22×C4—44no—
809C22×C4—44no—
810C22×C4—44no—
811C22×C4—44no—
812C22×C4—44no—
813C22×C4—44no—
814C22×C4—44no—
815C22×C4—44no—
816C22×C4—44no—
817C22×C4C22×C4×C1112yes—
818C22×C4C22×C4×C1112yes—
819C22×C4C22×C4×C1112yes—
820C22×C4C22×C4×C1112yes—
821C22×C4C22×C4×C1112yes—
822C22×C4C22×C4×C1112yes—
823C22×C4C2×D4×C1112yes—
824C22×C4C2×D4×C1112yes—
825C22×C4C2×D4×C1112yes—
826C22×C4C2×D4×C1112yes—
827C22×C4C2×D4×C1112yes—
828C22×C4C2×D4×C1112yes—
829C22×C4C2×D4×C1112yes—
830C22×C4C2×Q8×C1112yes—
831C22×C4C2×Q8×C1112yes—
832C22×C4C2×Q8×C1112yes—
833C22×C4C2×Q8×C1112yes—
834C22×C4C11×#4112yes—
835C22×C4C11×#4112yes—
836C22×C4C11×#4112yes—
837C4⋊C4—28no—
838C4⋊C4—28no—
839C4⋊C4—28no—
840C4⋊C4—44no—
841C4⋊C4—44no—
842C22⋊C4—28no—
843C22⋊C4—28no—
844C22⋊C4—44no—
845C22⋊C4C11×C22⋊C4116yes—
846C42—44no—
847C42—44no—
848C11#1405211yescharacteristic, direct product factor, Sylow
849C23—22no—
850C23—22no—
851C23—22no—
852C23—22no—
853C23—22no—
854C23—22no—
855C23—22no—
856C23—22no—
857C23—22no—
858C23—22no—
859C23—22no—
860C23—22no—
861C23—22no—
862C23—22no—
863C23—22no—
864C23—22no—
865C23—22no—
866C23—22no—
867C23—22no—
868C23—22no—
869C23—22no—
870C23—22no—
871C23—22no—
872C23—22no—
873C23—22no—
874C23—22no—
875C23—22no—
876C23—22no—
877C23C2×C11×C22⋊C414yes—
878C23C4×Q8×C1114yes—
879C23C4×Q8×C1114yes—
880C23C11×C22⋊Q814yes—
881C23C11×C22⋊Q814yes—
882C23C11×#12414yes—
883C23C11×C4⋊Q814yes—
884C23C23×C4×C1111yescharacteristic
885C23C22×D4×C1111yescharacteristic
886C23C22×D4×C1111yescharacteristic
887C23C22×D4×C1111yescharacteristic
888C23C22×Q8×C1111yescharacteristic
889C23C22×Q8×C1111yescharacteristic
890C23C2×C11×#4111yescharacteristic
891C23C2×C11×#4111yescharacteristic
892C23C2×C11×#4111yescharacteristic
893C23C2×C11×#4111yescharacteristic
894C23C2×C11×#4111yescharacteristic
895C23C11×H(5,𝔽2)11yescharacteristic
896C23C11×H(5,𝔽2)11yescharacteristic
897C23C11×H(5,𝔽2)11yescharacteristic
898C23C11×2−1+411yescharacteristic
899Q8—416no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—22no—
917C2×C4—22no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—22no—
923C2×C4—22no—
924C2×C4—22no—
925C2×C4—22no—
926C2×C4—22no—
927C2×C4—22no—
928C2×C4—22no—
929C2×C4—22no—
930C2×C4—22no—
931C2×C4—22no—
932C2×C4—22no—
933C2×C4—22no—
934C2×C4—22no—
935C2×C4—22no—
936C2×C4—22no—
937C2×C4—22no—
938C2×C4—22no—
939C2×C4—22no—
940C2×C4—22no—
941C2×C4—22no—
942C2×C4—22no—
943C2×C4—22no—
944C2×C4—22no—
945C2×C4—22no—
946C2×C4—22no—
947C2×C4—22no—
948C2×C4—416no—
949C2×C4—416no—
950C2×C4—416no—
951C2×C4—41no—
952C2×C4—41no—
953C2×C4—41no—
954C2×C4—41no—
955C2×C4—41no—
956C2×C4—41no—
957C2×C4—41no—
958C2×C4—41no—
959C2×C4—41no—
960C2×C4—41no—
961C2×C4—41no—
962C2×C4—41no—
963C2×C4—41no—
964C2×C4—41no—
965C2×C4—41no—
966C2×C4—41no—
967C2×C4—41no—
968C2×C4—41no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—41no—
973C2×C4—41no—
974C2×C4—41no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—41no—
978C2×C4—41no—
979C2×C4—41no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—41no—
986C2×C4—41no—
987C2×C4—41no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4C2×C11×C22⋊C414yes—
998C2×C4C2×C11×C22⋊C414yes—
999C2×C4C4×D4×C1114yes—
1000C2×C4C11×C22⋊Q814yescomplemented
1001C22—24no—
1002C22—24no—
1003C22—24no—
1004C22—24no—
1005C22—24no—
1006C22—24no—
1007C22—24no—
1008C22—24no—
1009C22—24no—
1010C22—24no—
1011C22—24no—
1012C22—24no—
1013C22—24no—
1014C22—24no—
1015C22C11×#39118yescomplemented
1016C22C22×C11×C22⋊C411yescharacteristic
1017C22C2×C4×D4×C1111yescharacteristic
1018C22C2×C4×Q8×C1111yescharacteristic
1019C22C2×C4×Q8×C1111yescharacteristic
1020C22C4×C11×#4111yescharacteristic
1021C22C11×#51811yescharacteristic
1022C22C11×#52011yescharacteristic
1023C22C2×C11×C22⋊Q811yescharacteristic
1024C22C2×C11×C22⋊Q811yescharacteristic
1025C22C2×C11×C22⋊Q811yescharacteristic
1026C22C11×#52511yescharacteristic
1027C22C2×C11×#12411yescharacteristic
1028C22C11×#52911yescharacteristic
1029C22C2×C11×C4⋊Q811yescharacteristic
1030C22C11×#53311yescharacteristic
1031C22C11×#53811yescharacteristic
1032C22C11×#53911yescharacteristic
1033C22C11×#54311yescharacteristic
1034C22C11×#54411yescharacteristic
1035C22D42×C1111yescharacteristic
1036C22D42×C1111yescharacteristic
1037C22C11×#54611yescharacteristic
1038C22C11×#54611yescharacteristic
1039C22C11×#54611yescharacteristic
1040C22C11×#54611yescharacteristic
1041C22C11×#54611yescharacteristic
1042C22C11×#54711yescharacteristic
1043C22C11×#54711yescharacteristic
1044C22D4×Q8×C1111yescharacteristic
1045C22C11×#55111yescharacteristic
1046C22C11×#55111yescharacteristic
1047C22C11×#55211yescharacteristic
1048C22C11×#55411yescharacteristic
1049C22C11×#55411yescharacteristic
1050C22C11×#55411yescharacteristic
1051C4—24no—
1052C4—24no—
1053C4—24no—
1054C4—24no—
1055C4—42no—
1056C4—42no—
1057C4—42no—
1058C4—42no—
1059C4—42no—
1060C4—42no—
1061C4—42no—
1062C4—42no—
1063C4—81no—
1064C4—81no—
1065C2—28no—
1066C2C2×C11×#39111yescharacteristic
1067C2C4×C11×C22⋊Q811yescharacteristic
1068C2C11×#232911yescharacteristic
1069C2D4×C11×C22⋊C411yescharacteristic
1070C2C11×#233911yescharacteristic
1071C2C11×#236011yescharacteristic
1072C2C11×#236811yescharacteristic
1073C2C11×#243711yescharacteristic
1074C2C11×#243811yescharacteristic
1075C2C11×#244011yescharacteristic
1076C2C11×#244911yescharacteristic
1077C2C11×#245011yescharacteristic
1078C2C11×#247211yescharacteristic
1079C2C11×#248811yescharacteristic
1080C2C11×#254911yescharacteristic
subgroupG/H
center, socleC24×C11C24
commutatorC23C23×C4×C11
Frattini, cosocleC24C24×C11
prime radicalC25×C11C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#391C2semidirect
6. C11×#1446C2semidirect
7. C11×#1445C2semidirect
8. C11×#1441C2semidirect
9. C11×#1441C2semidirect
10. C11×#1436C2semidirect
11. C11×#1436C2semidirect
12. C11×C4⋊#95C2semidirect
22. C2×C11×C22⋊Q8C4semidirect
65. C22×Q8×C11C2×C4semidirect
86. C23×C4×C11Q8semidirect
114. C2×C11×C4⋊C4C2×C4semidirect
115. C2×C11×C4⋊C4C2×C4semidirect
116. C2×C11×C4⋊C4C2×C4semidirect
128. C2×C11×C22⋊C4Q8semidirect
155. #14052C11direct (N × H)
310. C2×#391C2×C11semidirect
314. #1446C2×C11semidirect
315. #1445C2×C11semidirect
316. #1441C2×C11semidirect
317. #1441C2×C11semidirect
318. #1436C2×C11semidirect
319. #1436C2×C11semidirect
320. C4⋊#95C2×C11semidirect
475. C2×C4×C11C22⋊Q8semidirect
482. C2×C22⋊Q8C4×C11semidirect
532. C22×C11#391semidirect
589. C22×Q8C2×C4×C11semidirect
610. C23×C4Q8×C11semidirect
638. C2×C4⋊C4C2×C4×C11semidirect
639. C2×C4⋊C4C2×C4×C11semidirect
640. C2×C4⋊C4C2×C4×C11semidirect
652. C2×C22⋊C4Q8×C11semidirect
848. C11#14052direct (N × H)
1000. C2×C4C11×C22⋊Q8semidirect
1015. C22C11×#391semidirect

Maximal subgroups

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

subgroupindex
C22×C11×C22⋊Q82
C2×C11×#3912
C2×C11×#3852
C2×C4×C11×C22⋊C42
C22×C11×#952
C11×#14462
C11×#14452
C11×#14412
C11×#14362
C11×C4⋊#952
C11×C22⋊#952
#1405211