Finite Group Databasebeta

← C11×#15508 #14592701

Subgroups — C11×#15508 #14592701

Order 2816.

1782 conjugacy classes of subgroups.

The subgroup lattice has 1156 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#400C211yesmaximal, characteristic, complemented
2C2×C11×#396C211yesmaximal, characteristic, complemented
3C2×C11×#390C211yesmaximal, characteristic
4C2×C11×#386C211yesmaximal, characteristic
5C11×#1444C211yesmaximal, characteristic, complemented
6C11×#1439C211yesmaximal, characteristic, complemented
7C11×#1439C211yesmaximal, characteristic, complemented
8C11×#1439C211yesmaximal, characteristic, complemented
9C11×#1439C211yesmaximal, characteristic, complemented
10C11×#1439C211yesmaximal, characteristic, complemented
11C11×#1438C211yesmaximal, characteristic
12C11×#1436C211yesmaximal, characteristic, complemented
13C11×#1434C211yesmaximal, characteristic, complemented
14C11×C22⋊#95C211yesmaximal, characteristic, complemented
15C11×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×D4×C11C2211yescharacteristic
17C24×C4×C11C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×C11×C4⋊C4C2211yescharacteristic
20C22×C11×C4⋊C4C2211yescharacteristic
21C22×C11×C4⋊C4C2211yescharacteristic
22C22×C11×C4⋊C4C2211yescharacteristic
23C22×C11×C22⋊C4C2211yescharacteristic
24C22×C11×C22⋊C4C2211yescharacteristic
25C22×C11×C22⋊C4C2211yescharacteristic
26C22×C11×C22⋊C4C2211yescharacteristic
27C22×C11×C22⋊C4C2211yescharacteristic
28C22×C11×C22⋊C4C2211yescharacteristic
29C22×C11×C22⋊C4C2211yescharacteristic
30C22×C11×C22⋊C4C2211yescharacteristic
31C22×C11×C22⋊C4C2211yescharacteristic
32C22×C11×C22⋊C4C2211yescharacteristic
33C22×C11×C22⋊C4C2211yescharacteristic
34C22×C42×C11C2211yescharacteristic
35C11×#400—24no—
36C11×#396—24no—
37C11×#390—24no—
38C11×#386—24no—
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
55C25×C11C2311yescharacteristic
56C25×C11C2311yescharacteristic
57C22×D4×C11—22no—
58C22×D4×C11—22no—
59C22×D4×C11—22no—
60C22×D4×C11—22no—
61C22×D4×C11—41no—
62C22×D4×C11—41no—
63C22×D4×C11Q814yes—
64C23×C4×C11—22no—
65C23×C4×C11—22no—
66C23×C4×C11—22no—
67C23×C4×C11—41no—
68C23×C4×C11—41no—
69C23×C4×C11—41no—
70C23×C4×C11—41no—
71C23×C4×C11C2311yescharacteristic
72C23×C4×C11C2311yescharacteristic
73C23×C4×C11C2311yescharacteristic
74C23×C4×C11C2311yescharacteristic
75C23×C4×C11C2311yescharacteristic
76C23×C4×C11C2311yescharacteristic
77C23×C4×C11C2311yescharacteristic
78C23×C4×C11C2311yescharacteristic
79C23×C4×C11C2311yescharacteristic
80C23×C4×C11C2311yescharacteristic
81C23×C4×C11C2311yescharacteristic
82C23×C4×C11C2311yescharacteristic
83C23×C4×C11C2311yescharacteristic
84C2×C11×C4⋊C4—22no—
85C2×C11×C4⋊C4—22no—
86C2×C11×C4⋊C4—22no—
87C2×C11×C4⋊C4—22no—
88C2×C11×C4⋊C4—22no—
89C2×C11×C4⋊C4—22no—
90C2×C11×C4⋊C4—22no—
91C2×C11×C4⋊C4—41no—
92C2×C11×C4⋊C4—41no—
93C2×C11×C4⋊C4—41no—
94C2×C11×C4⋊C4—41no—
95C2×C11×C4⋊C4—41no—
96C2×C11×C4⋊C4—41no—
97C2×C11×C4⋊C4—41no—
98C2×C11×C4⋊C4—41no—
99C2×C11×C22⋊C4—22no—
100C2×C11×C22⋊C4—22no—
101C2×C11×C22⋊C4—22no—
102C2×C11×C22⋊C4—22no—
103C2×C11×C22⋊C4—22no—
104C2×C11×C22⋊C4—22no—
105C2×C11×C22⋊C4—22no—
106C2×C11×C22⋊C4—22no—
107C2×C11×C22⋊C4—22no—
108C2×C11×C22⋊C4—22no—
109C2×C11×C22⋊C4—22no—
110C2×C11×C22⋊C4—22no—
111C2×C11×C22⋊C4—22no—
112C2×C11×C22⋊C4—22no—
113C2×C11×C22⋊C4—22no—
114C2×C11×C22⋊C4—22no—
115C2×C11×C22⋊C4—41no—
116C2×C11×C22⋊C4—41no—
117C2×C11×C22⋊C4—41no—
118C2×C11×C22⋊C4—41no—
119C2×C11×C22⋊C4—41no—
120C2×C11×C22⋊C4—41no—
121C2×C11×C22⋊C4—41no—
122C2×C11×C22⋊C4—41no—
123C2×C11×C22⋊C4—41no—
124C2×C11×C22⋊C4—41no—
125C2×C11×C22⋊C4—41no—
126C2×C11×C22⋊C4—41no—
127C2×C11×C22⋊C4—41no—
128C2×C11×C22⋊C4—41no—
129C2×C11×C22⋊C4—41no—
130C2×C11×C22⋊C4—41no—
131C2×C11×C22⋊C4D414yes—
132C2×C42×C11—22no—
133C2×C42×C11—22no—
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—41no—
146C11×#95—41no—
147C11×#95—41no—
148C11×#95—41no—
149C11×#95—41no—
150C11×#95D414yes—
151#15508C1111yesmaximal, characteristic, direct product factor, Sylow
152C24×C11—21no—
153C24×C11—21no—
154C24×C11—21no—
155C24×C11—21no—
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×C11—21no—
165C24×C11—21no—
166C24×C11—21no—
167C24×C11—21no—
168C24×C11—21no—
169C24×C11—21no—
170C24×C11—21no—
171C24×C11—21no—
172C24×C11—21no—
173C24×C11—21no—
174C24×C11—21no—
175C24×C11—21no—
176C24×C11—21no—
177C24×C11—21no—
178C24×C11C2×D412yes—
179C24×C11C2×Q812yes—
180C24×C11C2×Q812yes—
181C24×C11#4112yes—
182C24×C11C2411yescharacteristic
183C2×D4×C11—28no—
184C2×D4×C11—28no—
185C2×D4×C11—44no—
186C2×D4×C11—44no—
187C2×D4×C11—44no—
188C2×D4×C11—44no—
189C2×D4×C11—44no—
190C22×C4×C11—21no—
191C22×C4×C11—21no—
192C22×C4×C11—21no—
193C22×C4×C11—21no—
194C22×C4×C11—21no—
195C22×C4×C11—21no—
196C22×C4×C11—21no—
197C22×C4×C11—21no—
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—21no—
247C22×C4×C11—21no—
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—21no—
263C22×C4×C11—21no—
264C22×C4×C11—21no—
265C22×C4×C11—21no—
266C22×C4×C11—21no—
267C22×C4×C11—21no—
268C22×C4×C11—21no—
269C22×C4×C11—21no—
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×C11C2×D412yes—
278C22×C4×C11C2×D412yes—
279C22×C4×C11C2×D412yes—
280C22×C4×C11C2×D412yes—
281C22×C4×C11C2×D412yes—
282C22×C4×C11C2×Q812yes—
283C22×C4×C11#4112yes—
284C22×C4×C11#4112yes—
285C22×C4×C11#4112yes—
286C22×C4×C11#4112yes—
287C22×C4×C11#4112yes—
288C11×C4⋊C4—44no—
289C11×C4⋊C4—44no—
290C11×C4⋊C4—44no—
291C11×C4⋊C4—44no—
292C11×C4⋊C4—44no—
293C11×C22⋊C4—44no—
294C11×C22⋊C4—44no—
295C11×C22⋊C4—44no—
296C11×C22⋊C4—44no—
297C11×C22⋊C4—44no—
298C11×C22⋊C4—44no—
299C11×C22⋊C4—44no—
300C11×C22⋊C4—44no—
301C11×C22⋊C4—44no—
302C11×C22⋊C4—44no—
303C11×C22⋊C4—44no—
304C42×C11—44no—
305C2×#400C2×C1111yescharacteristic, complemented
306C2×#396C2×C1111yescharacteristic, complemented
307C2×#390C2×C1111yescharacteristic
308C2×#386C2×C1111yescharacteristic
309#1444C2×C1111yescharacteristic, complemented
310#1439C2×C1111yescharacteristic, complemented
311#1439C2×C1111yescharacteristic, complemented
312#1439C2×C1111yescharacteristic, complemented
313#1439C2×C1111yescharacteristic, complemented
314#1439C2×C1111yescharacteristic, complemented
315#1438C2×C1111yescharacteristic
316#1436C2×C1111yescharacteristic, complemented
317#1434C2×C1111yescharacteristic, complemented
318C22⋊#95C2×C1111yescharacteristic, complemented
319C22⋊#95C2×C1111yescharacteristic, complemented
320C23×C11—22no—
321C23×C11—22no—
322C23×C11—22no—
323C23×C11—22no—
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—41no—
346C23×C11—41no—
347C23×C11—41no—
348C23×C11—41no—
349C23×C11—41no—
350C23×C11—41no—
351C23×C11—41no—
352C23×C11—41no—
353C23×C11—41no—
354C23×C11—41no—
355C23×C11—41no—
356C23×C11—41no—
357C23×C11—41no—
358C23×C11—41no—
359C23×C11—41no—
360C23×C11—41no—
361C23×C11—41no—
362C23×C11—41no—
363C23×C11—41no—
364C23×C11—41no—
365C23×C11—41no—
366C23×C11—41no—
367C23×C11—41no—
368C23×C11—41no—
369C23×C11—41no—
370C23×C11—41no—
371C23×C11—41no—
372C23×C11—41no—
373C23×C11—41no—
374C23×C11—41no—
375C23×C11—41no—
376C23×C11—41no—
377C23×C11—41no—
378C23×C11—41no—
379C23×C11—41no—
380C23×C11—41no—
381C23×C11—41no—
382C23×C11—41no—
383C23×C11—41no—
384C23×C11—41no—
385C23×C11—41no—
386C23×C11—41no—
387C23×C11—41no—
388C23×C11—41no—
389C23×C11C22⋊Q814yes—
390C23×C11C22×D411yescharacteristic
391C23×C11C22×D411yescharacteristic
392C23×C11C22×Q811yescharacteristic
393C23×C11C2×#4111yescharacteristic
394C23×C11C2×#4111yescharacteristic
395C23×C11C2×#4111yescharacteristic
396C23×C11C2×#4111yescharacteristic
397C23×C11C2×#4111yescharacteristic
398C23×C11C2×#4111yescharacteristic
399C23×C11H(5,𝔽2)11yescharacteristic
400C23×C11H(5,𝔽2)11yescharacteristic
401C23×C11H(5,𝔽2)11yescharacteristic
402C23×C11H(5,𝔽2)11yescharacteristic
403C23×C11H(5,𝔽2)11yescharacteristic
404C23×C11H(5,𝔽2)11yescharacteristic
405D4×C11—416no—
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—22no—
424C2×C4×C11—22no—
425C2×C4×C11—22no—
426C2×C4×C11—22no—
427C2×C4×C11—22no—
428C2×C4×C11—22no—
429C2×C4×C11—22no—
430C2×C4×C11—22no—
431C2×C4×C11—22no—
432C2×C4×C11—22no—
433C2×C4×C11—22no—
434C2×C4×C11—22no—
435C2×C4×C11—22no—
436C2×C4×C11—416no—
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×C11—41no—
473C2×C4×C11—41no—
474C2×C4×C11—41no—
475C2×C4×C11—41no—
476C2×C4×C11—41no—
477C2×C4×C11—41no—
478C2×C4×C11—41no—
479C2×C4×C11—41no—
480C2×C4×C11—41no—
481C2×C4×C11—41no—
482C2×C4×C11—41no—
483C2×C4×C11—41no—
484C2×C4×C11—41no—
485C2×C4×C11—41no—
486C2×C4×C11—41no—
487C2×C4×C11—41no—
488C2×C4×C11—41no—
489C2×C4×C11—41no—
490C2×C4×C11—41no—
491C2×C4×C11—41no—
492C2×C4×C11—41no—
493C2×C4×C11—41no—
494C2×C4×C11—41no—
495C2×C4×C11—41no—
496C2×C4×C11—41no—
497C2×C4×C11C22⋊Q814yes—
498C23×D4C22×C1111yescharacteristic
499C24×C4C22×C1111yescharacteristic
500C22×C4⋊C4C22×C1111yescharacteristic
501C22×C4⋊C4C22×C1111yescharacteristic
502C22×C4⋊C4C22×C1111yescharacteristic
503C22×C4⋊C4C22×C1111yescharacteristic
504C22×C4⋊C4C22×C1111yescharacteristic
505C22×C22⋊C4C22×C1111yescharacteristic
506C22×C22⋊C4C22×C1111yescharacteristic
507C22×C22⋊C4C22×C1111yescharacteristic
508C22×C22⋊C4C22×C1111yescharacteristic
509C22×C22⋊C4C22×C1111yescharacteristic
510C22×C22⋊C4C22×C1111yescharacteristic
511C22×C22⋊C4C22×C1111yescharacteristic
512C22×C22⋊C4C22×C1111yescharacteristic
513C22×C22⋊C4C22×C1111yescharacteristic
514C22×C22⋊C4C22×C1111yescharacteristic
515C22×C22⋊C4C22×C1111yescharacteristic
516C22×C42C22×C1111yescharacteristic
517#400—24no—
518#396—24no—
519#390—24no—
520#386—24no—
521C2×#95C22×C1111yescharacteristic
522C2×#95C22×C1111yescharacteristic
523C2×#95C22×C1111yescharacteristic
524C2×#95C22×C1111yescharacteristic
525C2×#95C22×C1111yescharacteristic
526C2×#95C22×C1111yescharacteristic
527C2×#95C22×C1111yescharacteristic
528C2×#95C22×C1111yescharacteristic
529C2×#95C22×C1111yescharacteristic
530C2×#95C22×C1111yescharacteristic
531C2×#95C22×C1111yescharacteristic
532C2×#95C22×C1111yescharacteristic
533C2×#95C22×C1111yescharacteristic
534C2×#95C22×C1111yescharacteristic
535C2×#95C22×C1111yescharacteristic
536C2×#95C22×C1111yescharacteristic
537C22×C11—24no—
538C22×C11—24no—
539C22×C11—24no—
540C22×C11—42no—
541C22×C11—42no—
542C22×C11—42no—
543C22×C11—42no—
544C22×C11—42no—
545C22×C11—42no—
546C22×C11—42no—
547C22×C11—42no—
548C22×C11—42no—
549C22×C11—42no—
550C22×C11—42no—
551C22×C11—42no—
552C22×C11—42no—
553C22×C11—42no—
554C22×C11—42no—
555C22×C11—42no—
556C22×C11—42no—
557C22×C11—42no—
558C22×C11—42no—
559C22×C11—81no—
560C22×C11—81no—
561C22×C11—81no—
562C22×C11—81no—
563C22×C11—81no—
564C22×C11—81no—
565C22×C11—81no—
566C22×C11—81no—
567C22×C11C2×C22⋊Q811yescharacteristic
568C22×C11C2×C22⋊Q811yescharacteristic
569C22×C11#52911yescharacteristic
570C22×C11#52911yescharacteristic
571C22×C11#53211yescharacteristic
572C22×C11#53211yescharacteristic
573C22×C11#53411yescharacteristic
574C22×C11#53511yescharacteristic
575C22×C11#53811yescharacteristic
576C22×C11#53811yescharacteristic
577C22×C11#53811yescharacteristic
578C22×C11#53811yescharacteristic
579C22×C11#54011yescharacteristic
580C22×C11#54011yescharacteristic
581C22×C11#54311yescharacteristic
582C22×C11D4211yescharacteristic
583C22×C11#54611yescharacteristic
584C22×C11#54611yescharacteristic
585C22×C11#54611yescharacteristic
586C22×C11#54611yescharacteristic
587C22×C11#54611yescharacteristic
588C22×C11#55011yescharacteristic
589C22×C11#55111yescharacteristic
590C22×C11#55111yescharacteristic
591C22×C11#55111yescharacteristic
592C22×C11#55311yescharacteristic
593C22×C11#55311yescharacteristic
594C22×C11#55311yescharacteristic
595C22×C11#55411yescharacteristic
596C22×C11#55411yescharacteristic
597C22×C11#55411yescharacteristic
598C22×C11#55411yescharacteristic
599C22×C11#55511yescharacteristic
600C22×C11#56011yescharacteristic
601C22×C11#56011yescharacteristic
602C4×C11—24no—
603C4×C11—42no—
604C4×C11—42no—
605C4×C11—42no—
606C4×C11—42no—
607C4×C11—42no—
608C4×C11—42no—
609C4×C11—42no—
610C4×C11—42no—
611C4×C11—81no—
612C4×C11—81no—
613C4×C11—81no—
614C4×C11—81no—
615C25C23×C1111yescharacteristic
616C25C23×C1111yescharacteristic
617C22×D4—22no—
618C22×D4—22no—
619C22×D4—22no—
620C22×D4—22no—
621C22×D4—41no—
622C22×D4—41no—
623C22×D4Q8×C1114yes—
624C23×C4—22no—
625C23×C4—22no—
626C23×C4—22no—
627C23×C4—41no—
628C23×C4—41no—
629C23×C4—41no—
630C23×C4—41no—
631C23×C4C23×C1111yescharacteristic
632C23×C4C23×C1111yescharacteristic
633C23×C4C23×C1111yescharacteristic
634C23×C4C23×C1111yescharacteristic
635C23×C4C23×C1111yescharacteristic
636C23×C4C23×C1111yescharacteristic
637C23×C4C23×C1111yescharacteristic
638C23×C4C23×C1111yescharacteristic
639C23×C4C23×C1111yescharacteristic
640C23×C4C23×C1111yescharacteristic
641C23×C4C23×C1111yescharacteristic
642C23×C4C23×C1111yescharacteristic
643C23×C4C23×C1111yescharacteristic
644C2×C4⋊C4—22no—
645C2×C4⋊C4—22no—
646C2×C4⋊C4—22no—
647C2×C4⋊C4—22no—
648C2×C4⋊C4—22no—
649C2×C4⋊C4—22no—
650C2×C4⋊C4—22no—
651C2×C4⋊C4—41no—
652C2×C4⋊C4—41no—
653C2×C4⋊C4—41no—
654C2×C4⋊C4—41no—
655C2×C4⋊C4—41no—
656C2×C4⋊C4—41no—
657C2×C4⋊C4—41no—
658C2×C4⋊C4—41no—
659C2×C22⋊C4—22no—
660C2×C22⋊C4—22no—
661C2×C22⋊C4—22no—
662C2×C22⋊C4—22no—
663C2×C22⋊C4—22no—
664C2×C22⋊C4—22no—
665C2×C22⋊C4—22no—
666C2×C22⋊C4—22no—
667C2×C22⋊C4—22no—
668C2×C22⋊C4—22no—
669C2×C22⋊C4—22no—
670C2×C22⋊C4—22no—
671C2×C22⋊C4—22no—
672C2×C22⋊C4—22no—
673C2×C22⋊C4—22no—
674C2×C22⋊C4—22no—
675C2×C22⋊C4—41no—
676C2×C22⋊C4—41no—
677C2×C22⋊C4—41no—
678C2×C22⋊C4—41no—
679C2×C22⋊C4—41no—
680C2×C22⋊C4—41no—
681C2×C22⋊C4—41no—
682C2×C22⋊C4—41no—
683C2×C22⋊C4—41no—
684C2×C22⋊C4—41no—
685C2×C22⋊C4—41no—
686C2×C22⋊C4—41no—
687C2×C22⋊C4—41no—
688C2×C22⋊C4—41no—
689C2×C22⋊C4—41no—
690C2×C22⋊C4—41no—
691C2×C22⋊C4D4×C1114yes—
692C2×C42—22no—
693C2×C42—22no—
694C2×C42—41no—
695#95—22no—
696#95—22no—
697#95—22no—
698#95—22no—
699#95—22no—
700#95—22no—
701#95—22no—
702#95—22no—
703#95—22no—
704#95—22no—
705#95—41no—
706#95—41no—
707#95—41no—
708#95—41no—
709#95—41no—
710#95D4×C1114yes—
711C2×C11—44no—
712C2×C11—82no—
713C2×C11#243711yescharacteristic
714C2×C11#245011yescharacteristic
715C2×C11#245411yescharacteristic
716C2×C11#252611yescharacteristic
717C2×C11#255411yescharacteristic
718C2×C11#255511yescharacteristic
719C2×C11#255911yescharacteristic
720C2×C11#256411yescharacteristic
721C2×C11#256611yescharacteristic
722C2×C11#267311yescharacteristic
723C2×C11#268511yescharacteristic
724C2×C11#268811yescharacteristic
725C2×C11#274911yescharacteristic
726C2×C11#278011yescharacteristic
727C2×C11#278411yescharacteristic
728C24—21no—
729C24—21no—
730C24—21no—
731C24—21no—
732C24—21no—
733C24—21no—
734C24—21no—
735C24—21no—
736C24—21no—
737C24—21no—
738C24—21no—
739C24—21no—
740C24—21no—
741C24—21no—
742C24—21no—
743C24—21no—
744C24—21no—
745C24—21no—
746C24—21no—
747C24—21no—
748C24—21no—
749C24—21no—
750C24—21no—
751C24—21no—
752C24—21no—
753C24—21no—
754C24C2×D4×C1112yes—
755C24C2×Q8×C1112yes—
756C24C2×Q8×C1112yes—
757C24C11×#4112yes—
758C24C24×C1111yescharacteristic
759C2×D4—28no—
760C2×D4—28no—
761C2×D4—44no—
762C2×D4—44no—
763C2×D4—44no—
764C2×D4—44no—
765C2×D4—44no—
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—21no—
786C22×C4—21no—
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—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—44no—
847C22×C4—44no—
848C22×C4—44no—
849C22×C4—44no—
850C22×C4—44no—
851C22×C4—44no—
852C22×C4—44no—
853C22×C4C2×D4×C1112yes—
854C22×C4C2×D4×C1112yes—
855C22×C4C2×D4×C1112yes—
856C22×C4C2×D4×C1112yes—
857C22×C4C2×D4×C1112yes—
858C22×C4C2×Q8×C1112yes—
859C22×C4C11×#4112yes—
860C22×C4C11×#4112yes—
861C22×C4C11×#4112yes—
862C22×C4C11×#4112yes—
863C22×C4C11×#4112yes—
864C4⋊C4—44no—
865C4⋊C4—44no—
866C4⋊C4—44no—
867C4⋊C4—44no—
868C4⋊C4—44no—
869C22⋊C4—44no—
870C22⋊C4—44no—
871C22⋊C4—44no—
872C22⋊C4—44no—
873C22⋊C4—44no—
874C22⋊C4—44no—
875C22⋊C4—44no—
876C22⋊C4—44no—
877C22⋊C4—44no—
878C22⋊C4—44no—
879C22⋊C4—44no—
880C42—44no—
881C11#1550811yescharacteristic, direct product factor, Sylow
882C23—22no—
883C23—22no—
884C23—22no—
885C23—22no—
886C23—22no—
887C23—22no—
888C23—22no—
889C23—22no—
890C23—22no—
891C23—22no—
892C23—22no—
893C23—22no—
894C23—22no—
895C23—22no—
896C23—22no—
897C23—22no—
898C23—22no—
899C23—22no—
900C23—22no—
901C23—22no—
902C23—22no—
903C23—22no—
904C23—22no—
905C23—22no—
906C23—22no—
907C23—41no—
908C23—41no—
909C23—41no—
910C23—41no—
911C23—41no—
912C23—41no—
913C23—41no—
914C23—41no—
915C23—41no—
916C23—41no—
917C23—41no—
918C23—41no—
919C23—41no—
920C23—41no—
921C23—41no—
922C23—41no—
923C23—41no—
924C23—41no—
925C23—41no—
926C23—41no—
927C23—41no—
928C23—41no—
929C23—41no—
930C23—41no—
931C23—41no—
932C23—41no—
933C23—41no—
934C23—41no—
935C23—41no—
936C23—41no—
937C23—41no—
938C23—41no—
939C23—41no—
940C23—41no—
941C23—41no—
942C23—41no—
943C23—41no—
944C23—41no—
945C23—41no—
946C23—41no—
947C23—41no—
948C23—41no—
949C23—41no—
950C23—41no—
951C23C11×C22⋊Q814yes—
952C23C22×D4×C1111yescharacteristic
953C23C22×D4×C1111yescharacteristic
954C23C22×Q8×C1111yescharacteristic
955C23C2×C11×#4111yescharacteristic
956C23C2×C11×#4111yescharacteristic
957C23C2×C11×#4111yescharacteristic
958C23C2×C11×#4111yescharacteristic
959C23C2×C11×#4111yescharacteristic
960C23C2×C11×#4111yescharacteristic
961C23C11×H(5,𝔽2)11yescharacteristic
962C23C11×H(5,𝔽2)11yescharacteristic
963C23C11×H(5,𝔽2)11yescharacteristic
964C23C11×H(5,𝔽2)11yescharacteristic
965C23C11×H(5,𝔽2)11yescharacteristic
966C23C11×H(5,𝔽2)11yescharacteristic
967D4—416no—
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—22no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—416no—
999C2×C4—41no—
1000C2×C4—41no—
1001C2×C4—41no—
1002C2×C4—41no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—41no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4C11×C22⋊Q814yes—
1060C22—24no—
1061C22—24no—
1062C22—24no—
1063C22—42no—
1064C22—42no—
1065C22—42no—
1066C22—42no—
1067C22—42no—
1068C22—42no—
1069C22—42no—
1070C22—42no—
1071C22—42no—
1072C22—42no—
1073C22—42no—
1074C22—42no—
1075C22—42no—
1076C22—42no—
1077C22—42no—
1078C22—42no—
1079C22—42no—
1080C22—42no—
1081C22—42no—
1082C22—81no—
1083C22—81no—
1084C22—81no—
1085C22—81no—
1086C22—81no—
1087C22—81no—
1088C22—81no—
1089C22—81no—
1090C22C2×C11×C22⋊Q811yescharacteristic
1091C22C2×C11×C22⋊Q811yescharacteristic
1092C22C11×#52911yescharacteristic
1093C22C11×#52911yescharacteristic
1094C22C11×#53211yescharacteristic
1095C22C11×#53211yescharacteristic
1096C22C11×#53411yescharacteristic
1097C22C11×#53511yescharacteristic
1098C22C11×#53811yescharacteristic
1099C22C11×#53811yescharacteristic
1100C22C11×#53811yescharacteristic
1101C22C11×#53811yescharacteristic
1102C22C11×#54011yescharacteristic
1103C22C11×#54011yescharacteristic
1104C22C11×#54311yescharacteristic
1105C22D42×C1111yescharacteristic
1106C22C11×#54611yescharacteristic
1107C22C11×#54611yescharacteristic
1108C22C11×#54611yescharacteristic
1109C22C11×#54611yescharacteristic
1110C22C11×#54611yescharacteristic
1111C22C11×#55011yescharacteristic
1112C22C11×#55111yescharacteristic
1113C22C11×#55111yescharacteristic
1114C22C11×#55111yescharacteristic
1115C22C11×#55311yescharacteristic
1116C22C11×#55311yescharacteristic
1117C22C11×#55311yescharacteristic
1118C22C11×#55411yescharacteristic
1119C22C11×#55411yescharacteristic
1120C22C11×#55411yescharacteristic
1121C22C11×#55411yescharacteristic
1122C22C11×#55511yescharacteristic
1123C22C11×#56011yescharacteristic
1124C22C11×#56011yescharacteristic
1125C4—24no—
1126C4—42no—
1127C4—42no—
1128C4—42no—
1129C4—42no—
1130C4—42no—
1131C4—42no—
1132C4—42no—
1133C4—42no—
1134C4—81no—
1135C4—81no—
1136C4—81no—
1137C4—81no—
1138C2—44no—
1139C2—82no—
1140C2C11×#243711yescharacteristic
1141C2C11×#245011yescharacteristic
1142C2C11×#245411yescharacteristic
1143C2C11×#252611yescharacteristic
1144C2C11×#255411yescharacteristic
1145C2C11×#255511yescharacteristic
1146C2C11×#255911yescharacteristic
1147C2C11×#256411yescharacteristic
1148C2C11×#256611yescharacteristic
1149C2C11×#267311yescharacteristic
1150C2C11×#268511yescharacteristic
1151C2C11×#268811yescharacteristic
1152C2C11×#274911yescharacteristic
1153C2C11×#278011yescharacteristic
1154C2C11×#278411yescharacteristic
subgroupG/H
center, socleC24×C11C24
commutator, Frattini, cosocleC24C24×C11
prime radicalC23×D4×C11C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#400C2semidirect
2. C2×C11×#396C2semidirect
5. C11×#1444C2semidirect
6. C11×#1439C2semidirect
7. C11×#1439C2semidirect
8. C11×#1439C2semidirect
9. C11×#1439C2semidirect
10. C11×#1439C2semidirect
12. C11×#1436C2semidirect
13. C11×#1434C2semidirect
14. C11×C22⋊#95C2semidirect
15. C11×C22⋊#95C2semidirect
151. #15508C11direct (N × H)
305. C2×#400C2×C11semidirect
306. C2×#396C2×C11semidirect
309. #1444C2×C11semidirect
310. #1439C2×C11semidirect
311. #1439C2×C11semidirect
312. #1439C2×C11semidirect
313. #1439C2×C11semidirect
314. #1439C2×C11semidirect
316. #1436C2×C11semidirect
317. #1434C2×C11semidirect
318. C22⋊#95C2×C11semidirect
319. C22⋊#95C2×C11semidirect
881. C11#15508direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4002
C2×C11×#3962
C2×C11×#3902
C2×C11×#3862
C11×#14442
C11×#14392
C11×#14382
C11×#14362
C11×#14342
C11×C22⋊#952
#1550811