Finite Group Databasebeta

← C11×#14100 #14591293

Subgroups — C11×#14100 #14591293

Order 2816.

2690 conjugacy classes of subgroups.

The subgroup lattice has 1360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×#121C211yesmaximal, characteristic
2C2×C11×#390C211yesmaximal, characteristic, complemented
3C2×C11×#388C211yesmaximal, characteristic, complemented
4C2×C11×#386C211yesmaximal, characteristic, complemented
5C2×C11×#386C211yesmaximal, characteristic, complemented
6C2×C4×C11×C22⋊C4C211yesmaximal, characteristic, complemented
7C2×C4×C11×C22⋊C4C211yesmaximal, characteristic, complemented
8C11×#1441C211yesmaximal, characteristic, complemented
9C11×#1438C211yesmaximal, characteristic, complemented
10C11×#1438C211yesmaximal, characteristic, complemented
11C11×#1438C211yesmaximal, characteristic, complemented
12C11×#1437C211yesmaximal, characteristic, complemented
13C11×#1437C211yesmaximal, characteristic, complemented
14C11×#1436C211yesmaximal, characteristic, complemented
15C11×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×D4×C11C2211yescharacteristic
17C23×D4×C11C2211yescharacteristic
18C23×D4×C11C2211yescharacteristic
19C24×C4×C11C2211yescharacteristic
20C24×C4×C11C2211yescharacteristic
21C2×C11×#121—24no—
22C2×C11×#121—24no—
23C2×C11×#121C418yescomplemented
24C22×C11×C4⋊C4C2211yescharacteristic
25C22×C11×C4⋊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×C11×C22⋊C4C2211yescharacteristic
35C22×C11×C22⋊C4C2211yescharacteristic
36C22×C11×C22⋊C4C2211yescharacteristic
37C22×C11×C22⋊C4C2211yescharacteristic
38C22×C11×C22⋊C4C2211yescharacteristic
39C22×C42×C11C2211yescharacteristic
40C22×C42×C11C2211yescharacteristic
41C22×C42×C11C2211yescharacteristic
42C11×#390—24no—
43C11×#388—24no—
44C11×#386—24no—
45C11×#386—24no—
46C4×C11×C22⋊C4—24no—
47C4×C11×C22⋊C4—24no—
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
58C2×C11×#95C2211yescharacteristic
59C2×C11×#95C2211yescharacteristic
60C25×C11C2311yescharacteristic
61C25×C11C2311yescharacteristic
62C25×C11C2311yescharacteristic
63C22×D4×C11—22no—
64C22×D4×C11—22no—
65C22×D4×C11—22no—
66C22×D4×C11—22no—
67C22×D4×C11—22no—
68C22×D4×C11—22no—
69C22×D4×C11—22no—
70C22×D4×C11—22no—
71C22×D4×C11—22no—
72C22×D4×C11—22no—
73C22×D4×C11—22no—
74C22×D4×C11—22no—
75C22×D4×C11—41no—
76C22×D4×C11—41no—
77C22×D4×C11—41no—
78C22×D4×C11—41no—
79C22×D4×C11—41no—
80C22×D4×C11—41no—
81C22×D4×C11C2×C414yes—
82C22×D4×C11C2×C414yes—
83C22×D4×C11C2×C414yescomplemented
84C23×C4×C11—22no—
85C23×C4×C11—22no—
86C23×C4×C11—22no—
87C23×C4×C11—22no—
88C23×C4×C11—22no—
89C23×C4×C11—22no—
90C23×C4×C11—22no—
91C23×C4×C11—22no—
92C23×C4×C11—22no—
93C23×C4×C11—41no—
94C23×C4×C11—41no—
95C23×C4×C11—41no—
96C23×C4×C11—41no—
97C23×C4×C11C2×C414yescomplemented
98C23×C4×C11C2311yescharacteristic
99C23×C4×C11C2311yescharacteristic
100C23×C4×C11C2311yescharacteristic
101C23×C4×C11C2311yescharacteristic
102C23×C4×C11C2311yescharacteristic
103C23×C4×C11C2311yescharacteristic
104C23×C4×C11C2311yescharacteristic
105C23×C4×C11C2311yescharacteristic
106C23×C4×C11C2311yescharacteristic
107C23×C4×C11C2311yescharacteristic
108C23×C4×C11C2311yescharacteristic
109C23×C4×C11C2311yescharacteristic
110C11×#121—232no—
111C2×C11×C4⋊C4—22no—
112C2×C11×C4⋊C4—22no—
113C2×C11×C4⋊C4—22no—
114C2×C11×C4⋊C4—22no—
115C2×C11×C4⋊C4—41no—
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⋊C4—22no—
125C2×C11×C22⋊C4—22no—
126C2×C11×C22⋊C4—22no—
127C2×C11×C22⋊C4—22no—
128C2×C11×C22⋊C4—22no—
129C2×C11×C22⋊C4—22no—
130C2×C11×C22⋊C4—22no—
131C2×C11×C22⋊C4—22no—
132C2×C11×C22⋊C4—22no—
133C2×C11×C22⋊C4—22no—
134C2×C11×C22⋊C4—22no—
135C2×C11×C22⋊C4—22no—
136C2×C11×C22⋊C4—22no—
137C2×C11×C22⋊C4—22no—
138C2×C11×C22⋊C4—22no—
139C2×C11×C22⋊C4—22no—
140C2×C11×C22⋊C4—22no—
141C2×C11×C22⋊C4—22no—
142C2×C11×C22⋊C4—22no—
143C2×C11×C22⋊C4—41no—
144C2×C11×C22⋊C4—41no—
145C2×C11×C22⋊C4—41no—
146C2×C11×C22⋊C4—41no—
147C2×C11×C22⋊C4—41no—
148C2×C11×C22⋊C4—41no—
149C2×C11×C22⋊C4—41no—
150C2×C11×C22⋊C4—41no—
151C2×C11×C22⋊C4C2×C414yes—
152C2×C11×C22⋊C4C2×C414yescomplemented
153C2×C11×C22⋊C4D414yes—
154C2×C11×C22⋊C4D414yes—
155C2×C11×C22⋊C4D414yescomplemented
156C2×C42×C11—22no—
157C2×C42×C11—22no—
158C2×C42×C11—22no—
159C2×C42×C11—22no—
160C2×C42×C11—22no—
161C2×C42×C11—22no—
162C2×C42×C11—41no—
163C2×C42×C11—41no—
164C2×C42×C11—41no—
165C11×#95—22no—
166C11×#95—22no—
167C11×#95—22no—
168C11×#95—22no—
169C11×#95—22no—
170C11×#95—22no—
171C11×#95—22no—
172C11×#95—22no—
173C11×#95—22no—
174C11×#95—41no—
175C11×#95—41no—
176C11×#95D414yescomplemented
177#14100C1111yesmaximal, characteristic, direct product factor, Sylow
178C24×C11—21no—
179C24×C11—21no—
180C24×C11—21no—
181C24×C11—21no—
182C24×C11—21no—
183C24×C11—21no—
184C24×C11—21no—
185C24×C11—21no—
186C24×C11—21no—
187C24×C11—21no—
188C24×C11—21no—
189C24×C11—21no—
190C24×C11—21no—
191C24×C11—21no—
192C24×C11—21no—
193C24×C11—21no—
194C24×C11—21no—
195C24×C11—21no—
196C24×C11—21no—
197C24×C11—21no—
198C24×C11—21no—
199C24×C11—21no—
200C24×C11—21no—
201C24×C11—21no—
202C24×C11—21no—
203C24×C11—21no—
204C24×C11—21no—
205C24×C11—21no—
206C24×C11—21no—
207C24×C11—21no—
208C24×C11—21no—
209C24×C11—21no—
210C24×C11—21no—
211C24×C11—21no—
212C24×C11—21no—
213C24×C11—21no—
214C24×C11—21no—
215C24×C11—21no—
216C24×C11C22×C412yes—
217C24×C11C22×C412yes—
218C24×C11C22×C412yes—
219C24×C11C2×D412yes—
220C24×C11C2×D412yes—
221C24×C11C2×D412yes—
222C24×C11#4112yes—
223C24×C11C2411yescharacteristic
224C2×D4×C11—28no—
225C2×D4×C11—28no—
226C2×D4×C11—28no—
227C2×D4×C11—28no—
228C2×D4×C11—28no—
229C2×D4×C11—28no—
230C2×D4×C11—44no—
231C2×D4×C11—44no—
232C2×D4×C11—44no—
233C2×D4×C11—44no—
234C2×D4×C11—44no—
235C2×D4×C11—44no—
236C2×D4×C11—44no—
237C2×D4×C11—44no—
238C2×D4×C11—44no—
239C2×D4×C11—44no—
240C2×D4×C11—44no—
241C2×D4×C11—44no—
242C2×D4×C11—44no—
243C2×D4×C11—44no—
244C2×D4×C11—44no—
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—28no—
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—21no—
271C22×C4×C11—21no—
272C22×C4×C11—21no—
273C22×C4×C11—21no—
274C22×C4×C11—21no—
275C22×C4×C11—21no—
276C22×C4×C11—21no—
277C22×C4×C11—21no—
278C22×C4×C11—21no—
279C22×C4×C11—21no—
280C22×C4×C11—21no—
281C22×C4×C11—21no—
282C22×C4×C11—21no—
283C22×C4×C11—21no—
284C22×C4×C11—21no—
285C22×C4×C11—21no—
286C22×C4×C11—21no—
287C22×C4×C11—21no—
288C22×C4×C11—21no—
289C22×C4×C11—21no—
290C22×C4×C11—21no—
291C22×C4×C11—21no—
292C22×C4×C11—21no—
293C22×C4×C11—21no—
294C22×C4×C11—21no—
295C22×C4×C11—21no—
296C22×C4×C11—21no—
297C22×C4×C11—21no—
298C22×C4×C11—28no—
299C22×C4×C11—28no—
300C22×C4×C11—21no—
301C22×C4×C11—21no—
302C22×C4×C11—21no—
303C22×C4×C11—21no—
304C22×C4×C11—21no—
305C22×C4×C11—21no—
306C22×C4×C11—21no—
307C22×C4×C11—21no—
308C22×C4×C11—21no—
309C22×C4×C11—21no—
310C22×C4×C11—21no—
311C22×C4×C11—21no—
312C22×C4×C11—21no—
313C22×C4×C11—21no—
314C22×C4×C11—44no—
315C22×C4×C11—44no—
316C22×C4×C11—44no—
317C22×C4×C11—44no—
318C22×C4×C11—44no—
319C22×C4×C11—44no—
320C22×C4×C11—44no—
321C22×C4×C11—44no—
322C22×C4×C11—44no—
323C22×C4×C11—44no—
324C22×C4×C11—44no—
325C22×C4×C11C22×C412yes—
326C22×C4×C11C22×C412yes—
327C22×C4×C11C22×C412yes—
328C22×C4×C11C22×C412yes—
329C22×C4×C11C2×D412yes—
330C22×C4×C11C2×D412yes—
331C22×C4×C11C2×D412yes—
332C22×C4×C11C2×D412yes—
333C22×C4×C11C2×D412yes—
334C22×C4×C11C2×D412yes—
335C22×C4×C11C2×D412yes—
336C22×C4×C11C2×D412yes—
337C22×C4×C11C2×D412yes—
338C22×C4×C11#4112yes—
339C22×C4×C11#4112yes—
340C22×C4×C11#4112yes—
341C22×C4×C11#4112yes—
342C22×C4×C11#4112yes—
343C11×C4⋊C4—28no—
344C11×C4⋊C4—44no—
345C11×C22⋊C4—28no—
346C11×C22⋊C4—28no—
347C11×C22⋊C4—28no—
348C11×C22⋊C4—28no—
349C11×C22⋊C4—44no—
350C11×C22⋊C4—44no—
351C11×C22⋊C4—44no—
352C11×C22⋊C4—44no—
353C11×C22⋊C4—44no—
354C11×C22⋊C4—44no—
355C11×C22⋊C4—44no—
356C11×C22⋊C4—44no—
357C11×C22⋊C4C22⋊C4116yescomplemented
358C42×C11—44no—
359C42×C11—44no—
360C42×C11—44no—
361C22×#121C2×C1111yescharacteristic
362C2×#390C2×C1111yescharacteristic, complemented
363C2×#388C2×C1111yescharacteristic, complemented
364C2×#386C2×C1111yescharacteristic, complemented
365C2×#386C2×C1111yescharacteristic, complemented
366C2×C4×C22⋊C4C2×C1111yescharacteristic, complemented
367C2×C4×C22⋊C4C2×C1111yescharacteristic, complemented
368#1441C2×C1111yescharacteristic, complemented
369#1438C2×C1111yescharacteristic, complemented
370#1438C2×C1111yescharacteristic, complemented
371#1438C2×C1111yescharacteristic, complemented
372#1437C2×C1111yescharacteristic, complemented
373#1437C2×C1111yescharacteristic, complemented
374#1436C2×C1111yescharacteristic, complemented
375C22⋊#95C2×C1111yescharacteristic, complemented
376C23×C11—22no—
377C23×C11—22no—
378C23×C11—22no—
379C23×C11—22no—
380C23×C11—22no—
381C23×C11—22no—
382C23×C11—22no—
383C23×C11—22no—
384C23×C11—22no—
385C23×C11—22no—
386C23×C11—22no—
387C23×C11—22no—
388C23×C11—22no—
389C23×C11—22no—
390C23×C11—22no—
391C23×C11—22no—
392C23×C11—22no—
393C23×C11—22no—
394C23×C11—22no—
395C23×C11—22no—
396C23×C11—22no—
397C23×C11—22no—
398C23×C11—22no—
399C23×C11—22no—
400C23×C11—22no—
401C23×C11—22no—
402C23×C11—22no—
403C23×C11—22no—
404C23×C11—22no—
405C23×C11—22no—
406C23×C11—22no—
407C23×C11—22no—
408C23×C11—22no—
409C23×C11—22no—
410C23×C11—22no—
411C23×C11—22no—
412C23×C11—22no—
413C23×C11—22no—
414C23×C11—22no—
415C23×C11—22no—
416C23×C11—22no—
417C23×C11—22no—
418C23×C11—22no—
419C23×C11—41no—
420C23×C11—41no—
421C23×C11—41no—
422C23×C11—41no—
423C23×C11—41no—
424C23×C11—41no—
425C23×C11—41no—
426C23×C11—41no—
427C23×C11—41no—
428C23×C11—41no—
429C23×C11—41no—
430C23×C11—41no—
431C23×C11—41no—
432C23×C11—41no—
433C23×C11—41no—
434C23×C11—41no—
435C23×C11—41no—
436C23×C11—41no—
437C23×C11—41no—
438C23×C11—41no—
439C23×C11—41no—
440C23×C11—41no—
441C23×C11—41no—
442C23×C11—41no—
443C23×C11—41no—
444C23×C11—41no—
445C23×C11—41no—
446C23×C11—41no—
447C23×C11—41no—
448C23×C11—41no—
449C23×C11—41no—
450C23×C11—41no—
451C23×C11—41no—
452C23×C11—41no—
453C23×C11—41no—
454C23×C11—41no—
455C23×C11—41no—
456C23×C11—41no—
457C23×C11—41no—
458C23×C11—41no—
459C23×C11—41no—
460C23×C11—41no—
461C23×C11—41no—
462C23×C11—41no—
463C23×C11—41no—
464C23×C11—41no—
465C23×C11—41no—
466C23×C11—41no—
467C23×C11—41no—
468C23×C11—41no—
469C23×C11—41no—
470C23×C11—41no—
471C23×C11—41no—
472C23×C11—41no—
473C23×C11—41no—
474C23×C11—41no—
475C23×C11—41no—
476C23×C11—41no—
477C23×C11—41no—
478C23×C11—41no—
479C23×C11C2×C22⋊C414yes—
480C23×C11C4×D414yes—
481C23×C11C23×C411yescharacteristic
482C23×C11C22×D411yescharacteristic
483C23×C11C22×D411yescharacteristic
484C23×C11C22×D411yescharacteristic
485C23×C11C22×D411yescharacteristic
486C23×C11C2×#4111yescharacteristic
487C23×C11C2×#4111yescharacteristic
488C23×C11C2×#4111yescharacteristic
489C23×C11C2×#4111yescharacteristic
490C23×C11C2×#4111yescharacteristic
491C23×C11C2×#4111yescharacteristic
492C23×C11H(5,𝔽2)11yescharacteristic
493C23×C11H(5,𝔽2)11yescharacteristic
494C23×C11H(5,𝔽2)11yescharacteristic
495C23×C11H(5,𝔽2)11yescharacteristic
496D4×C11—416no—
497D4×C11—416no—
498D4×C11—416no—
499C2×C4×C11—22no—
500C2×C4×C11—22no—
501C2×C4×C11—22no—
502C2×C4×C11—22no—
503C2×C4×C11—22no—
504C2×C4×C11—22no—
505C2×C4×C11—22no—
506C2×C4×C11—22no—
507C2×C4×C11—22no—
508C2×C4×C11—22no—
509C2×C4×C11—22no—
510C2×C4×C11—22no—
511C2×C4×C11—22no—
512C2×C4×C11—22no—
513C2×C4×C11—22no—
514C2×C4×C11—22no—
515C2×C4×C11—22no—
516C2×C4×C11—22no—
517C2×C4×C11—22no—
518C2×C4×C11—22no—
519C2×C4×C11—22no—
520C2×C4×C11—22no—
521C2×C4×C11—22no—
522C2×C4×C11—22no—
523C2×C4×C11—22no—
524C2×C4×C11—22no—
525C2×C4×C11—22no—
526C2×C4×C11—22no—
527C2×C4×C11—22no—
528C2×C4×C11—22no—
529C2×C4×C11—22no—
530C2×C4×C11—22no—
531C2×C4×C11—22no—
532C2×C4×C11—22no—
533C2×C4×C11—22no—
534C2×C4×C11—22no—
535C2×C4×C11—22no—
536C2×C4×C11—22no—
537C2×C4×C11—22no—
538C2×C4×C11—22no—
539C2×C4×C11—22no—
540C2×C4×C11—22no—
541C2×C4×C11—416no—
542C2×C4×C11—416no—
543C2×C4×C11—41no—
544C2×C4×C11—41no—
545C2×C4×C11—41no—
546C2×C4×C11—41no—
547C2×C4×C11—41no—
548C2×C4×C11—41no—
549C2×C4×C11—41no—
550C2×C4×C11—41no—
551C2×C4×C11—41no—
552C2×C4×C11—41no—
553C2×C4×C11—41no—
554C2×C4×C11—41no—
555C2×C4×C11—41no—
556C2×C4×C11—41no—
557C2×C4×C11—41no—
558C2×C4×C11—41no—
559C2×C4×C11—41no—
560C2×C4×C11—41no—
561C2×C4×C11—41no—
562C2×C4×C11—41no—
563C2×C4×C11—41no—
564C2×C4×C11—41no—
565C2×C4×C11—41no—
566C2×C4×C11—41no—
567C2×C4×C11—41no—
568C2×C4×C11—41no—
569C2×C4×C11—41no—
570C2×C4×C11—41no—
571C2×C4×C11—41no—
572C2×C4×C11—41no—
573C2×C4×C11—41no—
574C2×C4×C11—41no—
575C2×C4×C11—41no—
576C2×C4×C11—41no—
577C2×C4×C11—41no—
578C2×C4×C11—41no—
579C2×C4×C11—41no—
580C2×C4×C11—41no—
581C2×C4×C11C2×C22⋊C414yes—
582C2×C4×C11C2×C22⋊C414yes—
583C2×C4×C11C4×D414yes—
584C2×C4×C11#12114yescomplemented
585C23×D4C22×C1111yescharacteristic
586C23×D4C22×C1111yescharacteristic
587C23×D4C22×C1111yescharacteristic
588C24×C4C22×C1111yescharacteristic
589C24×C4C22×C1111yescharacteristic
590C2×#121—24no—
591C2×#121—24no—
592C2×#121C4×C1118yescomplemented
593C22×C4⋊C4C22×C1111yescharacteristic
594C22×C4⋊C4C22×C1111yescharacteristic
595C22×C22⋊C4C22×C1111yescharacteristic
596C22×C22⋊C4C22×C1111yescharacteristic
597C22×C22⋊C4C22×C1111yescharacteristic
598C22×C22⋊C4C22×C1111yescharacteristic
599C22×C22⋊C4C22×C1111yescharacteristic
600C22×C22⋊C4C22×C1111yescharacteristic
601C22×C22⋊C4C22×C1111yescharacteristic
602C22×C22⋊C4C22×C1111yescharacteristic
603C22×C22⋊C4C22×C1111yescharacteristic
604C22×C22⋊C4C22×C1111yescharacteristic
605C22×C22⋊C4C22×C1111yescharacteristic
606C22×C22⋊C4C22×C1111yescharacteristic
607C22×C22⋊C4C22×C1111yescharacteristic
608C22×C42C22×C1111yescharacteristic
609C22×C42C22×C1111yescharacteristic
610C22×C42C22×C1111yescharacteristic
611#390—24no—
612#388—24no—
613#386—24no—
614#386—24no—
615C4×C22⋊C4—24no—
616C4×C22⋊C4—24no—
617C2×#95C22×C1111yescharacteristic
618C2×#95C22×C1111yescharacteristic
619C2×#95C22×C1111yescharacteristic
620C2×#95C22×C1111yescharacteristic
621C2×#95C22×C1111yescharacteristic
622C2×#95C22×C1111yescharacteristic
623C2×#95C22×C1111yescharacteristic
624C2×#95C22×C1111yescharacteristic
625C2×#95C22×C1111yescharacteristic
626C2×#95C22×C1111yescharacteristic
627C2×#95C22×C1111yescharacteristic
628C2×#95C22×C1111yescharacteristic
629C22×C11—24no—
630C22×C11—24no—
631C22×C11—24no—
632C22×C11—24no—
633C22×C11—24no—
634C22×C11—24no—
635C22×C11—42no—
636C22×C11—42no—
637C22×C11—42no—
638C22×C11—42no—
639C22×C11—42no—
640C22×C11—42no—
641C22×C11—42no—
642C22×C11—42no—
643C22×C11—42no—
644C22×C11—42no—
645C22×C11—42no—
646C22×C11—42no—
647C22×C11—42no—
648C22×C11—42no—
649C22×C11—42no—
650C22×C11—42no—
651C22×C11—42no—
652C22×C11—42no—
653C22×C11—42no—
654C22×C11—42no—
655C22×C11—42no—
656C22×C11—42no—
657C22×C11—42no—
658C22×C11—42no—
659C22×C11—42no—
660C22×C11—42no—
661C22×C11—42no—
662C22×C11—42no—
663C22×C11—42no—
664C22×C11—42no—
665C22×C11—42no—
666C22×C11—81no—
667C22×C11—81no—
668C22×C11—81no—
669C22×C11—81no—
670C22×C11—81no—
671C22×C11—81no—
672C22×C11—81no—
673C22×C11—81no—
674C22×C11C22×C22⋊C411yescharacteristic
675C22×C11C2×C4×D411yescharacteristic
676C22×C11C2×C4×D411yescharacteristic
677C22×C11C4×#4111yescharacteristic
678C22×C11C4×#4111yescharacteristic
679C22×C11#51811yescharacteristic
680C22×C11#51811yescharacteristic
681C22×C11C2×#12111yescharacteristic
682C22×C11#52511yescharacteristic
683C22×C11#52511yescharacteristic
684C22×C11#52511yescharacteristic
685C22×C11#52911yescharacteristic
686C22×C11#53211yescharacteristic
687C22×C11#53211yescharacteristic
688C22×C11#53211yescharacteristic
689C22×C11#53811yescharacteristic
690C22×C11#53811yescharacteristic
691C22×C11#54011yescharacteristic
692C22×C11#54011yescharacteristic
693C22×C11D4211yescharacteristic
694C22×C11D4211yescharacteristic
695C22×C11D4211yescharacteristic
696C22×C11D4211yescharacteristic
697C22×C11#54611yescharacteristic
698C22×C11#54611yescharacteristic
699C22×C11#54611yescharacteristic
700C22×C11#54611yescharacteristic
701C22×C11#54611yescharacteristic
702C22×C11#54611yescharacteristic
703C22×C11#54611yescharacteristic
704C22×C11#55011yescharacteristic
705C22×C11#55311yescharacteristic
706C22×C11#55311yescharacteristic
707C22×C11#55311yescharacteristic
708C22×C11#55511yescharacteristic
709C4×C11—24no—
710C4×C11—24no—
711C4×C11—24no—
712C4×C11—24no—
713C4×C11—42no—
714C4×C11—42no—
715C4×C11—42no—
716C4×C11—42no—
717C4×C11—42no—
718C4×C11—42no—
719C4×C11—81no—
720C4×C11—81no—
721C25C23×C1111yescharacteristic
722C25C23×C1111yescharacteristic
723C25C23×C1111yescharacteristic
724C22×D4—22no—
725C22×D4—22no—
726C22×D4—22no—
727C22×D4—22no—
728C22×D4—22no—
729C22×D4—22no—
730C22×D4—22no—
731C22×D4—22no—
732C22×D4—22no—
733C22×D4—22no—
734C22×D4—22no—
735C22×D4—22no—
736C22×D4—41no—
737C22×D4—41no—
738C22×D4—41no—
739C22×D4—41no—
740C22×D4—41no—
741C22×D4—41no—
742C22×D4C2×C4×C1114yes—
743C22×D4C2×C4×C1114yes—
744C22×D4C2×C4×C1114yescomplemented
745C23×C4—22no—
746C23×C4—22no—
747C23×C4—22no—
748C23×C4—22no—
749C23×C4—22no—
750C23×C4—22no—
751C23×C4—22no—
752C23×C4—22no—
753C23×C4—22no—
754C23×C4—41no—
755C23×C4—41no—
756C23×C4—41no—
757C23×C4—41no—
758C23×C4C2×C4×C1114yescomplemented
759C23×C4C23×C1111yescharacteristic
760C23×C4C23×C1111yescharacteristic
761C23×C4C23×C1111yescharacteristic
762C23×C4C23×C1111yescharacteristic
763C23×C4C23×C1111yescharacteristic
764C23×C4C23×C1111yescharacteristic
765C23×C4C23×C1111yescharacteristic
766C23×C4C23×C1111yescharacteristic
767C23×C4C23×C1111yescharacteristic
768C23×C4C23×C1111yescharacteristic
769C23×C4C23×C1111yescharacteristic
770C23×C4C23×C1111yescharacteristic
771#121—232no—
772C2×C4⋊C4—22no—
773C2×C4⋊C4—22no—
774C2×C4⋊C4—22no—
775C2×C4⋊C4—22no—
776C2×C4⋊C4—41no—
777C2×C4⋊C4C2×C4×C1114yescomplemented
778C2×C22⋊C4—22no—
779C2×C22⋊C4—22no—
780C2×C22⋊C4—22no—
781C2×C22⋊C4—22no—
782C2×C22⋊C4—22no—
783C2×C22⋊C4—22no—
784C2×C22⋊C4—22no—
785C2×C22⋊C4—22no—
786C2×C22⋊C4—22no—
787C2×C22⋊C4—22no—
788C2×C22⋊C4—22no—
789C2×C22⋊C4—22no—
790C2×C22⋊C4—22no—
791C2×C22⋊C4—22no—
792C2×C22⋊C4—22no—
793C2×C22⋊C4—22no—
794C2×C22⋊C4—22no—
795C2×C22⋊C4—22no—
796C2×C22⋊C4—22no—
797C2×C22⋊C4—22no—
798C2×C22⋊C4—22no—
799C2×C22⋊C4—22no—
800C2×C22⋊C4—22no—
801C2×C22⋊C4—22no—
802C2×C22⋊C4—22no—
803C2×C22⋊C4—22no—
804C2×C22⋊C4—41no—
805C2×C22⋊C4—41no—
806C2×C22⋊C4—41no—
807C2×C22⋊C4—41no—
808C2×C22⋊C4—41no—
809C2×C22⋊C4—41no—
810C2×C22⋊C4—41no—
811C2×C22⋊C4—41no—
812C2×C22⋊C4C2×C4×C1114yes—
813C2×C22⋊C4C2×C4×C1114yescomplemented
814C2×C22⋊C4D4×C1114yes—
815C2×C22⋊C4D4×C1114yes—
816C2×C22⋊C4D4×C1114yescomplemented
817C2×C42—22no—
818C2×C42—22no—
819C2×C42—22no—
820C2×C42—22no—
821C2×C42—22no—
822C2×C42—22no—
823C2×C42—41no—
824C2×C42—41no—
825C2×C42—41no—
826#95—22no—
827#95—22no—
828#95—22no—
829#95—22no—
830#95—22no—
831#95—22no—
832#95—22no—
833#95—22no—
834#95—22no—
835#95—41no—
836#95—41no—
837#95D4×C1114yescomplemented
838C2×C11—44no—
839C2×C11—44no—
840C2×C11—82no—
841C2×C11#229711yescharacteristic
842C2×C11C4×#12111yescharacteristic
843C2×C11#233311yescharacteristic
844C2×C11D4×C22⋊C411yescharacteristic
845C2×C11D4×C22⋊C411yescharacteristic
846C2×C11#236311yescharacteristic
847C2×C11#236411yescharacteristic
848C2×C11#242411yescharacteristic
849C2×C11#242811yescharacteristic
850C2×C11#245611yescharacteristic
851C2×C11#246411yescharacteristic
852C2×C11#246411yescharacteristic
853C2×C11#247611yescharacteristic
854C2×C11#255511yescharacteristic
855C2×C11#255911yescharacteristic
856C24—21no—
857C24—21no—
858C24—21no—
859C24—21no—
860C24—21no—
861C24—21no—
862C24—21no—
863C24—21no—
864C24—21no—
865C24—21no—
866C24—21no—
867C24—21no—
868C24—21no—
869C24—21no—
870C24—21no—
871C24—21no—
872C24—21no—
873C24—21no—
874C24—21no—
875C24—21no—
876C24—21no—
877C24—21no—
878C24—21no—
879C24—21no—
880C24—21no—
881C24—21no—
882C24—21no—
883C24—21no—
884C24—21no—
885C24—21no—
886C24—21no—
887C24—21no—
888C24—21no—
889C24—21no—
890C24—21no—
891C24—21no—
892C24—21no—
893C24—21no—
894C24C22×C4×C1112yes—
895C24C22×C4×C1112yes—
896C24C22×C4×C1112yes—
897C24C2×D4×C1112yes—
898C24C2×D4×C1112yes—
899C24C2×D4×C1112yes—
900C24C11×#4112yes—
901C24C24×C1111yescharacteristic
902C2×D4—28no—
903C2×D4—28no—
904C2×D4—28no—
905C2×D4—28no—
906C2×D4—28no—
907C2×D4—28no—
908C2×D4—44no—
909C2×D4—44no—
910C2×D4—44no—
911C2×D4—44no—
912C2×D4—44no—
913C2×D4—44no—
914C2×D4—44no—
915C2×D4—44no—
916C2×D4—44no—
917C2×D4—44no—
918C2×D4—44no—
919C2×D4—44no—
920C2×D4—44no—
921C2×D4—44no—
922C2×D4—44no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—28no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—21no—
955C22×C4—21no—
956C22×C4—21no—
957C22×C4—21no—
958C22×C4—21no—
959C22×C4—21no—
960C22×C4—21no—
961C22×C4—21no—
962C22×C4—21no—
963C22×C4—21no—
964C22×C4—21no—
965C22×C4—21no—
966C22×C4—21no—
967C22×C4—21no—
968C22×C4—21no—
969C22×C4—21no—
970C22×C4—21no—
971C22×C4—21no—
972C22×C4—21no—
973C22×C4—21no—
974C22×C4—21no—
975C22×C4—21no—
976C22×C4—28no—
977C22×C4—28no—
978C22×C4—21no—
979C22×C4—21no—
980C22×C4—21no—
981C22×C4—21no—
982C22×C4—21no—
983C22×C4—21no—
984C22×C4—21no—
985C22×C4—21no—
986C22×C4—21no—
987C22×C4—21no—
988C22×C4—21no—
989C22×C4—21no—
990C22×C4—21no—
991C22×C4—21no—
992C22×C4—44no—
993C22×C4—44no—
994C22×C4—44no—
995C22×C4—44no—
996C22×C4—44no—
997C22×C4—44no—
998C22×C4—44no—
999C22×C4—44no—
1000C22×C4—44no—
1001C22×C4—44no—
1002C22×C4—44no—
1003C22×C4C22×C4×C1112yes—
1004C22×C4C22×C4×C1112yes—
1005C22×C4C22×C4×C1112yes—
1006C22×C4C22×C4×C1112yes—
1007C22×C4C2×D4×C1112yes—
1008C22×C4C2×D4×C1112yes—
1009C22×C4C2×D4×C1112yes—
1010C22×C4C2×D4×C1112yes—
1011C22×C4C2×D4×C1112yes—
1012C22×C4C2×D4×C1112yes—
1013C22×C4C2×D4×C1112yes—
1014C22×C4C2×D4×C1112yes—
1015C22×C4C2×D4×C1112yes—
1016C22×C4C11×#4112yes—
1017C22×C4C11×#4112yes—
1018C22×C4C11×#4112yes—
1019C22×C4C11×#4112yes—
1020C22×C4C11×#4112yes—
1021C4⋊C4—28no—
1022C4⋊C4—44no—
1023C22⋊C4—28no—
1024C22⋊C4—28no—
1025C22⋊C4—28no—
1026C22⋊C4—28no—
1027C22⋊C4—44no—
1028C22⋊C4—44no—
1029C22⋊C4—44no—
1030C22⋊C4—44no—
1031C22⋊C4—44no—
1032C22⋊C4—44no—
1033C22⋊C4—44no—
1034C22⋊C4—44no—
1035C22⋊C4C11×C22⋊C4116yescomplemented
1036C42—44no—
1037C42—44no—
1038C42—44no—
1039C11#1410011yescharacteristic, direct product factor, Sylow
1040C23—22no—
1041C23—22no—
1042C23—22no—
1043C23—22no—
1044C23—22no—
1045C23—22no—
1046C23—22no—
1047C23—22no—
1048C23—22no—
1049C23—22no—
1050C23—22no—
1051C23—22no—
1052C23—22no—
1053C23—22no—
1054C23—22no—
1055C23—22no—
1056C23—22no—
1057C23—22no—
1058C23—22no—
1059C23—22no—
1060C23—22no—
1061C23—22no—
1062C23—22no—
1063C23—22no—
1064C23—22no—
1065C23—22no—
1066C23—22no—
1067C23—22no—
1068C23—22no—
1069C23—22no—
1070C23—22no—
1071C23—22no—
1072C23—22no—
1073C23—22no—
1074C23—22no—
1075C23—22no—
1076C23—22no—
1077C23—22no—
1078C23—22no—
1079C23—22no—
1080C23—22no—
1081C23—22no—
1082C23—22no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—41no—
1117C23—41no—
1118C23—41no—
1119C23—41no—
1120C23—41no—
1121C23—41no—
1122C23—41no—
1123C23—41no—
1124C23—41no—
1125C23—41no—
1126C23—41no—
1127C23—41no—
1128C23—41no—
1129C23—41no—
1130C23—41no—
1131C23—41no—
1132C23—41no—
1133C23—41no—
1134C23—41no—
1135C23—41no—
1136C23—41no—
1137C23—41no—
1138C23—41no—
1139C23—41no—
1140C23—41no—
1141C23—41no—
1142C23—41no—
1143C23C2×C11×C22⋊C414yes—
1144C23C4×D4×C1114yes—
1145C23C23×C4×C1111yescharacteristic
1146C23C22×D4×C1111yescharacteristic
1147C23C22×D4×C1111yescharacteristic
1148C23C22×D4×C1111yescharacteristic
1149C23C22×D4×C1111yescharacteristic
1150C23C2×C11×#4111yescharacteristic
1151C23C2×C11×#4111yescharacteristic
1152C23C2×C11×#4111yescharacteristic
1153C23C2×C11×#4111yescharacteristic
1154C23C2×C11×#4111yescharacteristic
1155C23C2×C11×#4111yescharacteristic
1156C23C11×H(5,𝔽2)11yescharacteristic
1157C23C11×H(5,𝔽2)11yescharacteristic
1158C23C11×H(5,𝔽2)11yescharacteristic
1159C23C11×H(5,𝔽2)11yescharacteristic
1160D4—416no—
1161D4—416no—
1162D4—416no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—22no—
1166C2×C4—22no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—22no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—22no—
1173C2×C4—22no—
1174C2×C4—22no—
1175C2×C4—22no—
1176C2×C4—22no—
1177C2×C4—22no—
1178C2×C4—22no—
1179C2×C4—22no—
1180C2×C4—22no—
1181C2×C4—22no—
1182C2×C4—22no—
1183C2×C4—22no—
1184C2×C4—22no—
1185C2×C4—22no—
1186C2×C4—22no—
1187C2×C4—22no—
1188C2×C4—22no—
1189C2×C4—22no—
1190C2×C4—22no—
1191C2×C4—22no—
1192C2×C4—22no—
1193C2×C4—22no—
1194C2×C4—22no—
1195C2×C4—22no—
1196C2×C4—22no—
1197C2×C4—22no—
1198C2×C4—22no—
1199C2×C4—22no—
1200C2×C4—22no—
1201C2×C4—22no—
1202C2×C4—22no—
1203C2×C4—22no—
1204C2×C4—22no—
1205C2×C4—416no—
1206C2×C4—416no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—41no—
1234C2×C4—41no—
1235C2×C4—41no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—41no—
1239C2×C4—41no—
1240C2×C4—41no—
1241C2×C4—41no—
1242C2×C4—41no—
1243C2×C4—41no—
1244C2×C4—41no—
1245C2×C4C2×C11×C22⋊C414yes—
1246C2×C4C2×C11×C22⋊C414yes—
1247C2×C4C4×D4×C1114yes—
1248C2×C4C11×#12114yescomplemented
1249C22—24no—
1250C22—24no—
1251C22—24no—
1252C22—24no—
1253C22—24no—
1254C22—24no—
1255C22—42no—
1256C22—42no—
1257C22—42no—
1258C22—42no—
1259C22—42no—
1260C22—42no—
1261C22—42no—
1262C22—42no—
1263C22—42no—
1264C22—42no—
1265C22—42no—
1266C22—42no—
1267C22—42no—
1268C22—42no—
1269C22—42no—
1270C22—42no—
1271C22—42no—
1272C22—42no—
1273C22—42no—
1274C22—42no—
1275C22—42no—
1276C22—42no—
1277C22—42no—
1278C22—42no—
1279C22—42no—
1280C22—42no—
1281C22—42no—
1282C22—42no—
1283C22—42no—
1284C22—42no—
1285C22—42no—
1286C22—81no—
1287C22—81no—
1288C22—81no—
1289C22—81no—
1290C22—81no—
1291C22—81no—
1292C22—81no—
1293C22—81no—
1294C22C22×C11×C22⋊C411yescharacteristic
1295C22C2×C4×D4×C1111yescharacteristic
1296C22C2×C4×D4×C1111yescharacteristic
1297C22C4×C11×#4111yescharacteristic
1298C22C4×C11×#4111yescharacteristic
1299C22C11×#51811yescharacteristic
1300C22C11×#51811yescharacteristic
1301C22C2×C11×#12111yescharacteristic
1302C22C11×#52511yescharacteristic
1303C22C11×#52511yescharacteristic
1304C22C11×#52511yescharacteristic
1305C22C11×#52911yescharacteristic
1306C22C11×#53211yescharacteristic
1307C22C11×#53211yescharacteristic
1308C22C11×#53211yescharacteristic
1309C22C11×#53811yescharacteristic
1310C22C11×#53811yescharacteristic
1311C22C11×#54011yescharacteristic
1312C22C11×#54011yescharacteristic
1313C22D42×C1111yescharacteristic
1314C22D42×C1111yescharacteristic
1315C22D42×C1111yescharacteristic
1316C22D42×C1111yescharacteristic
1317C22C11×#54611yescharacteristic
1318C22C11×#54611yescharacteristic
1319C22C11×#54611yescharacteristic
1320C22C11×#54611yescharacteristic
1321C22C11×#54611yescharacteristic
1322C22C11×#54611yescharacteristic
1323C22C11×#54611yescharacteristic
1324C22C11×#55011yescharacteristic
1325C22C11×#55311yescharacteristic
1326C22C11×#55311yescharacteristic
1327C22C11×#55311yescharacteristic
1328C22C11×#55511yescharacteristic
1329C4—24no—
1330C4—24no—
1331C4—24no—
1332C4—24no—
1333C4—42no—
1334C4—42no—
1335C4—42no—
1336C4—42no—
1337C4—42no—
1338C4—42no—
1339C4—81no—
1340C4—81no—
1341C2—44no—
1342C2—44no—
1343C2—82no—
1344C2C11×#229711yescharacteristic
1345C2C4×C11×#12111yescharacteristic
1346C2C11×#233311yescharacteristic
1347C2D4×C11×C22⋊C411yescharacteristic
1348C2D4×C11×C22⋊C411yescharacteristic
1349C2C11×#236311yescharacteristic
1350C2C11×#236411yescharacteristic
1351C2C11×#242411yescharacteristic
1352C2C11×#242811yescharacteristic
1353C2C11×#245611yescharacteristic
1354C2C11×#246411yescharacteristic
1355C2C11×#246411yescharacteristic
1356C2C11×#247611yescharacteristic
1357C2C11×#255511yescharacteristic
1358C2C11×#255911yescharacteristic
subgroupG/H
center, socleC24×C11C24
commutatorC23C23×C4×C11
Frattini, cosocleC24C24×C11
prime radicalC22×C11×#121C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#390C2semidirect
3. C2×C11×#388C2semidirect
4. C2×C11×#386C2semidirect
5. C2×C11×#386C2semidirect
6. C2×C4×C11×C22⋊C4C2semidirect
7. C2×C4×C11×C22⋊C4C2semidirect
8. C11×#1441C2semidirect
9. C11×#1438C2semidirect
10. C11×#1438C2semidirect
11. C11×#1438C2semidirect
12. C11×#1437C2semidirect
13. C11×#1437C2semidirect
14. C11×#1436C2semidirect
15. C11×C22⋊#95C2semidirect
23. C2×C11×#121C4semidirect
83. C22×D4×C11C2×C4semidirect
97. C23×C4×C11C2×C4semidirect
116. C2×C11×C4⋊C4C2×C4semidirect
152. C2×C11×C22⋊C4C2×C4semidirect
155. C2×C11×C22⋊C4D4semidirect
176. C11×#95D4semidirect
177. #14100C11direct (N × H)
357. C11×C22⋊C4C22⋊C4semidirect
362. C2×#390C2×C11semidirect
363. C2×#388C2×C11semidirect
364. C2×#386C2×C11semidirect
365. C2×#386C2×C11semidirect
366. C2×C4×C22⋊C4C2×C11semidirect
367. C2×C4×C22⋊C4C2×C11semidirect
368. #1441C2×C11semidirect
369. #1438C2×C11semidirect
370. #1438C2×C11semidirect
371. #1438C2×C11semidirect
372. #1437C2×C11semidirect
373. #1437C2×C11semidirect
374. #1436C2×C11semidirect
375. C22⋊#95C2×C11semidirect
584. C2×C4×C11#121semidirect
592. C2×#121C4×C11semidirect
744. C22×D4C2×C4×C11semidirect
758. C23×C4C2×C4×C11semidirect
777. C2×C4⋊C4C2×C4×C11semidirect
813. C2×C22⋊C4C2×C4×C11semidirect
816. C2×C22⋊C4D4×C11semidirect
837. #95D4×C11semidirect
1035. C22⋊C4C11×C22⋊C4semidirect
1039. C11#14100direct (N × H)
1248. C2×C4C11×#121semidirect

Maximal subgroups

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

subgroupindex
C22×C11×#1212
C2×C11×#3902
C2×C11×#3882
C2×C11×#3862
C2×C4×C11×C22⋊C42
C11×#14412
C11×#14382
C11×#14372
C11×#14362
C11×C22⋊#952
#1410011