Finite Group Databasebeta

← C11×#24235 #14601428

Subgroups — C11×#24235 #14601428

Order 2816.

1376 conjugacy classes of subgroups.

The subgroup lattice has 994 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3500C211yesmaximal, characteristic
2C11×#3037C211yesmaximal, characteristic, complemented
3C2×C11×#456C211yesmaximal, characteristic, complemented
4C2×C11×#455C211yesmaximal, characteristic, complemented
5C4×C11×#137C211yesmaximal, characteristic, complemented
6C11×#2545C211yesmaximal, characteristic, complemented
7C11×#2038C211yesmaximal, characteristic, complemented
8C11×#2037C211yesmaximal, characteristic, complemented
9C11×#2005C211yesmaximal, characteristic, complemented
10C11×#2004C211yesmaximal, characteristic, complemented
11C11×#1980C211yesmaximal, characteristic, complemented
12C11×#1967C211yesmaximal, characteristic, complemented
13C11×#1806C211yesmaximal, characteristic, complemented
14C11×#1793C211yesmaximal, characteristic, complemented
15C11×#1792C211yesmaximal, characteristic, complemented
16C2×C11×2−1+4C2211yescharacteristic
17C2×C11×H(5,𝔽2)C2211yescharacteristic
18C2×C11×#137C2211yescharacteristic
19C2×C11×#137C2211yescharacteristic
20C2×C11×#137C2211yescharacteristic, complemented
21C11×#548—21no—
22C11×#548—21no—
23C11×#546—21no—
24C11×#546—21no—
25C11×#546—22no—
26C11×#546—22no—
27C11×#536—21no—
28C11×#536C2211yescharacteristic
29C11×#535—21no—
30C11×#535C2211yescharacteristic
31C11×#532—21no—
32C11×#532C2211yescharacteristic
33C2×C11×C4⋊Q8C2211yescharacteristic, complemented
34C2×C11×#124—21no—
35C2×C11×#124C2211yescharacteristic
36C2×C11×#124C2211yescharacteristic
37C4×C11×#41C2211yescharacteristic
38C2×C4×Q8×C11C2211yescharacteristic, complemented
39C11×#464—21no—
40C11×#464—21no—
41C11×#462—21no—
42C11×#460—21no—
43C11×#456—24no—
44C11×#455—24no—
45C11×#441—21no—
46C11×#440—21no—
47C4×C11×Q16—21no—
48C4×C11×SD16—21no—
49C11×#428C2211yescharacteristic, complemented
50C11×#423C2211yescharacteristic, complemented
51C2×C11×#104C2211yescharacteristic
52C2×C11×#104C2211yescharacteristic
53C2×C11×#104C2211yescharacteristic
54C2×C11×#104C2211yescharacteristic
55C2×C11×#104C2211yescharacteristic, complemented
56C2×C11×#104C2211yescharacteristic, complemented
57C11×#419C2211yescharacteristic, complemented
58C11×#417C2211yescharacteristic
59C11×#417C2211yescharacteristic
60C11×#417C2211yescharacteristic, complemented
61C2×C11×#101C2211yescharacteristic, complemented
62C2×C11×#101C2211yescharacteristic, complemented
63C2×C11×#100C2211yescharacteristic
64C2×C11×#100C2211yescharacteristic
65C4×C11×M16C2211yescharacteristic, complemented
66C11×#396—22no—
67C11×#391C2211yescharacteristic, complemented
68C11×#390C2211yescharacteristic
69C11×#388—22no—
70C4×C11×C4⋊C4C2211yescharacteristic, complemented
71C11×#339C2211yescharacteristic, complemented
72C11×#339C2211yescharacteristic, complemented
73C11×2−1+4—22no—
74C11×2−1+4—22no—
75C11×2−1+4—41no—
76C11×2−1+4—41no—
77C11×H(5,𝔽2)—22no—
78C11×H(5,𝔽2)—22no—
79C11×H(5,𝔽2)—41no—
80C11×H(5,𝔽2)—41no—
81C2×C11×#41—21no—
82C2×C11×#41—21no—
83C2×C11×#41—21no—
84C2×C11×#41—21no—
85C2×C11×#41—22no—
86C2×C11×#41C2311yescharacteristic
87C2×C11×#41C2311yescharacteristic
88C2×C11×#41C2311yescharacteristic
89C22×Q8×C11—21no—
90C22×Q8×C11—21no—
91C22×Q8×C11C2311yescharacteristic
92C22×Q8×C11C2311yescharacteristic
93C22×D4×C11—22no—
94C22×D4×C11—21no—
95C22×D4×C11—21no—
96C22×D4×C11C2311yescharacteristic
97C11×#137—22no—
98C11×#137—22no—
99C11×#137—22no—
100C11×#137—41no—
101C11×#137—41no—
102C11×#137D414yescomplemented
103C2×C11×Q16—21no—
104C2×C11×Q16—21no—
105C2×C11×Q16—21no—
106C2×C11×SD16—21no—
107C2×C11×SD16—21no—
108C2×C11×SD16—21no—
109C2×C11×M16C2311yescharacteristic
110C2×C11×M16C2311yescharacteristic
111C2×C11×M16C2311yescharacteristic
112C2×C11×M16C2311yescharacteristic
113C11×C4⋊Q8—21no—
114C11×C4⋊Q8—22no—
115C11×C4⋊Q8—41no—
116C11×C4⋊Q8D411yescharacteristic
117C11×#127—21no—
118C11×#127D411yescharacteristic
119C11×#124—22no—
120C11×#124—22no—
121C11×#124—21no—
122C11×#124—21no—
123C11×#124—22no—
124C11×#124—21no—
125C11×#124—21no—
126C11×#124—21no—
127C11×#124—21no—
128C11×#124—41no—
129C11×#124D411yescharacteristic
130C11×#124D411yescharacteristic
131C11×#123—22no—
132C11×#123—22no—
133C11×#123—22no—
134C11×C22⋊Q8—22no—
135C11×C22⋊Q8—22no—
136C11×C22⋊Q8—21no—
137C11×C22⋊Q8—21no—
138C11×#121—22no—
139C11×#121—22no—
140C11×#121—22no—
141C11×#121—22no—
142C11×#121—21no—
143C11×#121—21no—
144C11×#121—21no—
145C11×#121—21no—
146C11×#120—22no—
147C11×#120—22no—
148C11×#120—22no—
149C4×Q8×C11—21no—
150C4×Q8×C11—21no—
151C4×Q8×C11—21no—
152C4×Q8×C11—21no—
153C4×Q8×C11D411yescharacteristic
154C4×Q8×C11D411yescharacteristic
155C4×D4×C11—22no—
156C4×D4×C11—22no—
157C4×D4×C11—21no—
158C4×D4×C11—21no—
159C4×D4×C11—21no—
160C4×D4×C11—21no—
161C4×D4×C11D411yescharacteristic
162C4×D4×C11D411yescharacteristic
163C11×#117—21no—
164C11×#117C2311yescharacteristic
165C2×C11×C4⋊C4—21no—
166C2×C11×C4⋊C4—21no—
167C2×C11×C4⋊C4—22no—
168C2×C11×C4⋊C4C2311yescharacteristic
169C2×C11×C22⋊C4—22no—
170C2×C11×C22⋊C4—22no—
171C2×C11×C22⋊C4—22no—
172C2×C11×C22⋊C4—22no—
173C2×C11×C22⋊C4D412yes—
174C2×C11×C22⋊C4D412yes—
175C2×C42×C11—21no—
176C2×C42×C11—21no—
177C2×C42×C11C2311yescharacteristic
178C2×C42×C11C2311yescharacteristic
179C2×C42×C11C2311yescharacteristic
180C11×#107—21no—
181C11×#106—21no—
182C11×C4⋊C8—21no—
183C11×C4⋊C8—21no—
184C11×#104—22no—
185C11×#104—22no—
186C11×#104—22no—
187C11×#104—22no—
188C11×#104—41no—
189C11×#104—41no—
190C11×#103—21no—
191C11×#103—21no—
192C11×#103—21no—
193C11×#103—21no—
194C11×#103—21no—
195C11×#102—21no—
196C11×#102—21no—
197C11×#102—21no—
198C11×#101—22no—
199C11×#101—41no—
200C11×#100—22no—
201C11×#100—41no—
202C11×#97—21no—
203C4×C8×C11—21no—
204C11×#95—21no—
205C11×#95—22no—
206#24235C1111yesmaximal, characteristic, direct product factor, Sylow
207C24×C11—22no—
208C24×C11C2×D412yes—
209C11×#41—21no—
210C11×#41—21no—
211C11×#41—21no—
212C11×#41—21no—
213C11×#41—21no—
214C11×#41—21no—
215C11×#41—21no—
216C11×#41—21no—
217C11×#41—21no—
218C11×#41—21no—
219C11×#41—42no—
220C11×#41—42no—
221C11×#41—44no—
222C11×#41—44no—
223C11×#41—42no—
224C11×#41—42no—
225C11×#41—42no—
226C11×#41—42no—
227C11×#41—42no—
228C11×#41—42no—
229C11×#41C2×D412yes—
230C11×#41#4112yes—
231C2×Q8×C11—22no—
232C2×Q8×C11—21no—
233C2×Q8×C11—21no—
234C2×Q8×C11—21no—
235C2×Q8×C11—21no—
236C2×Q8×C11—21no—
237C2×Q8×C11—21no—
238C2×Q8×C11—21no—
239C2×Q8×C11—21no—
240C2×Q8×C11—21no—
241C2×Q8×C11—21no—
242C2×Q8×C11—21no—
243C2×Q8×C11—42no—
244C2×Q8×C11—42no—
245C2×Q8×C11—42no—
246C2×Q8×C11—42no—
247C2×Q8×C11C2×D411yescharacteristic
248C2×Q8×C11C2×D411yescharacteristic
249C2×Q8×C11C2×D412yes—
250C2×Q8×C11C2×D411yescharacteristic
251C2×D4×C11—21no—
252C2×D4×C11—22no—
253C2×D4×C11—22no—
254C2×D4×C11—22no—
255C2×D4×C11—21no—
256C2×D4×C11—21no—
257C2×D4×C11—22no—
258C2×D4×C11—22no—
259C2×D4×C11—21no—
260C2×D4×C11—21no—
261C2×D4×C11—21no—
262C2×D4×C11—21no—
263C2×D4×C11—21no—
264C2×D4×C11—21no—
265C2×D4×C11—21no—
266C2×D4×C11—21no—
267C2×D4×C11—42no—
268C2×D4×C11—42no—
269C2×D4×C11—44no—
270C2×D4×C11—44no—
271C2×D4×C11—42no—
272C2×D4×C11—42no—
273C2×D4×C11C2×D411yescharacteristic
274C2×D4×C11C2×D411yescharacteristic
275C2×D4×C11C2×D411yescharacteristic
276C22×C4×C11—21no—
277C22×C4×C11—22no—
278C22×C4×C11—22no—
279C22×C4×C11—22no—
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×C11C2×D412yes—
289C22×C4×C11C2×D411yescharacteristic
290C22×C4×C11C2×D411yescharacteristic
291C22×C4×C11C2411yescharacteristic
292C11×Q16—24no—
293C11×Q16—42no—
294C11×Q16—42no—
295C11×SD16—24no—
296C11×SD16—42no—
297C11×SD16—42no—
298C11×M16—21no—
299C11×M16—21no—
300C11×M16—21no—
301C11×M16—21no—
302C11×M16—21no—
303C11×M16—21no—
304C11×M16—21no—
305C11×M16C2×D412yes—
306C2×C8×C11—21no—
307C2×C8×C11—21no—
308C2×C8×C11—21no—
309C2×C8×C11—21no—
310C11×C4⋊C4—22no—
311C11×C4⋊C4—22no—
312C11×C4⋊C4—21no—
313C11×C4⋊C4—21no—
314C11×C4⋊C4—21no—
315C11×C4⋊C4—21no—
316C11×C4⋊C4—21no—
317C11×C4⋊C4—21no—
318C11×C4⋊C4—44no—
319C11×C4⋊C4—42no—
320C11×C4⋊C4—41no—
321C11×C4⋊C4—41no—
322C11×C4⋊C4C2×D411yescharacteristic
323C11×C4⋊C4C2×D411yescharacteristic
324C11×C22⋊C4—22no—
325C11×C22⋊C4—22no—
326C11×C22⋊C4—22no—
327C11×C22⋊C4—22no—
328C11×C22⋊C4—21no—
329C11×C22⋊C4—21no—
330C11×C22⋊C4—21no—
331C11×C22⋊C4—22no—
332C11×C22⋊C4—22no—
333C11×C22⋊C4—22no—
334C11×C22⋊C4—22no—
335C11×C22⋊C4—21no—
336C11×C22⋊C4—21no—
337C11×C22⋊C4—21no—
338C11×C22⋊C4—21no—
339C11×C22⋊C4—44no—
340C11×C22⋊C4—44no—
341C42×C11—21no—
342C42×C11—21no—
343C42×C11—21no—
344C42×C11—21no—
345C42×C11—21no—
346C42×C11—21no—
347C42×C11—21no—
348C42×C11—41no—
349C42×C11—41no—
350C42×C11C2×D411yescharacteristic
351C42×C11C2×D411yescharacteristic
352C42×C11C2×D411yescharacteristic
353C42×C11C2×D411yescharacteristic
354#3500C2×C1111yescharacteristic
355#3037C2×C1111yescharacteristic, complemented
356C2×#456C2×C1111yescharacteristic, complemented
357C2×#455C2×C1111yescharacteristic, complemented
358C4×#137C2×C1111yescharacteristic, complemented
359#2545C2×C1111yescharacteristic, complemented
360#2038C2×C1111yescharacteristic, complemented
361#2037C2×C1111yescharacteristic, complemented
362#2005C2×C1111yescharacteristic, complemented
363#2004C2×C1111yescharacteristic, complemented
364#1980C2×C1111yescharacteristic, complemented
365#1967C2×C1111yescharacteristic, complemented
366#1806C2×C1111yescharacteristic, complemented
367#1793C2×C1111yescharacteristic, complemented
368#1792C2×C1111yescharacteristic, complemented
369C23×C11—21no—
370C23×C11—22no—
371C23×C11—21no—
372C23×C11—21no—
373C23×C11—22no—
374C23×C11—22no—
375C23×C11—44no—
376C23×C11—42no—
377C23×C11—42no—
378C23×C11—82no—
379C23×C11—82no—
380C23×C11C22×D411yescharacteristic
381Q8×C11—21no—
382Q8×C11—22no—
383Q8×C11—22no—
384Q8×C11—21no—
385Q8×C11—21no—
386Q8×C11—21no—
387Q8×C11—21no—
388Q8×C11—44no—
389Q8×C11—41no—
390Q8×C11—41no—
391Q8×C11—41no—
392Q8×C11—41no—
393Q8×C11—41no—
394Q8×C11—41no—
395Q8×C11#12112yes—
396D4×C11—22no—
397D4×C11—22no—
398D4×C11—21no—
399D4×C11—21no—
400D4×C11—21no—
401D4×C11—21no—
402D4×C11—21no—
403D4×C11—44no—
404D4×C11—44no—
405D4×C11—44no—
406D4×C11—41no—
407D4×C11—41no—
408D4×C11—41no—
409D4×C11—41no—
410D4×C11—41no—
411D4×C11—41no—
412D4×C11—41no—
413D4×C11—41no—
414D4×C11—81no—
415D4×C11—81no—
416D4×C11—82no—
417D4×C11—82no—
418D4×C11#12112yes—
419C2×C4×C11—21no—
420C2×C4×C11—22no—
421C2×C4×C11—22no—
422C2×C4×C11—22no—
423C2×C4×C11—21no—
424C2×C4×C11—21no—
425C2×C4×C11—21no—
426C2×C4×C11—22no—
427C2×C4×C11—21no—
428C2×C4×C11—22no—
429C2×C4×C11—22no—
430C2×C4×C11—22no—
431C2×C4×C11—41no—
432C2×C4×C11—41no—
433C2×C4×C11—44no—
434C2×C4×C11—44no—
435C2×C4×C11—41no—
436C2×C4×C11—44no—
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—42no—
445C2×C4×C11—41no—
446C2×C4×C11—41no—
447C2×C4×C11—41no—
448C2×C4×C11—41no—
449C2×C4×C11—81no—
450C2×C4×C11—81no—
451C2×C4×C11#12011yescharacteristic
452C2×C4×C11#12011yescharacteristic
453C2×C4×C11#12011yescharacteristic
454C2×C4×C11#12011yescharacteristic
455C2×C4×C11C22×D411yescharacteristic
456C2×C4×C11C22×D411yescharacteristic
457C2×C4×C11C22×D411yescharacteristic
458C2×C4×C11C2×#4111yescharacteristic
459C2×C4×C11H(5,𝔽2)11yescharacteristic
460C2×C4×C11H(5,𝔽2)11yescharacteristic
461C8×C11—22no—
462C8×C11—41no—
463C8×C11—41no—
464C8×C11—41no—
465C2×2−1+4C22×C1111yescharacteristic
466C2×H(5,𝔽2)C22×C1111yescharacteristic
467C2×#137C22×C1111yescharacteristic
468C2×#137C22×C1111yescharacteristic
469C2×#137C22×C1111yescharacteristic, complemented
470#548—21no—
471#548—21no—
472#546—21no—
473#546—21no—
474#546—22no—
475#546—22no—
476#536—21no—
477#536C22×C1111yescharacteristic
478#535—21no—
479#535C22×C1111yescharacteristic
480#532—21no—
481#532C22×C1111yescharacteristic
482C2×C4⋊Q8C22×C1111yescharacteristic, complemented
483C2×#124—21no—
484C2×#124C22×C1111yescharacteristic
485C2×#124C22×C1111yescharacteristic
486C4×#41C22×C1111yescharacteristic
487C2×C4×Q8C22×C1111yescharacteristic, complemented
488#464—21no—
489#464—21no—
490#462—21no—
491#460—21no—
492#456—24no—
493#455—24no—
494#441—21no—
495#440—21no—
496C4×Q16—21no—
497C4×SD16—21no—
498#428C22×C1111yescharacteristic, complemented
499#423C22×C1111yescharacteristic, complemented
500C2×#104C22×C1111yescharacteristic
501C2×#104C22×C1111yescharacteristic
502C2×#104C22×C1111yescharacteristic
503C2×#104C22×C1111yescharacteristic
504C2×#104C22×C1111yescharacteristic, complemented
505C2×#104C22×C1111yescharacteristic, complemented
506#419C22×C1111yescharacteristic, complemented
507#417C22×C1111yescharacteristic
508#417C22×C1111yescharacteristic
509#417C22×C1111yescharacteristic, complemented
510C2×#101C22×C1111yescharacteristic, complemented
511C2×#101C22×C1111yescharacteristic, complemented
512C2×#100C22×C1111yescharacteristic
513C2×#100C22×C1111yescharacteristic
514C4×M16C22×C1111yescharacteristic, complemented
515#396—22no—
516#391C22×C1111yescharacteristic, complemented
517#390C22×C1111yescharacteristic
518#388—22no—
519C4×C4⋊C4C22×C1111yescharacteristic, complemented
520#339C22×C1111yescharacteristic, complemented
521#339C22×C1111yescharacteristic, complemented
522C22×C11—21no—
523C22×C11—21no—
524C22×C11—22no—
525C22×C11—41no—
526C22×C11—41no—
527C22×C11—41no—
528C22×C11—41no—
529C22×C11—42no—
530C22×C11—41no—
531C22×C11—42no—
532C22×C11—41no—
533C22×C11—41no—
534C22×C11—42no—
535C22×C11—41no—
536C22×C11—82no—
537C22×C11—82no—
538C22×C11—164no—
539C22×C11C2×#12011yescharacteristic
540C22×C11D4211yescharacteristic
541C22×C11#54611yescharacteristic
542C4×C11—22no—
543C4×C11—21no—
544C4×C11—21no—
545C4×C11—21no—
546C4×C11—21no—
547C4×C11—42no—
548C4×C11—42no—
549C4×C11—41no—
550C4×C11—41no—
551C4×C11—42no—
552C4×C11—41no—
553C4×C11—41no—
554C4×C11—81no—
555C4×C11—81no—
556C4×C11C2×#12111yescharacteristic
557C4×C11#53511yescharacteristic
558C4×C11D4211yescharacteristic
559C4×C11#54611yescharacteristic
5602−1+4—22no—
5612−1+4—22no—
5622−1+4—41no—
5632−1+4—41no—
564H(5,𝔽2)—22no—
565H(5,𝔽2)—22no—
566H(5,𝔽2)—41no—
567H(5,𝔽2)—41no—
568C2×#41—21no—
569C2×#41—21no—
570C2×#41—21no—
571C2×#41—21no—
572C2×#41—22no—
573C2×#41C23×C1111yescharacteristic
574C2×#41C23×C1111yescharacteristic
575C2×#41C23×C1111yescharacteristic
576C22×Q8—21no—
577C22×Q8—21no—
578C22×Q8C23×C1111yescharacteristic
579C22×Q8C23×C1111yescharacteristic
580C22×D4—22no—
581C22×D4—21no—
582C22×D4—21no—
583C22×D4C23×C1111yescharacteristic
584#137—22no—
585#137—22no—
586#137—22no—
587#137—41no—
588#137—41no—
589#137D4×C1114yescomplemented
590C2×Q16—21no—
591C2×Q16—21no—
592C2×Q16—21no—
593C2×SD16—21no—
594C2×SD16—21no—
595C2×SD16—21no—
596C2×M16C23×C1111yescharacteristic
597C2×M16C23×C1111yescharacteristic
598C2×M16C23×C1111yescharacteristic
599C2×M16C23×C1111yescharacteristic
600C4⋊Q8—21no—
601C4⋊Q8—22no—
602C4⋊Q8—41no—
603C4⋊Q8D4×C1111yescharacteristic
604#127—21no—
605#127D4×C1111yescharacteristic
606#124—22no—
607#124—22no—
608#124—21no—
609#124—21no—
610#124—22no—
611#124—21no—
612#124—21no—
613#124—21no—
614#124—21no—
615#124—41no—
616#124D4×C1111yescharacteristic
617#124D4×C1111yescharacteristic
618#123—22no—
619#123—22no—
620#123—22no—
621C22⋊Q8—22no—
622C22⋊Q8—22no—
623C22⋊Q8—21no—
624C22⋊Q8—21no—
625#121—22no—
626#121—22no—
627#121—22no—
628#121—22no—
629#121—21no—
630#121—21no—
631#121—21no—
632#121—21no—
633#120—22no—
634#120—22no—
635#120—22no—
636C4×Q8—21no—
637C4×Q8—21no—
638C4×Q8—21no—
639C4×Q8—21no—
640C4×Q8D4×C1111yescharacteristic
641C4×Q8D4×C1111yescharacteristic
642C4×D4—22no—
643C4×D4—22no—
644C4×D4—21no—
645C4×D4—21no—
646C4×D4—21no—
647C4×D4—21no—
648C4×D4D4×C1111yescharacteristic
649C4×D4D4×C1111yescharacteristic
650#117—21no—
651#117C23×C1111yescharacteristic
652C2×C4⋊C4—21no—
653C2×C4⋊C4—22no—
654C2×C4⋊C4—21no—
655C2×C4⋊C4C23×C1111yescharacteristic
656C2×C22⋊C4—22no—
657C2×C22⋊C4—22no—
658C2×C22⋊C4—22no—
659C2×C22⋊C4—22no—
660C2×C22⋊C4D4×C1112yes—
661C2×C22⋊C4D4×C1112yes—
662C2×C42—21no—
663C2×C42—21no—
664C2×C42C23×C1111yescharacteristic
665C2×C42C23×C1111yescharacteristic
666C2×C42C23×C1111yescharacteristic
667#107—21no—
668#106—21no—
669C4⋊C8—21no—
670C4⋊C8—21no—
671#104—22no—
672#104—22no—
673#104—22no—
674#104—22no—
675#104—41no—
676#104—41no—
677#103—21no—
678#103—21no—
679#103—21no—
680#103—21no—
681#103—21no—
682#102—21no—
683#102—21no—
684#102—21no—
685#101—22no—
686#101—41no—
687#100—22no—
688#100—41no—
689#97—21no—
690C4×C8—21no—
691#95—21no—
692#95—22no—
693C2×C11—21no—
694C2×C11—21no—
695C2×C11—42no—
696C2×C11—81no—
697C2×C11—82no—
698C2×C11—81no—
699C2×C11#240811yescharacteristic
700C2×C11#301811yescharacteristic
701C2×C11#302211yescharacteristic
702C24—22no—
703C24C2×D4×C1112yes—
704#41—21no—
705#41—21no—
706#41—21no—
707#41—21no—
708#41—21no—
709#41—21no—
710#41—21no—
711#41—21no—
712#41—21no—
713#41—21no—
714#41—42no—
715#41—42no—
716#41—44no—
717#41—44no—
718#41—42no—
719#41—42no—
720#41—42no—
721#41—42no—
722#41—42no—
723#41—42no—
724#41C2×D4×C1112yes—
725#41C11×#4112yes—
726C2×Q8—22no—
727C2×Q8—21no—
728C2×Q8—21no—
729C2×Q8—21no—
730C2×Q8—21no—
731C2×Q8—21no—
732C2×Q8—21no—
733C2×Q8—21no—
734C2×Q8—21no—
735C2×Q8—21no—
736C2×Q8—21no—
737C2×Q8—21no—
738C2×Q8—42no—
739C2×Q8—42no—
740C2×Q8—42no—
741C2×Q8—42no—
742C2×Q8C2×D4×C1111yescharacteristic
743C2×Q8C2×D4×C1111yescharacteristic
744C2×Q8C2×D4×C1112yes—
745C2×Q8C2×D4×C1111yescharacteristic
746C2×D4—21no—
747C2×D4—22no—
748C2×D4—22no—
749C2×D4—22no—
750C2×D4—21no—
751C2×D4—21no—
752C2×D4—22no—
753C2×D4—22no—
754C2×D4—21no—
755C2×D4—21no—
756C2×D4—21no—
757C2×D4—21no—
758C2×D4—21no—
759C2×D4—21no—
760C2×D4—21no—
761C2×D4—21no—
762C2×D4—42no—
763C2×D4—42no—
764C2×D4—44no—
765C2×D4—44no—
766C2×D4—42no—
767C2×D4—42no—
768C2×D4C2×D4×C1111yescharacteristic
769C2×D4C2×D4×C1111yescharacteristic
770C2×D4C2×D4×C1111yescharacteristic
771C22×C4—21no—
772C22×C4—22no—
773C22×C4—22no—
774C22×C4—22no—
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×C4C2×D4×C1112yes—
784C22×C4C2×D4×C1111yescharacteristic
785C22×C4C2×D4×C1111yescharacteristic
786C22×C4C24×C1111yescharacteristic
787Q16—24no—
788Q16—42no—
789Q16—42no—
790SD16—24no—
791SD16—42no—
792SD16—42no—
793M16—21no—
794M16—21no—
795M16—21no—
796M16—21no—
797M16—21no—
798M16—21no—
799M16—21no—
800M16C2×D4×C1112yes—
801C2×C8—21no—
802C2×C8—21no—
803C2×C8—21no—
804C2×C8—21no—
805C4⋊C4—22no—
806C4⋊C4—22no—
807C4⋊C4—21no—
808C4⋊C4—21no—
809C4⋊C4—21no—
810C4⋊C4—21no—
811C4⋊C4—21no—
812C4⋊C4—21no—
813C4⋊C4—44no—
814C4⋊C4—42no—
815C4⋊C4—41no—
816C4⋊C4—41no—
817C4⋊C4C2×D4×C1111yescharacteristic
818C4⋊C4C2×D4×C1111yescharacteristic
819C22⋊C4—22no—
820C22⋊C4—22no—
821C22⋊C4—22no—
822C22⋊C4—22no—
823C22⋊C4—21no—
824C22⋊C4—21no—
825C22⋊C4—21no—
826C22⋊C4—22no—
827C22⋊C4—22no—
828C22⋊C4—22no—
829C22⋊C4—22no—
830C22⋊C4—21no—
831C22⋊C4—21no—
832C22⋊C4—21no—
833C22⋊C4—21no—
834C22⋊C4—44no—
835C22⋊C4—44no—
836C42—21no—
837C42—21no—
838C42—21no—
839C42—21no—
840C42—21no—
841C42—21no—
842C42—21no—
843C42—41no—
844C42—41no—
845C42C2×D4×C1111yescharacteristic
846C42C2×D4×C1111yescharacteristic
847C42C2×D4×C1111yescharacteristic
848C42C2×D4×C1111yescharacteristic
849C11#2423511yescharacteristic, direct product factor, Sylow
850C23—21no—
851C23—22no—
852C23—21no—
853C23—21no—
854C23—22no—
855C23—22no—
856C23—44no—
857C23—42no—
858C23—42no—
859C23—82no—
860C23—82no—
861C23C22×D4×C1111yescharacteristic
862Q8—21no—
863Q8—22no—
864Q8—22no—
865Q8—21no—
866Q8—21no—
867Q8—21no—
868Q8—21no—
869Q8—44no—
870Q8—41no—
871Q8—41no—
872Q8—41no—
873Q8—41no—
874Q8—41no—
875Q8—41no—
876Q8C11×#12112yes—
877D4—22no—
878D4—22no—
879D4—21no—
880D4—21no—
881D4—21no—
882D4—21no—
883D4—21no—
884D4—44no—
885D4—44no—
886D4—44no—
887D4—41no—
888D4—41no—
889D4—41no—
890D4—41no—
891D4—41no—
892D4—41no—
893D4—41no—
894D4—41no—
895D4—81no—
896D4—81no—
897D4—82no—
898D4—82no—
899D4C11×#12112yes—
900C2×C4—21no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—21no—
905C2×C4—21no—
906C2×C4—21no—
907C2×C4—22no—
908C2×C4—21no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—44no—
915C2×C4—44no—
916C2×C4—41no—
917C2×C4—44no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—42no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—81no—
931C2×C4—81no—
932C2×C4C11×#12011yescharacteristic
933C2×C4C11×#12011yescharacteristic
934C2×C4C11×#12011yescharacteristic
935C2×C4C11×#12011yescharacteristic
936C2×C4C22×D4×C1111yescharacteristic
937C2×C4C22×D4×C1111yescharacteristic
938C2×C4C22×D4×C1111yescharacteristic
939C2×C4C2×C11×#4111yescharacteristic
940C2×C4C11×H(5,𝔽2)11yescharacteristic
941C2×C4C11×H(5,𝔽2)11yescharacteristic
942C8—22no—
943C8—41no—
944C8—41no—
945C8—41no—
946C22—21no—
947C22—21no—
948C22—22no—
949C22—41no—
950C22—41no—
951C22—41no—
952C22—41no—
953C22—42no—
954C22—41no—
955C22—42no—
956C22—41no—
957C22—41no—
958C22—42no—
959C22—41no—
960C22—82no—
961C22—82no—
962C22—164no—
963C22C2×C11×#12011yescharacteristic
964C22D42×C1111yescharacteristic
965C22C11×#54611yescharacteristic
966C4—22no—
967C4—21no—
968C4—21no—
969C4—21no—
970C4—21no—
971C4—42no—
972C4—42no—
973C4—41no—
974C4—41no—
975C4—42no—
976C4—41no—
977C4—41no—
978C4—81no—
979C4—81no—
980C4C2×C11×#12111yescharacteristic
981C4C11×#53511yescharacteristic
982C4D42×C1111yescharacteristic
983C4C11×#54611yescharacteristic
984C2—21no—
985C2—21no—
986C2—42no—
987C2—82no—
988C2—81no—
989C2—81no—
990C2C11×#240811yescharacteristic
991C2C11×#301811yescharacteristic
992C2C11×#302211yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#3500C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#3037C2semidirect
3. C2×C11×#456C2semidirect
4. C2×C11×#455C2semidirect
5. C4×C11×#137C2semidirect
6. C11×#2545C2semidirect
7. C11×#2038C2semidirect
8. C11×#2037C2semidirect
9. C11×#2005C2semidirect
10. C11×#2004C2semidirect
11. C11×#1980C2semidirect
12. C11×#1967C2semidirect
13. C11×#1806C2semidirect
14. C11×#1793C2semidirect
15. C11×#1792C2semidirect
20. C2×C11×#137C22semidirect
33. C2×C11×C4⋊Q8C22semidirect
38. C2×C4×Q8×C11C22semidirect
49. C11×#428C22semidirect
50. C11×#423C22semidirect
55. C2×C11×#104C22semidirect
56. C2×C11×#104C22semidirect
57. C11×#419C22semidirect
60. C11×#417C22semidirect
61. C2×C11×#101C22semidirect
62. C2×C11×#101C22semidirect
65. C4×C11×M16C22semidirect
67. C11×#391C22semidirect
70. C4×C11×C4⋊C4C22semidirect
71. C11×#339C22semidirect
72. C11×#339C22semidirect
102. C11×#137D4semidirect
206. #24235C11direct (N × H)
355. #3037C2×C11semidirect
356. C2×#456C2×C11semidirect
357. C2×#455C2×C11semidirect
358. C4×#137C2×C11semidirect
359. #2545C2×C11semidirect
360. #2038C2×C11semidirect
361. #2037C2×C11semidirect
362. #2005C2×C11semidirect
363. #2004C2×C11semidirect
364. #1980C2×C11semidirect
365. #1967C2×C11semidirect
366. #1806C2×C11semidirect
367. #1793C2×C11semidirect
368. #1792C2×C11semidirect
469. C2×#137C22×C11semidirect
482. C2×C4⋊Q8C22×C11semidirect
487. C2×C4×Q8C22×C11semidirect
498. #428C22×C11semidirect
499. #423C22×C11semidirect
504. C2×#104C22×C11semidirect
505. C2×#104C22×C11semidirect
506. #419C22×C11semidirect
509. #417C22×C11semidirect
510. C2×#101C22×C11semidirect
511. C2×#101C22×C11semidirect
514. C4×M16C22×C11semidirect
516. #391C22×C11semidirect
519. C4×C4⋊C4C22×C11semidirect
520. #339C22×C11semidirect
521. #339C22×C11semidirect
589. #137D4×C11semidirect
849. C11#24235direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35002
C11×#30372
C2×C11×#4562
C2×C11×#4552
C4×C11×#1372
C11×#25452
C11×#20382
C11×#20372
C11×#20052
C11×#20042
C11×#19802
C11×#19672
C11×#18062
C11×#17932
C11×#17922
#2423511