Finite Group Databasebeta

← C11×#24470 #14601663

Subgroups — C11×#24470 #14601663

Order 2816.

1360 conjugacy classes of subgroups.

The subgroup lattice has 1028 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3489C211yesmaximal, characteristic
2C11×#3056C211yesmaximal, characteristic, complemented
3C2×C11×#456C211yesmaximal, characteristic, complemented
4C11×#3007C211yesmaximal, characteristic, complemented
5C2×C11×#421C211yesmaximal, characteristic, complemented
6C11×#2621C211yesmaximal, characteristic, complemented
7C11×#2040C211yesmaximal, characteristic, complemented
8C11×#2038C211yesmaximal, characteristic, complemented
9C11×#2007C211yesmaximal, characteristic, complemented
10C11×#2005C211yesmaximal, characteristic, complemented
11C11×#1901C211yesmaximal, characteristic, complemented
12C11×#1897C211yesmaximal, characteristic, complemented
13C11×#1882C211yesmaximal, characteristic, complemented
14C11×#1860C211yesmaximal, characteristic, complemented
15C11×#1793C211yesmaximal, characteristic, complemented
16C2×C11×2−1+4C2211yescharacteristic
17C22×C11×#41C2211yescharacteristic
18C2×C11×#137C2211yescharacteristic
19C2×C11×#137C2211yescharacteristic
20C2×C11×#137C2211yescharacteristic, complemented
21C22×C11×M16C2211yescharacteristic
22D4×Q8×C11—21no—
23C11×#548—21no—
24C11×#547—21no—
25C11×#547—22no—
26C11×#546—21no—
27C11×#546—22no—
28C11×#537—21no—
29C11×#537C2211yescharacteristic
30C11×#536—21no—
31C11×#536C2211yescharacteristic
32C2×C11×C4⋊Q8C2211yescharacteristic, complemented
33C11×#525—21no—
34C11×#525C2211yescharacteristic
35C2×C11×C22⋊Q8—21no—
36C2×C11×C22⋊Q8C2211yescharacteristic
37C2×C11×C22⋊Q8C2211yescharacteristic
38C11×#520C2211yescharacteristic
39C2×C11×#117C2211yescharacteristic
40C11×#470—21no—
41C11×#468—21no—
42C11×#467—21no—
43C11×#465—21no—
44C11×#456—24no—
45C11×#452—21no—
46C11×#452—21no—
47C11×#451—21no—
48C11×#450—21no—
49C11×#428C2211yescharacteristic, complemented
50C11×#421—24no—
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
63C11×#407C2211yescharacteristic
64C11×#398—22no—
65C11×#397—22no—
66C11×#391C2211yescharacteristic, complemented
67C11×#391C2211yescharacteristic, complemented
68C11×#382C2211yescharacteristic, complemented
69C11×#343C2211yescharacteristic, complemented
70C11×#343C2211yescharacteristic, 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—
77C2×C11×#41—21no—
78C2×C11×#41—21no—
79C2×C11×#41—21no—
80C2×C11×#41—22no—
81C2×C11×#41—21no—
82C2×C11×#41—22no—
83C2×C11×#41—22no—
84C2×C11×#41—41no—
85C2×C11×#41—41no—
86C2×C11×#41D411yescharacteristic
87C2×C11×#41D411yescharacteristic
88C2×C11×#41C2311yescharacteristic
89C2×C11×#41C2311yescharacteristic
90C2×C11×#41C2311yescharacteristic
91C22×Q8×C11—21no—
92C22×Q8×C11—21no—
93C22×Q8×C11D411yescharacteristic
94C22×Q8×C11C2311yescharacteristic
95C22×Q8×C11C2311yescharacteristic
96C22×D4×C11—21no—
97C22×D4×C11D411yescharacteristic
98C23×C4×C11—21no—
99C23×C4×C11C2311yescharacteristic
100C11×#137—22no—
101C11×#137—22no—
102C11×#137—22no—
103C11×#137—41no—
104C11×#137—41no—
105C11×#137—41no—
106C2×C11×Q16—21no—
107C2×C11×Q16—21no—
108C2×C11×Q16—21no—
109C2×C11×SD16—21no—
110C2×C11×SD16—21no—
111C2×C11×SD16—21no—
112C2×C11×M16—21no—
113C2×C11×M16—22no—
114C2×C11×M16—41no—
115C2×C11×M16C2311yescharacteristic
116C2×C11×M16C2311yescharacteristic
117C2×C11×M16C2311yescharacteristic
118C2×C11×M16C2311yescharacteristic
119C22×C8×C11—21no—
120C11×C4⋊Q8—22no—
121C11×C4⋊Q8—21no—
122C11×C4⋊Q8—22no—
123C11×C4⋊Q8—41no—
124C11×#124—22no—
125C11×#124—21no—
126C11×#123—22no—
127C11×#123—22no—
128C11×#123—22no—
129C11×#123—21no—
130C11×#123—22no—
131C11×C22⋊Q8—22no—
132C11×C22⋊Q8—22no—
133C11×C22⋊Q8—22no—
134C11×C22⋊Q8—21no—
135C11×C22⋊Q8—21no—
136C11×C22⋊Q8—21no—
137C11×C22⋊Q8—21no—
138C11×C22⋊Q8—21no—
139C11×C22⋊Q8—21no—
140C11×C22⋊Q8—21no—
141C11×C22⋊Q8—21no—
142C11×C22⋊Q8—21no—
143C11×C22⋊Q8—21no—
144C11×C22⋊Q8—21no—
145C11×C22⋊Q8—21no—
146C11×C22⋊Q8D411yescharacteristic
147C11×C22⋊Q8D411yescharacteristic
148C11×#121—22no—
149C11×#121—22no—
150C11×#121—22no—
151C11×#121—21no—
152C11×#121—21no—
153C11×#121—22no—
154C11×#121D411yescharacteristic
155C11×#121D411yescharacteristic
156C11×#120—22no—
157C11×#120—21no—
158C4×Q8×C11—21no—
159C4×D4×C11—22no—
160C4×D4×C11—22no—
161C4×D4×C11—21no—
162C4×D4×C11—22no—
163C4×D4×C11—21no—
164C4×D4×C11—21no—
165C11×#117—21no—
166C11×#117—22no—
167C11×#117—41no—
168C11×#117C2311yescharacteristic
169C2×C11×C4⋊C4—22no—
170C2×C11×C4⋊C4—21no—
171C2×C11×C4⋊C4—21no—
172C2×C11×C4⋊C4—21no—
173C2×C11×C4⋊C4—22no—
174C2×C11×C4⋊C4D412yes—
175C2×C11×C4⋊C4C2311yescharacteristic
176C2×C11×C4⋊C4C2311yescharacteristic
177C2×C11×C22⋊C4—22no—
178C2×C11×C22⋊C4—21no—
179C2×C11×C22⋊C4—21no—
180C2×C11×C22⋊C4D412yes—
181C2×C42×C11C2311yescharacteristic
182C2×C42×C11C2311yescharacteristic
183C11×#107—21no—
184C11×#106—21no—
185C11×#104—22no—
186C11×#104—22no—
187C11×#104—22no—
188C11×#104—22no—
189C11×#104—41no—
190C11×#104D414yescomplemented
191C11×#103—21no—
192C11×#103—21no—
193C11×#103—21no—
194C11×#103—21no—
195C11×#103—21no—
196C11×#102—21no—
197C11×#102—21no—
198C11×#102—21no—
199C11×#101—22no—
200C11×#101—41no—
201C11×C22⋊C8—21no—
202C11×C22⋊C8—21no—
203C11×#95—22no—
204C11×#95—22no—
205C11×#95—22no—
206#24470C1111yesmaximal, characteristic, direct product factor, Sylow
207C24×C11—21no—
208C24×C11C2×D411yescharacteristic
209C11×#41—21no—
210C11×#41—21no—
211C11×#41—22no—
212C11×#41—22no—
213C11×#41—21no—
214C11×#41—21no—
215C11×#41—21no—
216C11×#41—21no—
217C11×#41—21no—
218C11×#41—21no—
219C11×#41—21no—
220C11×#41—21no—
221C11×#41—42no—
222C11×#41—42no—
223C11×#41—41no—
224C11×#41—41no—
225C11×#41—42no—
226C11×#41—42no—
227C11×#41—42no—
228C11×#41—42no—
229C11×#41—44no—
230C11×#41—44no—
231C11×#41—42no—
232C11×#41—42no—
233C11×#41C2×D412yes—
234C11×#41#4112yes—
235C2×Q8×C11—22no—
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—22no—
244C2×Q8×C11—21no—
245C2×Q8×C11—21no—
246C2×Q8×C11—21no—
247C2×Q8×C11—21no—
248C2×Q8×C11—21no—
249C2×Q8×C11—21no—
250C2×Q8×C11—41no—
251C2×Q8×C11—42no—
252C2×Q8×C11—42no—
253C2×Q8×C11—42no—
254C2×Q8×C11—42no—
255C2×Q8×C11C2×D411yescharacteristic
256C2×Q8×C11C2×D411yescharacteristic
257C2×Q8×C11C2×D411yescharacteristic
258C2×D4×C11—21no—
259C2×D4×C11—22no—
260C2×D4×C11—22no—
261C2×D4×C11—21no—
262C2×D4×C11—21no—
263C2×D4×C11—21no—
264C2×D4×C11—21no—
265C2×D4×C11—21no—
266C2×D4×C11—22no—
267C2×D4×C11—21no—
268C2×D4×C11—21no—
269C2×D4×C11—41no—
270C2×D4×C11—42no—
271C2×D4×C11—42no—
272C2×D4×C11C2×D411yescharacteristic
273C2×D4×C11C2×D411yescharacteristic
274C2×D4×C11C2×D411yescharacteristic
275C22×C4×C11—21no—
276C22×C4×C11—21no—
277C22×C4×C11—21no—
278C22×C4×C11—21no—
279C22×C4×C11—21no—
280C22×C4×C11—22no—
281C22×C4×C11—22no—
282C22×C4×C11—21no—
283C22×C4×C11—21no—
284C22×C4×C11—22no—
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—42no—
293C22×C4×C11—42no—
294C22×C4×C11C2×D412yes—
295C22×C4×C11C2×D411yescharacteristic
296C22×C4×C11C2×D411yescharacteristic
297C22×C4×C11C2×D411yescharacteristic
298C22×C4×C11C2×D411yescharacteristic
299C22×C4×C11C2×D411yescharacteristic
300C22×C4×C11C2×D412yes—
301C22×C4×C11C2411yescharacteristic
302C11×Q16—42no—
303C11×Q16—42no—
304C11×Q16—42no—
305C11×SD16—42no—
306C11×SD16—42no—
307C11×SD16—42no—
308C11×M16—21no—
309C11×M16—21no—
310C11×M16—21no—
311C11×M16—21no—
312C11×M16—21no—
313C11×M16—21no—
314C11×M16—21no—
315C11×M16—42no—
316C11×M16C2×D412yes—
317C2×C8×C11—21no—
318C2×C8×C11—21no—
319C2×C8×C11—21no—
320C2×C8×C11—21no—
321C2×C8×C11—42no—
322C11×C4⋊C4—22no—
323C11×C4⋊C4—22no—
324C11×C4⋊C4—22no—
325C11×C4⋊C4—22no—
326C11×C4⋊C4—21no—
327C11×C4⋊C4—22no—
328C11×C4⋊C4—22no—
329C11×C4⋊C4—21no—
330C11×C4⋊C4—21no—
331C11×C4⋊C4—21no—
332C11×C4⋊C4—21no—
333C11×C4⋊C4—21no—
334C11×C4⋊C4—42no—
335C11×C4⋊C4—44no—
336C11×C4⋊C4—41no—
337C11×C4⋊C4—41no—
338C11×C4⋊C4C2×D411yescharacteristic
339C11×C4⋊C4C2×D411yescharacteristic
340C11×C22⋊C4—22no—
341C11×C22⋊C4—22no—
342C11×C22⋊C4—22no—
343C11×C22⋊C4—22no—
344C11×C22⋊C4—22no—
345C11×C22⋊C4—21no—
346C11×C22⋊C4—22no—
347C11×C22⋊C4—22no—
348C11×C22⋊C4—21no—
349C11×C22⋊C4—21no—
350C11×C22⋊C4—21no—
351C11×C22⋊C4—21no—
352C11×C22⋊C4—42no—
353C11×C22⋊C4—41no—
354C11×C22⋊C4—41no—
355C42×C11—22no—
356C42×C11—21no—
357C42×C11—21no—
358C42×C11—21no—
359C42×C11—21no—
360C42×C11C2×D412yes—
361#3489C2×C1111yescharacteristic
362#3056C2×C1111yescharacteristic, complemented
363C2×#456C2×C1111yescharacteristic, complemented
364#3007C2×C1111yescharacteristic, complemented
365C2×#421C2×C1111yescharacteristic, complemented
366#2621C2×C1111yescharacteristic, complemented
367#2040C2×C1111yescharacteristic, complemented
368#2038C2×C1111yescharacteristic, complemented
369#2007C2×C1111yescharacteristic, complemented
370#2005C2×C1111yescharacteristic, complemented
371#1901C2×C1111yescharacteristic, complemented
372#1897C2×C1111yescharacteristic, complemented
373#1882C2×C1111yescharacteristic, complemented
374#1860C2×C1111yescharacteristic, complemented
375#1793C2×C1111yescharacteristic, complemented
376C23×C11—21no—
377C23×C11—21no—
378C23×C11—21no—
379C23×C11—21no—
380C23×C11—21no—
381C23×C11—41no—
382C23×C11—41no—
383C23×C11—42no—
384C23×C11—42no—
385C23×C11—81no—
386C23×C11#12011yescharacteristic
387C23×C11#12011yescharacteristic
388C23×C11C22×D411yescharacteristic
389Q8×C11—21no—
390Q8×C11—21no—
391Q8×C11—21no—
392Q8×C11—21no—
393Q8×C11—21no—
394Q8×C11—42no—
395Q8×C11—44no—
396Q8×C11—41no—
397Q8×C11—41no—
398Q8×C11—41no—
399Q8×C11—41no—
400Q8×C11—41no—
401Q8×C11—41no—
402Q8×C11—41no—
403Q8×C11—41no—
404Q8×C11#12112yes—
405D4×C11—22no—
406D4×C11—22no—
407D4×C11—21no—
408D4×C11—21no—
409D4×C11—21no—
410D4×C11—21no—
411D4×C11—21no—
412D4×C11—42no—
413D4×C11—42no—
414D4×C11—42no—
415D4×C11—42no—
416D4×C11—44no—
417D4×C11—41no—
418D4×C11—41no—
419D4×C11—41no—
420D4×C11—41no—
421D4×C11—81no—
422D4×C11—82no—
423D4×C11#12112yes—
424C2×C4×C11—21no—
425C2×C4×C11—21no—
426C2×C4×C11—21no—
427C2×C4×C11—21no—
428C2×C4×C11—21no—
429C2×C4×C11—21no—
430C2×C4×C11—21no—
431C2×C4×C11—21no—
432C2×C4×C11—21no—
433C2×C4×C11—22no—
434C2×C4×C11—21no—
435C2×C4×C11—21no—
436C2×C4×C11—22no—
437C2×C4×C11—21no—
438C2×C4×C11—22no—
439C2×C4×C11—21no—
440C2×C4×C11—21no—
441C2×C4×C11—22no—
442C2×C4×C11—21no—
443C2×C4×C11—22no—
444C2×C4×C11—22no—
445C2×C4×C11—22no—
446C2×C4×C11—42no—
447C2×C4×C11—42no—
448C2×C4×C11—42no—
449C2×C4×C11—44no—
450C2×C4×C11—41no—
451C2×C4×C11—41no—
452C2×C4×C11—44no—
453C2×C4×C11—41no—
454C2×C4×C11—41no—
455C2×C4×C11—41no—
456C2×C4×C11—41no—
457C2×C4×C11—42no—
458C2×C4×C11—41no—
459C2×C4×C11—41no—
460C2×C4×C11—42no—
461C2×C4×C11—41no—
462C2×C4×C11—41no—
463C2×C4×C11—41no—
464C2×C4×C11—41no—
465C2×C4×C11—41no—
466C2×C4×C11—82no—
467C2×C4×C11#12011yescharacteristic
468C2×C4×C11#12011yescharacteristic
469C2×C4×C11C22×D411yescharacteristic
470C2×C4×C11C22×D411yescharacteristic
471C2×C4×C11C22×D411yescharacteristic
472C2×C4×C11C2×#4111yescharacteristic
473C2×C4×C11H(5,𝔽2)11yescharacteristic
474C2×C4×C11H(5,𝔽2)11yescharacteristic
475C8×C11—22no—
476C8×C11—41no—
477C8×C11—41no—
478C8×C11—41no—
479C2×2−1+4C22×C1111yescharacteristic
480C22×#41C22×C1111yescharacteristic
481C2×#137C22×C1111yescharacteristic
482C2×#137C22×C1111yescharacteristic
483C2×#137C22×C1111yescharacteristic, complemented
484C22×M16C22×C1111yescharacteristic
485D4×Q8—21no—
486#548—21no—
487#547—21no—
488#547—22no—
489#546—21no—
490#546—22no—
491#537—21no—
492#537C22×C1111yescharacteristic
493#536—21no—
494#536C22×C1111yescharacteristic
495C2×C4⋊Q8C22×C1111yescharacteristic, complemented
496#525—21no—
497#525C22×C1111yescharacteristic
498C2×C22⋊Q8—21no—
499C2×C22⋊Q8C22×C1111yescharacteristic
500C2×C22⋊Q8C22×C1111yescharacteristic
501#520C22×C1111yescharacteristic
502C2×#117C22×C1111yescharacteristic
503#470—21no—
504#468—21no—
505#467—21no—
506#465—21no—
507#456—24no—
508#452—21no—
509#452—21no—
510#451—21no—
511#450—21no—
512#428C22×C1111yescharacteristic, complemented
513#421—24no—
514C2×#104C22×C1111yescharacteristic
515C2×#104C22×C1111yescharacteristic
516C2×#104C22×C1111yescharacteristic
517C2×#104C22×C1111yescharacteristic
518C2×#104C22×C1111yescharacteristic, complemented
519C2×#104C22×C1111yescharacteristic, complemented
520#419C22×C1111yescharacteristic, complemented
521#417C22×C1111yescharacteristic
522#417C22×C1111yescharacteristic
523#417C22×C1111yescharacteristic, complemented
524C2×#101C22×C1111yescharacteristic, complemented
525C2×#101C22×C1111yescharacteristic, complemented
526#407C22×C1111yescharacteristic
527#398—22no—
528#397—22no—
529#391C22×C1111yescharacteristic, complemented
530#391C22×C1111yescharacteristic, complemented
531#382C22×C1111yescharacteristic, complemented
532#343C22×C1111yescharacteristic, complemented
533#343C22×C1111yescharacteristic, complemented
534#339C22×C1111yescharacteristic, complemented
535#339C22×C1111yescharacteristic, complemented
536C22×C11—21no—
537C22×C11—21no—
538C22×C11—21no—
539C22×C11—21no—
540C22×C11—22no—
541C22×C11—21no—
542C22×C11—21no—
543C22×C11—21no—
544C22×C11—21no—
545C22×C11—41no—
546C22×C11—41no—
547C22×C11—41no—
548C22×C11—41no—
549C22×C11—41no—
550C22×C11—41no—
551C22×C11—41no—
552C22×C11—41no—
553C22×C11—81no—
554C22×C11—81no—
555C22×C11—84no—
556C22×C11C2×#12011yescharacteristic
557C22×C11D4211yescharacteristic
558C22×C11#54611yescharacteristic
559C4×C11—21no—
560C4×C11—21no—
561C4×C11—22no—
562C4×C11—42no—
563C4×C11—42no—
564C4×C11—41no—
565C4×C11—41no—
566C4×C11—41no—
567C4×C11—42no—
568C4×C11—41no—
569C4×C11—81no—
570C4×C11—81no—
571C4×C11—81no—
572C4×C11C2×#12111yescharacteristic
573C4×C11#53411yescharacteristic
574C4×C11D4211yescharacteristic
575C4×C11#54611yescharacteristic
5762−1+4—22no—
5772−1+4—22no—
5782−1+4—41no—
5792−1+4—41no—
580C2×#41—21no—
581C2×#41—21no—
582C2×#41—21no—
583C2×#41—22no—
584C2×#41—21no—
585C2×#41—22no—
586C2×#41—22no—
587C2×#41—41no—
588C2×#41—41no—
589C2×#41D4×C1111yescharacteristic
590C2×#41D4×C1111yescharacteristic
591C2×#41C23×C1111yescharacteristic
592C2×#41C23×C1111yescharacteristic
593C2×#41C23×C1111yescharacteristic
594C22×Q8—21no—
595C22×Q8—21no—
596C22×Q8D4×C1111yescharacteristic
597C22×Q8C23×C1111yescharacteristic
598C22×Q8C23×C1111yescharacteristic
599C22×D4—21no—
600C22×D4D4×C1111yescharacteristic
601C23×C4—21no—
602C23×C4C23×C1111yescharacteristic
603#137—22no—
604#137—22no—
605#137—22no—
606#137—41no—
607#137—41no—
608#137—41no—
609C2×Q16—21no—
610C2×Q16—21no—
611C2×Q16—21no—
612C2×SD16—21no—
613C2×SD16—21no—
614C2×SD16—21no—
615C2×M16—21no—
616C2×M16—22no—
617C2×M16—41no—
618C2×M16C23×C1111yescharacteristic
619C2×M16C23×C1111yescharacteristic
620C2×M16C23×C1111yescharacteristic
621C2×M16C23×C1111yescharacteristic
622C22×C8—21no—
623C4⋊Q8—22no—
624C4⋊Q8—21no—
625C4⋊Q8—22no—
626C4⋊Q8—41no—
627#124—22no—
628#124—21no—
629#123—22no—
630#123—22no—
631#123—22no—
632#123—21no—
633#123—22no—
634C22⋊Q8—22no—
635C22⋊Q8—22no—
636C22⋊Q8—22no—
637C22⋊Q8—21no—
638C22⋊Q8—21no—
639C22⋊Q8—21no—
640C22⋊Q8—21no—
641C22⋊Q8—21no—
642C22⋊Q8—21no—
643C22⋊Q8—21no—
644C22⋊Q8—21no—
645C22⋊Q8—21no—
646C22⋊Q8—21no—
647C22⋊Q8—21no—
648C22⋊Q8—21no—
649C22⋊Q8D4×C1111yescharacteristic
650C22⋊Q8D4×C1111yescharacteristic
651#121—22no—
652#121—22no—
653#121—22no—
654#121—21no—
655#121—21no—
656#121—22no—
657#121D4×C1111yescharacteristic
658#121D4×C1111yescharacteristic
659#120—22no—
660#120—21no—
661C4×Q8—21no—
662C4×D4—22no—
663C4×D4—22no—
664C4×D4—21no—
665C4×D4—22no—
666C4×D4—21no—
667C4×D4—21no—
668#117—21no—
669#117—22no—
670#117—41no—
671#117C23×C1111yescharacteristic
672C2×C4⋊C4—22no—
673C2×C4⋊C4—21no—
674C2×C4⋊C4—21no—
675C2×C4⋊C4—21no—
676C2×C4⋊C4—22no—
677C2×C4⋊C4D4×C1112yes—
678C2×C4⋊C4C23×C1111yescharacteristic
679C2×C4⋊C4C23×C1111yescharacteristic
680C2×C22⋊C4—22no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4D4×C1112yes—
684C2×C42C23×C1111yescharacteristic
685C2×C42C23×C1111yescharacteristic
686#107—21no—
687#106—21no—
688#104—22no—
689#104—22no—
690#104—22no—
691#104—22no—
692#104—41no—
693#104D4×C1114yescomplemented
694#103—21no—
695#103—21no—
696#103—21no—
697#103—21no—
698#103—21no—
699#102—21no—
700#102—21no—
701#102—21no—
702#101—22no—
703#101—41no—
704C22⋊C8—21no—
705C22⋊C8—21no—
706#95—22no—
707#95—22no—
708#95—22no—
709C2×C11—21no—
710C2×C11—21no—
711C2×C11—41no—
712C2×C11—41no—
713C2×C11—42no—
714C2×C11—81no—
715C2×C11—81no—
716C2×C11#241011yescharacteristic
717C2×C11#302011yescharacteristic
718C2×C11#302211yescharacteristic
719C24—21no—
720C24C2×D4×C1111yescharacteristic
721#41—21no—
722#41—21no—
723#41—22no—
724#41—22no—
725#41—21no—
726#41—21no—
727#41—21no—
728#41—21no—
729#41—21no—
730#41—21no—
731#41—21no—
732#41—21no—
733#41—42no—
734#41—42no—
735#41—41no—
736#41—41no—
737#41—42no—
738#41—42no—
739#41—42no—
740#41—42no—
741#41—44no—
742#41—44no—
743#41—42no—
744#41—42no—
745#41C2×D4×C1112yes—
746#41C11×#4112yes—
747C2×Q8—22no—
748C2×Q8—21no—
749C2×Q8—21no—
750C2×Q8—21no—
751C2×Q8—21no—
752C2×Q8—21no—
753C2×Q8—21no—
754C2×Q8—21no—
755C2×Q8—22no—
756C2×Q8—21no—
757C2×Q8—21no—
758C2×Q8—21no—
759C2×Q8—21no—
760C2×Q8—21no—
761C2×Q8—21no—
762C2×Q8—41no—
763C2×Q8—42no—
764C2×Q8—42no—
765C2×Q8—42no—
766C2×Q8—42no—
767C2×Q8C2×D4×C1111yescharacteristic
768C2×Q8C2×D4×C1111yescharacteristic
769C2×Q8C2×D4×C1111yescharacteristic
770C2×D4—21no—
771C2×D4—22no—
772C2×D4—22no—
773C2×D4—21no—
774C2×D4—21no—
775C2×D4—21no—
776C2×D4—21no—
777C2×D4—21no—
778C2×D4—22no—
779C2×D4—21no—
780C2×D4—21no—
781C2×D4—41no—
782C2×D4—42no—
783C2×D4—42no—
784C2×D4C2×D4×C1111yescharacteristic
785C2×D4C2×D4×C1111yescharacteristic
786C2×D4C2×D4×C1111yescharacteristic
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—22no—
793C22×C4—22no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—22no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—42no—
805C22×C4—42no—
806C22×C4C2×D4×C1112yes—
807C22×C4C2×D4×C1111yescharacteristic
808C22×C4C2×D4×C1111yescharacteristic
809C22×C4C2×D4×C1111yescharacteristic
810C22×C4C2×D4×C1111yescharacteristic
811C22×C4C2×D4×C1111yescharacteristic
812C22×C4C2×D4×C1112yes—
813C22×C4C24×C1111yescharacteristic
814Q16—42no—
815Q16—42no—
816Q16—42no—
817SD16—42no—
818SD16—42no—
819SD16—42no—
820M16—21no—
821M16—21no—
822M16—21no—
823M16—21no—
824M16—21no—
825M16—21no—
826M16—21no—
827M16—42no—
828M16C2×D4×C1112yes—
829C2×C8—21no—
830C2×C8—21no—
831C2×C8—21no—
832C2×C8—21no—
833C2×C8—42no—
834C4⋊C4—22no—
835C4⋊C4—22no—
836C4⋊C4—22no—
837C4⋊C4—22no—
838C4⋊C4—21no—
839C4⋊C4—22no—
840C4⋊C4—22no—
841C4⋊C4—21no—
842C4⋊C4—21no—
843C4⋊C4—21no—
844C4⋊C4—21no—
845C4⋊C4—21no—
846C4⋊C4—42no—
847C4⋊C4—44no—
848C4⋊C4—41no—
849C4⋊C4—41no—
850C4⋊C4C2×D4×C1111yescharacteristic
851C4⋊C4C2×D4×C1111yescharacteristic
852C22⋊C4—22no—
853C22⋊C4—22no—
854C22⋊C4—22no—
855C22⋊C4—22no—
856C22⋊C4—22no—
857C22⋊C4—21no—
858C22⋊C4—22no—
859C22⋊C4—22no—
860C22⋊C4—21no—
861C22⋊C4—21no—
862C22⋊C4—21no—
863C22⋊C4—21no—
864C22⋊C4—42no—
865C22⋊C4—41no—
866C22⋊C4—41no—
867C42—22no—
868C42—21no—
869C42—21no—
870C42—21no—
871C42—21no—
872C42C2×D4×C1112yes—
873C11#2447011yescharacteristic, direct product factor, Sylow
874C23—21no—
875C23—21no—
876C23—21no—
877C23—21no—
878C23—21no—
879C23—41no—
880C23—41no—
881C23—42no—
882C23—42no—
883C23—81no—
884C23C11×#12011yescharacteristic
885C23C11×#12011yescharacteristic
886C23C22×D4×C1111yescharacteristic
887Q8—21no—
888Q8—21no—
889Q8—21no—
890Q8—21no—
891Q8—21no—
892Q8—42no—
893Q8—44no—
894Q8—41no—
895Q8—41no—
896Q8—41no—
897Q8—41no—
898Q8—41no—
899Q8—41no—
900Q8—41no—
901Q8—41no—
902Q8C11×#12112yes—
903D4—22no—
904D4—22no—
905D4—21no—
906D4—21no—
907D4—21no—
908D4—21no—
909D4—21no—
910D4—42no—
911D4—42no—
912D4—42no—
913D4—42no—
914D4—44no—
915D4—41no—
916D4—41no—
917D4—41no—
918D4—41no—
919D4—81no—
920D4—82no—
921D4C11×#12112yes—
922C2×C4—21no—
923C2×C4—21no—
924C2×C4—21no—
925C2×C4—21no—
926C2×C4—21no—
927C2×C4—21no—
928C2×C4—21no—
929C2×C4—21no—
930C2×C4—21no—
931C2×C4—22no—
932C2×C4—21no—
933C2×C4—21no—
934C2×C4—22no—
935C2×C4—21no—
936C2×C4—22no—
937C2×C4—21no—
938C2×C4—21no—
939C2×C4—22no—
940C2×C4—21no—
941C2×C4—22no—
942C2×C4—22no—
943C2×C4—22no—
944C2×C4—42no—
945C2×C4—42no—
946C2×C4—42no—
947C2×C4—44no—
948C2×C4—41no—
949C2×C4—41no—
950C2×C4—44no—
951C2×C4—41no—
952C2×C4—41no—
953C2×C4—41no—
954C2×C4—41no—
955C2×C4—42no—
956C2×C4—41no—
957C2×C4—41no—
958C2×C4—42no—
959C2×C4—41no—
960C2×C4—41no—
961C2×C4—41no—
962C2×C4—41no—
963C2×C4—41no—
964C2×C4—82no—
965C2×C4C11×#12011yescharacteristic
966C2×C4C11×#12011yescharacteristic
967C2×C4C22×D4×C1111yescharacteristic
968C2×C4C22×D4×C1111yescharacteristic
969C2×C4C22×D4×C1111yescharacteristic
970C2×C4C2×C11×#4111yescharacteristic
971C2×C4C11×H(5,𝔽2)11yescharacteristic
972C2×C4C11×H(5,𝔽2)11yescharacteristic
973C8—22no—
974C8—41no—
975C8—41no—
976C8—41no—
977C22—21no—
978C22—21no—
979C22—21no—
980C22—21no—
981C22—22no—
982C22—21no—
983C22—21no—
984C22—21no—
985C22—21no—
986C22—41no—
987C22—41no—
988C22—41no—
989C22—41no—
990C22—41no—
991C22—41no—
992C22—41no—
993C22—41no—
994C22—81no—
995C22—81no—
996C22—84no—
997C22C2×C11×#12011yescharacteristic
998C22D42×C1111yescharacteristic
999C22C11×#54611yescharacteristic
1000C4—21no—
1001C4—21no—
1002C4—22no—
1003C4—42no—
1004C4—42no—
1005C4—41no—
1006C4—41no—
1007C4—41no—
1008C4—42no—
1009C4—41no—
1010C4—81no—
1011C4—81no—
1012C4—81no—
1013C4C2×C11×#12111yescharacteristic
1014C4C11×#53411yescharacteristic
1015C4D42×C1111yescharacteristic
1016C4C11×#54611yescharacteristic
1017C2—21no—
1018C2—21no—
1019C2—41no—
1020C2—41no—
1021C2—42no—
1022C2—81no—
1023C2—81no—
1024C2C11×#241011yescharacteristic
1025C2C11×#302011yescharacteristic
1026C2C11×#302211yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#3489C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#3056C2semidirect
3. C2×C11×#456C2semidirect
4. C11×#3007C2semidirect
5. C2×C11×#421C2semidirect
6. C11×#2621C2semidirect
7. C11×#2040C2semidirect
8. C11×#2038C2semidirect
9. C11×#2007C2semidirect
10. C11×#2005C2semidirect
11. C11×#1901C2semidirect
12. C11×#1897C2semidirect
13. C11×#1882C2semidirect
14. C11×#1860C2semidirect
15. C11×#1793C2semidirect
20. C2×C11×#137C22semidirect
32. C2×C11×C4⋊Q8C22semidirect
49. C11×#428C22semidirect
55. C2×C11×#104C22semidirect
56. C2×C11×#104C22semidirect
57. C11×#419C22semidirect
60. C11×#417C22semidirect
61. C2×C11×#101C22semidirect
62. C2×C11×#101C22semidirect
66. C11×#391C22semidirect
67. C11×#391C22semidirect
68. C11×#382C22semidirect
69. C11×#343C22semidirect
70. C11×#343C22semidirect
71. C11×#339C22semidirect
72. C11×#339C22semidirect
190. C11×#104D4semidirect
206. #24470C11direct (N × H)
362. #3056C2×C11semidirect
363. C2×#456C2×C11semidirect
364. #3007C2×C11semidirect
365. C2×#421C2×C11semidirect
366. #2621C2×C11semidirect
367. #2040C2×C11semidirect
368. #2038C2×C11semidirect
369. #2007C2×C11semidirect
370. #2005C2×C11semidirect
371. #1901C2×C11semidirect
372. #1897C2×C11semidirect
373. #1882C2×C11semidirect
374. #1860C2×C11semidirect
375. #1793C2×C11semidirect
483. C2×#137C22×C11semidirect
495. C2×C4⋊Q8C22×C11semidirect
512. #428C22×C11semidirect
518. C2×#104C22×C11semidirect
519. C2×#104C22×C11semidirect
520. #419C22×C11semidirect
523. #417C22×C11semidirect
524. C2×#101C22×C11semidirect
525. C2×#101C22×C11semidirect
529. #391C22×C11semidirect
530. #391C22×C11semidirect
531. #382C22×C11semidirect
532. #343C22×C11semidirect
533. #343C22×C11semidirect
534. #339C22×C11semidirect
535. #339C22×C11semidirect
693. #104D4×C11semidirect
873. C11#24470direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#34892
C11×#30562
C2×C11×#4562
C11×#30072
C2×C11×#4212
C11×#26212
C11×#20402
C11×#20382
C11×#20072
C11×#20052
C11×#19012
C11×#18972
C11×#18822
C11×#18602
C11×#17932
#2447011