Finite Group Databasebeta

← C11×#24028 #14601221

Subgroups — C11×#24028 #14601221

Order 2816.

1250 conjugacy classes of subgroups.

The subgroup lattice has 972 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3489C211yesmaximal, characteristic
2C11×#3093C211yesmaximal, characteristic, complemented
3C11×#2896C211yesmaximal, characteristic, complemented
4C11×#2499C211yesmaximal, characteristic, complemented
5C11×#2040C211yesmaximal, characteristic, complemented
6C11×#2039C211yesmaximal, characteristic, complemented
7C11×#2038C211yesmaximal, characteristic, complemented
8C11×#2038C211yesmaximal, characteristic, complemented
9C11×#1901C211yesmaximal, characteristic, complemented
10C11×#1871C211yesmaximal, characteristic, complemented
11C11×#1860C211yesmaximal, characteristic, complemented
12C11×#1859C211yesmaximal, characteristic, complemented
13C11×#1793C211yesmaximal, characteristic, complemented
14C11×#1793C211yesmaximal, characteristic, complemented
15C11×#1789C211yesmaximal, characteristic, complemented
16C2×C11×2−1+4C2211yescharacteristic
17C22×C11×#41C2211yescharacteristic
18C22×C11×M16C2211yescharacteristic
19D4×Q8×C11—21no—
20C11×#548—21no—
21C11×#547—21no—
22C11×#547—22no—
23C11×#546—21no—
24C11×#546—22no—
25C11×#537—21no—
26C11×#537C2211yescharacteristic
27C11×#536—21no—
28C11×#536C2211yescharacteristic
29C11×#525—21no—
30C11×#525C2211yescharacteristic
31C2×C11×C22⋊Q8—21no—
32C2×C11×C22⋊Q8C2211yescharacteristic
33C11×#520C2211yescharacteristic
34C2×C11×#117C2211yescharacteristic
35C11×#485—21no—
36C11×#485—21no—
37C11×#482—21no—
38C11×#482—21no—
39C11×#428C2211yescharacteristic, complemented
40C11×#428C2211yescharacteristic, complemented
41C2×C11×#104C2211yescharacteristic
42C2×C11×#104C2211yescharacteristic
43C2×C11×#104C2211yescharacteristic
44C2×C11×#104C2211yescharacteristic
45C2×C11×#104C2211yescharacteristic, complemented
46C2×C11×#104C2211yescharacteristic, complemented
47C11×#419—21no—
48C11×#418—21no—
49C11×#417C2211yescharacteristic
50C11×#417C2211yescharacteristic
51C11×#417C2211yescharacteristic
52C11×#417C2211yescharacteristic
53C11×#417C2211yescharacteristic, complemented
54C11×#417C2211yescharacteristic, complemented
55C11×#416—21no—
56C11×#416—21no—
57C2×C11×#101C2211yescharacteristic, complemented
58C2×C11×#101C2211yescharacteristic, complemented
59C11×#407C2211yescharacteristic
60C11×#397—22no—
61C11×#391C2211yescharacteristic, complemented
62C11×#391C2211yescharacteristic, complemented
63C11×#387—22no—
64C11×#384C2211yescharacteristic, complemented
65C11×#382C2211yescharacteristic, complemented
66C4×C11×C22⋊C4C2211yescharacteristic
67C11×#343C2211yescharacteristic, complemented
68C11×#343C2211yescharacteristic, complemented
69C11×#339C2211yescharacteristic, complemented
70C11×#339C2211yescharacteristic, complemented
71C11×2−1+4—22no—
72C11×2−1+4—22no—
73C11×2−1+4—41no—
74C11×2−1+4—41no—
75C2×C11×#41—21no—
76C2×C11×#41—21no—
77C2×C11×#41—21no—
78C2×C11×#41—22no—
79C2×C11×#41—21no—
80C2×C11×#41—22no—
81C2×C11×#41—22no—
82C2×C11×#41—41no—
83C2×C11×#41—41no—
84C2×C11×#41D411yescharacteristic
85C2×C11×#41D411yescharacteristic
86C2×C11×#41C2311yescharacteristic
87C2×C11×#41C2311yescharacteristic
88C2×C11×#41C2311yescharacteristic
89C22×Q8×C11—21no—
90C22×Q8×C11—21no—
91C22×Q8×C11D411yescharacteristic
92C22×Q8×C11C2311yescharacteristic
93C22×D4×C11—21no—
94C22×D4×C11D411yescharacteristic
95C23×C4×C11—21no—
96C23×C4×C11C2311yescharacteristic
97C2×C11×M16—21no—
98C2×C11×M16—41no—
99C2×C11×M16—41no—
100C2×C11×M16C2311yescharacteristic
101C2×C11×M16C2311yescharacteristic
102C2×C11×M16C2311yescharacteristic
103C2×C11×M16C2311yescharacteristic
104C22×C8×C11—21no—
105C11×C4⋊Q8—22no—
106C11×C4⋊Q8—21no—
107C11×#124—22no—
108C11×#124—21no—
109C11×#123—22no—
110C11×#123—22no—
111C11×#123—22no—
112C11×#123—21no—
113C11×#123—22no—
114C11×C22⋊Q8—22no—
115C11×C22⋊Q8—22no—
116C11×C22⋊Q8—22no—
117C11×C22⋊Q8—21no—
118C11×C22⋊Q8—21no—
119C11×C22⋊Q8—21no—
120C11×C22⋊Q8—21no—
121C11×C22⋊Q8—21no—
122C11×C22⋊Q8—21no—
123C11×C22⋊Q8—21no—
124C11×C22⋊Q8—21no—
125C11×C22⋊Q8D411yescharacteristic
126C11×C22⋊Q8D411yescharacteristic
127C11×#121—22no—
128C11×#121—22no—
129C11×#121—22no—
130C11×#121—21no—
131C11×#121—21no—
132C11×#121—22no—
133C11×#121D411yescharacteristic
134C11×#121D411yescharacteristic
135C11×#120—22no—
136C11×#120—21no—
137C4×Q8×C11—21no—
138C4×D4×C11—22no—
139C4×D4×C11—22no—
140C4×D4×C11—21no—
141C4×D4×C11—22no—
142C4×D4×C11—21no—
143C4×D4×C11—21no—
144C11×#117—21no—
145C11×#117—21no—
146C11×#117—21no—
147C11×#117—21no—
148C11×#117—21no—
149C11×#117C2311yescharacteristic
150C2×C11×C4⋊C4—22no—
151C2×C11×C4⋊C4—21no—
152C2×C11×C4⋊C4—22no—
153C2×C11×C4⋊C4D412yes—
154C2×C11×C4⋊C4C2311yescharacteristic
155C2×C11×C4⋊C4C2311yescharacteristic
156C2×C11×C4⋊C4C2311yescharacteristic
157C2×C11×C22⋊C4—22no—
158C2×C11×C22⋊C4—21no—
159C2×C11×C22⋊C4—21no—
160C2×C11×C22⋊C4D412yes—
161C2×C42×C11—21no—
162C2×C42×C11C2311yescharacteristic
163C2×C42×C11C2311yescharacteristic
164C11×#107—21no—
165C11×#107—21no—
166C11×#106—21no—
167C11×#106—21no—
168C11×#104—22no—
169C11×#104—22no—
170C11×#104—41no—
171C11×#104—41no—
172C11×#104—41no—
173C11×#104—41no—
174C11×#103—21no—
175C11×#103—21no—
176C11×#103—21no—
177C11×#103—21no—
178C11×#103—21no—
179C11×#103—21no—
180C11×#102—21no—
181C11×#102—21no—
182C11×#102—21no—
183C11×#102—21no—
184C11×#102—21no—
185C11×#102—21no—
186C11×#101—41no—
187C11×#101—41no—
188C11×C22⋊C8—21no—
189C11×C22⋊C8—21no—
190C11×#95—21no—
191C11×#95—22no—
192C11×#95—22no—
193C11×#95—22no—
194#24028C1111yesmaximal, characteristic, direct product factor, Sylow
195C24×C11—21no—
196C24×C11C2×D411yescharacteristic
197C11×#41—21no—
198C11×#41—21no—
199C11×#41—22no—
200C11×#41—22no—
201C11×#41—21no—
202C11×#41—21no—
203C11×#41—21no—
204C11×#41—21no—
205C11×#41—21no—
206C11×#41—21no—
207C11×#41—21no—
208C11×#41—21no—
209C11×#41—42no—
210C11×#41—42no—
211C11×#41—41no—
212C11×#41—41no—
213C11×#41—42no—
214C11×#41—42no—
215C11×#41—42no—
216C11×#41—42no—
217C11×#41—44no—
218C11×#41—44no—
219C11×#41—42no—
220C11×#41—42no—
221C11×#41#4112yes—
222C11×#41#4112yes—
223C2×Q8×C11—22no—
224C2×Q8×C11—21no—
225C2×Q8×C11—21no—
226C2×Q8×C11—21no—
227C2×Q8×C11—21no—
228C2×Q8×C11—21no—
229C2×Q8×C11—21no—
230C2×Q8×C11—21no—
231C2×Q8×C11—22no—
232C2×Q8×C11—41no—
233C2×Q8×C11—42no—
234C2×Q8×C11—42no—
235C2×Q8×C11—42no—
236C2×Q8×C11—42no—
237C2×Q8×C11C2×D411yescharacteristic
238C2×Q8×C11C2×D411yescharacteristic
239C2×Q8×C11C2×D411yescharacteristic
240C2×D4×C11—21no—
241C2×D4×C11—22no—
242C2×D4×C11—22no—
243C2×D4×C11—21no—
244C2×D4×C11—21no—
245C2×D4×C11—21no—
246C2×D4×C11—21no—
247C2×D4×C11—21no—
248C2×D4×C11—22no—
249C2×D4×C11—21no—
250C2×D4×C11—21no—
251C2×D4×C11—41no—
252C2×D4×C11—42no—
253C2×D4×C11—42no—
254C2×D4×C11C2×D411yescharacteristic
255C2×D4×C11C2×D411yescharacteristic
256C2×D4×C11C2×D411yescharacteristic
257C22×C4×C11—21no—
258C22×C4×C11—21no—
259C22×C4×C11—21no—
260C22×C4×C11—21no—
261C22×C4×C11—21no—
262C22×C4×C11—22no—
263C22×C4×C11—22no—
264C22×C4×C11—21no—
265C22×C4×C11—21no—
266C22×C4×C11—22no—
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—42no—
275C22×C4×C11—42no—
276C22×C4×C11C2×D412yes—
277C22×C4×C11C2×D411yescharacteristic
278C22×C4×C11C2×D411yescharacteristic
279C22×C4×C11C2×D411yescharacteristic
280C22×C4×C11C2×D411yescharacteristic
281C22×C4×C11C2×D411yescharacteristic
282C22×C4×C11C2×D412yes—
283C22×C4×C11C2411yescharacteristic
284C11×M16—21no—
285C11×M16—21no—
286C11×M16—21no—
287C11×M16—21no—
288C11×M16—21no—
289C11×M16—21no—
290C11×M16—21no—
291C11×M16—21no—
292C11×M16—42no—
293C2×C8×C11—21no—
294C2×C8×C11—21no—
295C2×C8×C11—21no—
296C2×C8×C11—21no—
297C2×C8×C11—42no—
298C11×C4⋊C4—22no—
299C11×C4⋊C4—22no—
300C11×C4⋊C4—22no—
301C11×C4⋊C4—22no—
302C11×C4⋊C4—21no—
303C11×C4⋊C4—22no—
304C11×C4⋊C4—22no—
305C11×C4⋊C4—21no—
306C11×C4⋊C4—21no—
307C11×C4⋊C4—21no—
308C11×C4⋊C4—21no—
309C11×C4⋊C4—21no—
310C11×C4⋊C4—21no—
311C11×C4⋊C4—21no—
312C11×C4⋊C4—44no—
313C11×C4⋊C4C2×D411yescharacteristic
314C11×C4⋊C4C2×D411yescharacteristic
315C11×C22⋊C4—22no—
316C11×C22⋊C4—22no—
317C11×C22⋊C4—22no—
318C11×C22⋊C4—22no—
319C11×C22⋊C4—22no—
320C11×C22⋊C4—21no—
321C11×C22⋊C4—22no—
322C11×C22⋊C4—22no—
323C11×C22⋊C4—21no—
324C11×C22⋊C4—21no—
325C11×C22⋊C4—21no—
326C11×C22⋊C4—21no—
327C11×C22⋊C4—42no—
328C11×C22⋊C4—41no—
329C11×C22⋊C4—41no—
330C42×C11—22no—
331C42×C11—21no—
332C42×C11—21no—
333C42×C11—21no—
334C42×C11—21no—
335C42×C11—21no—
336C42×C11—41no—
337C42×C11—41no—
338#3489C2×C1111yescharacteristic
339#3093C2×C1111yescharacteristic, complemented
340#2896C2×C1111yescharacteristic, complemented
341#2499C2×C1111yescharacteristic, complemented
342#2040C2×C1111yescharacteristic, complemented
343#2039C2×C1111yescharacteristic, complemented
344#2038C2×C1111yescharacteristic, complemented
345#2038C2×C1111yescharacteristic, complemented
346#1901C2×C1111yescharacteristic, complemented
347#1871C2×C1111yescharacteristic, complemented
348#1860C2×C1111yescharacteristic, complemented
349#1859C2×C1111yescharacteristic, complemented
350#1793C2×C1111yescharacteristic, complemented
351#1793C2×C1111yescharacteristic, complemented
352#1789C2×C1111yescharacteristic, complemented
353C23×C11—21no—
354C23×C11—21no—
355C23×C11—21no—
356C23×C11—21no—
357C23×C11—21no—
358C23×C11—41no—
359C23×C11—41no—
360C23×C11—42no—
361C23×C11—42no—
362C23×C11—81no—
363C23×C11#12011yescharacteristic
364C23×C11#12011yescharacteristic
365C23×C11C22×D411yescharacteristic
366Q8×C11—21no—
367Q8×C11—21no—
368Q8×C11—21no—
369Q8×C11—21no—
370Q8×C11—21no—
371Q8×C11—42no—
372Q8×C11—44no—
373Q8×C11—41no—
374Q8×C11—41no—
375Q8×C11—41no—
376Q8×C11—41no—
377Q8×C11#12312yes—
378D4×C11—22no—
379D4×C11—22no—
380D4×C11—21no—
381D4×C11—21no—
382D4×C11—21no—
383D4×C11—21no—
384D4×C11—21no—
385D4×C11—42no—
386D4×C11—42no—
387D4×C11—42no—
388D4×C11—42no—
389D4×C11—44no—
390D4×C11—41no—
391D4×C11—41no—
392D4×C11—41no—
393D4×C11—41no—
394D4×C11—81no—
395D4×C11—82no—
396D4×C11#12312yes—
397C2×C4×C11—21no—
398C2×C4×C11—21no—
399C2×C4×C11—21no—
400C2×C4×C11—21no—
401C2×C4×C11—21no—
402C2×C4×C11—21no—
403C2×C4×C11—21no—
404C2×C4×C11—21no—
405C2×C4×C11—21no—
406C2×C4×C11—21no—
407C2×C4×C11—21no—
408C2×C4×C11—22no—
409C2×C4×C11—22no—
410C2×C4×C11—22no—
411C2×C4×C11—21no—
412C2×C4×C11—22no—
413C2×C4×C11—21no—
414C2×C4×C11—21no—
415C2×C4×C11—22no—
416C2×C4×C11—21no—
417C2×C4×C11—22no—
418C2×C4×C11—22no—
419C2×C4×C11—42no—
420C2×C4×C11—42no—
421C2×C4×C11—42no—
422C2×C4×C11—44no—
423C2×C4×C11—41no—
424C2×C4×C11—44no—
425C2×C4×C11—41no—
426C2×C4×C11—41no—
427C2×C4×C11—41no—
428C2×C4×C11—41no—
429C2×C4×C11—41no—
430C2×C4×C11—42no—
431C2×C4×C11—41no—
432C2×C4×C11—42no—
433C2×C4×C11—41no—
434C2×C4×C11—42no—
435C2×C4×C11—41no—
436C2×C4×C11—41no—
437C2×C4×C11—41no—
438C2×C4×C11—82no—
439C2×C4×C11#12011yescharacteristic
440C2×C4×C11#12011yescharacteristic
441C2×C4×C11C22×D411yescharacteristic
442C2×C4×C11C22×D411yescharacteristic
443C2×C4×C11C2×#4111yescharacteristic
444C2×C4×C11C2×#4111yescharacteristic
445C2×C4×C11H(5,𝔽2)11yescharacteristic
446C2×C4×C11H(5,𝔽2)11yescharacteristic
447C8×C11—41no—
448C8×C11—41no—
449C8×C11—41no—
450C8×C11—41no—
451C2×2−1+4C22×C1111yescharacteristic
452C22×#41C22×C1111yescharacteristic
453C22×M16C22×C1111yescharacteristic
454D4×Q8—21no—
455#548—21no—
456#547—21no—
457#547—22no—
458#546—21no—
459#546—22no—
460#537—21no—
461#537C22×C1111yescharacteristic
462#536—21no—
463#536C22×C1111yescharacteristic
464#525—21no—
465#525C22×C1111yescharacteristic
466C2×C22⋊Q8—21no—
467C2×C22⋊Q8C22×C1111yescharacteristic
468#520C22×C1111yescharacteristic
469C2×#117C22×C1111yescharacteristic
470#485—21no—
471#485—21no—
472#482—21no—
473#482—21no—
474#428C22×C1111yescharacteristic, complemented
475#428C22×C1111yescharacteristic, complemented
476C2×#104C22×C1111yescharacteristic
477C2×#104C22×C1111yescharacteristic
478C2×#104C22×C1111yescharacteristic
479C2×#104C22×C1111yescharacteristic
480C2×#104C22×C1111yescharacteristic, complemented
481C2×#104C22×C1111yescharacteristic, complemented
482#419—21no—
483#418—21no—
484#417C22×C1111yescharacteristic
485#417C22×C1111yescharacteristic
486#417C22×C1111yescharacteristic
487#417C22×C1111yescharacteristic
488#417C22×C1111yescharacteristic, complemented
489#417C22×C1111yescharacteristic, complemented
490#416—21no—
491#416—21no—
492C2×#101C22×C1111yescharacteristic, complemented
493C2×#101C22×C1111yescharacteristic, complemented
494#407C22×C1111yescharacteristic
495#397—22no—
496#391C22×C1111yescharacteristic, complemented
497#391C22×C1111yescharacteristic, complemented
498#387—22no—
499#384C22×C1111yescharacteristic, complemented
500#382C22×C1111yescharacteristic, complemented
501C4×C22⋊C4C22×C1111yescharacteristic
502#343C22×C1111yescharacteristic, complemented
503#343C22×C1111yescharacteristic, complemented
504#339C22×C1111yescharacteristic, complemented
505#339C22×C1111yescharacteristic, complemented
506C22×C11—21no—
507C22×C11—21no—
508C22×C11—21no—
509C22×C11—21no—
510C22×C11—22no—
511C22×C11—21no—
512C22×C11—21no—
513C22×C11—21no—
514C22×C11—21no—
515C22×C11—41no—
516C22×C11—41no—
517C22×C11—41no—
518C22×C11—41no—
519C22×C11—41no—
520C22×C11—41no—
521C22×C11—41no—
522C22×C11—41no—
523C22×C11—81no—
524C22×C11—81no—
525C22×C11—84no—
526C22×C11C2×#12011yescharacteristic
527C22×C11#54611yescharacteristic
528C22×C11#54611yescharacteristic
529C4×C11—21no—
530C4×C11—21no—
531C4×C11—22no—
532C4×C11—42no—
533C4×C11—42no—
534C4×C11—41no—
535C4×C11—41no—
536C4×C11—42no—
537C4×C11—41no—
538C4×C11—41no—
539C4×C11—81no—
540C4×C11—81no—
541C4×C11—81no—
542C4×C11C2×#12311yescharacteristic
543C4×C11#53411yescharacteristic
544C4×C11#54611yescharacteristic
545C4×C11#54611yescharacteristic
5462−1+4—22no—
5472−1+4—22no—
5482−1+4—41no—
5492−1+4—41no—
550C2×#41—21no—
551C2×#41—21no—
552C2×#41—21no—
553C2×#41—22no—
554C2×#41—21no—
555C2×#41—22no—
556C2×#41—22no—
557C2×#41—41no—
558C2×#41—41no—
559C2×#41D4×C1111yescharacteristic
560C2×#41D4×C1111yescharacteristic
561C2×#41C23×C1111yescharacteristic
562C2×#41C23×C1111yescharacteristic
563C2×#41C23×C1111yescharacteristic
564C22×Q8—21no—
565C22×Q8—21no—
566C22×Q8D4×C1111yescharacteristic
567C22×Q8C23×C1111yescharacteristic
568C22×D4—21no—
569C22×D4D4×C1111yescharacteristic
570C23×C4—21no—
571C23×C4C23×C1111yescharacteristic
572C2×M16—21no—
573C2×M16—41no—
574C2×M16—41no—
575C2×M16C23×C1111yescharacteristic
576C2×M16C23×C1111yescharacteristic
577C2×M16C23×C1111yescharacteristic
578C2×M16C23×C1111yescharacteristic
579C22×C8—21no—
580C4⋊Q8—22no—
581C4⋊Q8—21no—
582#124—22no—
583#124—21no—
584#123—22no—
585#123—22no—
586#123—22no—
587#123—21no—
588#123—22no—
589C22⋊Q8—22no—
590C22⋊Q8—22no—
591C22⋊Q8—22no—
592C22⋊Q8—21no—
593C22⋊Q8—21no—
594C22⋊Q8—21no—
595C22⋊Q8—21no—
596C22⋊Q8—21no—
597C22⋊Q8—21no—
598C22⋊Q8—21no—
599C22⋊Q8—21no—
600C22⋊Q8D4×C1111yescharacteristic
601C22⋊Q8D4×C1111yescharacteristic
602#121—22no—
603#121—22no—
604#121—22no—
605#121—21no—
606#121—21no—
607#121—22no—
608#121D4×C1111yescharacteristic
609#121D4×C1111yescharacteristic
610#120—22no—
611#120—21no—
612C4×Q8—21no—
613C4×D4—22no—
614C4×D4—22no—
615C4×D4—21no—
616C4×D4—22no—
617C4×D4—21no—
618C4×D4—21no—
619#117—21no—
620#117—21no—
621#117—21no—
622#117—21no—
623#117—21no—
624#117C23×C1111yescharacteristic
625C2×C4⋊C4—22no—
626C2×C4⋊C4—21no—
627C2×C4⋊C4—22no—
628C2×C4⋊C4D4×C1112yes—
629C2×C4⋊C4C23×C1111yescharacteristic
630C2×C4⋊C4C23×C1111yescharacteristic
631C2×C4⋊C4C23×C1111yescharacteristic
632C2×C22⋊C4—22no—
633C2×C22⋊C4—21no—
634C2×C22⋊C4—21no—
635C2×C22⋊C4D4×C1112yes—
636C2×C42—21no—
637C2×C42C23×C1111yescharacteristic
638C2×C42C23×C1111yescharacteristic
639#107—21no—
640#107—21no—
641#106—21no—
642#106—21no—
643#104—22no—
644#104—22no—
645#104—41no—
646#104—41no—
647#104—41no—
648#104—41no—
649#103—21no—
650#103—21no—
651#103—21no—
652#103—21no—
653#103—21no—
654#103—21no—
655#102—21no—
656#102—21no—
657#102—21no—
658#102—21no—
659#102—21no—
660#102—21no—
661#101—41no—
662#101—41no—
663C22⋊C8—21no—
664C22⋊C8—21no—
665#95—21no—
666#95—22no—
667#95—22no—
668#95—22no—
669C2×C11—21no—
670C2×C11—21no—
671C2×C11—41no—
672C2×C11—41no—
673C2×C11—42no—
674C2×C11—81no—
675C2×C11—81no—
676C2×C11#240511yescharacteristic
677C2×C11#301811yescharacteristic
678C2×C11#302011yescharacteristic
679C24—21no—
680C24C2×D4×C1111yescharacteristic
681#41—21no—
682#41—21no—
683#41—22no—
684#41—22no—
685#41—21no—
686#41—21no—
687#41—21no—
688#41—21no—
689#41—21no—
690#41—21no—
691#41—21no—
692#41—21no—
693#41—42no—
694#41—42no—
695#41—41no—
696#41—41no—
697#41—42no—
698#41—42no—
699#41—42no—
700#41—42no—
701#41—44no—
702#41—44no—
703#41—42no—
704#41—42no—
705#41C11×#4112yes—
706#41C11×#4112yes—
707C2×Q8—22no—
708C2×Q8—21no—
709C2×Q8—21no—
710C2×Q8—21no—
711C2×Q8—21no—
712C2×Q8—21no—
713C2×Q8—21no—
714C2×Q8—21no—
715C2×Q8—22no—
716C2×Q8—41no—
717C2×Q8—42no—
718C2×Q8—42no—
719C2×Q8—42no—
720C2×Q8—42no—
721C2×Q8C2×D4×C1111yescharacteristic
722C2×Q8C2×D4×C1111yescharacteristic
723C2×Q8C2×D4×C1111yescharacteristic
724C2×D4—21no—
725C2×D4—22no—
726C2×D4—22no—
727C2×D4—21no—
728C2×D4—21no—
729C2×D4—21no—
730C2×D4—21no—
731C2×D4—21no—
732C2×D4—22no—
733C2×D4—21no—
734C2×D4—21no—
735C2×D4—41no—
736C2×D4—42no—
737C2×D4—42no—
738C2×D4C2×D4×C1111yescharacteristic
739C2×D4C2×D4×C1111yescharacteristic
740C2×D4C2×D4×C1111yescharacteristic
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—22no—
747C22×C4—22no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—22no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—42no—
759C22×C4—42no—
760C22×C4C2×D4×C1112yes—
761C22×C4C2×D4×C1111yescharacteristic
762C22×C4C2×D4×C1111yescharacteristic
763C22×C4C2×D4×C1111yescharacteristic
764C22×C4C2×D4×C1111yescharacteristic
765C22×C4C2×D4×C1111yescharacteristic
766C22×C4C2×D4×C1112yes—
767C22×C4C24×C1111yescharacteristic
768M16—21no—
769M16—21no—
770M16—21no—
771M16—21no—
772M16—21no—
773M16—21no—
774M16—21no—
775M16—21no—
776M16—42no—
777C2×C8—21no—
778C2×C8—21no—
779C2×C8—21no—
780C2×C8—21no—
781C2×C8—42no—
782C4⋊C4—22no—
783C4⋊C4—22no—
784C4⋊C4—22no—
785C4⋊C4—22no—
786C4⋊C4—21no—
787C4⋊C4—22no—
788C4⋊C4—22no—
789C4⋊C4—21no—
790C4⋊C4—21no—
791C4⋊C4—21no—
792C4⋊C4—21no—
793C4⋊C4—21no—
794C4⋊C4—21no—
795C4⋊C4—21no—
796C4⋊C4—44no—
797C4⋊C4C2×D4×C1111yescharacteristic
798C4⋊C4C2×D4×C1111yescharacteristic
799C22⋊C4—22no—
800C22⋊C4—22no—
801C22⋊C4—22no—
802C22⋊C4—22no—
803C22⋊C4—22no—
804C22⋊C4—21no—
805C22⋊C4—22no—
806C22⋊C4—22no—
807C22⋊C4—21no—
808C22⋊C4—21no—
809C22⋊C4—21no—
810C22⋊C4—21no—
811C22⋊C4—42no—
812C22⋊C4—41no—
813C22⋊C4—41no—
814C42—22no—
815C42—21no—
816C42—21no—
817C42—21no—
818C42—21no—
819C42—21no—
820C42—41no—
821C42—41no—
822C11#2402811yescharacteristic, direct product factor, Sylow
823C23—21no—
824C23—21no—
825C23—21no—
826C23—21no—
827C23—21no—
828C23—41no—
829C23—41no—
830C23—42no—
831C23—42no—
832C23—81no—
833C23C11×#12011yescharacteristic
834C23C11×#12011yescharacteristic
835C23C22×D4×C1111yescharacteristic
836Q8—21no—
837Q8—21no—
838Q8—21no—
839Q8—21no—
840Q8—21no—
841Q8—42no—
842Q8—44no—
843Q8—41no—
844Q8—41no—
845Q8—41no—
846Q8—41no—
847Q8C11×#12312yes—
848D4—22no—
849D4—22no—
850D4—21no—
851D4—21no—
852D4—21no—
853D4—21no—
854D4—21no—
855D4—42no—
856D4—42no—
857D4—42no—
858D4—42no—
859D4—44no—
860D4—41no—
861D4—41no—
862D4—41no—
863D4—41no—
864D4—81no—
865D4—82no—
866D4C11×#12312yes—
867C2×C4—21no—
868C2×C4—21no—
869C2×C4—21no—
870C2×C4—21no—
871C2×C4—21no—
872C2×C4—21no—
873C2×C4—21no—
874C2×C4—21no—
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—21no—
882C2×C4—22no—
883C2×C4—21no—
884C2×C4—21no—
885C2×C4—22no—
886C2×C4—21no—
887C2×C4—22no—
888C2×C4—22no—
889C2×C4—42no—
890C2×C4—42no—
891C2×C4—42no—
892C2×C4—44no—
893C2×C4—41no—
894C2×C4—44no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—42no—
901C2×C4—41no—
902C2×C4—42no—
903C2×C4—41no—
904C2×C4—42no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—82no—
909C2×C4C11×#12011yescharacteristic
910C2×C4C11×#12011yescharacteristic
911C2×C4C22×D4×C1111yescharacteristic
912C2×C4C22×D4×C1111yescharacteristic
913C2×C4C2×C11×#4111yescharacteristic
914C2×C4C2×C11×#4111yescharacteristic
915C2×C4C11×H(5,𝔽2)11yescharacteristic
916C2×C4C11×H(5,𝔽2)11yescharacteristic
917C8—41no—
918C8—41no—
919C8—41no—
920C8—41no—
921C22—21no—
922C22—21no—
923C22—21no—
924C22—21no—
925C22—22no—
926C22—21no—
927C22—21no—
928C22—21no—
929C22—21no—
930C22—41no—
931C22—41no—
932C22—41no—
933C22—41no—
934C22—41no—
935C22—41no—
936C22—41no—
937C22—41no—
938C22—81no—
939C22—81no—
940C22—84no—
941C22C2×C11×#12011yescharacteristic
942C22C11×#54611yescharacteristic
943C22C11×#54611yescharacteristic
944C4—21no—
945C4—21no—
946C4—22no—
947C4—42no—
948C4—42no—
949C4—41no—
950C4—41no—
951C4—42no—
952C4—41no—
953C4—41no—
954C4—81no—
955C4—81no—
956C4—81no—
957C4C2×C11×#12311yescharacteristic
958C4C11×#53411yescharacteristic
959C4C11×#54611yescharacteristic
960C4C11×#54611yescharacteristic
961C2—21no—
962C2—21no—
963C2—41no—
964C2—41no—
965C2—42no—
966C2—81no—
967C2—81no—
968C2C11×#240511yescharacteristic
969C2C11×#301811yescharacteristic
970C2C11×#302011yescharacteristic
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×#3093C2semidirect
3. C11×#2896C2semidirect
4. C11×#2499C2semidirect
5. C11×#2040C2semidirect
6. C11×#2039C2semidirect
7. C11×#2038C2semidirect
8. C11×#2038C2semidirect
9. C11×#1901C2semidirect
10. C11×#1871C2semidirect
11. C11×#1860C2semidirect
12. C11×#1859C2semidirect
13. C11×#1793C2semidirect
14. C11×#1793C2semidirect
15. C11×#1789C2semidirect
39. C11×#428C22semidirect
40. C11×#428C22semidirect
45. C2×C11×#104C22semidirect
46. C2×C11×#104C22semidirect
53. C11×#417C22semidirect
54. C11×#417C22semidirect
57. C2×C11×#101C22semidirect
58. C2×C11×#101C22semidirect
61. C11×#391C22semidirect
62. C11×#391C22semidirect
64. C11×#384C22semidirect
65. C11×#382C22semidirect
67. C11×#343C22semidirect
68. C11×#343C22semidirect
69. C11×#339C22semidirect
70. C11×#339C22semidirect
194. #24028C11direct (N × H)
339. #3093C2×C11semidirect
340. #2896C2×C11semidirect
341. #2499C2×C11semidirect
342. #2040C2×C11semidirect
343. #2039C2×C11semidirect
344. #2038C2×C11semidirect
345. #2038C2×C11semidirect
346. #1901C2×C11semidirect
347. #1871C2×C11semidirect
348. #1860C2×C11semidirect
349. #1859C2×C11semidirect
350. #1793C2×C11semidirect
351. #1793C2×C11semidirect
352. #1789C2×C11semidirect
474. #428C22×C11semidirect
475. #428C22×C11semidirect
480. C2×#104C22×C11semidirect
481. C2×#104C22×C11semidirect
488. #417C22×C11semidirect
489. #417C22×C11semidirect
492. C2×#101C22×C11semidirect
493. C2×#101C22×C11semidirect
496. #391C22×C11semidirect
497. #391C22×C11semidirect
499. #384C22×C11semidirect
500. #382C22×C11semidirect
502. #343C22×C11semidirect
503. #343C22×C11semidirect
504. #339C22×C11semidirect
505. #339C22×C11semidirect
822. C11#24028direct (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×#30932
C11×#28962
C11×#24992
C11×#20402
C11×#20392
C11×#20382
C11×#19012
C11×#18712
C11×#18602
C11×#18592
C11×#17932
C11×#17892
#2402811