Finite Group Databasebeta

← C11×#22588 #14599781

Subgroups — C11×#22588 #14599781

Order 2816.

888 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2924C211yesmaximal, characteristic, complemented
2C11×#2896C211yesmaximal, characteristic
3C11×#2880C211yesmaximal, characteristic
4C11×#1938C211yesmaximal, characteristic, complemented
5C11×#1937C211yesmaximal, characteristic, complemented
6C11×#1929C211yesmaximal, characteristic, complemented
7C11×#1929C211yesmaximal, characteristic, complemented
8C11×#1866C211yesmaximal, characteristic, complemented
9C11×#1866C211yesmaximal, characteristic, complemented
10C11×#1826C211yesmaximal, characteristic, complemented
11C11×#1811C211yesmaximal, characteristic, complemented
12C11×#1789C211yesmaximal, characteristic
13C11×#1765C211yesmaximal, characteristic, complemented
14C11×#1764C211yesmaximal, characteristic, complemented
15C11×#1753C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic
17C2×C11×#131C2211yescharacteristic
18C2×C11×#131C2211yescharacteristic
19C22×C11×M16C2211yescharacteristic
20C2×C11×#117C2211yescharacteristic
21C11×#433—21no—
22C11×#433—21no—
23C11×#432—21no—
24C11×#431—21no—
25C2×C11×#108C2211yescharacteristic, complemented
26C2×C11×#108C2211yescharacteristic, complemented
27C11×#424C2211yescharacteristic, complemented
28C11×#424C2211yescharacteristic, complemented
29C2×C11×#104C2211yescharacteristic
30C2×C11×#104C2211yescharacteristic
31C2×C11×#104C2211yescharacteristic
32C2×C11×#104C2211yescharacteristic
33C11×#419C411yescharacteristic, complemented
34C11×#419C411yescharacteristic, complemented
35C11×#418C411yescharacteristic, complemented
36C11×#418C411yescharacteristic, complemented
37C11×#417C411yescharacteristic, complemented
38C11×#417C411yescharacteristic, complemented
39C11×#417C411yescharacteristic, complemented
40C11×#417C411yescharacteristic, complemented
41C11×#416C2211yescharacteristic
42C11×#416C2211yescharacteristic
43C11×#416C2211yescharacteristic
44C11×#416C2211yescharacteristic
45C11×#408—21no—
46C11×#408—21no—
47C11×#408C2211yescharacteristic
48C11×#408C2211yescharacteristic
49C11×#407—21no—
50C11×#407C2211yescharacteristic
51C11×#407C2211yescharacteristic
52C2×C11×C22⋊C8—21no—
53C2×C11×C22⋊C8C2211yescharacteristic
54C11×#405C2211yescharacteristic, complemented
55C11×#405C2211yescharacteristic, complemented
56C2×C11×#97C2211yescharacteristic, complemented
57C2×C4×C8×C11C2211yescharacteristic, complemented
58C4×C11×C22⋊C4C2211yescharacteristic
59C11×#341C2211yescharacteristic, complemented
60C11×#341C2211yescharacteristic, complemented
61C11×#339C2211yescharacteristic, complemented
62C11×#339C2211yescharacteristic, complemented
63C11×#339C2211yescharacteristic, complemented
64C11×#339C2211yescharacteristic, complemented
65C11×#336C2211yescharacteristic, complemented
66C11×#336C2211yescharacteristic, complemented
67C2×C11×#41—21no—
68C2×C11×#41—21no—
69C2×C11×#41—22no—
70C2×C11×#41—22no—
71C2×C11×#41—41no—
72C2×C11×#41—41no—
73C2×C11×#41C2×C411yescharacteristic
74C2×C11×#41C2×C411yescharacteristic
75C2×C11×#41C2311yescharacteristic
76C2×C11×#41C2311yescharacteristic
77C22×Q8×C11C2×C411yescharacteristic
78C22×D4×C11—21no—
79C22×D4×C11C2×C411yescharacteristic
80C23×C4×C11—21no—
81C23×C4×C11C2311yescharacteristic
82C11×#131—22no—
83C11×#131—22no—
84C11×#131—41no—
85C11×#131—41no—
86C2×C11×M16—21no—
87C2×C11×M16—21no—
88C2×C11×M16—41no—
89C2×C11×M16—41no—
90C2×C11×M16C2×C411yescharacteristic
91C2×C11×M16C2×C411yescharacteristic
92C2×C11×M16C2×C411yescharacteristic
93C2×C11×M16C2×C411yescharacteristic
94C2×C11×M16C2311yescharacteristic
95C2×C11×M16C2311yescharacteristic
96C2×C11×M16C2311yescharacteristic
97C2×C11×M16C2311yescharacteristic
98C22×C8×C11—21no—
99C22×C8×C11—21no—
100C22×C8×C11C2311yescharacteristic
101C22×C8×C11C2311yescharacteristic
102C22×C8×C11C2311yescharacteristic
103C22×C8×C11C2311yescharacteristic
104C11×#117—21no—
105C11×#117—21no—
106C11×#117C2×C411yescharacteristic
107C11×#117C2×C411yescharacteristic
108C11×#117C2311yescharacteristic
109C11×#117C2311yescharacteristic
110C2×C11×C4⋊C4C2×C411yescharacteristic
111C2×C11×C4⋊C4C2×C411yescharacteristic
112C2×C11×C22⋊C4—21no—
113C2×C11×C22⋊C4—21no—
114C2×C42×C11—21no—
115C2×C42×C11C2311yescharacteristic
116C2×C42×C11C2311yescharacteristic
117C11×#108—41no—
118C11×#108—41no—
119C11×C4⋊C8—21no—
120C11×C4⋊C8—21no—
121C11×C4⋊C8—21no—
122C11×C4⋊C8—21no—
123C11×#104—22no—
124C11×#104—22no—
125C11×#104—41no—
126C11×#104—41no—
127C11×#103C2×C411yescharacteristic
128C11×#103C2×C411yescharacteristic
129C11×#103C2×C411yescharacteristic
130C11×#103C2×C411yescharacteristic
131C11×#103C2×C411yescharacteristic
132C11×#103C2×C411yescharacteristic
133C11×#103C2×C411yescharacteristic
134C11×#103C2×C411yescharacteristic
135C11×#102C2×C411yescharacteristic
136C11×#102C2×C411yescharacteristic
137C11×#102C2×C411yescharacteristic
138C11×#102C2×C411yescharacteristic
139C11×#102C2×C411yescharacteristic
140C11×#102C2×C411yescharacteristic
141C11×#102C2×C411yescharacteristic
142C11×#102C2×C411yescharacteristic
143C11×C22⋊C8—21no—
144C11×C22⋊C8—21no—
145C11×C22⋊C8—21no—
146C11×C22⋊C8—21no—
147C11×C22⋊C8—21no—
148C11×C22⋊C8—21no—
149C11×C22⋊C8—21no—
150C11×C22⋊C8—21no—
151C11×C22⋊C8D411yescharacteristic
152C11×C22⋊C8D411yescharacteristic
153C11×C22⋊C8D411yescharacteristic
154C11×C22⋊C8D411yescharacteristic
155C11×#97—21no—
156C11×#97—21no—
157C11×#97—41no—
158C4×C8×C11—21no—
159C4×C8×C11—21no—
160C4×C8×C11—41no—
161C11×#95—21no—
162#22588C1111yesmaximal, characteristic, direct product factor, Sylow
163C24×C11—21no—
164C24×C11#4111yescharacteristic
165C11×#41—21no—
166C11×#41—21no—
167C11×#41—22no—
168C11×#41—22no—
169C11×#41—21no—
170C11×#41—21no—
171C11×#41—21no—
172C11×#41—21no—
173C11×#41—42no—
174C11×#41—42no—
175C11×#41—41no—
176C11×#41—41no—
177C11×#41—42no—
178C11×#41—42no—
179C11×#41#4112yes—
180C11×#41#4112yes—
181C2×Q8×C11—21no—
182C2×Q8×C11—22no—
183C2×Q8×C11—41no—
184C2×Q8×C11C22×C411yescharacteristic
185C2×Q8×C11C22×C411yescharacteristic
186C2×D4×C11—21no—
187C2×D4×C11—22no—
188C2×D4×C11—21no—
189C2×D4×C11—21no—
190C2×D4×C11—21no—
191C2×D4×C11—21no—
192C2×D4×C11—41no—
193C2×D4×C11—42no—
194C2×D4×C11—42no—
195C2×D4×C11C22×C411yescharacteristic
196C2×D4×C11C22×C411yescharacteristic
197C22×C4×C11—21no—
198C22×C4×C11—21no—
199C22×C4×C11—21no—
200C22×C4×C11—21no—
201C22×C4×C11—21no—
202C22×C4×C11—21no—
203C22×C4×C11—21no—
204C22×C4×C11—21no—
205C22×C4×C11—21no—
206C22×C4×C11—21no—
207C22×C4×C11—21no—
208C22×C4×C11—21no—
209C22×C4×C11—21no—
210C22×C4×C11—42no—
211C22×C4×C11—42no—
212C22×C4×C11C22×C411yescharacteristic
213C22×C4×C11C22×C411yescharacteristic
214C22×C4×C11C2×D411yescharacteristic
215C22×C4×C11C2×D411yescharacteristic
216C22×C4×C11#4111yescharacteristic
217C22×C4×C11C2411yescharacteristic
218C11×M16—21no—
219C11×M16—21no—
220C11×M16—21no—
221C11×M16—21no—
222C11×M16—21no—
223C11×M16—21no—
224C11×M16—21no—
225C11×M16—21no—
226C11×M16—41no—
227C11×M16—41no—
228C11×M16—41no—
229C11×M16—41no—
230C11×M16—42no—
231C11×M16—42no—
232C2×C8×C11—21no—
233C2×C8×C11—21no—
234C2×C8×C11—21no—
235C2×C8×C11—21no—
236C2×C8×C11—21no—
237C2×C8×C11—21no—
238C2×C8×C11—21no—
239C2×C8×C11—21no—
240C2×C8×C11—21no—
241C2×C8×C11—21no—
242C2×C8×C11—21no—
243C2×C8×C11—21no—
244C2×C8×C11—42no—
245C2×C8×C11—42no—
246C2×C8×C11C22×C411yescharacteristic
247C2×C8×C11C22×C411yescharacteristic
248C2×C8×C11C22×C411yescharacteristic
249C2×C8×C11C22×C411yescharacteristic
250C2×C8×C11C2×D411yescharacteristic
251C2×C8×C11C2×D411yescharacteristic
252C2×C8×C11C2×D411yescharacteristic
253C2×C8×C11C2×D411yescharacteristic
254C11×C4⋊C4—21no—
255C11×C4⋊C4—21no—
256C11×C4⋊C4C22×C411yescharacteristic
257C11×C4⋊C4C22×C411yescharacteristic
258C11×C4⋊C4C22×C411yescharacteristic
259C11×C4⋊C4C22×C411yescharacteristic
260C11×C22⋊C4—21no—
261C11×C22⋊C4—21no—
262C11×C22⋊C4—21no—
263C11×C22⋊C4—21no—
264C11×C22⋊C4—42no—
265C42×C11—21no—
266C42×C11—21no—
267C42×C11—21no—
268C42×C11—21no—
269C42×C11—21no—
270C42×C11—21no—
271C42×C11—21no—
272C42×C11—21no—
273#2924C2×C1111yescharacteristic, complemented
274#2896C2×C1111yescharacteristic
275#2880C2×C1111yescharacteristic
276#1938C2×C1111yescharacteristic, complemented
277#1937C2×C1111yescharacteristic, complemented
278#1929C2×C1111yescharacteristic, complemented
279#1929C2×C1111yescharacteristic, complemented
280#1866C2×C1111yescharacteristic, complemented
281#1866C2×C1111yescharacteristic, complemented
282#1826C2×C1111yescharacteristic, complemented
283#1811C2×C1111yescharacteristic, complemented
284#1789C2×C1111yescharacteristic
285#1765C2×C1111yescharacteristic, complemented
286#1764C2×C1111yescharacteristic, complemented
287#1753C2×C1111yescharacteristic, complemented
288C23×C11—21no—
289C23×C11—21no—
290C23×C11—21no—
291C23×C11—21no—
292C23×C11—41no—
293C23×C11—41no—
294C23×C11—42no—
295C23×C11—42no—
296C23×C11—81no—
297C23×C11C4×D411yescharacteristic
298C23×C11C4×D411yescharacteristic
299C23×C11C2×#4111yescharacteristic
300Q8×C11—21no—
301Q8×C11—21no—
302Q8×C11—21no—
303Q8×C11—42no—
304Q8×C11#11712yes—
305D4×C11—22no—
306D4×C11—22no—
307D4×C11—21no—
308D4×C11—21no—
309D4×C11—21no—
310D4×C11—42no—
311D4×C11—42no—
312D4×C11—42no—
313D4×C11—41no—
314D4×C11—41no—
315D4×C11#11712yes—
316C2×C4×C11—21no—
317C2×C4×C11—21no—
318C2×C4×C11—21no—
319C2×C4×C11—21no—
320C2×C4×C11—21no—
321C2×C4×C11—21no—
322C2×C4×C11—21no—
323C2×C4×C11—22no—
324C2×C4×C11—22no—
325C2×C4×C11—21no—
326C2×C4×C11—21no—
327C2×C4×C11—21no—
328C2×C4×C11—21no—
329C2×C4×C11—22no—
330C2×C4×C11—21no—
331C2×C4×C11—21no—
332C2×C4×C11—21no—
333C2×C4×C11—21no—
334C2×C4×C11—21no—
335C2×C4×C11—42no—
336C2×C4×C11—42no—
337C2×C4×C11—42no—
338C2×C4×C11—41no—
339C2×C4×C11—42no—
340C2×C4×C11—41no—
341C2×C4×C11—41no—
342C2×C4×C11—41no—
343C2×C4×C11—41no—
344C2×C4×C11—41no—
345C2×C4×C11—41no—
346C2×C4×C11—81no—
347C2×C4×C11C4×D411yescharacteristic
348C2×C4×C11C4×D411yescharacteristic
349C2×C4×C11C23×C411yescharacteristic
350C2×C4×C11C22×D411yescharacteristic
351C2×C4×C11C2×#4111yescharacteristic
352C2×C4×C11C2×#4111yescharacteristic
353C2×C4×C11H(5,𝔽2)11yescharacteristic
354C2×C4×C11H(5,𝔽2)11yescharacteristic
355C8×C11—21no—
356C8×C11—21no—
357C8×C11—21no—
358C8×C11—21no—
359C8×C11—21no—
360C8×C11—21no—
361C8×C11—21no—
362C8×C11—21no—
363C8×C11—41no—
364C8×C11—41no—
365C8×C11—41no—
366C8×C11—41no—
367C22×#41C22×C1111yescharacteristic
368C2×#131C22×C1111yescharacteristic
369C2×#131C22×C1111yescharacteristic
370C22×M16C22×C1111yescharacteristic
371C2×#117C22×C1111yescharacteristic
372#433—21no—
373#433—21no—
374#432—21no—
375#431—21no—
376C2×#108C22×C1111yescharacteristic, complemented
377C2×#108C22×C1111yescharacteristic, complemented
378#424C22×C1111yescharacteristic, complemented
379#424C22×C1111yescharacteristic, complemented
380C2×#104C22×C1111yescharacteristic
381C2×#104C22×C1111yescharacteristic
382C2×#104C22×C1111yescharacteristic
383C2×#104C22×C1111yescharacteristic
384#419C4×C1111yescharacteristic, complemented
385#419C4×C1111yescharacteristic, complemented
386#418C4×C1111yescharacteristic, complemented
387#418C4×C1111yescharacteristic, complemented
388#417C4×C1111yescharacteristic, complemented
389#417C4×C1111yescharacteristic, complemented
390#417C4×C1111yescharacteristic, complemented
391#417C4×C1111yescharacteristic, complemented
392#416C22×C1111yescharacteristic
393#416C22×C1111yescharacteristic
394#416C22×C1111yescharacteristic
395#416C22×C1111yescharacteristic
396#408—21no—
397#408—21no—
398#408C22×C1111yescharacteristic
399#408C22×C1111yescharacteristic
400#407—21no—
401#407C22×C1111yescharacteristic
402#407C22×C1111yescharacteristic
403C2×C22⋊C8—21no—
404C2×C22⋊C8C22×C1111yescharacteristic
405#405C22×C1111yescharacteristic, complemented
406#405C22×C1111yescharacteristic, complemented
407C2×#97C22×C1111yescharacteristic, complemented
408C2×C4×C8C22×C1111yescharacteristic, complemented
409C4×C22⋊C4C22×C1111yescharacteristic
410#341C22×C1111yescharacteristic, complemented
411#341C22×C1111yescharacteristic, complemented
412#339C22×C1111yescharacteristic, complemented
413#339C22×C1111yescharacteristic, complemented
414#339C22×C1111yescharacteristic, complemented
415#339C22×C1111yescharacteristic, complemented
416#336C22×C1111yescharacteristic, complemented
417#336C22×C1111yescharacteristic, complemented
418C22×C11—21no—
419C22×C11—21no—
420C22×C11—21no—
421C22×C11—21no—
422C22×C11—22no—
423C22×C11—21no—
424C22×C11—21no—
425C22×C11—21no—
426C22×C11—21no—
427C22×C11—41no—
428C22×C11—41no—
429C22×C11—41no—
430C22×C11—41no—
431C22×C11—41no—
432C22×C11—81no—
433C22×C11—81no—
434C22×C11—84no—
435C22×C11C2×C4×D411yescharacteristic
436C22×C11#55111yescharacteristic
437C22×C11#55111yescharacteristic
438C4×C11—21no—
439C4×C11—21no—
440C4×C11—22no—
441C4×C11—42no—
442C4×C11—41no—
443C4×C11—41no—
444C4×C11—41no—
445C4×C11—41no—
446C4×C11—41no—
447C4×C11—81no—
448C4×C11C2×#11711yescharacteristic
449C4×C11#51811yescharacteristic
450C4×C11#54611yescharacteristic
451C4×C11#54611yescharacteristic
452C2×#41—21no—
453C2×#41—21no—
454C2×#41—22no—
455C2×#41—22no—
456C2×#41—41no—
457C2×#41—41no—
458C2×#41C2×C4×C1111yescharacteristic
459C2×#41C2×C4×C1111yescharacteristic
460C2×#41C23×C1111yescharacteristic
461C2×#41C23×C1111yescharacteristic
462C22×Q8C2×C4×C1111yescharacteristic
463C22×D4—21no—
464C22×D4C2×C4×C1111yescharacteristic
465C23×C4—21no—
466C23×C4C23×C1111yescharacteristic
467#131—22no—
468#131—22no—
469#131—41no—
470#131—41no—
471C2×M16—21no—
472C2×M16—21no—
473C2×M16—41no—
474C2×M16—41no—
475C2×M16C2×C4×C1111yescharacteristic
476C2×M16C2×C4×C1111yescharacteristic
477C2×M16C2×C4×C1111yescharacteristic
478C2×M16C2×C4×C1111yescharacteristic
479C2×M16C23×C1111yescharacteristic
480C2×M16C23×C1111yescharacteristic
481C2×M16C23×C1111yescharacteristic
482C2×M16C23×C1111yescharacteristic
483C22×C8—21no—
484C22×C8—21no—
485C22×C8C23×C1111yescharacteristic
486C22×C8C23×C1111yescharacteristic
487C22×C8C23×C1111yescharacteristic
488C22×C8C23×C1111yescharacteristic
489#117—21no—
490#117—21no—
491#117C2×C4×C1111yescharacteristic
492#117C2×C4×C1111yescharacteristic
493#117C23×C1111yescharacteristic
494#117C23×C1111yescharacteristic
495C2×C4⋊C4C2×C4×C1111yescharacteristic
496C2×C4⋊C4C2×C4×C1111yescharacteristic
497C2×C22⋊C4—21no—
498C2×C22⋊C4—21no—
499C2×C42—21no—
500C2×C42C23×C1111yescharacteristic
501C2×C42C23×C1111yescharacteristic
502#108—41no—
503#108—41no—
504C4⋊C8—21no—
505C4⋊C8—21no—
506C4⋊C8—21no—
507C4⋊C8—21no—
508#104—22no—
509#104—22no—
510#104—41no—
511#104—41no—
512#103C2×C4×C1111yescharacteristic
513#103C2×C4×C1111yescharacteristic
514#103C2×C4×C1111yescharacteristic
515#103C2×C4×C1111yescharacteristic
516#103C2×C4×C1111yescharacteristic
517#103C2×C4×C1111yescharacteristic
518#103C2×C4×C1111yescharacteristic
519#103C2×C4×C1111yescharacteristic
520#102C2×C4×C1111yescharacteristic
521#102C2×C4×C1111yescharacteristic
522#102C2×C4×C1111yescharacteristic
523#102C2×C4×C1111yescharacteristic
524#102C2×C4×C1111yescharacteristic
525#102C2×C4×C1111yescharacteristic
526#102C2×C4×C1111yescharacteristic
527#102C2×C4×C1111yescharacteristic
528C22⋊C8—21no—
529C22⋊C8—21no—
530C22⋊C8—21no—
531C22⋊C8—21no—
532C22⋊C8—21no—
533C22⋊C8—21no—
534C22⋊C8—21no—
535C22⋊C8—21no—
536C22⋊C8D4×C1111yescharacteristic
537C22⋊C8D4×C1111yescharacteristic
538C22⋊C8D4×C1111yescharacteristic
539C22⋊C8D4×C1111yescharacteristic
540#97—21no—
541#97—21no—
542#97—41no—
543C4×C8—21no—
544C4×C8—21no—
545C4×C8—41no—
546#95—21no—
547C2×C11—21no—
548C2×C11—21no—
549C2×C11—41no—
550C2×C11—41no—
551C2×C11—42no—
552C2×C11—81no—
553C2×C11#234211yescharacteristic
554C2×C11#295511yescharacteristic
555C2×C11#295611yescharacteristic
556C24—21no—
557C24C11×#4111yescharacteristic
558#41—21no—
559#41—21no—
560#41—22no—
561#41—22no—
562#41—21no—
563#41—21no—
564#41—21no—
565#41—21no—
566#41—42no—
567#41—42no—
568#41—41no—
569#41—41no—
570#41—42no—
571#41—42no—
572#41C11×#4112yes—
573#41C11×#4112yes—
574C2×Q8—21no—
575C2×Q8—22no—
576C2×Q8—41no—
577C2×Q8C22×C4×C1111yescharacteristic
578C2×Q8C22×C4×C1111yescharacteristic
579C2×D4—21no—
580C2×D4—22no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—41no—
586C2×D4—42no—
587C2×D4—42no—
588C2×D4C22×C4×C1111yescharacteristic
589C2×D4C22×C4×C1111yescharacteristic
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—42no—
604C22×C4—42no—
605C22×C4C22×C4×C1111yescharacteristic
606C22×C4C22×C4×C1111yescharacteristic
607C22×C4C2×D4×C1111yescharacteristic
608C22×C4C2×D4×C1111yescharacteristic
609C22×C4C11×#4111yescharacteristic
610C22×C4C24×C1111yescharacteristic
611M16—21no—
612M16—21no—
613M16—21no—
614M16—21no—
615M16—21no—
616M16—21no—
617M16—21no—
618M16—21no—
619M16—41no—
620M16—41no—
621M16—41no—
622M16—41no—
623M16—42no—
624M16—42no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—42no—
638C2×C8—42no—
639C2×C8C22×C4×C1111yescharacteristic
640C2×C8C22×C4×C1111yescharacteristic
641C2×C8C22×C4×C1111yescharacteristic
642C2×C8C22×C4×C1111yescharacteristic
643C2×C8C2×D4×C1111yescharacteristic
644C2×C8C2×D4×C1111yescharacteristic
645C2×C8C2×D4×C1111yescharacteristic
646C2×C8C2×D4×C1111yescharacteristic
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4C22×C4×C1111yescharacteristic
650C4⋊C4C22×C4×C1111yescharacteristic
651C4⋊C4C22×C4×C1111yescharacteristic
652C4⋊C4C22×C4×C1111yescharacteristic
653C22⋊C4—21no—
654C22⋊C4—21no—
655C22⋊C4—21no—
656C22⋊C4—21no—
657C22⋊C4—42no—
658C42—21no—
659C42—21no—
660C42—21no—
661C42—21no—
662C42—21no—
663C42—21no—
664C42—21no—
665C42—21no—
666C11#2258811yescharacteristic, direct product factor, Sylow
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—41no—
672C23—41no—
673C23—42no—
674C23—42no—
675C23—81no—
676C23C4×D4×C1111yescharacteristic
677C23C4×D4×C1111yescharacteristic
678C23C2×C11×#4111yescharacteristic
679Q8—21no—
680Q8—21no—
681Q8—21no—
682Q8—42no—
683Q8C11×#11712yes—
684D4—22no—
685D4—22no—
686D4—21no—
687D4—21no—
688D4—21no—
689D4—42no—
690D4—42no—
691D4—42no—
692D4—41no—
693D4—41no—
694D4C11×#11712yes—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—22no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—41no—
718C2×C4—42no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—81no—
726C2×C4C4×D4×C1111yescharacteristic
727C2×C4C4×D4×C1111yescharacteristic
728C2×C4C23×C4×C1111yescharacteristic
729C2×C4C22×D4×C1111yescharacteristic
730C2×C4C2×C11×#4111yescharacteristic
731C2×C4C2×C11×#4111yescharacteristic
732C2×C4C11×H(5,𝔽2)11yescharacteristic
733C2×C4C11×H(5,𝔽2)11yescharacteristic
734C8—21no—
735C8—21no—
736C8—21no—
737C8—21no—
738C8—21no—
739C8—21no—
740C8—21no—
741C8—21no—
742C8—41no—
743C8—41no—
744C8—41no—
745C8—41no—
746C22—21no—
747C22—21no—
748C22—21no—
749C22—21no—
750C22—21no—
751C22—21no—
752C22—21no—
753C22—21no—
754C22—22no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—81no—
761C22—81no—
762C22—84no—
763C22C2×C4×D4×C1111yescharacteristic
764C22C11×#55111yescharacteristic
765C22C11×#55111yescharacteristic
766C4—21no—
767C4—21no—
768C4—22no—
769C4—42no—
770C4—41no—
771C4—41no—
772C4—41no—
773C4—41no—
774C4—41no—
775C4—81no—
776C4C2×C11×#11711yescharacteristic
777C4C11×#51811yescharacteristic
778C4C11×#54611yescharacteristic
779C4C11×#54611yescharacteristic
780C2—21no—
781C2—21no—
782C2—41no—
783C2—41no—
784C2—42no—
785C2—81no—
786C2C11×#234211yescharacteristic
787C2C11×#295511yescharacteristic
788C2C11×#295611yescharacteristic
subgroupG/H
centerC2×C4×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
socleC22×C11C2×C4×D4
prime radicalC22×C11×#41C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C11 ◁ C2×C11×C22⋊C8 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#2924C2semidirect
4. C11×#1938C2semidirect
5. C11×#1937C2semidirect
6. C11×#1929C2semidirect
7. C11×#1929C2semidirect
8. C11×#1866C2semidirect
9. C11×#1866C2semidirect
10. C11×#1826C2semidirect
11. C11×#1811C2semidirect
13. C11×#1765C2semidirect
14. C11×#1764C2semidirect
15. C11×#1753C2semidirect
25. C2×C11×#108C22semidirect
26. C2×C11×#108C22semidirect
27. C11×#424C22semidirect
28. C11×#424C22semidirect
33. C11×#419C4semidirect
34. C11×#419C4semidirect
35. C11×#418C4semidirect
36. C11×#418C4semidirect
37. C11×#417C4semidirect
38. C11×#417C4semidirect
39. C11×#417C4semidirect
40. C11×#417C4semidirect
54. C11×#405C22semidirect
55. C11×#405C22semidirect
56. C2×C11×#97C22semidirect
57. C2×C4×C8×C11C22semidirect
59. C11×#341C22semidirect
60. C11×#341C22semidirect
61. C11×#339C22semidirect
62. C11×#339C22semidirect
63. C11×#339C22semidirect
64. C11×#339C22semidirect
65. C11×#336C22semidirect
66. C11×#336C22semidirect
162. #22588C11direct (N × H)
273. #2924C2×C11semidirect
276. #1938C2×C11semidirect
277. #1937C2×C11semidirect
278. #1929C2×C11semidirect
279. #1929C2×C11semidirect
280. #1866C2×C11semidirect
281. #1866C2×C11semidirect
282. #1826C2×C11semidirect
283. #1811C2×C11semidirect
285. #1765C2×C11semidirect
286. #1764C2×C11semidirect
287. #1753C2×C11semidirect
376. C2×#108C22×C11semidirect
377. C2×#108C22×C11semidirect
378. #424C22×C11semidirect
379. #424C22×C11semidirect
384. #419C4×C11semidirect
385. #419C4×C11semidirect
386. #418C4×C11semidirect
387. #418C4×C11semidirect
388. #417C4×C11semidirect
389. #417C4×C11semidirect
390. #417C4×C11semidirect
391. #417C4×C11semidirect
405. #405C22×C11semidirect
406. #405C22×C11semidirect
407. C2×#97C22×C11semidirect
408. C2×C4×C8C22×C11semidirect
410. #341C22×C11semidirect
411. #341C22×C11semidirect
412. #339C22×C11semidirect
413. #339C22×C11semidirect
414. #339C22×C11semidirect
415. #339C22×C11semidirect
416. #336C22×C11semidirect
417. #336C22×C11semidirect
666. C11#22588direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#29242
C11×#28962
C11×#28802
C11×#19382
C11×#19372
C11×#19292
C11×#18662
C11×#18262
C11×#18112
C11×#17892
C11×#17652
C11×#17642
C11×#17532
#2258811