Finite Group Databasebeta

← C11×#32968 #14610161

Subgroups — C11×#32968 #14610161

Order 2816.

1274 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#520C211yesmaximal, characteristic
2C2×C11×#479C211yesmaximal, characteristic, complemented
3C2×C11×#478C211yesmaximal, characteristic, complemented
4C11×#2629C211yesmaximal, characteristic, complemented
5C11×#1865C211yesmaximal, characteristic, complemented
6C11×#1864C211yesmaximal, characteristic, complemented
7C11×#1863C211yesmaximal, characteristic, complemented
8C11×#1862C211yesmaximal, characteristic, complemented
9C11×#1853C211yesmaximal, characteristic, complemented
10C11×#1852C211yesmaximal, characteristic, complemented
11C11×#1803C211yesmaximal, characteristic, complemented
12C11×#1802C211yesmaximal, characteristic, complemented
13C11×#1798C211yesmaximal, characteristic, complemented
14C11×#1788C211yesmaximal, characteristic
15C11×#1788C211yesmaximal, characteristic
16C22×C11×#41C2211yescharacteristic
17C2×C11×#125C2211yescharacteristic
18C11×#520—24no—
19C11×#520—24no—
20C2×C4×Q8×C11C2211yescharacteristic
21C2×C4×Q8×C11C2211yescharacteristic
22C2×C4×D4×C11—21no—
23C2×C4×D4×C11—21no—
24C2×C4×D4×C11C2211yescharacteristic
25C2×C4×D4×C11C2211yescharacteristic
26C2×C11×#117—21no—
27C2×C11×#117C2211yescharacteristic
28C22×C11×C4⋊C4—21no—
29C22×C11×C4⋊C4C2211yescharacteristic
30C11×#479—24no—
31C11×#478—24no—
32C2×C11×#107C2211yescharacteristic
33C2×C11×#107C2211yescharacteristic
34C2×C11×#106C2211yescharacteristic
35C2×C11×#106C2211yescharacteristic
36C2×C11×C4⋊C8C2211yescharacteristic
37C2×C11×C4⋊C8C2211yescharacteristic
38C2×C11×#103C2211yescharacteristic
39C2×C11×#103C2211yescharacteristic
40C2×C11×#103C2211yescharacteristic
41C2×C11×#103C2211yescharacteristic
42C2×C11×#102C2211yescharacteristic
43C2×C11×#102C2211yescharacteristic
44C2×C11×#102C2211yescharacteristic
45C2×C11×#102C2211yescharacteristic
46C2×C11×C22⋊C8C2211yescharacteristic
47C2×C11×C22⋊C8C2211yescharacteristic
48C11×#398—21no—
49C11×#398—21no—
50C11×#396—21no—
51C11×#396—21no—
52C11×#389C2211yescharacteristic
53C11×#389C2211yescharacteristic
54C11×#384C2211yescharacteristic
55C11×#380C2211yescharacteristic
56C11×#380C2211yescharacteristic
57C11×#340C2211yescharacteristic
58C11×#340C2211yescharacteristic
59C11×#340C2211yescharacteristic
60C11×#340C2211yescharacteristic
61C11×#336C2211yescharacteristic
62C11×#336C2211yescharacteristic
63C2×C11×#41—22no—
64C2×C11×#41—22no—
65C2×C11×#41—22no—
66C2×C11×#41—22no—
67C2×C11×#41—22no—
68C2×C11×#41Q814yes—
69C22×Q8×C11C2311yescharacteristic
70C22×D4×C11—21no—
71C22×D4×C11C2311yescharacteristic
72C23×C4×C11—21no—
73C23×C4×C11—21no—
74C23×C4×C11—21no—
75C23×C4×C11—21no—
76C23×C4×C11C2311yescharacteristic
77C22×C8×C11C2311yescharacteristic
78C22×C8×C11C2311yescharacteristic
79C22×C8×C11C2311yescharacteristic
80C22×C8×C11C2311yescharacteristic
81C11×#125—22no—
82C11×#125—22no—
83C4×Q8×C11—22no—
84C4×Q8×C11—22no—
85C4×Q8×C11—22no—
86C4×Q8×C11D414yes—
87C4×D4×C11—28no—
88C4×D4×C11—28no—
89C4×D4×C11—22no—
90C4×D4×C11—22no—
91C4×D4×C11—22no—
92C4×D4×C11D414yes—
93C11×#117—28no—
94C11×#117—22no—
95C11×#117—22no—
96C2×C11×C4⋊C4—28no—
97C2×C11×C4⋊C4—21no—
98C2×C11×C4⋊C4—21no—
99C2×C11×C4⋊C4—21no—
100C2×C11×C4⋊C4—22no—
101C2×C11×C4⋊C4—22no—
102C2×C11×C4⋊C4—21no—
103C2×C11×C4⋊C4—21no—
104C2×C11×C4⋊C4—21no—
105C2×C11×C4⋊C4—21no—
106C2×C11×C4⋊C4—21no—
107C2×C11×C4⋊C4—21no—
108C2×C11×C4⋊C4D411yescharacteristic
109C2×C11×C4⋊C4D411yescharacteristic
110C2×C11×C4⋊C4C2311yescharacteristic
111C2×C11×C4⋊C4C2311yescharacteristic
112C2×C11×C4⋊C4C2311yescharacteristic
113C2×C11×C4⋊C4C2311yescharacteristic
114C2×C11×C4⋊C4C2311yescharacteristic
115C2×C11×C4⋊C4C2311yescharacteristic
116C2×C11×C22⋊C4—21no—
117C2×C11×C22⋊C4—21no—
118C2×C11×C22⋊C4—21no—
119C2×C11×C22⋊C4—21no—
120C2×C11×C22⋊C4D411yescharacteristic
121C2×C11×C22⋊C4D411yescharacteristic
122C2×C42×C11—21no—
123C2×C42×C11—21no—
124C2×C42×C11C2311yescharacteristic
125C2×C42×C11C2311yescharacteristic
126C11×#107—22no—
127C11×#107—22no—
128C11×#106—22no—
129C11×#106—22no—
130C11×C4⋊C8—22no—
131C11×C4⋊C8—22no—
132C11×#103—22no—
133C11×#103—22no—
134C11×#103—22no—
135C11×#103—22no—
136C11×#102—22no—
137C11×#102—22no—
138C11×#102—22no—
139C11×#102—22no—
140C11×C22⋊C8—22no—
141C11×C22⋊C8—22no—
142C11×#95—21no—
143C11×#95—21no—
144C11×#95—21no—
145C11×#95—21no—
146#32968C1111yesmaximal, characteristic, direct product factor, Sylow
147C24×C11—21no—
148C24×C11C2×D411yescharacteristic
149C11×#41—28no—
150C11×#41—28no—
151C11×#41—28no—
152C11×#41—28no—
153C2×Q8×C11—21no—
154C2×Q8×C11—21no—
155C2×Q8×C11—21no—
156C2×Q8×C11C2×D412yes—
157C2×Q8×C11C2×Q812yes—
158C2×Q8×C11#4112yes—
159C2×D4×C11—24no—
160C2×D4×C11—24no—
161C2×D4×C11—24no—
162C2×D4×C11—21no—
163C2×D4×C11—21no—
164C2×D4×C11—21no—
165C2×D4×C11C2×D412yes—
166C2×D4×C11C2×Q812yes—
167C2×D4×C11#4112yes—
168C22×C4×C11—24no—
169C22×C4×C11—24no—
170C22×C4×C11—21no—
171C22×C4×C11—24no—
172C22×C4×C11—21no—
173C22×C4×C11—21no—
174C22×C4×C11—21no—
175C22×C4×C11—21no—
176C22×C4×C11—21no—
177C22×C4×C11—21no—
178C22×C4×C11—24no—
179C22×C4×C11—24no—
180C22×C4×C11—24no—
181C22×C4×C11—21no—
182C22×C4×C11—21no—
183C22×C4×C11—21no—
184C22×C4×C11—21no—
185C22×C4×C11—81no—
186C22×C4×C11—81no—
187C22×C4×C11—81no—
188C22×C4×C11—81no—
189C22×C4×C11—81no—
190C22×C4×C11—81no—
191C22×C4×C11C2×D411yescharacteristic
192C22×C4×C11C2×D411yescharacteristic
193C22×C4×C11C2×D411yescharacteristic
194C22×C4×C11C2×D411yescharacteristic
195C22×C4×C11C2×D411yescharacteristic
196C22×C4×C11C2×Q812yes—
197C22×C4×C11#4112yes—
198C22×C4×C11C2411yescharacteristic
199C2×C8×C11—21no—
200C2×C8×C11—21no—
201C2×C8×C11—21no—
202C2×C8×C11—21no—
203C2×C8×C11—21no—
204C2×C8×C11—21no—
205C2×C8×C11—21no—
206C2×C8×C11—21no—
207C2×C8×C11—21no—
208C2×C8×C11—21no—
209C2×C8×C11—21no—
210C2×C8×C11—21no—
211C11×C4⋊C4—24no—
212C11×C4⋊C4—24no—
213C11×C4⋊C4—22no—
214C11×C4⋊C4—24no—
215C11×C4⋊C4—22no—
216C11×C4⋊C4—21no—
217C11×C4⋊C4—21no—
218C11×C4⋊C4—21no—
219C11×C4⋊C4—21no—
220C11×C4⋊C4—21no—
221C11×C4⋊C4—21no—
222C11×C4⋊C4—21no—
223C11×C4⋊C4—21no—
224C11×C4⋊C4—21no—
225C11×C4⋊C4—21no—
226C11×C4⋊C4—42no—
227C11×C4⋊C4—42no—
228C11×C4⋊C4—81no—
229C11×C4⋊C4—81no—
230C11×C4⋊C4—81no—
231C11×C4⋊C4—81no—
232C11×C4⋊C4C2×D412yes—
233C11×C4⋊C4C2×D412yes—
234C11×C22⋊C4—24no—
235C11×C22⋊C4—24no—
236C11×C22⋊C4—22no—
237C11×C22⋊C4—22no—
238C11×C22⋊C4—81no—
239C11×C22⋊C4—81no—
240C42×C11—24no—
241C42×C11—24no—
242C42×C11—21no—
243C42×C11—21no—
244C42×C11C2×D412yes—
245C42×C11C2×D412yes—
246C2×#520C2×C1111yescharacteristic
247C2×#479C2×C1111yescharacteristic, complemented
248C2×#478C2×C1111yescharacteristic, complemented
249#2629C2×C1111yescharacteristic, complemented
250#1865C2×C1111yescharacteristic, complemented
251#1864C2×C1111yescharacteristic, complemented
252#1863C2×C1111yescharacteristic, complemented
253#1862C2×C1111yescharacteristic, complemented
254#1853C2×C1111yescharacteristic, complemented
255#1852C2×C1111yescharacteristic, complemented
256#1803C2×C1111yescharacteristic, complemented
257#1802C2×C1111yescharacteristic, complemented
258#1798C2×C1111yescharacteristic, complemented
259#1788C2×C1111yescharacteristic
260#1788C2×C1111yescharacteristic
261C23×C11—21no—
262C23×C11—22no—
263C23×C11—22no—
264C23×C11—21no—
265C23×C11—22no—
266C23×C11—21no—
267C23×C11—21no—
268C23×C11—21no—
269C23×C11—21no—
270C23×C11—41no—
271C23×C11—41no—
272C23×C11—41no—
273C23×C11—41no—
274C23×C11C22⋊Q812yes—
275C23×C11C22×D411yescharacteristic
276Q8×C11—22no—
277Q8×C11—22no—
278Q8×C11—22no—
279Q8×C11C22⋊Q814yes—
280D4×C11—216no—
281D4×C11—22no—
282D4×C11—22no—
283D4×C11—22no—
284D4×C11C22⋊Q814yes—
285C2×C4×C11—216no—
286C2×C4×C11—22no—
287C2×C4×C11—21no—
288C2×C4×C11—22no—
289C2×C4×C11—21no—
290C2×C4×C11—22no—
291C2×C4×C11—21no—
292C2×C4×C11—21no—
293C2×C4×C11—21no—
294C2×C4×C11—21no—
295C2×C4×C11—22no—
296C2×C4×C11—22no—
297C2×C4×C11—22no—
298C2×C4×C11—22no—
299C2×C4×C11—21no—
300C2×C4×C11—21no—
301C2×C4×C11—22no—
302C2×C4×C11—22no—
303C2×C4×C11—21no—
304C2×C4×C11—21no—
305C2×C4×C11—21no—
306C2×C4×C11—21no—
307C2×C4×C11—41no—
308C2×C4×C11—41no—
309C2×C4×C11—41no—
310C2×C4×C11—41no—
311C2×C4×C11—41no—
312C2×C4×C11—41no—
313C2×C4×C11—41no—
314C2×C4×C11—41no—
315C2×C4×C11—41no—
316C2×C4×C11—41no—
317C2×C4×C11—41no—
318C2×C4×C11—41no—
319C2×C4×C11—41no—
320C2×C4×C11—41no—
321C2×C4×C11—41no—
322C2×C4×C11—41no—
323C2×C4×C11—84no—
324C2×C4×C11—84no—
325C2×C4×C11—84no—
326C2×C4×C11#12012yes—
327C2×C4×C11#12012yes—
328C2×C4×C11C22⋊Q812yes—
329C2×C4×C11C22×D411yescharacteristic
330C2×C4×C11C22×D411yescharacteristic
331C2×C4×C11C22×Q811yescharacteristic
332C2×C4×C11C2×#4111yescharacteristic
333C2×C4×C11C2×#4111yescharacteristic
334C2×C4×C11C2×#4111yescharacteristic
335C8×C11—41no—
336C8×C11—41no—
337C8×C11—41no—
338C8×C11—41no—
339C22×#41C22×C1111yescharacteristic
340C2×#125C22×C1111yescharacteristic
341#520—24no—
342#520—24no—
343C2×C4×Q8C22×C1111yescharacteristic
344C2×C4×Q8C22×C1111yescharacteristic
345C2×C4×D4—21no—
346C2×C4×D4—21no—
347C2×C4×D4C22×C1111yescharacteristic
348C2×C4×D4C22×C1111yescharacteristic
349C2×#117—21no—
350C2×#117C22×C1111yescharacteristic
351C22×C4⋊C4—21no—
352C22×C4⋊C4C22×C1111yescharacteristic
353#479—24no—
354#478—24no—
355C2×#107C22×C1111yescharacteristic
356C2×#107C22×C1111yescharacteristic
357C2×#106C22×C1111yescharacteristic
358C2×#106C22×C1111yescharacteristic
359C2×C4⋊C8C22×C1111yescharacteristic
360C2×C4⋊C8C22×C1111yescharacteristic
361C2×#103C22×C1111yescharacteristic
362C2×#103C22×C1111yescharacteristic
363C2×#103C22×C1111yescharacteristic
364C2×#103C22×C1111yescharacteristic
365C2×#102C22×C1111yescharacteristic
366C2×#102C22×C1111yescharacteristic
367C2×#102C22×C1111yescharacteristic
368C2×#102C22×C1111yescharacteristic
369C2×C22⋊C8C22×C1111yescharacteristic
370C2×C22⋊C8C22×C1111yescharacteristic
371#398—21no—
372#398—21no—
373#396—21no—
374#396—21no—
375#389C22×C1111yescharacteristic
376#389C22×C1111yescharacteristic
377#384C22×C1111yescharacteristic
378#380C22×C1111yescharacteristic
379#380C22×C1111yescharacteristic
380#340C22×C1111yescharacteristic
381#340C22×C1111yescharacteristic
382#340C22×C1111yescharacteristic
383#340C22×C1111yescharacteristic
384#336C22×C1111yescharacteristic
385#336C22×C1111yescharacteristic
386C22×C11—22no—
387C22×C11—22no—
388C22×C11—22no—
389C22×C11—24no—
390C22×C11—42no—
391C22×C11—42no—
392C22×C11—41no—
393C22×C11—42no—
394C22×C11—41no—
395C22×C11—42no—
396C22×C11—41no—
397C22×C11—42no—
398C22×C11—41no—
399C22×C11—42no—
400C22×C11C2×#12011yescharacteristic
401C22×C11C2×C22⋊Q811yescharacteristic
402C22×C11#52511yescharacteristic
403C22×C11#57611yescharacteristic
404C22×C11#57711yescharacteristic
405C22×C11#57711yescharacteristic
406C22×C11#57811yescharacteristic
407C4×C11—22no—
408C4×C11—24no—
409C4×C11—22no—
410C4×C11—22no—
411C4×C11—41no—
412C4×C11—42no—
413C4×C11—42no—
414C4×C11—41no—
415C4×C11—81no—
416C4×C11—81no—
417C4×C11—81no—
418C4×C11—81no—
419C4×C11C2×C22⋊Q811yescharacteristic
420C4×C11C2×C22⋊Q811yescharacteristic
421C4×C11#52511yescharacteristic
422C4×C11#52511yescharacteristic
423C2×#41—22no—
424C2×#41—22no—
425C2×#41—22no—
426C2×#41—22no—
427C2×#41—22no—
428C2×#41Q8×C1114yes—
429C22×Q8C23×C1111yescharacteristic
430C22×D4—21no—
431C22×D4C23×C1111yescharacteristic
432C23×C4—21no—
433C23×C4—21no—
434C23×C4—21no—
435C23×C4—21no—
436C23×C4C23×C1111yescharacteristic
437C22×C8C23×C1111yescharacteristic
438C22×C8C23×C1111yescharacteristic
439C22×C8C23×C1111yescharacteristic
440C22×C8C23×C1111yescharacteristic
441#125—22no—
442#125—22no—
443C4×Q8—22no—
444C4×Q8—22no—
445C4×Q8—22no—
446C4×Q8D4×C1114yes—
447C4×D4—28no—
448C4×D4—28no—
449C4×D4—22no—
450C4×D4—22no—
451C4×D4—22no—
452C4×D4D4×C1114yes—
453#117—28no—
454#117—22no—
455#117—22no—
456C2×C4⋊C4—28no—
457C2×C4⋊C4—21no—
458C2×C4⋊C4—21no—
459C2×C4⋊C4—21no—
460C2×C4⋊C4—22no—
461C2×C4⋊C4—22no—
462C2×C4⋊C4—21no—
463C2×C4⋊C4—21no—
464C2×C4⋊C4—21no—
465C2×C4⋊C4—21no—
466C2×C4⋊C4—21no—
467C2×C4⋊C4—21no—
468C2×C4⋊C4D4×C1111yescharacteristic
469C2×C4⋊C4D4×C1111yescharacteristic
470C2×C4⋊C4C23×C1111yescharacteristic
471C2×C4⋊C4C23×C1111yescharacteristic
472C2×C4⋊C4C23×C1111yescharacteristic
473C2×C4⋊C4C23×C1111yescharacteristic
474C2×C4⋊C4C23×C1111yescharacteristic
475C2×C4⋊C4C23×C1111yescharacteristic
476C2×C22⋊C4—21no—
477C2×C22⋊C4—21no—
478C2×C22⋊C4—21no—
479C2×C22⋊C4—21no—
480C2×C22⋊C4D4×C1111yescharacteristic
481C2×C22⋊C4D4×C1111yescharacteristic
482C2×C42—21no—
483C2×C42—21no—
484C2×C42C23×C1111yescharacteristic
485C2×C42C23×C1111yescharacteristic
486#107—22no—
487#107—22no—
488#106—22no—
489#106—22no—
490C4⋊C8—22no—
491C4⋊C8—22no—
492#103—22no—
493#103—22no—
494#103—22no—
495#103—22no—
496#102—22no—
497#102—22no—
498#102—22no—
499#102—22no—
500C22⋊C8—22no—
501C22⋊C8—22no—
502#95—21no—
503#95—21no—
504#95—21no—
505#95—21no—
506C2×C11—42no—
507C2×C11—44no—
508C2×C11#284811yescharacteristic
509C2×C11#301211yescharacteristic
510C2×C11#301311yescharacteristic
511C2×C11#308311yescharacteristic
512C2×C11#308411yescharacteristic
513C2×C11#311911yescharacteristic
514C2×C11#312011yescharacteristic
515C24—21no—
516C24C2×D4×C1111yescharacteristic
517#41—28no—
518#41—28no—
519#41—28no—
520#41—28no—
521C2×Q8—21no—
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8C2×D4×C1112yes—
525C2×Q8C2×Q8×C1112yes—
526C2×Q8C11×#4112yes—
527C2×D4—24no—
528C2×D4—24no—
529C2×D4—24no—
530C2×D4—21no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4C2×D4×C1112yes—
534C2×D4C2×Q8×C1112yes—
535C2×D4C11×#4112yes—
536C22×C4—24no—
537C22×C4—24no—
538C22×C4—21no—
539C22×C4—24no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—24no—
547C22×C4—24no—
548C22×C4—24no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—81no—
554C22×C4—81no—
555C22×C4—81no—
556C22×C4—81no—
557C22×C4—81no—
558C22×C4—81no—
559C22×C4C2×D4×C1111yescharacteristic
560C22×C4C2×D4×C1111yescharacteristic
561C22×C4C2×D4×C1111yescharacteristic
562C22×C4C2×D4×C1111yescharacteristic
563C22×C4C2×D4×C1111yescharacteristic
564C22×C4C2×Q8×C1112yes—
565C22×C4C11×#4112yes—
566C22×C4C24×C1111yescharacteristic
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C4⋊C4—24no—
580C4⋊C4—24no—
581C4⋊C4—22no—
582C4⋊C4—24no—
583C4⋊C4—22no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—42no—
595C4⋊C4—42no—
596C4⋊C4—81no—
597C4⋊C4—81no—
598C4⋊C4—81no—
599C4⋊C4—81no—
600C4⋊C4C2×D4×C1112yes—
601C4⋊C4C2×D4×C1112yes—
602C22⋊C4—24no—
603C22⋊C4—24no—
604C22⋊C4—22no—
605C22⋊C4—22no—
606C22⋊C4—81no—
607C22⋊C4—81no—
608C42—24no—
609C42—24no—
610C42—21no—
611C42—21no—
612C42C2×D4×C1112yes—
613C42C2×D4×C1112yes—
614C11#3296811yescharacteristic, direct product factor, Sylow
615C23—21no—
616C23—22no—
617C23—22no—
618C23—21no—
619C23—22no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—41no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23C11×C22⋊Q812yes—
629C23C22×D4×C1111yescharacteristic
630Q8—22no—
631Q8—22no—
632Q8—22no—
633Q8C11×C22⋊Q814yes—
634D4—216no—
635D4—22no—
636D4—22no—
637D4—22no—
638D4C11×C22⋊Q814yes—
639C2×C4—216no—
640C2×C4—22no—
641C2×C4—21no—
642C2×C4—22no—
643C2×C4—21no—
644C2×C4—22no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—84no—
678C2×C4—84no—
679C2×C4—84no—
680C2×C4C11×#12012yes—
681C2×C4C11×#12012yes—
682C2×C4C11×C22⋊Q812yes—
683C2×C4C22×D4×C1111yescharacteristic
684C2×C4C22×D4×C1111yescharacteristic
685C2×C4C22×Q8×C1111yescharacteristic
686C2×C4C2×C11×#4111yescharacteristic
687C2×C4C2×C11×#4111yescharacteristic
688C2×C4C2×C11×#4111yescharacteristic
689C8—41no—
690C8—41no—
691C8—41no—
692C8—41no—
693C22—22no—
694C22—22no—
695C22—22no—
696C22—24no—
697C22—41no—
698C22—42no—
699C22—41no—
700C22—42no—
701C22—42no—
702C22—42no—
703C22—41no—
704C22—42no—
705C22—41no—
706C22—42no—
707C22C2×C11×#12011yescharacteristic
708C22C2×C11×C22⋊Q811yescharacteristic
709C22C11×#52511yescharacteristic
710C22C11×#57611yescharacteristic
711C22C11×#57711yescharacteristic
712C22C11×#57711yescharacteristic
713C22C11×#57811yescharacteristic
714C4—22no—
715C4—22no—
716C4—22no—
717C4—24no—
718C4—41no—
719C4—42no—
720C4—42no—
721C4—41no—
722C4—81no—
723C4—81no—
724C4—81no—
725C4—81no—
726C4C2×C11×C22⋊Q811yescharacteristic
727C4C2×C11×C22⋊Q811yescharacteristic
728C4C11×#52511yescharacteristic
729C4C11×#52511yescharacteristic
730C2—42no—
731C2—44no—
732C2C11×#284811yescharacteristic
733C2C11×#301211yescharacteristic
734C2C11×#301311yescharacteristic
735C2C11×#308311yescharacteristic
736C2C11×#308411yescharacteristic
737C2C11×#311911yescharacteristic
738C2C11×#312011yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC22×C11×#41C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C11×#117 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#479C2semidirect
3. C2×C11×#478C2semidirect
4. C11×#2629C2semidirect
5. C11×#1865C2semidirect
6. C11×#1864C2semidirect
7. C11×#1863C2semidirect
8. C11×#1862C2semidirect
9. C11×#1853C2semidirect
10. C11×#1852C2semidirect
11. C11×#1803C2semidirect
12. C11×#1802C2semidirect
13. C11×#1798C2semidirect
146. #32968C11direct (N × H)
247. C2×#479C2×C11semidirect
248. C2×#478C2×C11semidirect
249. #2629C2×C11semidirect
250. #1865C2×C11semidirect
251. #1864C2×C11semidirect
252. #1863C2×C11semidirect
253. #1862C2×C11semidirect
254. #1853C2×C11semidirect
255. #1852C2×C11semidirect
256. #1803C2×C11semidirect
257. #1802C2×C11semidirect
258. #1798C2×C11semidirect
614. C11#32968direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5202
C2×C11×#4792
C2×C11×#4782
C11×#26292
C11×#18652
C11×#18642
C11×#18632
C11×#18622
C11×#18532
C11×#18522
C11×#18032
C11×#18022
C11×#17982
C11×#17882
#3296811