Finite Group Databasebeta

← C11×#24863 #14602056

Subgroups — C11×#24863 #14602056

Order 2816.

1042 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#483C211yesmaximal, characteristic, complemented
2C22×C11×#103C211yesmaximal, characteristic, complemented
3C11×#2409C211yesmaximal, characteristic
4D4×C11×C4⋊C4C211yesmaximal, characteristic
5C11×#2096C211yesmaximal, characteristic, complemented
6C11×#2072C211yesmaximal, characteristic, complemented
7C11×#2035C211yesmaximal, characteristic, complemented
8C11×#2035C211yesmaximal, characteristic, complemented
9C11×#1927C211yesmaximal, characteristic, complemented
10C11×#1927C211yesmaximal, characteristic, complemented
11C11×#1872C211yesmaximal, characteristic, complemented
12C11×#1869C211yesmaximal, characteristic
13C11×#1853C211yesmaximal, characteristic, complemented
14C11×#1807C211yesmaximal, characteristic, complemented
15C11×#1787C211yesmaximal, characteristic, complemented
16C23×Q8×C11C2211yescharacteristic
17C23×C8×C11C2211yescharacteristic
18C2×C11×C22⋊Q8C2211yescharacteristic
19C2×C11×C22⋊Q8C2211yescharacteristic
20C2×C4×D4×C11—21no—
21C2×C4×D4×C11C2211yescharacteristic
22C22×C11×C4⋊C4C2211yescharacteristic
23C22×C11×C4⋊C4C2211yescharacteristic
24C11×#483—24no—
25C2×C11×#106C2211yescharacteristic
26C2×C11×#106C2211yescharacteristic
27C2×C11×#106C2211yescharacteristic
28C2×C11×#106C2211yescharacteristic
29C2×C11×#103—24no—
30C2×C11×#103C2211yescharacteristic
31C2×C11×#103C2211yescharacteristic
32C2×C11×#103C2211yescharacteristic
33C2×C11×#103C2211yescharacteristic
34C2×C11×#103C2211yescharacteristic
35C2×C11×#103C2211yescharacteristic
36C2×C11×#103C2211yescharacteristic
37C2×C11×#103C2211yescharacteristic
38C2×C11×C22⋊C8C2211yescharacteristic
39C2×C11×C22⋊C8C2211yescharacteristic
40C2×C11×C22⋊C8C2211yescharacteristic
41C11×#395—21no—
42C11×#393—21no—
43C11×#391C2211yescharacteristic
44C11×#391C2211yescharacteristic
45C11×#389—21no—
46C11×#386—21no—
47C11×#385—21no—
48C11×#385—21no—
49C11×#385—21no—
50C11×#384C2211yescharacteristic
51C11×#380C2211yescharacteristic
52C11×#380C2211yescharacteristic
53C11×#380C2211yescharacteristic
54C4×C11×C4⋊C4C2211yescharacteristic
55C11×#340C2211yescharacteristic
56C11×#340C2211yescharacteristic
57C11×#340C2211yescharacteristic
58C11×#340C2211yescharacteristic
59C11×#336C2211yescharacteristic
60C11×#336C2211yescharacteristic
61C22×Q8×C11—21no—
62C22×Q8×C11—22no—
63C22×Q8×C11—22no—
64C22×Q8×C11—22no—
65C22×Q8×C11—22no—
66C22×Q8×C11—41no—
67C22×Q8×C11—41no—
68C22×Q8×C11C2311yescharacteristic
69C22×Q8×C11C2311yescharacteristic
70C22×D4×C11D411yescharacteristic
71C23×C4×C11—21no—
72C23×C4×C11—21no—
73C23×C4×C11—21no—
74C23×C4×C11C2311yescharacteristic
75C23×C4×C11C2311yescharacteristic
76C22×C8×C11—22no—
77C22×C8×C11—22no—
78C22×C8×C11—41no—
79C22×C8×C11C2311yescharacteristic
80C22×C8×C11C2311yescharacteristic
81C22×C8×C11C2311yescharacteristic
82C22×C8×C11C2311yescharacteristic
83C11×C22⋊Q8—22no—
84C11×C22⋊Q8—22no—
85C11×C22⋊Q8—41no—
86C11×C22⋊Q8—41no—
87C4×D4×C11—22no—
88C4×D4×C11—22no—
89C4×D4×C11—44no—
90C2×C11×C4⋊C4—22no—
91C2×C11×C4⋊C4—22no—
92C2×C11×C4⋊C4—21no—
93C2×C11×C4⋊C4—21no—
94C2×C11×C4⋊C4—21no—
95C2×C11×C4⋊C4—21no—
96C2×C11×C4⋊C4—21no—
97C2×C11×C4⋊C4—21no—
98C2×C11×C4⋊C4—41no—
99C2×C11×C4⋊C4—41no—
100C2×C11×C4⋊C4D411yescharacteristic
101C2×C11×C4⋊C4C2311yescharacteristic
102C2×C11×C4⋊C4C2311yescharacteristic
103C2×C11×C4⋊C4C2311yescharacteristic
104C2×C11×C4⋊C4C2311yescharacteristic
105C2×C11×C4⋊C4C2311yescharacteristic
106C2×C11×C4⋊C4C2311yescharacteristic
107C2×C11×C22⋊C4—21no—
108C2×C11×C22⋊C4—21no—
109C2×C11×C22⋊C4—21no—
110C2×C11×C22⋊C4—21no—
111C2×C11×C22⋊C4—21no—
112C2×C11×C22⋊C4D411yescharacteristic
113C2×C11×C22⋊C4D411yescharacteristic
114C2×C42×C11—21no—
115C2×C42×C11C2311yescharacteristic
116C11×#106—22no—
117C11×#106—22no—
118C11×#106—41no—
119C11×#106—41no—
120C11×#103—22no—
121C11×#103—22no—
122C11×#103—22no—
123C11×#103—22no—
124C11×#103—22no—
125C11×#103—41no—
126C11×#103—41no—
127C11×#103D414yescomplemented
128C11×C22⋊C8—22no—
129C11×C22⋊C8—22no—
130C11×C22⋊C8—41no—
131C11×#95—21no—
132C11×#95—21no—
133C11×#95—21no—
134C11×#95—21no—
135C11×#95—21no—
136C11×#95—21no—
137C11×#95—21no—
138C11×#95—21no—
139#24863C1111yesmaximal, characteristic, direct product factor, Sylow
140C24×C11C2×D411yescharacteristic
141C24×C11C2×D411yescharacteristic
142C2×Q8×C11—21no—
143C2×Q8×C11—21no—
144C2×Q8×C11—28no—
145C2×Q8×C11—21no—
146C2×Q8×C11—21no—
147C2×Q8×C11—21no—
148C2×Q8×C11—21no—
149C2×Q8×C11—21no—
150C2×Q8×C11—21no—
151C2×Q8×C11—21no—
152C2×Q8×C11—21no—
153C2×Q8×C11—42no—
154C2×Q8×C11—42no—
155C2×Q8×C11—44no—
156C2×Q8×C11—44no—
157C2×Q8×C11—44no—
158C2×Q8×C11—42no—
159C2×Q8×C11C2×D412yes—
160C2×Q8×C11#4112yes—
161C2×D4×C11—22no—
162C2×D4×C11—22no—
163C2×D4×C11SD1614yes—
164C22×C4×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11—21no—
167C22×C4×C11—21no—
168C22×C4×C11—21no—
169C22×C4×C11—21no—
170C22×C4×C11—21no—
171C22×C4×C11—21no—
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—21no—
179C22×C4×C11—21no—
180C22×C4×C11—21no—
181C22×C4×C11—21no—
182C22×C4×C11—42no—
183C22×C4×C11—42no—
184C22×C4×C11—42no—
185C22×C4×C11—42no—
186C22×C4×C11—42no—
187C22×C4×C11—42no—
188C22×C4×C11—42no—
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×C11#4112yes—
196C22×C4×C11#4112yes—
197C22×C4×C11C2411yescharacteristic
198C2×C8×C11—21no—
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—44no—
210C2×C8×C11C2×D412yes—
211C11×C4⋊C4—22no—
212C11×C4⋊C4—21no—
213C11×C4⋊C4—21no—
214C11×C4⋊C4—21no—
215C11×C4⋊C4—21no—
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—42no—
224C11×C4⋊C4—42no—
225C11×C4⋊C4—42no—
226C11×C4⋊C4—42no—
227C11×C4⋊C4—42no—
228C11×C4⋊C4—81no—
229C11×C4⋊C4C2×D412yes—
230C11×C22⋊C4—22no—
231C11×C22⋊C4—22no—
232C11×C22⋊C4—42no—
233C11×C22⋊C4—42no—
234C11×C22⋊C4—42no—
235C11×C22⋊C4—42no—
236C11×C22⋊C4—42no—
237C42×C11—21no—
238C42×C11—21no—
239C42×C11—42no—
240C2×#483C2×C1111yescharacteristic, complemented
241C22×#103C2×C1111yescharacteristic, complemented
242#2409C2×C1111yescharacteristic
243D4×C4⋊C4C2×C1111yescharacteristic
244#2096C2×C1111yescharacteristic, complemented
245#2072C2×C1111yescharacteristic, complemented
246#2035C2×C1111yescharacteristic, complemented
247#2035C2×C1111yescharacteristic, complemented
248#1927C2×C1111yescharacteristic, complemented
249#1927C2×C1111yescharacteristic, complemented
250#1872C2×C1111yescharacteristic, complemented
251#1869C2×C1111yescharacteristic
252#1853C2×C1111yescharacteristic, complemented
253#1807C2×C1111yescharacteristic, complemented
254#1787C2×C1111yescharacteristic, complemented
255C23×C11—21no—
256C23×C11—21no—
257C23×C11—21no—
258C23×C11—21no—
259C23×C11—21no—
260C23×C11—21no—
261C23×C11—21no—
262C23×C11—21no—
263C23×C11—21no—
264C23×C11—21no—
265C23×C11#12312yes—
266C23×C11C2×SD1612yes—
267C23×C11C2×SD1612yes—
268C23×C11#13712yes—
269C23×C11C22×D411yescharacteristic
270Q8×C11—22no—
271Q8×C11—22no—
272Q8×C11—22no—
273Q8×C11—22no—
274Q8×C11—48no—
275Q8×C11—41no—
276Q8×C11—41no—
277Q8×C11—41no—
278Q8×C11—41no—
279D4×C11—28no—
280C2×C4×C11—21no—
281C2×C4×C11—21no—
282C2×C4×C11—21no—
283C2×C4×C11—21no—
284C2×C4×C11—22no—
285C2×C4×C11—22no—
286C2×C4×C11—22no—
287C2×C4×C11—22no—
288C2×C4×C11—21no—
289C2×C4×C11—21no—
290C2×C4×C11—22no—
291C2×C4×C11—22no—
292C2×C4×C11—21no—
293C2×C4×C11—22no—
294C2×C4×C11—21no—
295C2×C4×C11—21no—
296C2×C4×C11—21no—
297C2×C4×C11—48no—
298C2×C4×C11—41no—
299C2×C4×C11—41no—
300C2×C4×C11—41no—
301C2×C4×C11—41no—
302C2×C4×C11—41no—
303C2×C4×C11—41no—
304C2×C4×C11—41no—
305C2×C4×C11—41no—
306C2×C4×C11—41no—
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#12312yes—
326C2×C4×C11C2×SD1612yes—
327C2×C4×C11C22×D411yescharacteristic
328C2×C4×C11C2×#4111yescharacteristic
329C2×C4×C11C2×#4111yescharacteristic
330C2×C4×C11C2×#4111yescharacteristic
331C2×C4×C11H(5,𝔽2)11yescharacteristic
332C2×C4×C11H(5,𝔽2)11yescharacteristic
333C8×C11—22no—
334C8×C11—41no—
335C8×C11—41no—
336C8×C11—41no—
337C23×Q8C22×C1111yescharacteristic
338C23×C8C22×C1111yescharacteristic
339C2×C22⋊Q8C22×C1111yescharacteristic
340C2×C22⋊Q8C22×C1111yescharacteristic
341C2×C4×D4—21no—
342C2×C4×D4C22×C1111yescharacteristic
343C22×C4⋊C4C22×C1111yescharacteristic
344C22×C4⋊C4C22×C1111yescharacteristic
345#483—24no—
346C2×#106C22×C1111yescharacteristic
347C2×#106C22×C1111yescharacteristic
348C2×#106C22×C1111yescharacteristic
349C2×#106C22×C1111yescharacteristic
350C2×#103—24no—
351C2×#103C22×C1111yescharacteristic
352C2×#103C22×C1111yescharacteristic
353C2×#103C22×C1111yescharacteristic
354C2×#103C22×C1111yescharacteristic
355C2×#103C22×C1111yescharacteristic
356C2×#103C22×C1111yescharacteristic
357C2×#103C22×C1111yescharacteristic
358C2×#103C22×C1111yescharacteristic
359C2×C22⋊C8C22×C1111yescharacteristic
360C2×C22⋊C8C22×C1111yescharacteristic
361C2×C22⋊C8C22×C1111yescharacteristic
362#395—21no—
363#393—21no—
364#391C22×C1111yescharacteristic
365#391C22×C1111yescharacteristic
366#389—21no—
367#386—21no—
368#385—21no—
369#385—21no—
370#385—21no—
371#384C22×C1111yescharacteristic
372#380C22×C1111yescharacteristic
373#380C22×C1111yescharacteristic
374#380C22×C1111yescharacteristic
375C4×C4⋊C4C22×C1111yescharacteristic
376#340C22×C1111yescharacteristic
377#340C22×C1111yescharacteristic
378#340C22×C1111yescharacteristic
379#340C22×C1111yescharacteristic
380#336C22×C1111yescharacteristic
381#336C22×C1111yescharacteristic
382C22×C11—22no—
383C22×C11—22no—
384C22×C11—22no—
385C22×C11—22no—
386C22×C11—22no—
387C22×C11—22no—
388C22×C11—22no—
389C22×C11—22no—
390C22×C11—22no—
391C22×C11—41no—
392C22×C11—41no—
393C22×C11—41no—
394C22×C11—41no—
395C22×C11#48314yescomplemented
396C22×C11C2×#12311yescharacteristic
397C22×C11D4211yescharacteristic
398C22×C11#54611yescharacteristic
399C22×C11C22×SD1611yescharacteristic
400C22×C11C2×#13711yescharacteristic
401C22×C11#57711yescharacteristic
402C22×C11#57811yescharacteristic
403C4×C11—22no—
404C4×C11—22no—
405C4×C11—41no—
406C4×C11—41no—
407C4×C11—42no—
408C4×C11—42no—
409C4×C11—42no—
410C4×C11—81no—
411C4×C11—81no—
412C4×C11—81no—
413C4×C11—81no—
414C4×C11—81no—
415C4×C11#52511yescharacteristic
416C4×C11#53811yescharacteristic
417C4×C11#54611yescharacteristic
418C4×C11#55111yescharacteristic
419C22×Q8—21no—
420C22×Q8—22no—
421C22×Q8—22no—
422C22×Q8—22no—
423C22×Q8—22no—
424C22×Q8—41no—
425C22×Q8—41no—
426C22×Q8C23×C1111yescharacteristic
427C22×Q8C23×C1111yescharacteristic
428C22×D4D4×C1111yescharacteristic
429C23×C4—21no—
430C23×C4—21no—
431C23×C4—21no—
432C23×C4C23×C1111yescharacteristic
433C23×C4C23×C1111yescharacteristic
434C22×C8—22no—
435C22×C8—22no—
436C22×C8—41no—
437C22×C8C23×C1111yescharacteristic
438C22×C8C23×C1111yescharacteristic
439C22×C8C23×C1111yescharacteristic
440C22×C8C23×C1111yescharacteristic
441C22⋊Q8—22no—
442C22⋊Q8—22no—
443C22⋊Q8—41no—
444C22⋊Q8—41no—
445C4×D4—22no—
446C4×D4—22no—
447C4×D4—44no—
448C2×C4⋊C4—22no—
449C2×C4⋊C4—22no—
450C2×C4⋊C4—21no—
451C2×C4⋊C4—21no—
452C2×C4⋊C4—21no—
453C2×C4⋊C4—21no—
454C2×C4⋊C4—21no—
455C2×C4⋊C4—21no—
456C2×C4⋊C4—41no—
457C2×C4⋊C4—41no—
458C2×C4⋊C4D4×C1111yescharacteristic
459C2×C4⋊C4C23×C1111yescharacteristic
460C2×C4⋊C4C23×C1111yescharacteristic
461C2×C4⋊C4C23×C1111yescharacteristic
462C2×C4⋊C4C23×C1111yescharacteristic
463C2×C4⋊C4C23×C1111yescharacteristic
464C2×C4⋊C4C23×C1111yescharacteristic
465C2×C22⋊C4—21no—
466C2×C22⋊C4—21no—
467C2×C22⋊C4—21no—
468C2×C22⋊C4—21no—
469C2×C22⋊C4—21no—
470C2×C22⋊C4D4×C1111yescharacteristic
471C2×C22⋊C4D4×C1111yescharacteristic
472C2×C42—21no—
473C2×C42C23×C1111yescharacteristic
474#106—22no—
475#106—22no—
476#106—41no—
477#106—41no—
478#103—22no—
479#103—22no—
480#103—22no—
481#103—22no—
482#103—22no—
483#103—41no—
484#103—41no—
485#103D4×C1114yescomplemented
486C22⋊C8—22no—
487C22⋊C8—22no—
488C22⋊C8—41no—
489#95—21no—
490#95—21no—
491#95—21no—
492#95—21no—
493#95—21no—
494#95—21no—
495#95—21no—
496#95—21no—
497C2×C11—24no—
498C2×C11—42no—
499C2×C11#241811yescharacteristic
500C2×C11C2×#48311yescharacteristic
501C2×C11#309711yescharacteristic
502C2×C11#327011yescharacteristic
503C2×C11D4×SD1611yescharacteristic
504C2×C11#329811yescharacteristic
505C2×C11#331611yescharacteristic
506C24C2×D4×C1111yescharacteristic
507C24C2×D4×C1111yescharacteristic
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—28no—
511C2×Q8—21no—
512C2×Q8—21no—
513C2×Q8—21no—
514C2×Q8—21no—
515C2×Q8—21no—
516C2×Q8—21no—
517C2×Q8—21no—
518C2×Q8—21no—
519C2×Q8—42no—
520C2×Q8—42no—
521C2×Q8—44no—
522C2×Q8—44no—
523C2×Q8—44no—
524C2×Q8—42no—
525C2×Q8C2×D4×C1112yes—
526C2×Q8C11×#4112yes—
527C2×D4—22no—
528C2×D4—22no—
529C2×D4C11×SD1614yes—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—42no—
549C22×C4—42no—
550C22×C4—42no—
551C22×C4—42no—
552C22×C4—42no—
553C22×C4—42no—
554C22×C4—42no—
555C22×C4—81no—
556C22×C4—81no—
557C22×C4C2×D4×C1111yescharacteristic
558C22×C4C2×D4×C1111yescharacteristic
559C22×C4C2×D4×C1111yescharacteristic
560C22×C4C2×D4×C1111yescharacteristic
561C22×C4C11×#4112yes—
562C22×C4C11×#4112yes—
563C22×C4C24×C1111yescharacteristic
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—21no—
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—44no—
576C2×C8C2×D4×C1112yes—
577C4⋊C4—22no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—42no—
590C4⋊C4—42no—
591C4⋊C4—42no—
592C4⋊C4—42no—
593C4⋊C4—42no—
594C4⋊C4—81no—
595C4⋊C4C2×D4×C1112yes—
596C22⋊C4—22no—
597C22⋊C4—22no—
598C22⋊C4—42no—
599C22⋊C4—42no—
600C22⋊C4—42no—
601C22⋊C4—42no—
602C22⋊C4—42no—
603C42—21no—
604C42—21no—
605C42—42no—
606C11#2486311yescharacteristic, direct product factor, Sylow
607C23—21no—
608C23—21no—
609C23—21no—
610C23—21no—
611C23—21no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23C11×#12312yes—
618C23C2×C11×SD1612yes—
619C23C2×C11×SD1612yes—
620C23C11×#13712yes—
621C23C22×D4×C1111yescharacteristic
622Q8—22no—
623Q8—22no—
624Q8—22no—
625Q8—22no—
626Q8—48no—
627Q8—41no—
628Q8—41no—
629Q8—41no—
630Q8—41no—
631D4—28no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—21no—
645C2×C4—22no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—48no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
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—84no—
676C2×C4—84no—
677C2×C4C11×#12312yes—
678C2×C4C2×C11×SD1612yes—
679C2×C4C22×D4×C1111yescharacteristic
680C2×C4C2×C11×#4111yescharacteristic
681C2×C4C2×C11×#4111yescharacteristic
682C2×C4C2×C11×#4111yescharacteristic
683C2×C4C11×H(5,𝔽2)11yescharacteristic
684C2×C4C11×H(5,𝔽2)11yescharacteristic
685C8—22no—
686C8—41no—
687C8—41no—
688C8—41no—
689C22—22no—
690C22—22no—
691C22—22no—
692C22—22no—
693C22—22no—
694C22—22no—
695C22—22no—
696C22—22no—
697C22—22no—
698C22—41no—
699C22—41no—
700C22—41no—
701C22—41no—
702C22C11×#48314yescomplemented
703C22C2×C11×#12311yescharacteristic
704C22D42×C1111yescharacteristic
705C22C11×#54611yescharacteristic
706C22C22×C11×SD1611yescharacteristic
707C22C2×C11×#13711yescharacteristic
708C22C11×#57711yescharacteristic
709C22C11×#57811yescharacteristic
710C4—22no—
711C4—22no—
712C4—41no—
713C4—42no—
714C4—42no—
715C4—42no—
716C4—41no—
717C4—81no—
718C4—81no—
719C4—81no—
720C4—81no—
721C4—81no—
722C4C11×#52511yescharacteristic
723C4C11×#53811yescharacteristic
724C4C11×#54611yescharacteristic
725C4C11×#55111yescharacteristic
726C2—24no—
727C2—42no—
728C2C11×#241811yescharacteristic
729C2C2×C11×#48311yescharacteristic
730C2C11×#309711yescharacteristic
731C2C11×#327011yescharacteristic
732C2D4×C11×SD1611yescharacteristic
733C2C11×#329811yescharacteristic
734C2C11×#331611yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC22×D4×C11D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C4×D4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#483C2semidirect
2. C22×C11×#103C2semidirect
5. C11×#2096C2semidirect
6. C11×#2072C2semidirect
7. C11×#2035C2semidirect
8. C11×#2035C2semidirect
9. C11×#1927C2semidirect
10. C11×#1927C2semidirect
11. C11×#1872C2semidirect
13. C11×#1853C2semidirect
14. C11×#1807C2semidirect
15. C11×#1787C2semidirect
127. C11×#103D4semidirect
139. #24863C11direct (N × H)
240. C2×#483C2×C11semidirect
241. C22×#103C2×C11semidirect
244. #2096C2×C11semidirect
245. #2072C2×C11semidirect
246. #2035C2×C11semidirect
247. #2035C2×C11semidirect
248. #1927C2×C11semidirect
249. #1927C2×C11semidirect
250. #1872C2×C11semidirect
252. #1853C2×C11semidirect
253. #1807C2×C11semidirect
254. #1787C2×C11semidirect
395. C22×C11#483semidirect
485. #103D4×C11semidirect
606. C11#24863direct (N × H)
702. C22C11×#483semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#4832
C22×C11×#1032
C11×#24092
D4×C11×C4⋊C42
C11×#20962
C11×#20722
C11×#20352
C11×#19272
C11×#18722
C11×#18692
C11×#18532
C11×#18072
C11×#17872
#2486311