Finite Group Databasebeta

← C11×#23037 #14600230

Subgroups — C11×#23037 #14600230

Order 2816.

1082 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#469C211yesmaximal, characteristic
2C2×C4×C11×D8C211yesmaximal, characteristic, complemented
3C2×C11×#428C211yesmaximal, characteristic, complemented
4C11×#2363C211yesmaximal, characteristic, complemented
5C11×#2361C211yesmaximal, characteristic, complemented
6C11×#1972C211yesmaximal, characteristic, complemented
7C11×#1941C211yesmaximal, characteristic, complemented
8C11×#1926C211yesmaximal, characteristic, complemented
9C11×#1925C211yesmaximal, characteristic, complemented
10C11×#1875C211yesmaximal, characteristic, complemented
11C11×#1874C211yesmaximal, characteristic, complemented
12C11×#1864C211yesmaximal, characteristic, complemented
13C11×#1862C211yesmaximal, characteristic, complemented
14C11×#1776C211yesmaximal, characteristic, complemented
15C11×#1753C211yesmaximal, characteristic, complemented
16C22×C11×D8C2211yescharacteristic
17C22×C11×M16C2211yescharacteristic
18C2×C11×#121C2211yescharacteristic
19C2×C11×#121C2211yescharacteristic
20C2×C4×D4×C11—21no—
21C2×C4×D4×C11C2211yescharacteristic
22C2×C4×D4×C11C2211yescharacteristic
23C2×C11×#117C2211yescharacteristic
24C22×C11×C4⋊C4C2211yescharacteristic
25C11×#469C418yescomplemented
26C4×C11×D8—24no—
27C11×#428—24no—
28C2×C11×#107C2211yescharacteristic
29C2×C11×#107C2211yescharacteristic
30C2×C11×#106C2211yescharacteristic
31C2×C11×#106C2211yescharacteristic
32C2×C11×#106C2211yescharacteristic
33C2×C11×#102C2211yescharacteristic
34C2×C11×#102C2211yescharacteristic
35C2×C11×#102C2211yescharacteristic
36C2×C11×#102C2211yescharacteristic
37C2×C11×#102C2211yescharacteristic
38C2×C11×#102C2211yescharacteristic
39C2×C11×C22⋊C8C2211yescharacteristic
40C2×C11×#97C2211yescharacteristic
41C2×C4×C8×C11C2211yescharacteristic
42C11×#390—21no—
43C11×#390C2211yescharacteristic
44C11×#390C2211yescharacteristic
45C11×#389C2211yescharacteristic
46C11×#389C2211yescharacteristic
47C11×#388—21no—
48C11×#388—21no—
49C11×#386—21no—
50C11×#386—21no—
51C11×#385—21no—
52C4×C11×C4⋊C4C2211yescharacteristic
53C4×C11×C4⋊C4C2211yescharacteristic
54C4×C11×C22⋊C4—21no—
55C4×C11×C22⋊C4C2211yescharacteristic
56C11×#340C2211yescharacteristic
57C11×#340C2211yescharacteristic
58C11×#340C2211yescharacteristic
59C11×#340C2211yescharacteristic
60C11×#336C2211yescharacteristic
61C11×#336C2211yescharacteristic
62C22×D4×C11—21no—
63C22×D4×C11—21no—
64C22×D4×C11C2311yescharacteristic
65C22×D4×C11C2311yescharacteristic
66C23×C4×C11—21no—
67C23×C4×C11—21no—
68C23×C4×C11—21no—
69C23×C4×C11C2311yescharacteristic
70C2×C11×D8—22no—
71C2×C11×D8—22no—
72C2×C11×D8C2×C414yescomplemented
73C2×C11×M16—22no—
74C2×C11×M16—22no—
75C2×C11×M16C2×C414yescomplemented
76C22×C8×C11C2311yescharacteristic
77C22×C8×C11C2311yescharacteristic
78C22×C8×C11C2311yescharacteristic
79C22×C8×C11C2311yescharacteristic
80C11×#121—22no—
81C11×#121—22no—
82C11×#121C2×C414yescomplemented
83C11×#121C2×C414yescomplemented
84C4×D4×C11—22no—
85C4×D4×C11—22no—
86C4×D4×C11—41no—
87C4×D4×C11—41no—
88C4×D4×C11—44no—
89C11×#117—22no—
90C11×#117—41no—
91C2×C11×C4⋊C4—22no—
92C2×C11×C4⋊C4—21no—
93C2×C11×C4⋊C4—21no—
94C2×C11×C4⋊C4—21no—
95C2×C11×C4⋊C4—41no—
96C2×C11×C4⋊C4C2311yescharacteristic
97C2×C11×C4⋊C4C2311yescharacteristic
98C2×C11×C4⋊C4C2311yescharacteristic
99C2×C11×C4⋊C4C2311yescharacteristic
100C2×C11×C4⋊C4C2311yescharacteristic
101C2×C11×C4⋊C4C2311yescharacteristic
102C2×C11×C22⋊C4—21no—
103C2×C11×C22⋊C4—21no—
104C2×C11×C22⋊C4—21no—
105C2×C11×C22⋊C4—21no—
106C2×C11×C22⋊C4—21no—
107C2×C11×C22⋊C4—21no—
108C2×C11×C22⋊C4—21no—
109C2×C11×C22⋊C4—21no—
110C2×C11×C22⋊C4—21no—
111C2×C11×C22⋊C4D411yescharacteristic
112C2×C11×C22⋊C4D411yescharacteristic
113C2×C42×C11—21no—
114C2×C42×C11—21no—
115C2×C42×C11—21no—
116C2×C42×C11C2311yescharacteristic
117C2×C42×C11C2311yescharacteristic
118C11×#107—22no—
119C11×#107D414yescomplemented
120C11×#106—22no—
121C11×#106—22no—
122C11×#106C2×C414yescomplemented
123C11×#102—22no—
124C11×#102—22no—
125C11×#102—41no—
126C11×#102—41no—
127C11×#102C2×C414yescomplemented
128C11×#102C2×C414yescomplemented
129C11×C22⋊C8—22no—
130C11×#97—22no—
131C4×C8×C11—22no—
132C11×#95—21no—
133C11×#95—21no—
134C11×#95—21no—
135C11×#95—21no—
136C11×#95D411yescharacteristic
137C11×#95D411yescharacteristic
138#23037C1111yesmaximal, characteristic, direct product factor, Sylow
139C24×C11—21no—
140C24×C11—21no—
141C24×C11C2×D411yescharacteristic
142C2×D4×C11—24no—
143C2×D4×C11—24no—
144C2×D4×C11—21no—
145C2×D4×C11—21no—
146C2×D4×C11—21no—
147C2×D4×C11—21no—
148C2×D4×C11—21no—
149C2×D4×C11—21no—
150C2×D4×C11—21no—
151C2×D4×C11—21no—
152C2×D4×C11—21no—
153C2×D4×C11—21no—
154C2×D4×C11—42no—
155C2×D4×C11—42no—
156C2×D4×C11—81no—
157C2×D4×C11—81no—
158C2×D4×C11C22×C412yes—
159C2×D4×C11C22×C412yes—
160C22×C4×C11—21no—
161C22×C4×C11—21no—
162C22×C4×C11—21no—
163C22×C4×C11—21no—
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—42no—
171C22×C4×C11—42no—
172C22×C4×C11—42no—
173C22×C4×C11—42no—
174C22×C4×C11—42no—
175C22×C4×C11—42no—
176C22×C4×C11—81no—
177C22×C4×C11—81no—
178C22×C4×C11—81no—
179C22×C4×C11C22×C412yes—
180C22×C4×C11C2×D411yescharacteristic
181C22×C4×C11C2×D411yescharacteristic
182C22×C4×C11C2×D411yescharacteristic
183C22×C4×C11C2×D411yescharacteristic
184C22×C4×C11C2×D411yescharacteristic
185C22×C4×C11#4112yes—
186C22×C4×C11C2411yescharacteristic
187C11×D8—28no—
188C11×M16—28no—
189C2×C8×C11—21no—
190C2×C8×C11—21no—
191C2×C8×C11—21no—
192C2×C8×C11—21no—
193C2×C8×C11—21no—
194C2×C8×C11—21no—
195C2×C8×C11—21no—
196C2×C8×C11—21no—
197C2×C8×C11C22×C412yes—
198C2×C8×C11C22×C412yes—
199C2×C8×C11C2×D412yes—
200C2×C8×C11#4112yes—
201C11×C4⋊C4—21no—
202C11×C4⋊C4—21no—
203C11×C4⋊C4—21no—
204C11×C4⋊C4—21no—
205C11×C4⋊C4—21no—
206C11×C4⋊C4—21no—
207C11×C4⋊C4—21no—
208C11×C4⋊C4—21no—
209C11×C4⋊C4—42no—
210C11×C4⋊C4—42no—
211C11×C4⋊C4—81no—
212C11×C4⋊C4C22×C412yes—
213C11×C4⋊C4C22×C412yes—
214C11×C4⋊C4C2×D412yes—
215C11×C4⋊C4C2×D412yes—
216C11×C22⋊C4—24no—
217C11×C22⋊C4—24no—
218C11×C22⋊C4—22no—
219C11×C22⋊C4—41no—
220C11×C22⋊C4—42no—
221C11×C22⋊C4—42no—
222C11×C22⋊C4—42no—
223C11×C22⋊C4—42no—
224C11×C22⋊C4—42no—
225C11×C22⋊C4—81no—
226C11×C22⋊C4—81no—
227C42×C11—21no—
228C42×C11—21no—
229C42×C11—21no—
230C42×C11—21no—
231C42×C11—42no—
232C42×C11—42no—
233C42×C11—81no—
234C2×#469C2×C1111yescharacteristic
235C2×C4×D8C2×C1111yescharacteristic, complemented
236C2×#428C2×C1111yescharacteristic, complemented
237#2363C2×C1111yescharacteristic, complemented
238#2361C2×C1111yescharacteristic, complemented
239#1972C2×C1111yescharacteristic, complemented
240#1941C2×C1111yescharacteristic, complemented
241#1926C2×C1111yescharacteristic, complemented
242#1925C2×C1111yescharacteristic, complemented
243#1875C2×C1111yescharacteristic, complemented
244#1874C2×C1111yescharacteristic, complemented
245#1864C2×C1111yescharacteristic, complemented
246#1862C2×C1111yescharacteristic, complemented
247#1776C2×C1111yescharacteristic, complemented
248#1753C2×C1111yescharacteristic, complemented
249C23×C11—21no—
250C23×C11—21no—
251C23×C11—21no—
252C23×C11—21no—
253C23×C11—21no—
254C23×C11—21no—
255C23×C11—22no—
256C23×C11—22no—
257C23×C11—41no—
258C23×C11—41no—
259C23×C11—41no—
260C23×C11—41no—
261C23×C11—41no—
262C23×C11—41no—
263C23×C11—41no—
264C23×C11—41no—
265C23×C11—41no—
266C23×C11—41no—
267C23×C11—41no—
268C23×C11—41no—
269C23×C11C4×D412yes—
270C23×C11C22×D411yescharacteristic
271D4×C11—22no—
272D4×C11—22no—
273D4×C11—22no—
274D4×C11—22no—
275D4×C11—48no—
276D4×C11—41no—
277D4×C11—41no—
278D4×C11—41no—
279D4×C11—41no—
280D4×C11—84no—
281C2×C4×C11—21no—
282C2×C4×C11—21no—
283C2×C4×C11—21no—
284C2×C4×C11—21no—
285C2×C4×C11—22no—
286C2×C4×C11—22no—
287C2×C4×C11—22no—
288C2×C4×C11—22no—
289C2×C4×C11—22no—
290C2×C4×C11—22no—
291C2×C4×C11—21no—
292C2×C4×C11—22no—
293C2×C4×C11—22no—
294C2×C4×C11—21no—
295C2×C4×C11—21no—
296C2×C4×C11—21no—
297C2×C4×C11—21no—
298C2×C4×C11—21no—
299C2×C4×C11—21no—
300C2×C4×C11—21no—
301C2×C4×C11—21no—
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—84no—
317C2×C4×C11—84no—
318C2×C4×C11—84no—
319C2×C4×C11C4×D412yes—
320C2×C4×C11AGL(1,ℤ/8)12yes—
321C2×C4×C11C23×C411yescharacteristic
322C2×C4×C11C22×D411yescharacteristic
323C2×C4×C11C2×#4111yescharacteristic
324C2×C4×C11C2×#4111yescharacteristic
325C2×C4×C11H(5,𝔽2)11yescharacteristic
326C2×C4×C112−1+411yescharacteristic
327C8×C11—22no—
328C8×C11—41no—
329C8×C11—41no—
330C8×C11C4×D414yescomplemented
331C22×D8C22×C1111yescharacteristic
332C22×M16C22×C1111yescharacteristic
333C2×#121C22×C1111yescharacteristic
334C2×#121C22×C1111yescharacteristic
335C2×C4×D4—21no—
336C2×C4×D4C22×C1111yescharacteristic
337C2×C4×D4C22×C1111yescharacteristic
338C2×#117C22×C1111yescharacteristic
339C22×C4⋊C4C22×C1111yescharacteristic
340#469C4×C1118yescomplemented
341C4×D8—24no—
342#428—24no—
343C2×#107C22×C1111yescharacteristic
344C2×#107C22×C1111yescharacteristic
345C2×#106C22×C1111yescharacteristic
346C2×#106C22×C1111yescharacteristic
347C2×#106C22×C1111yescharacteristic
348C2×#102C22×C1111yescharacteristic
349C2×#102C22×C1111yescharacteristic
350C2×#102C22×C1111yescharacteristic
351C2×#102C22×C1111yescharacteristic
352C2×#102C22×C1111yescharacteristic
353C2×#102C22×C1111yescharacteristic
354C2×C22⋊C8C22×C1111yescharacteristic
355C2×#97C22×C1111yescharacteristic
356C2×C4×C8C22×C1111yescharacteristic
357#390—21no—
358#390C22×C1111yescharacteristic
359#390C22×C1111yescharacteristic
360#389C22×C1111yescharacteristic
361#389C22×C1111yescharacteristic
362#388—21no—
363#388—21no—
364#386—21no—
365#386—21no—
366#385—21no—
367C4×C4⋊C4C22×C1111yescharacteristic
368C4×C4⋊C4C22×C1111yescharacteristic
369C4×C22⋊C4—21no—
370C4×C22⋊C4C22×C1111yescharacteristic
371#340C22×C1111yescharacteristic
372#340C22×C1111yescharacteristic
373#340C22×C1111yescharacteristic
374#340C22×C1111yescharacteristic
375#336C22×C1111yescharacteristic
376#336C22×C1111yescharacteristic
377C22×C11—22no—
378C22×C11—22no—
379C22×C11—22no—
380C22×C11—41no—
381C22×C11—41no—
382C22×C11—41no—
383C22×C11—41no—
384C22×C11—42no—
385C22×C11—42no—
386C22×C11—42no—
387C22×C11—42no—
388C22×C11—42no—
389C22×C11—42no—
390C22×C11—81no—
391C22×C11—81no—
392C22×C11—81no—
393C22×C11—81no—
394C22×C11—81no—
395C22×C11—81no—
396C22×C11—81no—
397C22×C11—81no—
398C22×C11C2×C4×D411yescharacteristic
399C22×C11D4211yescharacteristic
400C22×C11#54711yescharacteristic
401C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
402C22×C11#57511yescharacteristic
403C22×C11#57611yescharacteristic
404C22×C11#57711yescharacteristic
405C4×C11—22no—
406C4×C11—22no—
407C4×C11—41no—
408C4×C11—41no—
409C4×C11—42no—
410C4×C11—42no—
411C4×C11—42no—
412C4×C11—42no—
413C4×C11—41no—
414C4×C11—81no—
415C4×C11—81no—
416C4×C11C2×C4×D411yescharacteristic
417C4×C11#52011yescharacteristic
418C4×C11#54811yescharacteristic
419C4×C11#55311yescharacteristic
420C22×D4—21no—
421C22×D4—21no—
422C22×D4C23×C1111yescharacteristic
423C22×D4C23×C1111yescharacteristic
424C23×C4—21no—
425C23×C4—21no—
426C23×C4—21no—
427C23×C4C23×C1111yescharacteristic
428C2×D8—22no—
429C2×D8—22no—
430C2×D8C2×C4×C1114yescomplemented
431C2×M16—22no—
432C2×M16—22no—
433C2×M16C2×C4×C1114yescomplemented
434C22×C8C23×C1111yescharacteristic
435C22×C8C23×C1111yescharacteristic
436C22×C8C23×C1111yescharacteristic
437C22×C8C23×C1111yescharacteristic
438#121—22no—
439#121—22no—
440#121C2×C4×C1114yescomplemented
441#121C2×C4×C1114yescomplemented
442C4×D4—22no—
443C4×D4—22no—
444C4×D4—41no—
445C4×D4—41no—
446C4×D4—44no—
447#117—22no—
448#117—41no—
449C2×C4⋊C4—22no—
450C2×C4⋊C4—21no—
451C2×C4⋊C4—21no—
452C2×C4⋊C4—21no—
453C2×C4⋊C4—41no—
454C2×C4⋊C4C23×C1111yescharacteristic
455C2×C4⋊C4C23×C1111yescharacteristic
456C2×C4⋊C4C23×C1111yescharacteristic
457C2×C4⋊C4C23×C1111yescharacteristic
458C2×C4⋊C4C23×C1111yescharacteristic
459C2×C4⋊C4C23×C1111yescharacteristic
460C2×C22⋊C4—21no—
461C2×C22⋊C4—21no—
462C2×C22⋊C4—21no—
463C2×C22⋊C4—21no—
464C2×C22⋊C4—21no—
465C2×C22⋊C4—21no—
466C2×C22⋊C4—21no—
467C2×C22⋊C4—21no—
468C2×C22⋊C4—21no—
469C2×C22⋊C4D4×C1111yescharacteristic
470C2×C22⋊C4D4×C1111yescharacteristic
471C2×C42—21no—
472C2×C42—21no—
473C2×C42—21no—
474C2×C42C23×C1111yescharacteristic
475C2×C42C23×C1111yescharacteristic
476#107—22no—
477#107D4×C1114yescomplemented
478#106—22no—
479#106—22no—
480#106C2×C4×C1114yescomplemented
481#102—22no—
482#102—22no—
483#102—41no—
484#102—41no—
485#102C2×C4×C1114yescomplemented
486#102C2×C4×C1114yescomplemented
487C22⋊C8—22no—
488#97—22no—
489C4×C8—22no—
490#95—21no—
491#95—21no—
492#95—21no—
493#95—21no—
494#95D4×C1111yescharacteristic
495#95D4×C1111yescharacteristic
496C2×C11—42no—
497C2×C11—82no—
498C2×C11—82no—
499C2×C11#236111yescharacteristic
500C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
501C2×C11#294611yescharacteristic
502C2×C11#326411yescharacteristic
503C2×C11#327111yescharacteristic
504C2×C11#335411yescharacteristic
505C2×C11#335511yescharacteristic
506C24—21no—
507C24—21no—
508C24C2×D4×C1111yescharacteristic
509C2×D4—24no—
510C2×D4—24no—
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—21no—
514C2×D4—21no—
515C2×D4—21no—
516C2×D4—21no—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—42no—
522C2×D4—42no—
523C2×D4—81no—
524C2×D4—81no—
525C2×D4C22×C4×C1112yes—
526C2×D4C22×C4×C1112yes—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—42no—
538C22×C4—42no—
539C22×C4—42no—
540C22×C4—42no—
541C22×C4—42no—
542C22×C4—42no—
543C22×C4—81no—
544C22×C4—81no—
545C22×C4—81no—
546C22×C4C22×C4×C1112yes—
547C22×C4C2×D4×C1111yescharacteristic
548C22×C4C2×D4×C1111yescharacteristic
549C22×C4C2×D4×C1111yescharacteristic
550C22×C4C2×D4×C1111yescharacteristic
551C22×C4C2×D4×C1111yescharacteristic
552C22×C4C11×#4112yes—
553C22×C4C24×C1111yescharacteristic
554D8—28no—
555M16—28no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8C22×C4×C1112yes—
565C2×C8C22×C4×C1112yes—
566C2×C8C2×D4×C1112yes—
567C2×C8C11×#4112yes—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—42no—
577C4⋊C4—42no—
578C4⋊C4—81no—
579C4⋊C4C22×C4×C1112yes—
580C4⋊C4C22×C4×C1112yes—
581C4⋊C4C2×D4×C1112yes—
582C4⋊C4C2×D4×C1112yes—
583C22⋊C4—24no—
584C22⋊C4—24no—
585C22⋊C4—22no—
586C22⋊C4—41no—
587C22⋊C4—42no—
588C22⋊C4—42no—
589C22⋊C4—42no—
590C22⋊C4—42no—
591C22⋊C4—42no—
592C22⋊C4—81no—
593C22⋊C4—81no—
594C42—21no—
595C42—21no—
596C42—21no—
597C42—21no—
598C42—42no—
599C42—42no—
600C42—81no—
601C11#2303711yescharacteristic, direct product factor, Sylow
602C23—21no—
603C23—21no—
604C23—21no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23—22no—
609C23—22no—
610C23—41no—
611C23—41no—
612C23—41no—
613C23—41no—
614C23—41no—
615C23—41no—
616C23—41no—
617C23—41no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23—41no—
622C23C4×D4×C1112yes—
623C23C22×D4×C1111yescharacteristic
624D4—22no—
625D4—22no—
626D4—22no—
627D4—22no—
628D4—48no—
629D4—41no—
630D4—41no—
631D4—41no—
632D4—41no—
633D4—84no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—21no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
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—84no—
670C2×C4—84no—
671C2×C4—84no—
672C2×C4C4×D4×C1112yes—
673C2×C4C11×AGL(1,ℤ/8)12yes—
674C2×C4C23×C4×C1111yescharacteristic
675C2×C4C22×D4×C1111yescharacteristic
676C2×C4C2×C11×#4111yescharacteristic
677C2×C4C2×C11×#4111yescharacteristic
678C2×C4C11×H(5,𝔽2)11yescharacteristic
679C2×C4C11×2−1+411yescharacteristic
680C8—22no—
681C8—41no—
682C8—41no—
683C8C4×D4×C1114yescomplemented
684C22—22no—
685C22—22no—
686C22—22no—
687C22—41no—
688C22—41no—
689C22—41no—
690C22—41no—
691C22—42no—
692C22—42no—
693C22—42no—
694C22—42no—
695C22—42no—
696C22—42no—
697C22—81no—
698C22—81no—
699C22—81no—
700C22—81no—
701C22—81no—
702C22—81no—
703C22—81no—
704C22—81no—
705C22C2×C4×D4×C1111yescharacteristic
706C22D42×C1111yescharacteristic
707C22C11×#54711yescharacteristic
708C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
709C22C11×#57511yescharacteristic
710C22C11×#57611yescharacteristic
711C22C11×#57711yescharacteristic
712C4—22no—
713C4—22no—
714C4—42no—
715C4—42no—
716C4—42no—
717C4—42no—
718C4—41no—
719C4—41no—
720C4—41no—
721C4—81no—
722C4—81no—
723C4C2×C4×D4×C1111yescharacteristic
724C4C11×#52011yescharacteristic
725C4C11×#54811yescharacteristic
726C4C11×#55311yescharacteristic
727C2—42no—
728C2—82no—
729C2—82no—
730C2C11×#236111yescharacteristic
731C2C4×C11×AGL(1,ℤ/8)11yescharacteristic
732C2C11×#294611yescharacteristic
733C2C11×#326411yescharacteristic
734C2C11×#327111yescharacteristic
735C2C11×#335411yescharacteristic
736C2C11×#335511yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#469C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C4×C11×C22⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C4×C11×D8C2semidirect
3. C2×C11×#428C2semidirect
4. C11×#2363C2semidirect
5. C11×#2361C2semidirect
6. C11×#1972C2semidirect
7. C11×#1941C2semidirect
8. C11×#1926C2semidirect
9. C11×#1925C2semidirect
10. C11×#1875C2semidirect
11. C11×#1874C2semidirect
12. C11×#1864C2semidirect
13. C11×#1862C2semidirect
14. C11×#1776C2semidirect
15. C11×#1753C2semidirect
25. C11×#469C4semidirect
72. C2×C11×D8C2×C4semidirect
75. C2×C11×M16C2×C4semidirect
82. C11×#121C2×C4semidirect
83. C11×#121C2×C4semidirect
119. C11×#107D4semidirect
122. C11×#106C2×C4semidirect
127. C11×#102C2×C4semidirect
128. C11×#102C2×C4semidirect
138. #23037C11direct (N × H)
235. C2×C4×D8C2×C11semidirect
236. C2×#428C2×C11semidirect
237. #2363C2×C11semidirect
238. #2361C2×C11semidirect
239. #1972C2×C11semidirect
240. #1941C2×C11semidirect
241. #1926C2×C11semidirect
242. #1925C2×C11semidirect
243. #1875C2×C11semidirect
244. #1874C2×C11semidirect
245. #1864C2×C11semidirect
246. #1862C2×C11semidirect
247. #1776C2×C11semidirect
248. #1753C2×C11semidirect
330. C8×C11C4×D4semidirect
340. #469C4×C11semidirect
430. C2×D8C2×C4×C11semidirect
433. C2×M16C2×C4×C11semidirect
440. #121C2×C4×C11semidirect
441. #121C2×C4×C11semidirect
477. #107D4×C11semidirect
480. #106C2×C4×C11semidirect
485. #102C2×C4×C11semidirect
486. #102C2×C4×C11semidirect
601. C11#23037direct (N × H)
683. C8C4×D4×C11semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#4692
C2×C4×C11×D82
C2×C11×#4282
C11×#23632
C11×#23612
C11×#19722
C11×#19412
C11×#19262
C11×#19252
C11×#18752
C11×#18742
C11×#18642
C11×#18622
C11×#17762
C11×#17532
#2303711