Finite Group Databasebeta

← C11×#23008 #14600201

Subgroups — C11×#23008 #14600201

Order 2816.

1122 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#459C211yesmaximal, characteristic
2C2×C11×#442C211yesmaximal, characteristic, complemented
3C2×C4×C11×D8C211yesmaximal, characteristic, complemented
4C11×#2366C211yesmaximal, characteristic, complemented
5C11×#2349C211yesmaximal, characteristic, complemented
6C11×#1961C211yesmaximal, characteristic, complemented
7C11×#1949C211yesmaximal, characteristic, complemented
8C11×#1936C211yesmaximal, characteristic, complemented
9C11×#1934C211yesmaximal, characteristic, complemented
10C11×#1879C211yesmaximal, characteristic, complemented
11C11×#1879C211yesmaximal, characteristic, complemented
12C11×#1864C211yesmaximal, characteristic, complemented
13C11×#1862C211yesmaximal, characteristic, complemented
14C11×#1771C211yesmaximal, characteristic, complemented
15C11×#1762C211yesmaximal, characteristic, complemented
16C22×C11×D8C2211yescharacteristic
17C22×C11×D8C2211yescharacteristic
18C2×C11×#127C2211yescharacteristic
19C2×C4×D4×C11—21no—
20C2×C4×D4×C11C2211yescharacteristic
21C2×C4×D4×C11C2211yescharacteristic
22C2×C4×D4×C11C2211yescharacteristic
23C2×C4×D4×C11C2211yescharacteristic
24C2×C4×D4×C11C2211yescharacteristic
25C11×#459C418yescomplemented
26C11×#442—24no—
27C4×C11×D8—24no—
28C2×C11×#107C2211yescharacteristic
29C2×C11×#106C2211yescharacteristic
30C2×C11×C4⋊C8C2211yescharacteristic
31C2×C11×#102C2211yescharacteristic
32C2×C11×#102C2211yescharacteristic
33C2×C11×#102C2211yescharacteristic
34C2×C11×#102C2211yescharacteristic
35C2×C11×#102C2211yescharacteristic
36C2×C11×#102C2211yescharacteristic
37C2×C11×#102C2211yescharacteristic
38C2×C11×#102C2211yescharacteristic
39C2×C11×#97C2211yescharacteristic
40C2×C11×#97C2211yescharacteristic
41C2×C4×C8×C11C2211yescharacteristic
42C11×#390—21no—
43C11×#390C2211yescharacteristic
44C11×#390C2211yescharacteristic
45C11×#389C2211yescharacteristic
46C11×#389C2211yescharacteristic
47C11×#386—21no—
48C11×#386—21no—
49C11×#385—21no—
50C11×#385—21no—
51C11×#382C2211yescharacteristic
52C11×#380—21no—
53C4×C11×C4⋊C4C2211yescharacteristic
54C4×C11×C4⋊C4C2211yescharacteristic
55C2×C11×#95—21no—
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
66C22×D4×C11C2311yescharacteristic
67C23×C4×C11—21no—
68C23×C4×C11—21no—
69C23×C4×C11—21no—
70C23×C4×C11—21no—
71C23×C4×C11—21no—
72C2×C11×D8—22no—
73C2×C11×D8—22no—
74C2×C11×D8—22no—
75C2×C11×D8—22no—
76C2×C11×D8C2×C414yescomplemented
77C2×C11×D8C2×C414yescomplemented
78C22×C8×C11C2311yescharacteristic
79C22×C8×C11C2311yescharacteristic
80C22×C8×C11C2311yescharacteristic
81C22×C8×C11C2311yescharacteristic
82C11×#127—22no—
83C11×#127C2×C414yescomplemented
84C4×D4×C11—22no—
85C4×D4×C11—22no—
86C4×D4×C11—22no—
87C4×D4×C11—22no—
88C4×D4×C11—22no—
89C4×D4×C11—41no—
90C4×D4×C11—41no—
91C4×D4×C11—41no—
92C4×D4×C11—41no—
93C4×D4×C11—44no—
94C4×D4×C11C2×C414yescomplemented
95C2×C11×C4⋊C4—21no—
96C2×C11×C4⋊C4—21no—
97C2×C11×C4⋊C4D411yescharacteristic
98C2×C11×C4⋊C4D411yescharacteristic
99C2×C11×C4⋊C4C2311yescharacteristic
100C2×C11×C4⋊C4C2311yescharacteristic
101C2×C11×C4⋊C4C2311yescharacteristic
102C2×C11×C4⋊C4C2311yescharacteristic
103C2×C11×C4⋊C4C2311yescharacteristic
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⋊C4—21no—
112C2×C11×C22⋊C4—21no—
113C2×C42×C11—21no—
114C2×C42×C11C2311yescharacteristic
115C2×C42×C11C2311yescharacteristic
116C2×C42×C11C2311yescharacteristic
117C11×#107—22no—
118C11×#106—22no—
119C11×C4⋊C8C2×C414yescomplemented
120C11×#102—22no—
121C11×#102—22no—
122C11×#102—22no—
123C11×#102—41no—
124C11×#102—41no—
125C11×#102C2×C414yescomplemented
126C11×#102C2×C414yescomplemented
127C11×#102D414yescomplemented
128C11×#97—22no—
129C11×#97—22no—
130C4×C8×C11—22no—
131C11×#95—21no—
132C11×#95—21no—
133C11×#95—21no—
134C11×#95—21no—
135C11×#95—21no—
136C11×#95D411yescharacteristic
137C11×#95D411yescharacteristic
138#23008C1111yesmaximal, characteristic, direct product factor, Sylow
139C24×C11—21no—
140C24×C11—21no—
141C24×C11—21no—
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—21no—
155C2×D4×C11—21no—
156C2×D4×C11—21no—
157C2×D4×C11—42no—
158C2×D4×C11—42no—
159C2×D4×C11—81no—
160C2×D4×C11—81no—
161C2×D4×C11C22×C412yes—
162C2×D4×C11C22×C412yes—
163C2×D4×C11C22×C412yes—
164C2×D4×C11C2×D412yes—
165C2×D4×C11#4112yes—
166C22×C4×C11—21no—
167C22×C4×C11—21no—
168C22×C4×C11—24no—
169C22×C4×C11—21no—
170C22×C4×C11—21no—
171C22×C4×C11—21no—
172C22×C4×C11—42no—
173C22×C4×C11—42no—
174C22×C4×C11—42no—
175C22×C4×C11—42no—
176C22×C4×C11—42no—
177C22×C4×C11—42no—
178C22×C4×C11—42no—
179C22×C4×C11—42no—
180C22×C4×C11—81no—
181C22×C4×C11—81no—
182C22×C4×C11—81no—
183C22×C4×C11—81no—
184C22×C4×C11—81no—
185C22×C4×C11—81no—
186C22×C4×C11C2×D411yescharacteristic
187C22×C4×C11C2×D411yescharacteristic
188C22×C4×C11C2×D411yescharacteristic
189C22×C4×C11C2×D411yescharacteristic
190C22×C4×C11C2×D411yescharacteristic
191C22×C4×C11C2×D411yescharacteristic
192C22×C4×C11C2411yescharacteristic
193C11×D8—28no—
194C11×D8—28no—
195C2×C8×C11—21no—
196C2×C8×C11—21no—
197C2×C8×C11—21no—
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×C11C22×C412yes—
205C2×C8×C11C22×C412yes—
206C2×C8×C11C2×D412yes—
207C11×C4⋊C4—22no—
208C11×C4⋊C4—21no—
209C11×C4⋊C4—21no—
210C11×C4⋊C4—21no—
211C11×C4⋊C4—21no—
212C11×C4⋊C4—21no—
213C11×C4⋊C4—21no—
214C11×C4⋊C4—21no—
215C11×C4⋊C4—21no—
216C11×C4⋊C4—41no—
217C11×C4⋊C4—81no—
218C11×C4⋊C4—81no—
219C11×C4⋊C4C22×C412yes—
220C11×C4⋊C4C2×D412yes—
221C11×C22⋊C4—24no—
222C11×C22⋊C4—42no—
223C11×C22⋊C4—42no—
224C11×C22⋊C4—42no—
225C11×C22⋊C4—42no—
226C11×C22⋊C4—42no—
227C11×C22⋊C4—42no—
228C11×C22⋊C4—81no—
229C11×C22⋊C4—81no—
230C42×C11—21no—
231C42×C11—21no—
232C42×C11—21no—
233C42×C11—21no—
234C42×C11—42no—
235C42×C11C22×C412yes—
236C42×C11#4112yes—
237C2×#459C2×C1111yescharacteristic
238C2×#442C2×C1111yescharacteristic, complemented
239C2×C4×D8C2×C1111yescharacteristic, complemented
240#2366C2×C1111yescharacteristic, complemented
241#2349C2×C1111yescharacteristic, complemented
242#1961C2×C1111yescharacteristic, complemented
243#1949C2×C1111yescharacteristic, complemented
244#1936C2×C1111yescharacteristic, complemented
245#1934C2×C1111yescharacteristic, complemented
246#1879C2×C1111yescharacteristic, complemented
247#1879C2×C1111yescharacteristic, complemented
248#1864C2×C1111yescharacteristic, complemented
249#1862C2×C1111yescharacteristic, complemented
250#1771C2×C1111yescharacteristic, complemented
251#1762C2×C1111yescharacteristic, complemented
252C23×C11—22no—
253C23×C11—22no—
254C23×C11—22no—
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×C11—41no—
270C23×C11—41no—
271C23×C11—41no—
272C23×C11—41no—
273C23×C11C22×D411yescharacteristic
274D4×C11—22no—
275D4×C11—22no—
276D4×C11—22no—
277D4×C11—22no—
278D4×C11—22no—
279D4×C11—22no—
280D4×C11—22no—
281D4×C11—48no—
282D4×C11—41no—
283D4×C11—41no—
284D4×C11—41no—
285D4×C11—41no—
286D4×C11—84no—
287D4×C11C4×D414yescomplemented
288C2×C4×C11—21no—
289C2×C4×C11—21no—
290C2×C4×C11—21no—
291C2×C4×C11—21no—
292C2×C4×C11—21no—
293C2×C4×C11—21no—
294C2×C4×C11—22no—
295C2×C4×C11—21no—
296C2×C4×C11—21no—
297C2×C4×C11—21no—
298C2×C4×C11—22no—
299C2×C4×C11—21no—
300C2×C4×C11—21no—
301C2×C4×C11—21no—
302C2×C4×C11—21no—
303C2×C4×C11—21no—
304C2×C4×C11—21no—
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—84no—
319C2×C4×C11—84no—
320C2×C4×C11—84no—
321C2×C4×C11—84no—
322C2×C4×C11—84no—
323C2×C4×C11C4×D412yes—
324C2×C4×C11C4×D412yes—
325C2×C4×C11AGL(1,ℤ/8)12yes—
326C2×C4×C11C23×C411yescharacteristic
327C2×C4×C11C22×D411yescharacteristic
328C2×C4×C11C2×#4111yescharacteristic
329C2×C4×C11C2×#4111yescharacteristic
330C2×C4×C11H(5,𝔽2)11yescharacteristic
331C2×C4×C112−1+411yescharacteristic
332C8×C11—22no—
333C8×C11—22no—
334C8×C11—22no—
335C8×C11—41no—
336C22×D8C22×C1111yescharacteristic
337C22×D8C22×C1111yescharacteristic
338C2×#127C22×C1111yescharacteristic
339C2×C4×D4—21no—
340C2×C4×D4C22×C1111yescharacteristic
341C2×C4×D4C22×C1111yescharacteristic
342C2×C4×D4C22×C1111yescharacteristic
343C2×C4×D4C22×C1111yescharacteristic
344C2×C4×D4C22×C1111yescharacteristic
345#459C4×C1118yescomplemented
346#442—24no—
347C4×D8—24no—
348C2×#107C22×C1111yescharacteristic
349C2×#106C22×C1111yescharacteristic
350C2×C4⋊C8C22×C1111yescharacteristic
351C2×#102C22×C1111yescharacteristic
352C2×#102C22×C1111yescharacteristic
353C2×#102C22×C1111yescharacteristic
354C2×#102C22×C1111yescharacteristic
355C2×#102C22×C1111yescharacteristic
356C2×#102C22×C1111yescharacteristic
357C2×#102C22×C1111yescharacteristic
358C2×#102C22×C1111yescharacteristic
359C2×#97C22×C1111yescharacteristic
360C2×#97C22×C1111yescharacteristic
361C2×C4×C8C22×C1111yescharacteristic
362#390—21no—
363#390C22×C1111yescharacteristic
364#390C22×C1111yescharacteristic
365#389C22×C1111yescharacteristic
366#389C22×C1111yescharacteristic
367#386—21no—
368#386—21no—
369#385—21no—
370#385—21no—
371#382C22×C1111yescharacteristic
372#380—21no—
373C4×C4⋊C4C22×C1111yescharacteristic
374C4×C4⋊C4C22×C1111yescharacteristic
375C2×#95—21no—
376#340C22×C1111yescharacteristic
377#340C22×C1111yescharacteristic
378#340C22×C1111yescharacteristic
379#340C22×C1111yescharacteristic
380#336C22×C1111yescharacteristic
381#336C22×C1111yescharacteristic
382C22×C11—24no—
383C22×C11—42no—
384C22×C11—42no—
385C22×C11—42no—
386C22×C11—42no—
387C22×C11—42no—
388C22×C11—42no—
389C22×C11—42no—
390C22×C11—42no—
391C22×C11—42no—
392C22×C11—42no—
393C22×C11—42no—
394C22×C11—42no—
395C22×C11—81no—
396C22×C11—81no—
397C22×C11—81no—
398C22×C11—81no—
399C22×C11—81no—
400C22×C11—81no—
401C22×C11—81no—
402C22×C11—81no—
403C22×C11C2×C4×D411yescharacteristic
404C22×C11D4211yescharacteristic
405C22×C11#54811yescharacteristic
406C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
407C22×C11#57511yescharacteristic
408C22×C11#57611yescharacteristic
409C22×C11#57611yescharacteristic
410C4×C11—22no—
411C4×C11—22no—
412C4×C11—22no—
413C4×C11—42no—
414C4×C11—41no—
415C4×C11—42no—
416C4×C11—41no—
417C4×C11—41no—
418C4×C11—81no—
419C4×C11—81no—
420C4×C11—81no—
421C4×C11C2×C4×D411yescharacteristic
422C4×C11#52011yescharacteristic
423C4×C11#54711yescharacteristic
424C4×C11#55311yescharacteristic
425C22×D4—21no—
426C22×D4—21no—
427C22×D4C23×C1111yescharacteristic
428C22×D4C23×C1111yescharacteristic
429C22×D4C23×C1111yescharacteristic
430C23×C4—21no—
431C23×C4—21no—
432C23×C4—21no—
433C23×C4—21no—
434C23×C4—21no—
435C2×D8—22no—
436C2×D8—22no—
437C2×D8—22no—
438C2×D8—22no—
439C2×D8C2×C4×C1114yescomplemented
440C2×D8C2×C4×C1114yescomplemented
441C22×C8C23×C1111yescharacteristic
442C22×C8C23×C1111yescharacteristic
443C22×C8C23×C1111yescharacteristic
444C22×C8C23×C1111yescharacteristic
445#127—22no—
446#127C2×C4×C1114yescomplemented
447C4×D4—22no—
448C4×D4—22no—
449C4×D4—22no—
450C4×D4—22no—
451C4×D4—22no—
452C4×D4—41no—
453C4×D4—41no—
454C4×D4—41no—
455C4×D4—41no—
456C4×D4—44no—
457C4×D4C2×C4×C1114yescomplemented
458C2×C4⋊C4—21no—
459C2×C4⋊C4—21no—
460C2×C4⋊C4D4×C1111yescharacteristic
461C2×C4⋊C4D4×C1111yescharacteristic
462C2×C4⋊C4C23×C1111yescharacteristic
463C2×C4⋊C4C23×C1111yescharacteristic
464C2×C4⋊C4C23×C1111yescharacteristic
465C2×C4⋊C4C23×C1111yescharacteristic
466C2×C4⋊C4C23×C1111yescharacteristic
467C2×C22⋊C4—21no—
468C2×C22⋊C4—21no—
469C2×C22⋊C4—21no—
470C2×C22⋊C4—21no—
471C2×C22⋊C4—21no—
472C2×C22⋊C4—21no—
473C2×C22⋊C4—21no—
474C2×C22⋊C4—21no—
475C2×C22⋊C4—21no—
476C2×C42—21no—
477C2×C42C23×C1111yescharacteristic
478C2×C42C23×C1111yescharacteristic
479C2×C42C23×C1111yescharacteristic
480#107—22no—
481#106—22no—
482C4⋊C8C2×C4×C1114yescomplemented
483#102—22no—
484#102—22no—
485#102—22no—
486#102—41no—
487#102—41no—
488#102C2×C4×C1114yescomplemented
489#102C2×C4×C1114yescomplemented
490#102D4×C1114yescomplemented
491#97—22no—
492#97—22no—
493C4×C8—22no—
494#95—21no—
495#95—21no—
496#95—21no—
497#95—21no—
498#95—21no—
499#95D4×C1111yescharacteristic
500#95D4×C1111yescharacteristic
501C2×C11—44no—
502C2×C11—82no—
503C2×C11—82no—
504C2×C11#236111yescharacteristic
505C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
506C2×C11#294811yescharacteristic
507C2×C11#326411yescharacteristic
508C2×C11#326811yescharacteristic
509C2×C11#336611yescharacteristic
510C2×C11#337011yescharacteristic
511C24—21no—
512C24—21no—
513C24—21no—
514C2×D4—24no—
515C2×D4—24no—
516C2×D4—21no—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—21no—
526C2×D4—21no—
527C2×D4—21no—
528C2×D4—21no—
529C2×D4—42no—
530C2×D4—42no—
531C2×D4—81no—
532C2×D4—81no—
533C2×D4C22×C4×C1112yes—
534C2×D4C22×C4×C1112yes—
535C2×D4C22×C4×C1112yes—
536C2×D4C2×D4×C1112yes—
537C2×D4C11×#4112yes—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—24no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—42no—
545C22×C4—42no—
546C22×C4—42no—
547C22×C4—42no—
548C22×C4—42no—
549C22×C4—42no—
550C22×C4—42no—
551C22×C4—42no—
552C22×C4—81no—
553C22×C4—81no—
554C22×C4—81no—
555C22×C4—81no—
556C22×C4—81no—
557C22×C4—81no—
558C22×C4C2×D4×C1111yescharacteristic
559C22×C4C2×D4×C1111yescharacteristic
560C22×C4C2×D4×C1111yescharacteristic
561C22×C4C2×D4×C1111yescharacteristic
562C22×C4C2×D4×C1111yescharacteristic
563C22×C4C2×D4×C1111yescharacteristic
564C22×C4C24×C1111yescharacteristic
565D8—28no—
566D8—28no—
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×C8C22×C4×C1112yes—
577C2×C8C22×C4×C1112yes—
578C2×C8C2×D4×C1112yes—
579C4⋊C4—22no—
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—41no—
589C4⋊C4—81no—
590C4⋊C4—81no—
591C4⋊C4C22×C4×C1112yes—
592C4⋊C4C2×D4×C1112yes—
593C22⋊C4—24no—
594C22⋊C4—42no—
595C22⋊C4—42no—
596C22⋊C4—42no—
597C22⋊C4—42no—
598C22⋊C4—42no—
599C22⋊C4—42no—
600C22⋊C4—81no—
601C22⋊C4—81no—
602C42—21no—
603C42—21no—
604C42—21no—
605C42—21no—
606C42—42no—
607C42C22×C4×C1112yes—
608C42C11×#4112yes—
609C11#2300811yescharacteristic, direct product factor, Sylow
610C23—22no—
611C23—22no—
612C23—22no—
613C23—22no—
614C23—22no—
615C23—41no—
616C23—41no—
617C23—41no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—41no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23C22×D4×C1111yescharacteristic
632D4—22no—
633D4—22no—
634D4—22no—
635D4—22no—
636D4—22no—
637D4—22no—
638D4—22no—
639D4—48no—
640D4—41no—
641D4—41no—
642D4—41no—
643D4—41no—
644D4—84no—
645D4C4×D4×C1114yescomplemented
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—22no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—22no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
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—84no—
677C2×C4—84no—
678C2×C4—84no—
679C2×C4—84no—
680C2×C4—84no—
681C2×C4C4×D4×C1112yes—
682C2×C4C4×D4×C1112yes—
683C2×C4C11×AGL(1,ℤ/8)12yes—
684C2×C4C23×C4×C1111yescharacteristic
685C2×C4C22×D4×C1111yescharacteristic
686C2×C4C2×C11×#4111yescharacteristic
687C2×C4C2×C11×#4111yescharacteristic
688C2×C4C11×H(5,𝔽2)11yescharacteristic
689C2×C4C11×2−1+411yescharacteristic
690C8—22no—
691C8—22no—
692C8—22no—
693C8—41no—
694C22—24no—
695C22—42no—
696C22—42no—
697C22—42no—
698C22—42no—
699C22—42no—
700C22—42no—
701C22—42no—
702C22—42no—
703C22—42no—
704C22—42no—
705C22—42no—
706C22—42no—
707C22—81no—
708C22—81no—
709C22—81no—
710C22—81no—
711C22—81no—
712C22—81no—
713C22—81no—
714C22—81no—
715C22C2×C4×D4×C1111yescharacteristic
716C22D42×C1111yescharacteristic
717C22C11×#54811yescharacteristic
718C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
719C22C11×#57511yescharacteristic
720C22C11×#57611yescharacteristic
721C22C11×#57611yescharacteristic
722C4—22no—
723C4—22no—
724C4—22no—
725C4—42no—
726C4—41no—
727C4—42no—
728C4—41no—
729C4—41no—
730C4—81no—
731C4—81no—
732C4—81no—
733C4C2×C4×D4×C1111yescharacteristic
734C4C11×#52011yescharacteristic
735C4C11×#54711yescharacteristic
736C4C11×#55311yescharacteristic
737C2—44no—
738C2—82no—
739C2—82no—
740C2C11×#236111yescharacteristic
741C2C4×C11×AGL(1,ℤ/8)11yescharacteristic
742C2C11×#294811yescharacteristic
743C2C11×#326411yescharacteristic
744C2C11×#326811yescharacteristic
745C2C11×#336611yescharacteristic
746C2C11×#337011yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#459C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C4×C11×C4⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#442C2semidirect
3. C2×C4×C11×D8C2semidirect
4. C11×#2366C2semidirect
5. C11×#2349C2semidirect
6. C11×#1961C2semidirect
7. C11×#1949C2semidirect
8. C11×#1936C2semidirect
9. C11×#1934C2semidirect
10. C11×#1879C2semidirect
11. C11×#1879C2semidirect
12. C11×#1864C2semidirect
13. C11×#1862C2semidirect
14. C11×#1771C2semidirect
15. C11×#1762C2semidirect
25. C11×#459C4semidirect
76. C2×C11×D8C2×C4semidirect
77. C2×C11×D8C2×C4semidirect
83. C11×#127C2×C4semidirect
94. C4×D4×C11C2×C4semidirect
119. C11×C4⋊C8C2×C4semidirect
125. C11×#102C2×C4semidirect
126. C11×#102C2×C4semidirect
127. C11×#102D4semidirect
138. #23008C11direct (N × H)
238. C2×#442C2×C11semidirect
239. C2×C4×D8C2×C11semidirect
240. #2366C2×C11semidirect
241. #2349C2×C11semidirect
242. #1961C2×C11semidirect
243. #1949C2×C11semidirect
244. #1936C2×C11semidirect
245. #1934C2×C11semidirect
246. #1879C2×C11semidirect
247. #1879C2×C11semidirect
248. #1864C2×C11semidirect
249. #1862C2×C11semidirect
250. #1771C2×C11semidirect
251. #1762C2×C11semidirect
287. D4×C11C4×D4semidirect
345. #459C4×C11semidirect
439. C2×D8C2×C4×C11semidirect
440. C2×D8C2×C4×C11semidirect
446. #127C2×C4×C11semidirect
457. C4×D4C2×C4×C11semidirect
482. C4⋊C8C2×C4×C11semidirect
488. #102C2×C4×C11semidirect
489. #102C2×C4×C11semidirect
490. #102D4×C11semidirect
609. C11#23008direct (N × H)
645. D4C4×D4×C11semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#4592
C2×C11×#4422
C2×C4×C11×D82
C11×#23662
C11×#23492
C11×#19612
C11×#19492
C11×#19362
C11×#19342
C11×#18792
C11×#18642
C11×#18622
C11×#17712
C11×#17622
#2300811