Finite Group Databasebeta

← C11×#22498 #14599691

Subgroups — C11×#22498 #14599691

Order 2816.

1186 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#553C211yesmaximal, characteristic
2C2×C11×#435C211yesmaximal, characteristic, complemented
3C11×#2354C211yesmaximal, characteristic, complemented
4C11×#1992C211yesmaximal, characteristic, complemented
5C11×#1989C211yesmaximal, characteristic, complemented
6C11×#1895C211yesmaximal, characteristic, complemented
7C11×#1893C211yesmaximal, characteristic, complemented
8C11×#1875C211yesmaximal, characteristic, complemented
9C11×#1875C211yesmaximal, characteristic, complemented
10C11×#1825C211yesmaximal, characteristic, complemented
11C11×#1823C211yesmaximal, characteristic, complemented
12C11×#1802C211yesmaximal, characteristic, complemented
13C11×#1762C211yesmaximal, characteristic, complemented
14C11×#1736C211yesmaximal, characteristic, complemented
15C11×#1735C211yesmaximal, characteristic, complemented
16C22×C11×M16C2211yescharacteristic
17C23×C8×C11C2211yescharacteristic
18C11×#553—24no—
19C11×#553C418yescomplemented
20C2×C11×#126—21no—
21C2×C11×#125C2211yescharacteristic
22C2×C11×#123—21no—
23C2×C11×#121—21no—
24C2×C11×#121C2211yescharacteristic
25C2×C11×#121C2211yescharacteristic
26C2×C4×D4×C11—21no—
27C2×C4×D4×C11C2211yescharacteristic
28C2×C4×D4×C11C2211yescharacteristic
29C2×C11×#117C2211yescharacteristic
30C2×C11×#117C2211yescharacteristic
31C2×C11×#117C2211yescharacteristic
32C22×C11×C4⋊C4C2211yescharacteristic
33C11×#435—24no—
34C2×C11×C4⋊C8C2211yescharacteristic
35C2×C11×#102C2211yescharacteristic
36C2×C11×#102C2211yescharacteristic
37C2×C11×#102C2211yescharacteristic
38C2×C11×#102C2211yescharacteristic
39C2×C11×C22⋊C8C2211yescharacteristic
40C2×C11×C22⋊C8C2211yescharacteristic
41C2×C11×#97C2211yescharacteristic
42C11×#390—21no—
43C11×#388—21no—
44C11×#388—21no—
45C11×#384C2211yescharacteristic
46C11×#380C2211yescharacteristic
47C11×#380C2211yescharacteristic
48C4×C11×C4⋊C4—21no—
49C4×C11×C4⋊C4C2211yescharacteristic
50C11×#340C2211yescharacteristic
51C11×#340C2211yescharacteristic
52C11×#340C2211yescharacteristic
53C11×#340C2211yescharacteristic
54C11×#340C2211yescharacteristic
55C11×#340C2211yescharacteristic
56C11×#340C2211yescharacteristic
57C11×#340C2211yescharacteristic
58C11×#340C2211yescharacteristic
59C11×#340C2211yescharacteristic
60C11×#340C2211yescharacteristic
61C11×#340C2211yescharacteristic
62C22×D4×C11—21no—
63C22×D4×C11—21no—
64C22×D4×C11D411yescharacteristic
65C22×D4×C11C2311yescharacteristic
66C23×C4×C11—21no—
67C23×C4×C11—21no—
68C23×C4×C11C2311yescharacteristic
69C23×C4×C11C2311yescharacteristic
70C2×C11×M16—22no—
71C2×C11×M16—22no—
72C2×C11×M16—41no—
73C22×C8×C11—22no—
74C22×C8×C11—22no—
75C22×C8×C11—41no—
76C22×C8×C11C2311yescharacteristic
77C22×C8×C11C2311yescharacteristic
78C22×C8×C11C2311yescharacteristic
79C22×C8×C11C2311yescharacteristic
80C11×#126—28no—
81C11×#125—22no—
82C11×#125C2×C414yes—
83C11×#123—28no—
84C11×#121—28no—
85C11×#121—22no—
86C11×#121—22no—
87C11×#121C2×C414yes—
88C11×#121C2×C414yes—
89C4×D4×C11—28no—
90C4×D4×C11—22no—
91C4×D4×C11C2×C414yes—
92C4×D4×C11C2×C414yes—
93C4×D4×C11D414yes—
94C11×#117—22no—
95C11×#117—22no—
96C11×#117—22no—
97C11×#117—41no—
98C11×#117—41no—
99C11×#117C2×C414yes—
100C2×C11×C4⋊C4—21no—
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⋊C4C2×C414yes—
107C2×C11×C4⋊C4D411yescharacteristic
108C2×C11×C4⋊C4C2311yescharacteristic
109C2×C11×C4⋊C4C2311yescharacteristic
110C2×C11×C4⋊C4C2311yescharacteristic
111C2×C11×C4⋊C4C2311yescharacteristic
112C2×C11×C4⋊C4C2311yescharacteristic
113C2×C11×C4⋊C4C2311yescharacteristic
114C2×C11×C4⋊C4C2311yescharacteristic
115C2×C11×C22⋊C4—21no—
116C2×C11×C22⋊C4—21no—
117C2×C11×C22⋊C4—21no—
118C2×C11×C22⋊C4—21no—
119C2×C11×C22⋊C4—21no—
120C2×C11×C22⋊C4—21no—
121C2×C11×C22⋊C4—21no—
122C2×C11×C22⋊C4—21no—
123C2×C11×C22⋊C4D411yescharacteristic
124C2×C11×C22⋊C4D411yescharacteristic
125C2×C42×C11—21no—
126C2×C42×C11—21no—
127C2×C42×C11—21no—
128C2×C42×C11—21no—
129C2×C42×C11C2311yescharacteristic
130C11×C4⋊C8—22no—
131C11×#102—22no—
132C11×#102—22no—
133C11×#102—41no—
134C11×#102—41no—
135C11×C22⋊C8—22no—
136C11×C22⋊C8—22no—
137C11×#97—22no—
138C11×#95—21no—
139C11×#95—21no—
140C11×#95—21no—
141#22498C1111yesmaximal, characteristic, direct product factor, Sylow
142C24×C11—21no—
143C24×C11C2×D411yescharacteristic
144C24×C11C2×D411yescharacteristic
145C2×D4×C11—24no—
146C2×D4×C11—24no—
147C2×D4×C11—21no—
148C2×D4×C11—21no—
149C2×D4×C11—21no—
150C2×D4×C11—21no—
151C2×D4×C11—21no—
152C2×D4×C11—41no—
153C2×D4×C11—41no—
154C2×D4×C11—42no—
155C2×D4×C11—42no—
156C2×D4×C11—81no—
157C2×D4×C11—81no—
158C2×D4×C11C22⋊C414yes—
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—21no—
171C22×C4×C11—21no—
172C22×C4×C11—24no—
173C22×C4×C11—24no—
174C22×C4×C11—21no—
175C22×C4×C11—21no—
176C22×C4×C11—21no—
177C22×C4×C11—81no—
178C22×C4×C11—81no—
179C22×C4×C11—81no—
180C22×C4×C11—81no—
181C22×C4×C11C22×C412yes—
182C22×C4×C11C22×C412yes—
183C22×C4×C11C2×D411yescharacteristic
184C22×C4×C11C2×D411yescharacteristic
185C22×C4×C11C2×D411yescharacteristic
186C22×C4×C11C2×D411yescharacteristic
187C22×C4×C11C2×D412yes—
188C22×C4×C11C2×D412yes—
189C22×C4×C11C2411yescharacteristic
190C11×M16—44no—
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×C11—21no—
198C2×C8×C11—21no—
199C2×C8×C11—21no—
200C2×C8×C11—21no—
201C2×C8×C11—21no—
202C2×C8×C11—44no—
203C2×C8×C11#4112yes—
204C11×C4⋊C4—24no—
205C11×C4⋊C4—24no—
206C11×C4⋊C4—24no—
207C11×C4⋊C4—21no—
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—21no—
217C11×C4⋊C4—42no—
218C11×C4⋊C4—81no—
219C11×C4⋊C4C22⋊C414yes—
220C11×C4⋊C4C22×C412yes—
221C11×C4⋊C4C22×C412yes—
222C11×C4⋊C4C22×C412yes—
223C11×C4⋊C4#4112yes—
224C11×C22⋊C4—24no—
225C11×C22⋊C4—24no—
226C11×C22⋊C4—24no—
227C11×C22⋊C4—24no—
228C11×C22⋊C4—42no—
229C11×C22⋊C4—42no—
230C11×C22⋊C4—81no—
231C11×C22⋊C4—81no—
232C11×C22⋊C4C22⋊C414yes—
233C11×C22⋊C4C22⋊C414yes—
234C42×C11—24no—
235C42×C11—42no—
236C42×C11—42no—
237C42×C11—42no—
238C42×C11C22×C412yes—
239C42×C11C2×D412yes—
240C2×#553C2×C1111yescharacteristic
241C2×#435C2×C1111yescharacteristic, complemented
242#2354C2×C1111yescharacteristic, complemented
243#1992C2×C1111yescharacteristic, complemented
244#1989C2×C1111yescharacteristic, complemented
245#1895C2×C1111yescharacteristic, complemented
246#1893C2×C1111yescharacteristic, complemented
247#1875C2×C1111yescharacteristic, complemented
248#1875C2×C1111yescharacteristic, complemented
249#1825C2×C1111yescharacteristic, complemented
250#1823C2×C1111yescharacteristic, complemented
251#1802C2×C1111yescharacteristic, complemented
252#1762C2×C1111yescharacteristic, complemented
253#1736C2×C1111yescharacteristic, complemented
254#1735C2×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—21no—
266C23×C11—21no—
267C23×C11—22no—
268C23×C11—41no—
269C23×C11—41no—
270C23×C11—41no—
271C23×C11—41no—
272C23×C11—41no—
273C23×C11—41no—
274C23×C11C2×C22⋊C412yes—
275C23×C11C2×C22⋊C412yes—
276C23×C11C22×D411yescharacteristic
277D4×C11—22no—
278D4×C11—22no—
279D4×C11—44no—
280D4×C11—48no—
281D4×C11—41no—
282D4×C11—41no—
283D4×C11—84no—
284C2×C4×C11—21no—
285C2×C4×C11—21no—
286C2×C4×C11—21no—
287C2×C4×C11—21no—
288C2×C4×C11—21no—
289C2×C4×C11—21no—
290C2×C4×C11—21no—
291C2×C4×C11—21no—
292C2×C4×C11—22no—
293C2×C4×C11—22no—
294C2×C4×C11—22no—
295C2×C4×C11—22no—
296C2×C4×C11—22no—
297C2×C4×C11—22no—
298C2×C4×C11—22no—
299C2×C4×C11—22no—
300C2×C4×C11—22no—
301C2×C4×C11—22no—
302C2×C4×C11—22no—
303C2×C4×C11—22no—
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—84no—
322C2×C4×C11—84no—
323C2×C4×C11C2×C22⋊C412yes—
324C2×C4×C11C2×C22⋊C412yes—
325C2×C4×C11C2×C22⋊C412yes—
326C2×C4×C11C2×C22⋊C412yes—
327C2×C4×C11C23×C411yescharacteristic
328C2×C4×C11C22×D411yescharacteristic
329C2×C4×C11C2×#4111yescharacteristic
330C2×C4×C11C2×#4111yescharacteristic
331C2×C4×C11H(5,𝔽2)11yescharacteristic
332C2×C4×C112−1+411yescharacteristic
333C8×C11—22no—
334C8×C11—41no—
335C8×C11—41no—
336C8×C11—41no—
337C22×M16C22×C1111yescharacteristic
338C23×C8C22×C1111yescharacteristic
339#553—24no—
340#553C4×C1118yescomplemented
341C2×#126—21no—
342C2×#125C22×C1111yescharacteristic
343C2×#123—21no—
344C2×#121—21no—
345C2×#121C22×C1111yescharacteristic
346C2×#121C22×C1111yescharacteristic
347C2×C4×D4—21no—
348C2×C4×D4C22×C1111yescharacteristic
349C2×C4×D4C22×C1111yescharacteristic
350C2×#117C22×C1111yescharacteristic
351C2×#117C22×C1111yescharacteristic
352C2×#117C22×C1111yescharacteristic
353C22×C4⋊C4C22×C1111yescharacteristic
354#435—24no—
355C2×C4⋊C8C22×C1111yescharacteristic
356C2×#102C22×C1111yescharacteristic
357C2×#102C22×C1111yescharacteristic
358C2×#102C22×C1111yescharacteristic
359C2×#102C22×C1111yescharacteristic
360C2×C22⋊C8C22×C1111yescharacteristic
361C2×C22⋊C8C22×C1111yescharacteristic
362C2×#97C22×C1111yescharacteristic
363#390—21no—
364#388—21no—
365#388—21no—
366#384C22×C1111yescharacteristic
367#380C22×C1111yescharacteristic
368#380C22×C1111yescharacteristic
369C4×C4⋊C4—21no—
370C4×C4⋊C4C22×C1111yescharacteristic
371#340C22×C1111yescharacteristic
372#340C22×C1111yescharacteristic
373#340C22×C1111yescharacteristic
374#340C22×C1111yescharacteristic
375#340C22×C1111yescharacteristic
376#340C22×C1111yescharacteristic
377#340C22×C1111yescharacteristic
378#340C22×C1111yescharacteristic
379#340C22×C1111yescharacteristic
380#340C22×C1111yescharacteristic
381#340C22×C1111yescharacteristic
382#340C22×C1111yescharacteristic
383C22×C11—22no—
384C22×C11—22no—
385C22×C11—22no—
386C22×C11—22no—
387C22×C11—22no—
388C22×C11—22no—
389C22×C11—41no—
390C22×C11—41no—
391C22×C11—41no—
392C22×C11—41no—
393C22×C11—41no—
394C22×C11—41no—
395C22×C11—41no—
396C22×C11—41no—
397C22×C11—42no—
398C22×C11—42no—
399C22×C11—42no—
400C22×C11—81no—
401C22×C11—81no—
402C22×C11—81no—
403C22×C11—81no—
404C22×C11C22×C22⋊C411yescharacteristic
405C22×C11#54611yescharacteristic
406C22×C11#54711yescharacteristic
407C22×C11#57511yescharacteristic
408C22×C11#57511yescharacteristic
409C22×C11#57611yescharacteristic
410C22×C11#57711yescharacteristic
411C4×C11—22no—
412C4×C11—22no—
413C4×C11—22no—
414C4×C11—22no—
415C4×C11—42no—
416C4×C11—42no—
417C4×C11—42no—
418C4×C11—42no—
419C4×C11—81no—
420C4×C11—81no—
421C4×C11—81no—
422C4×C11C4×#4111yescharacteristic
423C4×C11#52011yescharacteristic
424C4×C11#54611yescharacteristic
425C4×C11#54711yescharacteristic
426C22×D4—21no—
427C22×D4—21no—
428C22×D4D4×C1111yescharacteristic
429C22×D4C23×C1111yescharacteristic
430C23×C4—21no—
431C23×C4—21no—
432C23×C4C23×C1111yescharacteristic
433C23×C4C23×C1111yescharacteristic
434C2×M16—22no—
435C2×M16—22no—
436C2×M16—41no—
437C22×C8—22no—
438C22×C8—22no—
439C22×C8—41no—
440C22×C8C23×C1111yescharacteristic
441C22×C8C23×C1111yescharacteristic
442C22×C8C23×C1111yescharacteristic
443C22×C8C23×C1111yescharacteristic
444#126—28no—
445#125—22no—
446#125C2×C4×C1114yes—
447#123—28no—
448#121—28no—
449#121—22no—
450#121—22no—
451#121C2×C4×C1114yes—
452#121C2×C4×C1114yes—
453C4×D4—28no—
454C4×D4—22no—
455C4×D4C2×C4×C1114yes—
456C4×D4C2×C4×C1114yes—
457C4×D4D4×C1114yes—
458#117—22no—
459#117—22no—
460#117—22no—
461#117—41no—
462#117—41no—
463#117C2×C4×C1114yes—
464C2×C4⋊C4—21no—
465C2×C4⋊C4—22no—
466C2×C4⋊C4—21no—
467C2×C4⋊C4—21no—
468C2×C4⋊C4—21no—
469C2×C4⋊C4—21no—
470C2×C4⋊C4C2×C4×C1114yes—
471C2×C4⋊C4D4×C1111yescharacteristic
472C2×C4⋊C4C23×C1111yescharacteristic
473C2×C4⋊C4C23×C1111yescharacteristic
474C2×C4⋊C4C23×C1111yescharacteristic
475C2×C4⋊C4C23×C1111yescharacteristic
476C2×C4⋊C4C23×C1111yescharacteristic
477C2×C4⋊C4C23×C1111yescharacteristic
478C2×C4⋊C4C23×C1111yescharacteristic
479C2×C22⋊C4—21no—
480C2×C22⋊C4—21no—
481C2×C22⋊C4—21no—
482C2×C22⋊C4—21no—
483C2×C22⋊C4—21no—
484C2×C22⋊C4—21no—
485C2×C22⋊C4—21no—
486C2×C22⋊C4—21no—
487C2×C22⋊C4D4×C1111yescharacteristic
488C2×C22⋊C4D4×C1111yescharacteristic
489C2×C42—21no—
490C2×C42—21no—
491C2×C42—21no—
492C2×C42—21no—
493C2×C42C23×C1111yescharacteristic
494C4⋊C8—22no—
495#102—22no—
496#102—22no—
497#102—41no—
498#102—41no—
499C22⋊C8—22no—
500C22⋊C8—22no—
501#97—22no—
502#95—21no—
503#95—21no—
504#95—21no—
505C2×C11—42no—
506C2×C11—42no—
507C2×C11—82no—
508C2×C11#233911yescharacteristic
509C2×C11#289611yescharacteristic
510C2×C11#289711yescharacteristic
511C2×C11#330711yescharacteristic
512C2×C11#330911yescharacteristic
513C2×C11#334711yescharacteristic
514C2×C11#335011yescharacteristic
515C24—21no—
516C24C2×D4×C1111yescharacteristic
517C24C2×D4×C1111yescharacteristic
518C2×D4—24no—
519C2×D4—24no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—41no—
526C2×D4—41no—
527C2×D4—42no—
528C2×D4—42no—
529C2×D4—81no—
530C2×D4—81no—
531C2×D4C11×C22⋊C414yes—
532C2×D4C22×C4×C1112yes—
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—24no—
546C22×C4—24no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—81no—
551C22×C4—81no—
552C22×C4—81no—
553C22×C4—81no—
554C22×C4C22×C4×C1112yes—
555C22×C4C22×C4×C1112yes—
556C22×C4C2×D4×C1111yescharacteristic
557C22×C4C2×D4×C1111yescharacteristic
558C22×C4C2×D4×C1111yescharacteristic
559C22×C4C2×D4×C1111yescharacteristic
560C22×C4C2×D4×C1112yes—
561C22×C4C2×D4×C1112yes—
562C22×C4C24×C1111yescharacteristic
563M16—44no—
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×C8C11×#4112yes—
577C4⋊C4—24no—
578C4⋊C4—24no—
579C4⋊C4—24no—
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—21no—
590C4⋊C4—42no—
591C4⋊C4—81no—
592C4⋊C4C11×C22⋊C414yes—
593C4⋊C4C22×C4×C1112yes—
594C4⋊C4C22×C4×C1112yes—
595C4⋊C4C22×C4×C1112yes—
596C4⋊C4C11×#4112yes—
597C22⋊C4—24no—
598C22⋊C4—24no—
599C22⋊C4—24no—
600C22⋊C4—24no—
601C22⋊C4—42no—
602C22⋊C4—42no—
603C22⋊C4—81no—
604C22⋊C4—81no—
605C22⋊C4C11×C22⋊C414yes—
606C22⋊C4C11×C22⋊C414yes—
607C42—24no—
608C42—42no—
609C42—42no—
610C42—42no—
611C42C22×C4×C1112yes—
612C42C2×D4×C1112yes—
613C11#2249811yescharacteristic, direct product factor, Sylow
614C23—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—22no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23C2×C11×C22⋊C412yes—
634C23C2×C11×C22⋊C412yes—
635C23C22×D4×C1111yescharacteristic
636D4—22no—
637D4—22no—
638D4—44no—
639D4—48no—
640D4—41no—
641D4—41no—
642D4—84no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
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—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—84no—
681C2×C4—84no—
682C2×C4C2×C11×C22⋊C412yes—
683C2×C4C2×C11×C22⋊C412yes—
684C2×C4C2×C11×C22⋊C412yes—
685C2×C4C2×C11×C22⋊C412yes—
686C2×C4C23×C4×C1111yescharacteristic
687C2×C4C22×D4×C1111yescharacteristic
688C2×C4C2×C11×#4111yescharacteristic
689C2×C4C2×C11×#4111yescharacteristic
690C2×C4C11×H(5,𝔽2)11yescharacteristic
691C2×C4C11×2−1+411yescharacteristic
692C8—22no—
693C8—41no—
694C8—41no—
695C8—41no—
696C22—22no—
697C22—22no—
698C22—22no—
699C22—22no—
700C22—22no—
701C22—22no—
702C22—41no—
703C22—41no—
704C22—41no—
705C22—41no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—42no—
711C22—42no—
712C22—42no—
713C22—81no—
714C22—81no—
715C22—81no—
716C22—81no—
717C22C22×C11×C22⋊C411yescharacteristic
718C22C11×#54611yescharacteristic
719C22C11×#54711yescharacteristic
720C22C11×#57511yescharacteristic
721C22C11×#57511yescharacteristic
722C22C11×#57611yescharacteristic
723C22C11×#57711yescharacteristic
724C4—22no—
725C4—22no—
726C4—22no—
727C4—22no—
728C4—42no—
729C4—42no—
730C4—42no—
731C4—42no—
732C4—81no—
733C4—81no—
734C4—81no—
735C4C4×C11×#4111yescharacteristic
736C4C11×#52011yescharacteristic
737C4C11×#54611yescharacteristic
738C4C11×#54711yescharacteristic
739C2—42no—
740C2—42no—
741C2—82no—
742C2C11×#233911yescharacteristic
743C2C11×#289611yescharacteristic
744C2C11×#289711yescharacteristic
745C2C11×#330711yescharacteristic
746C2C11×#330911yescharacteristic
747C2C11×#334711yescharacteristic
748C2C11×#335011yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#553C2
LCSG ▷ C2×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
2. C2×C11×#435C2semidirect
3. C11×#2354C2semidirect
4. C11×#1992C2semidirect
5. C11×#1989C2semidirect
6. C11×#1895C2semidirect
7. C11×#1893C2semidirect
8. C11×#1875C2semidirect
9. C11×#1875C2semidirect
10. C11×#1825C2semidirect
11. C11×#1823C2semidirect
12. C11×#1802C2semidirect
13. C11×#1762C2semidirect
14. C11×#1736C2semidirect
15. C11×#1735C2semidirect
19. C11×#553C4semidirect
141. #22498C11direct (N × H)
241. C2×#435C2×C11semidirect
242. #2354C2×C11semidirect
243. #1992C2×C11semidirect
244. #1989C2×C11semidirect
245. #1895C2×C11semidirect
246. #1893C2×C11semidirect
247. #1875C2×C11semidirect
248. #1875C2×C11semidirect
249. #1825C2×C11semidirect
250. #1823C2×C11semidirect
251. #1802C2×C11semidirect
252. #1762C2×C11semidirect
253. #1736C2×C11semidirect
254. #1735C2×C11semidirect
340. #553C4×C11semidirect
613. C11#22498direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5532
C2×C11×#4352
C11×#23542
C11×#19922
C11×#19892
C11×#18952
C11×#18932
C11×#18752
C11×#18252
C11×#18232
C11×#18022
C11×#17622
C11×#17362
C11×#17352
#2249811