Finite Group Databasebeta

← C11×#24207 #14601400

Subgroups — C11×#24207 #14601400

Order 2816.

1076 conjugacy classes of subgroups.

The subgroup lattice has 714 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#556C211yesmaximal, characteristic
2C2×C11×#464C211yesmaximal, characteristic
3C2×C11×#441C211yesmaximal, characteristic, complemented
4C11×#2582C211yesmaximal, characteristic, complemented
5C11×#2043C211yesmaximal, characteristic, complemented
6C11×#2042C211yesmaximal, characteristic
7C11×#2016C211yesmaximal, characteristic, complemented
8C11×#2015C211yesmaximal, characteristic
9C11×#1985C211yesmaximal, characteristic, complemented
10C11×#1959C211yesmaximal, characteristic
11C11×#1878C211yesmaximal, characteristic, complemented
12C11×#1877C211yesmaximal, characteristic
13C11×#1865C211yesmaximal, characteristic, complemented
14C11×#1864C211yesmaximal, characteristic
15C11×#1803C211yesmaximal, characteristic, complemented
16C22×C11×Q16C2211yescharacteristic
17C22×C11×Q16C2211yescharacteristic
18C22×C11×SD16C2211yescharacteristic
19C11×#556—24no—
20C11×#556—24no—
21C2×C11×C4⋊Q8C2211yescharacteristic
22C2×C11×#126—21no—
23C2×C11×#126—21no—
24C2×C11×#124C2211yescharacteristic
25C2×C11×#124C2211yescharacteristic
26C2×C11×C22⋊Q8—21no—
27C2×C4×Q8×C11C2211yescharacteristic
28C2×C4×Q8×C11C2211yescharacteristic
29C2×C4×Q8×C11C2211yescharacteristic
30C2×C4×Q8×C11C2211yescharacteristic
31C2×C4×D4×C11C2211yescharacteristic
32C2×C11×#117—21no—
33C11×#464—24no—
34C11×#441—24no—
35C2×C11×#106C2211yescharacteristic
36C2×C11×C4⋊C8C2211yescharacteristic
37C2×C11×#103C2211yescharacteristic
38C2×C11×#103C2211yescharacteristic
39C2×C11×#103C2211yescharacteristic
40C2×C11×#103C2211yescharacteristic
41C2×C11×#103C2211yescharacteristic
42C2×C11×#103C2211yescharacteristic
43C2×C11×#103C2211yescharacteristic
44C2×C11×#102C2211yescharacteristic
45C2×C11×#102C2211yescharacteristic
46C2×C11×#102C2211yescharacteristic
47C2×C11×#97C2211yescharacteristic
48C11×#398—21no—
49C11×#398—21no—
50C11×#391—21no—
51C11×#391C2211yescharacteristic
52C11×#391C2211yescharacteristic
53C11×#389—21no—
54C11×#389C2211yescharacteristic
55C11×#389C2211yescharacteristic
56C11×#384C2211yescharacteristic
57C11×#340C2211yescharacteristic
58C11×#340C2211yescharacteristic
59C11×#336C2211yescharacteristic
60C11×#336C2211yescharacteristic
61C11×#336C2211yescharacteristic
62C11×#336C2211yescharacteristic
63C22×Q8×C11D411yescharacteristic
64C22×Q8×C11C2311yescharacteristic
65C22×Q8×C11C2311yescharacteristic
66C22×Q8×C11C2311yescharacteristic
67C22×D4×C11C2311yescharacteristic
68C23×C4×C11—21no—
69C2×C11×Q16—22no—
70C2×C11×Q16—22no—
71C2×C11×Q16—22no—
72C2×C11×Q16—22no—
73C2×C11×Q16—22no—
74C2×C11×Q16—41no—
75C2×C11×SD16—22no—
76C2×C11×SD16—22no—
77C2×C11×SD16—41no—
78C22×C8×C11C2311yescharacteristic
79C22×C8×C11C2311yescharacteristic
80C22×C8×C11C2311yescharacteristic
81C22×C8×C11C2311yescharacteristic
82C11×C4⋊Q8—22no—
83C11×C4⋊Q8—22no—
84C11×#126—28no—
85C11×#126—28no—
86C11×#124—22no—
87C11×#124—22no—
88C11×#124—22no—
89C11×#124D414yes—
90C11×C22⋊Q8—28no—
91C4×Q8×C11—22no—
92C4×Q8×C11—22no—
93C4×Q8×C11—22no—
94C4×Q8×C11—22no—
95C4×Q8×C11—22no—
96C4×Q8×C11—22no—
97C4×Q8×C11—22no—
98C4×Q8×C11D414yes—
99C4×D4×C11—22no—
100C4×D4×C11—22no—
101C11×#117—28no—
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⋊C4—21no—
109C2×C11×C4⋊C4—21no—
110C2×C11×C4⋊C4—21no—
111C2×C11×C4⋊C4D411yescharacteristic
112C2×C11×C4⋊C4D411yescharacteristic
113C2×C11×C4⋊C4D411yescharacteristic
114C2×C11×C4⋊C4C2311yescharacteristic
115C2×C11×C4⋊C4C2311yescharacteristic
116C2×C11×C4⋊C4C2311yescharacteristic
117C2×C11×C4⋊C4C2311yescharacteristic
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×C42×C11—21no—
124C2×C42×C11—21no—
125C2×C42×C11—21no—
126C2×C42×C11C2311yescharacteristic
127C2×C42×C11C2311yescharacteristic
128C2×C42×C11C2311yescharacteristic
129C11×#106—22no—
130C11×C4⋊C8—22no—
131C11×#103—22no—
132C11×#103—22no—
133C11×#103—22no—
134C11×#103—22no—
135C11×#103—41no—
136C11×#103—41no—
137C11×#103—41no—
138C11×#102—22no—
139C11×#102—22no—
140C11×#102—41no—
141C11×#97—22no—
142C11×#95—21no—
143C11×#95—21no—
144C11×#95—21no—
145C11×#95—21no—
146C11×#95—21no—
147C11×#95—21no—
148#24207C1111yesmaximal, characteristic, direct product factor, Sylow
149C24×C11—21no—
150C2×Q8×C11—22no—
151C2×Q8×C11—22no—
152C2×Q8×C11—21no—
153C2×Q8×C11—21no—
154C2×Q8×C11—21no—
155C2×Q8×C11—21no—
156C2×Q8×C11—21no—
157C2×Q8×C11—21no—
158C2×Q8×C11—21no—
159C2×Q8×C11—21no—
160C2×Q8×C11—21no—
161C2×Q8×C11—21no—
162C2×Q8×C11—21no—
163C2×Q8×C11—21no—
164C2×Q8×C11—21no—
165C2×Q8×C11—21no—
166C2×Q8×C11—21no—
167C2×Q8×C11—41no—
168C2×Q8×C11C2×D412yes—
169C2×Q8×C11C2×D412yes—
170C2×Q8×C11#4112yes—
171C2×D4×C11—21no—
172C2×D4×C11—21no—
173C2×D4×C11—21no—
174C2×D4×C11—21no—
175C2×D4×C11—21no—
176C2×D4×C11C2×D412yes—
177C22×C4×C11—24no—
178C22×C4×C11—21no—
179C22×C4×C11—21no—
180C22×C4×C11—21no—
181C22×C4×C11—21no—
182C22×C4×C11—21no—
183C22×C4×C11—21no—
184C22×C4×C11—21no—
185C22×C4×C11—42no—
186C22×C4×C11—42no—
187C22×C4×C11C2×D411yescharacteristic
188C22×C4×C11C2×D411yescharacteristic
189C22×C4×C11C2×D411yescharacteristic
190C22×C4×C11C2×D411yescharacteristic
191C22×C4×C11C2×D411yescharacteristic
192C22×C4×C11C2×D411yescharacteristic
193C22×C4×C11C2411yescharacteristic
194C11×Q16—28no—
195C11×Q16—44no—
196C11×SD16—44no—
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×C11—21no—
205C2×C8×C11—21no—
206C2×C8×C11—21no—
207C2×C8×C11—21no—
208C2×C8×C11#4112yes—
209C11×C4⋊C4—24no—
210C11×C4⋊C4—24no—
211C11×C4⋊C4—24no—
212C11×C4⋊C4—24no—
213C11×C4⋊C4—22no—
214C11×C4⋊C4—22no—
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—42no—
224C11×C4⋊C4—42no—
225C11×C4⋊C4—81no—
226C11×C4⋊C4—81no—
227C11×C4⋊C4—81no—
228C11×C4⋊C4C2×D412yes—
229C11×C22⋊C4—24no—
230C11×C22⋊C4—24no—
231C11×C22⋊C4—24no—
232C11×C22⋊C4—24no—
233C11×C22⋊C4—24no—
234C42×C11—24no—
235C42×C11—24no—
236C42×C11—21no—
237C42×C11—21no—
238C42×C11—21no—
239C42×C11—21no—
240C42×C11—42no—
241C42×C11C2×D412yes—
242C42×C11C2×D412yes—
243C2×#556C2×C1111yescharacteristic
244C2×#464C2×C1111yescharacteristic
245C2×#441C2×C1111yescharacteristic, complemented
246#2582C2×C1111yescharacteristic, complemented
247#2043C2×C1111yescharacteristic, complemented
248#2042C2×C1111yescharacteristic
249#2016C2×C1111yescharacteristic, complemented
250#2015C2×C1111yescharacteristic
251#1985C2×C1111yescharacteristic, complemented
252#1959C2×C1111yescharacteristic
253#1878C2×C1111yescharacteristic, complemented
254#1877C2×C1111yescharacteristic
255#1865C2×C1111yescharacteristic, complemented
256#1864C2×C1111yescharacteristic
257#1803C2×C1111yescharacteristic, complemented
258C23×C11—22no—
259C23×C11—41no—
260C23×C11—41no—
261C23×C11—41no—
262C23×C11—41no—
263C23×C11—41no—
264C23×C11—41no—
265C23×C11C22×D411yescharacteristic
266Q8×C11—22no—
267Q8×C11—22no—
268Q8×C11—22no—
269Q8×C11—22no—
270Q8×C11—22no—
271Q8×C11—22no—
272Q8×C11—44no—
273Q8×C11—41no—
274Q8×C11—41no—
275Q8×C11—41no—
276Q8×C11—41no—
277Q8×C11—41no—
278Q8×C11—41no—
279D4×C11—22no—
280D4×C11—22no—
281D4×C11—41no—
282D4×C11—41no—
283C2×C4×C11—21no—
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—22no—
291C2×C4×C11—21no—
292C2×C4×C11—22no—
293C2×C4×C11—22no—
294C2×C4×C11—21no—
295C2×C4×C11—22no—
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—48no—
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#12012yes—
321C2×C4×C11#12012yes—
322C2×C4×C11#13712yes—
323C2×C4×C11C22×D411yescharacteristic
324C2×C4×C11C22×D411yescharacteristic
325C2×C4×C11C2×#4111yescharacteristic
326C2×C4×C11C2×#4111yescharacteristic
327C2×C4×C11H(5,𝔽2)11yescharacteristic
328C2×C4×C112−1+411yescharacteristic
329C8×C11—22no—
330C8×C11—41no—
331C8×C11—41no—
332C8×C11—41no—
333C22×Q16C22×C1111yescharacteristic
334C22×Q16C22×C1111yescharacteristic
335C22×SD16C22×C1111yescharacteristic
336#556—24no—
337#556—24no—
338C2×C4⋊Q8C22×C1111yescharacteristic
339C2×#126—21no—
340C2×#126—21no—
341C2×#124C22×C1111yescharacteristic
342C2×#124C22×C1111yescharacteristic
343C2×C22⋊Q8—21no—
344C2×C4×Q8C22×C1111yescharacteristic
345C2×C4×Q8C22×C1111yescharacteristic
346C2×C4×Q8C22×C1111yescharacteristic
347C2×C4×Q8C22×C1111yescharacteristic
348C2×C4×D4C22×C1111yescharacteristic
349C2×#117—21no—
350#464—24no—
351#441—24no—
352C2×#106C22×C1111yescharacteristic
353C2×C4⋊C8C22×C1111yescharacteristic
354C2×#103C22×C1111yescharacteristic
355C2×#103C22×C1111yescharacteristic
356C2×#103C22×C1111yescharacteristic
357C2×#103C22×C1111yescharacteristic
358C2×#103C22×C1111yescharacteristic
359C2×#103C22×C1111yescharacteristic
360C2×#103C22×C1111yescharacteristic
361C2×#102C22×C1111yescharacteristic
362C2×#102C22×C1111yescharacteristic
363C2×#102C22×C1111yescharacteristic
364C2×#97C22×C1111yescharacteristic
365#398—21no—
366#398—21no—
367#391—21no—
368#391C22×C1111yescharacteristic
369#391C22×C1111yescharacteristic
370#389—21no—
371#389C22×C1111yescharacteristic
372#389C22×C1111yescharacteristic
373#384C22×C1111yescharacteristic
374#340C22×C1111yescharacteristic
375#340C22×C1111yescharacteristic
376#336C22×C1111yescharacteristic
377#336C22×C1111yescharacteristic
378#336C22×C1111yescharacteristic
379#336C22×C1111yescharacteristic
380C22×C11—42no—
381C22×C11—42no—
382C22×C11—42no—
383C22×C11—81no—
384C22×C11—81no—
385C22×C11—81no—
386C22×C11—81no—
387C22×C11C2×#12011yescharacteristic
388C22×C11#54811yescharacteristic
389C22×C11#55011yescharacteristic
390C22×C11C2×#13711yescharacteristic
391C22×C11#57511yescharacteristic
392C22×C11#57711yescharacteristic
393C22×C11#57811yescharacteristic
394C4×C11—22no—
395C4×C11—22no—
396C4×C11—22no—
397C4×C11—42no—
398C4×C11—42no—
399C4×C11—42no—
400C4×C11—41no—
401C4×C11—42no—
402C4×C11—41no—
403C4×C11—41no—
404C4×C11—81no—
405C4×C11—81no—
406C4×C11—81no—
407C4×C11#52511yescharacteristic
408C4×C11#53711yescharacteristic
409C4×C11#54611yescharacteristic
410C4×C11#54711yescharacteristic
411C22×Q8D4×C1111yescharacteristic
412C22×Q8C23×C1111yescharacteristic
413C22×Q8C23×C1111yescharacteristic
414C22×Q8C23×C1111yescharacteristic
415C22×D4C23×C1111yescharacteristic
416C23×C4—21no—
417C2×Q16—22no—
418C2×Q16—22no—
419C2×Q16—22no—
420C2×Q16—22no—
421C2×Q16—22no—
422C2×Q16—41no—
423C2×SD16—22no—
424C2×SD16—22no—
425C2×SD16—41no—
426C22×C8C23×C1111yescharacteristic
427C22×C8C23×C1111yescharacteristic
428C22×C8C23×C1111yescharacteristic
429C22×C8C23×C1111yescharacteristic
430C4⋊Q8—22no—
431C4⋊Q8—22no—
432#126—28no—
433#126—28no—
434#124—22no—
435#124—22no—
436#124—22no—
437#124D4×C1114yes—
438C22⋊Q8—28no—
439C4×Q8—22no—
440C4×Q8—22no—
441C4×Q8—22no—
442C4×Q8—22no—
443C4×Q8—22no—
444C4×Q8—22no—
445C4×Q8—22no—
446C4×Q8D4×C1114yes—
447C4×D4—22no—
448C4×D4—22no—
449#117—28no—
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—21no—
457C2×C4⋊C4—21no—
458C2×C4⋊C4—21no—
459C2×C4⋊C4D4×C1111yescharacteristic
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×C22⋊C4—21no—
467C2×C22⋊C4—21no—
468C2×C22⋊C4—21no—
469C2×C22⋊C4—21no—
470C2×C22⋊C4—21no—
471C2×C42—21no—
472C2×C42—21no—
473C2×C42—21no—
474C2×C42C23×C1111yescharacteristic
475C2×C42C23×C1111yescharacteristic
476C2×C42C23×C1111yescharacteristic
477#106—22no—
478C4⋊C8—22no—
479#103—22no—
480#103—22no—
481#103—22no—
482#103—22no—
483#103—41no—
484#103—41no—
485#103—41no—
486#102—22no—
487#102—22no—
488#102—41no—
489#97—22no—
490#95—21no—
491#95—21no—
492#95—21no—
493#95—21no—
494#95—21no—
495#95—21no—
496C2×C11—82no—
497C2×C11#240711yescharacteristic
498C2×C11#300711yescharacteristic
499C2×C11#301311yescharacteristic
500C2×C11#336911yescharacteristic
501C2×C11#337711yescharacteristic
502C2×C11#339811yescharacteristic
503C2×C11#340111yescharacteristic
504C24—21no—
505C2×Q8—22no—
506C2×Q8—22no—
507C2×Q8—21no—
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—21no—
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—21no—
520C2×Q8—21no—
521C2×Q8—21no—
522C2×Q8—41no—
523C2×Q8C2×D4×C1112yes—
524C2×Q8C2×D4×C1112yes—
525C2×Q8C11×#4112yes—
526C2×D4—21no—
527C2×D4—21no—
528C2×D4—21no—
529C2×D4—21no—
530C2×D4—21no—
531C2×D4C2×D4×C1112yes—
532C22×C4—24no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—42no—
541C22×C4—42no—
542C22×C4C2×D4×C1111yescharacteristic
543C22×C4C2×D4×C1111yescharacteristic
544C22×C4C2×D4×C1111yescharacteristic
545C22×C4C2×D4×C1111yescharacteristic
546C22×C4C2×D4×C1111yescharacteristic
547C22×C4C2×D4×C1111yescharacteristic
548C22×C4C24×C1111yescharacteristic
549Q16—28no—
550Q16—44no—
551SD16—44no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—21no—
563C2×C8C11×#4112yes—
564C4⋊C4—24no—
565C4⋊C4—24no—
566C4⋊C4—24no—
567C4⋊C4—24no—
568C4⋊C4—22no—
569C4⋊C4—22no—
570C4⋊C4—22no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—42no—
579C4⋊C4—42no—
580C4⋊C4—81no—
581C4⋊C4—81no—
582C4⋊C4—81no—
583C4⋊C4C2×D4×C1112yes—
584C22⋊C4—24no—
585C22⋊C4—24no—
586C22⋊C4—24no—
587C22⋊C4—24no—
588C22⋊C4—24no—
589C42—24no—
590C42—24no—
591C42—21no—
592C42—21no—
593C42—21no—
594C42—21no—
595C42—42no—
596C42C2×D4×C1112yes—
597C42C2×D4×C1112yes—
598C11#2420711yescharacteristic, direct product factor, Sylow
599C23—22no—
600C23—41no—
601C23—41no—
602C23—41no—
603C23—41no—
604C23—41no—
605C23—41no—
606C23C22×D4×C1111yescharacteristic
607Q8—22no—
608Q8—22no—
609Q8—22no—
610Q8—22no—
611Q8—22no—
612Q8—22no—
613Q8—44no—
614Q8—41no—
615Q8—41no—
616Q8—41no—
617Q8—41no—
618Q8—41no—
619Q8—41no—
620D4—22no—
621D4—22no—
622D4—41no—
623D4—41no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—22no—
632C2×C4—21no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—21no—
636C2×C4—22no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—48no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
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×C4C11×#12012yes—
662C2×C4C11×#12012yes—
663C2×C4C11×#13712yes—
664C2×C4C22×D4×C1111yescharacteristic
665C2×C4C22×D4×C1111yescharacteristic
666C2×C4C2×C11×#4111yescharacteristic
667C2×C4C2×C11×#4111yescharacteristic
668C2×C4C11×H(5,𝔽2)11yescharacteristic
669C2×C4C11×2−1+411yescharacteristic
670C8—22no—
671C8—41no—
672C8—41no—
673C8—41no—
674C22—42no—
675C22—42no—
676C22—42no—
677C22—81no—
678C22—81no—
679C22—81no—
680C22—81no—
681C22C2×C11×#12011yescharacteristic
682C22C11×#54811yescharacteristic
683C22C11×#55011yescharacteristic
684C22C2×C11×#13711yescharacteristic
685C22C11×#57511yescharacteristic
686C22C11×#57711yescharacteristic
687C22C11×#57811yescharacteristic
688C4—22no—
689C4—22no—
690C4—22no—
691C4—42no—
692C4—42no—
693C4—42no—
694C4—41no—
695C4—42no—
696C4—41no—
697C4—41no—
698C4—81no—
699C4—81no—
700C4—81no—
701C4C11×#52511yescharacteristic
702C4C11×#53711yescharacteristic
703C4C11×#54611yescharacteristic
704C4C11×#54711yescharacteristic
705C2—82no—
706C2C11×#240711yescharacteristic
707C2C11×#300711yescharacteristic
708C2C11×#301311yescharacteristic
709C2C11×#336911yescharacteristic
710C2C11×#337711yescharacteristic
711C2C11×#339811yescharacteristic
712C2C11×#340111yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC22×D4×C11C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C4×Q8×C11 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C11×#441C2semidirect
4. C11×#2582C2semidirect
5. C11×#2043C2semidirect
7. C11×#2016C2semidirect
9. C11×#1985C2semidirect
11. C11×#1878C2semidirect
13. C11×#1865C2semidirect
15. C11×#1803C2semidirect
148. #24207C11direct (N × H)
245. C2×#441C2×C11semidirect
246. #2582C2×C11semidirect
247. #2043C2×C11semidirect
249. #2016C2×C11semidirect
251. #1985C2×C11semidirect
253. #1878C2×C11semidirect
255. #1865C2×C11semidirect
257. #1803C2×C11semidirect
598. C11#24207direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5562
C2×C11×#4642
C2×C11×#4412
C11×#25822
C11×#20432
C11×#20422
C11×#20162
C11×#20152
C11×#19852
C11×#19592
C11×#18782
C11×#18772
C11×#18652
C11×#18642
C11×#18032
#2420711