Finite Group Databasebeta

← C11×#24490 #14601683

Subgroups — C11×#24490 #14601683

Order 2816.

1022 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#480C211yesmaximal, characteristic, complemented
2C2×C11×#417C211yesmaximal, characteristic, complemented
3C11×#2431C211yesmaximal, characteristic
4C11×#2345C211yesmaximal, characteristic, complemented
5C11×#2068C211yesmaximal, characteristic, complemented
6C11×#2067C211yesmaximal, characteristic, complemented
7C11×#2042C211yesmaximal, characteristic, complemented
8C11×#2041C211yesmaximal, characteristic, complemented
9C11×#1983C211yesmaximal, characteristic, complemented
10C11×#1982C211yesmaximal, characteristic, complemented
11C11×#1928C211yesmaximal, characteristic, complemented
12C11×#1925C211yesmaximal, characteristic, complemented
13C11×#1895C211yesmaximal, characteristic, complemented
14C11×#1851C211yesmaximal, characteristic, complemented
15C11×#1788C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic
17C22×C11×M16C2211yescharacteristic
18C2×C11×#127C2211yescharacteristic
19C2×C11×#124C2211yescharacteristic
20C2×C11×#121C2211yescharacteristic
21C22×C11×C4⋊C4C2211yescharacteristic
22C11×#480—24no—
23C2×C11×#107C2211yescharacteristic
24C2×C11×#107C2211yescharacteristic
25C2×C11×C4⋊C8C2211yescharacteristic
26C2×C11×C4⋊C8C2211yescharacteristic
27C11×#417—24no—
28C2×C11×#103C2211yescharacteristic
29C2×C11×#103C2211yescharacteristic
30C2×C11×#103C2211yescharacteristic
31C2×C11×#103C2211yescharacteristic
32C2×C11×#102C2211yescharacteristic
33C2×C11×#102C2211yescharacteristic
34C2×C11×#102C2211yescharacteristic
35C2×C11×#102C2211yescharacteristic
36C2×C11×#102C2211yescharacteristic
37C2×C11×#102C2211yescharacteristic
38C2×C11×#102C2211yescharacteristic
39C2×C11×#102C2211yescharacteristic
40C2×C11×C22⋊C8C2211yescharacteristic
41C11×#392—21no—
42C11×#392—21no—
43C11×#391C2211yescharacteristic
44C11×#390C2211yescharacteristic
45C11×#389C2211yescharacteristic
46C11×#389C2211yescharacteristic
47C11×#387—21no—
48C11×#387—21no—
49C11×#386—21no—
50C11×#386—21no—
51C11×#380—21no—
52C11×#380C2211yescharacteristic
53C4×C11×C4⋊C4C2211yescharacteristic
54C4×C11×C4⋊C4C2211yescharacteristic
55C4×C11×C22⋊C4—21no—
56C4×C11×C22⋊C4C2211yescharacteristic
57C11×#340C2211yescharacteristic
58C11×#340C2211yescharacteristic
59C11×#336C2211yescharacteristic
60C11×#336C2211yescharacteristic
61C2×C11×#41—22no—
62C2×C11×#41—22no—
63C2×C11×#41—22no—
64C2×C11×#41—22no—
65C2×C11×#41—41no—
66C2×C11×#41—41no—
67C22×Q8×C11C2311yescharacteristic
68C22×D4×C11—21no—
69C22×D4×C11—21no—
70C22×D4×C11—21no—
71C22×D4×C11—21no—
72C22×D4×C11C2311yescharacteristic
73C22×D4×C11C2311yescharacteristic
74C23×C4×C11—21no—
75C23×C4×C11—21no—
76C23×C4×C11C2311yescharacteristic
77C2×C11×M16—22no—
78C2×C11×M16—41no—
79C2×C11×M16—41no—
80C22×C8×C11C2311yescharacteristic
81C22×C8×C11C2311yescharacteristic
82C22×C8×C11C2311yescharacteristic
83C22×C8×C11C2311yescharacteristic
84C11×#127—22no—
85C11×#127—41no—
86C11×#124—22no—
87C11×#124—41no—
88C11×#121—22no—
89C11×#121—22no—
90C2×C11×C4⋊C4—21no—
91C2×C11×C4⋊C4—22no—
92C2×C11×C4⋊C4—21no—
93C2×C11×C4⋊C4—21no—
94C2×C11×C4⋊C4D414yescomplemented
95C2×C11×C4⋊C4C2311yescharacteristic
96C2×C11×C4⋊C4C2311yescharacteristic
97C2×C11×C4⋊C4C2311yescharacteristic
98C2×C11×C4⋊C4C2311yescharacteristic
99C2×C11×C4⋊C4C2311yescharacteristic
100C2×C11×C22⋊C4—21no—
101C2×C11×C22⋊C4—21no—
102C2×C11×C22⋊C4—21no—
103C2×C11×C22⋊C4—21no—
104C2×C11×C22⋊C4—21no—
105C2×C11×C22⋊C4—21no—
106C2×C11×C22⋊C4D411yescharacteristic
107C2×C11×C22⋊C4D411yescharacteristic
108C2×C42×C11—21no—
109C2×C42×C11—21no—
110C2×C42×C11C2311yescharacteristic
111C2×C42×C11C2311yescharacteristic
112C11×#107—22no—
113C11×#107—22no—
114C11×C4⋊C8—41no—
115C11×C4⋊C8—41no—
116C11×#103—22no—
117C11×#103—22no—
118C11×#103—22no—
119C11×#103—41no—
120C11×#102—22no—
121C11×#102—22no—
122C11×#102—22no—
123C11×#102—22no—
124C11×#102—22no—
125C11×#102—41no—
126C11×#102—41no—
127C11×#102—41no—
128C11×C22⋊C8—22no—
129C11×#95—21no—
130C11×#95—21no—
131C11×#95—21no—
132C11×#95—21no—
133C11×#95—21no—
134C11×#95—21no—
135C11×#95—21no—
136C11×#95D411yescharacteristic
137C11×#95D411yescharacteristic
138#24490C1111yesmaximal, characteristic, direct product factor, Sylow
139C24×C11—21no—
140C24×C11—21no—
141C24×C11C2×D411yescharacteristic
142C11×#41—28no—
143C11×#41—44no—
144C11×#41—44no—
145C11×#41—44no—
146C2×Q8×C11—21no—
147C2×Q8×C11—21no—
148C2×Q8×C11—21no—
149C2×Q8×C11—21no—
150C2×Q8×C11—21no—
151C2×Q8×C11#4112yes—
152C2×D4×C11—21no—
153C2×D4×C11—21no—
154C2×D4×C11—21no—
155C2×D4×C11—21no—
156C2×D4×C11—21no—
157C2×D4×C11—21no—
158C2×D4×C11—21no—
159C2×D4×C11—21no—
160C2×D4×C11—21no—
161C2×D4×C11—21no—
162C2×D4×C11—21no—
163C2×D4×C11—42no—
164C2×D4×C11—42no—
165C2×D4×C11—42no—
166C2×D4×C11—42no—
167C2×D4×C11—42no—
168C2×D4×C11—42no—
169C2×D4×C11—42no—
170C2×D4×C11—42no—
171C2×D4×C11—81no—
172C2×D4×C11—81no—
173C2×D4×C11—81no—
174C2×D4×C11—81no—
175C2×D4×C11#4112yes—
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—21no—
183C22×C4×C11—24no—
184C22×C4×C11—21no—
185C22×C4×C11—21no—
186C22×C4×C11—21no—
187C22×C4×C11—42no—
188C22×C4×C11—42no—
189C22×C4×C11—42no—
190C22×C4×C11—81no—
191C22×C4×C11—81no—
192C22×C4×C11C2×D411yescharacteristic
193C22×C4×C11C2×D411yescharacteristic
194C22×C4×C11C2×D411yescharacteristic
195C22×C4×C11C2×D411yescharacteristic
196C22×C4×C11C2×D412yes—
197C22×C4×C11C2×D411yescharacteristic
198C22×C4×C11#4112yes—
199C22×C4×C11C2411yescharacteristic
200C11×M16—44no—
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—21no—
210C2×C8×C11—21no—
211C2×C8×C11—21no—
212C2×C8×C11—21no—
213C11×C4⋊C4—24no—
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—81no—
223C11×C4⋊C4—81no—
224C11×C4⋊C4C2×D412yes—
225C11×C4⋊C4C2×D412yes—
226C11×C22⋊C4—22no—
227C11×C22⋊C4—41no—
228C11×C22⋊C4—42no—
229C11×C22⋊C4—42no—
230C11×C22⋊C4—42no—
231C11×C22⋊C4—42no—
232C11×C22⋊C4—81no—
233C11×C22⋊C4—81no—
234C42×C11—21no—
235C42×C11—21no—
236C42×C11—21no—
237C42×C11—21no—
238C42×C11—81no—
239C42×C11—81no—
240C2×#480C2×C1111yescharacteristic, complemented
241C2×#417C2×C1111yescharacteristic, complemented
242#2431C2×C1111yescharacteristic
243#2345C2×C1111yescharacteristic, complemented
244#2068C2×C1111yescharacteristic, complemented
245#2067C2×C1111yescharacteristic, complemented
246#2042C2×C1111yescharacteristic, complemented
247#2041C2×C1111yescharacteristic, complemented
248#1983C2×C1111yescharacteristic, complemented
249#1982C2×C1111yescharacteristic, complemented
250#1928C2×C1111yescharacteristic, complemented
251#1925C2×C1111yescharacteristic, complemented
252#1895C2×C1111yescharacteristic, complemented
253#1851C2×C1111yescharacteristic, complemented
254#1788C2×C1111yescharacteristic, complemented
255C23×C11—21no—
256C23×C11—21no—
257C23×C11—21no—
258C23×C11—21no—
259C23×C11—21no—
260C23×C11—21no—
261C23×C11—22no—
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×C11—41no—
274C23×C11—41no—
275C23×C11#12112yes—
276C23×C11C22×D411yescharacteristic
277Q8×C11—22no—
278Q8×C11—22no—
279Q8×C11—41no—
280Q8×C11—41no—
281D4×C11—22no—
282D4×C11—22no—
283D4×C11—48no—
284D4×C11—41no—
285D4×C11—41no—
286D4×C11—41no—
287D4×C11—41no—
288D4×C11—41no—
289D4×C11—41no—
290D4×C11—84no—
291D4×C11—84no—
292D4×C11—84no—
293C2×C4×C11—21no—
294C2×C4×C11—21no—
295C2×C4×C11—21no—
296C2×C4×C11—21no—
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—21no—
304C2×C4×C11—21no—
305C2×C4×C11—21no—
306C2×C4×C11—22no—
307C2×C4×C11—21no—
308C2×C4×C11—21no—
309C2×C4×C11—21no—
310C2×C4×C11—21no—
311C2×C4×C11—21no—
312C2×C4×C11—21no—
313C2×C4×C11—48no—
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—41no—
324C2×C4×C11—41no—
325C2×C4×C11—41no—
326C2×C4×C11—41no—
327C2×C4×C11—41no—
328C2×C4×C11—41no—
329C2×C4×C11—84no—
330C2×C4×C11#12112yes—
331C2×C4×C11#13712yes—
332C2×C4×C11C22×D411yescharacteristic
333C2×C4×C11C2×#4111yescharacteristic
334C2×C4×C11C2×#4111yescharacteristic
335C2×C4×C11C2×#4111yescharacteristic
336C2×C4×C11H(5,𝔽2)11yescharacteristic
337C2×C4×C11H(5,𝔽2)11yescharacteristic
338C8×C11—41no—
339C8×C11—41no—
340C8×C11—41no—
341C8×C11—41no—
342C22×#41C22×C1111yescharacteristic
343C22×M16C22×C1111yescharacteristic
344C2×#127C22×C1111yescharacteristic
345C2×#124C22×C1111yescharacteristic
346C2×#121C22×C1111yescharacteristic
347C22×C4⋊C4C22×C1111yescharacteristic
348#480—24no—
349C2×#107C22×C1111yescharacteristic
350C2×#107C22×C1111yescharacteristic
351C2×C4⋊C8C22×C1111yescharacteristic
352C2×C4⋊C8C22×C1111yescharacteristic
353#417—24no—
354C2×#103C22×C1111yescharacteristic
355C2×#103C22×C1111yescharacteristic
356C2×#103C22×C1111yescharacteristic
357C2×#103C22×C1111yescharacteristic
358C2×#102C22×C1111yescharacteristic
359C2×#102C22×C1111yescharacteristic
360C2×#102C22×C1111yescharacteristic
361C2×#102C22×C1111yescharacteristic
362C2×#102C22×C1111yescharacteristic
363C2×#102C22×C1111yescharacteristic
364C2×#102C22×C1111yescharacteristic
365C2×#102C22×C1111yescharacteristic
366C2×C22⋊C8C22×C1111yescharacteristic
367#392—21no—
368#392—21no—
369#391C22×C1111yescharacteristic
370#390C22×C1111yescharacteristic
371#389C22×C1111yescharacteristic
372#389C22×C1111yescharacteristic
373#387—21no—
374#387—21no—
375#386—21no—
376#386—21no—
377#380—21no—
378#380C22×C1111yescharacteristic
379C4×C4⋊C4C22×C1111yescharacteristic
380C4×C4⋊C4C22×C1111yescharacteristic
381C4×C22⋊C4—21no—
382C4×C22⋊C4C22×C1111yescharacteristic
383#340C22×C1111yescharacteristic
384#340C22×C1111yescharacteristic
385#336C22×C1111yescharacteristic
386#336C22×C1111yescharacteristic
387C22×C11—22no—
388C22×C11—22no—
389C22×C11—22no—
390C22×C11—41no—
391C22×C11—41no—
392C22×C11—41no—
393C22×C11—41no—
394C22×C11—42no—
395C22×C11—42no—
396C22×C11—42no—
397C22×C11—81no—
398C22×C11—81no—
399C22×C11—81no—
400C22×C11—81no—
401C22×C11—81no—
402C22×C11—81no—
403C22×C11—81no—
404C22×C11—81no—
405C22×C11—81no—
406C22×C11—81no—
407C22×C11—81no—
408C22×C11C2×#12111yescharacteristic
409C22×C11#54611yescharacteristic
410C22×C11#54611yescharacteristic
411C22×C11C2×#13711yescharacteristic
412C22×C11#57511yescharacteristic
413C22×C11#57611yescharacteristic
414C22×C11#57611yescharacteristic
415C4×C11—22no—
416C4×C11—22no—
417C4×C11—41no—
418C4×C11—42no—
419C4×C11—42no—
420C4×C11—42no—
421C4×C11—41no—
422C4×C11—41no—
423C4×C11—81no—
424C4×C11—81no—
425C4×C11—81no—
426C4×C11#52511yescharacteristic
427C4×C11#53511yescharacteristic
428C4×C11#55111yescharacteristic
429C4×C11#55111yescharacteristic
430C2×#41—22no—
431C2×#41—22no—
432C2×#41—22no—
433C2×#41—22no—
434C2×#41—41no—
435C2×#41—41no—
436C22×Q8C23×C1111yescharacteristic
437C22×D4—21no—
438C22×D4—21no—
439C22×D4—21no—
440C22×D4—21no—
441C22×D4C23×C1111yescharacteristic
442C22×D4C23×C1111yescharacteristic
443C23×C4—21no—
444C23×C4—21no—
445C23×C4C23×C1111yescharacteristic
446C2×M16—22no—
447C2×M16—41no—
448C2×M16—41no—
449C22×C8C23×C1111yescharacteristic
450C22×C8C23×C1111yescharacteristic
451C22×C8C23×C1111yescharacteristic
452C22×C8C23×C1111yescharacteristic
453#127—22no—
454#127—41no—
455#124—22no—
456#124—41no—
457#121—22no—
458#121—22no—
459C2×C4⋊C4—21no—
460C2×C4⋊C4—22no—
461C2×C4⋊C4—21no—
462C2×C4⋊C4—21no—
463C2×C4⋊C4D4×C1114yescomplemented
464C2×C4⋊C4C23×C1111yescharacteristic
465C2×C4⋊C4C23×C1111yescharacteristic
466C2×C4⋊C4C23×C1111yescharacteristic
467C2×C4⋊C4C23×C1111yescharacteristic
468C2×C4⋊C4C23×C1111yescharacteristic
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⋊C4D4×C1111yescharacteristic
476C2×C22⋊C4D4×C1111yescharacteristic
477C2×C42—21no—
478C2×C42—21no—
479C2×C42C23×C1111yescharacteristic
480C2×C42C23×C1111yescharacteristic
481#107—22no—
482#107—22no—
483C4⋊C8—41no—
484C4⋊C8—41no—
485#103—22no—
486#103—22no—
487#103—22no—
488#103—41no—
489#102—22no—
490#102—22no—
491#102—22no—
492#102—22no—
493#102—22no—
494#102—41no—
495#102—41no—
496#102—41no—
497C22⋊C8—22no—
498#95—21no—
499#95—21no—
500#95—21no—
501#95—21no—
502#95—21no—
503#95—21no—
504#95—21no—
505#95D4×C1111yescharacteristic
506#95D4×C1111yescharacteristic
507C2×C11—42no—
508C2×C11—82no—
509C2×C11—161no—
510C2×C11#241111yescharacteristic
511C2×C11#303711yescharacteristic
512C2×C11#304111yescharacteristic
513C2×C11#330911yescharacteristic
514C2×C11#331411yescharacteristic
515C2×C11#332211yescharacteristic
516C2×C11#333311yescharacteristic
517C24—21no—
518C24—21no—
519C24C2×D4×C1111yescharacteristic
520#41—28no—
521#41—44no—
522#41—44no—
523#41—44no—
524C2×Q8—21no—
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8—21no—
529C2×Q8C11×#4112yes—
530C2×D4—21no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—21no—
534C2×D4—21no—
535C2×D4—21no—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—42no—
542C2×D4—42no—
543C2×D4—42no—
544C2×D4—42no—
545C2×D4—42no—
546C2×D4—42no—
547C2×D4—42no—
548C2×D4—42no—
549C2×D4—81no—
550C2×D4—81no—
551C2×D4—81no—
552C2×D4—81no—
553C2×D4C11×#4112yes—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—24no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—42no—
566C22×C4—42no—
567C22×C4—42no—
568C22×C4—81no—
569C22×C4—81no—
570C22×C4C2×D4×C1111yescharacteristic
571C22×C4C2×D4×C1111yescharacteristic
572C22×C4C2×D4×C1111yescharacteristic
573C22×C4C2×D4×C1111yescharacteristic
574C22×C4C2×D4×C1112yes—
575C22×C4C2×D4×C1111yescharacteristic
576C22×C4C11×#4112yes—
577C22×C4C24×C1111yescharacteristic
578M16—44no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C4⋊C4—24no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—81no—
601C4⋊C4—81no—
602C4⋊C4C2×D4×C1112yes—
603C4⋊C4C2×D4×C1112yes—
604C22⋊C4—22no—
605C22⋊C4—41no—
606C22⋊C4—42no—
607C22⋊C4—42no—
608C22⋊C4—42no—
609C22⋊C4—42no—
610C22⋊C4—81no—
611C22⋊C4—81no—
612C42—21no—
613C42—21no—
614C42—21no—
615C42—21no—
616C42—81no—
617C42—81no—
618C11#2449011yescharacteristic, direct product factor, Sylow
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—22no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23C11×#12112yes—
640C23C22×D4×C1111yescharacteristic
641Q8—22no—
642Q8—22no—
643Q8—41no—
644Q8—41no—
645D4—22no—
646D4—22no—
647D4—48no—
648D4—41no—
649D4—41no—
650D4—41no—
651D4—41no—
652D4—41no—
653D4—41no—
654D4—84no—
655D4—84no—
656D4—84no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—22no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—48no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—84no—
694C2×C4C11×#12112yes—
695C2×C4C11×#13712yes—
696C2×C4C22×D4×C1111yescharacteristic
697C2×C4C2×C11×#4111yescharacteristic
698C2×C4C2×C11×#4111yescharacteristic
699C2×C4C2×C11×#4111yescharacteristic
700C2×C4C11×H(5,𝔽2)11yescharacteristic
701C2×C4C11×H(5,𝔽2)11yescharacteristic
702C8—41no—
703C8—41no—
704C8—41no—
705C8—41no—
706C22—22no—
707C22—22no—
708C22—22no—
709C22—41no—
710C22—41no—
711C22—41no—
712C22—41no—
713C22—42no—
714C22—42no—
715C22—42no—
716C22—81no—
717C22—81no—
718C22—81no—
719C22—81no—
720C22—81no—
721C22—81no—
722C22—81no—
723C22—81no—
724C22—81no—
725C22—81no—
726C22—81no—
727C22C2×C11×#12111yescharacteristic
728C22C11×#54611yescharacteristic
729C22C11×#54611yescharacteristic
730C22C2×C11×#13711yescharacteristic
731C22C11×#57511yescharacteristic
732C22C11×#57611yescharacteristic
733C22C11×#57611yescharacteristic
734C4—22no—
735C4—22no—
736C4—42no—
737C4—42no—
738C4—42no—
739C4—41no—
740C4—41no—
741C4—41no—
742C4—81no—
743C4—81no—
744C4—81no—
745C4C11×#52511yescharacteristic
746C4C11×#53511yescharacteristic
747C4C11×#55111yescharacteristic
748C4C11×#55111yescharacteristic
749C2—42no—
750C2—82no—
751C2—161no—
752C2C11×#241111yescharacteristic
753C2C11×#303711yescharacteristic
754C2C11×#304111yescharacteristic
755C2C11×#330911yescharacteristic
756C2C11×#331411yescharacteristic
757C2C11×#332211yescharacteristic
758C2C11×#333311yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#2431C2
LCSG ▷ C22×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
1. C2×C11×#480C2semidirect
2. C2×C11×#417C2semidirect
4. C11×#2345C2semidirect
5. C11×#2068C2semidirect
6. C11×#2067C2semidirect
7. C11×#2042C2semidirect
8. C11×#2041C2semidirect
9. C11×#1983C2semidirect
10. C11×#1982C2semidirect
11. C11×#1928C2semidirect
12. C11×#1925C2semidirect
13. C11×#1895C2semidirect
14. C11×#1851C2semidirect
15. C11×#1788C2semidirect
94. C2×C11×C4⋊C4D4semidirect
138. #24490C11direct (N × H)
240. C2×#480C2×C11semidirect
241. C2×#417C2×C11semidirect
243. #2345C2×C11semidirect
244. #2068C2×C11semidirect
245. #2067C2×C11semidirect
246. #2042C2×C11semidirect
247. #2041C2×C11semidirect
248. #1983C2×C11semidirect
249. #1982C2×C11semidirect
250. #1928C2×C11semidirect
251. #1925C2×C11semidirect
252. #1895C2×C11semidirect
253. #1851C2×C11semidirect
254. #1788C2×C11semidirect
463. C2×C4⋊C4D4×C11semidirect
618. C11#24490direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4802
C2×C11×#4172
C11×#24312
C11×#23452
C11×#20682
C11×#20672
C11×#20422
C11×#20412
C11×#19832
C11×#19822
C11×#19282
C11×#19252
C11×#18952
C11×#18512
C11×#17882
#2449011