Finite Group Databasebeta

← C11×#24512 #14601705

Subgroups — C11×#24512 #14601705

Order 2816.

1098 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#447C211yesmaximal, characteristic
2C2×C11×#433C211yesmaximal, characteristic, complemented
3C11×#2624C211yesmaximal, characteristic, complemented
4C11×#2309C211yesmaximal, characteristic, complemented
5C11×#2067C211yesmaximal, characteristic, complemented
6C11×#2065C211yesmaximal, characteristic, complemented
7C11×#2054C211yesmaximal, characteristic, complemented
8C11×#2054C211yesmaximal, characteristic, complemented
9C11×#1972C211yesmaximal, characteristic, complemented
10C11×#1970C211yesmaximal, characteristic, complemented
11C11×#1936C211yesmaximal, characteristic, complemented
12C11×#1934C211yesmaximal, characteristic, complemented
13C11×#1875C211yesmaximal, characteristic, complemented
14C11×#1854C211yesmaximal, characteristic, complemented
15C11×#1786C211yesmaximal, characteristic, complemented
16C23×D4×C11C2211yescharacteristic
17C22×C11×D8C2211yescharacteristic
18C22×C11×D8C2211yescharacteristic
19C2×C11×#121C2211yescharacteristic
20C2×C11×#117C2211yescharacteristic
21C2×C11×#117C2211yescharacteristic
22C11×#447—24no—
23C11×#433—24no—
24C2×C11×#107C2211yescharacteristic, complemented
25C2×C11×#106C2211yescharacteristic, complemented
26C2×C11×C4⋊C8C2211yescharacteristic, complemented
27C2×C11×C4⋊C8C2211yescharacteristic, complemented
28C2×C11×#102C2211yescharacteristic
29C2×C11×#102C2211yescharacteristic
30C2×C11×#102C2211yescharacteristic
31C2×C11×#102C2211yescharacteristic
32C2×C11×#102C2211yescharacteristic
33C2×C11×#102C2211yescharacteristic
34C2×C11×#102C2211yescharacteristic, complemented
35C2×C11×#102C2211yescharacteristic, complemented
36C2×C11×C22⋊C8C2211yescharacteristic
37C2×C11×C22⋊C8C2211yescharacteristic
38C2×C11×#97C2211yescharacteristic, complemented
39C2×C4×C8×C11C2211yescharacteristic, complemented
40C11×#399—21no—
41C11×#397—21no—
42C11×#394—21no—
43C11×#394—21no—
44C11×#390—21no—
45C11×#390—21no—
46C11×#390C2211yescharacteristic
47C11×#390C2211yescharacteristic
48C11×#390C2211yescharacteristic
49C11×#390C2211yescharacteristic
50C11×#390C2211yescharacteristic, complemented
51C11×#390C2211yescharacteristic, complemented
52C11×#389C2211yescharacteristic, complemented
53C11×#389C2211yescharacteristic, complemented
54C11×#380C2211yescharacteristic
55C11×#379—21no—
56C11×#379—21no—
57C11×#340C2211yescharacteristic, complemented
58C11×#340C2211yescharacteristic, complemented
59C11×#340C2211yescharacteristic, complemented
60C11×#340C2211yescharacteristic, complemented
61C25×C11—21no—
62C22×D4×C11—22no—
63C22×D4×C11—22no—
64C22×D4×C11—21no—
65C22×D4×C11—21no—
66C22×D4×C11—22no—
67C22×D4×C11—22no—
68C22×D4×C11—41no—
69C22×D4×C11—41no—
70C22×D4×C11C2311yescharacteristic
71C22×D4×C11C2311yescharacteristic
72C22×D4×C11C2311yescharacteristic
73C23×C4×C11C2311yescharacteristic
74C2×C11×D8—22no—
75C2×C11×D8—22no—
76C2×C11×D8—22no—
77C2×C11×D8—22no—
78C2×C11×D8—41no—
79C2×C11×D8—41no—
80C22×C8×C11C2311yescharacteristic
81C22×C8×C11C2311yescharacteristic
82C22×C8×C11C2311yescharacteristic
83C22×C8×C11C2311yescharacteristic
84C11×#121—22no—
85C11×#121—22no—
86C11×#117—22no—
87C11×#117—22no—
88C11×#117—41no—
89C11×#117—41no—
90C2×C11×C4⋊C4—21no—
91C2×C11×C4⋊C4—21no—
92C2×C11×C4⋊C4D411yescharacteristic
93C2×C11×C4⋊C4D411yescharacteristic
94C2×C11×C4⋊C4C2311yescharacteristic
95C2×C11×C4⋊C4C2311yescharacteristic
96C2×C11×C4⋊C4C2311yescharacteristic
97C2×C11×C4⋊C4C2311yescharacteristic
98C2×C11×C4⋊C4C2311yescharacteristic
99C2×C11×C22⋊C4—21no—
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⋊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×C11×C22⋊C4—21no—
114C2×C11×C22⋊C4D411yescharacteristic
115C2×C11×C22⋊C4D411yescharacteristic
116C2×C42×C11—21no—
117C2×C42×C11C2311yescharacteristic
118C2×C42×C11C2311yescharacteristic
119C11×#107—41no—
120C11×#106—41no—
121C11×C4⋊C8—22no—
122C11×C4⋊C8—22no—
123C11×#102—22no—
124C11×#102—22no—
125C11×#102—22no—
126C11×#102—22no—
127C11×#102—41no—
128C11×#102—41no—
129C11×#102—41no—
130C11×#102—41no—
131C11×C22⋊C8—22no—
132C11×C22⋊C8D414yes—
133C11×#97—22no—
134C4×C8×C11—22no—
135C11×#95—21no—
136C11×#95—21no—
137C11×#95—21no—
138#24512C1111yesmaximal, characteristic, direct product factor, Sylow
139C24×C11—24no—
140C24×C11—21no—
141C24×C11—21no—
142C24×C11—21no—
143C24×C11—42no—
144C24×C11—42no—
145C24×C11—81no—
146C24×C11—81no—
147C24×C11—81no—
148C24×C11—81no—
149C24×C11C2×D411yescharacteristic
150C2×D4×C11—24no—
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—21no—
158C2×D4×C11—21no—
159C2×D4×C11—21no—
160C2×D4×C11—21no—
161C2×D4×C11—21no—
162C2×D4×C11—21no—
163C2×D4×C11—21no—
164C2×D4×C11—21no—
165C2×D4×C11—21no—
166C2×D4×C11—21no—
167C2×D4×C11—44no—
168C2×D4×C11—44no—
169C2×D4×C11—44no—
170C2×D4×C11—44no—
171C2×D4×C11—42no—
172C2×D4×C11—42no—
173C2×D4×C11—42no—
174C2×D4×C11—81no—
175C2×D4×C11—81no—
176C2×D4×C11#4112yes—
177C2×D4×C11#4112yes—
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—21no—
186C22×C4×C11—21no—
187C22×C4×C11C2×D411yescharacteristic
188C22×C4×C11C2×D411yescharacteristic
189C22×C4×C11C2×D411yescharacteristic
190C22×C4×C11C2×D411yescharacteristic
191C22×C4×C11C2×D411yescharacteristic
192C22×C4×C11C2×D412yes—
193C22×C4×C11#4112yes—
194C22×C4×C11C2411yescharacteristic
195C11×D8—44no—
196C11×D8—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×C11C2×D412yes—
208C2×C8×C11C2×D412yes—
209C11×C4⋊C4—22no—
210C11×C4⋊C4—22no—
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—21no—
218C11×C4⋊C4—21no—
219C11×C4⋊C4—21no—
220C11×C4⋊C4—21no—
221C11×C4⋊C4—81no—
222C11×C4⋊C4—81no—
223C11×C22⋊C4—22no—
224C11×C22⋊C4—22no—
225C11×C22⋊C4—42no—
226C11×C22⋊C4—42no—
227C11×C22⋊C4—81no—
228C11×C22⋊C4—81no—
229C11×C22⋊C4—81no—
230C11×C22⋊C4—81no—
231C11×C22⋊C4—81no—
232C11×C22⋊C4—81no—
233C11×C22⋊C4—81no—
234C11×C22⋊C4—81no—
235C11×C22⋊C4—81no—
236C11×C22⋊C4—81no—
237C11×C22⋊C4—81no—
238C11×C22⋊C4—81no—
239C11×C22⋊C4—81no—
240C42×C11—21no—
241C42×C11—21no—
242C42×C11—21no—
243C42×C11—21no—
244C42×C11—42no—
245C2×#447C2×C1111yescharacteristic
246C2×#433C2×C1111yescharacteristic, complemented
247#2624C2×C1111yescharacteristic, complemented
248#2309C2×C1111yescharacteristic, complemented
249#2067C2×C1111yescharacteristic, complemented
250#2065C2×C1111yescharacteristic, complemented
251#2054C2×C1111yescharacteristic, complemented
252#2054C2×C1111yescharacteristic, complemented
253#1972C2×C1111yescharacteristic, complemented
254#1970C2×C1111yescharacteristic, complemented
255#1936C2×C1111yescharacteristic, complemented
256#1934C2×C1111yescharacteristic, complemented
257#1875C2×C1111yescharacteristic, complemented
258#1854C2×C1111yescharacteristic, complemented
259#1786C2×C1111yescharacteristic, complemented
260C23×C11—21no—
261C23×C11—21no—
262C23×C11—21no—
263C23×C11—21no—
264C23×C11—21no—
265C23×C11—21no—
266C23×C11—22no—
267C23×C11—22no—
268C23×C11—48no—
269C23×C11—41no—
270C23×C11—41no—
271C23×C11—41no—
272C23×C11—41no—
273C23×C11—41no—
274C23×C11—41no—
275C23×C11—41no—
276C23×C11—41no—
277C23×C11—41no—
278C23×C11—41no—
279C23×C11—41no—
280C23×C11—41no—
281C23×C11—41no—
282C23×C11—41no—
283C23×C11—41no—
284C23×C11—41no—
285C23×C11—41no—
286C23×C11—41no—
287C23×C11—41no—
288C23×C11—84no—
289C23×C11—84no—
290C23×C11—84no—
291C23×C11—84no—
292C23×C11—84no—
293C23×C11—84no—
294C23×C11#12112yes—
295C23×C11C22×D411yescharacteristic
296D4×C11—22no—
297D4×C11—22no—
298D4×C11—22no—
299D4×C11—22no—
300D4×C11—48no—
301D4×C11—41no—
302D4×C11—41no—
303D4×C11—41no—
304D4×C11—41no—
305D4×C11—41no—
306D4×C11—41no—
307D4×C11—41no—
308D4×C11—41no—
309D4×C11—84no—
310C2×C4×C11—21no—
311C2×C4×C11—21no—
312C2×C4×C11—22no—
313C2×C4×C11—22no—
314C2×C4×C11—22no—
315C2×C4×C11—22no—
316C2×C4×C11—21no—
317C2×C4×C11—21no—
318C2×C4×C11—21no—
319C2×C4×C11—21no—
320C2×C4×C11—21no—
321C2×C4×C11—21no—
322C2×C4×C11—21no—
323C2×C4×C11—21no—
324C2×C4×C11—21no—
325C2×C4×C11—21no—
326C2×C4×C11—21no—
327C2×C4×C11—21no—
328C2×C4×C11—41no—
329C2×C4×C11—41no—
330C2×C4×C11—41no—
331C2×C4×C11—41no—
332C2×C4×C11—41no—
333C2×C4×C11—41no—
334C2×C4×C11—41no—
335C2×C4×C11—41no—
336C2×C4×C11—41no—
337C2×C4×C11—41no—
338C2×C4×C11—41no—
339C2×C4×C11—41no—
340C2×C4×C11—41no—
341C2×C4×C11—41no—
342C2×C4×C11—41no—
343C2×C4×C11#12112yes—
344C2×C4×C11C22×D411yescharacteristic
345C2×C4×C11C2×#4111yescharacteristic
346C2×C4×C11C2×#4111yescharacteristic
347C2×C4×C11C2×#4111yescharacteristic
348C2×C4×C11H(5,𝔽2)11yescharacteristic
349C2×C4×C11H(5,𝔽2)11yescharacteristic
350C8×C11—22no—
351C8×C11—22no—
352C8×C11—41no—
353C8×C11—41no—
354C23×D4C22×C1111yescharacteristic
355C22×D8C22×C1111yescharacteristic
356C22×D8C22×C1111yescharacteristic
357C2×#121C22×C1111yescharacteristic
358C2×#117C22×C1111yescharacteristic
359C2×#117C22×C1111yescharacteristic
360#447—24no—
361#433—24no—
362C2×#107C22×C1111yescharacteristic, complemented
363C2×#106C22×C1111yescharacteristic, complemented
364C2×C4⋊C8C22×C1111yescharacteristic, complemented
365C2×C4⋊C8C22×C1111yescharacteristic, complemented
366C2×#102C22×C1111yescharacteristic
367C2×#102C22×C1111yescharacteristic
368C2×#102C22×C1111yescharacteristic
369C2×#102C22×C1111yescharacteristic
370C2×#102C22×C1111yescharacteristic
371C2×#102C22×C1111yescharacteristic
372C2×#102C22×C1111yescharacteristic, complemented
373C2×#102C22×C1111yescharacteristic, complemented
374C2×C22⋊C8C22×C1111yescharacteristic
375C2×C22⋊C8C22×C1111yescharacteristic
376C2×#97C22×C1111yescharacteristic, complemented
377C2×C4×C8C22×C1111yescharacteristic, complemented
378#399—21no—
379#397—21no—
380#394—21no—
381#394—21no—
382#390—21no—
383#390—21no—
384#390C22×C1111yescharacteristic
385#390C22×C1111yescharacteristic
386#390C22×C1111yescharacteristic
387#390C22×C1111yescharacteristic
388#390C22×C1111yescharacteristic, complemented
389#390C22×C1111yescharacteristic, complemented
390#389C22×C1111yescharacteristic, complemented
391#389C22×C1111yescharacteristic, complemented
392#380C22×C1111yescharacteristic
393#379—21no—
394#379—21no—
395#340C22×C1111yescharacteristic, complemented
396#340C22×C1111yescharacteristic, complemented
397#340C22×C1111yescharacteristic, complemented
398#340C22×C1111yescharacteristic, complemented
399C22×C11—22no—
400C22×C11—22no—
401C22×C11—22no—
402C22×C11—41no—
403C22×C11—41no—
404C22×C11—41no—
405C22×C11—41no—
406C22×C11—42no—
407C22×C11—42no—
408C22×C11—42no—
409C22×C11—42no—
410C22×C11—42no—
411C22×C11—42no—
412C22×C11—816no—
413C22×C11—81no—
414C22×C11—81no—
415C22×C11—81no—
416C22×C11—81no—
417C22×C11—81no—
418C22×C11—81no—
419C22×C11—81no—
420C22×C11—81no—
421C22×C11—81no—
422C22×C11—81no—
423C22×C11—81no—
424C22×C11—81no—
425C22×C11—81no—
426C22×C11—81no—
427C22×C11—81no—
428C22×C11C2×#12111yescharacteristic
429C22×C11#52511yescharacteristic
430C22×C11#53511yescharacteristic
431C22×C11#57611yescharacteristic
432C22×C11#57611yescharacteristic
433C22×C11#57611yescharacteristic
434C22×C11#57711yescharacteristic
435C4×C11—22no—
436C4×C11—41no—
437C4×C11—41no—
438C4×C11—41no—
439C4×C11—41no—
440C4×C11—81no—
441C4×C11—81no—
442C4×C11—81no—
443C4×C11—81no—
444C4×C11—81no—
445C4×C11#54611yescharacteristic
446C4×C11#54611yescharacteristic
447C4×C11#55111yescharacteristic
448C4×C11#55111yescharacteristic
449C25—21no—
450C22×D4—22no—
451C22×D4—22no—
452C22×D4—21no—
453C22×D4—21no—
454C22×D4—22no—
455C22×D4—22no—
456C22×D4—41no—
457C22×D4—41no—
458C22×D4C23×C1111yescharacteristic
459C22×D4C23×C1111yescharacteristic
460C22×D4C23×C1111yescharacteristic
461C23×C4C23×C1111yescharacteristic
462C2×D8—22no—
463C2×D8—22no—
464C2×D8—22no—
465C2×D8—22no—
466C2×D8—41no—
467C2×D8—41no—
468C22×C8C23×C1111yescharacteristic
469C22×C8C23×C1111yescharacteristic
470C22×C8C23×C1111yescharacteristic
471C22×C8C23×C1111yescharacteristic
472#121—22no—
473#121—22no—
474#117—22no—
475#117—22no—
476#117—41no—
477#117—41no—
478C2×C4⋊C4—21no—
479C2×C4⋊C4—21no—
480C2×C4⋊C4D4×C1111yescharacteristic
481C2×C4⋊C4D4×C1111yescharacteristic
482C2×C4⋊C4C23×C1111yescharacteristic
483C2×C4⋊C4C23×C1111yescharacteristic
484C2×C4⋊C4C23×C1111yescharacteristic
485C2×C4⋊C4C23×C1111yescharacteristic
486C2×C4⋊C4C23×C1111yescharacteristic
487C2×C22⋊C4—21no—
488C2×C22⋊C4—21no—
489C2×C22⋊C4—21no—
490C2×C22⋊C4—21no—
491C2×C22⋊C4—21no—
492C2×C22⋊C4—21no—
493C2×C22⋊C4—21no—
494C2×C22⋊C4—21no—
495C2×C22⋊C4—21no—
496C2×C22⋊C4—21no—
497C2×C22⋊C4—21no—
498C2×C22⋊C4—21no—
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—21no—
502C2×C22⋊C4D4×C1111yescharacteristic
503C2×C22⋊C4D4×C1111yescharacteristic
504C2×C42—21no—
505C2×C42C23×C1111yescharacteristic
506C2×C42C23×C1111yescharacteristic
507#107—41no—
508#106—41no—
509C4⋊C8—22no—
510C4⋊C8—22no—
511#102—22no—
512#102—22no—
513#102—22no—
514#102—22no—
515#102—41no—
516#102—41no—
517#102—41no—
518#102—41no—
519C22⋊C8—22no—
520C22⋊C8D4×C1114yes—
521#97—22no—
522C4×C8—22no—
523#95—21no—
524#95—21no—
525#95—21no—
526C2×C11—42no—
527C2×C11—82no—
528C2×C11—82no—
529C2×C11—161no—
530C2×C11#241111yescharacteristic
531C2×C11#305811yescharacteristic
532C2×C11#306211yescharacteristic
533C2×C11#311811yescharacteristic
534C2×C11#312211yescharacteristic
535C2×C11#322011yescharacteristic
536C2×C11#322411yescharacteristic
537C24—24no—
538C24—21no—
539C24—21no—
540C24—21no—
541C24—42no—
542C24—42no—
543C24—81no—
544C24—81no—
545C24—81no—
546C24—81no—
547C24C2×D4×C1111yescharacteristic
548C2×D4—24no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—44no—
566C2×D4—44no—
567C2×D4—44no—
568C2×D4—44no—
569C2×D4—42no—
570C2×D4—42no—
571C2×D4—42no—
572C2×D4—81no—
573C2×D4—81no—
574C2×D4C11×#4112yes—
575C2×D4C11×#4112yes—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4C2×D4×C1111yescharacteristic
586C22×C4C2×D4×C1111yescharacteristic
587C22×C4C2×D4×C1111yescharacteristic
588C22×C4C2×D4×C1111yescharacteristic
589C22×C4C2×D4×C1111yescharacteristic
590C22×C4C2×D4×C1112yes—
591C22×C4C11×#4112yes—
592C22×C4C24×C1111yescharacteristic
593D8—44no—
594D8—44no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8C2×D4×C1112yes—
606C2×C8C2×D4×C1112yes—
607C4⋊C4—22no—
608C4⋊C4—22no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—81no—
620C4⋊C4—81no—
621C22⋊C4—22no—
622C22⋊C4—22no—
623C22⋊C4—42no—
624C22⋊C4—42no—
625C22⋊C4—81no—
626C22⋊C4—81no—
627C22⋊C4—81no—
628C22⋊C4—81no—
629C22⋊C4—81no—
630C22⋊C4—81no—
631C22⋊C4—81no—
632C22⋊C4—81no—
633C22⋊C4—81no—
634C22⋊C4—81no—
635C22⋊C4—81no—
636C22⋊C4—81no—
637C22⋊C4—81no—
638C42—21no—
639C42—21no—
640C42—21no—
641C42—21no—
642C42—42no—
643C11#2451211yescharacteristic, direct product factor, Sylow
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—22no—
651C23—22no—
652C23—48no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—84no—
673C23—84no—
674C23—84no—
675C23—84no—
676C23—84no—
677C23—84no—
678C23C11×#12112yes—
679C23C22×D4×C1111yescharacteristic
680D4—22no—
681D4—22no—
682D4—22no—
683D4—22no—
684D4—48no—
685D4—41no—
686D4—41no—
687D4—41no—
688D4—41no—
689D4—41no—
690D4—41no—
691D4—41no—
692D4—41no—
693D4—84no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4C11×#12112yes—
728C2×C4C22×D4×C1111yescharacteristic
729C2×C4C2×C11×#4111yescharacteristic
730C2×C4C2×C11×#4111yescharacteristic
731C2×C4C2×C11×#4111yescharacteristic
732C2×C4C11×H(5,𝔽2)11yescharacteristic
733C2×C4C11×H(5,𝔽2)11yescharacteristic
734C8—22no—
735C8—22no—
736C8—41no—
737C8—41no—
738C22—22no—
739C22—22no—
740C22—22no—
741C22—41no—
742C22—41no—
743C22—41no—
744C22—41no—
745C22—42no—
746C22—42no—
747C22—42no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—816no—
752C22—81no—
753C22—81no—
754C22—81no—
755C22—81no—
756C22—81no—
757C22—81no—
758C22—81no—
759C22—81no—
760C22—81no—
761C22—81no—
762C22—81no—
763C22—81no—
764C22—81no—
765C22—81no—
766C22—81no—
767C22C2×C11×#12111yescharacteristic
768C22C11×#52511yescharacteristic
769C22C11×#53511yescharacteristic
770C22C11×#57611yescharacteristic
771C22C11×#57611yescharacteristic
772C22C11×#57611yescharacteristic
773C22C11×#57711yescharacteristic
774C4—22no—
775C4—41no—
776C4—41no—
777C4—41no—
778C4—41no—
779C4—81no—
780C4—81no—
781C4—81no—
782C4—81no—
783C4—81no—
784C4C11×#54611yescharacteristic
785C4C11×#54611yescharacteristic
786C4C11×#55111yescharacteristic
787C4C11×#55111yescharacteristic
788C2—42no—
789C2—82no—
790C2—82no—
791C2—161no—
792C2C11×#241111yescharacteristic
793C2C11×#305811yescharacteristic
794C2C11×#306211yescharacteristic
795C2C11×#311811yescharacteristic
796C2C11×#312211yescharacteristic
797C2C11×#322011yescharacteristic
798C2C11×#322411yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#447C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C11×#117 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#433C2semidirect
3. C11×#2624C2semidirect
4. C11×#2309C2semidirect
5. C11×#2067C2semidirect
6. C11×#2065C2semidirect
7. C11×#2054C2semidirect
8. C11×#2054C2semidirect
9. C11×#1972C2semidirect
10. C11×#1970C2semidirect
11. C11×#1936C2semidirect
12. C11×#1934C2semidirect
13. C11×#1875C2semidirect
14. C11×#1854C2semidirect
15. C11×#1786C2semidirect
24. C2×C11×#107C22semidirect
25. C2×C11×#106C22semidirect
26. C2×C11×C4⋊C8C22semidirect
27. C2×C11×C4⋊C8C22semidirect
34. C2×C11×#102C22semidirect
35. C2×C11×#102C22semidirect
38. C2×C11×#97C22semidirect
39. C2×C4×C8×C11C22semidirect
50. C11×#390C22semidirect
51. C11×#390C22semidirect
52. C11×#389C22semidirect
53. C11×#389C22semidirect
57. C11×#340C22semidirect
58. C11×#340C22semidirect
59. C11×#340C22semidirect
60. C11×#340C22semidirect
138. #24512C11direct (N × H)
246. C2×#433C2×C11semidirect
247. #2624C2×C11semidirect
248. #2309C2×C11semidirect
249. #2067C2×C11semidirect
250. #2065C2×C11semidirect
251. #2054C2×C11semidirect
252. #2054C2×C11semidirect
253. #1972C2×C11semidirect
254. #1970C2×C11semidirect
255. #1936C2×C11semidirect
256. #1934C2×C11semidirect
257. #1875C2×C11semidirect
258. #1854C2×C11semidirect
259. #1786C2×C11semidirect
362. C2×#107C22×C11semidirect
363. C2×#106C22×C11semidirect
364. C2×C4⋊C8C22×C11semidirect
365. C2×C4⋊C8C22×C11semidirect
372. C2×#102C22×C11semidirect
373. C2×#102C22×C11semidirect
376. C2×#97C22×C11semidirect
377. C2×C4×C8C22×C11semidirect
388. #390C22×C11semidirect
389. #390C22×C11semidirect
390. #389C22×C11semidirect
391. #389C22×C11semidirect
395. #340C22×C11semidirect
396. #340C22×C11semidirect
397. #340C22×C11semidirect
398. #340C22×C11semidirect
643. C11#24512direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4472
C2×C11×#4332
C11×#26242
C11×#23092
C11×#20672
C11×#20652
C11×#20542
C11×#19722
C11×#19702
C11×#19362
C11×#19342
C11×#18752
C11×#18542
C11×#17862
#2451211