Finite Group Databasebeta

← C11×#22052 #14599245

Subgroups — C11×#22052 #14599245

Order 2816.

1080 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#450C211yesmaximal, characteristic
2C11×#2323C211yesmaximal, characteristic, complemented
3C11×#2309C211yesmaximal, characteristic
4C11×#1973C211yesmaximal, characteristic, complemented
5C11×#1968C211yesmaximal, characteristic, complemented
6C11×#1936C211yesmaximal, characteristic, complemented
7C11×#1934C211yesmaximal, characteristic, complemented
8C11×#1926C211yesmaximal, characteristic, complemented
9C11×#1925C211yesmaximal, characteristic, complemented
10C11×#1880C211yesmaximal, characteristic, complemented
11C11×#1880C211yesmaximal, characteristic, complemented
12C11×#1873C211yesmaximal, characteristic, complemented
13C11×#1854C211yesmaximal, characteristic, complemented
14C11×#1786C211yesmaximal, characteristic
15C11×#1750C211yesmaximal, characteristic, complemented
16C23×D4×C11C2211yescharacteristic
17C22×C11×SD16C2211yescharacteristic
18C22×C11×SD16C2211yescharacteristic
19C2×C11×C22⋊Q8C2211yescharacteristic
20C2×C4×Q8×C11C2211yescharacteristic, complemented
21C2×C11×#117C2211yescharacteristic
22C2×C11×#117C2211yescharacteristic
23C11×#450C418yescomplemented
24C2×C11×#107C2211yescharacteristic, complemented
25C2×C11×#106C2211yescharacteristic, complemented
26C2×C11×#103C2211yescharacteristic, complemented
27C2×C11×#103C2211yescharacteristic, complemented
28C2×C11×#102C2211yescharacteristic
29C2×C11×#102C2211yescharacteristic
30C2×C11×#102C2211yescharacteristic
31C2×C11×#102C2211yescharacteristic
32C2×C11×#102C2211yescharacteristic
33C2×C11×#102C2211yescharacteristic
34C2×C11×C22⋊C8C2211yescharacteristic
35C2×C11×C22⋊C8C2211yescharacteristic
36C2×C11×#97C2211yescharacteristic, complemented
37C2×C4×C8×C11C2211yescharacteristic, complemented
38C11×#391C2211yescharacteristic, complemented
39C11×#390—21no—
40C11×#390—21no—
41C11×#390C2211yescharacteristic
42C11×#390C2211yescharacteristic
43C11×#390C2211yescharacteristic
44C11×#390C2211yescharacteristic
45C11×#389—21no—
46C11×#389C2211yescharacteristic, complemented
47C11×#388—21no—
48C11×#388—21no—
49C11×#387—21no—
50C11×#380C2211yescharacteristic
51C11×#379—21no—
52C11×#379—21no—
53C4×C11×C4⋊C4C2211yescharacteristic, complemented
54C11×#340C2211yescharacteristic, complemented
55C11×#340C2211yescharacteristic, complemented
56C11×#340C2211yescharacteristic, complemented
57C11×#340C2211yescharacteristic, complemented
58C11×#336C2211yescharacteristic, complemented
59C11×#336C2211yescharacteristic, complemented
60C25×C11—21no—
61C22×Q8×C11C2311yescharacteristic
62C22×D4×C11—21no—
63C22×D4×C11—22no—
64C22×D4×C11—41no—
65C22×D4×C11—41no—
66C22×D4×C11—41no—
67C22×D4×C11—41no—
68C22×D4×C11C2×C414yes—
69C22×D4×C11C2311yescharacteristic
70C22×D4×C11C2311yescharacteristic
71C23×C4×C11C2311yescharacteristic
72C2×C11×SD16—41no—
73C2×C11×SD16—41no—
74C2×C11×SD16—41no—
75C2×C11×SD16—41no—
76C2×C11×SD16C2×C414yes—
77C2×C11×SD16C2×C414yes—
78C22×C8×C11C2311yescharacteristic
79C22×C8×C11C2311yescharacteristic
80C22×C8×C11C2311yescharacteristic
81C22×C8×C11C2311yescharacteristic
82C11×C22⋊Q8—22no—
83C11×C22⋊Q8C2×C414yes—
84C4×Q8×C11—41no—
85C4×Q8×C11—41no—
86C11×#117—41no—
87C11×#117—41no—
88C11×#117—41no—
89C11×#117—41no—
90C2×C11×C4⋊C4—21no—
91C2×C11×C4⋊C4—21no—
92C2×C11×C4⋊C4—21no—
93C2×C11×C4⋊C4D411yescharacteristic
94C2×C11×C4⋊C4D411yescharacteristic
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⋊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⋊C4D411yescharacteristic
112C2×C11×C22⋊C4D411yescharacteristic
113C2×C42×C11—21no—
114C2×C42×C11—21no—
115C2×C42×C11—21no—
116C2×C42×C11C2311yescharacteristic
117C2×C42×C11C2311yescharacteristic
118C11×#107—41no—
119C11×#106—41no—
120C11×#103—41no—
121C11×#103—41no—
122C11×#102—41no—
123C11×#102—41no—
124C11×#102—41no—
125C11×#102—41no—
126C11×#102C2×C414yes—
127C11×#102C2×C414yes—
128C11×C22⋊C8—22no—
129C11×C22⋊C8C2×C414yes—
130C11×#97—41no—
131C4×C8×C11—41no—
132C11×#95—21no—
133C11×#95—21no—
134C11×#95—21no—
135C11×#95—21no—
136C11×#95—21no—
137#22052C1111yesmaximal, characteristic, direct product factor, Sylow
138C24×C11—21no—
139C24×C11—21no—
140C24×C11—24no—
141C24×C11—42no—
142C24×C11—42no—
143C24×C11—81no—
144C24×C11—81no—
145C24×C11—81no—
146C24×C11—81no—
147C24×C11C2×D411yescharacteristic
148C2×Q8×C11—21no—
149C2×Q8×C11—21no—
150C2×Q8×C11—21no—
151C2×Q8×C11—21no—
152C2×Q8×C11—21no—
153C2×Q8×C11C22×C412yes—
154C2×D4×C11—24no—
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—44no—
166C2×D4×C11—44no—
167C2×D4×C11—42no—
168C2×D4×C11—42no—
169C2×D4×C11—44no—
170C2×D4×C11—44no—
171C2×D4×C11C22×C412yes—
172C2×D4×C11C22×C412yes—
173C22×C4×C11—21no—
174C22×C4×C11—21no—
175C22×C4×C11—21no—
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×C11C22×C412yes—
184C22×C4×C11C2×D411yescharacteristic
185C22×C4×C11C2×D411yescharacteristic
186C22×C4×C11C2×D411yescharacteristic
187C22×C4×C11C2×D411yescharacteristic
188C22×C4×C11C2×D411yescharacteristic
189C22×C4×C11#4112yes—
190C22×C4×C11C2411yescharacteristic
191C11×SD16—44no—
192C11×SD16—44no—
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—21no—
203C2×C8×C11C22×C412yes—
204C2×C8×C11C22×C412yes—
205C11×C4⋊C4—24no—
206C11×C4⋊C4—21no—
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—41no—
216C11×C4⋊C4—41no—
217C11×C4⋊C4—42no—
218C11×C4⋊C4—81no—
219C11×C4⋊C4C22×C412yes—
220C11×C22⋊C4—24no—
221C11×C22⋊C4—41no—
222C11×C22⋊C4—41no—
223C11×C22⋊C4—42no—
224C11×C22⋊C4—81no—
225C11×C22⋊C4—81no—
226C11×C22⋊C4—81no—
227C11×C22⋊C4—81no—
228C11×C22⋊C4—81no—
229C11×C22⋊C4—81no—
230C11×C22⋊C4—81no—
231C11×C22⋊C4—81no—
232C11×C22⋊C4—81no—
233C42×C11—21no—
234C42×C11—21no—
235C42×C11—21no—
236C42×C11—21no—
237C42×C11—42no—
238C42×C11—42no—
239C42×C11—81no—
240C2×#450C2×C1111yescharacteristic
241#2323C2×C1111yescharacteristic, complemented
242#2309C2×C1111yescharacteristic
243#1973C2×C1111yescharacteristic, complemented
244#1968C2×C1111yescharacteristic, complemented
245#1936C2×C1111yescharacteristic, complemented
246#1934C2×C1111yescharacteristic, complemented
247#1926C2×C1111yescharacteristic, complemented
248#1925C2×C1111yescharacteristic, complemented
249#1880C2×C1111yescharacteristic, complemented
250#1880C2×C1111yescharacteristic, complemented
251#1873C2×C1111yescharacteristic, complemented
252#1854C2×C1111yescharacteristic, complemented
253#1786C2×C1111yescharacteristic
254#1750C2×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—22no—
263C23×C11—48no—
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—41no—
276C23×C11—84no—
277C23×C11—84no—
278C23×C11—84no—
279C23×C11—84no—
280C23×C11—84no—
281C23×C11—84no—
282C23×C11C4×D412yes—
283C23×C11C22×D411yescharacteristic
284Q8×C11—22no—
285Q8×C11—22no—
286Q8×C11—41no—
287Q8×C11—41no—
288D4×C11—22no—
289D4×C11—22no—
290D4×C11—22no—
291D4×C11—22no—
292D4×C11—48no—
293D4×C11—41no—
294D4×C11—41no—
295D4×C11—41no—
296D4×C11—41no—
297C2×C4×C11—21no—
298C2×C4×C11—21no—
299C2×C4×C11—22no—
300C2×C4×C11—22no—
301C2×C4×C11—22no—
302C2×C4×C11—22no—
303C2×C4×C11—22no—
304C2×C4×C11—22no—
305C2×C4×C11—21no—
306C2×C4×C11—21no—
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—21no—
314C2×C4×C11—21no—
315C2×C4×C11—21no—
316C2×C4×C11—21no—
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—41no—
330C2×C4×C11—41no—
331C2×C4×C11—41no—
332C2×C4×C11—41no—
333C2×C4×C11C4×D412yes—
334C2×C4×C11C23×C411yescharacteristic
335C2×C4×C11C2×#4111yescharacteristic
336C2×C4×C11H(5,𝔽2)11yescharacteristic
337C2×C4×C11H(5,𝔽2)11yescharacteristic
338C2×C4×C11H(5,𝔽2)11yescharacteristic
339C2×C4×C11H(5,𝔽2)11yescharacteristic
340C8×C11—22no—
341C8×C11—22no—
342C8×C11—41no—
343C8×C11—41no—
344C23×D4C22×C1111yescharacteristic
345C22×SD16C22×C1111yescharacteristic
346C22×SD16C22×C1111yescharacteristic
347C2×C22⋊Q8C22×C1111yescharacteristic
348C2×C4×Q8C22×C1111yescharacteristic, complemented
349C2×#117C22×C1111yescharacteristic
350C2×#117C22×C1111yescharacteristic
351#450C4×C1118yescomplemented
352C2×#107C22×C1111yescharacteristic, complemented
353C2×#106C22×C1111yescharacteristic, complemented
354C2×#103C22×C1111yescharacteristic, complemented
355C2×#103C22×C1111yescharacteristic, complemented
356C2×#102C22×C1111yescharacteristic
357C2×#102C22×C1111yescharacteristic
358C2×#102C22×C1111yescharacteristic
359C2×#102C22×C1111yescharacteristic
360C2×#102C22×C1111yescharacteristic
361C2×#102C22×C1111yescharacteristic
362C2×C22⋊C8C22×C1111yescharacteristic
363C2×C22⋊C8C22×C1111yescharacteristic
364C2×#97C22×C1111yescharacteristic, complemented
365C2×C4×C8C22×C1111yescharacteristic, complemented
366#391C22×C1111yescharacteristic, complemented
367#390—21no—
368#390—21no—
369#390C22×C1111yescharacteristic
370#390C22×C1111yescharacteristic
371#390C22×C1111yescharacteristic
372#390C22×C1111yescharacteristic
373#389—21no—
374#389C22×C1111yescharacteristic, complemented
375#388—21no—
376#388—21no—
377#387—21no—
378#380C22×C1111yescharacteristic
379#379—21no—
380#379—21no—
381C4×C4⋊C4C22×C1111yescharacteristic, complemented
382#340C22×C1111yescharacteristic, complemented
383#340C22×C1111yescharacteristic, complemented
384#340C22×C1111yescharacteristic, complemented
385#340C22×C1111yescharacteristic, complemented
386#336C22×C1111yescharacteristic, complemented
387#336C22×C1111yescharacteristic, complemented
388C22×C11—22no—
389C22×C11—22no—
390C22×C11—22no—
391C22×C11—41no—
392C22×C11—41no—
393C22×C11—41no—
394C22×C11—41no—
395C22×C11—42no—
396C22×C11—42no—
397C22×C11—42no—
398C22×C11—42no—
399C22×C11—42no—
400C22×C11—42no—
401C22×C11—816no—
402C22×C11—81no—
403C22×C11—81no—
404C22×C11—81no—
405C22×C11—81no—
406C22×C11—81no—
407C22×C11—81no—
408C22×C11—81no—
409C22×C11—81no—
410C22×C11C2×C4×D411yescharacteristic
411C22×C11#53411yescharacteristic
412C22×C11#53511yescharacteristic
413C22×C11#57611yescharacteristic
414C22×C11#57711yescharacteristic
415C22×C11#57711yescharacteristic
416C22×C11#57711yescharacteristic
417C4×C11—22no—
418C4×C11—42no—
419C4×C11—41no—
420C4×C11—41no—
421C4×C11—41no—
422C4×C11—41no—
423C4×C11—42no—
424C4×C11—81no—
425C4×C11—81no—
426C4×C11—81no—
427C4×C11—81no—
428C4×C11#51811yescharacteristic
429C4×C11#51811yescharacteristic
430C4×C11#53811yescharacteristic
431C4×C11#53811yescharacteristic
432C25—21no—
433C22×Q8C23×C1111yescharacteristic
434C22×D4—21no—
435C22×D4—22no—
436C22×D4—41no—
437C22×D4—41no—
438C22×D4—41no—
439C22×D4—41no—
440C22×D4C2×C4×C1114yes—
441C22×D4C23×C1111yescharacteristic
442C22×D4C23×C1111yescharacteristic
443C23×C4C23×C1111yescharacteristic
444C2×SD16—41no—
445C2×SD16—41no—
446C2×SD16—41no—
447C2×SD16—41no—
448C2×SD16C2×C4×C1114yes—
449C2×SD16C2×C4×C1114yes—
450C22×C8C23×C1111yescharacteristic
451C22×C8C23×C1111yescharacteristic
452C22×C8C23×C1111yescharacteristic
453C22×C8C23×C1111yescharacteristic
454C22⋊Q8—22no—
455C22⋊Q8C2×C4×C1114yes—
456C4×Q8—41no—
457C4×Q8—41no—
458#117—41no—
459#117—41no—
460#117—41no—
461#117—41no—
462C2×C4⋊C4—21no—
463C2×C4⋊C4—21no—
464C2×C4⋊C4—21no—
465C2×C4⋊C4D4×C1111yescharacteristic
466C2×C4⋊C4D4×C1111yescharacteristic
467C2×C4⋊C4C23×C1111yescharacteristic
468C2×C4⋊C4C23×C1111yescharacteristic
469C2×C4⋊C4C23×C1111yescharacteristic
470C2×C4⋊C4C23×C1111yescharacteristic
471C2×C4⋊C4C23×C1111yescharacteristic
472C2×C22⋊C4—21no—
473C2×C22⋊C4—21no—
474C2×C22⋊C4—21no—
475C2×C22⋊C4—21no—
476C2×C22⋊C4—21no—
477C2×C22⋊C4—21no—
478C2×C22⋊C4—21no—
479C2×C22⋊C4—21no—
480C2×C22⋊C4—21no—
481C2×C22⋊C4—21no—
482C2×C22⋊C4—21no—
483C2×C22⋊C4D4×C1111yescharacteristic
484C2×C22⋊C4D4×C1111yescharacteristic
485C2×C42—21no—
486C2×C42—21no—
487C2×C42—21no—
488C2×C42C23×C1111yescharacteristic
489C2×C42C23×C1111yescharacteristic
490#107—41no—
491#106—41no—
492#103—41no—
493#103—41no—
494#102—41no—
495#102—41no—
496#102—41no—
497#102—41no—
498#102C2×C4×C1114yes—
499#102C2×C4×C1114yes—
500C22⋊C8—22no—
501C22⋊C8C2×C4×C1114yes—
502#97—41no—
503C4×C8—41no—
504#95—21no—
505#95—21no—
506#95—21no—
507#95—21no—
508#95—21no—
509C2×C11—42no—
510C2×C11—82no—
511C2×C11—82no—
512C2×C11#232111yescharacteristic
513C2×C11#294611yescharacteristic
514C2×C11#294911yescharacteristic
515C2×C11#319811yescharacteristic
516C2×C11#320011yescharacteristic
517C2×C11#322211yescharacteristic
518C2×C11#322411yescharacteristic
519C24—21no—
520C24—21no—
521C24—24no—
522C24—42no—
523C24—42no—
524C24—81no—
525C24—81no—
526C24—81no—
527C24—81no—
528C24C2×D4×C1111yescharacteristic
529C2×Q8—21no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—21no—
533C2×Q8—21no—
534C2×Q8C22×C4×C1112yes—
535C2×D4—24no—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—44no—
547C2×D4—44no—
548C2×D4—42no—
549C2×D4—42no—
550C2×D4—44no—
551C2×D4—44no—
552C2×D4C22×C4×C1112yes—
553C2×D4C22×C4×C1112yes—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4C22×C4×C1112yes—
565C22×C4C2×D4×C1111yescharacteristic
566C22×C4C2×D4×C1111yescharacteristic
567C22×C4C2×D4×C1111yescharacteristic
568C22×C4C2×D4×C1111yescharacteristic
569C22×C4C2×D4×C1111yescharacteristic
570C22×C4C11×#4112yes—
571C22×C4C24×C1111yescharacteristic
572SD16—44no—
573SD16—44no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8C22×C4×C1112yes—
585C2×C8C22×C4×C1112yes—
586C4⋊C4—24no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—41no—
597C4⋊C4—41no—
598C4⋊C4—42no—
599C4⋊C4—81no—
600C4⋊C4C22×C4×C1112yes—
601C22⋊C4—24no—
602C22⋊C4—41no—
603C22⋊C4—41no—
604C22⋊C4—42no—
605C22⋊C4—81no—
606C22⋊C4—81no—
607C22⋊C4—81no—
608C22⋊C4—81no—
609C22⋊C4—81no—
610C22⋊C4—81no—
611C22⋊C4—81no—
612C22⋊C4—81no—
613C22⋊C4—81no—
614C42—21no—
615C42—21no—
616C42—21no—
617C42—21no—
618C42—42no—
619C42—42no—
620C42—81no—
621C11#2205211yescharacteristic, direct product factor, Sylow
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—22no—
629C23—22no—
630C23—48no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—84no—
644C23—84no—
645C23—84no—
646C23—84no—
647C23—84no—
648C23—84no—
649C23C4×D4×C1112yes—
650C23C22×D4×C1111yescharacteristic
651Q8—22no—
652Q8—22no—
653Q8—41no—
654Q8—41no—
655D4—22no—
656D4—22no—
657D4—22no—
658D4—22no—
659D4—48no—
660D4—41no—
661D4—41no—
662D4—41no—
663D4—41no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
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—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4C4×D4×C1112yes—
701C2×C4C23×C4×C1111yescharacteristic
702C2×C4C2×C11×#4111yescharacteristic
703C2×C4C11×H(5,𝔽2)11yescharacteristic
704C2×C4C11×H(5,𝔽2)11yescharacteristic
705C2×C4C11×H(5,𝔽2)11yescharacteristic
706C2×C4C11×H(5,𝔽2)11yescharacteristic
707C8—22no—
708C8—22no—
709C8—41no—
710C8—41no—
711C22—22no—
712C22—22no—
713C22—22no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—42no—
719C22—42no—
720C22—42no—
721C22—42no—
722C22—42no—
723C22—42no—
724C22—816no—
725C22—81no—
726C22—81no—
727C22—81no—
728C22—81no—
729C22—81no—
730C22—81no—
731C22—81no—
732C22—81no—
733C22C2×C4×D4×C1111yescharacteristic
734C22C11×#53411yescharacteristic
735C22C11×#53511yescharacteristic
736C22C11×#57611yescharacteristic
737C22C11×#57711yescharacteristic
738C22C11×#57711yescharacteristic
739C22C11×#57711yescharacteristic
740C4—22no—
741C4—41no—
742C4—41no—
743C4—41no—
744C4—41no—
745C4—42no—
746C4—42no—
747C4—81no—
748C4—81no—
749C4—81no—
750C4—81no—
751C4C11×#51811yescharacteristic
752C4C11×#51811yescharacteristic
753C4C11×#53811yescharacteristic
754C4C11×#53811yescharacteristic
755C2—42no—
756C2—82no—
757C2—82no—
758C2C11×#232111yescharacteristic
759C2C11×#294611yescharacteristic
760C2C11×#294911yescharacteristic
761C2C11×#319811yescharacteristic
762C2C11×#320011yescharacteristic
763C2C11×#322211yescharacteristic
764C2C11×#322411yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC23×D4×C11C22
LCSG ▷ C2×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. C11×#2323C2semidirect
4. C11×#1973C2semidirect
5. C11×#1968C2semidirect
6. C11×#1936C2semidirect
7. C11×#1934C2semidirect
8. C11×#1926C2semidirect
9. C11×#1925C2semidirect
10. C11×#1880C2semidirect
11. C11×#1880C2semidirect
12. C11×#1873C2semidirect
13. C11×#1854C2semidirect
15. C11×#1750C2semidirect
20. C2×C4×Q8×C11C22semidirect
23. C11×#450C4semidirect
24. C2×C11×#107C22semidirect
25. C2×C11×#106C22semidirect
26. C2×C11×#103C22semidirect
27. C2×C11×#103C22semidirect
36. C2×C11×#97C22semidirect
37. C2×C4×C8×C11C22semidirect
38. C11×#391C22semidirect
46. C11×#389C22semidirect
53. C4×C11×C4⋊C4C22semidirect
54. C11×#340C22semidirect
55. C11×#340C22semidirect
56. C11×#340C22semidirect
57. C11×#340C22semidirect
58. C11×#336C22semidirect
59. C11×#336C22semidirect
137. #22052C11direct (N × H)
241. #2323C2×C11semidirect
243. #1973C2×C11semidirect
244. #1968C2×C11semidirect
245. #1936C2×C11semidirect
246. #1934C2×C11semidirect
247. #1926C2×C11semidirect
248. #1925C2×C11semidirect
249. #1880C2×C11semidirect
250. #1880C2×C11semidirect
251. #1873C2×C11semidirect
252. #1854C2×C11semidirect
254. #1750C2×C11semidirect
348. C2×C4×Q8C22×C11semidirect
351. #450C4×C11semidirect
352. C2×#107C22×C11semidirect
353. C2×#106C22×C11semidirect
354. C2×#103C22×C11semidirect
355. C2×#103C22×C11semidirect
364. C2×#97C22×C11semidirect
365. C2×C4×C8C22×C11semidirect
366. #391C22×C11semidirect
374. #389C22×C11semidirect
381. C4×C4⋊C4C22×C11semidirect
382. #340C22×C11semidirect
383. #340C22×C11semidirect
384. #340C22×C11semidirect
385. #340C22×C11semidirect
386. #336C22×C11semidirect
387. #336C22×C11semidirect
621. C11#22052direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4502
C11×#23232
C11×#23092
C11×#19732
C11×#19682
C11×#19362
C11×#19342
C11×#19262
C11×#19252
C11×#18802
C11×#18732
C11×#18542
C11×#17862
C11×#17502
#2205211