Finite Group Databasebeta

← C11×#23192 #14600385

Subgroups — C11×#23192 #14600385

Order 2816.

986 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#497C211yesmaximal, characteristic
2C2×C11×#441C211yesmaximal, characteristic, complemented
3C2×C4×C11×SD16C211yesmaximal, characteristic
4C11×#2367C211yesmaximal, characteristic
5C11×#2365C211yesmaximal, characteristic, complemented
6C11×#1983C211yesmaximal, characteristic
7C11×#1981C211yesmaximal, characteristic, complemented
8C11×#1973C211yesmaximal, characteristic
9C11×#1969C211yesmaximal, characteristic, complemented
10C11×#1880C211yesmaximal, characteristic
11C11×#1878C211yesmaximal, characteristic, complemented
12C11×#1878C211yesmaximal, characteristic, complemented
13C11×#1877C211yesmaximal, characteristic
14C11×#1776C211yesmaximal, characteristic, complemented
15C11×#1771C211yesmaximal, characteristic, complemented
16C22×C11×Q16C2211yescharacteristic
17C22×C11×Q16C2211yescharacteristic
18C22×C11×SD16C2211yescharacteristic
19C22×C11×SD16C2211yescharacteristic
20C2×C11×C4⋊Q8C2211yescharacteristic
21C2×C11×#124C2211yescharacteristic
22C2×C4×Q8×C11C2211yescharacteristic
23C2×C4×Q8×C11C2211yescharacteristic
24C2×C4×Q8×C11C2211yescharacteristic
25C2×C4×D4×C11C2211yescharacteristic
26C11×#497C418yescomplemented
27C11×#441—24no—
28C4×C11×SD16—24no—
29C2×C11×#107C2211yescharacteristic
30C2×C11×#106C2211yescharacteristic
31C2×C11×C4⋊C8C2211yescharacteristic
32C2×C11×#103C2211yescharacteristic
33C2×C11×#103C2211yescharacteristic
34C2×C11×#103C2211yescharacteristic
35C2×C11×#103C2211yescharacteristic
36C2×C11×#103C2211yescharacteristic
37C2×C11×#103C2211yescharacteristic
38C2×C11×#102C2211yescharacteristic
39C2×C11×#102C2211yescharacteristic
40C2×C11×#97C2211yescharacteristic
41C2×C11×#97C2211yescharacteristic
42C2×C4×C8×C11C2211yescharacteristic
43C11×#391C2211yescharacteristic
44C11×#391C2211yescharacteristic
45C11×#391C2211yescharacteristic
46C11×#390C2211yescharacteristic
47C11×#389—21no—
48C11×#388—21no—
49C11×#388—21no—
50C11×#387—21no—
51C11×#387—21no—
52C11×#385—21no—
53C4×C11×C4⋊C4—21no—
54C4×C11×C4⋊C4C2211yescharacteristic
55C4×C11×C4⋊C4C2211yescharacteristic
56C4×C11×C4⋊C4C2211yescharacteristic
57C4×C11×C22⋊C4—21no—
58C11×#340C2211yescharacteristic
59C11×#340C2211yescharacteristic
60C11×#336C2211yescharacteristic
61C11×#336C2211yescharacteristic
62C22×Q8×C11C2311yescharacteristic
63C22×Q8×C11C2311yescharacteristic
64C22×Q8×C11C2311yescharacteristic
65C22×D4×C11C2311yescharacteristic
66C23×C4×C11—21no—
67C2×C11×Q16—22no—
68C2×C11×Q16—22no—
69C2×C11×Q16—41no—
70C2×C11×Q16—41no—
71C2×C11×Q16C2×C414yescomplemented
72C2×C11×Q16C2×C414yescomplemented
73C2×C11×SD16—22no—
74C2×C11×SD16—22no—
75C2×C11×SD16—41no—
76C2×C11×SD16—41no—
77C2×C11×SD16C2×C414yes—
78C2×C11×SD16C2×C414yes—
79C22×C8×C11C2311yescharacteristic
80C22×C8×C11C2311yescharacteristic
81C22×C8×C11C2311yescharacteristic
82C22×C8×C11C2311yescharacteristic
83C11×C4⋊Q8—22no—
84C11×C4⋊Q8C2×C414yescomplemented
85C11×#124—22no—
86C11×#124C2×C414yes—
87C4×Q8×C11—22no—
88C4×Q8×C11—22no—
89C4×Q8×C11—22no—
90C4×Q8×C11—41no—
91C4×Q8×C11—41no—
92C4×Q8×C11—41no—
93C4×D4×C11—22no—
94C4×D4×C11—41no—
95C2×C11×C4⋊C4—21no—
96C2×C11×C4⋊C4—21no—
97C2×C11×C4⋊C4—21no—
98C2×C11×C4⋊C4—21no—
99C2×C11×C4⋊C4—21no—
100C2×C11×C4⋊C4D411yescharacteristic
101C2×C11×C4⋊C4D411yescharacteristic
102C2×C11×C4⋊C4C2311yescharacteristic
103C2×C11×C4⋊C4C2311yescharacteristic
104C2×C11×C4⋊C4C2311yescharacteristic
105C2×C11×C4⋊C4C2311yescharacteristic
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×C42×C11—21no—
112C2×C42×C11—21no—
113C2×C42×C11—21no—
114C2×C42×C11—21no—
115C2×C42×C11—21no—
116C2×C42×C11C2311yescharacteristic
117C2×C42×C11C2311yescharacteristic
118C2×C42×C11C2311yescharacteristic
119C11×#107—22no—
120C11×#106D414yes—
121C11×C4⋊C8—22no—
122C11×#103—22no—
123C11×#103—22no—
124C11×#103—22no—
125C11×#103—41no—
126C11×#103—41no—
127C11×#103—41no—
128C11×#102—22no—
129C11×#102—41no—
130C11×#97—22no—
131C11×#97C2×C414yescomplemented
132C4×C8×C11—22no—
133C11×#95—21no—
134C11×#95—21no—
135C11×#95—21no—
136C11×#95—21no—
137C11×#95—21no—
138C11×#95—21no—
139C11×#95—21no—
140C11×#95—21no—
141C11×#95D411yescharacteristic
142C11×#95D411yescharacteristic
143#23192C1111yesmaximal, characteristic, direct product factor, Sylow
144C24×C11—21no—
145C2×Q8×C11—21no—
146C2×Q8×C11—21no—
147C2×Q8×C11—21no—
148C2×Q8×C11—21no—
149C2×Q8×C11—21no—
150C2×Q8×C11—21no—
151C2×Q8×C11—21no—
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×C11C22×C412yes—
161C2×Q8×C11C22×C412yes—
162C2×Q8×C11C22×C412yes—
163C2×D4×C11—21no—
164C2×D4×C11—21no—
165C2×D4×C11—21no—
166C2×D4×C11—21no—
167C2×D4×C11—21no—
168C2×D4×C11C22×C412yes—
169C22×C4×C11—21no—
170C22×C4×C11—21no—
171C22×C4×C11—21no—
172C22×C4×C11—21no—
173C22×C4×C11—21no—
174C22×C4×C11—21no—
175C22×C4×C11—21no—
176C22×C4×C11—42no—
177C22×C4×C11—42no—
178C22×C4×C11—81no—
179C22×C4×C11C2×D411yescharacteristic
180C22×C4×C11C2×D411yescharacteristic
181C22×C4×C11C2×D411yescharacteristic
182C22×C4×C11C2×D411yescharacteristic
183C22×C4×C11C2×D411yescharacteristic
184C22×C4×C11C2×D411yescharacteristic
185C22×C4×C11C2411yescharacteristic
186C11×Q16—28no—
187C11×Q16—44no—
188C11×SD16—28no—
189C11×SD16—44no—
190C2×C8×C11—21no—
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×C11C22×C412yes—
199C2×C8×C11C22×C412yes—
200C2×C8×C11C2×D412yes—
201C2×C8×C11#4112yes—
202C11×C4⋊C4—24no—
203C11×C4⋊C4—24no—
204C11×C4⋊C4—22no—
205C11×C4⋊C4—21no—
206C11×C4⋊C4—21no—
207C11×C4⋊C4—21no—
208C11×C4⋊C4—21no—
209C11×C4⋊C4—21no—
210C11×C4⋊C4—21no—
211C11×C4⋊C4—41no—
212C11×C4⋊C4—42no—
213C11×C4⋊C4—42no—
214C11×C4⋊C4—42no—
215C11×C4⋊C4C2×D412yes—
216C11×C4⋊C4C2×D412yes—
217C11×C22⋊C4—24no—
218C11×C22⋊C4—24no—
219C11×C22⋊C4—42no—
220C11×C22⋊C4—42no—
221C11×C22⋊C4—81no—
222C42×C11—21no—
223C42×C11—21no—
224C42×C11—21no—
225C42×C11—21no—
226C42×C11—42no—
227C42×C11—42no—
228C42×C11—42no—
229C42×C11—42no—
230C42×C11—81no—
231C42×C11C22×C412yes—
232C42×C11#4112yes—
233C2×#497C2×C1111yescharacteristic
234C2×#441C2×C1111yescharacteristic, complemented
235C2×C4×SD16C2×C1111yescharacteristic
236#2367C2×C1111yescharacteristic
237#2365C2×C1111yescharacteristic, complemented
238#1983C2×C1111yescharacteristic
239#1981C2×C1111yescharacteristic, complemented
240#1973C2×C1111yescharacteristic
241#1969C2×C1111yescharacteristic, complemented
242#1880C2×C1111yescharacteristic
243#1878C2×C1111yescharacteristic, complemented
244#1878C2×C1111yescharacteristic, complemented
245#1877C2×C1111yescharacteristic
246#1776C2×C1111yescharacteristic, complemented
247#1771C2×C1111yescharacteristic, complemented
248C23×C11—22no—
249C23×C11—41no—
250C23×C11—41no—
251C23×C11—41no—
252C23×C11—41no—
253C23×C11—41no—
254C23×C11—41no—
255C23×C11C22×D411yescharacteristic
256Q8×C11—22no—
257Q8×C11—22no—
258Q8×C11—22no—
259Q8×C11—22no—
260Q8×C11—22no—
261Q8×C11—22no—
262Q8×C11—41no—
263Q8×C11—41no—
264Q8×C11—41no—
265Q8×C11—41no—
266Q8×C11—41no—
267Q8×C11—41no—
268D4×C11—22no—
269D4×C11—22no—
270D4×C11—41no—
271D4×C11—41no—
272C2×C4×C11—21no—
273C2×C4×C11—21no—
274C2×C4×C11—21no—
275C2×C4×C11—21no—
276C2×C4×C11—21no—
277C2×C4×C11—21no—
278C2×C4×C11—22no—
279C2×C4×C11—22no—
280C2×C4×C11—22no—
281C2×C4×C11—21no—
282C2×C4×C11—21no—
283C2×C4×C11—21no—
284C2×C4×C11—22no—
285C2×C4×C11—22no—
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—41no—
293C2×C4×C11—41no—
294C2×C4×C11—41no—
295C2×C4×C11—41no—
296C2×C4×C11—41no—
297C2×C4×C11—41no—
298C2×C4×C11—41no—
299C2×C4×C11—41no—
300C2×C4×C11—41no—
301C2×C4×C11—41no—
302C2×C4×C11—41no—
303C2×C4×C11—41no—
304C2×C4×C11—41no—
305C2×C4×C11—41no—
306C2×C4×C11—41no—
307C2×C4×C11—41no—
308C2×C4×C11—84no—
309C2×C4×C11C4×D412yes—
310C2×C4×C11C4×D412yes—
311C2×C4×C11#13712yes—
312C2×C4×C11C23×C411yescharacteristic
313C2×C4×C11C22×D411yescharacteristic
314C2×C4×C11C2×#4111yescharacteristic
315C2×C4×C11C2×#4111yescharacteristic
316C2×C4×C11H(5,𝔽2)11yescharacteristic
317C2×C4×C11H(5,𝔽2)11yescharacteristic
318C8×C11—22no—
319C8×C11—41no—
320C8×C11—41no—
321C8×C11C4×D414yes—
322C22×Q16C22×C1111yescharacteristic
323C22×Q16C22×C1111yescharacteristic
324C22×SD16C22×C1111yescharacteristic
325C22×SD16C22×C1111yescharacteristic
326C2×C4⋊Q8C22×C1111yescharacteristic
327C2×#124C22×C1111yescharacteristic
328C2×C4×Q8C22×C1111yescharacteristic
329C2×C4×Q8C22×C1111yescharacteristic
330C2×C4×Q8C22×C1111yescharacteristic
331C2×C4×D4C22×C1111yescharacteristic
332#497C4×C1118yescomplemented
333#441—24no—
334C4×SD16—24no—
335C2×#107C22×C1111yescharacteristic
336C2×#106C22×C1111yescharacteristic
337C2×C4⋊C8C22×C1111yescharacteristic
338C2×#103C22×C1111yescharacteristic
339C2×#103C22×C1111yescharacteristic
340C2×#103C22×C1111yescharacteristic
341C2×#103C22×C1111yescharacteristic
342C2×#103C22×C1111yescharacteristic
343C2×#103C22×C1111yescharacteristic
344C2×#102C22×C1111yescharacteristic
345C2×#102C22×C1111yescharacteristic
346C2×#97C22×C1111yescharacteristic
347C2×#97C22×C1111yescharacteristic
348C2×C4×C8C22×C1111yescharacteristic
349#391C22×C1111yescharacteristic
350#391C22×C1111yescharacteristic
351#391C22×C1111yescharacteristic
352#390C22×C1111yescharacteristic
353#389—21no—
354#388—21no—
355#388—21no—
356#387—21no—
357#387—21no—
358#385—21no—
359C4×C4⋊C4—21no—
360C4×C4⋊C4C22×C1111yescharacteristic
361C4×C4⋊C4C22×C1111yescharacteristic
362C4×C4⋊C4C22×C1111yescharacteristic
363C4×C22⋊C4—21no—
364#340C22×C1111yescharacteristic
365#340C22×C1111yescharacteristic
366#336C22×C1111yescharacteristic
367#336C22×C1111yescharacteristic
368C22×C11—42no—
369C22×C11—42no—
370C22×C11—42no—
371C22×C11—81no—
372C22×C11—81no—
373C22×C11—81no—
374C22×C11—81no—
375C22×C11C2×C4×D411yescharacteristic
376C22×C11D4211yescharacteristic
377C22×C11#55011yescharacteristic
378C22×C11C2×#13711yescharacteristic
379C22×C11#57511yescharacteristic
380C22×C11#57711yescharacteristic
381C22×C11#57811yescharacteristic
382C4×C11—22no—
383C4×C11—22no—
384C4×C11—22no—
385C4×C11—42no—
386C4×C11—42no—
387C4×C11—42no—
388C4×C11—41no—
389C4×C11—42no—
390C4×C11—41no—
391C4×C11—41no—
392C4×C11—42no—
393C4×C11—81no—
394C4×C11—81no—
395C4×C11C2×C4×D411yescharacteristic
396C4×C11#51811yescharacteristic
397C4×C11#55011yescharacteristic
398C4×C11#55911yescharacteristic
399C22×Q8C23×C1111yescharacteristic
400C22×Q8C23×C1111yescharacteristic
401C22×Q8C23×C1111yescharacteristic
402C22×D4C23×C1111yescharacteristic
403C23×C4—21no—
404C2×Q16—22no—
405C2×Q16—22no—
406C2×Q16—41no—
407C2×Q16—41no—
408C2×Q16C2×C4×C1114yescomplemented
409C2×Q16C2×C4×C1114yescomplemented
410C2×SD16—22no—
411C2×SD16—22no—
412C2×SD16—41no—
413C2×SD16—41no—
414C2×SD16C2×C4×C1114yes—
415C2×SD16C2×C4×C1114yes—
416C22×C8C23×C1111yescharacteristic
417C22×C8C23×C1111yescharacteristic
418C22×C8C23×C1111yescharacteristic
419C22×C8C23×C1111yescharacteristic
420C4⋊Q8—22no—
421C4⋊Q8C2×C4×C1114yescomplemented
422#124—22no—
423#124C2×C4×C1114yes—
424C4×Q8—22no—
425C4×Q8—22no—
426C4×Q8—22no—
427C4×Q8—41no—
428C4×Q8—41no—
429C4×Q8—41no—
430C4×D4—22no—
431C4×D4—41no—
432C2×C4⋊C4—21no—
433C2×C4⋊C4—21no—
434C2×C4⋊C4—21no—
435C2×C4⋊C4—21no—
436C2×C4⋊C4—21no—
437C2×C4⋊C4D4×C1111yescharacteristic
438C2×C4⋊C4D4×C1111yescharacteristic
439C2×C4⋊C4C23×C1111yescharacteristic
440C2×C4⋊C4C23×C1111yescharacteristic
441C2×C4⋊C4C23×C1111yescharacteristic
442C2×C4⋊C4C23×C1111yescharacteristic
443C2×C22⋊C4—21no—
444C2×C22⋊C4—21no—
445C2×C22⋊C4—21no—
446C2×C22⋊C4—21no—
447C2×C22⋊C4—21no—
448C2×C42—21no—
449C2×C42—21no—
450C2×C42—21no—
451C2×C42—21no—
452C2×C42—21no—
453C2×C42C23×C1111yescharacteristic
454C2×C42C23×C1111yescharacteristic
455C2×C42C23×C1111yescharacteristic
456#107—22no—
457#106D4×C1114yes—
458C4⋊C8—22no—
459#103—22no—
460#103—22no—
461#103—22no—
462#103—41no—
463#103—41no—
464#103—41no—
465#102—22no—
466#102—41no—
467#97—22no—
468#97C2×C4×C1114yescomplemented
469C4×C8—22no—
470#95—21no—
471#95—21no—
472#95—21no—
473#95—21no—
474#95—21no—
475#95—21no—
476#95—21no—
477#95—21no—
478#95D4×C1111yescharacteristic
479#95D4×C1111yescharacteristic
480C2×C11—82no—
481C2×C11#236611yescharacteristic
482C2×C11C4×#13711yescharacteristic
483C2×C11#294711yescharacteristic
484C2×C11#326611yescharacteristic
485C2×C11#326911yescharacteristic
486C2×C11#339811yescharacteristic
487C2×C11#340111yescharacteristic
488C24—21no—
489C2×Q8—21no—
490C2×Q8—21no—
491C2×Q8—21no—
492C2×Q8—21no—
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8—21no—
499C2×Q8—21no—
500C2×Q8—21no—
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8—21no—
504C2×Q8C22×C4×C1112yes—
505C2×Q8C22×C4×C1112yes—
506C2×Q8C22×C4×C1112yes—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—21no—
512C2×D4C22×C4×C1112yes—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—42no—
521C22×C4—42no—
522C22×C4—81no—
523C22×C4C2×D4×C1111yescharacteristic
524C22×C4C2×D4×C1111yescharacteristic
525C22×C4C2×D4×C1111yescharacteristic
526C22×C4C2×D4×C1111yescharacteristic
527C22×C4C2×D4×C1111yescharacteristic
528C22×C4C2×D4×C1111yescharacteristic
529C22×C4C24×C1111yescharacteristic
530Q16—28no—
531Q16—44no—
532SD16—28no—
533SD16—44no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8C22×C4×C1112yes—
543C2×C8C22×C4×C1112yes—
544C2×C8C2×D4×C1112yes—
545C2×C8C11×#4112yes—
546C4⋊C4—24no—
547C4⋊C4—24no—
548C4⋊C4—22no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—41no—
556C4⋊C4—42no—
557C4⋊C4—42no—
558C4⋊C4—42no—
559C4⋊C4C2×D4×C1112yes—
560C4⋊C4C2×D4×C1112yes—
561C22⋊C4—24no—
562C22⋊C4—24no—
563C22⋊C4—42no—
564C22⋊C4—42no—
565C22⋊C4—81no—
566C42—21no—
567C42—21no—
568C42—21no—
569C42—21no—
570C42—42no—
571C42—42no—
572C42—42no—
573C42—42no—
574C42—81no—
575C42C22×C4×C1112yes—
576C42C11×#4112yes—
577C11#2319211yescharacteristic, direct product factor, Sylow
578C23—22no—
579C23—41no—
580C23—41no—
581C23—41no—
582C23—41no—
583C23—41no—
584C23—41no—
585C23C22×D4×C1111yescharacteristic
586Q8—22no—
587Q8—22no—
588Q8—22no—
589Q8—22no—
590Q8—22no—
591Q8—22no—
592Q8—41no—
593Q8—41no—
594Q8—41no—
595Q8—41no—
596Q8—41no—
597Q8—41no—
598D4—22no—
599D4—22no—
600D4—41no—
601D4—41no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—22no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—84no—
639C2×C4C4×D4×C1112yes—
640C2×C4C4×D4×C1112yes—
641C2×C4C11×#13712yes—
642C2×C4C23×C4×C1111yescharacteristic
643C2×C4C22×D4×C1111yescharacteristic
644C2×C4C2×C11×#4111yescharacteristic
645C2×C4C2×C11×#4111yescharacteristic
646C2×C4C11×H(5,𝔽2)11yescharacteristic
647C2×C4C11×H(5,𝔽2)11yescharacteristic
648C8—22no—
649C8—41no—
650C8—41no—
651C8C4×D4×C1114yes—
652C22—42no—
653C22—42no—
654C22—42no—
655C22—81no—
656C22—81no—
657C22—81no—
658C22—81no—
659C22C2×C4×D4×C1111yescharacteristic
660C22D42×C1111yescharacteristic
661C22C11×#55011yescharacteristic
662C22C2×C11×#13711yescharacteristic
663C22C11×#57511yescharacteristic
664C22C11×#57711yescharacteristic
665C22C11×#57811yescharacteristic
666C4—22no—
667C4—22no—
668C4—22no—
669C4—41no—
670C4—42no—
671C4—41no—
672C4—41no—
673C4—42no—
674C4—42no—
675C4—42no—
676C4—42no—
677C4—81no—
678C4—81no—
679C4C2×C4×D4×C1111yescharacteristic
680C4C11×#51811yescharacteristic
681C4C11×#55011yescharacteristic
682C4C11×#55911yescharacteristic
683C2—82no—
684C2C11×#236611yescharacteristic
685C2C4×C11×#13711yescharacteristic
686C2C11×#294711yescharacteristic
687C2C11×#326611yescharacteristic
688C2C11×#326911yescharacteristic
689C2C11×#339811yescharacteristic
690C2C11×#340111yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC22×D4×C11C23
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C4×C11×C4⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#441C2semidirect
5. C11×#2365C2semidirect
7. C11×#1981C2semidirect
9. C11×#1969C2semidirect
11. C11×#1878C2semidirect
12. C11×#1878C2semidirect
14. C11×#1776C2semidirect
15. C11×#1771C2semidirect
26. C11×#497C4semidirect
71. C2×C11×Q16C2×C4semidirect
72. C2×C11×Q16C2×C4semidirect
84. C11×C4⋊Q8C2×C4semidirect
131. C11×#97C2×C4semidirect
143. #23192C11direct (N × H)
234. C2×#441C2×C11semidirect
237. #2365C2×C11semidirect
239. #1981C2×C11semidirect
241. #1969C2×C11semidirect
243. #1878C2×C11semidirect
244. #1878C2×C11semidirect
246. #1776C2×C11semidirect
247. #1771C2×C11semidirect
332. #497C4×C11semidirect
408. C2×Q16C2×C4×C11semidirect
409. C2×Q16C2×C4×C11semidirect
421. C4⋊Q8C2×C4×C11semidirect
468. #97C2×C4×C11semidirect
577. C11#23192direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4972
C2×C11×#4412
C2×C4×C11×SD162
C11×#23672
C11×#23652
C11×#19832
C11×#19812
C11×#19732
C11×#19692
C11×#18802
C11×#18782
C11×#18772
C11×#17762
C11×#17712
#2319211