Finite Group Databasebeta

← C11×#22776 #14599969

Subgroups — C11×#22776 #14599969

Order 2816.

866 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#440C211yesmaximal, characteristic
2C11×#2355C211yesmaximal, characteristic, complemented
3C11×#2349C211yesmaximal, characteristic
4C11×#1935C211yesmaximal, characteristic, complemented
5C11×#1933C211yesmaximal, characteristic, complemented
6C11×#1921C211yesmaximal, characteristic, complemented
7C11×#1918C211yesmaximal, characteristic, complemented
8C11×#1877C211yesmaximal, characteristic
9C11×#1877C211yesmaximal, characteristic
10C11×#1836C211yesmaximal, characteristic, complemented
11C11×#1805C211yesmaximal, characteristic, complemented
12C11×#1802C211yesmaximal, characteristic
13C11×#1771C211yesmaximal, characteristic, complemented
14C11×#1762C211yesmaximal, characteristic
15C4×C11×#102C211yesmaximal, characteristic
16C22×C11×SD16C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C2×C4×D4×C11C2211yescharacteristic
19C2×C4×D4×C11C2211yescharacteristic
20C2×C4×D4×C11C2211yescharacteristic
21C11×#440C418yescomplemented
22C2×C11×#107C2211yescharacteristic
23C2×C11×C4⋊C8C2211yescharacteristic
24C2×C11×#103C2211yescharacteristic
25C2×C11×#103C2211yescharacteristic
26C2×C11×#103C2211yescharacteristic
27C2×C11×#102C2211yescharacteristic
28C2×C11×#102C2211yescharacteristic
29C2×C11×#102C2211yescharacteristic
30C2×C11×#97C2211yescharacteristic
31C2×C11×#97C2211yescharacteristic
32C2×C4×C8×C11C2211yescharacteristic
33C11×#391C2211yescharacteristic
34C11×#391C2211yescharacteristic
35C11×#389C2211yescharacteristic
36C11×#389C2211yescharacteristic
37C11×#387—21no—
38C11×#387—21no—
39C11×#385—21no—
40C11×#385—21no—
41C11×#384C2211yescharacteristic
42C11×#382—21no—
43C11×#382C2211yescharacteristic
44C11×#380—21no—
45C4×C11×C4⋊C4—21no—
46C4×C11×C4⋊C4C2211yescharacteristic
47C4×C11×C4⋊C4C2211yescharacteristic
48C4×C11×C4⋊C4C2211yescharacteristic
49C2×C11×#95—21no—
50C11×#340C2211yescharacteristic
51C11×#340C2211yescharacteristic
52C11×#340C2211yescharacteristic
53C11×#340C2211yescharacteristic
54C11×#340C2211yescharacteristic
55C11×#340C2211yescharacteristic
56C11×#340C2211yescharacteristic
57C11×#340C2211yescharacteristic
58C11×#336C2211yescharacteristic
59C11×#336C2211yescharacteristic
60C22×Q8×C11C2311yescharacteristic
61C22×D4×C11C2311yescharacteristic
62C23×C4×C11—21no—
63C23×C4×C11—21no—
64C23×C4×C11—21no—
65C2×C11×SD16—22no—
66C2×C11×SD16—22no—
67C2×C11×SD16C2×C414yes—
68C22×C8×C11C2311yescharacteristic
69C22×C8×C11C2311yescharacteristic
70C22×C8×C11C2311yescharacteristic
71C22×C8×C11C2311yescharacteristic
72C4×Q8×C11—22no—
73C4×Q8×C11C2×C414yescomplemented
74C4×D4×C11—22no—
75C4×D4×C11—22no—
76C4×D4×C11—22no—
77C4×D4×C11—41no—
78C4×D4×C11—41no—
79C4×D4×C11C2×C414yes—
80C2×C11×C4⋊C4—21no—
81C2×C11×C4⋊C4—21no—
82C2×C11×C4⋊C4—21no—
83C2×C11×C4⋊C4—21no—
84C2×C11×C4⋊C4—21no—
85C2×C11×C4⋊C4D411yescharacteristic
86C2×C11×C4⋊C4D411yescharacteristic
87C2×C11×C4⋊C4C2311yescharacteristic
88C2×C11×C4⋊C4C2311yescharacteristic
89C2×C11×C4⋊C4C2311yescharacteristic
90C2×C11×C4⋊C4C2311yescharacteristic
91C2×C11×C4⋊C4C2311yescharacteristic
92C2×C11×C4⋊C4C2311yescharacteristic
93C2×C11×C22⋊C4—21no—
94C2×C11×C22⋊C4—21no—
95C2×C11×C22⋊C4—21no—
96C2×C42×C11—21no—
97C2×C42×C11—21no—
98C2×C42×C11—21no—
99C2×C42×C11C2311yescharacteristic
100C2×C42×C11C2311yescharacteristic
101C2×C42×C11C2311yescharacteristic
102C11×#107C2×C414yescomplemented
103C11×C4⋊C8—22no—
104C11×#103—41no—
105C11×#103—41no—
106C11×#103C2×C414yescomplemented
107C11×#102—22no—
108C11×#102—22no—
109C11×#102C2×C414yes—
110C11×#97—41no—
111C11×#97C2×C414yescomplemented
112C4×C8×C11—41no—
113C11×#95—21no—
114C11×#95—21no—
115C11×#95—21no—
116C11×#95—21no—
117C11×#95—21no—
118C11×#95—21no—
119C11×#95—21no—
120C11×#95—21no—
121C11×#95—21no—
122C11×#95—21no—
123C11×#95D411yescharacteristic
124C11×#95D411yescharacteristic
125#22776C1111yesmaximal, characteristic, direct product factor, Sylow
126C24×C11—21no—
127C2×Q8×C11—21no—
128C2×Q8×C11—21no—
129C2×Q8×C11—21no—
130C2×Q8×C11—21no—
131C2×Q8×C11—21no—
132C2×Q8×C11C22×C412yes—
133C2×D4×C11—21no—
134C2×D4×C11—21no—
135C2×D4×C11—21no—
136C2×D4×C11C22×C412yes—
137C2×D4×C11#4112yes—
138C2×D4×C11#4112yes—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—24no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—42no—
148C22×C4×C11—42no—
149C22×C4×C11—42no—
150C22×C4×C11—42no—
151C22×C4×C11—81no—
152C22×C4×C11—81no—
153C22×C4×C11—81no—
154C22×C4×C11—81no—
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2×D411yescharacteristic
159C22×C4×C11C2×D411yescharacteristic
160C22×C4×C11C2×D411yescharacteristic
161C22×C4×C11C2411yescharacteristic
162C11×SD16—28no—
163C2×C8×C11—21no—
164C2×C8×C11—21no—
165C2×C8×C11—21no—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C2×C8×C11—21no—
172C2×C8×C11—21no—
173C2×C8×C11C22×C412yes—
174C2×C8×C11C22×C412yes—
175C11×C4⋊C4—24no—
176C11×C4⋊C4—22no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—21no—
186C11×C4⋊C4—21no—
187C11×C4⋊C4—41no—
188C11×C4⋊C4—42no—
189C11×C4⋊C4—81no—
190C11×C4⋊C4—81no—
191C11×C4⋊C4—81no—
192C11×C4⋊C4C22×C412yes—
193C11×C4⋊C4C22×C412yes—
194C11×C22⋊C4—24no—
195C11×C22⋊C4—42no—
196C11×C22⋊C4—42no—
197C42×C11—24no—
198C42×C11—21no—
199C42×C11—21no—
200C42×C11—21no—
201C42×C11—21no—
202C42×C11—81no—
203C42×C11—81no—
204C42×C11C22×C412yes—
205C42×C11#4112yes—
206C2×#440C2×C1111yescharacteristic
207#2355C2×C1111yescharacteristic, complemented
208#2349C2×C1111yescharacteristic
209#1935C2×C1111yescharacteristic, complemented
210#1933C2×C1111yescharacteristic, complemented
211#1921C2×C1111yescharacteristic, complemented
212#1918C2×C1111yescharacteristic, complemented
213#1877C2×C1111yescharacteristic
214#1877C2×C1111yescharacteristic
215#1836C2×C1111yescharacteristic, complemented
216#1805C2×C1111yescharacteristic, complemented
217#1802C2×C1111yescharacteristic
218#1771C2×C1111yescharacteristic, complemented
219#1762C2×C1111yescharacteristic
220C4×#102C2×C1111yescharacteristic
221C23×C11—22no—
222C23×C11—22no—
223C23×C11—22no—
224C23×C11—41no—
225C23×C11—41no—
226C23×C11—41no—
227C23×C11—41no—
228C23×C11C22×D411yescharacteristic
229Q8×C11—22no—
230Q8×C11—22no—
231Q8×C11—41no—
232Q8×C11—41no—
233D4×C11—22no—
234D4×C11—22no—
235D4×C11—22no—
236D4×C11#11714yes—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—22no—
244C2×C4×C11—22no—
245C2×C4×C11—22no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11—41no—
266C2×C4×C11—41no—
267C2×C4×C11—41no—
268C2×C4×C11—41no—
269C2×C4×C11—41no—
270C2×C4×C11—41no—
271C2×C4×C11—41no—
272C2×C4×C11—41no—
273C2×C4×C11—84no—
274C2×C4×C11—84no—
275C2×C4×C11—84no—
276C2×C4×C11C4×D412yes—
277C2×C4×C11C4×D412yes—
278C2×C4×C11#13712yes—
279C2×C4×C11C23×C411yescharacteristic
280C2×C4×C11C2×#4111yescharacteristic
281C2×C4×C11C2×#4111yescharacteristic
282C2×C4×C11C2×#4111yescharacteristic
283C2×C4×C11H(5,𝔽2)11yescharacteristic
284C2×C4×C112−1+411yescharacteristic
285C8×C11—22no—
286C8×C11—22no—
287C8×C11—41no—
288C8×C11—41no—
289C22×SD16C22×C1111yescharacteristic
290C2×C4×Q8C22×C1111yescharacteristic
291C2×C4×D4C22×C1111yescharacteristic
292C2×C4×D4C22×C1111yescharacteristic
293C2×C4×D4C22×C1111yescharacteristic
294#440C4×C1118yescomplemented
295C2×#107C22×C1111yescharacteristic
296C2×C4⋊C8C22×C1111yescharacteristic
297C2×#103C22×C1111yescharacteristic
298C2×#103C22×C1111yescharacteristic
299C2×#103C22×C1111yescharacteristic
300C2×#102C22×C1111yescharacteristic
301C2×#102C22×C1111yescharacteristic
302C2×#102C22×C1111yescharacteristic
303C2×#97C22×C1111yescharacteristic
304C2×#97C22×C1111yescharacteristic
305C2×C4×C8C22×C1111yescharacteristic
306#391C22×C1111yescharacteristic
307#391C22×C1111yescharacteristic
308#389C22×C1111yescharacteristic
309#389C22×C1111yescharacteristic
310#387—21no—
311#387—21no—
312#385—21no—
313#385—21no—
314#384C22×C1111yescharacteristic
315#382—21no—
316#382C22×C1111yescharacteristic
317#380—21no—
318C4×C4⋊C4—21no—
319C4×C4⋊C4C22×C1111yescharacteristic
320C4×C4⋊C4C22×C1111yescharacteristic
321C4×C4⋊C4C22×C1111yescharacteristic
322C2×#95—21no—
323#340C22×C1111yescharacteristic
324#340C22×C1111yescharacteristic
325#340C22×C1111yescharacteristic
326#340C22×C1111yescharacteristic
327#340C22×C1111yescharacteristic
328#340C22×C1111yescharacteristic
329#340C22×C1111yescharacteristic
330#340C22×C1111yescharacteristic
331#336C22×C1111yescharacteristic
332#336C22×C1111yescharacteristic
333C22×C11—24no—
334C22×C11—42no—
335C22×C11—42no—
336C22×C11—42no—
337C22×C11—42no—
338C22×C11—42no—
339C22×C11—42no—
340C22×C11C2×C4×D411yescharacteristic
341C22×C11#54611yescharacteristic
342C22×C11#54811yescharacteristic
343C22×C11C2×#13711yescharacteristic
344C22×C11#57511yescharacteristic
345C22×C11#57611yescharacteristic
346C22×C11#57711yescharacteristic
347C4×C11—22no—
348C4×C11—22no—
349C4×C11—22no—
350C4×C11—42no—
351C4×C11—42no—
352C4×C11—42no—
353C4×C11—41no—
354C4×C11—41no—
355C4×C11—41no—
356C4×C11—81no—
357C4×C11—81no—
358C4×C11—81no—
359C4×C11—81no—
360C4×C11C2×#11711yescharacteristic
361C4×C11#52011yescharacteristic
362C4×C11#55211yescharacteristic
363C4×C11#55311yescharacteristic
364C22×Q8C23×C1111yescharacteristic
365C22×D4C23×C1111yescharacteristic
366C23×C4—21no—
367C23×C4—21no—
368C23×C4—21no—
369C2×SD16—22no—
370C2×SD16—22no—
371C2×SD16C2×C4×C1114yes—
372C22×C8C23×C1111yescharacteristic
373C22×C8C23×C1111yescharacteristic
374C22×C8C23×C1111yescharacteristic
375C22×C8C23×C1111yescharacteristic
376C4×Q8—22no—
377C4×Q8C2×C4×C1114yescomplemented
378C4×D4—22no—
379C4×D4—22no—
380C4×D4—22no—
381C4×D4—41no—
382C4×D4—41no—
383C4×D4C2×C4×C1114yes—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4D4×C1111yescharacteristic
390C2×C4⋊C4D4×C1111yescharacteristic
391C2×C4⋊C4C23×C1111yescharacteristic
392C2×C4⋊C4C23×C1111yescharacteristic
393C2×C4⋊C4C23×C1111yescharacteristic
394C2×C4⋊C4C23×C1111yescharacteristic
395C2×C4⋊C4C23×C1111yescharacteristic
396C2×C4⋊C4C23×C1111yescharacteristic
397C2×C22⋊C4—21no—
398C2×C22⋊C4—21no—
399C2×C22⋊C4—21no—
400C2×C42—21no—
401C2×C42—21no—
402C2×C42—21no—
403C2×C42C23×C1111yescharacteristic
404C2×C42C23×C1111yescharacteristic
405C2×C42C23×C1111yescharacteristic
406#107C2×C4×C1114yescomplemented
407C4⋊C8—22no—
408#103—41no—
409#103—41no—
410#103C2×C4×C1114yescomplemented
411#102—22no—
412#102—22no—
413#102C2×C4×C1114yes—
414#97—41no—
415#97C2×C4×C1114yescomplemented
416C4×C8—41no—
417#95—21no—
418#95—21no—
419#95—21no—
420#95—21no—
421#95—21no—
422#95—21no—
423#95—21no—
424#95—21no—
425#95—21no—
426#95—21no—
427#95D4×C1111yescharacteristic
428#95D4×C1111yescharacteristic
429C2×C11—44no—
430C2×C11#235211yescharacteristic
431C2×C11C4×#13711yescharacteristic
432C2×C11#294611yescharacteristic
433C2×C11#331111yescharacteristic
434C2×C11#331411yescharacteristic
435C2×C11#337011yescharacteristic
436C2×C11#337211yescharacteristic
437C24—21no—
438C2×Q8—21no—
439C2×Q8—21no—
440C2×Q8—21no—
441C2×Q8—21no—
442C2×Q8—21no—
443C2×Q8C22×C4×C1112yes—
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—21no—
447C2×D4C22×C4×C1112yes—
448C2×D4C11×#4112yes—
449C2×D4C11×#4112yes—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—24no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—42no—
459C22×C4—42no—
460C22×C4—42no—
461C22×C4—42no—
462C22×C4—81no—
463C22×C4—81no—
464C22×C4—81no—
465C22×C4—81no—
466C22×C4C2×D4×C1111yescharacteristic
467C22×C4C2×D4×C1111yescharacteristic
468C22×C4C2×D4×C1111yescharacteristic
469C22×C4C2×D4×C1111yescharacteristic
470C22×C4C2×D4×C1111yescharacteristic
471C22×C4C2×D4×C1111yescharacteristic
472C22×C4C24×C1111yescharacteristic
473SD16—28no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8C22×C4×C1112yes—
485C2×C8C22×C4×C1112yes—
486C4⋊C4—24no—
487C4⋊C4—22no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—41no—
499C4⋊C4—42no—
500C4⋊C4—81no—
501C4⋊C4—81no—
502C4⋊C4—81no—
503C4⋊C4C22×C4×C1112yes—
504C4⋊C4C22×C4×C1112yes—
505C22⋊C4—24no—
506C22⋊C4—42no—
507C22⋊C4—42no—
508C42—24no—
509C42—21no—
510C42—21no—
511C42—21no—
512C42—21no—
513C42—81no—
514C42—81no—
515C42C22×C4×C1112yes—
516C42C11×#4112yes—
517C11#2277611yescharacteristic, direct product factor, Sylow
518C23—22no—
519C23—22no—
520C23—22no—
521C23—41no—
522C23—41no—
523C23—41no—
524C23—41no—
525C23C22×D4×C1111yescharacteristic
526Q8—22no—
527Q8—22no—
528Q8—41no—
529Q8—41no—
530D4—22no—
531D4—22no—
532D4—22no—
533D4C11×#11714yes—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—84no—
571C2×C4—84no—
572C2×C4—84no—
573C2×C4C4×D4×C1112yes—
574C2×C4C4×D4×C1112yes—
575C2×C4C11×#13712yes—
576C2×C4C23×C4×C1111yescharacteristic
577C2×C4C2×C11×#4111yescharacteristic
578C2×C4C2×C11×#4111yescharacteristic
579C2×C4C2×C11×#4111yescharacteristic
580C2×C4C11×H(5,𝔽2)11yescharacteristic
581C2×C4C11×2−1+411yescharacteristic
582C8—22no—
583C8—22no—
584C8—41no—
585C8—41no—
586C22—24no—
587C22—42no—
588C22—42no—
589C22—42no—
590C22—42no—
591C22—42no—
592C22—42no—
593C22C2×C4×D4×C1111yescharacteristic
594C22C11×#54611yescharacteristic
595C22C11×#54811yescharacteristic
596C22C2×C11×#13711yescharacteristic
597C22C11×#57511yescharacteristic
598C22C11×#57611yescharacteristic
599C22C11×#57711yescharacteristic
600C4—22no—
601C4—22no—
602C4—22no—
603C4—42no—
604C4—42no—
605C4—41no—
606C4—41no—
607C4—41no—
608C4—42no—
609C4—81no—
610C4—81no—
611C4—81no—
612C4—81no—
613C4C2×C11×#11711yescharacteristic
614C4C11×#52011yescharacteristic
615C4C11×#55211yescharacteristic
616C4C11×#55311yescharacteristic
617C2—44no—
618C2C11×#235211yescharacteristic
619C2C4×C11×#13711yescharacteristic
620C2C11×#294611yescharacteristic
621C2C11×#331111yescharacteristic
622C2C11×#331411yescharacteristic
623C2C11×#337011yescharacteristic
624C2C11×#337211yescharacteristic
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. C11×#2355C2semidirect
4. C11×#1935C2semidirect
5. C11×#1933C2semidirect
6. C11×#1921C2semidirect
7. C11×#1918C2semidirect
10. C11×#1836C2semidirect
11. C11×#1805C2semidirect
13. C11×#1771C2semidirect
21. C11×#440C4semidirect
73. C4×Q8×C11C2×C4semidirect
102. C11×#107C2×C4semidirect
106. C11×#103C2×C4semidirect
111. C11×#97C2×C4semidirect
125. #22776C11direct (N × H)
207. #2355C2×C11semidirect
209. #1935C2×C11semidirect
210. #1933C2×C11semidirect
211. #1921C2×C11semidirect
212. #1918C2×C11semidirect
215. #1836C2×C11semidirect
216. #1805C2×C11semidirect
218. #1771C2×C11semidirect
294. #440C4×C11semidirect
377. C4×Q8C2×C4×C11semidirect
406. #107C2×C4×C11semidirect
410. #103C2×C4×C11semidirect
415. #97C2×C4×C11semidirect
517. C11#22776direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4402
C11×#23552
C11×#23492
C11×#19352
C11×#19332
C11×#19212
C11×#19182
C11×#18772
C11×#18362
C11×#18052
C11×#18022
C11×#17712
C11×#17622
C4×C11×#1022
#2277611