Finite Group Databasebeta

← C11×#26177 #14603370

Subgroups — C11×#26177 #14603370

Order 2816.

834 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#464C211yesmaximal, characteristic
2C2×C11×#440C211yesmaximal, characteristic
3C11×#2447C211yesmaximal, characteristic
4Q8×C11×C4⋊C4C211yesmaximal, characteristic, complemented
5C11×#2095C211yesmaximal, characteristic, complemented
6C11×#2086C211yesmaximal, characteristic, complemented
7C11×#2071C211yesmaximal, characteristic
8C11×#2042C211yesmaximal, characteristic
9C11×#1935C211yesmaximal, characteristic, complemented
10C11×#1917C211yesmaximal, characteristic, complemented
11C11×#1880C211yesmaximal, characteristic
12C11×#1878C211yesmaximal, characteristic, complemented
13C11×#1878C211yesmaximal, characteristic, complemented
14C11×#1863C211yesmaximal, characteristic, complemented
15C11×#1862C211yesmaximal, characteristic
16C22×C11×Q16C2211yescharacteristic
17C22×C11×SD16C2211yescharacteristic
18C2×C11×#124C2211yescharacteristic
19C2×C4×Q8×C11C2211yescharacteristic
20C2×C4×Q8×C11C2211yescharacteristic
21C2×C4×Q8×C11C2211yescharacteristic
22C2×C4×D4×C11C2211yescharacteristic
23C11×#464—24no—
24C11×#440—24no—
25C2×C11×#107C2211yescharacteristic
26C2×C11×#107C2211yescharacteristic
27C2×C11×C4⋊C8C2211yescharacteristic
28C2×C11×#103C2211yescharacteristic
29C2×C11×#103C2211yescharacteristic
30C2×C11×#103C2211yescharacteristic
31C2×C11×#103C2211yescharacteristic
32C2×C11×#103C2211yescharacteristic
33C2×C11×#102C2211yescharacteristic
34C2×C11×#102C2211yescharacteristic
35C2×C11×#102C2211yescharacteristic
36C2×C11×#97C2211yescharacteristic
37C11×#397—21no—
38C11×#397—21no—
39C11×#391C2211yescharacteristic
40C11×#391C2211yescharacteristic
41C11×#390C2211yescharacteristic
42C11×#389—21no—
43C11×#389—21no—
44C11×#389C2211yescharacteristic
45C11×#389C2211yescharacteristic
46C11×#389C2211yescharacteristic
47C11×#385—21no—
48C11×#384—21no—
49C11×#384C2211yescharacteristic
50C11×#381—21no—
51C4×C11×C4⋊C4—21no—
52C4×C11×C4⋊C4C2211yescharacteristic
53C11×#340C2211yescharacteristic
54C11×#340C2211yescharacteristic
55C11×#340C2211yescharacteristic
56C11×#340C2211yescharacteristic
57C11×#336C2211yescharacteristic
58C11×#336C2211yescharacteristic
59C11×#336C2211yescharacteristic
60C11×#336C2211yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C22×Q8×C11C2311yescharacteristic
63C22×D4×C11C2311yescharacteristic
64C23×C4×C11—21no—
65C2×C11×Q16—22no—
66C2×C11×Q16—22no—
67C2×C11×Q16—22no—
68C2×C11×SD16—22no—
69C2×C11×SD16—22no—
70C2×C11×SD16D414yes—
71C22×C8×C11C2311yescharacteristic
72C22×C8×C11C2311yescharacteristic
73C22×C8×C11C2311yescharacteristic
74C22×C8×C11C2311yescharacteristic
75C11×#124—22no—
76C11×#124—41no—
77C4×Q8×C11—22no—
78C4×Q8×C11—22no—
79C4×Q8×C11—22no—
80C4×Q8×C11—22no—
81C4×Q8×C11—41no—
82C4×Q8×C11—41no—
83C4×D4×C11—22no—
84C4×D4×C11—41no—
85C2×C11×C4⋊C4—21no—
86C2×C11×C4⋊C4—21no—
87C2×C11×C4⋊C4—21no—
88C2×C11×C4⋊C4—21no—
89C2×C11×C4⋊C4—21no—
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×C42×C11—21no—
106C2×C42×C11—21no—
107C2×C42×C11—21no—
108C2×C42×C11C2311yescharacteristic
109C2×C42×C11C2311yescharacteristic
110C2×C42×C11C2311yescharacteristic
111C11×#107—22no—
112C11×#107—41no—
113C11×C4⋊C8—22no—
114C11×#103—22no—
115C11×#103—22no—
116C11×#103—22no—
117C11×#103—22no—
118C11×#103—41no—
119C11×#102—22no—
120C11×#102—22no—
121C11×#102—22no—
122C11×#97—22no—
123C11×#95—21no—
124C11×#95—21no—
125C11×#95—21no—
126C11×#95—21no—
127C11×#95—21no—
128C11×#95—21no—
129C11×#95—21no—
130C11×#95D411yescharacteristic
131C11×#95D411yescharacteristic
132#26177C1111yesmaximal, characteristic, direct product factor, Sylow
133C24×C11—21no—
134C2×Q8×C11—21no—
135C2×Q8×C11—21no—
136C2×Q8×C11—21no—
137C2×Q8×C11—21no—
138C2×Q8×C11—21no—
139C2×Q8×C11—21no—
140C2×Q8×C11—21no—
141C2×Q8×C11—21no—
142C2×Q8×C11—21no—
143C2×Q8×C11C2×D412yes—
144C2×Q8×C11#4112yes—
145C2×Q8×C11#4112yes—
146C2×D4×C11—21no—
147C2×D4×C11—21no—
148C2×D4×C11—21no—
149C2×D4×C11—21no—
150C2×D4×C11—21no—
151C2×D4×C11C2×D412yes—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—42no—
160C22×C4×C11—42no—
161C22×C4×C11—81no—
162C22×C4×C11C2×D411yescharacteristic
163C22×C4×C11C2×D411yescharacteristic
164C22×C4×C11C2×D411yescharacteristic
165C22×C4×C11C2×D411yescharacteristic
166C22×C4×C11C2×D411yescharacteristic
167C22×C4×C11C2×D411yescharacteristic
168C22×C4×C11C2411yescharacteristic
169C11×Q16—44no—
170C11×SD16—28no—
171C2×C8×C11—21no—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C2×C8×C11—21no—
179C2×C8×C11—21no—
180C2×C8×C11—21no—
181C2×C8×C11—21no—
182C2×C8×C11C2×D412yes—
183C11×C4⋊C4—24no—
184C11×C4⋊C4—22no—
185C11×C4⋊C4—21no—
186C11×C4⋊C4—21no—
187C11×C4⋊C4—21no—
188C11×C4⋊C4—21no—
189C11×C4⋊C4—21no—
190C11×C4⋊C4—21no—
191C11×C4⋊C4—21no—
192C11×C4⋊C4—21no—
193C11×C4⋊C4—21no—
194C11×C4⋊C4—41no—
195C11×C4⋊C4—42no—
196C11×C4⋊C4—42no—
197C11×C4⋊C4—42no—
198C11×C4⋊C4—81no—
199C11×C4⋊C4—81no—
200C11×C4⋊C4—81no—
201C11×C4⋊C4—81no—
202C11×C4⋊C4#4112yes—
203C11×C22⋊C4—42no—
204C11×C22⋊C4—42no—
205C11×C22⋊C4—42no—
206C11×C22⋊C4—42no—
207C11×C22⋊C4—81no—
208C42×C11—24no—
209C42×C11—21no—
210C42×C11—21no—
211C42×C11—21no—
212C42×C11—21no—
213C42×C11—21no—
214C42×C11—21no—
215C42×C11—42no—
216C42×C11—42no—
217C2×#464C2×C1111yescharacteristic
218C2×#440C2×C1111yescharacteristic
219#2447C2×C1111yescharacteristic
220Q8×C4⋊C4C2×C1111yescharacteristic, complemented
221#2095C2×C1111yescharacteristic, complemented
222#2086C2×C1111yescharacteristic, complemented
223#2071C2×C1111yescharacteristic
224#2042C2×C1111yescharacteristic
225#1935C2×C1111yescharacteristic, complemented
226#1917C2×C1111yescharacteristic, complemented
227#1880C2×C1111yescharacteristic
228#1878C2×C1111yescharacteristic, complemented
229#1878C2×C1111yescharacteristic, complemented
230#1863C2×C1111yescharacteristic, complemented
231#1862C2×C1111yescharacteristic
232C23×C11—22no—
233C23×C11—41no—
234C23×C11—41no—
235C23×C11—41no—
236C23×C11—41no—
237C23×C11—41no—
238C23×C11—41no—
239C23×C11C22×D411yescharacteristic
240Q8×C11—22no—
241Q8×C11—22no—
242Q8×C11—22no—
243Q8×C11—41no—
244Q8×C11—41no—
245Q8×C11—41no—
246Q8×C11—41no—
247Q8×C11#12314yes—
248D4×C11—22no—
249D4×C11—22no—
250D4×C11—41no—
251D4×C11—41no—
252C2×C4×C11—21no—
253C2×C4×C11—22no—
254C2×C4×C11—22no—
255C2×C4×C11—22no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—22no—
259C2×C4×C11—21no—
260C2×C4×C11—21no—
261C2×C4×C11—21no—
262C2×C4×C11—21no—
263C2×C4×C11—21no—
264C2×C4×C11—21no—
265C2×C4×C11—21no—
266C2×C4×C11—21no—
267C2×C4×C11—21no—
268C2×C4×C11—21no—
269C2×C4×C11—21no—
270C2×C4×C11—21no—
271C2×C4×C11—21no—
272C2×C4×C11—21no—
273C2×C4×C11—41no—
274C2×C4×C11—41no—
275C2×C4×C11—41no—
276C2×C4×C11—41no—
277C2×C4×C11—41no—
278C2×C4×C11—41no—
279C2×C4×C11—41no—
280C2×C4×C11—41no—
281C2×C4×C11—41no—
282C2×C4×C11—41no—
283C2×C4×C11—41no—
284C2×C4×C11—41no—
285C2×C4×C11—41no—
286C2×C4×C11—41no—
287C2×C4×C11—41no—
288C2×C4×C11—41no—
289C2×C4×C11—41no—
290C2×C4×C11—84no—
291C2×C4×C11#13712yes—
292C2×C4×C11C22×D411yescharacteristic
293C2×C4×C11C2×#4111yescharacteristic
294C2×C4×C11C2×#4111yescharacteristic
295C2×C4×C11C2×#4111yescharacteristic
296C2×C4×C11H(5,𝔽2)11yescharacteristic
297C2×C4×C112−1+411yescharacteristic
298C8×C11—22no—
299C8×C11—41no—
300C8×C11—41no—
301C8×C11—41no—
302C22×Q16C22×C1111yescharacteristic
303C22×SD16C22×C1111yescharacteristic
304C2×#124C22×C1111yescharacteristic
305C2×C4×Q8C22×C1111yescharacteristic
306C2×C4×Q8C22×C1111yescharacteristic
307C2×C4×Q8C22×C1111yescharacteristic
308C2×C4×D4C22×C1111yescharacteristic
309#464—24no—
310#440—24no—
311C2×#107C22×C1111yescharacteristic
312C2×#107C22×C1111yescharacteristic
313C2×C4⋊C8C22×C1111yescharacteristic
314C2×#103C22×C1111yescharacteristic
315C2×#103C22×C1111yescharacteristic
316C2×#103C22×C1111yescharacteristic
317C2×#103C22×C1111yescharacteristic
318C2×#103C22×C1111yescharacteristic
319C2×#102C22×C1111yescharacteristic
320C2×#102C22×C1111yescharacteristic
321C2×#102C22×C1111yescharacteristic
322C2×#97C22×C1111yescharacteristic
323#397—21no—
324#397—21no—
325#391C22×C1111yescharacteristic
326#391C22×C1111yescharacteristic
327#390C22×C1111yescharacteristic
328#389—21no—
329#389—21no—
330#389C22×C1111yescharacteristic
331#389C22×C1111yescharacteristic
332#389C22×C1111yescharacteristic
333#385—21no—
334#384—21no—
335#384C22×C1111yescharacteristic
336#381—21no—
337C4×C4⋊C4—21no—
338C4×C4⋊C4C22×C1111yescharacteristic
339#340C22×C1111yescharacteristic
340#340C22×C1111yescharacteristic
341#340C22×C1111yescharacteristic
342#340C22×C1111yescharacteristic
343#336C22×C1111yescharacteristic
344#336C22×C1111yescharacteristic
345#336C22×C1111yescharacteristic
346#336C22×C1111yescharacteristic
347C22×C11—42no—
348C22×C11—42no—
349C22×C11—42no—
350C22×C11—81no—
351C22×C11—81no—
352C22×C11—81no—
353C22×C11—81no—
354C22×C11#52511yescharacteristic
355C22×C11D4211yescharacteristic
356C22×C11#54811yescharacteristic
357C22×C11C2×#13711yescharacteristic
358C22×C11#57511yescharacteristic
359C22×C11#57611yescharacteristic
360C22×C11#57811yescharacteristic
361C4×C11—22no—
362C4×C11—24no—
363C4×C11—41no—
364C4×C11—42no—
365C4×C11—41no—
366C4×C11—41no—
367C4×C11—41no—
368C4×C11—41no—
369C4×C11—81no—
370C4×C11—81no—
371C4×C11—81no—
372C4×C11—81no—
373C4×C11—81no—
374C4×C11C2×#12311yescharacteristic
375C4×C11#53911yescharacteristic
376C4×C11#54711yescharacteristic
377C4×C11#55311yescharacteristic
378C22×Q8C23×C1111yescharacteristic
379C22×Q8C23×C1111yescharacteristic
380C22×D4C23×C1111yescharacteristic
381C23×C4—21no—
382C2×Q16—22no—
383C2×Q16—22no—
384C2×Q16—22no—
385C2×SD16—22no—
386C2×SD16—22no—
387C2×SD16D4×C1114yes—
388C22×C8C23×C1111yescharacteristic
389C22×C8C23×C1111yescharacteristic
390C22×C8C23×C1111yescharacteristic
391C22×C8C23×C1111yescharacteristic
392#124—22no—
393#124—41no—
394C4×Q8—22no—
395C4×Q8—22no—
396C4×Q8—22no—
397C4×Q8—22no—
398C4×Q8—41no—
399C4×Q8—41no—
400C4×D4—22no—
401C4×D4—41no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4D4×C1111yescharacteristic
411C2×C4⋊C4D4×C1111yescharacteristic
412C2×C4⋊C4C23×C1111yescharacteristic
413C2×C4⋊C4C23×C1111yescharacteristic
414C2×C4⋊C4C23×C1111yescharacteristic
415C2×C4⋊C4C23×C1111yescharacteristic
416C2×C4⋊C4C23×C1111yescharacteristic
417C2×C22⋊C4—21no—
418C2×C22⋊C4—21no—
419C2×C22⋊C4—21no—
420C2×C22⋊C4—21no—
421C2×C22⋊C4—21no—
422C2×C42—21no—
423C2×C42—21no—
424C2×C42—21no—
425C2×C42C23×C1111yescharacteristic
426C2×C42C23×C1111yescharacteristic
427C2×C42C23×C1111yescharacteristic
428#107—22no—
429#107—41no—
430C4⋊C8—22no—
431#103—22no—
432#103—22no—
433#103—22no—
434#103—22no—
435#103—41no—
436#102—22no—
437#102—22no—
438#102—22no—
439#97—22no—
440#95—21no—
441#95—21no—
442#95—21no—
443#95—21no—
444#95—21no—
445#95—21no—
446#95—21no—
447#95D4×C1111yescharacteristic
448#95D4×C1111yescharacteristic
449C2×C11—82no—
450C2×C11#244311yescharacteristic
451C2×C11#311711yescharacteristic
452C2×C11#312411yescharacteristic
453C2×C11#326811yescharacteristic
454C2×C11#327611yescharacteristic
455C2×C11#337511yescharacteristic
456C2×C11#337711yescharacteristic
457C24—21no—
458C2×Q8—21no—
459C2×Q8—21no—
460C2×Q8—21no—
461C2×Q8—21no—
462C2×Q8—21no—
463C2×Q8—21no—
464C2×Q8—21no—
465C2×Q8—21no—
466C2×Q8—21no—
467C2×Q8C2×D4×C1112yes—
468C2×Q8C11×#4112yes—
469C2×Q8C11×#4112yes—
470C2×D4—21no—
471C2×D4—21no—
472C2×D4—21no—
473C2×D4—21no—
474C2×D4—21no—
475C2×D4C2×D4×C1112yes—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—42no—
484C22×C4—42no—
485C22×C4—81no—
486C22×C4C2×D4×C1111yescharacteristic
487C22×C4C2×D4×C1111yescharacteristic
488C22×C4C2×D4×C1111yescharacteristic
489C22×C4C2×D4×C1111yescharacteristic
490C22×C4C2×D4×C1111yescharacteristic
491C22×C4C2×D4×C1111yescharacteristic
492C22×C4C24×C1111yescharacteristic
493Q16—44no—
494SD16—28no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8C2×D4×C1112yes—
507C4⋊C4—24no—
508C4⋊C4—22no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—41no—
519C4⋊C4—42no—
520C4⋊C4—42no—
521C4⋊C4—42no—
522C4⋊C4—81no—
523C4⋊C4—81no—
524C4⋊C4—81no—
525C4⋊C4—81no—
526C4⋊C4C11×#4112yes—
527C22⋊C4—42no—
528C22⋊C4—42no—
529C22⋊C4—42no—
530C22⋊C4—42no—
531C22⋊C4—81no—
532C42—24no—
533C42—21no—
534C42—21no—
535C42—21no—
536C42—21no—
537C42—21no—
538C42—21no—
539C42—42no—
540C42—42no—
541C11#2617711yescharacteristic, direct product factor, Sylow
542C23—22no—
543C23—41no—
544C23—41no—
545C23—41no—
546C23—41no—
547C23—41no—
548C23—41no—
549C23C22×D4×C1111yescharacteristic
550Q8—22no—
551Q8—22no—
552Q8—22no—
553Q8—41no—
554Q8—41no—
555Q8—41no—
556Q8—41no—
557Q8C11×#12314yes—
558D4—22no—
559D4—22no—
560D4—41no—
561D4—41no—
562C2×C4—21no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—22no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—84no—
601C2×C4C11×#13712yes—
602C2×C4C22×D4×C1111yescharacteristic
603C2×C4C2×C11×#4111yescharacteristic
604C2×C4C2×C11×#4111yescharacteristic
605C2×C4C2×C11×#4111yescharacteristic
606C2×C4C11×H(5,𝔽2)11yescharacteristic
607C2×C4C11×2−1+411yescharacteristic
608C8—22no—
609C8—41no—
610C8—41no—
611C8—41no—
612C22—42no—
613C22—42no—
614C22—42no—
615C22—81no—
616C22—81no—
617C22—81no—
618C22—81no—
619C22C11×#52511yescharacteristic
620C22D42×C1111yescharacteristic
621C22C11×#54811yescharacteristic
622C22C2×C11×#13711yescharacteristic
623C22C11×#57511yescharacteristic
624C22C11×#57611yescharacteristic
625C22C11×#57811yescharacteristic
626C4—24no—
627C4—22no—
628C4—41no—
629C4—41no—
630C4—41no—
631C4—41no—
632C4—41no—
633C4—42no—
634C4—81no—
635C4—81no—
636C4—81no—
637C4—81no—
638C4—81no—
639C4C2×C11×#12311yescharacteristic
640C4C11×#53911yescharacteristic
641C4C11×#54711yescharacteristic
642C4C11×#55311yescharacteristic
643C2—82no—
644C2C11×#244311yescharacteristic
645C2C11×#311711yescharacteristic
646C2C11×#312411yescharacteristic
647C2C11×#326811yescharacteristic
648C2C11×#327611yescharacteristic
649C2C11×#337511yescharacteristic
650C2C11×#337711yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC22×D4×C11C23
LCSG ▷ C22×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
4. Q8×C11×C4⋊C4C2semidirect
5. C11×#2095C2semidirect
6. C11×#2086C2semidirect
9. C11×#1935C2semidirect
10. C11×#1917C2semidirect
12. C11×#1878C2semidirect
13. C11×#1878C2semidirect
14. C11×#1863C2semidirect
132. #26177C11direct (N × H)
220. Q8×C4⋊C4C2×C11semidirect
221. #2095C2×C11semidirect
222. #2086C2×C11semidirect
225. #1935C2×C11semidirect
226. #1917C2×C11semidirect
228. #1878C2×C11semidirect
229. #1878C2×C11semidirect
230. #1863C2×C11semidirect
541. C11#26177direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4642
C2×C11×#4402
C11×#24472
Q8×C11×C4⋊C42
C11×#20952
C11×#20862
C11×#20712
C11×#20422
C11×#19352
C11×#19172
C11×#18802
C11×#18782
C11×#18632
C11×#18622
#2617711