Finite Group Databasebeta

← #14823648

Subgroups — #14823648

Order 2816.

924 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622684C211yesmaximal, characteristic, complemented
2C2×#10622627C211yesmaximal, characteristic, complemented
3#13072488C211yesmaximal, characteristic, complemented
4#13069990C211yesmaximal, characteristic, complemented
5#13069954C211yesmaximal, characteristic, complemented
6#13069926C211yesmaximal, characteristic, complemented
7#13069687C211yesmaximal, characteristic
8#13069481C211yesmaximal, characteristic, complemented
9#13069316C211yesmaximal, characteristic, complemented
10#13069312C211yesmaximal, characteristic, complemented
11#13069302C211yesmaximal, characteristic, complemented
12#13068967C211yesmaximal, characteristic, complemented
13#13068863C211yesmaximal, characteristic, complemented
14#13068485C211yesmaximal, characteristic, complemented
15C11×#2445C211yesmaximal, characteristic, complemented
16C2×C11×#127C2211yescharacteristic
17C2×C11×#123—21no—
18C2×C4×D4×C11C2211yescharacteristic
19C22×#4323C2211yescharacteristic
20C22×#4323C2211yescharacteristic
21C2×C4×D44C2211yescharacteristic
22C2×#66923C2211yescharacteristic
23C11×#394—21no—
24C11×#394—21no—
25C11×#390C2211yescharacteristic
26C11×#390C2211yescharacteristic
27C11×#390C2211yescharacteristic
28C11×#389C2211yescharacteristic
29C11×#386—21no—
30C4×C11×C4⋊C4C2211yescharacteristic
31C2×#66896C2211yescharacteristic
32C2×#66896C2211yescharacteristic
33C2×#66896C2211yescharacteristic
34C2×#66896C2211yescharacteristic
35C2×#66896C2211yescharacteristic
36C2×#66896C2211yescharacteristic
37#10622684—24no—
38#10622627—24no—
39#10622605—21no—
40#10622602—21no—
41C2×#66873C2211yescharacteristic
42C2×#66873C2211yescharacteristic
43C2×#66872C2211yescharacteristic
44C2×#66871C2211yescharacteristic
45#10622552C2211yescharacteristic
46#10622552C2211yescharacteristic
47#10622541C2211yescharacteristic
48#10622541C2211yescharacteristic
49C2×C4⋊(C11⋊C8)C2211yescharacteristic
50C2×#66867C2211yescharacteristic
51C2×#66867C2211yescharacteristic
52C2×C4×C11⋊C8C2211yescharacteristic
53#10622289—21no—
54#10622280—21no—
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622162C2211yescharacteristic
60#10622162C2211yescharacteristic
61C22×D4×C11—21no—
62C22×D4×C11—21no—
63C22×D4×C11C2311yescharacteristic
64C22×D4×C11C2311yescharacteristic
65C23×C4×C11—21no—
66C22×D44C2311yescharacteristic
67C22×C4×D11—21no—
68C11×#127—22no—
69C11×#127—41no—
70C11×#123—44no—
71C4×D4×C11—22no—
72C4×D4×C11—41no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4D411yescharacteristic
75C2×C11×C4⋊C4D411yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C22⋊C4—21no—
79C2×C11×C22⋊C4—21no—
80C2×C11×C22⋊C4—21no—
81C2×C11×C22⋊C4—21no—
82C2×C11×C22⋊C4—21no—
83C2×C11×C22⋊C4—21no—
84C2×C11×C22⋊C4—21no—
85C2×C42×C11C2311yescharacteristic
86C2×C42×C11C2311yescharacteristic
87C2×C42×C11C2311yescharacteristic
88C2×#4323—22no—
89C2×#4323—22no—
90C2×#4323—22no—
91C2×#4323—22no—
92C2×#4323—22no—
93C2×#4323—41no—
94C2×(C2×D11)⋊C4—21no—
95C2×(C2×D11)⋊C4—21no—
96C2×(C2×D11)⋊C4—21no—
97C2×(C2×D11)⋊C4—21no—
98C2×(C2×D11)⋊C4—21no—
99C2×C4⋊Dic11C2311yescharacteristic
100C2×C4⋊Dic11C2311yescharacteristic
101C2×C4⋊Dic11C2311yescharacteristic
102C2×Dic11⋊C4—21no—
103C2×Dic11⋊C4—21no—
104C2×Dic11⋊C4—21no—
105C2×Dic11⋊C4—21no—
106C22×C11⋊C8C2311yescharacteristic
107C22×C11⋊C8C2311yescharacteristic
108C22×C11⋊C8C2311yescharacteristic
109C22×C11⋊C8C2311yescharacteristic
110C4×D44—22no—
111C4×D44—41no—
112#66923—22no—
113#66923—41no—
114C11×#95—21no—
115C11×#95D411yescharacteristic
116C11×#95D411yescharacteristic
117#66896—22no—
118#66896—22no—
119#66896—22no—
120#66896—22no—
121#66896—22no—
122#66896D414yes—
123C11⋊#95—21no—
124C11⋊#95—21no—
125#66873—22no—
126#66873—22no—
127#66872—22no—
128#66871—41no—
129C4⋊(C11⋊C8)—22no—
130#66867—22no—
131#66867—22no—
132C4×C11⋊C8—22no—
133#26843—111nomaximal, Sylow
134C24×C11—21no—
135C24×C11—21no—
136C23×D11—21no—
137C2×D4×C11—21no—
138C2×D4×C11—21no—
139C2×D4×C11—21no—
140C2×D4×C11—21no—
141C2×D4×C11—21no—
142C2×D4×C11—21no—
143C2×D4×C11—21no—
144C2×D4×C11—21no—
145C2×D4×C11—21no—
146C2×D4×C11—21no—
147C2×D4×C11—21no—
148C2×D4×C11—42no—
149C2×D4×C11—42no—
150C2×D4×C11—42no—
151C2×D4×C11—42no—
152C2×D4×C11—81no—
153C2×D4×C11—81no—
154C2×D4×C11C2×D412yes—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11—42no—
158C22×C4×C11—42no—
159C22×C4×C11—81no—
160C22×C4×C11C2×D411yescharacteristic
161C22×C4×C11C2×D411yescharacteristic
162C22×C4×C11C2×D411yescharacteristic
163C22×C4×C11C2×D411yescharacteristic
164C22×C4×C11C2×D411yescharacteristic
165C22×C4×C11C2×D411yescharacteristic
166C22×C4×C11C2411yescharacteristic
167C22×Dic11—21no—
168C22×Dic11—21no—
169C22×Dic11—21no—
170C2×D44—21no—
171C2×D44—21no—
172C2×D44—21no—
173C2×D44—21no—
174C2×D44—21no—
175C2×D44#4112yes—
176C2×C4×D11—42no—
177C2×C4×D11—42no—
178C2×C4×D11—81no—
179C11×C4⋊C4—22no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—41no—
185C11×C4⋊C4—42no—
186C11×C22⋊C4—42no—
187C11×C22⋊C4—42no—
188C11×C22⋊C4—42no—
189C11×C22⋊C4—42no—
190C11×C22⋊C4—81no—
191C11×C22⋊C4—81no—
192C11×C22⋊C4—81no—
193C42×C11—21no—
194C42×C11—21no—
195C42×C11—21no—
196C42×C11—21no—
197C42×C11—21no—
198C42×C11—21no—
199#4323—28no—
200#4323—44no—
201(C2×D11)⋊C4—42no—
202(C2×D11)⋊C4—42no—
203(C2×D11)⋊C4—81no—
204(C2×D11)⋊C4—81no—
205(C2×D11)⋊C4—81no—
206C4⋊Dic11—21no—
207C4⋊Dic11—21no—
208C4⋊Dic11—21no—
209C4⋊Dic11—21no—
210C4⋊Dic11—21no—
211C4⋊Dic11C2×D412yes—
212Dic11⋊C4—42no—
213Dic11⋊C4—42no—
214Dic11⋊C4—81no—
215Dic11⋊C4—81no—
216C2×C11⋊C8—21no—
217C2×C11⋊C8—21no—
218C2×C11⋊C8—21no—
219C2×C11⋊C8—21no—
220C2×C11⋊C8—21no—
221C2×C11⋊C8—21no—
222C2×C11⋊C8—21no—
223C2×C11⋊C8—21no—
224C2×C11⋊C8—21no—
225C2×C11⋊C8C2×D412yes—
226C2×C11⋊C8#4112yes—
227C2×C11⋊C8#4112yes—
228C2×#490—111no—
229C2×#442—111no—
230#2454—111no—
231#2445D1111yescharacteristic, complemented
232#2065—111no—
233#2059—111no—
234#2054—111no—
235#2011—111no—
236#1970—111no—
237#1936—111no—
238#1936—111no—
239#1934—111no—
240#1879—111no—
241#1862—111no—
242#1770—111no—
243C23×C11—22no—
244C23×C11—41no—
245C23×C11—41no—
246C23×C11—41no—
247C23×C11—41no—
248C23×C11—41no—
249C23×C11—41no—
250C23×C11—41no—
251C23×C11—41no—
252C23×C11—41no—
253C23×C11—41no—
254C23×C11—41no—
255C23×C11—41no—
256C23×C11—41no—
257C23×C11C22×D411yescharacteristic
258C22×D11—22no—
259C22×D11—41no—
260C22×D11—41no—
261C22×D11—41no—
262C22×D11—41no—
263C22×D11—41no—
264C22×D11—41no—
265D4×C11—22no—
266D4×C11—22no—
267D4×C11—41no—
268D4×C11—41no—
269D4×C11—41no—
270D4×C11—41no—
271D4×C11—41no—
272D4×C11—41no—
273D4×C11—84no—
274D4×C11—84no—
275C2×C4×C11—21no—
276C2×C4×C11—21no—
277C2×C4×C11—21no—
278C2×C4×C11—21no—
279C2×C4×C11—21no—
280C2×C4×C11—21no—
281C2×C4×C11—21no—
282C2×C4×C11—21no—
283C2×C4×C11—21no—
284C2×C4×C11—21no—
285C2×C4×C11—21no—
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—84no—
299C2×C4×C11AGL(1,ℤ/8)12yes—
300C2×C4×C11C22×D411yescharacteristic
301C2×C4×C11C2×#4111yescharacteristic
302C2×C4×C11C2×#4111yescharacteristic
303C2×C4×C11C2×#4111yescharacteristic
304C2×C4×C11H(5,𝔽2)11yescharacteristic
305C2×C4×C112−1+411yescharacteristic
306C2×Dic11—22no—
307C2×Dic11—41no—
308C2×Dic11—41no—
309C2×Dic11—41no—
310C2×Dic11—41no—
311C2×Dic11—41no—
312C2×Dic11—41no—
313C2×Dic11—41no—
314C2×Dic11—41no—
315D44—22no—
316D44—22no—
317D44—41no—
318D44—41no—
319C4×D11—84no—
320C11⋊C8—22no—
321C11⋊C8—22no—
322C11⋊C8—22no—
323C11⋊C8—41no—
324C22×D8—111no—
325C22×D8—111no—
326C2×#127C2×D1111yescharacteristic
327C2×#125—111no—
328C2×#123—21no—
329C2×C4×D4—111no—
330C2×C4×D4C2×D1111yescharacteristic
331#490—224no—
332#442—224no—
333C2×#107—111no—
334C2×#106—111no—
335C2×C4⋊C8—111no—
336C2×#102—111no—
337C2×#102—111no—
338C2×#102—111no—
339C2×#102—111no—
340C2×#102—111no—
341C2×#102—111no—
342C2×#102—111no—
343C2×#102—111no—
344C2×#97—111no—
345C2×#97—111no—
346C2×C4×C8—111no—
347#399—221no—
348#396—221no—
349#394—21no—
350#394—21no—
351#390—111no—
352#390—111no—
353#390C2×D1111yescharacteristic
354#390C2×D1111yescharacteristic
355#390C2×D1111yescharacteristic
356#389—111no—
357#389—111no—
358#389C2×D1111yescharacteristic
359#386—21no—
360#385—221no—
361#380—221no—
362C4×C4⋊C4C2×D1111yescharacteristic
363#340—111no—
364#340—111no—
365#340—111no—
366#340—111no—
367#336—111no—
368#336—111no—
369C22×C11—42no—
370C22×C11—42no—
371C22×C11—42no—
372C22×C11—81no—
373C22×C11—81no—
374C22×C11—81no—
375C22×C11—81no—
376C22×C11—81no—
377C22×C11—81no—
378C22×C11—81no—
379C22×C11—81no—
380C22×C11—81no—
381C22×C11—81no—
382C22×C11—81no—
383C22×C11#53211yescharacteristic
384C22×C11D4211yescharacteristic
385C22×C11#54811yescharacteristic
386C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
387C22×C11#57511yescharacteristic
388C22×C11#57611yescharacteristic
389C22×C11#57611yescharacteristic
390C2×D11—42no—
391C2×D11—42no—
392C2×D11—42no—
393C2×D11—81no—
394C2×D11—81no—
395C2×D11—81no—
396C2×D11—81no—
397C4×C11—22no—
398C4×C11—41no—
399C4×C11—41no—
400C4×C11—41no—
401C4×C11—41no—
402C4×C11—41no—
403C4×C11—81no—
404C4×C11—81no—
405C4×C11#52511yescharacteristic
406C4×C11#54211yescharacteristic
407C4×C11#54711yescharacteristic
408C4×C11#55111yescharacteristic
409Dic11—42no—
410Dic11—81no—
411Dic11—81no—
412C22×D4—21no—
413C22×D4—21no—
414C22×D4—111no—
415C22×D4C22×D1111yescharacteristic
416C22×D4C22×D1111yescharacteristic
417C23×C4—21no—
418C23×C4—221no—
419C2×D8—222no—
420C2×D8—222no—
421C2×D8—222no—
422C2×D8—222no—
423C2×D8—222no—
424C2×D8—441no—
425C22×C8—111no—
426C22×C8—111no—
427C22×C8—111no—
428C22×C8—111no—
429#127—22no—
430#127—41no—
431#125—222no—
432#125—441no—
433#123—44no—
434C4×D4—22no—
435C4×D4—41no—
436C4×D4—222no—
437C4×D4—441no—
438C2×C4⋊C4—21no—
439C2×C4⋊C4—111no—
440C2×C4⋊C4—111no—
441C2×C4⋊C4—111no—
442C2×C4⋊C4—221no—
443C2×C4⋊C4—221no—
444C2×C4⋊C4—221no—
445C2×C4⋊C4—221no—
446C2×C4⋊C4C22⋊D1111yescharacteristic
447C2×C4⋊C4C22⋊D1111yescharacteristic
448C2×C4⋊C4C22×D1111yescharacteristic
449C2×C4⋊C4C22×D1111yescharacteristic
450C2×C22⋊C4—21no—
451C2×C22⋊C4—21no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—21no—
455C2×C22⋊C4—21no—
456C2×C22⋊C4—21no—
457C2×C22⋊C4—221no—
458C2×C22⋊C4—221no—
459C2×C22⋊C4—221no—
460C2×C22⋊C4—221no—
461C2×C22⋊C4—221no—
462C2×C42C22×D1111yescharacteristic
463C2×C42C22×D1111yescharacteristic
464C2×C42C22×D1111yescharacteristic
465#107—441no—
466#106—222no—
467C4⋊C8—222no—
468#102—114no—
469#102—222no—
470#102—222no—
471#102—222no—
472#102—222no—
473#102—222no—
474#102—222no—
475#102—222no—
476#97—222no—
477#97—222no—
478C4×C8—222no—
479#95—21no—
480#95—221no—
481#95—221no—
482#95C22⋊D1111yescharacteristic
483#95C22⋊D1111yescharacteristic
484C2×C11—82no—
485C2×C11—161no—
486C2×C11#246111yescharacteristic
487C2×C11#317611yescharacteristic
488C2×C11#318011yescharacteristic
489C2×C11#327311yescharacteristic
490C2×C11#327411yescharacteristic
491C2×C11#336611yescharacteristic
492C2×C11#337011yescharacteristic
493D11—82no—
494C24—21no—
495C24—21no—
496C24—221no—
497C2×D4—21no—
498C2×D4—21no—
499C2×D4—21no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4—42no—
509C2×D4—42no—
510C2×D4—42no—
511C2×D4—42no—
512C2×D4—81no—
513C2×D4—81no—
514C2×D4—112no—
515C2×D4—221no—
516C2×D4—221no—
517C2×D4—221no—
518C2×D4—221no—
519C2×D4—221no—
520C2×D4D4×D1112yes—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—42no—
524C22×C4—42no—
525C22×C4—81no—
526C22×C4—221no—
527C22×C4—221no—
528C22×C4—221no—
529C22×C4—442no—
530C22×C4—442no—
531C22×C4—881no—
532C22×C4C2×C22⋊D1111yescharacteristic
533C22×C4C2×C22⋊D1111yescharacteristic
534C22×C4C2×C22⋊D1111yescharacteristic
535C22×C4C2×C22⋊D1111yescharacteristic
536C22×C4C2×C22⋊D1111yescharacteristic
537C22×C4C2×C22⋊D1111yescharacteristic
538C22×C4C23×D1111yescharacteristic
539D8—228no—
540D8—444no—
541C2×C8—112no—
542C2×C8—112no—
543C2×C8—112no—
544C2×C8—221no—
545C2×C8—221no—
546C2×C8—221no—
547C2×C8—221no—
548C2×C8—221no—
549C2×C8—221no—
550C2×C8—221no—
551C2×C8—221no—
552C2×C8—221no—
553C4⋊C4—22no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—41no—
559C4⋊C4—42no—
560C4⋊C4—112no—
561C4⋊C4—221no—
562C4⋊C4—221no—
563C4⋊C4—221no—
564C4⋊C4—221no—
565C4⋊C4—221no—
566C4⋊C4—442no—
567C4⋊C4—442no—
568C4⋊C4—881no—
569C4⋊C4—881no—
570C22⋊C4—42no—
571C22⋊C4—42no—
572C22⋊C4—42no—
573C22⋊C4—42no—
574C22⋊C4—81no—
575C22⋊C4—81no—
576C22⋊C4—81no—
577C22⋊C4—442no—
578C22⋊C4—442no—
579C22⋊C4—881no—
580C22⋊C4—881no—
581C22⋊C4—881no—
582C42—21no—
583C42—21no—
584C42—21no—
585C42—21no—
586C42—21no—
587C42—21no—
588C11#2684311yescharacteristic, complemented, Sylow
589C23—22no—
590C23—41no—
591C23—41no—
592C23—41no—
593C23—41no—
594C23—41no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23—41no—
601C23—41no—
602C23—41no—
603C23—222no—
604C23—441no—
605C23—441no—
606C23—441no—
607C23—441no—
608C23—441no—
609C23—441no—
610C23C22×C22⋊D1111yescharacteristic
611D4—22no—
612D4—22no—
613D4—41no—
614D4—41no—
615D4—41no—
616D4—41no—
617D4—41no—
618D4—41no—
619D4—84no—
620D4—84no—
621D4—222no—
622D4—222no—
623D4—441no—
624D4—441no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—84no—
649C2×C4—222no—
650C2×C4—441no—
651C2×C4—441no—
652C2×C4—441no—
653C2×C4—441no—
654C2×C4—441no—
655C2×C4—441no—
656C2×C4—441no—
657C2×C4—441no—
658C2×C4—884no—
659C2×C4#6698512yes—
660C2×C4C2×D4×D1111yescharacteristic
661C2×C4#6703711yescharacteristic
662C2×C4#41×D1111yescharacteristic
663C2×C4#41×D1111yescharacteristic
664C2×C4#41×D1111yescharacteristic
665C2×C4#6704311yescharacteristic
666C8—222no—
667C8—222no—
668C8—222no—
669C8—441no—
670C22—42no—
671C22—42no—
672C22—42no—
673C22—81no—
674C22—81no—
675C22—81no—
676C22—81no—
677C22—81no—
678C22—81no—
679C22—81no—
680C22—81no—
681C22—81no—
682C22—81no—
683C22—81no—
684C22—442no—
685C22—442no—
686C22—442no—
687C22—881no—
688C22—881no—
689C22—881no—
690C22—881no—
691C22C2×#6698511yescharacteristic
692C22D4×C22⋊D1111yescharacteristic
693C22#1062335311yescharacteristic
694C22#1062336211yescharacteristic
695C22#1062336311yescharacteristic
696C22#1062336611yescharacteristic
697C22#1062336611yescharacteristic
698C4—22no—
699C4—41no—
700C4—41no—
701C4—41no—
702C4—41no—
703C4—41no—
704C4—81no—
705C4—81no—
706C4—442no—
707C4—881no—
708C4—881no—
709C4#1062318611yescharacteristic
710C4#1062318711yescharacteristic
711C4#1062319011yescharacteristic
712C4#1062319311yescharacteristic
713C2—82no—
714C2—161no—
715C2—882no—
716C2#1307258211yescharacteristic
717C2#1307926011yescharacteristic
718C2#1307930811yescharacteristic
719C2#1308022311yescharacteristic
720C2#1308023211yescharacteristic
721C2#1308131911yescharacteristic
722C2#1308136311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2445C2
socleC23×C11C22×D4
prime radical#13069687C2
hypercenter#2445D11
hypocenterC11#26843
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2445

Complements

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

NH ≅ G/Ntype
1. C2×#10622684C2semidirect
2. C2×#10622627C2semidirect
3. #13072488C2semidirect
4. #13069990C2semidirect
5. #13069954C2semidirect
6. #13069926C2semidirect
8. #13069481C2semidirect
9. #13069316C2semidirect
10. #13069312C2semidirect
11. #13069302C2semidirect
12. #13068967C2semidirect
13. #13068863C2semidirect
14. #13068485C2semidirect
15. C11×#2445C2semidirect
231. #2445D11semidirect
588. C11#26843semidirect

Maximal subgroups

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

subgroupindex
C2×#106226842
C2×#106226272
#130724882
#130699902
#130699542
#130699262
#130696872
#130694812
#130693162
#130693122
#130693022
#130689672
#130688632
#130684852
C11×#24452
#2684311