Finite Group Databasebeta

← #14804101

Subgroups — #14804101

Order 2816.

916 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622460C211yesmaximal, characteristic, complemented
2#13073782C211yesmaximal, characteristic, complemented
3#13073529C211yesmaximal, characteristic
4#13070049C211yesmaximal, characteristic, complemented
5#13070039C211yesmaximal, characteristic, complemented
6#13069806C211yesmaximal, characteristic, complemented
7#13069806C211yesmaximal, characteristic, complemented
8#13069585C211yesmaximal, characteristic, complemented
9#13069380C211yesmaximal, characteristic, complemented
10#13069054C211yesmaximal, characteristic, complemented
11#13069044C211yesmaximal, characteristic, complemented
12#13068649C211yesmaximal, characteristic, complemented
13#13068641C211yesmaximal, characteristic, complemented
14#13068442C211yesmaximal, characteristic, complemented
15C2×C11×#435C211yesmaximal, characteristic, complemented
16C22×C11×M16C2211yescharacteristic
17C23×C8×C11C2211yescharacteristic
18C2×C4×D4×C11C2211yescharacteristic
19C2×#66991—21no—
20C2×#66983C2211yescharacteristic
21C2×#66983C2211yescharacteristic
22C2×C4×D44C2211yescharacteristic
23C2×#66923C2211yescharacteristic
24C11×#435—24no—
25C2×C11×C4⋊C8C2211yescharacteristic
26C2×C11×C22⋊C8C2211yescharacteristic
27C2×C11×C22⋊C8C2211yescharacteristic
28C2×C11×#97C2211yescharacteristic
29#10622835—21no—
30#10622825C2211yescharacteristic
31#10622825C2211yescharacteristic
32#10622825C2211yescharacteristic
33#10622825C2211yescharacteristic
34#10622825C2211yescharacteristic
35#10622825C2211yescharacteristic
36C2×#66885C2211yescharacteristic
37C2×#66885C2211yescharacteristic
38C2×#66885C2211yescharacteristic
39C2×#66885C2211yescharacteristic
40C2×#66882C2211yescharacteristic
41C2×#66881C2211yescharacteristic
42C2×#66881C2211yescharacteristic
43C2×#66881C2211yescharacteristic
44#10622600—21no—
45#10622595—21no—
46#10622574—21no—
47#10622574—21no—
48#10622558—21no—
49#10622558—21no—
50#10622548C2211yescharacteristic
51C4×C4⋊Dic11C2211yescharacteristic
52#10622460—24no—
53#10622189C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622189C2211yescharacteristic
58#10622189C2211yescharacteristic
59#10622189C2211yescharacteristic
60#10622189C2211yescharacteristic
61C22×D4×C11D411yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C22×C22⋊D11—21no—
65C22×C22⋊D11—21no—
66C22×D44C2311yescharacteristic
67C22×C4×D11—21no—
68C2×C11×M16—22no—
69C2×C11×M16—22no—
70C2×C11×M16—41no—
71C22×C8×C11—22no—
72C22×C8×C11—22no—
73C22×C8×C11—41no—
74C22×C8×C11C2311yescharacteristic
75C22×C8×C11C2311yescharacteristic
76C22×C8×C11C2311yescharacteristic
77C22×C8×C11C2311yescharacteristic
78C4×D4×C11—22no—
79C4×D4×C11—22no—
80C2×C11×C4⋊C4D411yescharacteristic
81C2×C11×C22⋊C4D411yescharacteristic
82C2×C11×C22⋊C4D411yescharacteristic
83C2×C42×C11C2311yescharacteristic
84C2×C22⋊Dic11—21no—
85C2×C22⋊Dic11—21no—
86C2×C22⋊Dic11—21no—
87C2×C22⋊Dic11—21no—
88C2×C22⋊Dic11—21no—
89C2×C22⋊Dic11—21no—
90#66991—44no—
91#66983—22no—
92#66983—22no—
93#66983—41no—
94#66983—41no—
95C2×(C2×D11)⋊C4—21no—
96C2×(C2×D11)⋊C4—21no—
97C2×(C2×D11)⋊C4—21no—
98C2×C4⋊Dic11—21no—
99C2×C4⋊Dic11—21no—
100C2×C4⋊Dic11C2311yescharacteristic
101C2×C4⋊Dic11C2311yescharacteristic
102C2×C4⋊Dic11C2311yescharacteristic
103C2×C4⋊Dic11C2311yescharacteristic
104C2×C4⋊Dic11C2311yescharacteristic
105C2×C4⋊Dic11C2311yescharacteristic
106C2×C4⋊Dic11C2311yescharacteristic
107C2×Dic11⋊C4—21no—
108C2×Dic11⋊C4—21no—
109C2×C4×Dic11—21no—
110C4×D44—22no—
111C4×D44—22no—
112#66923—22no—
113#66923—22no—
114C11×C4⋊C8D414yescomplemented
115C11×C22⋊C8—22no—
116C11×C22⋊C8—22no—
117C11×#97—22no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95—21no—
124C11⋊#95—21no—
125#66885—22no—
126#66885—22no—
127#66885—22no—
128#66885—22no—
129#66882—22no—
130#66881—22no—
131#66881—41no—
132#66881—41no—
133#25355—111nomaximal, Sylow
134C24×C11C2×D411yescharacteristic
135C24×C11C2×D411yescharacteristic
136C23×D11—21no—
137C2×D4×C11—22no—
138C2×D4×C11—22no—
139C2×D4×C11—41no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2411yescharacteristic
157C2×C22⋊D11—42no—
158C2×C22⋊D11—42no—
159C2×C22⋊D11—42no—
160C2×C22⋊D11—42no—
161C2×C22⋊D11—81no—
162C2×C22⋊D11—81no—
163C22×Dic11—21no—
164C22×Dic11—21no—
165C22×Dic11—21no—
166C22×Dic11—21no—
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—42no—
179C11×M16—44no—
180C2×C8×C11—21no—
181C2×C8×C11—21no—
182C2×C8×C11—21no—
183C2×C8×C11—21no—
184C2×C8×C11—21no—
185C2×C8×C11—21no—
186C2×C8×C11—21no—
187C2×C8×C11—21no—
188C2×C8×C11—21no—
189C2×C8×C11—44no—
190C2×C8×C11C2×D412yes—
191C2×C8×C11C2×D412yes—
192C2×C8×C11#4112yes—
193C11×C4⋊C4—22no—
194C11×C22⋊C4—22no—
195C11×C22⋊C4—22no—
196C42×C11C2×D412yes—
197C42×C11#4112yes—
198C22⋊Dic11—42no—
199C22⋊Dic11—42no—
200C22⋊Dic11—42no—
201C22⋊Dic11—42no—
202C22⋊Dic11—81no—
203C22⋊Dic11—81no—
204(C2×D11)⋊C4—42no—
205(C2×D11)⋊C4—42no—
206(C2×D11)⋊C4—42no—
207C4⋊Dic11—21no—
208C4⋊Dic11—21no—
209C4⋊Dic11—21no—
210C4⋊Dic11—21no—
211C4⋊Dic11—21no—
212C4⋊Dic11—21no—
213C4⋊Dic11—21no—
214C4⋊Dic11—21no—
215C4⋊Dic11—21no—
216C4⋊Dic11—21no—
217C4⋊Dic11—21no—
218C4⋊Dic11—21no—
219C4⋊Dic11—21no—
220C4⋊Dic11—21no—
221C4⋊Dic11—42no—
222C4⋊Dic11—81no—
223Dic11⋊C4—42no—
224Dic11⋊C4—42no—
225C4×Dic11—81no—
226C2×#478—111no—
227C2×#435D1111yescharacteristic, complemented
228#2562—111no—
229#2537—111no—
230#2077—111no—
231#2075—111no—
232#2034—111no—
233#2034—111no—
234#1992—111no—
235#1948—111no—
236#1895—111no—
237#1893—111no—
238#1809—111no—
239#1807—111no—
240#1762—111no—
241C23×C11—21no—
242C23×C11—21no—
243C23×C11—21no—
244C23×C11—21no—
245C23×C11—21no—
246C23×C11—21no—
247C23×C11—21no—
248C23×C11—21no—
249C23×C11—21no—
250C23×C11—21no—
251C23×C11—21no—
252C23×C11—21no—
253C23×C11—21no—
254C23×C11AGL(1,ℤ/8)12yes—
255C23×C11C22×D411yescharacteristic
256C22×D11—22no—
257C22×D11—41no—
258C22×D11—41no—
259C22×D11—41no—
260C22×D11—41no—
261C22×D11—41no—
262C22×D11—41no—
263D4×C11—44no—
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—21no—
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#12112yes—
283C2×C4×C11#12112yes—
284C2×C4×C11C22×D411yescharacteristic
285C2×C4×C11C2×#4111yescharacteristic
286C2×C4×C11C2×#4111yescharacteristic
287C2×C4×C11C2×#4111yescharacteristic
288C2×C4×C11H(5,𝔽2)11yescharacteristic
289C2×C4×C112−1+411yescharacteristic
290C22⋊D11—84no—
291C22⋊D11—84no—
292C2×Dic11—41no—
293C2×Dic11—41no—
294C2×Dic11—41no—
295C2×Dic11—41no—
296C2×Dic11—41no—
297C2×Dic11—41no—
298C2×Dic11—41no—
299C2×Dic11—41no—
300C2×Dic11—41no—
301C2×Dic11—41no—
302C2×Dic11—41no—
303C2×Dic11—41no—
304C2×Dic11—41no—
305C2×Dic11—41no—
306C2×Dic11—41no—
307C2×Dic11—41no—
308C2×Dic11—41no—
309C2×Dic11—41no—
310C2×Dic11—41no—
311C2×Dic11—41no—
312C2×Dic11—41no—
313D44—22no—
314D44—22no—
315D44—41no—
316D44—41no—
317C4×D11—84no—
318C8×C11—22no—
319C8×C11—22no—
320C8×C11—22no—
321C8×C11—41no—
322C22×M16C2×D1111yescharacteristic
323C23×C8C2×D1111yescharacteristic
324C2×#125—111no—
325C2×#121—111no—
326C2×#121—111no—
327C2×#121—221no—
328C2×C4×D4—111no—
329C2×C4×D4C2×D1111yescharacteristic
330#478—224no—
331#435—24no—
332C2×#107—111no—
333C2×#106—111no—
334C2×#106—111no—
335C2×#106—111no—
336C2×C4⋊C8C2×D1111yescharacteristic
337C2×#102—111no—
338C2×#102—111no—
339C2×#102—111no—
340C2×#102—111no—
341C2×C22⋊C8C2×D1111yescharacteristic
342C2×C22⋊C8C2×D1111yescharacteristic
343C2×#97C2×D1111yescharacteristic
344#400—221no—
345#394—221no—
346#394—221no—
347#394—221no—
348#388—221no—
349#388—221no—
350#384—111no—
351#380—111no—
352#380—111no—
353#380—111no—
354#380—111no—
355#380—111no—
356#380—111no—
357#380—221no—
358C4×C4⋊C4—111no—
359#340—111no—
360#340—111no—
361#340—111no—
362#340—111no—
363#340—111no—
364#340—111no—
365#340—111no—
366#340—111no—
367C22×C11—22no—
368C22×C11—22no—
369C22×C11—22no—
370C22×C11—41no—
371C22×C11—41no—
372C22×C11—41no—
373C22×C11—41no—
374C22×C11—41no—
375C22×C11—41no—
376C22×C11—41no—
377C22×C11—41no—
378C22×C11—41no—
379C22×C11—41no—
380C22×C11—41no—
381C22×C11C2×#12111yescharacteristic
382C22×C11#54611yescharacteristic
383C22×C11#54711yescharacteristic
384C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
385C22×C11#57511yescharacteristic
386C22×C11#57711yescharacteristic
387C22×C11#57711yescharacteristic
388C2×D11—42no—
389C2×D11—42no—
390C2×D11—42no—
391C2×D11—81no—
392C2×D11—81no—
393C2×D11—81no—
394C2×D11—81no—
395C4×C11—22no—
396C4×C11—22no—
397C4×C11—41no—
398C4×C11—41no—
399C4×C11#52911yescharacteristic
400C4×C11#54211yescharacteristic
401C4×C11#54611yescharacteristic
402C4×C11#54811yescharacteristic
403Dic11—81no—
404Dic11—81no—
405Dic11—81no—
406Dic11—81no—
407Dic11—81no—
408Dic11—81no—
409Dic11—81no—
410C22×D4—111no—
411C22×D4—221no—
412C22×D4—221no—
413C22×D4D4411yescharacteristic
414C23×C4—221no—
415C23×C4C22×D1111yescharacteristic
416C23×C4C22×D1111yescharacteristic
417C2×M16—22no—
418C2×M16—22no—
419C2×M16—41no—
420C22×C8—22no—
421C22×C8—22no—
422C22×C8—41no—
423C22×C8C22×D1111yescharacteristic
424C22×C8C22×D1111yescharacteristic
425C22×C8C22×D1111yescharacteristic
426C22×C8C22×D1111yescharacteristic
427#125—222no—
428#125—222no—
429#121—222no—
430#121—222no—
431#121—441no—
432#121—441no—
433#121—444no—
434C4×D4—22no—
435C4×D4—22no—
436C4×D4—222no—
437C4×D4—222no—
438C2×C4⋊C4—111no—
439C2×C4⋊C4—111no—
440C2×C4⋊C4—111no—
441C2×C4⋊C4—111no—
442C2×C4⋊C4—111no—
443C2×C4⋊C4—111no—
444C2×C4⋊C4—111no—
445C2×C4⋊C4—221no—
446C2×C4⋊C4—221no—
447C2×C4⋊C4—221no—
448C2×C4⋊C4—221no—
449C2×C4⋊C4D4411yescharacteristic
450C2×C22⋊C4—221no—
451C2×C22⋊C4—221no—
452C2×C22⋊C4—221no—
453C2×C22⋊C4—221no—
454C2×C22⋊C4—221no—
455C2×C22⋊C4—221no—
456C2×C22⋊C4—221no—
457C2×C22⋊C4—221no—
458C2×C22⋊C4—221no—
459C2×C22⋊C4D4411yescharacteristic
460C2×C22⋊C4D4411yescharacteristic
461C2×C42—221no—
462C2×C42C22×D1111yescharacteristic
463#107—222no—
464#106—222no—
465#106—441no—
466#106—441no—
467C4⋊C8C22⋊D1114yescomplemented
468#102—222no—
469#102—222no—
470#102—222no—
471#102—222no—
472C22⋊C8—22no—
473C22⋊C8—22no—
474#97—22no—
475#95—221no—
476#95—221no—
477#95—221no—
478#95—221no—
479#95—221no—
480#95—221no—
481#95—221no—
482C2×C11—42no—
483C2×C11—81no—
484C2×C11#242711yescharacteristic
485C2×C11#305511yescharacteristic
486C2×C11#306011yescharacteristic
487C2×C11#330711yescharacteristic
488C2×C11#331011yescharacteristic
489C2×C11#334511yescharacteristic
490C2×C11#334811yescharacteristic
491D11—82no—
492C24—221no—
493C24C2×D4411yescharacteristic
494C24C2×D4411yescharacteristic
495C2×D4—22no—
496C2×D4—22no—
497C2×D4—41no—
498C2×D4—112no—
499C2×D4—221no—
500C2×D4—221no—
501C2×D4—221no—
502C2×D4—221no—
503C2×D4—221no—
504C2×D4—442no—
505C2×D4—442no—
506C2×D4—442no—
507C2×D4—442no—
508C2×D4—881no—
509C2×D4—881no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—221no—
523C22×C4—221no—
524C22×C4—221no—
525C22×C4—221no—
526C22×C4—221no—
527C22×C4—221no—
528C22×C4—221no—
529C22×C4—442no—
530C22×C4—442no—
531C22×C4—442no—
532C22×C4C2×D4411yescharacteristic
533C22×C4C2×D4411yescharacteristic
534C22×C4C2×D4411yescharacteristic
535C22×C4C2×D4411yescharacteristic
536C22×C4C23×D1111yescharacteristic
537M16—44no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—44no—
548C2×C8#434112yes—
549C2×C8C2×C22⋊D1112yes—
550C2×C8C2×C22⋊D1112yes—
551C4⋊C4—22no—
552C4⋊C4—221no—
553C4⋊C4—221no—
554C4⋊C4—221no—
555C4⋊C4—221no—
556C4⋊C4—221no—
557C4⋊C4—221no—
558C4⋊C4—221no—
559C4⋊C4—221no—
560C4⋊C4—221no—
561C4⋊C4—221no—
562C4⋊C4—221no—
563C4⋊C4—221no—
564C4⋊C4—221no—
565C4⋊C4—221no—
566C4⋊C4—442no—
567C4⋊C4—442no—
568C4⋊C4—442no—
569C4⋊C4—881no—
570C22⋊C4—22no—
571C22⋊C4—22no—
572C22⋊C4—442no—
573C22⋊C4—442no—
574C22⋊C4—442no—
575C22⋊C4—442no—
576C22⋊C4—442no—
577C22⋊C4—442no—
578C22⋊C4—442no—
579C22⋊C4—881no—
580C22⋊C4—881no—
581C42—881no—
582C42#433912yes—
583C42C2×C22⋊D1112yes—
584C11#2535511yescharacteristic, complemented, Sylow
585C23—21no—
586C23—21no—
587C23—21no—
588C23—21no—
589C23—21no—
590C23—21no—
591C23—21no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—222no—
599C23—441no—
600C23—441no—
601C23—441no—
602C23—441no—
603C23—441no—
604C23—441no—
605C23#6696112yes—
606C23C22×D4411yescharacteristic
607D4—44no—
608D4—222no—
609D4—222no—
610D4—441no—
611D4—441no—
612D4—884no—
613D4—884no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
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—441no—
633C2×C4—441no—
634C2×C4—441no—
635C2×C4—441no—
636C2×C4—441no—
637C2×C4—441no—
638C2×C4—441no—
639C2×C4—441no—
640C2×C4—441no—
641C2×C4—441no—
642C2×C4—441no—
643C2×C4—441no—
644C2×C4—441no—
645C2×C4—441no—
646C2×C4—441no—
647C2×C4—441no—
648C2×C4—441no—
649C2×C4—441no—
650C2×C4—441no—
651C2×C4—441no—
652C2×C4—441no—
653C2×C4—884no—
654C2×C4#6698312yes—
655C2×C4#6698312yes—
656C2×C4C2×#433911yescharacteristic
657C2×C4C2×#434111yescharacteristic
658C2×C4#6703711yescharacteristic
659C2×C4#41×D1111yescharacteristic
660C2×C4#6704311yescharacteristic
661C2×C4C22×C22⋊D1111yescharacteristic
662C8—22no—
663C8—22no—
664C8—22no—
665C8—41no—
666C22—22no—
667C22—22no—
668C22—22no—
669C22—41no—
670C22—41no—
671C22—41no—
672C22—41no—
673C22—41no—
674C22—41no—
675C22—41no—
676C22—41no—
677C22—41no—
678C22—41no—
679C22—41no—
680C22—442no—
681C22—442no—
682C22—442no—
683C22—881no—
684C22—881no—
685C22—881no—
686C22—881no—
687C22#1062308511yescharacteristic
688C22#1062308611yescharacteristic
689C22C2×#6696111yescharacteristic
690C22#1062327911yescharacteristic
691C22#1062328211yescharacteristic
692C22#1062328211yescharacteristic
693C22C2×#6698311yescharacteristic
694C4—22no—
695C4—22no—
696C4—41no—
697C4—41no—
698C4—881no—
699C4—881no—
700C4—881no—
701C4—881no—
702C4—881no—
703C4—881no—
704C4—881no—
705C4#1062308811yescharacteristic
706C4#1062309211yescharacteristic
707C4#1062333711yescharacteristic
708C4#1062336211yescharacteristic
709C2—42no—
710C2—81no—
711C2—882no—
712C2#1307218711yescharacteristic
713C2#1307823511yescharacteristic
714C2#1307827811yescharacteristic
715C2#1308059411yescharacteristic
716C2#1308063911yescharacteristic
717C2#1308108811yescharacteristic
718C2#1308113311yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#435C2
socleC23×C11C22×D4
prime radical#13073529C2
hypercenterC2×#435D11
hypocenterC11#25355
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
1. C2×#10622460C2semidirect
2. #13073782C2semidirect
4. #13070049C2semidirect
5. #13070039C2semidirect
6. #13069806C2semidirect
7. #13069806C2semidirect
8. #13069585C2semidirect
9. #13069380C2semidirect
10. #13069054C2semidirect
11. #13069044C2semidirect
12. #13068649C2semidirect
13. #13068641C2semidirect
14. #13068442C2semidirect
15. C2×C11×#435C2semidirect
114. C11×C4⋊C8D4semidirect
227. C2×#435D11semidirect
467. C4⋊C8C22⋊D11semidirect
584. C11#25355semidirect

Maximal subgroups

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

subgroupindex
C2×#106224602
#130737822
#130735292
#130700492
#130700392
#130698062
#130695852
#130693802
#130690542
#130690442
#130686492
#130686412
#130684422
C2×C11×#4352
#2535511