Finite Group Databasebeta

← #29739977

Subgroups — #29739977

Order 15616.

924 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840084C211yesmaximal, characteristic, complemented
2C2×#16839805C211yesmaximal, characteristic, complemented
3#21449260C211yesmaximal, characteristic
4#21448769C211yesmaximal, characteristic, complemented
5#21447345C211yesmaximal, characteristic, complemented
6#21447294C211yesmaximal, characteristic, complemented
7#21447251C211yesmaximal, characteristic, complemented
8#21446999C211yesmaximal, characteristic, complemented
9#21446449C211yesmaximal, characteristic, complemented
10#21446395C211yesmaximal, characteristic, complemented
11#21446258C211yesmaximal, characteristic, complemented
12#21446114C211yesmaximal, characteristic, complemented
13#21446021C211yesmaximal, characteristic, complemented
14#21446009C211yesmaximal, characteristic, complemented
15C61×#1875C211yesmaximal, characteristic, complemented
16C22×#11758194C2211yescharacteristic
17C2×#14519749—21no—
18C2×#14519748C2211yescharacteristic
19C2×C4×C22⋊D61C2211yescharacteristic
20C2×#14519735C2211yescharacteristic
21C22×C4⋊Dic61C2211yescharacteristic
22#16840084—24no—
23#16839805—24no—
24C2×#14519711C2211yescharacteristic
25C2×#14519711C2211yescharacteristic
26C2×#14519710C2211yescharacteristic
27C2×#14519710C2211yescharacteristic
28C2×#14519708C2211yescharacteristic
29C2×#14519708C2211yescharacteristic
30C2×#14519698C2211yescharacteristic
31C2×#14519698C2211yescharacteristic
32C2×#14519689C2211yescharacteristic
33C2×#14519689C2211yescharacteristic
34#16839685—21no—
35#16839678—21no—
36#16839665C2211yescharacteristic
37#16839662—21no—
38#16839658C2211yescharacteristic
39#16839653—21no—
40#16839650—21no—
41#16839642—21no—
42#16839631C2211yescharacteristic
43#16839622C2211yescharacteristic
44#16839619C2211yescharacteristic
45#16839619C2211yescharacteristic
46C4⋊C4×Dic61C2211yescharacteristic
47C4×#11758196—21no—
48#16839525C2211yescharacteristic
49#16839525C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839524C2211yescharacteristic
52#16839516C2211yescharacteristic
53#16839516C2211yescharacteristic
54C2×#121×C61C2211yescharacteristic
55C2×#117×C61C2211yescharacteristic
56C2×#102×C61C2211yescharacteristic
57C2×#102×C61C2211yescharacteristic
58C2×C22⋊C8×C61C2211yescharacteristic
59C61×#340C2211yescharacteristic
60C61×#340C2211yescharacteristic
61C22×C22⋊D61—21no—
62C22×C22⋊D61D411yescharacteristic
63C23×Dic61—21no—
64C22×C4×D61C2311yescharacteristic
65C2×#11758194—22no—
66C2×#11758194—22no—
67C2×#11758194—22no—
68C22×#92418C2311yescharacteristic
69C22×#92418C2311yescharacteristic
70#14519749—44no—
71#14519748—22no—
72#14519748—41no—
73C4×C22⋊D61—22no—
74C4×C22⋊D61—22no—
75#14519735—22no—
76#14519735—41no—
77C2×C4⋊Dic61—22no—
78C2×C4⋊Dic61—21no—
79C2×C4⋊Dic61—41no—
80C2×C4⋊Dic61C2311yescharacteristic
81C2×C4⋊Dic61C2311yescharacteristic
82C2×C4⋊Dic61C2311yescharacteristic
83C2×C4⋊Dic61C2311yescharacteristic
84C2×#11758196—21no—
85C2×#11758196—21no—
86C2×#11758196—21no—
87C2×#11758196D411yescharacteristic
88C2×C22⋊Dic61—21no—
89C2×C22⋊Dic61—21no—
90C2×C22⋊Dic61—21no—
91C2×C22⋊Dic61—21no—
92C2×C22⋊Dic61D411yescharacteristic
93C2×#11758198—21no—
94C2×#11758198—21no—
95C2×#11758198—21no—
96C2×#11758198D411yescharacteristic
97C2×C4×Dic61—21no—
98C2×C4×Dic61—21no—
99C2×C4×Dic61C2311yescharacteristic
100#14519711—22no—
101#14519711—41no—
102#14519710—22no—
103#14519710—22no—
104#14519708—22no—
105#14519708D414yescomplemented
106#14519698—22no—
107#14519698—22no—
108#14519689—22no—
109#14519689—22no—
110#14519684—21no—
111#14519684—21no—
112#14519684—21no—
113#14519684—21no—
114#14519684—21no—
115C22×D4×C61—21no—
116C22×D4×C61C2311yescharacteristic
117C23×C4×C61C2311yescharacteristic
118C22×C8×C61C2311yescharacteristic
119C22×C8×C61C2311yescharacteristic
120#121×C61—22no—
121#121×C61—22no—
122#117×C61—22no—
123#117×C61—41no—
124C2×C4⋊C4×C61C2311yescharacteristic
125C2×C4⋊C4×C61C2311yescharacteristic
126C2×C4⋊C4×C61C2311yescharacteristic
127C2×C22⋊C4×C61—21no—
128C2×C22⋊C4×C61—21no—
129C2×C42×C61—21no—
130#102×C61—22no—
131#102×C61—41no—
132C22⋊C8×C61—22no—
133C24×C61—21no—
134C24×C61C2×D411yescharacteristic
135C23×D61C2×D411yescharacteristic
136C2×D4×C61—21no—
137C2×D4×C61—21no—
138C2×D4×C61—21no—
139C2×D4×C61—21no—
140C2×D4×C61—21no—
141C2×D4×C61—21no—
142C2×D4×C61—42no—
143C2×D4×C61—42no—
144C2×D4×C61—42no—
145C22×C4×C61—21no—
146C22×C4×C61—21no—
147C22×C4×C61—21no—
148C22×C4×C61—21no—
149C22×C4×C61—21no—
150C22×C4×C61—21no—
151C22×C4×C61—21no—
152C22×C4×C61C2×D411yescharacteristic
153C22×C4×C61#4112yes—
154C22×C4×C61#4112yes—
155C22×C4×C61C2411yescharacteristic
156C2×C22⋊D61—22no—
157C2×C22⋊D61—22no—
158C2×C22⋊D61—41no—
159C2×C22⋊D61—42no—
160C2×C22⋊D61—42no—
161C2×C22⋊D61—81no—
162C22×Dic61—21no—
163C22×Dic61—21no—
164C22×Dic61—21no—
165C22×Dic61—21no—
166C22×Dic61—42no—
167C22×Dic61—42no—
168C22×Dic61—81no—
169C22×Dic61C2×D411yescharacteristic
170C22×Dic61C2×D411yescharacteristic
171C22×Dic61C2×D411yescharacteristic
172C2×C4×D61—21no—
173C2×C4×D61—21no—
174C2×C4×D61—21no—
175C2×C4×D61—21no—
176C2×C4×D61—21no—
177C2×C4×D61—21no—
178C2×C8×C61—21no—
179C2×C8×C61—21no—
180C2×C8×C61—21no—
181C2×C8×C61—21no—
182C2×C8×C61—21no—
183C2×C8×C61—21no—
184C4⋊C4×C61—21no—
185C4⋊C4×C61—21no—
186C4⋊C4×C61—21no—
187C4⋊C4×C61—21no—
188C4⋊C4×C61—21no—
189C4⋊C4×C61C2×D412yes—
190C22⋊C4×C61—42no—
191C22⋊C4×C61—42no—
192C42×C61—42no—
193C22⋊Dic61—22no—
194C22⋊Dic61—42no—
195C22⋊Dic61—42no—
196C22⋊Dic61—81no—
197C22⋊Dic61—81no—
198#11758198—22no—
199#11758198—42no—
200#11758198—42no—
201#11758198—81no—
202C4⋊Dic61—21no—
203C4⋊Dic61—21no—
204C4⋊Dic61—21no—
205C4⋊Dic61—21no—
206C4⋊Dic61—21no—
207C4⋊Dic61—21no—
208C4⋊Dic61—21no—
209C4⋊Dic61—42no—
210C4⋊Dic61C2×D412yes—
211#11758196—22no—
212#11758196—42no—
213#11758196—42no—
214#11758196—81no—
215C4×Dic61—21no—
216C4×Dic61—21no—
217C4×Dic61—42no—
218C4×Dic61—42no—
219#11758194—28no—
220C2×#92418—21no—
221C2×#92418—21no—
222C2×#92418—21no—
223C2×#92418—21no—
224C2×#92418C2×D412yes—
225C2×#92418#4112yes—
226C23×C61—21no—
227C23×C61—21no—
228C23×C61—21no—
229C23×C61—21no—
230C23×C61—21no—
231C23×C61—21no—
232C23×C61—41no—
233C23×C61—41no—
234C23×C61—41no—
235C23×C61—41no—
236C23×C61—41no—
237C23×C61—41no—
238C23×C61—41no—
239C23×C61#12312yes—
240C23×C61C22×D411yescharacteristic
241C22×D61—21no—
242C22×D61—21no—
243C22×D61—21no—
244C22×D61—21no—
245C22×D61—21no—
246C22×D61—21no—
247C22×D61—21no—
248D4×C61—41no—
249D4×C61—41no—
250D4×C61—41no—
251D4×C61—41no—
252D4×C61—84no—
253C2×C4×C61—21no—
254C2×C4×C61—21no—
255C2×C4×C61—22no—
256C2×C4×C61—22no—
257C2×C4×C61—22no—
258C2×C4×C61—22no—
259C2×C4×C61—22no—
260C2×C4×C61—41no—
261C2×C4×C61—41no—
262C2×C4×C61—41no—
263C2×C4×C61—41no—
264C2×C4×C61—41no—
265C2×C4×C61—41no—
266C2×C4×C61—41no—
267C2×C4×C61—41no—
268C2×C4×C61#12312yes—
269C2×C4×C61C22×D411yescharacteristic
270C2×C4×C61C2×#4111yescharacteristic
271C2×C4×C61C2×#4111yescharacteristic
272C2×C4×C61C2×#4111yescharacteristic
273C2×C4×C61H(5,𝔽2)11yescharacteristic
274C2×C4×C612−1+411yescharacteristic
275C22⋊D61—44no—
276C22⋊D61—84no—
277C2×Dic61—21no—
278C2×Dic61—21no—
279C2×Dic61—21no—
280C2×Dic61—21no—
281C2×Dic61—21no—
282C2×Dic61—22no—
283C2×Dic61—21no—
284C2×Dic61—21no—
285C2×Dic61—21no—
286C2×Dic61—41no—
287C2×Dic61—41no—
288C2×Dic61—41no—
289C2×Dic61—41no—
290C2×Dic61—41no—
291C2×Dic61—41no—
292C2×Dic61—41no—
293C2×Dic61—41no—
294C2×Dic61—41no—
295C2×Dic61—41no—
296C2×Dic61—41no—
297C2×Dic61—84no—
298C2×Dic61AGL(1,ℤ/8)12yes—
299C4×D61—41no—
300C4×D61—41no—
301C4×D61—41no—
302C4×D61—41no—
303C8×C61—41no—
304C8×C61—41no—
305#92418—22no—
306#92418—22no—
307#26157—611nomaximal, Sylow
308C22×C61—22no—
309C22×C61—22no—
310C22×C61—22no—
311C22×C61—41no—
312C22×C61—41no—
313C22×C61—41no—
314C22×C61—41no—
315C22×C61—81no—
316C22×C61—81no—
317C22×C61—81no—
318C22×C61—81no—
319C22×C61—81no—
320C22×C61—81no—
321C22×C61—81no—
322C22×C61C2×#12311yescharacteristic
323C22×C61D4211yescharacteristic
324C22×C61#54711yescharacteristic
325C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
326C22×C61#57511yescharacteristic
327C22×C61#57611yescharacteristic
328C22×C61#57811yescharacteristic
329C2×D61—41no—
330C2×D61—41no—
331C2×D61—41no—
332C2×D61—41no—
333C2×D61—41no—
334C2×D61—41no—
335C2×D61—41no—
336C4×C61—22no—
337C4×C61—42no—
338C4×C61—81no—
339C4×C61—81no—
340C4×C61#52511yescharacteristic
341C4×C61#53911yescharacteristic
342C4×C61#54811yescharacteristic
343C4×C61#55311yescharacteristic
344Dic61—22no—
345Dic61—41no—
346Dic61—41no—
347Dic61—42no—
348Dic61—81no—
349Dic61—81no—
350Dic61—81no—
351C2×#482—611no—
352C2×#428—611no—
353#2416—611no—
354#2354—611no—
355#2093—611no—
356#2083—611no—
357#2076—611no—
358#2033—611no—
359#1926—611no—
360#1919—611no—
361#1895—611no—
362#1875D6111yescharacteristic, complemented
363#1870—611no—
364#1854—611no—
365#1852—611no—
366C2×C61—42no—
367C2×C61—161no—
368C2×C61#244311yescharacteristic
369C2×C61#309411yescharacteristic
370C2×C61#309811yescharacteristic
371C2×C61#326911yescharacteristic
372C2×C61#327411yescharacteristic
373C2×C61#334711yescharacteristic
374C2×C61#335311yescharacteristic
375D61—81no—
376C22×M16—611no—
377C2×#121—611no—
378C2×#121—1221no—
379C2×#121C2×D6111yescharacteristic
380C2×C4×D4—611no—
381C2×#117—611no—
382C2×#117C2×D6111yescharacteristic
383C22×C4⋊C4—611no—
384#482—1224no—
385#428—1224no—
386C2×#107—611no—
387C2×#107—611no—
388C2×#107—611no—
389C2×#107—611no—
390C2×#106—611no—
391C2×#106—611no—
392C2×#102—611no—
393C2×#102—611no—
394C2×#102C2×D6111yescharacteristic
395C2×#102C2×D6111yescharacteristic
396C2×C22⋊C8—611no—
397C2×C22⋊C8—611no—
398C2×C22⋊C8C2×D6111yescharacteristic
399#396—1221no—
400#394—1221no—
401#390—611no—
402#390—1221no—
403#389—611no—
404#388—1221no—
405#388—1221no—
406#386—1221no—
407#384—611no—
408#380—611no—
409#380—611no—
410#380—611no—
411C4×C4⋊C4—611no—
412C4×C4⋊C4—1221no—
413#340—611no—
414#340—611no—
415#340—611no—
416#340—611no—
417#340C2×D6111yescharacteristic
418#340C2×D6111yescharacteristic
419#336—611no—
420#336—611no—
421C61#2615711yescharacteristic, complemented, Sylow
422C22×D4—21no—
423C22×D4—611no—
424C22×D4—1221no—
425C22×D4C22×D6111yescharacteristic
426C23×C4—611no—
427C23×C4—1221no—
428C23×C4C22×D6111yescharacteristic
429C2×M16—1222no—
430C2×M16—1222no—
431C2×M16—1222no—
432C22×C8—611no—
433C22×C8—611no—
434C22×C8C22×D6111yescharacteristic
435C22×C8C22×D6111yescharacteristic
436#121—22no—
437#121—22no—
438#121—1222no—
439#121—2441no—
440#121—2444no—
441C4×D4—1222no—
442C4×D4—1222no—
443#117—22no—
444#117—41no—
445#117—1222no—
446#117—2441no—
447C2×C4⋊C4—611no—
448C2×C4⋊C4—611no—
449C2×C4⋊C4—611no—
450C2×C4⋊C4—611no—
451C2×C4⋊C4—611no—
452C2×C4⋊C4—1222no—
453C2×C4⋊C4—1221no—
454C2×C4⋊C4—1221no—
455C2×C4⋊C4—1221no—
456C2×C4⋊C4—1221no—
457C2×C4⋊C4—2441no—
458C2×C4⋊C4C22×D6111yescharacteristic
459C2×C4⋊C4C22×D6111yescharacteristic
460C2×C4⋊C4C22×D6111yescharacteristic
461C2×C22⋊C4—21no—
462C2×C22⋊C4—21no—
463C2×C22⋊C4—611no—
464C2×C22⋊C4—611no—
465C2×C22⋊C4—1221no—
466C2×C22⋊C4—1221no—
467C2×C22⋊C4—1221no—
468C2×C22⋊C4—1221no—
469C2×C22⋊C4—1221no—
470C2×C22⋊C4—1221no—
471C2×C22⋊C4—1221no—
472C2×C42—21no—
473C2×C42—611no—
474C2×C42—1221no—
475C2×C42—1221no—
476#107—1222no—
477#107—1222no—
478#107—1222no—
479#107—2441no—
480#106—614no—
481#106—1222no—
482#102—22no—
483#102—41no—
484#102—1222no—
485#102—1222no—
486C22⋊C8—22no—
487C22⋊C8—1222no—
488C22⋊C8—1222no—
489#95—1221no—
490#95—1221no—
491#95—1221no—
492#95—1221no—
493#95—1221no—
494C24—21no—
495C24—611no—
496C24D4×D6111yescharacteristic
497C2×D4—21no—
498C2×D4—21no—
499C2×D4—21no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—42no—
504C2×D4—42no—
505C2×D4—42no—
506C2×D4—1222no—
507C2×D4—1222no—
508C2×D4—4881no—
509C2×D4—2442no—
510C2×D4—2441no—
511C2×D4—2442no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—611no—
520C22×C4—611no—
521C22×C4—611no—
522C22×C4—1221no—
523C22×C4—1221no—
524C22×C4—1221no—
525C22×C4—1221no—
526C22×C4—1221no—
527C22×C4—1221no—
528C22×C4—1221no—
529C22×C4—1221no—
530C22×C4—1221no—
531C22×C4—1221no—
532C22×C4—4881no—
533C22×C4—2442no—
534C22×C4—2442no—
535C22×C4#1175822212yes—
536C22×C4D4×D6111yescharacteristic
537C22×C4#1175822412yes—
538C22×C4C23×D6111yescharacteristic
539M16—1228no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—612no—
547C2×C8—612no—
548C2×C8—1221no—
549C2×C8—1221no—
550C2×C8—1221no—
551C2×C8—1221no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—612no—
558C4⋊C4—1221no—
559C4⋊C4—1222no—
560C4⋊C4—1221no—
561C4⋊C4—1221no—
562C4⋊C4—1221no—
563C4⋊C4—1221no—
564C4⋊C4—1221no—
565C4⋊C4—1221no—
566C4⋊C4—4881no—
567C4⋊C4—2442no—
568C4⋊C4—2442no—
569C4⋊C4—2442no—
570C4⋊C4D4×D6112yes—
571C22⋊C4—42no—
572C22⋊C4—42no—
573C22⋊C4—1222no—
574C22⋊C4—1222no—
575C22⋊C4—4881no—
576C22⋊C4—4881no—
577C22⋊C4—4881no—
578C22⋊C4—2442no—
579C22⋊C4—2442no—
580C22⋊C4—2442no—
581C22⋊C4—2442no—
582C42—42no—
583C42—1221no—
584C42—1221no—
585C42—2442no—
586C42—2442no—
587C23—21no—
588C23—21no—
589C23—21no—
590C23—21no—
591C23—21no—
592C23—21no—
593C23—41no—
594C23—41no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23—1221no—
601C23—1221no—
602C23—1221no—
603C23—1221no—
604C23—1221no—
605C23—1221no—
606C23—1221no—
607C23#1451975912yes—
608C23C2×D4×D6111yescharacteristic
609D4—41no—
610D4—41no—
611D4—41no—
612D4—41no—
613D4—84no—
614D4—4884no—
615D4—2444no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
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—612no—
632C2×C4—1221no—
633C2×C4—1221no—
634C2×C4—1221no—
635C2×C4—1221no—
636C2×C4—1221no—
637C2×C4—1221no—
638C2×C4—1221no—
639C2×C4—1222no—
640C2×C4—1221no—
641C2×C4—4884no—
642C2×C4—2441no—
643C2×C4—2441no—
644C2×C4—2441no—
645C2×C4—2441no—
646C2×C4—2441no—
647C2×C4—2441no—
648C2×C4—2441no—
649C2×C4—2441no—
650C2×C4—2441no—
651C2×C4—2441no—
652C2×C4—2441no—
653C2×C4—2441no—
654C2×C4—2441no—
655C2×C4—2441no—
656C2×C4—2441no—
657C2×C4#1451975912yes—
658C2×C4C2×D4×D6111yescharacteristic
659C2×C4#41×D6111yescharacteristic
660C2×C4C2×#1175822411yescharacteristic
661C2×C4C2×#1175822211yescharacteristic
662C2×C4#1451982211yescharacteristic
663C2×C4#1451982411yescharacteristic
664C8—41no—
665C8—41no—
666C8—1222no—
667C8—1222no—
668C22—22no—
669C22—22no—
670C22—22no—
671C22—41no—
672C22—41no—
673C22—41no—
674C22—41no—
675C22—81no—
676C22—81no—
677C22—81no—
678C22—81no—
679C22—81no—
680C22—81no—
681C22—81no—
682C22—2441no—
683C22—2441no—
684C22—2441no—
685C22—2441no—
686C22—2441no—
687C22—2441no—
688C22—2441no—
689C22C2×#1451975911yescharacteristic
690C22#1684039411yescharacteristic
691C22#1684041011yescharacteristic
692C22AGL(1,ℤ/8)×D6111yescharacteristic
693C22#1684055811yescharacteristic
694C22#1684056411yescharacteristic
695C22#1684057611yescharacteristic
696C4—22no—
697C4—42no—
698C4—81no—
699C4—81no—
700C4—1222no—
701C4—4881no—
702C4—4881no—
703C4—4881no—
704C4—2442no—
705C4—2441no—
706C4—2441no—
707C4#1684027111yescharacteristic
708C4#1684035411yescharacteristic
709C4#1684041811yescharacteristic
710C4#1684045511yescharacteristic
711C2—42no—
712C2—161no—
713C2—4881no—
714C2#2144955611yescharacteristic
715C2#2145575711yescharacteristic
716C2#2145579511yescharacteristic
717C2#2145737211yescharacteristic
718C2#2145743211yescharacteristic
719C2#2145831211yescharacteristic
720C2#2145840111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#1875C2
socleC23×C61C22×D4
prime radical#21449260C2
hypercenter#1875D61
hypocenterC61#26157
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1875

Complements

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

NH ≅ G/Ntype
1. C2×#16840084C2semidirect
2. C2×#16839805C2semidirect
4. #21448769C2semidirect
5. #21447345C2semidirect
6. #21447294C2semidirect
7. #21447251C2semidirect
8. #21446999C2semidirect
9. #21446449C2semidirect
10. #21446395C2semidirect
11. #21446258C2semidirect
12. #21446114C2semidirect
13. #21446021C2semidirect
14. #21446009C2semidirect
15. C61×#1875C2semidirect
105. #14519708D4semidirect
362. #1875D61semidirect
421. C61#26157semidirect

Maximal subgroups

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

subgroupindex
C2×#168400842
C2×#168398052
#214492602
#214487692
#214473452
#214472942
#214472512
#214469992
#214464492
#214463952
#214462582
#214461142
#214460212
#214460092
C61×#18752
#2615761