Finite Group Databasebeta

← #29730134

Subgroups — #29730134

Order 15616.

958 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840051C211yesmaximal, characteristic, complemented
2C2×C8×C22⋊D61C211yesmaximal, characteristic, complemented
3#21450989C211yesmaximal, characteristic, complemented
4#21450734C211yesmaximal, characteristic
5#21447255C211yesmaximal, characteristic, complemented
6#21447253C211yesmaximal, characteristic, complemented
7#21447010C211yesmaximal, characteristic, complemented
8#21447008C211yesmaximal, characteristic, complemented
9#21446778C211yesmaximal, characteristic, complemented
10#21446579C211yesmaximal, characteristic, complemented
11#21446247C211yesmaximal, characteristic, complemented
12#21446246C211yesmaximal, characteristic, complemented
13#21445843C211yesmaximal, characteristic, complemented
14#21445633C211yesmaximal, characteristic, complemented
15C61×#1807C211yesmaximal, characteristic, complemented
16C22×C8×D61C2211yescharacteristic
17C2×#14519776C2211yescharacteristic
18C2×#14519752C2211yescharacteristic
19C2×#14519751C2211yescharacteristic
20C2×#14519750—21no—
21C2×#14519739C2211yescharacteristic
22C2×C4×C22⋊D61C2211yescharacteristic
23#16840051—24no—
24C8×C22⋊D61—24no—
25C2×#14519708C2211yescharacteristic
26C2×#14519708C2211yescharacteristic
27C2×#14519706C2211yescharacteristic
28C2×#14519699C2211yescharacteristic
29C2×#14519699C2211yescharacteristic
30C2×#14519697C2211yescharacteristic
31C2×#14519697C2211yescharacteristic
32C2×C22⋊#92418C2211yescharacteristic
33C2×#14519689C2211yescharacteristic
34C2×C8×Dic61C2211yescharacteristic
35#16839680—21no—
36#16839677—21no—
37#16839675—21no—
38#16839674—21no—
39#16839662—21no—
40#16839631C2211yescharacteristic
41#16839626—21no—
42#16839622C2211yescharacteristic
43#16839621—21no—
44#16839619C2211yescharacteristic
45#16839619C2211yescharacteristic
46#16839619C2211yescharacteristic
47C4⋊C4×Dic61C2211yescharacteristic
48#16839525C2211yescharacteristic
49#16839525C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839524C2211yescharacteristic
52#16839524C2211yescharacteristic
53#16839524C2211yescharacteristic
54C23×C8×C61C2211yescharacteristic
55C2×#106×C61C2211yescharacteristic
56C2×#106×C61C2211yescharacteristic
57C61×#380C2211yescharacteristic
58C61×#380C2211yescharacteristic
59C61×#340C2211yescharacteristic
60C61×#340C2211yescharacteristic
61C22×Dic122—21no—
62C22×D244—21no—
63C22×D244C2311yescharacteristic
64C22×C22⋊D61—21no—
65C22×C22⋊D61D411yescharacteristic
66C22×C4×D61—21no—
67C22×C4×D61C2311yescharacteristic
68C22×#92418C2311yescharacteristic
69C22×#92418C2311yescharacteristic
70C2×C8×D61—22no—
71C2×C8×D61—22no—
72C2×C8×D61—41no—
73#14519776—22no—
74#14519776—22no—
75#14519752—22no—
76#14519752—41no—
77#14519751—22no—
78#14519751—41no—
79#14519750—44no—
80#14519739—22no—
81#14519739—22no—
82C4×C22⋊D61—22no—
83C4×C22⋊D61—22no—
84C2×C4⋊Dic61C2311yescharacteristic
85C2×C4⋊Dic61C2311yescharacteristic
86C2×C4⋊Dic61C2311yescharacteristic
87C2×#11758196—21no—
88C2×#11758196—21no—
89C2×#11758196—21no—
90C2×#11758196D411yescharacteristic
91C2×C22⋊Dic61—21no—
92C2×C22⋊Dic61D411yescharacteristic
93C2×#11758198—21no—
94C2×#11758198—21no—
95C2×#11758198—21no—
96C2×#11758198—21no—
97C2×#11758198—21no—
98C2×#11758198—21no—
99C2×#11758198D411yescharacteristic
100C2×C4×Dic61—21no—
101C2×C4×Dic61C2311yescharacteristic
102#14519708—22no—
103#14519708—41no—
104#14519706D414yescomplemented
105#14519699—22no—
106#14519699—22no—
107#14519697—22no—
108#14519697—22no—
109C22⋊#92418—22no—
110#14519689—22no—
111C8×Dic61—22no—
112#14519684—21no—
113#14519684—21no—
114#14519684—21no—
115#14519684—21no—
116#14519684—21no—
117C23×C4×C61C2311yescharacteristic
118C22×C8×C61—22no—
119C22×C8×C61—22no—
120C22×C8×C61—41no—
121C22×C8×C61C2311yescharacteristic
122C22×C8×C61C2311yescharacteristic
123C2×C4⋊C4×C61C2311yescharacteristic
124C2×C4⋊C4×C61C2311yescharacteristic
125C2×C4⋊C4×C61C2311yescharacteristic
126C2×C4⋊C4×C61C2311yescharacteristic
127C2×C22⋊C4×C61—21no—
128C2×C22⋊C4×C61—21no—
129#106×C61—22no—
130#106×C61—41no—
131#95×C61—21no—
132#95×C61—21no—
133C24×C61C2×D411yescharacteristic
134C23×D61—21no—
135C23×D61C2×D411yescharacteristic
136C22×C4×C61—21no—
137C22×C4×C61—21no—
138C22×C4×C61—21no—
139C22×C4×C61—21no—
140C22×C4×C61—21no—
141C22×C4×C61—21no—
142C22×C4×C61—21no—
143C22×C4×C61—21no—
144C22×C4×C61—21no—
145C22×C4×C61—21no—
146C22×C4×C61C2×D411yescharacteristic
147C22×C4×C61C2411yescharacteristic
148C2×C22⋊D61—22no—
149C2×C22⋊D61—22no—
150C2×C22⋊D61—42no—
151C2×C22⋊D61—42no—
152C2×C22⋊D61—81no—
153C2×C22⋊D61SD1614yes—
154C22×Dic61—21no—
155C22×Dic61—21no—
156C22×Dic61—21no—
157C22×Dic61C2×D411yescharacteristic
158C22×Dic61C2×D411yescharacteristic
159C22×Dic61C2×D411yescharacteristic
160C2×D244—21no—
161C2×D244—21no—
162C2×D244—21no—
163C2×D244—21no—
164C2×D244—21no—
165C2×D244—42no—
166C2×D244—42no—
167C2×D244—81no—
168C2×D244#4112yes—
169C2×C4×D61—21no—
170C2×C4×D61—21no—
171C2×C4×D61—21no—
172C2×C4×D61—21no—
173C2×C4×D61—21no—
174C2×C4×D61—21no—
175C2×C4×D61—42no—
176C2×C4×D61—42no—
177C2×C4×D61—42no—
178C2×Dic122—42no—
179C2×Dic122—81no—
180C2×Dic122—81no—
181C2×C8×C61—21no—
182C2×C8×C61—21no—
183C2×C8×C61—21no—
184C2×C8×C61—21no—
185C2×C8×C61—44no—
186C2×C8×C61C2×D412yes—
187C2×C8×C61#4112yes—
188C4⋊C4×C61—21no—
189C4⋊C4×C61—21no—
190C4⋊C4×C61—21no—
191C4⋊C4×C61—21no—
192C4⋊C4×C61—21no—
193C4⋊C4×C61—21no—
194C4⋊C4×C61—21no—
195C4⋊C4×C61—21no—
196C22⋊C4×C61—42no—
197C22⋊C4×C61—81no—
198C22⋊Dic61—22no—
199C22⋊Dic61—81no—
200#11758198—22no—
201#11758198—42no—
202#11758198—42no—
203#11758198—42no—
204#11758198—42no—
205#11758198—81no—
206#11758198—81no—
207C4⋊Dic61—21no—
208C4⋊Dic61—21no—
209C4⋊Dic61—21no—
210C4⋊Dic61—21no—
211C4⋊Dic61—21no—
212C4⋊Dic61—21no—
213#11758196—22no—
214#11758196—42no—
215#11758196—42no—
216#11758196—81no—
217C4×Dic61—42no—
218C4×Dic61C2×D412yes—
219C4×Dic61#4112yes—
220C2×#92418—21no—
221C2×#92418—21no—
222C2×#92418—21no—
223C2×#92418—21no—
224C2×#92418—21no—
225C2×#92418C2×D412yes—
226C8×D61—44no—
227C23×C61—21no—
228C23×C61—21no—
229C23×C61—21no—
230C23×C61—21no—
231C23×C61—21no—
232C23×C61—21no—
233C23×C61C2×SD1612yes—
234C23×C61C22×D411yescharacteristic
235C22×D61—21no—
236C22×D61—21no—
237C22×D61—21no—
238C22×D61—21no—
239C22×D61—21no—
240C22×D61—21no—
241C22×D61—22no—
242C22×D61—41no—
243C22×D61—41no—
244C22×D61—41no—
245C22×D61—41no—
246C22×D61—41no—
247C22×D61—41no—
248C22×D61C2×SD1612yes—
249C2×C4×C61—21no—
250C2×C4×C61—21no—
251C2×C4×C61—21no—
252C2×C4×C61—41no—
253C2×C4×C61—41no—
254C2×C4×C61—41no—
255C2×C4×C61—41no—
256C2×C4×C61—41no—
257C2×C4×C61—41no—
258C2×C4×C61—41no—
259C2×C4×C61—41no—
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×C61C22×D411yescharacteristic
269C2×C4×C61C2×#4111yescharacteristic
270C2×C4×C61C2×#4111yescharacteristic
271C2×C4×C61C2×#4111yescharacteristic
272C2×C4×C61H(5,𝔽2)11yescharacteristic
273C2×C4×C612−1+411yescharacteristic
274C22⋊D61—28no—
275C22⋊D61—84no—
276C2×Dic61—21no—
277C2×Dic61—21no—
278C2×Dic61—21no—
279C2×Dic61—21no—
280C2×Dic61—21no—
281C2×Dic61—41no—
282C2×Dic61—41no—
283C2×Dic61—41no—
284C2×Dic61—41no—
285C2×Dic61—41no—
286C2×Dic61—41no—
287C2×Dic61—41no—
288C2×Dic61—41no—
289C2×Dic61—41no—
290C2×Dic61#12112yes—
291C2×Dic61#12112yes—
292C2×Dic61C2×SD1612yes—
293C2×Dic61#13512yes—
294D244—22no—
295D244—22no—
296D244—41no—
297D244—41no—
298D244—84no—
299C4×D61—41no—
300C4×D61—41no—
301C4×D61—41no—
302C4×D61—41no—
303C4×D61—84no—
304Dic122—84no—
305C8×C61—22no—
306C8×C61—22no—
307#92418—22no—
308#92418—41no—
309#25339—611nomaximal, Sylow
310C22×C61—22no—
311C22×C61—22no—
312C22×C61—22no—
313C22×C61—41no—
314C22×C61—41no—
315C22×C61—41no—
316C22×C61—41no—
317C22×C61C2×#12111yescharacteristic
318C22×C61#54611yescharacteristic
319C22×C61#54711yescharacteristic
320C22×C61C22×SD1611yescharacteristic
321C22×C61C2×#13511yescharacteristic
322C22×C61#57611yescharacteristic
323C22×C61#57711yescharacteristic
324C2×D61—22no—
325C2×D61—22no—
326C2×D61—22no—
327C2×D61—41no—
328C2×D61—41no—
329C2×D61—41no—
330C2×D61—41no—
331C2×D61—42no—
332C2×D61—42no—
333C2×D61—42no—
334C2×D61—81no—
335C2×D61—81no—
336C2×D61—81no—
337C2×D61—81no—
338C4×C61—41no—
339C4×C61—81no—
340C4×C61—81no—
341C4×C61—81no—
342C4×C61—81no—
343C4×C61#52911yescharacteristic
344C4×C61#54211yescharacteristic
345C4×C61#54611yescharacteristic
346C4×C61#54811yescharacteristic
347Dic61—22no—
348Dic61—41no—
349Dic61—81no—
350Dic61—81no—
351Dic61—81no—
352Dic61#46514yes—
353C2×#476—611no—
354C2×C8×D4—611no—
355#2563—611no—
356#2537—611no—
357#2077—611no—
358#2077—611no—
359#2034—611no—
360#2034—611no—
361#1990—611no—
362#1948—611no—
363#1893—611no—
364#1893—611no—
365#1807—611no—
366#1807D6111yescharacteristic, complemented
367C4×#102—611no—
368C2×C61—42no—
369C2×C61#242711yescharacteristic
370C2×C61C2×#46511yescharacteristic
371C2×C61#306211yescharacteristic
372C2×C61#329511yescharacteristic
373C2×C61#330311yescharacteristic
374C2×C61#333511yescharacteristic
375C2×C61#334111yescharacteristic
376D61—42no—
377D61—82no—
378C23×C8—611no—
379C23×C8C2×D6111yescharacteristic
380C2×C4⋊Q8—611no—
381C2×#121—611no—
382C2×#121—611no—
383C2×#121—1221no—
384C2×C4×D4—611no—
385C2×C4×D4—611no—
386#476—1224no—
387C8×D4—1224no—
388C2×#106—611no—
389C2×#106—611no—
390C2×#106C2×D6111yescharacteristic
391C2×#106C2×D6111yescharacteristic
392C2×C4⋊C8—611no—
393C2×#102—611no—
394C2×#102—611no—
395C2×#102—611no—
396C2×#102—611no—
397C2×C22⋊C8—611no—
398C2×C22⋊C8—611no—
399C2×C4×C8—611no—
400#394—1221no—
401#394—1221no—
402#393—1221no—
403#393—1221no—
404#390—1221no—
405#384—611no—
406#382—1221no—
407#380—611no—
408#380—611no—
409#380—611no—
410#380—611no—
411#380—1221no—
412#380C2×D6111yescharacteristic
413#380C2×D6111yescharacteristic
414C4×C4⋊C4—611no—
415#340—611no—
416#340—611no—
417#340—611no—
418#340—611no—
419#340—611no—
420#340—611no—
421#340C2×D6111yescharacteristic
422#340C2×D6111yescharacteristic
423C61#2533911yescharacteristic, complemented, Sylow
424C22×Q8—1221no—
425C22×D4—611no—
426C22×D4—611no—
427C22×D4—1221no—
428C22×D4—1221no—
429C23×C4—611no—
430C23×C4—1221no—
431C23×C4C22×D6111yescharacteristic
432C22×C8—22no—
433C22×C8—22no—
434C22×C8—41no—
435C22×C8—611no—
436C22×C8—611no—
437C22×C8—1222no—
438C22×C8—1222no—
439C22×C8—2441no—
440C22×C8C22×D6111yescharacteristic
441C22×C8C22×D6111yescharacteristic
442C4⋊Q8—1222no—
443C4⋊Q8—1222no—
444#121—1222no—
445#121—1222no—
446#121—2444no—
447#121—2441no—
448#121—2441no—
449C4×D4—1222no—
450C4×D4—1222no—
451C4×D4—1222no—
452C4×D4—1222no—
453C2×C4⋊C4—611no—
454C2×C4⋊C4—611no—
455C2×C4⋊C4—611no—
456C2×C4⋊C4—611no—
457C2×C4⋊C4—1221no—
458C2×C4⋊C4—1221no—
459C2×C4⋊C4—1221no—
460C2×C4⋊C4C22×D6111yescharacteristic
461C2×C4⋊C4C22×D6111yescharacteristic
462C2×C4⋊C4C22×D6111yescharacteristic
463C2×C4⋊C4C22×D6111yescharacteristic
464C2×C22⋊C4—21no—
465C2×C22⋊C4—21no—
466C2×C22⋊C4—611no—
467C2×C22⋊C4—611no—
468C2×C22⋊C4—1221no—
469C2×C22⋊C4—1221no—
470C2×C22⋊C4—1221no—
471C2×C22⋊C4—1221no—
472C2×C22⋊C4—1221no—
473C2×C22⋊C4—1221no—
474C2×C22⋊C4—1221no—
475C2×C42—611no—
476C2×C42—1221no—
477#106—22no—
478#106—41no—
479#106—1222no—
480#106—2441no—
481C4⋊C8—614no—
482#102—1222no—
483#102—1222no—
484#102—1222no—
485#102—1222no—
486C22⋊C8—1222no—
487C22⋊C8—1222no—
488C4×C8—1222no—
489#95—21no—
490#95—21no—
491#95—1221no—
492#95—1221no—
493#95—1221no—
494#95—1221no—
495#95—1221no—
496C24—611no—
497C24—1221no—
498C24D4×D6111yescharacteristic
499C2×Q8—4881no—
500C2×Q8—4881no—
501C2×Q8—2442no—
502C2×D4—614no—
503C2×D4—612no—
504C2×D4—1222no—
505C2×D4—1222no—
506C2×D4—1221no—
507C2×D4—1221no—
508C2×D4—1221no—
509C2×D4—1221no—
510C2×D4—1221no—
511C2×D4—4881no—
512C2×D4—4881no—
513C2×D4—2442no—
514C2×D4—2442no—
515C2×D4—2442no—
516C2×D4—2442no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—611no—
528C22×C4—611no—
529C22×C4—611no—
530C22×C4—1221no—
531C22×C4—1221no—
532C22×C4—1221no—
533C22×C4—1221no—
534C22×C4—1221no—
535C22×C4—1221no—
536C22×C4—1221no—
537C22×C4—1221no—
538C22×C4—1221no—
539C22×C4—2442no—
540C22×C4—2442no—
541C22×C4—2442no—
542C22×C4D4×D6111yescharacteristic
543C22×C4C23×D6111yescharacteristic
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—44no—
549C2×C8—612no—
550C2×C8—1221no—
551C2×C8—1221no—
552C2×C8—1221no—
553C2×C8—1221no—
554C2×C8—1221no—
555C2×C8—2444no—
556C2×C8#1175822212yes—
557C2×C8D4×D6112yes—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—1222no—
567C4⋊C4—1221no—
568C4⋊C4—1221no—
569C4⋊C4—1221no—
570C4⋊C4—1221no—
571C4⋊C4—1221no—
572C4⋊C4—1221no—
573C4⋊C4—4881no—
574C4⋊C4—2442no—
575C4⋊C4—2442no—
576C22⋊C4—42no—
577C22⋊C4—81no—
578C22⋊C4—1222no—
579C22⋊C4—1222no—
580C22⋊C4—4881no—
581C22⋊C4—4881no—
582C22⋊C4—4881no—
583C22⋊C4—2442no—
584C22⋊C4—2442no—
585C22⋊C4—2442no—
586C22⋊C4—2442no—
587C42—612no—
588C42—612no—
589C42—2442no—
590C23—21no—
591C23—21no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—612no—
597C23—1221no—
598C23—1221no—
599C23—1221no—
600C23—1221no—
601C23—1221no—
602C23—1221no—
603C23—1222no—
604C23—2441no—
605C23—2441no—
606C23—2441no—
607C23—2441no—
608C23—2441no—
609C23—2441no—
610C23SD16×D6112yes—
611C23C2×D4×D6111yescharacteristic
612Q8—4884no—
613D4—1228no—
614D4—1222no—
615D4—1222no—
616D4—4884no—
617D4—4884no—
618D4—2441no—
619D4—2441no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
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—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—612no—
640C2×C4—612no—
641C2×C4—612no—
642C2×C4—612no—
643C2×C4—1221no—
644C2×C4—1221no—
645C2×C4—1221no—
646C2×C4—1221no—
647C2×C4—1221no—
648C2×C4—4884no—
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—2441no—
658C2×C4—2441no—
659C2×C4—2441no—
660C2×C4—2441no—
661C2×C4—2441no—
662C2×C4C2×D4×D6111yescharacteristic
663C2×C4#41×D6111yescharacteristic
664C2×C4#41×D6111yescharacteristic
665C2×C4C2×#1175822211yescharacteristic
666C2×C4#1451982211yescharacteristic
667C2×C4#1451982511yescharacteristic
668C8—22no—
669C8—22no—
670C8—1222no—
671C8—2441no—
672C22—22no—
673C22—22no—
674C22—22no—
675C22—41no—
676C22—41no—
677C22—41no—
678C22—41no—
679C22—1222no—
680C22—1222no—
681C22—1222no—
682C22—4881no—
683C22—4881no—
684C22—4881no—
685C22—4881no—
686C22—2442no—
687C22—2442no—
688C22—2442no—
689C22—2441no—
690C22—2441no—
691C22—2441no—
692C22—2441no—
693C22#121×D6111yescharacteristic
694C22#1684040111yescharacteristic
695C22#1684041311yescharacteristic
696C22C2×SD16×D6111yescharacteristic
697C22#135×D6111yescharacteristic
698C22#1684056411yescharacteristic
699C22#1684056811yescharacteristic
700C4—41no—
701C4—81no—
702C4—81no—
703C4—81no—
704C4—81no—
705C4—614no—
706C4—1222no—
707C4—4881no—
708C4—4881no—
709C4—4881no—
710C4—2441no—
711C4#1684029011yescharacteristic
712C4#1684038211yescharacteristic
713C4#1684040211yescharacteristic
714C4#1684042211yescharacteristic
715C2—42no—
716C2—4882no—
717C2—2442no—
718C2#2144939511yescharacteristic
719C2#465×D6111yescharacteristic
720C2#2145549211yescharacteristic
721C2#2145763811yescharacteristic
722C2#2145774211yescharacteristic
723C2#2145817211yescharacteristic
724C2#2145823911yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#1807C2
socleC23×C61C22×D4
prime radical#21450734C2
hypercenter#1807D61
hypocenterC61#25339
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1807

Complements

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

NH ≅ G/Ntype
1. C2×#16840051C2semidirect
2. C2×C8×C22⋊D61C2semidirect
3. #21450989C2semidirect
5. #21447255C2semidirect
6. #21447253C2semidirect
7. #21447010C2semidirect
8. #21447008C2semidirect
9. #21446778C2semidirect
10. #21446579C2semidirect
11. #21446247C2semidirect
12. #21446246C2semidirect
13. #21445843C2semidirect
14. #21445633C2semidirect
15. C61×#1807C2semidirect
104. #14519706D4semidirect
366. #1807D61semidirect
423. C61#25339semidirect

Maximal subgroups

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

subgroupindex
C2×#168400512
C2×C8×C22⋊D612
#214509892
#214507342
#214472552
#214472532
#214470102
#214470082
#214467782
#214465792
#214462472
#214462462
#214458432
#214456332
C61×#18072
#2533961