Finite Group Databasebeta

← #30615602

Subgroups — #30615602

Order 15616.

1954 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519856C211yesmaximal, characteristic, complemented
2C2×#16840753C212yesmaximal, complemented
3D61⋊#407C211yesmaximal, characteristic, complemented
4#21461807C214yesmaximal, complemented
5#21461805C214yesmaximal, complemented
6#21461508C212yesmaximal, complemented
7#525×D61C211yesmaximal, characteristic
8C2×D61⋊M16C2212yes—
9C2×#14519856—28no—
10C2×#14519856—22no—
11C2×#14519856C2214yes—
12C22×C4⋊#6923C2212yes—
13C22×C22⋊#6923—21no—
14C22×C4×#6923—21no—
15#16840753—28no—
16C2×#14519840C2214yescomplemented
17C2×#14519839C2214yescomplemented
18#16840734—21no—
19#16840733—22no—
20#16840732—21no—
21D61⋊(C22⋊C8)C2214yes—
22#16840635C2218yescomplemented
23C2×#41×D61C2211yescharacteristic
24C23×C4×D61C2211yescharacteristic
25#16840275C412yescomplemented
26#16840274C411yescharacteristic, complemented
27#16840273C411yescharacteristic, complemented
28#16840272C412yescomplemented
29#16840271—22no—
30#16840270—21no—
31#16840269C411yescharacteristic, complemented
32#16840268—21no—
33#123×D61—21no—
34C22⋊Q8×D61C2212yes—
35#121×D61C2212yes—
36#120×D61—21no—
37C4×D4×D61—22no—
38#117×D61C2211yescharacteristic
39C61×#525C411yescharacteristic, complemented
40C23×#6923—22no—
41C2×#11758213—22no—
42D61⋊M16—24no—
43D61⋊M16—24no—
44C2×#11758217—22no—
45C2×D61⋊C8C2314yes—
46#14519856—216no—
47#14519856—216no—
48C2×C4⋊#6923—22no—
49C2×C4⋊#6923—24no—
50C2×C4⋊#6923D418yescomplemented
51C2×C4⋊#6923C2314yes—
52C2×C22⋊#6923—28no—
53C2×C22⋊#6923—24no—
54C2×C4×#6923—28no—
55C2×C4×#6923—24no—
56#14519840—28no—
57#14519839—28no—
58#14519834—24no—
59C22⋊#92420—24no—
60C24×D61D411yescharacteristic
61C2×#11758226C2×C411yescharacteristic
62C2×#11758222—21no—
63C2×#11758222C2×C411yescharacteristic
64C2×#11758224—21no—
65C2×#11758224C2×C411yescharacteristic
66#41×D61—24no—
67#41×D61—24no—
68C2×Q8×D61C2311yescharacteristic
69C2×D4×D61—22no—
70C2×D4×D61—21no—
71C2×D4×D61C2311yescharacteristic
72C23×Dic61D411yescharacteristic
73C22×C4×D61—24no—
74C22×C4×D61—24no—
75C22×C4×D61—21no—
76C22×C4×D61C2×C411yescharacteristic
77C22×C4×D61C2×C412yes—
78C22×C4×D61D412yes—
79C22×C4×D61D411yescharacteristic
80C22×C4×D61D412yes—
81C22×C4×D61D411yescharacteristic
82C22×C4×D61C2312yes—
83C22×C4×D61C2311yescharacteristic
84#14519762—22no—
85#14519761—21no—
86#14519760—21no—
87#14519759—22no—
88#14519758—21no—
89#14519757C2×C412yescomplemented
90#14519756C2×C412yescomplemented
91#14519755—22no—
92#14519754—22no—
93#14519753C2×C412yescomplemented
94#14519752C2×C412yescomplemented
95#14519751C2×C412yescomplemented
96#14519750—22no—
97#14519749—22no—
98#14519748C2×C412yescomplemented
99#14519747—21no—
100#14519747—22no—
101#14519746—21no—
102#14519745—21no—
103#14519745—22no—
104C4×D244—22no—
105D4×Dic61—22no—
106#14519739—22no—
107C4×C22⋊D61—22no—
108C4×C22⋊D61—22no—
109#14519737—22no—
110#14519737—22no—
111#14519736C2×C411yescharacteristic
112#14519735C2×C412yes—
113#14519734—21no—
114#14519733—21no—
115C4⋊C4×D61—22no—
116C4⋊C4×D61C2312yes—
117C22⋊C4×D61—21no—
118C22⋊C4×D61—22no—
119C22⋊C4×D61—22no—
120C42×D61—21no—
121C2×#41×C61C2×C411yescharacteristic
122C23×C4×C61C2×C411yescharacteristic
123#123×C61—21no—
124C22⋊Q8×C61C2×C412yescomplemented
125#121×C61C2×C412yescomplemented
126#120×C61—21no—
127C4×D4×C61—22no—
128#117×C61C2×C411yescharacteristic
129C24×C61C22⋊C411yescharacteristic
130C23×D61—22no—
131C23×D61—22no—
132C23×D61—21no—
133C23×D61—44no—
134C23×D61C22⋊C411yescharacteristic
135C23×D61C22⋊C412yes—
136C23×D61C2×D412yes—
137C23×D61C2×D411yescharacteristic
138C22×#6923—28no—
139C22×#6923—24no—
140C22×#6923—48no—
141#41×C61—24no—
142C2×Q8×C61C22×C411yescharacteristic
143C2×D4×C61—21no—
144C2×D4×C61—22no—
145C2×D4×C61C22×C411yescharacteristic
146C22×C4×C61—24no—
147C22×C4×C61—21no—
148C22×C4×C61C22⋊C412yes—
149C22×C4×C61C22⋊C411yescharacteristic
150C22×C4×C61C22×C412yes—
151C22×C4×C61C22×C411yescharacteristic
152C2×C22⋊D61—21no—
153C2×C22⋊D61—22no—
154C2×C22⋊D61—21no—
155C2×C22⋊D61—22no—
156C2×C22⋊D61—21no—
157C22×Dic61—24no—
158C22×Dic61—21no—
159C22×Dic61C22⋊C412yes—
160C22×Dic61C22⋊C411yescharacteristic
161C22×Dic61C2×D412yes—
162C22×Dic61C2×D411yescharacteristic
163#11758226—24no—
164Q8×D61—22no—
165Q8×D61—22no—
166#11758224—24no—
167#11758224—44no—
168D4×D61—22no—
169D4×D61—22no—
170D4×D61—48no—
171D4×D61—42no—
172D4×D61—42no—
173#11758222—24no—
174#11758222—44no—
175C2×D244—21no—
176C2×D244—22no—
177C2×D244C22×C411yescharacteristic
178C2×C4×D61—22no—
179C2×C4×D61—22no—
180C2×C4×D61—24no—
181C2×C4×D61—24no—
182C2×C4×D61—28no—
183C2×C4×D61—24no—
184C2×C4×D61—28no—
185C2×C4×D61—24no—
186C2×C4×D61—24no—
187C2×C4×D61—24no—
188C2×C4×D61—21no—
189C2×C4×D61—22no—
190C2×C4×D61—21no—
191C2×C4×D61—21no—
192C2×C4×D61—42no—
193C2×C4×D61—42no—
194C2×C4×D61C22⋊C412yes—
195C2×C4×D61C22⋊C412yes—
196C2×C4×D61C22⋊C412yes—
197C2×C4×D61C22×C412yes—
198C2×C4×D61C22×C411yescharacteristic
199C2×C4×D61C2×D412yes—
200C2×C4×D61C2×D412yes—
201C2×C4×D61C2×D414yes—
202C2×C4×D61C2×D411yescharacteristic
203C2×C4×D61C2×D411yescharacteristic
204C2×C4×D61#4114yes—
205C2×C4×D61C2411yescharacteristic
206C2×Dic122—21no—
207C2×Dic122C22×C411yescharacteristic
208C22⋊#6923—216no—
209#11758217—44no—
210C2×#92420—24no—
211C4⋊#6923—28no—
212C4⋊#6923—24no—
213C4⋊#6923C2×D418yes—
214C4×#6923—216no—
215#11758213—44no—
216D61⋊C8—24no—
217D61⋊C8—24no—
218C4⋊C4×C61—22no—
219C4⋊C4×C61C22×C412yes—
220C22⋊C4×C61—21no—
221C22⋊C4×C61—22no—
222C22⋊C4×C61—22no—
223C42×C61—21no—
224C22⋊Dic61—21no—
225C22⋊Dic61—22no—
226C22⋊Dic61—22no—
227#11758198—22no—
228#11758198—22no—
229#11758198—22no—
230#11758198—22no—
231#11758198—22no—
232C4⋊Dic61—22no—
233C4⋊Dic61C22×C412yes—
234#11758196—22no—
235#11758196—22no—
236#11758196—22no—
237C4×Dic61—21no—
238C4×Dic61—22no—
239C23×C61—22no—
240C23×C61—21no—
241C23×C61—42no—
242C23×C61C2×C22⋊C412yes—
243C23×C61C2×C22⋊C411yescharacteristic
244C22×D61—24no—
245C22×D61—22no—
246C22×D61—22no—
247C22×D61—22no—
248C22×D61—24no—
249C22×D61—24no—
250C22×D61—24no—
251C22×D61—21no—
252C22×D61—42no—
253C22×D61—42no—
254C22×D61—42no—
255C22×D61—48no—
256C22×D61—48no—
257C22×D61—41no—
258C22×D61—41no—
259C22×D61—44no—
260C22×D61C2×C22⋊C412yes—
261C22×D61C2×C22⋊C411yescharacteristic
262C22×D61#12012yes—
263C22×D61#12312yes—
264C22×D61C22×D411yescharacteristic
265C2×#6923—28no—
266C2×#6923—416no—
267C2×#6923—48no—
268Q8×C61—22no—
269D4×C61—22no—
270D4×C61—44no—
271D4×C61—42no—
272C2×C4×C61—22no—
273C2×C4×C61—24no—
274C2×C4×C61—24no—
275C2×C4×C61—22no—
276C2×C4×C61—21no—
277C2×C4×C61—42no—
278C2×C4×C61C2×C22⋊C412yes—
279C2×C4×C61C2×C22⋊C411yescharacteristic
280C2×C4×C61C4×D414yes—
281C2×C4×C61C23×C411yescharacteristic
282C22⋊D61—44no—
283C22⋊D61—44no—
284C22⋊D61—42no—
285C22⋊D61—42no—
286C22⋊D61—42no—
287C2×Dic61—22no—
288C2×Dic61—24no—
289C2×Dic61—24no—
290C2×Dic61—22no—
291C2×Dic61—21no—
292C2×Dic61—42no—
293C2×Dic61C2×C22⋊C412yes—
294C2×Dic61C2×C22⋊C411yescharacteristic
295C2×Dic61#12114yes—
296C2×Dic61C22×D411yescharacteristic
297D244—22no—
298D244—44no—
299D244—42no—
300C4×D61—22no—
301C4×D61—22no—
302C4×D61—24no—
303C4×D61—24no—
304C4×D61—24no—
305C4×D61—24no—
306C4×D61—24no—
307C4×D61—41no—
308C4×D61—41no—
309C4×D61—44no—
310C4×D61—42no—
311C4×D61—42no—
312C4×D61C4×D414yes—
313C4×D61#12012yes—
314C4×D61#12114yes—
315C4×D61#12312yes—
316C4×D61C22×D412yes—
317C4×D61C2×#4112yes—
318Dic122—22no—
319Dic122—42no—
320#92420—44no—
321#20910—611nomaximal, Sylow
322C22×C61—22no—
323C22×C61—22no—
324C22×C61—22no—
325C22×C61—22no—
326C22×C61—44no—
327C22×C61—42no—
328C22×C61—41no—
329C22×C61#38612yes—
330C22×C61C22×C22⋊C411yescharacteristic
331C2×D61—22no—
332C2×D61—24no—
333C2×D61—24no—
334C2×D61—22no—
335C2×D61—22no—
336C2×D61—22no—
337C2×D61—48no—
338C2×D61—44no—
339C2×D61—44no—
340C2×D61—44no—
341C2×D61—42no—
342C2×D61—41no—
343C2×D61—82no—
344C2×D61—82no—
345C2×D61#38612yes—
346C2×D61C2×#12011yescharacteristic
347C2×D61C2×#12311yescharacteristic
348C2×D61#57514yes—
349#6923—48no—
350C4×C61—22no—
351C4×C61—42no—
352C4×C61—41no—
353C4×C61#38612yes—
354C4×C61C2×C4×D412yes—
355Dic61—22no—
356Dic61—42no—
357Dic61—41no—
358Dic61#38612yes—
359Dic61C2×#12112yes—
360C2×#525—611no—
361C22×#117—611no—
362C2×#417—612no—
363C2×#407—611no—
364#1875—614no—
365#1873—614no—
366#1736—612no—
367C2×C61—22no—
368C2×C61—42no—
369C2×C61—81no—
370C2×C61C2×#38611yescharacteristic
371C2×C61#289612yes—
372D61—22no—
373D61—42no—
374D61—81no—
375D61#300512yes—
376D61#309312yes—
377C22×#41—611no—
378C24×C4—611no—
379C22×M16—612no—
380#525—611no—
381#525—611no—
382#525—612no—
383#525—612no—
384#525—611no—
385#525—1222no—
386#525—1221no—
387#525—1221no—
388#525#692311yescharacteristic, complemented
389C2×#123—1221no—
390C2×C22⋊Q8—612no—
391C2×#121—612no—
392C2×#120—1221no—
393C2×C4×D4—1222no—
394C2×#117—611no—
395C2×#117—614no—
396C2×#117—1228no—
397C2×#117—1222no—
398C22×C4⋊C4—612no—
399C22×C22⋊C4—1221no—
400C22×C42—1221no—
401#417—1228no—
402C2×#103—614no—
403C2×#102—614no—
404#407—1221no—
405#407—1222no—
406#407—1221no—
407C2×C22⋊C8—614no—
408#340—618no—
409C61#2091011yescharacteristic, complemented, Sylow
410C25—611no—
411C2×#41—611no—
412C2×#41—611no—
413C2×#41—611no—
414C2×#41—1221no—
415C2×#41—1221no—
416C2×#41—1224no—
417C2×#41—1224no—
418C2×#41C2×#692311yescharacteristic
419C22×Q8—611no—
420C22×D4—611no—
421C22×D4—1222no—
422C22×D4—1221no—
423C23×C4—611no—
424C23×C4—611no—
425C23×C4—612no—
426C23×C4—611no—
427C23×C4—611no—
428C23×C4—612no—
429C23×C4—612no—
430C23×C4—612no—
431C23×C4—611no—
432C23×C4—1224no—
433C23×C4—1224no—
434C23×C4—1221no—
435C23×C4—1222no—
436C23×C4C2×#692311yescharacteristic
437C2×M16—1222no—
438C2×M16—1224no—
439C2×M16—1224no—
440C2×M16—1222no—
441C22×C8—614no—
442#123—21no—
443#123—1222no—
444#123—1221no—
445#123—1222no—
446#123—1221no—
447#123—1221no—
448C22⋊Q8—612no—
449C22⋊Q8—612no—
450C22⋊Q8—612no—
451C22⋊Q8—1222no—
452C22⋊Q8—1222no—
453C22⋊Q8C2×#692312yescomplemented
454#121—612no—
455#121—612no—
456#121—612no—
457#121—1222no—
458#121—1222no—
459#121C2×#692312yescomplemented
460#120—21no—
461#120—1221no—
462#120—1222no—
463#120—1222no—
464#120—1221no—
465#120—1221no—
466C4×D4—22no—
467C4×D4—1222no—
468C4×D4—1222no—
469C4×D4—1222no—
470C4×D4—1222no—
471C4×D4—1222no—
472C4×D4—1222no—
473C4×D4—1222no—
474#117—611no—
475#117—612no—
476#117—1221no—
477#117—1221no—
478#117—12216no—
479#117—12216no—
480#117C2×#692311yescharacteristic
481C2×C4⋊C4—614no—
482C2×C4⋊C4—618no—
483C2×C4⋊C4—612no—
484C2×C4⋊C4—1222no—
485C2×C4⋊C4—1222no—
486C2×C4⋊C4—1224no—
487C2×C22⋊C4—1222no—
488C2×C22⋊C4—1221no—
489C2×C22⋊C4—1222no—
490C2×C22⋊C4—1224no—
491C2×C22⋊C4—1228no—
492C2×C42—1221no—
493C2×C42—1224no—
494C2×C42—1228no—
495#103—1228no—
496#102—1228no—
497C22⋊C8—1224no—
498C22⋊C8—1224no—
499C24—611no—
500C24—612no—
501C24—612no—
502C24—611no—
503C24—1222no—
504C24—1222no—
505C24—1221no—
506C24—2444no—
507C24C22⋊#692311yescharacteristic
508#41—24no—
509#41—1224no—
510#41—1224no—
511#41—1224no—
512#41—2444no—
513#41—2444no—
514C2×Q8—611no—
515C2×Q8—1221no—
516C2×Q8—1222no—
517C2×Q8—1222no—
518C2×Q8C22×#692311yescharacteristic
519C2×D4—22no—
520C2×D4—21no—
521C2×D4—611no—
522C2×D4—1222no—
523C2×D4—1221no—
524C2×D4—1222no—
525C2×D4—1222no—
526C2×D4—1221no—
527C2×D4—1222no—
528C2×D4—1221no—
529C2×D4—1222no—
530C2×D4—1221no—
531C2×D4—2442no—
532C2×D4—2442no—
533C2×D4—2448no—
534C2×D4C22×#692311yescharacteristic
535C22×C4—24no—
536C22×C4—21no—
537C22×C4—611no—
538C22×C4—611no—
539C22×C4—611no—
540C22×C4—614no—
541C22×C4—614no—
542C22×C4—611no—
543C22×C4—611no—
544C22×C4—612no—
545C22×C4—612no—
546C22×C4—611no—
547C22×C4—612no—
548C22×C4—612no—
549C22×C4—612no—
550C22×C4—612no—
551C22×C4—612no—
552C22×C4—612no—
553C22×C4—1224no—
554C22×C4—1224no—
555C22×C4—1224no—
556C22×C4—1228no—
557C22×C4—1224no—
558C22×C4—1228no—
559C22×C4—1224no—
560C22×C4—1221no—
561C22×C4—1222no—
562C22×C4—1222no—
563C22×C4—1222no—
564C22×C4—1221no—
565C22×C4—1224no—
566C22×C4—1221no—
567C22×C4—1224no—
568C22×C4—1224no—
569C22×C4—1228no—
570C22×C4—1221no—
571C22×C4—2442no—
572C22×C4—2442no—
573C22×C4—2448no—
574C22×C4C22⋊#692312yes—
575C22×C4C22⋊#692311yescharacteristic
576C22×C4C22×#692312yes—
577C22×C4C22×#692311yescharacteristic
578M16—2444no—
579M16—2444no—
580C2×C8—1224no—
581C2×C8—1224no—
582C2×C8—1224no—
583C4⋊C4—22no—
584C4⋊C4—618no—
585C4⋊C4—612no—
586C4⋊C4—1222no—
587C4⋊C4—1222no—
588C4⋊C4—1222no—
589C4⋊C4—1228no—
590C4⋊C4—1224no—
591C4⋊C4—1222no—
592C4⋊C4C22×#692312yes—
593C22⋊C4—21no—
594C22⋊C4—22no—
595C22⋊C4—22no—
596C22⋊C4—1222no—
597C22⋊C4—1222no—
598C22⋊C4—1222no—
599C22⋊C4—1222no—
600C22⋊C4—1222no—
601C22⋊C4—12216no—
602C22⋊C4—1221no—
603C22⋊C4—1222no—
604C22⋊C4—1222no—
605C42—21no—
606C42—1222no—
607C42—12216no—
608C42—1221no—
609C23—22no—
610C23—21no—
611C23—42no—
612C23—611no—
613C23—612no—
614C23—612no—
615C23—611no—
616C23—612no—
617C23—1224no—
618C23—1222no—
619C23—1222no—
620C23—1224no—
621C23—1224no—
622C23—1224no—
623C23—1222no—
624C23—1221no—
625C23—2442no—
626C23—2442no—
627C23—2442no—
628C23—2441no—
629C23—2441no—
630C23—2444no—
631C23—2448no—
632C23—2448no—
633C23C2×C22⋊#692312yes—
634C23C2×C22⋊#692311yescharacteristic
635Q8—22no—
636Q8—1222no—
637Q8—2442no—
638D4—22no—
639D4—44no—
640D4—42no—
641D4—1222no—
642D4—2442no—
643D4—2444no—
644D4—2442no—
645D4—2444no—
646D4—2442no—
647D4—2444no—
648D4—2442no—
649C2×C4—22no—
650C2×C4—24no—
651C2×C4—24no—
652C2×C4—22no—
653C2×C4—21no—
654C2×C4—42no—
655C2×C4—614no—
656C2×C4—611no—
657C2×C4—611no—
658C2×C4—612no—
659C2×C4—614no—
660C2×C4—612no—
661C2×C4—614no—
662C2×C4—612no—
663C2×C4—612no—
664C2×C4—612no—
665C2×C4—1224no—
666C2×C4—1224no—
667C2×C4—1222no—
668C2×C4—1222no—
669C2×C4—1224no—
670C2×C4—1224no—
671C2×C4—1224no—
672C2×C4—1222no—
673C2×C4—1224no—
674C2×C4—1224no—
675C2×C4—1228no—
676C2×C4—1222no—
677C2×C4—1221no—
678C2×C4—2442no—
679C2×C4—2441no—
680C2×C4—2441no—
681C2×C4—2444no—
682C2×C4—2442no—
683C2×C4—2448no—
684C2×C4—24416no—
685C2×C4—2442no—
686C2×C4C2×C22⋊#692312yes—
687C2×C4C2×C22⋊#692311yescharacteristic
688C2×C4D4×#692314yes—
689C2×C4C23×#692311yescharacteristic
690C8—2444no—
691C22—22no—
692C22—22no—
693C22—22no—
694C22—22no—
695C22—44no—
696C22—42no—
697C22—41no—
698C22—614no—
699C22—611no—
700C22—611no—
701C22—612no—
702C22—1224no—
703C22—1224no—
704C22—1222no—
705C22—1222no—
706C22—1222no—
707C22—1222no—
708C22—4882no—
709C22—4882no—
710C22—2444no—
711C22—2444no—
712C22—2444no—
713C22—2448no—
714C22—2442no—
715C22—2441no—
716C22#1684071012yes—
717C22C22×C22⋊#692311yescharacteristic
718C4—22no—
719C4—42no—
720C4—41no—
721C4—612no—
722C4—612no—
723C4—1222no—
724C4—2448no—
725C4—2442no—
726C4—2441no—
727C4#1684071012yes—
728C4C2×D4×#692312yes—
729C2—22no—
730C2—42no—
731C2—81no—
732C2—612no—
733C2—612no—
734C2—1222no—
735C2—4881no—
736C2—2442no—
737C2C2×#1684071011yescharacteristic
738C2#2146243912yes—
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#525C4
socleC22×C61C22×C22⋊C4
prime radical#525×D61C2
cosocleC2×C4×D61C24
hypercenter#525#6923
hypocenterC61#20910
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #525

Complements

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

NH ≅ G/Ntype
1. C22×#14519856C2semidirect
2. C2×#16840753C2semidirect
3. D61⋊#407C2semidirect
4. #21461807C2semidirect
5. #21461805C2semidirect
6. #21461508C2semidirect
16. C2×#14519840C22semidirect
17. C2×#14519839C22semidirect
22. #16840635C22semidirect
25. #16840275C4semidirect
26. #16840274C4semidirect
27. #16840273C4semidirect
28. #16840272C4semidirect
31. #16840269C4semidirect
39. C61×#525C4semidirect
50. C2×C4⋊#6923D4semidirect
89. #14519757C2×C4semidirect
90. #14519756C2×C4semidirect
93. #14519753C2×C4semidirect
94. #14519752C2×C4semidirect
95. #14519751C2×C4semidirect
98. #14519748C2×C4semidirect
124. C22⋊Q8×C61C2×C4semidirect
125. #121×C61C2×C4semidirect
388. #525#6923semidirect
409. C61#20910semidirect
453. C22⋊Q8C2×#6923semidirect
459. #121C2×#6923semidirect

Maximal subgroups

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

subgroupindex
C22×#145198562
C2×#168407532
D61⋊#4072
#214618072
#214618052
#214615082
#525×D612
#2091061