Finite Group Databasebeta

← #30547642

Subgroups — #30547642

Order 15616.

2038 conjugacy classes of subgroups.

The subgroup lattice has 698 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459224C211yesmaximal, characteristic, complemented
2C2×#16840245C211yesmaximal, characteristic
3#21455685C214yesmaximal, complemented
4#21455679C214yesmaximal, complemented
5#21455674C214yesmaximal, complemented
6#21455668C214yesmaximal, complemented
7#21455621C214yesmaximal, complemented
8#21455613C214yesmaximal, complemented
9C2×#16839805C211yesmaximal, characteristic, complemented
10C2×#16839804C211yesmaximal, characteristic, complemented
11#21454382C211yesmaximal, characteristic, complemented
12#21454338C211yesmaximal, characteristic
13C61×#2896C211yesmaximal, characteristic
14C22×#11758194C2211yescharacteristic
15#16840393C2212yescomplemented
16#16840393C2212yescomplemented
17#16840390—21no—
18#16840390—21no—
19#16840390C2212yescomplemented
20#16840390C2212yescomplemented
21#16840388—22no—
22#16840319—22no—
23#16840315—22no—
24#16840315C2214yes—
25#16840245—22no—
26#16840245—22no—
27#16840245C2214yes—
28#16840245C2214yes—
29C2×Q8×Dic61C2212yes—
30C2×D4×Dic61—22no—
31C2×D4×Dic61C2212yes—
32C2×#14519736—21no—
33C2×#14519736C2211yescharacteristic
34C2×#14519736C2211yescharacteristic
35C22×C4⋊Dic61—21no—
36C22×C4⋊Dic61C2211yescharacteristic
37#16840071C2218yescomplemented
38#16840067C2218yescomplemented
39#16840064C2218yescomplemented
40#16840060C2218yescomplemented
41#16840055C2218yescomplemented
42#16840050C2218yescomplemented
43#16840045C2218yescomplemented
44#16840040C2218yescomplemented
45#16839805C2214yes—
46#16839805C2214yescomplemented
47#16839804C2214yes—
48#16839804C2214yescomplemented
49C2×#14519711C2212yescomplemented
50C2×#14519710C2212yescomplemented
51C2×#14519709C2212yescomplemented
52C2×#14519708C2212yescomplemented
53#16839790C2214yescomplemented
54#16839788C2214yescomplemented
55#16839785C2214yes—
56#16839771C2212yes—
57#16839767C2212yes—
58#16839763C2212yes—
59#16839763C2212yes—
60#16839758C2214yes—
61C22×#41×C61C2211yescharacteristic
62C22×M16×C61C2211yescharacteristic
63C2×#117×C61C2211yescharacteristic
64C61×#419C2212yes—
65C61×#418C2212yes—
66C61×#417C2212yes—
67C61×#417C2212yes—
68C61×#416C2214yes—
69C23×Dic61—21no—
70C23×Dic61—22no—
71C2×#11758194—24no—
72C2×#11758194C2312yes—
73C2×#11758194C2312yes—
74C22×#92418C2312yes—
75#14519777—22no—
76#14519777—22no—
77#14519776—22no—
78#14519776—22no—
79#14519776C2314yes—
80#14519776C2314yes—
81#14519769—22no—
82#14519769—22no—
83#14519768—22no—
84#14519768—22no—
85#14519768C2314yes—
86#14519768C2314yes—
87#14519756—24no—
88#14519756—24no—
89#14519754—24no—
90#14519754—24no—
91#14519754—24no—
92#14519754—24no—
93Q8×Dic61—24no—
94Q8×Dic61C2318yes—
95C4×Dic122—24no—
96C4×Dic122—24no—
97D4×Dic61—28no—
98D4×Dic61—28no—
99D4×Dic61—24no—
100D4×Dic61C2318yes—
101#14519736—21no—
102#14519736—21no—
103#14519736—24no—
104#14519736—24no—
105#14519736D412yes—
106#14519736D412yes—
107#14519736C2312yes—
108#14519736C2312yes—
109#14519736C2312yes—
110#14519736C2312yes—
111C2×C4⋊Dic61—21no—
112C2×C4⋊Dic61—21no—
113C2×C4⋊Dic61—21no—
114C2×C4⋊Dic61—22no—
115C2×C4⋊Dic61—24no—
116C2×C4⋊Dic61—24no—
117C2×C4⋊Dic61D411yescharacteristic
118C2×C4⋊Dic61D411yescharacteristic
119C2×C4⋊Dic61C2312yes—
120C2×C4⋊Dic61C2312yes—
121C2×C4⋊Dic61C2312yes—
122C2×C4⋊Dic61C2311yescharacteristic
123C2×C4⋊Dic61C2311yescharacteristic
124C2×C22⋊Dic61—21no—
125C2×C22⋊Dic61—22no—
126C2×C22⋊Dic61D412yes—
127C2×C4×Dic61—21no—
128C2×C4×Dic61—22no—
129C2×C4×Dic61C2312yes—
130#14519711C2318yes—
131#14519710C2318yes—
132#14519709C2318yes—
133#14519708C2318yes—
134#14519706C2318yes—
135#14519706C2318yes—
136#14519701C2314yes—
137#14519701C2314yes—
138#14519698C2314yes—
139#14519698C2314yes—
140C2×#41×C61—21no—
141C2×#41×C61—21no—
142C2×#41×C61—24no—
143C2×#41×C61Q818yescomplemented
144C2×#41×C61C2312yes—
145C2×#41×C61C2312yes—
146C22×Q8×C61C2311yescharacteristic
147C22×D4×C61—21no—
148C22×D4×C61C2311yescharacteristic
149C23×C4×C61—21no—
150C23×C4×C61C2311yescharacteristic
151C2×M16×C61—24no—
152C2×M16×C61C2312yes—
153C2×M16×C61C2312yes—
154C22×C8×C61C2312yes—
155#117×C61—21no—
156#117×C61—21no—
157#117×C61C2312yes—
158#117×C61C2312yes—
159C2×C4⋊C4×C61C2311yescharacteristic
160C2×C4⋊C4×C61C2311yescharacteristic
161C2×C22⋊C4×C61—21no—
162C2×C42×C61—21no—
163#103×C61C2314yes—
164#103×C61C2314yes—
165#102×C61C2314yes—
166#102×C61C2314yes—
167C24×C61—21no—
168C24×C61C2×D411yescharacteristic
169#41×C61—28no—
170#41×C61—28no—
171#41×C61—24no—
172#41×C61—24no—
173#41×C61C2×Q818yes—
174#41×C61C2×Q818yes—
175C2×Q8×C61—21no—
176C2×Q8×C61—22no—
177C2×Q8×C61C2×Q814yes—
178C2×Q8×C61C2412yes—
179C2×D4×C61—28no—
180C2×D4×C61—22no—
181C2×D4×C61—22no—
182C2×D4×C61—21no—
183C2×D4×C61—22no—
184C2×D4×C61C2×Q814yes—
185C2×D4×C61C2412yes—
186C22×C4×C61—21no—
187C22×C4×C61—28no—
188C22×C4×C61—22no—
189C22×C4×C61—22no—
190C22×C4×C61—21no—
191C22×C4×C61—21no—
192C22×C4×C61C2×D411yescharacteristic
193C22×C4×C61C2×D411yescharacteristic
194C22×C4×C61C2×D411yescharacteristic
195C22×C4×C61C2×Q814yes—
196C22×C4×C61#4114yes—
197C22×C4×C61C2411yescharacteristic
198C22×C4×C61C2411yescharacteristic
199C22×C4×C61C2411yescharacteristic
200C22×Dic61—22no—
201C22×Dic61—22no—
202C22×Dic61—22no—
203C22×Dic61—21no—
204C22×Dic61—21no—
205C22×Dic61—28no—
206C22×Dic61—84no—
207C22×Dic61—82no—
208C22×Dic61C2×D412yes—
209C22×Dic61C2×D412yes—
210C2×Dic122—24no—
211C2×Dic122—24no—
212M16×C61—24no—
213M16×C61—24no—
214C2×C8×C61—24no—
215C2×C8×C61C2414yes—
216C4⋊C4×C61—21no—
217C4⋊C4×C61—21no—
218C4⋊C4×C61C2412yes—
219C4⋊C4×C61C2412yes—
220C22⋊C4×C61—22no—
221C22⋊C4×C61—22no—
222C42×C61—22no—
223C42×C61—22no—
224C22⋊Dic61—22no—
225C22⋊Dic61—22no—
226C22⋊Dic61—28no—
227C22⋊Dic61C2×D414yes—
228C22⋊Dic61C2×D414yes—
229C4⋊Dic61—22no—
230C4⋊Dic61—22no—
231C4⋊Dic61—22no—
232C4⋊Dic61—21no—
233C4⋊Dic61—21no—
234C4⋊Dic61—28no—
235C4⋊Dic61—24no—
236C4⋊Dic61—24no—
237C4⋊Dic61C2×D412yes—
238C4⋊Dic61C2×D412yes—
239C4⋊Dic61C2×D412yes—
240C4⋊Dic61C2×D412yes—
241C4⋊Dic61C2412yes—
242C4⋊Dic61C2412yes—
243C4⋊Dic61C2414yes—
244#11758196—24no—
245#11758196—24no—
246#11758196—24no—
247#11758196—24no—
248C4×Dic61—22no—
249C4×Dic61—22no—
250C4×Dic61—28no—
251C4×Dic61C2×D414yes—
252C4×Dic61C2414yes—
253#11758194—24no—
254#11758194—24no—
255C2×#92418—24no—
256C2×#92418C2414yes—
257C23×C61—24no—
258C23×C61—22no—
259C23×C61—41no—
260C23×C61—41no—
261C23×C61—42no—
262C23×C61—42no—
263C23×C61C22⋊Q814yes—
264C23×C61C22×D411yescharacteristic
265C23×C61C22×D411yescharacteristic
266C23×C61C22×D411yescharacteristic
267Q8×C61—24no—
268Q8×C61—22no—
269Q8×C61C22×Q814yes—
270D4×C61—28no—
271D4×C61—28no—
272D4×C61—24no—
273D4×C61—22no—
274D4×C61C22×Q814yes—
275C2×C4×C61—24no—
276C2×C4×C61—22no—
277C2×C4×C61—28no—
278C2×C4×C61—28no—
279C2×C4×C61—22no—
280C2×C4×C61—22no—
281C2×C4×C61—81no—
282C2×C4×C61—81no—
283C2×C4×C61C22⋊Q814yes—
284C2×C4×C61C22⋊Q814yes—
285C2×C4×C61C22⋊Q814yes—
286C2×C4×C61C22×D411yescharacteristic
287C2×C4×C61C22×D411yescharacteristic
288C2×C4×C61C22×D411yescharacteristic
289C2×C4×C61C22×Q812yes—
290C2×C4×C61C22×Q812yes—
291C2×C4×C61C22×Q812yes—
292C2×C4×C61C2×#4112yes—
293C2×C4×C61C2×#4112yes—
294C2×C4×C61C2×#4112yes—
295C2×C4×C61C2511yescharacteristic
296C2×Dic61—22no—
297C2×Dic61—22no—
298C2×Dic61—24no—
299C2×Dic61—42no—
300C2×Dic61—42no—
301C2×Dic61—44no—
302C2×Dic61—88no—
303C2×Dic61—81no—
304C2×Dic61—81no—
305C2×Dic61—82no—
306C2×Dic61—82no—
307C2×Dic61C22×D414yes—
308C2×Dic61C22×D414yes—
309Dic122—84no—
310Dic122—84no—
311C8×C61—24no—
312#92418—24no—
313#60492—611nomaximal, Sylow
314C22×C61—21no—
315C22×C61—21no—
316C22×C61—21no—
317C22×C61—21no—
318C22×C61—21no—
319C22×C61—21no—
320C22×C61—24no—
321C22×C61—44no—
322C22×C61—48no—
323C22×C61—42no—
324C22×C61—42no—
325C22×C61C2×C22⋊Q812yes—
326C22×C61C2×C22⋊Q812yes—
327C22×C61C2×C22⋊Q812yes—
328C22×C61C23×D411yescharacteristic
329C4×C61—24no—
330C4×C61—42no—
331C4×C61—42no—
332C4×C61C2×C22⋊Q812yes—
333C4×C61C2×C22⋊Q812yes—
334C4×C61C2×C22⋊Q812yes—
335C4×C61C23×Q811yescharacteristic
336C4×C61C22×#4111yescharacteristic
337Dic61—24no—
338Dic61—24no—
339Dic61—42no—
340Dic61—44no—
341Dic61—42no—
342#3458—611no—
343C2×#520—611no—
344#3084—614no—
345#3084—614no—
346#3083—614no—
347#3083—614no—
348#3078—614no—
349#3077—614no—
350C2×#428—611no—
351C2×#428—611no—
352#2905—611no—
353#2896—611no—
354#2896D6111yescharacteristic
355C2×C61—22no—
356C2×C61—22no—
357C2×C61—22no—
358C2×C61—44no—
359C2×C61C22×C22⋊Q811yescharacteristic
360C2×C61#358511yescharacteristic
361C2×C61#358611yescharacteristic
362C22×#41C2×D6111yescharacteristic
363C22×M16—611no—
364C22×M16C2×D6111yescharacteristic
365#544—612no—
366#544—612no—
367#544—612no—
368#544—612no—
369#544—1221no—
370#544—1221no—
371#543—1222no—
372#533—614no—
373#533—1222no—
374#533—1222no—
375#520—614no—
376#520—614no—
377#520—1222no—
378#520—1222no—
379C2×C4×Q8—612no—
380C2×C4×D4—612no—
381C2×C4×D4—1222no—
382C2×#117—611no—
383C2×#117—611no—
384C2×#117—1221no—
385C2×#117C2×D6111yescharacteristic
386C22×C4⋊C4—611no—
387C22×C4⋊C4—1221no—
388#479—618no—
389#479—618no—
390#478—618no—
391#478—618no—
392#477—618no—
393#476—618no—
394#475—618no—
395#474—618no—
396#428—614no—
397#428—614no—
398#428—614no—
399#428—614no—
400C2×#107—612no—
401C2×#107—612no—
402C2×#106—612no—
403C2×#106—612no—
404#424—614no—
405#424—614no—
406#423—614no—
407#419—612no—
408#419C2×D6112yes—
409#418—612no—
410#418C2×D6112yes—
411#417—612no—
412#417—612no—
413#417C2×D6112yes—
414#417C2×D6112yes—
415#416—614no—
416#416C2×D6114yes—
417C61#6049211yescharacteristic, complemented, Sylow
418C2×#41—21no—
419C2×#41—21no—
420C2×#41—24no—
421C2×#41Dic12218yescomplemented
422C2×#41C22×D6112yes—
423C2×#41C22×D6112yes—
424C22×Q8C22×D6111yescharacteristic
425C22×D4—21no—
426C22×D4C22×D6111yescharacteristic
427C23×C4—21no—
428C23×C4—1222no—
429C23×C4—1221no—
430C23×C4C22×D6111yescharacteristic
431C2×M16—24no—
432C2×M16—612no—
433C2×M16—612no—
434C2×M16—1224no—
435C2×M16C22×D6112yes—
436C2×M16C22×D6112yes—
437C22×C8—612no—
438C22×C8C22×D6112yes—
439C4⋊Q8—614no—
440C4⋊Q8—614no—
441C4⋊Q8—1222no—
442C4⋊Q8—1222no—
443C4⋊Q8—1222no—
444C4⋊Q8—1222no—
445#125—614no—
446#125—614no—
447#125—1222no—
448#125—1222no—
449#125—1222no—
450#125—1222no—
451C22⋊Q8—1224no—
452C22⋊Q8—1224no—
453C22⋊Q8—1224no—
454C22⋊Q8—1224no—
455C22⋊Q8—1224no—
456C22⋊Q8—1224no—
457C4×Q8—618no—
458C4×Q8—1224no—
459C4×Q8—1224no—
460C4×Q8—1224no—
461C4×D4—618no—
462C4×D4—1224no—
463C4×D4—1228no—
464C4×D4—1228no—
465#117—21no—
466#117—21no—
467#117—612no—
468#117—612no—
469#117—612no—
470#117—612no—
471#117—612no—
472#117—612no—
473#117—1224no—
474#117—1224no—
475#117—1221no—
476#117—1221no—
477#117C22×D6112yes—
478#117C22×D6112yes—
479C2×C4⋊C4—611no—
480C2×C4⋊C4—611no—
481C2×C4⋊C4—612no—
482C2×C4⋊C4—612no—
483C2×C4⋊C4—612no—
484C2×C4⋊C4—611no—
485C2×C4⋊C4—611no—
486C2×C4⋊C4—1224no—
487C2×C4⋊C4—1224no—
488C2×C4⋊C4—1222no—
489C2×C4⋊C4—1221no—
490C2×C4⋊C4—1221no—
491C2×C4⋊C4—1221no—
492C2×C4⋊C4C22×D6111yescharacteristic
493C2×C4⋊C4C22×D6111yescharacteristic
494C2×C22⋊C4—21no—
495C2×C22⋊C4—612no—
496C2×C22⋊C4—1222no—
497C2×C22⋊C4—1221no—
498C2×C42—21no—
499C2×C42—612no—
500C2×C42—1222no—
501C2×C42—1221no—
502#107—618no—
503#107—618no—
504#106—618no—
505#106—618no—
506C4⋊C8—618no—
507C4⋊C8—618no—
508#103—614no—
509#103—614no—
510#103C22×D6114yes—
511#103C22×D6114yes—
512#102—614no—
513#102—614no—
514#102C22×D6114yes—
515#102C22×D6114yes—
516C24—21no—
517C24D4×D6111yescharacteristic
518#41—24no—
519#41—24no—
520#41—28no—
521#41—28no—
522#41C2×Dic12218yes—
523#41C2×Dic12218yes—
524C2×Q8—21no—
525C2×Q8—22no—
526C2×Q8—1224no—
527C2×Q8—1224no—
528C2×Q8C2×Dic12214yes—
529C2×Q8C23×D6112yes—
530C2×D4—22no—
531C2×D4—22no—
532C2×D4—28no—
533C2×D4—21no—
534C2×D4—22no—
535C2×D4C2×Dic12214yes—
536C2×D4C23×D6112yes—
537C22×C4—21no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—28no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—612no—
544C22×C4—612no—
545C22×C4—1228no—
546C22×C4—1221no—
547C22×C4—1221no—
548C22×C4—1222no—
549C22×C4—1222no—
550C22×C4—1222no—
551C22×C4—4884no—
552C22×C4—4882no—
553C22×C4C2×Dic12214yes—
554C22×C4D4×D6111yescharacteristic
555C22×C4D4×D6111yescharacteristic
556C22×C4D4×D6111yescharacteristic
557C22×C4#1175822414yes—
558C22×C4C23×D6111yescharacteristic
559C22×C4C23×D6111yescharacteristic
560C22×C4C23×D6111yescharacteristic
561M16—24no—
562M16—24no—
563M16—1224no—
564M16—1224no—
565C2×C8—24no—
566C2×C8—614no—
567C2×C8—1224no—
568C2×C8C23×D6114yes—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—612no—
572C4⋊C4—612no—
573C4⋊C4—612no—
574C4⋊C4—612no—
575C4⋊C4—612no—
576C4⋊C4—612no—
577C4⋊C4—614no—
578C4⋊C4—1228no—
579C4⋊C4—1224no—
580C4⋊C4—1224no—
581C4⋊C4—1224no—
582C4⋊C4—1224no—
583C4⋊C4—1224no—
584C4⋊C4—1224no—
585C4⋊C4—1222no—
586C4⋊C4—1222no—
587C4⋊C4—1222no—
588C4⋊C4—1221no—
589C4⋊C4—1221no—
590C4⋊C4C23×D6112yes—
591C4⋊C4C23×D6112yes—
592C22⋊C4—22no—
593C22⋊C4—22no—
594C22⋊C4—614no—
595C22⋊C4—614no—
596C22⋊C4—1228no—
597C22⋊C4—1222no—
598C22⋊C4—1222no—
599C42—22no—
600C42—22no—
601C42—614no—
602C42—614no—
603C42—1228no—
604C42—1222no—
605C42—1222no—
606C23—24no—
607C23—22no—
608C23—41no—
609C23—41no—
610C23—42no—
611C23—42no—
612C23#1451975414yes—
613C23C2×D4×D6111yescharacteristic
614C23C2×D4×D6111yescharacteristic
615C23C2×D4×D6111yescharacteristic
616Q8—24no—
617Q8—22no—
618Q8—4884no—
619Q8—4884no—
620Q8C22×Dic12214yes—
621D4—28no—
622D4—28no—
623D4—24no—
624D4—22no—
625D4C22×Dic12214yes—
626C2×C4—24no—
627C2×C4—22no—
628C2×C4—28no—
629C2×C4—28no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—81no—
633C2×C4—81no—
634C2×C4—614no—
635C2×C4—614no—
636C2×C4—1222no—
637C2×C4—1222no—
638C2×C4—1224no—
639C2×C4—4888no—
640C2×C4—4881no—
641C2×C4—4881no—
642C2×C4—4882no—
643C2×C4—4882no—
644C2×C4—2442no—
645C2×C4—2442no—
646C2×C4—2444no—
647C2×C4#1451975414yes—
648C2×C4#1451975414yes—
649C2×C4#1451975414yes—
650C2×C4C2×D4×D6111yescharacteristic
651C2×C4C2×D4×D6111yescharacteristic
652C2×C4C2×D4×D6111yescharacteristic
653C2×C4C22×Dic12212yes—
654C2×C4C22×Dic12212yes—
655C2×C4C22×Dic12212yes—
656C2×C4C2×#1175822412yes—
657C2×C4C2×#1175822412yes—
658C2×C4C2×#1175822412yes—
659C2×C4C24×D6111yescharacteristic
660C8—24no—
661C8—1224no—
662C22—21no—
663C22—21no—
664C22—21no—
665C22—21no—
666C22—21no—
667C22—21no—
668C22—24no—
669C22—44no—
670C22—48no—
671C22—42no—
672C22—42no—
673C22C2×#1451975412yes—
674C22C2×#1451975412yes—
675C22C2×#1451975412yes—
676C22C22×D4×D6111yescharacteristic
677C4—24no—
678C4—42no—
679C4—42no—
680C4—1224no—
681C4—1224no—
682C4—2444no—
683C4—2442no—
684C4—2442no—
685C4C2×#1451975412yes—
686C4C2×#1451975412yes—
687C4C2×#1451975412yes—
688C4C23×Dic12211yescharacteristic
689C4C22×#1175822411yescharacteristic
690C2—22no—
691C2—22no—
692C2—22no—
693C2—44no—
694C2C22×#1451975411yescharacteristic
695C2#2146059611yescharacteristic
696C2#2146060311yescharacteristic
subgroupG/H
centerC22C22×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#2896C2
socleC22×C61C23×D4
prime radicalC22×#41×C61C22
hypercenter#2896D61
hypocenterC61#60492
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2896

Complements

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

NH ≅ G/Ntype
1. #21459224C2semidirect
3. #21455685C2semidirect
4. #21455679C2semidirect
5. #21455674C2semidirect
6. #21455668C2semidirect
7. #21455621C2semidirect
8. #21455613C2semidirect
9. C2×#16839805C2semidirect
10. C2×#16839804C2semidirect
11. #21454382C2semidirect
15. #16840393C22semidirect
16. #16840393C22semidirect
19. #16840390C22semidirect
20. #16840390C22semidirect
37. #16840071C22semidirect
38. #16840067C22semidirect
39. #16840064C22semidirect
40. #16840060C22semidirect
41. #16840055C22semidirect
42. #16840050C22semidirect
43. #16840045C22semidirect
44. #16840040C22semidirect
46. #16839805C22semidirect
48. #16839804C22semidirect
49. C2×#14519711C22semidirect
50. C2×#14519710C22semidirect
51. C2×#14519709C22semidirect
52. C2×#14519708C22semidirect
53. #16839790C22semidirect
54. #16839788C22semidirect
143. C2×#41×C61Q8semidirect
417. C61#60492semidirect
421. C2×#41Dic122semidirect

Maximal subgroups

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

subgroupindex
#214592242
C2×#168402452
#214556852
#214556792
#214556742
#214556682
#214556212
#214556132
C2×#168398052
C2×#168398042
#214543822
#214543382
C61×#28962
#6049261