Finite Group Databasebeta

← #29700429

Subgroups — #29700429

Order 15616.

1114 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
1C2×#16839899C211yesmaximal, characteristic
2C2×#16839769C211yesmaximal, characteristic, complemented
3#21448853C211yesmaximal, characteristic
4Q8×#11758198C211yesmaximal, characteristic, complemented
5#21446674C211yesmaximal, characteristic, complemented
6#21446509C211yesmaximal, characteristic, complemented
7#21446459C211yesmaximal, characteristic, complemented
8#21446254C211yesmaximal, characteristic
9#21446176C211yesmaximal, characteristic, complemented
10#21446153C211yesmaximal, characteristic, complemented
11#21446087C211yesmaximal, characteristic, complemented
12#21446015C211yesmaximal, characteristic, complemented
13#103×Dic61C211yesmaximal, characteristic, complemented
14#21445604C211yesmaximal, characteristic, complemented
15C2×C61×#440C211yesmaximal, characteristic, complemented
16C22×Q8×D61C2211yescharacteristic
17C22×#11758200C2211yescharacteristic
18C22×#11758189C2211yescharacteristic
19C2×#14519748C2211yescharacteristic
20C2×Q8×Dic61C2211yescharacteristic
21C2×#14519735C2211yescharacteristic
22#16839899C418yescomplemented
23C2×#14519708C2211yescharacteristic
24#16839769—24no—
25C2×#14519702C2211yescharacteristic
26C2×#14519702C2211yescharacteristic
27C2×#14519701C2211yescharacteristic
28C2×#14519701C2211yescharacteristic
29C2×#14519700C2211yescharacteristic
30C2×#14519698C2211yescharacteristic
31C2×#14519689C2211yescharacteristic
32C2×C8×Dic61C2211yescharacteristic
33#16839668—21no—
34#16839668C2211yescharacteristic
35#16839667—21no—
36#16839667C2211yescharacteristic
37#16839665C2211yescharacteristic
38#16839662—21no—
39#16839660C2211yescharacteristic
40#16839650—21no—
41#16839641—21no—
42#16839619—21no—
43#16839619C2211yescharacteristic
44C4⋊C4×Dic61C2211yescharacteristic
45C4×#11758198—21no—
46C4×#11758198C2211yescharacteristic
47C4×C22⋊Dic61—21no—
48#16839525C2211yescharacteristic
49#16839525C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839524C2211yescharacteristic
52#16839517C2211yescharacteristic
53#16839516C2211yescharacteristic
54C22×SD16×C61C2211yescharacteristic
55C2×C4×Q8×C61C2211yescharacteristic
56C2×C4×D4×C61C2211yescharacteristic
57C61×#440—24no—
58C2×#107×C61C2211yescharacteristic
59C2×#103×C61C2211yescharacteristic
60C2×#102×C61C2211yescharacteristic
61C2×#97×C61C2211yescharacteristic
62C22×Dic122—21no—
63C22×Dic122C2311yescharacteristic
64C2×Q8×D61—22no—
65C2×Q8×D61—22no—
66C2×Q8×D61—22no—
67C2×Q8×D61—41no—
68C2×Q8×D61—41no—
69C2×Q8×D61C2×C414yescomplemented
70C22×C22⋊D61—21no—
71C22×C4×D61—21no—
72C22×C4×D61C2311yescharacteristic
73C2×#11758200—41no—
74C2×#11758200—41no—
75C2×#11758200C2×C414yes—
76C2×#11758189—22no—
77C2×#11758189—22no—
78C2×#11758189—41no—
79C22×#92418C2311yescharacteristic
80C22×#92418C2311yescharacteristic
81#14519748—22no—
82#14519748C2×C414yes—
83Q8×Dic61—22no—
84Q8×Dic61—41no—
85#14519735—22no—
86#14519735—41no—
87C2×C4⋊Dic61—21no—
88C2×C4⋊Dic61C2311yescharacteristic
89C2×C4⋊Dic61C2311yescharacteristic
90C2×C4⋊Dic61C2311yescharacteristic
91C2×#11758196—21no—
92C2×C22⋊Dic61—21no—
93C2×C22⋊Dic61—21no—
94C2×C22⋊Dic61—21no—
95C2×#11758198—21no—
96C2×#11758198—21no—
97C2×#11758198D411yescharacteristic
98C2×#11758198D411yescharacteristic
99C2×C4×Dic61—21no—
100C2×C4×Dic61—21no—
101C2×C4×Dic61—21no—
102C2×C4×Dic61C2311yescharacteristic
103#14519708—41no—
104#14519702—22no—
105#14519702C2×C414yescomplemented
106#14519701—22no—
107#14519701C2×C414yescomplemented
108#14519700—22no—
109#14519698—41no—
110#14519689C2×C414yescomplemented
111C8×Dic61—41no—
112#14519684—21no—
113#14519684—21no—
114#14519684—21no—
115#14519684—21no—
116#14519684—21no—
117#14519684—21no—
118#14519684—21no—
119#14519684D411yescharacteristic
120#14519684D411yescharacteristic
121C22×Q8×C61C2311yescharacteristic
122C22×D4×C61C2311yescharacteristic
123C23×C4×C61—21no—
124C2×SD16×C61—22no—
125C2×SD16×C61—22no—
126C2×SD16×C61C2×C414yes—
127C22×C8×C61C2311yescharacteristic
128C22×C8×C61C2311yescharacteristic
129C4×Q8×C61—22no—
130C4×Q8×C61—41no—
131C4×D4×C61—22no—
132C4×D4×C61—41no—
133C2×C4⋊C4×C61—21no—
134C2×C4⋊C4×C61C2311yescharacteristic
135C2×C4⋊C4×C61C2311yescharacteristic
136C2×C22⋊C4×C61—21no—
137C2×C42×C61—21no—
138C2×C42×C61C2311yescharacteristic
139#107×C61—22no—
140#103×C61D414yescomplemented
141#102×C61—22no—
142#97×C61—22no—
143C24×C61—21no—
144C23×D61C2×D411yescharacteristic
145C2×Q8×C61—21no—
146C2×Q8×C61—21no—
147C2×Q8×C61—21no—
148C2×Q8×C61C22×C412yes—
149C2×Q8×C61C2×D412yes—
150C2×Q8×C61#4112yes—
151C2×D4×C61—21no—
152C2×D4×C61—21no—
153C2×D4×C61—21no—
154C2×D4×C61—21no—
155C2×D4×C61—21no—
156C2×D4×C61C22×C412yes—
157C22×C4×C61—21no—
158C22×C4×C61—21no—
159C22×C4×C61—21no—
160C22×C4×C61—42no—
161C22×C4×C61—42no—
162C22×C4×C61—81no—
163C22×C4×C61C2×D411yescharacteristic
164C22×C4×C61C2×D411yescharacteristic
165C22×C4×C61C2411yescharacteristic
166C2×C22⋊D61—24no—
167C2×C22⋊D61—81no—
168C2×C22⋊D61—81no—
169C22×Dic61—21no—
170C22×Dic61—21no—
171C22×Dic61—21no—
172C22×Dic61—21no—
173C22×Dic61C2×D411yescharacteristic
174C22×Dic61C2×D411yescharacteristic
175C22×Dic61C2×D411yescharacteristic
176Q8×D61—28no—
177Q8×D61—44no—
178Q8×D61—44no—
179Q8×D61—44no—
180C2×C4×D61—21no—
181C2×C4×D61—21no—
182C2×C4×D61—21no—
183C2×C4×D61—21no—
184C2×C4×D61—24no—
185C2×C4×D61—42no—
186C2×C4×D61—42no—
187C2×C4×D61C22×C412yes—
188C2×C4×D61#4112yes—
189C2×Dic122—21no—
190C2×Dic122—21no—
191C2×Dic122—21no—
192C2×Dic122—21no—
193C2×Dic122—21no—
194C2×Dic122—24no—
195C2×Dic122—42no—
196C2×Dic122—42no—
197C2×Dic122C22×C412yes—
198SD16×C61—28no—
199C2×C8×C61—21no—
200C2×C8×C61—21no—
201C2×C8×C61—21no—
202C2×C8×C61—21no—
203C2×C8×C61C22×C412yes—
204C2×C8×C61C2×D412yes—
205C4⋊C4×C61—21no—
206C4⋊C4×C61—21no—
207C4⋊C4×C61—21no—
208C4⋊C4×C61—42no—
209C4⋊C4×C61C2×D412yes—
210C22⋊C4×C61—42no—
211C42×C61—21no—
212C42×C61—21no—
213C42×C61—42no—
214C22⋊Dic61—24no—
215C22⋊Dic61—42no—
216C22⋊Dic61—81no—
217#11758200—44no—
218#11758198—22no—
219#11758198—41no—
220#11758198—42no—
221#11758198—42no—
222C4⋊Dic61—21no—
223C4⋊Dic61—21no—
224C4⋊Dic61—21no—
225C4⋊Dic61—21no—
226C4⋊Dic61—21no—
227C4⋊Dic61—42no—
228C4⋊Dic61C22×C412yes—
229#11758196—81no—
230C4×Dic61—21no—
231C4×Dic61—21no—
232C4×Dic61—42no—
233C4×Dic61—42no—
234C4×Dic61—81no—
235C2×#92418—21no—
236C2×#92418—21no—
237C2×#92418—21no—
238C2×#92418—21no—
239C2×#92418—21no—
240C2×#92418C22×C412yes—
241#11758189—44no—
242C23×C61—22no—
243C23×C61—41no—
244C23×C61—41no—
245C23×C61—41no—
246C23×C61—41no—
247C23×C61—41no—
248C23×C61—41no—
249C23×C61C22×D411yescharacteristic
250C22×D61—21no—
251C22×D61—21no—
252C22×D61—21no—
253C22×D61—21no—
254C22×D61—21no—
255C22×D61—21no—
256C22×D61C4×D412yes—
257Q8×C61—22no—
258Q8×C61—22no—
259Q8×C61—22no—
260Q8×C61C4×D414yes—
261D4×C61—22no—
262D4×C61—22no—
263D4×C61—41no—
264D4×C61—41no—
265C2×C4×C61—22no—
266C2×C4×C61—22no—
267C2×C4×C61—22no—
268C2×C4×C61—22no—
269C2×C4×C61—21no—
270C2×C4×C61—21no—
271C2×C4×C61—21no—
272C2×C4×C61—21no—
273C2×C4×C61—21no—
274C2×C4×C61—21no—
275C2×C4×C61—41no—
276C2×C4×C61—41no—
277C2×C4×C61—41no—
278C2×C4×C61—41no—
279C2×C4×C61—41no—
280C2×C4×C61—84no—
281C2×C4×C61C23×C411yescharacteristic
282C2×C4×C61C22×D411yescharacteristic
283C2×C4×C61C2×#4111yescharacteristic
284C2×C4×C61C2×#4111yescharacteristic
285C2×C4×C61H(5,𝔽2)11yescharacteristic
286C2×C4×C61H(5,𝔽2)11yescharacteristic
287C22⋊D61—84no—
288C2×Dic61—21no—
289C2×Dic61—21no—
290C2×Dic61—21no—
291C2×Dic61—21no—
292C2×Dic61—22no—
293C2×Dic61—22no—
294C2×Dic61—21no—
295C2×Dic61—21no—
296C2×Dic61—21no—
297C2×Dic61—41no—
298C2×Dic61—41no—
299C2×Dic61—41no—
300C2×Dic61—41no—
301C2×Dic61—41no—
302C2×Dic61—41no—
303C2×Dic61—41no—
304C2×Dic61—41no—
305C2×Dic61—41no—
306C2×Dic61—41no—
307C2×Dic61C4×D412yes—
308C2×Dic61#13712yes—
309C4×D61—22no—
310C4×D61—22no—
311C4×D61—22no—
312C4×D61—22no—
313C4×D61—48no—
314Dic122—22no—
315Dic122—22no—
316Dic122—48no—
317Dic122—41no—
318Dic122—41no—
319C8×C61—22no—
320C8×C61—22no—
321#92418—22no—
322#92418—41no—
323#22865—611nomaximal, Sylow
324C22×C61—42no—
325C22×C61—42no—
326C22×C61—42no—
327C22×C61—81no—
328C22×C61—81no—
329C22×C61—81no—
330C22×C61—81no—
331C22×C61C2×C4×D411yescharacteristic
332C22×C61D4211yescharacteristic
333C22×C61#54611yescharacteristic
334C22×C61C2×#13711yescharacteristic
335C22×C61#57511yescharacteristic
336C22×C61#57711yescharacteristic
337C22×C61#57711yescharacteristic
338C2×D61—22no—
339C2×D61—22no—
340C2×D61—22no—
341C2×D61—41no—
342C2×D61—41no—
343C2×D61—41no—
344C2×D61—41no—
345C4×C61—24no—
346C4×C61—41no—
347C4×C61—42no—
348C4×C61—41no—
349C4×C61—81no—
350C4×C61C2×C4×D411yescharacteristic
351C4×C61#51811yescharacteristic
352C4×C61#54611yescharacteristic
353C4×C61#55111yescharacteristic
354Dic61—22no—
355Dic61—22no—
356Dic61—42no—
357Dic61—42no—
358Dic61—41no—
359Dic61—81no—
360Dic61—81no—
361C2×#448—611no—
362C2×#440D6111yescharacteristic, complemented
363C2×#419—611no—
364#2363—611no—
365Q8×C22⋊C4—611no—
366#1968—611no—
367#1935—611no—
368#1928—611no—
369#1895—611no—
370#1880—611no—
371#1877—611no—
372#1865—611no—
373#1854—611no—
374C4×#103—611no—
375#1753—611no—
376C2×C61—82no—
377C2×C61#235811yescharacteristic
378C2×C61C4×#13711yescharacteristic
379C2×C61#294911yescharacteristic
380C2×C61#327511yescharacteristic
381C2×C61#327811yescharacteristic
382C2×C61#332011yescharacteristic
383C2×C61#332111yescharacteristic
384D61—42no—
385C23×Q8—611no—
386C22×SD16—611no—
387C22×SD16C2×D6111yescharacteristic
388C22×M16—611no—
389C2×#121—611no—
390C2×C4×Q8—611no—
391C2×C4×Q8C2×D6111yescharacteristic
392C2×C4×D4C2×D6111yescharacteristic
393C2×#117—611no—
394#448—618no—
395#440—24no—
396C2×#107C2×D6111yescharacteristic
397C2×#106—611no—
398#419—1224no—
399C2×#103—611no—
400C2×#103—611no—
401C2×#103—611no—
402C2×#103—611no—
403C2×#103—611no—
404C2×#103C2×D6111yescharacteristic
405C2×#102—611no—
406C2×#102C2×D6111yescharacteristic
407C2×C22⋊C8—611no—
408C2×#97C2×D6111yescharacteristic
409C2×C4×C8—611no—
410#391—611no—
411#391—611no—
412#391—1221no—
413#391—1221no—
414#390—611no—
415#390—1221no—
416#389—611no—
417#388—1221no—
418#386—1221no—
419#380—611no—
420#380—1221no—
421C4×C4⋊C4—611no—
422C4×C22⋊C4—611no—
423C4×C22⋊C4—1221no—
424C4×C22⋊C4—1221no—
425#340—611no—
426#340—611no—
427#340—611no—
428#340—611no—
429#336—611no—
430#336—611no—
431C61#2286511yescharacteristic, complemented, Sylow
432C22×Q8—614no—
433C22×Q8—611no—
434C22×Q8—1221no—
435C22×Q8—1222no—
436C22×Q8—1222no—
437C22×Q8—1222no—
438C22×Q8—2441no—
439C22×Q8—2441no—
440C22×Q8C22×D6111yescharacteristic
441C22×D4—1221no—
442C22×D4C22×D6111yescharacteristic
443C23×C4—21no—
444C23×C4—611no—
445C23×C4—1221no—
446C2×SD16—22no—
447C2×SD16—22no—
448C2×SD16—614no—
449C2×SD16—2441no—
450C2×SD16—2441no—
451C2×SD16C4×D6114yes—
452C2×M16—1222no—
453C2×M16—1222no—
454C2×M16—2441no—
455C22×C8—611no—
456C22×C8—611no—
457C22×C8C22×D6111yescharacteristic
458C22×C8C22×D6111yescharacteristic
459#121—614no—
460#121—1222no—
461C4×Q8—22no—
462C4×Q8—41no—
463C4×Q8—1222no—
464C4×Q8—2441no—
465C4×D4—22no—
466C4×D4—41no—
467#117—1222no—
468#117—2441no—
469C2×C4⋊C4—21no—
470C2×C4⋊C4—611no—
471C2×C4⋊C4—611no—
472C2×C4⋊C4—611no—
473C2×C4⋊C4—1221no—
474C2×C4⋊C4—1221no—
475C2×C4⋊C4C22×D6111yescharacteristic
476C2×C4⋊C4C22×D6111yescharacteristic
477C2×C22⋊C4—21no—
478C2×C22⋊C4—611no—
479C2×C22⋊C4—611no—
480C2×C22⋊C4—1221no—
481C2×C22⋊C4—1221no—
482C2×C22⋊C4—1221no—
483C2×C22⋊C4—1221no—
484C2×C22⋊C4—1221no—
485C2×C42—21no—
486C2×C42—611no—
487C2×C42—1221no—
488C2×C42—1221no—
489C2×C42—1221no—
490C2×C42C22×D6111yescharacteristic
491#107—22no—
492#106—2441no—
493#103—614no—
494#103—614no—
495#103—1222no—
496#103—1222no—
497#103—1222no—
498#103C22⋊D6114yescomplemented
499#102—22no—
500#102—2441no—
501C22⋊C8—614no—
502#97—22no—
503C4×C8—2441no—
504#95—611no—
505#95—611no—
506#95—1221no—
507#95—1221no—
508#95—1221no—
509#95—1221no—
510#95—1221no—
511#95—1221no—
512#95—1221no—
513C24—21no—
514C24—611no—
515C2×Q8—21no—
516C2×Q8—21no—
517C2×Q8—21no—
518C2×Q8—612no—
519C2×Q8—1224no—
520C2×Q8—1221no—
521C2×Q8—1228no—
522C2×Q8—1221no—
523C2×Q8—1221no—
524C2×Q8—1221no—
525C2×Q8—1221no—
526C2×Q8—2442no—
527C2×Q8—2442no—
528C2×Q8—2444no—
529C2×Q8—2444no—
530C2×Q8—2444no—
531C2×Q8C2×C4×D6112yes—
532C2×Q8#1175822212yes—
533C2×Q8C2×C22⋊D6112yes—
534C2×D4—21no—
535C2×D4—21no—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—1224no—
540C2×D4—4881no—
541C2×D4—4881no—
542C2×D4C2×C4×D6112yes—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—42no—
547C22×C4—42no—
548C22×C4—81no—
549C22×C4—611no—
550C22×C4—611no—
551C22×C4—612no—
552C22×C4—612no—
553C22×C4—611no—
554C22×C4—1224no—
555C22×C4—1221no—
556C22×C4—1221no—
557C22×C4—1221no—
558C22×C4—1221no—
559C22×C4—1221no—
560C22×C4—1221no—
561C22×C4—1221no—
562C22×C4—1221no—
563C22×C4—2442no—
564C22×C4—2442no—
565C22×C4D4×D6111yescharacteristic
566C22×C4D4×D6111yescharacteristic
567C22×C4C23×D6111yescharacteristic
568SD16—28no—
569SD16—2444no—
570M16—2444no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—612no—
576C2×C8—1221no—
577C2×C8—1221no—
578C2×C8—1221no—
579C2×C8—1221no—
580C2×C8—1221no—
581C2×C8C2×C4×D6112yes—
582C2×C8C2×C22⋊D6112yes—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—42no—
587C4⋊C4—612no—
588C4⋊C4—1221no—
589C4⋊C4—1221no—
590C4⋊C4—1221no—
591C4⋊C4—1221no—
592C4⋊C4—1221no—
593C4⋊C4—4881no—
594C4⋊C4—2442no—
595C4⋊C4C2×C22⋊D6112yes—
596C22⋊C4—42no—
597C22⋊C4—1222no—
598C22⋊C4—1224no—
599C22⋊C4—4881no—
600C22⋊C4—2441no—
601C22⋊C4—2442no—
602C22⋊C4—2442no—
603C22⋊C4—2442no—
604C42—21no—
605C42—21no—
606C42—42no—
607C42—1221no—
608C42—1221no—
609C42—4881no—
610C42—2442no—
611C42—2442no—
612C23—22no—
613C23—41no—
614C23—41no—
615C23—41no—
616C23—41no—
617C23—41no—
618C23—41no—
619C23—612no—
620C23—1221no—
621C23—1221no—
622C23—1221no—
623C23—1221no—
624C23—1221no—
625C23—1221no—
626C23C2×D4×D6111yescharacteristic
627Q8—22no—
628Q8—22no—
629Q8—22no—
630Q8—1222no—
631Q8—1222no—
632Q8—2448no—
633Q8—2441no—
634Q8—2441no—
635Q8C4×C22⋊D6114yes—
636D4—22no—
637D4—22no—
638D4—41no—
639D4—41no—
640D4—4884no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—22no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—84no—
657C2×C4—612no—
658C2×C4—612no—
659C2×C4—1221no—
660C2×C4—1221no—
661C2×C4—1221no—
662C2×C4—1221no—
663C2×C4—1222no—
664C2×C4—1222no—
665C2×C4—1222no—
666C2×C4—1222no—
667C2×C4—1222no—
668C2×C4—1222no—
669C2×C4—1221no—
670C2×C4—1221no—
671C2×C4—1221no—
672C2×C4—2448no—
673C2×C4—2441no—
674C2×C4—2441no—
675C2×C4—2441no—
676C2×C4—2441no—
677C2×C4—2441no—
678C2×C4—2441no—
679C2×C4—2441no—
680C2×C4—2441no—
681C2×C4—2441no—
682C2×C4—2441no—
683C2×C4C22×C4×D6111yescharacteristic
684C2×C4C22×C22⋊D6111yescharacteristic
685C2×C4#41×D6111yescharacteristic
686C2×C4C2×#1175822211yescharacteristic
687C2×C4#1451982211yescharacteristic
688C2×C4#1451982311yescharacteristic
689C8—22no—
690C8—22no—
691C8—1222no—
692C8—2441no—
693C22—42no—
694C22—42no—
695C22—42no—
696C22—81no—
697C22—81no—
698C22—81no—
699C22—81no—
700C22—1222no—
701C22—1222no—
702C22—1222no—
703C22—2441no—
704C22—2441no—
705C22—2441no—
706C22—2441no—
707C22C4×D4×D6111yescharacteristic
708C22D4×C22⋊D6111yescharacteristic
709C22#1684040811yescharacteristic
710C22#137×D6111yescharacteristic
711C22#1684055811yescharacteristic
712C22#1684057111yescharacteristic
713C22#1684057211yescharacteristic
714C4—24no—
715C4—41no—
716C4—42no—
717C4—41no—
718C4—81no—
719C4—1222no—
720C4—1222no—
721C4—4881no—
722C4—4881no—
723C4—2442no—
724C4—2441no—
725C4—2442no—
726C4C2×C4×C22⋊D6111yescharacteristic
727C4#1684023411yescharacteristic
728C4#1684040011yescharacteristic
729C4#1684044111yescharacteristic
730C2—82no—
731C2—2442no—
732C2#2144879611yescharacteristic
733C2#2145464111yescharacteristic
734C2#2145467511yescharacteristic
735C2#2145745011yescharacteristic
736C2#2145747911yescharacteristic
737C2#2145799511yescharacteristic
738C2#2145801011yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#440C2
socleC23×C61C22×D4
prime radicalC2×#14519748C22
cosocleC22×C4×C61C24
hypercenterC2×#440D61
hypocenterC61#22865
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#440

Complements

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

NH ≅ G/Ntype
2. C2×#16839769C2semidirect
4. Q8×#11758198C2semidirect
5. #21446674C2semidirect
6. #21446509C2semidirect
7. #21446459C2semidirect
9. #21446176C2semidirect
10. #21446153C2semidirect
11. #21446087C2semidirect
12. #21446015C2semidirect
13. #103×Dic61C2semidirect
14. #21445604C2semidirect
15. C2×C61×#440C2semidirect
22. #16839899C4semidirect
69. C2×Q8×D61C2×C4semidirect
105. #14519702C2×C4semidirect
107. #14519701C2×C4semidirect
110. #14519689C2×C4semidirect
140. #103×C61D4semidirect
362. C2×#440D61semidirect
431. C61#22865semidirect
498. #103C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168398992
C2×#168397692
#214488532
Q8×#117581982
#214466742
#214465092
#214464592
#214462542
#214461762
#214461532
#214460872
#214460152
#103×Dic612
#214456042
C2×C61×#4402
#2286561