Finite Group Databasebeta

← #29686391

Subgroups — #29686391

Order 15616.

1120 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839954C211yesmaximal, characteristic
2C2×#16839872C211yesmaximal, characteristic, complemented
3C2×C4×#11758199C211yesmaximal, characteristic, complemented
4#21448181C211yesmaximal, characteristic, complemented
5#21446747C211yesmaximal, characteristic, complemented
6#21446585C211yesmaximal, characteristic, complemented
7#21446443C211yesmaximal, characteristic, complemented
8#21446436C211yesmaximal, characteristic, complemented
9#21446170C211yesmaximal, characteristic, complemented
10#21446170C211yesmaximal, characteristic, complemented
11#21445826C211yesmaximal, characteristic, complemented
12#21445676C211yesmaximal, characteristic, complemented
13#21445644C211yesmaximal, characteristic, complemented
14C4×#14519698C211yesmaximal, characteristic, complemented
15C61×#2328C211yesmaximal, characteristic, complemented
16C22×#11758199C2211yescharacteristic
17C22×#11758199C2211yescharacteristic
18C2×C4×D244C2211yescharacteristic
19C2×C4×D244C2211yescharacteristic
20C2×C4×D244C2211yescharacteristic
21#16839954C418yescomplemented
22#16839872—24no—
23C4×#11758199—24no—
24C2×#14519710C2211yescharacteristic
25C2×#14519708C2211yescharacteristic
26C2×C4⋊#92418C2211yescharacteristic
27C2×C4⋊#92418C2211yescharacteristic
28C2×#14519698C2211yescharacteristic
29C2×#14519698C2211yescharacteristic
30C2×#14519698C2211yescharacteristic
31C2×#14519698C2211yescharacteristic
32C2×#14519698C2211yescharacteristic
33C2×#14519698C2211yescharacteristic
34C2×#14519697C2211yescharacteristic
35C2×#14519697C2211yescharacteristic
36C2×#14519688C2211yescharacteristic
37C2×C4×#92418C2211yescharacteristic
38C4×C4⋊Dic61C2211yescharacteristic
39C4×C4⋊Dic61C2211yescharacteristic
40C4×C4⋊Dic61C2211yescharacteristic
41#16839609—21no—
42#16839609—21no—
43#16839609—21no—
44#95×D61—21no—
45#16839524C2211yescharacteristic
46#16839524C2211yescharacteristic
47#16839524C2211yescharacteristic
48#16839524C2211yescharacteristic
49#16839517C2211yescharacteristic
50#16839517C2211yescharacteristic
51C2×#127×C61C2211yescharacteristic
52C2×C4×D4×C61C2211yescharacteristic
53C2×C4×D4×C61C2211yescharacteristic
54C61×#390C2211yescharacteristic
55C61×#390C2211yescharacteristic
56C61×#386—21no—
57C61×#386—21no—
58C61×#386—21no—
59C61×#386—21no—
60C61×#382C2211yescharacteristic
61C61×#376C2211yescharacteristic
62C22×D244C2311yescharacteristic
63C22×C4×D61—21no—
64C22×C4×D61—21no—
65C22×C4×D61—21no—
66C2×#11758199—22no—
67C2×#11758199—22no—
68C2×#11758199—22no—
69C2×#11758199—22no—
70C2×#11758199C2×C414yescomplemented
71C2×#11758199C2×C414yescomplemented
72C22×#92418C2311yescharacteristic
73C22×#92418C2311yescharacteristic
74C22×#92418C2311yescharacteristic
75C22×#92418C2311yescharacteristic
76C4×D244—22no—
77C4×D244—22no—
78C4×D244—22no—
79C4×D244—22no—
80C4×D244C2×C414yescomplemented
81C4×D244D414yescomplemented
82C2×C4⋊Dic61C2311yescharacteristic
83C2×C4⋊Dic61C2311yescharacteristic
84C2×C4⋊Dic61C2311yescharacteristic
85C2×#11758198—21no—
86C2×#11758198—21no—
87C2×#11758198—21no—
88C2×C4×Dic61—21no—
89C2×C4×Dic61—21no—
90C2×C4×Dic61—21no—
91#14519710—22no—
92#14519708—22no—
93C4⋊#92418—22no—
94C4⋊#92418C2×C414yescomplemented
95#14519698—22no—
96#14519698—22no—
97#14519698—22no—
98#14519698—22no—
99#14519698C2×C414yescomplemented
100#14519698C2×C414yescomplemented
101#14519697—22no—
102#14519697—22no—
103#14519688—22no—
104C4×#92418—22no—
105#14519684—21no—
106#14519684—21no—
107#14519684—21no—
108C22×D4×C61—21no—
109C22×D4×C61—21no—
110C22×D4×C61C2311yescharacteristic
111C22×D4×C61C2311yescharacteristic
112C23×C4×C61—21no—
113C23×C4×C61—21no—
114#127×C61—22no—
115#127×C61C2×C414yescomplemented
116C4×D4×C61—22no—
117C4×D4×C61—22no—
118C4×D4×C61—22no—
119C4×D4×C61—22no—
120C2×C4⋊C4×C61C2311yescharacteristic
121C2×C4⋊C4×C61C2311yescharacteristic
122C2×C22⋊C4×C61—21no—
123C2×C22⋊C4×C61—21no—
124C2×C22⋊C4×C61—21no—
125C2×C22⋊C4×C61—21no—
126C2×C22⋊C4×C61—21no—
127C2×C22⋊C4×C61—21no—
128C2×C42×C61C2311yescharacteristic
129C2×C42×C61C2311yescharacteristic
130C2×C42×C61C2311yescharacteristic
131#95×C61—21no—
132#95×C61—21no—
133#95×C61D411yescharacteristic
134#95×C61D411yescharacteristic
135#95×C61D411yescharacteristic
136#95×C61D411yescharacteristic
137C24×C61—21no—
138C24×C61—21no—
139C23×D61—21no—
140C2×D4×C61—24no—
141C2×D4×C61—24no—
142C2×D4×C61—21no—
143C2×D4×C61—21no—
144C2×D4×C61—21no—
145C2×D4×C61—21no—
146C2×D4×C61—21no—
147C2×D4×C61—21no—
148C2×D4×C61—21no—
149C2×D4×C61—21no—
150C2×D4×C61—21no—
151C2×D4×C61—21no—
152C2×D4×C61—81no—
153C2×D4×C61—81no—
154C2×D4×C61—81no—
155C2×D4×C61—81no—
156C2×D4×C61C22×C412yes—
157C2×D4×C61C22×C412yes—
158C22×C4×C61—21no—
159C22×C4×C61—21no—
160C22×C4×C61—42no—
161C22×C4×C61—42no—
162C22×C4×C61—81no—
163C22×C4×C61—81no—
164C22×C4×C61—81no—
165C22×C4×C61—81no—
166C22×C4×C61C2×D411yescharacteristic
167C22×C4×C61C2×D411yescharacteristic
168C22×C4×C61C2×D411yescharacteristic
169C22×C4×C61C2×D411yescharacteristic
170C22×C4×C61C2×D411yescharacteristic
171C22×C4×C61C2×D411yescharacteristic
172C22×C4×C61C2411yescharacteristic
173C22×Dic61—21no—
174C22×Dic61—21no—
175C22×Dic61—21no—
176C2×D244—21no—
177C2×D244—21no—
178C2×D244—21no—
179C2×D244C22×C412yes—
180C2×D244C2×D412yes—
181C2×D244#4112yes—
182C2×C4×D61—24no—
183C2×C4×D61—24no—
184C2×C4×D61—24no—
185C2×C4×D61—81no—
186C2×C4×D61—81no—
187C2×C4×D61—81no—
188C2×C4×D61—81no—
189C2×C4×D61—81no—
190C2×C4×D61—81no—
191C4⋊C4×C61—21no—
192C4⋊C4×C61—21no—
193C4⋊C4×C61—21no—
194C4⋊C4×C61—21no—
195C22⋊C4×C61—42no—
196C22⋊C4×C61—42no—
197C22⋊C4×C61—81no—
198C22⋊C4×C61—81no—
199C22⋊C4×C61—81no—
200C22⋊C4×C61—81no—
201C42×C61—21no—
202C42×C61—21no—
203C42×C61C22×C412yes—
204C42×C61C2×D412yes—
205C42×C61#4112yes—
206C42×C61#4112yes—
207#11758199—28no—
208#11758199—28no—
209#11758198—24no—
210#11758198—24no—
211#11758198—24no—
212C4⋊Dic61—21no—
213C4⋊Dic61—21no—
214C4⋊Dic61—21no—
215C4⋊Dic61C22×C412yes—
216C4⋊Dic61C2×D412yes—
217C4⋊Dic61#4112yes—
218C4×Dic61—81no—
219C4×Dic61—81no—
220C4×Dic61—81no—
221C2×#92418—21no—
222C2×#92418—21no—
223C2×#92418—21no—
224C2×#92418—21no—
225C2×#92418—21no—
226C2×#92418—21no—
227C2×#92418—21no—
228C2×#92418—21no—
229C2×#92418—21no—
230C2×#92418—21no—
231C2×#92418C22×C412yes—
232C2×#92418C22×C412yes—
233C23×C61—22no—
234C23×C61—22no—
235C23×C61—41no—
236C23×C61—41no—
237C23×C61—41no—
238C23×C61—41no—
239C23×C61—41no—
240C23×C61—41no—
241C23×C61—41no—
242C23×C61—41no—
243C23×C61—41no—
244C23×C61—41no—
245C23×C61—41no—
246C23×C61—41no—
247C23×C61C22×D411yescharacteristic
248C22×D61—22no—
249C22×D61—22no—
250C22×D61—22no—
251C22×D61—41no—
252C22×D61—41no—
253C22×D61—41no—
254C22×D61—41no—
255D4×C61—22no—
256D4×C61—22no—
257D4×C61—22no—
258D4×C61—22no—
259D4×C61—41no—
260D4×C61—41no—
261D4×C61—41no—
262D4×C61—41no—
263D4×C61—84no—
264D4×C61—84no—
265C2×C4×C61—21no—
266C2×C4×C61—21no—
267C2×C4×C61—21no—
268C2×C4×C61—21no—
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—21no—
276C2×C4×C61—21no—
277C2×C4×C61—21no—
278C2×C4×C61—21no—
279C2×C4×C61—41no—
280C2×C4×C61—41no—
281C2×C4×C61—41no—
282C2×C4×C61—41no—
283C2×C4×C61—41no—
284C2×C4×C61—41no—
285C2×C4×C61—84no—
286C2×C4×C61—84no—
287C2×C4×C61C4×D412yes—
288C2×C4×C61C4×D412yes—
289C2×C4×C61#12112yes—
290C2×C4×C61#12112yes—
291C2×C4×C61C23×C411yescharacteristic
292C2×C4×C61C22×D411yescharacteristic
293C2×C4×C61C2×#4111yescharacteristic
294C2×C4×C61C2×#4111yescharacteristic
295C2×C4×C61C2×#4111yescharacteristic
296C2×C4×C61C2×#4111yescharacteristic
297C2×Dic61—22no—
298C2×Dic61—22no—
299C2×Dic61—22no—
300C2×Dic61—41no—
301C2×Dic61—41no—
302C2×Dic61—41no—
303C2×Dic61—41no—
304C2×Dic61—41no—
305C2×Dic61—41no—
306D244—22no—
307D244—22no—
308D244—22no—
309D244C4×D414yes—
310C4×D61—84no—
311C4×D61—84no—
312C4×D61—84no—
313#92418—22no—
314#92418—22no—
315#92418—41no—
316#92418—41no—
317#21513—611nomaximal, Sylow
318C22×C61—42no—
319C22×C61—42no—
320C22×C61—42no—
321C22×C61—42no—
322C22×C61—42no—
323C22×C61—42no—
324C22×C61—81no—
325C22×C61—81no—
326C22×C61—81no—
327C22×C61—81no—
328C22×C61—81no—
329C22×C61—81no—
330C22×C61—81no—
331C22×C61—81no—
332C22×C61C2×C4×D411yescharacteristic
333C22×C61C2×#12111yescharacteristic
334C22×C61#52511yescharacteristic
335C22×C61#57611yescharacteristic
336C22×C61#57611yescharacteristic
337C22×C61#57611yescharacteristic
338C22×C61#57711yescharacteristic
339C2×D61—24no—
340C2×D61—42no—
341C2×D61—42no—
342C2×D61—42no—
343C2×D61—42no—
344C2×D61—42no—
345C2×D61—42no—
346C4×C61—22no—
347C4×C61—22no—
348C4×C61—22no—
349C4×C61—22no—
350C4×C61—41no—
351C4×C61—41no—
352C4×C61—81no—
353C4×C61—81no—
354C4×C61C2×C4×D411yescharacteristic
355C4×C61C4×#4111yescharacteristic
356C4×C61#52911yescharacteristic
357C4×C61#53211yescharacteristic
358Dic61—42no—
359Dic61—42no—
360Dic61—42no—
361C2×#459—611no—
362C2×#442—611no—
363C2×C4×D8—611no—
364#2328D6111yescharacteristic, complemented
365#2275—611no—
366#1982—611no—
367#1949—611no—
368#1926—611no—
369#1925—611no—
370#1879—611no—
371#1879—611no—
372#1804—611no—
373#1768—611no—
374#1762—611no—
375C4×#102—611no—
376C2×C61—82no—
377C2×C61—82no—
378C2×C61C4×#12111yescharacteristic
379C2×C61#294611yescharacteristic
380C2×C61#294811yescharacteristic
381C2×C61#304111yescharacteristic
382C2×C61#304511yescharacteristic
383C2×C61#311911yescharacteristic
384C2×C61#312211yescharacteristic
385D61—44no—
386C22×D8—611no—
387C22×D8—611no—
388C2×#127C2×D6111yescharacteristic
389C2×C4×D4—611no—
390C2×C4×D4—611no—
391C2×C4×D4—611no—
392C2×C4×D4C2×D6111yescharacteristic
393C2×C4×D4C2×D6111yescharacteristic
394#459—618no—
395#442—1224no—
396C4×D8—1224no—
397C2×#107—611no—
398C2×#106—611no—
399C2×C4⋊C8—611no—
400C2×C4⋊C8—611no—
401C2×#102—611no—
402C2×#102—611no—
403C2×#102—611no—
404C2×#102—611no—
405C2×#102—611no—
406C2×#102—611no—
407C2×#102—611no—
408C2×#102—611no—
409C2×#97—611no—
410C2×C4×C8—611no—
411#390C2×D6111yescharacteristic
412#390C2×D6111yescharacteristic
413#386—21no—
414#386—21no—
415#386—21no—
416#386—21no—
417#382C2×D6111yescharacteristic
418C4×C4⋊C4—611no—
419C4×C4⋊C4—611no—
420C4×C4⋊C4—611no—
421C4×C22⋊C4—1221no—
422C4×C22⋊C4—1221no—
423C4×C22⋊C4—1221no—
424#376C2×D6111yescharacteristic
425C2×#95—1221no—
426#340—611no—
427#340—611no—
428#340—611no—
429#340—611no—
430#336—611no—
431#336—611no—
432C61#2151311yescharacteristic, complemented, Sylow
433C22×D4—21no—
434C22×D4—21no—
435C22×D4—611no—
436C22×D4C22×D6111yescharacteristic
437C22×D4C22×D6111yescharacteristic
438C23×C4—21no—
439C23×C4—21no—
440C23×C4—1221no—
441C23×C4—1221no—
442C23×C4—1221no—
443C2×D8—614no—
444C2×D8—614no—
445C2×D8—1222no—
446C2×D8—1222no—
447C2×D8—1222no—
448C2×D8—1222no—
449C22×C8—611no—
450C22×C8—611no—
451C22×C8—611no—
452C22×C8—611no—
453#127—22no—
454#127C4×D6114yescomplemented
455C4×D4—22no—
456C4×D4—22no—
457C4×D4—22no—
458C4×D4—22no—
459C4×D4—614no—
460C4×D4—614no—
461C4×D4—1222no—
462C4×D4—1222no—
463C4×D4—1222no—
464C4×D4—1222no—
465C2×C4⋊C4—611no—
466C2×C4⋊C4—611no—
467C2×C4⋊C4—611no—
468C2×C4⋊C4C22×D6111yescharacteristic
469C2×C4⋊C4C22×D6111yescharacteristic
470C2×C22⋊C4—21no—
471C2×C22⋊C4—21no—
472C2×C22⋊C4—21no—
473C2×C22⋊C4—21no—
474C2×C22⋊C4—21no—
475C2×C22⋊C4—21no—
476C2×C22⋊C4—1221no—
477C2×C22⋊C4—1221no—
478C2×C22⋊C4—1221no—
479C2×C42—1221no—
480C2×C42—1221no—
481C2×C42—1221no—
482C2×C42C22×D6111yescharacteristic
483C2×C42C22×D6111yescharacteristic
484C2×C42C22×D6111yescharacteristic
485#107—1222no—
486#106—1222no—
487C4⋊C8—614no—
488C4⋊C8—1222no—
489#102—614no—
490#102—614no—
491#102—1222no—
492#102—1222no—
493#102—1222no—
494#102—1222no—
495#102—1222no—
496#102—1222no—
497#97—1222no—
498C4×C8—1222no—
499#95—21no—
500#95—21no—
501#95—1221no—
502#95—1221no—
503#95—1221no—
504#95C22⋊D6111yescharacteristic
505#95C22⋊D6111yescharacteristic
506#95C22⋊D6111yescharacteristic
507#95C22⋊D6111yescharacteristic
508C24—21no—
509C24—21no—
510C24—1221no—
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—21no—
514C2×D4—21no—
515C2×D4—21no—
516C2×D4—21no—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—24no—
522C2×D4—24no—
523C2×D4—81no—
524C2×D4—81no—
525C2×D4—81no—
526C2×D4—81no—
527C2×D4—612no—
528C2×D4—612no—
529C2×D4—612no—
530C2×D4—1221no—
531C2×D4—1221no—
532C2×D4—1221no—
533C2×D4C2×C4×D6112yes—
534C2×D4C2×C4×D6112yes—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—42no—
538C22×C4—42no—
539C22×C4—81no—
540C22×C4—81no—
541C22×C4—81no—
542C22×C4—81no—
543C22×C4—1224no—
544C22×C4—1221no—
545C22×C4—1221no—
546C22×C4—1221no—
547C22×C4—1224no—
548C22×C4—1224no—
549C22×C4—4881no—
550C22×C4—4881no—
551C22×C4—4881no—
552C22×C4—4881no—
553C22×C4—4881no—
554C22×C4—4881no—
555C22×C4C2×C22⋊D6111yescharacteristic
556C22×C4C2×C22⋊D6111yescharacteristic
557C22×C4C2×C22⋊D6111yescharacteristic
558C22×C4C2×C22⋊D6111yescharacteristic
559C22×C4C2×C22⋊D6111yescharacteristic
560C22×C4C2×C22⋊D6111yescharacteristic
561C22×C4C23×D6111yescharacteristic
562D8—1228no—
563D8—1228no—
564C2×C8—612no—
565C2×C8—612no—
566C2×C8—1221no—
567C2×C8—1221no—
568C2×C8—1221no—
569C2×C8—1221no—
570C2×C8—1221no—
571C2×C8—1221no—
572C2×C8—1221no—
573C2×C8—1221no—
574C2×C8—1221no—
575C2×C8—1221no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—612no—
581C4⋊C4—612no—
582C4⋊C4—612no—
583C4⋊C4—1221no—
584C4⋊C4—1221no—
585C4⋊C4—1221no—
586C22⋊C4—42no—
587C22⋊C4—42no—
588C22⋊C4—81no—
589C22⋊C4—81no—
590C22⋊C4—81no—
591C22⋊C4—81no—
592C22⋊C4—1224no—
593C22⋊C4—1224no—
594C22⋊C4—1224no—
595C42—21no—
596C42—21no—
597C42—4881no—
598C42—4881no—
599C42—4881no—
600C42C2×C4×D6112yes—
601C42#1175822212yes—
602C42D4×D6112yes—
603C42#1175822412yes—
604C23—22no—
605C23—22no—
606C23—41no—
607C23—41no—
608C23—41no—
609C23—41no—
610C23—41no—
611C23—41no—
612C23—41no—
613C23—41no—
614C23—41no—
615C23—41no—
616C23—41no—
617C23—41no—
618C23—1222no—
619C23—1222no—
620C23—1222no—
621C23—2441no—
622C23—2441no—
623C23—2441no—
624C23—2441no—
625C23C22×C22⋊D6111yescharacteristic
626D4—22no—
627D4—22no—
628D4—22no—
629D4—22no—
630D4—41no—
631D4—41no—
632D4—41no—
633D4—41no—
634D4—84no—
635D4—84no—
636D4—614no—
637D4—1222no—
638D4—1222no—
639D4—1222no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—84no—
661C2×C4—84no—
662C2×C4—1222no—
663C2×C4—1222no—
664C2×C4—1222no—
665C2×C4—4884no—
666C2×C4—4884no—
667C2×C4—4884no—
668C2×C4—2441no—
669C2×C4—2441no—
670C2×C4—2441no—
671C2×C4—2441no—
672C2×C4—2441no—
673C2×C4—2441no—
674C2×C4C4×C22⋊D6112yes—
675C2×C4C4×C22⋊D6112yes—
676C2×C4#1451974812yes—
677C2×C4#1451974812yes—
678C2×C4C22×C4×D6111yescharacteristic
679C2×C4C2×D4×D6111yescharacteristic
680C2×C4#41×D6111yescharacteristic
681C2×C4#41×D6111yescharacteristic
682C2×C4C2×#1175822411yescharacteristic
683C2×C4C2×#1175822211yescharacteristic
684C8—1222no—
685C8—1222no—
686C8—2441no—
687C8—2441no—
688C22—42no—
689C22—42no—
690C22—42no—
691C22—42no—
692C22—42no—
693C22—42no—
694C22—81no—
695C22—81no—
696C22—81no—
697C22—81no—
698C22—81no—
699C22—81no—
700C22—81no—
701C22—81no—
702C22—1224no—
703C22—2442no—
704C22—2442no—
705C22—2442no—
706C22—2442no—
707C22—2442no—
708C22—2442no—
709C22C2×C4×C22⋊D6111yescharacteristic
710C22C2×#1451974811yescharacteristic
711C22#1684026911yescharacteristic
712C22#1684056511yescharacteristic
713C22#1684056511yescharacteristic
714C22#1684056511yescharacteristic
715C22#1684057311yescharacteristic
716C4—22no—
717C4—22no—
718C4—22no—
719C4—22no—
720C4—41no—
721C4—41no—
722C4—81no—
723C4—81no—
724C4—2442no—
725C4—2442no—
726C4—2442no—
727C4C4×D4×D6111yescharacteristic
728C4C4×#1175822411yescharacteristic
729C4#1684029411yescharacteristic
730C4#1684030911yescharacteristic
731C2—82no—
732C2—82no—
733C2—2444no—
734C2C4×#1451974811yescharacteristic
735C2#2145465111yescharacteristic
736C2#2145466911yescharacteristic
737C2#2145531811yescharacteristic
738C2#2145535411yescharacteristic
739C2#2145601211yescharacteristic
740C2#2145605711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#2328C2
socleC23×C61C22×D4
prime radicalC2×#16839954C2
cosocleC22×C4×C61C24
hypercenter#2328D61
hypocenterC61#21513
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ #376 ◁ #2328

Complements

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

NH ≅ G/Ntype
2. C2×#16839872C2semidirect
3. C2×C4×#11758199C2semidirect
4. #21448181C2semidirect
5. #21446747C2semidirect
6. #21446585C2semidirect
7. #21446443C2semidirect
8. #21446436C2semidirect
9. #21446170C2semidirect
10. #21446170C2semidirect
11. #21445826C2semidirect
12. #21445676C2semidirect
13. #21445644C2semidirect
14. C4×#14519698C2semidirect
15. C61×#2328C2semidirect
21. #16839954C4semidirect
70. C2×#11758199C2×C4semidirect
71. C2×#11758199C2×C4semidirect
80. C4×D244C2×C4semidirect
81. C4×D244D4semidirect
94. C4⋊#92418C2×C4semidirect
99. #14519698C2×C4semidirect
100. #14519698C2×C4semidirect
115. #127×C61C2×C4semidirect
364. #2328D61semidirect
432. C61#21513semidirect
454. #127C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168399542
C2×#168398722
C2×C4×#117581992
#214481812
#214467472
#214465852
#214464432
#214464362
#214461702
#214458262
#214456762
#214456442
C4×#145196982
C61×#23282
#2151361