Finite Group Databasebeta

← #29686281

Subgroups — #29686281

Order 15616.

1140 conjugacy classes of subgroups.

The subgroup lattice has 718 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839960C211yesmaximal, characteristic
2C2×#16839860C211yesmaximal, characteristic, complemented
3C4×#14519773C211yesmaximal, characteristic
4C4×Q8×Dic61C211yesmaximal, characteristic, complemented
5#21446744C211yesmaximal, characteristic
6#21446574C211yesmaximal, characteristic, complemented
7#21446442C211yesmaximal, characteristic, complemented
8#21446438C211yesmaximal, characteristic, complemented
9#21446176C211yesmaximal, characteristic, complemented
10#21446172C211yesmaximal, characteristic, complemented
11#21445822C211yesmaximal, characteristic, complemented
12#21445673C211yesmaximal, characteristic, complemented
13#21445645C211yesmaximal, characteristic, complemented
14#21445644C211yesmaximal, characteristic, complemented
15C2×C61×#440C211yesmaximal, characteristic, complemented
16C22×#11758201C2211yescharacteristic
17C2×#14519773C2211yescharacteristic
18C2×Q8×Dic61C2211yescharacteristic
19C2×Q8×Dic61C2211yescharacteristic
20C2×C4×D244C2211yescharacteristic
21C2×C4×C22⋊D61—21no—
22C2×C4×C22⋊D61—21no—
23#16839960C418yescomplemented
24#16839860—24no—
25C2×#14519710C2211yescharacteristic
26C2×#14519706C2211yescharacteristic
27C2×#14519706C2211yescharacteristic
28C2×#14519701C2211yescharacteristic
29C2×#14519699C2211yescharacteristic
30C2×#14519699C2211yescharacteristic
31C2×#14519698C2211yescharacteristic
32C2×#14519698C2211yescharacteristic
33C2×#14519697C2211yescharacteristic
34C2×#14519688C2211yescharacteristic
35#16839665C2211yescharacteristic
36#16839663C2211yescharacteristic
37#16839662—21no—
38#16839662—21no—
39#16839631C2211yescharacteristic
40C4⋊C4×Dic61—21no—
41C4⋊C4×Dic61—21no—
42C4⋊C4×Dic61C2211yescharacteristic
43C4⋊C4×Dic61C2211yescharacteristic
44C4×C4⋊Dic61—21no—
45C4×C4⋊Dic61C2211yescharacteristic
46C42×Dic61—21no—
47C42×Dic61C2211yescharacteristic
48#16839525C2211yescharacteristic
49#16839525C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839524C2211yescharacteristic
52#16839516C2211yescharacteristic
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×D244C2311yescharacteristic
63C22×C22⋊D61—21no—
64C22×C22⋊D61—21no—
65C22×C4×D61—21no—
66C2×#11758201—22no—
67C2×#11758201—22no—
68C2×#11758201C2×C414yescomplemented
69C22×#92418C2311yescharacteristic
70C22×#92418C2311yescharacteristic
71#14519773—22no—
72#14519773C2×C414yes—
73Q8×Dic61—22no—
74Q8×Dic61—22no—
75Q8×Dic61—22no—
76Q8×Dic61C2×C414yescomplemented
77C4×D244—22no—
78C4×D244—22no—
79C4×C22⋊D61—44no—
80C4×C22⋊D61—44no—
81C2×C4⋊Dic61—21no—
82C2×C4⋊Dic61—21no—
83C2×C4⋊Dic61C2311yescharacteristic
84C2×C4⋊Dic61C2311yescharacteristic
85C2×C4⋊Dic61C2311yescharacteristic
86C2×#11758196—21no—
87C2×#11758196—21no—
88C2×C22⋊Dic61—21no—
89C2×C22⋊Dic61—21no—
90C2×#11758198—21no—
91C2×#11758198—21no—
92C2×#11758198—21no—
93C2×C4×Dic61—21no—
94C2×C4×Dic61—21no—
95C2×C4×Dic61—21no—
96C2×C4×Dic61—21no—
97C2×C4×Dic61—21no—
98C2×C4×Dic61D411yescharacteristic
99C2×C4×Dic61D411yescharacteristic
100C2×C4×Dic61D411yescharacteristic
101C2×C4×Dic61D411yescharacteristic
102C2×C4×Dic61C2311yescharacteristic
103C2×C4×Dic61C2311yescharacteristic
104#14519710—22no—
105#14519706—22no—
106#14519706C2×C414yescomplemented
107#14519701—22no—
108#14519699—22no—
109#14519699C2×C414yescomplemented
110#14519698—22no—
111#14519698C2×C414yescomplemented
112#14519697—22no—
113#14519688—22no—
114#14519684—21no—
115#14519684—21no—
116#14519684—21no—
117C22×Q8×C61C2311yescharacteristic
118C22×D4×C61C2311yescharacteristic
119C23×C4×C61—21no—
120C2×SD16×C61—22no—
121C2×SD16×C61—22no—
122C2×SD16×C61C2×C414yescomplemented
123C22×C8×C61C2311yescharacteristic
124C22×C8×C61C2311yescharacteristic
125C4×Q8×C61—22no—
126C4×Q8×C61D414yescomplemented
127C4×D4×C61—22no—
128C4×D4×C61—22no—
129C2×C4⋊C4×C61—21no—
130C2×C4⋊C4×C61C2311yescharacteristic
131C2×C4⋊C4×C61C2311yescharacteristic
132C2×C22⋊C4×C61—21no—
133C2×C42×C61—21no—
134C2×C42×C61C2311yescharacteristic
135#107×C61—22no—
136#103×C61—22no—
137#102×C61—22no—
138#97×C61—22no—
139C24×C61—21no—
140C23×D61—21no—
141C2×Q8×C61—21no—
142C2×Q8×C61—21no—
143C2×Q8×C61—21no—
144C2×Q8×C61C22×C412yes—
145C2×Q8×C61C2×D412yes—
146C2×Q8×C61#4112yes—
147C2×D4×C61—21no—
148C2×D4×C61—21no—
149C2×D4×C61—21no—
150C2×D4×C61—21no—
151C2×D4×C61—21no—
152C2×D4×C61C22×C412yes—
153C22×C4×C61—21no—
154C22×C4×C61—21no—
155C22×C4×C61—21no—
156C22×C4×C61—42no—
157C22×C4×C61—42no—
158C22×C4×C61—42no—
159C22×C4×C61C2×D411yescharacteristic
160C22×C4×C61C2×D411yescharacteristic
161C22×C4×C61C2411yescharacteristic
162C2×C22⋊D61—24no—
163C2×C22⋊D61—24no—
164C2×C22⋊D61—42no—
165C2×C22⋊D61—42no—
166C2×C22⋊D61—42no—
167C2×C22⋊D61—42no—
168C22×Dic61—21no—
169C22×Dic61—21no—
170C22×Dic61—21no—
171C22×Dic61C2×D411yescharacteristic
172C22×Dic61C2×D411yescharacteristic
173C22×Dic61C2×D411yescharacteristic
174C22×Dic61C2×D411yescharacteristic
175C2×D244—21no—
176C2×D244—21no—
177C2×D244—21no—
178C2×D244—21no—
179C2×D244—21no—
180C2×D244C22×C412yes—
181C2×C4×D61—42no—
182C2×C4×D61—42no—
183C2×C4×D61—42no—
184SD16×C61—28no—
185C2×C8×C61—21no—
186C2×C8×C61—21no—
187C2×C8×C61—21no—
188C2×C8×C61—21no—
189C2×C8×C61—21no—
190C2×C8×C61C22×C412yes—
191C4⋊C4×C61—24no—
192C4⋊C4×C61—21no—
193C4⋊C4×C61—21no—
194C4⋊C4×C61—21no—
195C4⋊C4×C61C2×D412yes—
196C22⋊C4×C61—42no—
197C42×C61—24no—
198C42×C61C2×D412yes—
199C42×C61#4112yes—
200C22⋊Dic61—42no—
201C22⋊Dic61—42no—
202#11758201—28no—
203#11758198—42no—
204#11758198—42no—
205#11758198—42no—
206C4⋊Dic61—24no—
207C4⋊Dic61—21no—
208C4⋊Dic61—21no—
209C4⋊Dic61—24no—
210C4⋊Dic61—21no—
211C4⋊Dic61—21no—
212C4⋊Dic61C22×C412yes—
213C4⋊Dic61#4112yes—
214#11758196—42no—
215#11758196—42no—
216C4×Dic61—24no—
217C4×Dic61—21no—
218C4×Dic61—21no—
219C4×Dic61—24no—
220C4×Dic61—22no—
221C4×Dic61—22no—
222C4×Dic61—22no—
223C4×Dic61—41no—
224C4×Dic61—42no—
225C4×Dic61—42no—
226C4×Dic61—42no—
227C4×Dic61C22×C412yes—
228C4×Dic61#4112yes—
229C2×#92418—21no—
230C2×#92418—21no—
231C2×#92418—21no—
232C2×#92418—21no—
233C2×#92418—21no—
234C2×#92418C22×C412yes—
235C23×C61—22no—
236C23×C61—41no—
237C23×C61—41no—
238C23×C61—41no—
239C23×C61—41no—
240C23×C61—41no—
241C23×C61—41no—
242C23×C61C22×D411yescharacteristic
243C22×D61—22no—
244C22×D61—41no—
245C22×D61—41no—
246C22×D61—41no—
247C22×D61—41no—
248C22×D61—41no—
249C22×D61—41no—
250Q8×C61—22no—
251Q8×C61—22no—
252Q8×C61—22no—
253Q8×C61C4×D414yescomplemented
254D4×C61—22no—
255D4×C61—22no—
256D4×C61—41no—
257D4×C61—41no—
258C2×C4×C61—22no—
259C2×C4×C61—22no—
260C2×C4×C61—22no—
261C2×C4×C61—21no—
262C2×C4×C61—21no—
263C2×C4×C61—21no—
264C2×C4×C61—21no—
265C2×C4×C61—22no—
266C2×C4×C61—41no—
267C2×C4×C61—41no—
268C2×C4×C61—41no—
269C2×C4×C61—41no—
270C2×C4×C61—41no—
271C2×C4×C61—84no—
272C2×C4×C61#12112yes—
273C2×C4×C61#12112yes—
274C2×C4×C61C23×C411yescharacteristic
275C2×C4×C61C22×D411yescharacteristic
276C2×C4×C61C2×#4111yescharacteristic
277C2×C4×C61C2×#4111yescharacteristic
278C2×C4×C61C2×#4111yescharacteristic
279C2×C4×C61C2×#4111yescharacteristic
280C22⋊D61—48no—
281C22⋊D61—48no—
282C2×Dic61—21no—
283C2×Dic61—21no—
284C2×Dic61—21no—
285C2×Dic61—21no—
286C2×Dic61—22no—
287C2×Dic61—21no—
288C2×Dic61—22no—
289C2×Dic61—21no—
290C2×Dic61—21no—
291C2×Dic61—41no—
292C2×Dic61—41no—
293C2×Dic61—41no—
294C2×Dic61—41no—
295C2×Dic61—41no—
296C2×Dic61—41no—
297C2×Dic61—41no—
298C2×Dic61C4×D412yes—
299C2×Dic61C4×D412yes—
300C2×Dic61AGL(1,ℤ/8)12yes—
301C2×Dic61AGL(1,ℤ/8)12yes—
302C2×Dic61#13712yes—
303D244—22no—
304D244—22no—
305D244—41no—
306D244—41no—
307C4×D61—84no—
308C8×C61—22no—
309C8×C61—41no—
310#92418—22no—
311#92418—41no—
312#21505—611nomaximal, Sylow
313C22×C61—42no—
314C22×C61—42no—
315C22×C61—42no—
316C22×C61—81no—
317C22×C61—81no—
318C22×C61—81no—
319C22×C61—81no—
320C22×C61C2×C4×D411yescharacteristic
321C22×C61C2×#12111yescharacteristic
322C22×C61#52511yescharacteristic
323C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
324C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
325C22×C61C2×#13711yescharacteristic
326C22×C61#57511yescharacteristic
327C2×D61—42no—
328C2×D61—42no—
329C2×D61—42no—
330C2×D61—81no—
331C2×D61—81no—
332C2×D61—81no—
333C2×D61—81no—
334C4×C61—22no—
335C4×C61—22no—
336C4×C61—24no—
337C4×C61—42no—
338C4×C61—81no—
339C4×C61C2×C4×D411yescharacteristic
340C4×C61C4×#4111yescharacteristic
341C4×C61#52911yescharacteristic
342C4×C61#53211yescharacteristic
343Dic61—22no—
344Dic61—22no—
345Dic61—41no—
346Dic61—42no—
347Dic61—42no—
348Dic61—81no—
349Dic61#44014yescomplemented
350C2×#460—611no—
351C2×#440—611no—
352C2×#440D6111yescharacteristic, complemented
353C4×#127—611no—
354C42×Q8—611no—
355#1982—611no—
356#1947—611no—
357#1925—611no—
358#1925—611no—
359#1880—611no—
360#1880—611no—
361#1803—611no—
362#1767—611no—
363#1762—611no—
364#1762—611no—
365C2×C61—82no—
366C2×C61C4×#12111yescharacteristic
367C2×C61C2×#44011yescharacteristic
368C2×C61C4×AGL(1,ℤ/8)11yescharacteristic
369C2×C61#303711yescharacteristic
370C2×C61#303811yescharacteristic
371C2×C61#311211yescharacteristic
372C2×C61#311511yescharacteristic
373D61—82no—
374C22×SD16—611no—
375C22×SD16C2×D6111yescharacteristic
376C2×#127—611no—
377C2×C4×Q8—611no—
378C2×C4×Q8—611no—
379C2×C4×Q8C2×D6111yescharacteristic
380C2×C4×D4—611no—
381C2×C4×D4—1221no—
382C2×C4×D4—1221no—
383C2×C4×D4C2×D6111yescharacteristic
384#460—618no—
385#440—24no—
386#440—1224no—
387C2×#107—611no—
388C2×#107C2×D6111yescharacteristic
389C2×C4⋊C8—611no—
390C2×C4⋊C8—611no—
391C2×#103—611no—
392C2×#103C2×D6111yescharacteristic
393C2×#102—611no—
394C2×#102—611no—
395C2×#102—611no—
396C2×#102—611no—
397C2×#102—611no—
398C2×#102C2×D6111yescharacteristic
399C2×#97—611no—
400C2×#97C2×D6111yescharacteristic
401#390—611no—
402#390—611no—
403#390—1221no—
404#390—1221no—
405#384—611no—
406C4×C4⋊C4—611no—
407C4×C4⋊C4—611no—
408C4×C4⋊C4—611no—
409C4×C4⋊C4—1221no—
410C4×C4⋊C4—1221no—
411C4×C4⋊C4—1221no—
412C43—611no—
413C43—1221no—
414#340—611no—
415#340—611no—
416#340—611no—
417#340—611no—
418#336—611no—
419#336—611no—
420C61#2150511yescharacteristic, complemented, Sylow
421C22×Q8C22×D6111yescharacteristic
422C22×D4—611no—
423C22×D4—1221no—
424C22×D4—1221no—
425C22×D4C22×D6111yescharacteristic
426C23×C4—21no—
427C23×C4—1221no—
428C2×SD16—22no—
429C2×SD16—22no—
430C2×SD16—614no—
431C2×SD16—1222no—
432C2×SD16—1222no—
433C2×SD16C4×D6114yescomplemented
434C22×C8—611no—
435C22×C8—611no—
436C22×C8C22×D6111yescharacteristic
437C22×C8C22×D6111yescharacteristic
438#127—614no—
439#127—1222no—
440C4×Q8—22no—
441C4×Q8—614no—
442C4×Q8—1222no—
443C4×Q8—1222no—
444C4×Q8—1222no—
445C4×Q8C22⋊D6114yescomplemented
446C4×D4—22no—
447C4×D4—22no—
448C4×D4—1222no—
449C4×D4—1222no—
450C4×D4—2444no—
451C4×D4—2444no—
452C2×C4⋊C4—21no—
453C2×C4⋊C4—611no—
454C2×C4⋊C4—611no—
455C2×C4⋊C4—611no—
456C2×C4⋊C4—1221no—
457C2×C4⋊C4—1221no—
458C2×C4⋊C4—1221no—
459C2×C4⋊C4—1221no—
460C2×C4⋊C4C22×D6111yescharacteristic
461C2×C4⋊C4C22×D6111yescharacteristic
462C2×C22⋊C4—21no—
463C2×C22⋊C4—1221no—
464C2×C22⋊C4—1221no—
465C2×C22⋊C4—1221no—
466C2×C22⋊C4—1221no—
467C2×C22⋊C4—1221no—
468C2×C42—21no—
469C2×C42—611no—
470C2×C42—611no—
471C2×C42—611no—
472C2×C42—611no—
473C2×C42—611no—
474C2×C42—611no—
475C2×C42—1221no—
476C2×C42—1221no—
477C2×C42—1221no—
478C2×C42—1221no—
479C2×C42—1221no—
480C2×C42C22×D6111yescharacteristic
481#107—22no—
482#107—1222no—
483C4⋊C8—614no—
484C4⋊C8—1222no—
485#103—22no—
486#103—1222no—
487#102—22no—
488#102—614no—
489#102—614no—
490#102—1222no—
491#102—1222no—
492#102—1222no—
493#97—22no—
494#97—1222no—
495#95—1221no—
496#95—1221no—
497#95—1221no—
498C24—21no—
499C24—1221no—
500C2×Q8—21no—
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8C2×C4×D6112yes—
504C2×Q8#1175822212yes—
505C2×Q8C2×C22⋊D6112yes—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—612no—
512C2×D4—1224no—
513C2×D4—1224no—
514C2×D4—1221no—
515C2×D4—1221no—
516C2×D4—1221no—
517C2×D4—1221no—
518C2×D4—1221no—
519C2×D4—2442no—
520C2×D4—2442no—
521C2×D4—2442no—
522C2×D4—2442no—
523C2×D4C2×C4×D6112yes—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—42no—
528C22×C4—42no—
529C22×C4—42no—
530C22×C4—611no—
531C22×C4—611no—
532C22×C4—611no—
533C22×C4—611no—
534C22×C4—1221no—
535C22×C4—1221no—
536C22×C4—1221no—
537C22×C4—2442no—
538C22×C4—2442no—
539C22×C4—2442no—
540C22×C4D4×D6111yescharacteristic
541C22×C4D4×D6111yescharacteristic
542C22×C4C23×D6111yescharacteristic
543SD16—28no—
544SD16—1228no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—612no—
551C2×C8—1221no—
552C2×C8—1221no—
553C2×C8—1221no—
554C2×C8—1221no—
555C2×C8—1221no—
556C2×C8C2×C4×D6112yes—
557C4⋊C4—21no—
558C4⋊C4—24no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—612no—
562C4⋊C4—612no—
563C4⋊C4—1224no—
564C4⋊C4—1224no—
565C4⋊C4—1221no—
566C4⋊C4—1221no—
567C4⋊C4—1221no—
568C4⋊C4—1221no—
569C4⋊C4—2442no—
570C4⋊C4—2442no—
571C4⋊C4C2×C22⋊D6112yes—
572C22⋊C4—42no—
573C22⋊C4—2442no—
574C22⋊C4—2442no—
575C22⋊C4—2442no—
576C22⋊C4—2442no—
577C22⋊C4—2442no—
578C42—24no—
579C42—612no—
580C42—612no—
581C42—1222no—
582C42—1222no—
583C42—1222no—
584C42—1224no—
585C42—1224no—
586C42—1221no—
587C42—1221no—
588C42—2441no—
589C42—2442no—
590C42—2442no—
591C42—2442no—
592C42#1175822412yes—
593C42C2×C22⋊D6112yes—
594C23—22no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23—41no—
601C23—1222no—
602C23—2441no—
603C23—2441no—
604C23—2441no—
605C23—2441no—
606C23—2441no—
607C23—2441no—
608C23C2×D4×D6111yescharacteristic
609Q8—22no—
610Q8—22no—
611Q8—22no—
612Q8C4×C22⋊D6114yescomplemented
613D4—22no—
614D4—22no—
615D4—41no—
616D4—41no—
617D4—1222no—
618D4—1222no—
619D4—2448no—
620D4—2448no—
621D4—2441no—
622D4—2441no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—22no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—84no—
637C2×C4—612no—
638C2×C4—612no—
639C2×C4—612no—
640C2×C4—612no—
641C2×C4—612no—
642C2×C4—1221no—
643C2×C4—1221no—
644C2×C4—1221no—
645C2×C4—1221no—
646C2×C4—1222no—
647C2×C4—1222no—
648C2×C4—1221no—
649C2×C4—1221no—
650C2×C4—1221no—
651C2×C4—4884no—
652C2×C4—2441no—
653C2×C4—2441no—
654C2×C4—2441no—
655C2×C4—2441no—
656C2×C4—2441no—
657C2×C4—2441no—
658C2×C4—2441no—
659C2×C4#1451974912yes—
660C2×C4#1451974912yes—
661C2×C4C22×C4×D6111yescharacteristic
662C2×C4C22×C22⋊D6111yescharacteristic
663C2×C4#41×D6111yescharacteristic
664C2×C4#41×D6111yescharacteristic
665C2×C4C2×#1175822411yescharacteristic
666C2×C4C2×#1175822211yescharacteristic
667C8—22no—
668C8—41no—
669C8—1222no—
670C8—2441no—
671C22—42no—
672C22—42no—
673C22—42no—
674C22—81no—
675C22—81no—
676C22—81no—
677C22—81no—
678C22—4881no—
679C22—4881no—
680C22—4881no—
681C22—4881no—
682C22—2442no—
683C22—2442no—
684C22—2442no—
685C22C4×D4×D6111yescharacteristic
686C22C2×#1451974911yescharacteristic
687C22#1684027111yescharacteristic
688C22AGL(1,ℤ/8)×D6111yescharacteristic
689C22AGL(1,ℤ/8)×D6111yescharacteristic
690C22#137×D6111yescharacteristic
691C22#1684056111yescharacteristic
692C4—24no—
693C4—22no—
694C4—22no—
695C4—42no—
696C4—81no—
697C4—614no—
698C4—1222no—
699C4—1222no—
700C4—4881no—
701C4—2442no—
702C4—2441no—
703C4—2442no—
704C4C2×C4×C22⋊D6111yescharacteristic
705C4C4×#1175822411yescharacteristic
706C4#1684029211yescharacteristic
707C4#1684030811yescharacteristic
708C2—82no—
709C2—4882no—
710C2C4×#1451974911yescharacteristic
711C2#440×D6111yescharacteristic
712C2#2145462411yescharacteristic
713C2#2145528811yescharacteristic
714C2#2145529711yescharacteristic
715C2#2145593911yescharacteristic
716C2#2145596811yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#440C2
socleC23×C61C22×D4
prime radicalC2×#14519773C22
cosocleC22×C4×C61C24
hypercenterC2×#440D61
hypocenterC61#21505
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×#16839860C2semidirect
4. C4×Q8×Dic61C2semidirect
6. #21446574C2semidirect
7. #21446442C2semidirect
8. #21446438C2semidirect
9. #21446176C2semidirect
10. #21446172C2semidirect
11. #21445822C2semidirect
12. #21445673C2semidirect
13. #21445645C2semidirect
14. #21445644C2semidirect
15. C2×C61×#440C2semidirect
23. #16839960C4semidirect
68. C2×#11758201C2×C4semidirect
76. Q8×Dic61C2×C4semidirect
106. #14519706C2×C4semidirect
109. #14519699C2×C4semidirect
111. #14519698C2×C4semidirect
122. C2×SD16×C61C2×C4semidirect
126. C4×Q8×C61D4semidirect
253. Q8×C61C4×D4semidirect
349. Dic61#440semidirect
352. C2×#440D61semidirect
420. C61#21505semidirect
433. C2×SD16C4×D61semidirect
445. C4×Q8C22⋊D61semidirect
612. Q8C4×C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168399602
C2×#168398602
C4×#145197732
C4×Q8×Dic612
#214467442
#214465742
#214464422
#214464382
#214461762
#214461722
#214458222
#214456732
#214456452
#214456442
C2×C61×#4402
#2150561