Finite Group Databasebeta

← #29686401

Subgroups — #29686401

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×#16839955C211yesmaximal, characteristic
2C2×C4×#11758199C211yesmaximal, characteristic, complemented
3#21448541C211yesmaximal, characteristic, complemented
4#21448180C211yesmaximal, characteristic, complemented
5#21446744C211yesmaximal, characteristic, complemented
6#21446588C211yesmaximal, characteristic, complemented
7#21446445C211yesmaximal, characteristic, complemented
8#21446442C211yesmaximal, characteristic, complemented
9#21446169C211yesmaximal, characteristic, complemented
10#21446165C211yesmaximal, characteristic, complemented
11#21445827C211yesmaximal, characteristic, complemented
12#21445679C211yesmaximal, characteristic, complemented
13#21445645C211yesmaximal, characteristic, complemented
14C4×#14519698C211yesmaximal, characteristic, complemented
15C2×C61×#442C211yesmaximal, characteristic, complemented
16C22×#11758199C2211yescharacteristic
17C2×#14519773C2211yescharacteristic
18C2×C4×D244C2211yescharacteristic
19C2×D4×Dic61C2211yescharacteristic
20C2×D4×Dic61C2211yescharacteristic
21#16839955C418yescomplemented
22C4×#11758199—24no—
23C2×#14519710C2211yescharacteristic
24C2×#14519706C2211yescharacteristic
25C2×#14519706C2211yescharacteristic
26C2×#14519699C2211yescharacteristic
27C2×#14519699C2211yescharacteristic
28C2×#14519698C2211yescharacteristic
29C2×#14519698C2211yescharacteristic
30C2×#14519698C2211yescharacteristic
31C2×#14519697C2211yescharacteristic
32C2×C4×#92418C2211yescharacteristic
33#16839665C2211yescharacteristic
34#16839663C2211yescharacteristic
35#16839641—21no—
36#16839641—21no—
37#16839638—21no—
38#16839638—21no—
39#16839627C2211yescharacteristic
40C4⋊C4×Dic61C2211yescharacteristic
41C4⋊C4×Dic61C2211yescharacteristic
42C4×C4⋊Dic61C2211yescharacteristic
43C22⋊C4×Dic61—21no—
44C22⋊C4×Dic61—21no—
45C4×C22⋊Dic61—21no—
46#16839608C2211yescharacteristic
47C2×#14519684—21no—
48#16839525C2211yescharacteristic
49#16839525C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839524C2211yescharacteristic
52#16839516C2211yescharacteristic
53#16839516C2211yescharacteristic
54C22×D8×C61C2211yescharacteristic
55C2×C4×D4×C61C2211yescharacteristic
56C2×C4×D4×C61C2211yescharacteristic
57C61×#442—24no—
58C2×#106×C61C2211yescharacteristic
59C2×#102×C61C2211yescharacteristic
60C2×#102×C61C2211yescharacteristic
61C2×#97×C61C2211yescharacteristic
62C22×D244C2311yescharacteristic
63C22×C22⋊D61—21no—
64C22×C22⋊D61—21no—
65C23×Dic61—21no—
66C23×Dic61—21no—
67C22×C4×D61—21no—
68C2×#11758199—22no—
69C2×#11758199—22no—
70C2×#11758199C2×C414yescomplemented
71C22×#92418C2311yescharacteristic
72C22×#92418C2311yescharacteristic
73#14519773—22no—
74#14519773C2×C414yescomplemented
75C4×D244—22no—
76C4×D244—22no—
77D4×Dic61—22no—
78D4×Dic61—22no—
79D4×Dic61—22no—
80D4×Dic61C2×C414yescomplemented
81C2×C4⋊Dic61C2311yescharacteristic
82C2×C4⋊Dic61C2311yescharacteristic
83C2×C4⋊Dic61C2311yescharacteristic
84C2×C22⋊Dic61—21no—
85C2×C22⋊Dic61—21no—
86C2×C22⋊Dic61—21no—
87C2×C22⋊Dic61—21no—
88C2×#11758198—21no—
89C2×#11758198—21no—
90C2×#11758198—21no—
91C2×C4×Dic61—21no—
92C2×C4×Dic61—21no—
93C2×C4×Dic61—21no—
94C2×C4×Dic61C2311yescharacteristic
95C2×C4×Dic61C2311yescharacteristic
96#14519710—22no—
97#14519706—22no—
98#14519706C2×C414yescomplemented
99#14519699—22no—
100#14519699C2×C414yescomplemented
101#14519698—22no—
102#14519698—22no—
103#14519698C2×C414yescomplemented
104#14519697—22no—
105C4×#92418—22no—
106#14519684—21no—
107#14519684—21no—
108#14519684—21no—
109#14519684—21no—
110#14519684—21no—
111#14519684D411yescharacteristic
112#14519684D411yescharacteristic
113#14519684D411yescharacteristic
114#14519684D411yescharacteristic
115C22×D4×C61C2311yescharacteristic
116C22×D4×C61C2311yescharacteristic
117C23×C4×C61—21no—
118C23×C4×C61—21no—
119C2×D8×C61—22no—
120C2×D8×C61—22no—
121C2×D8×C61C2×C414yescomplemented
122C22×C8×C61C2311yescharacteristic
123C22×C8×C61C2311yescharacteristic
124C4×D4×C61—22no—
125C4×D4×C61—22no—
126C4×D4×C61—22no—
127C4×D4×C61D414yescomplemented
128C2×C4⋊C4×C61C2311yescharacteristic
129C2×C4⋊C4×C61C2311yescharacteristic
130C2×C22⋊C4×C61—21no—
131C2×C22⋊C4×C61—21no—
132C2×C42×C61C2311yescharacteristic
133#106×C61—22no—
134#102×C61—22no—
135#102×C61—22no—
136#97×C61—22no—
137C24×C61—21no—
138C24×C61—21no—
139C23×D61—21no—
140C2×D4×C61—21no—
141C2×D4×C61—21no—
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×C61C22×C412yes—
149C2×D4×C61C22×C412yes—
150C2×D4×C61C2×D412yes—
151C2×D4×C61#4112yes—
152C22×C4×C61—21no—
153C22×C4×C61—24no—
154C22×C4×C61—21no—
155C22×C4×C61—42no—
156C22×C4×C61—81no—
157C22×C4×C61—81no—
158C22×C4×C61—81no—
159C22×C4×C61—81no—
160C22×C4×C61C2×D411yescharacteristic
161C22×C4×C61C2×D411yescharacteristic
162C22×C4×C61C2411yescharacteristic
163C2×C22⋊D61—24no—
164C2×C22⋊D61—24no—
165C2×C22⋊D61—81no—
166C2×C22⋊D61—81no—
167C2×C22⋊D61—81no—
168C2×C22⋊D61—81no—
169C22×Dic61—21no—
170C22×Dic61—21no—
171C22×Dic61—24no—
172C22×Dic61—24no—
173C22×Dic61—21no—
174C22×Dic61—81no—
175C22×Dic61—81no—
176C22×Dic61—81no—
177C22×Dic61—81no—
178C22×Dic61C2×D411yescharacteristic
179C22×Dic61C2×D411yescharacteristic
180C22×Dic61C2×D411yescharacteristic
181C22×Dic61C2×D411yescharacteristic
182C2×D244—21no—
183C2×D244—21no—
184C2×D244—21no—
185C2×D244—21no—
186C2×D244—21no—
187C2×D244C22×C412yes—
188C2×C4×D61—42no—
189C2×C4×D61—81no—
190C2×C4×D61—81no—
191D8×C61—28no—
192C2×C8×C61—21no—
193C2×C8×C61—21no—
194C2×C8×C61—21no—
195C2×C8×C61—21no—
196C2×C8×C61—21no—
197C2×C8×C61C22×C412yes—
198C4⋊C4×C61—21no—
199C4⋊C4×C61—21no—
200C4⋊C4×C61—21no—
201C4⋊C4×C61C2×D412yes—
202C22⋊C4×C61—24no—
203C22⋊C4×C61—42no—
204C42×C61C2×D412yes—
205C42×C61#4112yes—
206C22⋊Dic61—24no—
207C22⋊Dic61—24no—
208C22⋊Dic61—81no—
209C22⋊Dic61—81no—
210#11758199—28no—
211#11758198—42no—
212#11758198—81no—
213#11758198—81no—
214C4⋊Dic61—21no—
215C4⋊Dic61—21no—
216C4⋊Dic61—21no—
217C4⋊Dic61—21no—
218C4⋊Dic61C22×C412yes—
219C4⋊Dic61#4112yes—
220C4×Dic61—21no—
221C4×Dic61—21no—
222C4×Dic61—81no—
223C4×Dic61—81no—
224C4×Dic61—81no—
225C4×Dic61C22×C412yes—
226C4×Dic61#4112yes—
227C2×#92418—21no—
228C2×#92418—21no—
229C2×#92418—21no—
230C2×#92418—21no—
231C2×#92418—21no—
232C2×#92418C22×C412yes—
233C23×C61—22no—
234C23×C61—22no—
235C23×C61—22no—
236C23×C61—22no—
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—41no—
250C22×D61—41no—
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—22no—
260D4×C61—41no—
261D4×C61—41no—
262D4×C61C4×D414yes—
263C2×C4×C61—21no—
264C2×C4×C61—21no—
265C2×C4×C61—21no—
266C2×C4×C61—21no—
267C2×C4×C61—22no—
268C2×C4×C61—41no—
269C2×C4×C61—41no—
270C2×C4×C61—41no—
271C2×C4×C61—41no—
272C2×C4×C61—41no—
273C2×C4×C61—84no—
274C2×C4×C61—84no—
275C2×C4×C61#12112yes—
276C2×C4×C61#12112yes—
277C2×C4×C61C23×C411yescharacteristic
278C2×C4×C61C22×D411yescharacteristic
279C2×C4×C61C2×#4111yescharacteristic
280C2×C4×C61C2×#4111yescharacteristic
281C2×C4×C61C2×#4111yescharacteristic
282C2×C4×C61C2×#4111yescharacteristic
283C22⋊D61—84no—
284C22⋊D61—84no—
285C2×Dic61—21no—
286C2×Dic61—21no—
287C2×Dic61—21no—
288C2×Dic61—21no—
289C2×Dic61—22no—
290C2×Dic61—21no—
291C2×Dic61—21no—
292C2×Dic61—22no—
293C2×Dic61—21no—
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—84no—
305C2×Dic61—84no—
306C2×Dic61C4×D412yes—
307C2×Dic61C4×D412yes—
308D244—22no—
309D244—22no—
310D244—41no—
311D244—41no—
312C4×D61—84no—
313C8×C61—22no—
314C8×C61—41no—
315#92418—22no—
316#92418—41no—
317#21513—611nomaximal, Sylow
318C22×C61—24no—
319C22×C61—42no—
320C22×C61—42no—
321C22×C61—42no—
322C22×C61—42no—
323C22×C61—42no—
324C22×C61—42no—
325C22×C61—42no—
326C22×C61—42no—
327C22×C61—42no—
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—42no—
340C2×D61—42no—
341C2×D61—42no—
342C2×D61—81no—
343C2×D61—81no—
344C2×D61—81no—
345C2×D61—81no—
346C4×C61—22no—
347C4×C61—22no—
348C4×C61—42no—
349C4×C61—81no—
350C4×C61C2×C4×D411yescharacteristic
351C4×C61C4×#4111yescharacteristic
352C4×C61#52911yescharacteristic
353C4×C61#53211yescharacteristic
354Dic61—22no—
355Dic61—22no—
356Dic61—41no—
357Dic61—41no—
358Dic61—42no—
359Dic61—42no—
360Dic61—81no—
361C2×#459—611no—
362C2×#442D6111yescharacteristic, complemented
363C2×C4×D8—611no—
364#2328—611no—
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—44no—
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—82no—
386C22×D8—611no—
387C22×D8C2×D6111yescharacteristic
388C2×#127—611no—
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—24no—
396C4×D8—1224no—
397C2×#107—611no—
398C2×#106C2×D6111yescharacteristic
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×#102C2×D6111yescharacteristic
408C2×#102C2×D6111yescharacteristic
409C2×#97C2×D6111yescharacteristic
410C2×C4×C8—611no—
411#390—611no—
412#390—611no—
413#386—1221no—
414#386—1221no—
415#386—1221no—
416#386—1221no—
417#382—611no—
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#376—611no—
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—611no—
434C22×D4—1221no—
435C22×D4—1221no—
436C22×D4C22×D6111yescharacteristic
437C22×D4C22×D6111yescharacteristic
438C23×C4—21no—
439C23×C4—21no—
440C23×C4—1221no—
441C23×C4—1221no—
442C23×C4—1221no—
443C2×D8—22no—
444C2×D8—22no—
445C2×D8—614no—
446C2×D8—1222no—
447C2×D8—1222no—
448C2×D8C4×D6114yescomplemented
449C22×C8—611no—
450C22×C8—611no—
451C22×C8C22×D6111yescharacteristic
452C22×C8C22×D6111yescharacteristic
453#127—614no—
454#127—1222no—
455C4×D4—22no—
456C4×D4—22no—
457C4×D4—22no—
458C4×D4—614no—
459C4×D4—1222no—
460C4×D4—1222no—
461C4×D4—1222no—
462C4×D4—1222no—
463C4×D4—1222no—
464C4×D4C22⋊D6114yescomplemented
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—1221no—
473C2×C22⋊C4—1221no—
474C2×C22⋊C4—1221no—
475C2×C22⋊C4—1221no—
476C2×C22⋊C4—1221no—
477C2×C22⋊C4—1221no—
478C2×C22⋊C4—1221no—
479C2×C42—611no—
480C2×C42—611no—
481C2×C42—1221no—
482C2×C42—1221no—
483C2×C42—1221no—
484C2×C42C22×D6111yescharacteristic
485#107—1222no—
486#106—22no—
487C4⋊C8—614no—
488C4⋊C8—1222no—
489#102—22no—
490#102—22no—
491#102—614no—
492#102—614no—
493#102—1222no—
494#102—1222no—
495#102—1222no—
496#102—1222no—
497#97—22no—
498C4×C8—1222no—
499#95—611no—
500#95—611no—
501#95—611no—
502#95—611no—
503#95—1221no—
504#95—1221no—
505#95—1221no—
506#95—1221no—
507#95—1221no—
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—612no—
520C2×D4—1224no—
521C2×D4—1224no—
522C2×D4—1221no—
523C2×D4—1221no—
524C2×D4—1221no—
525C2×D4—1221no—
526C2×D4—1221no—
527C2×D4—4881no—
528C2×D4—4881no—
529C2×D4—4881no—
530C2×D4—4881no—
531C2×D4C2×C4×D6112yes—
532C2×D4C2×C4×D6112yes—
533C2×D4#1175822212yes—
534C2×D4C2×C22⋊D6112yes—
535C22×C4—21no—
536C22×C4—24no—
537C22×C4—21no—
538C22×C4—42no—
539C22×C4—81no—
540C22×C4—81no—
541C22×C4—81no—
542C22×C4—81no—
543C22×C4—611no—
544C22×C4—611no—
545C22×C4—611no—
546C22×C4—611no—
547C22×C4—1224no—
548C22×C4—1224no—
549C22×C4—1221no—
550C22×C4—1221no—
551C22×C4—1221no—
552C22×C4—4881no—
553C22×C4—4881no—
554C22×C4—4881no—
555C22×C4—4881no—
556C22×C4—4881no—
557C22×C4—4881no—
558C22×C4—2442no—
559C22×C4D4×D6111yescharacteristic
560C22×C4D4×D6111yescharacteristic
561C22×C4C23×D6111yescharacteristic
562D8—28no—
563D8—1228no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—612no—
570C2×C8—1221no—
571C2×C8—1221no—
572C2×C8—1221no—
573C2×C8—1221no—
574C2×C8—1221no—
575C2×C8C2×C4×D6112yes—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—612no—
580C4⋊C4—612no—
581C4⋊C4—1221no—
582C4⋊C4—1221no—
583C4⋊C4—1221no—
584C4⋊C4—1221no—
585C4⋊C4C2×C22⋊D6112yes—
586C22⋊C4—24no—
587C22⋊C4—42no—
588C22⋊C4—1224no—
589C22⋊C4—1224no—
590C22⋊C4—4881no—
591C22⋊C4—4881no—
592C22⋊C4—4881no—
593C22⋊C4—4881no—
594C22⋊C4—2442no—
595C42—612no—
596C42—612no—
597C42—1221no—
598C42—1221no—
599C42—4881no—
600C42—4881no—
601C42—4881no—
602C42#1175822412yes—
603C42C2×C22⋊D6112yes—
604C23—22no—
605C23—22no—
606C23—22no—
607C23—22no—
608C23—41no—
609C23—41no—
610C23—41no—
611C23—41no—
612C23—41no—
613C23—41no—
614C23—41no—
615C23—41no—
616C23—41no—
617C23—41no—
618C23—1222no—
619C23—2441no—
620C23—2441no—
621C23—2441no—
622C23—2441no—
623C23—2441no—
624C23—2441no—
625C23C2×D4×D6111yescharacteristic
626D4—22no—
627D4—22no—
628D4—22no—
629D4—22no—
630D4—22no—
631D4—41no—
632D4—41no—
633D4—1222no—
634D4—1222no—
635D4—4884no—
636D4—4884no—
637D4—2441no—
638D4—2441no—
639D4C4×C22⋊D6114yes—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—22no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—84no—
651C2×C4—84no—
652C2×C4—612no—
653C2×C4—612no—
654C2×C4—1221no—
655C2×C4—1221no—
656C2×C4—1221no—
657C2×C4—1221no—
658C2×C4—1222no—
659C2×C4—1221no—
660C2×C4—1221no—
661C2×C4—1222no—
662C2×C4—1221no—
663C2×C4—1221no—
664C2×C4—1221no—
665C2×C4—1221no—
666C2×C4—4884no—
667C2×C4—4884no—
668C2×C4—4884no—
669C2×C4—2441no—
670C2×C4—2441no—
671C2×C4—2441no—
672C2×C4—2441no—
673C2×C4—2441no—
674C2×C4—2441no—
675C2×C4—2441no—
676C2×C4#1451974912yes—
677C2×C4#1451974912yes—
678C2×C4C22×C4×D6111yescharacteristic
679C2×C4C22×C22⋊D6111yescharacteristic
680C2×C4#41×D6111yescharacteristic
681C2×C4#41×D6111yescharacteristic
682C2×C4C2×#1175822411yescharacteristic
683C2×C4C2×#1175822211yescharacteristic
684C8—22no—
685C8—41no—
686C8—1222no—
687C8—2441no—
688C22—24no—
689C22—42no—
690C22—42no—
691C22—42no—
692C22—42no—
693C22—42no—
694C22—42no—
695C22—42no—
696C22—42no—
697C22—42no—
698C22—81no—
699C22—81no—
700C22—81no—
701C22—81no—
702C22—4881no—
703C22—4881no—
704C22—4881no—
705C22—4881no—
706C22—2442no—
707C22—2442no—
708C22—2442no—
709C22C4×D4×D6111yescharacteristic
710C22C2×#1451974911yescharacteristic
711C22#1684027111yescharacteristic
712C22#1684056611yescharacteristic
713C22#1684056611yescharacteristic
714C22#1684056611yescharacteristic
715C22#1684057211yescharacteristic
716C4—22no—
717C4—22no—
718C4—42no—
719C4—81no—
720C4—1222no—
721C4—1222no—
722C4—4881no—
723C4—2442no—
724C4—2441no—
725C4—2441no—
726C4—2442no—
727C4C2×C4×C22⋊D6111yescharacteristic
728C4C4×#1175822411yescharacteristic
729C4#1684029211yescharacteristic
730C4#1684030811yescharacteristic
731C2—44no—
732C2—82no—
733C2—4882no—
734C2C4×#1451974911yescharacteristic
735C2#2145464811yescharacteristic
736C2#2145466811yescharacteristic
737C2#2145532411yescharacteristic
738C2#2145536211yescharacteristic
739C2#2145602211yescharacteristic
740C2#2145606111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#442C2
socleC23×C61C22×D4
prime radicalC2×#16839955C2
cosocleC22×C4×C61C24
hypercenterC2×#442D61
hypocenterC61#21513
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#442

Complements

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

NH ≅ G/Ntype
2. C2×C4×#11758199C2semidirect
3. #21448541C2semidirect
4. #21448180C2semidirect
5. #21446744C2semidirect
6. #21446588C2semidirect
7. #21446445C2semidirect
8. #21446442C2semidirect
9. #21446169C2semidirect
10. #21446165C2semidirect
11. #21445827C2semidirect
12. #21445679C2semidirect
13. #21445645C2semidirect
14. C4×#14519698C2semidirect
15. C2×C61×#442C2semidirect
21. #16839955C4semidirect
70. C2×#11758199C2×C4semidirect
74. #14519773C2×C4semidirect
80. D4×Dic61C2×C4semidirect
98. #14519706C2×C4semidirect
100. #14519699C2×C4semidirect
103. #14519698C2×C4semidirect
121. C2×D8×C61C2×C4semidirect
127. C4×D4×C61D4semidirect
362. C2×#442D61semidirect
432. C61#21513semidirect
448. C2×D8C4×D61semidirect
464. C4×D4C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168399552
C2×C4×#117581992
#214485412
#214481802
#214467442
#214465882
#214464452
#214464422
#214461692
#214461652
#214458272
#214456792
#214456452
C4×#145196982
C2×C61×#4422
#2151361