Finite Group Databasebeta

← #29686398

Subgroups — #29686398

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×#16839874C211yesmaximal, characteristic, complemented
2C2×D8×Dic61C211yesmaximal, characteristic, complemented
3#21448545C211yesmaximal, characteristic, complemented
4#21448180C211yesmaximal, characteristic, complemented
5#21446747C211yesmaximal, characteristic, complemented
6#21446589C211yesmaximal, characteristic, complemented
7#21446448C211yesmaximal, characteristic, complemented
8#21446441C211yesmaximal, characteristic, complemented
9#21446169C211yesmaximal, characteristic, complemented
10#21446169C211yesmaximal, characteristic, complemented
11#21445829C211yesmaximal, characteristic, complemented
12#21445678C211yesmaximal, characteristic, complemented
13#21445646C211yesmaximal, characteristic, complemented
14#102×Dic61C211yesmaximal, characteristic, complemented
15C2×C61×#459C211yesmaximal, characteristic
16C2×D4×Dic61C2211yescharacteristic
17C2×D4×Dic61C2211yescharacteristic
18C2×D4×Dic61C2211yescharacteristic
19C2×D4×Dic61C2211yescharacteristic
20#16839874—24no—
21D8×Dic61—24no—
22C2×#14519711C2211yescharacteristic
23C2×#14519709C2211yescharacteristic
24C2×C4⋊#92418C2211yescharacteristic
25C2×#14519698C2211yescharacteristic
26C2×#14519698C2211yescharacteristic
27C2×#14519698C2211yescharacteristic
28C2×#14519698C2211yescharacteristic
29C2×#14519698C2211yescharacteristic
30C2×#14519698C2211yescharacteristic
31C2×#14519687C2211yescharacteristic
32C2×C8×Dic61C2211yescharacteristic
33#16839665C2211yescharacteristic
34#16839665C2211yescharacteristic
35#16839642—21no—
36#16839642—21no—
37#16839642—21no—
38#16839642—21no—
39#16839628C2211yescharacteristic
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
55C22×D8×C61C2211yescharacteristic
56C2×#127×C61C2211yescharacteristic
57C2×C4×D4×C61C2211yescharacteristic
58C61×#459C418yescomplemented
59C2×C4⋊C8×C61C2211yescharacteristic
60C2×#102×C61C2211yescharacteristic
61C2×#102×C61C2211yescharacteristic
62C23×Dic61—21no—
63C23×Dic61—21no—
64C23×Dic61—21no—
65C23×Dic61—21no—
66C22×#92418C2311yescharacteristic
67C22×#92418C2311yescharacteristic
68D4×Dic61—22no—
69D4×Dic61—22no—
70D4×Dic61—22no—
71D4×Dic61—22no—
72D4×Dic61—22no—
73D4×Dic61—22no—
74D4×Dic61—22no—
75D4×Dic61D414yescomplemented
76C2×C4⋊Dic61C2311yescharacteristic
77C2×C4⋊Dic61C2311yescharacteristic
78C2×C4⋊Dic61C2311yescharacteristic
79C2×C4⋊Dic61C2311yescharacteristic
80C2×C22⋊Dic61—21no—
81C2×C22⋊Dic61—21no—
82C2×C22⋊Dic61—21no—
83C2×C22⋊Dic61—21no—
84C2×C22⋊Dic61—21no—
85C2×C22⋊Dic61—21no—
86C2×C22⋊Dic61—21no—
87C2×C22⋊Dic61—21no—
88C2×C4×Dic61—21no—
89C2×C4×Dic61—21no—
90C2×C4×Dic61—21no—
91C2×C4×Dic61C2311yescharacteristic
92C2×C4×Dic61C2311yescharacteristic
93#14519711—22no—
94#14519709—22no—
95C4⋊#92418—22no—
96#14519698—22no—
97#14519698—22no—
98#14519698—22no—
99#14519698—22no—
100#14519698—22no—
101#14519698—22no—
102#14519687—22no—
103C8×Dic61—22no—
104#14519684—21no—
105#14519684—21no—
106#14519684—21no—
107#14519684—21no—
108#14519684—21no—
109#14519684D411yescharacteristic
110#14519684D411yescharacteristic
111#14519684D411yescharacteristic
112#14519684D411yescharacteristic
113C22×D4×C61—21no—
114C22×D4×C61—21no—
115C22×D4×C61C2311yescharacteristic
116C22×D4×C61C2311yescharacteristic
117C22×D4×C61C2311yescharacteristic
118C23×C4×C61—21no—
119C2×D8×C61—22no—
120C2×D8×C61—22no—
121C2×D8×C61—22no—
122C2×D8×C61—22no—
123C2×D8×C61C2×C414yescomplemented
124C2×D8×C61C2×C414yescomplemented
125C22×C8×C61C2311yescharacteristic
126C22×C8×C61C2311yescharacteristic
127#127×C61—22no—
128#127×C61C2×C414yescomplemented
129C4×D4×C61—22no—
130C4×D4×C61C2×C414yescomplemented
131C2×C4⋊C4×C61C2311yescharacteristic
132C2×C22⋊C4×C61—21no—
133C2×C42×C61C2311yescharacteristic
134C4⋊C8×C61C2×C414yescomplemented
135#102×C61C2×C414yescomplemented
136#102×C61C2×C414yescomplemented
137C24×C61—21no—
138C24×C61—21no—
139C24×C61—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—21no—
153C2×D4×C61—21no—
154C2×D4×C61—21no—
155C2×D4×C61—81no—
156C2×D4×C61—81no—
157C2×D4×C61—81no—
158C2×D4×C61—81no—
159C2×D4×C61C22×C412yes—
160C2×D4×C61C22×C412yes—
161C2×D4×C61C22×C412yes—
162C2×D4×C61C2×D412yes—
163C2×D4×C61#4112yes—
164C22×C4×C61—21no—
165C22×C4×C61—24no—
166C22×C4×C61—81no—
167C22×C4×C61—81no—
168C22×C4×C61C2×D411yescharacteristic
169C22×C4×C61C2×D411yescharacteristic
170C22×C4×C61C2411yescharacteristic
171C22×Dic61—21no—
172C22×Dic61—21no—
173C22×Dic61—24no—
174C22×Dic61—24no—
175C22×Dic61—21no—
176C22×Dic61—21no—
177C22×Dic61—42no—
178C22×Dic61—42no—
179C22×Dic61—81no—
180C22×Dic61—81no—
181C22×Dic61—81no—
182C22×Dic61—81no—
183C22×Dic61—81no—
184C22×Dic61—81no—
185C22×Dic61—81no—
186C22×Dic61—81no—
187C22×Dic61C2×D411yescharacteristic
188C22×Dic61C2×D411yescharacteristic
189C22×Dic61C2×D411yescharacteristic
190C22×Dic61C2×D411yescharacteristic
191D8×C61—28no—
192D8×C61—28no—
193C2×C8×C61—21no—
194C2×C8×C61—21no—
195C2×C8×C61—21no—
196C2×C8×C61—21no—
197C2×C8×C61C22×C412yes—
198C2×C8×C61C22×C412yes—
199C4⋊C4×C61—21no—
200C4⋊C4×C61C22×C412yes—
201C22⋊C4×C61—24no—
202C42×C61C22×C412yes—
203C42×C61#4112yes—
204C22⋊Dic61—24no—
205C22⋊Dic61—24no—
206C22⋊Dic61—42no—
207C22⋊Dic61—42no—
208C22⋊Dic61—81no—
209C22⋊Dic61—81no—
210C22⋊Dic61—81no—
211C22⋊Dic61—81no—
212C4⋊Dic61—21no—
213C4⋊Dic61—21no—
214C4⋊Dic61—21no—
215C4⋊Dic61—21no—
216C4⋊Dic61—21no—
217C4⋊Dic61—21no—
218C4⋊Dic61C2×D412yes—
219C4⋊Dic61#4112yes—
220C4×Dic61—21no—
221C4×Dic61—21no—
222C4×Dic61—81no—
223C4×Dic61—81no—
224C4×Dic61—81no—
225C4×Dic61C2×D412yes—
226C4×Dic61#4112yes—
227C2×#92418—21no—
228C2×#92418—21no—
229C2×#92418—21no—
230C2×#92418—21no—
231C2×#92418—21no—
232C2×#92418—21no—
233C23×C61—22no—
234C23×C61—22no—
235C23×C61—22no—
236C23×C61—22no—
237C23×C61—22no—
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×C61—41no—
248C23×C61—41no—
249C23×C61—41no—
250C23×C61—41no—
251C23×C61—41no—
252C23×C61—41no—
253C23×C61—41no—
254C23×C61C22×D411yescharacteristic
255D4×C61—22no—
256D4×C61—22no—
257D4×C61—22no—
258D4×C61—22no—
259D4×C61—22no—
260D4×C61—22no—
261D4×C61—22no—
262D4×C61—41no—
263D4×C61—41no—
264D4×C61—41no—
265D4×C61—41no—
266D4×C61—84no—
267D4×C61—84no—
268D4×C61C4×D414yes—
269C2×C4×C61—21no—
270C2×C4×C61—21no—
271C2×C4×C61—21no—
272C2×C4×C61—21no—
273C2×C4×C61—22no—
274C2×C4×C61—41no—
275C2×C4×C61—41no—
276C2×C4×C61—84no—
277C2×C4×C61C4×D412yes—
278C2×C4×C61C4×D412yes—
279C2×C4×C61C23×C411yescharacteristic
280C2×C4×C61C22×D411yescharacteristic
281C2×C4×C61C2×#4111yescharacteristic
282C2×C4×C61C2×#4111yescharacteristic
283C2×C4×C61C2×#4111yescharacteristic
284C2×C4×C61C2×#4111yescharacteristic
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—41no—
305C2×Dic61—41no—
306C2×Dic61—41no—
307C2×Dic61—84no—
308C2×Dic61—84no—
309C2×Dic61—84no—
310C2×Dic61—84no—
311C2×Dic61#12112yes—
312C2×Dic61#12112yes—
313C8×C61—22no—
314C8×C61—22no—
315#92418—41no—
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—42no—
329C22×C61—42no—
330C22×C61—42no—
331C22×C61—81no—
332C22×C61—81no—
333C22×C61—81no—
334C22×C61—81no—
335C22×C61—81no—
336C22×C61—81no—
337C22×C61—81no—
338C22×C61—81no—
339C22×C61C2×C4×D411yescharacteristic
340C22×C61C2×#12111yescharacteristic
341C22×C61#52511yescharacteristic
342C22×C61#57611yescharacteristic
343C22×C61#57611yescharacteristic
344C22×C61#57611yescharacteristic
345C22×C61#57711yescharacteristic
346C4×C61—22no—
347C4×C61—22no—
348C4×C61—42no—
349C4×C61C2×C4×D411yescharacteristic
350C4×C61C4×#4111yescharacteristic
351C4×C61#52911yescharacteristic
352C4×C61#53211yescharacteristic
353Dic61—22no—
354Dic61—22no—
355Dic61—41no—
356Dic61—41no—
357Dic61—42no—
358Dic61—42no—
359Dic61—81no—
360Dic61—81no—
361C2×#459D6111yescharacteristic
362C2×#442—611no—
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×C61—82no—
379C2×C61C4×#12111yescharacteristic
380C2×C61#294611yescharacteristic
381C2×C61#294811yescharacteristic
382C2×C61#304111yescharacteristic
383C2×C61#304511yescharacteristic
384C2×C61#311911yescharacteristic
385C2×C61#312211yescharacteristic
386C22×D8C2×D6111yescharacteristic
387C22×D8C2×D6111yescharacteristic
388C2×#127C2×D6111yescharacteristic
389C2×C4×D4—611no—
390C2×C4×D4—611no—
391C2×C4×D4—611no—
392C2×C4×D4—611no—
393C2×C4×D4C2×D6111yescharacteristic
394#459Dic6118yescomplemented
395#442—1224no—
396C4×D8—1224no—
397C2×#107—611no—
398C2×#106—611no—
399C2×C4⋊C8—611no—
400C2×C4⋊C8C2×D6111yescharacteristic
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×#97—611no—
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—21no—
434C22×D4—21no—
435C22×D4C22×D6111yescharacteristic
436C22×D4C22×D6111yescharacteristic
437C22×D4C22×D6111yescharacteristic
438C23×C4—21no—
439C23×C4—1221no—
440C23×C4—1221no—
441C23×C4—1221no—
442C23×C4—1221no—
443C2×D8—22no—
444C2×D8—22no—
445C2×D8—22no—
446C2×D8—22no—
447C2×D8C2×Dic6114yescomplemented
448C2×D8C2×Dic6114yescomplemented
449C22×C8—611no—
450C22×C8—611no—
451C22×C8C22×D6111yescharacteristic
452C22×C8C22×D6111yescharacteristic
453#127—22no—
454#127C2×Dic6114yescomplemented
455C4×D4—22no—
456C4×D4—614no—
457C4×D4—1222no—
458C4×D4—1222no—
459C4×D4—1222no—
460C4×D4—1222no—
461C4×D4—1222no—
462C4×D4—1222no—
463C4×D4—1222no—
464C4×D4C2×Dic6114yescomplemented
465C2×C4⋊C4—611no—
466C2×C4⋊C4—611no—
467C2×C4⋊C4—611no—
468C2×C4⋊C4—611no—
469C2×C4⋊C4C22×D6111yescharacteristic
470C2×C22⋊C4—21no—
471C2×C22⋊C4—1221no—
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—1222no—
487C4⋊C8—1222no—
488C4⋊C8C2×Dic6114yescomplemented
489#102—1222no—
490#102—1222no—
491#102—1222no—
492#102—1222no—
493#102—1222no—
494#102—1222no—
495#102C2×Dic6114yescomplemented
496#102C2×Dic6114yescomplemented
497#97—1222no—
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—21no—
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—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—24no—
525C2×D4—24no—
526C2×D4—81no—
527C2×D4—81no—
528C2×D4—81no—
529C2×D4—81no—
530C2×D4D4×D6112yes—
531C2×D4#1175822412yes—
532C2×D4C22×Dic6112yes—
533C2×D4C22×Dic6112yes—
534C2×D4C22×Dic6112yes—
535C22×C4—21no—
536C22×C4—24no—
537C22×C4—81no—
538C22×C4—81no—
539C22×C4—611no—
540C22×C4—611no—
541C22×C4—611no—
542C22×C4—611no—
543C22×C4—1224no—
544C22×C4—1224no—
545C22×C4—1221no—
546C22×C4—1221no—
547C22×C4—1221no—
548C22×C4—1221no—
549C22×C4—4881no—
550C22×C4—4881no—
551C22×C4—4881no—
552C22×C4—4881no—
553C22×C4—4881no—
554C22×C4—4881no—
555C22×C4—4881no—
556C22×C4—4881no—
557C22×C4—2442no—
558C22×C4—2442no—
559C22×C4D4×D6111yescharacteristic
560C22×C4D4×D6111yescharacteristic
561C22×C4C23×D6111yescharacteristic
562D8—28no—
563D8—28no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—1221no—
569C2×C8—1221no—
570C2×C8—1221no—
571C2×C8—1221no—
572C2×C8—1221no—
573C2×C8—1221no—
574C2×C8C22×Dic6112yes—
575C2×C8C22×Dic6112yes—
576C4⋊C4—21no—
577C4⋊C4—612no—
578C4⋊C4—612no—
579C4⋊C4—1221no—
580C4⋊C4—1221no—
581C4⋊C4—1221no—
582C4⋊C4—1221no—
583C4⋊C4—1221no—
584C4⋊C4—1221no—
585C4⋊C4C22×Dic6112yes—
586C22⋊C4—24no—
587C22⋊C4—1224no—
588C22⋊C4—1224no—
589C22⋊C4—4881no—
590C22⋊C4—4881no—
591C22⋊C4—4881no—
592C22⋊C4—4881no—
593C22⋊C4—2442no—
594C22⋊C4—2442no—
595C42—612no—
596C42—612no—
597C42—1221no—
598C42—1221no—
599C42—4881no—
600C42—4881no—
601C42—4881no—
602C42#1175822412yes—
603C42C22×Dic6112yes—
604C23—22no—
605C23—22no—
606C23—22no—
607C23—22no—
608C23—22no—
609C23—41no—
610C23—41no—
611C23—41no—
612C23—41no—
613C23—41no—
614C23—41no—
615C23—41no—
616C23—41no—
617C23—41no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—41no—
625C23C2×D4×D6111yescharacteristic
626D4—22no—
627D4—22no—
628D4—22no—
629D4—22no—
630D4—22no—
631D4—22no—
632D4—22no—
633D4—41no—
634D4—41no—
635D4—41no—
636D4—41no—
637D4—84no—
638D4—84no—
639D4D4×Dic6114yes—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—22no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—84no—
648C2×C4—612no—
649C2×C4—612no—
650C2×C4—1221no—
651C2×C4—1221no—
652C2×C4—1221no—
653C2×C4—1221no—
654C2×C4—1222no—
655C2×C4—1221no—
656C2×C4—1221no—
657C2×C4—1222no—
658C2×C4—1221no—
659C2×C4—1221no—
660C2×C4—1221no—
661C2×C4—1221no—
662C2×C4—4884no—
663C2×C4—4884no—
664C2×C4—4884no—
665C2×C4—4884no—
666C2×C4—2441no—
667C2×C4—2441no—
668C2×C4—2441no—
669C2×C4—2441no—
670C2×C4—2441no—
671C2×C4—2441no—
672C2×C4—2441no—
673C2×C4—2441no—
674C2×C4—2441no—
675C2×C4—2441no—
676C2×C4D4×Dic6112yes—
677C2×C4D4×Dic6112yes—
678C2×C4C23×Dic6111yescharacteristic
679C2×C4C2×D4×D6111yescharacteristic
680C2×C4#41×D6111yescharacteristic
681C2×C4#41×D6111yescharacteristic
682C2×C4C2×#1175822411yescharacteristic
683C2×C4C2×#1175822411yescharacteristic
684C8—22no—
685C8—22no—
686C8—2441no—
687C8—2441no—
688C22—24no—
689C22—42no—
690C22—42no—
691C22—42no—
692C22—42no—
693C22—42no—
694C22—42no—
695C22—42no—
696C22—42no—
697C22—42no—
698C22—42no—
699C22—42no—
700C22—42no—
701C22—81no—
702C22—81no—
703C22—81no—
704C22—81no—
705C22—81no—
706C22—81no—
707C22—81no—
708C22—81no—
709C22C2×D4×Dic6111yescharacteristic
710C22#121×D6111yescharacteristic
711C22#1684027211yescharacteristic
712C22#1684056311yescharacteristic
713C22#1684056311yescharacteristic
714C22#1684056611yescharacteristic
715C22#1684057211yescharacteristic
716C4—22no—
717C4—22no—
718C4—42no—
719C4—1222no—
720C4—1222no—
721C4—4881no—
722C4—4881no—
723C4—2441no—
724C4—2441no—
725C4—2442no—
726C4—2442no—
727C4C2×D4×Dic6111yescharacteristic
728C4#41×Dic6111yescharacteristic
729C4#1684029311yescharacteristic
730C4#1684030711yescharacteristic
731C2—44no—
732C2—82no—
733C2—82no—
734C2#121×Dic6111yescharacteristic
735C2#2145465211yescharacteristic
736C2#2145467111yescharacteristic
737C2#2145531711yescharacteristic
738C2#2145535311yescharacteristic
739C2#2145601511yescharacteristic
740C2#2145606011yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
Fitting, prime radicalC2×C61×#459C2
socleC23×C61C22×D4
cosocleC22×C4×C61C24
hypercenterC2×#459D61
hypocenterC61#21513
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#459

Complements

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

NH ≅ G/Ntype
1. C2×#16839874C2semidirect
2. C2×D8×Dic61C2semidirect
3. #21448545C2semidirect
4. #21448180C2semidirect
5. #21446747C2semidirect
6. #21446589C2semidirect
7. #21446448C2semidirect
8. #21446441C2semidirect
9. #21446169C2semidirect
10. #21446169C2semidirect
11. #21445829C2semidirect
12. #21445678C2semidirect
13. #21445646C2semidirect
14. #102×Dic61C2semidirect
58. C61×#459C4semidirect
75. D4×Dic61D4semidirect
123. C2×D8×C61C2×C4semidirect
124. C2×D8×C61C2×C4semidirect
128. #127×C61C2×C4semidirect
130. C4×D4×C61C2×C4semidirect
134. C4⋊C8×C61C2×C4semidirect
135. #102×C61C2×C4semidirect
136. #102×C61C2×C4semidirect
394. #459Dic61semidirect
432. C61#21513semidirect
447. C2×D8C2×Dic61semidirect
448. C2×D8C2×Dic61semidirect
454. #127C2×Dic61semidirect
464. C4×D4C2×Dic61semidirect
488. C4⋊C8C2×Dic61semidirect
495. #102C2×Dic61semidirect
496. #102C2×Dic61semidirect

Maximal subgroups

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

subgroupindex
C2×#168398742
C2×D8×Dic612
#214485452
#214481802
#214467472
#214465892
#214464482
#214464412
#214461692
#214458292
#214456782
#214456462
#102×Dic612
C2×C61×#4592
#2151361