Finite Group Databasebeta

← #29696899

Subgroups — #29696899

Order 15616.

1118 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839893C211yesmaximal, characteristic, complemented
2#21448776C211yesmaximal, characteristic, complemented
3#21446752C211yesmaximal, characteristic, complemented
4#21446752C211yesmaximal, characteristic, complemented
5#21446747C211yesmaximal, characteristic
6#21446644C211yesmaximal, characteristic
7#21446636C211yesmaximal, characteristic, complemented
8#21446631C211yesmaximal, characteristic, complemented
9#21445834C211yesmaximal, characteristic, complemented
10#21445829C211yesmaximal, characteristic, complemented
11#21445819C211yesmaximal, characteristic, complemented
12#21445649C211yesmaximal, characteristic, complemented
13#21445644C211yesmaximal, characteristic, complemented
14C4×#14519698C211yesmaximal, characteristic, complemented
15C2×C61×#559C211yesmaximal, characteristic
16#16839893—24no—
17C2×C4⋊#92418C2211yescharacteristic
18C2×C4⋊#92418C2211yescharacteristic
19C2×C4⋊#92418C2211yescharacteristic
20C2×#14519701C2211yescharacteristic
21C2×#14519701C2211yescharacteristic
22C2×#14519701C2211yescharacteristic
23C2×#14519701C2211yescharacteristic
24C2×#14519698C2211yescharacteristic
25C2×#14519698C2211yescharacteristic
26C2×#14519698C2211yescharacteristic
27C2×#14519698C2211yescharacteristic
28C2×#14519698C2211yescharacteristic
29C2×#14519698C2211yescharacteristic
30C2×#14519698C2211yescharacteristic
31C2×#14519698C2211yescharacteristic
32C2×#14519688C2211yescharacteristic
33C2×#14519688C2211yescharacteristic
34C2×C4×#92418C2211yescharacteristic
35#16839669—21no—
36#16839648—21no—
37#16839648—21no—
38#16839632C2211yescharacteristic
39#16839628C2211yescharacteristic
40#16839628C2211yescharacteristic
41C4⋊C4×Dic61—21no—
42C4×C4⋊Dic61C2211yescharacteristic
43C4×C4⋊Dic61C2211yescharacteristic
44C4×C4⋊Dic61C2211yescharacteristic
45#16839524C2211yescharacteristic
46#16839524C2211yescharacteristic
47#16839524C2211yescharacteristic
48#16839524C2211yescharacteristic
49C61×#559—24no—
50C61×#559C418yescomplemented
51C2×#127×C61C2211yescharacteristic
52C2×#124×C61—21no—
53C2×#124×C61C2211yescharacteristic
54C2×#124×C61C2211yescharacteristic
55C2×#123×C61—21no—
56C2×#123×C61—21no—
57C2×C4×Q8×C61C2211yescharacteristic
58C2×C4×Q8×C61C2211yescharacteristic
59C2×C4×D4×C61—21no—
60C2×C4×D4×C61C2211yescharacteristic
61C2×C4×D4×C61C2211yescharacteristic
62C22×#92418C2311yescharacteristic
63C22×#92418C2311yescharacteristic
64C22×#92418C2311yescharacteristic
65C22×#92418C2311yescharacteristic
66C2×C4⋊Dic61—21no—
67C2×C4⋊Dic61—21no—
68C2×C4⋊Dic61C2311yescharacteristic
69C2×C4⋊Dic61C2311yescharacteristic
70C2×C4⋊Dic61C2311yescharacteristic
71C2×C4⋊Dic61C2311yescharacteristic
72C2×C4×Dic61—21no—
73C2×C4×Dic61—21no—
74C2×C4×Dic61—21no—
75C4⋊#92418—22no—
76C4⋊#92418—22no—
77C4⋊#92418—22no—
78#14519701—22no—
79#14519701—22no—
80#14519701—41no—
81#14519701—41no—
82#14519698—22no—
83#14519698—22no—
84#14519698—22no—
85#14519698—22no—
86#14519698—41no—
87#14519698—41no—
88#14519698—41no—
89#14519698—41no—
90#14519688—22no—
91#14519688—22no—
92C4×#92418—22no—
93#14519684—21no—
94#14519684—21no—
95#14519684—21no—
96#14519684—21no—
97#14519684—21no—
98#14519684—21no—
99#14519684—21no—
100C22×Q8×C61D411yescharacteristic
101C22×Q8×C61C2311yescharacteristic
102C22×D4×C61—21no—
103C22×D4×C61—21no—
104C22×D4×C61C2311yescharacteristic
105C22×D4×C61C2311yescharacteristic
106C23×C4×C61—21no—
107C23×C4×C61—21no—
108#127×C61—22no—
109#127×C61C2×C414yes—
110#124×C61—28no—
111#124×C61—22no—
112#124×C61—22no—
113#124×C61C2×C414yes—
114#124×C61C2×C414yes—
115#123×C61—28no—
116#123×C61—28no—
117C4×Q8×C61—22no—
118C4×Q8×C61C2×C414yes—
119C4×Q8×C61C2×C414yes—
120C4×Q8×C61D414yes—
121C4×D4×C61—28no—
122C4×D4×C61—22no—
123C4×D4×C61—22no—
124C4×D4×C61C2×C414yes—
125C4×D4×C61C2×C414yes—
126C2×C4⋊C4×C61—21no—
127C2×C4⋊C4×C61D411yescharacteristic
128C2×C4⋊C4×C61D411yescharacteristic
129C2×C4⋊C4×C61D411yescharacteristic
130C2×C4⋊C4×C61C2311yescharacteristic
131C2×C22⋊C4×C61—21no—
132C2×C22⋊C4×C61—21no—
133C2×C22⋊C4×C61—21no—
134C2×C22⋊C4×C61—21no—
135C2×C22⋊C4×C61—21no—
136C2×C22⋊C4×C61—21no—
137C2×C42×C61—21no—
138C2×C42×C61C2311yescharacteristic
139C2×C42×C61C2311yescharacteristic
140C2×C42×C61C2311yescharacteristic
141C24×C61—21no—
142C24×C61—21no—
143C2×Q8×C61—21no—
144C2×Q8×C61—21no—
145C2×Q8×C61—21no—
146C2×Q8×C61—21no—
147C2×Q8×C61—21no—
148C2×Q8×C61—41no—
149C2×Q8×C61—41no—
150C2×Q8×C61C22⋊C414yes—
151C2×Q8×C61C22×C412yes—
152C2×D4×C61—24no—
153C2×D4×C61—24no—
154C2×D4×C61—21no—
155C2×D4×C61—21no—
156C2×D4×C61—21no—
157C2×D4×C61—21no—
158C2×D4×C61—21no—
159C2×D4×C61—21no—
160C2×D4×C61—21no—
161C2×D4×C61—21no—
162C2×D4×C61—21no—
163C2×D4×C61—21no—
164C2×D4×C61—42no—
165C2×D4×C61—42no—
166C2×D4×C61—81no—
167C2×D4×C61—81no—
168C2×D4×C61C22×C412yes—
169C2×D4×C61C22×C412yes—
170C22×C4×C61—21no—
171C22×C4×C61—21no—
172C22×C4×C61—24no—
173C22×C4×C61—24no—
174C22×C4×C61—81no—
175C22×C4×C61—81no—
176C22×C4×C61—81no—
177C22×C4×C61—81no—
178C22×C4×C61C2×D411yescharacteristic
179C22×C4×C61C2×D411yescharacteristic
180C22×C4×C61C2×D411yescharacteristic
181C22×C4×C61C2×D411yescharacteristic
182C22×C4×C61C2×D411yescharacteristic
183C22×C4×C61C2×D411yescharacteristic
184C22×C4×C61C2411yescharacteristic
185C22×Dic61—21no—
186C22×Dic61—21no—
187C22×Dic61—21no—
188C22×Dic61—21no—
189C4⋊C4×C61—24no—
190C4⋊C4×C61—21no—
191C4⋊C4×C61C22⋊C414yes—
192C4⋊C4×C61C22⋊C414yes—
193C4⋊C4×C61C22⋊C414yes—
194C4⋊C4×C61C22×C412yes—
195C22⋊C4×C61—24no—
196C22⋊C4×C61—24no—
197C22⋊C4×C61—24no—
198C22⋊C4×C61—24no—
199C22⋊C4×C61—24no—
200C22⋊C4×C61—24no—
201C42×C61—24no—
202C42×C61C22×C412yes—
203C42×C61C22×C412yes—
204C42×C61C22×C412yes—
205C42×C61C2×D412yes—
206C42×C61C2×D412yes—
207C42×C61C2×D412yes—
208C4⋊Dic61—21no—
209C4⋊Dic61—21no—
210C4⋊Dic61—21no—
211C4⋊Dic61—21no—
212C4⋊Dic61—21no—
213C4⋊Dic61—21no—
214C4⋊Dic61—21no—
215C4⋊Dic61—42no—
216C4⋊Dic61—81no—
217C4⋊Dic61#4112yes—
218C4×Dic61—42no—
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×#92418—21no—
232C2×#92418#4112yes—
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
248Q8×C61—22no—
249Q8×C61—22no—
250Q8×C61—44no—
251Q8×C61—41no—
252Q8×C61—41no—
253D4×C61—22no—
254D4×C61—22no—
255D4×C61—22no—
256D4×C61—22no—
257D4×C61—48no—
258D4×C61—41no—
259D4×C61—41no—
260D4×C61—41no—
261D4×C61—41no—
262D4×C61—84no—
263C2×C4×C61—21no—
264C2×C4×C61—21no—
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—22no—
276C2×C4×C61—22no—
277C2×C4×C61—41no—
278C2×C4×C61—41no—
279C2×C4×C61—41no—
280C2×C4×C61—41no—
281C2×C4×C61—84no—
282C2×C4×C61—84no—
283C2×C4×C61C2×C22⋊C412yes—
284C2×C4×C61C2×C22⋊C412yes—
285C2×C4×C61C2×C22⋊C412yes—
286C2×C4×C61C2×C22⋊C412yes—
287C2×C4×C61C2×C22⋊C412yes—
288C2×C4×C61C2×C22⋊C412yes—
289C2×C4×C61C23×C411yescharacteristic
290C2×C4×C61C22×D411yescharacteristic
291C2×C4×C61C2×#4111yescharacteristic
292C2×C4×C61C2×#4111yescharacteristic
293C2×C4×C61H(5,𝔽2)11yescharacteristic
294C2×C4×C612−1+411yescharacteristic
295C2×Dic61—22no—
296C2×Dic61—41no—
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—
307#92418—22no—
308#92418—41no—
309#92418—41no—
310#92418—41no—
311#22549—611nomaximal, Sylow
312C22×C61—42no—
313C22×C61—42no—
314C22×C61—42no—
315C22×C61—42no—
316C22×C61—42no—
317C22×C61—42no—
318C22×C61—81no—
319C22×C61—81no—
320C22×C61—81no—
321C22×C61—81no—
322C22×C61—81no—
323C22×C61—81no—
324C22×C61—81no—
325C22×C61—81no—
326C22×C61C22×C22⋊C411yescharacteristic
327C22×C61#54811yescharacteristic
328C22×C61#55011yescharacteristic
329C22×C61#57511yescharacteristic
330C22×C61#57511yescharacteristic
331C22×C61#57611yescharacteristic
332C22×C61#57711yescharacteristic
333C4×C61—22no—
334C4×C61—22no—
335C4×C61—22no—
336C4×C61—22no—
337C4×C61—22no—
338C4×C61—22no—
339C4×C61—42no—
340C4×C61—42no—
341C4×C61C4×#4111yescharacteristic
342C4×C61#52011yescharacteristic
343C4×C61#54811yescharacteristic
344C4×C61#55011yescharacteristic
345Dic61—42no—
346Dic61—81no—
347Dic61—81no—
348Dic61—81no—
349C2×#559D6111yescharacteristic
350C2×#446—611no—
351#2355—611no—
352#1983—611no—
353#1983—611no—
354#1982—611no—
355#1961—611no—
356#1959—611no—
357#1958—611no—
358#1805—611no—
359#1804—611no—
360#1802—611no—
361#1763—611no—
362#1762—611no—
363C4×#102—611no—
364C2×C61—82no—
365C2×C61—82no—
366C2×C61#234111yescharacteristic
367C2×C61#289611yescharacteristic
368C2×C61#289711yescharacteristic
369C2×C61#337011yescharacteristic
370C2×C61#337111yescharacteristic
371C2×C61#340111yescharacteristic
372C2×C61#340311yescharacteristic
373#559—24no—
374#559Dic6118yescomplemented
375C2×#127C2×D6111yescharacteristic
376C2×#124—21no—
377C2×#124C2×D6111yescharacteristic
378C2×#124C2×D6111yescharacteristic
379C2×#123—21no—
380C2×#123—21no—
381C2×C4×Q8C2×D6111yescharacteristic
382C2×C4×Q8C2×D6111yescharacteristic
383C2×C4×D4—21no—
384C2×C4×D4C2×D6111yescharacteristic
385C2×C4×D4C2×D6111yescharacteristic
386#446—1224no—
387C2×C4⋊C8—611no—
388C2×C4⋊C8—611no—
389C2×C4⋊C8—611no—
390C2×#103—611no—
391C2×#103—611no—
392C2×#103—611no—
393C2×#103—611no—
394C2×#102—611no—
395C2×#102—611no—
396C2×#102—611no—
397C2×#102—611no—
398C2×#102—611no—
399C2×#102—611no—
400C2×#102—611no—
401C2×#102—611no—
402C2×#97—611no—
403C2×#97—611no—
404C2×C4×C8—611no—
405#391—1221no—
406#387—1221no—
407#387—1221no—
408#384—611no—
409#382—611no—
410#382—611no—
411C4×C4⋊C4—611no—
412C4×C4⋊C4—611no—
413C4×C4⋊C4—611no—
414C4×C4⋊C4—1221no—
415#340—611no—
416#340—611no—
417#340—611no—
418#340—611no—
419C61#2254911yescharacteristic, complemented, Sylow
420C22×Q8C22⋊D6111yescharacteristic
421C22×Q8C22×D6111yescharacteristic
422C22×D4—21no—
423C22×D4—21no—
424C22×D4C22×D6111yescharacteristic
425C22×D4C22×D6111yescharacteristic
426C23×C4—21no—
427C23×C4—21no—
428C22×C8—611no—
429C22×C8—611no—
430C22×C8—611no—
431C22×C8—611no—
432#127—22no—
433#127C2×Dic6114yes—
434#124—28no—
435#124—22no—
436#124—22no—
437#124C2×Dic6114yes—
438#124C2×Dic6114yes—
439#123—28no—
440#123—28no—
441C4×Q8—22no—
442C4×Q8C2×Dic6114yes—
443C4×Q8C2×Dic6114yes—
444C4×Q8C22⋊D6114yes—
445C4×D4—28no—
446C4×D4—22no—
447C4×D4—22no—
448C4×D4C2×Dic6114yes—
449C4×D4C2×Dic6114yes—
450C2×C4⋊C4—21no—
451C2×C4⋊C4—611no—
452C2×C4⋊C4—611no—
453C2×C4⋊C4—611no—
454C2×C4⋊C4—611no—
455C2×C4⋊C4—1221no—
456C2×C4⋊C4—1221no—
457C2×C4⋊C4C22⋊D6111yescharacteristic
458C2×C4⋊C4C22⋊D6111yescharacteristic
459C2×C4⋊C4C22⋊D6111yescharacteristic
460C2×C4⋊C4C22×D6111yescharacteristic
461C2×C22⋊C4—21no—
462C2×C22⋊C4—21no—
463C2×C22⋊C4—21no—
464C2×C22⋊C4—21no—
465C2×C22⋊C4—21no—
466C2×C22⋊C4—21no—
467C2×C42—21no—
468C2×C42—1221no—
469C2×C42—1221no—
470C2×C42—1221no—
471C2×C42C22×D6111yescharacteristic
472C2×C42C22×D6111yescharacteristic
473C2×C42C22×D6111yescharacteristic
474C4⋊C8—1222no—
475C4⋊C8—1222no—
476C4⋊C8—1222no—
477#103—1222no—
478#103—1222no—
479#103—2441no—
480#103—2441no—
481#102—1222no—
482#102—1222no—
483#102—1222no—
484#102—1222no—
485#102—2441no—
486#102—2441no—
487#102—2441no—
488#102—2441no—
489#97—1222no—
490#97—1222no—
491C4×C8—1222no—
492#95—1221no—
493#95—1221no—
494#95—1221no—
495#95—1221no—
496#95—1221no—
497#95—1221no—
498#95—1221no—
499C24—21no—
500C24—21no—
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8—21no—
504C2×Q8—21no—
505C2×Q8—21no—
506C2×Q8—41no—
507C2×Q8—41no—
508C2×Q8C22⋊Dic6114yes—
509C2×Q8C22×Dic6112yes—
510C2×D4—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—24no—
521C2×D4—24no—
522C2×D4—42no—
523C2×D4—42no—
524C2×D4—81no—
525C2×D4—81no—
526C2×D4C22×Dic6112yes—
527C2×D4C22×Dic6112yes—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—24no—
531C22×C4—24no—
532C22×C4—81no—
533C22×C4—81no—
534C22×C4—81no—
535C22×C4—81no—
536C22×C4—1221no—
537C22×C4—1221no—
538C22×C4—1221no—
539C22×C4—1221no—
540C22×C4C2×C22⋊D6111yescharacteristic
541C22×C4C2×C22⋊D6111yescharacteristic
542C22×C4C2×C22⋊D6111yescharacteristic
543C22×C4C2×C22⋊D6111yescharacteristic
544C22×C4C2×C22⋊D6111yescharacteristic
545C22×C4C2×C22⋊D6111yescharacteristic
546C22×C4C23×D6111yescharacteristic
547C2×C8—612no—
548C2×C8—1221no—
549C2×C8—1221no—
550C2×C8—1221no—
551C2×C8—1221no—
552C2×C8—1221no—
553C2×C8—1221no—
554C2×C8—1221no—
555C2×C8—1221no—
556C2×C8—1221no—
557C2×C8—1221no—
558C2×C8—1221no—
559C4⋊C4—21no—
560C4⋊C4—24no—
561C4⋊C4—612no—
562C4⋊C4—1221no—
563C4⋊C4—1221no—
564C4⋊C4—1221no—
565C4⋊C4—1221no—
566C4⋊C4—1221no—
567C4⋊C4—1221no—
568C4⋊C4—1221no—
569C4⋊C4—4881no—
570C4⋊C4—2442no—
571C4⋊C4C22⋊Dic6114yes—
572C4⋊C4C22⋊Dic6114yes—
573C4⋊C4C22⋊Dic6114yes—
574C4⋊C4C22×Dic6112yes—
575C22⋊C4—24no—
576C22⋊C4—24no—
577C22⋊C4—24no—
578C22⋊C4—24no—
579C22⋊C4—24no—
580C22⋊C4—24no—
581C42—24no—
582C42—4881no—
583C42—4881no—
584C42—2442no—
585C42C22×Dic6112yes—
586C42C22×Dic6112yes—
587C42C22×Dic6112yes—
588C42C2×C22⋊D6112yes—
589C42C2×C22⋊D6112yes—
590C42C2×C22⋊D6112yes—
591C23—22no—
592C23—22no—
593C23—41no—
594C23—41no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23—41no—
601C23—41no—
602C23—41no—
603C23—41no—
604C23—41no—
605C23C22×C22⋊D6111yescharacteristic
606Q8—22no—
607Q8—22no—
608Q8—44no—
609Q8—41no—
610Q8—41no—
611D4—22no—
612D4—22no—
613D4—22no—
614D4—22no—
615D4—48no—
616D4—41no—
617D4—41no—
618D4—41no—
619D4—41no—
620D4—84no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—84no—
640C2×C4—84no—
641C2×C4—1222no—
642C2×C4—2441no—
643C2×C4—2441no—
644C2×C4—2441no—
645C2×C4—2441no—
646C2×C4—2441no—
647C2×C4—2441no—
648C2×C4—2441no—
649C2×C4—2441no—
650C2×C4—2441no—
651C2×C4—2441no—
652C2×C4—2441no—
653C2×C4C2×C22⋊Dic6112yes—
654C2×C4C2×C22⋊Dic6112yes—
655C2×C4C2×C22⋊Dic6112yes—
656C2×C4C2×C22⋊Dic6112yes—
657C2×C4C2×C22⋊Dic6112yes—
658C2×C4C2×C22⋊Dic6112yes—
659C2×C4C23×Dic6111yescharacteristic
660C2×C4C22×C22⋊D6111yescharacteristic
661C2×C4#41×D6111yescharacteristic
662C2×C4#41×D6111yescharacteristic
663C2×C4#1451982311yescharacteristic
664C2×C4#1451982411yescharacteristic
665C8—1222no—
666C8—2441no—
667C8—2441no—
668C8—2441no—
669C22—42no—
670C22—42no—
671C22—42no—
672C22—42no—
673C22—42no—
674C22—42no—
675C22—81no—
676C22—81no—
677C22—81no—
678C22—81no—
679C22—81no—
680C22—81no—
681C22—81no—
682C22—81no—
683C22C22×C22⋊Dic6111yescharacteristic
684C22#1684041911yescharacteristic
685C22#1684043111yescharacteristic
686C22#1684056011yescharacteristic
687C22#1684056011yescharacteristic
688C22#1684056511yescharacteristic
689C22#1684057311yescharacteristic
690C4—22no—
691C4—22no—
692C4—22no—
693C4—22no—
694C4—22no—
695C4—22no—
696C4—42no—
697C4—42no—
698C4—4881no—
699C4—4881no—
700C4—4881no—
701C4—2442no—
702C4#41×Dic6111yescharacteristic
703C4#1684024511yescharacteristic
704C4#1684041911yescharacteristic
705C4#1684043111yescharacteristic
706C2—82no—
707C2—82no—
708C2#2144866011yescharacteristic
709C2#2145433811yescharacteristic
710C2#2145434511yescharacteristic
711C2#2145856611yescharacteristic
712C2#2145858111yescharacteristic
713C2#2145887911yescharacteristic
714C2#2145890311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#559C2
socleC23×C61C22×D4
prime radicalC2×#127×C61C22
cosocleC22×C4×C61C24
hypercenterC2×#559D61
hypocenterC61#22549
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#559

Complements

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

NH ≅ G/Ntype
1. C2×#16839893C2semidirect
2. #21448776C2semidirect
3. #21446752C2semidirect
4. #21446752C2semidirect
7. #21446636C2semidirect
8. #21446631C2semidirect
9. #21445834C2semidirect
10. #21445829C2semidirect
11. #21445819C2semidirect
12. #21445649C2semidirect
13. #21445644C2semidirect
14. C4×#14519698C2semidirect
50. C61×#559C4semidirect
374. #559Dic61semidirect
419. C61#22549semidirect

Maximal subgroups

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

subgroupindex
C2×#168398932
#214487762
#214467522
#214467472
#214466442
#214466362
#214466312
#214458342
#214458292
#214458192
#214456492
#214456442
C4×#145196982
C2×C61×#5592
#2254961