Finite Group Databasebeta

← #29682697

Subgroups — #29682697

Order 15616.

1234 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839765C211yesmaximal, characteristic
2C2×#102×D61C211yesmaximal, characteristic
3C2×#16839719C211yesmaximal, characteristic, complemented
4#21448441C211yesmaximal, characteristic, complemented
5#21448398C211yesmaximal, characteristic
6#21446517C211yesmaximal, characteristic, complemented
7#21446516C211yesmaximal, characteristic, complemented
8#21446513C211yesmaximal, characteristic, complemented
9#21446505C211yesmaximal, characteristic, complemented
10#21446504C211yesmaximal, characteristic, complemented
11#21446501C211yesmaximal, characteristic, complemented
12#21446500C211yesmaximal, characteristic, complemented
13#21445537C211yesmaximal, characteristic, complemented
14#21445534C211yesmaximal, characteristic, complemented
15C61×#1936C211yesmaximal, characteristic, complemented
16C22×D4×D61C2211yescharacteristic
17C22×#11758189C2211yescharacteristic
18C22×C8×D61C2211yescharacteristic
19C2×#14519735C2211yescharacteristic
20C2×#14519735C2211yescharacteristic
21C2×#14519734C2211yescharacteristic
22C2×C4⋊C4×D61C2211yescharacteristic
23#16839765C418yescomplemented
24C2×#14519699C2211yescharacteristic
25C2×#14519699C2211yescharacteristic
26C2×#14519698C2211yescharacteristic
27C2×#14519698C2211yescharacteristic
28C2×#14519697C2211yescharacteristic
29C2×#14519697C2211yescharacteristic
30#102×D61—24no—
31#16839719—24no—
32C2×#14519687C2211yescharacteristic, complemented
33C2×C4×#92418C2211yescharacteristic, complemented
34C2×C8×Dic61C2211yescharacteristic, complemented
35#16839665C2211yescharacteristic
36#16839664C2211yescharacteristic
37#16839663C2211yescharacteristic
38#16839662—21no—
39#16839662—21no—
40#16839661C2211yescharacteristic, complemented
41#16839660C2211yescharacteristic, complemented
42#16839658C2211yescharacteristic, complemented
43#16839636—21no—
44#16839633—21no—
45#16839631—21no—
46#16839626—21no—
47#16839617—21no—
48#16839617—21no—
49#16839525C2211yescharacteristic, complemented
50#16839525C2211yescharacteristic, complemented
51#16839524C2211yescharacteristic, complemented
52#16839524C2211yescharacteristic, complemented
53#16839524C2211yescharacteristic, complemented
54#16839524C2211yescharacteristic, complemented
55C2×#102×C61C2211yescharacteristic
56C2×#102×C61C2211yescharacteristic
57C2×#97×C61C2211yescharacteristic, complemented
58C61×#390C2211yescharacteristic
59C61×#389C2211yescharacteristic, complemented
60C61×#340C2211yescharacteristic, complemented
61C61×#340C2211yescharacteristic, complemented
62C24×D61—21no—
63C22×D244C2311yescharacteristic
64C22×C22⋊D61—21no—
65C2×D4×D61—22no—
66C2×D4×D61—22no—
67C2×D4×D61—22no—
68C2×D4×D61—22no—
69C2×D4×D61—22no—
70C2×D4×D61C2×C414yes—
71C22×C4×D61—21no—
72C22×C4×D61C2311yescharacteristic
73C2×#11758189—22no—
74C2×#11758189—22no—
75C2×#11758189C2×C414yes—
76C22×#92418C2311yescharacteristic
77C22×#92418C2311yescharacteristic
78C2×C8×D61—22no—
79C2×C8×D61—22no—
80C2×C8×D61D414yes—
81#14519735—22no—
82#14519735—22no—
83#14519735—22no—
84#14519735C2×C414yes—
85#14519734—22no—
86#14519734—22no—
87C2×C4⋊Dic61—21no—
88C2×C4⋊Dic61C2311yescharacteristic
89C2×C4⋊Dic61C2311yescharacteristic
90C2×C4⋊Dic61C2311yescharacteristic
91C2×#11758196—21no—
92C2×#11758196—21no—
93C2×#11758196—21no—
94C2×#11758196D411yescharacteristic
95C2×#11758196D411yescharacteristic
96C4⋊C4×D61—22no—
97C4⋊C4×D61—22no—
98C2×C22⋊Dic61—21no—
99C2×C22⋊Dic61—21no—
100C2×#11758198—21no—
101C2×#11758198—21no—
102C2×#11758198—21no—
103C2×#11758198—21no—
104C2×#11758198—21no—
105C2×#11758198—21no—
106C2×#11758198D411yescharacteristic
107C2×#11758198D411yescharacteristic
108C2×C4×Dic61—21no—
109C2×C4×Dic61—21no—
110C2×C4×Dic61C2311yescharacteristic
111#14519699—22no—
112#14519699C2×C414yescomplemented
113#14519698—22no—
114#14519698C2×C414yescomplemented
115#14519697—22no—
116#14519697C2×C414yescomplemented
117#14519687—22no—
118C4×#92418—22no—
119C8×Dic61—22no—
120#14519684—21no—
121#14519684—21no—
122#14519684—21no—
123C22×D4×C61C2311yescharacteristic
124C22×C8×C61C2311yescharacteristic
125C22×C8×C61C2311yescharacteristic
126C2×C4⋊C4×C61—21no—
127C2×C4⋊C4×C61C2311yescharacteristic
128C2×C4⋊C4×C61C2311yescharacteristic
129C2×C4⋊C4×C61C2311yescharacteristic
130C2×C22⋊C4×C61—21no—
131C2×C22⋊C4×C61—21no—
132C2×C42×C61C2311yescharacteristic
133#102×C61—22no—
134#102×C61C2×C414yescomplemented
135#97×C61—22no—
136#95×C61—21no—
137C24×C61—21no—
138C23×D61—21no—
139C23×D61—24no—
140C23×D61—42no—
141C23×D61—42no—
142C23×D61—81no—
143C23×D61—81no—
144C23×D61—81no—
145C23×D61—81no—
146C23×D61C2×D411yescharacteristic
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×C61C2×D411yescharacteristic
157C22×C4×C61C2×D411yescharacteristic
158C22×C4×C61C2411yescharacteristic
159C2×C22⋊D61—24no—
160C2×C22⋊D61—42no—
161C2×C22⋊D61—42no—
162C22×Dic61—21no—
163C22×Dic61—21no—
164C22×Dic61—21no—
165C22×Dic61C2×D411yescharacteristic
166C22×Dic61C2×D411yescharacteristic
167C22×Dic61C2×D411yescharacteristic
168D4×D61—28no—
169D4×D61—28no—
170D4×D61—44no—
171D4×D61—44no—
172C2×D244—21no—
173C2×D244—21no—
174C2×D244—21no—
175C2×D244—21no—
176C2×D244—21no—
177C2×D244C22×C412yes—
178C2×C4×D61—42no—
179C2×C4×D61—81no—
180C2×C4×D61—81no—
181C2×C4×D61C22×C412yes—
182C2×C4×D61C2×D412yes—
183C2×C4×D61#4112yes—
184C2×C4×D61#4112yes—
185C2×C4×D61#4112yes—
186C2×C4×D61#4112yes—
187C2×C8×C61—21no—
188C2×C8×C61—21no—
189C2×C8×C61—21no—
190C2×C8×C61—21no—
191C2×C8×C61C22×C412yes—
192C2×C8×C61C2×D412yes—
193C4⋊C4×C61—21no—
194C4⋊C4×C61—21no—
195C4⋊C4×C61—21no—
196C4⋊C4×C61—21no—
197C4⋊C4×C61—21no—
198C4⋊C4×C61—81no—
199C4⋊C4×C61C22×C412yes—
200C22⋊C4×C61—81no—
201C22⋊C4×C61—81no—
202C42×C61—21no—
203C42×C61—21no—
204C22⋊Dic61—81no—
205C22⋊Dic61—81no—
206#11758198—24no—
207#11758198—22no—
208#11758198—22no—
209#11758198—42no—
210#11758198—81no—
211#11758198—81no—
212#11758198—81no—
213#11758198—81no—
214C4⋊Dic61—21no—
215C4⋊Dic61—21no—
216C4⋊Dic61—21no—
217C4⋊Dic61—21no—
218C4⋊Dic61—21no—
219C4⋊Dic61—81no—
220C4⋊Dic61C22×C412yes—
221#11758196—22no—
222#11758196—22no—
223#11758196—42no—
224#11758196—81no—
225#11758196—81no—
226C4×Dic61—21no—
227C4×Dic61—21no—
228C4×Dic61—24no—
229C4×Dic61—42no—
230C2×#92418—21no—
231C2×#92418—21no—
232C2×#92418—21no—
233C2×#92418—21no—
234C2×#92418C22×C412yes—
235C2×#92418C2×D412yes—
236#11758189—28no—
237C8×D61—28no—
238C23×C61—22no—
239C23×C61—41no—
240C23×C61—41no—
241C23×C61—41no—
242C23×C61—41no—
243C23×C61—41no—
244C23×C61—41no—
245C23×C61C22×D411yescharacteristic
246C22×D61—21no—
247C22×D61—21no—
248C22×D61—21no—
249C22×D61—21no—
250C22×D61—22no—
251C22×D61—41no—
252C22×D61—41no—
253C22×D61—41no—
254C22×D61—41no—
255C22×D61—41no—
256C22×D61—41no—
257C22×D61—48no—
258C22×D61—84no—
259C22×D61—84no—
260C22×D61—84no—
261C22×D61—84no—
262C22×D61—84no—
263C22×D61—84no—
264C22×D61C4×D412yes—
265C22×D61#12112yes—
266C22×D61#12412yes—
267D4×C61—22no—
268D4×C61—22no—
269D4×C61—41no—
270D4×C61—41no—
271C2×C4×C61—22no—
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—41no—
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—41no—
286C2×C4×C61C23×C411yescharacteristic
287C2×C4×C61C22×D411yescharacteristic
288C2×C4×C61C2×#4111yescharacteristic
289C2×C4×C61C2×#4111yescharacteristic
290C2×C4×C61C2×#4111yescharacteristic
291C2×C4×C61C2×#4111yescharacteristic
292C22⋊D61—48no—
293C2×Dic61—22no—
294C2×Dic61—21no—
295C2×Dic61—21no—
296C2×Dic61—21no—
297C2×Dic61—21no—
298C2×Dic61—21no—
299C2×Dic61—21no—
300C2×Dic61—41no—
301C2×Dic61—41no—
302C2×Dic61—41no—
303C2×Dic61—41no—
304C2×Dic61—41no—
305C2×Dic61—41no—
306C2×Dic61—41no—
307C2×Dic61—41no—
308C2×Dic61C4×D412yes—
309C2×Dic61#12112yes—
310C2×Dic61#12412yes—
311D244—22no—
312D244—22no—
313D244—41no—
314D244—41no—
315C4×D61—84no—
316C4×D61#11714yes—
317C4×D61C4×D414yes—
318C4×D61#12314yes—
319C4×D61#12614yes—
320C8×C61—22no—
321C8×C61—22no—
322#92418—22no—
323#92418—22no—
324#21091—611nomaximal, Sylow
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×C61C2×#12411yescharacteristic
335C22×C61#57611yescharacteristic
336C22×C61#57611yescharacteristic
337C22×C61#57711yescharacteristic
338C22×C61#57711yescharacteristic
339C2×D61—22no—
340C2×D61—22no—
341C2×D61—22no—
342C2×D61—22no—
343C2×D61—22no—
344C2×D61—22no—
345C2×D61—42no—
346C2×D61—42no—
347C2×D61—42no—
348C2×D61—816no—
349C2×D61—81no—
350C2×D61—81no—
351C2×D61—81no—
352C2×D61—81no—
353C2×D61#38814yes—
354C4×C61—42no—
355C4×C61—41no—
356C4×C61—41no—
357C4×C61—81no—
358C4×C61—81no—
359C4×C61C2×#11711yescharacteristic
360C4×C61C2×C4×D411yescharacteristic
361C4×C61C2×#12311yescharacteristic
362C4×C61C2×#12611yescharacteristic
363Dic61—42no—
364Dic61—41no—
365Dic61—41no—
366Dic61—81no—
367Dic61—81no—
368Dic61#38814yes—
369C2×#418—611no—
370C22×#102—611no—
371C2×#405—611no—
372#2317—611no—
373#2309—611no—
374#1936—611no—
375#1936—611no—
376#1936—611no—
377#1936D6111yescharacteristic, complemented
378#1934—611no—
379#1934—611no—
380#1934—611no—
381#1934—611no—
382#1736—611no—
383#1735—611no—
384C2×C61—82no—
385C2×C61C2×#38811yescharacteristic
386C2×C61#294611yescharacteristic
387C2×C61#294611yescharacteristic
388C2×C61#305711yescharacteristic
389C2×C61#305811yescharacteristic
390C2×C61#313611yescharacteristic
391C2×C61#313611yescharacteristic
392D61—24no—
393D61—82no—
394C23×D4—611no—
395C22×M16—611no—
396C23×C8—611no—
397C2×#117—611no—
398C2×#117—611no—
399C2×#117—611no—
400C22×C4⋊C4—611no—
401#418—618no—
402C2×#102—611no—
403C2×#102—611no—
404C2×#102—611no—
405C2×#102—611no—
406C2×#102—611no—
407C2×#102—611no—
408C2×#102—1224no—
409C2×#102C2×D6111yescharacteristic
410C2×#102C2×D6111yescharacteristic
411#405—1224no—
412C2×#97—611no—
413C2×#97C2×D6111yescharacteristic, complemented
414C2×C4×C8—611no—
415C2×C4×C8—611no—
416#390—611no—
417#390—611no—
418#390—611no—
419#390—1221no—
420#390—1221no—
421#390C2×D6111yescharacteristic
422#389—611no—
423#389—611no—
424#389—611no—
425#389C2×D6111yescharacteristic, complemented
426#385—1221no—
427#385—1221no—
428#384—1221no—
429#382—1221no—
430#379—1221no—
431#379—1221no—
432#340—611no—
433#340—611no—
434#340—611no—
435#340—611no—
436#340—611no—
437#340—611no—
438#340C2×D6111yescharacteristic, complemented
439#340C2×D6111yescharacteristic, complemented
440C61#2109111yescharacteristic, complemented, Sylow
441C25—1221no—
442C22×D4—614no—
443C22×D4—611no—
444C22×D4—1222no—
445C22×D4—1222no—
446C22×D4—1222no—
447C22×D4—1222no—
448C22×D4—1222no—
449C22×D4—1221no—
450C22×D4C22×D6111yescharacteristic
451C23×C4—611no—
452C23×C4—1221no—
453C2×M16—614no—
454C2×M16—1222no—
455C2×M16—1222no—
456C22×C8—611no—
457C22×C8—611no—
458C22×C8—614no—
459C22×C8—1222no—
460C22×C8—1222no—
461C22×C8C22×D6111yescharacteristic
462C22×C8C22×D6111yescharacteristic
463#117—614no—
464#117—1222no—
465#117—1222no—
466#117—1222no—
467#117—1222no—
468#117—1222no—
469C2×C4⋊C4—21no—
470C2×C4⋊C4—611no—
471C2×C4⋊C4—611no—
472C2×C4⋊C4—611no—
473C2×C4⋊C4—611no—
474C2×C4⋊C4—611no—
475C2×C4⋊C4—1222no—
476C2×C4⋊C4—1222no—
477C2×C4⋊C4—1221no—
478C2×C4⋊C4—1221no—
479C2×C4⋊C4—1221no—
480C2×C4⋊C4—1221no—
481C2×C4⋊C4C22×D6111yescharacteristic
482C2×C4⋊C4C22×D6111yescharacteristic
483C2×C4⋊C4C22×D6111yescharacteristic
484C2×C22⋊C4—21no—
485C2×C22⋊C4—21no—
486C2×C22⋊C4—611no—
487C2×C22⋊C4—611no—
488C2×C22⋊C4—1221no—
489C2×C22⋊C4—1221no—
490C2×C22⋊C4—1221no—
491C2×C22⋊C4—1221no—
492C2×C22⋊C4—1221no—
493C2×C22⋊C4—1221no—
494C2×C22⋊C4—1221no—
495C2×C22⋊C4—1221no—
496C2×C42—611no—
497C2×C42—1221no—
498C2×C42—1221no—
499C2×C42C22×D6111yescharacteristic
500#102—22no—
501#102—614no—
502#102—614no—
503#102—614no—
504#102—1222no—
505#102—1222no—
506#102—1222no—
507#102C4×D6114yescomplemented
508#97—22no—
509#97—1222no—
510C4×C8—1222no—
511C4×C8—1222no—
512#95—21no—
513#95—1221no—
514#95—1221no—
515#95—1221no—
516C24—21no—
517C24—611no—
518C24—1224no—
519C24—1221no—
520C24—4881no—
521C24—4881no—
522C24—4881no—
523C24—4881no—
524C24—2442no—
525C24—2442no—
526C2×D4—21no—
527C2×D4—21no—
528C2×D4—21no—
529C2×D4—21no—
530C2×D4—21no—
531C2×D4—612no—
532C2×D4—1228no—
533C2×D4—1228no—
534C2×D4—1224no—
535C2×D4—1221no—
536C2×D4—1221no—
537C2×D4—1221no—
538C2×D4—1221no—
539C2×D4—1221no—
540C2×D4—2444no—
541C2×D4—2444no—
542C2×D4—2442no—
543C2×D4—2442no—
544C2×D4C2×C4×D6112yes—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—611no—
549C22×C4—612no—
550C22×C4—612no—
551C22×C4—612no—
552C22×C4—612no—
553C22×C4—612no—
554C22×C4—612no—
555C22×C4—611no—
556C22×C4—611no—
557C22×C4—1221no—
558C22×C4—1221no—
559C22×C4—1221no—
560C22×C4—4881no—
561C22×C4—4881no—
562C22×C4—2442no—
563C22×C4D4×D6111yescharacteristic
564C22×C4D4×D6111yescharacteristic
565C22×C4C23×D6111yescharacteristic
566M16—1228no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—612no—
572C2×C8—612no—
573C2×C8—1228no—
574C2×C8—1221no—
575C2×C8—1221no—
576C2×C8—1221no—
577C2×C8—1221no—
578C2×C8C2×C4×D6112yes—
579C2×C8D4×D6112yes—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—81no—
586C4⋊C4—612no—
587C4⋊C4—1222no—
588C4⋊C4—1222no—
589C4⋊C4—1221no—
590C4⋊C4—1221no—
591C4⋊C4—1221no—
592C4⋊C4—1221no—
593C4⋊C4—1221no—
594C4⋊C4—4881no—
595C4⋊C4—4881no—
596C4⋊C4—4881no—
597C4⋊C4—2442no—
598C4⋊C4C2×C4×D6112yes—
599C22⋊C4—81no—
600C22⋊C4—81no—
601C22⋊C4—1222no—
602C22⋊C4—1222no—
603C22⋊C4—1224no—
604C22⋊C4—4881no—
605C22⋊C4—4881no—
606C22⋊C4—4881no—
607C22⋊C4—4881no—
608C22⋊C4—4881no—
609C22⋊C4—4881no—
610C22⋊C4—2442no—
611C42—21no—
612C42—21no—
613C42—1224no—
614C42—1221no—
615C42—1221no—
616C42—2442no—
617C23—22no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—612no—
625C23—612no—
626C23—612no—
627C23—1221no—
628C23—1221no—
629C23—1221no—
630C23—1221no—
631C23—1222no—
632C23—4884no—
633C23—4884no—
634C23—4884no—
635C23—4884no—
636C23—4884no—
637C23—4884no—
638C23—2448no—
639C23—2441no—
640C23—2441no—
641C23—2441no—
642C23—2441no—
643C23—2441no—
644C23—2441no—
645C23C2×D4×D6111yescharacteristic
646D4—22no—
647D4—22no—
648D4—41no—
649D4—41no—
650D4—1222no—
651D4—1222no—
652D4—2448no—
653D4—2441no—
654D4—2441no—
655C2×C4—22no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—612no—
671C2×C4—612no—
672C2×C4—612no—
673C2×C4—614no—
674C2×C4—614no—
675C2×C4—614no—
676C2×C4—614no—
677C2×C4—1222no—
678C2×C4—1221no—
679C2×C4—1221no—
680C2×C4—1221no—
681C2×C4—1221no—
682C2×C4—1221no—
683C2×C4—1221no—
684C2×C4—4884no—
685C2×C4—2441no—
686C2×C4—2441no—
687C2×C4—2441no—
688C2×C4—2441no—
689C2×C4—2441no—
690C2×C4—2441no—
691C2×C4—2441no—
692C2×C4—2441no—
693C2×C4C22×C4×D6111yescharacteristic
694C2×C4C2×D4×D6111yescharacteristic
695C2×C4#41×D6111yescharacteristic
696C2×C4#41×D6111yescharacteristic
697C2×C4#41×D6111yescharacteristic
698C2×C4#41×D6111yescharacteristic
699C8—22no—
700C8—22no—
701C8—1222no—
702C8—1222no—
703C22—42no—
704C22—42no—
705C22—42no—
706C22—81no—
707C22—81no—
708C22—81no—
709C22—81no—
710C22—614no—
711C22—1222no—
712C22—1222no—
713C22—1222no—
714C22—1222no—
715C22—1222no—
716C22—1222no—
717C22—48816no—
718C22—4881no—
719C22—4881no—
720C22—4881no—
721C22—4881no—
722C22—2442no—
723C22—2442no—
724C22—2442no—
725C22C4×D4×D6111yescharacteristic
726C22#121×D6111yescharacteristic
727C22#124×D6111yescharacteristic
728C22#1684056611yescharacteristic
729C22#1684056611yescharacteristic
730C22#1684057111yescharacteristic
731C22#1684057211yescharacteristic
732C4—42no—
733C4—41no—
734C4—41no—
735C4—81no—
736C4—81no—
737C4—614no—
738C4—4881no—
739C4—4881no—
740C4—2442no—
741C4—2441no—
742C4—2441no—
743C4#117×D6111yescharacteristic
744C4C4×D4×D6111yescharacteristic
745C4#123×D6111yescharacteristic
746C4#126×D6111yescharacteristic
747C2—82no—
748C2—1224no—
749C2—4882no—
750C2#388×D6111yescharacteristic
751C2#2145464811yescharacteristic
752C2#2145465011yescharacteristic
753C2#2145545611yescharacteristic
754C2#2145546511yescharacteristic
755C2#2145617011yescharacteristic
756C2#2145617411yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1936C2
socleC23×C61C22×D4
prime radicalC22×D4×D61C22
cosocleC22×C4×C61C24
hypercenter#1936D61
hypocenterC61#21091
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1936

Complements

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

NH ≅ G/Ntype
3. C2×#16839719C2semidirect
4. #21448441C2semidirect
6. #21446517C2semidirect
7. #21446516C2semidirect
8. #21446513C2semidirect
9. #21446505C2semidirect
10. #21446504C2semidirect
11. #21446501C2semidirect
12. #21446500C2semidirect
13. #21445537C2semidirect
14. #21445534C2semidirect
15. C61×#1936C2semidirect
23. #16839765C4semidirect
32. C2×#14519687C22semidirect
33. C2×C4×#92418C22semidirect
34. C2×C8×Dic61C22semidirect
40. #16839661C22semidirect
41. #16839660C22semidirect
42. #16839658C22semidirect
49. #16839525C22semidirect
50. #16839525C22semidirect
51. #16839524C22semidirect
52. #16839524C22semidirect
53. #16839524C22semidirect
54. #16839524C22semidirect
57. C2×#97×C61C22semidirect
59. C61×#389C22semidirect
60. C61×#340C22semidirect
61. C61×#340C22semidirect
112. #14519699C2×C4semidirect
114. #14519698C2×C4semidirect
116. #14519697C2×C4semidirect
134. #102×C61C2×C4semidirect
377. #1936D61semidirect
413. C2×#97C2×D61semidirect
425. #389C2×D61semidirect
438. #340C2×D61semidirect
439. #340C2×D61semidirect
440. C61#21091semidirect
507. #102C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168397652
C2×#102×D612
C2×#168397192
#214484412
#214483982
#214465172
#214465162
#214465132
#214465052
#214465042
#214465012
#214465002
#214455372
#214455342
C61×#19362
#2109161