Finite Group Databasebeta

← #29697197

Subgroups — #29697197

Order 15616.

1190 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#102×D61C211yesmaximal, characteristic
2#21448695C211yesmaximal, characteristic, complemented
3#21448640C211yesmaximal, characteristic
4#21446504C211yesmaximal, characteristic, complemented
5#21446449C211yesmaximal, characteristic, complemented
6#21446443C211yesmaximal, characteristic, complemented
7#21446081C211yesmaximal, characteristic, complemented
8#21446079C211yesmaximal, characteristic, complemented
9#21445908C211yesmaximal, characteristic, complemented
10#21445843C211yesmaximal, characteristic, complemented
11#21445748C211yesmaximal, characteristic
12C4×#14519699C211yesmaximal, characteristic, complemented
13#21445633C211yesmaximal, characteristic, complemented
14C8×#11758198C211yesmaximal, characteristic, complemented
15C61×#1934C211yesmaximal, characteristic, complemented
16C22×D4×D61C2211yescharacteristic
17C22×C8×D61C2211yescharacteristic
18C2×C4×D244C2211yescharacteristic
19C2×#14519739C2211yescharacteristic
20C2×C4⋊C4×D61C2211yescharacteristic
21C2×C22⋊C4×D61—21no—
22C2×#14519708C2211yescharacteristic, complemented
23C2×#14519708C2211yescharacteristic, complemented
24C2×#14519699C2211yescharacteristic
25C2×#14519699C2211yescharacteristic
26C2×#14519698C2211yescharacteristic
27C2×#14519698C2211yescharacteristic
28C2×#14519697C2211yescharacteristic
29C2×#14519697C2211yescharacteristic
30#102×D61C418yescomplemented
31C2×#14519689C2211yescharacteristic
32C2×C8×Dic61C2211yescharacteristic, complemented
33#16839665C2211yescharacteristic
34#16839661C2211yescharacteristic, complemented
35#16839649—21no—
36#16839643—21no—
37#16839638—21no—
38#16839638—21no—
39#16839619—21no—
40#16839619C2211yescharacteristic
41#16839619C2211yescharacteristic
42#16839617—21no—
43C4⋊C4×Dic61C2211yescharacteristic, complemented
44C4×C4⋊Dic61C2211yescharacteristic, complemented
45C4×#11758198C2211yescharacteristic
46#16839609—21no—
47#16839525C2211yescharacteristic, complemented
48#16839525C2211yescharacteristic, complemented
49#16839524C2211yescharacteristic, complemented
50#16839524C2211yescharacteristic, complemented
51#16839517C2211yescharacteristic, complemented
52#16839516C2211yescharacteristic, complemented
53C2×#102×C61C2211yescharacteristic
54C2×#102×C61C2211yescharacteristic
55C2×C4×C8×C61C2211yescharacteristic, complemented
56C61×#390C2211yescharacteristic
57C61×#389C2211yescharacteristic, complemented
58C61×#340C2211yescharacteristic, complemented
59C61×#340C2211yescharacteristic, complemented
60C24×D61—21no—
61C22×D244C2311yescharacteristic
62C22×C22⋊D61—21no—
63C2×D4×D61—22no—
64C2×D4×D61—22no—
65C2×D4×D61—22no—
66C2×D4×D61—41no—
67C2×D4×D61—41no—
68C2×D4×D61C2×C414yes—
69C22×C4×D61—21no—
70C22×C4×D61—21no—
71C22×C4×D61—21no—
72C22×C4×D61C2311yescharacteristic
73C22×#92418C2311yescharacteristic
74C22×#92418C2311yescharacteristic
75C2×C8×D61—41no—
76C2×C8×D61—41no—
77C2×C8×D61C2×C414yescomplemented
78C4×D244—22no—
79C4×D244—41no—
80#14519739—22no—
81#14519739—41no—
82C2×C4⋊Dic61—21no—
83C2×C4⋊Dic61C2311yescharacteristic
84C2×C4⋊Dic61C2311yescharacteristic
85C2×C4⋊Dic61C2311yescharacteristic
86C2×#11758196—21no—
87C4⋊C4×D61—22no—
88C4⋊C4×D61C2×C414yescomplemented
89C2×C22⋊Dic61—21no—
90C2×C22⋊Dic61—21no—
91C2×#11758198—21no—
92C2×#11758198—21no—
93C2×#11758198—21no—
94C2×#11758198—21no—
95C2×#11758198D411yescharacteristic
96C2×#11758198D411yescharacteristic
97C22⋊C4×D61—44no—
98C2×C4×Dic61—21no—
99C2×C4×Dic61—21no—
100C2×C4×Dic61C2311yescharacteristic
101#14519708—41no—
102#14519708—41no—
103#14519699—22no—
104#14519699C2×C414yes—
105#14519698—41no—
106#14519698C2×C414yescomplemented
107#14519697—22no—
108#14519697C2×C414yes—
109#14519689—22no—
110C8×Dic61—41no—
111#14519684—21no—
112#14519684—21no—
113#14519684—21no—
114#14519684—21no—
115#14519684—21no—
116#14519684D411yescharacteristic
117#14519684D411yescharacteristic
118C22×D4×C61C2311yescharacteristic
119C22×C8×C61C2311yescharacteristic
120C22×C8×C61C2311yescharacteristic
121C2×C4⋊C4×C61—21no—
122C2×C4⋊C4×C61C2311yescharacteristic
123C2×C4⋊C4×C61C2311yescharacteristic
124C2×C4⋊C4×C61C2311yescharacteristic
125C2×C22⋊C4×C61—21no—
126C2×C22⋊C4×C61—21no—
127C2×C42×C61C2311yescharacteristic
128#102×C61—41no—
129#102×C61C2×C414yescomplemented
130C4×C8×C61—41no—
131#95×C61—21no—
132C24×C61—21no—
133C23×D61—21no—
134C23×D61—24no—
135C23×D61—42no—
136C23×D61—42no—
137C23×D61—42no—
138C23×D61—42no—
139C23×D61—81no—
140C23×D61—81no—
141C23×D61C2×D411yescharacteristic
142C2×D4×C61—21no—
143C2×D4×C61—21no—
144C2×D4×C61—21no—
145C2×D4×C61—21no—
146C2×D4×C61—21no—
147C2×D4×C61C22×C412yes—
148C22×C4×C61—21no—
149C22×C4×C61—21no—
150C22×C4×C61—21no—
151C22×C4×C61C2×D411yescharacteristic
152C22×C4×C61C2×D411yescharacteristic
153C22×C4×C61C2411yescharacteristic
154C2×C22⋊D61—24no—
155C2×C22⋊D61—42no—
156C2×C22⋊D61—42no—
157C22×Dic61—21no—
158C22×Dic61—21no—
159C22×Dic61—21no—
160C22×Dic61C2×D411yescharacteristic
161C22×Dic61C2×D411yescharacteristic
162C22×Dic61C2×D411yescharacteristic
163D4×D61—28no—
164D4×D61—44no—
165D4×D61—44no—
166D4×D61—44no—
167C2×D244—21no—
168C2×D244—21no—
169C2×D244—21no—
170C2×D244C22×C412yes—
171C2×D244#4112yes—
172C2×D244#4112yes—
173C2×C4×D61—21no—
174C2×C4×D61—21no—
175C2×C4×D61—21no—
176C2×C4×D61—21no—
177C2×C4×D61—24no—
178C2×C4×D61—42no—
179C2×C4×D61—42no—
180C2×C4×D61—42no—
181C2×C4×D61—42no—
182C2×C4×D61—81no—
183C2×C4×D61—81no—
184C2×C4×D61—81no—
185C2×C4×D61—81no—
186C2×C4×D61C22×C412yes—
187C2×C4×D61#4112yes—
188C2×C8×C61—21no—
189C2×C8×C61—21no—
190C2×C8×C61—21no—
191C2×C8×C61—21no—
192C2×C8×C61—21no—
193C2×C8×C61C22×C412yes—
194C4⋊C4×C61—21no—
195C4⋊C4×C61—21no—
196C4⋊C4×C61—21no—
197C4⋊C4×C61—21no—
198C4⋊C4×C61—21no—
199C4⋊C4×C61—81no—
200C4⋊C4×C61C22×C412yes—
201C22⋊C4×C61—42no—
202C22⋊C4×C61—81no—
203C42×C61—21no—
204C42×C61—21no—
205C22⋊Dic61—42no—
206C22⋊Dic61—81no—
207#11758198—22no—
208#11758198—42no—
209#11758198—42no—
210#11758198—42no—
211#11758198—42no—
212#11758198SD1614yes—
213C4⋊Dic61—21no—
214C4⋊Dic61—21no—
215C4⋊Dic61—21no—
216C4⋊Dic61—21no—
217C4⋊Dic61—21no—
218C4⋊Dic61—81no—
219C4⋊Dic61C22×C412yes—
220#11758196—24no—
221C4×Dic61—21no—
222C4×Dic61—21no—
223C4×Dic61—81no—
224C4×Dic61—81no—
225C2×#92418—21no—
226C2×#92418—21no—
227C2×#92418—21no—
228C2×#92418—21no—
229C2×#92418—21no—
230C2×#92418C22×C412yes—
231C8×D61—44no—
232C23×C61—22no—
233C23×C61—41no—
234C23×C61—41no—
235C23×C61—41no—
236C23×C61—41no—
237C23×C61—41no—
238C23×C61—41no—
239C23×C61C22×D411yescharacteristic
240C22×D61—21no—
241C22×D61—21no—
242C22×D61—21no—
243C22×D61—21no—
244C22×D61—22no—
245C22×D61—22no—
246C22×D61—22no—
247C22×D61—48no—
248C22×D61—41no—
249C22×D61—41no—
250C22×D61—41no—
251C22×D61—41no—
252C22×D61—48no—
253C22×D61—84no—
254C22×D61—84no—
255C22×D61—84no—
256C22×D61—84no—
257C22×D61—84no—
258C22×D61C4×D412yes—
259C22×D61C2×SD1612yes—
260C22×D61#13512yes—
261D4×C61—22no—
262D4×C61—22no—
263D4×C61—41no—
264D4×C61—41no—
265C2×C4×C61—21no—
266C2×C4×C61—21no—
267C2×C4×C61—22no—
268C2×C4×C61—21no—
269C2×C4×C61—21no—
270C2×C4×C61—21no—
271C2×C4×C61—41no—
272C2×C4×C61—41no—
273C2×C4×C61—41no—
274C2×C4×C61—41no—
275C2×C4×C61—41no—
276C2×C4×C61—41no—
277C2×C4×C61—41no—
278C2×C4×C61—41no—
279C2×C4×C61C2×SD1612yes—
280C2×C4×C61C23×C411yescharacteristic
281C2×C4×C61C2×#4111yescharacteristic
282C2×C4×C61C2×#4111yescharacteristic
283C2×C4×C61C2×#4111yescharacteristic
284C2×C4×C61H(5,𝔽2)11yescharacteristic
285C2×C4×C61H(5,𝔽2)11yescharacteristic
286C22⋊D61—48no—
287C2×Dic61—21no—
288C2×Dic61—21no—
289C2×Dic61—21no—
290C2×Dic61—21no—
291C2×Dic61—22no—
292C2×Dic61—21no—
293C2×Dic61—21no—
294C2×Dic61—21no—
295C2×Dic61—41no—
296C2×Dic61—41no—
297C2×Dic61—41no—
298C2×Dic61—41no—
299C2×Dic61—41no—
300C2×Dic61—41no—
301C2×Dic61—41no—
302C2×Dic61—41no—
303C2×Dic61C4×D412yes—
304C2×Dic61C2×SD1612yes—
305D244—22no—
306D244—22no—
307D244—22no—
308D244#11714yes—
309C4×D61—22no—
310C4×D61—22no—
311C4×D61—22no—
312C4×D61—22no—
313C4×D61—84no—
314C4×D61—84no—
315C4×D61—84no—
316C8×C61—22no—
317C8×C61—41no—
318#92418—22no—
319#92418—41no—
320#22574—611nomaximal, Sylow
321C22×C61—42no—
322C22×C61—42no—
323C22×C61—42no—
324C22×C61—81no—
325C22×C61—81no—
326C22×C61—81no—
327C22×C61—81no—
328C22×C61C2×C4×D411yescharacteristic
329C22×C61#54611yescharacteristic
330C22×C61#54611yescharacteristic
331C22×C61C22×SD1611yescharacteristic
332C22×C61C2×#13511yescharacteristic
333C22×C61#57611yescharacteristic
334C22×C61#57611yescharacteristic
335C2×D61—22no—
336C2×D61—22no—
337C2×D61—22no—
338C2×D61—22no—
339C2×D61—22no—
340C2×D61—22no—
341C2×D61—24no—
342C2×D61—42no—
343C2×D61—42no—
344C2×D61—42no—
345C2×D61—42no—
346C2×D61—42no—
347C2×D61—42no—
348C2×D61—816no—
349C2×D61C4×SD1614yes—
350C4×C61—22no—
351C4×C61—42no—
352C4×C61—41no—
353C4×C61—81no—
354C4×C61—81no—
355C4×C61C2×#11711yescharacteristic
356C4×C61#51811yescharacteristic
357C4×C61#55111yescharacteristic
358C4×C61#55111yescharacteristic
359Dic61—22no—
360Dic61—22no—
361Dic61—42no—
362Dic61—41no—
363Dic61—81no—
364Dic61—81no—
365C22×#102—611no—
366#2345—611no—
367D4×C22⋊C4—611no—
368#1934—611no—
369#1934D6111yescharacteristic, complemented
370#1926—611no—
371#1926—611no—
372#1864—611no—
373#1864—611no—
374#1824—611no—
375#1807—611no—
376#1786—611no—
377C4×#102—611no—
378C4×#102—611no—
379C8×C22⋊C4—611no—
380C2×C61—82no—
381C2×C61#234211yescharacteristic
382C2×C61C2×C4×SD1611yescharacteristic
383C2×C61#294811yescharacteristic
384C2×C61#329511yescharacteristic
385C2×C61#329511yescharacteristic
386C2×C61#329711yescharacteristic
387C2×C61#329711yescharacteristic
388D61—24no—
389D61—44no—
390C23×D4—611no—
391C23×C8—611no—
392C2×C4×D4—611no—
393C2×C4×D4—611no—
394C22×C4⋊C4—611no—
395C22×C22⋊C4—1221no—
396C2×#106—611no—
397C2×#106—611no—
398C2×#102—611no—
399C2×#102—611no—
400C2×#102—611no—
401C2×#102—618no—
402C2×#102—611no—
403C2×#102—611no—
404C2×#102—611no—
405C2×#102C2×D6111yescharacteristic
406C2×#102C2×D6111yescharacteristic
407C2×C22⋊C8—611no—
408C2×C4×C8—611no—
409C2×C4×C8C2×D6111yescharacteristic, complemented
410#390—611no—
411#390C2×D6111yescharacteristic
412#389—611no—
413#389C2×D6111yescharacteristic, complemented
414#387—1221no—
415#387—1221no—
416#386—1221no—
417#386—1221no—
418#380—611no—
419#380—611no—
420#380—1221no—
421#379—1221no—
422C4×C4⋊C4—611no—
423C4×C4⋊C4—611no—
424C4×C22⋊C4—611no—
425C4×C22⋊C4—1221no—
426#340—611no—
427#340—611no—
428#340—611no—
429#340—611no—
430#340C2×D6111yescharacteristic, complemented
431#340C2×D6111yescharacteristic, complemented
432#336—611no—
433#336—611no—
434C61#2257411yescharacteristic, complemented, Sylow
435C25—1221no—
436C22×D4—614no—
437C22×D4—611no—
438C22×D4—1222no—
439C22×D4—1221no—
440C22×D4—1222no—
441C22×D4—1222no—
442C22×D4—2441no—
443C22×D4—2441no—
444C22×D4C22×D6111yescharacteristic
445C23×C4—611no—
446C23×C4—1221no—
447C23×C4—1221no—
448C23×C4—1221no—
449C22×C8—611no—
450C22×C8—614no—
451C22×C8—611no—
452C22×C8—2441no—
453C22×C8—2441no—
454C22×C8C22×D6111yescharacteristic
455C22×C8C22×D6111yescharacteristic
456C4×D4—1222no—
457C4×D4—1222no—
458C4×D4—2441no—
459C4×D4—2441no—
460C2×C4⋊C4—21no—
461C2×C4⋊C4—611no—
462C2×C4⋊C4—614no—
463C2×C4⋊C4—611no—
464C2×C4⋊C4—611no—
465C2×C4⋊C4—1222no—
466C2×C4⋊C4—1221no—
467C2×C4⋊C4—1221no—
468C2×C4⋊C4C22×D6111yescharacteristic
469C2×C4⋊C4C22×D6111yescharacteristic
470C2×C4⋊C4C22×D6111yescharacteristic
471C2×C22⋊C4—21no—
472C2×C22⋊C4—21no—
473C2×C22⋊C4—611no—
474C2×C22⋊C4—611no—
475C2×C22⋊C4—1221no—
476C2×C22⋊C4—1221no—
477C2×C22⋊C4—1221no—
478C2×C22⋊C4—1221no—
479C2×C22⋊C4—1221no—
480C2×C22⋊C4—1221no—
481C2×C22⋊C4—2444no—
482C2×C42—611no—
483C2×C42—1221no—
484C2×C42—1221no—
485C2×C42C22×D6111yescharacteristic
486#106—2441no—
487#106—2441no—
488#102—41no—
489#102—614no—
490#102—614no—
491#102—614no—
492#102—1222no—
493#102—1222no—
494#102—2441no—
495#102C4×D6114yescomplemented
496C22⋊C8—1222no—
497C4×C8—41no—
498C4×C8—2441no—
499#95—21no—
500#95—611no—
501#95—611no—
502#95—1221no—
503#95—1221no—
504#95—1221no—
505#95—1221no—
506#95—1221no—
507C24—21no—
508C24—611no—
509C24—1224no—
510C24—1221no—
511C24—4881no—
512C24—4881no—
513C24—2442no—
514C24—2442no—
515C24—2442no—
516C24—2442no—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—612no—
523C2×D4—612no—
524C2×D4—612no—
525C2×D4—1224no—
526C2×D4—1228no—
527C2×D4—1221no—
528C2×D4—1221no—
529C2×D4—1221no—
530C2×D4—2444no—
531C2×D4—2444no—
532C2×D4—2444no—
533C2×D4—2442no—
534C2×D4—2442no—
535C2×D4C2×C4×D6112yes—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—611no—
540C22×C4—611no—
541C22×C4—612no—
542C22×C4—612no—
543C22×C4—611no—
544C22×C4—1224no—
545C22×C4—1221no—
546C22×C4—1221no—
547C22×C4—1221no—
548C22×C4—1221no—
549C22×C4—1221no—
550C22×C4—1221no—
551C22×C4—1221no—
552C22×C4—4881no—
553C22×C4—4881no—
554C22×C4—4881no—
555C22×C4—4881no—
556C22×C4—2442no—
557C22×C4—2442no—
558C22×C4—2442no—
559C22×C4—2442no—
560C22×C4D4×D6111yescharacteristic
561C22×C4D4×D6111yescharacteristic
562C22×C4C23×D6111yescharacteristic
563C2×C8—21no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—612no—
569C2×C8—1221no—
570C2×C8—1221no—
571C2×C8—1221no—
572C2×C8—1221no—
573C2×C8—1221no—
574C2×C8—2444no—
575C2×C8C2×C4×D6112yes—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—81no—
582C4⋊C4—612no—
583C4⋊C4—1224no—
584C4⋊C4—1221no—
585C4⋊C4—1221no—
586C4⋊C4—1221no—
587C4⋊C4—1221no—
588C4⋊C4—1221no—
589C4⋊C4—4881no—
590C4⋊C4C2×C4×D6112yes—
591C22⋊C4—42no—
592C22⋊C4—81no—
593C22⋊C4—614no—
594C22⋊C4—1222no—
595C22⋊C4—4881no—
596C22⋊C4—2442no—
597C22⋊C4—2442no—
598C22⋊C4—2442no—
599C22⋊C4—2442no—
600C22⋊C4—2442no—
601C42—21no—
602C42—21no—
603C42—1221no—
604C42—1221no—
605C42—4881no—
606C42—4881no—
607C23—22no—
608C23—41no—
609C23—41no—
610C23—41no—
611C23—41no—
612C23—41no—
613C23—41no—
614C23—612no—
615C23—612no—
616C23—612no—
617C23—1221no—
618C23—1221no—
619C23—1221no—
620C23—1221no—
621C23—1222no—
622C23—1222no—
623C23—1222no—
624C23—4884no—
625C23—4884no—
626C23—4884no—
627C23—4884no—
628C23—4884no—
629C23—2448no—
630C23—2448no—
631C23—2441no—
632C23—2441no—
633C23—2441no—
634C23—2441no—
635C23C2×D4×D6111yescharacteristic
636D4—22no—
637D4—22no—
638D4—41no—
639D4—41no—
640D4—614no—
641D4—1222no—
642D4—1222no—
643D4—1222no—
644D4—2448no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—22no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—612no—
660C2×C4—612no—
661C2×C4—1221no—
662C2×C4—1221no—
663C2×C4—1221no—
664C2×C4—1221no—
665C2×C4—1222no—
666C2×C4—1222no—
667C2×C4—1222no—
668C2×C4—1222no—
669C2×C4—1222no—
670C2×C4—1221no—
671C2×C4—1221no—
672C2×C4—1221no—
673C2×C4—4884no—
674C2×C4—4884no—
675C2×C4—4884no—
676C2×C4—2441no—
677C2×C4—2441no—
678C2×C4—2441no—
679C2×C4—2441no—
680C2×C4—2441no—
681C2×C4—2441no—
682C2×C4—2441no—
683C2×C4—2441no—
684C2×C4SD16×D6112yes—
685C2×C4C22×C4×D6111yescharacteristic
686C2×C4#41×D6111yescharacteristic
687C2×C4#41×D6111yescharacteristic
688C2×C4#41×D6111yescharacteristic
689C2×C4#1451982211yescharacteristic
690C2×C4#1451982311yescharacteristic
691C8—22no—
692C8—41no—
693C8—1222no—
694C8—2441no—
695C22—42no—
696C22—42no—
697C22—42no—
698C22—81no—
699C22—81no—
700C22—81no—
701C22—81no—
702C22—614no—
703C22—1222no—
704C22—1222no—
705C22—1222no—
706C22—1222no—
707C22—1222no—
708C22—1222no—
709C22—1224no—
710C22—48816no—
711C22—2442no—
712C22—2442no—
713C22—2442no—
714C22—2442no—
715C22—2442no—
716C22—2442no—
717C22C4×D4×D6111yescharacteristic
718C22#1684040111yescharacteristic
719C22#1684040511yescharacteristic
720C22C2×SD16×D6111yescharacteristic
721C22#135×D6111yescharacteristic
722C22#1684056311yescharacteristic
723C22#1684056411yescharacteristic
724C4—22no—
725C4—41no—
726C4—42no—
727C4—81no—
728C4—81no—
729C4—1222no—
730C4—1222no—
731C4—4881no—
732C4—4881no—
733C4—2441no—
734C4—2442no—
735C4#117×D6111yescharacteristic
736C4#1684023411yescharacteristic
737C4#1684043711yescharacteristic
738C4#1684044011yescharacteristic
739C2—82no—
740C2—1224no—
741C2—2444no—
742C2#2144866711yescharacteristic
743C2C4×SD16×D6111yescharacteristic
744C2#2145466611yescharacteristic
745C2#2145763811yescharacteristic
746C2#2145764211yescharacteristic
747C2#2145766411yescharacteristic
748C2#2145766811yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1934C2
socleC23×C61C22×D4
prime radicalC22×D4×D61C22
cosocleC22×C4×C61C24
hypercenter#1934D61
hypocenterC61#22574
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1934

Complements

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

NH ≅ G/Ntype
2. #21448695C2semidirect
4. #21446504C2semidirect
5. #21446449C2semidirect
6. #21446443C2semidirect
7. #21446081C2semidirect
8. #21446079C2semidirect
9. #21445908C2semidirect
10. #21445843C2semidirect
12. C4×#14519699C2semidirect
13. #21445633C2semidirect
14. C8×#11758198C2semidirect
15. C61×#1934C2semidirect
22. C2×#14519708C22semidirect
23. C2×#14519708C22semidirect
30. #102×D61C4semidirect
32. C2×C8×Dic61C22semidirect
34. #16839661C22semidirect
43. C4⋊C4×Dic61C22semidirect
44. C4×C4⋊Dic61C22semidirect
47. #16839525C22semidirect
48. #16839525C22semidirect
49. #16839524C22semidirect
50. #16839524C22semidirect
51. #16839517C22semidirect
52. #16839516C22semidirect
55. C2×C4×C8×C61C22semidirect
57. C61×#389C22semidirect
58. C61×#340C22semidirect
59. C61×#340C22semidirect
77. C2×C8×D61C2×C4semidirect
88. C4⋊C4×D61C2×C4semidirect
106. #14519698C2×C4semidirect
129. #102×C61C2×C4semidirect
369. #1934D61semidirect
409. C2×C4×C8C2×D61semidirect
413. #389C2×D61semidirect
430. #340C2×D61semidirect
431. #340C2×D61semidirect
434. C61#22574semidirect
495. #102C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#102×D612
#214486952
#214486402
#214465042
#214464492
#214464432
#214460812
#214460792
#214459082
#214458432
#214457482
C4×#145196992
#214456332
C8×#117581982
C61×#19342
#2257461