Finite Group Databasebeta

← #29732219

Subgroups — #29732219

Order 15616.

1194 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×#16840314C211yesmaximal, characteristic, complemented
2C2×#16839993C211yesmaximal, characteristic
3C2×#16839991C211yesmaximal, characteristic
4#21454151C211yesmaximal, characteristic
5#21447151C211yesmaximal, characteristic, complemented
6#21447064C211yesmaximal, characteristic, complemented
7#21446954C211yesmaximal, characteristic, complemented
8#21446903C211yesmaximal, characteristic, complemented
9#21446240C211yesmaximal, characteristic, complemented
10#21446175C211yesmaximal, characteristic, complemented
11#21446172C211yesmaximal, characteristic, complemented
12#21446089C211yesmaximal, characteristic, complemented
13#21446088C211yesmaximal, characteristic, complemented
14C2×#16839516C211yesmaximal, characteristic, complemented
15C61×#1892C211yesmaximal, characteristic, complemented
16C22×#11758190C2211yescharacteristic
17C22×#11758201C2211yescharacteristic
18C23×#92418C2211yescharacteristic
19#16840314—24no—
20#16840314—24no—
21C2×#14519776C2211yescharacteristic
22C2×#14519775C2211yescharacteristic
23C2×#14519767—21no—
24C2×#14519761—21no—
25C2×#14519756C2211yescharacteristic
26C2×#14519754—21no—
27C2×#14519751C2211yescharacteristic
28C2×Q8×Dic61C2211yescharacteristic
29C2×#14519742—21no—
30C2×#14519742C2211yescharacteristic
31C2×#14519733—21no—
32C22×C4×Dic61C2211yescharacteristic
33#16839993—24no—
34#16839991—24no—
35C2×#14519709C2211yescharacteristic
36C2×#14519708C2211yescharacteristic
37C2×#14519702C2211yescharacteristic
38C2×#14519701C2211yescharacteristic
39C2×#14519700C2211yescharacteristic
40C2×#14519700C2211yescharacteristic
41C2×#14519699C2211yescharacteristic
42C2×#14519697C2211yescharacteristic
43#16839663C2211yescharacteristic
44#16839663C2211yescharacteristic
45#16839661C2211yescharacteristic
46#16839661C2211yescharacteristic
47#16839654—21no—
48#16839654—21no—
49#16839639—21no—
50#16839524C2211yescharacteristic
51#16839524C2211yescharacteristic
52#16839516C2211yescharacteristic
53#16839516C2211yescharacteristic
54#16839516C2211yescharacteristic
55#16839516C2211yescharacteristic
56C23×C8×C61C2211yescharacteristic
57C2×C22⋊Q8×C61C2211yescharacteristic
58C2×#103×C61C2211yescharacteristic
59C2×#103×C61C2211yescharacteristic
60C61×#380C2211yescharacteristic
61C61×#340C2211yescharacteristic
62C61×#340C2211yescharacteristic
63C22×Dic122—21no—
64C22×Dic122C2311yescharacteristic
65C22×D244C2311yescharacteristic
66C22×C22⋊D61—21no—
67C23×Dic61D411yescharacteristic
68C23×Dic61D411yescharacteristic
69C2×#11758190—22no—
70C2×#11758190—22no—
71C2×#11758190—41no—
72C2×#11758201—22no—
73C2×#11758201—22no—
74C2×#11758201—41no—
75C22×#92418—22no—
76C22×#92418—22no—
77C22×#92418—41no—
78C22×#92418C2311yescharacteristic
79C22×#92418C2311yescharacteristic
80#14519776—22no—
81#14519776—22no—
82#14519775—22no—
83#14519775—22no—
84#14519767—28no—
85#14519761—44no—
86#14519756—22no—
87#14519756D414yes—
88#14519754—28no—
89#14519751—22no—
90#14519751—22no—
91Q8×Dic61—22no—
92Q8×Dic61—22no—
93#14519742—28no—
94#14519742—22no—
95#14519742—22no—
96#14519733—28no—
97C2×C4⋊Dic61—21no—
98C2×C4⋊Dic61—21no—
99C2×C4⋊Dic61—21no—
100C2×C4⋊Dic61C2311yescharacteristic
101C2×C4⋊Dic61C2311yescharacteristic
102C2×#11758196—21no—
103C2×#11758196—21no—
104C2×#11758196—21no—
105C2×#11758196—21no—
106C2×#11758196—21no—
107C2×C22⋊Dic61—21no—
108C2×#11758198—21no—
109C2×#11758198—21no—
110C2×#11758198—21no—
111C2×#11758198—21no—
112C2×#11758198—21no—
113C2×C4×Dic61—22no—
114C2×C4×Dic61—22no—
115C2×C4×Dic61—21no—
116C2×C4×Dic61—21no—
117C2×C4×Dic61D411yescharacteristic
118C2×C4×Dic61D411yescharacteristic
119C2×C4×Dic61C2311yescharacteristic
120C2×C4×Dic61C2311yescharacteristic
121#14519709—22no—
122#14519708—22no—
123#14519702—22no—
124#14519701—22no—
125#14519700—22no—
126#14519700—41no—
127#14519699—22no—
128#14519697—22no—
129#14519684—21no—
130#14519684—21no—
131C22×Q8×C61C2311yescharacteristic
132C23×C4×C61C2311yescharacteristic
133C22×C8×C61—22no—
134C22×C8×C61—22no—
135C22×C8×C61—41no—
136C22×C8×C61C2311yescharacteristic
137C22×C8×C61C2311yescharacteristic
138C22⋊Q8×C61—22no—
139C22⋊Q8×C61D414yes—
140C2×C4⋊C4×C61—21no—
141C2×C4⋊C4×C61C2311yescharacteristic
142C2×C4⋊C4×C61C2311yescharacteristic
143C2×C4⋊C4×C61C2311yescharacteristic
144C2×C22⋊C4×C61—21no—
145C2×C22⋊C4×C61—21no—
146#103×C61—22no—
147#103×C61—41no—
148#95×C61—21no—
149C24×C61C2×D411yescharacteristic
150C23×D61—21no—
151C2×Q8×C61—21no—
152C2×Q8×C61—21no—
153C2×Q8×C61—21no—
154C2×Q8×C61—21no—
155C2×Q8×C61—21no—
156C2×Q8×C61C2×D412yes—
157C22×C4×C61—21no—
158C22×C4×C61—21no—
159C22×C4×C61—21no—
160C22×C4×C61—21no—
161C22×C4×C61—21no—
162C22×C4×C61—21no—
163C22×C4×C61—21no—
164C22×C4×C61—21no—
165C22×C4×C61C2×D411yescharacteristic
166C22×C4×C61C2×D412yes—
167C22×C4×C61C2×D412yes—
168C22×C4×C61C2411yescharacteristic
169C2×C22⋊D61—42no—
170C2×C22⋊D61—42no—
171C2×C22⋊D61—42no—
172C22×Dic61—22no—
173C22×Dic61—22no—
174C22×Dic61—22no—
175C22×Dic61—21no—
176C22×Dic61—21no—
177C22×Dic61—22no—
178C22×Dic61—21no—
179C22×Dic61—41no—
180C22×Dic61SD1614yescomplemented
181C22×Dic61C2×D411yescharacteristic
182C22×Dic61C2×D411yescharacteristic
183C22×Dic61C2×D411yescharacteristic
184C22×Dic61C2×D411yescharacteristic
185C2×D244—21no—
186C2×D244—21no—
187C2×D244—21no—
188C2×D244—21no—
189C2×D244—21no—
190C2×D244—21no—
191C2×Dic122—21no—
192C2×Dic122—21no—
193C2×Dic122—21no—
194C2×Dic122—21no—
195C2×Dic122—24no—
196C2×Dic122—21no—
197C2×Dic122—42no—
198C2×Dic122—42no—
199C2×Dic122C2×D412yes—
200C2×C8×C61—21no—
201C2×C8×C61—21no—
202C2×C8×C61—21no—
203C2×C8×C61—21no—
204C2×C8×C61—21no—
205C2×C8×C61—44no—
206C2×C8×C61#4112yes—
207C4⋊C4×C61—24no—
208C4⋊C4×C61—21no—
209C4⋊C4×C61—21no—
210C4⋊C4×C61—21no—
211C4⋊C4×C61—21no—
212C4⋊C4×C61—21no—
213C4⋊C4×C61C2×D412yes—
214C22⋊C4×C61—24no—
215C22⋊C4×C61—42no—
216C22⋊Dic61—24no—
217#11758201—44no—
218#11758198—42no—
219#11758198—42no—
220#11758198—42no—
221#11758198—42no—
222#11758198—42no—
223C4⋊Dic61—24no—
224C4⋊Dic61—21no—
225C4⋊Dic61—21no—
226C4⋊Dic61—21no—
227C4⋊Dic61—42no—
228C4⋊Dic61—42no—
229C4⋊Dic61C2×D412yes—
230#11758196—24no—
231#11758196—24no—
232#11758196—24no—
233#11758196—24no—
234#11758196—24no—
235C4×Dic61—24no—
236C4×Dic61—24no—
237C4×Dic61—22no—
238C4×Dic61—22no—
239C4×Dic61—21no—
240C4×Dic61—21no—
241C4×Dic61—21no—
242C4×Dic61—21no—
243C2×#92418—21no—
244C2×#92418—21no—
245C2×#92418—21no—
246C2×#92418—21no—
247C2×#92418—21no—
248C2×#92418—44no—
249C2×#92418#4112yes—
250#11758190—44no—
251C23×C61—21no—
252C23×C61—21no—
253C23×C61—21no—
254C23×C61—21no—
255C23×C61#12012yes—
256C23×C61C2×SD1612yes—
257C23×C61#13712yes—
258C23×C61C22×D411yescharacteristic
259C22×D61—41no—
260C22×D61—41no—
261C22×D61—41no—
262C22×D61—41no—
263C22×D61—41no—
264C22×D61—41no—
265C22×D61—41no—
266Q8×C61—22no—
267Q8×C61—22no—
268Q8×C61—41no—
269Q8×C61—41no—
270C2×C4×C61—21no—
271C2×C4×C61—21no—
272C2×C4×C61—22no—
273C2×C4×C61—22no—
274C2×C4×C61—22no—
275C2×C4×C61—22no—
276C2×C4×C61—22no—
277C2×C4×C61—22no—
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×C61—41no—
287C2×C4×C61—41no—
288C2×C4×C61#12012yes—
289C2×C4×C61C22×D411yescharacteristic
290C2×C4×C61C22×D411yescharacteristic
291C2×C4×C61C2×#4111yescharacteristic
292C2×C4×C61C2×#4111yescharacteristic
293C2×C4×C61H(5,𝔽2)11yescharacteristic
294C2×C4×C612−1+411yescharacteristic
295C22⋊D61—84no—
296C2×Dic61—21no—
297C2×Dic61—21no—
298C2×Dic61—21no—
299C2×Dic61—21no—
300C2×Dic61—21no—
301C2×Dic61—21no—
302C2×Dic61—28no—
303C2×Dic61—21no—
304C2×Dic61—22no—
305C2×Dic61—22no—
306C2×Dic61—21no—
307C2×Dic61—21no—
308C2×Dic61—44no—
309C2×Dic61—41no—
310C2×Dic61—41no—
311C2×Dic61—41no—
312C2×Dic61—41no—
313C2×Dic61—41no—
314C2×Dic61—41no—
315C2×Dic61—41no—
316C2×Dic61C2×SD1612yes—
317C2×Dic61C2×SD1612yes—
318C2×Dic61#13512yes—
319D244—41no—
320D244—41no—
321D244—41no—
322D244—41no—
323Dic122—22no—
324Dic122—22no—
325Dic122—48no—
326Dic122—41no—
327Dic122—41no—
328C8×C61—22no—
329C8×C61—41no—
330#92418—22no—
331#92418—41no—
332#25497—611nomaximal, Sylow
333C22×C61—22no—
334C22×C61—22no—
335C22×C61—22no—
336C22×C61—22no—
337C22×C61—22no—
338C22×C61—22no—
339C22×C61#44814yes—
340C22×C61C2×#12011yescharacteristic
341C22×C61#53211yescharacteristic
342C22×C61#53711yescharacteristic
343C22×C61C22×SD1611yescharacteristic
344C22×C61C2×#13511yescharacteristic
345C22×C61C2×#13711yescharacteristic
346C22×C61#57511yescharacteristic
347C2×D61—81no—
348C2×D61—81no—
349C2×D61—81no—
350C2×D61—81no—
351C2×D61—81no—
352C2×D61—81no—
353C2×D61—81no—
354C4×C61—22no—
355C4×C61—42no—
356C4×C61—42no—
357C4×C61—81no—
358C4×C61—81no—
359C4×C61#54611yescharacteristic
360C4×C61#54611yescharacteristic
361C4×C61#54711yescharacteristic
362C4×C61#54711yescharacteristic
363Dic61—22no—
364Dic61—22no—
365Dic61—22no—
366Dic61—42no—
367Dic61—42no—
368Dic61—41no—
369Dic61—81no—
370C2×#533—611no—
371C2×#465—611no—
372C2×#465—611no—
373#2854—611no—
374#2058—611no—
375#2043—611no—
376#2023—611no—
377#2013—611no—
378#1892—611no—
379#1892D6111yescharacteristic, complemented
380#1880—611no—
381#1880—611no—
382#1865—611no—
383#1865—611no—
384C2×#336—611no—
385C2×C61—24no—
386C2×C61#243011yescharacteristic
387C2×C61C2×#44811yescharacteristic
388C2×C61#300211yescharacteristic
389C2×C61#316711yescharacteristic
390C2×C61#318111yescharacteristic
391C2×C61#324611yescharacteristic
392C2×C61#324811yescharacteristic
393D61—161no—
394C22×SD16—611no—
395C22×SD16—611no—
396C23×C8—611no—
397C23×C8C2×D6111yescharacteristic
398#533—1224no—
399#533—1224no—
400C2×C4⋊Q8—611no—
401C2×C4⋊Q8—611no—
402C2×#125—1221no—
403C2×#123—1221no—
404C2×C22⋊Q8—611no—
405C2×C22⋊Q8—1221no—
406C2×C22⋊Q8C2×D6111yescharacteristic
407C2×#121—611no—
408C2×C4×Q8—611no—
409C2×C4×Q8—611no—
410C2×C4×Q8—1221no—
411C2×#117—1221no—
412C22×C42—611no—
413#465—1224no—
414#465—1224no—
415C2×#106—611no—
416C2×#106—611no—
417C2×#103—611no—
418C2×#103—611no—
419C2×#103—611no—
420C2×#103—611no—
421C2×#103C2×D6111yescharacteristic
422C2×#103C2×D6111yescharacteristic
423C2×#102—611no—
424C2×#102—611no—
425#390—611no—
426#390—611no—
427#389—611no—
428#389—611no—
429#388—1221no—
430#388—1221no—
431#386—1221no—
432#380C2×D6111yescharacteristic
433#340—611no—
434#340—611no—
435#340C2×D6111yescharacteristic
436#340C2×D6111yescharacteristic
437#336—611no—
438#336—611no—
439#336—611no—
440#336—611no—
441C61#2549711yescharacteristic, complemented, Sylow
442C22×Q8—611no—
443C22×Q8—1221no—
444C22×Q8C22×D6111yescharacteristic
445C22×D4—611no—
446C22×D4—1221no—
447C23×C4—611no—
448C23×C4—611no—
449C23×C4C22×D6111yescharacteristic
450C2×SD16—1222no—
451C2×SD16—1222no—
452C2×SD16—1222no—
453C2×SD16—1222no—
454C2×SD16—2441no—
455C2×SD16—2441no—
456C22×C8—22no—
457C22×C8—22no—
458C22×C8—41no—
459C22×C8—611no—
460C22×C8—611no—
461C22×C8—1222no—
462C22×C8—1222no—
463C22×C8—2441no—
464C22×C8C22×D6111yescharacteristic
465C22×C8C22×D6111yescharacteristic
466C4⋊Q8—1222no—
467C4⋊Q8—1222no—
468C4⋊Q8—1222no—
469C4⋊Q8—1222no—
470#125—1228no—
471#123—2444no—
472C22⋊Q8—22no—
473C22⋊Q8—614no—
474C22⋊Q8—1228no—
475C22⋊Q8—1222no—
476C22⋊Q8D24414yes—
477#121—1222no—
478#121—1222no—
479C4×Q8—1222no—
480C4×Q8—1228no—
481C4×Q8—1222no—
482C4×Q8—1222no—
483C4×Q8—1222no—
484#117—1228no—
485C2×C4⋊C4—21no—
486C2×C4⋊C4—611no—
487C2×C4⋊C4—611no—
488C2×C4⋊C4—1221no—
489C2×C4⋊C4—1221no—
490C2×C4⋊C4—1221no—
491C2×C4⋊C4—1221no—
492C2×C4⋊C4—1221no—
493C2×C4⋊C4—1221no—
494C2×C4⋊C4—1221no—
495C2×C4⋊C4—1221no—
496C2×C4⋊C4C22×D6111yescharacteristic
497C2×C4⋊C4C22×D6111yescharacteristic
498C2×C4⋊C4C22×D6111yescharacteristic
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—1221no—
502C2×C22⋊C4—1221no—
503C2×C22⋊C4—1221no—
504C2×C22⋊C4—1221no—
505C2×C22⋊C4—1221no—
506C2×C22⋊C4—1221no—
507C2×C42—611no—
508C2×C42—611no—
509C2×C42—611no—
510C2×C42—611no—
511C2×C42—1221no—
512C2×C42—1221no—
513C2×C42—1222no—
514C2×C42—1222no—
515#106—1222no—
516#106—1222no—
517#103—22no—
518#103—41no—
519#103—1222no—
520#103—1222no—
521#103—1222no—
522#103—2441no—
523#102—1222no—
524#102—1222no—
525#95—21no—
526#95—1221no—
527#95—1221no—
528C24—1221no—
529C24D4×D6111yescharacteristic
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—21no—
533C2×Q8—21no—
534C2×Q8—21no—
535C2×Q8—612no—
536C2×Q8—1224no—
537C2×Q8—1221no—
538C2×Q8—1221no—
539C2×Q8—1221no—
540C2×Q8—1221no—
541C2×Q8—1221no—
542C2×Q8—2442no—
543C2×Q8—2442no—
544C2×Q8C2×D24412yes—
545C2×D4—1221no—
546C2×D4—1221no—
547C2×D4—1221no—
548C2×D4—1221no—
549C2×D4—1221no—
550C2×D4—1221no—
551C2×D4—2442no—
552C2×D4—2442no—
553C2×D4—2442no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—611no—
563C22×C4—611no—
564C22×C4—611no—
565C22×C4—614no—
566C22×C4—611no—
567C22×C4—1222no—
568C22×C4—1222no—
569C22×C4—1222no—
570C22×C4—1221no—
571C22×C4—1221no—
572C22×C4—1222no—
573C22×C4—1221no—
574C22×C4—2441no—
575C22×C4C2×D24412yes—
576C22×C4D4×D6112yes—
577C22×C4D4×D6111yescharacteristic
578C22×C4C23×D6111yescharacteristic
579SD16—2444no—
580SD16—2444no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—44no—
587C2×C8—612no—
588C2×C8—1221no—
589C2×C8—1221no—
590C2×C8—1221no—
591C2×C8—1221no—
592C2×C8—1221no—
593C2×C8—2444no—
594C2×C8#1175822412yes—
595C4⋊C4—21no—
596C4⋊C4—24no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—612no—
602C4⋊C4—1224no—
603C4⋊C4—1224no—
604C4⋊C4—1224no—
605C4⋊C4—1224no—
606C4⋊C4—1224no—
607C4⋊C4—1221no—
608C4⋊C4—1224no—
609C4⋊C4—1221no—
610C4⋊C4—1221no—
611C4⋊C4—2442no—
612C4⋊C4—2442no—
613C4⋊C4C2×D24412yes—
614C22⋊C4—24no—
615C22⋊C4—42no—
616C22⋊C4—1224no—
617C22⋊C4—2442no—
618C22⋊C4—2442no—
619C22⋊C4—2442no—
620C22⋊C4—2442no—
621C22⋊C4—2442no—
622C42—1224no—
623C42—1224no—
624C42—1221no—
625C42—1221no—
626C42—1221no—
627C42—1221no—
628C42—1222no—
629C42—1222no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—2441no—
635C23—2441no—
636C23—2441no—
637C23—2441no—
638C23—2441no—
639C23—2441no—
640C23—2441no—
641C23#1451974712yes—
642C23SD16×D6112yes—
643C23#1451980912yes—
644C23C2×D4×D6111yescharacteristic
645Q8—22no—
646Q8—22no—
647Q8—41no—
648Q8—41no—
649Q8—1222no—
650Q8—1222no—
651Q8—2448no—
652Q8—2441no—
653Q8—2441no—
654D4—4884no—
655D4—2441no—
656D4—2441no—
657D4—2441no—
658D4—2441no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—612no—
678C2×C4—612no—
679C2×C4—612no—
680C2×C4—1221no—
681C2×C4—1221no—
682C2×C4—1221no—
683C2×C4—1221no—
684C2×C4—1221no—
685C2×C4—1221no—
686C2×C4—1228no—
687C2×C4—1221no—
688C2×C4—1222no—
689C2×C4—1222no—
690C2×C4—1221no—
691C2×C4—1221no—
692C2×C4—2444no—
693C2×C4—2441no—
694C2×C4—2441no—
695C2×C4—2441no—
696C2×C4—2441no—
697C2×C4—2441no—
698C2×C4—2441no—
699C2×C4—2441no—
700C2×C4#1451974712yes—
701C2×C4C2×D4×D6111yescharacteristic
702C2×C4C22×D24411yescharacteristic
703C2×C4#41×D6111yescharacteristic
704C2×C4C2×#1175822411yescharacteristic
705C2×C4#1451982211yescharacteristic
706C2×C4#1451982411yescharacteristic
707C8—22no—
708C8—41no—
709C8—1222no—
710C8—2441no—
711C22—22no—
712C22—22no—
713C22—22no—
714C22—22no—
715C22—22no—
716C22—22no—
717C22—4881no—
718C22—4881no—
719C22—4881no—
720C22—4881no—
721C22—4881no—
722C22—4881no—
723C22—4881no—
724C22#1683990214yes—
725C22C2×#1451974711yescharacteristic
726C22#1684030711yescharacteristic
727C22#1684033911yescharacteristic
728C22C2×SD16×D6111yescharacteristic
729C22#135×D6111yescharacteristic
730C22C2×#1451980911yescharacteristic
731C22#1684055911yescharacteristic
732C4—22no—
733C4—42no—
734C4—42no—
735C4—81no—
736C4—81no—
737C4—1222no—
738C4—1222no—
739C4—1222no—
740C4—4881no—
741C4—2441no—
742C4—2442no—
743C4—2442no—
744C4#1684039911yescharacteristic
745C4#1684040711yescharacteristic
746C4#1684041011yescharacteristic
747C4#1684041611yescharacteristic
748C2—24no—
749C2—9761no—
750C2#2144942711yescharacteristic
751C2C2×#1683990211yescharacteristic
752C2#2145503911yescharacteristic
753C2#2145637311yescharacteristic
754C2#2145652311yescharacteristic
755C2#2145713011yescharacteristic
756C2#2145715111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#1892C2
socleC23×C61C22×D4
prime radicalC2×#14519751C22
hypercenter#1892D61
hypocenterC61#25497
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1892

Complements

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

NH ≅ G/Ntype
1. C2×#16840314C2semidirect
5. #21447151C2semidirect
6. #21447064C2semidirect
7. #21446954C2semidirect
8. #21446903C2semidirect
9. #21446240C2semidirect
10. #21446175C2semidirect
11. #21446172C2semidirect
12. #21446089C2semidirect
13. #21446088C2semidirect
14. C2×#16839516C2semidirect
15. C61×#1892C2semidirect
180. C22×Dic61SD16semidirect
379. #1892D61semidirect
441. C61#25497semidirect

Maximal subgroups

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

subgroupindex
C2×#168403142
C2×#168399932
C2×#168399912
#214541512
#214471512
#214470642
#214469542
#214469032
#214462402
#214461752
#214461722
#214460892
#214460882
C2×#168395162
C61×#18922
#2549761