Finite Group Databasebeta

← #29733125

Subgroups — #29733125

Order 15616.

1124 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×#16840467C211yesmaximal, characteristic
2C2×#16840092C211yesmaximal, characteristic, complemented
3C2×#16840020C211yesmaximal, characteristic, complemented
4#21449242C211yesmaximal, characteristic
5#21447151C211yesmaximal, characteristic, complemented
6#21447018C211yesmaximal, characteristic, complemented
7#21446959C211yesmaximal, characteristic, complemented
8#21446830C211yesmaximal, characteristic, complemented
9#21446161C211yesmaximal, characteristic, complemented
10#21446131C211yesmaximal, characteristic, complemented
11#21446125C211yesmaximal, characteristic, complemented
12#21446116C211yesmaximal, characteristic
13#21446088C211yesmaximal, characteristic, complemented
14#21446013C211yesmaximal, characteristic, complemented
15C61×#1736C211yesmaximal, characteristic, complemented
16C22×Dic244C2211yescharacteristic
17#16840467—24no—
18#16840467—24no—
19C2×#14519776C2211yescharacteristic
20C2×#14519767—21no—
21C2×#14519757C2211yescharacteristic
22C2×#14519757C2211yescharacteristic
23C2×#14519756—21no—
24C2×#14519756C2211yescharacteristic
25C2×#14519756C2211yescharacteristic
26C2×#14519755—21no—
27C2×#14519742C2211yescharacteristic
28C2×C4×C22⋊D61—21no—
29C2×C4×C22⋊D61C2211yescharacteristic
30C2×C4⋊C4×D61C2211yescharacteristic
31#16840092—24no—
32#16840020—24no—
33C2×#14519709C2211yescharacteristic
34C2×#14519708C2211yescharacteristic
35C2×#14519708C2211yescharacteristic
36C2×#14519702C2211yescharacteristic
37C2×#14519702C2211yescharacteristic
38C2×#14519700C2211yescharacteristic
39C2×#14519700C2211yescharacteristic
40C2×#14519700C2211yescharacteristic
41C2×#14519700C2211yescharacteristic
42C2×C22⋊#92418C2211yescharacteristic
43C2×#14519689C2211yescharacteristic
44C2×#14519689C2211yescharacteristic
45#16839687—21no—
46#16839678—21no—
47#16839667C2211yescharacteristic
48#16839661C2211yescharacteristic
49#16839660—21no—
50#16839653—21no—
51#16839619C2211yescharacteristic
52#16839524C2211yescharacteristic
53#16839524C2211yescharacteristic
54#16839516C2211yescharacteristic
55#16839516C2211yescharacteristic
56C22×M16×C61C2211yescharacteristic
57C2×#117×C61C2211yescharacteristic
58C22×C4⋊C4×C61C2211yescharacteristic
59C61×#340C2211yescharacteristic
60C61×#340C2211yescharacteristic
61C61×#340C2211yescharacteristic
62C61×#340C2211yescharacteristic
63C22×Dic122—21no—
64C22×Dic122C2311yescharacteristic
65C22×Dic122C2311yescharacteristic
66C22×C22⋊D61D411yescharacteristic
67C22×C4×D61—21no—
68C22×C4×D61C2311yescharacteristic
69C2×Dic244—22no—
70C2×Dic244—22no—
71C2×Dic244—41no—
72C22×#92418C2311yescharacteristic
73C22×#92418C2311yescharacteristic
74#14519776—22no—
75#14519776—22no—
76#14519767—28no—
77#14519757—22no—
78#14519757—22no—
79#14519757—22no—
80#14519757—41no—
81#14519756—28no—
82#14519756—22no—
83#14519756—22no—
84#14519756—22no—
85#14519756D414yes—
86#14519755—28no—
87#14519742—22no—
88#14519742—22no—
89C4×C22⋊D61—28no—
90C4×C22⋊D61—22no—
91C4×C22⋊D61—22no—
92C2×C4⋊Dic61—21no—
93C2×C4⋊Dic61—21no—
94C2×C4⋊Dic61—21no—
95C2×C4⋊Dic61C2311yescharacteristic
96C2×C4⋊Dic61C2311yescharacteristic
97C2×#11758196—21no—
98C2×#11758196—21no—
99C2×#11758196—21no—
100C2×#11758196—21no—
101C2×#11758196—21no—
102C2×#11758196D411yescharacteristic
103C4⋊C4×D61—22no—
104C4⋊C4×D61—22no—
105C2×C22⋊Dic61—21no—
106C2×C22⋊Dic61—21no—
107C2×C22⋊Dic61D411yescharacteristic
108C2×#11758198—21no—
109C2×#11758198—21no—
110C2×#11758198—21no—
111C2×#11758198D411yescharacteristic
112C2×C4×Dic61—21no—
113C2×C4×Dic61C2311yescharacteristic
114#14519709—22no—
115#14519708—22no—
116#14519708—22no—
117#14519702—22no—
118#14519702—22no—
119#14519700—22no—
120#14519700—22no—
121#14519700—22no—
122#14519700—41no—
123C22⋊#92418—22no—
124#14519689—22no—
125#14519689—41no—
126#14519684—21no—
127#14519684—21no—
128#14519684—21no—
129#14519684—21no—
130C23×C4×C61—21no—
131C23×C4×C61C2311yescharacteristic
132C2×M16×C61—22no—
133C2×M16×C61—22no—
134C2×M16×C61—41no—
135C22×C8×C61C2311yescharacteristic
136C22×C8×C61C2311yescharacteristic
137#117×C61—22no—
138#117×C61—41no—
139C2×C4⋊C4×C61—22no—
140C2×C4⋊C4×C61—21no—
141C2×C4⋊C4×C61D414yes—
142C2×C4⋊C4×C61C2311yescharacteristic
143C2×C4⋊C4×C61C2311yescharacteristic
144C2×C4⋊C4×C61C2311yescharacteristic
145C2×C4⋊C4×C61C2311yescharacteristic
146C2×C22⋊C4×C61—21no—
147C2×C42×C61—21no—
148C24×C61C2×D411yescharacteristic
149C23×D61C2×D411yescharacteristic
150C22×C4×C61—21no—
151C22×C4×C61—21no—
152C22×C4×C61—21no—
153C22×C4×C61—21no—
154C22×C4×C61—21no—
155C22×C4×C61—21no—
156C22×C4×C61—21no—
157C22×C4×C61—24no—
158C22×C4×C61—21no—
159C22×C4×C61—81no—
160C22×C4×C61—81no—
161C22×C4×C61C2×D411yescharacteristic
162C22×C4×C61C2×D412yes—
163C22×C4×C61C2×D412yes—
164C22×C4×C61C2411yescharacteristic
165C2×C22⋊D61—22no—
166C2×C22⋊D61—22no—
167C2×C22⋊D61—22no—
168C22×Dic61—21no—
169C22×Dic61—21no—
170C22×Dic61—21no—
171C22×Dic61—21no—
172C22×Dic61C2×D411yescharacteristic
173C22×Dic61C2×D411yescharacteristic
174C22×Dic61C2×D411yescharacteristic
175C2×C4×D61—21no—
176C2×C4×D61—21no—
177C2×C4×D61—21no—
178C2×C4×D61—21no—
179C2×C4×D61—21no—
180C2×C4×D61—21no—
181C2×C4×D61—24no—
182C2×C4×D61—81no—
183C2×C4×D61—81no—
184C2×Dic122—21no—
185C2×Dic122—21no—
186C2×Dic122—21no—
187C2×Dic122—21no—
188C2×Dic122—21no—
189C2×Dic122—21no—
190C2×Dic122—21no—
191C2×Dic122—21no—
192C2×Dic122—21no—
193C2×Dic122—21no—
194C2×Dic122—21no—
195C2×Dic122—24no—
196C2×Dic122—81no—
197C2×Dic122—81no—
198C2×Dic122C2×D412yes—
199M16×C61—44no—
200C2×C8×C61—21no—
201C2×C8×C61—21no—
202C2×C8×C61—21no—
203C2×C8×C61—21no—
204C2×C8×C61—21no—
205C2×C8×C61#4112yes—
206C4⋊C4×C61—24no—
207C4⋊C4×C61—21no—
208C4⋊C4×C61—21no—
209C4⋊C4×C61—21no—
210C4⋊C4×C61—21no—
211C4⋊C4×C61—21no—
212C4⋊C4×C61C2×D412yes—
213C4⋊C4×C61C2×D412yes—
214C4⋊C4×C61#4112yes—
215C22⋊C4×C61—42no—
216C42×C61—42no—
217C22⋊Dic61—24no—
218C22⋊Dic61—22no—
219C22⋊Dic61—42no—
220#11758198—24no—
221#11758198—22no—
222#11758198—42no—
223#11758198—42no—
224C4⋊Dic61—24no—
225C4⋊Dic61—21no—
226C4⋊Dic61—21no—
227C4⋊Dic61—21no—
228C4⋊Dic61—42no—
229C4⋊Dic61—42no—
230C4⋊Dic61C2×D412yes—
231#11758196—24no—
232#11758196—24no—
233#11758196—24no—
234#11758196—24no—
235#11758196—22no—
236#11758196—42no—
237C4×Dic61—24no—
238C4×Dic61—21no—
239C4×Dic61—21no—
240C2×#92418—21no—
241C2×#92418—21no—
242C2×#92418—21no—
243C2×#92418—21no—
244C2×#92418—21no—
245C2×#92418—21no—
246Dic244—44no—
247C23×C61—21no—
248C23×C61—21no—
249C23×C61—21no—
250C23×C61—21no—
251C23×C61—21no—
252C23×C61—21no—
253C23×C61#12012yes—
254C23×C61C22×D411yescharacteristic
255C22×D61—21no—
256C22×D61—21no—
257C22×D61—21no—
258C22×D61—21no—
259C22×D61—21no—
260C22×D61—21no—
261C22×D61#13712yes—
262C2×C4×C61—21no—
263C2×C4×C61—21no—
264C2×C4×C61—22no—
265C2×C4×C61—22no—
266C2×C4×C61—22no—
267C2×C4×C61—22no—
268C2×C4×C61—22no—
269C2×C4×C61—22no—
270C2×C4×C61—22no—
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×C61—41no—
280C2×C4×C61—84no—
281C2×C4×C61#12012yes—
282C2×C4×C61C22×D411yescharacteristic
283C2×C4×C61C22×D411yescharacteristic
284C2×C4×C61C2×#4111yescharacteristic
285C2×C4×C61C2×#4111yescharacteristic
286C2×C4×C61H(5,𝔽2)11yescharacteristic
287C2×C4×C612−1+411yescharacteristic
288C22⋊D61—28no—
289C2×Dic61—21no—
290C2×Dic61—21no—
291C2×Dic61—22no—
292C2×Dic61—21no—
293C2×Dic61—21no—
294C2×Dic61—22no—
295C2×Dic61—21no—
296C2×Dic61—21no—
297C2×Dic61—21no—
298C2×Dic61—21no—
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—41no—
308C2×Dic61—41no—
309C2×Dic61#13712yes—
310C4×D61—41no—
311C4×D61—41no—
312C4×D61—41no—
313C4×D61—41no—
314C4×D61—84no—
315Dic122—22no—
316Dic122—22no—
317Dic122—41no—
318Dic122—41no—
319Dic122—41no—
320Dic122—41no—
321Dic122—41no—
322Dic122—41no—
323Dic122—84no—
324C8×C61—22no—
325C8×C61—41no—
326#92418—41no—
327#92418—41no—
328#25561—611nomaximal, Sylow
329C22×C61—22no—
330C22×C61—22no—
331C22×C61—22no—
332C22×C61—41no—
333C22×C61—41no—
334C22×C61—41no—
335C22×C61—41no—
336C22×C61C2×#12011yescharacteristic
337C22×C61#54611yescharacteristic
338C22×C61#54711yescharacteristic
339C22×C61C2×#13711yescharacteristic
340C22×C61C2×#13711yescharacteristic
341C22×C61#57711yescharacteristic
342C22×C61#57711yescharacteristic
343C2×D61—22no—
344C2×D61—22no—
345C2×D61—22no—
346C2×D61—41no—
347C2×D61—41no—
348C2×D61—41no—
349C2×D61—41no—
350C4×C61—22no—
351C4×C61—42no—
352C4×C61—42no—
353C4×C61—42no—
354C4×C61—81no—
355C4×C61#53211yescharacteristic
356C4×C61#53711yescharacteristic
357C4×C61#54611yescharacteristic
358C4×C61#54711yescharacteristic
359Dic61—22no—
360Dic61—42no—
361Dic61—41no—
362Dic61—41no—
363Dic61—42no—
364Dic61—81no—
365Dic61—81no—
366C2×#554—611no—
367C2×#483—611no—
368C2×#470—611no—
369#2415—611no—
370#2058—611no—
371#2035—611no—
372#2024—611no—
373#2001—611no—
374#1878—611no—
375#1873—611no—
376#1872—611no—
377#1870—611no—
378#1865—611no—
379#1853—611no—
380#1736D6111yescharacteristic, complemented
381C2×C61—42no—
382C2×C61#243011yescharacteristic
383C2×C61#300411yescharacteristic
384C2×C61#300911yescharacteristic
385C2×C61#331611yescharacteristic
386C2×C61#333111yescharacteristic
387C2×C61#334411yescharacteristic
388C2×C61#335611yescharacteristic
389D61—42no—
390C22×Q16—611no—
391C22×M16C2×D6111yescharacteristic
392#554—1224no—
393#554—1224no—
394C2×C4⋊Q8—611no—
395C2×#125—1221no—
396C2×C22⋊Q8—611no—
397C2×C22⋊Q8—611no—
398C2×C22⋊Q8—611no—
399C2×C22⋊Q8—611no—
400C2×C22⋊Q8—1221no—
401C2×C22⋊Q8—1221no—
402C2×C4×Q8—611no—
403C2×C4×D4—611no—
404C2×C4×D4—1221no—
405C2×#117C2×D6111yescharacteristic
406C22×C4⋊C4—611no—
407C22×C4⋊C4C2×D6111yescharacteristic
408#483—1224no—
409#470—1224no—
410C2×#106—611no—
411C2×#106—611no—
412C2×#106—611no—
413C2×#103—611no—
414C2×#103—611no—
415C2×#103—611no—
416C2×#103—611no—
417C2×#103—611no—
418C2×#103—611no—
419C2×C22⋊C8—611no—
420C2×C22⋊C8—611no—
421C2×C22⋊C8—611no—
422#397—1221no—
423#394—1221no—
424#391—611no—
425#389—611no—
426#389—1221no—
427#388—1221no—
428#380—611no—
429#340—611no—
430#340—611no—
431#340C2×D6111yescharacteristic
432#340C2×D6111yescharacteristic
433#340C2×D6111yescharacteristic
434#340C2×D6111yescharacteristic
435#336—611no—
436#336—611no—
437C61#2556111yescharacteristic, complemented, Sylow
438C22×Q8—611no—
439C22×Q8—611no—
440C22×Q8—1221no—
441C22×D4—611no—
442C23×C4—21no—
443C23×C4—611no—
444C23×C4—1221no—
445C23×C4C22×D6111yescharacteristic
446C2×Q16—1222no—
447C2×Q16—1222no—
448C2×Q16—2441no—
449C2×M16—22no—
450C2×M16—22no—
451C2×M16—41no—
452C22×C8—611no—
453C22×C8—611no—
454C22×C8C22×D6111yescharacteristic
455C22×C8C22×D6111yescharacteristic
456C4⋊Q8—1222no—
457C4⋊Q8—1222no—
458#125—1228no—
459C22⋊Q8—614no—
460C22⋊Q8—1222no—
461C22⋊Q8—1228no—
462C22⋊Q8—1228no—
463C22⋊Q8—1222no—
464C22⋊Q8—1222no—
465C22⋊Q8—1222no—
466C22⋊Q8—1222no—
467C22⋊Q8—1222no—
468C22⋊Q8—2441no—
469C4×Q8—1222no—
470C4×Q8—1222no—
471C4×D4—1228no—
472C4×D4—1222no—
473C4×D4—1222no—
474#117—22no—
475#117—41no—
476C2×C4⋊C4—21no—
477C2×C4⋊C4—22no—
478C2×C4⋊C4—611no—
479C2×C4⋊C4—611no—
480C2×C4⋊C4—611no—
481C2×C4⋊C4—1222no—
482C2×C4⋊C4—1221no—
483C2×C4⋊C4—1221no—
484C2×C4⋊C4—1221no—
485C2×C4⋊C4—1221no—
486C2×C4⋊C4—1221no—
487C2×C4⋊C4—1222no—
488C2×C4⋊C4—1221no—
489C2×C4⋊C4—1221no—
490C2×C4⋊C4—1221no—
491C2×C4⋊C4D24414yes—
492C2×C4⋊C4C22×D6111yescharacteristic
493C2×C4⋊C4C22×D6111yescharacteristic
494C2×C4⋊C4C22×D6111yescharacteristic
495C2×C4⋊C4C22×D6111yescharacteristic
496C2×C22⋊C4—21no—
497C2×C22⋊C4—611no—
498C2×C22⋊C4—611no—
499C2×C22⋊C4—1221no—
500C2×C22⋊C4—1221no—
501C2×C22⋊C4—1221no—
502C2×C22⋊C4—1221no—
503C2×C22⋊C4—1221no—
504C2×C42—21no—
505C2×C42—611no—
506C2×C42—1221no—
507#106—1222no—
508#106—1222no—
509#106—1222no—
510#103—1222no—
511#103—1222no—
512#103—1222no—
513#103—1222no—
514#103—1222no—
515#103—2441no—
516C22⋊C8—1222no—
517C22⋊C8—1222no—
518C22⋊C8—2441no—
519#95—1221no—
520#95—1221no—
521#95—1221no—
522#95—1221no—
523C24—611no—
524C24D4×D6111yescharacteristic
525C2×Q8—612no—
526C2×Q8—1224no—
527C2×Q8—1221no—
528C2×Q8—1221no—
529C2×Q8—1221no—
530C2×Q8—1221no—
531C2×Q8—1221no—
532C2×Q8—1221no—
533C2×Q8—1221no—
534C2×Q8—1221no—
535C2×Q8—1221no—
536C2×Q8—1221no—
537C2×Q8—1221no—
538C2×Q8—4881no—
539C2×Q8—4881no—
540C2×D4—1222no—
541C2×D4—1222no—
542C2×D4—1222no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—24no—
551C22×C4—21no—
552C22×C4—81no—
553C22×C4—81no—
554C22×C4—611no—
555C22×C4—611no—
556C22×C4—611no—
557C22×C4—1224no—
558C22×C4—1221no—
559C22×C4—1221no—
560C22×C4—1221no—
561C22×C4—1221no—
562C22×C4—1221no—
563C22×C4—1221no—
564C22×C4—1221no—
565C22×C4—1221no—
566C22×C4—1221no—
567C22×C4—1221no—
568C22×C4—4881no—
569C22×C4—4881no—
570C22×C4C2×D24412yes—
571C22×C4D4×D6112yes—
572C22×C4D4×D6111yescharacteristic
573C22×C4C23×D6111yescharacteristic
574Q16—2444no—
575M16—44no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—1221no—
582C2×C8—1221no—
583C2×C8—1221no—
584C2×C8—1221no—
585C2×C8—1221no—
586C2×C8—1221no—
587C2×C8#1175822212yes—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—24no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—612no—
595C4⋊C4—1224no—
596C4⋊C4—1224no—
597C4⋊C4—1224no—
598C4⋊C4—1224no—
599C4⋊C4—1221no—
600C4⋊C4—1222no—
601C4⋊C4—1224no—
602C4⋊C4—1221no—
603C4⋊C4—1221no—
604C4⋊C4—2442no—
605C4⋊C4—2442no—
606C4⋊C4—2442no—
607C4⋊C4C2×D24412yes—
608C4⋊C4C2×D24412yes—
609C4⋊C4#1175822212yes—
610C22⋊C4—42no—
611C22⋊C4—1224no—
612C22⋊C4—1222no—
613C22⋊C4—1224no—
614C22⋊C4—1222no—
615C22⋊C4—2442no—
616C22⋊C4—2442no—
617C22⋊C4—2442no—
618C42—42no—
619C42—1224no—
620C42—1221no—
621C42—1221no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—612no—
629C23—1221no—
630C23—1221no—
631C23—1221no—
632C23—1221no—
633C23—1221no—
634C23—1221no—
635C23#1451974712yes—
636C23C2×D4×D6111yescharacteristic
637Q8—1222no—
638Q8—1222no—
639Q8—4884no—
640Q8—2441no—
641Q8—2441no—
642Q8—2441no—
643Q8—2441no—
644Q8—2441no—
645Q8—2441no—
646D4—1228no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—84no—
666C2×C4—612no—
667C2×C4—1221no—
668C2×C4—1221no—
669C2×C4—1222no—
670C2×C4—1221no—
671C2×C4—1222no—
672C2×C4—1221no—
673C2×C4—1221no—
674C2×C4—1221no—
675C2×C4—1221no—
676C2×C4—1221no—
677C2×C4—4884no—
678C2×C4—2441no—
679C2×C4—2441no—
680C2×C4—2441no—
681C2×C4—2441no—
682C2×C4—2441no—
683C2×C4—2441no—
684C2×C4—2441no—
685C2×C4—2441no—
686C2×C4—2441no—
687C2×C4—2441no—
688C2×C4—2441no—
689C2×C4—2441no—
690C2×C4—2441no—
691C2×C4—2441no—
692C2×C4#1451974712yes—
693C2×C4C2×D4×D6111yescharacteristic
694C2×C4C22×D24411yescharacteristic
695C2×C4C2×#1175822211yescharacteristic
696C2×C4C2×#1175822211yescharacteristic
697C2×C4#1451982211yescharacteristic
698C2×C4#1451982511yescharacteristic
699C8—22no—
700C8—41no—
701C8—2441no—
702C8—2441no—
703C22—22no—
704C22—22no—
705C22—22no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—1222no—
711C22—1222no—
712C22—1222no—
713C22—2441no—
714C22—2441no—
715C22—2441no—
716C22—2441no—
717C22C2×#1451974711yescharacteristic
718C22#1684040211yescharacteristic
719C22#1684041311yescharacteristic
720C22#137×D6111yescharacteristic
721C22#137×D6111yescharacteristic
722C22#1684057211yescharacteristic
723C22#1684057211yescharacteristic
724C4—22no—
725C4—42no—
726C4—42no—
727C4—42no—
728C4—81no—
729C4—1222no—
730C4—4881no—
731C4—4881no—
732C4—2441no—
733C4—2442no—
734C4—2441no—
735C4—2442no—
736C4#1684031211yescharacteristic
737C4#1684034311yescharacteristic
738C4#1684040211yescharacteristic
739C4#1684041311yescharacteristic
740C2—42no—
741C2—2442no—
742C2#2144942911yescharacteristic
743C2#2145505511yescharacteristic
744C2#2145509711yescharacteristic
745C2#2145793111yescharacteristic
746C2#2145813111yescharacteristic
747C2#2145827511yescharacteristic
748C2#2145843011yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#1736C2
socleC23×C61C22×D4
prime radicalC22×C22⋊D61D4
hypercenter#1736D61
hypocenterC61#25561
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1736

Complements

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

NH ≅ G/Ntype
2. C2×#16840092C2semidirect
3. C2×#16840020C2semidirect
5. #21447151C2semidirect
6. #21447018C2semidirect
7. #21446959C2semidirect
8. #21446830C2semidirect
9. #21446161C2semidirect
10. #21446131C2semidirect
11. #21446125C2semidirect
13. #21446088C2semidirect
14. #21446013C2semidirect
15. C61×#1736C2semidirect
380. #1736D61semidirect
437. C61#25561semidirect

Maximal subgroups

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

subgroupindex
C2×#168404672
C2×#168400922
C2×#168400202
#214492422
#214471512
#214470182
#214469592
#214468302
#214461612
#214461312
#214461252
#214461162
#214460882
#214460132
C61×#17362
#2556161