Finite Group Databasebeta

← #29733127

Subgroups — #29733127

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×#16840018C211yesmaximal, characteristic, complemented
3#21449249C211yesmaximal, characteristic
4#21447150C211yesmaximal, characteristic, complemented
5#21447017C211yesmaximal, characteristic, complemented
6#21446958C211yesmaximal, characteristic, complemented
7#21446828C211yesmaximal, characteristic, complemented
8#21446157C211yesmaximal, characteristic, complemented
9#21446129C211yesmaximal, characteristic, complemented
10#21446123C211yesmaximal, characteristic, complemented
11#21446114C211yesmaximal, characteristic
12#21446084C211yesmaximal, characteristic, complemented
13#21446010C211yesmaximal, characteristic, complemented
14#21445538C211yesmaximal, characteristic, complemented
15C2×C61×#483C211yesmaximal, characteristic, complemented
16C22×#11758202C2211yescharacteristic
17C22×#11758194C2211yescharacteristic
18#16840467—24no—
19#16840467—24no—
20C2×#14519776C2211yescharacteristic
21C2×#14519767—21no—
22C2×#14519757C2211yescharacteristic
23C2×#14519756—21no—
24C2×#14519756C2211yescharacteristic
25C2×#14519755—21no—
26C2×#14519753C2211yescharacteristic
27C2×#14519742C2211yescharacteristic
28C2×C4×C22⋊D61—21no—
29C2×C4×C22⋊D61C2211yescharacteristic
30C2×#14519736C2211yescharacteristic
31C2×C4⋊C4×D61C2211yescharacteristic
32#16840018—24no—
33C2×#14519708C2211yescharacteristic
34C2×#14519702C2211yescharacteristic
35C2×#14519702C2211yescharacteristic
36C2×#14519701C2211yescharacteristic
37C2×#14519700C2211yescharacteristic
38C2×#14519689C2211yescharacteristic
39C2×#14519689C2211yescharacteristic
40#16839690—21no—
41#16839677—21no—
42#16839669C2211yescharacteristic
43#16839658C2211yescharacteristic
44#16839657—21no—
45#16839652—21no—
46#16839619C2211yescharacteristic
47#16839525C2211yescharacteristic
48#16839525C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839524C2211yescharacteristic
52#16839524C2211yescharacteristic
53#16839516C2211yescharacteristic
54#16839516C2211yescharacteristic
55C2×C22⋊Q8×C61C2211yescharacteristic
56C22×C4⋊C4×C61C2211yescharacteristic
57C61×#483—24no—
58C2×#106×C61C2211yescharacteristic
59C2×#106×C61C2211yescharacteristic
60C2×#103×C61C2211yescharacteristic
61C2×#103×C61C2211yescharacteristic
62C2×C22⋊C8×C61C2211yescharacteristic
63C22×Dic122—21no—
64C22×Dic122C2311yescharacteristic
65C22×C22⋊D61D411yescharacteristic
66C22×C4×D61—21no—
67C22×C4×D61C2311yescharacteristic
68C2×#11758202—22no—
69C2×#11758202—22no—
70C2×#11758202—41no—
71C2×#11758194—22no—
72C2×#11758194—22no—
73C2×#11758194—41no—
74C22×#92418C2311yescharacteristic
75C22×#92418C2311yescharacteristic
76#14519776—22no—
77#14519776—22no—
78#14519767—28no—
79#14519757—22no—
80#14519757—22no—
81#14519756—28no—
82#14519756—22no—
83#14519756D414yes—
84#14519755—28no—
85#14519753—22no—
86#14519753—41no—
87#14519742—22no—
88#14519742—22no—
89C4×C22⋊D61—28no—
90C4×C22⋊D61—22no—
91C4×C22⋊D61—22no—
92#14519736—22no—
93#14519736—41no—
94C2×C4⋊Dic61—21no—
95C2×C4⋊Dic61C2311yescharacteristic
96C2×C4⋊Dic61C2311yescharacteristic
97C2×C4⋊Dic61C2311yescharacteristic
98C2×#11758196—21no—
99C2×#11758196—21no—
100C2×#11758196—21no—
101C2×#11758196—21no—
102C2×#11758196—21no—
103C2×#11758196—21no—
104C2×#11758196D411yescharacteristic
105C4⋊C4×D61—22no—
106C4⋊C4×D61—22no—
107C2×C22⋊Dic61—21no—
108C2×C22⋊Dic61—21no—
109C2×C22⋊Dic61D411yescharacteristic
110C2×#11758198—21no—
111C2×#11758198—21no—
112C2×#11758198—21no—
113C2×#11758198D411yescharacteristic
114C2×C4×Dic61—21no—
115C2×C4×Dic61—21no—
116C2×C4×Dic61C2311yescharacteristic
117#14519708—22no—
118#14519702—22no—
119#14519702—41no—
120#14519701—22no—
121#14519700—22no—
122#14519689—22no—
123#14519689—41no—
124#14519684—21no—
125#14519684—21no—
126#14519684—21no—
127#14519684—21no—
128C22×Q8×C61C2311yescharacteristic
129C23×C4×C61—21no—
130C23×C4×C61C2311yescharacteristic
131C22×C8×C61C2311yescharacteristic
132C22×C8×C61C2311yescharacteristic
133C22⋊Q8×C61—22no—
134C22⋊Q8×C61—22no—
135C2×C4⋊C4×C61—22no—
136C2×C4⋊C4×C61—21no—
137C2×C4⋊C4×C61—21no—
138C2×C4⋊C4×C61D414yes—
139C2×C4⋊C4×C61C2311yescharacteristic
140C2×C4⋊C4×C61C2311yescharacteristic
141C2×C4⋊C4×C61C2311yescharacteristic
142C2×C22⋊C4×C61—21no—
143#106×C61—22no—
144#106×C61—22no—
145#103×C61—22no—
146#103×C61—22no—
147C22⋊C8×C61—22no—
148C24×C61C2×D411yescharacteristic
149C23×D61C2×D411yescharacteristic
150C2×Q8×C61—21no—
151C2×Q8×C61—21no—
152C2×Q8×C61—21no—
153C2×Q8×C61—21no—
154C2×Q8×C61—21no—
155C2×Q8×C61—21no—
156C22×C4×C61—21no—
157C22×C4×C61—21no—
158C22×C4×C61—21no—
159C22×C4×C61—21no—
160C22×C4×C61—21no—
161C22×C4×C61—21no—
162C22×C4×C61—24no—
163C22×C4×C61—21no—
164C22×C4×C61—21no—
165C22×C4×C61—81no—
166C22×C4×C61—81no—
167C22×C4×C61C2×D411yescharacteristic
168C22×C4×C61C2×D412yes—
169C22×C4×C61C2×D412yes—
170C22×C4×C61C2411yescharacteristic
171C2×C22⋊D61—22no—
172C2×C22⋊D61—22no—
173C2×C22⋊D61—22no—
174C22×Dic61—21no—
175C22×Dic61—21no—
176C22×Dic61—21no—
177C22×Dic61—21no—
178C22×Dic61C2×D411yescharacteristic
179C22×Dic61C2×D411yescharacteristic
180C22×Dic61C2×D411yescharacteristic
181C2×C4×D61—21no—
182C2×C4×D61—21no—
183C2×C4×D61—21no—
184C2×C4×D61—21no—
185C2×C4×D61—21no—
186C2×C4×D61—21no—
187C2×C4×D61—24no—
188C2×C4×D61—81no—
189C2×C4×D61—81no—
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—
199C2×C8×C61—21no—
200C2×C8×C61—21no—
201C2×C8×C61—21no—
202C2×C8×C61—21no—
203C2×C8×C61—21no—
204C2×C8×C61—21no—
205C4⋊C4×C61—24no—
206C4⋊C4×C61—21no—
207C4⋊C4×C61—21no—
208C4⋊C4×C61—21no—
209C4⋊C4×C61—21no—
210C4⋊C4×C61—42no—
211C4⋊C4×C61C2×D412yes—
212C4⋊C4×C61C2×D412yes—
213C22⋊C4×C61—42no—
214C22⋊Dic61—24no—
215C22⋊Dic61—22no—
216C22⋊Dic61—42no—
217#11758202—44no—
218#11758198—24no—
219#11758198—22no—
220#11758198—42no—
221#11758198—42no—
222C4⋊Dic61—24no—
223C4⋊Dic61—21no—
224C4⋊Dic61—21no—
225C4⋊Dic61—21no—
226C4⋊Dic61—21no—
227C4⋊Dic61C2×D412yes—
228C4⋊Dic61#4112yes—
229#11758196—24no—
230#11758196—24no—
231#11758196—24no—
232#11758196—24no—
233#11758196—22no—
234#11758196—42no—
235#11758196—42no—
236C4×Dic61—24no—
237C4×Dic61—21no—
238C4×Dic61—21no—
239C4×Dic61—42no—
240#11758194—44no—
241C2×#92418—21no—
242C2×#92418—21no—
243C2×#92418—21no—
244C2×#92418—21no—
245C2×#92418—21no—
246C2×#92418#4112yes—
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—
262Q8×C61—41no—
263Q8×C61—41no—
264Q8×C61—41no—
265Q8×C61—41no—
266C2×C4×C61—21no—
267C2×C4×C61—21no—
268C2×C4×C61—22no—
269C2×C4×C61—22no—
270C2×C4×C61—22no—
271C2×C4×C61—22no—
272C2×C4×C61—22no—
273C2×C4×C61—22no—
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—41no—
281C2×C4×C61—41no—
282C2×C4×C61—41no—
283C2×C4×C61—41no—
284C2×C4×C61—84no—
285C2×C4×C61#12012yes—
286C2×C4×C61C22×D411yescharacteristic
287C2×C4×C61C22×D411yescharacteristic
288C2×C4×C61C2×#4111yescharacteristic
289C2×C4×C61C2×#4111yescharacteristic
290C2×C4×C61H(5,𝔽2)11yescharacteristic
291C2×C4×C612−1+411yescharacteristic
292C22⋊D61—28no—
293C2×Dic61—21no—
294C2×Dic61—21no—
295C2×Dic61—22no—
296C2×Dic61—21no—
297C2×Dic61—21no—
298C2×Dic61—22no—
299C2×Dic61—22no—
300C2×Dic61—21no—
301C2×Dic61—21no—
302C2×Dic61—21no—
303C2×Dic61—21no—
304C2×Dic61—41no—
305C2×Dic61—41no—
306C2×Dic61—41no—
307C2×Dic61—41no—
308C2×Dic61—41no—
309C2×Dic61—41no—
310C2×Dic61—41no—
311C2×Dic61—41no—
312C2×Dic61—41no—
313C2×Dic61#13712yes—
314C4×D61—41no—
315C4×D61—41no—
316C4×D61—41no—
317C4×D61—41no—
318C4×D61—84no—
319Dic122—22no—
320Dic122—22no—
321Dic122—41no—
322Dic122—41no—
323Dic122—84no—
324C8×C61—41no—
325C8×C61—41no—
326#92418—22no—
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—81no—
354C4×C61—81no—
355C4×C61#53211yescharacteristic
356C4×C61#53711yescharacteristic
357C4×C61#54611yescharacteristic
358C4×C61#54711yescharacteristic
359Dic61—22no—
360Dic61—42no—
361Dic61—42no—
362Dic61—41no—
363Dic61—41no—
364Dic61—42no—
365Dic61—81no—
366C2×#554—611no—
367C2×#483D6111yescharacteristic, complemented
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#1736—611no—
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×M16—611no—
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—1221no—
400C2×C22⋊Q8—1221no—
401C2×C22⋊Q8C2×D6111yescharacteristic
402C2×C4×Q8—611no—
403C2×C4×D4—611no—
404C2×C4×D4—1221no—
405C2×#117—611no—
406C22×C4⋊C4—611no—
407C22×C4⋊C4C2×D6111yescharacteristic
408#483—24no—
409#470—1224no—
410C2×#106—611no—
411C2×#106C2×D6111yescharacteristic
412C2×#106C2×D6111yescharacteristic
413C2×#103—611no—
414C2×#103—611no—
415C2×#103—611no—
416C2×#103—611no—
417C2×#103C2×D6111yescharacteristic
418C2×#103C2×D6111yescharacteristic
419C2×C22⋊C8—611no—
420C2×C22⋊C8—611no—
421C2×C22⋊C8C2×D6111yescharacteristic
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#340—611no—
432#340—611no—
433#340—611no—
434#340—611no—
435#336—611no—
436#336—611no—
437C61#2556111yescharacteristic, complemented, Sylow
438C22×Q8—611no—
439C22×Q8—1221no—
440C22×Q8C22×D6111yescharacteristic
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—1222no—
450C2×M16—1222no—
451C2×M16—2441no—
452C22×C8—611no—
453C22×C8—611no—
454C22×C8C22×D6111yescharacteristic
455C22×C8C22×D6111yescharacteristic
456C4⋊Q8—1222no—
457C4⋊Q8—1222no—
458#125—1228no—
459C22⋊Q8—22no—
460C22⋊Q8—22no—
461C22⋊Q8—614no—
462C22⋊Q8—1222no—
463C22⋊Q8—1228no—
464C22⋊Q8—1228no—
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—1222no—
475#117—2441no—
476C2×C4⋊C4—21no—
477C2×C4⋊C4—22no—
478C2×C4⋊C4—21no—
479C2×C4⋊C4—611no—
480C2×C4⋊C4—611no—
481C2×C4⋊C4—611no—
482C2×C4⋊C4—611no—
483C2×C4⋊C4—1222no—
484C2×C4⋊C4—1221no—
485C2×C4⋊C4—1221no—
486C2×C4⋊C4—1221no—
487C2×C4⋊C4—1221no—
488C2×C4⋊C4—1221no—
489C2×C4⋊C4—1222no—
490C2×C4⋊C4—1221no—
491C2×C4⋊C4—1221no—
492C2×C4⋊C4C22⋊D6114yes—
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—611no—
505C2×C42—1221no—
506C2×C42—1221no—
507#106—22no—
508#106—22no—
509#106—1222no—
510#103—22no—
511#103—22no—
512#103—1222no—
513#103—1222no—
514#103—1222no—
515#103—2441no—
516C22⋊C8—22no—
517C22⋊C8—1222no—
518C22⋊C8—2441no—
519#95—1221no—
520#95—1221no—
521#95—1221no—
522#95—1221no—
523C24—611no—
524C24D4×D6111yescharacteristic
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8—21no—
529C2×Q8—21no—
530C2×Q8—21no—
531C2×Q8—612no—
532C2×Q8—1224no—
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—24no—
550C22×C4—21no—
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×C4D4×D6112yes—
571C22×C4D4×D6111yescharacteristic
572C22×C4C2×C22⋊D6112yes—
573C22×C4C23×D6111yescharacteristic
574Q16—2444no—
575M16—2444no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—612no—
583C2×C8—1221no—
584C2×C8—1221no—
585C2×C8—1221no—
586C2×C8—1221no—
587C2×C8—1221no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—24no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—42no—
594C4⋊C4—612no—
595C4⋊C4—612no—
596C4⋊C4—1224no—
597C4⋊C4—1224no—
598C4⋊C4—1224no—
599C4⋊C4—1224no—
600C4⋊C4—1221no—
601C4⋊C4—1221no—
602C4⋊C4—1222no—
603C4⋊C4—1224no—
604C4⋊C4—1221no—
605C4⋊C4—1221no—
606C4⋊C4—2442no—
607C4⋊C4—2442no—
608C4⋊C4C2×C22⋊D6112yes—
609C4⋊C4C2×C22⋊D6112yes—
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—1224no—
619C42—1221no—
620C42—1221no—
621C42—2442no—
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#1451974512yes—
636C23C2×D4×D6111yescharacteristic
637Q8—41no—
638Q8—41no—
639Q8—41no—
640Q8—41no—
641Q8—1222no—
642Q8—1222no—
643Q8—4884no—
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—41no—
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—1222no—
676C2×C4—1221no—
677C2×C4—1221no—
678C2×C4—4884no—
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#1451974512yes—
693C2×C4C2×D4×D6111yescharacteristic
694C2×C4C22×C22⋊D6111yescharacteristic
695C2×C4#41×D6111yescharacteristic
696C2×C4#41×D6111yescharacteristic
697C2×C4#1451982311yescharacteristic
698C2×C4#1451982411yescharacteristic
699C8—41no—
700C8—41no—
701C8—1222no—
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×#1451974511yescharacteristic
718C22#1684040411yescharacteristic
719C22#1684041011yescharacteristic
720C22#137×D6111yescharacteristic
721C22#137×D6111yescharacteristic
722C22#1684056811yescharacteristic
723C22#1684056811yescharacteristic
724C4—22no—
725C4—42no—
726C4—42no—
727C4—81no—
728C4—81no—
729C4—1222no—
730C4—4881no—
731C4—2442no—
732C4—2441no—
733C4—2442no—
734C4—2441no—
735C4—2442no—
736C4#1684030811yescharacteristic
737C4#1684034011yescharacteristic
738C4#1684040411yescharacteristic
739C4#1684041011yescharacteristic
740C2—42no—
741C2—2442no—
742C2#2144943111yescharacteristic
743C2#2145505111yescharacteristic
744C2#2145509211yescharacteristic
745C2#2145793311yescharacteristic
746C2#2145813311yescharacteristic
747C2#2145827711yescharacteristic
748C2#2145842711yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#483C2
socleC23×C61C22×D4
prime radicalC22×C22⋊D61D4
hypercenterC2×#483D61
hypocenterC61#25561
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#483

Complements

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

NH ≅ G/Ntype
2. C2×#16840018C2semidirect
4. #21447150C2semidirect
5. #21447017C2semidirect
6. #21446958C2semidirect
7. #21446828C2semidirect
8. #21446157C2semidirect
9. #21446129C2semidirect
10. #21446123C2semidirect
12. #21446084C2semidirect
13. #21446010C2semidirect
14. #21445538C2semidirect
15. C2×C61×#483C2semidirect
367. C2×#483D61semidirect
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×#168400182
#214492492
#214471502
#214470172
#214469582
#214468282
#214461572
#214461292
#214461232
#214461142
#214460842
#214460102
#214455382
C2×C61×#4832
#2556161