Finite Group Databasebeta

← #29685181

Subgroups — #29685181

Order 15616.

1214 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840363C211yesmaximal, characteristic
2C2×#16839824C211yesmaximal, characteristic, complemented
3#21448173C211yesmaximal, characteristic, complemented
4#21446775C211yesmaximal, characteristic, complemented
5#21446773C211yesmaximal, characteristic, complemented
6#21446744C211yesmaximal, characteristic, complemented
7#21446744C211yesmaximal, characteristic, complemented
8#21446140C211yesmaximal, characteristic, complemented
9#21446138C211yesmaximal, characteristic, complemented
10#21446135C211yesmaximal, characteristic, complemented
11#21446133C211yesmaximal, characteristic, complemented
12#21445645C211yesmaximal, characteristic, complemented
13C4×#14519697C211yesmaximal, characteristic, complemented
14C4×#14519698C211yesmaximal, characteristic, complemented
15C61×#1762C211yesmaximal, characteristic, complemented
16#16840363—24no—
17#16840363C418yescomplemented
18C2×#14519773C2211yescharacteristic
19C2×#14519768C2211yescharacteristic
20C2×#14519760—21no—
21C2×#14519759—21no—
22C2×#14519752C2211yescharacteristic
23C2×#14519751—21no—
24C2×#14519750—21no—
25C2×#14519748C2211yescharacteristic
26C2×C4×D244C2211yescharacteristic
27C2×#14519735C2211yescharacteristic
28C2×#14519734C2211yescharacteristic
29C2×C4⋊C4×D61C2211yescharacteristic
30#16839824—24no—
31C2×#14519706C2211yescharacteristic
32C2×#14519706C2211yescharacteristic
33C2×#14519699C2211yescharacteristic
34C2×#14519699C2211yescharacteristic
35C2×#14519698C2211yescharacteristic
36C2×#14519698C2211yescharacteristic
37C2×#14519697C2211yescharacteristic
38C2×#14519697C2211yescharacteristic
39C2×#14519689C2211yescharacteristic
40C2×#14519689C2211yescharacteristic
41C2×C4×#92418C2211yescharacteristic
42C4⋊C4×Dic61C2211yescharacteristic
43C4⋊C4×Dic61C2211yescharacteristic
44C4×#11758196—21no—
45C4×C4⋊Dic61C2211yescharacteristic
46#16839613—21no—
47C4×#11758198—21no—
48#16839609—21no—
49#16839525C2211yescharacteristic
50#16839525C2211yescharacteristic
51#16839524C2211yescharacteristic
52#16839524C2211yescharacteristic
53#16839524C2211yescharacteristic
54#16839524C2211yescharacteristic
55C2×C4×D4×C61C2211yescharacteristic
56C2×#102×C61C2211yescharacteristic
57C2×#102×C61C2211yescharacteristic
58C2×#97×C61C2211yescharacteristic
59C4×C4⋊C4×C61C2211yescharacteristic
60C61×#340C2211yescharacteristic
61C61×#340C2211yescharacteristic
62C22×D244—21no—
63C22×D244C2311yescharacteristic
64C22×C22⋊D61—21no—
65C22×C22⋊D61—21no—
66C22×C22⋊D61—21no—
67C22×C4×D61—21no—
68C22×C4×D61—21no—
69C22×C4×D61C2311yescharacteristic
70C22×#92418C2311yescharacteristic
71C22×#92418C2311yescharacteristic
72#14519773—22no—
73#14519773C2×C414yescomplemented
74#14519768—22no—
75#14519768C2×C414yescomplemented
76#14519760—28no—
77#14519759—28no—
78#14519752—22no—
79#14519752C2×C414yes—
80#14519751—28no—
81#14519750—28no—
82#14519748—22no—
83#14519748C2×C414yes—
84C4×D244—22no—
85C4×D244C2×C414yescomplemented
86#14519735—22no—
87#14519735—22no—
88#14519734C2×C414yes—
89#14519734D414yes—
90C2×C4⋊Dic61—21no—
91C2×C4⋊Dic61C2311yescharacteristic
92C2×C4⋊Dic61C2311yescharacteristic
93C2×C4⋊Dic61C2311yescharacteristic
94C2×#11758196—21no—
95C2×#11758196—21no—
96C2×#11758196D411yescharacteristic
97C2×#11758196D411yescharacteristic
98C4⋊C4×D61—22no—
99C4⋊C4×D61—22no—
100C2×C22⋊Dic61—21no—
101C2×#11758198—21no—
102C2×#11758198—21no—
103C2×#11758198—21no—
104C2×#11758198D411yescharacteristic
105C2×#11758198D411yescharacteristic
106C2×C4×Dic61—21no—
107C2×C4×Dic61—21no—
108C2×C4×Dic61—21no—
109C2×C4×Dic61—21no—
110C2×C4×Dic61C2311yescharacteristic
111#14519706—22no—
112#14519706—22no—
113#14519699—22no—
114#14519699—22no—
115#14519698—22no—
116#14519698—22no—
117#14519697—22no—
118#14519697—22no—
119#14519689—22no—
120#14519689—22no—
121C4×#92418—22no—
122#14519684—21no—
123#14519684—21no—
124#14519684—21no—
125C22×D4×C61C2311yescharacteristic
126C23×C4×C61—21no—
127C22×C8×C61C2311yescharacteristic
128C22×C8×C61C2311yescharacteristic
129C4×D4×C61—22no—
130C4×D4×C61C2×C414yescomplemented
131C2×C4⋊C4×C61C2311yescharacteristic
132C2×C4⋊C4×C61C2311yescharacteristic
133C2×C4⋊C4×C61C2311yescharacteristic
134C2×C22⋊C4×C61—21no—
135C2×C42×C61—21no—
136C2×C42×C61C2311yescharacteristic
137#102×C61—22no—
138#102×C61—22no—
139#97×C61—22no—
140#95×C61—21no—
141C24×C61—21no—
142C23×D61—21no—
143C23×D61C2×D411yescharacteristic
144C2×D4×C61—21no—
145C2×D4×C61—21no—
146C2×D4×C61—21no—
147C2×D4×C61—21no—
148C2×D4×C61—21no—
149C2×D4×C61C22×C412yes—
150C22×C4×C61—21no—
151C22×C4×C61—21no—
152C22×C4×C61—21no—
153C22×C4×C61—24no—
154C22×C4×C61—81no—
155C22×C4×C61—81no—
156C22×C4×C61C2×D411yescharacteristic
157C22×C4×C61C2×D411yescharacteristic
158C22×C4×C61C2411yescharacteristic
159C2×C22⋊D61—24no—
160C2×C22⋊D61—24no—
161C2×C22⋊D61—24no—
162C2×C22⋊D61—81no—
163C2×C22⋊D61—81no—
164C2×C22⋊D61—81no—
165C2×C22⋊D61—81no—
166C2×C22⋊D61—81no—
167C2×C22⋊D61—81no—
168C22×Dic61—21no—
169C22×Dic61—21no—
170C22×Dic61—21no—
171C22×Dic61C2×D411yescharacteristic
172C22×Dic61C2×D411yescharacteristic
173C22×Dic61C2×D411yescharacteristic
174C2×D244—21no—
175C2×D244—21no—
176C2×D244—21no—
177C2×D244—21no—
178C2×D244—21no—
179C2×D244—24no—
180C2×D244—81no—
181C2×D244—81no—
182C2×D244C22×C412yes—
183C2×C4×D61—21no—
184C2×C4×D61—21no—
185C2×C4×D61—21no—
186C2×C4×D61—21no—
187C2×C4×D61—24no—
188C2×C4×D61—24no—
189C2×C4×D61—81no—
190C2×C4×D61—81no—
191C2×C4×D61—81no—
192C2×C4×D61—81no—
193C2×C4×D61C22×C412yes—
194C2×C4×D61C2×D412yes—
195C2×C8×C61—21no—
196C2×C8×C61—21no—
197C2×C8×C61—21no—
198C2×C8×C61—21no—
199C2×C8×C61—21no—
200C2×C8×C61—21no—
201C4⋊C4×C61—21no—
202C4⋊C4×C61—21no—
203C4⋊C4×C61—21no—
204C4⋊C4×C61C22×C412yes—
205C4⋊C4×C61#4112yes—
206C4⋊C4×C61#4112yes—
207C22⋊C4×C61—24no—
208C42×C61—81no—
209C42×C61C22×C412yes—
210C42×C61C2×D412yes—
211C22⋊Dic61—24no—
212#11758198—24no—
213#11758198—24no—
214#11758198—24no—
215#11758198C22⋊C414yes—
216#11758198C22⋊C414yes—
217C4⋊Dic61—21no—
218C4⋊Dic61—21no—
219C4⋊Dic61—21no—
220C4⋊Dic61—24no—
221C4⋊Dic61C22×C412yes—
222C4⋊Dic61#4112yes—
223C4⋊Dic61#4112yes—
224#11758196—24no—
225#11758196—24no—
226#11758196C22⋊C414yes—
227#11758196C22⋊C414yes—
228C4×Dic61—24no—
229C4×Dic61—81no—
230C4×Dic61—81no—
231C4×Dic61—81no—
232C4×Dic61C22×C412yes—
233C4×Dic61C2×D412yes—
234C2×#92418—21no—
235C2×#92418—21no—
236C2×#92418—21no—
237C2×#92418—21no—
238C2×#92418—21no—
239C2×#92418—21no—
240C23×C61—22no—
241C23×C61—41no—
242C23×C61—41no—
243C23×C61—41no—
244C23×C61—41no—
245C23×C61—41no—
246C23×C61—41no—
247C23×C61C22×D411yescharacteristic
248C22×D61—21no—
249C22×D61—21no—
250C22×D61—21no—
251C22×D61—21no—
252C22×D61—21no—
253C22×D61—21no—
254C22×D61—22no—
255C22×D61—41no—
256C22×D61—41no—
257C22×D61—41no—
258C22×D61—41no—
259C22×D61—41no—
260C22×D61—41no—
261C22×D61C2×C22⋊C412yes—
262D4×C61—22no—
263D4×C61—22no—
264D4×C61—41no—
265D4×C61—41no—
266C2×C4×C61—21no—
267C2×C4×C61—21no—
268C2×C4×C61—21no—
269C2×C4×C61—21no—
270C2×C4×C61—22no—
271C2×C4×C61—22no—
272C2×C4×C61—22no—
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—84no—
280C2×C4×C61C2×C22⋊C412yes—
281C2×C4×C61C2×C22⋊C412yes—
282C2×C4×C61C23×C411yescharacteristic
283C2×C4×C61C22×D411yescharacteristic
284C2×C4×C61C2×#4111yescharacteristic
285C2×C4×C61C2×#4111yescharacteristic
286C2×C4×C61C2×#4111yescharacteristic
287C2×C4×C61C2×#4111yescharacteristic
288C22⋊D61—84no—
289C22⋊D61—84no—
290C22⋊D61—84no—
291C2×Dic61—21no—
292C2×Dic61—21no—
293C2×Dic61—21no—
294C2×Dic61—21no—
295C2×Dic61—21no—
296C2×Dic61—21no—
297C2×Dic61—22no—
298C2×Dic61—22no—
299C2×Dic61—22no—
300C2×Dic61—41no—
301C2×Dic61—41no—
302C2×Dic61—41no—
303C2×Dic61—41no—
304C2×Dic61—41no—
305C2×Dic61—41no—
306C2×Dic61C2×C22⋊C412yes—
307C2×Dic61C2×C22⋊C412yes—
308C2×Dic61C2×C22⋊C412yes—
309D244—22no—
310D244—22no—
311D244—41no—
312D244—41no—
313D244—84no—
314C4×D61—22no—
315C4×D61—22no—
316C4×D61—22no—
317C4×D61—22no—
318C4×D61—84no—
319C4×D61—84no—
320C8×C61—41no—
321C8×C61—41no—
322#92418—41no—
323#92418—41no—
324#21399—611nomaximal, Sylow
325C22×C61—42no—
326C22×C61—42no—
327C22×C61—42no—
328C22×C61—81no—
329C22×C61—81no—
330C22×C61—81no—
331C22×C61—81no—
332C22×C61C22×C22⋊C411yescharacteristic
333C22×C61#52511yescharacteristic
334C22×C61#52511yescharacteristic
335C22×C61#57611yescharacteristic
336C22×C61#57611yescharacteristic
337C22×C61#57711yescharacteristic
338C22×C61#57711yescharacteristic
339C2×D61—22no—
340C2×D61—22no—
341C2×D61—22no—
342C2×D61—41no—
343C2×D61—41no—
344C2×D61—41no—
345C2×D61—41no—
346C2×D61—42no—
347C2×D61—42no—
348C2×D61—42no—
349C2×D61—81no—
350C2×D61—81no—
351C2×D61—81no—
352C2×D61—81no—
353C4×C61—22no—
354C4×C61—22no—
355C4×C61—42no—
356C4×C61—42no—
357C4×C61—42no—
358C4×C61C4×#4111yescharacteristic
359C4×C61C4×#4111yescharacteristic
360C4×C61#53211yescharacteristic
361C4×C61#53211yescharacteristic
362Dic61—22no—
363Dic61—22no—
364Dic61—22no—
365Dic61—42no—
366Dic61—42no—
367Dic61—42no—
368C2×#540—611no—
369C2×#433—611no—
370#2274—611no—
371#1989—611no—
372#1989—611no—
373#1982—611no—
374#1982—611no—
375#1875—611no—
376#1875—611no—
377#1874—611no—
378#1874—611no—
379#1762—611no—
380#1762D6111yescharacteristic, complemented
381C4×#102—611no—
382C4×#102—611no—
383C2×C61—82no—
384C2×C61#229711yescharacteristic
385C2×C61#289711yescharacteristic
386C2×C61#289711yescharacteristic
387C2×C61#311911yescharacteristic
388C2×C61#311911yescharacteristic
389C2×C61#312211yescharacteristic
390C2×C61#312611yescharacteristic
391D61—42no—
392D61—82no—
393#540—618no—
394#540—1224no—
395C2×#127—611no—
396C2×#125—611no—
397C2×#123—1221no—
398C2×#123—1221no—
399C2×#121—611no—
400C2×#121—611no—
401C2×#121—1221no—
402C2×#121—1221no—
403C2×C4×D4—611no—
404C2×C4×D4C2×D6111yescharacteristic
405C2×#117—611no—
406C2×#117—611no—
407C22×C4⋊C4—611no—
408#433—1224no—
409C2×C4⋊C8—611no—
410C2×C4⋊C8—611no—
411C2×#102—611no—
412C2×#102—611no—
413C2×#102—611no—
414C2×#102—611no—
415C2×#102—611no—
416C2×#102—611no—
417C2×#102C2×D6111yescharacteristic
418C2×#102C2×D6111yescharacteristic
419C2×C22⋊C8—611no—
420C2×C22⋊C8—611no—
421C2×#97C2×D6111yescharacteristic
422C2×C4×C8—611no—
423C4×C4⋊C4—611no—
424C4×C4⋊C4—611no—
425C4×C4⋊C4—611no—
426C4×C4⋊C4—1221no—
427C4×C4⋊C4—1221no—
428C4×C4⋊C4C2×D6111yescharacteristic
429C4×C22⋊C4—1221no—
430C4×C22⋊C4—1221no—
431#340—611no—
432#340—611no—
433#340—611no—
434#340—611no—
435#340—611no—
436#340—611no—
437#340C2×D6111yescharacteristic
438#340C2×D6111yescharacteristic
439C61#2139911yescharacteristic, complemented, Sylow
440C22×D4—611no—
441C22×D4—1221no—
442C22×D4—1221no—
443C22×D4—1221no—
444C22×D4—1221no—
445C22×D4C22×D6111yescharacteristic
446C23×C4—21no—
447C23×C4—611no—
448C23×C4—1221no—
449C23×C4—1221no—
450C22×C8—611no—
451C22×C8—611no—
452C22×C8C22×D6111yescharacteristic
453C22×C8C22×D6111yescharacteristic
454#127—614no—
455#127—1222no—
456#125—614no—
457#125—1222no—
458#123—1228no—
459#123—1228no—
460#121—614no—
461#121—614no—
462#121—1228no—
463#121—1228no—
464#121—1222no—
465#121—1222no—
466C4×D4—22no—
467C4×D4—614no—
468C4×D4—1222no—
469C4×D4C4×D6114yescomplemented
470#117—614no—
471#117—614no—
472#117—1222no—
473#117—1222no—
474C2×C4⋊C4—611no—
475C2×C4⋊C4—611no—
476C2×C4⋊C4—611no—
477C2×C4⋊C4—611no—
478C2×C4⋊C4—611no—
479C2×C4⋊C4—1222no—
480C2×C4⋊C4—1221no—
481C2×C4⋊C4—1221no—
482C2×C4⋊C4—1221no—
483C2×C4⋊C4—1222no—
484C2×C4⋊C4C22×D6111yescharacteristic
485C2×C4⋊C4C22×D6111yescharacteristic
486C2×C4⋊C4C22×D6111yescharacteristic
487C2×C22⋊C4—21no—
488C2×C22⋊C4—611no—
489C2×C22⋊C4—611no—
490C2×C22⋊C4—1221no—
491C2×C22⋊C4—1221no—
492C2×C22⋊C4—1221no—
493C2×C22⋊C4—1221no—
494C2×C42—21no—
495C2×C42—611no—
496C2×C42—1221no—
497C2×C42—1221no—
498C2×C42—1221no—
499C2×C42—1221no—
500C2×C42C22×D6111yescharacteristic
501C4⋊C8—1222no—
502C4⋊C8—1222no—
503#102—22no—
504#102—22no—
505#102—1222no—
506#102—1222no—
507#102—1222no—
508#102—1222no—
509#102—1222no—
510#102—1222no—
511C22⋊C8—1222no—
512C22⋊C8—1222no—
513#97—22no—
514C4×C8—1222no—
515#95—21no—
516#95—1221no—
517#95—1221no—
518#95—1221no—
519C24—21no—
520C24—611no—
521C24—1221no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—21no—
526C2×D4—21no—
527C2×D4—612no—
528C2×D4—1224no—
529C2×D4—1224no—
530C2×D4—1224no—
531C2×D4—1224no—
532C2×D4—1221no—
533C2×D4—1221no—
534C2×D4—1221no—
535C2×D4—1221no—
536C2×D4—1221no—
537C2×D4—4881no—
538C2×D4—4881no—
539C2×D4—4881no—
540C2×D4—4881no—
541C2×D4—4881no—
542C2×D4—4881no—
543C2×D4—4881no—
544C2×D4—4881no—
545C2×D4C2×C4×D6112yes—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—24no—
550C22×C4—81no—
551C22×C4—81no—
552C22×C4—611no—
553C22×C4—611no—
554C22×C4—611no—
555C22×C4—612no—
556C22×C4—612no—
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—1224no—
566C22×C4—4881no—
567C22×C4—4881no—
568C22×C4—4881no—
569C22×C4—4881no—
570C22×C4D4×D6111yescharacteristic
571C22×C4D4×D6111yescharacteristic
572C22×C4C23×D6111yescharacteristic
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—1221no—
580C2×C8—1221no—
581C2×C8—1221no—
582C2×C8—1221no—
583C2×C8—1221no—
584C2×C8—1221no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—614no—
589C4⋊C4—614no—
590C4⋊C4—612no—
591C4⋊C4—612no—
592C4⋊C4—612no—
593C4⋊C4—1224no—
594C4⋊C4—1224no—
595C4⋊C4—1224no—
596C4⋊C4—1221no—
597C4⋊C4—1221no—
598C4⋊C4—1221no—
599C4⋊C4C2×C4×D6112yes—
600C4⋊C4#1175822212yes—
601C4⋊C4#1175822212yes—
602C22⋊C4—24no—
603C22⋊C4—614no—
604C22⋊C4—614no—
605C22⋊C4—1224no—
606C22⋊C4—1224no—
607C22⋊C4—1224no—
608C22⋊C4—1224no—
609C42—81no—
610C42—612no—
611C42—612no—
612C42—1224no—
613C42—4881no—
614C42—4881no—
615C42—4881no—
616C42C2×C4×D6112yes—
617C42D4×D6112yes—
618C23—22no—
619C23—41no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—41no—
625C23—612no—
626C23—1221no—
627C23—1221no—
628C23—1221no—
629C23—1221no—
630C23—1221no—
631C23—1221no—
632C23—1222no—
633C23—2441no—
634C23—2441no—
635C23—2441no—
636C23—2441no—
637C23—2441no—
638C23—2441no—
639C23C2×D4×D6111yescharacteristic
640D4—22no—
641D4—22no—
642D4—41no—
643D4—41no—
644D4—1222no—
645D4—1222no—
646D4—4884no—
647D4—4884no—
648D4—4884no—
649D4—4884no—
650D4—2441no—
651D4—2441no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
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—612no—
668C2×C4—612no—
669C2×C4—1221no—
670C2×C4—1221no—
671C2×C4—1221no—
672C2×C4—1221no—
673C2×C4—1221no—
674C2×C4—1221no—
675C2×C4—1222no—
676C2×C4—1222no—
677C2×C4—1222no—
678C2×C4—1222no—
679C2×C4—1222no—
680C2×C4—1222no—
681C2×C4—1222no—
682C2×C4—4884no—
683C2×C4—4884no—
684C2×C4—2441no—
685C2×C4—2441no—
686C2×C4—2441no—
687C2×C4—2441no—
688C2×C4—2441no—
689C2×C4—2441no—
690C2×C4C22⋊C4×D6112yes—
691C2×C4C22⋊C4×D6112yes—
692C2×C4C22×C4×D6111yescharacteristic
693C2×C4C2×D4×D6111yescharacteristic
694C2×C4#41×D6111yescharacteristic
695C2×C4#41×D6111yescharacteristic
696C2×C4C2×#1175822211yescharacteristic
697C2×C4C2×#1175822211yescharacteristic
698C8—41no—
699C8—41no—
700C8—2441no—
701C8—2441no—
702C22—42no—
703C22—42no—
704C22—42no—
705C22—81no—
706C22—81no—
707C22—81no—
708C22—81no—
709C22—1222no—
710C22—1222no—
711C22—1222no—
712C22—4881no—
713C22—4881no—
714C22—4881no—
715C22—4881no—
716C22—2442no—
717C22—2442no—
718C22—2442no—
719C22—2441no—
720C22—2441no—
721C22—2441no—
722C22—2441no—
723C22C2×C22⋊C4×D6111yescharacteristic
724C22#1684027111yescharacteristic
725C22#1684027111yescharacteristic
726C22#1684056611yescharacteristic
727C22#1684056611yescharacteristic
728C22#1684057111yescharacteristic
729C22#1684057211yescharacteristic
730C4—22no—
731C4—22no—
732C4—42no—
733C4—42no—
734C4—42no—
735C4—1222no—
736C4—1222no—
737C4—1222no—
738C4—2442no—
739C4—2442no—
740C4—2442no—
741C4#1684023011yescharacteristic
742C4C4×#1175822211yescharacteristic
743C4#1684030911yescharacteristic
744C4#1684030911yescharacteristic
745C2—82no—
746C2—4882no—
747C2—2442no—
748C2#2144830511yescharacteristic
749C2#2145434311yescharacteristic
750C2#2145434411yescharacteristic
751C2#2145601611yescharacteristic
752C2#2145602211yescharacteristic
753C2#2145606111yescharacteristic
754C2#2145610911yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1762C2
socleC23×C61C22×D4
prime radicalC2×#16840363C2
cosocleC22×C4×C61C24
hypercenter#1762D61
hypocenterC61#21399
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1762

Complements

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

NH ≅ G/Ntype
2. C2×#16839824C2semidirect
3. #21448173C2semidirect
4. #21446775C2semidirect
5. #21446773C2semidirect
6. #21446744C2semidirect
7. #21446744C2semidirect
8. #21446140C2semidirect
9. #21446138C2semidirect
10. #21446135C2semidirect
11. #21446133C2semidirect
12. #21445645C2semidirect
13. C4×#14519697C2semidirect
14. C4×#14519698C2semidirect
15. C61×#1762C2semidirect
17. #16840363C4semidirect
73. #14519773C2×C4semidirect
75. #14519768C2×C4semidirect
85. C4×D244C2×C4semidirect
130. C4×D4×C61C2×C4semidirect
380. #1762D61semidirect
439. C61#21399semidirect
469. C4×D4C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168403632
C2×#168398242
#214481732
#214467752
#214467732
#214467442
#214461402
#214461382
#214461352
#214461332
#214456452
C4×#145196972
C4×#145196982
C61×#17622
#2139961