Finite Group Databasebeta

← #29696268

Subgroups — #29696268

Order 15616.

1226 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840460C211yesmaximal, characteristic
2C2×#16839825C211yesmaximal, characteristic, complemented
3#21448750C211yesmaximal, characteristic, complemented
4#21446782C211yesmaximal, characteristic, complemented
5#21446773C211yesmaximal, characteristic, complemented
6#21446246C211yesmaximal, characteristic, complemented
7#21446245C211yesmaximal, characteristic, complemented
8#21446140C211yesmaximal, characteristic, complemented
9#21446134C211yesmaximal, characteristic, complemented
10#21445913C211yesmaximal, characteristic, complemented
11#21445828C211yesmaximal, characteristic, complemented
12#21445633C211yesmaximal, characteristic, complemented
13#21445534C211yesmaximal, characteristic, complemented
14C2×#16839524C211yesmaximal, characteristic, complemented
15C61×#1824C211yesmaximal, characteristic, complemented
16C23×#92418C2211yescharacteristic
17C22×C8×D61C2211yescharacteristic
18#16840460—24no—
19#16840460C418yescomplemented
20C2×#14519772—21no—
21C2×#14519768C2211yescharacteristic
22C2×#14519762—21no—
23C2×#14519752C2211yescharacteristic
24C2×#14519751—21no—
25C2×#14519751C2211yescharacteristic
26C2×#14519739C2211yescharacteristic
27C2×C4×C22⋊D61—21no—
28C2×C4×C22⋊D61C2211yescharacteristic
29C2×#14519735C2211yescharacteristic
30C2×#14519735C2211yescharacteristic
31C22×C4⋊Dic61C2211yescharacteristic
32#16839825—24no—
33C2×#14519706C2211yescharacteristic
34C2×#14519699C2211yescharacteristic
35C2×#14519699C2211yescharacteristic
36C2×#14519697C2211yescharacteristic
37C2×#14519697C2211yescharacteristic
38C2×#14519689C2211yescharacteristic
39C2×C8×Dic61C2211yescharacteristic
40#16839654—21no—
41#16839649—21no—
42#16839639—21no—
43#16839627C2211yescharacteristic
44#16839619C2211yescharacteristic
45C4⋊C4×Dic61C2211yescharacteristic
46C22⋊C4×Dic61—21no—
47#16839525C2211yescharacteristic
48#16839525C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839524C2211yescharacteristic
52#16839524C2211yescharacteristic
53#16839524C2211yescharacteristic
54#16839524C2211yescharacteristic
55C22×C4⋊C4×C61C2211yescharacteristic
56C2×C22⋊C8×C61C2211yescharacteristic
57C61×#380C2211yescharacteristic
58C61×#340C2211yescharacteristic
59C61×#340C2211yescharacteristic
60C61×#340C2211yescharacteristic
61C61×#340C2211yescharacteristic
62C22×D244—21no—
63C22×D244C2311yescharacteristic
64C22×C22⋊D61—21no—
65C22×C22⋊D61D411yescharacteristic
66C23×Dic61—21no—
67C22×C4×D61—21no—
68C22×C4×D61C2311yescharacteristic
69C22×#92418—22no—
70C22×#92418—22no—
71C22×#92418—41no—
72C22×#92418C2311yescharacteristic
73C22×#92418C2311yescharacteristic
74C2×C8×D61—22no—
75C2×C8×D61—22no—
76C2×C8×D61—41no—
77#14519772—28no—
78#14519768—22no—
79#14519768C2×C414yescomplemented
80#14519762—28no—
81#14519752—22no—
82#14519752C2×C414yescomplemented
83#14519751—22no—
84#14519751—28no—
85#14519751C2×C414yes—
86#14519739—22no—
87#14519739C2×C414yescomplemented
88C4×C22⋊D61—28no—
89C4×C22⋊D61C2×C414yes—
90C4×C22⋊D61D414yes—
91#14519735—22no—
92#14519735—22no—
93#14519735—41no—
94#14519735C2×C414yescomplemented
95C2×C4⋊Dic61—21no—
96C2×C4⋊Dic61—22no—
97C2×C4⋊Dic61—21no—
98C2×C4⋊Dic61—41no—
99C2×C4⋊Dic61C2311yescharacteristic
100C2×C4⋊Dic61C2311yescharacteristic
101C2×C4⋊Dic61C2311yescharacteristic
102C2×#11758196—21no—
103C2×#11758196D411yescharacteristic
104C2×C22⋊Dic61D411yescharacteristic
105C2×#11758198—21no—
106C2×#11758198—21no—
107C2×#11758198—21no—
108C2×#11758198—21no—
109C2×#11758198—21no—
110C2×#11758198—21no—
111C2×#11758198D411yescharacteristic
112C2×C4×Dic61—21no—
113C2×C4×Dic61—21no—
114C2×C4×Dic61—21no—
115C2×C4×Dic61C2311yescharacteristic
116#14519706—22no—
117#14519699—22no—
118#14519699—41no—
119#14519697—22no—
120#14519697—41no—
121#14519689—22no—
122C8×Dic61—22no—
123#14519684—21no—
124#14519684—21no—
125#14519684—21no—
126#14519684—21no—
127C23×C4×C61—21no—
128C23×C4×C61C2311yescharacteristic
129C22×C8×C61C2311yescharacteristic
130C22×C8×C61C2311yescharacteristic
131C2×C4⋊C4×C61—22no—
132C2×C4⋊C4×C61—21no—
133C2×C4⋊C4×C61C2×C414yes—
134C2×C4⋊C4×C61C2311yescharacteristic
135C2×C4⋊C4×C61C2311yescharacteristic
136C2×C4⋊C4×C61C2311yescharacteristic
137C2×C4⋊C4×C61C2311yescharacteristic
138C2×C22⋊C4×C61—21no—
139C22⋊C8×C61—22no—
140#95×C61—21no—
141C24×C61C2×D411yescharacteristic
142C23×D61—21no—
143C23×D61C2×D411yescharacteristic
144C22×C4×C61—21no—
145C22×C4×C61—21no—
146C22×C4×C61—21no—
147C22×C4×C61—21no—
148C22×C4×C61—21no—
149C22×C4×C61—21no—
150C22×C4×C61—24no—
151C22×C4×C61—21no—
152C22×C4×C61—21no—
153C22×C4×C61—81no—
154C22×C4×C61—81no—
155C22×C4×C61C22×C412yes—
156C22×C4×C61C2×D411yescharacteristic
157C22×C4×C61C2×D412yes—
158C22×C4×C61C2411yescharacteristic
159C2×C22⋊D61—22no—
160C2×C22⋊D61—22no—
161C2×C22⋊D61—24no—
162C2×C22⋊D61—42no—
163C2×C22⋊D61—42no—
164C2×C22⋊D61C22⋊C414yes—
165C22×Dic61—21no—
166C22×Dic61—21no—
167C22×Dic61—21no—
168C22×Dic61—42no—
169C22×Dic61—42no—
170C22×Dic61—81no—
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—81no—
189C2×C4×D61—81no—
190C2×C4×D61C22×C412yes—
191C2×C4×D61C2×D412yes—
192C2×C8×C61—21no—
193C2×C8×C61—21no—
194C2×C8×C61—21no—
195C2×C8×C61—21no—
196C2×C8×C61—21no—
197C2×C8×C61—21no—
198C4⋊C4×C61—24no—
199C4⋊C4×C61—21no—
200C4⋊C4×C61—21no—
201C4⋊C4×C61—21no—
202C4⋊C4×C61—21no—
203C4⋊C4×C61—21no—
204C4⋊C4×C61—21no—
205C4⋊C4×C61C22×C412yes—
206C4⋊C4×C61C22×C412yes—
207C22⋊C4×C61—42no—
208C22⋊Dic61C22⋊C414yes—
209#11758198—24no—
210#11758198—24no—
211#11758198—24no—
212#11758198—24no—
213#11758198—42no—
214#11758198—81no—
215#11758198C22⋊C414yes—
216C4⋊Dic61—21no—
217C4⋊Dic61—21no—
218C4⋊Dic61—24no—
219C4⋊Dic61—21no—
220C4⋊Dic61—21no—
221C4⋊Dic61—42no—
222C4⋊Dic61C22×C412yes—
223C4⋊Dic61#4112yes—
224#11758196—24no—
225#11758196C22⋊C414yes—
226C4×Dic61—24no—
227C4×Dic61—42no—
228C4×Dic61—81no—
229C4×Dic61C22×C412yes—
230C4×Dic61C2×D412yes—
231C2×#92418—21no—
232C2×#92418—21no—
233C2×#92418—21no—
234C2×#92418—21no—
235C2×#92418—21no—
236C2×#92418—44no—
237C2×#92418#4112yes—
238C8×D61—44no—
239C23×C61—21no—
240C23×C61—21no—
241C23×C61—21no—
242C23×C61—21no—
243C23×C61C2×C22⋊C412yes—
244C23×C61#13512yes—
245C23×C61#13512yes—
246C23×C61C22×D411yescharacteristic
247C22×D61—21no—
248C22×D61—21no—
249C22×D61—21no—
250C22×D61—21no—
251C22×D61—21no—
252C22×D61—21no—
253C22×D61—22no—
254C22×D61—41no—
255C22×D61—41no—
256C22×D61—41no—
257C22×D61—41no—
258C22×D61—41no—
259C22×D61—41no—
260C22×D61C2×C22⋊C412yes—
261C2×C4×C61—21no—
262C2×C4×C61—21no—
263C2×C4×C61—22no—
264C2×C4×C61—22no—
265C2×C4×C61—22no—
266C2×C4×C61—22no—
267C2×C4×C61—22no—
268C2×C4×C61—22no—
269C2×C4×C61—41no—
270C2×C4×C61—41no—
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—84no—
280C2×C4×C61C2×C22⋊C412yes—
281C2×C4×C61C23×C411yescharacteristic
282C2×C4×C61C22×D411yescharacteristic
283C2×C4×C61C2×#4111yescharacteristic
284C2×C4×C61C2×#4111yescharacteristic
285C2×C4×C61H(5,𝔽2)11yescharacteristic
286C2×C4×C612−1+411yescharacteristic
287C22⋊D61—28no—
288C22⋊D61—48no—
289C2×Dic61—21no—
290C2×Dic61—21no—
291C2×Dic61—21no—
292C2×Dic61—21no—
293C2×Dic61—21no—
294C2×Dic61—21no—
295C2×Dic61—22no—
296C2×Dic61—22no—
297C2×Dic61—41no—
298C2×Dic61—41no—
299C2×Dic61—41no—
300C2×Dic61—41no—
301C2×Dic61—41no—
302C2×Dic61—41no—
303C2×Dic61—41no—
304C2×Dic61—84no—
305C2×Dic61C2×C22⋊C412yes—
306C2×Dic61C2×C22⋊C412yes—
307C2×Dic61C2×C22⋊C412yes—
308D244—22no—
309D244—22no—
310D244—41no—
311D244—41no—
312D244—84no—
313C4×D61—22no—
314C4×D61—22no—
315C4×D61—22no—
316C4×D61—22no—
317C4×D61—84no—
318C8×C61—41no—
319C8×C61—41no—
320#92418—22no—
321#92418—41no—
322#22488—611nomaximal, Sylow
323C22×C61—22no—
324C22×C61—22no—
325C22×C61—22no—
326C22×C61—22no—
327C22×C61—22no—
328C22×C61—22no—
329C22×C61#41614yes—
330C22×C61C22×C22⋊C411yescharacteristic
331C22×C61#54611yescharacteristic
332C22×C61#54711yescharacteristic
333C22×C61C2×#13511yescharacteristic
334C22×C61C2×#13511yescharacteristic
335C22×C61#57611yescharacteristic
336C22×C61#57711yescharacteristic
337C2×D61—22no—
338C2×D61—22no—
339C2×D61—22no—
340C2×D61—41no—
341C2×D61—41no—
342C2×D61—41no—
343C2×D61—41no—
344C2×D61—42no—
345C2×D61—42no—
346C2×D61—42no—
347C2×D61—81no—
348C2×D61—81no—
349C2×D61—81no—
350C2×D61—81no—
351C4×C61—22no—
352C4×C61—42no—
353C4×C61—42no—
354C4×C61—81no—
355C4×C61—81no—
356C4×C61C4×#4111yescharacteristic
357C4×C61#52011yescharacteristic
358C4×C61#54611yescharacteristic
359C4×C61#54711yescharacteristic
360Dic61—22no—
361Dic61—22no—
362Dic61—22no—
363Dic61—42no—
364Dic61—42no—
365Dic61—81no—
366C2×#553—611no—
367C2×C8×D4—611no—
368#2352—611no—
369#1991—611no—
370#1989—611no—
371#1893—611no—
372#1893—611no—
373#1875—611no—
374#1874—611no—
375#1825—611no—
376#1824D6111yescharacteristic, complemented
377#1804—611no—
378C4×#102—611no—
379#1735—611no—
380C2×#340—611no—
381C2×C61—24no—
382C2×C61#233911yescharacteristic
383C2×C61C2×#41611yescharacteristic
384C2×C61#289711yescharacteristic
385C2×C61#329711yescharacteristic
386C2×C61#330111yescharacteristic
387C2×C61#333711yescharacteristic
388C2×C61#333911yescharacteristic
389D61—42no—
390D61—82no—
391C23×C8—611no—
392C23×C8—611no—
393#553—618no—
394#553—1224no—
395C2×#126—1221no—
396C2×#125—611no—
397C2×#123—1221no—
398C2×#121—611no—
399C2×#121—611no—
400C2×#121—1221no—
401C2×C4×D4—611no—
402C2×C4×D4—611no—
403C2×C4×D4—1221no—
404C2×#117—611no—
405C2×#117—611no—
406C22×C4⋊C4—611no—
407C22×C4⋊C4C2×D6111yescharacteristic
408C8×D4—1224no—
409C2×C4⋊C8—611no—
410C2×#102—611no—
411C2×#102—611no—
412C2×#102—611no—
413C2×#102—611no—
414C2×C22⋊C8—611no—
415C2×C22⋊C8C2×D6111yescharacteristic
416C2×C4×C8—611no—
417#388—1221no—
418#387—1221no—
419#386—1221no—
420#382—611no—
421#380—611no—
422#380C2×D6111yescharacteristic
423C4×C4⋊C4—611no—
424C4×C22⋊C4—1221no—
425#340—611no—
426#340—611no—
427#340—611no—
428#340—611no—
429#340—611no—
430#340—611no—
431#340—611no—
432#340—611no—
433#340C2×D6111yescharacteristic
434#340C2×D6111yescharacteristic
435#340C2×D6111yescharacteristic
436#340C2×D6111yescharacteristic
437C61#2248811yescharacteristic, complemented, Sylow
438C22×D4—611no—
439C22×D4—611no—
440C22×D4—1221no—
441C22×D4—1221no—
442C23×C4—21no—
443C23×C4—611no—
444C23×C4—1221no—
445C23×C4—1221no—
446C23×C4C22×D6111yescharacteristic
447C22×C8—611no—
448C22×C8—611no—
449C22×C8—1222no—
450C22×C8—1222no—
451C22×C8—1222no—
452C22×C8—1222no—
453C22×C8—2441no—
454C22×C8—2441no—
455C22×C8C22×D6111yescharacteristic
456C22×C8C22×D6111yescharacteristic
457#126—1228no—
458#125—614no—
459#125—1222no—
460#123—1228no—
461#121—614no—
462#121—614no—
463#121—1222no—
464#121—1228no—
465#121—1222no—
466C4×D4—614no—
467C4×D4—614no—
468C4×D4—614no—
469C4×D4—1222no—
470C4×D4—1228no—
471#117—614no—
472#117—1222no—
473#117—1222no—
474#117—2441no—
475C2×C4⋊C4—21no—
476C2×C4⋊C4—22no—
477C2×C4⋊C4—611no—
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—2441no—
486C2×C4⋊C4C4×D6114yes—
487C2×C4⋊C4C22×D6111yescharacteristic
488C2×C4⋊C4C22×D6111yescharacteristic
489C2×C4⋊C4C22×D6111yescharacteristic
490C2×C4⋊C4C22×D6111yescharacteristic
491C2×C22⋊C4—21no—
492C2×C22⋊C4—611no—
493C2×C22⋊C4—611no—
494C2×C22⋊C4—1221no—
495C2×C22⋊C4—1221no—
496C2×C22⋊C4—1221no—
497C2×C22⋊C4—1221no—
498C2×C22⋊C4—1221no—
499C2×C22⋊C4—1221no—
500C2×C42—611no—
501C2×C42—1221no—
502C2×C42—1221no—
503C2×C42—1221no—
504C4⋊C8—1222no—
505#102—1222no—
506#102—1222no—
507#102—2441no—
508#102—2441no—
509C22⋊C8—22no—
510C22⋊C8—1222no—
511C4×C8—1222no—
512#95—21no—
513#95—1221no—
514#95—1221no—
515#95—1221no—
516#95—1221no—
517C24—611no—
518C24—1221no—
519C24D4×D6111yescharacteristic
520C2×D4—614no—
521C2×D4—612no—
522C2×D4—1224no—
523C2×D4—1222no—
524C2×D4—1222no—
525C2×D4—1224no—
526C2×D4—1221no—
527C2×D4—1221no—
528C2×D4—1221no—
529C2×D4—1221no—
530C2×D4—1221no—
531C2×D4—4881no—
532C2×D4—4881no—
533C2×D4—2442no—
534C2×D4—2442no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—24no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—81no—
545C22×C4—81no—
546C22×C4—611no—
547C22×C4—611no—
548C22×C4—611no—
549C22×C4—612no—
550C22×C4—612no—
551C22×C4—1224no—
552C22×C4—1221no—
553C22×C4—1221no—
554C22×C4—1221no—
555C22×C4—1221no—
556C22×C4—1221no—
557C22×C4—1221no—
558C22×C4—1221no—
559C22×C4—4881no—
560C22×C4—4881no—
561C22×C4—4881no—
562C22×C4—2442no—
563C22×C4—2442no—
564C22×C4C2×C4×D6112yes—
565C22×C4D4×D6112yes—
566C22×C4D4×D6111yescharacteristic
567C22×C4C23×D6111yescharacteristic
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—612no—
575C2×C8—1221no—
576C2×C8—1221no—
577C2×C8—1221no—
578C2×C8—1221no—
579C2×C8—1221no—
580C2×C8—2444no—
581C2×C8—2444no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—24no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—614no—
590C4⋊C4—612no—
591C4⋊C4—612no—
592C4⋊C4—1224no—
593C4⋊C4—1224no—
594C4⋊C4—1221no—
595C4⋊C4—1221no—
596C4⋊C4—1221no—
597C4⋊C4—1221no—
598C4⋊C4—2442no—
599C4⋊C4C2×C4×D6112yes—
600C4⋊C4C2×C4×D6112yes—
601C22⋊C4—42no—
602C22⋊C4—614no—
603C22⋊C4—614no—
604C22⋊C4—1224no—
605C22⋊C4—1224no—
606C22⋊C4—1224no—
607C22⋊C4—1224no—
608C22⋊C4—4881no—
609C22⋊C4—2442no—
610C42—612no—
611C42—612no—
612C42—1224no—
613C42—4881no—
614C42—2442no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—612no—
620C23—1221no—
621C23—1221no—
622C23—1221no—
623C23—1221no—
624C23—1221no—
625C23—1221no—
626C23—1222no—
627C23—2441no—
628C23—2441no—
629C23—2441no—
630C23—2441no—
631C23—2441no—
632C23—2441no—
633C23C22⋊C4×D6112yes—
634C23#1451979812yes—
635C23#1451980012yes—
636C23C2×D4×D6111yescharacteristic
637D4—1228no—
638D4—1222no—
639D4—1222no—
640D4—4884no—
641D4—2448no—
642D4—2441no—
643D4—2441no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—84no—
663C2×C4—612no—
664C2×C4—612no—
665C2×C4—612no—
666C2×C4—1221no—
667C2×C4—1221no—
668C2×C4—1221no—
669C2×C4—1221no—
670C2×C4—1221no—
671C2×C4—1221no—
672C2×C4—1222no—
673C2×C4—1222no—
674C2×C4—1222no—
675C2×C4—1222no—
676C2×C4—1222no—
677C2×C4—1222no—
678C2×C4—4884no—
679C2×C4—4884no—
680C2×C4—2441no—
681C2×C4—2441no—
682C2×C4—2441no—
683C2×C4—2441no—
684C2×C4—2441no—
685C2×C4—2441no—
686C2×C4—2441no—
687C2×C4C22⋊C4×D6112yes—
688C2×C4C22×C4×D6111yescharacteristic
689C2×C4C2×D4×D6111yescharacteristic
690C2×C4#41×D6111yescharacteristic
691C2×C4#41×D6111yescharacteristic
692C2×C4#1451982311yescharacteristic
693C2×C4#1451982411yescharacteristic
694C8—41no—
695C8—41no—
696C8—1222no—
697C8—2441no—
698C22—22no—
699C22—22no—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—22no—
704C22—1222no—
705C22—1222no—
706C22—1222no—
707C22—4881no—
708C22—4881no—
709C22—4881no—
710C22—4881no—
711C22—2442no—
712C22—2442no—
713C22—2442no—
714C22—2441no—
715C22—2441no—
716C22—2441no—
717C22—2441no—
718C22#1683975714yes—
719C22C2×C22⋊C4×D6111yescharacteristic
720C22#1684040411yescharacteristic
721C22#1684041011yescharacteristic
722C22C2×#1451979811yescharacteristic
723C22C2×#1451980011yescharacteristic
724C22#1684056611yescharacteristic
725C22#1684057211yescharacteristic
726C4—22no—
727C4—42no—
728C4—42no—
729C4—81no—
730C4—81no—
731C4—1222no—
732C4—1222no—
733C4—1222no—
734C4—4881no—
735C4—2442no—
736C4—2442no—
737C4#1684023011yescharacteristic
738C4#1684024211yescharacteristic
739C4#1684040411yescharacteristic
740C4#1684041011yescharacteristic
741C2—24no—
742C2—4882no—
743C2—2442no—
744C2#2144864311yescharacteristic
745C2C2×#1683975711yescharacteristic
746C2#2145434411yescharacteristic
747C2#2145766711yescharacteristic
748C2#2145771911yescharacteristic
749C2#2145819611yescharacteristic
750C2#2145821911yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1824C2
socleC23×C61C22×D4
prime radicalC2×#16840460C2
cosocleC22×C4×C61C24
hypercenter#1824D61
hypocenterC61#22488
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1824

Complements

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

NH ≅ G/Ntype
2. C2×#16839825C2semidirect
3. #21448750C2semidirect
4. #21446782C2semidirect
5. #21446773C2semidirect
6. #21446246C2semidirect
7. #21446245C2semidirect
8. #21446140C2semidirect
9. #21446134C2semidirect
10. #21445913C2semidirect
11. #21445828C2semidirect
12. #21445633C2semidirect
13. #21445534C2semidirect
14. C2×#16839524C2semidirect
15. C61×#1824C2semidirect
19. #16840460C4semidirect
79. #14519768C2×C4semidirect
82. #14519752C2×C4semidirect
87. #14519739C2×C4semidirect
94. #14519735C2×C4semidirect
376. #1824D61semidirect
437. C61#22488semidirect

Maximal subgroups

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

subgroupindex
C2×#168404602
C2×#168398252
#214487502
#214467822
#214467732
#214462462
#214462452
#214461402
#214461342
#214459132
#214458282
#214456332
#214455342
C2×#168395242
C61×#18242
#2248861