Finite Group Databasebeta

← #29685178

Subgroups — #29685178

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×#16840365C211yesmaximal, characteristic
2C2×#16839820C211yesmaximal, characteristic, complemented
3#21448176C211yesmaximal, characteristic, complemented
4#21446775C211yesmaximal, characteristic, complemented
5#21446773C211yesmaximal, characteristic, complemented
6#21446744C211yesmaximal, characteristic, complemented
7#21446744C211yesmaximal, characteristic, complemented
8#21446142C211yesmaximal, characteristic, complemented
9#21446139C211yesmaximal, characteristic, complemented
10#21446136C211yesmaximal, characteristic, complemented
11#21445646C211yesmaximal, characteristic, complemented
12#21445643C211yesmaximal, characteristic, complemented
13#102×Dic61C211yesmaximal, characteristic, complemented
14#21445633C211yesmaximal, characteristic, complemented
15C61×#1874C211yesmaximal, characteristic, complemented
16#16840365—24no—
17#16840365C418yescomplemented
18C2×#14519773C2211yescharacteristic
19C2×#14519768C2211yescharacteristic
20C2×#14519761—21no—
21C2×#14519759—21no—
22C2×#14519751C2211yescharacteristic
23C2×#14519749—21no—
24C2×#14519748—21no—
25C2×D4×Dic61C2211yescharacteristic
26C2×#14519739C2211yescharacteristic
27C2×#14519736C2211yescharacteristic
28C2×#14519736C2211yescharacteristic
29#16839820—24no—
30C2×#14519706C2211yescharacteristic
31C2×#14519706C2211yescharacteristic
32C2×#14519699C2211yescharacteristic
33C2×#14519699C2211yescharacteristic
34C2×#14519698C2211yescharacteristic
35C2×#14519698C2211yescharacteristic
36C2×#14519697C2211yescharacteristic
37C2×#14519697C2211yescharacteristic
38C2×C22⋊#92418C2211yescharacteristic
39C2×#14519687C2211yescharacteristic
40C2×C8×Dic61C2211yescharacteristic
41C4⋊C4×Dic61—21no—
42C4⋊C4×Dic61—21no—
43C4⋊C4×Dic61C2211yescharacteristic
44C4⋊C4×Dic61C2211yescharacteristic
45C4⋊C4×Dic61C2211yescharacteristic
46C4⋊C4×Dic61C2211yescharacteristic
47C4×C22⋊Dic61—21no—
48C4×C22⋊Dic61—21no—
49#16839525C2211yescharacteristic
50#16839525C2211yescharacteristic
51#16839524C2211yescharacteristic
52#16839524C2211yescharacteristic
53#16839524C2211yescharacteristic
54#16839524C2211yescharacteristic
55C2×#121×C61C2211yescharacteristic
56C22×C4⋊C4×C61C2211yescharacteristic
57C2×#102×C61C2211yescharacteristic
58C2×#102×C61C2211yescharacteristic
59C2×C22⋊C8×C61C2211yescharacteristic
60C61×#340C2211yescharacteristic
61C61×#340C2211yescharacteristic
62C22×D244C2311yescharacteristic
63C22×C22⋊D61—21no—
64C22×C22⋊D61—21no—
65C22×C22⋊D61—21no—
66C23×Dic61—21no—
67C22×C4×D61—21no—
68C22×#92418C2311yescharacteristic
69C22×#92418C2311yescharacteristic
70#14519773—22no—
71#14519773C2×C414yescomplemented
72#14519768—22no—
73#14519768C2×C414yescomplemented
74#14519761—28no—
75#14519759—28no—
76#14519751—22no—
77#14519751C2×C414yes—
78#14519749—28no—
79#14519748—28no—
80D4×Dic61—22no—
81D4×Dic61C2×C414yescomplemented
82#14519739—22no—
83#14519739C2×C414yescomplemented
84#14519736—22no—
85#14519736—22no—
86#14519736C2×C414yes—
87#14519736D414yes—
88C2×C4⋊Dic61—21no—
89C2×C4⋊Dic61D411yescharacteristic
90C2×C4⋊Dic61D411yescharacteristic
91C2×C4⋊Dic61C2311yescharacteristic
92C2×C4⋊Dic61C2311yescharacteristic
93C2×C4⋊Dic61C2311yescharacteristic
94C2×#11758196—21no—
95C2×C22⋊Dic61—21no—
96C2×C22⋊Dic61—21no—
97C2×C22⋊Dic61D411yescharacteristic
98C2×C22⋊Dic61D411yescharacteristic
99C2×#11758198—21no—
100C2×#11758198—21no—
101C2×C4×Dic61—21no—
102C2×C4×Dic61—21no—
103C2×C4×Dic61—21no—
104C2×C4×Dic61—21no—
105C2×C4×Dic61—21no—
106C2×C4×Dic61C2311yescharacteristic
107C2×C4×Dic61C2311yescharacteristic
108#14519706—22no—
109#14519706—22no—
110#14519699—22no—
111#14519699—22no—
112#14519698—22no—
113#14519698—22no—
114#14519697—22no—
115#14519697—22no—
116C22⋊#92418—22no—
117#14519687—22no—
118C8×Dic61—22no—
119#14519684—21no—
120#14519684—21no—
121#14519684—21no—
122#14519684—21no—
123C22×D4×C61—21no—
124C22×D4×C61C2311yescharacteristic
125C23×C4×C61—21no—
126C23×C4×C61C2311yescharacteristic
127C22×C8×C61C2311yescharacteristic
128C22×C8×C61C2311yescharacteristic
129#121×C61—22no—
130#121×C61C2×C414yes—
131C2×C4⋊C4×C61—21no—
132C2×C4⋊C4×C61—22no—
133C2×C4⋊C4×C61—22no—
134C2×C4⋊C4×C61C2311yescharacteristic
135C2×C4⋊C4×C61C2311yescharacteristic
136C2×C4⋊C4×C61C2311yescharacteristic
137C2×C22⋊C4×C61—21no—
138#102×C61—22no—
139#102×C61—22no—
140C22⋊C8×C61—22no—
141C24×C61—21no—
142C24×C61C2×D411yescharacteristic
143C23×D61—21no—
144C2×D4×C61—24no—
145C2×D4×C61—21no—
146C2×D4×C61—21no—
147C2×D4×C61—21no—
148C2×D4×C61—21no—
149C2×D4×C61—21no—
150C2×D4×C61—81no—
151C2×D4×C61—81no—
152C2×D4×C61C22×C412yes—
153C22×C4×C61—21no—
154C22×C4×C61—21no—
155C22×C4×C61—21no—
156C22×C4×C61—21no—
157C22×C4×C61—21no—
158C22×C4×C61—21no—
159C22×C4×C61—21no—
160C22×C4×C61—24no—
161C22×C4×C61—81no—
162C22×C4×C61—81no—
163C22×C4×C61C22×C412yes—
164C22×C4×C61C2×D411yescharacteristic
165C22×C4×C61C2×D412yes—
166C22×C4×C61C2411yescharacteristic
167C2×C22⋊D61—24no—
168C2×C22⋊D61—24no—
169C2×C22⋊D61—24no—
170C2×C22⋊D61—81no—
171C2×C22⋊D61—81no—
172C2×C22⋊D61—81no—
173C2×C22⋊D61—81no—
174C2×C22⋊D61—81no—
175C2×C22⋊D61—81no—
176C22×Dic61—21no—
177C22×Dic61—21no—
178C22×Dic61—21no—
179C22×Dic61—24no—
180C22×Dic61—81no—
181C22×Dic61—81no—
182C22×Dic61C2×D411yescharacteristic
183C22×Dic61C2×D411yescharacteristic
184C22×Dic61C2×D411yescharacteristic
185C22×Dic61C2×D411yescharacteristic
186C2×D244—21no—
187C2×D244—21no—
188C2×D244—21no—
189C2×D244—21no—
190C2×D244—21no—
191C2×D244C22×C412yes—
192C2×C4×D61—24no—
193C2×C4×D61—81no—
194C2×C4×D61—81no—
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—24no—
202C4⋊C4×C61—21no—
203C4⋊C4×C61—21no—
204C4⋊C4×C61—21no—
205C4⋊C4×C61C22×C412yes—
206C4⋊C4×C61#4112yes—
207C4⋊C4×C61#4112yes—
208C22⋊C4×C61—24no—
209C22⋊Dic61—24no—
210C22⋊Dic61—24no—
211C22⋊Dic61C22⋊C414yes—
212C22⋊Dic61C22⋊C414yes—
213#11758198—24no—
214#11758198—24no—
215C4⋊Dic61—21no—
216C4⋊Dic61—21no—
217C4⋊Dic61—21no—
218C4⋊Dic61—24no—
219C4⋊Dic61C22⋊C414yes—
220C4⋊Dic61C22⋊C414yes—
221C4⋊Dic61C22×C412yes—
222C4⋊Dic61#4112yes—
223C4⋊Dic61#4112yes—
224#11758196—24no—
225C4×Dic61—24no—
226C4×Dic61—81no—
227C4×Dic61—81no—
228C4×Dic61—81no—
229C4×Dic61—81no—
230C4×Dic61C22×C412yes—
231C4×Dic61C22×C412yes—
232C4×Dic61C2×D412yes—
233C4×Dic61C2×D412yes—
234C2×#92418—21no—
235C2×#92418—21no—
236C2×#92418—21no—
237C2×#92418—21no—
238C2×#92418—21no—
239C2×#92418—21no—
240C23×C61—21no—
241C23×C61—21no—
242C23×C61—21no—
243C23×C61—21no—
244C23×C61—21no—
245C23×C61—21no—
246C23×C61—22no—
247C23×C61—41no—
248C23×C61—41no—
249C23×C61—41no—
250C23×C61—41no—
251C23×C61—41no—
252C23×C61—41no—
253C23×C61C2×C22⋊C412yes—
254C23×C61C22×D411yescharacteristic
255C22×D61—22no—
256C22×D61—41no—
257C22×D61—41no—
258C22×D61—41no—
259C22×D61—41no—
260C22×D61—41no—
261C22×D61—41no—
262D4×C61—22no—
263D4×C61—22no—
264D4×C61—41no—
265D4×C61—41no—
266D4×C61—84no—
267C2×C4×C61—21no—
268C2×C4×C61—21no—
269C2×C4×C61—22no—
270C2×C4×C61—22no—
271C2×C4×C61—22no—
272C2×C4×C61—22no—
273C2×C4×C61—22no—
274C2×C4×C61—22no—
275C2×C4×C61—22no—
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—84no—
283C2×C4×C61C2×C22⋊C412yes—
284C2×C4×C61C23×C411yescharacteristic
285C2×C4×C61C22×D411yescharacteristic
286C2×C4×C61C2×#4111yescharacteristic
287C2×C4×C61C2×#4111yescharacteristic
288C2×C4×C61C2×#4111yescharacteristic
289C2×C4×C61C2×#4111yescharacteristic
290C22⋊D61—84no—
291C22⋊D61—84no—
292C22⋊D61—84no—
293C2×Dic61—21no—
294C2×Dic61—21no—
295C2×Dic61—21no—
296C2×Dic61—21no—
297C2×Dic61—21no—
298C2×Dic61—21no—
299C2×Dic61—21no—
300C2×Dic61—21no—
301C2×Dic61—22no—
302C2×Dic61—22no—
303C2×Dic61—22no—
304C2×Dic61—41no—
305C2×Dic61—41no—
306C2×Dic61—41no—
307C2×Dic61—41no—
308C2×Dic61—41no—
309C2×Dic61—41no—
310C2×Dic61—84no—
311C2×Dic61C2×C22⋊C412yes—
312C2×Dic61C2×C22⋊C412yes—
313C2×Dic61C2×C22⋊C412yes—
314C2×Dic61C2×C22⋊C412yes—
315D244—22no—
316D244—22no—
317D244—41no—
318D244—41no—
319C4×D61—84no—
320C8×C61—41no—
321C8×C61—41no—
322#92418—41no—
323#92418—41no—
324#21399—611nomaximal, Sylow
325C22×C61—22no—
326C22×C61—22no—
327C22×C61—22no—
328C22×C61—41no—
329C22×C61—41no—
330C22×C61—41no—
331C22×C61—41no—
332C22×C61—42no—
333C22×C61—42no—
334C22×C61—42no—
335C22×C61—81no—
336C22×C61—81no—
337C22×C61—81no—
338C22×C61—81no—
339C22×C61C22×C22⋊C411yescharacteristic
340C22×C61#52511yescharacteristic
341C22×C61#52511yescharacteristic
342C22×C61#57611yescharacteristic
343C22×C61#57611yescharacteristic
344C22×C61#57711yescharacteristic
345C22×C61#57711yescharacteristic
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—42no—
355C4×C61—42no—
356C4×C61—42no—
357C4×C61C4×#4111yescharacteristic
358C4×C61C4×#4111yescharacteristic
359C4×C61#53211yescharacteristic
360C4×C61#53211yescharacteristic
361Dic61—22no—
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#1874D6111yescharacteristic, complemented
379#1762—611no—
380#1762—611no—
381C4×#102—611no—
382C4×#102—611no—
383C2×C61—42no—
384C2×C61—82no—
385C2×C61#229711yescharacteristic
386C2×C61#289711yescharacteristic
387C2×C61#289711yescharacteristic
388C2×C61#311911yescharacteristic
389C2×C61#311911yescharacteristic
390C2×C61#312211yescharacteristic
391C2×C61#312611yescharacteristic
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—1221no—
401C2×#121—1221no—
402C2×#121C2×D6111yescharacteristic
403C2×C4×D4—611no—
404C2×C4×D4—611no—
405C2×#117—611no—
406C2×#117—611no—
407C22×C4⋊C4C2×D6111yescharacteristic
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⋊C8C2×D6111yescharacteristic
421C2×#97—611no—
422C2×C4×C8—611no—
423C4×C4⋊C4—611no—
424C4×C4⋊C4—611no—
425C4×C4⋊C4—611no—
426C4×C4⋊C4—611no—
427C4×C4⋊C4—1221no—
428C4×C4⋊C4—1221no—
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—21no—
441C22×D4—611no—
442C22×D4—1221no—
443C22×D4—1221no—
444C22×D4—1221no—
445C22×D4C22×D6111yescharacteristic
446C23×C4—21no—
447C23×C4—1221no—
448C23×C4—1221no—
449C23×C4C22×D6111yescharacteristic
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—22no—
461#121—614no—
462#121—1228no—
463#121—1228no—
464#121—1222no—
465#121C4×D6114yes—
466C4×D4—614no—
467C4×D4—614no—
468C4×D4—1222no—
469C4×D4—1222no—
470#117—614no—
471#117—614no—
472#117—1222no—
473#117—1222no—
474C2×C4⋊C4—21no—
475C2×C4⋊C4—22no—
476C2×C4⋊C4—22no—
477C2×C4⋊C4—611no—
478C2×C4⋊C4—611no—
479C2×C4⋊C4—611no—
480C2×C4⋊C4—611no—
481C2×C4⋊C4—611no—
482C2×C4⋊C4—1221no—
483C2×C4⋊C4—1221no—
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—611no—
495C2×C42—611no—
496C2×C42—1221no—
497C2×C42—1221no—
498C2×C42—1221no—
499C2×C42—1221no—
500C2×C42—1221no—
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—22no—
512C22⋊C8—1222no—
513#97—1222no—
514C4×C8—1222no—
515#95—1221no—
516#95—1221no—
517#95—1221no—
518#95—1221no—
519C24—21no—
520C24—1221no—
521C24D4×D6111yescharacteristic
522C2×D4—24no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—21no—
526C2×D4—21no—
527C2×D4—21no—
528C2×D4—81no—
529C2×D4—81no—
530C2×D4—612no—
531C2×D4—1224no—
532C2×D4—1224no—
533C2×D4—1224no—
534C2×D4—1221no—
535C2×D4—1221no—
536C2×D4—1221no—
537C2×D4—1221no—
538C2×D4—1221no—
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—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—24no—
554C22×C4—81no—
555C22×C4—81no—
556C22×C4—611no—
557C22×C4—611no—
558C22×C4—611no—
559C22×C4—611no—
560C22×C4—1224no—
561C22×C4—1224no—
562C22×C4—1221no—
563C22×C4—1221no—
564C22×C4—1221no—
565C22×C4—4881no—
566C22×C4—4881no—
567C22×C4—4881no—
568C22×C4—4881no—
569C22×C4C2×C4×D6112yes—
570C22×C4D4×D6112yes—
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—24no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—614no—
590C4⋊C4—614no—
591C4⋊C4—612no—
592C4⋊C4—612no—
593C4⋊C4—612no—
594C4⋊C4—1224no—
595C4⋊C4—1224no—
596C4⋊C4—1221no—
597C4⋊C4—1221no—
598C4⋊C4—1221no—
599C4⋊C4C2×C4×D6112yes—
600C4⋊C4#1175822412yes—
601C4⋊C4#1175822412yes—
602C22⋊C4—24no—
603C22⋊C4—614no—
604C22⋊C4—614no—
605C22⋊C4—1224no—
606C22⋊C4—1224no—
607C22⋊C4—1224no—
608C22⋊C4—1224no—
609C42—612no—
610C42—612no—
611C42—612no—
612C42—612no—
613C42—1224no—
614C42—4881no—
615C42—4881no—
616C42—4881no—
617C42—4881no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—22no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—1222no—
632C23—2441no—
633C23—2441no—
634C23—2441no—
635C23—2441no—
636C23—2441no—
637C23—2441no—
638C23C22⋊C4×D6112yes—
639C23C2×D4×D6111yescharacteristic
640D4—22no—
641D4—22no—
642D4—41no—
643D4—41no—
644D4—84no—
645D4—1222no—
646D4—1222no—
647D4—4884no—
648D4—4884no—
649D4—4884no—
650D4—2441no—
651D4—2441no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—84no—
668C2×C4—612no—
669C2×C4—612no—
670C2×C4—612no—
671C2×C4—612no—
672C2×C4—1221no—
673C2×C4—1221no—
674C2×C4—1221no—
675C2×C4—1221no—
676C2×C4—1221no—
677C2×C4—1221no—
678C2×C4—1221no—
679C2×C4—1221no—
680C2×C4—1222no—
681C2×C4—1222no—
682C2×C4—1222no—
683C2×C4—4884no—
684C2×C4—4884no—
685C2×C4—2441no—
686C2×C4—2441no—
687C2×C4—2441no—
688C2×C4—2441no—
689C2×C4—2441no—
690C2×C4—2441no—
691C2×C4C22⋊C4×D6112yes—
692C2×C4C22×C4×D6111yescharacteristic
693C2×C4C2×D4×D6111yescharacteristic
694C2×C4#41×D6111yescharacteristic
695C2×C4#41×D6111yescharacteristic
696C2×C4C2×#1175822411yescharacteristic
697C2×C4C2×#1175822411yescharacteristic
698C8—41no—
699C8—41no—
700C8—2441no—
701C8—2441no—
702C22—22no—
703C22—22no—
704C22—22no—
705C22—41no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22—42no—
710C22—42no—
711C22—42no—
712C22—81no—
713C22—81no—
714C22—81no—
715C22—81no—
716C22—4881no—
717C22—4881no—
718C22—4881no—
719C22—4881no—
720C22—2442no—
721C22—2442no—
722C22—2442no—
723C22C2×C22⋊C4×D6111yescharacteristic
724C22#1684026811yescharacteristic
725C22#1684027011yescharacteristic
726C22#1684056311yescharacteristic
727C22#1684056611yescharacteristic
728C22#1684056811yescharacteristic
729C22#1684057111yescharacteristic
730C4—22no—
731C4—42no—
732C4—42no—
733C4—42no—
734C4—1222no—
735C4—1222no—
736C4—1222no—
737C4—1222no—
738C4—2442no—
739C4—2442no—
740C4—2442no—
741C4C4×#1175822411yescharacteristic
742C4C4×#1175822411yescharacteristic
743C4#1684030711yescharacteristic
744C4#1684030711yescharacteristic
745C2—42no—
746C2—82no—
747C2—4882no—
748C2#2144830411yescharacteristic
749C2#2145434011yescharacteristic
750C2#2145434311yescharacteristic
751C2#2145601311yescharacteristic
752C2#2145602111yescharacteristic
753C2#2145605611yescharacteristic
754C2#2145610411yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1874C2
socleC23×C61C22×D4
prime radicalC2×#16840365C2
cosocleC22×C4×C61C24
hypercenter#1874D61
hypocenterC61#21399
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1874

Complements

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

NH ≅ G/Ntype
2. C2×#16839820C2semidirect
3. #21448176C2semidirect
4. #21446775C2semidirect
5. #21446773C2semidirect
6. #21446744C2semidirect
7. #21446744C2semidirect
8. #21446142C2semidirect
9. #21446139C2semidirect
10. #21446136C2semidirect
11. #21445646C2semidirect
12. #21445643C2semidirect
13. #102×Dic61C2semidirect
14. #21445633C2semidirect
15. C61×#1874C2semidirect
17. #16840365C4semidirect
71. #14519773C2×C4semidirect
73. #14519768C2×C4semidirect
81. D4×Dic61C2×C4semidirect
83. #14519739C2×C4semidirect
378. #1874D61semidirect
439. C61#21399semidirect

Maximal subgroups

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

subgroupindex
C2×#168403652
C2×#168398202
#214481762
#214467752
#214467732
#214467442
#214461422
#214461392
#214461362
#214456462
#214456432
#102×Dic612
#214456332
C61×#18742
#2139961