Finite Group Databasebeta

← #29733267

Subgroups — #29733267

Order 15616.

1238 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840458C211yesmaximal, characteristic, complemented
2C2×#16840116C211yesmaximal, characteristic, complemented
3C2×#16839974C211yesmaximal, characteristic, complemented
4#21446820C211yesmaximal, characteristic, complemented
5#21446820C211yesmaximal, characteristic, complemented
6#21446815C211yesmaximal, characteristic, complemented
7#21446815C211yesmaximal, characteristic, complemented
8#21446776C211yesmaximal, characteristic, complemented
9#21446614C211yesmaximal, characteristic, complemented
10#21446142C211yesmaximal, characteristic, complemented
11#21446137C211yesmaximal, characteristic, complemented
12#21446132C211yesmaximal, characteristic, complemented
13#21446127C211yesmaximal, characteristic, complemented
14C4×#14519697C211yesmaximal, characteristic, complemented
15C61×#2540C211yesmaximal, characteristic, complemented
16C22×#11758201C2211yescharacteristic
17C22×#11758199C2211yescharacteristic
18#16840458—24no—
19#16840458—24no—
20C2×#14519772—21no—
21C2×#14519769C2211yescharacteristic
22C2×#14519759—21no—
23C2×#14519751C2211yescharacteristic
24C2×#14519751C2211yescharacteristic
25C2×#14519749—21no—
26C2×C4×D244C2211yescharacteristic
27C2×#14519737—21no—
28C2×#14519736C2211yescharacteristic
29C22×C4⋊Dic61C2211yescharacteristic
30#16840116—24no—
31#16839974—24no—
32C2×C4⋊#92418C2211yescharacteristic
33C2×#14519701C2211yescharacteristic
34C2×#14519701C2211yescharacteristic
35C2×#14519701C2211yescharacteristic
36C2×#14519698C2211yescharacteristic
37C2×#14519698C2211yescharacteristic
38C2×#14519698C2211yescharacteristic
39C2×#14519697C2211yescharacteristic
40C2×#14519697C2211yescharacteristic
41C2×C22⋊#92418C2211yescharacteristic
42C2×C22⋊#92418C2211yescharacteristic
43C2×C22⋊#92418C2211yescharacteristic
44C2×C22⋊#92418C2211yescharacteristic
45C2×C4×#92418C2211yescharacteristic
46#16839524C2211yescharacteristic
47#16839524C2211yescharacteristic
48#16839524C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839524C2211yescharacteristic
52C2×#124×C61C2211yescharacteristic
53C2×C22⋊Q8×C61C2211yescharacteristic
54C2×C22⋊Q8×C61C2211yescharacteristic
55C2×#121×C61C2211yescharacteristic
56C2×#121×C61C2211yescharacteristic
57C2×C4×D4×C61C2211yescharacteristic
58C61×#399—21no—
59C61×#392—21no—
60C61×#390—21no—
61C61×#390—21no—
62C4×C4⋊C4×C61C2211yescharacteristic
63C22×D244C2311yescharacteristic
64C22×C22⋊D61—21no—
65C22×C22⋊D61—21no—
66C23×Dic61—21no—
67C22×C4×D61—21no—
68C2×#11758201—22no—
69C2×#11758201—41no—
70C2×#11758201—41no—
71C2×#11758199—22no—
72C2×#11758199—41no—
73C2×#11758199—41no—
74C22×#92418C2311yescharacteristic
75C22×#92418C2311yescharacteristic
76C22×#92418C2311yescharacteristic
77C22×#92418C2311yescharacteristic
78#14519772—28no—
79#14519769—22no—
80#14519769D414yescomplemented
81#14519759—28no—
82#14519751—22no—
83#14519751—22no—
84#14519751—22no—
85#14519751—22no—
86#14519749—28no—
87C4×D244—22no—
88C4×D244D414yescomplemented
89#14519737—28no—
90#14519736—22no—
91#14519736—22no—
92C2×C4⋊Dic61—21no—
93C2×C4⋊Dic61—22no—
94C2×C4⋊Dic61—22no—
95C2×C4⋊Dic61C2311yescharacteristic
96C2×C4⋊Dic61C2311yescharacteristic
97C2×C4⋊Dic61C2311yescharacteristic
98C2×#11758196—21no—
99C2×#11758196—21no—
100C2×C22⋊Dic61—21no—
101C2×#11758198—21no—
102C2×#11758198—21no—
103C2×#11758198—21no—
104C2×C4×Dic61—21no—
105C4⋊#92418—22no—
106#14519701—22no—
107#14519701—22no—
108#14519701—22no—
109#14519698—22no—
110#14519698—22no—
111#14519698—22no—
112#14519697—22no—
113#14519697—22no—
114C22⋊#92418—41no—
115C22⋊#92418—41no—
116C22⋊#92418—41no—
117C22⋊#92418—41no—
118C4×#92418—22no—
119C22×Q8×C61C2311yescharacteristic
120C22×D4×C61—21no—
121C22×D4×C61—21no—
122C22×D4×C61D411yescharacteristic
123C22×D4×C61C2311yescharacteristic
124C23×C4×C61C2311yescharacteristic
125C23×C4×C61C2311yescharacteristic
126#124×C61—22no—
127#124×C61—22no—
128C22⋊Q8×C61—22no—
129C22⋊Q8×C61—22no—
130C22⋊Q8×C61—41no—
131C22⋊Q8×C61—41no—
132#121×C61—22no—
133#121×C61—22no—
134#121×C61—41no—
135#121×C61—41no—
136C4×D4×C61—22no—
137C4×D4×C61—22no—
138C2×C4⋊C4×C61—21no—
139C2×C4⋊C4×C61—21no—
140C2×C4⋊C4×C61D411yescharacteristic
141C2×C4⋊C4×C61C2311yescharacteristic
142C2×C4⋊C4×C61C2311yescharacteristic
143C2×C22⋊C4×C61—21no—
144C2×C22⋊C4×C61—21no—
145C2×C22⋊C4×C61—21no—
146C2×C22⋊C4×C61—21no—
147C2×C22⋊C4×C61—21no—
148C2×C22⋊C4×C61—21no—
149C2×C22⋊C4×C61D411yescharacteristic
150C2×C22⋊C4×C61D411yescharacteristic
151C2×C42×C61—21no—
152C2×C42×C61C2311yescharacteristic
153#95×C61—21no—
154C24×C61—21no—
155C24×C61C2×D411yescharacteristic
156C24×C61C2×D411yescharacteristic
157C23×D61—21no—
158C2×Q8×C61—21no—
159C2×Q8×C61—21no—
160C2×Q8×C61—21no—
161C2×Q8×C61—21no—
162C2×Q8×C61—21no—
163C2×Q8×C61—21no—
164C2×D4×C61—22no—
165C2×D4×C61—22no—
166C2×D4×C61—21no—
167C2×D4×C61—21no—
168C2×D4×C61—21no—
169C2×D4×C61—21no—
170C2×D4×C61—21no—
171C2×D4×C61—21no—
172C2×D4×C61—41no—
173C2×D4×C61—42no—
174C2×D4×C61—42no—
175C2×D4×C61—42no—
176C2×D4×C61—42no—
177C2×D4×C61—81no—
178C2×D4×C61—81no—
179C22×C4×C61—21no—
180C22×C4×C61—21no—
181C22×C4×C61—21no—
182C22×C4×C61—21no—
183C22×C4×C61—21no—
184C22×C4×C61—21no—
185C22×C4×C61—21no—
186C22×C4×C61—21no—
187C22×C4×C61—21no—
188C22×C4×C61—21no—
189C22×C4×C61—21no—
190C22×C4×C61—21no—
191C22×C4×C61—21no—
192C22×C4×C61—21no—
193C22×C4×C61—21no—
194C22×C4×C61C2×D411yescharacteristic
195C22×C4×C61C2×D411yescharacteristic
196C22×C4×C61C2×D411yescharacteristic
197C22×C4×C61C2×D411yescharacteristic
198C22×C4×C61C2411yescharacteristic
199C2×C22⋊D61—24no—
200C2×C22⋊D61—24no—
201C2×C22⋊D61—42no—
202C2×C22⋊D61—42no—
203C2×C22⋊D61—81no—
204C2×C22⋊D61—81no—
205C22×Dic61—21no—
206C22×Dic61—21no—
207C22×Dic61—21no—
208C22×Dic61—24no—
209C22×Dic61—81no—
210C22×Dic61—81no—
211C2×D244—21no—
212C2×D244—21no—
213C2×D244—21no—
214C2×D244—21no—
215C2×D244—21no—
216C2×D244C2×D412yes—
217C2×C4×D61—24no—
218C2×C4×D61—81no—
219C2×C4×D61—81no—
220C4⋊C4×C61—22no—
221C4⋊C4×C61—21no—
222C4⋊C4×C61—21no—
223C4⋊C4×C61—42no—
224C4⋊C4×C61—42no—
225C4⋊C4×C61#4112yes—
226C4⋊C4×C61#4112yes—
227C22⋊C4×C61—22no—
228C22⋊C4×C61—22no—
229C22⋊C4×C61—42no—
230C22⋊C4×C61—42no—
231C22⋊C4×C61—42no—
232C22⋊C4×C61—42no—
233C22⋊C4×C61—42no—
234C22⋊C4×C61—42no—
235C42×C61—81no—
236C42×C61C2×D412yes—
237C42×C61C2×D412yes—
238C22⋊Dic61—24no—
239#11758201—44no—
240#11758199—44no—
241#11758198—24no—
242#11758198—24no—
243#11758198—24no—
244C4⋊Dic61—24no—
245C4⋊Dic61—21no—
246C4⋊Dic61—21no—
247C4⋊Dic61—21no—
248C4⋊Dic61C2×D412yes—
249C4⋊Dic61C2×D412yes—
250C4⋊Dic61C2×D412yes—
251#11758196—24no—
252#11758196—24no—
253C4×Dic61—24no—
254C2×#92418—21no—
255C2×#92418—21no—
256C2×#92418—21no—
257C2×#92418—21no—
258C2×#92418—21no—
259C2×#92418—21no—
260C2×#92418—21no—
261C2×#92418—21no—
262C2×#92418—21no—
263C2×#92418—21no—
264C2×#92418—21no—
265C2×#92418—21no—
266C23×C61—21no—
267C23×C61—21no—
268C23×C61—21no—
269C23×C61—21no—
270C23×C61—21no—
271C23×C61—21no—
272C23×C61—21no—
273C23×C61—21no—
274C23×C61—21no—
275C23×C61—21no—
276C23×C61—21no—
277C23×C61—21no—
278C23×C61—21no—
279C23×C61—41no—
280C23×C61—41no—
281C23×C61—41no—
282C23×C61—41no—
283C23×C61—41no—
284C23×C61—41no—
285C23×C61—41no—
286C23×C61#13512yes—
287C23×C61C22×D411yescharacteristic
288C22×D61—22no—
289C22×D61—41no—
290C22×D61—41no—
291C22×D61—41no—
292C22×D61—41no—
293C22×D61—41no—
294C22×D61—41no—
295Q8×C61—41no—
296Q8×C61—41no—
297Q8×C61—41no—
298Q8×C61—41no—
299D4×C61—44no—
300D4×C61—41no—
301D4×C61—41no—
302D4×C61—41no—
303D4×C61—41no—
304D4×C61—84no—
305D4×C61—84no—
306C2×C4×C61—21no—
307C2×C4×C61—21no—
308C2×C4×C61—21no—
309C2×C4×C61—21no—
310C2×C4×C61—21no—
311C2×C4×C61—21no—
312C2×C4×C61—22no—
313C2×C4×C61—22no—
314C2×C4×C61—21no—
315C2×C4×C61—21no—
316C2×C4×C61—21no—
317C2×C4×C61—21no—
318C2×C4×C61—41no—
319C2×C4×C61—41no—
320C2×C4×C61—41no—
321C2×C4×C61—41no—
322C2×C4×C61—41no—
323C2×C4×C61—41no—
324C2×C4×C61—41no—
325C2×C4×C61—41no—
326C2×C4×C61—41no—
327C2×C4×C61—41no—
328C2×C4×C61—41no—
329C2×C4×C61—41no—
330C2×C4×C61—41no—
331C2×C4×C61—41no—
332C2×C4×C61—41no—
333C2×C4×C61#12012yes—
334C2×C4×C61#12012yes—
335C2×C4×C61C22×D411yescharacteristic
336C2×C4×C61C22×D411yescharacteristic
337C2×C4×C61C2×#4111yescharacteristic
338C2×C4×C61C2×#4111yescharacteristic
339C2×C4×C61H(5,𝔽2)11yescharacteristic
340C2×C4×C61H(5,𝔽2)11yescharacteristic
341C22⋊D61—48no—
342C22⋊D61—84no—
343C2×Dic61—22no—
344C2×Dic61—22no—
345C2×Dic61—22no—
346C2×Dic61—41no—
347C2×Dic61—41no—
348C2×Dic61—41no—
349C2×Dic61—41no—
350C2×Dic61—41no—
351C2×Dic61—41no—
352C2×Dic61—84no—
353D244—22no—
354D244—22no—
355D244—41no—
356D244—41no—
357C4×D61—84no—
358#92418—41no—
359#92418—41no—
360#92418—41no—
361#92418—41no—
362#25575—611nomaximal, Sylow
363C22×C61—22no—
364C22×C61—22no—
365C22×C61—22no—
366C22×C61—41no—
367C22×C61—41no—
368C22×C61—41no—
369C22×C61—41no—
370C22×C61—41no—
371C22×C61—41no—
372C22×C61—41no—
373C22×C61—41no—
374C22×C61—41no—
375C22×C61—41no—
376C22×C61—41no—
377C22×C61—81no—
378C22×C61—81no—
379C22×C61—81no—
380C22×C61—81no—
381C22×C61—81no—
382C22×C61—81no—
383C22×C61—81no—
384C22×C61C2×#12011yescharacteristic
385C22×C61#54611yescharacteristic
386C22×C61#54611yescharacteristic
387C22×C61C2×#13511yescharacteristic
388C22×C61#57511yescharacteristic
389C22×C61#57611yescharacteristic
390C22×C61#57711yescharacteristic
391C2×D61—42no—
392C2×D61—42no—
393C2×D61—42no—
394C2×D61—81no—
395C2×D61—81no—
396C2×D61—81no—
397C2×D61—81no—
398C4×C61—22no—
399C4×C61—22no—
400C4×C61—41no—
401C4×C61—41no—
402C4×C61—42no—
403C4×C61—42no—
404C4×C61—81no—
405C4×C61#53211yescharacteristic
406C4×C61#53511yescharacteristic
407C4×C61#55011yescharacteristic
408C4×C61#55011yescharacteristic
409Dic61—42no—
410Dic61—42no—
411Dic61—42no—
412C2×#553—611no—
413C2×#488—611no—
414C2×#463—611no—
415#2540D6111yescharacteristic, complemented
416#2000—611no—
417#2000—611no—
418#1999—611no—
419#1999—611no—
420#1989—611no—
421#1954—611no—
422#1875—611no—
423#1874—611no—
424#1873—611no—
425#1872—611no—
426C4×#102—611no—
427C2×C61—42no—
428C2×C61—81no—
429C2×C61—161no—
430C2×C61#243111yescharacteristic
431C2×C61#300211yescharacteristic
432C2×C61#301211yescharacteristic
433C2×C61#329711yescharacteristic
434C2×C61#330111yescharacteristic
435C2×C61#332211yescharacteristic
436C2×C61#332611yescharacteristic
437D61—82no—
438C22×SD16—611no—
439C22×D8—611no—
440#553—1224no—
441#553—1224no—
442C2×#126—1221no—
443C2×#125—611no—
444C2×#124C2×D6111yescharacteristic
445C2×#123—1221no—
446C2×C22⋊Q8C2×D6111yescharacteristic
447C2×C22⋊Q8C2×D6111yescharacteristic
448C2×#121—611no—
449C2×#121—611no—
450C2×#121—1221no—
451C2×#121C2×D6111yescharacteristic
452C2×#121C2×D6111yescharacteristic
453C2×C4×D4—611no—
454C2×C4×D4—1221no—
455C2×C4×D4C2×D6111yescharacteristic
456C2×#117—611no—
457C22×C4⋊C4—611no—
458#488—1224no—
459#463—1224no—
460C2×C4⋊C8—611no—
461C2×#103—611no—
462C2×#103—611no—
463C2×#103—611no—
464C2×#102—611no—
465C2×#102—611no—
466C2×#102—611no—
467C2×#102—611no—
468C2×#102—611no—
469C2×C22⋊C8—611no—
470C2×C22⋊C8—611no—
471C2×C22⋊C8—611no—
472C2×C22⋊C8—611no—
473C2×C4×C8—611no—
474#399—21no—
475#392—21no—
476#390—21no—
477#390—21no—
478C4×C4⋊C4C2×D6111yescharacteristic
479#340—611no—
480#340—611no—
481#340—611no—
482#340—611no—
483#340—611no—
484#340—611no—
485C61#2557511yescharacteristic, complemented, Sylow
486C22×Q8C22×D6111yescharacteristic
487C22×D4—21no—
488C22×D4—21no—
489C22×D4—611no—
490C22×D4—1221no—
491C22×D4—1221no—
492C22×D4C22⋊D6111yescharacteristic
493C22×D4C22×D6111yescharacteristic
494C23×C4—1221no—
495C23×C4—1221no—
496C23×C4C22×D6111yescharacteristic
497C23×C4C22×D6111yescharacteristic
498C2×SD16—1222no—
499C2×SD16—2441no—
500C2×SD16—2441no—
501C2×D8—1222no—
502C2×D8—2441no—
503C2×D8—2441no—
504C22×C8—611no—
505C22×C8—611no—
506C22×C8—611no—
507C22×C8—611no—
508#126—1228no—
509#125—614no—
510#125—1222no—
511#124—22no—
512#124—22no—
513#123—1228no—
514C22⋊Q8—22no—
515C22⋊Q8—22no—
516C22⋊Q8—41no—
517C22⋊Q8—41no—
518#121—22no—
519#121—22no—
520#121—41no—
521#121—41no—
522#121—1222no—
523#121—1222no—
524#121—1222no—
525#121—1222no—
526#121—1228no—
527C4×D4—22no—
528C4×D4—22no—
529C4×D4—614no—
530C4×D4—1228no—
531C4×D4—1222no—
532#117—1222no—
533#117—1222no—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—611no—
537C2×C4⋊C4—611no—
538C2×C4⋊C4—611no—
539C2×C4⋊C4—1222no—
540C2×C4⋊C4—1222no—
541C2×C4⋊C4—1221no—
542C2×C4⋊C4—1221no—
543C2×C4⋊C4—1221no—
544C2×C4⋊C4C22⋊D6111yescharacteristic
545C2×C4⋊C4C22×D6111yescharacteristic
546C2×C4⋊C4C22×D6111yescharacteristic
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—21no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—1221no—
554C2×C22⋊C4—1221no—
555C2×C22⋊C4—1221no—
556C2×C22⋊C4—1221no—
557C2×C22⋊C4C22⋊D6111yescharacteristic
558C2×C22⋊C4C22⋊D6111yescharacteristic
559C2×C42—21no—
560C2×C42—1221no—
561C2×C42C22×D6111yescharacteristic
562C4⋊C8—1222no—
563#103—1222no—
564#103—1222no—
565#103—1222no—
566#102—1222no—
567#102—1222no—
568#102—1222no—
569#102—1222no—
570#102—1222no—
571C22⋊C8—2441no—
572C22⋊C8—2441no—
573C22⋊C8—2441no—
574C22⋊C8—2441no—
575C4×C8—1222no—
576#95—21no—
577C24—21no—
578C24—1221no—
579C24C2×C22⋊D6111yescharacteristic
580C24C2×C22⋊D6111yescharacteristic
581C2×Q8—21no—
582C2×Q8—21no—
583C2×Q8—21no—
584C2×Q8—21no—
585C2×Q8—21no—
586C2×Q8—21no—
587C2×D4—22no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—22no—
595C2×D4—41no—
596C2×D4—42no—
597C2×D4—42no—
598C2×D4—42no—
599C2×D4—42no—
600C2×D4—81no—
601C2×D4—81no—
602C2×D4—612no—
603C2×D4—1224no—
604C2×D4—1224no—
605C2×D4—1221no—
606C2×D4—1221no—
607C2×D4—1221no—
608C2×D4—1221no—
609C2×D4—1221no—
610C2×D4—4881no—
611C2×D4—4881no—
612C2×D4—2442no—
613C2×D4—2442no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—1224no—
630C22×C4—1221no—
631C22×C4—1221no—
632C22×C4—1221no—
633C22×C4—1224no—
634C22×C4—4881no—
635C22×C4—4881no—
636C22×C4—4881no—
637C22×C4—4881no—
638C22×C4C2×C22⋊D6111yescharacteristic
639C22×C4C2×C22⋊D6111yescharacteristic
640C22×C4C2×C22⋊D6111yescharacteristic
641C22×C4C2×C22⋊D6111yescharacteristic
642C22×C4C23×D6111yescharacteristic
643SD16—2444no—
644D8—2444no—
645C2×C8—1221no—
646C2×C8—1221no—
647C2×C8—1221no—
648C2×C8—1221no—
649C2×C8—1221no—
650C2×C8—1221no—
651C2×C8—1221no—
652C2×C8—1221no—
653C2×C8—1221no—
654C2×C8—1221no—
655C2×C8—1221no—
656C2×C8—1221no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—22no—
660C4⋊C4—42no—
661C4⋊C4—42no—
662C4⋊C4—612no—
663C4⋊C4—612no—
664C4⋊C4—612no—
665C4⋊C4—1224no—
666C4⋊C4—1221no—
667C4⋊C4—1221no—
668C4⋊C4—1221no—
669C4⋊C4—1224no—
670C4⋊C4—1224no—
671C4⋊C4#1175822412yes—
672C4⋊C4#1175822412yes—
673C22⋊C4—22no—
674C22⋊C4—22no—
675C22⋊C4—42no—
676C22⋊C4—42no—
677C22⋊C4—42no—
678C22⋊C4—42no—
679C22⋊C4—42no—
680C22⋊C4—42no—
681C22⋊C4—1224no—
682C22⋊C4—1224no—
683C22⋊C4—1224no—
684C22⋊C4—1224no—
685C42—81no—
686C42—1224no—
687C42D4×D6112yes—
688C42D4×D6112yes—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—41no—
703C23—41no—
704C23—41no—
705C23—41no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23—1222no—
710C23—2441no—
711C23—2441no—
712C23—2441no—
713C23—2441no—
714C23—2441no—
715C23—2441no—
716C23#1451979712yes—
717C23C22×C22⋊D6111yescharacteristic
718Q8—41no—
719Q8—41no—
720Q8—41no—
721Q8—41no—
722D4—44no—
723D4—41no—
724D4—41no—
725D4—41no—
726D4—41no—
727D4—84no—
728D4—84no—
729D4—1222no—
730D4—1222no—
731D4—4884no—
732D4—2448no—
733D4—2441no—
734D4—2441no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—1222no—
763C2×C4—1222no—
764C2×C4—1222no—
765C2×C4—4884no—
766C2×C4—4884no—
767C2×C4—2441no—
768C2×C4—2441no—
769C2×C4—2441no—
770C2×C4—2441no—
771C2×C4—2441no—
772C2×C4—2441no—
773C2×C4#1451974512yes—
774C2×C4#1451974512yes—
775C2×C4C2×D4×D6111yescharacteristic
776C2×C4C2×D4×D6111yescharacteristic
777C2×C4C2×#1175822411yescharacteristic
778C2×C4C2×#1175822411yescharacteristic
779C2×C4#1451982211yescharacteristic
780C2×C4#1451982211yescharacteristic
781C8—2441no—
782C8—2441no—
783C8—2441no—
784C8—2441no—
785C22—22no—
786C22—22no—
787C22—22no—
788C22—41no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—41no—
796C22—41no—
797C22—41no—
798C22—41no—
799C22—81no—
800C22—81no—
801C22—81no—
802C22—81no—
803C22—81no—
804C22—81no—
805C22—81no—
806C22—4881no—
807C22—4881no—
808C22—4881no—
809C22—4881no—
810C22—2442no—
811C22—2442no—
812C22—2442no—
813C22C2×#1451974511yescharacteristic
814C22#1684040611yescharacteristic
815C22#1684040611yescharacteristic
816C22C2×#1451979711yescharacteristic
817C22#1684056011yescharacteristic
818C22#1684056511yescharacteristic
819C22#1684057011yescharacteristic
820C4—22no—
821C4—22no—
822C4—42no—
823C4—42no—
824C4—41no—
825C4—41no—
826C4—81no—
827C4—2442no—
828C4—2442no—
829C4—2442no—
830C4#1684031011yescharacteristic
831C4#1684032511yescharacteristic
832C4#1684043211yescharacteristic
833C4#1684043211yescharacteristic
834C2—42no—
835C2—81no—
836C2—161no—
837C2—4882no—
838C2#2144943511yescharacteristic
839C2#2145503511yescharacteristic
840C2#2145512011yescharacteristic
841C2#2145766911yescharacteristic
842C2#2145772111yescharacteristic
843C2#2145802011yescharacteristic
844C2#2145807211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2540C2
socleC23×C61C22×D4
hypercenter#2540D61
hypocenterC61#25575
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2540

Complements

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

NH ≅ G/Ntype
1. C2×#16840458C2semidirect
2. C2×#16840116C2semidirect
3. C2×#16839974C2semidirect
4. #21446820C2semidirect
5. #21446820C2semidirect
6. #21446815C2semidirect
7. #21446815C2semidirect
8. #21446776C2semidirect
9. #21446614C2semidirect
10. #21446142C2semidirect
11. #21446137C2semidirect
12. #21446132C2semidirect
13. #21446127C2semidirect
14. C4×#14519697C2semidirect
15. C61×#2540C2semidirect
80. #14519769D4semidirect
88. C4×D244D4semidirect
415. #2540D61semidirect
485. C61#25575semidirect

Maximal subgroups

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

subgroupindex
C2×#168404582
C2×#168401162
C2×#168399742
#214468202
#214468152
#214467762
#214466142
#214461422
#214461372
#214461322
#214461272
C4×#145196972
C61×#25402
#2557561