Finite Group Databasebeta

← #29733265

Subgroups — #29733265

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×#16840119C211yesmaximal, characteristic, complemented
2C2×#16839977C211yesmaximal, characteristic, complemented
3#21450758C211yesmaximal, characteristic, complemented
4#21446822C211yesmaximal, characteristic, complemented
5#21446822C211yesmaximal, characteristic, complemented
6#21446815C211yesmaximal, characteristic, complemented
7#21446815C211yesmaximal, characteristic, complemented
8#21446777C211yesmaximal, characteristic, complemented
9#21446614C211yesmaximal, characteristic, complemented
10#21446141C211yesmaximal, characteristic, complemented
11#21446136C211yesmaximal, characteristic, complemented
12#21446131C211yesmaximal, characteristic, complemented
13#21446126C211yesmaximal, characteristic, complemented
14C4×#14519698C211yesmaximal, characteristic, complemented
15C2×C61×#553C211yesmaximal, characteristic, complemented
16C22×#11758200C2211yescharacteristic
17C22×#11758199C2211yescharacteristic
18C2×#14519765C2211yescharacteristic
19C2×#14519756C2211yescharacteristic
20C2×#14519756C2211yescharacteristic
21C2×#14519751C2211yescharacteristic
22C2×#14519751C2211yescharacteristic
23#16840119—24no—
24#16839977—24no—
25C2×C4⋊#92418C2211yescharacteristic
26C2×#14519700C2211yescharacteristic
27C2×#14519700C2211yescharacteristic
28C2×#14519700C2211yescharacteristic
29C2×#14519698C2211yescharacteristic
30C2×#14519698C2211yescharacteristic
31C2×#14519697C2211yescharacteristic
32C2×#14519697C2211yescharacteristic
33C2×#14519697C2211yescharacteristic
34C2×C22⋊#92418C2211yescharacteristic
35C2×C22⋊#92418C2211yescharacteristic
36C2×C22⋊#92418C2211yescharacteristic
37C2×C22⋊#92418C2211yescharacteristic
38C2×C4×#92418C2211yescharacteristic
39#16839697—21no—
40#16839670—21no—
41#16839662—21no—
42#16839662—21no—
43C4×C4⋊Dic61C2211yescharacteristic
44#16839524C2211yescharacteristic
45#16839524C2211yescharacteristic
46#16839524C2211yescharacteristic
47#16839524C2211yescharacteristic
48#16839524C2211yescharacteristic
49#16839524C2211yescharacteristic
50C61×#553—24no—
51C61×#553—24no—
52C2×#126×C61—21no—
53C2×#125×C61C2211yescharacteristic
54C2×#123×C61—21no—
55C2×#121×C61—21no—
56C2×#121×C61C2211yescharacteristic
57C2×#121×C61C2211yescharacteristic
58C2×C4×D4×C61—21no—
59C2×C4×D4×C61C2211yescharacteristic
60C2×C4×D4×C61C2211yescharacteristic
61C2×#117×C61C2211yescharacteristic
62C22×C4⋊C4×C61C2211yescharacteristic
63C22×Dic122C2311yescharacteristic
64C22×D244C2311yescharacteristic
65C22×C22⋊D61—21no—
66C22×C22⋊D61—21no—
67C2×#11758200—22no—
68C2×#11758200—41no—
69C2×#11758200—41no—
70C2×#11758199—22no—
71C2×#11758199—41no—
72C2×#11758199—41no—
73C22×#92418C2311yescharacteristic
74C22×#92418C2311yescharacteristic
75C22×#92418C2311yescharacteristic
76C22×#92418C2311yescharacteristic
77#14519765—22no—
78#14519765—22no—
79#14519756—22no—
80#14519756—22no—
81#14519756—41no—
82#14519756—41no—
83#14519751—22no—
84#14519751—22no—
85#14519751—41no—
86#14519751—41no—
87C2×C4⋊Dic61C2311yescharacteristic
88C2×C4⋊Dic61C2311yescharacteristic
89C2×#11758196—21no—
90C2×#11758196—21no—
91C2×C22⋊Dic61—21no—
92C2×C22⋊Dic61—21no—
93C2×#11758198—21no—
94C2×#11758198—21no—
95C2×#11758198—21no—
96C2×#11758198—21no—
97C2×C4×Dic61—21no—
98C4⋊#92418—22no—
99#14519700—22no—
100#14519700—22no—
101#14519700—22no—
102#14519698—22no—
103#14519698—22no—
104#14519697—22no—
105#14519697—22no—
106#14519697—22no—
107C22⋊#92418—41no—
108C22⋊#92418—41no—
109C22⋊#92418—41no—
110C22⋊#92418—41no—
111C4×#92418—22no—
112#14519684—21no—
113C22×D4×C61—21no—
114C22×D4×C61—21no—
115C22×D4×C61D411yescharacteristic
116C22×D4×C61C2311yescharacteristic
117C23×C4×C61—21no—
118C23×C4×C61—21no—
119C23×C4×C61C2311yescharacteristic
120C23×C4×C61C2311yescharacteristic
121#126×C61—28no—
122#125×C61—22no—
123#125×C61D414yescomplemented
124#123×C61—28no—
125#121×C61—28no—
126#121×C61—22no—
127#121×C61—22no—
128#121×C61—22no—
129#121×C61—22no—
130C4×D4×C61—28no—
131C4×D4×C61—22no—
132C4×D4×C61—22no—
133C4×D4×C61—22no—
134C4×D4×C61D414yescomplemented
135#117×C61—22no—
136#117×C61—22no—
137C2×C4⋊C4×C61—21no—
138C2×C4⋊C4×C61—21no—
139C2×C4⋊C4×C61—21no—
140C2×C4⋊C4×C61—22no—
141C2×C4⋊C4×C61—22no—
142C2×C4⋊C4×C61D411yescharacteristic
143C2×C4⋊C4×C61C2311yescharacteristic
144C2×C4⋊C4×C61C2311yescharacteristic
145C2×C4⋊C4×C61C2311yescharacteristic
146C2×C22⋊C4×C61—21no—
147C2×C22⋊C4×C61—21no—
148C2×C22⋊C4×C61—21no—
149C2×C22⋊C4×C61—21no—
150C2×C22⋊C4×C61D411yescharacteristic
151C2×C22⋊C4×C61D411yescharacteristic
152C2×C42×C61—21no—
153C2×C42×C61C2311yescharacteristic
154C24×C61—21no—
155C24×C61C2×D411yescharacteristic
156C24×C61C2×D411yescharacteristic
157C23×D61—21no—
158C2×D4×C61—24no—
159C2×D4×C61—22no—
160C2×D4×C61—24no—
161C2×D4×C61—22no—
162C2×D4×C61—21no—
163C2×D4×C61—21no—
164C2×D4×C61—21no—
165C2×D4×C61—21no—
166C2×D4×C61—21no—
167C2×D4×C61—41no—
168C2×D4×C61—42no—
169C2×D4×C61—42no—
170C2×D4×C61—81no—
171C2×D4×C61—81no—
172C2×D4×C61C2×D412yes—
173C22×C4×C61—21no—
174C22×C4×C61—21no—
175C22×C4×C61—21no—
176C22×C4×C61—24no—
177C22×C4×C61—21no—
178C22×C4×C61—21no—
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—24no—
190C22×C4×C61—81no—
191C22×C4×C61—81no—
192C22×C4×C61—81no—
193C22×C4×C61—81no—
194C22×C4×C61C2×D411yescharacteristic
195C22×C4×C61C2×D411yescharacteristic
196C22×C4×C61C2×D411yescharacteristic
197C22×C4×C61C2×D411yescharacteristic
198C22×C4×C61C2411yescharacteristic
199C2×C22⋊D61—42no—
200C2×C22⋊D61—42no—
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—
208C2×D244—21no—
209C2×D244—21no—
210C2×D244—21no—
211C2×D244—21no—
212C2×D244—21no—
213C2×D244—21no—
214C2×Dic122—21no—
215C2×Dic122—21no—
216C2×Dic122—21no—
217C2×Dic122—21no—
218C2×Dic122—21no—
219C2×Dic122—21no—
220C4⋊C4×C61—24no—
221C4⋊C4×C61—24no—
222C4⋊C4×C61—24no—
223C4⋊C4×C61—22no—
224C4⋊C4×C61—21no—
225C4⋊C4×C61—21no—
226C4⋊C4×C61—21no—
227C4⋊C4×C61C2×D412yes—
228C4⋊C4×C61C2×D412yes—
229C4⋊C4×C61C2×D412yes—
230C22⋊C4×C61—24no—
231C22⋊C4×C61—24no—
232C22⋊C4×C61—24no—
233C22⋊C4×C61—24no—
234C22⋊C4×C61—22no—
235C22⋊C4×C61—22no—
236C42×C61—24no—
237C42×C61C2×D412yes—
238C42×C61C2×D412yes—
239C22⋊Dic61—42no—
240C22⋊Dic61—42no—
241#11758200—44no—
242#11758199—44no—
243#11758198—42no—
244#11758198—42no—
245#11758198—42no—
246#11758198—42no—
247C4⋊Dic61—21no—
248C4⋊Dic61—21no—
249C4⋊Dic61#4112yes—
250C4⋊Dic61#4112yes—
251#11758196—42no—
252#11758196—42no—
253C4×Dic61—81no—
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—22no—
274C23×C61—21no—
275C23×C61—21no—
276C23×C61—21no—
277C23×C61—21no—
278C23×C61—21no—
279C23×C61—21no—
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—41no—
289C22×D61—41no—
290C22×D61—41no—
291C22×D61—41no—
292C22×D61—41no—
293C22×D61—41no—
294C22×D61—41no—
295D4×C61—22no—
296D4×C61—22no—
297D4×C61—44no—
298D4×C61—48no—
299D4×C61—41no—
300D4×C61—41no—
301D4×C61—84no—
302C2×C4×C61—21no—
303C2×C4×C61—21no—
304C2×C4×C61—21no—
305C2×C4×C61—21no—
306C2×C4×C61—21no—
307C2×C4×C61—22no—
308C2×C4×C61—22no—
309C2×C4×C61—21no—
310C2×C4×C61—22no—
311C2×C4×C61—21no—
312C2×C4×C61—21no—
313C2×C4×C61—21no—
314C2×C4×C61—21no—
315C2×C4×C61—41no—
316C2×C4×C61—41no—
317C2×C4×C61—41no—
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—84no—
330C2×C4×C61—84no—
331C2×C4×C61#12012yes—
332C2×C4×C61#12012yes—
333C2×C4×C61C22×D411yescharacteristic
334C2×C4×C61C22×D411yescharacteristic
335C2×C4×C61C2×#4111yescharacteristic
336C2×C4×C61C2×#4111yescharacteristic
337C2×C4×C61H(5,𝔽2)11yescharacteristic
338C2×C4×C61H(5,𝔽2)11yescharacteristic
339C22⋊D61—84no—
340C22⋊D61—84no—
341C2×Dic61—22no—
342C2×Dic61—22no—
343C2×Dic61—41no—
344C2×Dic61—41no—
345C2×Dic61—41no—
346C2×Dic61—41no—
347C2×Dic61—41no—
348C2×Dic61—41no—
349C2×Dic61—41no—
350D244—41no—
351D244—41no—
352D244—41no—
353D244—41no—
354Dic122—41no—
355Dic122—41no—
356Dic122—41no—
357Dic122—41no—
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—42no—
372C22×C61—41no—
373C22×C61—42no—
374C22×C61—42no—
375C22×C61—41no—
376C22×C61—41no—
377C22×C61—41no—
378C22×C61—41no—
379C22×C61—41no—
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—81no—
392C2×D61—81no—
393C2×D61—81no—
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—42no—
405C4×C61#53211yescharacteristic
406C4×C61#53511yescharacteristic
407C4×C61#55011yescharacteristic
408C4×C61#55011yescharacteristic
409Dic61—42no—
410Dic61—42no—
411Dic61—81no—
412C2×#553D6111yescharacteristic, complemented
413C2×#488—611no—
414C2×#463—611no—
415#2540—611no—
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—82no—
430C2×C61#243111yescharacteristic
431C2×C61#300211yescharacteristic
432C2×C61#301211yescharacteristic
433C2×C61#329711yescharacteristic
434C2×C61#330111yescharacteristic
435C2×C61#332211yescharacteristic
436C2×C61#332611yescharacteristic
437D61—161no—
438C22×SD16—611no—
439C22×D8—611no—
440#553—24no—
441#553—24no—
442C2×#126—21no—
443C2×#125C2×D6111yescharacteristic
444C2×#124—611no—
445C2×#123—21no—
446C2×C22⋊Q8—611no—
447C2×C22⋊Q8—611no—
448C2×#121—21no—
449C2×#121—611no—
450C2×#121—611no—
451C2×#121C2×D6111yescharacteristic
452C2×#121C2×D6111yescharacteristic
453C2×C4×D4—21no—
454C2×C4×D4C2×D6111yescharacteristic
455C2×C4×D4C2×D6111yescharacteristic
456C2×#117C2×D6111yescharacteristic
457C22×C4⋊C4C2×D6111yescharacteristic
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—1221no—
475#392—1221no—
476#390—1221no—
477#390—1221no—
478C4×C4⋊C4—611no—
479#340—611no—
480#340—611no—
481#340—611no—
482#340—611no—
483#340—611no—
484#340—611no—
485C61#2557511yescharacteristic, complemented, Sylow
486C22×Q8—611no—
487C22×D4—21no—
488C22×D4—21no—
489C22×D4—611no—
490C22×D4—1221no—
491C22×D4—1221no—
492C22×D4C22⋊D6111yescharacteristic
493C22×D4C22×D6111yescharacteristic
494C23×C4—21no—
495C23×C4—21no—
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—28no—
509#125—22no—
510#125C22⋊D6114yescomplemented
511#124—1222no—
512#124—1222no—
513#123—28no—
514C22⋊Q8—1222no—
515C22⋊Q8—1222no—
516C22⋊Q8—2441no—
517C22⋊Q8—2441no—
518#121—28no—
519#121—22no—
520#121—22no—
521#121—22no—
522#121—22no—
523#121—1222no—
524#121—1222no—
525#121—2441no—
526#121—2441no—
527C4×D4—28no—
528C4×D4—22no—
529C4×D4—22no—
530C4×D4—22no—
531C4×D4C22⋊D6114yescomplemented
532#117—22no—
533#117—22no—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4—22no—
538C2×C4⋊C4—22no—
539C2×C4⋊C4—611no—
540C2×C4⋊C4—611no—
541C2×C4⋊C4—1221no—
542C2×C4⋊C4—1221no—
543C2×C4⋊C4C22⋊D6111yescharacteristic
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—1221no—
552C2×C22⋊C4—1221no—
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—1221no—
577C24—21no—
578C24—1221no—
579C24C2×C22⋊D6111yescharacteristic
580C24C2×C22⋊D6111yescharacteristic
581C2×Q8—1221no—
582C2×Q8—1221no—
583C2×Q8—1221no—
584C2×Q8—1221no—
585C2×Q8—1221no—
586C2×Q8—1221no—
587C2×D4—24no—
588C2×D4—22no—
589C2×D4—24no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—22no—
596C2×D4—41no—
597C2×D4—42no—
598C2×D4—42no—
599C2×D4—81no—
600C2×D4—81no—
601C2×D4—1221no—
602C2×D4—1221no—
603C2×D4—1221no—
604C2×D4—1221no—
605C2×D4—1221no—
606C2×D4—1221no—
607C2×D4—4881no—
608C2×D4—4881no—
609C2×D4—2442no—
610C2×D4—2442no—
611C2×D4—2442no—
612C2×D4—2442no—
613C2×D4C2×C22⋊D6112yes—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—24no—
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—21no—
630C22×C4—24no—
631C22×C4—81no—
632C22×C4—81no—
633C22×C4—81no—
634C22×C4—81no—
635C22×C4—1221no—
636C22×C4—1221no—
637C22×C4—1221no—
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—24no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—24no—
662C4⋊C4—24no—
663C4⋊C4—22no—
664C4⋊C4—612no—
665C4⋊C4—612no—
666C4⋊C4—1221no—
667C4⋊C4—1221no—
668C4⋊C4—2442no—
669C4⋊C4—2442no—
670C4⋊C4C2×C22⋊D6112yes—
671C4⋊C4C2×C22⋊D6112yes—
672C4⋊C4C2×C22⋊D6112yes—
673C22⋊C4—24no—
674C22⋊C4—24no—
675C22⋊C4—24no—
676C22⋊C4—24no—
677C22⋊C4—22no—
678C22⋊C4—22no—
679C22⋊C4—2442no—
680C22⋊C4—2442no—
681C22⋊C4—2442no—
682C22⋊C4—2442no—
683C22⋊C4—2442no—
684C22⋊C4—2442no—
685C42—24no—
686C42—4881no—
687C42C2×C22⋊D6112yes—
688C42C2×C22⋊D6112yes—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—22no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—41no—
704C23—41no—
705C23—41no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23—2441no—
710C23—2441no—
711C23—2441no—
712C23—2441no—
713C23—2441no—
714C23—2441no—
715C23—2441no—
716C23#1451979712yes—
717C23C22×C22⋊D6111yescharacteristic
718Q8—2441no—
719Q8—2441no—
720Q8—2441no—
721Q8—2441no—
722D4—22no—
723D4—22no—
724D4—44no—
725D4—48no—
726D4—41no—
727D4—41no—
728D4—84no—
729D4—4884no—
730D4—4884no—
731D4—2441no—
732D4—2441no—
733D4—2441no—
734D4—2441no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—21no—
743C2×C4—22no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—21no—
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—84no—
763C2×C4—84no—
764C2×C4—1222no—
765C2×C4—1222no—
766C2×C4—2441no—
767C2×C4—2441no—
768C2×C4—2441no—
769C2×C4—2441no—
770C2×C4—2441no—
771C2×C4—2441no—
772C2×C4—2441no—
773C2×C4#1451974612yes—
774C2×C4#1451974612yes—
775C2×C4C22×C22⋊D6111yescharacteristic
776C2×C4C22×C22⋊D6111yescharacteristic
777C2×C4#41×D6111yescharacteristic
778C2×C4#41×D6111yescharacteristic
779C2×C4#1451982311yescharacteristic
780C2×C4#1451982311yescharacteristic
781C8—2441no—
782C8—2441no—
783C8—2441no—
784C8—2441no—
785C22—22no—
786C22—22no—
787C22—22no—
788C22—41no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—42no—
793C22—41no—
794C22—41no—
795C22—41no—
796C22—41no—
797C22—41no—
798C22—42no—
799C22—41no—
800C22—42no—
801C22—41no—
802C22—81no—
803C22—81no—
804C22—81no—
805C22—81no—
806C22—4881no—
807C22—4881no—
808C22—4881no—
809C22—4881no—
810C22—4881no—
811C22—4881no—
812C22—4881no—
813C22C2×#1451974611yescharacteristic
814C22#1684040011yescharacteristic
815C22#1684040011yescharacteristic
816C22C2×#1451979711yescharacteristic
817C22#1684056011yescharacteristic
818C22#1684056511yescharacteristic
819C22#1684057311yescharacteristic
820C4—22no—
821C4—22no—
822C4—42no—
823C4—42no—
824C4—42no—
825C4—41no—
826C4—41no—
827C4—4881no—
828C4—2442no—
829C4—2442no—
830C4#1684030811yescharacteristic
831C4#1684032611yescharacteristic
832C4#1684043111yescharacteristic
833C4#1684043111yescharacteristic
834C2—42no—
835C2—81no—
836C2—82no—
837C2—9761no—
838C2#2144943411yescharacteristic
839C2#2145503711yescharacteristic
840C2#2145512311yescharacteristic
841C2#2145766311yescharacteristic
842C2#2145771511yescharacteristic
843C2#2145801411yescharacteristic
844C2#2145806611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#553C2
socleC23×C61C22×D4
hypercenterC2×#553D61
hypocenterC61#25575
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#553

Complements

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

NH ≅ G/Ntype
1. C2×#16840119C2semidirect
2. C2×#16839977C2semidirect
3. #21450758C2semidirect
4. #21446822C2semidirect
5. #21446822C2semidirect
6. #21446815C2semidirect
7. #21446815C2semidirect
8. #21446777C2semidirect
9. #21446614C2semidirect
10. #21446141C2semidirect
11. #21446136C2semidirect
12. #21446131C2semidirect
13. #21446126C2semidirect
14. C4×#14519698C2semidirect
15. C2×C61×#553C2semidirect
123. #125×C61D4semidirect
134. C4×D4×C61D4semidirect
412. C2×#553D61semidirect
485. C61#25575semidirect
510. #125C22⋊D61semidirect
531. C4×D4C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168401192
C2×#168399772
#214507582
#214468222
#214468152
#214467772
#214466142
#214461412
#214461362
#214461312
#214461262
C4×#145196982
C2×C61×#5532
#2557561