Finite Group Databasebeta

← #29723873

Subgroups — #29723873

Order 15616.

1156 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839913C211yesmaximal, characteristic
2C2×C4×#11758200C211yesmaximal, characteristic, complemented
3#21449344C211yesmaximal, characteristic, complemented
4#21447352C211yesmaximal, characteristic, complemented
5#21447255C211yesmaximal, characteristic, complemented
6#21447136C211yesmaximal, characteristic, complemented
7#21447015C211yesmaximal, characteristic, complemented
8#21446505C211yesmaximal, characteristic, complemented
9#21446427C211yesmaximal, characteristic, complemented
10#21446177C211yesmaximal, characteristic, complemented
11#21446153C211yesmaximal, characteristic, complemented
12#21446080C211yesmaximal, characteristic, complemented
13#21445819C211yesmaximal, characteristic, complemented
14#21445750C211yesmaximal, characteristic
15D4×C22⋊C4×C61C211yesmaximal, characteristic
16C22×#11758200C2211yescharacteristic
17C22×#11758200C2211yescharacteristic
18C2×#14519756C2211yescharacteristic
19C2×C4×Dic122C2211yescharacteristic, complemented
20#16839913—24no—
21C4×#11758200—24no—
22C2×#14519708C2211yescharacteristic, complemented
23C2×#14519708C2211yescharacteristic, complemented
24C2×C4⋊#92418C2211yescharacteristic, complemented
25C2×#14519700C2211yescharacteristic, complemented
26C2×#14519700C2211yescharacteristic, complemented
27C2×#14519698C2211yescharacteristic
28C2×#14519698C2211yescharacteristic
29C2×#14519698C2211yescharacteristic
30C2×#14519698C2211yescharacteristic
31C2×#14519698C2211yescharacteristic
32C2×#14519698C2211yescharacteristic
33C2×C22⋊#92418C2211yescharacteristic
34C2×C22⋊#92418C2211yescharacteristic
35C2×C4×#92418C2211yescharacteristic, complemented
36#16839698—21no—
37#16839696—21no—
38#16839668C2211yescharacteristic, complemented
39#16839660C2211yescharacteristic, complemented
40#16839655—21no—
41#16839645—21no—
42#16839632C2211yescharacteristic, complemented
43#16839622C2211yescharacteristic
44#16839524C2211yescharacteristic, complemented
45#16839524C2211yescharacteristic, complemented
46#16839524C2211yescharacteristic, complemented
47#16839524C2211yescharacteristic, complemented
48#16839517C2211yescharacteristic, complemented
49#16839517C2211yescharacteristic, complemented
50C23×D4×C61C2211yescharacteristic
51C2×C4×D4×C61C2211yescharacteristic
52C2×C4×D4×C61C2211yescharacteristic
53C22×C22⋊C4×C61—21no—
54C61×#390C2211yescharacteristic
55C61×#390C2211yescharacteristic
56C61×#386—21no—
57C61×#386—21no—
58C61×#380C2211yescharacteristic
59C61×#379—21no—
60C4×C22⋊C4×C61C2211yescharacteristic
61C22×Dic122C2311yescharacteristic
62C2×#11758200—22no—
63C2×#11758200—22no—
64C2×#11758200—22no—
65C2×#11758200—22no—
66C2×#11758200—41no—
67C2×#11758200D414yes—
68C22×#92418C2311yescharacteristic
69C22×#92418C2311yescharacteristic
70C22×#92418C2311yescharacteristic
71C22×#92418C2311yescharacteristic
72#14519756—22no—
73#14519756—41no—
74C4×Dic122—22no—
75C4×Dic122—41no—
76C2×C4⋊Dic61—21no—
77C2×C4⋊Dic61—21no—
78C2×C4⋊Dic61C2311yescharacteristic
79C2×C4⋊Dic61C2311yescharacteristic
80C2×C4⋊Dic61C2311yescharacteristic
81C2×#11758196—21no—
82C2×#11758196—21no—
83C2×#11758196—21no—
84C2×C22⋊Dic61—21no—
85C2×C22⋊Dic61—21no—
86C2×C4×Dic61—21no—
87#14519708—22no—
88#14519708—41no—
89C4⋊#92418—41no—
90#14519700—22no—
91#14519700—41no—
92#14519698—22no—
93#14519698—22no—
94#14519698—22no—
95#14519698—22no—
96#14519698—22no—
97#14519698—41no—
98C22⋊#92418—22no—
99C22⋊#92418—41no—
100C4×#92418—22no—
101#14519684—21no—
102#14519684—21no—
103#14519684—21no—
104#14519684—21no—
105C25×C61—21no—
106C22×D4×C61—22no—
107C22×D4×C61—22no—
108C22×D4×C61—22no—
109C22×D4×C61—22no—
110C22×D4×C61—21no—
111C22×D4×C61—41no—
112C22×D4×C61—41no—
113C22×D4×C61C2311yescharacteristic
114C22×D4×C61C2311yescharacteristic
115C23×C4×C61—21no—
116C23×C4×C61—21no—
117C23×C4×C61C2311yescharacteristic
118C4×D4×C61—22no—
119C4×D4×C61—22no—
120C4×D4×C61—41no—
121C4×D4×C61—41no—
122C2×C4⋊C4×C61C2311yescharacteristic
123C2×C4⋊C4×C61C2311yescharacteristic
124C2×C22⋊C4×C61—21no—
125C2×C22⋊C4×C61—21no—
126C2×C22⋊C4×C61—21no—
127C2×C22⋊C4×C61—21no—
128C2×C22⋊C4×C61—21no—
129C2×C22⋊C4×C61—21no—
130C2×C22⋊C4×C61—21no—
131C2×C22⋊C4×C61—44no—
132C2×C22⋊C4×C61D411yescharacteristic
133C2×C22⋊C4×C61D411yescharacteristic
134C2×C42×C61C2311yescharacteristic
135C2×C42×C61C2311yescharacteristic
136#95×C61—21no—
137#95×C61D411yescharacteristic
138#95×C61D411yescharacteristic
139C24×C61—21no—
140C24×C61—24no—
141C24×C61—21no—
142C24×C61—42no—
143C24×C61—42no—
144C24×C61—42no—
145C24×C61—42no—
146C24×C61—81no—
147C24×C61—81no—
148C24×C61C2×D411yescharacteristic
149C2×D4×C61—24no—
150C2×D4×C61—21no—
151C2×D4×C61—21no—
152C2×D4×C61—21no—
153C2×D4×C61—21no—
154C2×D4×C61—21no—
155C2×D4×C61—21no—
156C2×D4×C61—21no—
157C2×D4×C61—21no—
158C2×D4×C61—42no—
159C2×D4×C61—42no—
160C2×D4×C61—44no—
161C2×D4×C61—44no—
162C2×D4×C61—44no—
163C2×D4×C61—44no—
164C2×D4×C61C2×D412yes—
165C2×D4×C61#4112yes—
166C2×D4×C61#4112yes—
167C2×D4×C61#4112yes—
168C22×C4×C61—21no—
169C22×C4×C61—21no—
170C22×C4×C61—21no—
171C22×C4×C61—21no—
172C22×C4×C61—21no—
173C22×C4×C61—21no—
174C22×C4×C61—21no—
175C22×C4×C61—21no—
176C22×C4×C61—42no—
177C22×C4×C61—42no—
178C22×C4×C61—42no—
179C22×C4×C61—42no—
180C22×C4×C61—81no—
181C22×C4×C61—81no—
182C22×C4×C61C2×D411yescharacteristic
183C22×C4×C61C2×D411yescharacteristic
184C22×C4×C61C2×D411yescharacteristic
185C22×C4×C61C2×D411yescharacteristic
186C22×C4×C61C2×D411yescharacteristic
187C22×C4×C61C2411yescharacteristic
188C22×Dic61—21no—
189C22×Dic61—21no—
190C22×Dic61—21no—
191C22×Dic61—21no—
192C2×Dic122—21no—
193C2×Dic122—21no—
194C2×Dic122—21no—
195C2×Dic122—21no—
196C2×Dic122—21no—
197C2×Dic122C2×D412yes—
198C4⋊C4×C61—21no—
199C4⋊C4×C61—21no—
200C4⋊C4×C61—21no—
201C4⋊C4×C61—21no—
202C22⋊C4×C61—41no—
203C22⋊C4×C61—42no—
204C22⋊C4×C61—42no—
205C22⋊C4×C61—42no—
206C22⋊C4×C61—42no—
207C22⋊C4×C61—42no—
208C22⋊C4×C61—81no—
209C22⋊C4×C61—81no—
210C22⋊C4×C61SD1614yescomplemented
211C42×C61—21no—
212C42×C61—21no—
213C42×C61—21no—
214C42×C61—21no—
215C22⋊Dic61—42no—
216C22⋊Dic61—81no—
217#11758200—28no—
218#11758200—44no—
219C4⋊Dic61—21no—
220C4⋊Dic61—21no—
221C4⋊Dic61—21no—
222C4⋊Dic61—21no—
223C4⋊Dic61—21no—
224C4⋊Dic61—21no—
225C4⋊Dic61—42no—
226C4⋊Dic61—81no—
227#11758196—42no—
228#11758196—42no—
229#11758196—81no—
230C4×Dic61—42no—
231C2×#92418—21no—
232C2×#92418—21no—
233C2×#92418—21no—
234C2×#92418—21no—
235C2×#92418—21no—
236C2×#92418—21no—
237C2×#92418—21no—
238C2×#92418—21no—
239C2×#92418—21no—
240C2×#92418—21no—
241C2×#92418—21no—
242C2×#92418C2×D412yes—
243C23×C61—21no—
244C23×C61—22no—
245C23×C61—21no—
246C23×C61—22no—
247C23×C61—22no—
248C23×C61—21no—
249C23×C61—21no—
250C23×C61—21no—
251C23×C61—21no—
252C23×C61—22no—
253C23×C61—48no—
254C23×C61—48no—
255C23×C61—41no—
256C23×C61—41no—
257C23×C61—41no—
258C23×C61—41no—
259C23×C61—41no—
260C23×C61—41no—
261C23×C61—41no—
262C23×C61—41no—
263C23×C61—41no—
264C23×C61—41no—
265C23×C61—84no—
266C23×C61—84no—
267C23×C61—84no—
268C23×C61—84no—
269C23×C61—84no—
270C23×C61C2×SD1612yes—
271C23×C61C22×D411yescharacteristic
272D4×C61—22no—
273D4×C61—22no—
274D4×C61—22no—
275D4×C61—22no—
276D4×C61—22no—
277D4×C61—48no—
278D4×C61—41no—
279D4×C61—41no—
280D4×C61#12314yes—
281C2×C4×C61—21no—
282C2×C4×C61—21no—
283C2×C4×C61—21no—
284C2×C4×C61—21no—
285C2×C4×C61—21no—
286C2×C4×C61—21no—
287C2×C4×C61—21no—
288C2×C4×C61—21no—
289C2×C4×C61—21no—
290C2×C4×C61—21no—
291C2×C4×C61—21no—
292C2×C4×C61—21no—
293C2×C4×C61—21no—
294C2×C4×C61—41no—
295C2×C4×C61—41no—
296C2×C4×C61—41no—
297C2×C4×C61—41no—
298C2×C4×C61—41no—
299C2×C4×C61—41no—
300C2×C4×C61—41no—
301C2×C4×C61—41no—
302C2×C4×C61—41no—
303C2×C4×C61—41no—
304C2×C4×C61—84no—
305C2×C4×C61—84no—
306C2×C4×C61C2×SD1612yes—
307C2×C4×C61C2×SD1612yes—
308C2×C4×C61C22×D411yescharacteristic
309C2×C4×C61C2×#4111yescharacteristic
310C2×C4×C61C2×#4111yescharacteristic
311C2×C4×C61C2×#4111yescharacteristic
312C2×C4×C61H(5,𝔽2)11yescharacteristic
313C2×C4×C61H(5,𝔽2)11yescharacteristic
314C2×Dic61—22no—
315C2×Dic61—41no—
316C2×Dic61—41no—
317C2×Dic61—41no—
318C2×Dic61—41no—
319C2×Dic61—41no—
320C2×Dic61—41no—
321C2×Dic61—41no—
322C2×Dic61—41no—
323C2×Dic61—41no—
324C2×Dic61—41no—
325C2×Dic61—41no—
326Dic122—22no—
327Dic122—22no—
328Dic122—41no—
329Dic122—41no—
330#92418—22no—
331#92418—41no—
332#92418—41no—
333#92418—41no—
334#24901—611nomaximal, Sylow
335C22×C61—22no—
336C22×C61—24no—
337C22×C61—22no—
338C22×C61—22no—
339C22×C61—42no—
340C22×C61—41no—
341C22×C61—42no—
342C22×C61—41no—
343C22×C61—41no—
344C22×C61—42no—
345C22×C61—42no—
346C22×C61—42no—
347C22×C61—41no—
348C22×C61—42no—
349C22×C61—42no—
350C22×C61—42no—
351C22×C61—42no—
352C22×C61—816no—
353C22×C61—81no—
354C22×C61—81no—
355C22×C61—81no—
356C22×C61—81no—
357C22×C61#52511yescharacteristic
358C22×C61D4211yescharacteristic
359C22×C61#54611yescharacteristic
360C22×C61C22×SD1611yescharacteristic
361C22×C61#57511yescharacteristic
362C22×C61#57611yescharacteristic
363C22×C61#57711yescharacteristic
364C4×C61—22no—
365C4×C61—22no—
366C4×C61—41no—
367C4×C61—41no—
368C4×C61—41no—
369C4×C61—81no—
370C4×C61—81no—
371C4×C61C2×#12311yescharacteristic
372C4×C61#53811yescharacteristic
373C4×C61#54611yescharacteristic
374C4×C61#55111yescharacteristic
375Dic61—42no—
376Dic61—81no—
377Dic61—81no—
378Dic61—81no—
379C2×#450—611no—
380C2×C4×SD16—611no—
381#2423—611no—
382D4×C22⋊C4D6111yescharacteristic
383#2094—611no—
384#2077—611no—
385#2055—611no—
386#2035—611no—
387#1934—611no—
388#1923—611no—
389#1880—611no—
390#1877—611no—
391#1864—611no—
392#1802—611no—
393#1786—611no—
394C2×C61—42no—
395C2×C61—44no—
396C2×C61—82no—
397C2×C61#241811yescharacteristic
398C2×C61#310111yescharacteristic
399C2×C61#311811yescharacteristic
400C2×C61#326811yescharacteristic
401C2×C61D4×SD1611yescharacteristic
402C2×C61#329511yescharacteristic
403C2×C61#332311yescharacteristic
404C23×D4C2×D6111yescharacteristic
405C22×SD16—611no—
406C22×SD16—611no—
407C2×C22⋊Q8—611no—
408C2×C4×Q8—611no—
409C2×C4×D4C2×D6111yescharacteristic
410C2×C4×D4C2×D6111yescharacteristic
411C22×C22⋊C4—21no—
412#450—1224no—
413C4×SD16—1224no—
414C2×#106—611no—
415C2×#106—611no—
416C2×C4⋊C8—611no—
417C2×#103—611no—
418C2×#103—611no—
419C2×#102—611no—
420C2×#102—611no—
421C2×#102—611no—
422C2×#102—611no—
423C2×#102—611no—
424C2×#102—611no—
425C2×C22⋊C8—611no—
426C2×C22⋊C8—611no—
427C2×C4×C8—611no—
428#399—1221no—
429#398—1221no—
430#391—611no—
431#390C2×D6111yescharacteristic
432#390C2×D6111yescharacteristic
433#389—611no—
434#388—1221no—
435#387—1221no—
436#386—21no—
437#386—21no—
438#384—611no—
439#380—611no—
440#380C2×D6111yescharacteristic
441#379—21no—
442C4×C22⋊C4C2×D6111yescharacteristic
443#340—611no—
444#340—611no—
445#340—611no—
446#340—611no—
447#336—611no—
448#336—611no—
449C61#2490111yescharacteristic, complemented, Sylow
450C25—21no—
451C22×Q8—611no—
452C22×D4—22no—
453C22×D4—22no—
454C22×D4—22no—
455C22×D4—22no—
456C22×D4—21no—
457C22×D4—41no—
458C22×D4—41no—
459C22×D4C22×D6111yescharacteristic
460C22×D4C22×D6111yescharacteristic
461C23×C4—21no—
462C23×C4—21no—
463C23×C4C22×D6111yescharacteristic
464C2×SD16—614no—
465C2×SD16—1222no—
466C2×SD16—1222no—
467C2×SD16—1222no—
468C2×SD16—1222no—
469C2×SD16—2441no—
470C22×C8—611no—
471C22×C8—611no—
472C22×C8—611no—
473C22×C8—611no—
474C22⋊Q8—1222no—
475C22⋊Q8—2441no—
476C4×Q8—1222no—
477C4×Q8—2441no—
478C4×D4—22no—
479C4×D4—22no—
480C4×D4—41no—
481C4×D4—41no—
482C2×C4⋊C4—611no—
483C2×C4⋊C4—611no—
484C2×C4⋊C4—611no—
485C2×C4⋊C4—1221no—
486C2×C4⋊C4—1221no—
487C2×C4⋊C4—1221no—
488C2×C4⋊C4—1221no—
489C2×C4⋊C4—1221no—
490C2×C4⋊C4C22×D6111yescharacteristic
491C2×C4⋊C4C22×D6111yescharacteristic
492C2×C22⋊C4—21no—
493C2×C22⋊C4—21no—
494C2×C22⋊C4—21no—
495C2×C22⋊C4—21no—
496C2×C22⋊C4—21no—
497C2×C22⋊C4—21no—
498C2×C22⋊C4—21no—
499C2×C22⋊C4—44no—
500C2×C22⋊C4—1221no—
501C2×C22⋊C4—1221no—
502C2×C22⋊C4C22⋊D6111yescharacteristic
503C2×C22⋊C4C22⋊D6111yescharacteristic
504C2×C42—1221no—
505C2×C42C22×D6111yescharacteristic
506C2×C42C22×D6111yescharacteristic
507#106—1222no—
508#106—2441no—
509C4⋊C8—2441no—
510#103—1222no—
511#103—2441no—
512#102—1222no—
513#102—1222no—
514#102—1222no—
515#102—1222no—
516#102—1222no—
517#102—2441no—
518C22⋊C8—1222no—
519C22⋊C8—2441no—
520C4×C8—1222no—
521#95—21no—
522#95—1221no—
523#95—1221no—
524#95—1221no—
525#95—1221no—
526#95C22⋊D6111yescharacteristic
527#95C22⋊D6111yescharacteristic
528C24—21no—
529C24—24no—
530C24—21no—
531C24—42no—
532C24—42no—
533C24—42no—
534C24—42no—
535C24—81no—
536C24—81no—
537C24C2×C22⋊D6111yescharacteristic
538C2×Q8—612no—
539C2×Q8—1221no—
540C2×Q8—1221no—
541C2×Q8—1221no—
542C2×Q8—1221no—
543C2×Q8—1221no—
544C2×D4—24no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—42no—
554C2×D4—42no—
555C2×D4—44no—
556C2×D4—44no—
557C2×D4—44no—
558C2×D4—44no—
559C2×D4#1175822212yes—
560C2×D4#1175822212yes—
561C2×D4D4×D6112yes—
562C2×D4#1175822412yes—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—42no—
572C22×C4—42no—
573C22×C4—42no—
574C22×C4—42no—
575C22×C4—81no—
576C22×C4—81no—
577C22×C4—1221no—
578C22×C4—1221no—
579C22×C4—1221no—
580C22×C4—1221no—
581C22×C4C2×C22⋊D6111yescharacteristic
582C22×C4C2×C22⋊D6111yescharacteristic
583C22×C4C2×C22⋊D6111yescharacteristic
584C22×C4C2×C22⋊D6111yescharacteristic
585C22×C4C2×C22⋊D6111yescharacteristic
586C22×C4C23×D6111yescharacteristic
587SD16—1228no—
588SD16—2444no—
589C2×C8—612no—
590C2×C8—1221no—
591C2×C8—1221no—
592C2×C8—1221no—
593C2×C8—1221no—
594C2×C8—1221no—
595C2×C8—1221no—
596C2×C8—1221no—
597C2×C8—1221no—
598C2×C8—1221no—
599C2×C8—1221no—
600C2×C8—1221no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—1221no—
606C4⋊C4—1221no—
607C4⋊C4—1221no—
608C4⋊C4—1221no—
609C4⋊C4—1221no—
610C4⋊C4—1221no—
611C4⋊C4—4881no—
612C4⋊C4—4881no—
613C4⋊C4—2442no—
614C4⋊C4—2442no—
615C4⋊C4—2442no—
616C22⋊C4—41no—
617C22⋊C4—42no—
618C22⋊C4—42no—
619C22⋊C4—42no—
620C22⋊C4—42no—
621C22⋊C4—42no—
622C22⋊C4—81no—
623C22⋊C4—81no—
624C22⋊C4—4881no—
625C22⋊C4—2442no—
626C22⋊C4#1175820014yescomplemented
627C42—21no—
628C42—21no—
629C42—21no—
630C42—21no—
631C42—2442no—
632C23—21no—
633C23—22no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—22no—
638C23—21no—
639C23—22no—
640C23—21no—
641C23—22no—
642C23—48no—
643C23—48no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—84no—
655C23—84no—
656C23—84no—
657C23—84no—
658C23—84no—
659C23C2×#1175820012yes—
660C23C22×C22⋊D6111yescharacteristic
661Q8—1222no—
662Q8—1222no—
663Q8—2441no—
664Q8—2441no—
665D4—22no—
666D4—22no—
667D4—22no—
668D4—22no—
669D4—22no—
670D4—48no—
671D4—41no—
672D4—41no—
673D4#1451975914yes—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—84no—
698C2×C4—84no—
699C2×C4—1222no—
700C2×C4—2441no—
701C2×C4—2441no—
702C2×C4—2441no—
703C2×C4—2441no—
704C2×C4—2441no—
705C2×C4—2441no—
706C2×C4—2441no—
707C2×C4—2441no—
708C2×C4—2441no—
709C2×C4—2441no—
710C2×C4—2441no—
711C2×C4C2×#1175820012yes—
712C2×C4C2×#1175820012yes—
713C2×C4C2×D4×D6111yescharacteristic
714C2×C4C2×#1175822411yescharacteristic
715C2×C4C2×#1175822211yescharacteristic
716C2×C4C2×#1175822211yescharacteristic
717C2×C4#1451982211yescharacteristic
718C2×C4#1451982211yescharacteristic
719C8—1222no—
720C8—2441no—
721C8—2441no—
722C8—2441no—
723C22—24no—
724C22—22no—
725C22—22no—
726C22—22no—
727C22—41no—
728C22—42no—
729C22—41no—
730C22—42no—
731C22—41no—
732C22—42no—
733C22—41no—
734C22—42no—
735C22—42no—
736C22—42no—
737C22—42no—
738C22—42no—
739C22—42no—
740C22—816no—
741C22—81no—
742C22—81no—
743C22—81no—
744C22—81no—
745C22#1684027311yescharacteristic
746C22D4×C22⋊D6111yescharacteristic
747C22#1684040611yescharacteristic
748C22C22×#1175820011yescharacteristic
749C22#1684056011yescharacteristic
750C22#1684056511yescharacteristic
751C22#1684057311yescharacteristic
752C4—22no—
753C4—22no—
754C4—41no—
755C4—41no—
756C4—41no—
757C4—81no—
758C4—81no—
759C4—4881no—
760C4—4881no—
761C4—4881no—
762C4—2442no—
763C4C2×#1451975911yescharacteristic
764C4#1684035011yescharacteristic
765C4#1684040211yescharacteristic
766C4#1684043811yescharacteristic
767C2—42no—
768C2—44no—
769C2—82no—
770C2#2144928111yescharacteristic
771C2#2145582711yescharacteristic
772C2#2145600311yescharacteristic
773C2#2145735511yescharacteristic
774C2D4×#1175820011yescharacteristic
775C2#2145764311yescharacteristic
776C2#2145803511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingD4×C22⋊C4×C61C2
socleC23×C61C22×D4
prime radicalC23×D4×C61C22
hypercenterD4×C22⋊C4D61
hypocenterC61#24901
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ D4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×#11758200C2semidirect
3. #21449344C2semidirect
4. #21447352C2semidirect
5. #21447255C2semidirect
6. #21447136C2semidirect
7. #21447015C2semidirect
8. #21446505C2semidirect
9. #21446427C2semidirect
10. #21446177C2semidirect
11. #21446153C2semidirect
12. #21446080C2semidirect
13. #21445819C2semidirect
19. C2×C4×Dic122C22semidirect
22. C2×#14519708C22semidirect
23. C2×#14519708C22semidirect
24. C2×C4⋊#92418C22semidirect
25. C2×#14519700C22semidirect
26. C2×#14519700C22semidirect
35. C2×C4×#92418C22semidirect
38. #16839668C22semidirect
39. #16839660C22semidirect
42. #16839632C22semidirect
44. #16839524C22semidirect
45. #16839524C22semidirect
46. #16839524C22semidirect
47. #16839524C22semidirect
48. #16839517C22semidirect
49. #16839517C22semidirect
210. C22⋊C4×C61SD16semidirect
449. C61#24901semidirect
626. C22⋊C4#11758200semidirect

Maximal subgroups

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

subgroupindex
C2×#168399132
C2×C4×#117582002
#214493442
#214473522
#214472552
#214471362
#214470152
#214465052
#214464272
#214461772
#214461532
#214460802
#214458192
#214457502
D4×C22⋊C4×C612
#2490161