Finite Group Databasebeta

← #29700420

Subgroups — #29700420

Order 15616.

1274 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839913C211yesmaximal, characteristic
2C2×#16839859C211yesmaximal, characteristic, complemented
3#21448846C211yesmaximal, characteristic, complemented
4D4×C22⋊Dic61C211yesmaximal, characteristic
5#21446674C211yesmaximal, characteristic, complemented
6#21446513C211yesmaximal, characteristic, complemented
7#21446442C211yesmaximal, characteristic, complemented
8#21446252C211yesmaximal, characteristic, complemented
9#21446171C211yesmaximal, characteristic, complemented
10#21446151C211yesmaximal, characteristic, complemented
11#21446078C211yesmaximal, characteristic, complemented
12#21446018C211yesmaximal, characteristic, complemented
13#102×Dic61C211yesmaximal, characteristic, complemented
14#21445600C211yesmaximal, characteristic, complemented
15C2×C61×#418C211yesmaximal, characteristic
16C22×#11758200C2211yescharacteristic
17C22×#11758200C2211yescharacteristic
18C2×#14519756C2211yescharacteristic
19C2×#14519742C2211yescharacteristic, complemented
20C2×D4×Dic61C2211yescharacteristic
21C2×D4×Dic61C2211yescharacteristic
22C22×C22⋊Dic61—21no—
23#16839913C418yescomplemented
24#16839859—24no—
25C2×#14519710C2211yescharacteristic, complemented
26C2×#14519708C2211yescharacteristic, complemented
27C2×#14519702C2211yescharacteristic, complemented
28C2×#14519702C2211yescharacteristic, complemented
29C2×#14519698C2211yescharacteristic
30C2×#14519698C2211yescharacteristic
31C2×C22⋊#92418C2211yescharacteristic
32C2×#14519687C2211yescharacteristic, complemented
33C2×C8×Dic61C2211yescharacteristic, complemented
34#16839667C2211yescharacteristic, complemented
35#16839665C2211yescharacteristic
36#16839665C2211yescharacteristic
37#16839658C2211yescharacteristic, complemented
38#16839656—21no—
39#16839650—21no—
40#16839646—21no—
41#16839642—21no—
42#16839642—21no—
43#16839622C2211yescharacteristic
44#16839618—21no—
45C4⋊C4×Dic61C2211yescharacteristic, complemented
46C4×#11758196—21no—
47C4×C22⋊Dic61C2211yescharacteristic
48#16839525C2211yescharacteristic, complemented
49#16839525C2211yescharacteristic, complemented
50#16839524C2211yescharacteristic, complemented
51#16839524C2211yescharacteristic, complemented
52#16839516C2211yescharacteristic, complemented
53#16839516C2211yescharacteristic, complemented
54C23×D4×C61C2211yescharacteristic
55C22×M16×C61C2211yescharacteristic
56C2×#117×C61C2211yescharacteristic
57C61×#418—24no—
58C2×#102×C61C2211yescharacteristic
59C2×#102×C61C2211yescharacteristic
60C2×#102×C61C2211yescharacteristic
61C2×#102×C61C2211yescharacteristic
62C22×Dic122C2311yescharacteristic
63C23×Dic61—21no—
64C23×Dic61—21no—
65C2×#11758200—22no—
66C2×#11758200—22no—
67C2×#11758200—41no—
68C2×#11758200—41no—
69C2×#11758200C2×C414yes—
70C2×#11758200C2×C414yescomplemented
71C22×#92418C2311yescharacteristic
72C22×#92418C2311yescharacteristic
73#14519756—22no—
74#14519756C2×C414yescomplemented
75#14519742—22no—
76#14519742—41no—
77D4×Dic61—22no—
78D4×Dic61—22no—
79D4×Dic61—41no—
80D4×Dic61—41no—
81C2×C4⋊Dic61C2311yescharacteristic
82C2×C4⋊Dic61C2311yescharacteristic
83C2×C4⋊Dic61C2311yescharacteristic
84C2×#11758196—21no—
85C2×#11758196—21no—
86C2×#11758196—21no—
87C2×C22⋊Dic61—21no—
88C2×C22⋊Dic61—21no—
89C2×C22⋊Dic61—21no—
90C2×C22⋊Dic61—21no—
91C2×C22⋊Dic61—21no—
92C2×C22⋊Dic61—21no—
93C2×C22⋊Dic61—21no—
94C2×C22⋊Dic61—21no—
95C2×C22⋊Dic61—44no—
96C2×C22⋊Dic61D411yescharacteristic
97C2×C22⋊Dic61D411yescharacteristic
98C2×C4×Dic61—21no—
99C2×C4×Dic61—21no—
100C2×C4×Dic61C2311yescharacteristic
101C2×C4×Dic61C2311yescharacteristic
102#14519710—22no—
103#14519708—41no—
104#14519702—22no—
105#14519702—41no—
106#14519698C2×C414yes—
107#14519698C2×C414yescomplemented
108C22⋊#92418C2×C414yescomplemented
109#14519687—22no—
110C8×Dic61—41no—
111#14519684—21no—
112#14519684—21no—
113#14519684—21no—
114#14519684—21no—
115#14519684—21no—
116#14519684D411yescharacteristic
117#14519684D411yescharacteristic
118C25×C61—21no—
119C22×D4×C61—22no—
120C22×D4×C61—22no—
121C22×D4×C61—21no—
122C22×D4×C61—22no—
123C22×D4×C61—41no—
124C22×D4×C61—41no—
125C22×D4×C61C2×C414yes—
126C22×D4×C61C2311yescharacteristic
127C22×D4×C61C2311yescharacteristic
128C23×C4×C61C2311yescharacteristic
129C2×M16×C61—22no—
130C2×M16×C61—22no—
131C2×M16×C61—41no—
132C22×C8×C61C2311yescharacteristic
133C22×C8×C61C2311yescharacteristic
134#117×C61—22no—
135#117×C61—41no—
136C2×C4⋊C4×C61C2311yescharacteristic
137C2×C4⋊C4×C61C2311yescharacteristic
138C2×C22⋊C4×C61—21no—
139C2×C42×C61—21no—
140#102×C61—22no—
141#102×C61—22no—
142#102×C61—22no—
143#102×C61D414yes—
144C24×C61—21no—
145C24×C61—21no—
146C24×C61—24no—
147C24×C61—42no—
148C24×C61—42no—
149C24×C61—42no—
150C24×C61—42no—
151C24×C61—81no—
152C24×C61—81no—
153C24×C61C2×D411yescharacteristic
154C2×D4×C61—28no—
155C2×D4×C61—24no—
156C2×D4×C61—21no—
157C2×D4×C61—21no—
158C2×D4×C61—21no—
159C2×D4×C61—21no—
160C2×D4×C61—21no—
161C2×D4×C61—21no—
162C2×D4×C61—21no—
163C2×D4×C61—21no—
164C2×D4×C61—44no—
165C2×D4×C61—44no—
166C2×D4×C61—44no—
167C2×D4×C61—42no—
168C2×D4×C61—42no—
169C2×D4×C61C22×C412yes—
170C2×D4×C61C22×C412yes—
171C2×D4×C61C2×D412yes—
172C2×D4×C61#4112yes—
173C22×C4×C61—21no—
174C22×C4×C61—21no—
175C22×C4×C61—21no—
176C22×C4×C61—21no—
177C22×C4×C61—21no—
178C22×C4×C61—21no—
179C22×C4×C61C22×C412yes—
180C22×C4×C61C2×D411yescharacteristic
181C22×C4×C61#4112yes—
182C22×C4×C61C2411yescharacteristic
183C22×Dic61—21no—
184C22×Dic61—21no—
185C22×Dic61—21no—
186C22×Dic61—21no—
187C22×Dic61—42no—
188C22×Dic61—42no—
189C22×Dic61—42no—
190C22×Dic61—42no—
191C22×Dic61—81no—
192C22×Dic61—81no—
193C22×Dic61C2×D411yescharacteristic
194C22×Dic61C2×D411yescharacteristic
195C22×Dic61C2×D411yescharacteristic
196C22×Dic61C2×D411yescharacteristic
197C2×Dic122—21no—
198C2×Dic122—21no—
199C2×Dic122—21no—
200C2×Dic122—21no—
201C2×Dic122—21no—
202C2×Dic122C22×C412yes—
203M16×C61—44no—
204C2×C8×C61—21no—
205C2×C8×C61—21no—
206C2×C8×C61—21no—
207C2×C8×C61—21no—
208C2×C8×C61—21no—
209C2×C8×C61C2×D412yes—
210C4⋊C4×C61—21no—
211C4⋊C4×C61—21no—
212C4⋊C4×C61—21no—
213C4⋊C4×C61C2×D412yes—
214C22⋊C4×C61—42no—
215C42×C61—42no—
216C22⋊Dic61—24no—
217C22⋊Dic61—22no—
218C22⋊Dic61—41no—
219C22⋊Dic61—42no—
220C22⋊Dic61—42no—
221C22⋊Dic61—42no—
222C22⋊Dic61—42no—
223C22⋊Dic61—42no—
224C22⋊Dic61—81no—
225C22⋊Dic61—81no—
226#11758200—28no—
227#11758200—44no—
228C4⋊Dic61—21no—
229C4⋊Dic61—21no—
230C4⋊Dic61—21no—
231C4⋊Dic61—21no—
232C4⋊Dic61—21no—
233C4⋊Dic61C22×C412yes—
234#11758196—24no—
235#11758196—42no—
236#11758196—42no—
237C4×Dic61—21no—
238C4×Dic61—21no—
239C4×Dic61—21no—
240C4×Dic61—21no—
241C4×Dic61—42no—
242C4×Dic61—42no—
243C2×#92418—21no—
244C2×#92418—21no—
245C2×#92418—21no—
246C2×#92418—21no—
247C2×#92418C22×C412yes—
248C2×#92418C22×C412yes—
249C23×C61—22no—
250C23×C61—22no—
251C23×C61—21no—
252C23×C61—22no—
253C23×C61—21no—
254C23×C61—21no—
255C23×C61—21no—
256C23×C61—21no—
257C23×C61—21no—
258C23×C61—22no—
259C23×C61—48no—
260C23×C61—48no—
261C23×C61—41no—
262C23×C61—41no—
263C23×C61—41no—
264C23×C61—41no—
265C23×C61—41no—
266C23×C61—41no—
267C23×C61—41no—
268C23×C61—41no—
269C23×C61—41no—
270C23×C61—41no—
271C23×C61—84no—
272C23×C61—84no—
273C23×C61—84no—
274C23×C61—84no—
275C23×C61—84no—
276C23×C61C4×D412yes—
277C23×C61C22×D411yescharacteristic
278D4×C61—22no—
279D4×C61—22no—
280D4×C61—22no—
281D4×C61—22no—
282D4×C61—22no—
283D4×C61—48no—
284D4×C61—41no—
285D4×C61—41no—
286D4×C61C4×D414yes—
287C2×C4×C61—21no—
288C2×C4×C61—21no—
289C2×C4×C61—22no—
290C2×C4×C61—22no—
291C2×C4×C61—22no—
292C2×C4×C61—22no—
293C2×C4×C61—22no—
294C2×C4×C61—41no—
295C2×C4×C61—41no—
296C2×C4×C61—41no—
297C2×C4×C61—41no—
298C2×C4×C61—41no—
299C2×C4×C61C4×D412yes—
300C2×C4×C61C23×C411yescharacteristic
301C2×C4×C61C22×D411yescharacteristic
302C2×C4×C61C2×#4111yescharacteristic
303C2×C4×C61C2×#4111yescharacteristic
304C2×C4×C61H(5,𝔽2)11yescharacteristic
305C2×C4×C61H(5,𝔽2)11yescharacteristic
306C2×Dic61—21no—
307C2×Dic61—21no—
308C2×Dic61—22no—
309C2×Dic61—22no—
310C2×Dic61—21no—
311C2×Dic61—21no—
312C2×Dic61—21no—
313C2×Dic61—21no—
314C2×Dic61—21no—
315C2×Dic61—21no—
316C2×Dic61—21no—
317C2×Dic61—21no—
318C2×Dic61—21no—
319C2×Dic61—41no—
320C2×Dic61—41no—
321C2×Dic61—41no—
322C2×Dic61—41no—
323C2×Dic61—41no—
324C2×Dic61—41no—
325C2×Dic61—41no—
326C2×Dic61—41no—
327C2×Dic61—41no—
328C2×Dic61—41no—
329C2×Dic61—84no—
330C2×Dic61—84no—
331C2×Dic61AGL(1,ℤ/8)12yes—
332Dic122—22no—
333Dic122—22no—
334Dic122—41no—
335Dic122—41no—
336C8×C61—22no—
337C8×C61—41no—
338#92418—22no—
339#92418—22no—
340#22864—611nomaximal, Sylow
341C22×C61—22no—
342C22×C61—24no—
343C22×C61—22no—
344C22×C61—22no—
345C22×C61—42no—
346C22×C61—42no—
347C22×C61—42no—
348C22×C61—41no—
349C22×C61—41no—
350C22×C61—42no—
351C22×C61—42no—
352C22×C61—41no—
353C22×C61—41no—
354C22×C61—42no—
355C22×C61—42no—
356C22×C61—42no—
357C22×C61—42no—
358C22×C61—816no—
359C22×C61—81no—
360C22×C61—81no—
361C22×C61—81no—
362C22×C61—81no—
363C22×C61C2×C4×D411yescharacteristic
364C22×C61D4211yescharacteristic
365C22×C61#54611yescharacteristic
366C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
367C22×C61#57511yescharacteristic
368C22×C61#57711yescharacteristic
369C22×C61#57711yescharacteristic
370C4×C61—22no—
371C4×C61—42no—
372C4×C61—81no—
373C4×C61C2×C4×D411yescharacteristic
374C4×C61#51811yescharacteristic
375C4×C61#54611yescharacteristic
376C4×C61#55111yescharacteristic
377Dic61—22no—
378Dic61—42no—
379Dic61—42no—
380Dic61—41no—
381Dic61—41no—
382Dic61—41no—
383Dic61—81no—
384Dic61—81no—
385C2×#450—611no—
386C2×#440—611no—
387C2×#418D6111yescharacteristic
388#2362—611no—
389D4×C22⋊C4—611no—
390#1968—611no—
391#1936—611no—
392#1925—611no—
393#1894—611no—
394#1880—611no—
395#1877—611no—
396#1864—611no—
397#1854—611no—
398C4×#102—611no—
399#1753—611no—
400C2×C61—42no—
401C2×C61—44no—
402C2×C61—82no—
403C2×C61#235811yescharacteristic
404C2×C61C4×AGL(1,ℤ/8)11yescharacteristic
405C2×C61#294911yescharacteristic
406C2×C61#327211yescharacteristic
407C2×C61#327511yescharacteristic
408C2×C61#331011yescharacteristic
409C2×C61#331111yescharacteristic
410C23×D4C2×D6111yescharacteristic
411C22×SD16—611no—
412C22×SD16—611no—
413C22×M16C2×D6111yescharacteristic
414C2×C22⋊Q8—611no—
415C2×C4×Q8—611no—
416C2×C4×D4—611no—
417C2×C4×D4—611no—
418C2×#117C2×D6111yescharacteristic
419C22×C22⋊C4—1221no—
420#450—618no—
421#440—1224no—
422C2×#107—611no—
423C2×#106—611no—
424#418—24no—
425C2×#103—611no—
426C2×#103—611no—
427C2×#102—611no—
428C2×#102—611no—
429C2×#102C2×D6111yescharacteristic
430C2×#102C2×D6111yescharacteristic
431C2×#102C2×D6111yescharacteristic
432C2×#102C2×D6111yescharacteristic
433C2×C22⋊C8—611no—
434C2×#97—611no—
435C2×C4×C8—611no—
436#391—611no—
437#390—611no—
438#390—611no—
439#389—611no—
440#388—1221no—
441#388—1221no—
442#387—1221no—
443#386—1221no—
444#386—1221no—
445#380—611no—
446#379—1221no—
447C4×C4⋊C4—611no—
448C4×C4⋊C4—1221no—
449C4×C22⋊C4—611no—
450#340—611no—
451#340—611no—
452#340—611no—
453#340—611no—
454#336—611no—
455#336—611no—
456C61#2286411yescharacteristic, complemented, Sylow
457C25—21no—
458C22×Q8—611no—
459C22×D4—22no—
460C22×D4—22no—
461C22×D4—21no—
462C22×D4—22no—
463C22×D4—41no—
464C22×D4—41no—
465C22×D4C4×D6114yes—
466C22×D4C22×D6111yescharacteristic
467C22×D4C22×D6111yescharacteristic
468C23×C4—1221no—
469C23×C4—1221no—
470C23×C4C22×D6111yescharacteristic
471C2×SD16—614no—
472C2×SD16—614no—
473C2×SD16—1222no—
474C2×SD16—1222no—
475C2×SD16—2441no—
476C2×SD16—2441no—
477C2×M16—22no—
478C2×M16—22no—
479C2×M16—41no—
480C22×C8—611no—
481C22×C8—611no—
482C22×C8C22×D6111yescharacteristic
483C22×C8C22×D6111yescharacteristic
484C22⋊Q8—614no—
485C22⋊Q8—1222no—
486C4×Q8—1222no—
487C4×Q8—2441no—
488C4×D4—1222no—
489C4×D4—1222no—
490C4×D4—2441no—
491C4×D4—2441no—
492#117—22no—
493#117—41no—
494C2×C4⋊C4—611no—
495C2×C4⋊C4—611no—
496C2×C4⋊C4—611no—
497C2×C4⋊C4—1221no—
498C2×C4⋊C4—1221no—
499C2×C4⋊C4—1221no—
500C2×C4⋊C4C22×D6111yescharacteristic
501C2×C4⋊C4C22×D6111yescharacteristic
502C2×C22⋊C4—21no—
503C2×C22⋊C4—611no—
504C2×C22⋊C4—611no—
505C2×C22⋊C4—1221no—
506C2×C22⋊C4—1221no—
507C2×C22⋊C4—1221no—
508C2×C22⋊C4—1221no—
509C2×C22⋊C4—1221no—
510C2×C22⋊C4—1221no—
511C2×C22⋊C4—1221no—
512C2×C22⋊C4—1221no—
513C2×C22⋊C4—2444no—
514C2×C42—21no—
515C2×C42—611no—
516C2×C42—611no—
517C2×C42—1221no—
518C2×C42—1221no—
519#107—1222no—
520#106—2441no—
521#103—1222no—
522#103—2441no—
523#102—22no—
524#102—22no—
525#102—22no—
526#102—614no—
527#102—614no—
528#102C22⋊D6114yes—
529C22⋊C8—614no—
530#97—1222no—
531C4×C8—2441no—
532#95—611no—
533#95—611no—
534#95—1221no—
535#95—1221no—
536#95—1221no—
537#95—1221no—
538#95—1221no—
539C24—21no—
540C24—21no—
541C24—24no—
542C24—42no—
543C24—42no—
544C24—42no—
545C24—42no—
546C24—81no—
547C24—81no—
548C24D4×D6111yescharacteristic
549C2×Q8—612no—
550C2×Q8—1221no—
551C2×Q8—1221no—
552C2×Q8—1221no—
553C2×Q8—1221no—
554C2×Q8—1221no—
555C2×D4—28no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—24no—
565C2×D4—44no—
566C2×D4—44no—
567C2×D4—44no—
568C2×D4—42no—
569C2×D4—42no—
570C2×D4C2×C4×D6112yes—
571C2×D4C2×C4×D6112yes—
572C2×D4#1175822212yes—
573C2×D4C2×C22⋊D6112yes—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—611no—
581C22×C4—611no—
582C22×C4—611no—
583C22×C4—611no—
584C22×C4—1221no—
585C22×C4—1221no—
586C22×C4—1221no—
587C22×C4—1221no—
588C22×C4—4881no—
589C22×C4—4881no—
590C22×C4—2442no—
591C22×C4—2442no—
592C22×C4—2442no—
593C22×C4—2442no—
594C22×C4C2×C4×D6112yes—
595C22×C4D4×D6111yescharacteristic
596C22×C4#1175822412yes—
597C22×C4C23×D6111yescharacteristic
598SD16—1228no—
599SD16—2444no—
600M16—44no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—612no—
607C2×C8—612no—
608C2×C8—1221no—
609C2×C8—1221no—
610C2×C8—1221no—
611C2×C8—1221no—
612C2×C8C2×C22⋊D6112yes—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—612no—
617C4⋊C4—1221no—
618C4⋊C4—1224no—
619C4⋊C4—1221no—
620C4⋊C4—1221no—
621C4⋊C4—1221no—
622C4⋊C4—1221no—
623C4⋊C4—2442no—
624C4⋊C4—2442no—
625C4⋊C4C2×C22⋊D6112yes—
626C22⋊C4—42no—
627C22⋊C4—1222no—
628C22⋊C4—1224no—
629C22⋊C4—4881no—
630C22⋊C4—4881no—
631C22⋊C4—2442no—
632C22⋊C4—2441no—
633C22⋊C4—2442no—
634C22⋊C4—2442no—
635C22⋊C4—2442no—
636C22⋊C4—2442no—
637C42—42no—
638C42—1221no—
639C42—1221no—
640C42—1221no—
641C42—1221no—
642C42—2442no—
643C42—2442no—
644C23—22no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—22no—
651C23—22no—
652C23—21no—
653C23—22no—
654C23—48no—
655C23—48no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—84no—
667C23—84no—
668C23—84no—
669C23—84no—
670C23—84no—
671C23#1451973712yes—
672C23C2×D4×D6111yescharacteristic
673Q8—1222no—
674Q8—1222no—
675Q8—2441no—
676Q8—2441no—
677D4—22no—
678D4—22no—
679D4—22no—
680D4—22no—
681D4—22no—
682D4—48no—
683D4—41no—
684D4—41no—
685D4C4×C22⋊D6114yes—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—612no—
699C2×C4—1221no—
700C2×C4—1221no—
701C2×C4—1222no—
702C2×C4—1222no—
703C2×C4—1221no—
704C2×C4—1221no—
705C2×C4—1221no—
706C2×C4—1221no—
707C2×C4—1221no—
708C2×C4—1221no—
709C2×C4—1221no—
710C2×C4—1221no—
711C2×C4—1221no—
712C2×C4—4884no—
713C2×C4—4884no—
714C2×C4—2441no—
715C2×C4—2441no—
716C2×C4—2441no—
717C2×C4—2441no—
718C2×C4—2441no—
719C2×C4—2441no—
720C2×C4—2441no—
721C2×C4—2441no—
722C2×C4—2441no—
723C2×C4—2441no—
724C2×C4#1451973712yes—
725C2×C4C22×C4×D6111yescharacteristic
726C2×C4C22×C22⋊D6111yescharacteristic
727C2×C4C2×#1175822411yescharacteristic
728C2×C4C2×#1175822211yescharacteristic
729C2×C4#1451982211yescharacteristic
730C2×C4#1451982211yescharacteristic
731C8—22no—
732C8—41no—
733C8—1222no—
734C8—1222no—
735C22—22no—
736C22—22no—
737C22—22no—
738C22—24no—
739C22—42no—
740C22—41no—
741C22—42no—
742C22—41no—
743C22—42no—
744C22—42no—
745C22—42no—
746C22—41no—
747C22—41no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—816no—
753C22—81no—
754C22—81no—
755C22—81no—
756C22—81no—
757C22C2×#1451973711yescharacteristic
758C22D4×C22⋊D6111yescharacteristic
759C22#1684040211yescharacteristic
760C22AGL(1,ℤ/8)×D6111yescharacteristic
761C22#1684055811yescharacteristic
762C22#1684057211yescharacteristic
763C22#1684057211yescharacteristic
764C4—22no—
765C4—42no—
766C4—81no—
767C4—1222no—
768C4—4881no—
769C4—4881no—
770C4—2441no—
771C4—2442no—
772C4—2441no—
773C4—2442no—
774C4—2441no—
775C4C2×C4×C22⋊D6111yescharacteristic
776C4#1684023511yescharacteristic
777C4#1684040611yescharacteristic
778C4#1684043811yescharacteristic
779C2—42no—
780C2—44no—
781C2—82no—
782C2#2144879811yescharacteristic
783C2#2145462311yescharacteristic
784C2#2145468111yescharacteristic
785C2#2145741311yescharacteristic
786C2#2145745011yescharacteristic
787C2#2145784111yescharacteristic
788C2#2145785611yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#418C2
socleC23×C61C22×D4
prime radicalC23×D4×C61C22
cosocleC22×C4×C61C24
hypercenterC2×#418D61
hypocenterC61#22864
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#418

Complements

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

NH ≅ G/Ntype
2. C2×#16839859C2semidirect
3. #21448846C2semidirect
5. #21446674C2semidirect
6. #21446513C2semidirect
7. #21446442C2semidirect
8. #21446252C2semidirect
9. #21446171C2semidirect
10. #21446151C2semidirect
11. #21446078C2semidirect
12. #21446018C2semidirect
13. #102×Dic61C2semidirect
14. #21445600C2semidirect
19. C2×#14519742C22semidirect
23. #16839913C4semidirect
25. C2×#14519710C22semidirect
26. C2×#14519708C22semidirect
27. C2×#14519702C22semidirect
28. C2×#14519702C22semidirect
32. C2×#14519687C22semidirect
33. C2×C8×Dic61C22semidirect
34. #16839667C22semidirect
37. #16839658C22semidirect
45. C4⋊C4×Dic61C22semidirect
48. #16839525C22semidirect
49. #16839525C22semidirect
50. #16839524C22semidirect
51. #16839524C22semidirect
52. #16839516C22semidirect
53. #16839516C22semidirect
70. C2×#11758200C2×C4semidirect
74. #14519756C2×C4semidirect
107. #14519698C2×C4semidirect
108. C22⋊#92418C2×C4semidirect
456. C61#22864semidirect

Maximal subgroups

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

subgroupindex
C2×#168399132
C2×#168398592
#214488462
D4×C22⋊Dic612
#214466742
#214465132
#214464422
#214462522
#214461712
#214461512
#214460782
#214460182
#102×Dic612
#214456002
C2×C61×#4182
#2286461