Finite Group Databasebeta

← #29715682

Subgroups — #29715682

Order 15616.

1606 conjugacy classes of subgroups.

The subgroup lattice has 918 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×SD16×D61C211yesmaximal, characteristic, complemented
2C2×#16839991C211yesmaximal, characteristic, complemented
3C2×C8×C22⋊D61C211yesmaximal, characteristic, complemented
4#21449180C211yesmaximal, characteristic, complemented
5#21449171C211yesmaximal, characteristic
6#21447135C211yesmaximal, characteristic, complemented
7#21447133C211yesmaximal, characteristic, complemented
8#21446822C211yesmaximal, characteristic, complemented
9#21446820C211yesmaximal, characteristic, complemented
10#21446675C211yesmaximal, characteristic, complemented
11#21446671C211yesmaximal, characteristic, complemented
12#21445841C211yesmaximal, characteristic, complemented
13#21445752C211yesmaximal, characteristic, complemented
14#21445748C211yesmaximal, characteristic, complemented
15C2×C61×#465C211yesmaximal, characteristic, complemented
16C22×Q8×D61C2211yescharacteristic
17C22×D4×D61C2211yescharacteristic
18C22×#11758190C2211yescharacteristic
19C22×#11758200C2211yescharacteristic
20C22×#11758201C2211yescharacteristic
21C2×SD16×D61—24no—
22C2×SD16×D61—24no—
23C2×SD16×D61—24no—
24C22×C8×D61C2211yescharacteristic
25C2×#14519756C2211yescharacteristic, complemented
26C2×#14519751C2211yescharacteristic
27C2×#14519745—21no—
28C2×C4×C22⋊D61C2211yescharacteristic
29#16839991—24no—
30C8×C22⋊D61—24no—
31C2×#14519709C2211yescharacteristic, complemented
32C2×#14519706C2211yescharacteristic, complemented
33C2×#14519702C2211yescharacteristic, complemented
34C2×#14519701C2211yescharacteristic, complemented
35C2×#14519700C2211yescharacteristic, complemented
36C2×#14519699C2211yescharacteristic
37C2×#14519698C2211yescharacteristic
38C2×#14519697C2211yescharacteristic
39C2×C22⋊#92418C2211yescharacteristic, complemented
40C2×#14519689C2211yescharacteristic
41C2×C8×Dic61C2211yescharacteristic, complemented
42#16839682—21no—
43#16839677—21no—
44#16839674—21no—
45#16839670—21no—
46#16839669C2211yescharacteristic, complemented
47#16839667C2211yescharacteristic, complemented
48#16839665C2211yescharacteristic
49#16839663C2211yescharacteristic
50#16839638—21no—
51#16839633—21no—
52#16839619C2211yescharacteristic
53#16839619C2211yescharacteristic
54#16839617—21no—
55#16839524C2211yescharacteristic, complemented
56#16839524C2211yescharacteristic, complemented
57C22×SD16×C61C2211yescharacteristic
58C23×C8×C61C2211yescharacteristic, complemented
59C2×C22⋊Q8×C61C2211yescharacteristic, complemented
60C2×#121×C61C2211yescharacteristic
61C61×#465—24no—
62C2×#106×C61C2211yescharacteristic, complemented
63C2×#103×C61C2211yescharacteristic, complemented
64C2×#102×C61C2211yescharacteristic
65C24×D61—21no—
66C22×Dic122—21no—
67C22×Dic122C2311yescharacteristic
68C2×Q8×D61—22no—
69C2×Q8×D61—22no—
70C2×Q8×D61—22no—
71C2×Q8×D61—22no—
72C2×Q8×D61—41no—
73C2×Q8×D61—41no—
74C22×D244C2311yescharacteristic
75C22×C22⋊D61—21no—
76C22×C22⋊D61—21no—
77C22×C22⋊D61D411yescharacteristic
78C2×D4×D61—22no—
79C2×D4×D61—22no—
80C2×D4×D61—22no—
81C2×D4×D61—22no—
82C2×D4×D61—41no—
83C2×D4×D61—41no—
84C22×C4×D61—21no—
85C22×C4×D61C2311yescharacteristic
86C2×#11758190—22no—
87C2×#11758190—22no—
88C2×#11758190D414yescomplemented
89C2×#11758200—22no—
90C2×#11758200—22no—
91C2×#11758200—22no—
92C2×#11758201—22no—
93C2×#11758201—22no—
94C2×#11758201—22no—
95SD16×D61—232no—
96C22×#92418C2311yescharacteristic
97C22×#92418C2311yescharacteristic
98C2×C8×D61—22no—
99C2×C8×D61—22no—
100C2×C8×D61D414yescomplemented
101#14519756—22no—
102#14519756—41no—
103#14519751—22no—
104#14519751—41no—
105#14519745—44no—
106C4×C22⋊D61—22no—
107C4×C22⋊D61—22no—
108C2×C4⋊Dic61C2311yescharacteristic
109C2×C4⋊Dic61C2311yescharacteristic
110C2×#11758196—21no—
111C2×#11758196D411yescharacteristic
112C2×C22⋊Dic61—21no—
113C2×C22⋊Dic61—21no—
114C2×C22⋊Dic61—21no—
115C2×C22⋊Dic61D411yescharacteristic
116C2×#11758198—21no—
117C2×#11758198—21no—
118C2×#11758198—21no—
119C2×#11758198—21no—
120C2×#11758198—21no—
121C2×#11758198D411yescharacteristic
122C2×C4×Dic61C2311yescharacteristic
123#14519709—22no—
124#14519706—22no—
125#14519702—22no—
126#14519701—41no—
127#14519700—41no—
128#14519699—22no—
129#14519698—41no—
130#14519697—41no—
131C22⋊#92418—22no—
132#14519689—22no—
133C8×Dic61—22no—
134#14519684—21no—
135#14519684—21no—
136#14519684—21no—
137#14519684—21no—
138#14519684—21no—
139#14519684—21no—
140C22×Q8×C61C2311yescharacteristic
141C22×D4×C61—21no—
142C22×D4×C61C2311yescharacteristic
143C23×C4×C61C2311yescharacteristic
144C2×SD16×C61—22no—
145C2×SD16×C61—22no—
146C2×SD16×C61D414yescomplemented
147C22×C8×C61—22no—
148C22×C8×C61—22no—
149C22×C8×C61—22no—
150C22×C8×C61C2311yescharacteristic
151C22×C8×C61C2311yescharacteristic
152C22⋊Q8×C61—22no—
153C22⋊Q8×C61—41no—
154#121×C61—22no—
155#121×C61—41no—
156C2×C4⋊C4×C61—21no—
157C2×C4⋊C4×C61C2311yescharacteristic
158C2×C4⋊C4×C61C2311yescharacteristic
159C2×C22⋊C4×C61—21no—
160C2×C22⋊C4×C61—21no—
161#106×C61—22no—
162#103×C61—22no—
163#102×C61—22no—
164C24×C61—21no—
165C24×C61C2×D411yescharacteristic
166C23×D61—21no—
167C23×D61—42no—
168C23×D61—42no—
169C23×D61—42no—
170C23×D61—42no—
171C23×D61—42no—
172C23×D61—81no—
173C23×D61—81no—
174C23×D61C2×D411yescharacteristic
175C2×Q8×C61—21no—
176C2×Q8×C61—21no—
177C2×Q8×C61—21no—
178C2×Q8×C61—21no—
179C2×Q8×C61—21no—
180C2×Q8×C61C2×D412yes—
181C2×D4×C61—21no—
182C2×D4×C61—21no—
183C2×D4×C61—21no—
184C2×D4×C61—21no—
185C2×D4×C61—21no—
186C2×D4×C61—42no—
187C2×D4×C61—42no—
188C2×D4×C61—81no—
189C2×D4×C61C2×D412yes—
190C22×C4×C61—21no—
191C22×C4×C61—21no—
192C22×C4×C61—21no—
193C22×C4×C61—21no—
194C22×C4×C61—21no—
195C22×C4×C61—21no—
196C22×C4×C61—21no—
197C22×C4×C61—21no—
198C22×C4×C61—21no—
199C22×C4×C61C2×D411yescharacteristic
200C22×C4×C61C2411yescharacteristic
201C2×C22⋊D61—22no—
202C2×C22⋊D61—22no—
203C2×C22⋊D61—42no—
204C2×C22⋊D61—42no—
205C2×C22⋊D61—42no—
206C2×C22⋊D61—42no—
207C2×C22⋊D61—42no—
208C2×C22⋊D61—81no—
209C2×C22⋊D61SD1614yescomplemented
210C22×Dic61—21no—
211C22×Dic61—21no—
212C22×Dic61—21no—
213C22×Dic61C2×D411yescharacteristic
214C22×Dic61C2×D411yescharacteristic
215C22×Dic61C2×D411yescharacteristic
216Q8×D61—28no—
217Q8×D61—44no—
218Q8×D61—44no—
219Q8×D61—44no—
220D4×D61—28no—
221D4×D61—44no—
222D4×D61—44no—
223D4×D61—44no—
224C2×D244—21no—
225C2×D244—21no—
226C2×D244—21no—
227C2×D244—21no—
228C2×D244—21no—
229C2×D244C2×D412yes—
230C2×C4×D61—21no—
231C2×C4×D61—21no—
232C2×C4×D61—21no—
233C2×C4×D61—21no—
234C2×C4×D61—42no—
235C2×C4×D61—42no—
236C2×C4×D61—42no—
237C2×C4×D61C2×D412yes—
238C2×C4×D61#4112yes—
239C2×Dic122—21no—
240C2×Dic122—21no—
241C2×Dic122—21no—
242C2×Dic122—21no—
243C2×Dic122—21no—
244C2×Dic122—42no—
245C2×Dic122—42no—
246C2×Dic122—42no—
247C2×Dic122C2×D412yes—
248SD16×C61—28no—
249C2×C8×C61—21no—
250C2×C8×C61—21no—
251C2×C8×C61—21no—
252C2×C8×C61—44no—
253C2×C8×C61C2×D412yes—
254C2×C8×C61C2×D412yes—
255C2×C8×C61C2×D412yes—
256C4⋊C4×C61—21no—
257C4⋊C4×C61—21no—
258C4⋊C4×C61—21no—
259C4⋊C4×C61—21no—
260C4⋊C4×C61—42no—
261C22⋊C4×C61—42no—
262C22⋊C4×C61—42no—
263C22⋊Dic61—22no—
264C22⋊Dic61—42no—
265C22⋊Dic61—42no—
266C22⋊Dic61—81no—
267#11758201—28no—
268#11758200—28no—
269#11758198—22no—
270#11758198—42no—
271#11758198—42no—
272#11758198—42no—
273#11758198—42no—
274#11758198—81no—
275C4⋊Dic61—21no—
276C4⋊Dic61—21no—
277C4⋊Dic61—21no—
278C4⋊Dic61—21no—
279#11758196—22no—
280#11758196—42no—
281C4×Dic61—21no—
282C4×Dic61—21no—
283C2×#92418—21no—
284C2×#92418—21no—
285C2×#92418—21no—
286C2×#92418—21no—
287C2×#92418—21no—
288C2×#92418C2×D412yes—
289#11758190—28no—
290C8×D61—28no—
291C23×C61—21no—
292C23×C61—21no—
293C23×C61—21no—
294C23×C61—21no—
295C23×C61—21no—
296C23×C61—21no—
297C23×C61—22no—
298C23×C61—41no—
299C23×C61—41no—
300C23×C61—41no—
301C23×C61—41no—
302C23×C61—41no—
303C23×C61—41no—
304C23×C61C2×SD1612yescomplemented
305C23×C61C22×D411yescharacteristic
306C22×D61—21no—
307C22×D61—21no—
308C22×D61—21no—
309C22×D61—21no—
310C22×D61—22no—
311C22×D61—48no—
312C22×D61—41no—
313C22×D61—41no—
314C22×D61—41no—
315C22×D61—41no—
316C22×D61—41no—
317C22×D61—41no—
318C22×D61—84no—
319C22×D61—84no—
320C22×D61—84no—
321C22×D61—84no—
322C22×D61—84no—
323C22×D61—84no—
324C22×D61#12112yes—
325C22×D61C2×SD1612yes—
326C22×D61#13512yes—
327Q8×C61—22no—
328Q8×C61—22no—
329Q8×C61—41no—
330Q8×C61—41no—
331D4×C61—22no—
332D4×C61—22no—
333D4×C61—41no—
334D4×C61—41no—
335D4×C61—84no—
336C2×C4×C61—21no—
337C2×C4×C61—21no—
338C2×C4×C61—21no—
339C2×C4×C61—22no—
340C2×C4×C61—41no—
341C2×C4×C61—41no—
342C2×C4×C61—41no—
343C2×C4×C61—41no—
344C2×C4×C61—41no—
345C2×C4×C61—41no—
346C2×C4×C61—41no—
347C2×C4×C61—41no—
348C2×C4×C61—41no—
349C2×C4×C61—41no—
350C2×C4×C61—41no—
351C2×C4×C61—41no—
352C2×C4×C61C22×D411yescharacteristic
353C2×C4×C61C22×D411yescharacteristic
354C2×C4×C61C22×D411yescharacteristic
355C2×C4×C61C2×#4111yescharacteristic
356C2×C4×C61H(5,𝔽2)11yescharacteristic
357C2×C4×C61H(5,𝔽2)11yescharacteristic
358C22⋊D61—28no—
359C22⋊D61—48no—
360C22⋊D61—84no—
361C2×Dic61—21no—
362C2×Dic61—21no—
363C2×Dic61—21no—
364C2×Dic61—21no—
365C2×Dic61—21no—
366C2×Dic61—22no—
367C2×Dic61—21no—
368C2×Dic61—21no—
369C2×Dic61—41no—
370C2×Dic61—41no—
371C2×Dic61—41no—
372C2×Dic61—41no—
373C2×Dic61—41no—
374C2×Dic61—41no—
375C2×Dic61—41no—
376C2×Dic61—41no—
377C2×Dic61#12112yes—
378C2×Dic61C2×SD1612yescomplemented
379D244—22no—
380D244—22no—
381D244—41no—
382D244—41no—
383C4×D61—22no—
384C4×D61—22no—
385C4×D61—22no—
386C4×D61—22no—
387C4×D61—48no—
388Dic122—22no—
389Dic122—22no—
390Dic122—48no—
391Dic122—41no—
392Dic122—41no—
393C8×C61—41no—
394C8×C61#12014yescomplemented
395#92418—22no—
396#92418—41no—
397#24264—611nomaximal, Sylow
398C22×C61—22no—
399C22×C61—22no—
400C22×C61—22no—
401C22×C61—41no—
402C22×C61—41no—
403C22×C61—41no—
404C22×C61—41no—
405C22×C61—42no—
406C22×C61—42no—
407C22×C61—42no—
408C22×C61—81no—
409C22×C61—81no—
410C22×C61—81no—
411C22×C61—81no—
412C22×C61C2×#12111yescharacteristic
413C22×C61D4211yescharacteristic
414C22×C61D4211yescharacteristic
415C22×C61C22×SD1611yescharacteristic
416C22×C61C2×#13511yescharacteristic
417C22×C61#57711yescharacteristic
418C22×C61#57711yescharacteristic
419C2×D61—22no—
420C2×D61—22no—
421C2×D61—22no—
422C2×D61—22no—
423C2×D61—22no—
424C2×D61—22no—
425C2×D61—42no—
426C2×D61—42no—
427C2×D61—42no—
428C2×D61—816no—
429C2×D61—81no—
430C2×D61—81no—
431C2×D61—81no—
432C2×D61—81no—
433C2×D61#46514yescomplemented
434C4×C61—42no—
435C4×C61—41no—
436C4×C61—81no—
437C4×C61—81no—
438C4×C61C2×#12011yescharacteristic
439C4×C61#53511yescharacteristic
440C4×C61#54611yescharacteristic
441C4×C61#54611yescharacteristic
442Dic61—22no—
443Dic61—22no—
444Dic61—42no—
445Dic61—41no—
446Dic61—81no—
447Dic61—81no—
448C23×SD16—611no—
449C2×#465—611no—
450C2×#465D6111yescharacteristic, complemented
451C2×C8×D4—611no—
452#2409—611no—
453#2408—611no—
454#2055—611no—
455#2055—611no—
456#2000—611no—
457#2000—611no—
458#1968—611no—
459#1968—611no—
460#1807—611no—
461#1787—611no—
462#1786—611no—
463C2×C61—42no—
464C2×C61—82no—
465C2×C61#240811yescharacteristic
466C2×C61C2×#46511yescharacteristic
467C2×C61#305711yescharacteristic
468C2×C61D4×SD1611yescharacteristic
469C2×C61D4×SD1611yescharacteristic
470C2×C61#328211yescharacteristic
471C2×C61#328211yescharacteristic
472D61—24no—
473D61—82no—
474C23×Q8—611no—
475C23×D4—611no—
476C22×SD16—611no—
477C22×SD16—611no—
478C22×SD16—611no—
479C22×SD16—1224no—
480C22×SD16—1224no—
481C22×SD16—1224no—
482C22×SD16C2×D6111yescharacteristic
483C23×C8—611no—
484C23×C8C2×D6111yescharacteristic, complemented
485C2×C22⋊Q8—611no—
486C2×C22⋊Q8C2×D6111yescharacteristic, complemented
487C2×#121—611no—
488C2×#121C2×D6111yescharacteristic
489C2×#120—1221no—
490C2×C4×D4—611no—
491#465—24no—
492#465—1224no—
493C8×D4—1224no—
494C2×#106—611no—
495C2×#106C2×D6111yescharacteristic, complemented
496C2×C4⋊C8—611no—
497C2×#103—611no—
498C2×#103—611no—
499C2×#103—611no—
500C2×#103C2×D6111yescharacteristic, complemented
501C2×#102—611no—
502C2×#102—611no—
503C2×#102—611no—
504C2×#102C2×D6111yescharacteristic
505C2×C22⋊C8—611no—
506C2×C22⋊C8—611no—
507C2×C4×C8—611no—
508#395—1221no—
509#394—1221no—
510#393—1221no—
511#392—1221no—
512#391—611no—
513#391—611no—
514#390—611no—
515#390—611no—
516#386—1221no—
517#385—1221no—
518#380—611no—
519#380—611no—
520#379—1221no—
521#340—611no—
522#340—611no—
523C61#2426411yescharacteristic, complemented, Sylow
524C25—1221no—
525C22×Q8—611no—
526C22×Q8—1221no—
527C22×Q8—1222no—
528C22×Q8—1222no—
529C22×Q8—1222no—
530C22×Q8—1222no—
531C22×Q8—2441no—
532C22×Q8—2441no—
533C22×Q8C22×D6111yescharacteristic
534C22×D4—21no—
535C22×D4—611no—
536C22×D4—611no—
537C22×D4—1222no—
538C22×D4—1222no—
539C22×D4—1221no—
540C22×D4—1222no—
541C22×D4—1222no—
542C22×D4—1221no—
543C22×D4—2441no—
544C22×D4—2441no—
545C22×D4C22×D6111yescharacteristic
546C23×C4—611no—
547C23×C4—1221no—
548C23×C4C22×D6111yescharacteristic
549C2×SD16—22no—
550C2×SD16—22no—
551C2×SD16—614no—
552C2×SD16—1222no—
553C2×SD16—1222no—
554C2×SD16—12232no—
555C2×SD16—1222no—
556C2×SD16—1222no—
557C2×SD16—1222no—
558C2×SD16—1222no—
559C2×SD16—1222no—
560C2×SD16—1222no—
561C2×SD16C22⋊D6114yescomplemented
562C22×C8—22no—
563C22×C8—22no—
564C22×C8—22no—
565C22×C8—611no—
566C22×C8—614no—
567C22×C8—611no—
568C22×C8—1222no—
569C22×C8—1222no—
570C22×C8C22×D6111yescharacteristic
571C22×C8C22×D6111yescharacteristic
572C22⋊Q8—22no—
573C22⋊Q8—41no—
574C22⋊Q8—1222no—
575C22⋊Q8—2441no—
576#121—22no—
577#121—41no—
578#121—1222no—
579#121—2441no—
580#120—2444no—
581C4×D4—1222no—
582C4×D4—1222no—
583C2×C4⋊C4—21no—
584C2×C4⋊C4—611no—
585C2×C4⋊C4—611no—
586C2×C4⋊C4—611no—
587C2×C4⋊C4—1221no—
588C2×C4⋊C4C22×D6111yescharacteristic
589C2×C4⋊C4C22×D6111yescharacteristic
590C2×C22⋊C4—21no—
591C2×C22⋊C4—21no—
592C2×C22⋊C4—611no—
593C2×C22⋊C4—611no—
594C2×C22⋊C4—1221no—
595C2×C22⋊C4—1221no—
596C2×C22⋊C4—1221no—
597C2×C22⋊C4—1221no—
598C2×C22⋊C4—1221no—
599C2×C22⋊C4—1221no—
600C2×C22⋊C4—1221no—
601C2×C22⋊C4—1221no—
602C2×C42—611no—
603#106—22no—
604#106—1222no—
605C4⋊C8—1222no—
606#103—22no—
607#103—1222no—
608#103—2441no—
609#103—2441no—
610#102—22no—
611#102—1222no—
612#102—2441no—
613#102—2441no—
614C22⋊C8—1222no—
615C22⋊C8—1222no—
616C4×C8—1222no—
617#95—1221no—
618#95—1221no—
619#95—1221no—
620#95—1221no—
621#95—1221no—
622#95—1221no—
623C24—21no—
624C24—611no—
625C24—1221no—
626C24—4881no—
627C24—4881no—
628C24—2442no—
629C24—2442no—
630C24—2442no—
631C24—2442no—
632C24—2442no—
633C24D4×D6111yescharacteristic
634C2×Q8—21no—
635C2×Q8—21no—
636C2×Q8—21no—
637C2×Q8—21no—
638C2×Q8—21no—
639C2×Q8—612no—
640C2×Q8—1221no—
641C2×Q8—1228no—
642C2×Q8—1221no—
643C2×Q8—1221no—
644C2×Q8—1221no—
645C2×Q8—1221no—
646C2×Q8—2442no—
647C2×Q8—2442no—
648C2×Q8—2442no—
649C2×Q8—2444no—
650C2×Q8—2444no—
651C2×Q8—2444no—
652C2×Q8C2×C22⋊D6112yes—
653C2×D4—21no—
654C2×D4—21no—
655C2×D4—21no—
656C2×D4—21no—
657C2×D4—21no—
658C2×D4—42no—
659C2×D4—42no—
660C2×D4—81no—
661C2×D4—614no—
662C2×D4—612no—
663C2×D4—1228no—
664C2×D4—1222no—
665C2×D4—1222no—
666C2×D4—1221no—
667C2×D4—1221no—
668C2×D4—1221no—
669C2×D4—1221no—
670C2×D4—1221no—
671C2×D4—4881no—
672C2×D4—2442no—
673C2×D4—2444no—
674C2×D4—2444no—
675C2×D4—2444no—
676C2×D4—2442no—
677C2×D4—2442no—
678C2×D4—2442no—
679C2×D4—2442no—
680C2×D4C2×C22⋊D6112yes—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—611no—
691C22×C4—611no—
692C22×C4—612no—
693C22×C4—612no—
694C22×C4—611no—
695C22×C4—1221no—
696C22×C4—1221no—
697C22×C4—1221no—
698C22×C4—1221no—
699C22×C4—1221no—
700C22×C4—1221no—
701C22×C4—1221no—
702C22×C4—2442no—
703C22×C4—2442no—
704C22×C4—2442no—
705C22×C4D4×D6111yescharacteristic
706C22×C4C23×D6111yescharacteristic
707SD16—28no—
708SD16—1228no—
709SD16—1228no—
710SD16—1228no—
711C2×C8—21no—
712C2×C8—21no—
713C2×C8—21no—
714C2×C8—44no—
715C2×C8—612no—
716C2×C8—1221no—
717C2×C8—1221no—
718C2×C8—1228no—
719C2×C8—1221no—
720C2×C8—1221no—
721C2×C8—1221no—
722C2×C8D4×D6112yes—
723C2×C8D4×D6112yes—
724C2×C8C2×C22⋊D6112yes—
725C4⋊C4—21no—
726C4⋊C4—21no—
727C4⋊C4—21no—
728C4⋊C4—21no—
729C4⋊C4—42no—
730C4⋊C4—1222no—
731C4⋊C4—1221no—
732C4⋊C4—1221no—
733C4⋊C4—1221no—
734C4⋊C4—1221no—
735C4⋊C4—2442no—
736C22⋊C4—42no—
737C22⋊C4—42no—
738C22⋊C4—1222no—
739C22⋊C4—1222no—
740C22⋊C4—4881no—
741C22⋊C4—4881no—
742C22⋊C4—2442no—
743C22⋊C4—2442no—
744C22⋊C4—2442no—
745C22⋊C4—2442no—
746C22⋊C4—2442no—
747C22⋊C4—2442no—
748C42—1221no—
749C42—1221no—
750C23—21no—
751C23—21no—
752C23—21no—
753C23—21no—
754C23—21no—
755C23—21no—
756C23—22no—
757C23—41no—
758C23—41no—
759C23—41no—
760C23—41no—
761C23—41no—
762C23—41no—
763C23—612no—
764C23—612no—
765C23—612no—
766C23—1221no—
767C23—1221no—
768C23—1221no—
769C23—1221no—
770C23—1222no—
771C23—4884no—
772C23—4884no—
773C23—4884no—
774C23—4884no—
775C23—4884no—
776C23—4884no—
777C23—2448no—
778C23—2441no—
779C23—2441no—
780C23—2441no—
781C23—2441no—
782C23—2441no—
783C23—2441no—
784C23SD16×D6112yescomplemented
785C23C2×D4×D6111yescharacteristic
786Q8—22no—
787Q8—22no—
788Q8—41no—
789Q8—41no—
790Q8—1222no—
791Q8—1222no—
792Q8—2448no—
793Q8—2441no—
794Q8—2441no—
795D4—22no—
796D4—22no—
797D4—41no—
798D4—41no—
799D4—84no—
800D4—1228no—
801D4—1222no—
802D4—1222no—
803D4—4884no—
804D4—2448no—
805D4—2441no—
806D4—2441no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—22no—
810C2×C4—21no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—612no—
824C2×C4—612no—
825C2×C4—1221no—
826C2×C4—1221no—
827C2×C4—1221no—
828C2×C4—1221no—
829C2×C4—1222no—
830C2×C4—1222no—
831C2×C4—1222no—
832C2×C4—1222no—
833C2×C4—1221no—
834C2×C4—1221no—
835C2×C4—1221no—
836C2×C4—1222no—
837C2×C4—2448no—
838C2×C4—2441no—
839C2×C4—2441no—
840C2×C4—2441no—
841C2×C4—2441no—
842C2×C4—2441no—
843C2×C4—2441no—
844C2×C4—2441no—
845C2×C4—2441no—
846C2×C4C2×D4×D6111yescharacteristic
847C2×C4C2×D4×D6111yescharacteristic
848C2×C4C22×C22⋊D6111yescharacteristic
849C2×C4#41×D6111yescharacteristic
850C2×C4#1451982211yescharacteristic
851C2×C4#1451982311yescharacteristic
852C8—41no—
853C8—1222no—
854C8—2441no—
855C8#1451974514yescomplemented
856C22—22no—
857C22—22no—
858C22—22no—
859C22—41no—
860C22—41no—
861C22—41no—
862C22—41no—
863C22—42no—
864C22—42no—
865C22—42no—
866C22—81no—
867C22—81no—
868C22—81no—
869C22—81no—
870C22—614no—
871C22—1222no—
872C22—1222no—
873C22—1222no—
874C22—1222no—
875C22—1222no—
876C22—1222no—
877C22—48816no—
878C22—4881no—
879C22—4881no—
880C22—4881no—
881C22—4881no—
882C22—2442no—
883C22—2442no—
884C22—2442no—
885C22#121×D6111yescharacteristic
886C22D4×C22⋊D6111yescharacteristic
887C22#1684039611yescharacteristic
888C22C2×SD16×D6111yescharacteristic
889C22#135×D6111yescharacteristic
890C22#1684056811yescharacteristic
891C22#1684056911yescharacteristic
892C4—41no—
893C4—42no—
894C4—81no—
895C4—81no—
896C4—1222no—
897C4—1222no—
898C4—4881no—
899C4—4881no—
900C4—2441no—
901C4—2442no—
902C4C2×#1451974511yescharacteristic
903C4#1684032811yescharacteristic
904C4#1684040011yescharacteristic
905C4#1684040911yescharacteristic
906C2—42no—
907C2—82no—
908C2—1224no—
909C2—4882no—
910C2#2144917111yescharacteristic
911C2#465×D6111yescharacteristic
912C2#2145545311yescharacteristic
913C2SD16×C22⋊D6111yescharacteristic
914C2#2145751211yescharacteristic
915C2#2145752011yescharacteristic
916C2#2145753311yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#465C2
socleC23×C61C22×D4
prime radical#21449171C2
hypercenterC2×#465D61
hypocenterC61#24264
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#465

Complements

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

NH ≅ G/Ntype
1. C22×SD16×D61C2semidirect
2. C2×#16839991C2semidirect
3. C2×C8×C22⋊D61C2semidirect
4. #21449180C2semidirect
6. #21447135C2semidirect
7. #21447133C2semidirect
8. #21446822C2semidirect
9. #21446820C2semidirect
10. #21446675C2semidirect
11. #21446671C2semidirect
12. #21445841C2semidirect
13. #21445752C2semidirect
14. #21445748C2semidirect
15. C2×C61×#465C2semidirect
25. C2×#14519756C22semidirect
31. C2×#14519709C22semidirect
32. C2×#14519706C22semidirect
33. C2×#14519702C22semidirect
34. C2×#14519701C22semidirect
35. C2×#14519700C22semidirect
39. C2×C22⋊#92418C22semidirect
41. C2×C8×Dic61C22semidirect
46. #16839669C22semidirect
47. #16839667C22semidirect
55. #16839524C22semidirect
56. #16839524C22semidirect
58. C23×C8×C61C22semidirect
59. C2×C22⋊Q8×C61C22semidirect
62. C2×#106×C61C22semidirect
63. C2×#103×C61C22semidirect
88. C2×#11758190D4semidirect
100. C2×C8×D61D4semidirect
146. C2×SD16×C61D4semidirect
209. C2×C22⋊D61SD16semidirect
304. C23×C61C2×SD16semidirect
378. C2×Dic61C2×SD16semidirect
394. C8×C61#120semidirect
433. C2×D61#465semidirect
450. C2×#465D61semidirect
484. C23×C8C2×D61semidirect
486. C2×C22⋊Q8C2×D61semidirect
495. C2×#106C2×D61semidirect
500. C2×#103C2×D61semidirect
523. C61#24264semidirect
561. C2×SD16C22⋊D61semidirect
784. C23SD16×D61semidirect
855. C8#14519745semidirect

Maximal subgroups

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

subgroupindex
C22×SD16×D612
C2×#168399912
C2×C8×C22⋊D612
#214491802
#214491712
#214471352
#214471332
#214468222
#214468202
#214466752
#214466712
#214458412
#214457522
#214457482
C2×C61×#4652
#2426461