Finite Group Databasebeta

← #29695498

Subgroups — #29695498

Order 15616.

1670 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840407C211yesmaximal, characteristic
2C2×#16839835C211yesmaximal, characteristic, complemented
3C2×#16839760C211yesmaximal, characteristic, complemented
4C2×#102×D61C211yesmaximal, characteristic, complemented
5C4⋊C4×D244C211yesmaximal, characteristic, complemented
6#21446751C211yesmaximal, characteristic, complemented
7#21446635C211yesmaximal, characteristic, complemented
8#21446256C211yesmaximal, characteristic, complemented
9#21446241C211yesmaximal, characteristic, complemented
10#21446135C211yesmaximal, characteristic, complemented
11#21446125C211yesmaximal, characteristic, complemented
12#21445819C211yesmaximal, characteristic, complemented
13#21445756C211yesmaximal, characteristic, complemented
14#21445748C211yesmaximal, characteristic, complemented
15C61×#1762C211yesmaximal, characteristic, complemented
16C22×#11758224C2211yescharacteristic
17C22×D4×D61C2211yescharacteristic
18C22×#11758189C2211yescharacteristic, complemented
19C22×C8×D61C2211yescharacteristic
20#16840407—24no—
21#16840407C418yescomplemented
22C2×#14519765C2211yescharacteristic
23C2×#14519761—21no—
24C2×#14519757C2211yescharacteristic
25C2×#14519752C2211yescharacteristic
26C2×#14519751—21no—
27C2×#14519747—21no—
28C2×C4×D244—21no—
29C2×C4×D244C2211yescharacteristic
30C2×C4⋊C4×D61C2211yescharacteristic
31C2×C4⋊C4×D61C2211yescharacteristic, complemented
32C22×#11758198—21no—
33#16839835—24no—
34C2×C4⋊#92418C2211yescharacteristic, complemented
35#16839760—24no—
36C2×#14519702C2211yescharacteristic, complemented
37C2×#14519702C2211yescharacteristic, complemented
38C2×#14519700C2211yescharacteristic, complemented
39C2×#14519700C2211yescharacteristic, complemented
40C2×#14519699C2211yescharacteristic
41C2×#14519699C2211yescharacteristic
42C2×#14519698C2211yescharacteristic
43C2×#14519698C2211yescharacteristic
44C2×#14519697C2211yescharacteristic
45C2×#14519697C2211yescharacteristic
46#102×D61—24no—
47C2×#14519689C2211yescharacteristic
48C2×#14519689C2211yescharacteristic, complemented
49#16839660—21no—
50#16839636—21no—
51#16839636—21no—
52#16839632C2211yescharacteristic, complemented
53#16839619C2211yescharacteristic
54#16839619C2211yescharacteristic, complemented
55#16839524C2211yescharacteristic, complemented
56#16839524C2211yescharacteristic, complemented
57C2×C4×D4×C61C2211yescharacteristic
58C2×#102×C61C2211yescharacteristic
59C2×#102×C61C2211yescharacteristic
60C2×#97×C61C2211yescharacteristic, complemented
61C4×C4⋊C4×C61C2211yescharacteristic, complemented
62C61×#340C2211yescharacteristic, complemented
63C61×#340C2211yescharacteristic, complemented
64C24×D61—21no—
65C2×#11758224—22no—
66C2×#11758224—22no—
67C2×#11758224—22no—
68C2×#11758224—41no—
69C2×#11758224—41no—
70C2×#11758224C2×C414yescomplemented
71C22×Dic122C2311yescharacteristic
72C22×D244—21no—
73C22×D244D411yescharacteristic
74C22×D244C2311yescharacteristic
75C22×C22⋊D61—21no—
76C22×C22⋊D61—21no—
77C2×D4×D61—22no—
78C2×D4×D61—22no—
79C2×D4×D61—22no—
80C2×D4×D61—41no—
81C2×D4×D61—41no—
82C2×D4×D61C2×C414yescomplemented
83C23×Dic61—21no—
84C22×C4×D61—21no—
85C22×C4×D61—21no—
86C22×C4×D61C2311yescharacteristic
87C22×C4×D61C2311yescharacteristic
88C2×#11758189—22no—
89C2×#11758189—22no—
90C2×#11758189—41no—
91C22×#92418C2311yescharacteristic
92C22×#92418C2311yescharacteristic
93C2×C8×D61—22no—
94C2×C8×D61—22no—
95C2×C8×D61—41no—
96#14519765—22no—
97#14519765C2×C414yescomplemented
98#14519761—28no—
99#14519757—22no—
100#14519757C2×C414yescomplemented
101#14519752—22no—
102#14519752C2×C414yescomplemented
103#14519751—28no—
104#14519747—28no—
105C4×D244—44no—
106C4×D244C2×C414yes—
107C4×D244D414yes—
108C2×C4⋊Dic61—21no—
109C2×C4⋊Dic61—21no—
110C2×C4⋊Dic61—21no—
111C2×C4⋊Dic61D411yescharacteristic
112C2×C4⋊Dic61C2311yescharacteristic
113C2×C4⋊Dic61C2311yescharacteristic
114C2×#11758196—21no—
115C2×#11758196—21no—
116C4⋊C4×D61—22no—
117C4⋊C4×D61—22no—
118C4⋊C4×D61—41no—
119C4⋊C4×D61—41no—
120C2×#11758198—21no—
121C2×#11758198—21no—
122C2×#11758198—21no—
123C2×#11758198—21no—
124C2×#11758198—28no—
125C2×#11758198—21no—
126C2×#11758198—21no—
127C2×#11758198D411yescharacteristic
128C2×#11758198D411yescharacteristic
129C4⋊#92418—22no—
130#14519702—22no—
131#14519702—41no—
132#14519700—22no—
133#14519700—41no—
134#14519699—22no—
135#14519699—41no—
136#14519698—22no—
137#14519698—22no—
138#14519697—22no—
139#14519697—41no—
140#14519689—22no—
141#14519689—22no—
142#14519684—21no—
143#14519684—21no—
144C22×D4×C61C2311yescharacteristic
145C23×C4×C61—21no—
146C22×C8×C61C2311yescharacteristic
147C22×C8×C61C2311yescharacteristic
148C4×D4×C61—22no—
149C4×D4×C61C2×C414yescomplemented
150C2×C4⋊C4×C61C2311yescharacteristic
151C2×C4⋊C4×C61C2311yescharacteristic
152C2×C4⋊C4×C61C2311yescharacteristic
153C2×C22⋊C4×C61—21no—
154C2×C42×C61—21no—
155C2×C42×C61C2311yescharacteristic
156#102×C61—22no—
157#102×C61D414yescomplemented
158#97×C61—22no—
159#95×C61—21no—
160C24×C61—21no—
161C23×D61—21no—
162C23×D61—24no—
163C23×D61—42no—
164C23×D61—42no—
165C23×D61—42no—
166C23×D61—42no—
167C23×D61—81no—
168C23×D61—81no—
169C23×D61C2×D411yescharacteristic
170C23×D61C2×D411yescharacteristic
171C2×D4×C61—21no—
172C2×D4×C61—21no—
173C2×D4×C61—21no—
174C2×D4×C61C22×C412yes—
175C2×D4×C61C2×D412yes—
176C2×D4×C61#4112yes—
177C22×C4×C61—21no—
178C22×C4×C61—21no—
179C22×C4×C61—24no—
180C22×C4×C61—21no—
181C22×C4×C61—81no—
182C22×C4×C61—81no—
183C22×C4×C61C2×D411yescharacteristic
184C22×C4×C61C2×D411yescharacteristic
185C22×C4×C61C2411yescharacteristic
186C2×C22⋊D61—24no—
187C2×C22⋊D61—24no—
188C2×C22⋊D61—42no—
189C2×C22⋊D61—42no—
190C2×C22⋊D61—42no—
191C2×C22⋊D61—42no—
192C22×Dic61—21no—
193C22×Dic61—24no—
194C22×Dic61—21no—
195C22×Dic61—21no—
196C22×Dic61—42no—
197C22×Dic61—42no—
198C22×Dic61C2×D411yescharacteristic
199C22×Dic61C2×D411yescharacteristic
200#11758224—28no—
201#11758224—44no—
202#11758224—44no—
203#11758224—44no—
204D4×D61—28no—
205D4×D61—44no—
206D4×D61—44no—
207D4×D61—44no—
208C2×D244—22no—
209C2×D244—22no—
210C2×D244—21no—
211C2×D244—21no—
212C2×D244—21no—
213C2×D244—21no—
214C2×D244—21no—
215C2×D244—24no—
216C2×D244—81no—
217C2×D244—81no—
218C2×D244C22⋊C414yes—
219C2×D244C22×C412yes—
220C2×C4×D61—21no—
221C2×C4×D61—21no—
222C2×C4×D61—21no—
223C2×C4×D61—21no—
224C2×C4×D61—21no—
225C2×C4×D61—21no—
226C2×C4×D61—21no—
227C2×C4×D61—21no—
228C2×C4×D61—42no—
229C2×C4×D61—42no—
230C2×C4×D61—42no—
231C2×C4×D61—42no—
232C2×C4×D61—81no—
233C2×C4×D61—81no—
234C2×C4×D61C22×C412yes—
235C2×C4×D61C22×C412yes—
236C2×C4×D61C2×D412yes—
237C2×C4×D61C2×D412yes—
238C2×Dic122—21no—
239C2×Dic122—21no—
240C2×Dic122—21no—
241C2×Dic122—21no—
242C2×Dic122—21no—
243C2×Dic122C22×C412yes—
244C2×C8×C61—21no—
245C2×C8×C61—21no—
246C2×C8×C61—21no—
247C2×C8×C61—21no—
248C2×C8×C61—21no—
249C2×C8×C61C2×D412yes—
250C4⋊C4×C61—21no—
251C4⋊C4×C61—21no—
252C4⋊C4×C61—21no—
253C4⋊C4×C61—21no—
254C4⋊C4×C61C22×C412yes—
255C4⋊C4×C61C2×D412yes—
256C22⋊C4×C61—24no—
257C42×C61—42no—
258C42×C61C22×C412yes—
259C42×C61C2×D412yes—
260#11758198—24no—
261#11758198—24no—
262#11758198—24no—
263#11758198—24no—
264#11758198—42no—
265#11758198—42no—
266#11758198C22⋊C414yes—
267#11758198C22⋊C414yes—
268C4⋊Dic61—24no—
269C4⋊Dic61—21no—
270C4⋊Dic61—21no—
271C4⋊Dic61—21no—
272C4⋊Dic61—21no—
273C4⋊Dic61—42no—
274C4⋊Dic61—81no—
275C4⋊Dic61C22⋊C414yes—
276#11758196—42no—
277#11758196—42no—
278C2×#92418—21no—
279C2×#92418—21no—
280C2×#92418—21no—
281C2×#92418—21no—
282C2×#92418—21no—
283C2×#92418—21no—
284#11758189—44no—
285C8×D61—44no—
286C23×C61—22no—
287C23×C61—22no—
288C23×C61—22no—
289C23×C61—41no—
290C23×C61—41no—
291C23×C61—41no—
292C23×C61—41no—
293C23×C61C22×D411yescharacteristic
294C22×D61—21no—
295C22×D61—21no—
296C22×D61—21no—
297C22×D61—21no—
298C22×D61—21no—
299C22×D61—21no—
300C22×D61—21no—
301C22×D61—21no—
302C22×D61—21no—
303C22×D61—21no—
304C22×D61—22no—
305C22×D61—48no—
306C22×D61—41no—
307C22×D61—41no—
308C22×D61—41no—
309C22×D61—41no—
310C22×D61—41no—
311C22×D61—41no—
312C22×D61—48no—
313C22×D61—84no—
314C22×D61—84no—
315C22×D61—84no—
316C22×D61—84no—
317C22×D61—84no—
318C22×D61C2×C22⋊C412yes—
319C22×D61C2×C22⋊C412yes—
320C22×D61AGL(1,ℤ/8)12yes—
321C22×D61#13712yes—
322D4×C61—22no—
323D4×C61—22no—
324D4×C61—22no—
325D4×C61C4×D414yescomplemented
326C2×C4×C61—21no—
327C2×C4×C61—21no—
328C2×C4×C61—21no—
329C2×C4×C61—21no—
330C2×C4×C61—22no—
331C2×C4×C61—22no—
332C2×C4×C61—41no—
333C2×C4×C61—41no—
334C2×C4×C61—41no—
335C2×C4×C61—41no—
336C2×C4×C61—41no—
337C2×C4×C61—41no—
338C2×C4×C61—41no—
339C2×C4×C61—84no—
340C2×C4×C61C2×C22⋊C412yes—
341C2×C4×C61C2×C22⋊C412yes—
342C2×C4×C61C23×C411yescharacteristic
343C2×C4×C61C22×D411yescharacteristic
344C2×C4×C61C22×D411yescharacteristic
345C2×C4×C61C2×#4111yescharacteristic
346C2×C4×C61H(5,𝔽2)11yescharacteristic
347C2×C4×C61H(5,𝔽2)11yescharacteristic
348C22⋊D61—48no—
349C22⋊D61—48no—
350C2×Dic61—21no—
351C2×Dic61—21no—
352C2×Dic61—21no—
353C2×Dic61—21no—
354C2×Dic61—22no—
355C2×Dic61—48no—
356C2×Dic61—41no—
357C2×Dic61—41no—
358C2×Dic61—41no—
359C2×Dic61—41no—
360C2×Dic61—41no—
361C2×Dic61—41no—
362C2×Dic61—41no—
363C2×Dic61—41no—
364C2×Dic61C2×C22⋊C412yes—
365C2×Dic61C2×C22⋊C412yes—
366D244—28no—
367D244—22no—
368D244—22no—
369D244—41no—
370D244—41no—
371D244—84no—
372C4×D61—22no—
373C4×D61—22no—
374C4×D61—22no—
375C4×D61—22no—
376C4×D61—22no—
377C4×D61—22no—
378C4×D61—22no—
379C4×D61—22no—
380C4×D61—84no—
381C4×D61—84no—
382Dic122—22no—
383Dic122—22no—
384Dic122—41no—
385Dic122—41no—
386C8×C61—22no—
387C8×C61—41no—
388#92418—41no—
389#92418—41no—
390#22419—611nomaximal, Sylow
391C22×C61—24no—
392C22×C61—42no—
393C22×C61—42no—
394C22×C61—42no—
395C22×C61—42no—
396C22×C61—42no—
397C22×C61—42no—
398C22×C61C22×C22⋊C411yescharacteristic
399C22×C61D4211yescharacteristic
400C22×C61#54611yescharacteristic
401C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
402C22×C61C2×#13711yescharacteristic
403C22×C61#57611yescharacteristic
404C22×C61#57711yescharacteristic
405C2×D61—22no—
406C2×D61—22no—
407C2×D61—22no—
408C2×D61—22no—
409C2×D61—22no—
410C2×D61—22no—
411C2×D61—22no—
412C2×D61—22no—
413C2×D61—22no—
414C2×D61—41no—
415C2×D61—41no—
416C2×D61—41no—
417C2×D61—41no—
418C2×D61—42no—
419C2×D61—42no—
420C2×D61—42no—
421C2×D61—816no—
422C2×D61—81no—
423C2×D61—81no—
424C2×D61—81no—
425C2×D61—81no—
426C2×D61#41714yescomplemented
427C4×C61—22no—
428C4×C61—22no—
429C4×C61—42no—
430C4×C61—42no—
431C4×C61—81no—
432C4×C61C2×C4×D411yescharacteristic
433C4×C61#51811yescharacteristic
434C4×C61D4211yescharacteristic
435C4×C61#54611yescharacteristic
436Dic61—22no—
437Dic61—22no—
438Dic61—42no—
439Dic61—81no—
440Dic61—81no—
441C2×#546—611no—
442C2×#435—611no—
443C2×#417—611no—
444C22×#102—611no—
445D4×C4⋊C4—611no—
446#1983—611no—
447#1959—611no—
448#1895—611no—
449#1892—611no—
450#1874—611no—
451#1872—611no—
452#1802—611no—
453#1788—611no—
454#1786—611no—
455#1762D6111yescharacteristic, complemented
456C2×C61—44no—
457C2×C61D4×C22⋊C411yescharacteristic
458C2×C61C2×#41711yescharacteristic
459C2×C61#289711yescharacteristic
460C2×C61#326411yescharacteristic
461C2×C61#326611yescharacteristic
462C2×C61#330611yescharacteristic
463C2×C61#331411yescharacteristic
464D61—24no—
465D61—42no—
466D61—82no—
467C22×#41—611no—
468C23×D4—611no—
469C22×M16—611no—
470C23×C8—611no—
471#546—618no—
472#546—1224no—
473C2×#124—611no—
474C2×#123—1221no—
475C2×C22⋊Q8—611no—
476C2×#121—611no—
477C2×#121—1221no—
478C2×#120—1221no—
479C2×C4×D4—611no—
480C2×C4×D4—1221no—
481C2×C4×D4C2×D6111yescharacteristic
482C22×C4⋊C4—611no—
483C22×C4⋊C4—611no—
484C22×C22⋊C4—1221no—
485#435—1224no—
486C2×C4⋊C8—611no—
487#417—1224no—
488C2×#103—611no—
489C2×#103—611no—
490C2×#103—611no—
491C2×#103—611no—
492C2×#102—611no—
493C2×#102—611no—
494C2×#102—611no—
495C2×#102—611no—
496C2×#102—611no—
497C2×#102—611no—
498C2×#102—1224no—
499C2×#102C2×D6111yescharacteristic
500C2×#102C2×D6111yescharacteristic
501C2×C22⋊C8—611no—
502C2×C22⋊C8—611no—
503C2×#97C2×D6111yescharacteristic, complemented
504#389—1221no—
505#385—1221no—
506#385—1221no—
507#384—611no—
508#380—611no—
509#380—611no—
510C4×C4⋊C4C2×D6111yescharacteristic, complemented
511#340—611no—
512#340—611no—
513#340C2×D6111yescharacteristic, complemented
514#340C2×D6111yescharacteristic, complemented
515C61#2241911yescharacteristic, complemented, Sylow
516C25—1221no—
517C2×#41—614no—
518C2×#41—1222no—
519C2×#41—1222no—
520C2×#41—1222no—
521C2×#41—2441no—
522C2×#41—2441no—
523C22×Q8—611no—
524C22×D4—614no—
525C22×D4—611no—
526C22×D4—611no—
527C22×D4—1221no—
528C22×D4—1222no—
529C22×D4—1221no—
530C22×D4—1222no—
531C22×D4—1222no—
532C22×D4—1221no—
533C22×D4—2441no—
534C22×D4—2441no—
535C22×D4C22×D6111yescharacteristic
536C23×C4—21no—
537C23×C4—611no—
538C23×C4—611no—
539C23×C4—1221no—
540C23×C4—1221no—
541C23×C4—1221no—
542C2×M16—1222no—
543C2×M16—1222no—
544C2×M16—2441no—
545C22×C8—611no—
546C22×C8—611no—
547C22×C8—1222no—
548C22×C8—1222no—
549C22×C8—2441no—
550C22×C8C22×D6111yescharacteristic
551C22×C8C22×D6111yescharacteristic
552#124—614no—
553#124—1222no—
554#123—1228no—
555C22⋊Q8—614no—
556C22⋊Q8—1222no—
557#121—614no—
558#121—1228no—
559#121—1222no—
560#120—1228no—
561C4×D4—22no—
562C4×D4—614no—
563C4×D4—614no—
564C4×D4—2444no—
565C4×D4C4×D6114yescomplemented
566C2×C4⋊C4—611no—
567C2×C4⋊C4—611no—
568C2×C4⋊C4—611no—
569C2×C4⋊C4—1221no—
570C2×C4⋊C4—1222no—
571C2×C4⋊C4—1222no—
572C2×C4⋊C4—1221no—
573C2×C4⋊C4—1221no—
574C2×C4⋊C4—1221no—
575C2×C4⋊C4—1221no—
576C2×C4⋊C4—2441no—
577C2×C4⋊C4—2441no—
578C2×C4⋊C4C22×D6111yescharacteristic
579C2×C4⋊C4C22×D6111yescharacteristic
580C2×C4⋊C4C22×D6111yescharacteristic
581C2×C22⋊C4—21no—
582C2×C22⋊C4—611no—
583C2×C22⋊C4—611no—
584C2×C22⋊C4—1228no—
585C2×C22⋊C4—1221no—
586C2×C22⋊C4—1221no—
587C2×C22⋊C4—1221no—
588C2×C22⋊C4—1221no—
589C2×C22⋊C4—1221no—
590C2×C22⋊C4—1221no—
591C2×C42—21no—
592C2×C42C22×D6111yescharacteristic
593C4⋊C8—1222no—
594#103—1222no—
595#103—1222no—
596#103—2441no—
597#103—2441no—
598#102—22no—
599#102—1222no—
600#102—1222no—
601#102—1222no—
602#102—1222no—
603#102—2441no—
604#102—2441no—
605#102D24414yescomplemented
606C22⋊C8—1222no—
607C22⋊C8—1222no—
608#97—22no—
609#95—21no—
610#95—1221no—
611#95—1221no—
612C24—21no—
613C24—611no—
614C24—611no—
615C24—1224no—
616C24—1221no—
617C24—4881no—
618C24—4881no—
619C24—2442no—
620C24—2442no—
621C24—2442no—
622C24—2442no—
623#41—1228no—
624#41—2444no—
625#41—2444no—
626#41—2444no—
627C2×Q8—612no—
628C2×Q8—1221no—
629C2×Q8—1221no—
630C2×Q8—1221no—
631C2×Q8—1221no—
632C2×Q8—1221no—
633C2×D4—21no—
634C2×D4—21no—
635C2×D4—21no—
636C2×D4—612no—
637C2×D4—614no—
638C2×D4—1222no—
639C2×D4—1222no—
640C2×D4—1224no—
641C2×D4—1224no—
642C2×D4—1228no—
643C2×D4—1224no—
644C2×D4—1221no—
645C2×D4—1221no—
646C2×D4—1221no—
647C2×D4—1221no—
648C2×D4—1221no—
649C2×D4—4881no—
650C2×D4—4881no—
651C2×D4—2444no—
652C2×D4—2444no—
653C2×D4—2444no—
654C2×D4—2442no—
655C2×D4—2442no—
656C2×D4—2442no—
657C2×D4—2442no—
658C2×D4C2×C4×D6112yes—
659C2×D4C2×D24412yes—
660C2×D4#1175822212yes—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—24no—
664C22×C4—21no—
665C22×C4—81no—
666C22×C4—81no—
667C22×C4—611no—
668C22×C4—611no—
669C22×C4—612no—
670C22×C4—612no—
671C22×C4—612no—
672C22×C4—612no—
673C22×C4—1224no—
674C22×C4—1221no—
675C22×C4—1221no—
676C22×C4—1221no—
677C22×C4—1221no—
678C22×C4—1221no—
679C22×C4—1221no—
680C22×C4—1221no—
681C22×C4—1221no—
682C22×C4—1221no—
683C22×C4—1221no—
684C22×C4—1221no—
685C22×C4—4881no—
686C22×C4—4881no—
687C22×C4—2442no—
688C22×C4—2442no—
689C22×C4—2442no—
690C22×C4—2442no—
691C22×C4—2442no—
692C22×C4—2442no—
693C22×C4D4×D6111yescharacteristic
694C22×C4D4×D6111yescharacteristic
695C22×C4C23×D6111yescharacteristic
696M16—2444no—
697C2×C8—21no—
698C2×C8—21no—
699C2×C8—21no—
700C2×C8—21no—
701C2×C8—21no—
702C2×C8—1221no—
703C2×C8—1221no—
704C2×C8—1221no—
705C2×C8—1221no—
706C2×C8—1221no—
707C2×C8—1221no—
708C2×C8—2444no—
709C2×C8C2×D24412yes—
710C4⋊C4—21no—
711C4⋊C4—21no—
712C4⋊C4—21no—
713C4⋊C4—21no—
714C4⋊C4—614no—
715C4⋊C4—1224no—
716C4⋊C4—1221no—
717C4⋊C4—1221no—
718C4⋊C4—1221no—
719C4⋊C4—1221no—
720C4⋊C4—4881no—
721C4⋊C4—2442no—
722C4⋊C4—2442no—
723C4⋊C4—2442no—
724C4⋊C4C2×C4×D6112yes—
725C4⋊C4C2×D24412yes—
726C22⋊C4—24no—
727C22⋊C4—614no—
728C22⋊C4—614no—
729C22⋊C4—1224no—
730C22⋊C4—1224no—
731C22⋊C4—1224no—
732C22⋊C4—1224no—
733C22⋊C4—2442no—
734C22⋊C4—2442no—
735C42—42no—
736C42C2×C4×D6112yes—
737C42D4×D6112yes—
738C23—22no—
739C23—22no—
740C23—22no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—612no—
746C23—612no—
747C23—612no—
748C23—612no—
749C23—1221no—
750C23—1221no—
751C23—1221no—
752C23—1221no—
753C23—1221no—
754C23—1221no—
755C23—1221no—
756C23—1221no—
757C23—1221no—
758C23—1221no—
759C23—1222no—
760C23—4884no—
761C23—4884no—
762C23—4884no—
763C23—4884no—
764C23—4884no—
765C23—2448no—
766C23—2448no—
767C23—2441no—
768C23—2441no—
769C23—2441no—
770C23—2441no—
771C23—2441no—
772C23—2441no—
773C23C2×D4×D6111yescharacteristic
774Q8—1222no—
775Q8—1222no—
776Q8—2441no—
777Q8—2441no—
778D4—22no—
779D4—22no—
780D4—22no—
781D4—1228no—
782D4—1222no—
783D4—1222no—
784D4—4884no—
785D4—2448no—
786D4—2448no—
787D4—2441no—
788D4—2441no—
789D4C4×D24414yescomplemented
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—84no—
804C2×C4—612no—
805C2×C4—612no—
806C2×C4—1221no—
807C2×C4—1221no—
808C2×C4—1221no—
809C2×C4—1221no—
810C2×C4—1222no—
811C2×C4—1222no—
812C2×C4—1222no—
813C2×C4—1222no—
814C2×C4—1222no—
815C2×C4—1222no—
816C2×C4—1222no—
817C2×C4—1222no—
818C2×C4—1222no—
819C2×C4—4884no—
820C2×C4—4884no—
821C2×C4—2448no—
822C2×C4—2441no—
823C2×C4—2441no—
824C2×C4—2441no—
825C2×C4—2441no—
826C2×C4—2441no—
827C2×C4—2441no—
828C2×C4—2441no—
829C2×C4—2441no—
830C2×C4C22⋊C4×D6112yes—
831C2×C4C22⋊C4×D6112yes—
832C2×C4C22×C4×D6111yescharacteristic
833C2×C4C2×D4×D6111yescharacteristic
834C2×C4C22×D24411yescharacteristic
835C2×C4C2×#1175822211yescharacteristic
836C2×C4#1451982311yescharacteristic
837C2×C4#1451982311yescharacteristic
838C8—22no—
839C8—41no—
840C8—2441no—
841C8—2441no—
842C22—24no—
843C22—42no—
844C22—42no—
845C22—42no—
846C22—42no—
847C22—42no—
848C22—42no—
849C22—614no—
850C22—1222no—
851C22—1222no—
852C22—1222no—
853C22—1222no—
854C22—1222no—
855C22—1222no—
856C22—1222no—
857C22—1222no—
858C22—1222no—
859C22—48816no—
860C22—4881no—
861C22—4881no—
862C22—4881no—
863C22—4881no—
864C22—2442no—
865C22—2442no—
866C22—2442no—
867C22—2441no—
868C22—2441no—
869C22—2441no—
870C22—2441no—
871C22C2×C22⋊C4×D6111yescharacteristic
872C22D4×D24411yescharacteristic
873C22#1684040811yescharacteristic
874C22AGL(1,ℤ/8)×D6111yescharacteristic
875C22#137×D6111yescharacteristic
876C22#1684056611yescharacteristic
877C22#1684057211yescharacteristic
878C4—22no—
879C4—22no—
880C4—42no—
881C4—42no—
882C4—81no—
883C4—1222no—
884C4—1222no—
885C4—4881no—
886C4—4881no—
887C4—2442no—
888C4C2×C4×D24411yescharacteristic
889C4#1684023611yescharacteristic
890C4D4×D24411yescharacteristic
891C4#1684040811yescharacteristic
892C2—44no—
893C2—1224no—
894C2—4882no—
895C2—2442no—
896C2C22⋊C4×D24411yescharacteristic
897C2#417×D6111yescharacteristic
898C2#2145434411yescharacteristic
899C2#2145730111yescharacteristic
900C2#2145733111yescharacteristic
901C2#2145778511yescharacteristic
902C2#2145790511yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1762C2
socleC23×C61C22×D4
prime radicalC2×#16840407C2
cosocleC22×C4×C61C24
hypercenter#1762D61
hypocenterC61#22419
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1762

Complements

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

NH ≅ G/Ntype
2. C2×#16839835C2semidirect
3. C2×#16839760C2semidirect
4. C2×#102×D61C2semidirect
5. C4⋊C4×D244C2semidirect
6. #21446751C2semidirect
7. #21446635C2semidirect
8. #21446256C2semidirect
9. #21446241C2semidirect
10. #21446135C2semidirect
11. #21446125C2semidirect
12. #21445819C2semidirect
13. #21445756C2semidirect
14. #21445748C2semidirect
15. C61×#1762C2semidirect
18. C22×#11758189C22semidirect
21. #16840407C4semidirect
31. C2×C4⋊C4×D61C22semidirect
34. C2×C4⋊#92418C22semidirect
36. C2×#14519702C22semidirect
37. C2×#14519702C22semidirect
38. C2×#14519700C22semidirect
39. C2×#14519700C22semidirect
48. C2×#14519689C22semidirect
52. #16839632C22semidirect
54. #16839619C22semidirect
55. #16839524C22semidirect
56. #16839524C22semidirect
60. C2×#97×C61C22semidirect
61. C4×C4⋊C4×C61C22semidirect
62. C61×#340C22semidirect
63. C61×#340C22semidirect
70. C2×#11758224C2×C4semidirect
82. C2×D4×D61C2×C4semidirect
97. #14519765C2×C4semidirect
100. #14519757C2×C4semidirect
102. #14519752C2×C4semidirect
149. C4×D4×C61C2×C4semidirect
157. #102×C61D4semidirect
325. D4×C61C4×D4semidirect
426. C2×D61#417semidirect
455. #1762D61semidirect
503. C2×#97C2×D61semidirect
510. C4×C4⋊C4C2×D61semidirect
513. #340C2×D61semidirect
514. #340C2×D61semidirect
515. C61#22419semidirect
565. C4×D4C4×D61semidirect
605. #102D244semidirect
789. D4C4×D244semidirect

Maximal subgroups

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

subgroupindex
C2×#168404072
C2×#168398352
C2×#168397602
C2×#102×D612
C4⋊C4×D2442
#214467512
#214466352
#214462562
#214462412
#214461352
#214461252
#214458192
#214457562
#214457482
C61×#17622
#2241961