Finite Group Databasebeta

← #29695494

Subgroups — #29695494

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×#16840400C211yesmaximal, characteristic
2C2×#16839831C211yesmaximal, characteristic, complemented
3C2×#102×D61C211yesmaximal, characteristic, complemented
4C4⋊C4×C22⋊D61C211yesmaximal, characteristic, complemented
5#21446748C211yesmaximal, characteristic, complemented
6#21446632C211yesmaximal, characteristic, complemented
7#21446257C211yesmaximal, characteristic, complemented
8#21446239C211yesmaximal, characteristic, complemented
9#21446136C211yesmaximal, characteristic, complemented
10#21446123C211yesmaximal, characteristic, complemented
11#21445817C211yesmaximal, characteristic, complemented
12#21445759C211yesmaximal, characteristic, complemented
13#21445748C211yesmaximal, characteristic, complemented
14#21445646C211yesmaximal, characteristic, complemented
15C2×C61×#417C211yesmaximal, characteristic, complemented
16C22×D4×D61C2211yescharacteristic
17C22×C8×D61C2211yescharacteristic
18#16840400—24no—
19#16840400C418yescomplemented
20C2×#14519766C2211yescharacteristic
21C2×#14519760—21no—
22C2×#14519753C2211yescharacteristic
23C2×#14519751C2211yescharacteristic
24C2×#14519749—21no—
25C2×#14519745—21no—
26C2×D4×Dic61C2211yescharacteristic
27C2×C4×C22⋊D61—21no—
28C2×C4×C22⋊D61C2211yescharacteristic
29C2×C4⋊C4×D61C2211yescharacteristic
30C22×#11758198—21no—
31#16839831—24no—
32C2×#14519706C2211yescharacteristic, complemented
33C2×#14519701C2211yescharacteristic, complemented
34C2×#14519701C2211yescharacteristic, complemented
35C2×#14519699C2211yescharacteristic
36C2×#14519699C2211yescharacteristic
37C2×#14519698C2211yescharacteristic
38C2×#14519698C2211yescharacteristic
39C2×#14519697C2211yescharacteristic
40C2×#14519697C2211yescharacteristic
41#102×D61—24no—
42C2×C22⋊#92418C2211yescharacteristic, complemented
43C2×#14519689C2211yescharacteristic
44C2×#14519687C2211yescharacteristic, complemented
45#16839657—21no—
46#16839635—21no—
47#16839633—21no—
48#16839631C2211yescharacteristic, complemented
49#16839622C2211yescharacteristic, complemented
50#16839619C2211yescharacteristic
51C4⋊C4×Dic61C2211yescharacteristic, complemented
52#16839525C2211yescharacteristic, complemented
53#16839525C2211yescharacteristic, complemented
54#16839524C2211yescharacteristic, complemented
55#16839524C2211yescharacteristic, complemented
56C22×#41×C61C2211yescharacteristic
57C22×M16×C61C2211yescharacteristic, complemented
58C22×C4⋊C4×C61C2211yescharacteristic, complemented
59C61×#417—24no—
60C2×#103×C61C2211yescharacteristic, complemented
61C2×#103×C61C2211yescharacteristic, complemented
62C2×#102×C61C2211yescharacteristic
63C2×#102×C61C2211yescharacteristic
64C24×D61—21no—
65C22×D244C2311yescharacteristic
66C22×C22⋊D61—21no—
67C22×C22⋊D61—21no—
68C22×C22⋊D61D411yescharacteristic
69C2×D4×D61—22no—
70C2×D4×D61—22no—
71C2×D4×D61—22no—
72C2×D4×D61—41no—
73C2×D4×D61—41no—
74C2×D4×D61C2×C414yescomplemented
75C23×Dic61—21no—
76C22×C4×D61—21no—
77C22×C4×D61C2311yescharacteristic
78C22×#92418C2311yescharacteristic
79C22×#92418C2311yescharacteristic
80C2×C8×D61—22no—
81C2×C8×D61—22no—
82C2×C8×D61—41no—
83#14519766—22no—
84#14519766C2×C414yescomplemented
85#14519760—28no—
86#14519753—22no—
87#14519753C2×C414yescomplemented
88#14519751—22no—
89#14519751C2×C414yescomplemented
90#14519749—28no—
91#14519745—28no—
92D4×Dic61—22no—
93D4×Dic61C2×C414yescomplemented
94C4×C22⋊D61—44no—
95C4×C22⋊D61C2×C414yes—
96C4×C22⋊D61D414yes—
97C2×C4⋊Dic61C2311yescharacteristic
98C2×C4⋊Dic61C2311yescharacteristic
99C2×C4⋊Dic61C2311yescharacteristic
100C2×#11758196—21no—
101C2×#11758196—21no—
102C2×#11758196—21no—
103C2×#11758196—21no—
104C2×#11758196D411yescharacteristic
105C4⋊C4×D61—22no—
106C4⋊C4×D61—41no—
107C2×C22⋊Dic61—21no—
108C2×C22⋊Dic61—21no—
109C2×C22⋊Dic61D411yescharacteristic
110C2×#11758198—21no—
111C2×#11758198—21no—
112C2×#11758198—21no—
113C2×#11758198—21no—
114C2×#11758198—28no—
115C2×#11758198—21no—
116C2×#11758198D411yescharacteristic
117C2×C4×Dic61—21no—
118C2×C4×Dic61C2311yescharacteristic
119#14519706—22no—
120#14519701—41no—
121#14519701—41no—
122#14519699—22no—
123#14519699—41no—
124#14519698—22no—
125#14519698—22no—
126#14519697—22no—
127#14519697—41no—
128C22⋊#92418—22no—
129#14519689—22no—
130#14519687—22no—
131#14519684—21no—
132#14519684—21no—
133#14519684—21no—
134C2×#41×C61—22no—
135C2×#41×C61—22no—
136C2×#41×C61—22no—
137C2×#41×C61—41no—
138C2×#41×C61—41no—
139C2×#41×C61C2×C414yescomplemented
140C22×Q8×C61C2311yescharacteristic
141C22×D4×C61—21no—
142C22×D4×C61C2311yescharacteristic
143C23×C4×C61—21no—
144C23×C4×C61—21no—
145C23×C4×C61C2311yescharacteristic
146C2×M16×C61—22no—
147C2×M16×C61—22no—
148C2×M16×C61—41no—
149C22×C8×C61C2311yescharacteristic
150C22×C8×C61C2311yescharacteristic
151C2×C4⋊C4×C61—22no—
152C2×C4⋊C4×C61—21no—
153C2×C4⋊C4×C61—41no—
154C2×C4⋊C4×C61C2311yescharacteristic
155C2×C4⋊C4×C61C2311yescharacteristic
156#103×C61—22no—
157#103×C61—22no—
158#102×C61—22no—
159#102×C61D414yescomplemented
160C24×C61—21no—
161C24×C61C2×D411yescharacteristic
162C23×D61—21no—
163C23×D61—24no—
164C23×D61—42no—
165C23×D61—42no—
166C23×D61—42no—
167C23×D61—42no—
168C23×D61—81no—
169C23×D61—81no—
170C23×D61C2×D411yescharacteristic
171#41×C61—28no—
172#41×C61—44no—
173#41×C61—44no—
174#41×C61—44no—
175C2×Q8×C61—21no—
176C2×Q8×C61—21no—
177C2×Q8×C61—21no—
178C2×Q8×C61—21no—
179C2×Q8×C61—21no—
180C2×Q8×C61C22×C412yes—
181C2×D4×C61—24no—
182C2×D4×C61—21no—
183C2×D4×C61—21no—
184C2×D4×C61—21no—
185C2×D4×C61—42no—
186C2×D4×C61—42no—
187C2×D4×C61C22×C412yes—
188C2×D4×C61C2×D412yes—
189C2×D4×C61#4112yes—
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—24no—
197C22×C4×C61—21no—
198C22×C4×C61—42no—
199C22×C4×C61—42no—
200C22×C4×C61—42no—
201C22×C4×C61—42no—
202C22×C4×C61—81no—
203C22×C4×C61C22×C412yes—
204C22×C4×C61C2×D411yescharacteristic
205C22×C4×C61C2×D412yes—
206C22×C4×C61C2411yescharacteristic
207C2×C22⋊D61—22no—
208C2×C22⋊D61—22no—
209C2×C22⋊D61—24no—
210C2×C22⋊D61—24no—
211C2×C22⋊D61—42no—
212C2×C22⋊D61—42no—
213C2×C22⋊D61—81no—
214C2×C22⋊D61—81no—
215C2×C22⋊D61C22⋊C414yes—
216C22×Dic61—21no—
217C22×Dic61—24no—
218C22×Dic61—21no—
219C22×Dic61—21no—
220C22×Dic61—81no—
221C22×Dic61—81no—
222C22×Dic61C2×D411yescharacteristic
223C22×Dic61C2×D411yescharacteristic
224C22×Dic61C2×D411yescharacteristic
225D4×D61—28no—
226D4×D61—44no—
227D4×D61—44no—
228D4×D61—44no—
229C2×D244—21no—
230C2×D244—21no—
231C2×D244—21no—
232C2×D244—21no—
233C2×D244—21no—
234C2×D244C22×C412yes—
235C2×C4×D61—21no—
236C2×C4×D61—21no—
237C2×C4×D61—21no—
238C2×C4×D61—21no—
239C2×C4×D61—42no—
240C2×C4×D61—42no—
241C2×C4×D61—81no—
242C2×C4×D61C22×C412yes—
243C2×C4×D61C2×D412yes—
244M16×C61—44no—
245C2×C8×C61—21no—
246C2×C8×C61—21no—
247C2×C8×C61—21no—
248C2×C8×C61—21no—
249C2×C8×C61—21no—
250C2×C8×C61C2×D412yes—
251C4⋊C4×C61—21no—
252C4⋊C4×C61—21no—
253C4⋊C4×C61—21no—
254C4⋊C4×C61—42no—
255C4⋊C4×C61C2×D412yes—
256C22⋊Dic61—24no—
257C22⋊Dic61—42no—
258C22⋊Dic61C22⋊C414yes—
259#11758198—24no—
260#11758198—24no—
261#11758198—24no—
262#11758198—24no—
263#11758198—42no—
264#11758198C22⋊C414yes—
265C4⋊Dic61—21no—
266C4⋊Dic61—21no—
267C4⋊Dic61—21no—
268C4⋊Dic61—21no—
269C4⋊Dic61—21no—
270C4⋊Dic61C22×C412yes—
271#11758196—24no—
272#11758196—42no—
273#11758196—42no—
274#11758196—81no—
275#11758196C22⋊C414yes—
276C4×Dic61—42no—
277C4×Dic61C22×C412yes—
278C4×Dic61C2×D412yes—
279C2×#92418—21no—
280C2×#92418—21no—
281C2×#92418—21no—
282C2×#92418—21no—
283C2×#92418—21no—
284C2×#92418—21no—
285C8×D61—44no—
286C23×C61—22no—
287C23×C61—22no—
288C23×C61—21no—
289C23×C61—22no—
290C23×C61—21no—
291C23×C61—21no—
292C23×C61—21no—
293C23×C61—21no—
294C23×C61—21no—
295C23×C61—41no—
296C23×C61—41no—
297C23×C61—41no—
298C23×C61—41no—
299C23×C61C2×C22⋊C412yes—
300C23×C61C22×D411yescharacteristic
301C22×D61—21no—
302C22×D61—21no—
303C22×D61—21no—
304C22×D61—21no—
305C22×D61—22no—
306C22×D61—48no—
307C22×D61—41no—
308C22×D61—41no—
309C22×D61—41no—
310C22×D61—41no—
311C22×D61—41no—
312C22×D61—41no—
313C22×D61—48no—
314C22×D61—84no—
315C22×D61—84no—
316C22×D61—84no—
317C22×D61—84no—
318C22×D61—84no—
319C22×D61C2×C22⋊C412yes—
320C22×D61AGL(1,ℤ/8)12yes—
321C22×D61#13712yes—
322Q8×C61—22no—
323Q8×C61—22no—
324Q8×C61—41no—
325Q8×C61—41no—
326D4×C61—22no—
327D4×C61—22no—
328D4×C61—22no—
329D4×C61—48no—
330D4×C61C4×D414yescomplemented
331C2×C4×C61—21no—
332C2×C4×C61—21no—
333C2×C4×C61—22no—
334C2×C4×C61—22no—
335C2×C4×C61—22no—
336C2×C4×C61—22no—
337C2×C4×C61—22no—
338C2×C4×C61—22no—
339C2×C4×C61—48no—
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—84no—
348C2×C4×C61C2×C22⋊C412yes—
349C2×C4×C61C23×C411yescharacteristic
350C2×C4×C61C22×D411yescharacteristic
351C2×C4×C61C22×D411yescharacteristic
352C2×C4×C61C2×#4111yescharacteristic
353C2×C4×C61H(5,𝔽2)11yescharacteristic
354C2×C4×C61H(5,𝔽2)11yescharacteristic
355C22⋊D61—28no—
356C22⋊D61—48no—
357C22⋊D61—84no—
358C2×Dic61—21no—
359C2×Dic61—21no—
360C2×Dic61—21no—
361C2×Dic61—21no—
362C2×Dic61—21no—
363C2×Dic61—21no—
364C2×Dic61—22no—
365C2×Dic61—41no—
366C2×Dic61—41no—
367C2×Dic61—41no—
368C2×Dic61—41no—
369C2×Dic61—41no—
370C2×Dic61—41no—
371C2×Dic61—41no—
372C2×Dic61—41no—
373C2×Dic61—84no—
374C2×Dic61C2×C22⋊C412yes—
375C2×Dic61C2×C22⋊C412yes—
376C2×Dic61C2×C22⋊C412yes—
377D244—22no—
378D244—22no—
379D244—41no—
380D244—41no—
381C4×D61—22no—
382C4×D61—22no—
383C4×D61—22no—
384C4×D61—22no—
385C4×D61—84no—
386C8×C61—22no—
387C8×C61—41no—
388#92418—41no—
389#92418—41no—
390#22419—611nomaximal, Sylow
391C22×C61—24no—
392C22×C61—22no—
393C22×C61—22no—
394C22×C61—22no—
395C22×C61—42no—
396C22×C61—42no—
397C22×C61—41no—
398C22×C61—42no—
399C22×C61—42no—
400C22×C61—41no—
401C22×C61—42no—
402C22×C61—41no—
403C22×C61—42no—
404C22×C61—41no—
405C22×C61C22×C22⋊C411yescharacteristic
406C22×C61D4211yescharacteristic
407C22×C61#54611yescharacteristic
408C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
409C22×C61C2×#13711yescharacteristic
410C22×C61#57611yescharacteristic
411C22×C61#57711yescharacteristic
412C2×D61—22no—
413C2×D61—22no—
414C2×D61—22no—
415C2×D61—22no—
416C2×D61—22no—
417C2×D61—22no—
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—42no—
429C4×C61—42no—
430C4×C61—81no—
431C4×C61C2×C4×D411yescharacteristic
432C4×C61#51811yescharacteristic
433C4×C61D4211yescharacteristic
434C4×C61#54611yescharacteristic
435Dic61—22no—
436Dic61—22no—
437Dic61—22no—
438Dic61—42no—
439Dic61—81no—
440Dic61—81no—
441C2×#546—611no—
442C2×#435—611no—
443C2×#417D6111yescharacteristic, complemented
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#1762—611no—
456C2×C61—44no—
457C2×C61—42no—
458C2×C61D4×C22⋊C411yescharacteristic
459C2×C61C2×#41711yescharacteristic
460C2×C61#289711yescharacteristic
461C2×C61#326411yescharacteristic
462C2×C61#326611yescharacteristic
463C2×C61#330611yescharacteristic
464C2×C61#331411yescharacteristic
465D61—24no—
466D61—82no—
467C22×#41C2×D6111yescharacteristic
468C23×D4—611no—
469C22×M16C2×D6111yescharacteristic, complemented
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—611no—
481C2×C4×D4—1221no—
482C22×C4⋊C4—611no—
483C22×C4⋊C4C2×D6111yescharacteristic, complemented
484C22×C22⋊C4—1221no—
485#435—1224no—
486C2×C4⋊C8—611no—
487#417—24no—
488C2×#103—611no—
489C2×#103—611no—
490C2×#103C2×D6111yescharacteristic, complemented
491C2×#103C2×D6111yescharacteristic, complemented
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×#97—611no—
504#389—1221no—
505#385—1221no—
506#385—1221no—
507#384—611no—
508#380—611no—
509#380—611no—
510C4×C4⋊C4—611no—
511#340—611no—
512#340—611no—
513#340—611no—
514#340—611no—
515C61#2241911yescharacteristic, complemented, Sylow
516C25—1221no—
517C2×#41—22no—
518C2×#41—22no—
519C2×#41—22no—
520C2×#41—41no—
521C2×#41—41no—
522C2×#41C4×D6114yescomplemented
523C22×Q8C22×D6111yescharacteristic
524C22×D4—21no—
525C22×D4—611no—
526C22×D4—614no—
527C22×D4—611no—
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—21no—
538C23×C4—611no—
539C23×C4—1221no—
540C23×C4—1221no—
541C23×C4C22×D6111yescharacteristic
542C2×M16—22no—
543C2×M16—22no—
544C2×M16—41no—
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—614no—
562C4×D4—614no—
563C4×D4—614no—
564C4×D4—1222no—
565C4×D4—2444no—
566C2×C4⋊C4—22no—
567C2×C4⋊C4—21no—
568C2×C4⋊C4—41no—
569C2×C4⋊C4—611no—
570C2×C4⋊C4—611no—
571C2×C4⋊C4—611no—
572C2×C4⋊C4—611no—
573C2×C4⋊C4—1221no—
574C2×C4⋊C4—1222no—
575C2×C4⋊C4—1221no—
576C2×C4⋊C4—1221no—
577C2×C4⋊C4—1221no—
578C2×C4⋊C4—2441no—
579C2×C4⋊C4C22×D6111yescharacteristic
580C2×C4⋊C4C22×D6111yescharacteristic
581C2×C22⋊C4—611no—
582C2×C22⋊C4—611no—
583C2×C22⋊C4—1228no—
584C2×C22⋊C4—1221no—
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—611no—
592C2×C42—1221no—
593C4⋊C8—1222no—
594#103—22no—
595#103—22no—
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#102C22⋊D6114yescomplemented
606C22⋊C8—1222no—
607C22⋊C8—1222no—
608#97—1222no—
609#95—1221no—
610#95—1221no—
611#95—1221no—
612C24—21no—
613C24—611no—
614C24—1224no—
615C24—1221no—
616C24—4881no—
617C24—4881no—
618C24—2442no—
619C24—2442no—
620C24—2442no—
621C24—2442no—
622C24D4×D6111yescharacteristic
623#41—28no—
624#41—44no—
625#41—44no—
626#41—44no—
627C2×Q8—21no—
628C2×Q8—21no—
629C2×Q8—21no—
630C2×Q8—21no—
631C2×Q8—21no—
632C2×Q8C2×C4×D6112yes—
633C2×D4—24no—
634C2×D4—21no—
635C2×D4—21no—
636C2×D4—21no—
637C2×D4—42no—
638C2×D4—42no—
639C2×D4—614no—
640C2×D4—612no—
641C2×D4—1224no—
642C2×D4—1222no—
643C2×D4—1222no—
644C2×D4—1228no—
645C2×D4—1224no—
646C2×D4—1221no—
647C2×D4—1221no—
648C2×D4—1221no—
649C2×D4—1221no—
650C2×D4—1221no—
651C2×D4—4881no—
652C2×D4—4881no—
653C2×D4—2444no—
654C2×D4—2444no—
655C2×D4—2444no—
656C2×D4—2442no—
657C2×D4—2442no—
658C2×D4C2×C4×D6112yes—
659C2×D4#1175822212yes—
660C2×D4C2×C22⋊D6112yes—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—24no—
668C22×C4—21no—
669C22×C4—42no—
670C22×C4—42no—
671C22×C4—42no—
672C22×C4—42no—
673C22×C4—81no—
674C22×C4—611no—
675C22×C4—611no—
676C22×C4—611no—
677C22×C4—612no—
678C22×C4—612no—
679C22×C4—1224no—
680C22×C4—1221no—
681C22×C4—1221no—
682C22×C4—1221no—
683C22×C4—1221no—
684C22×C4—1221no—
685C22×C4—1221no—
686C22×C4—1221no—
687C22×C4—4881no—
688C22×C4—4881no—
689C22×C4—4881no—
690C22×C4—2442no—
691C22×C4—2442no—
692C22×C4C2×C4×D6112yes—
693C22×C4D4×D6112yes—
694C22×C4D4×D6111yescharacteristic
695C22×C4C23×D6111yescharacteristic
696M16—44no—
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×C22⋊D6112yes—
710C4⋊C4—21no—
711C4⋊C4—21no—
712C4⋊C4—21no—
713C4⋊C4—42no—
714C4⋊C4—614no—
715C4⋊C4—612no—
716C4⋊C4—1224no—
717C4⋊C4—1221no—
718C4⋊C4—1221no—
719C4⋊C4—1221no—
720C4⋊C4—1221no—
721C4⋊C4—1221no—
722C4⋊C4—4881no—
723C4⋊C4—2442no—
724C4⋊C4—2442no—
725C4⋊C4C2×C22⋊D6112yes—
726C22⋊C4—614no—
727C22⋊C4—614no—
728C22⋊C4—1224no—
729C22⋊C4—1224no—
730C22⋊C4—1224no—
731C22⋊C4—1224no—
732C22⋊C4—1224no—
733C22⋊C4—2442no—
734C22⋊C4—2442no—
735C42—612no—
736C42—612no—
737C42—2442no—
738C23—22no—
739C23—21no—
740C23—21no—
741C23—21no—
742C23—21no—
743C23—21no—
744C23—22no—
745C23—21no—
746C23—22no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—612no—
752C23—612no—
753C23—612no—
754C23—1221no—
755C23—1221no—
756C23—1221no—
757C23—1221no—
758C23—1222no—
759C23—4884no—
760C23—4884no—
761C23—4884no—
762C23—4884no—
763C23—4884no—
764C23—2448no—
765C23—2448no—
766C23—2441no—
767C23—2441no—
768C23—2441no—
769C23—2441no—
770C23—2441no—
771C23—2441no—
772C23C22⋊C4×D6112yes—
773C23C2×D4×D6111yescharacteristic
774Q8—22no—
775Q8—22no—
776Q8—41no—
777Q8—41no—
778D4—22no—
779D4—22no—
780D4—22no—
781D4—48no—
782D4—1228no—
783D4—1222no—
784D4—1222no—
785D4—4884no—
786D4—2448no—
787D4—2441no—
788D4—2441no—
789D4C4×C22⋊D6114yescomplemented
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—48no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—84no—
807C2×C4—612no—
808C2×C4—612no—
809C2×C4—612no—
810C2×C4—1221no—
811C2×C4—1221no—
812C2×C4—1221no—
813C2×C4—1221no—
814C2×C4—1221no—
815C2×C4—1221no—
816C2×C4—1222no—
817C2×C4—1222no—
818C2×C4—1222no—
819C2×C4—1222no—
820C2×C4—1222no—
821C2×C4—4884no—
822C2×C4—4884no—
823C2×C4—2441no—
824C2×C4—2441no—
825C2×C4—2441no—
826C2×C4—2441no—
827C2×C4—2441no—
828C2×C4—2441no—
829C2×C4—2441no—
830C2×C4—2441no—
831C2×C4C22⋊C4×D6112yes—
832C2×C4C22×C4×D6111yescharacteristic
833C2×C4C2×D4×D6111yescharacteristic
834C2×C4C22×C22⋊D6111yescharacteristic
835C2×C4C2×#1175822211yescharacteristic
836C2×C4#1451982211yescharacteristic
837C2×C4#1451982211yescharacteristic
838C8—22no—
839C8—41no—
840C8—2441no—
841C8—2441no—
842C22—22no—
843C22—22no—
844C22—24no—
845C22—22no—
846C22—42no—
847C22—41no—
848C22—42no—
849C22—41no—
850C22—42no—
851C22—41no—
852C22—42no—
853C22—41no—
854C22—42no—
855C22—42no—
856C22—614no—
857C22—1222no—
858C22—1222no—
859C22—1222no—
860C22—1222no—
861C22—1222no—
862C22—1222no—
863C22—48816no—
864C22—4881no—
865C22—4881no—
866C22—4881no—
867C22—4881no—
868C22—2442no—
869C22—2442no—
870C22—2442no—
871C22C2×C22⋊C4×D6111yescharacteristic
872C22D4×C22⋊D6111yescharacteristic
873C22#1684040211yescharacteristic
874C22AGL(1,ℤ/8)×D6111yescharacteristic
875C22#137×D6111yescharacteristic
876C22#1684056611yescharacteristic
877C22#1684057111yescharacteristic
878C4—22no—
879C4—42no—
880C4—42no—
881C4—81no—
882C4—1222no—
883C4—1222no—
884C4—1222no—
885C4—4881no—
886C4—4881no—
887C4—2442no—
888C4C2×C4×C22⋊D6111yescharacteristic
889C4#1684023511yescharacteristic
890C4D4×C22⋊D6111yescharacteristic
891C4#1684040211yescharacteristic
892C2—42no—
893C2—44no—
894C2—1224no—
895C2—4882no—
896C2C22⋊C4×C22⋊D6111yescharacteristic
897C2#417×D6111yescharacteristic
898C2#2145434311yescharacteristic
899C2#2145729311yescharacteristic
900C2#2145732311yescharacteristic
901C2#2145778111yescharacteristic
902C2#2145790111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#417C2
socleC23×C61C22×D4
prime radicalC2×#16840400C2
cosocleC22×C4×C61C24
hypercenterC2×#417D61
hypocenterC61#22419
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#417

Complements

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

NH ≅ G/Ntype
2. C2×#16839831C2semidirect
3. C2×#102×D61C2semidirect
4. C4⋊C4×C22⋊D61C2semidirect
5. #21446748C2semidirect
6. #21446632C2semidirect
7. #21446257C2semidirect
8. #21446239C2semidirect
9. #21446136C2semidirect
10. #21446123C2semidirect
11. #21445817C2semidirect
12. #21445759C2semidirect
13. #21445748C2semidirect
14. #21445646C2semidirect
15. C2×C61×#417C2semidirect
19. #16840400C4semidirect
32. C2×#14519706C22semidirect
33. C2×#14519701C22semidirect
34. C2×#14519701C22semidirect
42. C2×C22⋊#92418C22semidirect
44. C2×#14519687C22semidirect
48. #16839631C22semidirect
49. #16839622C22semidirect
51. C4⋊C4×Dic61C22semidirect
52. #16839525C22semidirect
53. #16839525C22semidirect
54. #16839524C22semidirect
55. #16839524C22semidirect
57. C22×M16×C61C22semidirect
58. C22×C4⋊C4×C61C22semidirect
60. C2×#103×C61C22semidirect
61. C2×#103×C61C22semidirect
74. C2×D4×D61C2×C4semidirect
84. #14519766C2×C4semidirect
87. #14519753C2×C4semidirect
89. #14519751C2×C4semidirect
93. D4×Dic61C2×C4semidirect
139. C2×#41×C61C2×C4semidirect
159. #102×C61D4semidirect
330. D4×C61C4×D4semidirect
426. C2×D61#417semidirect
443. C2×#417D61semidirect
469. C22×M16C2×D61semidirect
483. C22×C4⋊C4C2×D61semidirect
490. C2×#103C2×D61semidirect
491. C2×#103C2×D61semidirect
515. C61#22419semidirect
522. C2×#41C4×D61semidirect
605. #102C22⋊D61semidirect
789. D4C4×C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168404002
C2×#168398312
C2×#102×D612
C4⋊C4×C22⋊D612
#214467482
#214466322
#214462572
#214462392
#214461362
#214461232
#214458172
#214457592
#214457482
#214456462
C2×C61×#4172
#2241961