Finite Group Databasebeta

← #29695554

Subgroups — #29695554

Order 15616.

1930 conjugacy classes of subgroups.

The subgroup lattice has 960 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×C22⋊D61C211yesmaximal, characteristic
2C2×#16839831C211yesmaximal, characteristic, complemented
3C2×#102×D61C211yesmaximal, characteristic, complemented
4#21448749C211yesmaximal, characteristic, complemented
5#21446744C211yesmaximal, characteristic, complemented
6#21446641C211yesmaximal, characteristic, complemented
7#21446257C211yesmaximal, characteristic, complemented
8#21446244C211yesmaximal, characteristic, complemented
9#21446141C211yesmaximal, characteristic, complemented
10#21446133C211yesmaximal, characteristic, complemented
11#21445827C211yesmaximal, characteristic, complemented
12#21445750C211yesmaximal, characteristic, complemented
13#21445748C211yesmaximal, characteristic, complemented
14#21445646C211yesmaximal, characteristic, complemented
15C2×C61×#418C211yesmaximal, characteristic, complemented
16C23×C22⋊D61—21no—
17C22×D4×D61C2211yescharacteristic
18C22×C8×D61C2211yescharacteristic, complemented
19D4×C22⋊D61—24no—
20D4×C22⋊D61C418yescomplemented
21C2×#14519773C2211yescharacteristic
22C2×#14519751C2211yescharacteristic
23C2×#14519749—21no—
24C2×#14519748C2211yescharacteristic
25C2×#14519746—21no—
26C2×#14519745—21no—
27C2×D4×Dic61C2211yescharacteristic
28C2×C4×C22⋊D61C2211yescharacteristic
29C2×C4⋊C4×D61C2211yescharacteristic, complemented
30#16839831—24no—
31C2×#14519706C2211yescharacteristic, complemented
32C2×#14519699C2211yescharacteristic, complemented
33C2×#14519699C2211yescharacteristic, complemented
34C2×#14519698C2211yescharacteristic
35C2×#14519698C2211yescharacteristic
36C2×#14519698C2211yescharacteristic, complemented
37C2×#14519698C2211yescharacteristic, complemented
38C2×#14519697C2211yescharacteristic, complemented
39C2×#14519697C2211yescharacteristic, complemented
40#102×D61—24no—
41C2×C22⋊#92418C2211yescharacteristic, complemented
42C2×#14519689C2211yescharacteristic, complemented
43C2×#14519687C2211yescharacteristic, complemented
44#16839656—21no—
45#16839646—21no—
46#16839638—21no—
47#16839627C2211yescharacteristic, complemented
48#16839622C2211yescharacteristic, complemented
49#16839619C2211yescharacteristic, complemented
50C4⋊C4×Dic61C2211yescharacteristic, complemented
51C4×#11758198—21no—
52#16839525C2211yescharacteristic, complemented
53#16839525C2211yescharacteristic, complemented
54#16839524C2211yescharacteristic, complemented
55#16839524C2211yescharacteristic, complemented
56C23×D4×C61C2211yescharacteristic
57C22×M16×C61C2211yescharacteristic, complemented
58C2×#117×C61C2211yescharacteristic, complemented
59C61×#418—24no—
60C2×#102×C61C2211yescharacteristic
61C2×#102×C61C2211yescharacteristic
62C2×#102×C61C2211yescharacteristic, complemented
63C2×#102×C61C2211yescharacteristic, complemented
64C24×D61—21no—
65C22×D244C2311yescharacteristic
66C22×C22⋊D61—21no—
67C22×C22⋊D61—21no—
68C22×C22⋊D61—28no—
69C22×C22⋊D61—21no—
70C22×C22⋊D61—21no—
71C22×C22⋊D61—21no—
72C22×C22⋊D61—44no—
73C22×C22⋊D61—44no—
74C22×C22⋊D61D411yescharacteristic
75C2×D4×D61—22no—
76C2×D4×D61—22no—
77C2×D4×D61—22no—
78C2×D4×D61—41no—
79C2×D4×D61—41no—
80C2×D4×D61C2×C414yes—
81C23×Dic61—21no—
82C22×C4×D61—21no—
83C22×C4×D61C2311yescharacteristic
84C22×#92418C2311yescharacteristic
85C22×#92418C2311yescharacteristic
86C2×C8×D61—22no—
87C2×C8×D61—22no—
88C2×C8×D61—41no—
89#14519773—22no—
90#14519773C2×C414yescomplemented
91#14519751—22no—
92#14519751C2×C414yescomplemented
93#14519749—28no—
94#14519748—22no—
95#14519748C2×C414yes—
96#14519746—28no—
97#14519745—28no—
98D4×Dic61—22no—
99D4×Dic61C2×C414yescomplemented
100C4×C22⋊D61C2×C414yes—
101C4×C22⋊D61D414yes—
102C2×C4⋊Dic61C2311yescharacteristic
103C2×C4⋊Dic61C2311yescharacteristic
104C2×C4⋊Dic61C2311yescharacteristic
105C2×#11758196—21no—
106C2×#11758196D411yescharacteristic
107C4⋊C4×D61—22no—
108C4⋊C4×D61—41no—
109C2×C22⋊Dic61—21no—
110C2×C22⋊Dic61—21no—
111C2×C22⋊Dic61—21no—
112C2×C22⋊Dic61D411yescharacteristic
113C2×#11758198—21no—
114C2×#11758198—21no—
115C2×#11758198D411yescharacteristic
116C2×C4×Dic61—21no—
117C2×C4×Dic61C2311yescharacteristic
118#14519706—22no—
119#14519699—22no—
120#14519699—41no—
121#14519698—22no—
122#14519698—22no—
123#14519698—41no—
124#14519698—41no—
125#14519697—22no—
126#14519697—41no—
127C22⋊#92418—22no—
128#14519689—22no—
129#14519687—22no—
130#14519684—21no—
131#14519684—21no—
132#14519684—21no—
133#14519684—21no—
134#14519684—21no—
135C25×C61—21no—
136C22×D4×C61—22no—
137C22×D4×C61—22no—
138C22×D4×C61—21no—
139C22×D4×C61—22no—
140C22×D4×C61—41no—
141C22×D4×C61—41no—
142C22×D4×C61C2×C414yescomplemented
143C22×D4×C61C2311yescharacteristic
144C22×D4×C61C2311yescharacteristic
145C23×C4×C61C2311yescharacteristic
146C2×M16×C61—22no—
147C2×M16×C61—22no—
148C2×M16×C61—41no—
149C22×C8×C61C2311yescharacteristic
150C22×C8×C61C2311yescharacteristic
151#117×C61—22no—
152#117×C61—41no—
153C2×C4⋊C4×C61C2311yescharacteristic
154C2×C4⋊C4×C61C2311yescharacteristic
155C2×C22⋊C4×C61—21no—
156C2×C42×C61—21no—
157#102×C61—22no—
158#102×C61—22no—
159#102×C61—22no—
160#102×C61D414yescomplemented
161C24×C61—21no—
162C24×C61—21no—
163C24×C61—24no—
164C24×C61—42no—
165C24×C61—42no—
166C24×C61—42no—
167C24×C61—42no—
168C24×C61—81no—
169C24×C61—81no—
170C24×C61C2×D411yescharacteristic
171C23×D61—21no—
172C23×D61—24no—
173C23×D61—42no—
174C23×D61—42no—
175C23×D61—42no—
176C23×D61—42no—
177C23×D61—81no—
178C23×D61—81no—
179C23×D61C2×D411yescharacteristic
180C2×D4×C61—28no—
181C2×D4×C61—24no—
182C2×D4×C61—21no—
183C2×D4×C61—21no—
184C2×D4×C61—21no—
185C2×D4×C61—21no—
186C2×D4×C61—21no—
187C2×D4×C61—21no—
188C2×D4×C61—21no—
189C2×D4×C61—21no—
190C2×D4×C61—44no—
191C2×D4×C61—44no—
192C2×D4×C61—44no—
193C2×D4×C61—42no—
194C2×D4×C61—42no—
195C2×D4×C61C22×C412yes—
196C2×D4×C61C22×C412yes—
197C2×D4×C61C2×D412yes—
198C2×D4×C61#4112yes—
199C22×C4×C61—21no—
200C22×C4×C61—21no—
201C22×C4×C61—21no—
202C22×C4×C61—21no—
203C22×C4×C61—21no—
204C22×C4×C61—21no—
205C22×C4×C61C22×C412yes—
206C22×C4×C61C2×D411yescharacteristic
207C22×C4×C61C2×D412yes—
208C22×C4×C61C2411yescharacteristic
209C2×C22⋊D61—22no—
210C2×C22⋊D61—22no—
211C2×C22⋊D61—24no—
212C2×C22⋊D61—24no—
213C2×C22⋊D61—24no—
214C2×C22⋊D61—24no—
215C2×C22⋊D61—24no—
216C2×C22⋊D61—42no—
217C2×C22⋊D61—42no—
218C2×C22⋊D61—42no—
219C2×C22⋊D61—42no—
220C2×C22⋊D61—432no—
221C2×C22⋊D61—42no—
222C2×C22⋊D61—42no—
223C2×C22⋊D61—42no—
224C2×C22⋊D61—42no—
225C2×C22⋊D61—81no—
226C2×C22⋊D61—81no—
227C2×C22⋊D61C22⋊C414yes—
228C22×Dic61—21no—
229C22×Dic61—24no—
230C22×Dic61—21no—
231C22×Dic61—21no—
232C22×Dic61—42no—
233C22×Dic61—42no—
234C22×Dic61C2×D411yescharacteristic
235C22×Dic61C2×D411yescharacteristic
236C22×Dic61C2×D411yescharacteristic
237D4×D61—28no—
238D4×D61—44no—
239D4×D61—44no—
240D4×D61—44no—
241C2×D244—21no—
242C2×D244—21no—
243C2×D244—21no—
244C2×D244—21no—
245C2×D244—21no—
246C2×D244C22×C412yes—
247C2×C4×D61—21no—
248C2×C4×D61—21no—
249C2×C4×D61—21no—
250C2×C4×D61—21no—
251C2×C4×D61—42no—
252C2×C4×D61—42no—
253C2×C4×D61—81no—
254C2×C4×D61C22×C412yes—
255C2×C4×D61C2×D412yes—
256M16×C61—44no—
257C2×C8×C61—21no—
258C2×C8×C61—21no—
259C2×C8×C61—21no—
260C2×C8×C61—21no—
261C2×C8×C61—21no—
262C2×C8×C61C2×D412yescomplemented
263C4⋊C4×C61—21no—
264C4⋊C4×C61—21no—
265C4⋊C4×C61—21no—
266C4⋊C4×C61C2×D412yescomplemented
267C22⋊C4×C61—42no—
268C42×C61—42no—
269C22⋊Dic61—24no—
270C22⋊Dic61—24no—
271C22⋊Dic61—81no—
272C22⋊Dic61C22⋊C414yes—
273#11758198—24no—
274#11758198—42no—
275#11758198C22⋊C414yes—
276C4⋊Dic61—21no—
277C4⋊Dic61—21no—
278C4⋊Dic61—21no—
279C4⋊Dic61—21no—
280C4⋊Dic61—21no—
281C4⋊Dic61C22×C412yes—
282#11758196—42no—
283#11758196C22⋊C414yes—
284C4×Dic61—81no—
285C4×Dic61C22×C412yes—
286C4×Dic61C2×D412yes—
287C2×#92418—21no—
288C2×#92418—21no—
289C2×#92418—21no—
290C2×#92418—21no—
291C2×#92418—21no—
292C2×#92418—21no—
293C8×D61—44no—
294C23×C61—22no—
295C23×C61—21no—
296C23×C61—22no—
297C23×C61—22no—
298C23×C61—21no—
299C23×C61—21no—
300C23×C61—21no—
301C23×C61—21no—
302C23×C61—21no—
303C23×C61—22no—
304C23×C61—48no—
305C23×C61—48no—
306C23×C61—41no—
307C23×C61—41no—
308C23×C61—41no—
309C23×C61—41no—
310C23×C61—41no—
311C23×C61—41no—
312C23×C61—41no—
313C23×C61—41no—
314C23×C61—41no—
315C23×C61—41no—
316C23×C61—84no—
317C23×C61—84no—
318C23×C61—84no—
319C23×C61—84no—
320C23×C61—84no—
321C23×C61C2×C22⋊C412yes—
322C23×C61C22×D411yescharacteristic
323C22×D61—21no—
324C22×D61—21no—
325C22×D61—21no—
326C22×D61—21no—
327C22×D61—22no—
328C22×D61—48no—
329C22×D61—41no—
330C22×D61—41no—
331C22×D61—41no—
332C22×D61—41no—
333C22×D61—41no—
334C22×D61—41no—
335C22×D61—48no—
336C22×D61—84no—
337C22×D61—84no—
338C22×D61—84no—
339C22×D61—84no—
340C22×D61—84no—
341C22×D61C2×C22⋊C412yes—
342C22×D61AGL(1,ℤ/8)12yes—
343C22×D61AGL(1,ℤ/8)12yes—
344D4×C61—22no—
345D4×C61—22no—
346D4×C61—22no—
347D4×C61—22no—
348D4×C61—22no—
349D4×C61—48no—
350D4×C61—41no—
351D4×C61—41no—
352D4×C61C4×D414yes—
353C2×C4×C61—21no—
354C2×C4×C61—21no—
355C2×C4×C61—22no—
356C2×C4×C61—22no—
357C2×C4×C61—22no—
358C2×C4×C61—22no—
359C2×C4×C61—22no—
360C2×C4×C61—41no—
361C2×C4×C61—41no—
362C2×C4×C61—41no—
363C2×C4×C61—41no—
364C2×C4×C61—41no—
365C2×C4×C61C2×C22⋊C412yes—
366C2×C4×C61C23×C411yescharacteristic
367C2×C4×C61C22×D411yescharacteristic
368C2×C4×C61C22×D411yescharacteristic
369C2×C4×C61C2×#4111yescharacteristic
370C2×C4×C61H(5,𝔽2)11yescharacteristic
371C2×C4×C61H(5,𝔽2)11yescharacteristic
372C22⋊D61—28no—
373C22⋊D61—48no—
374C22⋊D61—48no—
375C22⋊D61—48no—
376C22⋊D61—48no—
377C22⋊D61—84no—
378C2×Dic61—21no—
379C2×Dic61—21no—
380C2×Dic61—21no—
381C2×Dic61—21no—
382C2×Dic61—21no—
383C2×Dic61—21no—
384C2×Dic61—22no—
385C2×Dic61—48no—
386C2×Dic61—41no—
387C2×Dic61—41no—
388C2×Dic61—41no—
389C2×Dic61—41no—
390C2×Dic61—41no—
391C2×Dic61—41no—
392C2×Dic61—41no—
393C2×Dic61—41no—
394C2×Dic61C2×C22⋊C412yes—
395C2×Dic61C2×C22⋊C412yes—
396C2×Dic61C2×C22⋊C412yes—
397D244—22no—
398D244—22no—
399D244—41no—
400D244—41no—
401C4×D61—22no—
402C4×D61—22no—
403C4×D61—22no—
404C4×D61—22no—
405C4×D61—84no—
406C8×C61—22no—
407C8×C61—41no—
408#92418—41no—
409#92418—41no—
410#22423—611nomaximal, Sylow
411C22×C61—24no—
412C22×C61—22no—
413C22×C61—22no—
414C22×C61—22no—
415C22×C61—42no—
416C22×C61—42no—
417C22×C61—42no—
418C22×C61—41no—
419C22×C61—42no—
420C22×C61—41no—
421C22×C61—42no—
422C22×C61—41no—
423C22×C61—42no—
424C22×C61—41no—
425C22×C61—42no—
426C22×C61—42no—
427C22×C61—42no—
428C22×C61—816no—
429C22×C61—81no—
430C22×C61—81no—
431C22×C61—81no—
432C22×C61—81no—
433C22×C61C22×C22⋊C411yescharacteristic
434C22×C61D4211yescharacteristic
435C22×C61#54611yescharacteristic
436C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
437C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
438C22×C61#57611yescharacteristic
439C22×C61#57711yescharacteristic
440C2×D61—22no—
441C2×D61—22no—
442C2×D61—22no—
443C2×D61—22no—
444C2×D61—22no—
445C2×D61—22no—
446C2×D61—42no—
447C2×D61—42no—
448C2×D61—42no—
449C2×D61—816no—
450C2×D61—81no—
451C2×D61—81no—
452C2×D61—81no—
453C2×D61—81no—
454C2×D61#41814yescomplemented
455C4×C61—22no—
456C4×C61—42no—
457C4×C61—81no—
458C4×C61C2×C4×D411yescharacteristic
459C4×C61#51811yescharacteristic
460C4×C61D4211yescharacteristic
461C4×C61#54611yescharacteristic
462Dic61—22no—
463Dic61—22no—
464Dic61—22no—
465Dic61—42no—
466Dic61—81no—
467Dic61—81no—
468C2×D42—611no—
469C2×#435—611no—
470C2×#418D6111yescharacteristic, complemented
471C22×#102—611no—
472#2352—611no—
473#1982—611no—
474#1961—611no—
475#1895—611no—
476#1893—611no—
477#1875—611no—
478#1874—611no—
479#1804—611no—
480#1786—611no—
481#1786—611no—
482#1762—611no—
483C2×C61—44no—
484C2×C61—42no—
485C2×C61—82no—
486C2×C61D4×C22⋊C411yescharacteristic
487C2×C61C2×#41811yescharacteristic
488C2×C61#289711yescharacteristic
489C2×C61#326411yescharacteristic
490C2×C61#326511yescharacteristic
491C2×C61#331011yescharacteristic
492C2×C61#331811yescharacteristic
493D61—24no—
494D61—82no—
495C23×D4—611no—
496C23×D4—1221no—
497C23×D4C2×D6111yescharacteristic
498C22×M16C2×D6111yescharacteristic, complemented
499C23×C8—611no—
500D42—618no—
501D42—1224no—
502C2×#127—611no—
503C2×#121—611no—
504C2×#121—611no—
505C2×#121—1221no—
506C2×#120—1221no—
507C2×#120—1221no—
508C2×C4×D4—611no—
509C2×C4×D4—611no—
510C2×#117C2×D6111yescharacteristic, complemented
511C22×C4⋊C4—611no—
512#435—1224no—
513C2×C4⋊C8—611no—
514#418—24no—
515C2×#102—611no—
516C2×#102—611no—
517C2×#102—611no—
518C2×#102—611no—
519C2×#102—611no—
520C2×#102—611no—
521C2×#102—611no—
522C2×#102—611no—
523C2×#102—1224no—
524C2×#102C2×D6111yescharacteristic
525C2×#102C2×D6111yescharacteristic
526C2×#102C2×D6111yescharacteristic, complemented
527C2×#102C2×D6111yescharacteristic, complemented
528C2×C22⋊C8—611no—
529C2×C22⋊C8—611no—
530C2×#97—611no—
531#388—1221no—
532#387—1221no—
533#386—1221no—
534#382—611no—
535#380—611no—
536#380—611no—
537C4×C4⋊C4—611no—
538C4×C22⋊C4—1221no—
539#340—611no—
540#340—611no—
541#340—611no—
542#340—611no—
543C61#2242311yescharacteristic, complemented, Sylow
544C25—21no—
545C25—1221no—
546C22×D4—22no—
547C22×D4—22no—
548C22×D4—21no—
549C22×D4—22no—
550C22×D4—41no—
551C22×D4—41no—
552C22×D4—611no—
553C22×D4—614no—
554C22×D4—611no—
555C22×D4—1222no—
556C22×D4—1221no—
557C22×D4—1221no—
558C22×D4—1221no—
559C22×D4—1228no—
560C22×D4—1222no—
561C22×D4—1222no—
562C22×D4—1221no—
563C22×D4—1221no—
564C22×D4—2441no—
565C22×D4—2441no—
566C22×D4—2444no—
567C22×D4—2444no—
568C22×D4C4×D6114yescomplemented
569C22×D4C22×D6111yescharacteristic
570C22×D4C22×D6111yescharacteristic
571C23×C4—611no—
572C23×C4—1221no—
573C23×C4—1221no—
574C23×C4C22×D6111yescharacteristic
575C2×M16—22no—
576C2×M16—22no—
577C2×M16—41no—
578C22×C8—611no—
579C22×C8—611no—
580C22×C8—1222no—
581C22×C8—1222no—
582C22×C8—2441no—
583C22×C8C22×D6111yescharacteristic
584C22×C8C22×D6111yescharacteristic
585#127—614no—
586#127—1222no—
587#121—614no—
588#121—614no—
589#121—1228no—
590#121—1222no—
591#121—1222no—
592#120—1228no—
593#120—1228no—
594C4×D4—614no—
595C4×D4—614no—
596C4×D4—614no—
597C4×D4—1222no—
598#117—22no—
599#117—41no—
600C2×C4⋊C4—611no—
601C2×C4⋊C4—611no—
602C2×C4⋊C4—611no—
603C2×C4⋊C4—611no—
604C2×C4⋊C4—1222no—
605C2×C4⋊C4—1221no—
606C2×C4⋊C4—2441no—
607C2×C4⋊C4C22×D6111yescharacteristic
608C2×C4⋊C4C22×D6111yescharacteristic
609C2×C22⋊C4—21no—
610C2×C22⋊C4—611no—
611C2×C22⋊C4—611no—
612C2×C22⋊C4—1221no—
613C2×C22⋊C4—1221no—
614C2×C22⋊C4—1221no—
615C2×C22⋊C4—1221no—
616C2×C22⋊C4—1221no—
617C2×C42—21no—
618C2×C42—611no—
619C2×C42—1221no—
620C4⋊C8—1222no—
621#102—22no—
622#102—22no—
623#102—22no—
624#102—1222no—
625#102—1222no—
626#102—1222no—
627#102—1222no—
628#102—2441no—
629#102—2441no—
630#102—2441no—
631#102—2441no—
632#102C22⋊D6114yescomplemented
633C22⋊C8—1222no—
634C22⋊C8—1222no—
635#97—1222no—
636#95—1221no—
637#95—1221no—
638#95—1221no—
639#95—1221no—
640#95—1221no—
641C24—21no—
642C24—21no—
643C24—24no—
644C24—42no—
645C24—42no—
646C24—42no—
647C24—42no—
648C24—81no—
649C24—81no—
650C24—611no—
651C24—1224no—
652C24—1221no—
653C24—4881no—
654C24—4881no—
655C24—2442no—
656C24—2442no—
657C24—2442no—
658C24—2442no—
659C24D4×D6111yescharacteristic
660C2×D4—28no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—21no—
668C2×D4—21no—
669C2×D4—24no—
670C2×D4—44no—
671C2×D4—44no—
672C2×D4—44no—
673C2×D4—42no—
674C2×D4—42no—
675C2×D4—614no—
676C2×D4—612no—
677C2×D4—1224no—
678C2×D4—1224no—
679C2×D4—1224no—
680C2×D4—1222no—
681C2×D4—1222no—
682C2×D4—1228no—
683C2×D4—1224no—
684C2×D4—1224no—
685C2×D4—1221no—
686C2×D4—1221no—
687C2×D4—1221no—
688C2×D4—1221no—
689C2×D4—1221no—
690C2×D4—4881no—
691C2×D4—4881no—
692C2×D4—2444no—
693C2×D4—2444no—
694C2×D4—2444no—
695C2×D4—2442no—
696C2×D4—2442no—
697C2×D4—2442no—
698C2×D4—2442no—
699C2×D4—24432no—
700C2×D4—2442no—
701C2×D4—2442no—
702C2×D4—2442no—
703C2×D4—2442no—
704C2×D4C2×C4×D6112yes—
705C2×D4C2×C4×D6112yes—
706C2×D4#1175822212yes—
707C2×D4C2×C22⋊D6112yes—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—611no—
715C22×C4—611no—
716C22×C4—611no—
717C22×C4—612no—
718C22×C4—612no—
719C22×C4—1224no—
720C22×C4—1221no—
721C22×C4—1221no—
722C22×C4—1221no—
723C22×C4—1221no—
724C22×C4—1221no—
725C22×C4—1221no—
726C22×C4—1221no—
727C22×C4—4881no—
728C22×C4—2442no—
729C22×C4—2442no—
730C22×C4—2442no—
731C22×C4—2442no—
732C22×C4C2×C4×D6112yes—
733C22×C4D4×D6112yes—
734C22×C4D4×D6111yescharacteristic
735C22×C4C23×D6111yescharacteristic
736M16—44no—
737C2×C8—21no—
738C2×C8—21no—
739C2×C8—21no—
740C2×C8—21no—
741C2×C8—21no—
742C2×C8—1221no—
743C2×C8—1221no—
744C2×C8—1221no—
745C2×C8—1221no—
746C2×C8—1221no—
747C2×C8—1221no—
748C2×C8—2444no—
749C2×C8C2×C22⋊D6112yescomplemented
750C4⋊C4—21no—
751C4⋊C4—21no—
752C4⋊C4—21no—
753C4⋊C4—614no—
754C4⋊C4—612no—
755C4⋊C4—1221no—
756C4⋊C4—1221no—
757C4⋊C4—1221no—
758C4⋊C4—1221no—
759C4⋊C4—1221no—
760C4⋊C4—2442no—
761C4⋊C4C2×C22⋊D6112yescomplemented
762C22⋊C4—42no—
763C22⋊C4—614no—
764C22⋊C4—614no—
765C22⋊C4—1224no—
766C22⋊C4—1224no—
767C22⋊C4—1224no—
768C22⋊C4—4881no—
769C22⋊C4—2442no—
770C42—42no—
771C42—612no—
772C42—612no—
773C42—4881no—
774C23—22no—
775C23—21no—
776C23—21no—
777C23—21no—
778C23—21no—
779C23—21no—
780C23—22no—
781C23—21no—
782C23—22no—
783C23—22no—
784C23—48no—
785C23—48no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23—84no—
797C23—84no—
798C23—84no—
799C23—84no—
800C23—84no—
801C23—612no—
802C23—612no—
803C23—612no—
804C23—1221no—
805C23—1221no—
806C23—1221no—
807C23—1221no—
808C23—1222no—
809C23—4884no—
810C23—4884no—
811C23—4884no—
812C23—4884no—
813C23—4884no—
814C23—2448no—
815C23—2448no—
816C23—2441no—
817C23—2441no—
818C23—2441no—
819C23—2441no—
820C23—2441no—
821C23—2441no—
822C23C22⋊C4×D6112yes—
823C23C2×D4×D6111yescharacteristic
824D4—22no—
825D4—22no—
826D4—22no—
827D4—22no—
828D4—22no—
829D4—48no—
830D4—41no—
831D4—41no—
832D4—1228no—
833D4—1222no—
834D4—1222no—
835D4—4884no—
836D4—2448no—
837D4—2448no—
838D4—2448no—
839D4—2448no—
840D4—2441no—
841D4—2441no—
842D4C4×C22⋊D6114yes—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—612no—
856C2×C4—612no—
857C2×C4—612no—
858C2×C4—1221no—
859C2×C4—1221no—
860C2×C4—1221no—
861C2×C4—1221no—
862C2×C4—1221no—
863C2×C4—1221no—
864C2×C4—1222no—
865C2×C4—1222no—
866C2×C4—1222no—
867C2×C4—1222no—
868C2×C4—1222no—
869C2×C4—4884no—
870C2×C4—2448no—
871C2×C4—2441no—
872C2×C4—2441no—
873C2×C4—2441no—
874C2×C4—2441no—
875C2×C4—2441no—
876C2×C4—2441no—
877C2×C4—2441no—
878C2×C4—2441no—
879C2×C4C22⋊C4×D6112yes—
880C2×C4C22×C4×D6111yescharacteristic
881C2×C4C2×D4×D6111yescharacteristic
882C2×C4C22×C22⋊D6111yescharacteristic
883C2×C4C2×#1175822211yescharacteristic
884C2×C4#1451982211yescharacteristic
885C2×C4#1451982211yescharacteristic
886C8—22no—
887C8—41no—
888C8—2441no—
889C8—2441no—
890C22—22no—
891C22—22no—
892C22—24no—
893C22—22no—
894C22—42no—
895C22—41no—
896C22—42no—
897C22—41no—
898C22—42no—
899C22—41no—
900C22—42no—
901C22—41no—
902C22—42no—
903C22—42no—
904C22—42no—
905C22—42no—
906C22—42no—
907C22—816no—
908C22—81no—
909C22—81no—
910C22—81no—
911C22—81no—
912C22—614no—
913C22—1222no—
914C22—1222no—
915C22—1222no—
916C22—1222no—
917C22—1222no—
918C22—1222no—
919C22—48816no—
920C22—4881no—
921C22—4881no—
922C22—4881no—
923C22—4881no—
924C22—2442no—
925C22—2442no—
926C22—2442no—
927C22C2×C22⋊C4×D6111yescharacteristic
928C22D4×C22⋊D6111yescharacteristic
929C22#1684040211yescharacteristic
930C22AGL(1,ℤ/8)×D6111yescharacteristic
931C22AGL(1,ℤ/8)×D6111yescharacteristic
932C22#1684056611yescharacteristic
933C22#1684057211yescharacteristic
934C4—22no—
935C4—42no—
936C4—81no—
937C4—1222no—
938C4—1222no—
939C4—1222no—
940C4—4881no—
941C4—4881no—
942C4—2442no—
943C4C2×C4×C22⋊D6111yescharacteristic
944C4#1684023511yescharacteristic
945C4D4×C22⋊D6111yescharacteristic
946C4#1684040211yescharacteristic
947C2—42no—
948C2—44no—
949C2—82no—
950C2—1224no—
951C2—4882no—
952C2C22⋊C4×C22⋊D6111yescharacteristic
953C2#418×D6111yescharacteristic
954C2#2145434411yescharacteristic
955C2#2145729311yescharacteristic
956C2#2145730811yescharacteristic
957C2#2145784111yescharacteristic
958C2#2145796111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#418C2
socleC23×C61C22×D4
prime radicalC2×D4×C22⋊D61C2
cosocleC22×C4×C61C24
hypercenterC2×#418D61
hypocenterC61#22423
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×#16839831C2semidirect
3. C2×#102×D61C2semidirect
4. #21448749C2semidirect
5. #21446744C2semidirect
6. #21446641C2semidirect
7. #21446257C2semidirect
8. #21446244C2semidirect
9. #21446141C2semidirect
10. #21446133C2semidirect
11. #21445827C2semidirect
12. #21445750C2semidirect
13. #21445748C2semidirect
14. #21445646C2semidirect
15. C2×C61×#418C2semidirect
18. C22×C8×D61C22semidirect
20. D4×C22⋊D61C4semidirect
29. C2×C4⋊C4×D61C22semidirect
31. C2×#14519706C22semidirect
32. C2×#14519699C22semidirect
33. C2×#14519699C22semidirect
36. C2×#14519698C22semidirect
37. C2×#14519698C22semidirect
38. C2×#14519697C22semidirect
39. C2×#14519697C22semidirect
41. C2×C22⋊#92418C22semidirect
42. C2×#14519689C22semidirect
43. C2×#14519687C22semidirect
47. #16839627C22semidirect
48. #16839622C22semidirect
49. #16839619C22semidirect
50. C4⋊C4×Dic61C22semidirect
52. #16839525C22semidirect
53. #16839525C22semidirect
54. #16839524C22semidirect
55. #16839524C22semidirect
57. C22×M16×C61C22semidirect
58. C2×#117×C61C22semidirect
62. C2×#102×C61C22semidirect
63. C2×#102×C61C22semidirect
90. #14519773C2×C4semidirect
92. #14519751C2×C4semidirect
99. D4×Dic61C2×C4semidirect
142. C22×D4×C61C2×C4semidirect
160. #102×C61D4semidirect
262. C2×C8×C61C2×D4semidirect
266. C4⋊C4×C61C2×D4semidirect
454. C2×D61#418semidirect
470. C2×#418D61semidirect
498. C22×M16C2×D61semidirect
510. C2×#117C2×D61semidirect
526. C2×#102C2×D61semidirect
527. C2×#102C2×D61semidirect
543. C61#22423semidirect
568. C22×D4C4×D61semidirect
632. #102C22⋊D61semidirect
749. C2×C8C2×C22⋊D61semidirect
761. C4⋊C4C2×C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
C2×D4×C22⋊D612
C2×#168398312
C2×#102×D612
#214487492
#214467442
#214466412
#214462572
#214462442
#214461412
#214461332
#214458272
#214457502
#214457482
#214456462
C2×C61×#4182
#2242361