Finite Group Databasebeta

← #29695557

Subgroups — #29695557

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×#16839830C211yesmaximal, characteristic, complemented
3C2×#16839765C211yesmaximal, characteristic, complemented
4C22×#14519698C211yesmaximal, characteristic, complemented
5#21448750C211yesmaximal, characteristic, complemented
6#21446744C211yesmaximal, characteristic, complemented
7#21446641C211yesmaximal, characteristic, complemented
8#21446254C211yesmaximal, characteristic, complemented
9#21446245C211yesmaximal, characteristic, complemented
10#21446138C211yesmaximal, characteristic, complemented
11#21446134C211yesmaximal, characteristic, complemented
12#21445827C211yesmaximal, characteristic, complemented
13#21445748C211yesmaximal, characteristic, complemented
14#21445646C211yesmaximal, characteristic, complemented
15C61×#1786C211yesmaximal, characteristic, complemented
16C23×C22⋊D61—21no—
17C22×D4×D61C2211yescharacteristic
18C22×#11758189C2211yescharacteristic, complemented
19C23×#92418C2211yescharacteristic, complemented
20D4×C22⋊D61—24no—
21D4×C22⋊D61C418yescomplemented
22C2×#14519773C2211yescharacteristic
23C2×#14519751C2211yescharacteristic
24C2×#14519749—21no—
25C2×#14519748C2211yescharacteristic
26C2×#14519746—21no—
27C2×#14519745—21no—
28C2×D4×Dic61C2211yescharacteristic
29C2×C4×C22⋊D61C2211yescharacteristic
30C2×#14519735C2211yescharacteristic, complemented
31C22×C4⋊Dic61C2211yescharacteristic, complemented
32#16839830—24no—
33C2×#14519706C2211yescharacteristic, complemented
34#16839765—24no—
35C2×#14519699C2211yescharacteristic, complemented
36C2×#14519699C2211yescharacteristic, complemented
37C2×#14519698—24no—
38C2×#14519698C2211yescharacteristic
39C2×#14519698C2211yescharacteristic
40C2×#14519698C2211yescharacteristic, complemented
41C2×#14519698C2211yescharacteristic, complemented
42C2×#14519697C2211yescharacteristic, complemented
43C2×#14519697C2211yescharacteristic, complemented
44C2×#14519689C2211yescharacteristic, complemented
45C2×#14519687C2211yescharacteristic, complemented
46#16839654—21no—
47#16839649—21no—
48#16839639—21no—
49#16839627C2211yescharacteristic, complemented
50#16839619C2211yescharacteristic, complemented
51C4⋊C4×Dic61C2211yescharacteristic, complemented
52C22⋊C4×Dic61—21no—
53#16839525C2211yescharacteristic, complemented
54#16839525C2211yescharacteristic, complemented
55#16839524C2211yescharacteristic, complemented
56#16839524C2211yescharacteristic, complemented
57C23×D4×C61C2211yescharacteristic
58C2×#102×C61C2211yescharacteristic
59C2×#102×C61C2211yescharacteristic
60C2×#102×C61C2211yescharacteristic, complemented
61C2×#102×C61C2211yescharacteristic, complemented
62C2×C22⋊C8×C61C2211yescharacteristic, complemented
63C61×#380C2211yescharacteristic, 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×C414yescomplemented
81C23×Dic61—21no—
82C23×Dic61—21no—
83C22×C4×D61C2311yescharacteristic
84C2×#11758189—22no—
85C2×#11758189—22no—
86C2×#11758189—41no—
87C22×#92418—22no—
88C22×#92418—22no—
89C22×#92418—41no—
90C22×#92418C2311yescharacteristic
91C22×#92418C2311yescharacteristic
92#14519773—22no—
93#14519773C2×C414yescomplemented
94#14519751—22no—
95#14519751C2×C414yes—
96#14519749—28no—
97#14519748—22no—
98#14519748C2×C414yescomplemented
99#14519746—28no—
100#14519745—28no—
101D4×Dic61—22no—
102D4×Dic61C2×C414yescomplemented
103C4×C22⋊D61C2×C414yes—
104C4×C22⋊D61D414yes—
105#14519735—22no—
106#14519735—41no—
107C2×C4⋊Dic61—22no—
108C2×C4⋊Dic61—21no—
109C2×C4⋊Dic61—41no—
110C2×C4⋊Dic61C2311yescharacteristic
111C2×C4⋊Dic61C2311yescharacteristic
112C2×C4⋊Dic61C2311yescharacteristic
113C2×#11758196D411yescharacteristic
114C2×C22⋊Dic61—21no—
115C2×C22⋊Dic61—21no—
116C2×C22⋊Dic61D411yescharacteristic
117C2×#11758198—21no—
118C2×#11758198—21no—
119C2×#11758198—21no—
120C2×#11758198D411yescharacteristic
121C2×C4×Dic61—21no—
122C2×C4×Dic61—21no—
123C2×C4×Dic61C2311yescharacteristic
124#14519706—22no—
125#14519699—22no—
126#14519699—41no—
127#14519698—22no—
128#14519698—22no—
129#14519698—22no—
130#14519698D414yescomplemented
131#14519697—22no—
132#14519697—41no—
133#14519689—22no—
134#14519687—22no—
135#14519684—21no—
136#14519684—21no—
137#14519684—21no—
138#14519684—21no—
139C25×C61—21no—
140C22×D4×C61—22no—
141C22×D4×C61—22no—
142C22×D4×C61—21no—
143C22×D4×C61—22no—
144C22×D4×C61—41no—
145C22×D4×C61—41no—
146C22×D4×C61C2×C414yes—
147C22×D4×C61C2311yescharacteristic
148C22×D4×C61C2311yescharacteristic
149C23×C4×C61C2311yescharacteristic
150C22×C8×C61C2311yescharacteristic
151C22×C8×C61C2311yescharacteristic
152C2×C4⋊C4×C61C2311yescharacteristic
153C2×C4⋊C4×C61C2311yescharacteristic
154C2×C22⋊C4×C61—21no—
155#102×C61—22no—
156#102×C61—22no—
157#102×C61—41no—
158#102×C61—41no—
159C22⋊C8×C61—22no—
160#95×C61—21no—
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—21no—
230C22×Dic61—24no—
231C22×Dic61—21no—
232C22×Dic61—42no—
233C22×Dic61—42no—
234C22×Dic61—42no—
235C22×Dic61—42no—
236C22×Dic61—81no—
237C22×Dic61C2×D411yescharacteristic
238C22×Dic61C2×D411yescharacteristic
239C22×Dic61C2×D411yescharacteristic
240D4×D61—28no—
241D4×D61—44no—
242D4×D61—44no—
243D4×D61—44no—
244C2×D244—21no—
245C2×D244—21no—
246C2×D244—21no—
247C2×D244—21no—
248C2×D244—21no—
249C2×D244C22×C412yes—
250C2×C4×D61—21no—
251C2×C4×D61—21no—
252C2×C4×D61—21no—
253C2×C4×D61—21no—
254C2×C4×D61C22×C412yes—
255C2×C4×D61C2×D412yes—
256C2×C8×C61—21no—
257C2×C8×C61—21no—
258C2×C8×C61—21no—
259C2×C8×C61—21no—
260C2×C8×C61—21no—
261C2×C8×C61—21no—
262C4⋊C4×C61—21no—
263C4⋊C4×C61—21no—
264C4⋊C4×C61—21no—
265C4⋊C4×C61—21no—
266C22⋊C4×C61—42no—
267C22⋊Dic61—24no—
268C22⋊Dic61—24no—
269C22⋊Dic61C22⋊C414yes—
270#11758198—24no—
271#11758198—42no—
272#11758198—81no—
273#11758198C22⋊C414yes—
274C4⋊Dic61—21no—
275C4⋊Dic61—21no—
276C4⋊Dic61—21no—
277C4⋊Dic61—21no—
278C4⋊Dic61—42no—
279C4⋊Dic61C22×C412yes—
280C4⋊Dic61C2×D412yescomplemented
281#11758196C22⋊C414yes—
282C4×Dic61—42no—
283C4×Dic61—81no—
284C4×Dic61C22×C412yes—
285C4×Dic61C2×D412yes—
286C2×#92418—21no—
287C2×#92418—21no—
288C2×#92418—21no—
289C2×#92418—21no—
290C2×#92418—21no—
291C2×#92418—44no—
292C2×#92418C2×D412yescomplemented
293#11758189—44no—
294C23×C61—21no—
295C23×C61—21no—
296C23×C61—21no—
297C23×C61—21no—
298C23×C61—22no—
299C23×C61—22no—
300C23×C61—22no—
301C23×C61—22no—
302C23×C61—48no—
303C23×C61—41no—
304C23×C61—41no—
305C23×C61—41no—
306C23×C61—41no—
307C23×C61—41no—
308C23×C61—41no—
309C23×C61—41no—
310C23×C61—41no—
311C23×C61—41no—
312C23×C61—41no—
313C23×C61—48no—
314C23×C61—84no—
315C23×C61—84no—
316C23×C61—84no—
317C23×C61—84no—
318C23×C61—84no—
319C23×C61C2×C22⋊C412yes—
320C23×C61AGL(1,ℤ/8)12yes—
321C23×C61AGL(1,ℤ/8)12yes—
322C23×C61C22×D411yescharacteristic
323C22×D61—21no—
324C22×D61—21no—
325C22×D61—21no—
326C22×D61—21no—
327C22×D61—21no—
328C22×D61—21no—
329C22×D61—22no—
330C22×D61—48no—
331C22×D61—48no—
332C22×D61—41no—
333C22×D61—41no—
334C22×D61—41no—
335C22×D61—41no—
336C22×D61—41no—
337C22×D61—41no—
338C22×D61—84no—
339C22×D61—84no—
340C22×D61—84no—
341C22×D61—84no—
342C22×D61—84no—
343C22×D61C2×C22⋊C412yes—
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—41no—
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—22no—
386C2×Dic61—48no—
387C2×Dic61—41no—
388C2×Dic61—41no—
389C2×Dic61—41no—
390C2×Dic61—41no—
391C2×Dic61—41no—
392C2×Dic61—41no—
393C2×Dic61—41no—
394C2×Dic61—84no—
395C2×Dic61C2×C22⋊C412yes—
396C2×Dic61C2×C22⋊C412yes—
397C2×Dic61C2×C22⋊C412yes—
398D244—22no—
399D244—22no—
400D244—41no—
401D244—41no—
402C4×D61—22no—
403C4×D61—22no—
404C4×D61—22no—
405C4×D61—22no—
406C8×C61—41no—
407C8×C61—41no—
408#92418—22no—
409#92418—41no—
410#22423—611nomaximal, Sylow
411C22×C61—22no—
412C22×C61—22no—
413C22×C61—22no—
414C22×C61—22no—
415C22×C61—22no—
416C22×C61—22no—
417C22×C61—24no—
418C22×C61—42no—
419C22×C61—42no—
420C22×C61—42no—
421C22×C61—42no—
422C22×C61—42no—
423C22×C61—42no—
424C22×C61—42no—
425C22×C61—42no—
426C22×C61—42no—
427C22×C61—816no—
428C22×C61—81no—
429C22×C61—81no—
430C22×C61—81no—
431C22×C61—81no—
432C22×C61#41814yescomplemented
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—41no—
444C2×D61—41no—
445C2×D61—41no—
446C2×D61—41no—
447C2×D61—42no—
448C2×D61—42no—
449C2×D61—42no—
450C2×D61—816no—
451C2×D61—81no—
452C2×D61—81no—
453C2×D61—81no—
454C2×D61—81no—
455C4×C61—22no—
456C4×C61—81no—
457C4×C61—81no—
458C4×C61C2×C4×D411yescharacteristic
459C4×C61#51811yescharacteristic
460C4×C61D4211yescharacteristic
461C4×C61#54611yescharacteristic
462Dic61—22no—
463Dic61—22no—
464Dic61—22no—
465Dic61—42no—
466Dic61—42no—
467Dic61—81no—
468C2×D42—611no—
469C2×#435—611no—
470C2×#418—611no—
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#1786D6111yescharacteristic, complemented
482#1762—611no—
483C2×C61—24no—
484C2×C61—44no—
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—42no—
494D61—82no—
495C23×D4—611no—
496C23×D4—1221no—
497C23×D4C2×D6111yescharacteristic
498C22×M16—611no—
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×#117—611no—
511C22×C4⋊C4—611no—
512#435—1224no—
513C2×C4⋊C8—611no—
514#418—1224no—
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⋊C8C2×D6111yescharacteristic, complemented
530C2×#97—611no—
531#388—1221no—
532#387—1221no—
533#386—1221no—
534#382—611no—
535#380—611no—
536#380C2×D6111yescharacteristic, complemented
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×D6114yes—
569C22×D4C22×D6111yescharacteristic
570C22×D4C22×D6111yescharacteristic
571C23×C4—611no—
572C23×C4—1221no—
573C23×C4—1221no—
574C23×C4C22×D6111yescharacteristic
575C2×M16—1222no—
576C2×M16—1222no—
577C2×M16—2441no—
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—1222no—
599#117—2441no—
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—611no—
618C2×C42—1221no—
619C2×C42—1221no—
620C4⋊C8—1222no—
621#102—22no—
622#102—22no—
623#102—41no—
624#102—41no—
625#102—614no—
626#102—1222no—
627#102—1222no—
628#102—1222no—
629#102—1222no—
630#102—1222no—
631#102—2441no—
632#102—2441no—
633C22⋊C8—22no—
634C22⋊C8—1222no—
635#97—1222no—
636#95—21no—
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×D4D4×D6112yes—
707C2×D4#1175822412yes—
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—2444no—
737C2×C8—21no—
738C2×C8—21no—
739C2×C8—21no—
740C2×C8—21no—
741C2×C8—21no—
742C2×C8—21no—
743C2×C8—612no—
744C2×C8—1221no—
745C2×C8—1221no—
746C2×C8—1221no—
747C2×C8—1221no—
748C2×C8—1221no—
749C2×C8—2444no—
750C4⋊C4—21no—
751C4⋊C4—21no—
752C4⋊C4—21no—
753C4⋊C4—21no—
754C4⋊C4—614no—
755C4⋊C4—612no—
756C4⋊C4—612no—
757C4⋊C4—1221no—
758C4⋊C4—1221no—
759C4⋊C4—1221no—
760C4⋊C4—1221no—
761C4⋊C4—2442no—
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—612no—
771C42—612no—
772C42—4881no—
773C42—2442no—
774C23—21no—
775C23—21no—
776C23—21no—
777C23—21no—
778C23—22no—
779C23—22no—
780C23—22no—
781C23—22no—
782C23—48no—
783C23—41no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—48no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—41no—
794C23—84no—
795C23—84no—
796C23—84no—
797C23—84no—
798C23—84no—
799C23—612no—
800C23—1221no—
801C23—1221no—
802C23—1221no—
803C23—1221no—
804C23—1221no—
805C23—1221no—
806C23—1222no—
807C23—4884no—
808C23—4884no—
809C23—4884no—
810C23—4884no—
811C23—4884no—
812C23—2448no—
813C23—2448no—
814C23—2441no—
815C23—2441no—
816C23—2441no—
817C23—2441no—
818C23—2441no—
819C23—2441no—
820C23C22⋊C4×D6112yes—
821C23#1451980112yes—
822C23#1451980412yes—
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—
842D4#1451973714yes—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—41no—
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—1222no—
870C2×C4—4884no—
871C2×C4—2448no—
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×C4C2×D4×D6111yescharacteristic
883C2×C4C2×#1175822411yescharacteristic
884C2×C4#1451982211yescharacteristic
885C2×C4#1451982211yescharacteristic
886C8—41no—
887C8—41no—
888C8—1222no—
889C8—2441no—
890C22—22no—
891C22—22no—
892C22—22no—
893C22—22no—
894C22—22no—
895C22—22no—
896C22—24no—
897C22—42no—
898C22—42no—
899C22—42no—
900C22—42no—
901C22—42no—
902C22—42no—
903C22—42no—
904C22—42no—
905C22—42no—
906C22—816no—
907C22—81no—
908C22—81no—
909C22—81no—
910C22—81no—
911C22—1222no—
912C22—1222no—
913C22—1222no—
914C22—48816no—
915C22—4881no—
916C22—4881no—
917C22—4881no—
918C22—4881no—
919C22—2442no—
920C22—2442no—
921C22—2442no—
922C22—2441no—
923C22—2441no—
924C22—2441no—
925C22—2441no—
926C22#1683976514yescomplemented
927C22C2×C22⋊C4×D6111yescharacteristic
928C22#1684039411yescharacteristic
929C22#1684039911yescharacteristic
930C22C2×#1451980111yescharacteristic
931C22C2×#1451980411yescharacteristic
932C22#1684056611yescharacteristic
933C22#1684057211yescharacteristic
934C4—22no—
935C4—81no—
936C4—81no—
937C4—1222no—
938C4—1222no—
939C4—1222no—
940C4—4881no—
941C4—2442no—
942C4—2442no—
943C4C2×#1451973711yescharacteristic
944C4#1684023511yescharacteristic
945C4#1684039411yescharacteristic
946C4#1684039911yescharacteristic
947C2—24no—
948C2—44no—
949C2—82no—
950C2—4882no—
951C2—2442no—
952C2#2144863511yescharacteristic
953C2C2×#1683976511yescharacteristic
954C2#2145434411yescharacteristic
955C2#2145730311yescharacteristic
956C2#2145731811yescharacteristic
957C2#2145784411yescharacteristic
958C2#2145796411yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1786C2
socleC23×C61C22×D4
prime radicalC2×D4×C22⋊D61C2
cosocleC22×C4×C61C24
hypercenter#1786D61
hypocenterC61#22423
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1786

Complements

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

NH ≅ G/Ntype
2. C2×#16839830C2semidirect
3. C2×#16839765C2semidirect
4. C22×#14519698C2semidirect
5. #21448750C2semidirect
6. #21446744C2semidirect
7. #21446641C2semidirect
8. #21446254C2semidirect
9. #21446245C2semidirect
10. #21446138C2semidirect
11. #21446134C2semidirect
12. #21445827C2semidirect
13. #21445748C2semidirect
14. #21445646C2semidirect
15. C61×#1786C2semidirect
18. C22×#11758189C22semidirect
19. C23×#92418C22semidirect
21. D4×C22⋊D61C4semidirect
30. C2×#14519735C22semidirect
31. C22×C4⋊Dic61C22semidirect
33. C2×#14519706C22semidirect
35. C2×#14519699C22semidirect
36. C2×#14519699C22semidirect
40. C2×#14519698C22semidirect
41. C2×#14519698C22semidirect
42. C2×#14519697C22semidirect
43. C2×#14519697C22semidirect
44. C2×#14519689C22semidirect
45. C2×#14519687C22semidirect
49. #16839627C22semidirect
50. #16839619C22semidirect
51. C4⋊C4×Dic61C22semidirect
53. #16839525C22semidirect
54. #16839525C22semidirect
55. #16839524C22semidirect
56. #16839524C22semidirect
60. C2×#102×C61C22semidirect
61. C2×#102×C61C22semidirect
62. C2×C22⋊C8×C61C22semidirect
63. C61×#380C22semidirect
80. C2×D4×D61C2×C4semidirect
93. #14519773C2×C4semidirect
98. #14519748C2×C4semidirect
102. D4×Dic61C2×C4semidirect
130. #14519698D4semidirect
280. C4⋊Dic61C2×D4semidirect
292. C2×#92418C2×D4semidirect
432. C22×C61#418semidirect
481. #1786D61semidirect
526. C2×#102C2×D61semidirect
527. C2×#102C2×D61semidirect
529. C2×C22⋊C8C2×D61semidirect
536. #380C2×D61semidirect
543. C61#22423semidirect
926. C22#16839765semidirect

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×#168398302
C2×#168397652
C22×#145196982
#214487502
#214467442
#214466412
#214462542
#214462452
#214461382
#214461342
#214458272
#214457482
#214456462
C61×#17862
#2242361