Finite Group Databasebeta

← #29695621

Subgroups — #29695621

Order 15616.

1910 conjugacy classes of subgroups.

The subgroup lattice has 958 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×C22⋊D61C211yesmaximal, characteristic
2C2×#16839837C211yesmaximal, characteristic, complemented
3C2×#16839767C211yesmaximal, characteristic, complemented
4C2×#16839765C211yesmaximal, characteristic, complemented
5#21448763C211yesmaximal, characteristic, complemented
6#21446744C211yesmaximal, characteristic, complemented
7#21446623C211yesmaximal, characteristic, complemented
8#21446255C211yesmaximal, characteristic, complemented
9#21446254C211yesmaximal, characteristic, complemented
10#21446139C211yesmaximal, characteristic, complemented
11#21446138C211yesmaximal, characteristic, complemented
12#21445817C211yesmaximal, characteristic, complemented
13#21445748C211yesmaximal, characteristic, complemented
14#102×Dic61C211yesmaximal, characteristic, complemented
15C61×#1786C211yesmaximal, characteristic, complemented
16C23×C22⋊D61—21no—
17C22×D4×D61C2211yescharacteristic
18C22×#11758194C2211yescharacteristic, complemented
19C22×#11758189C2211yescharacteristic, 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×#14519736C2211yescharacteristic, complemented
31C2×#14519735C2211yescharacteristic, complemented
32#16839837—24no—
33C2×#14519706C2211yescharacteristic, complemented
34#16839767—24no—
35#16839765—24no—
36C2×#14519699C2211yescharacteristic, complemented
37C2×#14519699C2211yescharacteristic, complemented
38C2×#14519698C2211yescharacteristic
39C2×#14519698C2211yescharacteristic
40C2×#14519698C2211yescharacteristic, complemented
41C2×#14519698C2211yescharacteristic, complemented
42C2×#14519697C2211yescharacteristic, complemented
43C2×#14519697C2211yescharacteristic, complemented
44C2×#14519689C2211yescharacteristic, complemented
45C2×C8×Dic61C2211yescharacteristic, complemented
46#16839662—21no—
47#16839656—21no—
48#16839651—21no—
49#16839631C2211yescharacteristic, complemented
50#16839619C2211yescharacteristic, complemented
51C4⋊C4×Dic61C2211yescharacteristic, complemented
52#16839613—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×C414yes—
81C23×Dic61—21no—
82C22×C4×D61C2311yescharacteristic
83C2×#11758194—22no—
84C2×#11758194—22no—
85C2×#11758194—41no—
86C2×#11758189—22no—
87C2×#11758189—22no—
88C2×#11758189—41no—
89C22×#92418C2311yescharacteristic
90C22×#92418C2311yescharacteristic
91#14519773—22no—
92#14519773C2×C414yes—
93#14519751—22no—
94#14519751C2×C414yes—
95#14519749—28no—
96#14519748—22no—
97#14519748C2×C414yes—
98#14519746—28no—
99#14519745—28no—
100D4×Dic61—22no—
101D4×Dic61C2×C414yes—
102C4×C22⋊D61C2×C414yes—
103C4×C22⋊D61D414yes—
104#14519736—22no—
105#14519736—41no—
106#14519735—22no—
107#14519735—41no—
108C2×C4⋊Dic61C2311yescharacteristic
109C2×C4⋊Dic61C2311yescharacteristic
110C2×C4⋊Dic61C2311yescharacteristic
111C2×#11758196—21no—
112C2×#11758196—21no—
113C2×#11758196D411yescharacteristic
114C2×C22⋊Dic61—21no—
115C2×C22⋊Dic61—21no—
116C2×C22⋊Dic61—21no—
117C2×C22⋊Dic61D411yescharacteristic
118C2×#11758198—21no—
119C2×#11758198—21no—
120C2×#11758198—21no—
121C2×#11758198D411yescharacteristic
122C2×C4×Dic61—21no—
123C2×C4×Dic61—21no—
124C2×C4×Dic61—21no—
125C2×C4×Dic61C2311yescharacteristic
126#14519706—22no—
127#14519699—22no—
128#14519699—41no—
129#14519698—22no—
130#14519698—22no—
131#14519698—22no—
132#14519698D414yescomplemented
133#14519697—22no—
134#14519697—41no—
135#14519689—22no—
136C8×Dic61—22no—
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—24no—
210C2×C22⋊D61—24no—
211C2×C22⋊D61—24no—
212C2×C22⋊D61—24no—
213C2×C22⋊D61—24no—
214C2×C22⋊D61—22no—
215C2×C22⋊D61—22no—
216C2×C22⋊D61—42no—
217C2×C22⋊D61—42no—
218C2×C22⋊D61—432no—
219C2×C22⋊D61—42no—
220C2×C22⋊D61—42no—
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×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×D61C22×C412yes—
252C2×C4×D61C2×D412yes—
253C2×C8×C61—21no—
254C2×C8×C61—21no—
255C2×C8×C61—21no—
256C2×C8×C61—21no—
257C2×C8×C61—21no—
258C2×C8×C61—21no—
259C4⋊C4×C61—21no—
260C4⋊C4×C61—21no—
261C4⋊C4×C61—21no—
262C4⋊C4×C61—21no—
263C22⋊C4×C61—81no—
264C22⋊Dic61—24no—
265C22⋊Dic61—24no—
266C22⋊Dic61—42no—
267C22⋊Dic61C22⋊C414yes—
268#11758198—24no—
269#11758198—42no—
270#11758198—81no—
271#11758198C22⋊C414yes—
272C4⋊Dic61—21no—
273C4⋊Dic61—21no—
274C4⋊Dic61—21no—
275C4⋊Dic61—21no—
276C4⋊Dic61C22×C412yes—
277C4⋊Dic61C2×D412yescomplemented
278#11758196—42no—
279#11758196—81no—
280#11758196C22⋊C414yes—
281C4×Dic61—42no—
282C4×Dic61—42no—
283C4×Dic61—42no—
284C4×Dic61C22×C412yes—
285C4×Dic61C2×D412yes—
286#11758194—44no—
287C2×#92418—21no—
288C2×#92418—21no—
289C2×#92418—21no—
290C2×#92418—21no—
291C2×#92418—21no—
292C2×#92418C2×D412yescomplemented
293#11758189—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—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—22no—
383C2×Dic61—22no—
384C2×Dic61—41no—
385C2×Dic61—41no—
386C2×Dic61—41no—
387C2×Dic61—41no—
388C2×Dic61—48no—
389C2×Dic61—41no—
390C2×Dic61—41no—
391C2×Dic61—41no—
392C2×Dic61C2×C22⋊C412yes—
393C2×Dic61C2×C22⋊C412yes—
394C2×Dic61C2×C22⋊C412yes—
395C2×Dic61AGL(1,ℤ/8)12yes—
396C2×Dic61AGL(1,ℤ/8)12yes—
397D244—22no—
398D244—22no—
399D244—41no—
400D244—41no—
401C4×D61—22no—
402C4×D61—22no—
403C4×D61—22no—
404C4×D61—22no—
405C8×C61—41no—
406C8×C61—41no—
407#92418—22no—
408#92418—41no—
409#22428—611nomaximal, Sylow
410C22×C61—24no—
411C22×C61—22no—
412C22×C61—22no—
413C22×C61—22no—
414C22×C61—42no—
415C22×C61—42no—
416C22×C61—42no—
417C22×C61—41no—
418C22×C61—42no—
419C22×C61—41no—
420C22×C61—42no—
421C22×C61—41no—
422C22×C61—42no—
423C22×C61—41no—
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×C61C22×C22⋊C411yescharacteristic
433C22×C61D4211yescharacteristic
434C22×C61#54611yescharacteristic
435C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
436C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
437C22×C61#57611yescharacteristic
438C22×C61#57711yescharacteristic
439C2×D61—22no—
440C2×D61—22no—
441C2×D61—22no—
442C2×D61—41no—
443C2×D61—41no—
444C2×D61—41no—
445C2×D61—41no—
446C2×D61—42no—
447C2×D61—42no—
448C2×D61—42no—
449C2×D61—816no—
450C2×D61—81no—
451C2×D61—81no—
452C2×D61—81no—
453C2×D61—81no—
454C4×C61—22no—
455C4×C61—81no—
456C4×C61—81no—
457C4×C61C2×C4×D411yescharacteristic
458C4×C61#51811yescharacteristic
459C4×C61D4211yescharacteristic
460C4×C61#54611yescharacteristic
461Dic61—22no—
462Dic61—22no—
463Dic61—42no—
464Dic61—42no—
465Dic61—81no—
466Dic61#41814yescomplemented
467C2×D42—611no—
468C2×#436—611no—
469C2×#418—611no—
470C2×#418—611no—
471#2354—611no—
472#1982—611no—
473#1957—611no—
474#1895—611no—
475#1895—611no—
476#1875—611no—
477#1875—611no—
478#1802—611no—
479#1786—611no—
480#1786D6111yescharacteristic, complemented
481C4×#102—611no—
482C2×C61—44no—
483C2×C61—42no—
484C2×C61—82no—
485C2×C61D4×C22⋊C411yescharacteristic
486C2×C61C2×#41811yescharacteristic
487C2×C61#289711yescharacteristic
488C2×C61#327211yescharacteristic
489C2×C61#327411yescharacteristic
490C2×C61#332411yescharacteristic
491C2×C61#332511yescharacteristic
492D61—42no—
493D61—82no—
494C23×D4—611no—
495C23×D4—1221no—
496C23×D4C2×D6111yescharacteristic
497C22×M16—611no—
498C22×M16—611no—
499D42—618no—
500D42—1224no—
501C2×#127—611no—
502C2×#121—611no—
503C2×#121—611no—
504C2×#121—1221no—
505C2×#120—1221no—
506C2×#120—1221no—
507C2×C4×D4—611no—
508C2×C4×D4—611no—
509C2×#117—611no—
510C2×#117—611no—
511#436—1224no—
512C2×C4⋊C8—611no—
513#418—1224no—
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×#102C2×D6111yescharacteristic
524C2×#102C2×D6111yescharacteristic
525C2×#102C2×D6111yescharacteristic, complemented
526C2×#102C2×D6111yescharacteristic, complemented
527C2×C22⋊C8—611no—
528C2×C22⋊C8C2×D6111yescharacteristic, complemented
529C2×C4×C8—611no—
530#390—1221no—
531#388—1221no—
532#388—1221no—
533#384—611no—
534#380—611no—
535#380C2×D6111yescharacteristic, complemented
536C4×C4⋊C4—611no—
537C4×C4⋊C4—1221no—
538#340—611no—
539#340—611no—
540#340—611no—
541#340—611no—
542C61#2242811yescharacteristic, complemented, Sylow
543C25—21no—
544C25—1221no—
545C22×D4—22no—
546C22×D4—22no—
547C22×D4—21no—
548C22×D4—22no—
549C22×D4—41no—
550C22×D4—41no—
551C22×D4—611no—
552C22×D4—614no—
553C22×D4—611no—
554C22×D4—1222no—
555C22×D4—1221no—
556C22×D4—1221no—
557C22×D4—1221no—
558C22×D4—1228no—
559C22×D4—1222no—
560C22×D4—1222no—
561C22×D4—1221no—
562C22×D4—1221no—
563C22×D4—2441no—
564C22×D4—2441no—
565C22×D4—2444no—
566C22×D4—2444no—
567C22×D4C4×D6114yes—
568C22×D4C22×D6111yescharacteristic
569C22×D4C22×D6111yescharacteristic
570C23×C4—611no—
571C23×C4—1221no—
572C23×C4C22×D6111yescharacteristic
573C2×M16—1222no—
574C2×M16—1222no—
575C2×M16—1222no—
576C2×M16—1222no—
577C2×M16—2441no—
578C2×M16—2441no—
579C22×C8—611no—
580C22×C8—611no—
581C22×C8C22×D6111yescharacteristic
582C22×C8C22×D6111yescharacteristic
583#127—614no—
584#127—1222no—
585#121—614no—
586#121—614no—
587#121—1228no—
588#121—1222no—
589#121—1222no—
590#120—1228no—
591#120—1228no—
592C4×D4—614no—
593C4×D4—614no—
594C4×D4—614no—
595C4×D4—1222no—
596#117—1222no—
597#117—1222no—
598#117—2441no—
599#117—2441no—
600C2×C4⋊C4—611no—
601C2×C4⋊C4—611no—
602C2×C4⋊C4—611no—
603C2×C4⋊C4—611no—
604C2×C4⋊C4—1221no—
605C2×C4⋊C4—1221no—
606C2×C4⋊C4C22×D6111yescharacteristic
607C2×C4⋊C4C22×D6111yescharacteristic
608C2×C22⋊C4—21no—
609C2×C22⋊C4—611no—
610C2×C22⋊C4—611no—
611C2×C22⋊C4—1221no—
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—
620C2×C42—1221no—
621C4⋊C8—1222no—
622#102—22no—
623#102—22no—
624#102—41no—
625#102—41no—
626#102—614no—
627#102—1222no—
628#102—1222no—
629#102—1222no—
630#102—1222no—
631#102—1222no—
632#102—2441no—
633#102—2441no—
634C22⋊C8—22no—
635C22⋊C8—1222no—
636C4×C8—1222no—
637#95—21no—
638#95—1221no—
639#95—1221no—
640C24—21no—
641C24—21no—
642C24—24no—
643C24—42no—
644C24—42no—
645C24—42no—
646C24—42no—
647C24—81no—
648C24—81no—
649C24—611no—
650C24—1224no—
651C24—1221no—
652C24—4881no—
653C24—4881no—
654C24—2442no—
655C24—2442no—
656C24—2442no—
657C24—2442no—
658C24D4×D6111yescharacteristic
659C2×D4—28no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—21no—
668C2×D4—24no—
669C2×D4—44no—
670C2×D4—44no—
671C2×D4—44no—
672C2×D4—42no—
673C2×D4—42no—
674C2×D4—614no—
675C2×D4—612no—
676C2×D4—1222no—
677C2×D4—1222no—
678C2×D4—1224no—
679C2×D4—1224no—
680C2×D4—1224no—
681C2×D4—1228no—
682C2×D4—1224no—
683C2×D4—1224no—
684C2×D4—1221no—
685C2×D4—1221no—
686C2×D4—1221no—
687C2×D4—1221no—
688C2×D4—1221no—
689C2×D4—4881no—
690C2×D4—4881no—
691C2×D4—2442no—
692C2×D4—2442no—
693C2×D4—2444no—
694C2×D4—2444no—
695C2×D4—2444no—
696C2×D4—2442no—
697C2×D4—2442no—
698C2×D4—24432no—
699C2×D4—2442no—
700C2×D4—2442no—
701C2×D4—2442no—
702C2×D4—2442no—
703C2×D4C2×C4×D6112yes—
704C2×D4C2×C4×D6112yes—
705C2×D4D4×D6112yes—
706C2×D4#1175822412yes—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—611no—
714C22×C4—611no—
715C22×C4—611no—
716C22×C4—612no—
717C22×C4—612no—
718C22×C4—1224no—
719C22×C4—1221no—
720C22×C4—1221no—
721C22×C4—1221no—
722C22×C4—1221no—
723C22×C4—1221no—
724C22×C4—1221no—
725C22×C4—1221no—
726C22×C4—2442no—
727C22×C4—2442no—
728C22×C4C2×C4×D6112yes—
729C22×C4D4×D6112yes—
730C22×C4D4×D6111yescharacteristic
731C22×C4C23×D6111yescharacteristic
732M16—2444no—
733M16—2444no—
734C2×C8—21no—
735C2×C8—21no—
736C2×C8—21no—
737C2×C8—21no—
738C2×C8—21no—
739C2×C8—21no—
740C2×C8—612no—
741C2×C8—1221no—
742C2×C8—1221no—
743C2×C8—1221no—
744C2×C8—1221no—
745C2×C8—1221no—
746C4⋊C4—21no—
747C4⋊C4—21no—
748C4⋊C4—21no—
749C4⋊C4—21no—
750C4⋊C4—614no—
751C4⋊C4—612no—
752C4⋊C4—612no—
753C4⋊C4—1221no—
754C4⋊C4—1221no—
755C4⋊C4—1221no—
756C4⋊C4—1221no—
757C4⋊C4—4881no—
758C4⋊C4—2442no—
759C22⋊C4—81no—
760C22⋊C4—614no—
761C22⋊C4—614no—
762C22⋊C4—1224no—
763C22⋊C4—1224no—
764C22⋊C4—1224no—
765C22⋊C4—4881no—
766C22⋊C4—2442no—
767C22⋊C4—2442no—
768C42—612no—
769C42—612no—
770C42—2442no—
771C42—2442no—
772C42—2442no—
773C23—22no—
774C23—21no—
775C23—21no—
776C23—21no—
777C23—21no—
778C23—21no—
779C23—22no—
780C23—21no—
781C23—22no—
782C23—22no—
783C23—48no—
784C23—48no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—84no—
796C23—84no—
797C23—84no—
798C23—84no—
799C23—84no—
800C23—612no—
801C23—1221no—
802C23—1221no—
803C23—1221no—
804C23—1221no—
805C23—1221no—
806C23—1221no—
807C23—1222no—
808C23—4884no—
809C23—4884no—
810C23—4884no—
811C23—4884no—
812C23—4884no—
813C23—2448no—
814C23—2448no—
815C23—2441no—
816C23—2441no—
817C23—2441no—
818C23—2441no—
819C23—2441no—
820C23—2441no—
821C23C22⋊C4×D6112yes—
822C23C2×D4×D6111yescharacteristic
823D4—22no—
824D4—22no—
825D4—22no—
826D4—22no—
827D4—22no—
828D4—48no—
829D4—41no—
830D4—41no—
831D4—1228no—
832D4—1222no—
833D4—1222no—
834D4—4884no—
835D4—2448no—
836D4—2448no—
837D4—2448no—
838D4—2448no—
839D4—2441no—
840D4—2441no—
841D4#1451973714yes—
842C2×C4—21no—
843C2×C4—21no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—612no—
855C2×C4—612no—
856C2×C4—612no—
857C2×C4—612no—
858C2×C4—612no—
859C2×C4—1221no—
860C2×C4—1221no—
861C2×C4—1221no—
862C2×C4—1221no—
863C2×C4—1222no—
864C2×C4—1222no—
865C2×C4—1222no—
866C2×C4—1222no—
867C2×C4—1222no—
868C2×C4—1222no—
869C2×C4—2448no—
870C2×C4—2441no—
871C2×C4—2441no—
872C2×C4—2441no—
873C2×C4—2441no—
874C2×C4—2441no—
875C2×C4—2441no—
876C2×C4—2441no—
877C2×C4C22⋊C4×D6112yes—
878C2×C4C22×C4×D6111yescharacteristic
879C2×C4C2×D4×D6111yescharacteristic
880C2×C4C2×D4×D6111yescharacteristic
881C2×C4C2×#1175822411yescharacteristic
882C2×C4#1451982211yescharacteristic
883C2×C4#1451982211yescharacteristic
884C8—41no—
885C8—41no—
886C8—1222no—
887C8—2441no—
888C22—22no—
889C22—22no—
890C22—24no—
891C22—22no—
892C22—42no—
893C22—41no—
894C22—42no—
895C22—41no—
896C22—42no—
897C22—41no—
898C22—42no—
899C22—41no—
900C22—42no—
901C22—42no—
902C22—42no—
903C22—42no—
904C22—42no—
905C22—816no—
906C22—81no—
907C22—81no—
908C22—81no—
909C22—81no—
910C22—1222no—
911C22—1222no—
912C22—1222no—
913C22—48816no—
914C22—4881no—
915C22—4881no—
916C22—4881no—
917C22—4881no—
918C22—2442no—
919C22—2442no—
920C22—2442no—
921C22—2441no—
922C22—2441no—
923C22—2441no—
924C22—2441no—
925C22C2×C22⋊C4×D6111yescharacteristic
926C22#1684039411yescharacteristic
927C22#1684039911yescharacteristic
928C22AGL(1,ℤ/8)×D6111yescharacteristic
929C22AGL(1,ℤ/8)×D6111yescharacteristic
930C22#1684056311yescharacteristic
931C22#1684056811yescharacteristic
932C4—22no—
933C4—81no—
934C4—81no—
935C4—614no—
936C4—1222no—
937C4—1222no—
938C4—4881no—
939C4—2442no—
940C4—2442no—
941C4C2×#1451973711yescharacteristic
942C4#1684023511yescharacteristic
943C4#1684039411yescharacteristic
944C4#1684039911yescharacteristic
945C2—42no—
946C2—44no—
947C2—82no—
948C2—4882no—
949C2—2442no—
950C2#2144863511yescharacteristic
951C2#418×D6111yescharacteristic
952C2#2145434011yescharacteristic
953C2#2145741711yescharacteristic
954C2#2145743711yescharacteristic
955C2#2145804311yescharacteristic
956C2#2145805411yescharacteristic
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#22428
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×#16839837C2semidirect
3. C2×#16839767C2semidirect
4. C2×#16839765C2semidirect
5. #21448763C2semidirect
6. #21446744C2semidirect
7. #21446623C2semidirect
8. #21446255C2semidirect
9. #21446254C2semidirect
10. #21446139C2semidirect
11. #21446138C2semidirect
12. #21445817C2semidirect
13. #21445748C2semidirect
14. #102×Dic61C2semidirect
15. C61×#1786C2semidirect
18. C22×#11758194C22semidirect
19. C22×#11758189C22semidirect
21. D4×C22⋊D61C4semidirect
30. C2×#14519736C22semidirect
31. C2×#14519735C22semidirect
33. C2×#14519706C22semidirect
36. C2×#14519699C22semidirect
37. C2×#14519699C22semidirect
40. C2×#14519698C22semidirect
41. C2×#14519698C22semidirect
42. C2×#14519697C22semidirect
43. C2×#14519697C22semidirect
44. C2×#14519689C22semidirect
45. C2×C8×Dic61C22semidirect
49. #16839631C22semidirect
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
132. #14519698D4semidirect
277. C4⋊Dic61C2×D4semidirect
292. C2×#92418C2×D4semidirect
466. Dic61#418semidirect
480. #1786D61semidirect
525. C2×#102C2×D61semidirect
526. C2×#102C2×D61semidirect
528. C2×C22⋊C8C2×D61semidirect
535. #380C2×D61semidirect
542. C61#22428semidirect

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×#168398372
C2×#168397672
C2×#168397652
#214487632
#214467442
#214466232
#214462552
#214462542
#214461392
#214461382
#214458172
#214457482
#102×Dic612
C61×#17862
#2242861