Finite Group Databasebeta

← #29695549

Subgroups — #29695549

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×#16839833C211yesmaximal, characteristic, complemented
3C2×#16839765C211yesmaximal, characteristic, complemented
4#21448744C211yesmaximal, characteristic, complemented
5#21446744C211yesmaximal, characteristic, complemented
6#21446641C211yesmaximal, characteristic, complemented
7#21446254C211yesmaximal, characteristic, complemented
8#21446247C211yesmaximal, characteristic, complemented
9#21446138C211yesmaximal, characteristic, complemented
10#21446136C211yesmaximal, characteristic, complemented
11#21445827C211yesmaximal, characteristic, complemented
12#21445750C211yesmaximal, characteristic, complemented
13#21445748C211yesmaximal, characteristic, complemented
14#21445646C211yesmaximal, characteristic, complemented
15C22×#102×C61C211yesmaximal, characteristic, complemented
16C23×C22⋊D61—21no—
17C22×D4×D61C2211yescharacteristic
18C22×#11758189C2211yescharacteristic, 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×#14519735C2211yescharacteristic, complemented
30#16839833—24no—
31C2×#14519706C2211yescharacteristic, complemented
32#16839765—24no—
33C2×#14519699C2211yescharacteristic, complemented
34C2×#14519699C2211yescharacteristic, complemented
35C2×#14519698C2211yescharacteristic
36C2×#14519698C2211yescharacteristic
37C2×#14519698C2211yescharacteristic, complemented
38C2×#14519698C2211yescharacteristic, complemented
39C2×#14519697C2211yescharacteristic, complemented
40C2×#14519697C2211yescharacteristic, complemented
41C2×C22⋊#92418C2211yescharacteristic, complemented
42C2×#14519689C2211yescharacteristic, complemented
43C2×#14519687C2211yescharacteristic, complemented
44#16839652—21no—
45#16839643—21no—
46#16839641—21no—
47#16839627C2211yescharacteristic, complemented
48#16839622C2211yescharacteristic, complemented
49#16839619C2211yescharacteristic, complemented
50C4⋊C4×Dic61C2211yescharacteristic, complemented
51C4×C22⋊Dic61—21no—
52#16839525C2211yescharacteristic, complemented
53#16839525C2211yescharacteristic, complemented
54#16839524C2211yescharacteristic, complemented
55#16839524C2211yescharacteristic, complemented
56C23×D4×C61C2211yescharacteristic
57C23×C8×C61C2211yescharacteristic, complemented
58C22×C4⋊C4×C61C2211yescharacteristic, complemented
59C2×#102×C61—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×C414yescomplemented
81C23×Dic61—21no—
82C22×C4×D61C2311yescharacteristic
83C2×#11758189—22no—
84C2×#11758189—22no—
85C2×#11758189—41no—
86C22×#92418C2311yescharacteristic
87C22×#92418C2311yescharacteristic
88#14519773—22no—
89#14519773C2×C414yescomplemented
90#14519751—22no—
91#14519751C2×C414yes—
92#14519749—28no—
93#14519748—22no—
94#14519748C2×C414yescomplemented
95#14519746—28no—
96#14519745—28no—
97D4×Dic61—22no—
98D4×Dic61C2×C414yescomplemented
99C4×C22⋊D61C2×C414yes—
100C4×C22⋊D61D414yes—
101#14519735—22no—
102#14519735—41no—
103C2×C4⋊Dic61C2311yescharacteristic
104C2×C4⋊Dic61C2311yescharacteristic
105C2×C4⋊Dic61C2311yescharacteristic
106C2×#11758196D411yescharacteristic
107C2×C22⋊Dic61—21no—
108C2×C22⋊Dic61—21no—
109C2×C22⋊Dic61—21no—
110C2×C22⋊Dic61D411yescharacteristic
111C2×#11758198—21no—
112C2×#11758198—21no—
113C2×#11758198—21no—
114C2×#11758198D411yescharacteristic
115C2×C4×Dic61—21no—
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×C414yes—
143C22×D4×C61C2311yescharacteristic
144C22×D4×C61C2311yescharacteristic
145C23×C4×C61—21no—
146C23×C4×C61C2311yescharacteristic
147C22×C8×C61—22no—
148C22×C8×C61—22no—
149C22×C8×C61—41no—
150C22×C8×C61C2311yescharacteristic
151C22×C8×C61C2311yescharacteristic
152C2×C4⋊C4×C61—22no—
153C2×C4⋊C4×C61—21no—
154C2×C4⋊C4×C61—41no—
155C2×C4⋊C4×C61C2311yescharacteristic
156C2×C4⋊C4×C61C2311yescharacteristic
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×C61—42no—
206C22×C4×C61—42no—
207C22×C4×C61—81no—
208C22×C4×C61C22×C412yes—
209C22×C4×C61C2×D411yescharacteristic
210C22×C4×C61C2×D412yes—
211C22×C4×C61C2411yescharacteristic
212C2×C22⋊D61—22no—
213C2×C22⋊D61—22no—
214C2×C22⋊D61—24no—
215C2×C22⋊D61—24no—
216C2×C22⋊D61—24no—
217C2×C22⋊D61—24no—
218C2×C22⋊D61—24no—
219C2×C22⋊D61—42no—
220C2×C22⋊D61—42no—
221C2×C22⋊D61—42no—
222C2×C22⋊D61—42no—
223C2×C22⋊D61—432no—
224C2×C22⋊D61—42no—
225C2×C22⋊D61—42no—
226C2×C22⋊D61—42no—
227C2×C22⋊D61—42no—
228C2×C22⋊D61—81no—
229C2×C22⋊D61—81no—
230C2×C22⋊D61C22⋊C414yes—
231C22×Dic61—21no—
232C22×Dic61—24no—
233C22×Dic61—21no—
234C22×Dic61—21no—
235C22×Dic61—42no—
236C22×Dic61—42no—
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—44no—
262C2×C8×C61C2×D412yescomplemented
263C4⋊C4×C61—21no—
264C4⋊C4×C61—21no—
265C4⋊C4×C61—21no—
266C4⋊C4×C61—42no—
267C4⋊C4×C61C2×D412yescomplemented
268C22⋊Dic61—24no—
269C22⋊Dic61—24no—
270C22⋊Dic61—42no—
271C22⋊Dic61C22⋊C414yes—
272#11758198—24no—
273#11758198—42no—
274#11758198—81no—
275#11758198C22⋊C414yes—
276C4⋊Dic61—21no—
277C4⋊Dic61—21no—
278C4⋊Dic61—21no—
279C4⋊Dic61—21no—
280C4⋊Dic61—21no—
281C4⋊Dic61C22×C412yes—
282#11758196C22⋊C414yes—
283C4×Dic61—42no—
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—
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—22no—
360C2×C4×C61—41no—
361C2×C4×C61—41no—
362C2×C4×C61—41no—
363C2×C4×C61—41no—
364C2×C4×C61—41no—
365C2×C4×C61—84no—
366C2×C4×C61C2×C22⋊C412yes—
367C2×C4×C61C23×C411yescharacteristic
368C2×C4×C61C22×D411yescharacteristic
369C2×C4×C61C22×D411yescharacteristic
370C2×C4×C61C2×#4111yescharacteristic
371C2×C4×C61H(5,𝔽2)11yescharacteristic
372C2×C4×C61H(5,𝔽2)11yescharacteristic
373C22⋊D61—28no—
374C22⋊D61—48no—
375C22⋊D61—48no—
376C22⋊D61—48no—
377C22⋊D61—48no—
378C22⋊D61—84no—
379C2×Dic61—21no—
380C2×Dic61—21no—
381C2×Dic61—21no—
382C2×Dic61—21no—
383C2×Dic61—21no—
384C2×Dic61—21no—
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—41no—
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—22no—
407C8×C61—41no—
408#92418—41no—
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—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×#418—611no—
471C22×#102D6111yescharacteristic, complemented
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—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×C8C2×D6111yescharacteristic, complemented
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⋊C4C2×D6111yescharacteristic, complemented
512#435—1224no—
513C2×C4⋊C8—611no—
514#418—1224no—
515C2×#102—24no—
516C2×#102—611no—
517C2×#102—611no—
518C2×#102—611no—
519C2×#102—611no—
520C2×#102—611no—
521C2×#102—611no—
522C2×#102—611no—
523C2×#102—611no—
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×D6114yes—
569C22×D4C22×D6111yescharacteristic
570C22×D4C22×D6111yescharacteristic
571C23×C4—21no—
572C23×C4—611no—
573C23×C4—1221no—
574C23×C4C22×D6111yescharacteristic
575C2×M16—1222no—
576C2×M16—1222no—
577C2×M16—2441no—
578C22×C8—22no—
579C22×C8—22no—
580C22×C8—41no—
581C22×C8—611no—
582C22×C8—611no—
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—22no—
601C2×C4⋊C4—21no—
602C2×C4⋊C4—41no—
603C2×C4⋊C4—611no—
604C2×C4⋊C4—611no—
605C2×C4⋊C4—611no—
606C2×C4⋊C4—611no—
607C2×C4⋊C4C22×D6111yescharacteristic
608C2×C4⋊C4C22×D6111yescharacteristic
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—
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—42no—
715C22×C4—42no—
716C22×C4—81no—
717C22×C4—611no—
718C22×C4—611no—
719C22×C4—611no—
720C22×C4—612no—
721C22×C4—612no—
722C22×C4—1224no—
723C22×C4—1221no—
724C22×C4—1221no—
725C22×C4—1221no—
726C22×C4—1221no—
727C22×C4—1221no—
728C22×C4—1221no—
729C22×C4—1221no—
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—44no—
743C2×C8—1221no—
744C2×C8—1221no—
745C2×C8—1221no—
746C2×C8—1221no—
747C2×C8—1221no—
748C2×C8—1221no—
749C2×C8C2×C22⋊D6112yescomplemented
750C4⋊C4—21no—
751C4⋊C4—21no—
752C4⋊C4—21no—
753C4⋊C4—42no—
754C4⋊C4—614no—
755C4⋊C4—612no—
756C4⋊C4—1221no—
757C4⋊C4—1221no—
758C4⋊C4—1221no—
759C4⋊C4—1221no—
760C4⋊C4—1221no—
761C4⋊C4C2×C22⋊D6112yescomplemented
762C22⋊C4—614no—
763C22⋊C4—614no—
764C22⋊C4—1224no—
765C22⋊C4—1224no—
766C22⋊C4—1224no—
767C22⋊C4—4881no—
768C22⋊C4—2442no—
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—
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—84no—
856C2×C4—612no—
857C2×C4—612no—
858C2×C4—612no—
859C2×C4—1221no—
860C2×C4—1221no—
861C2×C4—1221no—
862C2×C4—1221no—
863C2×C4—1221no—
864C2×C4—1221no—
865C2×C4—1222no—
866C2×C4—1222no—
867C2×C4—1222no—
868C2×C4—1222no—
869C2×C4—1222no—
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—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
928C22D4×C22⋊D6111yescharacteristic
929C22#1684040211yescharacteristic
930C22C2×#1451980111yescharacteristic
931C22C2×#1451980411yescharacteristic
932C22#1684056311yescharacteristic
933C22#1684056811yescharacteristic
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—24no—
948C2—44no—
949C2—82no—
950C2—4882no—
951C2—2442no—
952C2C22⋊C4×C22⋊D6111yescharacteristic
953C2C2×#1683976511yescharacteristic
954C2#2145434011yescharacteristic
955C2#2145729911yescharacteristic
956C2#2145731411yescharacteristic
957C2#2145783611yescharacteristic
958C2#2145795611yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC22×#102×C61C2
socleC23×C61C22×D4
prime radicalC2×D4×C22⋊D61C2
cosocleC22×C4×C61C24
hypercenterC22×#102D61
hypocenterC61#22423
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#102

Complements

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

NH ≅ G/Ntype
2. C2×#16839833C2semidirect
3. C2×#16839765C2semidirect
4. #21448744C2semidirect
5. #21446744C2semidirect
6. #21446641C2semidirect
7. #21446254C2semidirect
8. #21446247C2semidirect
9. #21446138C2semidirect
10. #21446136C2semidirect
11. #21445827C2semidirect
12. #21445750C2semidirect
13. #21445748C2semidirect
14. #21445646C2semidirect
15. C22×#102×C61C2semidirect
18. C22×#11758189C22semidirect
20. D4×C22⋊D61C4semidirect
29. C2×#14519735C22semidirect
31. C2×#14519706C22semidirect
33. C2×#14519699C22semidirect
34. C2×#14519699C22semidirect
37. C2×#14519698C22semidirect
38. C2×#14519698C22semidirect
39. C2×#14519697C22semidirect
40. 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. C23×C8×C61C22semidirect
58. C22×C4⋊C4×C61C22semidirect
62. C2×#102×C61C22semidirect
63. C2×#102×C61C22semidirect
80. C2×D4×D61C2×C4semidirect
89. #14519773C2×C4semidirect
94. #14519748C2×C4semidirect
98. D4×Dic61C2×C4semidirect
160. #102×C61D4semidirect
262. C2×C8×C61C2×D4semidirect
267. C4⋊C4×C61C2×D4semidirect
432. C22×C61#418semidirect
471. C22×#102D61semidirect
499. C23×C8C2×D61semidirect
511. C22×C4⋊C4C2×D61semidirect
526. C2×#102C2×D61semidirect
527. C2×#102C2×D61semidirect
543. C61#22423semidirect
632. #102C22⋊D61semidirect
749. C2×C8C2×C22⋊D61semidirect
761. C4⋊C4C2×C22⋊D61semidirect
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×#168398332
C2×#168397652
#214487442
#214467442
#214466412
#214462542
#214462472
#214461382
#214461362
#214458272
#214457502
#214457482
#214456462
C22×#102×C612
#2242361