Finite Group Databasebeta

← #29695547

Subgroups — #29695547

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×D244C211yesmaximal, characteristic
2C2×#16839834C211yesmaximal, characteristic, complemented
3C2×#16839766C211yesmaximal, characteristic, complemented
4C22×#14519697C211yesmaximal, characteristic, complemented
5#21446746C211yesmaximal, characteristic, complemented
6#21446642C211yesmaximal, characteristic, complemented
7#21446255C211yesmaximal, characteristic, complemented
8#21446245C211yesmaximal, characteristic, complemented
9#21446141C211yesmaximal, characteristic, complemented
10#21446136C211yesmaximal, characteristic, complemented
11#21445826C211yesmaximal, characteristic, complemented
12#21445749C211yesmaximal, characteristic, complemented
13#21445749C211yesmaximal, characteristic, complemented
14#21445647C211yesmaximal, characteristic, complemented
15C61×#2352C211yesmaximal, characteristic, complemented
16C23×D244C2211yescharacteristic
17C23×D244C2211yescharacteristic
18C22×D4×D61—21no—
19C22×#11758194C2211yescharacteristic, complemented
20C23×#92418C2211yescharacteristic, complemented
21D4×D244—24no—
22D4×D244C418yescomplemented
23C2×#14519774C2211yescharacteristic
24C2×#14519752—21no—
25C2×#14519751C2211yescharacteristic
26C2×#14519751C2211yescharacteristic
27C2×#14519747—21no—
28C2×#14519747—21no—
29C2×C4×D244C2211yescharacteristic
30#16839834—24no—
31C2×C4⋊#92418C2211yescharacteristic, complemented
32#16839766—24no—
33C2×#14519697—24no—
34C2×#14519697C2211yescharacteristic
35C2×#14519697C2211yescharacteristic
36C2×#14519697C2211yescharacteristic
37C2×#14519697C2211yescharacteristic
38C2×#14519697C2211yescharacteristic, complemented
39C2×#14519697C2211yescharacteristic, complemented
40C2×#14519697C2211yescharacteristic, complemented
41C2×#14519697C2211yescharacteristic, complemented
42C2×#14519697C2211yescharacteristic, complemented
43C2×#14519697C2211yescharacteristic, complemented
44C2×#14519697C2211yescharacteristic, complemented
45C2×#14519697C2211yescharacteristic, complemented
46C2×C22⋊#92418C2211yescharacteristic, complemented
47C2×C22⋊#92418C2211yescharacteristic, complemented
48C2×#14519688C2211yescharacteristic, complemented
49#16839524C2211yescharacteristic, complemented
50#16839524C2211yescharacteristic, complemented
51#16839524C2211yescharacteristic, complemented
52#16839524C2211yescharacteristic, complemented
53C2×C4×D4×C61C2211yescharacteristic
54C2×#117×C61C2211yescharacteristic, complemented
55C22×C4⋊C4×C61C2211yescharacteristic, complemented
56C61×#388—21no—
57C61×#387—21no—
58C61×#386—21no—
59C61×#382C2211yescharacteristic, complemented
60C61×#380C2211yescharacteristic, complemented
61C61×#380C2211yescharacteristic, complemented
62C4×C4⋊C4×C61C2211yescharacteristic, complemented
63C4×C22⋊C4×C61—21no—
64C24×D61—21no—
65C24×D61—21no—
66C22×D244—22no—
67C22×D244—22no—
68C22×D244—22no—
69C22×D244—22no—
70C22×D244—21no—
71C22×D244—21no—
72C22×D244—21no—
73C22×D244—22no—
74C22×D244—22no—
75C22×D244—21no—
76C22×D244—41no—
77C22×D244—41no—
78C22×D244—41no—
79C22×D244—41no—
80C22×D244C2×C414yes—
81C22×D244C2×C414yescomplemented
82C22×D244C2311yescharacteristic
83C22×D244C2311yescharacteristic
84C22×D244C2311yescharacteristic
85C22×C22⋊D61—21no—
86C22×C22⋊D61—21no—
87C2×D4×D61—28no—
88C2×D4×D61—44no—
89C2×D4×D61—44no—
90C22×C4×D61—21no—
91C2×#11758194—22no—
92C2×#11758194—22no—
93C2×#11758194—41no—
94C22×#92418—22no—
95C22×#92418—22no—
96C22×#92418—41no—
97C22×#92418C2311yescharacteristic
98C22×#92418C2311yescharacteristic
99C22×#92418C2311yescharacteristic
100C22×#92418C2311yescharacteristic
101#14519774—22no—
102#14519774C2×C414yescomplemented
103#14519752—28no—
104#14519751—22no—
105#14519751—22no—
106#14519751C2×C414yes—
107#14519751C2×C414yescomplemented
108#14519747—28no—
109#14519747—28no—
110C4×D244—22no—
111C4×D244C2×C414yescomplemented
112C2×C4⋊Dic61C2311yescharacteristic
113C2×#11758198—21no—
114C2×#11758198—21no—
115C2×#11758198—21no—
116C4⋊#92418—22no—
117#14519697—22no—
118#14519697—22no—
119#14519697—22no—
120#14519697—22no—
121#14519697—22no—
122#14519697—22no—
123#14519697—22no—
124#14519697—41no—
125#14519697—41no—
126#14519697—41no—
127#14519697—41no—
128#14519697D414yescomplemented
129C22⋊#92418—22no—
130C22⋊#92418—22no—
131#14519688—22no—
132C22×D4×C61D411yescharacteristic
133C23×C4×C61—21no—
134C23×C4×C61C2311yescharacteristic
135C23×C4×C61C2311yescharacteristic
136C4×D4×C61C2×C414yes—
137C4×D4×C61D414yes—
138#117×C61—22no—
139#117×C61—41no—
140C2×C4⋊C4×C61—22no—
141C2×C4⋊C4×C61—21no—
142C2×C4⋊C4×C61—41no—
143C2×C4⋊C4×C61D411yescharacteristic
144C2×C4⋊C4×C61C2311yescharacteristic
145C2×C4⋊C4×C61C2311yescharacteristic
146C2×C4⋊C4×C61C2311yescharacteristic
147C2×C4⋊C4×C61C2311yescharacteristic
148C2×C22⋊C4×C61—21no—
149C2×C22⋊C4×C61—21no—
150C2×C22⋊C4×C61—21no—
151C2×C22⋊C4×C61D411yescharacteristic
152C2×C22⋊C4×C61D411yescharacteristic
153C2×C42×C61—21no—
154C2×C42×C61—21no—
155C2×C42×C61C2311yescharacteristic
156#95×C61—21no—
157#95×C61—21no—
158#95×C61—21no—
159#95×C61—21no—
160#95×C61—21no—
161C24×C61C2×D411yescharacteristic
162C24×C61C2×D411yescharacteristic
163C23×D61—21no—
164C23×D61—21no—
165C23×D61—21no—
166C23×D61—24no—
167C23×D61—24no—
168C23×D61—42no—
169C23×D61—42no—
170C23×D61—42no—
171C23×D61—42no—
172C23×D61—42no—
173C23×D61—42no—
174C23×D61—42no—
175C23×D61—42no—
176C23×D61—81no—
177C23×D61—81no—
178C23×D61—81no—
179C23×D61—81no—
180C2×D4×C61—22no—
181C2×D4×C61—22no—
182C2×D4×C61C22⋊C414yes—
183C22×C4×C61—21no—
184C22×C4×C61—21no—
185C22×C4×C61—21no—
186C22×C4×C61—21no—
187C22×C4×C61—21no—
188C22×C4×C61—21no—
189C22×C4×C61—21no—
190C22×C4×C61—21no—
191C22×C4×C61—21no—
192C22×C4×C61—21no—
193C22×C4×C61—21no—
194C22×C4×C61—21no—
195C22×C4×C61—42no—
196C22×C4×C61—42no—
197C22×C4×C61—81no—
198C22×C4×C61C22×C412yes—
199C22×C4×C61C22×C412yes—
200C22×C4×C61C2×D411yescharacteristic
201C22×C4×C61C2×D411yescharacteristic
202C22×C4×C61C2×D411yescharacteristic
203C22×C4×C61C2×D411yescharacteristic
204C22×C4×C61C2×D412yes—
205C22×C4×C61C2×D412yes—
206C22×C4×C61C2411yescharacteristic
207C2×C22⋊D61—24no—
208C2×C22⋊D61—24no—
209C2×C22⋊D61—42no—
210C2×C22⋊D61—42no—
211C2×C22⋊D61—42no—
212C2×C22⋊D61—42no—
213C22×Dic61—21no—
214D4×D61—432no—
215C2×D244—21no—
216C2×D244—21no—
217C2×D244—21no—
218C2×D244—21no—
219C2×D244—21no—
220C2×D244—21no—
221C2×D244—21no—
222C2×D244—21no—
223C2×D244—21no—
224C2×D244—21no—
225C2×D244—21no—
226C2×D244—28no—
227C2×D244—28no—
228C2×D244—24no—
229C2×D244—24no—
230C2×D244—24no—
231C2×D244—21no—
232C2×D244—21no—
233C2×D244—24no—
234C2×D244—44no—
235C2×D244—44no—
236C2×D244—44no—
237C2×D244—44no—
238C2×D244—44no—
239C2×D244—44no—
240C2×D244—42no—
241C2×D244—42no—
242C2×D244—42no—
243C2×D244—42no—
244C2×D244—42no—
245C2×D244—42no—
246C2×D244—81no—
247C2×D244—81no—
248C2×D244C22×C412yes—
249C2×D244C22×C412yes—
250C2×D244C22×C412yes—
251C2×D244C2×D412yes—
252C2×D244#4112yes—
253C2×C4×D61—24no—
254C2×C4×D61—42no—
255C2×C4×D61—42no—
256C4⋊C4×C61—21no—
257C4⋊C4×C61—21no—
258C4⋊C4×C61—21no—
259C4⋊C4×C61—21no—
260C4⋊C4×C61—21no—
261C4⋊C4×C61—21no—
262C4⋊C4×C61—21no—
263C4⋊C4×C61—42no—
264C4⋊C4×C61C22⋊C414yes—
265C4⋊C4×C61C2×D412yescomplemented
266C22⋊C4×C61—42no—
267C22⋊C4×C61—42no—
268C22⋊C4×C61—81no—
269C22⋊C4×C61C22⋊C414yes—
270C22⋊C4×C61C22⋊C414yes—
271C42×C61—42no—
272C42×C61—81no—
273C42×C61C22×C412yes—
274C42×C61C2×D412yes—
275#11758198—24no—
276#11758198—24no—
277#11758198—24no—
278C4⋊Dic61—21no—
279C4⋊Dic61C22×C412yes—
280#11758194—44no—
281C2×#92418—21no—
282C2×#92418—21no—
283C2×#92418—21no—
284C2×#92418—21no—
285C2×#92418—21no—
286C2×#92418—21no—
287C2×#92418—21no—
288C2×#92418—21no—
289C2×#92418—21no—
290C2×#92418—21no—
291C2×#92418—21no—
292C2×#92418—44no—
293C2×#92418C2×D412yescomplemented
294C23×C61—21no—
295C23×C61—21no—
296C23×C61—21no—
297C23×C61—21no—
298C23×C61—21no—
299C23×C61—21no—
300C23×C61—21no—
301C23×C61—21no—
302C23×C61—21no—
303C23×C61—21no—
304C23×C61C2×C22⋊C412yes—
305C23×C61C2×C22⋊C412yes—
306C23×C61AGL(1,ℤ/8)12yes—
307C23×C61AGL(1,ℤ/8)12yes—
308C23×C61C22×D411yescharacteristic
309C22×D61—22no—
310C22×D61—22no—
311C22×D61—22no—
312C22×D61—22no—
313C22×D61—22no—
314C22×D61—48no—
315C22×D61—48no—
316C22×D61—41no—
317C22×D61—41no—
318C22×D61—41no—
319C22×D61—41no—
320C22×D61—48no—
321C22×D61—41no—
322C22×D61—41no—
323C22×D61—41no—
324C22×D61—41no—
325C22×D61—41no—
326C22×D61—41no—
327C22×D61—41no—
328C22×D61—41no—
329C22×D61—41no—
330C22×D61—41no—
331C22×D61—41no—
332C22×D61—41no—
333C22×D61—48no—
334C22×D61—84no—
335C22×D61—84no—
336C22×D61—84no—
337C22×D61—84no—
338C22×D61—84no—
339C22×D61—84no—
340C22×D61—84no—
341C22×D61—84no—
342C22×D61—84no—
343C22×D61—84no—
344D4×C61—28no—
345C2×C4×C61—21no—
346C2×C4×C61—21no—
347C2×C4×C61—21no—
348C2×C4×C61—21no—
349C2×C4×C61—21no—
350C2×C4×C61—21no—
351C2×C4×C61—21no—
352C2×C4×C61—21no—
353C2×C4×C61—22no—
354C2×C4×C61—22no—
355C2×C4×C61—22no—
356C2×C4×C61—22no—
357C2×C4×C61—22no—
358C2×C4×C61—22no—
359C2×C4×C61—22no—
360C2×C4×C61—22no—
361C2×C4×C61—22no—
362C2×C4×C61—41no—
363C2×C4×C61—41no—
364C2×C4×C61—41no—
365C2×C4×C61—41no—
366C2×C4×C61—41no—
367C2×C4×C61—41no—
368C2×C4×C61—41no—
369C2×C4×C61—41no—
370C2×C4×C61—41no—
371C2×C4×C61—41no—
372C2×C4×C61—41no—
373C2×C4×C61—84no—
374C2×C4×C61C2×C22⋊C412yes—
375C2×C4×C61C2×C22⋊C412yes—
376C2×C4×C61C2×C22⋊C412yes—
377C2×C4×C61C2×C22⋊C412yes—
378C2×C4×C61C23×C411yescharacteristic
379C2×C4×C61C22×D411yescharacteristic
380C2×C4×C61C22×D411yescharacteristic
381C2×C4×C61C2×#4111yescharacteristic
382C2×C4×C61H(5,𝔽2)11yescharacteristic
383C2×C4×C61H(5,𝔽2)11yescharacteristic
384C22⋊D61—48no—
385C22⋊D61—48no—
386C2×Dic61—22no—
387C2×Dic61—41no—
388C2×Dic61—41no—
389D244—22no—
390D244—22no—
391D244—22no—
392D244—22no—
393D244—22no—
394D244—22no—
395D244—22no—
396D244—48no—
397D244—48no—
398D244—48no—
399D244—41no—
400D244—41no—
401D244—41no—
402D244—41no—
403D244—84no—
404D244C4×D414yes—
405C4×D61—48no—
406#92418—22no—
407#92418—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—22no—
418C22×C61—22no—
419C22×C61—22no—
420C22×C61—41no—
421C22×C61—41no—
422C22×C61—41no—
423C22×C61—41no—
424C22×C61#41814yescomplemented
425C22×C61C22×C22⋊C411yescharacteristic
426C22×C61D4211yescharacteristic
427C22×C61#54611yescharacteristic
428C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
429C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
430C22×C61#57611yescharacteristic
431C22×C61#57711yescharacteristic
432C2×D61—24no—
433C2×D61—42no—
434C2×D61—42no—
435C2×D61—42no—
436C2×D61—42no—
437C2×D61—42no—
438C2×D61—42no—
439C2×D61—42no—
440C2×D61—42no—
441C2×D61—42no—
442C2×D61—42no—
443C2×D61—42no—
444C2×D61—42no—
445C2×D61—816no—
446C2×D61—816no—
447C2×D61—81no—
448C2×D61—81no—
449C2×D61—81no—
450C2×D61—81no—
451C2×D61—81no—
452C2×D61—81no—
453C2×D61—81no—
454C2×D61—81no—
455C4×C61—22no—
456C4×C61—22no—
457C4×C61—22no—
458C4×C61—22no—
459C4×C61—42no—
460C4×C61—81no—
461C4×C61—81no—
462C4×C61—81no—
463C4×C61C2×C4×D411yescharacteristic
464C4×C61#51811yescharacteristic
465C4×C61D4211yescharacteristic
466C4×C61#54611yescharacteristic
467Dic61—42no—
468C2×D42—611no—
469C2×#435—611no—
470C2×#418—611no—
471C22×#102—611no—
472#2352D6111yescharacteristic, complemented
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—42no—
485C2×C61D4×C22⋊C411yescharacteristic
486C2×C61C2×#41811yescharacteristic
487C2×C61#289711yescharacteristic
488C2×C61#326411yescharacteristic
489C2×C61#326511yescharacteristic
490C2×C61#331011yescharacteristic
491C2×C61#331811yescharacteristic
492D61—44no—
493D61—82no—
494D61—82no—
495C23×D4—611no—
496C23×D4—611no—
497C23×D4—1221no—
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×D4C2×D6111yescharacteristic
510C2×#117C2×D6111yescharacteristic, complemented
511C22×C4⋊C4C2×D6111yescharacteristic, complemented
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—611no—
524C2×#102—611no—
525C2×#102—611no—
526C2×#102—611no—
527C2×#102—1224no—
528C2×C22⋊C8—611no—
529C2×C22⋊C8—611no—
530C2×#97—611no—
531#388—21no—
532#387—21no—
533#386—21no—
534#382C2×D6111yescharacteristic, complemented
535#380C2×D6111yescharacteristic, complemented
536#380C2×D6111yescharacteristic, complemented
537C4×C4⋊C4C2×D6111yescharacteristic, complemented
538C4×C22⋊C4—21no—
539#340—611no—
540#340—611no—
541#340—611no—
542#340—611no—
543C61#2242311yescharacteristic, complemented, Sylow
544C25—1221no—
545C25—1221no—
546C22×D4—614no—
547C22×D4—614no—
548C22×D4—611no—
549C22×D4—611no—
550C22×D4—611no—
551C22×D4—1222no—
552C22×D4—1222no—
553C22×D4—1222no—
554C22×D4—1222no—
555C22×D4—1221no—
556C22×D4—1221no—
557C22×D4—1228no—
558C22×D4—1222no—
559C22×D4—1222no—
560C22×D4—1221no—
561C22×D4—1221no—
562C22×D4—1221no—
563C22×D4—1221no—
564C22×D4—2441no—
565C22×D4—2441no—
566C22×D4—2441no—
567C22×D4—2441no—
568C22×D4—2444no—
569C22×D4—2444no—
570C22×D4C22⋊D6111yescharacteristic
571C23×C4—21no—
572C23×C4—1221no—
573C23×C4C22×D6111yescharacteristic
574C23×C4C22×D6111yescharacteristic
575C2×M16—1222no—
576C2×M16—1222no—
577C2×M16—2441no—
578C22×C8—611no—
579C22×C8—611no—
580C22×C8—611no—
581C22×C8—611no—
582C22×C8—1222no—
583C22×C8—1222no—
584C22×C8—2441no—
585#127—614no—
586#127—1222no—
587#121—614no—
588#121—614no—
589#121—1222no—
590#121—1222no—
591#121—1228no—
592#120—1228no—
593#120—1228no—
594C4×D4—614no—
595C4×D4—1222no—
596C4×D4C4×D6114yes—
597C4×D4D24414yes—
598#117—22no—
599#117—41no—
600C2×C4⋊C4—22no—
601C2×C4⋊C4—21no—
602C2×C4⋊C4—41no—
603C2×C4⋊C4—611no—
604C2×C4⋊C4C22⋊D6111yescharacteristic
605C2×C4⋊C4C22×D6111yescharacteristic
606C2×C4⋊C4C22×D6111yescharacteristic
607C2×C4⋊C4C22×D6111yescharacteristic
608C2×C4⋊C4C22×D6111yescharacteristic
609C2×C22⋊C4—21no—
610C2×C22⋊C4—21no—
611C2×C22⋊C4—21no—
612C2×C22⋊C4—1221no—
613C2×C22⋊C4—1221no—
614C2×C22⋊C4—1221no—
615C2×C22⋊C4C22⋊D6111yescharacteristic
616C2×C22⋊C4C22⋊D6111yescharacteristic
617C2×C42—21no—
618C2×C42—21no—
619C2×C42C22×D6111yescharacteristic
620C4⋊C8—1222no—
621#102—614no—
622#102—1222no—
623#102—1222no—
624#102—1222no—
625#102—1222no—
626#102—1222no—
627#102—1222no—
628#102—1222no—
629#102—2441no—
630#102—2441no—
631#102—2441no—
632#102—2441no—
633C22⋊C8—1222no—
634C22⋊C8—1222no—
635#97—1222no—
636#95—21no—
637#95—21no—
638#95—21no—
639#95—21no—
640#95—21no—
641C24—1221no—
642C24—1224no—
643C24—1224no—
644C24—1221no—
645C24—1221no—
646C24—4881no—
647C24—4881no—
648C24—4881no—
649C24—4881no—
650C24—2442no—
651C24—2442no—
652C24—2442no—
653C24—2442no—
654C24—2442no—
655C24—2442no—
656C24—2442no—
657C24—2442no—
658C24C2×C22⋊D6111yescharacteristic
659C24C2×C22⋊D6111yescharacteristic
660C2×D4—22no—
661C2×D4—22no—
662C2×D4—612no—
663C2×D4—612no—
664C2×D4—612no—
665C2×D4—612no—
666C2×D4—612no—
667C2×D4—1228no—
668C2×D4—1228no—
669C2×D4—1224no—
670C2×D4—1224no—
671C2×D4—1221no—
672C2×D4—1221no—
673C2×D4—1221no—
674C2×D4—1221no—
675C2×D4—1221no—
676C2×D4—1221no—
677C2×D4—1221no—
678C2×D4—1221no—
679C2×D4—1221no—
680C2×D4—1221no—
681C2×D4—1221no—
682C2×D4—1221no—
683C2×D4—1221no—
684C2×D4—1224no—
685C2×D4—1224no—
686C2×D4—1224no—
687C2×D4—1224no—
688C2×D4—4881no—
689C2×D4—4881no—
690C2×D4—2444no—
691C2×D4—2444no—
692C2×D4—2444no—
693C2×D4—2444no—
694C2×D4—2444no—
695C2×D4—2444no—
696C2×D4—2442no—
697C2×D4—2442no—
698C2×D4—2442no—
699C2×D4—2442no—
700C2×D4—2442no—
701C2×D4—2442no—
702C2×D4—24432no—
703C2×D4—2442no—
704C2×D4—2442no—
705C2×D4—2442no—
706C2×D4—2442no—
707C2×D4#1175819814yes—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—42no—
721C22×C4—42no—
722C22×C4—81no—
723C22×C4—1221no—
724C22×C4—1224no—
725C22×C4—2442no—
726C22×C4—2442no—
727C22×C4C2×C4×D6112yes—
728C22×C4C2×C4×D6112yes—
729C22×C4C2×D24412yes—
730C22×C4C2×D24412yes—
731C22×C4C2×C22⋊D6111yescharacteristic
732C22×C4C2×C22⋊D6111yescharacteristic
733C22×C4C2×C22⋊D6111yescharacteristic
734C22×C4C2×C22⋊D6111yescharacteristic
735C22×C4C23×D6111yescharacteristic
736M16—2444no—
737C2×C8—612no—
738C2×C8—1221no—
739C2×C8—1221no—
740C2×C8—1221no—
741C2×C8—1221no—
742C2×C8—1221no—
743C2×C8—1221no—
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—21no—
755C4⋊C4—21no—
756C4⋊C4—21no—
757C4⋊C4—42no—
758C4⋊C4—612no—
759C4⋊C4—1221no—
760C4⋊C4#1175819814yes—
761C4⋊C4D4×D6112yescomplemented
762C22⋊C4—42no—
763C22⋊C4—42no—
764C22⋊C4—81no—
765C22⋊C4—1224no—
766C22⋊C4—1224no—
767C22⋊C4—1224no—
768C22⋊C4#1175819814yes—
769C22⋊C4#1175819814yes—
770C42—42no—
771C42—81no—
772C42C2×C4×D6112yes—
773C42C2×D24412yes—
774C23—21no—
775C23—21no—
776C23—21no—
777C23—21no—
778C23—21no—
779C23—21no—
780C23—21no—
781C23—21no—
782C23—21no—
783C23—21no—
784C23—1222no—
785C23—1222no—
786C23—1222no—
787C23—1222no—
788C23—1222no—
789C23—4884no—
790C23—4884no—
791C23—4884no—
792C23—4884no—
793C23—4884no—
794C23—4884no—
795C23—4884no—
796C23—4884no—
797C23—4884no—
798C23—4884no—
799C23—2448no—
800C23—2448no—
801C23—2448no—
802C23—2448no—
803C23—2441no—
804C23—2441no—
805C23—2441no—
806C23—2441no—
807C23—2441no—
808C23—2441no—
809C23—2441no—
810C23—2441no—
811C23—2441no—
812C23—2441no—
813C23—2441no—
814C23—2441no—
815C23—2441no—
816C23—2441no—
817C23—2441no—
818C23—2441no—
819C23C2×#1175819812yes—
820C23C2×#1175819812yes—
821C23#1451980212yes—
822C23#1451980212yes—
823C23C22×C22⋊D6111yescharacteristic
824D4—28no—
825D4—614no—
826D4—1222no—
827D4—1222no—
828D4—1222no—
829D4—1222no—
830D4—1222no—
831D4—1222no—
832D4—1222no—
833D4—4884no—
834D4—2448no—
835D4—2448no—
836D4—2448no—
837D4—2448no—
838D4—2448no—
839D4—2441no—
840D4—2441no—
841D4—2441no—
842D4—2441no—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—21no—
848C2×C4—21no—
849C2×C4—21no—
850C2×C4—21no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—84no—
872C2×C4—1222no—
873C2×C4—2448no—
874C2×C4—2441no—
875C2×C4—2441no—
876C2×C4C2×#1175819812yes—
877C2×C4C2×#1175819812yes—
878C2×C4C2×#1175819812yes—
879C2×C4C2×#1175819812yes—
880C2×C4C22×C4×D6111yescharacteristic
881C2×C4C2×D4×D6111yescharacteristic
882C2×C4C22×D24411yescharacteristic
883C2×C4#41×D6111yescharacteristic
884C2×C4#1451982211yescharacteristic
885C2×C4#1451982311yescharacteristic
886C8—1222no—
887C8—2441no—
888C8—2441no—
889C8—2441no—
890C22—22no—
891C22—22no—
892C22—22no—
893C22—22no—
894C22—22no—
895C22—22no—
896C22—22no—
897C22—22no—
898C22—22no—
899C22—41no—
900C22—41no—
901C22—41no—
902C22—41no—
903C22—1224no—
904C22—48816no—
905C22—48816no—
906C22—4881no—
907C22—4881no—
908C22—4881no—
909C22—4881no—
910C22—4881no—
911C22—4881no—
912C22—4881no—
913C22—4881no—
914C22—2442no—
915C22—2442no—
916C22—2442no—
917C22—2442no—
918C22—2442no—
919C22—2442no—
920C22—2442no—
921C22—2442no—
922C22—2442no—
923C22—2442no—
924C22—2442no—
925C22—2442no—
926C22#1683976614yescomplemented
927C22C22×#1175819811yescharacteristic
928C22D4×C22⋊D6111yescharacteristic
929C22#1684040011yescharacteristic
930C22C2×#1451980211yescharacteristic
931C22C2×#1451980211yescharacteristic
932C22#1684056511yescharacteristic
933C22#1684057011yescharacteristic
934C4—22no—
935C4—22no—
936C4—22no—
937C4—22no—
938C4—42no—
939C4—81no—
940C4—81no—
941C4—81no—
942C4—2442no—
943C4C4×D4×D6111yescharacteristic
944C4#1684023411yescharacteristic
945C4D4×D24411yescharacteristic
946C4#1684040711yescharacteristic
947C2—24no—
948C2—42no—
949C2—4882no—
950C2—4882no—
951C2—2444no—
952C2D4×#1175819811yescharacteristic
953C2C2×#1683976611yescharacteristic
954C2#2145434211yescharacteristic
955C2#2145730011yescharacteristic
956C2#2145731511yescharacteristic
957C2#2145783411yescharacteristic
958C2#2145795411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#2352C2
socleC23×C61C22×D4
prime radicalC2×D4×D244C2
cosocleC22×C4×C61C24
hypercenter#2352D61
hypocenterC61#22423
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2352

Complements

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

NH ≅ G/Ntype
2. C2×#16839834C2semidirect
3. C2×#16839766C2semidirect
4. C22×#14519697C2semidirect
5. #21446746C2semidirect
6. #21446642C2semidirect
7. #21446255C2semidirect
8. #21446245C2semidirect
9. #21446141C2semidirect
10. #21446136C2semidirect
11. #21445826C2semidirect
12. #21445749C2semidirect
13. #21445749C2semidirect
14. #21445647C2semidirect
15. C61×#2352C2semidirect
19. C22×#11758194C22semidirect
20. C23×#92418C22semidirect
22. D4×D244C4semidirect
31. C2×C4⋊#92418C22semidirect
38. C2×#14519697C22semidirect
39. C2×#14519697C22semidirect
40. C2×#14519697C22semidirect
41. C2×#14519697C22semidirect
42. C2×#14519697C22semidirect
43. C2×#14519697C22semidirect
44. C2×#14519697C22semidirect
45. C2×#14519697C22semidirect
46. C2×C22⋊#92418C22semidirect
47. C2×C22⋊#92418C22semidirect
48. C2×#14519688C22semidirect
49. #16839524C22semidirect
50. #16839524C22semidirect
51. #16839524C22semidirect
52. #16839524C22semidirect
54. C2×#117×C61C22semidirect
55. C22×C4⋊C4×C61C22semidirect
59. C61×#382C22semidirect
60. C61×#380C22semidirect
61. C61×#380C22semidirect
62. C4×C4⋊C4×C61C22semidirect
81. C22×D244C2×C4semidirect
102. #14519774C2×C4semidirect
107. #14519751C2×C4semidirect
111. C4×D244C2×C4semidirect
128. #14519697D4semidirect
265. C4⋊C4×C61C2×D4semidirect
293. C2×#92418C2×D4semidirect
424. C22×C61#418semidirect
472. #2352D61semidirect
510. C2×#117C2×D61semidirect
511. C22×C4⋊C4C2×D61semidirect
534. #382C2×D61semidirect
535. #380C2×D61semidirect
536. #380C2×D61semidirect
537. C4×C4⋊C4C2×D61semidirect
543. C61#22423semidirect
761. C4⋊C4D4×D61semidirect
926. C22#16839766semidirect

Maximal subgroups

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

subgroupindex
C2×D4×D2442
C2×#168398342
C2×#168397662
C22×#145196972
#214467462
#214466422
#214462552
#214462452
#214461412
#214461362
#214458262
#214457492
#214456472
C61×#23522
#2242361