Finite Group Databasebeta

← #29689141

Subgroups — #29689141

Order 15616.

1622 conjugacy classes of subgroups.

The subgroup lattice has 1076 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#525×D61C211yesmaximal, characteristic
2C2×#16839725C211yesmaximal, characteristic, complemented
3C4×C22⋊C4×D61C211yesmaximal, characteristic, complemented
4#21446261C212yesmaximal, complemented
5#21446259C212yesmaximal, complemented
6#21446122C211yesmaximal, characteristic, complemented
7#21446121C211yesmaximal, characteristic, complemented
8#21446119C211yesmaximal, characteristic, complemented
9#21445917C212yesmaximal, complemented
10#21445761C212yesmaximal, complemented
11C61×#1871C211yesmaximal, characteristic, complemented
12C2×#41×D61C2211yescharacteristic
13C23×C4×D61C2211yescharacteristic
14C22×#11758194C2211yescharacteristic, complemented
15#16840275C411yescharacteristic, complemented
16#16840275C411yescharacteristic, complemented
17#16840274C2211yescharacteristic
18#16840273C2211yescharacteristic
19#16840272C411yescharacteristic, complemented
20#16840272C411yescharacteristic, complemented
21#16840271—21no—
22#16840271—21no—
23#16840270—21no—
24#16840269C2211yescharacteristic
25#16840268—21no—
26#123×D61—21no—
27C22⋊Q8×D61C411yescharacteristic, complemented
28C22⋊Q8×D61C411yescharacteristic, complemented
29#121×D61C411yescharacteristic, complemented
30#121×D61C411yescharacteristic, complemented
31#120×D61—21no—
32C4×D4×D61—21no—
33C4×D4×D61—21no—
34#117×D61C2211yescharacteristic
35C2×C22⋊C4×D61—21no—
36C2×C42×D61C2212yescomplemented
37C2×#14519705C2212yescomplemented
38C2×#14519704C2212yescomplemented
39C2×#14519703C2212yescomplemented
40#16839725—21no—
41#16839725—21no—
42#16839725C2212yes—
43#16839725C2212yescomplemented
44C2×#14519689—21no—
45C2×#14519689—21no—
46C22⋊C4×Dic61—21no—
47C4×#11758198C2212yes—
48C4×C22⋊Dic61C2211yescharacteristic, complemented
49#16839609—21no—
50#95×D61—21no—
51#16839523C2212yescomplemented
52#16839522C2212yescomplemented
53#16839521C2212yescomplemented
54C22×M16×C61C2211yescharacteristic, complemented
55C61×#525C2211yescharacteristic
56C2×#104×C61C2212yescomplemented
57C4×C22⋊C4×C61C2211yescharacteristic, complemented
58C61×#339C2212yescomplemented
59C24×D61D411yescharacteristic
60C2×#11758226C2×C411yescharacteristic, complemented
61C2×#11758222—21no—
62C2×#11758222C2311yescharacteristic
63C2×#11758224—21no—
64C2×#11758224C2×C411yescharacteristic, complemented
65#41×D61—42no—
66#41×D61—42no—
67C2×Q8×D61C2×C411yescharacteristic, complemented
68C2×D4×D61—21no—
69C2×D4×D61—21no—
70C2×D4×D61—21no—
71C2×D4×D61C2×C411yescharacteristic, complemented
72C23×Dic61D411yescharacteristic
73C22×C4×D61—22no—
74C22×C4×D61—21no—
75C22×C4×D61—42no—
76C22×C4×D61—42no—
77C22×C4×D61C2×C411yescharacteristic
78C22×C4×D61C2×C411yescharacteristic
79C22×C4×D61C2×C411yescharacteristic
80C22×C4×D61C2×C411yescharacteristic
81C22×C4×D61D411yescharacteristic
82C22×C4×D61D411yescharacteristic
83C22×C4×D61D411yescharacteristic
84C22×C4×D61D411yescharacteristic
85C22×C4×D61D411yescharacteristic
86C22×C4×D61D411yescharacteristic
87C22×C4×D61C2311yescharacteristic
88C22×C4×D61C2311yescharacteristic
89C2×#11758194—21no—
90C2×#11758194—42no—
91C2×#11758194C2312yes—
92C22×#92418—21no—
93#14519762—21no—
94#14519762—21no—
95#14519761—21no—
96#14519760—21no—
97#14519759—21no—
98#14519759—21no—
99#14519758—21no—
100#14519757C2×C411yescharacteristic
101#14519757C2×C411yescharacteristic
102#14519756C2×C411yescharacteristic, complemented
103#14519756C2×C411yescharacteristic, complemented
104#14519755—21no—
105#14519755—21no—
106#14519754—21no—
107#14519754—21no—
108#14519753C2×C411yescharacteristic
109#14519753C2×C411yescharacteristic
110#14519752C2×C411yescharacteristic
111#14519752C2×C411yescharacteristic
112#14519751C2×C411yescharacteristic, complemented
113#14519751C2×C411yescharacteristic, complemented
114#14519750—21no—
115#14519750—21no—
116#14519749—21no—
117#14519749—21no—
118#14519748C2×C411yescharacteristic
119#14519748C2×C411yescharacteristic
120#14519747—21no—
121#14519747—21no—
122#14519747—21no—
123#14519746—21no—
124#14519745—21no—
125#14519745—21no—
126#14519745—21no—
127C4×D244—21no—
128C4×D244—21no—
129D4×Dic61—21no—
130D4×Dic61—21no—
131#14519739—21no—
132#14519739—21no—
133C4×C22⋊D61—21no—
134C4×C22⋊D61—21no—
135C4×C22⋊D61—21no—
136C4×C22⋊D61—21no—
137#14519737—21no—
138#14519737—21no—
139#14519737—21no—
140#14519737—21no—
141#14519736C2311yescharacteristic
142#14519735C2×C411yescharacteristic, complemented
143#14519735C2×C411yescharacteristic, complemented
144#14519734—21no—
145#14519733—21no—
146C4⋊C4×D61—21no—
147C4⋊C4×D61—21no—
148C4⋊C4×D61C2×C411yescharacteristic, complemented
149C4⋊C4×D61C2×C411yescharacteristic, complemented
150C2×C22⋊Dic61—21no—
151C2×#11758198—22no—
152C22⋊C4×D61—28no—
153C22⋊C4×D61—21no—
154C22⋊C4×D61—21no—
155C22⋊C4×D61—21no—
156C22⋊C4×D61—21no—
157C22⋊C4×D61—21no—
158C2×C4×Dic61—22no—
159C2×C4×Dic61C2312yes—
160C42×D61—21no—
161C42×D61—42no—
162C42×D61—42no—
163#14519705—42no—
164#14519704—42no—
165#14519703—42no—
166#14519689—22no—
167#14519689—22no—
168#14519689—22no—
169#14519689—22no—
170#14519684—21no—
171#14519684—22no—
172C2×#41×C61C2311yescharacteristic
173C23×C4×C61C2311yescharacteristic
174C2×M16×C61—21no—
175C2×M16×C61—42no—
176C2×M16×C61C2312yes—
177C22×C8×C61—21no—
178#123×C61—21no—
179C22⋊Q8×C61C2×C411yescharacteristic, complemented
180C22⋊Q8×C61C2×C411yescharacteristic, complemented
181#121×C61C2×C411yescharacteristic, complemented
182#121×C61C2×C411yescharacteristic, complemented
183#120×C61—21no—
184C4×D4×C61—21no—
185C4×D4×C61—21no—
186#117×C61C2311yescharacteristic
187C2×C22⋊C4×C61—21no—
188C2×C42×C61C2312yes—
189#104×C61—42no—
190#95×C61—21no—
191C24×C61C2×D411yescharacteristic
192C23×D61—24no—
193C23×D61—21no—
194C23×D61—42no—
195C23×D61—42no—
196C23×D61C22⋊C411yescharacteristic
197C23×D61C22⋊C411yescharacteristic
198C23×D61C22⋊C411yescharacteristic
199C23×D61C22⋊C411yescharacteristic
200C23×D61C2×D411yescharacteristic
201C23×D61C2×D411yescharacteristic
202#41×C61—22no—
203#41×C61—22no—
204C2×Q8×C61C22×C411yescharacteristic
205C2×D4×C61—21no—
206C2×D4×C61—21no—
207C2×D4×C61—21no—
208C2×D4×C61C22×C411yescharacteristic
209C22×C4×C61—22no—
210C22×C4×C61—22no—
211C22×C4×C61—22no—
212C22×C4×C61—21no—
213C22×C4×C61C22×C411yescharacteristic
214C22×C4×C61C22×C411yescharacteristic
215C22×C4×C61C2×D411yescharacteristic
216C22×C4×C61C2×D411yescharacteristic
217C22×C4×C61C2×D411yescharacteristic
218C22×C4×C61C2411yescharacteristic
219C2×C22⋊D61—21no—
220C2×C22⋊D61—21no—
221C2×C22⋊D61—21no—
222C2×C22⋊D61—21no—
223C2×C22⋊D61—21no—
224C2×C22⋊D61—21no—
225C2×C22⋊D61—21no—
226C22×Dic61—22no—
227C22×Dic61—21no—
228C22×Dic61—42no—
229C22×Dic61C22⋊C411yescharacteristic
230C22×Dic61C22⋊C411yescharacteristic
231C22×Dic61C22⋊C411yescharacteristic
232C22×Dic61C22⋊C411yescharacteristic
233C22×Dic61C2×D411yescharacteristic
234C22×Dic61C2×D411yescharacteristic
235#11758226—42no—
236Q8×D61—42no—
237#11758224—42no—
238#11758224—44no—
239D4×D61—42no—
240D4×D61—44no—
241D4×D61—44no—
242D4×D61—44no—
243#11758222—22no—
244#11758222—22no—
245#11758222—42no—
246#11758222—42no—
247C2×D244—21no—
248C2×D244—21no—
249C2×D244—21no—
250C2×D244C22×C411yescharacteristic
251C2×C4×D61—22no—
252C2×C4×D61—22no—
253C2×C4×D61—22no—
254C2×C4×D61—22no—
255C2×C4×D61—28no—
256C2×C4×D61—21no—
257C2×C4×D61—21no—
258C2×C4×D61—21no—
259C2×C4×D61—21no—
260C2×C4×D61—21no—
261C2×C4×D61—42no—
262C2×C4×D61—42no—
263C2×C4×D61—42no—
264C2×C4×D61—42no—
265C2×C4×D61—41no—
266C2×C4×D61—41no—
267C2×C4×D61—41no—
268C2×C4×D61—41no—
269C2×C4×D61—41no—
270C2×C4×D61—41no—
271C2×C4×D61—41no—
272C2×C4×D61—41no—
273C2×C4×D61—42no—
274C2×C4×D61—42no—
275C2×C4×D61—42no—
276C2×C4×D61—42no—
277C2×C4×D61—44no—
278C2×C4×D61—44no—
279C2×C4×D61C22⋊C411yescharacteristic
280C2×C4×D61C22⋊C411yescharacteristic
281C2×C4×D61C22⋊C411yescharacteristic
282C2×C4×D61C22⋊C411yescharacteristic
283C2×C4×D61C22⋊C411yescharacteristic
284C2×C4×D61C22⋊C411yescharacteristic
285C2×C4×D61C22⋊C411yescharacteristic
286C2×C4×D61C22⋊C411yescharacteristic
287C2×C4×D61C22×C411yescharacteristic
288C2×C4×D61C22×C411yescharacteristic
289C2×C4×D61C22×C411yescharacteristic
290C2×C4×D61C22×C411yescharacteristic
291C2×C4×D61C2×D411yescharacteristic
292C2×C4×D61C2×D411yescharacteristic
293C2×C4×D61C2×D411yescharacteristic
294C2×C4×D61C2×D411yescharacteristic
295C2×Dic122—21no—
296C2×Dic122C22×C411yescharacteristic
297M16×C61—22no—
298M16×C61—22no—
299M16×C61—42no—
300C2×C8×C61—22no—
301C2×C8×C61—42no—
302C4⋊C4×C61—21no—
303C4⋊C4×C61—21no—
304C4⋊C4×C61C22×C411yescharacteristic
305C4⋊C4×C61C22×C411yescharacteristic
306C22⋊C4×C61—24no—
307C22⋊C4×C61—21no—
308C22⋊C4×C61—21no—
309C22⋊C4×C61—21no—
310C22⋊C4×C61—21no—
311C22⋊C4×C61—21no—
312C42×C61—21no—
313C42×C61—22no—
314C42×C61—22no—
315C22⋊Dic61—24no—
316C22⋊Dic61—21no—
317C22⋊Dic61—21no—
318C22⋊Dic61—21no—
319C22⋊Dic61—21no—
320C22⋊Dic61—21no—
321#11758198—28no—
322#11758198—21no—
323#11758198—21no—
324#11758198—21no—
325#11758198—21no—
326#11758198—21no—
327#11758198—21no—
328#11758198—21no—
329#11758198—21no—
330#11758198—21no—
331#11758198—21no—
332C4⋊Dic61—21no—
333C4⋊Dic61—21no—
334C4⋊Dic61C22×C411yescharacteristic
335C4⋊Dic61C22×C411yescharacteristic
336#11758196—21no—
337#11758196—21no—
338#11758196—21no—
339#11758196—21no—
340#11758196—21no—
341#11758196—21no—
342C4×Dic61—21no—
343C4×Dic61—21no—
344C4×Dic61—21no—
345C4×Dic61—22no—
346C4×Dic61—22no—
347C4×Dic61—44no—
348#11758194—22no—
349#11758194—22no—
350#11758194—42no—
351C2×#92418—22no—
352C2×#92418—42no—
353C23×C61—22no—
354C23×C61—22no—
355C23×C61—21no—
356C23×C61—41no—
357C23×C61C2×C22⋊C411yescharacteristic
358C23×C61C2×C22⋊C411yescharacteristic
359C23×C61C22×D411yescharacteristic
360C22×D61—22no—
361C22×D61—22no—
362C22×D61—22no—
363C22×D61—22no—
364C22×D61—22no—
365C22×D61—22no—
366C22×D61—22no—
367C22×D61—22no—
368C22×D61—22no—
369C22×D61—22no—
370C22×D61—21no—
371C22×D61—41no—
372C22×D61—41no—
373C22×D61—41no—
374C22×D61—41no—
375C22×D61—41no—
376C22×D61—41no—
377C22×D61—41no—
378C22×D61—416no—
379C22×D61—42no—
380C22×D61—42no—
381C22×D61—42no—
382C22×D61#10414yescomplemented
383C22×D61C2×C22⋊C411yescharacteristic
384C22×D61C2×C22⋊C411yescharacteristic
385C22×D61C2×C22⋊C411yescharacteristic
386C22×D61C2×C22⋊C411yescharacteristic
387Q8×C61—22no—
388D4×C61—22no—
389D4×C61—42no—
390D4×C61—42no—
391D4×C61—42no—
392C2×C4×C61—22no—
393C2×C4×C61—22no—
394C2×C4×C61—22no—
395C2×C4×C61—21no—
396C2×C4×C61—21no—
397C2×C4×C61—21no—
398C2×C4×C61—21no—
399C2×C4×C61—24no—
400C2×C4×C61—21no—
401C2×C4×C61—21no—
402C2×C4×C61—21no—
403C2×C4×C61—42no—
404C2×C4×C61—42no—
405C2×C4×C61—41no—
406C2×C4×C61—41no—
407C2×C4×C61C2×C22⋊C411yescharacteristic
408C2×C4×C61C2×C22⋊C411yescharacteristic
409C2×C4×C61C23×C411yescharacteristic
410C2×C4×C61C22×D411yescharacteristic
411C2×C4×C61H(5,𝔽2)12yes—
412C2×C4×C61H(5,𝔽2)12yes—
413C22⋊D61—42no—
414C22⋊D61—42no—
415C22⋊D61—42no—
416C22⋊D61—42no—
417C22⋊D61—42no—
418C22⋊D61—42no—
419C22⋊D61—42no—
420C2×Dic61—22no—
421C2×Dic61—22no—
422C2×Dic61—24no—
423C2×Dic61—21no—
424C2×Dic61—21no—
425C2×Dic61—21no—
426C2×Dic61—41no—
427C2×Dic61—41no—
428C2×Dic61—41no—
429C2×Dic61—41no—
430C2×Dic61—42no—
431C2×Dic61—42no—
432C2×Dic61—42no—
433C2×Dic61C2×C22⋊C411yescharacteristic
434C2×Dic61C2×C22⋊C411yescharacteristic
435C2×Dic61C2×C22⋊C411yescharacteristic
436C2×Dic61C2×C22⋊C411yescharacteristic
437D244—22no—
438D244—42no—
439D244—42no—
440D244—42no—
441C4×D61—22no—
442C4×D61—22no—
443C4×D61—22no—
444C4×D61—22no—
445C4×D61—21no—
446C4×D61—21no—
447C4×D61—21no—
448C4×D61—21no—
449C4×D61—21no—
450C4×D61—21no—
451C4×D61—21no—
452C4×D61—21no—
453C4×D61—41no—
454C4×D61—41no—
455C4×D61—41no—
456C4×D61—41no—
457C4×D61—41no—
458C4×D61—41no—
459C4×D61—41no—
460C4×D61—41no—
461C4×D61—42no—
462C4×D61—416no—
463C4×D61—42no—
464C4×D61—42no—
465C4×D61—42no—
466C4×D61—41no—
467C4×D61—41no—
468Dic122—22no—
469Dic122—42no—
470C8×C61—42no—
471#92418—42no—
472#21773—611nomaximal, Sylow
473C22×C61—21no—
474C22×C61—21no—
475C22×C61—21no—
476C22×C61—21no—
477C22×C61—21no—
478C22×C61—21no—
479C22×C61—21no—
480C22×C61—44no—
481C22×C61—41no—
482C22×C61—41no—
483C22×C61—41no—
484C22×C61C2×#10412yes—
485C22×C61C22×C22⋊C411yescharacteristic
486C22×C61#53412yes—
487C2×D61—28no—
488C2×D61—21no—
489C2×D61—21no—
490C2×D61—21no—
491C2×D61—21no—
492C2×D61—21no—
493C2×D61—21no—
494C2×D61—21no—
495C2×D61—21no—
496C2×D61—21no—
497C2×D61—44no—
498C2×D61—44no—
499C2×D61—44no—
500C2×D61—44no—
501C2×D61—44no—
502C2×D61—41no—
503C2×D61—41no—
504C2×D61—41no—
505C2×D61—84no—
506C2×D61C2×#10412yes—
507C2×D61C2×#10412yes—
508C2×D61#42112yes—
509C4×C61—21no—
510C4×C61—21no—
511C4×C61—44no—
512C4×C61—41no—
513C4×C61—41no—
514C4×C61—41no—
515C4×C61#51812yes—
516C4×C61#53411yescharacteristic
517C4×C61#53411yescharacteristic
518Dic61—21no—
519Dic61—21no—
520Dic61—21no—
521Dic61—21no—
522Dic61—44no—
523Dic61—41no—
524Dic61—41no—
525Dic61—41no—
526C2×#525—611no—
527C2×#407—611no—
528C2×C4×C22⋊C4—611no—
529#1896—612no—
530#1896—612no—
531#1871—611no—
532#1871—611no—
533#1871—611no—
534#1871D6111yescharacteristic, complemented
535#1826—612no—
536#1789—612no—
537C2×C61—22no—
538C2×C61—22no—
539C2×C61—41no—
540C2×C61—81no—
541C2×C61#230811yescharacteristic
542C2×C61C22×#10411yescharacteristic
543C2×C61C2×#42111yescharacteristic
544D61—22no—
545D61—22no—
546D61—22no—
547D61—41no—
548D61—81no—
549C22×#41—611no—
550C24×C4—611no—
551C22×M16—611no—
552C22×M16C2×D6111yescharacteristic, complemented
553#525—611no—
554#525—611no—
555#525—611no—
556#525—611no—
557#525—611no—
558#525—611no—
559#525—611no—
560#525—1221no—
561#525—1221no—
562#525—1221no—
563#525—1221no—
564#525C2×D6111yescharacteristic
565C2×#123—1221no—
566C2×C22⋊Q8—611no—
567C2×C22⋊Q8—611no—
568C2×#121—611no—
569C2×#121—611no—
570C2×#120—1221no—
571C2×C4×D4—1221no—
572C2×C4×D4—1221no—
573C2×#117—611no—
574C22×C22⋊C4—1221no—
575C22×C42—612no—
576C2×#104—612no—
577C2×#104—612no—
578C2×#104—612no—
579C2×#104C2×D6112yescomplemented
580#407—612no—
581#407—612no—
582#407—1221no—
583#407—1221no—
584C2×C22⋊C8—1221no—
585C2×C22⋊C8—1221no—
586C4×C22⋊C4—611no—
587C4×C22⋊C4—612no—
588C4×C22⋊C4—1221no—
589C4×C22⋊C4—1221no—
590C4×C22⋊C4C2×D6111yescharacteristic, complemented
591C2×#95—1221no—
592#339—612no—
593#339—612no—
594#339—612no—
595#339C2×D6112yescomplemented
596C61#2177311yescharacteristic, complemented, Sylow
597C25—611no—
598C2×#41—611no—
599C2×#41—611no—
600C2×#41—611no—
601C2×#41—1221no—
602C2×#41—1221no—
603C2×#41—2442no—
604C2×#41—2442no—
605C2×#41C22×D6111yescharacteristic
606C22×Q8—611no—
607C22×D4—611no—
608C22×D4—1221no—
609C22×D4—1221no—
610C22×D4—1221no—
611C23×C4—611no—
612C23×C4—611no—
613C23×C4—611no—
614C23×C4—611no—
615C23×C4—611no—
616C23×C4—611no—
617C23×C4—611no—
618C23×C4—611no—
619C23×C4—611no—
620C23×C4—611no—
621C23×C4—611no—
622C23×C4—611no—
623C23×C4—611no—
624C23×C4—1221no—
625C23×C4—1222no—
626C23×C4—2442no—
627C23×C4—2442no—
628C23×C4C22×D6111yescharacteristic
629C2×M16—21no—
630C2×M16—42no—
631C2×M16—612no—
632C2×M16—1221no—
633C2×M16—2442no—
634C2×M16C22×D6112yes—
635C22×C8—21no—
636C22×C8—1221no—
637#123—21no—
638#123—1221no—
639#123—1221no—
640#123—1221no—
641#123—1221no—
642#123—1221no—
643#123—1221no—
644#123—1221no—
645C22⋊Q8—611no—
646C22⋊Q8—611no—
647C22⋊Q8—611no—
648C22⋊Q8—611no—
649C22⋊Q8—611no—
650C22⋊Q8—611no—
651C22⋊Q8—1221no—
652C22⋊Q8—1221no—
653C22⋊Q8—1221no—
654C22⋊Q8—1221no—
655C22⋊Q8C4×D6111yescharacteristic, complemented
656C22⋊Q8C4×D6111yescharacteristic, complemented
657#121—611no—
658#121—611no—
659#121—611no—
660#121—611no—
661#121—611no—
662#121—611no—
663#121—1221no—
664#121—1221no—
665#121—1221no—
666#121—1221no—
667#121C4×D6111yescharacteristic, complemented
668#121C4×D6111yescharacteristic, complemented
669#120—21no—
670#120—1221no—
671#120—1221no—
672#120—1221no—
673#120—1221no—
674#120—1221no—
675#120—1221no—
676#120—1221no—
677C4×D4—21no—
678C4×D4—21no—
679C4×D4—1221no—
680C4×D4—1221no—
681C4×D4—1221no—
682C4×D4—1221no—
683C4×D4—1221no—
684C4×D4—1221no—
685C4×D4—1221no—
686C4×D4—1221no—
687C4×D4—1221no—
688C4×D4—1221no—
689C4×D4—1221no—
690C4×D4—1221no—
691C4×D4—1221no—
692C4×D4—1221no—
693#117—611no—
694#117—611no—
695#117—611no—
696#117—1221no—
697#117—1221no—
698#117C22×D6111yescharacteristic
699C2×C4⋊C4—611no—
700C2×C4⋊C4—611no—
701C2×C4⋊C4—1221no—
702C2×C4⋊C4—1221no—
703C2×C22⋊C4—21no—
704C2×C22⋊C4—1221no—
705C2×C22⋊C4—1221no—
706C2×C22⋊C4—1221no—
707C2×C22⋊C4—1221no—
708C2×C22⋊C4—1221no—
709C2×C22⋊C4—1228no—
710C2×C22⋊C4—1222no—
711C2×C22⋊C4—1221no—
712C2×C42—612no—
713C2×C42—1221no—
714C2×C42—1222no—
715C2×C42—2442no—
716C2×C42—2442no—
717C2×C42C22×D6112yes—
718#104—42no—
719#104—2442no—
720#104—2442no—
721#104—2442no—
722C22⋊C8—1222no—
723C22⋊C8—1222no—
724C22⋊C8—1222no—
725C22⋊C8—1222no—
726#95—21no—
727#95—1222no—
728#95—1221no—
729C24—611no—
730C24—611no—
731C24—611no—
732C24—611no—
733C24—611no—
734C24—611no—
735C24—1224no—
736C24—1221no—
737C24—2442no—
738C24—2442no—
739C24D4×D6111yescharacteristic
740#41—22no—
741#41—22no—
742#41—1222no—
743#41—1222no—
744#41—2442no—
745#41—2442no—
746#41—2442no—
747#41—2444no—
748#41—2442no—
749C2×Q8—611no—
750C2×Q8—1221no—
751C2×Q8—2442no—
752C2×Q8C2×C4×D6111yescharacteristic
753C2×D4—21no—
754C2×D4—21no—
755C2×D4—21no—
756C2×D4—611no—
757C2×D4—1221no—
758C2×D4—1221no—
759C2×D4—1221no—
760C2×D4—1221no—
761C2×D4—1221no—
762C2×D4—1221no—
763C2×D4—1221no—
764C2×D4—1221no—
765C2×D4—1221no—
766C2×D4—1221no—
767C2×D4—2442no—
768C2×D4—2444no—
769C2×D4—2444no—
770C2×D4—2444no—
771C2×D4C2×C4×D6111yescharacteristic
772C22×C4—22no—
773C22×C4—22no—
774C22×C4—22no—
775C22×C4—21no—
776C22×C4—611no—
777C22×C4—611no—
778C22×C4—611no—
779C22×C4—611no—
780C22×C4—611no—
781C22×C4—611no—
782C22×C4—611no—
783C22×C4—611no—
784C22×C4—611no—
785C22×C4—611no—
786C22×C4—611no—
787C22×C4—611no—
788C22×C4—611no—
789C22×C4—611no—
790C22×C4—611no—
791C22×C4—611no—
792C22×C4—611no—
793C22×C4—611no—
794C22×C4—611no—
795C22×C4—611no—
796C22×C4—611no—
797C22×C4—611no—
798C22×C4—1221no—
799C22×C4—1221no—
800C22×C4—1221no—
801C22×C4—1221no—
802C22×C4—1228no—
803C22×C4—1221no—
804C22×C4—1222no—
805C22×C4—1222no—
806C22×C4—1222no—
807C22×C4—1222no—
808C22×C4—1222no—
809C22×C4—1221no—
810C22×C4—2442no—
811C22×C4—2442no—
812C22×C4—2442no—
813C22×C4—2442no—
814C22×C4—2441no—
815C22×C4—2441no—
816C22×C4—2441no—
817C22×C4—2441no—
818C22×C4—2441no—
819C22×C4—2441no—
820C22×C4—2441no—
821C22×C4—2441no—
822C22×C4—2442no—
823C22×C4—2442no—
824C22×C4—2442no—
825C22×C4—2442no—
826C22×C4—2444no—
827C22×C4—2444no—
828C22×C4—2442no—
829C22×C4C2×C4×D6111yescharacteristic
830C22×C4C2×C4×D6111yescharacteristic
831C22×C4D4×D6111yescharacteristic
832C22×C4D4×D6111yescharacteristic
833C22×C4D4×D6111yescharacteristic
834C22×C4C23×D6111yescharacteristic
835M16—22no—
836M16—22no—
837M16—42no—
838M16—1222no—
839M16—1222no—
840M16—2442no—
841C2×C8—22no—
842C2×C8—42no—
843C2×C8—1222no—
844C2×C8—2442no—
845C4⋊C4—21no—
846C4⋊C4—21no—
847C4⋊C4—611no—
848C4⋊C4—611no—
849C4⋊C4—1221no—
850C4⋊C4—1221no—
851C4⋊C4—1221no—
852C4⋊C4—1221no—
853C4⋊C4—1221no—
854C4⋊C4—1221no—
855C4⋊C4—1221no—
856C4⋊C4—1221no—
857C4⋊C4C2×C4×D6111yescharacteristic
858C4⋊C4C2×C4×D6111yescharacteristic
859C22⋊C4—24no—
860C22⋊C4—21no—
861C22⋊C4—21no—
862C22⋊C4—21no—
863C22⋊C4—21no—
864C22⋊C4—21no—
865C22⋊C4—1221no—
866C22⋊C4—1221no—
867C22⋊C4—1221no—
868C22⋊C4—1221no—
869C22⋊C4—1221no—
870C22⋊C4—1221no—
871C22⋊C4—1221no—
872C22⋊C4—1221no—
873C22⋊C4—1228no—
874C22⋊C4—1221no—
875C22⋊C4—1221no—
876C22⋊C4—1224no—
877C22⋊C4—1221no—
878C22⋊C4—1221no—
879C22⋊C4—1221no—
880C22⋊C4—1221no—
881C22⋊C4—1221no—
882C42—21no—
883C42—22no—
884C42—22no—
885C42—1221no—
886C42—1221no—
887C42—1221no—
888C42—1222no—
889C42—1222no—
890C42—2444no—
891C23—22no—
892C23—22no—
893C23—21no—
894C23—41no—
895C23—611no—
896C23—611no—
897C23—611no—
898C23—614no—
899C23—611no—
900C23—1222no—
901C23—1222no—
902C23—1222no—
903C23—1222no—
904C23—1222no—
905C23—1222no—
906C23—1222no—
907C23—1222no—
908C23—1222no—
909C23—1222no—
910C23—1221no—
911C23—2441no—
912C23—2441no—
913C23—2441no—
914C23—2441no—
915C23—2441no—
916C23—2441no—
917C23—2441no—
918C23—2442no—
919C23—2442no—
920C23—2442no—
921C23—24416no—
922C23C22⋊C4×D6111yescharacteristic
923C23C22⋊C4×D6111yescharacteristic
924C23C2×D4×D6111yescharacteristic
925Q8—22no—
926Q8—1222no—
927Q8—2442no—
928D4—22no—
929D4—42no—
930D4—42no—
931D4—42no—
932D4—1222no—
933D4—2442no—
934D4—2442no—
935D4—2442no—
936D4—2442no—
937D4—2442no—
938D4—2442no—
939D4—2442no—
940D4—2442no—
941D4—2442no—
942D4—2442no—
943C2×C4—22no—
944C2×C4—22no—
945C2×C4—22no—
946C2×C4—21no—
947C2×C4—21no—
948C2×C4—21no—
949C2×C4—21no—
950C2×C4—24no—
951C2×C4—21no—
952C2×C4—21no—
953C2×C4—21no—
954C2×C4—42no—
955C2×C4—42no—
956C2×C4—41no—
957C2×C4—41no—
958C2×C4—611no—
959C2×C4—611no—
960C2×C4—611no—
961C2×C4—611no—
962C2×C4—1222no—
963C2×C4—1222no—
964C2×C4—1222no—
965C2×C4—1222no—
966C2×C4—1222no—
967C2×C4—1222no—
968C2×C4—1221no—
969C2×C4—1221no—
970C2×C4—1221no—
971C2×C4—1221no—
972C2×C4—1221no—
973C2×C4—1221no—
974C2×C4—1221no—
975C2×C4—1221no—
976C2×C4—1224no—
977C2×C4—1221no—
978C2×C4—1221no—
979C2×C4—1221no—
980C2×C4—2441no—
981C2×C4—2441no—
982C2×C4—2441no—
983C2×C4—2441no—
984C2×C4—2441no—
985C2×C4—2441no—
986C2×C4—2441no—
987C2×C4—2441no—
988C2×C4—2442no—
989C2×C4—2442no—
990C2×C4—24416no—
991C2×C4—2442no—
992C2×C4—2442no—
993C2×C4—2441no—
994C2×C4—2441no—
995C2×C4—2441no—
996C2×C4—2441no—
997C2×C4—2442no—
998C2×C4—2442no—
999C2×C4—2442no—
1000C2×C4—2441no—
1001C2×C4—2441no—
1002C2×C4C22⋊C4×D6111yescharacteristic
1003C2×C4C22⋊C4×D6111yescharacteristic
1004C2×C4C22×C4×D6111yescharacteristic
1005C2×C4C2×D4×D6111yescharacteristic
1006C2×C4#1451982212yes—
1007C2×C4#1451982312yes—
1008C8—42no—
1009C8—2442no—
1010C22—21no—
1011C22—21no—
1012C22—21no—
1013C22—21no—
1014C22—21no—
1015C22—21no—
1016C22—21no—
1017C22—44no—
1018C22—41no—
1019C22—41no—
1020C22—41no—
1021C22—612no—
1022C22—612no—
1023C22—612no—
1024C22—1228no—
1025C22—1221no—
1026C22—1221no—
1027C22—1221no—
1028C22—1221no—
1029C22—1221no—
1030C22—1221no—
1031C22—1221no—
1032C22—1221no—
1033C22—1221no—
1034C22—4884no—
1035C22—2444no—
1036C22—2444no—
1037C22—2444no—
1038C22—2444no—
1039C22—2444no—
1040C22—2441no—
1041C22—2441no—
1042C22—2441no—
1043C22#104×D6112yes—
1044C22C2×C22⋊C4×D6111yescharacteristic
1045C22#1684032012yes—
1046C4—21no—
1047C4—21no—
1048C4—44no—
1049C4—41no—
1050C4—41no—
1051C4—41no—
1052C4—1221no—
1053C4—1221no—
1054C4—1221no—
1055C4—1221no—
1056C4—2444no—
1057C4—2441no—
1058C4—2441no—
1059C4—2441no—
1060C4#1684023412yes—
1061C4#1684032211yescharacteristic
1062C4#1684032311yescharacteristic
1063C2—22no—
1064C2—22no—
1065C2—41no—
1066C2—81no—
1067C2—1222no—
1068C2—1222no—
1069C2—1222no—
1070C2—4881no—
1071C2—2441no—
1072C2#2144839311yescharacteristic
1073C2C2×#104×D6111yescharacteristic
1074C2#421×D6111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1871C2
socleC22×C61C22×C22⋊C4
prime radical#525×D61C2
cosocleC22×C4×C61C24
hypercenter#1871D61
hypocenterC61#21773
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1871

Complements

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

NH ≅ G/Ntype
2. C2×#16839725C2semidirect
3. C4×C22⋊C4×D61C2semidirect
4. #21446261C2semidirect
5. #21446259C2semidirect
6. #21446122C2semidirect
7. #21446121C2semidirect
8. #21446119C2semidirect
9. #21445917C2semidirect
10. #21445761C2semidirect
11. C61×#1871C2semidirect
14. C22×#11758194C22semidirect
15. #16840275C4semidirect
16. #16840275C4semidirect
19. #16840272C4semidirect
20. #16840272C4semidirect
27. C22⋊Q8×D61C4semidirect
28. C22⋊Q8×D61C4semidirect
29. #121×D61C4semidirect
30. #121×D61C4semidirect
36. C2×C42×D61C22semidirect
37. C2×#14519705C22semidirect
38. C2×#14519704C22semidirect
39. C2×#14519703C22semidirect
43. #16839725C22semidirect
48. C4×C22⋊Dic61C22semidirect
51. #16839523C22semidirect
52. #16839522C22semidirect
53. #16839521C22semidirect
54. C22×M16×C61C22semidirect
56. C2×#104×C61C22semidirect
57. C4×C22⋊C4×C61C22semidirect
58. C61×#339C22semidirect
60. C2×#11758226C2×C4semidirect
64. C2×#11758224C2×C4semidirect
67. C2×Q8×D61C2×C4semidirect
71. C2×D4×D61C2×C4semidirect
102. #14519756C2×C4semidirect
103. #14519756C2×C4semidirect
112. #14519751C2×C4semidirect
113. #14519751C2×C4semidirect
142. #14519735C2×C4semidirect
143. #14519735C2×C4semidirect
148. C4⋊C4×D61C2×C4semidirect
149. C4⋊C4×D61C2×C4semidirect
179. C22⋊Q8×C61C2×C4semidirect
180. C22⋊Q8×C61C2×C4semidirect
181. #121×C61C2×C4semidirect
182. #121×C61C2×C4semidirect
382. C22×D61#104semidirect
534. #1871D61semidirect
552. C22×M16C2×D61semidirect
579. C2×#104C2×D61semidirect
590. C4×C22⋊C4C2×D61semidirect
595. #339C2×D61semidirect
596. C61#21773semidirect
655. C22⋊Q8C4×D61semidirect
656. C22⋊Q8C4×D61semidirect
667. #121C4×D61semidirect
668. #121C4×D61semidirect

Maximal subgroups

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

subgroupindex
#525×D612
C2×#168397252
C4×C22⋊C4×D612
#214462612
#214462592
#214461222
#214461212
#214461192
#214459172
#214457612
C61×#18712
#2177361