Finite Group Databasebeta

← #29689138

Subgroups — #29689138

Order 15616.

1622 conjugacy classes of subgroups.

The subgroup lattice has 1090 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#525×D61C211yesmaximal, characteristic
2#407×D61C211yesmaximal, characteristic, complemented
3C2×C4×#11758198C211yesmaximal, characteristic, complemented
4#21446263C211yesmaximal, characteristic, complemented
5#21446262C211yesmaximal, characteristic, complemented
6#21446260C211yesmaximal, characteristic, complemented
7#21446120C212yesmaximal, complemented
8#21446118C212yesmaximal, complemented
9#21445917C212yesmaximal, complemented
10#21445761C212yesmaximal, complemented
11C61×#1896C211yesmaximal, characteristic, complemented
12C2×#41×D61C2211yescharacteristic
13C23×C4×D61C2211yescharacteristic
14C2×M16×D61C2212yescomplemented
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
35C22×#11758198—21no—
36C22×C4×Dic61C2211yescharacteristic, complemented
37C2×#14519705C2212yescomplemented
38C2×#14519704C2212yescomplemented
39C2×#14519703C2212yescomplemented
40#16839726C2211yescharacteristic, complemented
41#16839725C2212yes—
42#16839724—21no—
43#16839724—21no—
44C22⋊C8×D61—21no—
45C22⋊C8×D61—21no—
46C4×#11758198—21no—
47C4×#11758198—21no—
48C4×#11758198C2212yes—
49C4×#11758198C2212yescomplemented
50C2×#14519684—21no—
51#16839523C2212yescomplemented
52#16839522C2212yescomplemented
53#16839521C2212yescomplemented
54C61×#525C2211yescharacteristic
55C22×C42×C61C2211yescharacteristic, complemented
56C2×#104×C61C2212yescomplemented
57C61×#407C2211yescharacteristic, 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×Dic61—21no—
73C23×Dic61D411yescharacteristic
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×#11758194C2312yes—
90C2×#11758189—22no—
91M16×D61—42no—
92M16×D61—42no—
93C2×C8×D61—22no—
94#14519762—21no—
95#14519762—21no—
96#14519761—21no—
97#14519760—21no—
98#14519759—21no—
99#14519759—21no—
100#14519758—21no—
101#14519757C2×C411yescharacteristic, complemented
102#14519757C2×C411yescharacteristic, complemented
103#14519756C2×C411yescharacteristic
104#14519756C2×C411yescharacteristic
105#14519755—21no—
106#14519755—21no—
107#14519754—21no—
108#14519754—21no—
109#14519753C2×C411yescharacteristic, complemented
110#14519753C2×C411yescharacteristic, complemented
111#14519752C2×C411yescharacteristic, complemented
112#14519752C2×C411yescharacteristic, complemented
113#14519751C2×C411yescharacteristic
114#14519751C2×C411yescharacteristic
115#14519750—21no—
116#14519750—21no—
117#14519749—21no—
118#14519749—21no—
119#14519748C2×C411yescharacteristic, complemented
120#14519748C2×C411yescharacteristic, complemented
121#14519747—21no—
122#14519747—21no—
123#14519747—21no—
124#14519746—21no—
125#14519745—21no—
126#14519745—21no—
127#14519745—21no—
128C4×D244—21no—
129C4×D244—21no—
130D4×Dic61—21no—
131D4×Dic61—21no—
132#14519739—21no—
133#14519739—21no—
134C4×C22⋊D61—21no—
135C4×C22⋊D61—21no—
136C4×C22⋊D61—21no—
137C4×C22⋊D61—21no—
138#14519737—21no—
139#14519737—21no—
140#14519737—21no—
141#14519737—21no—
142#14519736C2311yescharacteristic
143#14519735C2×C411yescharacteristic, complemented
144#14519735C2×C411yescharacteristic, complemented
145#14519734—21no—
146#14519733—21no—
147C4⋊C4×D61—21no—
148C4⋊C4×D61—21no—
149C4⋊C4×D61C2×C411yescharacteristic, complemented
150C4⋊C4×D61C2×C411yescharacteristic, complemented
151C2×#11758198—28no—
152C2×#11758198—22no—
153C2×#11758198—22no—
154C22⋊C4×D61—21no—
155C22⋊C4×D61—21no—
156C22⋊C4×D61—21no—
157C22⋊C4×D61—21no—
158C22⋊C4×D61—21no—
159C2×C4×Dic61—21no—
160C2×C4×Dic61—42no—
161C2×C4×Dic61C2312yes—
162C42×D61—21no—
163#14519705—42no—
164#14519704—42no—
165#14519703—42no—
166C22⋊#92418—21no—
167C22⋊#92418—21no—
168#14519689—22no—
169#14519689—22no—
170#14519684—22no—
171#14519684—22no—
172C2×#41×C61C2311yescharacteristic
173C23×C4×C61—21no—
174C23×C4×C61C2311yescharacteristic
175C2×M16×C61C2312yes—
176#123×C61—21no—
177C22⋊Q8×C61C2×C411yescharacteristic
178C22⋊Q8×C61C2×C411yescharacteristic
179#121×C61C2×C411yescharacteristic
180#121×C61C2×C411yescharacteristic
181#120×C61—21no—
182C4×D4×C61—21no—
183C4×D4×C61—21no—
184#117×C61C2311yescharacteristic
185C2×C42×C61—21no—
186C2×C42×C61—42no—
187C2×C42×C61C2312yes—
188#104×C61—42no—
189C22⋊C8×C61—21no—
190C22⋊C8×C61—21no—
191C24×C61C2×D411yescharacteristic
192C23×D61—24no—
193C23×D61—21no—
194C23×D61—41no—
195C23×D61—41no—
196C23×D61—42no—
197C23×D61C22⋊C411yescharacteristic
198C23×D61C22⋊C411yescharacteristic
199C23×D61C22⋊C411yescharacteristic
200C23×D61C22⋊C411yescharacteristic
201C23×D61C2×D411yescharacteristic
202C23×D61C2×D411yescharacteristic
203#41×C61—22no—
204#41×C61—22no—
205C2×Q8×C61C22×C411yescharacteristic
206C2×D4×C61—21no—
207C2×D4×C61—21no—
208C2×D4×C61—21no—
209C2×D4×C61C22×C411yescharacteristic
210C22×C4×C61—22no—
211C22×C4×C61—22no—
212C22×C4×C61—24no—
213C22×C4×C61—22no—
214C22×C4×C61—21no—
215C22×C4×C61—42no—
216C22×C4×C61—42no—
217C22×C4×C61C22×C411yescharacteristic
218C22×C4×C61C22×C411yescharacteristic
219C22×C4×C61C2×D411yescharacteristic
220C22×C4×C61C2×D411yescharacteristic
221C22×C4×C61C2×D411yescharacteristic
222C22×C4×C61C2411yescharacteristic
223C2×C22⋊D61—21no—
224C2×C22⋊D61—21no—
225C2×C22⋊D61—21no—
226C2×C22⋊D61—21no—
227C2×C22⋊D61—21no—
228C2×C22⋊D61—21no—
229C2×C22⋊D61—21no—
230C22×Dic61—24no—
231C22×Dic61—22no—
232C22×Dic61—21no—
233C22×Dic61—41no—
234C22×Dic61—41no—
235C22×Dic61—42no—
236C22×Dic61—42no—
237C22×Dic61C22⋊C411yescharacteristic
238C22×Dic61C22⋊C411yescharacteristic
239C22×Dic61C22⋊C411yescharacteristic
240C22×Dic61C22⋊C411yescharacteristic
241C22×Dic61C2×D411yescharacteristic
242C22×Dic61C2×D411yescharacteristic
243#11758226—42no—
244Q8×D61—42no—
245#11758224—42no—
246#11758224—42no—
247#11758224—42no—
248D4×D61—42no—
249D4×D61—44no—
250D4×D61—42no—
251D4×D61—42no—
252D4×D61—44no—
253#11758222—22no—
254#11758222—22no—
255#11758222—44no—
256C2×D244—21no—
257C2×D244—21no—
258C2×D244—21no—
259C2×D244C22×C411yescharacteristic
260C2×C4×D61—22no—
261C2×C4×D61—22no—
262C2×C4×D61—22no—
263C2×C4×D61—22no—
264C2×C4×D61—21no—
265C2×C4×D61—21no—
266C2×C4×D61—21no—
267C2×C4×D61—21no—
268C2×C4×D61—21no—
269C2×C4×D61—42no—
270C2×C4×D61—42no—
271C2×C4×D61—42no—
272C2×C4×D61—42no—
273C2×C4×D61—42no—
274C2×C4×D61—42no—
275C2×C4×D61—42no—
276C2×C4×D61—42no—
277C2×C4×D61—44no—
278C2×C4×D61—41no—
279C2×C4×D61—41no—
280C2×C4×D61—41no—
281C2×C4×D61—41no—
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×D61C22×C411yescharacteristic
292C2×C4×D61C22×C411yescharacteristic
293C2×C4×D61C22×C411yescharacteristic
294C2×C4×D61C2×D411yescharacteristic
295C2×C4×D61C2×D411yescharacteristic
296C2×C4×D61C2×D411yescharacteristic
297C2×C4×D61C2×D411yescharacteristic
298C2×Dic122—21no—
299C2×Dic122C22×C411yescharacteristic
300M16×C61—22no—
301M16×C61—22no—
302C2×C8×C61—22no—
303C4⋊C4×C61—21no—
304C4⋊C4×C61—21no—
305C4⋊C4×C61C22×C411yescharacteristic
306C4⋊C4×C61C22×C411yescharacteristic
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—
315C42×C61—42no—
316C22⋊Dic61—21no—
317C22⋊Dic61—21no—
318C22⋊Dic61—21no—
319C22⋊Dic61—21no—
320C22⋊Dic61—21no—
321#11758198—28no—
322#11758198—28no—
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—
332#11758198—21no—
333C4⋊Dic61—21no—
334C4⋊Dic61—21no—
335C4⋊Dic61C22×C411yescharacteristic
336C4⋊Dic61C22×C411yescharacteristic
337#11758196—21no—
338#11758196—21no—
339#11758196—21no—
340#11758196—21no—
341#11758196—21no—
342#11758196—21no—
343C4×Dic61—21no—
344C4×Dic61—21no—
345C4×Dic61—21no—
346C4×Dic61—22no—
347C4×Dic61—22no—
348C4×Dic61—42no—
349#11758194—22no—
350#11758194—22no—
351C2×#92418—22no—
352#11758189—44no—
353C8×D61—44no—
354C23×C61—21no—
355C23×C61—21no—
356C23×C61—22no—
357C23×C61—22no—
358C23×C61—21no—
359C23×C61C2×C22⋊C411yescharacteristic
360C23×C61C2×C22⋊C411yescharacteristic
361C23×C61C22×D411yescharacteristic
362C22×D61—21no—
363C22×D61—21no—
364C22×D61—21no—
365C22×D61—21no—
366C22×D61—22no—
367C22×D61—22no—
368C22×D61—22no—
369C22×D61—22no—
370C22×D61—22no—
371C22×D61—22no—
372C22×D61—22no—
373C22×D61—21no—
374C22×D61—41no—
375C22×D61—41no—
376C22×D61—41no—
377C22×D61—41no—
378C22×D61—41no—
379C22×D61—41no—
380C22×D61—41no—
381C22×D61—41no—
382C22×D61—42no—
383C22×D61—42no—
384C22×D61—48no—
385C22×D61—48no—
386C22×D61—42no—
387C22×D61#10414yescomplemented
388C22×D61C2×C22⋊C411yescharacteristic
389C22×D61C2×C22⋊C411yescharacteristic
390C22×D61C2×C22⋊C411yescharacteristic
391C22×D61C2×C22⋊C411yescharacteristic
392Q8×C61—22no—
393D4×C61—22no—
394D4×C61—41no—
395D4×C61—41no—
396D4×C61—42no—
397D4×C61—42no—
398C2×C4×C61—21no—
399C2×C4×C61—21no—
400C2×C4×C61—22no—
401C2×C4×C61—22no—
402C2×C4×C61—22no—
403C2×C4×C61—22no—
404C2×C4×C61—24no—
405C2×C4×C61—21no—
406C2×C4×C61—21no—
407C2×C4×C61—21no—
408C2×C4×C61—48no—
409C2×C4×C61—42no—
410C2×C4×C61—42no—
411C2×C4×C61—42no—
412C2×C4×C61C2×C22⋊C411yescharacteristic
413C2×C4×C61C2×C22⋊C411yescharacteristic
414C2×C4×C61C23×C411yescharacteristic
415C2×C4×C61C22×D411yescharacteristic
416C2×C4×C61H(5,𝔽2)12yes—
417C2×C4×C61H(5,𝔽2)12yes—
418C22⋊D61—42no—
419C22⋊D61—42no—
420C22⋊D61—42no—
421C22⋊D61—41no—
422C22⋊D61—41no—
423C22⋊D61—42no—
424C22⋊D61—42no—
425C22⋊D61—42no—
426C2×Dic61—21no—
427C2×Dic61—21no—
428C2×Dic61—21no—
429C2×Dic61—21no—
430C2×Dic61—24no—
431C2×Dic61—21no—
432C2×Dic61—21no—
433C2×Dic61—21no—
434C2×Dic61—41no—
435C2×Dic61—41no—
436C2×Dic61—41no—
437C2×Dic61—41no—
438C2×Dic61—42no—
439C2×Dic61—48no—
440C2×Dic61—42no—
441C2×Dic61—42no—
442C2×Dic61C2×C22⋊C411yescharacteristic
443C2×Dic61C2×C22⋊C411yescharacteristic
444C2×Dic61C2×C22⋊C411yescharacteristic
445C2×Dic61C2×C22⋊C411yescharacteristic
446D244—22no—
447D244—42no—
448D244—42no—
449D244—42no—
450C4×D61—22no—
451C4×D61—22no—
452C4×D61—22no—
453C4×D61—22no—
454C4×D61—22no—
455C4×D61—22no—
456C4×D61—22no—
457C4×D61—22no—
458C4×D61—41no—
459C4×D61—41no—
460C4×D61—41no—
461C4×D61—41no—
462C4×D61—41no—
463C4×D61—41no—
464C4×D61—41no—
465C4×D61—41no—
466C4×D61—42no—
467C4×D61—42no—
468C4×D61—42no—
469C4×D61—42no—
470C4×D61—42no—
471Dic122—22no—
472Dic122—42no—
473C8×C61—42no—
474#92418—42no—
475#21773—611nomaximal, Sylow
476C22×C61—24no—
477C22×C61—24no—
478C22×C61—21no—
479C22×C61—21no—
480C22×C61—21no—
481C22×C61—21no—
482C22×C61—21no—
483C22×C61—21no—
484C22×C61—41no—
485C22×C61—41no—
486C22×C61—41no—
487C22×C61C2×#10412yes—
488C22×C61#42112yes—
489C22×C61C22×C22⋊C411yescharacteristic
490C22×C61#53411yescharacteristic
491C22×C61#53411yescharacteristic
492C2×D61—21no—
493C2×D61—21no—
494C2×D61—21no—
495C2×D61—21no—
496C2×D61—21no—
497C2×D61—21no—
498C2×D61—21no—
499C2×D61—21no—
500C2×D61—21no—
501C2×D61—21no—
502C2×D61—44no—
503C2×D61—42no—
504C2×D61—42no—
505C2×D61—44no—
506C2×D61—42no—
507C2×D61—42no—
508C2×D61—44no—
509C2×D61—44no—
510C2×D61—41no—
511C2×D61—41no—
512C2×D61—41no—
513C2×D61—84no—
514C2×D61C2×#10412yes—
515C2×D61C2×#10412yes—
516C4×C61—21no—
517C4×C61—21no—
518C4×C61—44no—
519C4×C61—41no—
520C4×C61—41no—
521C4×C61—41no—
522C4×C61#51812yes—
523C4×C61#53412yes—
524Dic61—21no—
525Dic61—21no—
526Dic61—21no—
527Dic61—21no—
528Dic61—44no—
529Dic61—41no—
530Dic61—41no—
531Dic61—41no—
532C2×#525—611no—
533C2×#407—611no—
534C2×C4×C22⋊C4—611no—
535#1896—611no—
536#1896—611no—
537#1896—611no—
538#1896D6111yescharacteristic, complemented
539#1871—612no—
540#1871—612no—
541#1826—612no—
542#1789—612no—
543C2×C61—21no—
544C2×C61—21no—
545C2×C61—22no—
546C2×C61—22no—
547C2×C61—81no—
548C2×C61#230811yescharacteristic
549C2×C61C22×#10411yescharacteristic
550C2×C61C2×#42111yescharacteristic
551D61—22no—
552D61—22no—
553D61—41no—
554D61—41no—
555D61—81no—
556C22×#41—611no—
557C24×C4—611no—
558C22×M16—612no—
559#525—611no—
560#525—611no—
561#525—611no—
562#525—611no—
563#525—611no—
564#525—611no—
565#525—611no—
566#525—1221no—
567#525—1221no—
568#525—1221no—
569#525—1221no—
570#525C2×D6111yescharacteristic
571C2×#123—1221no—
572C2×C22⋊Q8—611no—
573C2×C22⋊Q8—611no—
574C2×#121—611no—
575C2×#121—611no—
576C2×#120—1221no—
577C2×C4×D4—1221no—
578C2×C4×D4—1221no—
579C2×#117—611no—
580C22×C22⋊C4—1221no—
581C22×C42—611no—
582C22×C42C2×D6111yescharacteristic, complemented
583C2×#104—612no—
584C2×#104—612no—
585C2×#104—612no—
586C2×#104C2×D6112yescomplemented
587#407—611no—
588#407—612no—
589#407—1221no—
590#407—1221no—
591#407C2×D6111yescharacteristic, complemented
592C2×C22⋊C8—1221no—
593C2×C22⋊C8—1221no—
594C4×C22⋊C4—612no—
595C4×C22⋊C4—612no—
596C4×C22⋊C4—1221no—
597C4×C22⋊C4—1221no—
598C2×#95—1221no—
599#339—612no—
600#339—612no—
601#339—612no—
602#339C2×D6112yescomplemented
603C61#2177311yescharacteristic, complemented, Sylow
604C25—611no—
605C2×#41—611no—
606C2×#41—611no—
607C2×#41—611no—
608C2×#41—1221no—
609C2×#41—1221no—
610C2×#41—2442no—
611C2×#41—2442no—
612C2×#41C22×D6111yescharacteristic
613C22×Q8—611no—
614C22×D4—611no—
615C22×D4—1221no—
616C22×D4—1221no—
617C22×D4—1221no—
618C23×C4—21no—
619C23×C4—611no—
620C23×C4—611no—
621C23×C4—611no—
622C23×C4—611no—
623C23×C4—611no—
624C23×C4—611no—
625C23×C4—611no—
626C23×C4—611no—
627C23×C4—611no—
628C23×C4—611no—
629C23×C4—611no—
630C23×C4—611no—
631C23×C4—611no—
632C23×C4—1221no—
633C23×C4—1221no—
634C23×C4—2442no—
635C23×C4—2442no—
636C23×C4C22×D6111yescharacteristic
637C2×M16—612no—
638C2×M16—1222no—
639C2×M16—2442no—
640C2×M16—2442no—
641C2×M16C22×D6112yes—
642C22×C8—1222no—
643#123—21no—
644#123—1221no—
645#123—1221no—
646#123—1221no—
647#123—1221no—
648#123—1221no—
649#123—1221no—
650#123—1221no—
651C22⋊Q8—611no—
652C22⋊Q8—611no—
653C22⋊Q8—611no—
654C22⋊Q8—611no—
655C22⋊Q8—611no—
656C22⋊Q8—611no—
657C22⋊Q8—1221no—
658C22⋊Q8—1221no—
659C22⋊Q8—1221no—
660C22⋊Q8—1221no—
661C22⋊Q8C4×D6111yescharacteristic
662C22⋊Q8C4×D6111yescharacteristic
663#121—611no—
664#121—611no—
665#121—611no—
666#121—611no—
667#121—611no—
668#121—611no—
669#121—1221no—
670#121—1221no—
671#121—1221no—
672#121—1221no—
673#121C4×D6111yescharacteristic
674#121C4×D6111yescharacteristic
675#120—21no—
676#120—1221no—
677#120—1221no—
678#120—1221no—
679#120—1221no—
680#120—1221no—
681#120—1221no—
682#120—1221no—
683C4×D4—21no—
684C4×D4—21no—
685C4×D4—1221no—
686C4×D4—1221no—
687C4×D4—1221no—
688C4×D4—1221no—
689C4×D4—1221no—
690C4×D4—1221no—
691C4×D4—1221no—
692C4×D4—1221no—
693C4×D4—1221no—
694C4×D4—1221no—
695C4×D4—1221no—
696C4×D4—1221no—
697C4×D4—1221no—
698C4×D4—1221no—
699#117—611no—
700#117—611no—
701#117—611no—
702#117—1221no—
703#117—1221no—
704#117C22×D6111yescharacteristic
705C2×C4⋊C4—611no—
706C2×C4⋊C4—611no—
707C2×C4⋊C4—1221no—
708C2×C4⋊C4—1221no—
709C2×C22⋊C4—1221no—
710C2×C22⋊C4—1221no—
711C2×C22⋊C4—1221no—
712C2×C22⋊C4—1221no—
713C2×C22⋊C4—1221no—
714C2×C22⋊C4—1222no—
715C2×C22⋊C4—1222no—
716C2×C22⋊C4—1228no—
717C2×C42—21no—
718C2×C42—42no—
719C2×C42—612no—
720C2×C42—1221no—
721C2×C42—1221no—
722C2×C42—2442no—
723C2×C42C22×D6112yes—
724#104—42no—
725#104—2442no—
726#104—2442no—
727#104—2442no—
728C22⋊C8—21no—
729C22⋊C8—21no—
730C22⋊C8—1222no—
731C22⋊C8—1222no—
732C22⋊C8—1221no—
733C22⋊C8—1221no—
734#95—1222no—
735#95—1222no—
736C24—611no—
737C24—611no—
738C24—611no—
739C24—611no—
740C24—611no—
741C24—611no—
742C24—1224no—
743C24—1221no—
744C24—2441no—
745C24—2441no—
746C24—2442no—
747C24D4×D6111yescharacteristic
748#41—22no—
749#41—22no—
750#41—1222no—
751#41—1222no—
752#41—2444no—
753#41—2442no—
754#41—2442no—
755#41—2442no—
756#41—2442no—
757C2×Q8—611no—
758C2×Q8—1221no—
759C2×Q8—2442no—
760C2×Q8C2×C4×D6111yescharacteristic
761C2×D4—21no—
762C2×D4—21no—
763C2×D4—21no—
764C2×D4—611no—
765C2×D4—1221no—
766C2×D4—1221no—
767C2×D4—1221no—
768C2×D4—1221no—
769C2×D4—1221no—
770C2×D4—1221no—
771C2×D4—1221no—
772C2×D4—1221no—
773C2×D4—1221no—
774C2×D4—1221no—
775C2×D4—2442no—
776C2×D4—2444no—
777C2×D4—2442no—
778C2×D4—2442no—
779C2×D4—2444no—
780C2×D4C2×C4×D6111yescharacteristic
781C22×C4—22no—
782C22×C4—22no—
783C22×C4—24no—
784C22×C4—22no—
785C22×C4—21no—
786C22×C4—42no—
787C22×C4—42no—
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—611no—
799C22×C4—611no—
800C22×C4—611no—
801C22×C4—611no—
802C22×C4—611no—
803C22×C4—611no—
804C22×C4—611no—
805C22×C4—611no—
806C22×C4—611no—
807C22×C4—611no—
808C22×C4—611no—
809C22×C4—611no—
810C22×C4—1221no—
811C22×C4—1221no—
812C22×C4—1221no—
813C22×C4—1221no—
814C22×C4—1221no—
815C22×C4—1222no—
816C22×C4—1222no—
817C22×C4—1222no—
818C22×C4—1222no—
819C22×C4—1224no—
820C22×C4—1222no—
821C22×C4—1221no—
822C22×C4—2442no—
823C22×C4—2442no—
824C22×C4—2442no—
825C22×C4—2442no—
826C22×C4—2442no—
827C22×C4—2442no—
828C22×C4—2442no—
829C22×C4—2442no—
830C22×C4—2441no—
831C22×C4—2441no—
832C22×C4—2441no—
833C22×C4—2441no—
834C22×C4—2444no—
835C22×C4—2441no—
836C22×C4—2441no—
837C22×C4—2442no—
838C22×C4—2442no—
839C22×C4C2×C4×D6111yescharacteristic
840C22×C4C2×C4×D6111yescharacteristic
841C22×C4D4×D6111yescharacteristic
842C22×C4D4×D6111yescharacteristic
843C22×C4D4×D6111yescharacteristic
844C22×C4C23×D6111yescharacteristic
845M16—22no—
846M16—22no—
847M16—1222no—
848M16—1222no—
849M16—2444no—
850C2×C8—22no—
851C2×C8—1222no—
852C2×C8—2444no—
853C4⋊C4—21no—
854C4⋊C4—21no—
855C4⋊C4—611no—
856C4⋊C4—611no—
857C4⋊C4—1221no—
858C4⋊C4—1221no—
859C4⋊C4—1221no—
860C4⋊C4—1221no—
861C4⋊C4—1221no—
862C4⋊C4—1221no—
863C4⋊C4—1221no—
864C4⋊C4—1221no—
865C4⋊C4C2×C4×D6111yescharacteristic
866C4⋊C4C2×C4×D6111yescharacteristic
867C22⋊C4—21no—
868C22⋊C4—21no—
869C22⋊C4—21no—
870C22⋊C4—21no—
871C22⋊C4—21no—
872C22⋊C4—1221no—
873C22⋊C4—1221no—
874C22⋊C4—1221no—
875C22⋊C4—1221no—
876C22⋊C4—1221no—
877C22⋊C4—1221no—
878C22⋊C4—1221no—
879C22⋊C4—1221no—
880C22⋊C4—1228no—
881C22⋊C4—1228no—
882C22⋊C4—1221no—
883C22⋊C4—1221no—
884C22⋊C4—1221no—
885C22⋊C4—1221no—
886C22⋊C4—1221no—
887C22⋊C4—1221no—
888C22⋊C4—1221no—
889C42—21no—
890C42—22no—
891C42—22no—
892C42—42no—
893C42—1221no—
894C42—1221no—
895C42—1221no—
896C42—1222no—
897C42—1222no—
898C42—2442no—
899C23—22no—
900C23—22no—
901C23—21no—
902C23—21no—
903C23—21no—
904C23—611no—
905C23—611no—
906C23—614no—
907C23—611no—
908C23—611no—
909C23—1222no—
910C23—1222no—
911C23—1222no—
912C23—1222no—
913C23—1222no—
914C23—1222no—
915C23—1222no—
916C23—1221no—
917C23—1221no—
918C23—1221no—
919C23—1221no—
920C23—1221no—
921C23—2441no—
922C23—2441no—
923C23—2441no—
924C23—2441no—
925C23—2441no—
926C23—2441no—
927C23—2441no—
928C23—2441no—
929C23—2448no—
930C23—2448no—
931C23—2442no—
932C23—2442no—
933C23—2442no—
934C23C22⋊C4×D6111yescharacteristic
935C23C22⋊C4×D6111yescharacteristic
936C23C2×D4×D6111yescharacteristic
937Q8—22no—
938Q8—1222no—
939Q8—2442no—
940D4—22no—
941D4—42no—
942D4—42no—
943D4—41no—
944D4—41no—
945D4—1222no—
946D4—2442no—
947D4—2442no—
948D4—2442no—
949D4—2442no—
950D4—2442no—
951D4—2442no—
952D4—2442no—
953D4—2442no—
954D4—2442no—
955D4—2441no—
956D4—2441no—
957C2×C4—21no—
958C2×C4—21no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—24no—
964C2×C4—21no—
965C2×C4—21no—
966C2×C4—21no—
967C2×C4—48no—
968C2×C4—42no—
969C2×C4—42no—
970C2×C4—42no—
971C2×C4—611no—
972C2×C4—611no—
973C2×C4—611no—
974C2×C4—611no—
975C2×C4—1221no—
976C2×C4—1221no—
977C2×C4—1221no—
978C2×C4—1221no—
979C2×C4—1222no—
980C2×C4—1222no—
981C2×C4—1222no—
982C2×C4—1222no—
983C2×C4—1222no—
984C2×C4—1222no—
985C2×C4—1222no—
986C2×C4—1222no—
987C2×C4—1224no—
988C2×C4—1221no—
989C2×C4—1221no—
990C2×C4—1221no—
991C2×C4—2441no—
992C2×C4—2441no—
993C2×C4—2441no—
994C2×C4—2441no—
995C2×C4—2441no—
996C2×C4—2441no—
997C2×C4—2441no—
998C2×C4—2441no—
999C2×C4—2442no—
1000C2×C4—2442no—
1001C2×C4—2442no—
1002C2×C4—2442no—
1003C2×C4—2441no—
1004C2×C4—2441no—
1005C2×C4—2441no—
1006C2×C4—2441no—
1007C2×C4—2442no—
1008C2×C4—2448no—
1009C2×C4—2442no—
1010C2×C4—2442no—
1011C2×C4—2442no—
1012C2×C4C22⋊C4×D6111yescharacteristic
1013C2×C4C22⋊C4×D6111yescharacteristic
1014C2×C4C22×C4×D6111yescharacteristic
1015C2×C4C2×D4×D6111yescharacteristic
1016C2×C4#1451982212yes—
1017C2×C4#1451982312yes—
1018C8—42no—
1019C8—2442no—
1020C22—24no—
1021C22—24no—
1022C22—21no—
1023C22—21no—
1024C22—21no—
1025C22—21no—
1026C22—21no—
1027C22—21no—
1028C22—41no—
1029C22—41no—
1030C22—41no—
1031C22—612no—
1032C22—612no—
1033C22—1221no—
1034C22—1221no—
1035C22—1221no—
1036C22—1221no—
1037C22—1221no—
1038C22—1221no—
1039C22—1221no—
1040C22—1221no—
1041C22—1221no—
1042C22—1221no—
1043C22—4884no—
1044C22—2444no—
1045C22—2442no—
1046C22—2442no—
1047C22—2442no—
1048C22—2442no—
1049C22—2444no—
1050C22—2444no—
1051C22—2444no—
1052C22—2441no—
1053C22—2441no—
1054C22—2441no—
1055C22#104×D6112yes—
1056C22#1683977712yes—
1057C22C2×C22⋊C4×D6111yescharacteristic
1058C22#1684032211yescharacteristic
1059C22#1684032311yescharacteristic
1060C4—21no—
1061C4—21no—
1062C4—44no—
1063C4—41no—
1064C4—41no—
1065C4—41no—
1066C4—1221no—
1067C4—1221no—
1068C4—1221no—
1069C4—1221no—
1070C4—2444no—
1071C4—2441no—
1072C4—2441no—
1073C4—2441no—
1074C4#1684023412yes—
1075C4#1684032012yes—
1076C2—21no—
1077C2—21no—
1078C2—22no—
1079C2—22no—
1080C2—81no—
1081C2—1222no—
1082C2—1222no—
1083C2—4881no—
1084C2—2441no—
1085C2—2441no—
1086C2#2144839311yescharacteristic
1087C2C2×#104×D6111yescharacteristic
1088C2C2×#1683977711yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1896C2
socleC22×C61C22×C22⋊C4
prime radical#525×D61C2
cosocleC22×C4×C61C24
hypercenter#1896D61
hypocenterC61#21773
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1896

Complements

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

NH ≅ G/Ntype
2. #407×D61C2semidirect
3. C2×C4×#11758198C2semidirect
4. #21446263C2semidirect
5. #21446262C2semidirect
6. #21446260C2semidirect
7. #21446120C2semidirect
8. #21446118C2semidirect
9. #21445917C2semidirect
10. #21445761C2semidirect
11. C61×#1896C2semidirect
14. C2×M16×D61C22semidirect
15. #16840275C4semidirect
16. #16840275C4semidirect
19. #16840272C4semidirect
20. #16840272C4semidirect
27. C22⋊Q8×D61C4semidirect
28. C22⋊Q8×D61C4semidirect
29. #121×D61C4semidirect
30. #121×D61C4semidirect
36. C22×C4×Dic61C22semidirect
37. C2×#14519705C22semidirect
38. C2×#14519704C22semidirect
39. C2×#14519703C22semidirect
40. #16839726C22semidirect
49. C4×#11758198C22semidirect
51. #16839523C22semidirect
52. #16839522C22semidirect
53. #16839521C22semidirect
55. C22×C42×C61C22semidirect
56. C2×#104×C61C22semidirect
57. C61×#407C22semidirect
58. C61×#339C22semidirect
60. C2×#11758226C2×C4semidirect
64. C2×#11758224C2×C4semidirect
67. C2×Q8×D61C2×C4semidirect
71. C2×D4×D61C2×C4semidirect
101. #14519757C2×C4semidirect
102. #14519757C2×C4semidirect
109. #14519753C2×C4semidirect
110. #14519753C2×C4semidirect
111. #14519752C2×C4semidirect
112. #14519752C2×C4semidirect
119. #14519748C2×C4semidirect
120. #14519748C2×C4semidirect
143. #14519735C2×C4semidirect
144. #14519735C2×C4semidirect
149. C4⋊C4×D61C2×C4semidirect
150. C4⋊C4×D61C2×C4semidirect
387. C22×D61#104semidirect
538. #1896D61semidirect
582. C22×C42C2×D61semidirect
586. C2×#104C2×D61semidirect
591. #407C2×D61semidirect
602. #339C2×D61semidirect
603. C61#21773semidirect

Maximal subgroups

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

subgroupindex
#525×D612
#407×D612
C2×C4×#117581982
#214462632
#214462622
#214462602
#214461202
#214461182
#214459172
#214457612
C61×#18962
#2177361