Finite Group Databasebeta

← #29647466

Subgroups — #29647466

Order 15616.

1466 conjugacy classes of subgroups.

The subgroup lattice has 1030 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×#16839624C211yesmaximal, characteristic, complemented
4#21444374C212yesmaximal, complemented
5#21444372C212yesmaximal, complemented
6#21444350C212yesmaximal, complemented
7#21444346C212yesmaximal, complemented
8#21444324C211yesmaximal, characteristic, complemented
9#21444323C211yesmaximal, characteristic, complemented
10#21444321C211yesmaximal, characteristic, complemented
11C61×#1504C211yesmaximal, characteristic, complemented
12C2×#41×D61C411yescharacteristic, complemented
13C23×C4×D61C2211yescharacteristic
14C2×M16×D61—21no—
15#16840275C411yescharacteristic, complemented
16#16840275C2211yescharacteristic
17#16840274C411yescharacteristic, complemented
18#16840273C2211yescharacteristic
19#16840272C411yescharacteristic, complemented
20#16840272C2211yescharacteristic
21#16840271—21no—
22#16840271—21no—
23#16840270—21no—
24#16840269C411yescharacteristic, complemented
25#16840268—21no—
26#123×D61—21no—
27C22⋊Q8×D61C411yescharacteristic, complemented
28C22⋊Q8×D61C2211yescharacteristic
29#121×D61C411yescharacteristic, complemented
30#121×D61C2211yescharacteristic
31#120×D61—21no—
32C4×D4×D61—21no—
33C4×D4×D61—21no—
34#117×D61C411yescharacteristic, complemented
35C22×#11758198—21no—
36#16839726C2211yescharacteristic, complemented
37#16839725—21no—
38#16839724—21no—
39#16839724C2212yes—
40C22⋊C8×D61—21no—
41C22⋊C8×D61C2212yescomplemented
42#16839624—21no—
43#16839624—21no—
44#16839624C2212yes—
45#16839624C2212yescomplemented
46C2×#14519684—21no—
47C2×#14519684C2211yescharacteristic, complemented
48#16839500C2212yescomplemented
49#16839499C2212yescomplemented
50#16839498C2212yescomplemented
51#16839497C2212yescomplemented
52#16839496C2212yescomplemented
53#16839495C2212yescomplemented
54C61×#525C2211yescharacteristic
55C61×#407C2211yescharacteristic, complemented
56C2×#95×C61C2211yescharacteristic, complemented
57C61×#328C2212yescomplemented
58C61×#327C2212yescomplemented
59C24×D61D411yescharacteristic
60C2×#11758226C2×C411yescharacteristic, complemented
61C2×#11758222—21no—
62C2×#11758222C2×C411yescharacteristic
63C2×#11758224—21no—
64C2×#11758224C2×C411yescharacteristic, complemented
65#41×D61—44no—
66C2×Q8×D61C2×C411yescharacteristic, complemented
67C2×D4×D61—21no—
68C2×D4×D61—21no—
69C2×D4×D61—21no—
70C2×D4×D61C2×C411yescharacteristic, complemented
71C23×Dic61—21no—
72C23×Dic61D411yescharacteristic
73C22×C4×D61—21no—
74C22×C4×D61—44no—
75C22×C4×D61C2×C411yescharacteristic
76C22×C4×D61C2×C411yescharacteristic
77C22×C4×D61C2×C411yescharacteristic
78C22×C4×D61C2×C411yescharacteristic
79C22×C4×D61D411yescharacteristic
80C22×C4×D61D411yescharacteristic
81C22×C4×D61D411yescharacteristic
82C22×C4×D61D411yescharacteristic
83C22×C4×D61D411yescharacteristic
84C22×C4×D61D411yescharacteristic
85C22×C4×D61C2311yescharacteristic
86C22×C4×D61C2311yescharacteristic
87C2×#11758194—21no—
88C2×#11758189—22no—
89M16×D61—44no—
90C2×C8×D61—22no—
91#14519762—21no—
92#14519762—21no—
93#14519761—21no—
94#14519760—21no—
95#14519759—21no—
96#14519759—21no—
97#14519758—21no—
98#14519757C2×C411yescharacteristic, complemented
99#14519757C2×C411yescharacteristic, complemented
100#14519756C2×C411yescharacteristic
101#14519756C2311yescharacteristic
102#14519755—21no—
103#14519755—21no—
104#14519754—21no—
105#14519754—21no—
106#14519753C2×C411yescharacteristic, complemented
107#14519753C2×C411yescharacteristic, complemented
108#14519752C2×C411yescharacteristic, complemented
109#14519752C2×C411yescharacteristic, complemented
110#14519751C2×C411yescharacteristic
111#14519751C2311yescharacteristic
112#14519750—21no—
113#14519750—21no—
114#14519749—21no—
115#14519749—21no—
116#14519748C2×C411yescharacteristic, complemented
117#14519748C2×C411yescharacteristic, complemented
118#14519747—21no—
119#14519747—21no—
120#14519747—21no—
121#14519746—21no—
122#14519745—21no—
123#14519745—21no—
124#14519745—21no—
125C4×D244—21no—
126C4×D244—21no—
127D4×Dic61—21no—
128D4×Dic61—21no—
129#14519739—21no—
130#14519739—21no—
131C4×C22⋊D61—21no—
132C4×C22⋊D61—21no—
133C4×C22⋊D61—21no—
134C4×C22⋊D61—21no—
135#14519737—21no—
136#14519737—21no—
137#14519737—21no—
138#14519737—21no—
139#14519736C2×C411yescharacteristic
140#14519735C2×C411yescharacteristic, complemented
141#14519735C2×C411yescharacteristic, complemented
142#14519734—21no—
143#14519733—21no—
144C4⋊C4×D61—21no—
145C4⋊C4×D61—21no—
146C4⋊C4×D61C2×C411yescharacteristic, complemented
147C4⋊C4×D61C2×C411yescharacteristic, complemented
148C2×#11758198—22no—
149C2×#11758198—22no—
150C2×#11758198—44no—
151C22⋊C4×D61—21no—
152C22⋊C4×D61—21no—
153C22⋊C4×D61—21no—
154C22⋊C4×D61—21no—
155C22⋊C4×D61—21no—
156C42×D61—21no—
157C22⋊#92418—21no—
158C22⋊#92418C2312yes—
159#14519689—22no—
160#14519689—22no—
161#14519684—21no—
162#14519684—22no—
163#14519684—22no—
164#14519684C2312yes—
165C2×#41×C61C2×C411yescharacteristic
166C23×C4×C61—21no—
167C23×C4×C61C2311yescharacteristic
168C2×M16×C61—21no—
169#123×C61—21no—
170C22⋊Q8×C61C2×C411yescharacteristic
171C22⋊Q8×C61C2311yescharacteristic
172#121×C61C2×C411yescharacteristic
173#121×C61C2311yescharacteristic
174#120×C61—21no—
175C4×D4×C61—21no—
176C4×D4×C61—21no—
177#117×C61C2×C411yescharacteristic
178C22⋊C8×C61—21no—
179C22⋊C8×C61C2312yes—
180#95×C61—21no—
181#95×C61C2312yes—
182C24×C61C2×D411yescharacteristic
183C23×D61—24no—
184C23×D61—21no—
185C23×D61—41no—
186C23×D61—41no—
187C23×D61—42no—
188C23×D61C22⋊C411yescharacteristic
189C23×D61C22⋊C411yescharacteristic
190C23×D61C22⋊C411yescharacteristic
191C23×D61C22⋊C411yescharacteristic
192C23×D61C2×D411yescharacteristic
193C23×D61C2×D411yescharacteristic
194#41×C61—42no—
195C2×Q8×C61C22×C411yescharacteristic
196C2×D4×C61—21no—
197C2×D4×C61—21no—
198C2×D4×C61—21no—
199C2×D4×C61C22×C411yescharacteristic
200C22×C4×C61—21no—
201C22×C4×C61—22no—
202C22×C4×C61—42no—
203C22×C4×C61—42no—
204C22×C4×C61—42no—
205C22×C4×C61—42no—
206C22×C4×C61C22×C411yescharacteristic
207C22×C4×C61C22×C411yescharacteristic
208C22×C4×C61C2×D411yescharacteristic
209C22×C4×C61C2×D411yescharacteristic
210C22×C4×C61C2×D411yescharacteristic
211C22×C4×C61C2411yescharacteristic
212C2×C22⋊D61—21no—
213C2×C22⋊D61—21no—
214C2×C22⋊D61—21no—
215C2×C22⋊D61—21no—
216C2×C22⋊D61—21no—
217C2×C22⋊D61—21no—
218C2×C22⋊D61—21no—
219C22×Dic61—21no—
220C22×Dic61—22no—
221C22×Dic61—42no—
222C22×Dic61—42no—
223C22×Dic61—42no—
224C22×Dic61—42no—
225C22×Dic61C22⋊C411yescharacteristic
226C22×Dic61C22⋊C411yescharacteristic
227C22×Dic61C22⋊C411yescharacteristic
228C22×Dic61C22⋊C411yescharacteristic
229C22×Dic61C2×D411yescharacteristic
230C22×Dic61C2×D411yescharacteristic
231#11758226—42no—
232Q8×D61—42no—
233#11758224—42no—
234#11758224—44no—
235D4×D61—42no—
236D4×D61—42no—
237D4×D61—42no—
238D4×D61—44no—
239D4×D61—44no—
240#11758222—44no—
241#11758222—42no—
242C2×D244—21no—
243C2×D244—21no—
244C2×D244—21no—
245C2×D244C22×C411yescharacteristic
246C2×C4×D61—24no—
247C2×C4×D61—24no—
248C2×C4×D61—21no—
249C2×C4×D61—21no—
250C2×C4×D61—21no—
251C2×C4×D61—21no—
252C2×C4×D61—21no—
253C2×C4×D61—42no—
254C2×C4×D61—42no—
255C2×C4×D61—42no—
256C2×C4×D61—42no—
257C2×C4×D61—42no—
258C2×C4×D61—42no—
259C2×C4×D61—42no—
260C2×C4×D61—42no—
261C2×C4×D61—44no—
262C2×C4×D61—42no—
263C2×C4×D61—42no—
264C2×C4×D61C22⋊C411yescharacteristic
265C2×C4×D61C22⋊C411yescharacteristic
266C2×C4×D61C22⋊C411yescharacteristic
267C2×C4×D61C22⋊C411yescharacteristic
268C2×C4×D61C22⋊C411yescharacteristic
269C2×C4×D61C22⋊C411yescharacteristic
270C2×C4×D61C22⋊C411yescharacteristic
271C2×C4×D61C22⋊C411yescharacteristic
272C2×C4×D61C22×C411yescharacteristic
273C2×C4×D61C22×C411yescharacteristic
274C2×C4×D61C22×C411yescharacteristic
275C2×C4×D61C22×C411yescharacteristic
276C2×C4×D61C2×D411yescharacteristic
277C2×C4×D61C2×D411yescharacteristic
278C2×C4×D61C2×D411yescharacteristic
279C2×C4×D61C2×D411yescharacteristic
280C2×Dic122—21no—
281C2×Dic122C22×C411yescharacteristic
282M16×C61—42no—
283C2×C8×C61—22no—
284C4⋊C4×C61—21no—
285C4⋊C4×C61—21no—
286C4⋊C4×C61C22×C411yescharacteristic
287C4⋊C4×C61C22×C411yescharacteristic
288C22⋊C4×C61—21no—
289C22⋊C4×C61—21no—
290C22⋊C4×C61—21no—
291C22⋊C4×C61—21no—
292C22⋊C4×C61—21no—
293C42×C61—21no—
294C22⋊Dic61—21no—
295C22⋊Dic61—21no—
296C22⋊Dic61—21no—
297C22⋊Dic61—21no—
298C22⋊Dic61—21no—
299#11758198—21no—
300#11758198—21no—
301#11758198—21no—
302#11758198—21no—
303#11758198—21no—
304#11758198—21no—
305#11758198—21no—
306#11758198—21no—
307#11758198—21no—
308#11758198—21no—
309#11758198—44no—
310#11758198—44no—
311C4⋊Dic61—21no—
312C4⋊Dic61—21no—
313C4⋊Dic61C22×C411yescharacteristic
314C4⋊Dic61C22×C411yescharacteristic
315#11758196—21no—
316#11758196—21no—
317#11758196—21no—
318#11758196—21no—
319#11758196—21no—
320#11758196—21no—
321C4×Dic61—21no—
322C4×Dic61—21no—
323C4×Dic61—21no—
324#11758194—42no—
325C2×#92418—22no—
326#11758189—44no—
327C8×D61—44no—
328C23×C61—21no—
329C23×C61—21no—
330C23×C61—22no—
331C23×C61—22no—
332C23×C61—21no—
333C23×C61C2×C22⋊C411yescharacteristic
334C23×C61C2×C22⋊C411yescharacteristic
335C23×C61C22×D411yescharacteristic
336C22×D61—21no—
337C22×D61—21no—
338C22×D61—21no—
339C22×D61—21no—
340C22×D61—22no—
341C22×D61—22no—
342C22×D61—22no—
343C22×D61—22no—
344C22×D61—22no—
345C22×D61—22no—
346C22×D61—22no—
347C22×D61—21no—
348C22×D61—41no—
349C22×D61—41no—
350C22×D61—41no—
351C22×D61—41no—
352C22×D61—41no—
353C22×D61—41no—
354C22×D61—41no—
355C22×D61—41no—
356C22×D61—42no—
357C22×D61—42no—
358C22×D61—48no—
359C22×D61—48no—
360C22×D61—42no—
361C22×D61#9914yes—
362C22×D61C2×C22⋊C411yescharacteristic
363C22×D61C2×C22⋊C411yescharacteristic
364C22×D61C2×C22⋊C411yescharacteristic
365C22×D61C2×C22⋊C411yescharacteristic
366Q8×C61—41no—
367D4×C61—41no—
368D4×C61—41no—
369D4×C61—41no—
370D4×C61—42no—
371D4×C61—42no—
372C2×C4×C61—22no—
373C2×C4×C61—22no—
374C2×C4×C61—21no—
375C2×C4×C61—21no—
376C2×C4×C61—21no—
377C2×C4×C61—41no—
378C2×C4×C61—41no—
379C2×C4×C61—41no—
380C2×C4×C61—41no—
381C2×C4×C61—42no—
382C2×C4×C61—42no—
383C2×C4×C61—42no—
384C2×C4×C61—42no—
385C2×C4×C61—84no—
386C2×C4×C61C2×C22⋊C411yescharacteristic
387C2×C4×C61C2×C22⋊C411yescharacteristic
388C2×C4×C61C23×C411yescharacteristic
389C2×C4×C61C22×D411yescharacteristic
390C22⋊D61—42no—
391C22⋊D61—42no—
392C22⋊D61—42no—
393C22⋊D61—41no—
394C22⋊D61—41no—
395C22⋊D61—42no—
396C22⋊D61—42no—
397C22⋊D61—42no—
398C2×Dic61—22no—
399C2×Dic61—22no—
400C2×Dic61—21no—
401C2×Dic61—21no—
402C2×Dic61—21no—
403C2×Dic61—41no—
404C2×Dic61—41no—
405C2×Dic61—41no—
406C2×Dic61—41no—
407C2×Dic61—42no—
408C2×Dic61—42no—
409C2×Dic61—42no—
410C2×Dic61—42no—
411C2×Dic61—84no—
412C2×Dic61C2×C22⋊C411yescharacteristic
413C2×Dic61C2×C22⋊C411yescharacteristic
414C2×Dic61C2×C22⋊C411yescharacteristic
415C2×Dic61C2×C22⋊C411yescharacteristic
416D244—41no—
417D244—42no—
418D244—42no—
419D244—42no—
420C4×D61—22no—
421C4×D61—22no—
422C4×D61—22no—
423C4×D61—22no—
424C4×D61—22no—
425C4×D61—22no—
426C4×D61—22no—
427C4×D61—22no—
428C4×D61—41no—
429C4×D61—41no—
430C4×D61—41no—
431C4×D61—41no—
432C4×D61—41no—
433C4×D61—41no—
434C4×D61—41no—
435C4×D61—41no—
436C4×D61—42no—
437C4×D61—42no—
438C4×D61—42no—
439C4×D61—42no—
440C4×D61—42no—
441Dic122—42no—
442Dic122—41no—
443C8×C61—42no—
444#92418—42no—
445#17587—611nomaximal, Sylow
446C22×C61—24no—
447C22×C61—24no—
448C22×C61—21no—
449C22×C61—21no—
450C22×C61—21no—
451C22×C61—21no—
452C22×C61—21no—
453C22×C61—21no—
454C22×C61—41no—
455C22×C61—41no—
456C22×C61—41no—
457C22×C61C2×#9912yes—
458C22×C61#42112yes—
459C22×C61C22×C22⋊C411yescharacteristic
460C22×C61#57511yescharacteristic
461C22×C61#57511yescharacteristic
462C2×D61—21no—
463C2×D61—21no—
464C2×D61—21no—
465C2×D61—21no—
466C2×D61—21no—
467C2×D61—21no—
468C2×D61—21no—
469C2×D61—21no—
470C2×D61—21no—
471C2×D61—21no—
472C2×D61—44no—
473C2×D61—42no—
474C2×D61—42no—
475C2×D61—44no—
476C2×D61—42no—
477C2×D61—42no—
478C2×D61—44no—
479C2×D61—44no—
480C2×D61—41no—
481C2×D61—41no—
482C2×D61—41no—
483C2×D61—84no—
484C2×D61C2×#9912yes—
485C2×D61C2×#9912yes—
486C4×C61—21no—
487C4×C61—21no—
488C4×C61—21no—
489C4×C61—21no—
490C4×C61—41no—
491C4×C61—41no—
492C4×C61—41no—
493C4×C61—82no—
494Dic61—21no—
495Dic61—21no—
496Dic61—21no—
497Dic61—21no—
498Dic61—41no—
499Dic61—41no—
500Dic61—41no—
501Dic61—82no—
502C2×#525—611no—
503C2×#407—611no—
504C2×#381—611no—
505#1516—612no—
506#1516—612no—
507#1511—612no—
508#1510—612no—
509#1504—611no—
510#1504—611no—
511#1504—611no—
512#1504D6111yescharacteristic, complemented
513C2×C61—21no—
514C2×C61—21no—
515C2×C61—22no—
516C2×C61—22no—
517C2×C61—81no—
518C2×C61C22×#9911yescharacteristic
519C2×C61#289611yescharacteristic
520C2×C61C2×#42111yescharacteristic
521D61—22no—
522D61—22no—
523D61—41no—
524D61—41no—
525D61—81no—
526C22×#41—611no—
527C24×C4—611no—
528C22×M16—1221no—
529#525—611no—
530#525—611no—
531#525—611no—
532#525—611no—
533#525—611no—
534#525—611no—
535#525—611no—
536#525—1221no—
537#525—1221no—
538#525—1221no—
539#525—1221no—
540#525C2×D6111yescharacteristic
541C2×#123—1221no—
542C2×C22⋊Q8—611no—
543C2×C22⋊Q8—611no—
544C2×#121—611no—
545C2×#121—611no—
546C2×#120—1221no—
547C2×C4×D4—1221no—
548C2×C4×D4—1221no—
549C2×#117—611no—
550C22×C22⋊C4—1221no—
551#407—611no—
552#407—612no—
553#407—1221no—
554#407—1221no—
555#407C2×D6111yescharacteristic, complemented
556C2×C22⋊C8—612no—
557C2×C22⋊C8—1221no—
558#381—612no—
559#381—612no—
560#381—1221no—
561#381—1221no—
562C2×#95—611no—
563C2×#95—1221no—
564C2×#95C2×D6111yescharacteristic, complemented
565#328—612no—
566#328—612no—
567#328—612no—
568#328C2×D6112yescomplemented
569#327—612no—
570#327—612no—
571#327—612no—
572#327C2×D6112yescomplemented
573C61#1758711yescharacteristic, complemented, Sylow
574C25—611no—
575C2×#41—611no—
576C2×#41—611no—
577C2×#41—611no—
578C2×#41—1221no—
579C2×#41—1221no—
580C2×#41—2444no—
581C2×#41C4×D6111yescharacteristic
582C22×Q8—611no—
583C22×D4—611no—
584C22×D4—1221no—
585C22×D4—1221no—
586C22×D4—1221no—
587C23×C4—21no—
588C23×C4—611no—
589C23×C4—611no—
590C23×C4—611no—
591C23×C4—611no—
592C23×C4—611no—
593C23×C4—611no—
594C23×C4—611no—
595C23×C4—611no—
596C23×C4—611no—
597C23×C4—611no—
598C23×C4—611no—
599C23×C4—611no—
600C23×C4—611no—
601C23×C4—1221no—
602C23×C4—1221no—
603C23×C4—2444no—
604C23×C4C22×D6111yescharacteristic
605C2×M16—21no—
606C2×M16—1222no—
607C2×M16—1221no—
608C2×M16—2444no—
609C22×C8—1222no—
610#123—21no—
611#123—1221no—
612#123—1221no—
613#123—1221no—
614#123—1221no—
615#123—1221no—
616#123—1221no—
617#123—1221no—
618C22⋊Q8—611no—
619C22⋊Q8—611no—
620C22⋊Q8—611no—
621C22⋊Q8—611no—
622C22⋊Q8—611no—
623C22⋊Q8—611no—
624C22⋊Q8—1221no—
625C22⋊Q8—1221no—
626C22⋊Q8—1221no—
627C22⋊Q8—1221no—
628C22⋊Q8C4×D6111yescharacteristic
629C22⋊Q8C22×D6111yescharacteristic
630#121—611no—
631#121—611no—
632#121—611no—
633#121—611no—
634#121—611no—
635#121—611no—
636#121—1221no—
637#121—1221no—
638#121—1221no—
639#121—1221no—
640#121C4×D6111yescharacteristic
641#121C22×D6111yescharacteristic
642#120—21no—
643#120—1221no—
644#120—1221no—
645#120—1221no—
646#120—1221no—
647#120—1221no—
648#120—1221no—
649#120—1221no—
650C4×D4—21no—
651C4×D4—21no—
652C4×D4—1221no—
653C4×D4—1221no—
654C4×D4—1221no—
655C4×D4—1221no—
656C4×D4—1221no—
657C4×D4—1221no—
658C4×D4—1221no—
659C4×D4—1221no—
660C4×D4—1221no—
661C4×D4—1221no—
662C4×D4—1221no—
663C4×D4—1221no—
664C4×D4—1221no—
665C4×D4—1221no—
666#117—611no—
667#117—611no—
668#117—611no—
669#117—1221no—
670#117—1221no—
671#117C4×D6111yescharacteristic
672C2×C4⋊C4—611no—
673C2×C4⋊C4—611no—
674C2×C4⋊C4—1221no—
675C2×C4⋊C4—1221no—
676C2×C22⋊C4—1221no—
677C2×C22⋊C4—1221no—
678C2×C22⋊C4—1221no—
679C2×C22⋊C4—1221no—
680C2×C22⋊C4—1221no—
681C2×C22⋊C4—1222no—
682C2×C22⋊C4—1222no—
683C2×C22⋊C4—2444no—
684C2×C42—1221no—
685C22⋊C8—21no—
686C22⋊C8—612no—
687C22⋊C8—1222no—
688C22⋊C8—1222no—
689C22⋊C8—1221no—
690C22⋊C8C22×D6112yes—
691#95—21no—
692#95—612no—
693#95—1222no—
694#95—1222no—
695#95—1221no—
696#95C22×D6112yes—
697C24—611no—
698C24—611no—
699C24—611no—
700C24—611no—
701C24—611no—
702C24—611no—
703C24—1224no—
704C24—1221no—
705C24—2442no—
706C24—2441no—
707C24—2441no—
708C24D4×D6111yescharacteristic
709#41—42no—
710#41—2442no—
711#41—2444no—
712#41—2444no—
713#41—2442no—
714#41—2442no—
715C2×Q8—611no—
716C2×Q8—1221no—
717C2×Q8—2442no—
718C2×Q8C2×C4×D6111yescharacteristic
719C2×D4—21no—
720C2×D4—21no—
721C2×D4—21no—
722C2×D4—611no—
723C2×D4—1221no—
724C2×D4—1221no—
725C2×D4—1221no—
726C2×D4—1221no—
727C2×D4—1221no—
728C2×D4—1221no—
729C2×D4—1221no—
730C2×D4—1221no—
731C2×D4—1221no—
732C2×D4—1221no—
733C2×D4—2442no—
734C2×D4—2444no—
735C2×D4—2444no—
736C2×D4—2442no—
737C2×D4—2442no—
738C2×D4C2×C4×D6111yescharacteristic
739C22×C4—21no—
740C22×C4—22no—
741C22×C4—42no—
742C22×C4—42no—
743C22×C4—42no—
744C22×C4—42no—
745C22×C4—611no—
746C22×C4—611no—
747C22×C4—611no—
748C22×C4—611no—
749C22×C4—611no—
750C22×C4—611no—
751C22×C4—611no—
752C22×C4—611no—
753C22×C4—611no—
754C22×C4—611no—
755C22×C4—611no—
756C22×C4—611no—
757C22×C4—611no—
758C22×C4—611no—
759C22×C4—611no—
760C22×C4—611no—
761C22×C4—611no—
762C22×C4—611no—
763C22×C4—611no—
764C22×C4—611no—
765C22×C4—611no—
766C22×C4—611no—
767C22×C4—1221no—
768C22×C4—1224no—
769C22×C4—1224no—
770C22×C4—1221no—
771C22×C4—1221no—
772C22×C4—1221no—
773C22×C4—1221no—
774C22×C4—1221no—
775C22×C4—1222no—
776C22×C4—2442no—
777C22×C4—2442no—
778C22×C4—2442no—
779C22×C4—2442no—
780C22×C4—2442no—
781C22×C4—2442no—
782C22×C4—2442no—
783C22×C4—2442no—
784C22×C4—2442no—
785C22×C4—2442no—
786C22×C4—2444no—
787C22×C4—2442no—
788C22×C4—2442no—
789C22×C4—2442no—
790C22×C4—2442no—
791C22×C4C2×C4×D6111yescharacteristic
792C22×C4C2×C4×D6111yescharacteristic
793C22×C4D4×D6111yescharacteristic
794C22×C4D4×D6111yescharacteristic
795C22×C4D4×D6111yescharacteristic
796C22×C4C23×D6111yescharacteristic
797M16—42no—
798M16—2444no—
799M16—2442no—
800C2×C8—22no—
801C2×C8—1222no—
802C2×C8—2444no—
803C4⋊C4—21no—
804C4⋊C4—21no—
805C4⋊C4—611no—
806C4⋊C4—611no—
807C4⋊C4—1221no—
808C4⋊C4—1221no—
809C4⋊C4—1221no—
810C4⋊C4—1221no—
811C4⋊C4—1221no—
812C4⋊C4—1221no—
813C4⋊C4—1221no—
814C4⋊C4—1221no—
815C4⋊C4C2×C4×D6111yescharacteristic
816C4⋊C4C2×C4×D6111yescharacteristic
817C22⋊C4—21no—
818C22⋊C4—21no—
819C22⋊C4—21no—
820C22⋊C4—21no—
821C22⋊C4—21no—
822C22⋊C4—1221no—
823C22⋊C4—1221no—
824C22⋊C4—1221no—
825C22⋊C4—1221no—
826C22⋊C4—1221no—
827C22⋊C4—1221no—
828C22⋊C4—1221no—
829C22⋊C4—1221no—
830C22⋊C4—1221no—
831C22⋊C4—1221no—
832C22⋊C4—1221no—
833C22⋊C4—1221no—
834C22⋊C4—1221no—
835C22⋊C4—1221no—
836C22⋊C4—1221no—
837C22⋊C4—2444no—
838C22⋊C4—2444no—
839C42—21no—
840C42—1221no—
841C42—1221no—
842C42—1221no—
843C23—22no—
844C23—22no—
845C23—21no—
846C23—21no—
847C23—21no—
848C23—611no—
849C23—611no—
850C23—614no—
851C23—611no—
852C23—611no—
853C23—1222no—
854C23—1222no—
855C23—1222no—
856C23—1222no—
857C23—1222no—
858C23—1222no—
859C23—1222no—
860C23—1221no—
861C23—1221no—
862C23—1221no—
863C23—1221no—
864C23—1221no—
865C23—2441no—
866C23—2441no—
867C23—2441no—
868C23—2441no—
869C23—2441no—
870C23—2441no—
871C23—2441no—
872C23—2441no—
873C23—2448no—
874C23—2448no—
875C23—2442no—
876C23—2442no—
877C23—2442no—
878C23C22⋊C4×D6111yescharacteristic
879C23C22⋊C4×D6111yescharacteristic
880C23C2×D4×D6111yescharacteristic
881Q8—41no—
882Q8—2441no—
883Q8—2442no—
884D4—41no—
885D4—42no—
886D4—42no—
887D4—41no—
888D4—41no—
889D4—2441no—
890D4—2442no—
891D4—2442no—
892D4—2442no—
893D4—2442no—
894D4—2442no—
895D4—2442no—
896D4—2442no—
897D4—2442no—
898D4—2442no—
899D4—2441no—
900D4—2441no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—21no—
904C2×C4—21no—
905C2×C4—21no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—42no—
911C2×C4—42no—
912C2×C4—42no—
913C2×C4—42no—
914C2×C4—84no—
915C2×C4—611no—
916C2×C4—611no—
917C2×C4—611no—
918C2×C4—611no—
919C2×C4—1222no—
920C2×C4—1222no—
921C2×C4—1222no—
922C2×C4—1222no—
923C2×C4—1222no—
924C2×C4—1222no—
925C2×C4—1222no—
926C2×C4—1222no—
927C2×C4—1222no—
928C2×C4—1222no—
929C2×C4—1221no—
930C2×C4—1221no—
931C2×C4—1221no—
932C2×C4—4884no—
933C2×C4—2441no—
934C2×C4—2441no—
935C2×C4—2441no—
936C2×C4—2441no—
937C2×C4—2441no—
938C2×C4—2441no—
939C2×C4—2441no—
940C2×C4—2441no—
941C2×C4—2442no—
942C2×C4—2442no—
943C2×C4—2442no—
944C2×C4—2442no—
945C2×C4—2442no—
946C2×C4—2441no—
947C2×C4—2441no—
948C2×C4—2441no—
949C2×C4—2441no—
950C2×C4—2442no—
951C2×C4—2442no—
952C2×C4—2442no—
953C2×C4—2442no—
954C2×C4C22⋊C4×D6111yescharacteristic
955C2×C4C22⋊C4×D6111yescharacteristic
956C2×C4C22×C4×D6111yescharacteristic
957C2×C4C2×D4×D6111yescharacteristic
958C8—42no—
959C8—2442no—
960C22—24no—
961C22—24no—
962C22—21no—
963C22—21no—
964C22—21no—
965C22—21no—
966C22—21no—
967C22—21no—
968C22—41no—
969C22—41no—
970C22—41no—
971C22—612no—
972C22—612no—
973C22—1221no—
974C22—1221no—
975C22—1221no—
976C22—1221no—
977C22—1221no—
978C22—1221no—
979C22—1221no—
980C22—1221no—
981C22—1221no—
982C22—1221no—
983C22—4884no—
984C22—2444no—
985C22—2442no—
986C22—2442no—
987C22—2442no—
988C22—2442no—
989C22—2444no—
990C22—2444no—
991C22—2444no—
992C22—2441no—
993C22—2441no—
994C22—2441no—
995C22#99×D6112yes—
996C22#1683977712yes—
997C22C2×C22⋊C4×D6111yescharacteristic
998C22#1684055811yescharacteristic
999C22#1684056111yescharacteristic
1000C4—21no—
1001C4—21no—
1002C4—21no—
1003C4—21no—
1004C4—41no—
1005C4—41no—
1006C4—41no—
1007C4—82no—
1008C4—1221no—
1009C4—1221no—
1010C4—1221no—
1011C4—1221no—
1012C4—4882no—
1013C4—2441no—
1014C4—2441no—
1015C4—2441no—
1016C2—21no—
1017C2—21no—
1018C2—22no—
1019C2—22no—
1020C2—81no—
1021C2—1222no—
1022C2—1222no—
1023C2—4881no—
1024C2—2441no—
1025C2—2441no—
1026C2C2×#99×D6111yescharacteristic
1027C2#2145433511yescharacteristic
1028C2C2×#1683977711yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1504C2
socleC22×C61C22×C22⋊C4
prime radical#525×D61C2
cosocleC22×C4×C61C24
hypercenter#1504D61
hypocenterC61#17587
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1504

Complements

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

NH ≅ G/Ntype
2. #407×D61C2semidirect
3. C2×#16839624C2semidirect
4. #21444374C2semidirect
5. #21444372C2semidirect
6. #21444350C2semidirect
7. #21444346C2semidirect
8. #21444324C2semidirect
9. #21444323C2semidirect
10. #21444321C2semidirect
11. C61×#1504C2semidirect
12. C2×#41×D61C4semidirect
15. #16840275C4semidirect
17. #16840274C4semidirect
19. #16840272C4semidirect
24. #16840269C4semidirect
27. C22⋊Q8×D61C4semidirect
29. #121×D61C4semidirect
34. #117×D61C4semidirect
36. #16839726C22semidirect
41. C22⋊C8×D61C22semidirect
45. #16839624C22semidirect
47. C2×#14519684C22semidirect
48. #16839500C22semidirect
49. #16839499C22semidirect
50. #16839498C22semidirect
51. #16839497C22semidirect
52. #16839496C22semidirect
53. #16839495C22semidirect
55. C61×#407C22semidirect
56. C2×#95×C61C22semidirect
57. C61×#328C22semidirect
58. C61×#327C22semidirect
60. C2×#11758226C2×C4semidirect
64. C2×#11758224C2×C4semidirect
66. C2×Q8×D61C2×C4semidirect
70. C2×D4×D61C2×C4semidirect
98. #14519757C2×C4semidirect
99. #14519757C2×C4semidirect
106. #14519753C2×C4semidirect
107. #14519753C2×C4semidirect
108. #14519752C2×C4semidirect
109. #14519752C2×C4semidirect
116. #14519748C2×C4semidirect
117. #14519748C2×C4semidirect
140. #14519735C2×C4semidirect
141. #14519735C2×C4semidirect
146. C4⋊C4×D61C2×C4semidirect
147. C4⋊C4×D61C2×C4semidirect
512. #1504D61semidirect
555. #407C2×D61semidirect
564. C2×#95C2×D61semidirect
568. #328C2×D61semidirect
572. #327C2×D61semidirect
573. C61#17587semidirect

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×#168396242
#214443742
#214443722
#214443502
#214443462
#214443242
#214443232
#214443212
C61×#15042
#1758761