Finite Group Databasebeta

← #29647289

Subgroups — #29647289

Order 15616.

1438 conjugacy classes of subgroups.

The subgroup lattice has 1024 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
3#21448201C211yesmaximal, characteristic, complemented
4#21444363C211yesmaximal, characteristic, complemented
5#21444362C211yesmaximal, characteristic, complemented
6#21444360C211yesmaximal, characteristic, complemented
7#21444350C212yesmaximal, complemented
8#21444346C212yesmaximal, complemented
9#21444309C212yesmaximal, complemented
10#21444307C212yesmaximal, complemented
11C61×#1513C211yesmaximal, 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—
34C2×#14519735—21no—
35#117×D61C411yescharacteristic, complemented
36#16839726C2211yescharacteristic, complemented
37#16839725—21no—
38#16839724—21no—
39#16839724C2212yes—
40C22⋊C8×D61—21no—
41C22⋊C8×D61C2212yescomplemented
42#16839624C2212yes—
43#16839622C2211yescharacteristic, complemented
44#16839619—21no—
45#16839617—21no—
46C22⋊C4×Dic61—21no—
47#16839609C2212yescomplemented
48#16839500C2212yescomplemented
49#16839499C2212yescomplemented
50#16839498C2212yescomplemented
51#16839497C2212yescomplemented
52#16839496C2212yescomplemented
53#16839495C2212yescomplemented
54C61×#525C2211yescharacteristic
55C61×#407C2211yescharacteristic, complemented
56C61×#380C2211yescharacteristic, complemented
57C61×#328C2212yescomplemented
58C61×#327C2212yescomplemented
59C24×D61D411yescharacteristic
60C2×#11758226C2×C411yescharacteristic
61C2×#11758222—21no—
62C2×#11758222C2×C411yescharacteristic
63C2×#11758224—21no—
64C2×#11758224C2×C411yescharacteristic
65#41×D61—44no—
66C2×Q8×D61C2×C411yescharacteristic
67C2×D4×D61—21no—
68C2×D4×D61—21no—
69C2×D4×D61—21no—
70C2×D4×D61C2×C411yescharacteristic
71C23×Dic61D411yescharacteristic
72C22×C4×D61—21no—
73C22×C4×D61—44no—
74C22×C4×D61C2×C411yescharacteristic
75C22×C4×D61C2×C411yescharacteristic
76C22×C4×D61C2×C411yescharacteristic
77C22×C4×D61C2×C411yescharacteristic
78C22×C4×D61D411yescharacteristic
79C22×C4×D61D411yescharacteristic
80C22×C4×D61D411yescharacteristic
81C22×C4×D61D411yescharacteristic
82C22×C4×D61D411yescharacteristic
83C22×C4×D61D411yescharacteristic
84C22×C4×D61C2311yescharacteristic
85C22×C4×D61C2311yescharacteristic
86C2×#11758194—21no—
87C2×#11758189—22no—
88M16×D61—44no—
89C2×C8×D61—22no—
90#14519762—21no—
91#14519762—21no—
92#14519761—21no—
93#14519760—21no—
94#14519759—21no—
95#14519759—21no—
96#14519758—21no—
97#14519757C2×C411yescharacteristic
98#14519757C2×C411yescharacteristic
99#14519756C2×C411yescharacteristic
100#14519756C2311yescharacteristic
101#14519755—21no—
102#14519755—21no—
103#14519754—21no—
104#14519754—21no—
105#14519753C2×C411yescharacteristic
106#14519753C2×C411yescharacteristic
107#14519752C2×C411yescharacteristic
108#14519752C2×C411yescharacteristic
109#14519751C2×C411yescharacteristic
110#14519751C2311yescharacteristic
111#14519750—21no—
112#14519750—21no—
113#14519749—21no—
114#14519749—21no—
115#14519748C2×C411yescharacteristic
116#14519748C2×C411yescharacteristic
117#14519747—21no—
118#14519747—21no—
119#14519747—21no—
120#14519746—21no—
121#14519745—21no—
122#14519745—21no—
123#14519745—21no—
124C4×D244—21no—
125C4×D244—21no—
126D4×Dic61—21no—
127D4×Dic61—21no—
128#14519739—21no—
129#14519739—21no—
130C4×C22⋊D61—21no—
131C4×C22⋊D61—21no—
132C4×C22⋊D61—21no—
133C4×C22⋊D61—21no—
134#14519737—21no—
135#14519737—21no—
136#14519737—21no—
137#14519737—21no—
138#14519736C2×C411yescharacteristic
139#14519735—44no—
140#14519735C2×C411yescharacteristic
141#14519735C2×C411yescharacteristic
142#14519734—21no—
143#14519733—21no—
144C2×C4⋊Dic61—21no—
145C4⋊C4×D61—21no—
146C4⋊C4×D61—21no—
147C4⋊C4×D61C2×C411yescharacteristic
148C4⋊C4×D61C2×C411yescharacteristic
149C2×C22⋊Dic61—21no—
150C2×#11758198—22no—
151C2×#11758198—22no—
152C22⋊C4×D61—21no—
153C22⋊C4×D61—21no—
154C22⋊C4×D61—21no—
155C22⋊C4×D61—21no—
156C22⋊C4×D61—21no—
157C2×C4×Dic61—22no—
158C42×D61—21no—
159C22⋊#92418—21no—
160C22⋊#92418C2312yes—
161#14519689—22no—
162#14519689—22no—
163#14519684—22no—
164#14519684C2312yes—
165C2×#41×C61C2×C411yescharacteristic
166C23×C4×C61C2311yescharacteristic
167C2×M16×C61—21no—
168#123×C61—21no—
169C22⋊Q8×C61C2×C411yescharacteristic
170C22⋊Q8×C61C2311yescharacteristic
171#121×C61C2×C411yescharacteristic
172#121×C61C2311yescharacteristic
173#120×C61—21no—
174C4×D4×C61—21no—
175C4×D4×C61—21no—
176#117×C61C2×C411yescharacteristic
177C2×C4⋊C4×C61—21no—
178C2×C22⋊C4×C61—21no—
179C22⋊C8×C61—21no—
180C22⋊C8×C61C2312yes—
181#95×C61C2312yes—
182C24×C61C2×D411yescharacteristic
183C23×D61—21no—
184C23×D61—42no—
185C23×D61—42no—
186C23×D61—41no—
187C23×D61—41no—
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×C61C22×C411yescharacteristic
204C22×C4×C61C22×C411yescharacteristic
205C22×C4×C61C2×D411yescharacteristic
206C22×C4×C61C2×D411yescharacteristic
207C22×C4×C61C2×D411yescharacteristic
208C22×C4×C61C2411yescharacteristic
209C2×C22⋊D61—21no—
210C2×C22⋊D61—21no—
211C2×C22⋊D61—21no—
212C2×C22⋊D61—21no—
213C2×C22⋊D61—21no—
214C2×C22⋊D61—21no—
215C2×C22⋊D61—21no—
216C22×Dic61—21no—
217C22×Dic61—22no—
218C22×Dic61—42no—
219C22×Dic61C22⋊C411yescharacteristic
220C22×Dic61C22⋊C411yescharacteristic
221C22×Dic61C22⋊C411yescharacteristic
222C22×Dic61C22⋊C411yescharacteristic
223C22×Dic61C2×D411yescharacteristic
224C22×Dic61C2×D411yescharacteristic
225#11758226—42no—
226Q8×D61—42no—
227#11758224—42no—
228#11758224—44no—
229D4×D61—42no—
230D4×D61—42no—
231D4×D61—42no—
232D4×D61—44no—
233D4×D61—44no—
234#11758222—44no—
235#11758222—42no—
236C2×D244—21no—
237C2×D244—21no—
238C2×D244—21no—
239C2×D244C22×C411yescharacteristic
240C2×C4×D61—24no—
241C2×C4×D61—24no—
242C2×C4×D61—24no—
243C2×C4×D61—21no—
244C2×C4×D61—21no—
245C2×C4×D61—21no—
246C2×C4×D61—21no—
247C2×C4×D61—21no—
248C2×C4×D61—42no—
249C2×C4×D61—42no—
250C2×C4×D61—42no—
251C2×C4×D61—42no—
252C2×C4×D61—42no—
253C2×C4×D61—42no—
254C2×C4×D61—42no—
255C2×C4×D61—42no—
256C2×C4×D61—42no—
257C2×C4×D61—44no—
258C2×C4×D61C22⋊C411yescharacteristic
259C2×C4×D61C22⋊C411yescharacteristic
260C2×C4×D61C22⋊C411yescharacteristic
261C2×C4×D61C22⋊C411yescharacteristic
262C2×C4×D61C22⋊C411yescharacteristic
263C2×C4×D61C22⋊C411yescharacteristic
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×D61C2×D411yescharacteristic
271C2×C4×D61C2×D411yescharacteristic
272C2×C4×D61C2×D411yescharacteristic
273C2×C4×D61C2×D411yescharacteristic
274C2×Dic122—21no—
275C2×Dic122C22×C411yescharacteristic
276M16×C61—42no—
277C2×C8×C61—22no—
278C4⋊C4×C61—21no—
279C4⋊C4×C61—21no—
280C4⋊C4×C61—42no—
281C4⋊C4×C61C22×C411yescharacteristic
282C4⋊C4×C61C22×C411yescharacteristic
283C22⋊C4×C61—21no—
284C22⋊C4×C61—21no—
285C22⋊C4×C61—21no—
286C22⋊C4×C61—21no—
287C22⋊C4×C61—21no—
288C22⋊C4×C61—42no—
289C42×C61—21no—
290C22⋊Dic61—21no—
291C22⋊Dic61—21no—
292C22⋊Dic61—21no—
293C22⋊Dic61—21no—
294C22⋊Dic61—21no—
295C22⋊Dic61—42no—
296#11758198—21no—
297#11758198—21no—
298#11758198—21no—
299#11758198—21no—
300#11758198—21no—
301#11758198—21no—
302#11758198—21no—
303#11758198—21no—
304#11758198—21no—
305#11758198—21no—
306#11758198—44no—
307#11758198—44no—
308C4⋊Dic61—21no—
309C4⋊Dic61—21no—
310C4⋊Dic61—42no—
311C4⋊Dic61C22×C411yescharacteristic
312C4⋊Dic61C22×C411yescharacteristic
313#11758196—21no—
314#11758196—21no—
315#11758196—21no—
316#11758196—21no—
317#11758196—21no—
318#11758196—21no—
319C4×Dic61—21no—
320C4×Dic61—21no—
321C4×Dic61—21no—
322C4×Dic61—44no—
323#11758194—42no—
324C2×#92418—22no—
325#11758189—44no—
326C8×D61—44no—
327C23×C61—21no—
328C23×C61—21no—
329C23×C61—21no—
330C23×C61—41no—
331C23×C61—41no—
332C23×C61C2×C22⋊C411yescharacteristic
333C23×C61C2×C22⋊C411yescharacteristic
334C23×C61C22×D411yescharacteristic
335C22×D61—21no—
336C22×D61—21no—
337C22×D61—21no—
338C22×D61—21no—
339C22×D61—22no—
340C22×D61—22no—
341C22×D61—22no—
342C22×D61—22no—
343C22×D61—22no—
344C22×D61—22no—
345C22×D61—21no—
346C22×D61—41no—
347C22×D61—41no—
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×D61C2×C22⋊C411yescharacteristic
362C22×D61C2×C22⋊C411yescharacteristic
363C22×D61C2×C22⋊C411yescharacteristic
364C22×D61C2×C22⋊C411yescharacteristic
365Q8×C61—41no—
366D4×C61—41no—
367D4×C61—42no—
368D4×C61—42no—
369D4×C61—41no—
370D4×C61—41no—
371C2×C4×C61—22no—
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—42no—
381C2×C4×C61—42no—
382C2×C4×C61—42no—
383C2×C4×C61—42no—
384C2×C4×C61C2×C22⋊C411yescharacteristic
385C2×C4×C61C2×C22⋊C411yescharacteristic
386C2×C4×C61C23×C411yescharacteristic
387C2×C4×C61C22×D411yescharacteristic
388C22⋊D61—42no—
389C22⋊D61—42no—
390C22⋊D61—42no—
391C22⋊D61—42no—
392C22⋊D61—42no—
393C22⋊D61—41no—
394C22⋊D61—41no—
395C22⋊D61—42no—
396C2×Dic61—22no—
397C2×Dic61—22no—
398C2×Dic61—22no—
399C2×Dic61—21no—
400C2×Dic61—21no—
401C2×Dic61—21no—
402C2×Dic61—41no—
403C2×Dic61—41no—
404C2×Dic61—41no—
405C2×Dic61—42no—
406C2×Dic61—42no—
407C2×Dic61—42no—
408C2×Dic61—42no—
409C2×Dic61C2×C22⋊C411yescharacteristic
410C2×Dic61C2×C22⋊C411yescharacteristic
411C2×Dic61C2×C22⋊C411yescharacteristic
412C2×Dic61C2×C22⋊C411yescharacteristic
413D244—41no—
414D244—42no—
415D244—42no—
416D244—42no—
417C4×D61—22no—
418C4×D61—22no—
419C4×D61—22no—
420C4×D61—22no—
421C4×D61—22no—
422C4×D61—22no—
423C4×D61—22no—
424C4×D61—22no—
425C4×D61—22no—
426C4×D61—41no—
427C4×D61—41no—
428C4×D61—41no—
429C4×D61—41no—
430C4×D61—41no—
431C4×D61—41no—
432C4×D61—42no—
433C4×D61—42no—
434C4×D61—42no—
435C4×D61—42no—
436C4×D61—42no—
437C4×D61#9914yes—
438Dic122—42no—
439Dic122—41no—
440C8×C61—42no—
441#92418—42no—
442#17559—611nomaximal, Sylow
443C22×C61—21no—
444C22×C61—21no—
445C22×C61—21no—
446C22×C61—21no—
447C22×C61—21no—
448C22×C61—21no—
449C22×C61—21no—
450C22×C61—21no—
451C22×C61—42no—
452C22×C61—42no—
453C22×C61—41no—
454C22×C61—41no—
455C22×C61—41no—
456C22×C61C22×C22⋊C411yescharacteristic
457C22×C61#57511yescharacteristic
458C22×C61#57511yescharacteristic
459C2×D61—21no—
460C2×D61—21no—
461C2×D61—21no—
462C2×D61—21no—
463C2×D61—21no—
464C2×D61—21no—
465C2×D61—21no—
466C2×D61—21no—
467C2×D61—21no—
468C2×D61—21no—
469C2×D61—44no—
470C2×D61—42no—
471C2×D61—42no—
472C2×D61—42no—
473C2×D61—42no—
474C2×D61—44no—
475C2×D61—44no—
476C2×D61—44no—
477C2×D61—41no—
478C2×D61—41no—
479C2×D61—41no—
480C2×D61—84no—
481C2×D61C2×#9912yes—
482C2×D61#42112yes—
483C4×C61—21no—
484C4×C61—21no—
485C4×C61—21no—
486C4×C61—41no—
487C4×C61—41no—
488C4×C61—41no—
489C4×C61—82no—
490C4×C61C2×#9912yes—
491Dic61—21no—
492Dic61—21no—
493Dic61—21no—
494Dic61—41no—
495Dic61—41no—
496Dic61—41no—
497Dic61—82no—
498Dic61C2×#9912yes—
499C2×#525—611no—
500C2×#407—611no—
501#2280—611no—
502#1513—611no—
503#1513—611no—
504#1513—611no—
505#1513D6111yescharacteristic, complemented
506#1511—612no—
507#1510—612no—
508#1501—612no—
509#1501—612no—
510C2×C61—21no—
511C2×C61—21no—
512C2×C61—41no—
513C2×C61—41no—
514C2×C61—81no—
515C2×C61C22×#9911yescharacteristic
516C2×C61#289611yescharacteristic
517C2×C61C2×#42111yescharacteristic
518D61—22no—
519D61—22no—
520D61—41no—
521D61—41no—
522D61—81no—
523C22×#41—611no—
524C24×C4—611no—
525C22×M16—1221no—
526#525—611no—
527#525—611no—
528#525—611no—
529#525—611no—
530#525—611no—
531#525—611no—
532#525—611no—
533#525—1221no—
534#525—1221no—
535#525—1221no—
536#525—1221no—
537#525C2×D6111yescharacteristic
538C2×#123—1221no—
539C2×C22⋊Q8—611no—
540C2×C22⋊Q8—611no—
541C2×#121—611no—
542C2×#121—611no—
543C2×#120—1221no—
544C2×C4×D4—1221no—
545C2×C4×D4—1221no—
546C2×#117—611no—
547C2×#117—1221no—
548#407—611no—
549#407—612no—
550#407—1221no—
551#407—1221no—
552#407C2×D6111yescharacteristic, complemented
553C2×C22⋊C8—612no—
554C2×C22⋊C8—1221no—
555#381—612no—
556#380—611no—
557#380—1221no—
558#380C2×D6111yescharacteristic, complemented
559#379—1221no—
560C4×C22⋊C4—612no—
561C4×C22⋊C4—1221no—
562#328—612no—
563#328—612no—
564#328—612no—
565#328C2×D6112yescomplemented
566#327—612no—
567#327—612no—
568#327—612no—
569#327C2×D6112yescomplemented
570C61#1755911yescharacteristic, complemented, Sylow
571C25—611no—
572C2×#41—611no—
573C2×#41—611no—
574C2×#41—611no—
575C2×#41—1221no—
576C2×#41—1221no—
577C2×#41—2444no—
578C2×#41C4×D6111yescharacteristic
579C22×Q8—611no—
580C22×D4—611no—
581C22×D4—1221no—
582C22×D4—1221no—
583C22×D4—1221no—
584C23×C4—611no—
585C23×C4—611no—
586C23×C4—611no—
587C23×C4—611no—
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—1221no—
598C23×C4—2444no—
599C23×C4C22×D6111yescharacteristic
600C2×M16—21no—
601C2×M16—1222no—
602C2×M16—1221no—
603C2×M16—2444no—
604C22×C8—1222no—
605#123—21no—
606#123—1221no—
607#123—1221no—
608#123—1221no—
609#123—1221no—
610#123—1221no—
611#123—1221no—
612#123—1221no—
613C22⋊Q8—611no—
614C22⋊Q8—611no—
615C22⋊Q8—611no—
616C22⋊Q8—611no—
617C22⋊Q8—611no—
618C22⋊Q8—611no—
619C22⋊Q8—1221no—
620C22⋊Q8—1221no—
621C22⋊Q8—1221no—
622C22⋊Q8—1221no—
623C22⋊Q8C4×D6111yescharacteristic
624C22⋊Q8C22×D6111yescharacteristic
625#121—611no—
626#121—611no—
627#121—611no—
628#121—611no—
629#121—611no—
630#121—611no—
631#121—1221no—
632#121—1221no—
633#121—1221no—
634#121—1221no—
635#121C4×D6111yescharacteristic
636#121C22×D6111yescharacteristic
637#120—21no—
638#120—1221no—
639#120—1221no—
640#120—1221no—
641#120—1221no—
642#120—1221no—
643#120—1221no—
644#120—1221no—
645C4×D4—21no—
646C4×D4—21no—
647C4×D4—1221no—
648C4×D4—1221no—
649C4×D4—1221no—
650C4×D4—1221no—
651C4×D4—1221no—
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—
661#117—611no—
662#117—611no—
663#117—611no—
664#117—1221no—
665#117—1221no—
666#117—2444no—
667#117C4×D6111yescharacteristic
668C2×C4⋊C4—21no—
669C2×C4⋊C4—611no—
670C2×C4⋊C4—611no—
671C2×C4⋊C4—1221no—
672C2×C4⋊C4—1221no—
673C2×C4⋊C4—1221no—
674C2×C22⋊C4—21no—
675C2×C22⋊C4—1221no—
676C2×C22⋊C4—1221no—
677C2×C22⋊C4—1221no—
678C2×C22⋊C4—1221no—
679C2×C22⋊C4—1221no—
680C2×C22⋊C4—1222no—
681C2×C22⋊C4—1222no—
682C2×C22⋊C4—1221no—
683C2×C42—1221no—
684C2×C42—1222no—
685C22⋊C8—21no—
686C22⋊C8—612no—
687C22⋊C8—1222no—
688C22⋊C8—1222no—
689C22⋊C8—1221no—
690C22⋊C8C22×D6112yes—
691#95—612no—
692#95—1222no—
693#95C22×D6112yes—
694C24—611no—
695C24—611no—
696C24—611no—
697C24—611no—
698C24—611no—
699C24—611no—
700C24—1221no—
701C24—2441no—
702C24—2441no—
703C24—2442no—
704C24—2442no—
705C24D4×D6111yescharacteristic
706#41—42no—
707#41—2442no—
708#41—2444no—
709#41—2444no—
710#41—2442no—
711#41—2442no—
712C2×Q8—611no—
713C2×Q8—1221no—
714C2×Q8—2442no—
715C2×Q8C2×C4×D6111yescharacteristic
716C2×D4—21no—
717C2×D4—21no—
718C2×D4—21no—
719C2×D4—611no—
720C2×D4—1221no—
721C2×D4—1221no—
722C2×D4—1221no—
723C2×D4—1221no—
724C2×D4—1221no—
725C2×D4—1221no—
726C2×D4—1221no—
727C2×D4—1221no—
728C2×D4—1221no—
729C2×D4—1221no—
730C2×D4—2442no—
731C2×D4—2444no—
732C2×D4—2444no—
733C2×D4—2442no—
734C2×D4—2442no—
735C2×D4C2×C4×D6111yescharacteristic
736C22×C4—21no—
737C22×C4—22no—
738C22×C4—42no—
739C22×C4—611no—
740C22×C4—611no—
741C22×C4—611no—
742C22×C4—611no—
743C22×C4—611no—
744C22×C4—611no—
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—1224no—
762C22×C4—1224no—
763C22×C4—1224no—
764C22×C4—1221no—
765C22×C4—1221no—
766C22×C4—1221no—
767C22×C4—1221no—
768C22×C4—1221no—
769C22×C4—1221no—
770C22×C4—1222no—
771C22×C4—2442no—
772C22×C4—2442no—
773C22×C4—2442no—
774C22×C4—2444no—
775C22×C4—2442no—
776C22×C4—2442no—
777C22×C4—2442no—
778C22×C4—2442no—
779C22×C4—2442no—
780C22×C4—2442no—
781C22×C4—2442no—
782C22×C4C2×C4×D6111yescharacteristic
783C22×C4C2×C4×D6111yescharacteristic
784C22×C4D4×D6111yescharacteristic
785C22×C4D4×D6111yescharacteristic
786C22×C4D4×D6111yescharacteristic
787C22×C4C23×D6111yescharacteristic
788M16—42no—
789M16—2444no—
790M16—2442no—
791C2×C8—22no—
792C2×C8—1222no—
793C2×C8—2444no—
794C4⋊C4—21no—
795C4⋊C4—21no—
796C4⋊C4—42no—
797C4⋊C4—611no—
798C4⋊C4—611no—
799C4⋊C4—1221no—
800C4⋊C4—1221no—
801C4⋊C4—1221no—
802C4⋊C4—1221no—
803C4⋊C4—1221no—
804C4⋊C4—1221no—
805C4⋊C4—1221no—
806C4⋊C4—1221no—
807C4⋊C4—2442no—
808C4⋊C4C2×C4×D6111yescharacteristic
809C4⋊C4C2×C4×D6111yescharacteristic
810C22⋊C4—21no—
811C22⋊C4—21no—
812C22⋊C4—21no—
813C22⋊C4—21no—
814C22⋊C4—21no—
815C22⋊C4—42no—
816C22⋊C4—1221no—
817C22⋊C4—1221no—
818C22⋊C4—1221no—
819C22⋊C4—1221no—
820C22⋊C4—1221no—
821C22⋊C4—1221no—
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—2444no—
832C22⋊C4—2444no—
833C22⋊C4—2442no—
834C42—21no—
835C42—1221no—
836C42—1221no—
837C42—1221no—
838C42—2444no—
839C23—21no—
840C23—21no—
841C23—21no—
842C23—41no—
843C23—41no—
844C23—611no—
845C23—611no—
846C23—611no—
847C23—611no—
848C23—1222no—
849C23—1222no—
850C23—1222no—
851C23—1222no—
852C23—1222no—
853C23—1222no—
854C23—1221no—
855C23—1221no—
856C23—1221no—
857C23—1221no—
858C23—1221no—
859C23—2441no—
860C23—2441no—
861C23—2441no—
862C23—2441no—
863C23—2441no—
864C23—2441no—
865C23—2441no—
866C23—2441no—
867C23—2441no—
868C23—2441no—
869C23—2442no—
870C23—2442no—
871C23—2442no—
872C23—2448no—
873C23—2448no—
874C23C22⋊C4×D6111yescharacteristic
875C23C22⋊C4×D6111yescharacteristic
876C23C2×D4×D6111yescharacteristic
877Q8—41no—
878Q8—2441no—
879Q8—2442no—
880D4—41no—
881D4—42no—
882D4—42no—
883D4—41no—
884D4—41no—
885D4—2441no—
886D4—2442no—
887D4—2442no—
888D4—2442no—
889D4—2442no—
890D4—2442no—
891D4—2442no—
892D4—2442no—
893D4—2442no—
894D4—2442no—
895D4—2441no—
896D4—2441no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—21no—
901C2×C4—21no—
902C2×C4—21no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—42no—
907C2×C4—42no—
908C2×C4—42no—
909C2×C4—42no—
910C2×C4—611no—
911C2×C4—614no—
912C2×C4—611no—
913C2×C4—611no—
914C2×C4—611no—
915C2×C4—1222no—
916C2×C4—1222no—
917C2×C4—1222no—
918C2×C4—1222no—
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—1221no—
928C2×C4—1221no—
929C2×C4—1221no—
930C2×C4—2441no—
931C2×C4—2441no—
932C2×C4—2441no—
933C2×C4—2441no—
934C2×C4—2441no—
935C2×C4—2441no—
936C2×C4—2442no—
937C2×C4—2442no—
938C2×C4—2442no—
939C2×C4—2442no—
940C2×C4—2442no—
941C2×C4—2441no—
942C2×C4—2441no—
943C2×C4—2441no—
944C2×C4—2442no—
945C2×C4—2442no—
946C2×C4—2442no—
947C2×C4—2442no—
948C2×C4C22⋊C4×D6111yescharacteristic
949C2×C4C22⋊C4×D6111yescharacteristic
950C2×C4C22×C4×D6111yescharacteristic
951C2×C4C2×D4×D6111yescharacteristic
952C8—42no—
953C8—2442no—
954C22—21no—
955C22—21no—
956C22—21no—
957C22—21no—
958C22—21no—
959C22—21no—
960C22—21no—
961C22—21no—
962C22—42no—
963C22—42no—
964C22—41no—
965C22—41no—
966C22—41no—
967C22—612no—
968C22—612no—
969C22—1221no—
970C22—1221no—
971C22—1221no—
972C22—1221no—
973C22—1221no—
974C22—1221no—
975C22—1221no—
976C22—1221no—
977C22—1221no—
978C22—1221no—
979C22—4884no—
980C22—2442no—
981C22—2442no—
982C22—2442no—
983C22—2442no—
984C22—2444no—
985C22—2444no—
986C22—2444no—
987C22—2444no—
988C22—2441no—
989C22—2441no—
990C22—2441no—
991C22C2×C22⋊C4×D6111yescharacteristic
992C22#1684055811yescharacteristic
993C22#1684056111yescharacteristic
994C4—21no—
995C4—21no—
996C4—21no—
997C4—41no—
998C4—41no—
999C4—41no—
1000C4—82no—
1001C4—612no—
1002C4—1221no—
1003C4—1221no—
1004C4—1221no—
1005C4—4882no—
1006C4—2441no—
1007C4—2441no—
1008C4—2441no—
1009C4#99×D6112yes—
1010C2—21no—
1011C2—21no—
1012C2—41no—
1013C2—41no—
1014C2—81no—
1015C2—1222no—
1016C2—1222no—
1017C2—4881no—
1018C2—2441no—
1019C2—2441no—
1020C2C2×#99×D6111yescharacteristic
1021C2#2145433511yescharacteristic
1022C2#421×D6111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1513C2
socleC22×C61C22×C22⋊C4
prime radical#525×D61C2
cosocleC22×C4×C61C24
hypercenter#1513D61
hypocenterC61#17559
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1513

Complements

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

NH ≅ G/Ntype
2. #407×D61C2semidirect
3. #21448201C2semidirect
4. #21444363C2semidirect
5. #21444362C2semidirect
6. #21444360C2semidirect
7. #21444350C2semidirect
8. #21444346C2semidirect
9. #21444309C2semidirect
10. #21444307C2semidirect
11. C61×#1513C2semidirect
12. C2×#41×D61C4semidirect
15. #16840275C4semidirect
17. #16840274C4semidirect
19. #16840272C4semidirect
24. #16840269C4semidirect
27. C22⋊Q8×D61C4semidirect
29. #121×D61C4semidirect
35. #117×D61C4semidirect
36. #16839726C22semidirect
41. C22⋊C8×D61C22semidirect
43. #16839622C22semidirect
47. #16839609C22semidirect
48. #16839500C22semidirect
49. #16839499C22semidirect
50. #16839498C22semidirect
51. #16839497C22semidirect
52. #16839496C22semidirect
53. #16839495C22semidirect
55. C61×#407C22semidirect
56. C61×#380C22semidirect
57. C61×#328C22semidirect
58. C61×#327C22semidirect
505. #1513D61semidirect
552. #407C2×D61semidirect
558. #380C2×D61semidirect
565. #328C2×D61semidirect
569. #327C2×D61semidirect
570. C61#17559semidirect

Maximal subgroups

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

subgroupindex
#525×D612
#407×D612
#214482012
#214443632
#214443622
#214443602
#214443502
#214443462
#214443092
#214443072
C61×#15132
#1755961