Finite Group Databasebeta

← #30615692

Subgroups — #30615692

Order 15616.

1986 conjugacy classes of subgroups.

The subgroup lattice has 1068 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D61⋊M16C211yesmaximal, characteristic, complemented
2C2×#16840753C212yesmaximal, complemented
3C2×#16840704C211yesmaximal, characteristic, complemented
4#21461835C212yesmaximal, complemented
5#21461834C212yesmaximal, complemented
6#21461833C212yesmaximal, complemented
7#21461832C212yesmaximal, complemented
8#21461508C212yesmaximal, complemented
9#525×D61C211yesmaximal, characteristic
10C22×#11758213—21no—
11C2×D61⋊M16—28no—
12C2×D61⋊M16—21no—
13C2×D61⋊M16—21no—
14C2×D61⋊M16C2212yes—
15C2×D61⋊M16C2212yes—
16C22×#11758217—21no—
17C22×D61⋊C8C2212yes—
18C22×C4⋊#6923C2212yes—
19C22×C22⋊#6923—21no—
20#16840753—28no—
21C2×#14519840C2214yescomplemented
22C2×#14519839C2214yescomplemented
23#16840704—21no—
24#16840704—21no—
25#16840704C2212yes—
26#16840704C2212yes—
27C2×(C2×#6923)⋊C4—21no—
28#16840635C2214yescomplemented
29#16840635C2214yescomplemented
30C2×#41×D61C2211yescharacteristic
31C23×C4×D61C2211yescharacteristic
32#16840275C411yescharacteristic, complemented
33#16840275C411yescharacteristic, complemented
34#16840274C411yescharacteristic, complemented
35#16840273C411yescharacteristic, complemented
36#16840272C411yescharacteristic, complemented
37#16840272C411yescharacteristic, complemented
38#16840271—21no—
39#16840271—21no—
40#16840270—21no—
41#16840269C411yescharacteristic, complemented
42#16840268—21no—
43#123×D61—21no—
44C22⋊Q8×D61C2211yescharacteristic
45C22⋊Q8×D61C2211yescharacteristic
46#121×D61C2211yescharacteristic
47#121×D61C2211yescharacteristic
48#120×D61—21no—
49C4×D4×D61—21no—
50C4×D4×D61—21no—
51#117×D61C2211yescharacteristic
52C61×#525C411yescharacteristic, complemented
53C23×#6923—22no—
54C2×#11758213—28no—
55C2×#11758213—22no—
56C2×#11758213—22no—
57D61⋊M16—28no—
58D61⋊M16—28no—
59D61⋊M16—24no—
60D61⋊M16—28no—
61D61⋊M16D418yescomplemented
62C2×#11758217—28no—
63C2×#11758217—22no—
64C2×#11758217—22no—
65C2×D61⋊C8—22no—
66C2×D61⋊C8—28no—
67C2×D61⋊C8C2314yes—
68C22×#92420—22no—
69C2×C4⋊#6923—24no—
70C2×C4⋊#6923—24no—
71C2×C4⋊#6923—22no—
72C2×C4⋊#6923C2314yes—
73C2×C22⋊#6923—22no—
74C2×C22⋊#6923—22no—
75C2×C22⋊#6923—44no—
76#14519840—28no—
77#14519839—28no—
78(C2×#6923)⋊C4—22no—
79(C2×#6923)⋊C4—22no—
80C24×D61D411yescharacteristic
81C2×#11758226C2×C411yescharacteristic
82C2×#11758222—21no—
83C2×#11758222C2×C411yescharacteristic
84C2×#11758224—21no—
85C2×#11758224C2×C411yescharacteristic
86#41×D61—24no—
87#41×D61—24no—
88C2×Q8×D61C2311yescharacteristic
89C2×D4×D61—21no—
90C2×D4×D61—21no—
91C2×D4×D61—21no—
92C2×D4×D61C2311yescharacteristic
93C23×Dic61D411yescharacteristic
94C22×C4×D61—24no—
95C22×C4×D61—24no—
96C22×C4×D61—21no—
97C22×C4×D61C2×C411yescharacteristic
98C22×C4×D61C2×C411yescharacteristic
99C22×C4×D61C2×C411yescharacteristic
100C22×C4×D61D411yescharacteristic
101C22×C4×D61D411yescharacteristic
102C22×C4×D61D411yescharacteristic
103C22×C4×D61D411yescharacteristic
104C22×C4×D61D411yescharacteristic
105C22×C4×D61D411yescharacteristic
106C22×C4×D61C2311yescharacteristic
107C22×C4×D61C2311yescharacteristic
108C22×C4×D61C2311yescharacteristic
109#14519762—21no—
110#14519762—21no—
111#14519761—21no—
112#14519760—21no—
113#14519759—21no—
114#14519759—21no—
115#14519758—21no—
116#14519757C2×C411yescharacteristic, complemented
117#14519757C2×C411yescharacteristic, complemented
118#14519756C2×C411yescharacteristic, complemented
119#14519756C2×C411yescharacteristic, complemented
120#14519755—21no—
121#14519755—21no—
122#14519754—21no—
123#14519754—21no—
124#14519753C2×C411yescharacteristic, complemented
125#14519753C2×C411yescharacteristic, complemented
126#14519752C2×C411yescharacteristic, complemented
127#14519752C2×C411yescharacteristic, complemented
128#14519751C2×C411yescharacteristic, complemented
129#14519751C2×C411yescharacteristic, complemented
130#14519750—21no—
131#14519750—21no—
132#14519749—21no—
133#14519749—21no—
134#14519748C2×C411yescharacteristic, complemented
135#14519748C2×C411yescharacteristic, complemented
136#14519747—21no—
137#14519747—21no—
138#14519747—21no—
139#14519746—21no—
140#14519745—21no—
141#14519745—21no—
142#14519745—21no—
143C4×D244—21no—
144C4×D244—21no—
145D4×Dic61—21no—
146D4×Dic61—21no—
147#14519739—21no—
148#14519739—21no—
149C4×C22⋊D61—21no—
150C4×C22⋊D61—21no—
151C4×C22⋊D61—21no—
152C4×C22⋊D61—21no—
153#14519737—21no—
154#14519737—21no—
155#14519737—21no—
156#14519737—21no—
157#14519736C2×C411yescharacteristic
158#14519735C2×C411yescharacteristic
159#14519735C2×C411yescharacteristic
160#14519734—21no—
161#14519733—21no—
162C4⋊C4×D61—21no—
163C4⋊C4×D61—21no—
164C4⋊C4×D61C2311yescharacteristic
165C4⋊C4×D61C2311yescharacteristic
166C22⋊C4×D61—21no—
167C22⋊C4×D61—21no—
168C22⋊C4×D61—21no—
169C22⋊C4×D61—21no—
170C22⋊C4×D61—21no—
171C42×D61—21no—
172C2×#41×C61C2×C411yescharacteristic
173C23×C4×C61C2×C411yescharacteristic
174#123×C61—21no—
175C22⋊Q8×C61C2×C411yescharacteristic, complemented
176C22⋊Q8×C61C2×C411yescharacteristic, complemented
177#121×C61C2×C411yescharacteristic, complemented
178#121×C61C2×C411yescharacteristic, complemented
179#120×C61—21no—
180C4×D4×C61—21no—
181C4×D4×C61—21no—
182#117×C61C2×C411yescharacteristic
183C24×C61C22⋊C411yescharacteristic
184C23×D61—24no—
185C23×D61—22no—
186C23×D61—22no—
187C23×D61—21no—
188C23×D61—42no—
189C23×D61C22⋊C411yescharacteristic
190C23×D61C22⋊C411yescharacteristic
191C23×D61C22⋊C411yescharacteristic
192C23×D61C2×D411yescharacteristic
193C23×D61C2×D411yescharacteristic
194C23×D61C2×D411yescharacteristic
195C22×#6923—24no—
196C22×#6923—44no—
197C22×#6923—44no—
198C22×#6923—44no—
199#41×C61—24no—
200C2×Q8×C61C22×C411yescharacteristic
201C2×D4×C61—21no—
202C2×D4×C61—21no—
203C2×D4×C61—21no—
204C2×D4×C61C22×C411yescharacteristic
205C22×C4×C61—24no—
206C22×C4×C61—21no—
207C22×C4×C61C22⋊C411yescharacteristic
208C22×C4×C61C22⋊C411yescharacteristic
209C22×C4×C61C22⋊C411yescharacteristic
210C22×C4×C61C22×C411yescharacteristic
211C22×C4×C61C22×C411yescharacteristic
212C22×C4×C61C22×C411yescharacteristic
213C2×C22⋊D61—21no—
214C2×C22⋊D61—21no—
215C2×C22⋊D61—21no—
216C2×C22⋊D61—21no—
217C2×C22⋊D61—21no—
218C2×C22⋊D61—21no—
219C2×C22⋊D61—21no—
220C22×Dic61—22no—
221C22×Dic61—22no—
222C22×Dic61—21no—
223C22×Dic61C22⋊C411yescharacteristic
224C22×Dic61C22⋊C411yescharacteristic
225C22×Dic61C22⋊C411yescharacteristic
226C22×Dic61C2×D411yescharacteristic
227C22×Dic61C2×D411yescharacteristic
228C22×Dic61C2×D411yescharacteristic
229#11758226—24no—
230Q8×D61—22no—
231Q8×D61—22no—
232#11758224—24no—
233#11758224—42no—
234#11758224—42no—
235D4×D61—22no—
236D4×D61—22no—
237D4×D61—44no—
238D4×D61—44no—
239D4×D61—42no—
240D4×D61—42no—
241#11758222—24no—
242#11758222—42no—
243#11758222—42no—
244C2×D244—21no—
245C2×D244—21no—
246C2×D244—21no—
247C2×D244C22×C411yescharacteristic
248C2×C4×D61—24no—
249C2×C4×D61—24no—
250C2×C4×D61—22no—
251C2×C4×D61—22no—
252C2×C4×D61—24no—
253C2×C4×D61—24no—
254C2×C4×D61—22no—
255C2×C4×D61—22no—
256C2×C4×D61—24no—
257C2×C4×D61—24no—
258C2×C4×D61—22no—
259C2×C4×D61—22no—
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—44no—
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×D61C22×C411yescharacteristic
277C2×C4×D61C22×C411yescharacteristic
278C2×C4×D61C22×C411yescharacteristic
279C2×C4×D61C2×D411yescharacteristic
280C2×C4×D61C2×D411yescharacteristic
281C2×C4×D61C2×D411yescharacteristic
282C2×C4×D61C2×D411yescharacteristic
283C2×C4×D61C2×D414yes—
284C2×C4×D61C2×D411yescharacteristic
285C2×C4×D61C2×D411yescharacteristic
286C2×C4×D61#4114yes—
287C2×C4×D61C2411yescharacteristic
288C2×Dic122—21no—
289C2×Dic122C22×C411yescharacteristic
290C22⋊#6923—44no—
291C22⋊#6923—44no—
292#11758217—28no—
293#11758217—28no—
294C2×#92420—28no—
295C2×#92420—24no—
296C4⋊#6923—24no—
297C4⋊#6923—24no—
298C4⋊#6923—44no—
299#11758213—28no—
300#11758213—28no—
301D61⋊C8—28no—
302D61⋊C8—24no—
303D61⋊C8C2×D418yes—
304C4⋊C4×C61—21no—
305C4⋊C4×C61—21no—
306C4⋊C4×C61C22×C411yescharacteristic
307C4⋊C4×C61C22×C411yescharacteristic
308C22⋊C4×C61—21no—
309C22⋊C4×C61—21no—
310C22⋊C4×C61—21no—
311C22⋊C4×C61—21no—
312C22⋊C4×C61—21no—
313C42×C61—21no—
314C22⋊Dic61—21no—
315C22⋊Dic61—21no—
316C22⋊Dic61—21no—
317C22⋊Dic61—21no—
318C22⋊Dic61—21no—
319#11758198—21no—
320#11758198—21no—
321#11758198—21no—
322#11758198—21no—
323#11758198—21no—
324#11758198—21no—
325#11758198—21no—
326#11758198—21no—
327#11758198—21no—
328#11758198—21no—
329C4⋊Dic61—21no—
330C4⋊Dic61—21no—
331C4⋊Dic61C22×C411yescharacteristic
332C4⋊Dic61C22×C411yescharacteristic
333#11758196—21no—
334#11758196—21no—
335#11758196—21no—
336#11758196—21no—
337#11758196—21no—
338#11758196—21no—
339C4×Dic61—21no—
340C4×Dic61—21no—
341C4×Dic61—21no—
342C23×C61—22no—
343C23×C61—22no—
344C23×C61—21no—
345C23×C61—41no—
346C23×C61C2×C22⋊C411yescharacteristic
347C23×C61C2×C22⋊C411yescharacteristic
348C23×C61C2×C22⋊C411yescharacteristic
349C22×D61—22no—
350C22×D61—21no—
351C22×D61—21no—
352C22×D61—22no—
353C22×D61—22no—
354C22×D61—22no—
355C22×D61—22no—
356C22×D61—22no—
357C22×D61—21no—
358C22×D61—21no—
359C22×D61—22no—
360C22×D61—22no—
361C22×D61—22no—
362C22×D61—22no—
363C22×D61—22no—
364C22×D61—21no—
365C22×D61—41no—
366C22×D61—41no—
367C22×D61—41no—
368C22×D61—48no—
369C22×D61—48no—
370C22×D61—42no—
371C22×D61—41no—
372C22×D61—41no—
373C22×D61—42no—
374C22×D61C2×C22⋊C411yescharacteristic
375C22×D61C2×C22⋊C411yescharacteristic
376C22×D61C2×C22⋊C411yescharacteristic
377C22×D61#12114yes—
378C22×D61AGL(1,ℤ/8)12yes—
379C22×D61#13712yes—
380C22×D61C22×D411yescharacteristic
381C2×#6923—44no—
382C2×#6923—44no—
383C2×#6923—44no—
384C2×#6923—88no—
385Q8×C61—22no—
386D4×C61—22no—
387D4×C61—42no—
388D4×C61—42no—
389D4×C61—42no—
390C2×C4×C61—22no—
391C2×C4×C61—22no—
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—42no—
399C2×C4×C61C2×C22⋊C411yescharacteristic
400C2×C4×C61C2×C22⋊C411yescharacteristic
401C2×C4×C61C2×C22⋊C411yescharacteristic
402C2×C4×C61C4×D414yes—
403C2×C4×C61C23×C411yescharacteristic
404C22⋊D61—42no—
405C22⋊D61—42no—
406C22⋊D61—42no—
407C22⋊D61—42no—
408C22⋊D61—42no—
409C22⋊D61—42no—
410C22⋊D61—41no—
411C22⋊D61—41no—
412C2×Dic61—22no—
413C2×Dic61—21no—
414C2×Dic61—21no—
415C2×Dic61—21no—
416C2×Dic61—21no—
417C2×Dic61—22no—
418C2×Dic61—22no—
419C2×Dic61—21no—
420C2×Dic61—21no—
421C2×Dic61—21no—
422C2×Dic61—42no—
423C2×Dic61C2×C22⋊C411yescharacteristic
424C2×Dic61C2×C22⋊C411yescharacteristic
425C2×Dic61C2×C22⋊C411yescharacteristic
426C2×Dic61#12012yes—
427C2×Dic61#12312yes—
428C2×Dic61C22×D411yescharacteristic
429D244—22no—
430D244—42no—
431D244—42no—
432D244—42no—
433C4×D61—22no—
434C4×D61—22no—
435C4×D61—22no—
436C4×D61—22no—
437C4×D61—22no—
438C4×D61—22no—
439C4×D61—22no—
440C4×D61—22no—
441C4×D61—21no—
442C4×D61—21no—
443C4×D61—21no—
444C4×D61—21no—
445C4×D61—22no—
446C4×D61—22no—
447C4×D61—42no—
448C4×D61—41no—
449C4×D61—41no—
450C4×D61—42no—
451C4×D61—42no—
452C4×D61—42no—
453C4×D61C4×D414yes—
454C4×D61#12012yes—
455C4×D61#12114yes—
456C4×D61#12312yes—
457C4×D61C22×D412yes—
458C4×D61C2×#4112yes—
459Dic122—22no—
460Dic122—41no—
461Dic122—41no—
462#92420—28no—
463#20971—611nomaximal, Sylow
464C22×C61—21no—
465C22×C61—21no—
466C22×C61—21no—
467C22×C61—21no—
468C22×C61—21no—
469C22×C61—21no—
470C22×C61—21no—
471C22×C61—44no—
472C22×C61—41no—
473C22×C61—41no—
474C22×C61—41no—
475C22×C61#38612yes—
476C22×C61#41712yescomplemented
477C22×C61C22×C22⋊C411yescharacteristic
478C2×D61—21no—
479C2×D61—21no—
480C2×D61—21no—
481C2×D61—21no—
482C2×D61—24no—
483C2×D61—24no—
484C2×D61—24no—
485C2×D61—24no—
486C2×D61—21no—
487C2×D61—21no—
488C2×D61—21no—
489C2×D61—44no—
490C2×D61—44no—
491C2×D61—44no—
492C2×D61—42no—
493C2×D61—42no—
494C2×D61—41no—
495C2×D61—41no—
496C2×D61—41no—
497C2×D61—82no—
498C2×D61—82no—
499C2×D61#38612yes—
500C2×D61#41712yescomplemented
501C2×D61C2×#12112yes—
502C2×D61C2×AGL(1,ℤ/8)11yescharacteristic
503C2×D61C2×#13711yescharacteristic
504C2×D61#57512yes—
505#6923—84no—
506C4×C61—21no—
507C4×C61—21no—
508C4×C61—41no—
509C4×C61—41no—
510C4×C61—41no—
511C4×C61#38612yes—
512C4×C61C2×C4×D412yes—
513Dic61—21no—
514Dic61—21no—
515Dic61—41no—
516Dic61—41no—
517Dic61—41no—
518Dic61#38612yes—
519Dic61C2×#12011yescharacteristic
520Dic61C2×#12311yescharacteristic
521C23×M16—611no—
522C2×#525—611no—
523C2×#417—612no—
524C2×#380—611no—
525#1895—612no—
526#1894—612no—
527#1893—612no—
528#1892—612no—
529#1736—612no—
530C2×C61—22no—
531C2×C61—22no—
532C2×C61—41no—
533C2×C61—81no—
534C2×C61C2×#38611yescharacteristic
535C2×C61C2×#41711yescharacteristic
536C2×C61#289611yescharacteristic
537D61—22no—
538D61—22no—
539D61—41no—
540D61—81no—
541D61#305512yes—
542D61#305612yes—
543C22×#41—611no—
544C24×C4—611no—
545C22×M16—612no—
546C22×M16—612no—
547C22×M16—1228no—
548C22×M16—1221no—
549C22×M16—1221no—
550C22×M16—1221no—
551C22×M16—1221no—
552C23×C8—612no—
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#525#692311yescharacteristic, complemented
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×C4⋊C4—612no—
575C22×C22⋊C4—1221no—
576#417—1228no—
577C2×#103—614no—
578C2×#102—614no—
579#380—612no—
580#380—612no—
581#380—1221no—
582#380—1221no—
583C2×#95—1221no—
584#340—614no—
585#340—614no—
586C61#2097111yescharacteristic, complemented, Sylow
587C25—611no—
588C2×#41—611no—
589C2×#41—611no—
590C2×#41—611no—
591C2×#41—1221no—
592C2×#41—1221no—
593C2×#41—1224no—
594C2×#41—1224no—
595C2×#41C2×#692311yescharacteristic
596C22×Q8—611no—
597C22×D4—611no—
598C22×D4—1221no—
599C22×D4—1221no—
600C22×D4—1221no—
601C23×C4—611no—
602C23×C4—611no—
603C23×C4—611no—
604C23×C4—611no—
605C23×C4—611no—
606C23×C4—611no—
607C23×C4—611no—
608C23×C4—611no—
609C23×C4—611no—
610C23×C4—611no—
611C23×C4—611no—
612C23×C4—611no—
613C23×C4—611no—
614C23×C4—1224no—
615C23×C4—1224no—
616C23×C4—1221no—
617C23×C4—1222no—
618C23×C4C2×#692311yescharacteristic
619C2×M16—618no—
620C2×M16—1228no—
621C2×M16—1222no—
622C2×M16—1222no—
623C2×M16—1224no—
624C2×M16—1222no—
625C2×M16—1222no—
626C2×M16—1228no—
627C2×M16—1228no—
628C2×M16—1228no—
629C2×M16—1228no—
630C22×C8—614no—
631C22×C8—1228no—
632C22×C8—1222no—
633C22×C8—1222no—
634#123—21no—
635#123—1221no—
636#123—1221no—
637#123—1221no—
638#123—1221no—
639#123—1221no—
640#123—1221no—
641#123—1221no—
642C22⋊Q8—611no—
643C22⋊Q8—611no—
644C22⋊Q8—611no—
645C22⋊Q8—611no—
646C22⋊Q8—611no—
647C22⋊Q8—611no—
648C22⋊Q8—1221no—
649C22⋊Q8—1221no—
650C22⋊Q8—1221no—
651C22⋊Q8—1221no—
652C22⋊Q8C2×#692311yescharacteristic, complemented
653C22⋊Q8C2×#692311yescharacteristic, complemented
654#121—611no—
655#121—611no—
656#121—611no—
657#121—611no—
658#121—611no—
659#121—611no—
660#121—1221no—
661#121—1221no—
662#121—1221no—
663#121—1221no—
664#121C2×#692311yescharacteristic, complemented
665#121C2×#692311yescharacteristic, complemented
666#120—21no—
667#120—1221no—
668#120—1221no—
669#120—1221no—
670#120—1221no—
671#120—1221no—
672#120—1221no—
673#120—1221no—
674C4×D4—21no—
675C4×D4—21no—
676C4×D4—1221no—
677C4×D4—1221no—
678C4×D4—1221no—
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—
690#117—611no—
691#117—611no—
692#117—611no—
693#117—1221no—
694#117—1221no—
695#117C2×#692311yescharacteristic
696C2×C4⋊C4—611no—
697C2×C4⋊C4—611no—
698C2×C4⋊C4—614no—
699C2×C4⋊C4—1221no—
700C2×C4⋊C4—1221no—
701C2×C4⋊C4—1224no—
702C2×C4⋊C4—1224no—
703C2×C4⋊C4—1222no—
704C2×C22⋊C4—1221no—
705C2×C22⋊C4—1221no—
706C2×C22⋊C4—1221no—
707C2×C22⋊C4—1221no—
708C2×C22⋊C4—1221no—
709C2×C22⋊C4—1222no—
710C2×C22⋊C4—1222no—
711C2×C22⋊C4—2444no—
712C2×C42—1221no—
713#103—1228no—
714#102—1228no—
715#95—1222no—
716#95—1222no—
717C24—611no—
718C24—611no—
719C24—611no—
720C24—611no—
721C24—611no—
722C24—611no—
723C24—1222no—
724C24—1224no—
725C24—1222no—
726C24—1221no—
727C24—2442no—
728C24C22⋊#692311yescharacteristic
729#41—24no—
730#41—1224no—
731#41—1224no—
732#41—1224no—
733#41—2442no—
734#41—2442no—
735#41—2442no—
736#41—2442no—
737C2×Q8—611no—
738C2×Q8—1221no—
739C2×Q8—1222no—
740C2×Q8—1222no—
741C2×Q8C22×#692311yescharacteristic
742C2×D4—21no—
743C2×D4—21no—
744C2×D4—21no—
745C2×D4—611no—
746C2×D4—1221no—
747C2×D4—1221no—
748C2×D4—1221no—
749C2×D4—1222no—
750C2×D4—1222no—
751C2×D4—1221no—
752C2×D4—1221no—
753C2×D4—1221no—
754C2×D4—1221no—
755C2×D4—1221no—
756C2×D4—1221no—
757C2×D4—1221no—
758C2×D4—2444no—
759C2×D4—2442no—
760C2×D4—2442no—
761C2×D4—2444no—
762C2×D4C22×#692311yescharacteristic
763C22×C4—24no—
764C22×C4—21no—
765C22×C4—611no—
766C22×C4—611no—
767C22×C4—611no—
768C22×C4—614no—
769C22×C4—614no—
770C22×C4—611no—
771C22×C4—611no—
772C22×C4—611no—
773C22×C4—611no—
774C22×C4—611no—
775C22×C4—611no—
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—1222no—
790C22×C4—1222no—
791C22×C4—1222no—
792C22×C4—1222no—
793C22×C4—1222no—
794C22×C4—1222no—
795C22×C4—1224no—
796C22×C4—1224no—
797C22×C4—1222no—
798C22×C4—1222no—
799C22×C4—1224no—
800C22×C4—1224no—
801C22×C4—1222no—
802C22×C4—1222no—
803C22×C4—1221no—
804C22×C4—1224no—
805C22×C4—1221no—
806C22×C4—1221no—
807C22×C4—1221no—
808C22×C4—1222no—
809C22×C4—1222no—
810C22×C4—1221no—
811C22×C4—1224no—
812C22×C4—1221no—
813C22×C4—1224no—
814C22×C4—2444no—
815C22×C4—2444no—
816C22×C4—2444no—
817C22×C4—2444no—
818C22×C4C22⋊#692311yescharacteristic
819C22×C4C22⋊#692311yescharacteristic
820C22×C4C22⋊#692311yescharacteristic
821C22×C4C22×#692311yescharacteristic
822C22×C4C22×#692311yescharacteristic
823C22×C4C22×#692311yescharacteristic
824M16—1228no—
825M16—1228no—
826M16—1228no—
827M16—1228no—
828C2×C8—618no—
829C2×C8—1224no—
830C2×C8—1224no—
831C2×C8—1228no—
832C2×C8—1228no—
833C4⋊C4—21no—
834C4⋊C4—21no—
835C4⋊C4—611no—
836C4⋊C4—611no—
837C4⋊C4—1221no—
838C4⋊C4—1221no—
839C4⋊C4—1221no—
840C4⋊C4—1221no—
841C4⋊C4—1221no—
842C4⋊C4—1221no—
843C4⋊C4—1224no—
844C4⋊C4—1224no—
845C4⋊C4—1221no—
846C4⋊C4—1221no—
847C4⋊C4—2444no—
848C4⋊C4C22×#692311yescharacteristic
849C4⋊C4C22×#692311yescharacteristic
850C22⋊C4—21no—
851C22⋊C4—21no—
852C22⋊C4—21no—
853C22⋊C4—21no—
854C22⋊C4—21no—
855C22⋊C4—1221no—
856C22⋊C4—1221no—
857C22⋊C4—1221no—
858C22⋊C4—1221no—
859C22⋊C4—1221no—
860C22⋊C4—1221no—
861C22⋊C4—1221no—
862C22⋊C4—1221no—
863C22⋊C4—1221no—
864C22⋊C4—1221no—
865C22⋊C4—1221no—
866C22⋊C4—1221no—
867C22⋊C4—1221no—
868C22⋊C4—1221no—
869C22⋊C4—1221no—
870C22⋊C4—2444no—
871C22⋊C4—2444no—
872C42—21no—
873C42—1221no—
874C42—1221no—
875C42—1221no—
876C23—22no—
877C23—22no—
878C23—21no—
879C23—41no—
880C23—611no—
881C23—614no—
882C23—612no—
883C23—612no—
884C23—611no—
885C23—611no—
886C23—611no—
887C23—1222no—
888C23—1221no—
889C23—1222no—
890C23—1221no—
891C23—1222no—
892C23—1221no—
893C23—1222no—
894C23—1222no—
895C23—1222no—
896C23—1222no—
897C23—1222no—
898C23—1221no—
899C23—1222no—
900C23—1222no—
901C23—1222no—
902C23—1221no—
903C23—2441no—
904C23—2441no—
905C23—2441no—
906C23—2442no—
907C23—2441no—
908C23—2441no—
909C23—2442no—
910C23—2448no—
911C23—2448no—
912C23C2×C22⋊#692311yescharacteristic
913C23C2×C22⋊#692311yescharacteristic
914C23C2×C22⋊#692311yescharacteristic
915Q8—22no—
916Q8—1222no—
917Q8—2441no—
918Q8—2441no—
919D4—22no—
920D4—42no—
921D4—42no—
922D4—42no—
923D4—1222no—
924D4—2442no—
925D4—2442no—
926D4—2442no—
927D4—2441no—
928D4—2441no—
929D4—2442no—
930D4—2442no—
931D4—2442no—
932D4—2442no—
933D4—2442no—
934D4—2442no—
935C2×C4—22no—
936C2×C4—22no—
937C2×C4—22no—
938C2×C4—22no—
939C2×C4—22no—
940C2×C4—21no—
941C2×C4—21no—
942C2×C4—21no—
943C2×C4—42no—
944C2×C4—612no—
945C2×C4—612no—
946C2×C4—611no—
947C2×C4—611no—
948C2×C4—612no—
949C2×C4—614no—
950C2×C4—612no—
951C2×C4—614no—
952C2×C4—612no—
953C2×C4—612no—
954C2×C4—611no—
955C2×C4—611no—
956C2×C4—1221no—
957C2×C4—1221no—
958C2×C4—1221no—
959C2×C4—1221no—
960C2×C4—1222no—
961C2×C4—1222no—
962C2×C4—1222no—
963C2×C4—1222no—
964C2×C4—1222no—
965C2×C4—1222no—
966C2×C4—1221no—
967C2×C4—1221no—
968C2×C4—1221no—
969C2×C4—1221no—
970C2×C4—1222no—
971C2×C4—1222no—
972C2×C4—1222no—
973C2×C4—1222no—
974C2×C4—1222no—
975C2×C4—1222no—
976C2×C4—1222no—
977C2×C4—1221no—
978C2×C4—1221no—
979C2×C4—1221no—
980C2×C4—4888no—
981C2×C4—2442no—
982C2×C4—2442no—
983C2×C4—2441no—
984C2×C4—2441no—
985C2×C4—2442no—
986C2×C4—2442no—
987C2×C4—2444no—
988C2×C4—2444no—
989C2×C4—2444no—
990C2×C4—2442no—
991C2×C4C2×C22⋊#692311yescharacteristic
992C2×C4C2×C22⋊#692311yescharacteristic
993C2×C4C2×C22⋊#692311yescharacteristic
994C2×C4D4×#692314yes—
995C2×C4C23×#692311yescharacteristic
996C8—1228no—
997C22—21no—
998C22—21no—
999C22—21no—
1000C22—21no—
1001C22—21no—
1002C22—21no—
1003C22—21no—
1004C22—44no—
1005C22—41no—
1006C22—41no—
1007C22—41no—
1008C22—611no—
1009C22—611no—
1010C22—612no—
1011C22—612no—
1012C22—612no—
1013C22—612no—
1014C22—1224no—
1015C22—1224no—
1016C22—1224no—
1017C22—1224no—
1018C22—1221no—
1019C22—1221no—
1020C22—1221no—
1021C22—1221no—
1022C22—1221no—
1023C22—1221no—
1024C22—1221no—
1025C22—4882no—
1026C22—4882no—
1027C22—2444no—
1028C22—2444no—
1029C22—2442no—
1030C22—2442no—
1031C22—2444no—
1032C22—2441no—
1033C22—2441no—
1034C22—2441no—
1035C22#1684071012yes—
1036C22#1684075312yescomplemented
1037C22C22×C22⋊#692311yescharacteristic
1038C4—21no—
1039C4—21no—
1040C4—41no—
1041C4—41no—
1042C4—41no—
1043C4—611no—
1044C4—611no—
1045C4—612no—
1046C4—1221no—
1047C4—1221no—
1048C4—4884no—
1049C4—2441no—
1050C4—2441no—
1051C4—2441no—
1052C4#1684071012yes—
1053C4C2×D4×#692312yes—
1054C2—22no—
1055C2—22no—
1056C2—41no—
1057C2—81no—
1058C2—612no—
1059C2—612no—
1060C2—1222no—
1061C2—1222no—
1062C2—4881no—
1063C2—2441no—
1064C2C2×#1684071011yescharacteristic
1065C2C2×#1684075311yescharacteristic
1066C2#2146243911yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#525C4
socleC22×C61C22×C22⋊C4
prime radical#525×D61C2
cosocleC2×C4×D61C24
hypercenter#525#6923
hypocenterC61#20971
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #525

Complements

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

NH ≅ G/Ntype
1. C22×D61⋊M16C2semidirect
2. C2×#16840753C2semidirect
3. C2×#16840704C2semidirect
4. #21461835C2semidirect
5. #21461834C2semidirect
6. #21461833C2semidirect
7. #21461832C2semidirect
8. #21461508C2semidirect
21. C2×#14519840C22semidirect
22. C2×#14519839C22semidirect
28. #16840635C22semidirect
29. #16840635C22semidirect
32. #16840275C4semidirect
33. #16840275C4semidirect
34. #16840274C4semidirect
35. #16840273C4semidirect
36. #16840272C4semidirect
37. #16840272C4semidirect
41. #16840269C4semidirect
52. C61×#525C4semidirect
61. D61⋊M16D4semidirect
116. #14519757C2×C4semidirect
117. #14519757C2×C4semidirect
118. #14519756C2×C4semidirect
119. #14519756C2×C4semidirect
124. #14519753C2×C4semidirect
125. #14519753C2×C4semidirect
126. #14519752C2×C4semidirect
127. #14519752C2×C4semidirect
128. #14519751C2×C4semidirect
129. #14519751C2×C4semidirect
134. #14519748C2×C4semidirect
135. #14519748C2×C4semidirect
175. C22⋊Q8×C61C2×C4semidirect
176. C22⋊Q8×C61C2×C4semidirect
177. #121×C61C2×C4semidirect
178. #121×C61C2×C4semidirect
476. C22×C61#417semidirect
500. C2×D61#417semidirect
564. #525#6923semidirect
586. C61#20971semidirect
652. C22⋊Q8C2×#6923semidirect
653. C22⋊Q8C2×#6923semidirect
664. #121C2×#6923semidirect
665. #121C2×#6923semidirect
1036. C22#16840753semidirect

Maximal subgroups

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

subgroupindex
C22×D61⋊M162
C2×#168407532
C2×#168407042
#214618352
#214618342
#214618332
#214618322
#214615082
#525×D612
#2097161