Finite Group Databasebeta

← #30616370

Subgroups — #30616370

Order 15616.

868 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840787C211yesmaximal, characteristic, complemented
2C2×#16840778C211yesmaximal, characteristic, complemented
3#21461944C211yesmaximal, characteristic
4#21461942C211yesmaximal, characteristic
5#21461921C211yesmaximal, characteristic, complemented
6#21461916C211yesmaximal, characteristic, complemented
7#21461894C211yesmaximal, characteristic, complemented
8#21461892C211yesmaximal, characteristic, complemented
9#21461891C211yesmaximal, characteristic, complemented
10#21461888C211yesmaximal, characteristic, complemented
11#21461607C211yesmaximal, characteristic, complemented
12#21461548C211yesmaximal, characteristic, complemented
13#21461545C211yesmaximal, characteristic, complemented
14#21461476C211yesmaximal, characteristic, complemented
15#21448255C211yesmaximal, characteristic
16#16840787—24no—
17#16840778—24no—
18C2×#14519844C2211yescharacteristic
19C2×#14519844C2211yescharacteristic
20C2×C4⋊#92420C2211yescharacteristic
21C2×C4⋊#92420C2211yescharacteristic
22C2×C4⋊#92420C2211yescharacteristic
23C2×C4⋊#92420C2211yescharacteristic
24C2×#14519834C2211yescharacteristic
25C2×#14519834C2211yescharacteristic
26C2×#14519834C2211yescharacteristic
27C2×#14519834C2211yescharacteristic
28C2×C22⋊#92420C2211yescharacteristic
29C2×C22⋊#92420C2211yescharacteristic
30C2×C22⋊#92420C2211yescharacteristic
31C2×C22⋊#92420C2211yescharacteristic
32C2×#14519832C2211yescharacteristic
33C2×#14519832C2211yescharacteristic
34C2×#14519832C2211yescharacteristic
35C2×#14519832C2211yescharacteristic
36C2×C4×#92420C2211yescharacteristic
37C2×C4×#92420C2211yescharacteristic
38C2×C4×#92420C2211yescharacteristic
39C2×C4×#92420C2211yescharacteristic
40#16840628C2211yescharacteristic
41#16840628C2211yescharacteristic
42#16840628C2211yescharacteristic
43#16840628C2211yescharacteristic
44#16840628C2211yescharacteristic
45#16840628C2211yescharacteristic
46C2×#14519737C2211yescharacteristic
47C2×#14519735C2211yescharacteristic
48C22×C4×Dic61C2211yescharacteristic
49#16839654C411yescharacteristic
50#16839652C411yescharacteristic
51#16839649C411yescharacteristic
52#16839643C411yescharacteristic
53#16839641C411yescharacteristic
54#16839639C411yescharacteristic
55#16839637C411yescharacteristic
56C4⋊C4×Dic61C2211yescharacteristic
57C22⋊C4×Dic61C2211yescharacteristic
58#16839609C2211yescharacteristic
59#16839607C2211yescharacteristic
60C61×#385C411yescharacteristic
61C22×#92420C2311yescharacteristic
62C22×#92420C2311yescharacteristic
63C22×#92420C2311yescharacteristic
64C22×#92420C2311yescharacteristic
65C22×#92420C2311yescharacteristic
66C22×#92420C2311yescharacteristic
67C22×#92420C2311yescharacteristic
68C22×#92420C2311yescharacteristic
69#14519844—22no—
70#14519844—22no—
71C4⋊#92420—22no—
72C4⋊#92420—22no—
73C4⋊#92420—22no—
74C4⋊#92420—22no—
75#14519834—22no—
76#14519834—22no—
77#14519834—22no—
78#14519834—22no—
79C22⋊#92420—22no—
80C22⋊#92420—22no—
81C22⋊#92420—22no—
82C22⋊#92420—22no—
83#14519832—22no—
84#14519832—22no—
85#14519832—22no—
86#14519832—22no—
87C4×#92420—22no—
88C4×#92420—22no—
89C4×#92420—22no—
90C4×#92420D414yescomplemented
91C22×C22⋊D61C2×C411yescharacteristic
92C23×Dic61C2×C411yescharacteristic
93C23×Dic61C2311yescharacteristic
94C22×C4×D61C2311yescharacteristic
95#14519737—22no—
96#14519737—22no—
97#14519735—22no—
98#14519735—22no—
99C2×C4⋊Dic61C2×C411yescharacteristic
100C2×C4⋊Dic61C2×C411yescharacteristic
101C2×#11758196C2×C411yescharacteristic
102C2×C22⋊Dic61C2×C411yescharacteristic
103C2×#11758198C2×C411yescharacteristic
104C2×#11758198C2×C411yescharacteristic
105C2×#11758198C2×C411yescharacteristic
106C2×#11758198C2×C411yescharacteristic
107C2×#11758198C2×C411yescharacteristic
108C2×C4×Dic61—22no—
109C2×C4×Dic61—22no—
110C2×C4×Dic61C2×C411yescharacteristic
111C2×C4×Dic61C2×C411yescharacteristic
112C2×C4×Dic61C2311yescharacteristic
113C2×C4×Dic61C2311yescharacteristic
114C2×C4×Dic61C2311yescharacteristic
115C2×C4×Dic61C2311yescharacteristic
116C2×C4×Dic61C2311yescharacteristic
117#14519684C2×C411yescharacteristic
118#14519684C2×C411yescharacteristic
119#14519684C2×C411yescharacteristic
120#14519684C2×C411yescharacteristic
121#14519684C2×C411yescharacteristic
122#14519684C2×C411yescharacteristic
123#14519684C2×C411yescharacteristic
124#14519684C2×C411yescharacteristic
125C23×C4×C61C2×C411yescharacteristic
126C2×C4⋊C4×C61C2×C411yescharacteristic
127C2×C4⋊C4×C61C2×C411yescharacteristic
128C2×C22⋊C4×C61C2×C411yescharacteristic
129C2×C22⋊C4×C61C2×C411yescharacteristic
130#95×C61C2×C411yescharacteristic
131#95×C61C2×C411yescharacteristic
132C24×C61C22×C411yescharacteristic
133C23×D61C22×C411yescharacteristic
134C22×C4×C61—22no—
135C22×C4×C61—22no—
136C22×C4×C61—22no—
137C22×C4×C61C22×C411yescharacteristic
138C22×C4×C61C22×C411yescharacteristic
139C22×C4×C61C22×C411yescharacteristic
140C22×C4×C61C22×C411yescharacteristic
141C22×C4×C61C22×C411yescharacteristic
142C22×C4×C61C22×C411yescharacteristic
143C2×C22⋊D61—22no—
144C2×C22⋊D61—22no—
145C2×C22⋊D61—41no—
146C22×Dic61—22no—
147C22×Dic61—21no—
148C22×Dic61—21no—
149C22×Dic61—21no—
150C22×Dic61—21no—
151C22×Dic61—21no—
152C22×Dic61—21no—
153C22×Dic61—41no—
154C22×Dic61—41no—
155C22×Dic61C22×C411yescharacteristic
156C22×Dic61C22×C411yescharacteristic
157C22×Dic61C22×C411yescharacteristic
158C22×Dic61C22×C411yescharacteristic
159C22×Dic61C22×C411yescharacteristic
160C22×Dic61C22×C411yescharacteristic
161C22×Dic61C2411yescharacteristic
162C2×C4×D61—21no—
163C2×C4×D61—21no—
164C2×C4×D61—21no—
165C2×C4×D61—21no—
166C2×C4×D61—21no—
167C2×C4×D61—21no—
168C2×#92420—21no—
169C2×#92420—21no—
170C2×#92420—21no—
171C2×#92420—21no—
172C2×#92420—21no—
173C2×#92420—21no—
174C2×#92420—21no—
175C2×#92420—21no—
176C2×#92420—21no—
177C2×#92420—21no—
178C2×#92420—21no—
179C2×#92420—21no—
180C2×#92420—21no—
181C2×#92420—21no—
182C2×#92420—21no—
183C2×#92420—21no—
184C2×#92420—21no—
185C2×#92420—21no—
186C2×#92420—21no—
187C2×#92420—21no—
188C2×#92420C2×D412yes—
189C2×#92420C2×D412yes—
190C2×#92420#4112yes—
191C2×#92420#4112yes—
192C4⋊C4×C61—22no—
193C4⋊C4×C61—22no—
194C22⋊C4×C61—22no—
195C22⋊C4×C61—22no—
196C22⋊Dic61—41no—
197#11758198—22no—
198#11758198—22no—
199#11758198—22no—
200#11758198—22no—
201#11758198—41no—
202C4⋊Dic61—22no—
203C4⋊Dic61—41no—
204#11758196—22no—
205C4×Dic61—22no—
206C4×Dic61—22no—
207C4×Dic61—21no—
208C4×Dic61—21no—
209C4×Dic61—21no—
210C4×Dic61—21no—
211C4×Dic61—21no—
212C4×Dic61—21no—
213C4×Dic61C2×D412yes—
214C4×Dic61#4112yes—
215C4×Dic61#4112yes—
216C4×Dic61#4112yes—
217C23×C61—21no—
218C23×C61—21no—
219C23×C61—21no—
220C23×C61—21no—
221C23×C61—21no—
222C23×C61—21no—
223C23×C61#13112yes—
224C23×C61C23×C411yescharacteristic
225C22×D61—21no—
226C22×D61—21no—
227C22×D61—21no—
228C22×D61—21no—
229C22×D61—21no—
230C22×D61—21no—
231C22×D61—21no—
232C2×C4×C61—28no—
233C2×C4×C61—21no—
234C2×C4×C61—21no—
235C2×C4×C61—21no—
236C2×C4×C61—21no—
237C2×C4×C61—21no—
238C2×C4×C61—21no—
239C2×C4×C61—21no—
240C2×C4×C61—21no—
241C2×C4×C61—21no—
242C2×C4×C61—21no—
243C2×C4×C61—21no—
244C2×C4×C61—21no—
245C2×C4×C61—21no—
246C2×C4×C61—21no—
247C2×C4×C61—21no—
248C2×C4×C61#11712yes—
249C2×C4×C61C4×D412yes—
250C2×C4×C61#13112yes—
251C22⋊D61—44no—
252C2×Dic61—21no—
253C2×Dic61—21no—
254C2×Dic61—21no—
255C2×Dic61—21no—
256C2×Dic61—21no—
257C2×Dic61—21no—
258C2×Dic61—21no—
259C2×Dic61—21no—
260C2×Dic61—21no—
261C2×Dic61—21no—
262C2×Dic61—21no—
263C2×Dic61—21no—
264C2×Dic61—21no—
265C2×Dic61—21no—
266C2×Dic61—21no—
267C2×Dic61—21no—
268C2×Dic61—44no—
269C2×Dic61—41no—
270C2×Dic61—41no—
271C2×Dic61—41no—
272C2×Dic61—41no—
273C2×Dic61#11712yes—
274C2×Dic61C4×D412yes—
275C2×Dic61C22×D411yescharacteristic
276C2×Dic61C2×#4111yescharacteristic
277C2×Dic61C2×#4111yescharacteristic
278C2×Dic61C2×#4111yescharacteristic
279C2×Dic61C2×#4111yescharacteristic
280C2×Dic61C2×#4111yescharacteristic
281C4×D61—41no—
282C4×D61—41no—
283C4×D61—41no—
284C4×D61—41no—
285#92420—22no—
286#92420—22no—
287#92420—22no—
288#92420—22no—
289#92420—41no—
290#92420—41no—
291#92420—41no—
292#92420—41no—
293#21272—611nomaximal, Sylow
294C22×C61—22no—
295C22×C61—22no—
296C22×C61—22no—
297C22×C61—41no—
298C22×C61—41no—
299C22×C61—41no—
300C22×C61—41no—
301C22×C61C2×#11711yescharacteristic
302C22×C61C2×C4×D411yescharacteristic
303C22×C61C4×#4111yescharacteristic
304C22×C61C2×#13111yescharacteristic
305C22×C61C2×#13111yescharacteristic
306C22×C61#56811yescharacteristic
307C22×C61#56811yescharacteristic
308C2×D61—41no—
309C2×D61—41no—
310C2×D61—41no—
311C2×D61—41no—
312C2×D61—41no—
313C2×D61—41no—
314C2×D61—41no—
315C4×C61—22no—
316C4×C61—22no—
317C4×C61—22no—
318C4×C61—41no—
319C4×C61—41no—
320C4×C61—41no—
321Dic61—22no—
322Dic61—22no—
323Dic61—41no—
324Dic61—41no—
325Dic61—41no—
326Dic61—41no—
327Dic61#52911yescharacteristic
328Dic61#52911yescharacteristic
329Dic61#53211yescharacteristic
330Dic61#53211yescharacteristic
331C2×#433—611no—
332C2×#431—611no—
333#2290—611no—
334#1955—611no—
335#1954—611no—
336#1940—611no—
337#1939—611no—
338#1924—611no—
339#1924—611no—
340#1923—611no—
341#1923—611no—
342#1768—611no—
343#1750—611no—
344#1749—611no—
345#1726—611no—
346C2×C61—42no—
347C2×C61#229311yescharacteristic
348C2×C61#292411yescharacteristic
349C2×C61#292511yescharacteristic
350C2×C61#292911yescharacteristic
351C2×C61#293011yescharacteristic
352C2×C61#296811yescharacteristic
353C2×C61#296911yescharacteristic
354D61—81no—
355C2×C4×D4—611no—
356C2×#117—611no—
357C22×C42—611no—
358#433—1224no—
359#431—1224no—
360C2×C4⋊C8—611no—
361C2×C4⋊C8—611no—
362C2×C4⋊C8—611no—
363C2×C4⋊C8—611no—
364C2×C4⋊C8—611no—
365C2×C4⋊C8—611no—
366C2×C22⋊C8—611no—
367C2×C22⋊C8—611no—
368C2×C22⋊C8—611no—
369C2×C22⋊C8—611no—
370C2×C22⋊C8—611no—
371C2×C22⋊C8—611no—
372C2×C22⋊C8—611no—
373C2×C22⋊C8—611no—
374C2×#97—611no—
375C2×#97—611no—
376C2×#97—611no—
377C2×#97—611no—
378C2×C4×C8—611no—
379C2×C4×C8—611no—
380C2×C4×C8—611no—
381C2×C4×C8—611no—
382#388—611no—
383#388—611no—
384#387—611no—
385#387—611no—
386#386—611no—
387#386—611no—
388#385—611no—
389#385#692311yescharacteristic
390C4×C4⋊C4—611no—
391C4×C22⋊C4—611no—
392C4×C22⋊C4—611no—
393#376—611no—
394#336—611no—
395#336—611no—
396#336—611no—
397#336—611no—
398#336—611no—
399#336—611no—
400C61#2127211yescharacteristic, complemented, Sylow
401C22×D4—611no—
402C23×C4—611no—
403C23×C4—611no—
404C23×C4—611no—
405C23×C4C2×#692311yescharacteristic
406C22×C8—611no—
407C22×C8—611no—
408C22×C8—611no—
409C22×C8—611no—
410C22×C8—611no—
411C22×C8—611no—
412C22×C8—611no—
413C22×C8—611no—
414C4×D4—1222no—
415C4×D4—1222no—
416#117—1222no—
417#117—1222no—
418C2×C4⋊C4—611no—
419C2×C4⋊C4—611no—
420C2×C4⋊C4—611no—
421C2×C4⋊C4C2×#692311yescharacteristic
422C2×C4⋊C4C2×#692311yescharacteristic
423C2×C22⋊C4—611no—
424C2×C22⋊C4—611no—
425C2×C22⋊C4—611no—
426C2×C22⋊C4—611no—
427C2×C22⋊C4—611no—
428C2×C22⋊C4—611no—
429C2×C22⋊C4C2×#692311yescharacteristic
430C2×C22⋊C4C2×#692311yescharacteristic
431C2×C42—611no—
432C2×C42—611no—
433C2×C42—611no—
434C2×C42—611no—
435C2×C42—611no—
436C2×C42—611no—
437C2×C42—611no—
438C2×C42—1222no—
439C2×C42—1222no—
440C4⋊C8—1222no—
441C4⋊C8—1222no—
442C4⋊C8—1222no—
443C4⋊C8—1222no—
444C4⋊C8—1222no—
445C4⋊C8—1222no—
446C22⋊C8—1222no—
447C22⋊C8—1222no—
448C22⋊C8—1222no—
449C22⋊C8—1222no—
450C22⋊C8—1222no—
451C22⋊C8—1222no—
452C22⋊C8—1222no—
453C22⋊C8—1222no—
454#97—1222no—
455#97—1222no—
456#97—1222no—
457#97—1222no—
458C4×C8—614no—
459C4×C8—1222no—
460C4×C8—1222no—
461C4×C8—1222no—
462#95—611no—
463#95—611no—
464#95—611no—
465#95—611no—
466#95—611no—
467#95—611no—
468#95—611no—
469#95—611no—
470#95C2×#692311yescharacteristic
471#95C2×#692311yescharacteristic
472C24—611no—
473C24C22×#692311yescharacteristic
474C2×D4—1222no—
475C2×D4—1222no—
476C2×D4—2441no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—611no—
481C22×C4—611no—
482C22×C4—611no—
483C22×C4—611no—
484C22×C4—611no—
485C22×C4—611no—
486C22×C4—611no—
487C22×C4—1221no—
488C22×C4—1221no—
489C22×C4—1221no—
490C22×C4—1221no—
491C22×C4—1221no—
492C22×C4—1221no—
493C22×C4—1221no—
494C22×C4—1221no—
495C22×C4—1221no—
496C22×C4—1221no—
497C22×C4—1222no—
498C22×C4—1221no—
499C22×C4—1221no—
500C22×C4—2441no—
501C22×C4—2441no—
502C22×C4C22×#692311yescharacteristic
503C22×C4C22×#692311yescharacteristic
504C22×C4C22×#692311yescharacteristic
505C22×C4C22×#692311yescharacteristic
506C22×C4C22×#692311yescharacteristic
507C22×C4C22×#692311yescharacteristic
508C2×C8—612no—
509C2×C8—612no—
510C2×C8—612no—
511C2×C8—612no—
512C2×C8—1221no—
513C2×C8—1221no—
514C2×C8—1221no—
515C2×C8—1221no—
516C2×C8—1221no—
517C2×C8—1221no—
518C2×C8—1221no—
519C2×C8—1221no—
520C2×C8—1221no—
521C2×C8—1221no—
522C2×C8—1221no—
523C2×C8—1221no—
524C2×C8—1221no—
525C2×C8—1221no—
526C2×C8—1221no—
527C2×C8—1221no—
528C2×C8—1221no—
529C2×C8—1221no—
530C2×C8—1221no—
531C2×C8—1221no—
532C4⋊C4—22no—
533C4⋊C4—22no—
534C4⋊C4—1222no—
535C4⋊C4—1222no—
536C4⋊C4—2441no—
537C22⋊C4—22no—
538C22⋊C4—22no—
539C22⋊C4—1222no—
540C22⋊C4—1222no—
541C22⋊C4—1222no—
542C22⋊C4—1222no—
543C22⋊C4—2441no—
544C22⋊C4—2441no—
545C42—612no—
546C42—612no—
547C42—612no—
548C42—612no—
549C42—1221no—
550C42—1221no—
551C42—1221no—
552C42—1221no—
553C42—1221no—
554C42—1222no—
555C42—1221no—
556C42—1222no—
557C23—21no—
558C23—21no—
559C23—21no—
560C23—21no—
561C23—21no—
562C23—21no—
563C23—1221no—
564C23—1221no—
565C23—1221no—
566C23—1221no—
567C23—1221no—
568C23—1221no—
569C23—1221no—
570C23#1451986412yes—
571C23C23×#692311yescharacteristic
572D4—2444no—
573C2×C4—28no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—611no—
590C2×C4—611no—
591C2×C4—611no—
592C2×C4—611no—
593C2×C4—611no—
594C2×C4—611no—
595C2×C4—612no—
596C2×C4—612no—
597C2×C4—1221no—
598C2×C4—1221no—
599C2×C4—1221no—
600C2×C4—1221no—
601C2×C4—1221no—
602C2×C4—1221no—
603C2×C4—1221no—
604C2×C4—1221no—
605C2×C4—1221no—
606C2×C4—1221no—
607C2×C4—1221no—
608C2×C4—1221no—
609C2×C4—1221no—
610C2×C4—1221no—
611C2×C4—1221no—
612C2×C4—1221no—
613C2×C4—2441no—
614C2×C4—2441no—
615C2×C4—2441no—
616C2×C4—2441no—
617C2×C4—2441no—
618C2×C4—2441no—
619C2×C4—2441no—
620C2×C4—2441no—
621C2×C4—2444no—
622C2×C4#1451985612yes—
623C2×C4D4×#692312yes—
624C2×C4#1451986412yes—
625C8—1222no—
626C8—1222no—
627C8—1222no—
628C8—1222no—
629C8—2441no—
630C8—2441no—
631C8—2441no—
632C8—2441no—
633C22—22no—
634C22—22no—
635C22—22no—
636C22—41no—
637C22—41no—
638C22—41no—
639C22—41no—
640C22—2441no—
641C22—2441no—
642C22—2441no—
643C22—2441no—
644C22—2441no—
645C22—2441no—
646C22—2441no—
647C22C2×#1451985611yescharacteristic
648C22C2×D4×#692311yescharacteristic
649C22#41×#692311yescharacteristic
650C22C2×#1451986411yescharacteristic
651C22C2×#1451986411yescharacteristic
652C22#1684084111yescharacteristic
653C22#1684084211yescharacteristic
654C4—22no—
655C4—22no—
656C4—22no—
657C4—41no—
658C4—41no—
659C4—41no—
660C4—611no—
661C4—611no—
662C4—611no—
663C4—611no—
664C4—1222no—
665C4—1222no—
666C4—2441no—
667C4—2441no—
668C4—2441no—
669C4—2441no—
670C2—42no—
671C2—4881no—
672C2#2146227611yescharacteristic
673C2#2146250911yescharacteristic
674C2#2146251411yescharacteristic
675C2#2146253411yescharacteristic
676C2#2146253911yescharacteristic
677C2#2146264611yescharacteristic
678C2#2146265211yescharacteristic
subgroupG/H
center, FrattiniC23C23×#6923
commutator, socleC23×C61C23×C4
FittingC61×#385C4
prime radicalC22×C22⋊D61C2×C4
cosocleC22×Dic61C24
hypercenter#385#6923
hypocenterC61#21272
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
1. C2×#16840787C2semidirect
2. C2×#16840778C2semidirect
5. #21461921C2semidirect
6. #21461916C2semidirect
7. #21461894C2semidirect
8. #21461892C2semidirect
9. #21461891C2semidirect
10. #21461888C2semidirect
11. #21461607C2semidirect
12. #21461548C2semidirect
13. #21461545C2semidirect
14. #21461476C2semidirect
90. C4×#92420D4semidirect
400. C61#21272semidirect

Maximal subgroups

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

subgroupindex
C2×#168407872
C2×#168407782
#214619442
#214619422
#214619212
#214619162
#214618942
#214618922
#214618912
#214618882
#214616072
#214615482
#214615452
#214614762
#214482552
#2127261