Finite Group Databasebeta

← #30609204

Subgroups — #30609204

Order 15616.

1926 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519856C211yesmaximal, characteristic
2C2×#16840713C212yesmaximal, complemented
3C2×#16840704C211yesmaximal, characteristic
4#21461007C212yesmaximal, complemented
5#21461005C212yesmaximal, complemented
6#21461002C214yesmaximal
7#21460996C212yesmaximal, complemented
8#380×D61C211yesmaximal, characteristic
9C2×#14519856—28no—
10C2×#14519856—24no—
11C22×C4⋊#6923C2211yescharacteristic
12C22×C4⋊#6923C2211yescharacteristic
13C22×C4⋊#6923C2211yescharacteristic
14C22×C4⋊#6923C2211yescharacteristic
15C22×C4⋊#6923C2214yes—
16C22×C22⋊#6923C2212yes—
17C22×C22⋊#6923C2212yes—
18C22×C4×#6923C2212yes—
19#16840713—28no—
20#16840704—24no—
21C2×(C2×#6923)⋊C4C2214yes—
22C2×(C2×#6923)⋊C4C2212yes—
23C2×(C2×#6923)⋊C4C2214yes—
24C2×(C2×#6923)⋊C4C2214yes—
25C23×C4×D61C2211yescharacteristic
26C2×C4⋊C4×D61C2212yes—
27C2×C22⋊C4×D61C2212yes—
28#16839622C411yescharacteristic, complemented
29#16839621C412yescomplemented
30#16839620C412yescomplemented
31#16839619C412yescomplemented
32#95×D61C2212yes—
33C61×#380C411yescharacteristic, complemented
34C23×#6923C2312yes—
35C23×#6923C2312yes—
36C23×#6923C2312yes—
37C23×#6923C2312yes—
38#14519856—232no—
39C2×C4⋊#6923—24no—
40C2×C4⋊#6923—24no—
41C2×C4⋊#6923—22no—
42C2×C4⋊#6923—22no—
43C2×C4⋊#6923—28no—
44C2×C4⋊#6923—22no—
45C2×C4⋊#6923—22no—
46C2×C4⋊#6923—24no—
47C2×C4⋊#6923—24no—
48C2×C4⋊#6923—44no—
49C2×C4⋊#6923—44no—
50C2×C22⋊#6923—24no—
51C2×C22⋊#6923—24no—
52C2×C22⋊#6923—24no—
53C2×C22⋊#6923—24no—
54C2×C22⋊#6923—44no—
55C2×C4×#6923—24no—
56C2×C4×#6923—24no—
57C2×C4×#6923D418yes—
58(C2×#6923)⋊C4—28no—
59(C2×#6923)⋊C4—24no—
60(C2×#6923)⋊C4—44no—
61(C2×#6923)⋊C4—44no—
62C24×D61C2311yescharacteristic
63C23×Dic61C2×C411yescharacteristic
64C22×C4×D61—24no—
65C22×C4×D61—24no—
66C22×C4×D61C2×C411yescharacteristic
67C22×C4×D61C2×C411yescharacteristic
68C22×C4×D61D414yes—
69C22×C4×D61Q814yes—
70C22×C4×D61C2314yes—
71C22×C4×D61C2311yescharacteristic
72C22×C4×D61C2311yescharacteristic
73C2×C4⋊Dic61C2×C412yes—
74C2×#11758196C2×C414yes—
75C4⋊C4×D61—24no—
76C4⋊C4×D61—24no—
77C2×C22⋊Dic61C2×C412yes—
78C2×#11758198C2×C414yes—
79C22⋊C4×D61—42no—
80C22⋊C4×D61—42no—
81#14519684C2×C414yes—
82#14519684C2×C412yes—
83C23×C4×C61C2×C411yescharacteristic
84C2×C4⋊C4×C61C2×C412yes—
85C2×C22⋊C4×C61C2×C412yes—
86#95×C61C2×C412yes—
87C24×C61C22×C411yescharacteristic
88C23×D61—22no—
89C23×D61—22no—
90C23×D61—22no—
91C23×D61—21no—
92C23×D61—21no—
93C23×D61—21no—
94C23×D61—21no—
95C23×D61—22no—
96C23×D61C22×C411yescharacteristic
97C23×D61C2×D412yes—
98C23×D61C2×Q812yes—
99C23×D61C2411yescharacteristic
100C22×#6923—22no—
101C22×#6923—22no—
102C22×#6923—22no—
103C22×#6923—22no—
104C22×#6923—22no—
105C22×#6923—22no—
106C22×#6923—22no—
107C22×#6923—22no—
108C22×#6923—22no—
109C22×#6923—22no—
110C22×#6923—22no—
111C22×#6923—22no—
112C22×#6923—22no—
113C22×#6923—22no—
114C22×#6923—24no—
115C22×#6923—24no—
116C22×#6923—22no—
117C22×#6923—24no—
118C22×#6923—24no—
119C22×#6923—22no—
120C22×#6923—22no—
121C22×#6923—22no—
122C22×#6923C2×D414yes—
123C22×#6923C2×D414yes—
124C22×C4×C61—24no—
125C22×C4×C61C4⋊C414yescomplemented
126C22×C4×C61C22×C414yes—
127C22×C4×C61C22×C411yescharacteristic
128C22×C4×C61C22×C411yescharacteristic
129C22×Dic61—24no—
130C22×Dic61C4⋊C414yescomplemented
131C22×Dic61C22×C414yes—
132C22×Dic61C22×C411yescharacteristic
133C22×Dic61C22×C411yescharacteristic
134C2×C4×D61—22no—
135C2×C4×D61—22no—
136C2×C4×D61—24no—
137C2×C4×D61—24no—
138C2×C4×D61—28no—
139C2×C4×D61—216no—
140C2×C4×D61—28no—
141C2×C4×D61—24no—
142C2×C4×D61—24no—
143C2×C4×D61—24no—
144C2×C4×D61—24no—
145C2×C4×D61—24no—
146C2×C4×D61—24no—
147C2×C4×D61C4⋊C414yescomplemented
148C2×C4×D61C4⋊C414yescomplemented
149C2×C4×D61C2×D412yes—
150C2×C4×D61C2×D414yes—
151C2×C4×D61C2×D412yes—
152C2×C4×D61C2×Q812yes—
153C2×C4×D61C2×Q812yes—
154C2×C4×D61#4114yes—
155C22⋊#6923—216no—
156C22⋊#6923—48no—
157C4⋊#6923—28no—
158C4⋊#6923—28no—
159C4⋊#6923—416no—
160C4⋊#6923—44no—
161C4⋊#6923—44no—
162C4×#6923—216no—
163C4⋊C4×C61—24no—
164C22⋊C4×C61—42no—
165C22⋊Dic61—42no—
166#11758198—44no—
167C4⋊Dic61—24no—
168#11758196—28no—
169C23×C61—22no—
170C23×C61—21no—
171C23×C61—21no—
172C23×C61—22no—
173C23×C61C2×C4⋊C412yes—
174C23×C61C23×C411yescharacteristic
175C22×D61—22no—
176C22×D61—21no—
177C22×D61—21no—
178C22×D61—22no—
179C22×D61—22no—
180C22×D61—24no—
181C22×D61—22no—
182C22×D61—22no—
183C22×D61—22no—
184C22×D61—22no—
185C22×D61—22no—
186C22×D61—22no—
187C22×D61—22no—
188C22×D61—24no—
189C22×D61—42no—
190C22×D61—42no—
191C22×D61—42no—
192C22×D61—42no—
193C22×D61—42no—
194C22×D61—42no—
195C22×D61—42no—
196C22×D61—42no—
197C22×D61C2×C4⋊C412yes—
198C22×D61C22×D412yes—
199C22×D61C22×D411yescharacteristic
200C22×D61C22×Q811yescharacteristic
201C22×D61C2×#4112yes—
202C22×D61H(5,𝔽2)12yes—
203C22×D61H(5,𝔽2)11yescharacteristic
204C22×D61H(5,𝔽2)11yescharacteristic
205C22×D612−1+412yes—
206C22×D612−1+411yescharacteristic
207C22×D612−1+411yescharacteristic
208C2×#6923—24no—
209C2×#6923—24no—
210C2×#6923—24no—
211C2×#6923—24no—
212C2×#6923—24no—
213C2×#6923—24no—
214C2×#6923—42no—
215C2×#6923—42no—
216C2×#6923—42no—
217C2×#6923—42no—
218C2×#6923—42no—
219C2×#6923—42no—
220C2×#6923—42no—
221C2×#6923—42no—
222C2×#6923—42no—
223C2×#6923—42no—
224C2×#6923—44no—
225C2×#6923—42no—
226C2×#6923—42no—
227C2×#6923—42no—
228C2×#6923—44no—
229C2×#6923—42no—
230C2×#6923—44no—
231C2×#6923—44no—
232C2×C4×C61—22no—
233C2×C4×C61—28no—
234C2×C4×C61—24no—
235C2×C4×C61—24no—
236C2×C4×C61—24no—
237C2×C4×C61C2×C4⋊C412yes—
238C2×C4×C61C2×C4⋊C412yes—
239C2×C4×C61C4×D414yes—
240C2×Dic61—22no—
241C2×Dic61—28no—
242C2×Dic61—24no—
243C2×Dic61—24no—
244C2×Dic61—24no—
245C2×Dic61C2×C4⋊C412yes—
246C2×Dic61C2×C4⋊C412yes—
247C2×Dic61C4×D414yes—
248C4×D61—22no—
249C4×D61—24no—
250C4×D61—22no—
251C4×D61—28no—
252C4×D61—28no—
253C4×D61—44no—
254C4×D61—44no—
255C4×D61—44no—
256C4×D61—44no—
257C4×D61#12014yes—
258C4×D61C22⋊Q818yes—
259C4×D61#12314yes—
260#14264—611nomaximal, Sylow
261C22×C61—22no—
262C22×C61—22no—
263C22×C61—22no—
264C22×C61—42no—
265C22×C61—42no—
266C22×C61C22×C4⋊C411yescharacteristic
267C22×C61C2×C4×D412yes—
268C22×C61#51811yescharacteristic
269C22×C61#51911yescharacteristic
270C22×C61#52012yes—
271C2×D61—22no—
272C2×D61—22no—
273C2×D61—22no—
274C2×D61—42no—
275C2×D61—42no—
276C2×D61—42no—
277C2×D61—42no—
278C2×D61—42no—
279C2×D61—42no—
280C2×D61—44no—
281C2×D61—44no—
282C2×D61C2×#12011yescharacteristic
283C2×D61C2×C22⋊Q812yes—
284C2×D61C2×#12311yescharacteristic
285C2×D61#53511yescharacteristic
286C2×D61#53512yes—
287C2×D61#53611yescharacteristic
288C2×D61#53612yes—
289C2×D61#53711yescharacteristic
290C2×D61#53712yes—
291C2×D61#53711yescharacteristic
292C2×D61#53712yes—
293C2×D61#54012yes—
294C2×D61#54112yes—
295C2×D61#54212yes—
296C2×D61#54212yes—
297C2×D61#54411yescharacteristic
298C2×D61#54412yes—
299C2×D61#54411yescharacteristic
300#6923—44no—
301#6923—44no—
302#6923—82no—
303#6923—82no—
304C4×C61—22no—
305C4×C61—44no—
306C4×C61#38514yes—
307Dic61—22no—
308Dic61—44no—
309Dic61#38514yes—
310C22×#117—611no—
311C2×#389—612no—
312C2×#380—611no—
313C2×#380—611no—
314#1444—612no—
315#1442—612no—
316#1439—614no—
317C4⋊#95—612no—
318C2×C61—42no—
319C2×C61C2×#38511yescharacteristic
320C2×C61#231611yescharacteristic
321C2×C61#231711yescharacteristic
322C2×C61#232312yes—
323C2×C61#232412yes—
324D61—42no—
325D61#261511yescharacteristic
326D61#261611yescharacteristic
327D61#262411yescharacteristic
328D61#262511yescharacteristic
329D61#262812yes—
330D61#262912yes—
331C24×C4—611no—
332C2×#117—1228no—
333C2×#117—1224no—
334C22×C4⋊C4—612no—
335C22×C4⋊C4—611no—
336C22×C4⋊C4—611no—
337C22×C4⋊C4—611no—
338C22×C4⋊C4—611no—
339C22×C4⋊C4—614no—
340C22×C22⋊C4—612no—
341C22×C22⋊C4—612no—
342C22×C22⋊C4—612no—
343C22×C42—612no—
344#389—1228no—
345#380—611no—
346#380—612no—
347#380—612no—
348#380—612no—
349#380—1224no—
350#380#692311yescharacteristic, complemented
351C2×#95—612no—
352C2×#95—614no—
353C2×#95—612no—
354C2×#95—614no—
355C2×#95—614no—
356C61#1426411yescharacteristic, complemented, Sylow
357C25—611no—
358C23×C4—611no—
359C23×C4—611no—
360C23×C4—614no—
361C23×C4—614no—
362C23×C4—611no—
363C23×C4—611no—
364C23×C4—611no—
365C23×C4—612no—
366C23×C4—612no—
367C23×C4—614no—
368C23×C4—612no—
369C23×C4—612no—
370C23×C4—1224no—
371C23×C4—1224no—
372C23×C4C2×#692311yescharacteristic
373#117—12232no—
374C2×C4⋊C4—614no—
375C2×C4⋊C4—612no—
376C2×C4⋊C4—1224no—
377C2×C4⋊C4—1224no—
378C2×C4⋊C4—1222no—
379C2×C4⋊C4—1222no—
380C2×C4⋊C4—1224no—
381C2×C4⋊C4—1224no—
382C2×C4⋊C4—1224no—
383C2×C4⋊C4—1222no—
384C2×C4⋊C4—1222no—
385C2×C4⋊C4—1224no—
386C2×C4⋊C4—1228no—
387C2×C4⋊C4—2444no—
388C2×C4⋊C4—2444no—
389C2×C4⋊C4C2×#692312yes—
390C2×C22⋊C4—612no—
391C2×C22⋊C4—614no—
392C2×C22⋊C4—1224no—
393C2×C22⋊C4—1224no—
394C2×C22⋊C4—1224no—
395C2×C22⋊C4—1224no—
396C2×C22⋊C4—2442no—
397C2×C22⋊C4—2442no—
398C2×C22⋊C4—2444no—
399C2×C22⋊C4C2×#692312yes—
400C2×C42—618no—
401C2×C42—1224no—
402C2×C42—1224no—
403#95—614no—
404#95—612no—
405#95—1224no—
406#95—1228no—
407#95—2444no—
408#95—2444no—
409#95C2×#692312yes—
410C24—611no—
411C24—612no—
412C24—612no—
413C24—611no—
414C24—1222no—
415C24—1221no—
416C24—1221no—
417C24—1222no—
418C24—1222no—
419C24—1221no—
420C24—1221no—
421C24—1222no—
422C24C22×#692311yescharacteristic
423C22×C4—24no—
424C22×C4—611no—
425C22×C4—612no—
426C22×C4—612no—
427C22×C4—614no—
428C22×C4—614no—
429C22×C4—614no—
430C22×C4—611no—
431C22×C4—612no—
432C22×C4—614no—
433C22×C4—614no—
434C22×C4—612no—
435C22×C4—614no—
436C22×C4—614no—
437C22×C4—614no—
438C22×C4—1228no—
439C22×C4—1224no—
440C22×C4—12216no—
441C22×C4—1228no—
442C22×C4—1222no—
443C22×C4—1222no—
444C22×C4—1224no—
445C22×C4—1224no—
446C22×C4—1224no—
447C22×C4—1224no—
448C22×C4—1224no—
449C22×C4—1224no—
450C22×C4—1224no—
451C22×C4—1224no—
452C22×C4—1222no—
453C22×C4—1222no—
454C22×C4—1222no—
455C22×C4—1222no—
456C22×C4—1222no—
457C22×C4—1222no—
458C22×C4—1222no—
459C22×C4—1222no—
460C22×C4—1222no—
461C22×C4—1222no—
462C22×C4—1222no—
463C22×C4—1222no—
464C22×C4—1222no—
465C22×C4—1222no—
466C22×C4—1224no—
467C22×C4—1222no—
468C22×C4—1224no—
469C22×C4—1224no—
470C22×C4—1224no—
471C22×C4—1222no—
472C22×C4—1222no—
473C22×C4—1222no—
474C22×C4C4⋊#692314yescomplemented
475C22×C4C22×#692314yes—
476C22×C4C22×#692311yescharacteristic
477C22×C4C22×#692311yescharacteristic
478C4⋊C4—24no—
479C4⋊C4—1228no—
480C4⋊C4—1228no—
481C4⋊C4—1228no—
482C4⋊C4—1224no—
483C4⋊C4—2444no—
484C4⋊C4—2444no—
485C4⋊C4—24416no—
486C22⋊C4—42no—
487C22⋊C4—12216no—
488C22⋊C4—2444no—
489C22⋊C4—2442no—
490C22⋊C4—2448no—
491C42—12216no—
492C23—22no—
493C23—21no—
494C23—21no—
495C23—22no—
496C23—611no—
497C23—611no—
498C23—612no—
499C23—612no—
500C23—611no—
501C23—611no—
502C23—611no—
503C23—611no—
504C23—612no—
505C23—612no—
506C23—612no—
507C23—1222no—
508C23—1222no—
509C23—1222no—
510C23—1224no—
511C23—1222no—
512C23—1222no—
513C23—1222no—
514C23—1222no—
515C23—1222no—
516C23—1224no—
517C23—1222no—
518C23—1221no—
519C23—1221no—
520C23—1222no—
521C23—2442no—
522C23—2442no—
523C23—2442no—
524C23—2442no—
525C23—2442no—
526C23—2442no—
527C23—2442no—
528C23—2442no—
529C23C2×C4⋊#692312yes—
530C23C23×#692311yescharacteristic
531C2×C4—22no—
532C2×C4—28no—
533C2×C4—24no—
534C2×C4—24no—
535C2×C4—24no—
536C2×C4—612no—
537C2×C4—614no—
538C2×C4—614no—
539C2×C4—618no—
540C2×C4—614no—
541C2×C4—612no—
542C2×C4—1228no—
543C2×C4—1222no—
544C2×C4—1222no—
545C2×C4—1224no—
546C2×C4—1228no—
547C2×C4—1222no—
548C2×C4—1228no—
549C2×C4—1224no—
550C2×C4—1224no—
551C2×C4—1224no—
552C2×C4—1224no—
553C2×C4—1224no—
554C2×C4—1224no—
555C2×C4—1224no—
556C2×C4—1224no—
557C2×C4—1224no—
558C2×C4—2444no—
559C2×C4—2444no—
560C2×C4—2444no—
561C2×C4—2444no—
562C2×C4—2442no—
563C2×C4—2442no—
564C2×C4—2444no—
565C2×C4—2442no—
566C2×C4—2442no—
567C2×C4—2442no—
568C2×C4—2442no—
569C2×C4—2444no—
570C2×C4—2444no—
571C2×C4—2444no—
572C2×C4—2442no—
573C2×C4—2442no—
574C2×C4—2442no—
575C2×C4—2442no—
576C2×C4—2442no—
577C2×C4—2442no—
578C2×C4—2442no—
579C2×C4—2442no—
580C2×C4C2×C4⋊#692312yes—
581C2×C4C2×C4⋊#692312yes—
582C2×C4D4×#692314yes—
583C22—22no—
584C22—22no—
585C22—22no—
586C22—42no—
587C22—42no—
588C22—611no—
589C22—611no—
590C22—611no—
591C22—611no—
592C22—611no—
593C22—611no—
594C22—612no—
595C22—612no—
596C22—612no—
597C22—612no—
598C22—612no—
599C22—612no—
600C22—612no—
601C22—612no—
602C22—612no—
603C22—611no—
604C22—611no—
605C22—612no—
606C22—1222no—
607C22—1222no—
608C22—1222no—
609C22—2442no—
610C22—2442no—
611C22—2442no—
612C22—2442no—
613C22—2444no—
614C22—2444no—
615C22—2442no—
616C22—2442no—
617C22C22×C4⋊#692311yescharacteristic
618C22C2×D4×#692312yes—
619C22#1684082911yescharacteristic
620C22#1684083011yescharacteristic
621C22#1684083112yes—
622C4—22no—
623C4—44no—
624C4—614no—
625C4—1222no—
626C4—4882no—
627C4—4882no—
628C4—2444no—
629C4—2444no—
630C4—2444no—
631C4#1684070914yes—
632C2—42no—
633C2—611no—
634C2—611no—
635C2—611no—
636C2—611no—
637C2—612no—
638C2—612no—
639C2—2442no—
640C2C2×#1684070911yescharacteristic
641C2#2146229911yescharacteristic
642C2#2146230011yescharacteristic
643C2#2146230612yes—
644C2#2146230712yes—
subgroupG/H
center, FrattiniC23C23×#6923
commutator, socleC23×C61C23×C4
FittingC61×#380C4
prime radicalC24×D61C23
cosocleC23×D61C24
hypercenter#380#6923
hypocenterC61#14264
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #380

Complements

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

NH ≅ G/Ntype
2. C2×#16840713C2semidirect
4. #21461007C2semidirect
5. #21461005C2semidirect
7. #21460996C2semidirect
28. #16839622C4semidirect
29. #16839621C4semidirect
30. #16839620C4semidirect
31. #16839619C4semidirect
33. C61×#380C4semidirect
125. C22×C4×C61C4⋊C4semidirect
130. C22×Dic61C4⋊C4semidirect
147. C2×C4×D61C4⋊C4semidirect
148. C2×C4×D61C4⋊C4semidirect
350. #380#6923semidirect
356. C61#14264semidirect
474. C22×C4C4⋊#6923semidirect

Maximal subgroups

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

subgroupindex
C22×#145198562
C2×#168407132
C2×#168407042
#214610072
#214610052
#214610022
#214609962
#380×D612
#1426461