Finite Group Databasebeta

← #29681805

Subgroups — #29681805

Order 15616.

1994 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840273C211yesmaximal, characteristic
2C22×#14519736C211yesmaximal, characteristic, complemented
3C2×#16839735C212yesmaximal, complemented
4#21446275C214yesmaximal, complemented
5#21446270C214yesmaximal, complemented
6#21445551C212yesmaximal, complemented
7C61×#2280C211yesmaximal, characteristic, complemented
8C22×#11758222C2211yescharacteristic
9#16840273—21no—
10#16840273—21no—
11#16840273—21no—
12#16840273—21no—
13#16840273—22no—
14#16840273—22no—
15C2×#14519760C2212yes—
16C2×#14519756C412yescomplemented
17C2×#14519751C412yescomplemented
18C2×#14519746C2212yes—
19C2×C4×C22⋊D61C414yescomplemented
20C2×#14519736—28no—
21C2×#14519736—21no—
22C2×#14519736—21no—
23C2×#14519736C2212yes—
24C2×#14519736C2212yes—
25C2×#14519736C2211yescharacteristic
26C22×C4⋊Dic61—21no—
27C22×C22⋊Dic61C2212yes—
28C22×C4×Dic61—21no—
29#16839735—28no—
30C2×#14519691C2218yes—
31#16839528C2218yes—
32C24×C4×C61C2211yescharacteristic
33C2×#117×C61C2212yes—
34C61×#381C2212yes—
35C61×#380—22no—
36C61×#379C2212yes—
37C4×C22⋊C4×C61—22no—
38C2×#11758222—24no—
39C2×#11758222—21no—
40C2×#11758222—21no—
41C2×#11758222—21no—
42C2×#11758222—21no—
43C2×#11758222—24no—
44C22×Dic122C2×C411yescharacteristic, complemented
45C22×D244C2×C411yescharacteristic, complemented
46C22×C22⋊D61C2×C414yes—
47C22×C22⋊D61C2312yes—
48C23×Dic61—22no—
49C22×C4×D61C2×C412yescomplemented
50#14519760—22no—
51#14519760—22no—
52#14519760—24no—
53#14519756—22no—
54#14519756—22no—
55#14519756—22no—
56#14519756—22no—
57#14519751—22no—
58#14519751—22no—
59#14519751—22no—
60#14519751—22no—
61#14519746—22no—
62#14519746—22no—
63#14519746—24no—
64C4×C22⋊D61—24no—
65C4×C22⋊D61—24no—
66C4×C22⋊D61—24no—
67C4×C22⋊D61—24no—
68#14519736—28no—
69#14519736—28no—
70#14519736—24no—
71#14519736—21no—
72#14519736—21no—
73#14519736—21no—
74#14519736—21no—
75#14519736—28no—
76#14519736D418yescomplemented
77C2×C4⋊Dic61—28no—
78C2×C4⋊Dic61—22no—
79C2×C4⋊Dic61—22no—
80C2×C4⋊Dic61C2×C412yescomplemented
81C2×#11758196C2×C414yescomplemented
82C2×C22⋊Dic61—22no—
83C2×C22⋊Dic61—28no—
84C2×C22⋊Dic61C2×C414yes—
85C2×C22⋊Dic61C2312yes—
86C2×C22⋊Dic61C2314yes—
87C2×#11758198C2×C414yescomplemented
88C2×C4×Dic61—28no—
89C2×C4×Dic61—22no—
90C2×C4×Dic61—22no—
91C2×C4×Dic61C2×C412yescomplemented
92#14519691—216no—
93C25×C61C2311yescharacteristic
94C23×C4×C61—24no—
95C23×C4×C61—24no—
96C23×C4×C61C2×C412yes—
97C23×C4×C61C2×C412yes—
98C23×C4×C61D411yescharacteristic
99C23×C4×C61D411yescharacteristic
100C23×C4×C61D411yescharacteristic
101C23×C4×C61D411yescharacteristic
102C23×C4×C61D412yes—
103C23×C4×C61D412yes—
104C23×C4×C61C2311yescharacteristic
105C23×C4×C61C2311yescharacteristic
106#117×C61—24no—
107#117×C61—24no—
108C2×C4⋊C4×C61—22no—
109C2×C22⋊C4×C61—24no—
110C2×C22⋊C4×C61C2314yes—
111C2×C42×C61—22no—
112#95×C61—24no—
113C24×C61—22no—
114C24×C61—22no—
115C24×C61—44no—
116C24×C61C22×C412yes—
117C24×C61C2×D411yescharacteristic
118C24×C61C2×D412yes—
119C24×C61C2×D411yescharacteristic
120C24×C61C2411yescharacteristic
121C23×D61C22×C412yes—
122C22×C4×C61—22no—
123C22×C4×C61—22no—
124C22×C4×C61—28no—
125C22×C4×C61—28no—
126C22×C4×C61—22no—
127C22×C4×C61—22no—
128C22×C4×C61—22no—
129C22×C4×C61—22no—
130C22×C4×C61—28no—
131C22×C4×C61—28no—
132C22×C4×C61—22no—
133C22×C4×C61—22no—
134C22×C4×C61—22no—
135C22×C4×C61—22no—
136C22×C4×C61—24no—
137C22×C4×C61C22⋊C412yes—
138C22×C4×C61C22⋊C412yes—
139C22×C4×C61C22⋊C412yes—
140C22×C4×C61C22⋊C412yes—
141C22×C4×C61C22⋊C412yes—
142C22×C4×C61C22⋊C412yes—
143C22×C4×C61C22⋊C412yes—
144C22×C4×C61C22⋊C412yes—
145C22×C4×C61C22×C412yes—
146C22×C4×C61C22×C411yescharacteristic
147C22×C4×C61C22×C411yescharacteristic
148C22×C4×C61C2×D411yescharacteristic
149C22×C4×C61C2×D411yescharacteristic
150C22×C4×C61C2×D412yes—
151C22×C4×C61C2×D411yescharacteristic
152C22×C4×C61C2×D411yescharacteristic
153C22×C4×C61C2×D411yescharacteristic
154C22×C4×C61C2×D411yescharacteristic
155C22×C4×C61C2×D414yes—
156C22×C4×C61#4114yes—
157C2×C22⋊D61—24no—
158C2×C22⋊D61—24no—
159C2×C22⋊D61—24no—
160C2×C22⋊D61—22no—
161C2×C22⋊D61—22no—
162C2×C22⋊D61—24no—
163C2×C22⋊D61—48no—
164C22×Dic61—28no—
165C22×Dic61—24no—
166C22×Dic61—48no—
167C22×Dic61C22×C412yes—
168C22×Dic61C22×C414yes—
169#11758222—42no—
170#11758222—42no—
171#11758222—44no—
172#11758222—44no—
173#11758222—42no—
174#11758222—42no—
175C2×D244—21no—
176C2×D244—21no—
177C2×D244—24no—
178C2×C4×D61—22no—
179C2×C4×D61—22no—
180C2×C4×D61—28no—
181C2×Dic122—21no—
182C2×Dic122—21no—
183C2×Dic122—24no—
184C4⋊C4×C61—44no—
185C22⋊C4×C61—24no—
186C22⋊C4×C61—24no—
187C22⋊C4×C61—48no—
188C42×C61—44no—
189C22⋊Dic61—28no—
190C22⋊Dic61—24no—
191C22⋊Dic61—24no—
192C22⋊Dic61—24no—
193C22⋊Dic61—22no—
194C22⋊Dic61—22no—
195C22⋊Dic61C2×D418yes—
196#11758198—24no—
197#11758198—24no—
198C4⋊Dic61—28no—
199C4⋊Dic61—22no—
200C4⋊Dic61—22no—
201C4⋊Dic61—28no—
202#11758196—24no—
203#11758196—24no—
204C4×Dic61—28no—
205C4×Dic61—22no—
206C4×Dic61—22no—
207C4×Dic61—28no—
208C23×C61—21no—
209C23×C61—21no—
210C23×C61—24no—
211C23×C61—24no—
212C23×C61—21no—
213C23×C61—24no—
214C23×C61—21no—
215C23×C61—24no—
216C23×C61—24no—
217C23×C61—42no—
218C23×C61—42no—
219C23×C61—42no—
220C23×C61—42no—
221C23×C61—48no—
222C23×C61—48no—
223C23×C61C2×C22⋊C412yes—
224C23×C61C2×C22⋊C412yes—
225C23×C61C23×C411yescharacteristic
226C23×C61C22×D411yescharacteristic
227C23×C61C22×D411yescharacteristic
228C23×C61C22×D412yes—
229C23×C61C2×#4112yes—
230C22×D61—22no—
231C22×D61—24no—
232C22×D61—44no—
233C2×C4×C61—24no—
234C2×C4×C61—21no—
235C2×C4×C61—21no—
236C2×C4×C61—24no—
237C2×C4×C61—21no—
238C2×C4×C61—21no—
239C2×C4×C61—24no—
240C2×C4×C61—24no—
241C2×C4×C61—24no—
242C2×C4×C61—24no—
243C2×C4×C61—24no—
244C2×C4×C61—24no—
245C2×C4×C61—24no—
246C2×C4×C61—24no—
247C2×C4×C61—48no—
248C2×C4×C61—44no—
249C2×C4×C61C2×C22⋊C412yes—
250C2×C4×C61C2×C22⋊C412yes—
251C2×C4×C61C2×C22⋊C411yescharacteristic
252C2×C4×C61C2×C22⋊C411yescharacteristic
253C2×C4×C61C2×C22⋊C411yescharacteristic
254C2×C4×C61C2×C22⋊C411yescharacteristic
255C2×C4×C61C4×D414yes—
256C2×C4×C61C4×D414yes—
257C2×C4×C61#12012yes—
258C2×C4×C61#12012yes—
259C2×C4×C61#12114yes—
260C2×C4×C61#12114yes—
261C2×C4×C61#12312yes—
262C2×C4×C61#12312yes—
263C22⋊D61—48no—
264C22⋊D61—42no—
265C22⋊D61—44no—
266C22⋊D61—42no—
267C22⋊D61—48no—
268C2×Dic61—24no—
269C2×Dic61—22no—
270C2×Dic61—24no—
271C2×Dic61—28no—
272C2×Dic61—416no—
273C2×Dic61—48no—
274C2×Dic61—44no—
275D244—42no—
276D244—42no—
277C4×D61—44no—
278C4×D61—44no—
279Dic122—42no—
280Dic122—42no—
281#20983—611nomaximal, Sylow
282C22×C61—24no—
283C22×C61—24no—
284C22×C61—22no—
285C22×C61—22no—
286C22×C61—22no—
287C22×C61—22no—
288C22×C61—22no—
289C22×C61—22no—
290C22×C61—22no—
291C22×C61—22no—
292C22×C61—42no—
293C22×C61—42no—
294C22×C61—48no—
295C22×C61—48no—
296C22×C61—42no—
297C22×C61—42no—
298C22×C61#41014yescomplemented
299C22×C61C22×C22⋊C411yescharacteristic
300C22×C61C2×C4×D412yes—
301C22×C61C2×#12011yescharacteristic
302C22×C61C2×#12112yes—
303C22×C61C2×#12311yescharacteristic
304C2×D61—44no—
305C2×D61—42no—
306C2×D61—84no—
307C4×C61—22no—
308C4×C61—22no—
309C4×C61—84no—
310C4×C61#38612yes—
311C4×C61#38612yes—
312C4×C61#38612yes—
313C4×C61#38612yes—
314Dic61—48no—
315Dic61—44no—
316Dic61—42no—
317C2×#525—611no—
318C22×#117—611no—
319C2×#410—612no—
320#2280D6111yescharacteristic, complemented
321#1899—614no—
322#1898—614no—
323#1740—612no—
324C2×C61—21no—
325C2×C61—22no—
326C2×C61—22no—
327C2×C61—21no—
328C2×C61—24no—
329C2×C61—42no—
330C2×C61C2×#38611yescharacteristic
331C2×C61C2×#41012yes—
332D61—82no—
333C22×#41—611no—
334C24×C4C2×D6111yescharacteristic
335#525—1221no—
336#525—1221no—
337#525—1221no—
338#525—1221no—
339#525—1222no—
340#525—1222no—
341C2×#123—612no—
342C2×C22⋊Q8—612no—
343C2×#121—612no—
344C2×#120—612no—
345C2×C4×D4—614no—
346C2×#117—611no—
347C2×#117—612no—
348C2×#117—612no—
349C2×#117—1228no—
350C2×#117—1221no—
351C2×#117—1221no—
352C2×#117C2×D6112yes—
353C22×C4⋊C4—1221no—
354C22×C22⋊C4—612no—
355C22×C42—1221no—
356#410—1228no—
357C2×#99—618no—
358#381C2×D6112yes—
359#380—22no—
360#379C2×D6112yes—
361C4×C22⋊C4—22no—
362#342—618no—
363C61#2098311yescharacteristic, complemented, Sylow
364C25C22×D6111yescharacteristic
365C2×#41—1221no—
366C2×#41—1221no—
367C2×#41—1224no—
368C2×#41—1224no—
369C2×#41—1221no—
370C2×#41—1221no—
371C22×Q8—611no—
372C22×D4—612no—
373C22×D4—614no—
374C22×D4—611no—
375C23×C4—24no—
376C23×C4—24no—
377C23×C4—612no—
378C23×C4—1222no—
379C23×C4C4×D6112yes—
380C23×C4C4×D6112yes—
381C23×C4D24411yescharacteristic
382C23×C4D24411yescharacteristic
383C23×C4D24411yescharacteristic
384C23×C4D24411yescharacteristic
385C23×C4C22⋊D6112yes—
386C23×C4C22⋊D6112yes—
387C23×C4C22×D6111yescharacteristic
388C23×C4C22×D6111yescharacteristic
389#123—1222no—
390#123—1222no—
391#123—1224no—
392C22⋊Q8—1222no—
393C22⋊Q8—1222no—
394C22⋊Q8—1222no—
395C22⋊Q8—1222no—
396#121—1222no—
397#121—1222no—
398#121—1222no—
399#121—1222no—
400#120—1222no—
401#120—1222no—
402#120—1224no—
403C4×D4—1224no—
404C4×D4—1224no—
405C4×D4—1224no—
406C4×D4—1224no—
407#117—24no—
408#117—24no—
409#117—618no—
410#117—1228no—
411#117—1228no—
412#117—1228no—
413#117—1221no—
414#117—1221no—
415#117—1224no—
416#117—1221no—
417#117—1221no—
418C2×C4⋊C4—22no—
419C2×C4⋊C4—612no—
420C2×C4⋊C4—614no—
421C2×C4⋊C4—1228no—
422C2×C4⋊C4—1222no—
423C2×C4⋊C4—1222no—
424C2×C22⋊C4—24no—
425C2×C22⋊C4—614no—
426C2×C22⋊C4—614no—
427C2×C22⋊C4—612no—
428C2×C22⋊C4—614no—
429C2×C22⋊C4—1228no—
430C2×C22⋊C4—1222no—
431C2×C22⋊C4C22×D6114yes—
432C2×C42—22no—
433C2×C42—612no—
434C2×C42—1228no—
435C2×C42—1222no—
436C2×C42—1222no—
437#99—12216no—
438#95—24no—
439C24—22no—
440C24—22no—
441C24—44no—
442C24—612no—
443C24C2×C4×D6112yes—
444C24C2×D24411yescharacteristic
445C24C2×D24411yescharacteristic
446C24C2×C22⋊D6112yes—
447C24C23×D6111yescharacteristic
448#41—2442no—
449#41—2442no—
450#41—2444no—
451#41—2444no—
452#41—2442no—
453#41—2442no—
454C2×Q8—1221no—
455C2×Q8—1221no—
456C2×Q8—1224no—
457C2×D4—1224no—
458C2×D4—1222no—
459C2×D4—1222no—
460C2×D4—1224no—
461C2×D4—1224no—
462C2×D4—1224no—
463C2×D4—1221no—
464C2×D4—1221no—
465C2×D4—1224no—
466C2×D4—2448no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—28no—
470C22×C4—28no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—28no—
476C22×C4—28no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—24no—
482C22×C4—612no—
483C22×C4—614no—
484C22×C4—1228no—
485C22×C4—1224no—
486C22×C4—1222no—
487C22×C4—1222no—
488C22×C4—1228no—
489C22×C4—2448no—
490C22×C4#1175819812yes—
491C22×C4#1175819812yes—
492C22×C4#1175819812yes—
493C22×C4#1175819812yes—
494C22×C4#1175819812yes—
495C22×C4#1175819812yes—
496C22×C4#1175819812yes—
497C22×C4#1175819812yes—
498C22×C4C2×C4×D6112yes—
499C22×C4C2×C4×D6111yescharacteristic
500C22×C4C2×C4×D6111yescharacteristic
501C22×C4C2×D24411yescharacteristic
502C22×C4C2×D24411yescharacteristic
503C22×C4C2×D24411yescharacteristic
504C22×C4C2×D24411yescharacteristic
505C22×C4D4×D6114yes—
506C22×C4#1175822414yes—
507C22×C4C2×C22⋊D6112yes—
508C22×C4C2×C22⋊D6111yescharacteristic
509C22×C4C2×C22⋊D6111yescharacteristic
510C4⋊C4—44no—
511C4⋊C4—1228no—
512C4⋊C4—1224no—
513C4⋊C4—1224no—
514C4⋊C4—1222no—
515C4⋊C4—1222no—
516C4⋊C4—1228no—
517C22⋊C4—24no—
518C22⋊C4—24no—
519C22⋊C4—48no—
520C22⋊C4—618no—
521C22⋊C4—1228no—
522C22⋊C4—1224no—
523C22⋊C4—1222no—
524C22⋊C4—1222no—
525C22⋊C4—1224no—
526C22⋊C4—1224no—
527C22⋊C4—1224no—
528C22⋊C4—1224no—
529C42—44no—
530C42—1228no—
531C42—1222no—
532C42—1222no—
533C42—1228no—
534C23—24no—
535C23—21no—
536C23—21no—
537C23—24no—
538C23—24no—
539C23—24no—
540C23—21no—
541C23—24no—
542C23—21no—
543C23—42no—
544C23—42no—
545C23—42no—
546C23—42no—
547C23—48no—
548C23—48no—
549C23—1224no—
550C23—1222no—
551C23—2444no—
552C23C2×#1175819812yes—
553C23C2×#1175819812yes—
554C23C22×C4×D6111yescharacteristic
555C23C2×D4×D6112yes—
556C23C22×C22⋊D6111yescharacteristic
557C23C22×D24411yescharacteristic
558C23C2×#1175822412yes—
559Q8—2442no—
560Q8—2442no—
561D4—2448no—
562D4—2448no—
563D4—2442no—
564D4—2444no—
565D4—2442no—
566D4—2442no—
567D4—2442no—
568C2×C4—24no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—24no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—24no—
575C2×C4—24no—
576C2×C4—24no—
577C2×C4—24no—
578C2×C4—24no—
579C2×C4—24no—
580C2×C4—24no—
581C2×C4—24no—
582C2×C4—48no—
583C2×C4—44no—
584C2×C4—1224no—
585C2×C4—1222no—
586C2×C4—1224no—
587C2×C4—1228no—
588C2×C4—24416no—
589C2×C4—2448no—
590C2×C4—2444no—
591C2×C4—2444no—
592C2×C4—2444no—
593C2×C4C2×#1175819812yes—
594C2×C4C2×#1175819812yes—
595C2×C4C2×#1175819811yescharacteristic
596C2×C4C2×#1175819811yescharacteristic
597C2×C4C2×#1175819811yescharacteristic
598C2×C4C2×#1175819811yescharacteristic
599C2×C4#1451973714yes—
600C2×C4#1451973714yes—
601C2×C4#1451974712yes—
602C2×C4#1451974712yes—
603C2×C4#1451974914yes—
604C2×C4#1451974914yes—
605C2×C4#1451976112yes—
606C2×C4#1451976112yes—
607C22—24no—
608C22—24no—
609C22—22no—
610C22—22no—
611C22—22no—
612C22—22no—
613C22—22no—
614C22—22no—
615C22—22no—
616C22—22no—
617C22—42no—
618C22—42no—
619C22—48no—
620C22—48no—
621C22—42no—
622C22—42no—
623C22—4884no—
624C22—2442no—
625C22—2444no—
626C22#1683973514yescomplemented
627C22C22×#1175819811yescharacteristic
628C22C2×#1451973712yes—
629C22C2×#1451974711yescharacteristic
630C22C2×#1451974912yes—
631C22C2×#1451976111yescharacteristic
632C4—22no—
633C4—22no—
634C4—84no—
635C4—2448no—
636C4—2442no—
637C4—2444no—
638C4#1683963912yes—
639C4#1683963912yes—
640C4#1683963912yes—
641C4#1683963912yes—
642C2—22no—
643C2—21no—
644C2—24no—
645C2—21no—
646C2—22no—
647C2—42no—
648C2—4882no—
649C2C2×#1683963911yescharacteristic
650C2C2×#1683973512yes—
subgroupG/H
centerC2×C4C2×#11758198
commutatorC23×C61C23×C4
FrattiniC24C23×D61
FittingC61×#2280C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840273C2
cosocleC24×C61C24
hypercenter#2280D61
hypocenterC61#20983
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C24×C4 ◁ #2280

Complements

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

NH ≅ G/Ntype
2. C22×#14519736C2semidirect
3. C2×#16839735C2semidirect
4. #21446275C2semidirect
5. #21446270C2semidirect
6. #21445551C2semidirect
7. C61×#2280C2semidirect
16. C2×#14519756C4semidirect
17. C2×#14519751C4semidirect
19. C2×C4×C22⋊D61C4semidirect
44. C22×Dic122C2×C4semidirect
45. C22×D244C2×C4semidirect
49. C22×C4×D61C2×C4semidirect
76. #14519736D4semidirect
80. C2×C4⋊Dic61C2×C4semidirect
81. C2×#11758196C2×C4semidirect
87. C2×#11758198C2×C4semidirect
91. C2×C4×Dic61C2×C4semidirect
298. C22×C61#410semidirect
320. #2280D61semidirect
363. C61#20983semidirect
626. C22#16839735semidirect

Maximal subgroups

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

subgroupindex
C2×#168402732
C22×#145197362
C2×#168397352
#214462752
#214462702
#214455512
C61×#22802
#2098361