Finite Group Databasebeta

← #30602782

Subgroups — #30602782

Order 15616.

1338 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840704C211yesmaximal, characteristic
2C2×C4×C22⋊#6923C211yesmaximal, characteristic
3C2×#16840640C214yesmaximal
4C2×#16839619C211yesmaximal, characteristic
5C22×C4⋊#6923—21no—
6C22×C22⋊#6923C2212yes—
7C22×C22⋊#6923C2212yes—
8C22×C4×#6923—21no—
9#16840704—22no—
10#16840704C414yescomplemented
11C4×C22⋊#6923—22no—
12C4×C22⋊#6923C414yescomplemented
13C2×(C2×#6923)⋊C4—21no—
14C2×(C2×#6923)⋊C4—21no—
15#16840640—28no—
16C23×C4×D61C2211yescharacteristic
17C22×C4⋊Dic61C411yescharacteristic, complemented
18C22×#11758198C2212yes—
19#16839619—21no—
20#16839619—21no—
21#16839619—21no—
22#16839619—21no—
23C2×#14519684C412yescomplemented
24C22×C4⋊C4×C61C411yescharacteristic, complemented
25C23×#6923—22no—
26C23×#6923—22no—
27C2×C4⋊#6923—24no—
28C2×C4⋊#6923—42no—
29C2×C4⋊#6923—42no—
30C2×C22⋊#6923—22no—
31C2×C22⋊#6923—22no—
32C2×C22⋊#6923—22no—
33C2×C22⋊#6923—24no—
34C2×C22⋊#6923—24no—
35C2×C22⋊#6923—22no—
36C2×C22⋊#6923C2×C414yes—
37C2×C22⋊#6923C2×C414yes—
38C2×C22⋊#6923D414yes—
39C2×C22⋊#6923Q814yes—
40C2×C4×#6923—24no—
41C2×C4×#6923—42no—
42C2×C4×#6923—42no—
43(C2×#6923)⋊C4—24no—
44(C2×#6923)⋊C4—24no—
45C24×D61C2311yescharacteristic
46C23×Dic61C2×C412yes—
47C23×Dic61C2×C411yescharacteristic
48C22×C4×D61—42no—
49C22×C4×D61—42no—
50C22×C4×D61C2×C412yes—
51C22×C4×D61C2×C412yes—
52C22×C4×D61D411yescharacteristic
53C22×C4×D61D411yescharacteristic
54C22×C4×D61D412yes—
55C22×C4×D61D411yescharacteristic
56C22×C4×D61D411yescharacteristic
57C22×C4×D61Q812yes—
58C2×C4⋊Dic61—21no—
59C2×C4⋊Dic61—21no—
60C2×C4⋊Dic61—42no—
61C2×#11758198—24no—
62C2×#11758198—22no—
63C2×#11758198—22no—
64C2×#11758198—24no—
65#14519684—22no—
66#14519684—22no—
67C23×C4×C61C2×C412yes—
68C23×C4×C61C2×C411yescharacteristic
69C2×C4⋊C4×C61—21no—
70C2×C4⋊C4×C61—21no—
71C2×C4⋊C4×C61—42no—
72C24×C61C22×C411yescharacteristic
73C23×D61—41no—
74C23×D61—41no—
75C23×D61—41no—
76C23×D61—41no—
77C23×D61C22×C411yescharacteristic
78C23×D61C22×C411yescharacteristic
79C23×D61C2×D411yescharacteristic
80C23×D61C2×D411yescharacteristic
81C23×D61C2×D411yescharacteristic
82C23×D61C2×D412yes—
83C23×D61C2×Q811yescharacteristic
84C23×D61C2×Q812yes—
85C23×D61#4112yes—
86C23×D61#4112yes—
87C22×#6923—24no—
88C22×#6923—24no—
89C22×#6923—24no—
90C22×#6923—24no—
91C22×#6923—42no—
92C22×#6923—42no—
93C22×#6923—42no—
94C22×#6923—42no—
95C22×#6923—42no—
96C22×#6923—42no—
97C22×#6923—42no—
98C22×#6923—42no—
99C22×#6923—42no—
100C22×#6923—42no—
101C22×C4×C61—22no—
102C22×C4×C61—22no—
103C22×C4×C61—22no—
104C22×C4×C61—24no—
105C22×C4×C61—42no—
106C22×C4×C61—42no—
107C22×C4×C61C4212yes—
108C22×C4×C61C22⋊C411yescharacteristic
109C22×C4×C61C22⋊C411yescharacteristic
110C22×C4×C61C4⋊C412yes—
111C22×Dic61—22no—
112C22×Dic61—24no—
113C22×Dic61—41no—
114C22×Dic61—41no—
115C22×Dic61—42no—
116C22×Dic61—42no—
117C22×Dic61C4212yes—
118C22×Dic61C22⋊C411yescharacteristic
119C22×Dic61C22⋊C411yescharacteristic
120C22×Dic61C4⋊C412yes—
121C2×C4×D61—22no—
122C2×C4×D61—22no—
123C2×C4×D61—22no—
124C2×C4×D61—22no—
125C2×C4×D61—44no—
126C2×C4×D61—44no—
127C2×C4×D61—44no—
128C2×C4×D61—44no—
129C2×C4×D61—41no—
130C2×C4×D61—41no—
131C2×C4×D61—41no—
132C2×C4×D61—41no—
133C2×C4×D61C22⋊C412yes—
134C2×C4×D61C22⋊C412yes—
135C2×C4×D61C22⋊C412yes—
136C2×C4×D61C22⋊C412yes—
137C2×C4×D61C4⋊C412yes—
138C2×C4×D61C4⋊C412yes—
139C2×C4×D61C4⋊C412yes—
140C2×C4×D61C4⋊C412yes—
141C22⋊#6923—24no—
142C22⋊#6923—24no—
143C22⋊#6923—24no—
144C22⋊#6923—28no—
145C22⋊#6923—44no—
146C22⋊#6923C4⋊C418yescomplemented
147C4⋊#6923—48no—
148C4×#6923—48no—
149C4⋊C4×C61—42no—
150C4⋊C4×C61—42no—
151#11758198—44no—
152#11758198—42no—
153#11758198—42no—
154C4⋊Dic61—42no—
155C4⋊Dic61—42no—
156C23×C61—21no—
157C23×C61—21no—
158C23×C61—21no—
159C23×C61—21no—
160C23×C61C2×C4211yescharacteristic
161C23×C61C2×C22⋊C411yescharacteristic
162C23×C61C2×C4⋊C411yescharacteristic
163C23×C61C4×D412yes—
164C23×C61C4×Q812yes—
165C22×D61—21no—
166C22×D61—21no—
167C22×D61—21no—
168C22×D61—21no—
169C22×D61—21no—
170C22×D61—21no—
171C22×D61—21no—
172C22×D61—21no—
173C22×D61—41no—
174C22×D61—41no—
175C22×D61—41no—
176C22×D61—41no—
177C22×D61—41no—
178C22×D61—41no—
179C22×D61—42no—
180C22×D61—42no—
181C22×D61—41no—
182C22×D61—41no—
183C22×D61—42no—
184C22×D61—42no—
185C22×D61—42no—
186C22×D61—42no—
187C22×D61—42no—
188C22×D61—42no—
189C22×D61C2×C22⋊C411yescharacteristic
190C22×D61C2×C22⋊C411yescharacteristic
191C22×D61C2×C4⋊C411yescharacteristic
192C22×D61C2×C4⋊C411yescharacteristic
193C22×D61C2×C4⋊C412yes—
194C22×D61#11712yes—
195C22×D61C4×D412yes—
196C22×D61C4×Q812yes—
197C22×D61#12112yes—
198C22×D61#12112yes—
199C22×D61C22⋊Q812yes—
200C22×D61C22⋊Q812yes—
201C22×D61#12411yescharacteristic
202C22×D61#12411yescharacteristic
203C22×D61#12512yes—
204C22×D61#12711yescharacteristic
205C22×D61C4⋊Q811yescharacteristic
206C22×D61C4⋊Q812yes—
207C2×#6923—28no—
208C2×#6923—44no—
209C2×#6923—44no—
210C2×#6923—44no—
211C2×#6923—44no—
212C2×#6923—44no—
213C2×#6923—44no—
214C2×#6923—44no—
215C2×#6923—44no—
216C2×#6923—44no—
217C2×#6923—82no—
218C2×#6923—82no—
219C2×#6923—82no—
220C2×#6923—82no—
221C2×C4×C61—21no—
222C2×C4×C61—21no—
223C2×C4×C61—24no—
224C2×C4×C61—24no—
225C2×C4×C61—42no—
226C2×C4×C61—42no—
227C2×C4×C61—42no—
228C2×C4×C61—84no—
229C2×C4×C61#9512yes—
230C2×C4×C61#9512yes—
231C2×C4×C61#9912yes—
232C2×C4×C61#9912yes—
233C2×Dic61—21no—
234C2×Dic61—21no—
235C2×Dic61—21no—
236C2×Dic61—21no—
237C2×Dic61—42no—
238C2×Dic61—42no—
239C2×Dic61—42no—
240C2×Dic61—42no—
241C2×Dic61—42no—
242C2×Dic61—84no—
243C2×Dic61#9512yes—
244C2×Dic61#9512yes—
245C4×D61—24no—
246C4×D61—24no—
247C4×D61—24no—
248C4×D61—24no—
249C4×D61—42no—
250C4×D61—42no—
251C4×D61—42no—
252C4×D61—42no—
253#10854—611nomaximal, Sylow
254C22×C61—22no—
255C22×C61—22no—
256C22×C61—21no—
257C22×C61—21no—
258C22×C61—21no—
259C22×C61—21no—
260C22×C61—22no—
261C22×C61—22no—
262C22×C61C2×#9511yescharacteristic
263C22×C61C4×C4⋊C412yes—
264C22×C61#38912yes—
265C22×C61#39011yescharacteristic
266C22×C61#39111yescharacteristic
267C22×C61C2×#9911yescharacteristic
268C22×C61C2×#9911yescharacteristic
269C22×C61#41011yescharacteristic
270C22×C61#41011yescharacteristic
271C2×D61—22no—
272C2×D61—22no—
273C2×D61—21no—
274C2×D61—21no—
275C2×D61—21no—
276C2×D61—21no—
277C2×D61—21no—
278C2×D61—21no—
279C2×D61—21no—
280C2×D61—21no—
281C2×D61—21no—
282C2×D61—21no—
283C2×D61—21no—
284C2×D61—21no—
285C2×D61—22no—
286C2×D61—22no—
287C2×D61—21no—
288C2×D61—21no—
289C2×D61—21no—
290C2×D61—21no—
291C2×D61—42no—
292C2×D61—42no—
293C2×D61—42no—
294C2×D61—42no—
295C2×D61—42no—
296C2×D61—42no—
297C2×D61—42no—
298C2×D61—42no—
299C2×D61#38012yes—
300C2×D61#38211yescharacteristic
301C2×D61#38411yescharacteristic
302C2×D61#38912yes—
303C2×D61#39011yescharacteristic
304C2×D61#39111yescharacteristic
305#6923—48no—
306#6923—84no—
307C4×C61—22no—
308C4×C61—82no—
309C4×C61#34214yescomplemented
310Dic61—22no—
311Dic61—22no—
312Dic61—82no—
313C2×#380—611no—
314C2×#380—611no—
315C2×C4×C22⋊C4—611no—
316C2×#342—614no—
317C2×C61—22no—
318C2×C61—22no—
319C2×C61C4⋊#9511yescharacteristic
320C2×C61C2×#34211yescharacteristic
321C2×C61#174011yescharacteristic
322C2×C61#196411yescharacteristic
323C2×C61#196411yescharacteristic
324C2×C61#199611yescharacteristic
325C2×C61#199611yescharacteristic
326D61—22no—
327D61—21no—
328D61—21no—
329D61—21no—
330D61—22no—
331D61—21no—
332C24×C4—611no—
333C22×C4⋊C4—611no—
334C22×C4⋊C4—1221no—
335C22×C4⋊C4#692311yescharacteristic, complemented
336C22×C22⋊C4—612no—
337C22×C22⋊C4—612no—
338C22×C22⋊C4—612no—
339C22×C42—1221no—
340#380—614no—
341#380—1221no—
342#380—1221no—
343#380—1221no—
344#380—1221no—
345#380—1222no—
346C4×C22⋊C4—614no—
347C4×C22⋊C4—1222no—
348C2×#95—612no—
349C2×#95—1221no—
350C2×#95—1221no—
351#342—1228no—
352C61#1085411yescharacteristic, complemented, Sylow
353C25—611no—
354C23×C4—611no—
355C23×C4—611no—
356C23×C4—611no—
357C23×C4—612no—
358C23×C4—612no—
359C23×C4—612no—
360C23×C4—612no—
361C23×C4—611no—
362C23×C4—611no—
363C23×C4—612no—
364C23×C4—1222no—
365C23×C4—1222no—
366C23×C4—2442no—
367C23×C4—2442no—
368C23×C4C2×#692312yes—
369C23×C4C2×#692311yescharacteristic
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—42no—
373C2×C4⋊C4—1224no—
374C2×C4⋊C4—1221no—
375C2×C4⋊C4—1221no—
376C2×C4⋊C4—2442no—
377C2×C4⋊C4—2442no—
378C2×C4⋊C4—2442no—
379C2×C22⋊C4—614no—
380C2×C22⋊C4—614no—
381C2×C22⋊C4—614no—
382C2×C22⋊C4—614no—
383C2×C22⋊C4—1222no—
384C2×C22⋊C4—1222no—
385C2×C22⋊C4—1222no—
386C2×C22⋊C4—1224no—
387C2×C22⋊C4—1224no—
388C2×C22⋊C4—1224no—
389C2×C22⋊C4—1222no—
390C2×C22⋊C4—1222no—
391C2×C22⋊C4—1224no—
392C2×C22⋊C4—1222no—
393C2×C42—1224no—
394C2×C42—2442no—
395C2×C42—2442no—
396#95—1222no—
397#95—1222no—
398#95—1224no—
399#95—1224no—
400C24—611no—
401C24—611no—
402C24—611no—
403C24—611no—
404C24—611no—
405C24—611no—
406C24—612no—
407C24—612no—
408C24—612no—
409C24—612no—
410C24—2441no—
411C24—2441no—
412C24—2441no—
413C24—2441no—
414C24C22×#692311yescharacteristic
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—24no—
419C22×C4—42no—
420C22×C4—42no—
421C22×C4—611no—
422C22×C4—611no—
423C22×C4—612no—
424C22×C4—612no—
425C22×C4—612no—
426C22×C4—612no—
427C22×C4—612no—
428C22×C4—612no—
429C22×C4—612no—
430C22×C4—612no—
431C22×C4—612no—
432C22×C4—612no—
433C22×C4—1222no—
434C22×C4—1222no—
435C22×C4—1222no—
436C22×C4—1222no—
437C22×C4—1224no—
438C22×C4—1224no—
439C22×C4—1224no—
440C22×C4—1224no—
441C22×C4—1224no—
442C22×C4—1222no—
443C22×C4—2444no—
444C22×C4—2444no—
445C22×C4—2444no—
446C22×C4—2444no—
447C22×C4—2441no—
448C22×C4—2441no—
449C22×C4—2441no—
450C22×C4—2441no—
451C22×C4—2441no—
452C22×C4—2441no—
453C22×C4—2442no—
454C22×C4—2442no—
455C22×C4—2442no—
456C22×C4—2442no—
457C22×C4—2442no—
458C22×C4—2442no—
459C22×C4—2442no—
460C22×C4—2442no—
461C22×C4—2442no—
462C22×C4—2442no—
463C22×C4—2442no—
464C22×C4—2442no—
465C22×C4C4×#692312yes—
466C22×C4C4⋊#692312yes—
467C22×C4C22⋊#692311yescharacteristic
468C22×C4C22⋊#692311yescharacteristic
469C4⋊C4—42no—
470C4⋊C4—42no—
471C4⋊C4—2442no—
472C4⋊C4—2448no—
473C4⋊C4—2442no—
474C22⋊C4—618no—
475C22⋊C4—1224no—
476C22⋊C4—1224no—
477C22⋊C4—1224no—
478C22⋊C4—1228no—
479C22⋊C4—2444no—
480C22⋊C4—2442no—
481C22⋊C4—2442no—
482C22⋊C4—2444no—
483C42—2448no—
484C23—21no—
485C23—21no—
486C23—21no—
487C23—21no—
488C23—612no—
489C23—611no—
490C23—611no—
491C23—612no—
492C23—611no—
493C23—611no—
494C23—611no—
495C23—611no—
496C23—611no—
497C23—611no—
498C23—612no—
499C23—612no—
500C23—612no—
501C23—612no—
502C23—612no—
503C23—612no—
504C23—612no—
505C23—612no—
506C23—1221no—
507C23—1221no—
508C23—1221no—
509C23—1221no—
510C23—1221no—
511C23—1221no—
512C23—1221no—
513C23—1221no—
514C23—2441no—
515C23—2441no—
516C23—2441no—
517C23—2441no—
518C23—2441no—
519C23—2441no—
520C23—2441no—
521C23—2441no—
522C23—2442no—
523C23—2442no—
524C23—2442no—
525C23—2442no—
526C23—2442no—
527C23—2442no—
528C23—2442no—
529C23—2442no—
530C23C2×C4×#692311yescharacteristic
531C23C2×C22⋊#692311yescharacteristic
532C23C2×C4⋊#692311yescharacteristic
533C23D4×#692312yes—
534C23Q8×#692312yes—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—24no—
538C2×C4—24no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—84no—
543C2×C4—612no—
544C2×C4—612no—
545C2×C4—1221no—
546C2×C4—1221no—
547C2×C4—1221no—
548C2×C4—1221no—
549C2×C4—1224no—
550C2×C4—1224no—
551C2×C4—1224no—
552C2×C4—1224no—
553C2×C4—1228no—
554C2×C4—4882no—
555C2×C4—4882no—
556C2×C4—4882no—
557C2×C4—4882no—
558C2×C4—4884no—
559C2×C4—2442no—
560C2×C4—2442no—
561C2×C4—2442no—
562C2×C4—2442no—
563C2×C4—2442no—
564C2×C4—2442no—
565C2×C4—2444no—
566C2×C4—2444no—
567C2×C4—2444no—
568C2×C4—2442no—
569C2×C4—2442no—
570C2×C4—2442no—
571C2×C4—2444no—
572C2×C4—2444no—
573C2×C4—2444no—
574C2×C4—2444no—
575C2×C4—2444no—
576C2×C4—2444no—
577C2×C4(C2×#6923)⋊C412yes—
578C2×C4(C2×#6923)⋊C412yes—
579C2×C4#1451983512yes—
580C2×C4#1451983612yes—
581C22—21no—
582C22—21no—
583C22—21no—
584C22—21no—
585C22—22no—
586C22—22no—
587C22—22no—
588C22—22no—
589C22—612no—
590C22—611no—
591C22—611no—
592C22—611no—
593C22—612no—
594C22—611no—
595C22—1221no—
596C22—1221no—
597C22—1221no—
598C22—1221no—
599C22—1221no—
600C22—1221no—
601C22—1221no—
602C22—1221no—
603C22—1221no—
604C22—1222no—
605C22—1221no—
606C22—1221no—
607C22—1222no—
608C22—1221no—
609C22—1221no—
610C22—1222no—
611C22—1221no—
612C22—1221no—
613C22—1222no—
614C22—1221no—
615C22—2442no—
616C22—2442no—
617C22—2442no—
618C22—2442no—
619C22—2442no—
620C22—2442no—
621C22—2442no—
622C22—2442no—
623C22C2×(C2×#6923)⋊C411yescharacteristic
624C22C4⋊C4×#692312yes—
625C22#1684071312yes—
626C22#1684071411yescharacteristic
627C22(C2×#6923)⋊Q811yescharacteristic
628C22C2×#1451983511yescharacteristic
629C22C2×#1451983611yescharacteristic
630C22#1684074211yescharacteristic
631C22#1684074311yescharacteristic
632C4—22no—
633C4—82no—
634C4—1222no—
635C4—1222no—
636C4—4884no—
637C4—4882no—
638C4—2448no—
639C4#1684064014yescomplemented
640C2—22no—
641C2—22no—
642C2—1221no—
643C2—1222no—
644C2—1221no—
645C2—1221no—
646C2—1222no—
647C2—1221no—
648C2#2146099611yescharacteristic
649C2C2×#1684064011yescharacteristic
650C2#2146151911yescharacteristic
651C2#2146195811yescharacteristic
652C2#2146195911yescharacteristic
653C2#2146200811yescharacteristic
654C2#2146200911yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC23×C61C2×C42
FrattiniC24C22×#6923
FittingC22×C4⋊C4×C61C4
socleC23×C61C2×C22⋊C4
prime radical, cosocleC24×D61C23
hypercenterC22×C4⋊C4#6923
hypocenterC61#10854
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
10. #16840704C4semidirect
12. C4×C22⋊#6923C4semidirect
17. C22×C4⋊Dic61C4semidirect
23. C2×#14519684C4semidirect
24. C22×C4⋊C4×C61C4semidirect
146. C22⋊#6923C4⋊C4semidirect
309. C4×C61#342semidirect
335. C22×C4⋊C4#6923semidirect
352. C61#10854semidirect
639. C4#16840640semidirect

Maximal subgroups

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

subgroupindex
C2×#168407042
C2×C4×C22⋊#69232
C2×#168406402
C2×#168396192
#1085461