Finite Group Databasebeta

← #30617799

Subgroups — #30617799

Order 15616.

1442 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840787C212yesmaximal, complemented
2#21461944C212yesmaximal, complemented
3#21461943C212yesmaximal, complemented
4#21461942C212yesmaximal, complemented
5#21461940C212yesmaximal, complemented
6#21461643C212yesmaximal, complemented
7#21461642C211yesmaximal, characteristic, complemented
8#21461642C211yesmaximal, characteristic, complemented
9C2×#16840272C211yesmaximal, characteristic
10#16840787—28no—
11C2×#14519844C2212yescomplemented
12C2×C4⋊#92420C2212yescomplemented
13C2×#14519834C2212yes—
14C2×#14519834C2212yes—
15C2×#14519834C2211yescharacteristic
16C2×#14519834C2212yes—
17C2×#14519834C2211yescharacteristic
18C2×C22⋊#92420C2211yescharacteristic
19C2×C22⋊#92420C2212yes—
20C2×C22⋊#92420C2211yescharacteristic
21C2×C22⋊#92420C2212yescomplemented
22C2×C22⋊#92420C2212yescomplemented
23C2×C22⋊#92420C2212yescomplemented
24C2×C22⋊#92420C2212yescomplemented
25C2×#14519832C2212yescomplemented
26C2×C4×#92420C2212yescomplemented
27C22×#11758224C2211yescharacteristic
28C23×C4×D61C2211yescharacteristic
29#16840272—28no—
30C2×#14519759C412yes—
31C2×#14519757C411yescharacteristic
32C2×#14519756C411yescharacteristic
33C2×#14519748C411yescharacteristic
34C2×#14519745C412yes—
35C2×D4×Dic61C2212yes—
36C2×#14519737C2212yes—
37C2×#14519735C2211yescharacteristic
38C2×#121×C61C411yescharacteristic
39C22×#92420C2312yes—
40C22×#92420C2312yes—
41C22×#92420C2312yes—
42C22×#92420C2312yes—
43#14519844—24no—
44C4⋊#92420—24no—
45#14519834—24no—
46#14519834—24no—
47#14519834—41no—
48#14519834—42no—
49#14519834—41no—
50C22⋊#92420—41no—
51C22⋊#92420—42no—
52C22⋊#92420—41no—
53C22⋊#92420—42no—
54C22⋊#92420—42no—
55C22⋊#92420—42no—
56C22⋊#92420—42no—
57#14519832—24no—
58C4×#92420—24no—
59C24×D61C2×C411yescharacteristic
60C2×#11758224—24no—
61C2×#11758224—41no—
62C2×#11758224—41no—
63C2×#11758224—42no—
64C22×Dic122C2×C411yescharacteristic
65C22×C22⋊D61C2×C412yes—
66C22×C22⋊D61C2×C412yes—
67C23×Dic61C2311yescharacteristic
68C23×Dic61C2312yes—
69C22×C4×D61—24no—
70C22×C4×D61—42no—
71C22×C4×D61—41no—
72C22×C4×D61—41no—
73C22×C4×D61C2×C411yescharacteristic
74C22×C4×D61C2×C411yescharacteristic
75C22×C4×D61C2311yescharacteristic
76C22×C4×D61C2311yescharacteristic
77#14519759—28no—
78#14519757—24no—
79#14519756—24no—
80#14519748—24no—
81#14519745—28no—
82D4×Dic61—24no—
83D4×Dic61—24no—
84#14519737—24no—
85#14519737—24no—
86#14519735D418yes—
87C2×C4⋊Dic61C2×C412yes—
88C2×C4⋊Dic61C2×C411yescharacteristic
89C2×#11758196C2×C412yes—
90C2×C22⋊Dic61C2×C412yes—
91C2×C22⋊Dic61C2×C412yes—
92C2×#11758198C2×C412yes—
93C2×#11758198C2×C412yes—
94C2×C4×Dic61C2312yes—
95C22×D4×C61C2×C412yes—
96C22×D4×C61C2×C411yescharacteristic
97C23×C4×C61C2×C411yescharacteristic
98#121×C61—24no—
99C2×C4⋊C4×C61C2×C411yescharacteristic
100C2×C22⋊C4×C61C2×C412yes—
101C24×C61C22×C412yes—
102C24×C61C22×C411yescharacteristic
103C23×D61—22no—
104C23×D61—22no—
105C23×D61—22no—
106C23×D61—41no—
107C23×D61—41no—
108C23×D61—41no—
109C23×D61—41no—
110C23×D61C22×C411yescharacteristic
111C23×D61C22×C411yescharacteristic
112C2×D4×C61—24no—
113C2×D4×C61—22no—
114C2×D4×C61—24no—
115C2×D4×C61—41no—
116C2×D4×C61—41no—
117C2×D4×C61—42no—
118C22×C4×C61—22no—
119C22×C4×C61—41no—
120C22×C4×C61—41no—
121C22×C4×C61C22×C411yescharacteristic
122C22×C4×C61C22×C411yescharacteristic
123C22×C4×C61C22×C412yes—
124C2×C22⋊D61—24no—
125C2×C22⋊D61—24no—
126C2×C22⋊D61—24no—
127C2×C22⋊D61—42no—
128C2×C22⋊D61—42no—
129C2×C22⋊D61—42no—
130C22×Dic61—22no—
131C22×Dic61—22no—
132C22×Dic61—22no—
133C22×Dic61—21no—
134C22×Dic61—21no—
135C22×Dic61—22no—
136C22×Dic61—22no—
137C22×Dic61—22no—
138C22×Dic61—22no—
139C22×Dic61—22no—
140C22×Dic61C22×C411yescharacteristic
141C22×Dic61C22×C412yes—
142C22×Dic61C22×C412yes—
143C22×Dic61C2411yescharacteristic
144#11758224—48no—
145#11758224—48no—
146C2×C4×D61—21no—
147C2×C4×D61—21no—
148C2×C4×D61—22no—
149C2×C4×D61—22no—
150C2×C4×D61—22no—
151C2×C4×D61—22no—
152C2×C4×D61—21no—
153C2×C4×D61—21no—
154C2×C4×D61—22no—
155C2×C4×D61—48no—
156C2×C4×D61—48no—
157C2×C4×D61—41no—
158C2×C4×D61—41no—
159C2×C4×D61—41no—
160C2×C4×D61—41no—
161C2×C4×D61C2×D414yes—
162C2×Dic122—22no—
163C2×Dic122—41no—
164C2×Dic122—41no—
165C2×#92420—22no—
166C2×#92420—22no—
167C2×#92420—22no—
168C2×#92420—22no—
169C2×#92420—22no—
170C2×#92420—22no—
171C2×#92420—22no—
172C2×#92420—22no—
173C2×#92420—22no—
174C2×#92420—22no—
175C2×#92420—22no—
176C2×#92420—22no—
177C4⋊C4×C61C22⋊C414yes—
178C22⋊C4×C61—24no—
179C22⋊Dic61—24no—
180C22⋊Dic61—24no—
181#11758198—24no—
182#11758198C22⋊C418yes—
183C4⋊Dic61—24no—
184C4⋊Dic61C22⋊C414yes—
185#11758196—24no—
186C4×Dic61C2×D414yes—
187C4×Dic61C2×D414yes—
188C23×C61—21no—
189C23×C61—21no—
190C23×C61—21no—
191C23×C61—21no—
192C23×C61—21no—
193C23×C61—21no—
194C23×C61—22no—
195C23×C61—22no—
196C23×C61—22no—
197C23×C61—22no—
198C23×C61—22no—
199C23×C61—22no—
200C23×C61—22no—
201C23×C61#13112yes—
202C23×C61C23×C411yescharacteristic
203C22×D61—21no—
204C22×D61—21no—
205C22×D61—21no—
206C22×D61—21no—
207C22×D61—21no—
208C22×D61—21no—
209C22×D61—21no—
210C22×D61—21no—
211C22×D61—21no—
212C22×D61—21no—
213C22×D61—21no—
214C22×D61—21no—
215C22×D61—44no—
216C22×D61—44no—
217C22×D61—44no—
218C22×D61—44no—
219C22×D61—44no—
220C22×D61—44no—
221C22×D61—44no—
222C22×D61C2×C22⋊C412yes—
223C22×D61#13112yes—
224D4×C61—48no—
225D4×C61—44no—
226C2×C4×C61—21no—
227C2×C4×C61—21no—
228C2×C4×C61—22no—
229C2×C4×C61—22no—
230C2×C4×C61—21no—
231C2×C4×C61—21no—
232C2×C4×C61—21no—
233C2×C4×C61—44no—
234C2×C4×C61C2×C22⋊C414yes—
235C2×C4×C61C2×C22⋊C412yes—
236C22⋊D61—48no—
237C22⋊D61—48no—
238C2×Dic61—22no—
239C2×Dic61—22no—
240C2×Dic61—22no—
241C2×Dic61—21no—
242C2×Dic61—22no—
243C2×Dic61—22no—
244C2×Dic61—21no—
245C2×Dic61—21no—
246C2×Dic61—42no—
247C2×Dic61—42no—
248C2×Dic61—42no—
249C2×Dic61—42no—
250C2×Dic61—42no—
251C2×Dic61—42no—
252C2×Dic61C2×C22⋊C414yes—
253C2×Dic61C22×D412yes—
254C2×Dic61H(5,𝔽2)11yescharacteristic
255C2×Dic61H(5,𝔽2)11yescharacteristic
256C2×Dic61H(5,𝔽2)12yes—
257C4×D61—24no—
258C4×D61—24no—
259C4×D61—44no—
260C4×D61—44no—
261C4×D61—42no—
262C4×D61—42no—
263Dic122—44no—
264#92420—42no—
265#92420—42no—
266#92420—42no—
267#92420—42no—
268#21792—611nomaximal, Sylow
269C22×C61—22no—
270C22×C61—22no—
271C22×C61—22no—
272C22×C61—41no—
273C22×C61—41no—
274C22×C61—41no—
275C22×C61—41no—
276C22×C61—42no—
277C22×C61—42no—
278C22×C61—42no—
279C22×C61—42no—
280C22×C61—42no—
281C22×C61—42no—
282C22×C61—42no—
283C22×C61C22×C22⋊C411yescharacteristic
284C22×C61#51811yescharacteristic
285C22×C61#51811yescharacteristic
286C22×C61C2×#13111yescharacteristic
287C22×C61C2×#13111yescharacteristic
288C22×C61#56811yescharacteristic
289C22×C61#56811yescharacteristic
290C2×D61—22no—
291C2×D61—22no—
292C2×D61—22no—
293C2×D61—22no—
294C2×D61—22no—
295C2×D61—22no—
296C2×D61—416no—
297C2×D61—41no—
298C2×D61—41no—
299C2×D61—41no—
300C2×D61—41no—
301C2×D61—41no—
302C2×D61—41no—
303C2×D61—41no—
304C2×D61—41no—
305C4×C61—22no—
306C4×C61—24no—
307C4×C61—41no—
308Dic61—24no—
309Dic61—42no—
310Dic61—41no—
311Dic61#53512yes—
312Dic61#53512yes—
313C2×#525—611no—
314C2×#433—612no—
315#1955—612no—
316#1955—612no—
317#1954—612no—
318#1954—612no—
319#1780—612no—
320#1779—611no—
321#1779—611no—
322C2×C61—42no—
323C2×C61—82no—
324C2×C61#230911yescharacteristic
325C2×C61#288011yescharacteristic
326C2×C61#288011yescharacteristic
327C2×C61#297611yescharacteristic
328C2×C61#297611yescharacteristic
329C2×C61#297711yescharacteristic
330C2×C61#297811yescharacteristic
331D61—42no—
332D61—42no—
333C22×#41—611no—
334C24×C4—611no—
335#525—1228no—
336C2×#123—612no—
337C2×C22⋊Q8—611no—
338C2×C22⋊Q8—611no—
339C2×#121—611no—
340C2×#121#692311yescharacteristic
341C2×#120—612no—
342C2×C4×D4—612no—
343C2×C4×D4—612no—
344C2×#117—611no—
345#433—1228no—
346C2×C4⋊C8—612no—
347C2×C4⋊C8—612no—
348C2×C22⋊C8—612no—
349C2×C22⋊C8—612no—
350C2×C22⋊C8—611no—
351C2×C22⋊C8—612no—
352C2×C22⋊C8—611no—
353C2×C22⋊C8—612no—
354C2×C22⋊C8—612no—
355C2×C22⋊C8—612no—
356C2×C22⋊C8—612no—
357C2×C22⋊C8—611no—
358C2×C22⋊C8—612no—
359C2×C22⋊C8—611no—
360C2×#97—612no—
361C2×C4×C8—612no—
362C61#2179211yescharacteristic, complemented, Sylow
363C25—611no—
364C2×#41—1224no—
365C2×#41—2441no—
366C2×#41—2441no—
367C2×#41—2442no—
368C22×Q8—611no—
369C22×D4—612no—
370C22×D4—612no—
371C22×D4C2×#692312yes—
372C22×D4C2×#692311yescharacteristic
373C23×C4—611no—
374C23×C4—611no—
375C23×C4—612no—
376C23×C4—611no—
377C23×C4—611no—
378C23×C4—611no—
379C23×C4—1224no—
380C23×C4—2442no—
381C23×C4—2441no—
382C23×C4—2441no—
383C23×C4C2×#692311yescharacteristic
384C22×C8—612no—
385C22×C8—612no—
386C22×C8—612no—
387C22×C8—612no—
388#123—1228no—
389C22⋊Q8—1224no—
390C22⋊Q8—1224no—
391#121—24no—
392#121—1224no—
393#120—1228no—
394C4×D4—1224no—
395C4×D4—1224no—
396C4×D4—1224no—
397C4×D4—1224no—
398#117—618no—
399C2×C4⋊C4—611no—
400C2×C4⋊C4—612no—
401C2×C4⋊C4—612no—
402C2×C4⋊C4C2×#692311yescharacteristic
403C2×C22⋊C4—612no—
404C2×C22⋊C4—612no—
405C2×C22⋊C4—612no—
406C2×C22⋊C4—612no—
407C2×C22⋊C4C2×#692312yes—
408C2×C42—612no—
409C4⋊C8—1224no—
410C4⋊C8—1224no—
411C22⋊C8—1224no—
412C22⋊C8—1224no—
413C22⋊C8—2441no—
414C22⋊C8—2442no—
415C22⋊C8—2441no—
416C22⋊C8—2442no—
417C22⋊C8—2442no—
418C22⋊C8—2442no—
419C22⋊C8—2442no—
420C22⋊C8—2441no—
421C22⋊C8—2442no—
422C22⋊C8—2441no—
423#97—1224no—
424C4×C8—1224no—
425C24—611no—
426C24—611no—
427C24—1222no—
428C24—1222no—
429C24—1222no—
430C24—2441no—
431C24—2441no—
432C24—2441no—
433C24—2441no—
434C24C22×#692312yes—
435C24C22×#692311yescharacteristic
436#41—2448no—
437#41—2448no—
438C2×Q8—1222no—
439C2×Q8—2441no—
440C2×Q8—2441no—
441C2×D4—24no—
442C2×D4—24no—
443C2×D4—22no—
444C2×D4—41no—
445C2×D4—41no—
446C2×D4—42no—
447C2×D4—1224no—
448C2×D4—1224no—
449C2×D4—1224no—
450C2×D4—2442no—
451C2×D4—2442no—
452C2×D4—2442no—
453C22×C4—22no—
454C22×C4—41no—
455C22×C4—41no—
456C22×C4—611no—
457C22×C4—612no—
458C22×C4—614no—
459C22×C4—611no—
460C22×C4—612no—
461C22×C4—1221no—
462C22×C4—1221no—
463C22×C4—1222no—
464C22×C4—1221no—
465C22×C4—1221no—
466C22×C4—1222no—
467C22×C4—1222no—
468C22×C4—1222no—
469C22×C4—1221no—
470C22×C4—1221no—
471C22×C4—1222no—
472C22×C4—1222no—
473C22×C4—1222no—
474C22×C4—1222no—
475C22×C4—1222no—
476C22×C4—1222no—
477C22×C4—1222no—
478C22×C4—1222no—
479C22×C4—1222no—
480C22×C4—2441no—
481C22×C4—2441no—
482C22×C4—2441no—
483C22×C4—2441no—
484C22×C4—2448no—
485C22×C4—2448no—
486C22×C4C22×#692311yescharacteristic
487C22×C4C22×#692312yes—
488C22×C4C22×#692311yescharacteristic
489C2×C8—1222no—
490C2×C8—1222no—
491C2×C8—1222no—
492C2×C8—1222no—
493C2×C8—1222no—
494C2×C8—1222no—
495C2×C8—1222no—
496C2×C8—1222no—
497C2×C8—1222no—
498C2×C8—1222no—
499C2×C8—1222no—
500C2×C8—1222no—
501C4⋊C4—614no—
502C4⋊C4—1224no—
503C4⋊C4—1224no—
504C4⋊C4C22⋊#692314yes—
505C22⋊C4—24no—
506C22⋊C4—618no—
507C22⋊C4—1224no—
508C22⋊C4—1224no—
509C22⋊C4—1224no—
510C42—614no—
511C42—614no—
512C23—21no—
513C23—21no—
514C23—21no—
515C23—21no—
516C23—21no—
517C23—21no—
518C23—22no—
519C23—22no—
520C23—22no—
521C23—22no—
522C23—22no—
523C23—22no—
524C23—22no—
525C23—612no—
526C23—612no—
527C23—1221no—
528C23—1221no—
529C23—1221no—
530C23—1221no—
531C23—1221no—
532C23—1221no—
533C23—1221no—
534C23—1221no—
535C23—1221no—
536C23—1221no—
537C23—1221no—
538C23—1221no—
539C23—2444no—
540C23—2444no—
541C23—2444no—
542C23—2444no—
543C23—2444no—
544C23—2444no—
545C23—2444no—
546C23#1451986412yes—
547C23C23×#692311yescharacteristic
548Q8—2444no—
549D4—48no—
550D4—44no—
551D4—2448no—
552D4—2448no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—44no—
561C2×C4—612no—
562C2×C4—611no—
563C2×C4—611no—
564C2×C4—612no—
565C2×C4—614no—
566C2×C4—1224no—
567C2×C4—1224no—
568C2×C4—1222no—
569C2×C4—1222no—
570C2×C4—1221no—
571C2×C4—1222no—
572C2×C4—1221no—
573C2×C4—1221no—
574C2×C4—1222no—
575C2×C4—1222no—
576C2×C4—2444no—
577C2×C4—2442no—
578C2×C4—2442no—
579C2×C4—2444no—
580C2×C4—2442no—
581C2×C4—2442no—
582C2×C4—2442no—
583C2×C4—2442no—
584C2×C4—2442no—
585C2×C4—2442no—
586C2×C4C2×C22⋊#692314yes—
587C2×C4C2×C22⋊#692312yes—
588C8—2442no—
589C8—2442no—
590C8—2442no—
591C8—2442no—
592C22—22no—
593C22—22no—
594C22—22no—
595C22—41no—
596C22—41no—
597C22—41no—
598C22—41no—
599C22—42no—
600C22—42no—
601C22—42no—
602C22—42no—
603C22—42no—
604C22—42no—
605C22—42no—
606C22—1222no—
607C22—1222no—
608C22—1222no—
609C22—1222no—
610C22—1222no—
611C22—1222no—
612C22—24416no—
613C22—2441no—
614C22—2441no—
615C22—2441no—
616C22—2441no—
617C22—2441no—
618C22—2441no—
619C22—2441no—
620C22—2441no—
621C22C22×C22⋊#692311yescharacteristic
622C22#1684082911yescharacteristic
623C22#1684082911yescharacteristic
624C22C2×#1451986411yescharacteristic
625C22D61⋊#13111yescharacteristic
626C22#1684084011yescharacteristic
627C22#1684084111yescharacteristic
628C4—22no—
629C4—24no—
630C4—41no—
631C4—612no—
632C4—612no—
633C4—1224no—
634C4—2441no—
635C4—2442no—
636C2—42no—
637C2—82no—
638C2—2442no—
639C2—2442no—
640C2#2146229211yescharacteristic
641C2#2146240711yescharacteristic
642C2#2146241011yescharacteristic
643C2#2146268611yescharacteristic
644C2#2146268811yescharacteristic
645C2#2146269211yescharacteristic
646C2#2146269611yescharacteristic
subgroupG/H
center, FrattiniC23C23×#6923
commutator, socleC23×C61C23×C4
FittingC2×#121×C61C4
prime radicalC2×#16840272C2
cosocleC22×Dic61C24
hypercenterC2×#121#6923
hypocenterC61#21792
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C2×#16840787C2semidirect
2. #21461944C2semidirect
3. #21461943C2semidirect
4. #21461942C2semidirect
5. #21461940C2semidirect
6. #21461643C2semidirect
7. #21461642C2semidirect
8. #21461642C2semidirect
11. C2×#14519844C22semidirect
12. C2×C4⋊#92420C22semidirect
21. C2×C22⋊#92420C22semidirect
22. C2×C22⋊#92420C22semidirect
23. C2×C22⋊#92420C22semidirect
24. C2×C22⋊#92420C22semidirect
25. C2×#14519832C22semidirect
26. C2×C4×#92420C22semidirect
362. C61#21792semidirect

Maximal subgroups

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

subgroupindex
C2×#168407872
#214619442
#214619432
#214619422
#214619402
#214616432
#214616422
C2×#168402722
#2179261