Finite Group Databasebeta

← #30610328

Subgroups — #30610328

Order 15616.

922 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462719C212yesmaximal, complemented
2#21461101C212yesmaximal, complemented
3#21461100C212yesmaximal, complemented
4#21461091C212yesmaximal, complemented
5#21461079C211yesmaximal, characteristic
6#21461071C211yesmaximal, characteristic, complemented
7#21461070C211yesmaximal, characteristic, complemented
8#21461059C211yesmaximal, characteristic
9#21461051C211yesmaximal, characteristic, complemented
10#21461050C211yesmaximal, characteristic, complemented
11C2×#16840449C211yesmaximal, characteristic
12#16840814—22no—
13#16840814—22no—
14#16840812—22no—
15#16840811—22no—
16#16840783C2212yes—
17#16840782C2212yes—
18#16840782C2212yes—
19#16840779C2212yes—
20#16840778C2212yes—
21#16840778C2212yes—
22#16840608C2212yes—
23#16840608C2212yes—
24#16840607C2212yes—
25#16840607C2212yes—
26#16840605C2211yescharacteristic
27#16840605C2211yescharacteristic
28#16840605C2211yescharacteristic
29#16840605C2211yescharacteristic
30#16840605C2212yes—
31#16840605C2212yes—
32#16840449—22no—
33#16840449—22no—
34#16840449—22no—
35#16840449—22no—
36C2×#14519770C2211yescharacteristic
37C2×#14519770C2211yescharacteristic
38C2×#14519768C411yescharacteristic
39C2×#14519767C411yescharacteristic
40C2×#14519767C2211yescharacteristic
41C2×#14519758C411yescharacteristic
42C2×#14519754C411yescharacteristic
43C2×#14519754C411yescharacteristic
44C2×#14519742C2211yescharacteristic
45C2×D4×Dic61C2211yescharacteristic
46C2×#14519736C2211yescharacteristic
47C2×#14519733C411yescharacteristic
48C2×#14519733C2211yescharacteristic
49C22×#11758196C411yescharacteristic
50C2×#123×C61C411yescharacteristic
51#14519844—22no—
52#14519844—22no—
53#14519844—22no—
54C4⋊#92420—22no—
55C4⋊#92420—22no—
56C4⋊#92420—22no—
57C22⋊#92420C2312yes—
58C22⋊#92420C2312yes—
59C22⋊#92420C2312yes—
60C22⋊#92420C2312yes—
61#14519832—22no—
62#14519832—22no—
63#14519832—22no—
64C4×#92420—22no—
65C4×#92420—22no—
66C4×#92420—22no—
67C22×Dic122C2×C411yescharacteristic
68C23×Dic61C2×C411yescharacteristic
69C23×Dic61C2×C411yescharacteristic
70C23×Dic61C2×C411yescharacteristic
71#14519770—22no—
72#14519770—22no—
73#14519770—22no—
74#14519770—22no—
75#14519768—22no—
76#14519768—22no—
77#14519767—22no—
78#14519767—22no—
79#14519767—22no—
80#14519767—22no—
81#14519758—22no—
82#14519758—22no—
83#14519754—22no—
84#14519754—22no—
85#14519754—22no—
86#14519754—22no—
87#14519742D412yes—
88#14519742D412yes—
89#14519742D412yes—
90#14519742D412yes—
91D4×Dic61—22no—
92D4×Dic61—22no—
93#14519736—22no—
94#14519736—22no—
95#14519733—21no—
96#14519733—21no—
97#14519733—21no—
98#14519733—21no—
99#14519733—22no—
100#14519733—22no—
101C2×C4⋊Dic61C2×C411yescharacteristic
102C2×C4⋊Dic61C2×C411yescharacteristic
103C2×C4⋊Dic61C2×C411yescharacteristic
104C2×C4⋊Dic61C2311yescharacteristic
105C2×#11758196—21no—
106C2×#11758196—21no—
107C2×#11758196—21no—
108C2×#11758196—21no—
109C2×#11758196C2×C411yescharacteristic
110C2×#11758196C2×C411yescharacteristic
111C2×#11758196C2×C411yescharacteristic
112C2×#11758196C2×C411yescharacteristic
113C2×#11758196C2×C411yescharacteristic
114C2×#11758196C2×C411yescharacteristic
115C2×#11758196C2×C411yescharacteristic
116C2×#11758196C2×C411yescharacteristic
117C2×#11758196C2×C411yescharacteristic
118C2×#11758196C2311yescharacteristic
119C2×C22⋊Dic61C2×C411yescharacteristic
120C2×C22⋊Dic61C2×C411yescharacteristic
121C2×C22⋊Dic61C2×C411yescharacteristic
122C2×C22⋊Dic61C2311yescharacteristic
123C2×C22⋊Dic61C2311yescharacteristic
124C2×C4×Dic61C2×C411yescharacteristic
125C2×C4×Dic61C2×C411yescharacteristic
126C2×C4×Dic61C2311yescharacteristic
127C2×C4×Dic61C2311yescharacteristic
128C2×C4×Dic61C2311yescharacteristic
129C22×D4×C61C2×C411yescharacteristic
130C23×C4×C61C2×C411yescharacteristic
131#123×C61—22no—
132#123×C61—22no—
133C2×C4⋊C4×C61C2×C411yescharacteristic
134C2×C4⋊C4×C61C2×C411yescharacteristic
135C2×C22⋊C4×C61C2×C411yescharacteristic
136C2×C22⋊C4×C61C2×C411yescharacteristic
137C2×C22⋊C4×C61C2×C411yescharacteristic
138C24×C61C22×C411yescharacteristic
139C24×C61C22×C411yescharacteristic
140C2×D4×C61—22no—
141C2×D4×C61—22no—
142C2×D4×C61—41no—
143C22×C4×C61—22no—
144C22×C4×C61—21no—
145C22×C4×C61—21no—
146C22×C4×C61—41no—
147C22×C4×C61C22×C411yescharacteristic
148C22×C4×C61C22×C411yescharacteristic
149C22×C4×C61C22×C411yescharacteristic
150C22×C4×C61C22×C411yescharacteristic
151C22×C4×C61C22×C411yescharacteristic
152C22×Dic61—22no—
153C22×Dic61—21no—
154C22×Dic61—21no—
155C22×Dic61—21no—
156C22×Dic61—21no—
157C22×Dic61—21no—
158C22×Dic61—21no—
159C22×Dic61—41no—
160C22×Dic61—42no—
161C22×Dic61—42no—
162C22×Dic61C22×C411yescharacteristic
163C22×Dic61C22×C411yescharacteristic
164C22×Dic61C22×C411yescharacteristic
165C22×Dic61C22×C411yescharacteristic
166C22×Dic61C22×C411yescharacteristic
167C22×Dic61C22×C411yescharacteristic
168C22×Dic61C22×C411yescharacteristic
169C22×Dic61C2411yescharacteristic
170C2×Dic122—42no—
171C2×Dic122C22⋊C412yes—
172C2×Dic122C22⋊C412yes—
173C2×#92420—22no—
174C2×#92420—22no—
175C2×#92420—22no—
176C2×#92420—22no—
177C4⋊C4×C61—22no—
178C4⋊C4×C61C22⋊C412yes—
179C4⋊C4×C61C22⋊C412yes—
180C22⋊C4×C61—22no—
181C22⋊C4×C61—21no—
182C22⋊C4×C61—21no—
183C22⋊C4×C61—22no—
184C22⋊Dic61—21no—
185C22⋊Dic61—21no—
186C22⋊Dic61—22no—
187C22⋊Dic61—22no—
188C22⋊Dic61—22no—
189C22⋊Dic61—22no—
190C4⋊Dic61—22no—
191C4⋊Dic61—22no—
192C4⋊Dic61—22no—
193C4⋊Dic61—22no—
194#11758196—21no—
195#11758196—21no—
196#11758196—22no—
197#11758196—22no—
198#11758196—22no—
199#11758196—21no—
200#11758196—21no—
201#11758196—21no—
202#11758196—21no—
203#11758196—21no—
204#11758196—21no—
205#11758196—22no—
206#11758196C22⋊C411yescharacteristic
207#11758196C22⋊C411yescharacteristic
208#11758196C22⋊C411yescharacteristic
209#11758196C22⋊C411yescharacteristic
210#11758196C22⋊C412yes—
211#11758196C22⋊C412yes—
212C4×Dic61—21no—
213C4×Dic61—21no—
214C4×Dic61—21no—
215C4×Dic61—21no—
216C4×Dic61C2×D412yes—
217C4×Dic61C2×D412yes—
218C4×Dic61C2×D412yes—
219C4×Dic61C2×D412yes—
220C4×Dic61C2×D412yes—
221C4×Dic61C2×D412yes—
222C23×C61—21no—
223C23×C61—21no—
224C23×C61—21no—
225C23×C61—21no—
226C23×C61—21no—
227C23×C61—41no—
228C23×C61—41no—
229C23×C61—41no—
230C23×C61—41no—
231C23×C61#13112yes—
232C23×C61C23×C411yescharacteristic
233D4×C61—44no—
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—41no—
243C2×C4×C61—42no—
244C2×C4×C61—42no—
245C2×C4×C61—41no—
246C2×C4×C61C2×C22⋊C411yescharacteristic
247C2×C4×C61C2×C22⋊C411yescharacteristic
248C2×C4×C61C2×C22⋊C412yes—
249C2×C4×C61C2×C22⋊C412yes—
250C2×Dic61—21no—
251C2×Dic61—21no—
252C2×Dic61—22no—
253C2×Dic61—21no—
254C2×Dic61—21no—
255C2×Dic61—21no—
256C2×Dic61—21no—
257C2×Dic61—21no—
258C2×Dic61—21no—
259C2×Dic61—41no—
260C2×Dic61—41no—
261C2×Dic61—42no—
262C2×Dic61—42no—
263C2×Dic61—42no—
264C2×Dic61—42no—
265C2×Dic61—42no—
266C2×Dic61—42no—
267C2×Dic61—41no—
268C2×Dic61—41no—
269C2×Dic61—41no—
270C2×Dic61C2×C22⋊C411yescharacteristic
271C2×Dic61C2×C22⋊C411yescharacteristic
272C2×Dic61C2×C22⋊C411yescharacteristic
273C2×Dic61C2×C22⋊C412yes—
274C2×Dic61C2×C22⋊C411yescharacteristic
275C2×Dic61C22×D412yes—
276Dic122—24no—
277Dic122—42no—
278#92420—42no—
279#92420—42no—
280#92420—42no—
281#92420—42no—
282#17423—611nomaximal, Sylow
283C22×C61—21no—
284C22×C61—21no—
285C22×C61—22no—
286C22×C61—42no—
287C22×C61—42no—
288C22×C61—41no—
289C22×C61—41no—
290C22×C61—41no—
291C22×C61—41no—
292C22×C61—41no—
293C22×C61—81no—
294C22×C61—81no—
295C22×C61C22×C22⋊C411yescharacteristic
296C22×C61C2×#13111yescharacteristic
297C22×C61#56811yescharacteristic
298C4×C61—21no—
299C4×C61—21no—
300C4×C61—22no—
301C4×C61—22no—
302C4×C61—41no—
303C4×C61—41no—
304Dic61—21no—
305Dic61—21no—
306Dic61—22no—
307Dic61—22no—
308Dic61—21no—
309Dic61—41no—
310Dic61—41no—
311Dic61—41no—
312Dic61—41no—
313Dic61#41312yes—
314C2×#552—611no—
315#2984—612no—
316#1473—612no—
317#1473—612no—
318#1470—612no—
319#1466—611no—
320#1464—611no—
321#1464—611no—
322#1460—611no—
323#1458—611no—
324#1458—611no—
325C2×C61—21no—
326C2×C61—21no—
327C2×C61—42no—
328C2×C61—81no—
329C2×C61#288011yescharacteristic
330C2×C61#288411yescharacteristic
331C2×C61C2×#41311yescharacteristic
332#552—1222no—
333#552—1222no—
334#552—1222no—
335#552—1222no—
336C2×#126—611no—
337C2×#126—611no—
338C2×#125—611no—
339C2×#125—611no—
340C2×#125—611no—
341C2×#123—611no—
342C2×#123#692311yescharacteristic
343C2×C22⋊Q8—611no—
344C2×C22⋊Q8—611no—
345C2×C4×Q8—611no—
346C2×C4×D4—611no—
347C2×#117—611no—
348C2×#117—611no—
349C2×#117—611no—
350C22×C4⋊C4—611no—
351#446—1222no—
352#446—1222no—
353#446—1222no—
354C8×Q8—1222no—
355#432—612no—
356#432—612no—
357#432—612no—
358#431—612no—
359#431—612no—
360#431—612no—
361#324—612no—
362#324—612no—
363#324—612no—
364#324—612no—
365#323—611no—
366#323—611no—
367#323—611no—
368#323—611no—
369#323—612no—
370#323—612no—
371C61#1742311yescharacteristic, complemented, Sylow
372C22×Q8—611no—
373C22×D4C2×#692311yescharacteristic
374C23×C4—611no—
375C23×C4—611no—
376C23×C4—611no—
377C23×C4C2×#692311yescharacteristic
378#126—1222no—
379#126—1222no—
380#126—1222no—
381#126—1222no—
382#125—1222no—
383#125—1222no—
384#125—1222no—
385#125—1222no—
386#125—1222no—
387#125—1222no—
388#123—22no—
389#123—22no—
390#123—1222no—
391#123—1222no—
392C22⋊Q8—1222no—
393C22⋊Q8—1222no—
394C22⋊Q8—1222no—
395C22⋊Q8—1222no—
396C4×Q8—612no—
397C4×Q8—612no—
398C4×Q8—612no—
399C4×Q8—612no—
400C4×D4—1222no—
401C4×D4—1222no—
402#117—1222no—
403#117—1222no—
404#117—1222no—
405#117—1222no—
406#117—1221no—
407#117—1221no—
408#117—1221no—
409#117—1221no—
410C2×C4⋊C4—611no—
411C2×C4⋊C4—611no—
412C2×C4⋊C4—611no—
413C2×C4⋊C4—611no—
414C2×C4⋊C4—611no—
415C2×C4⋊C4—611no—
416C2×C4⋊C4—611no—
417C2×C4⋊C4—611no—
418C2×C4⋊C4—611no—
419C2×C4⋊C4—611no—
420C2×C4⋊C4—611no—
421C2×C4⋊C4—611no—
422C2×C4⋊C4—611no—
423C2×C4⋊C4—611no—
424C2×C4⋊C4—1221no—
425C2×C4⋊C4—1221no—
426C2×C4⋊C4—1221no—
427C2×C4⋊C4—1221no—
428C2×C4⋊C4C2×#692311yescharacteristic
429C2×C4⋊C4C2×#692311yescharacteristic
430C2×C22⋊C4—611no—
431C2×C22⋊C4—611no—
432C2×C22⋊C4—611no—
433C2×C22⋊C4—611no—
434C2×C22⋊C4—611no—
435C2×C22⋊C4C2×#692311yescharacteristic
436C2×C22⋊C4C2×#692311yescharacteristic
437C2×C22⋊C4C2×#692311yescharacteristic
438C2×C42—611no—
439C2×C42—611no—
440C2×C42—611no—
441C2×C42—611no—
442C2×C42—611no—
443C4⋊C8—1222no—
444C4⋊C8—1222no—
445C4⋊C8—1222no—
446C4⋊C8—1222no—
447C4⋊C8—1222no—
448C4⋊C8—1222no—
449C22⋊C8—612no—
450C22⋊C8—612no—
451C22⋊C8—612no—
452C22⋊C8—612no—
453#97—1222no—
454#97—1222no—
455#97—1222no—
456C4×C8—1222no—
457C4×C8—1222no—
458C4×C8—1222no—
459C24C22×#692311yescharacteristic
460C24C22×#692311yescharacteristic
461C2×Q8—612no—
462C2×Q8—612no—
463C2×Q8—2442no—
464C2×D4—22no—
465C2×D4—22no—
466C2×D4—41no—
467C22×C4—22no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—41no—
471C22×C4—611no—
472C22×C4—611no—
473C22×C4—611no—
474C22×C4—611no—
475C22×C4—611no—
476C22×C4—611no—
477C22×C4—611no—
478C22×C4—611no—
479C22×C4—1221no—
480C22×C4—1221no—
481C22×C4—1221no—
482C22×C4—1221no—
483C22×C4—1221no—
484C22×C4—1221no—
485C22×C4—1222no—
486C22×C4—2441no—
487C22×C4—2442no—
488C22×C4—2442no—
489C22×C4C22×#692311yescharacteristic
490C22×C4C22×#692311yescharacteristic
491C22×C4C22×#692311yescharacteristic
492C22×C4C22×#692311yescharacteristic
493C22×C4C22×#692311yescharacteristic
494C2×C8—1222no—
495C2×C8—1222no—
496C2×C8—1222no—
497C2×C8—1222no—
498C4⋊C4—22no—
499C4⋊C4—611no—
500C4⋊C4—611no—
501C4⋊C4—611no—
502C4⋊C4—611no—
503C4⋊C4—612no—
504C4⋊C4—612no—
505C4⋊C4—1221no—
506C4⋊C4—1221no—
507C4⋊C4—1221no—
508C4⋊C4—1221no—
509C4⋊C4—1221no—
510C4⋊C4—1221no—
511C4⋊C4—1222no—
512C4⋊C4—1222no—
513C4⋊C4—1222no—
514C4⋊C4—1222no—
515C4⋊C4—1221no—
516C4⋊C4—1221no—
517C4⋊C4—1222no—
518C4⋊C4—1222no—
519C4⋊C4—1222no—
520C4⋊C4—1222no—
521C4⋊C4C22⋊#692312yes—
522C4⋊C4C22⋊#692312yes—
523C22⋊C4—22no—
524C22⋊C4—21no—
525C22⋊C4—21no—
526C22⋊C4—22no—
527C22⋊C4—1222no—
528C22⋊C4—1222no—
529C22⋊C4—1221no—
530C22⋊C4—1221no—
531C22⋊C4—1222no—
532C22⋊C4—1222no—
533C42—612no—
534C42—612no—
535C42—612no—
536C42—612no—
537C42—612no—
538C42—612no—
539C42—1221no—
540C42—1221no—
541C42—1221no—
542C42—1221no—
543C23—21no—
544C23—21no—
545C23—21no—
546C23—21no—
547C23—21no—
548C23—41no—
549C23—41no—
550C23—41no—
551C23—41no—
552C23#1451986412yes—
553C23C23×#692311yescharacteristic
554Q8—1224no—
555Q8—2442no—
556D4—44no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—41no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—41no—
569C2×C4—611no—
570C2×C4—611no—
571C2×C4—611no—
572C2×C4—612no—
573C2×C4—611no—
574C2×C4—612no—
575C2×C4—1222no—
576C2×C4—1221no—
577C2×C4—1221no—
578C2×C4—1221no—
579C2×C4—1221no—
580C2×C4—1221no—
581C2×C4—1221no—
582C2×C4—1221no—
583C2×C4—1221no—
584C2×C4—2442no—
585C2×C4—2442no—
586C2×C4—2441no—
587C2×C4—2441no—
588C2×C4—2442no—
589C2×C4—2442no—
590C2×C4—2442no—
591C2×C4—2442no—
592C2×C4—2441no—
593C2×C4—2441no—
594C2×C4—2441no—
595C2×C4C2×C22⋊#692311yescharacteristic
596C2×C4C2×C22⋊#692311yescharacteristic
597C2×C4C2×C22⋊#692312yes—
598C2×C4C2×C22⋊#692312yes—
599C8—2442no—
600C8—2442no—
601C8—2442no—
602C8—2442no—
603C22—21no—
604C22—21no—
605C22—22no—
606C22—42no—
607C22—42no—
608C22—41no—
609C22—41no—
610C22—41no—
611C22—41no—
612C22—41no—
613C22—81no—
614C22—81no—
615C22C22×C22⋊#692311yescharacteristic
616C22C2×#1451986411yescharacteristic
617C22#1684084011yescharacteristic
618C4—21no—
619C4—21no—
620C4—22no—
621C4—22no—
622C4—41no—
623C4—41no—
624C4—612no—
625C4—1221no—
626C4—1221no—
627C4—1222no—
628C4—1221no—
629C4—1222no—
630C4—2441no—
631C4—2441no—
632C4—2441no—
633C4—2441no—
634C2—21no—
635C2—21no—
636C2—42no—
637C2—81no—
638C2#2146240711yescharacteristic
639C2#2146242111yescharacteristic
640C2D61⋊#41311yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC23×C61C23×C4
FrattiniC23C23×#6923
FittingC2×#123×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC22×D4×C61C2×C4
cosocleC22×Dic61C24
hypercenterC2×#123#6923
hypocenterC61#17423
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C4⋊C4 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
1. #21462719C2semidirect
2. #21461101C2semidirect
3. #21461100C2semidirect
4. #21461091C2semidirect
6. #21461071C2semidirect
7. #21461070C2semidirect
9. #21461051C2semidirect
10. #21461050C2semidirect
371. C61#17423semidirect

Maximal subgroups

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

subgroupindex
#214627192
#214611012
#214611002
#214610912
#214610792
#214610712
#214610702
#214610592
#214610512
#214610502
C2×#168404492
#1742361