Finite Group Databasebeta

← #30615218

Subgroups — #30615218

Order 15616.

1306 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D61⋊#432C211yesmaximal, characteristic
2#21462266C211yesmaximal, characteristic
3#21461723C212yesmaximal
4#21461690C214yesmaximal, complemented
5#21461658C212yesmaximal
6#21461591C214yesmaximal, complemented
7C2×C4×Q8×D61C211yesmaximal, characteristic
8#16840785—21no—
9#16840784—21no—
10#16840783—21no—
11#16840782—21no—
12D61⋊(C4⋊C8)C2212yes—
13C2×#14519840C2218yes—
14D61⋊(C22⋊C8)C2212yes—
15#16840721C2212yes—
16#16840707—21no—
17#16840706C2212yes—
18#16840705—21no—
19#16840704C2212yes—
20C4×C4⋊#6923C2212yes—
21C4×C22⋊#6923—21no—
22#16840698—21no—
23#16840635C2218yes—
24C22×Q8×D61C2211yescharacteristic
25C2×Q8×Dic61C411yescharacteristic, complemented
26C2×C4×Dic122—21no—
27C2×C4×Dic122C411yescharacteristic, complemented
28C2×#14519742—21no—
29C2×#14519742C411yescharacteristic, complemented
30C4×Q8×D61—21no—
31C4×Q8×D61—21no—
32C4×Q8×D61—21no—
33C4×Q8×D61—21no—
34C4×Q8×D61C412yescomplemented
35C4×Q8×D61C412yescomplemented
36C4×Q8×D61C2212yes—
37C4×Q8×D61C2212yes—
38C2×C4⋊C4×D61—21no—
39C2×C4⋊C4×D61C2211yescharacteristic
40C2×C42×D61—21no—
41C2×C42×D61C2211yescharacteristic
42C2×C4×Q8×C61C411yescharacteristic, complemented
43C2×D61⋊C8C2314yes—
44C2×C4⋊#6923C2314yes—
45C2×C22⋊#6923—22no—
46C2×C4×#6923—22no—
47#14519844—22no—
48C4⋊#92420—22no—
49#14519840—216no—
50#14519834—22no—
51C22⋊#92420—22no—
52#14519832—22no—
53#14519832—22no—
54(C2×#6923)⋊C4—22no—
55(C2×#6923)⋊C4—22no—
56(C2×#6923)⋊C4—22no—
57(C2×#6923)⋊C4—22no—
58C22×Dic122—21no—
59C22×Dic122C2×C411yescharacteristic
60C2×Q8×D61—28no—
61C2×Q8×D61—21no—
62C2×Q8×D61—21no—
63C2×Q8×D61C2×C412yes—
64C2×Q8×D61C2312yes—
65C22×C4×D61—21no—
66C22×C4×D61—21no—
67C22×C4×D61D411yescharacteristic
68C22×C4×D61D411yescharacteristic
69C22×C4×D61C2311yescharacteristic
70Q8×Dic61—21no—
71Q8×Dic61—21no—
72Q8×Dic61C2×C412yes—
73Q8×Dic61C2×C412yes—
74C4×Dic122—21no—
75C4×Dic122—21no—
76C4×Dic122—22no—
77C4×Dic122—22no—
78C4×Dic122—22no—
79C4×Dic122—22no—
80C4×Dic122C2×C412yes—
81C4×Dic122C2×C412yes—
82#14519742—21no—
83#14519742—21no—
84#14519742—22no—
85#14519742—22no—
86#14519742—22no—
87#14519742—22no—
88#14519742C2×C412yes—
89#14519742C2×C412yes—
90C2×C4⋊Dic61—21no—
91C2×C4⋊Dic61C2×C411yescharacteristic
92C2×#11758196—21no—
93C2×#11758196—21no—
94C2×#11758196—21no—
95C4⋊C4×D61—22no—
96C4⋊C4×D61—22no—
97C4⋊C4×D61—22no—
98C4⋊C4×D61—22no—
99C4⋊C4×D61—21no—
100C4⋊C4×D61—21no—
101C4⋊C4×D61C2×C412yes—
102C4⋊C4×D61C2312yes—
103C2×C4×Dic61—21no—
104C2×C4×Dic61—21no—
105C2×C4×Dic61—21no—
106C2×C4×Dic61C2×C411yescharacteristic
107C2×C4×Dic61D411yescharacteristic
108C2×C4×Dic61D411yescharacteristic
109C42×D61—22no—
110C42×D61—22no—
111C42×D61—22no—
112C42×D61—22no—
113C42×D61C2×C411yescharacteristic
114C42×D61C2×C411yescharacteristic
115C42×D61D411yescharacteristic
116C42×D61D411yescharacteristic
117C42×D61D411yescharacteristic
118C42×D61D411yescharacteristic
119C42×D61C2311yescharacteristic
120C42×D61C2311yescharacteristic
121C22×Q8×C61C2×C411yescharacteristic
122C4×Q8×C61—21no—
123C4×Q8×C61—21no—
124C4×Q8×C61C2×C412yes—
125C4×Q8×C61C2×C412yes—
126C2×C4⋊C4×C61—21no—
127C2×C4⋊C4×C61C2×C411yescharacteristic
128C2×C42×C61—21no—
129C2×C42×C61C2×C411yescharacteristic
130C23×D61C2×D411yescharacteristic
131C22×#6923—24no—
132C2×Q8×C61—24no—
133C2×Q8×C61—21no—
134C2×Q8×C61C22×C412yes—
135C22×C4×C61—21no—
136C22×C4×C61—21no—
137C22×C4×C61C22⋊C411yescharacteristic
138C22×C4×C61C22⋊C411yescharacteristic
139C22×C4×C61C22×C411yescharacteristic
140C22×Dic61—21no—
141C22×Dic61—21no—
142C22×Dic61C22⋊C411yescharacteristic
143C22×Dic61C22⋊C411yescharacteristic
144C22×Dic61C2×D411yescharacteristic
145Q8×D61—28no—
146Q8×D61—28no—
147Q8×D61—24no—
148Q8×D61—24no—
149Q8×D61—24no—
150Q8×D61#4118yes—
151C2×C4×D61—28no—
152C2×C4×D61—22no—
153C2×C4×D61—24no—
154C2×C4×D61—22no—
155C2×C4×D61—24no—
156C2×C4×D61—22no—
157C2×C4×D61—22no—
158C2×C4×D61—42no—
159C2×C4×D61—44no—
160C2×C4×D61C22⋊C411yescharacteristic
161C2×C4×D61C22⋊C411yescharacteristic
162C2×C4×D61C22⋊C411yescharacteristic
163C2×C4×D61C22⋊C411yescharacteristic
164C2×C4×D61C22×C411yescharacteristic
165C2×C4×D61C2×D411yescharacteristic
166C2×C4×D61C2×D411yescharacteristic
167C2×C4×D61C2×D411yescharacteristic
168C2×C4×D61C2×D411yescharacteristic
169C2×C4×D61C2×D411yescharacteristic
170C2×C4×D61C2×D411yescharacteristic
171C2×C4×D61C2411yescharacteristic
172C2×Dic122—28no—
173C2×Dic122—21no—
174C2×Dic122—22no—
175C2×Dic122—22no—
176C2×Dic122—24no—
177C2×Dic122C22×C412yes—
178C22⋊#6923—44no—
179C2×#92420—24no—
180C4⋊#6923—28no—
181C4×#6923—44no—
182D61⋊C8—28no—
183C4⋊C4×C61—22no—
184C4⋊C4×C61—22no—
185C4⋊C4×C61—21no—
186C4⋊C4×C61C22×C412yes—
187C42×C61—22no—
188C42×C61—22no—
189C42×C61C22⋊C411yescharacteristic
190C42×C61C22⋊C411yescharacteristic
191C42×C61C22×C411yescharacteristic
192C42×C61C22×C411yescharacteristic
193C4⋊Dic61—21no—
194C4⋊Dic61—22no—
195C4⋊Dic61—22no—
196C4⋊Dic61C22×C412yes—
197#11758196—22no—
198#11758196—22no—
199#11758196—22no—
200#11758196—22no—
201#11758196—22no—
202#11758196—22no—
203C4×Dic61—22no—
204C4×Dic61—22no—
205C4×Dic61—22no—
206C4×Dic61—22no—
207C4×Dic61—22no—
208C4×Dic61—22no—
209C4×Dic61C22⋊C411yescharacteristic
210C4×Dic61C22⋊C411yescharacteristic
211C4×Dic61C22⋊C411yescharacteristic
212C4×Dic61C22⋊C411yescharacteristic
213C4×Dic61C22⋊C411yescharacteristic
214C4×Dic61C22⋊C411yescharacteristic
215C4×Dic61C22×C411yescharacteristic
216C4×Dic61C22×C411yescharacteristic
217C4×Dic61C2×D411yescharacteristic
218C4×Dic61C2×D411yescharacteristic
219C4×Dic61C2×D411yescharacteristic
220C4×Dic61C2×D411yescharacteristic
221C23×C61C2×C22⋊C411yescharacteristic
222C22×D61—22no—
223C22×D61—22no—
224C22×D61C2×C22⋊C411yescharacteristic
225C22×D61#13714yes—
226C22×D61C22×D411yescharacteristic
227C2×#6923—44no—
228C2×#6923—44no—
229C2×#6923—44no—
230Q8×C61—24no—
231Q8×C61—22no—
232Q8×C61#11714yes—
233C2×C4×C61—24no—
234C2×C4×C61—22no—
235C2×C4×C61—22no—
236C2×C4×C61—22no—
237C2×C4×C61—22no—
238C2×C4×C61—41no—
239C2×C4×C61—42no—
240C2×C4×C61C2×C22⋊C411yescharacteristic
241C2×C4×C61C2×C22⋊C411yescharacteristic
242C2×C4×C61C2×C22⋊C411yescharacteristic
243C2×C4×C61C2×C22⋊C411yescharacteristic
244C2×C4×C61C2×C22⋊C411yescharacteristic
245C2×C4×C61C23×C411yescharacteristic
246C2×Dic61—24no—
247C2×Dic61—22no—
248C2×Dic61—22no—
249C2×Dic61—22no—
250C2×Dic61—22no—
251C2×Dic61—41no—
252C2×Dic61—42no—
253C2×Dic61C2×C22⋊C411yescharacteristic
254C2×Dic61C2×C22⋊C411yescharacteristic
255C2×Dic61C2×C22⋊C411yescharacteristic
256C2×Dic61C2×C22⋊C411yescharacteristic
257C2×Dic61C2×C22⋊C411yescharacteristic
258C2×Dic61C22×D411yescharacteristic
259C4×D61—28no—
260C4×D61—28no—
261C4×D61—22no—
262C4×D61—22no—
263C4×D61—22no—
264C4×D61—22no—
265C4×D61—22no—
266C4×D61—22no—
267C4×D61—22no—
268C4×D61—22no—
269C4×D61—22no—
270C4×D61—41no—
271C4×D61—41no—
272C4×D61—44no—
273C4×D61—44no—
274C4×D61C2×#4114yes—
275Dic122—28no—
276Dic122—24no—
277Dic122—22no—
278Dic122—28no—
279Dic122#11714yes—
280#92420—44no—
281#20741—611nomaximal, Sylow
282C22×C61—21no—
283C22×C61—21no—
284C22×C61#41912yes—
285C22×C61C22×C22⋊C411yescharacteristic
286C2×D61—21no—
287C2×D61—21no—
288C2×D61—28no—
289C2×D61#41912yes—
290C2×D61#52512yes—
291C2×D61C2×#13712yes—
292C2×D61#57512yes—
293#6923—84no—
294C4×C61—21no—
295C4×C61—21no—
296C4×C61—21no—
297C4×C61—21no—
298C4×C61—24no—
299C4×C61—21no—
300C4×C61—42no—
301C4×C61C2×#11712yes—
302Dic61—21no—
303Dic61—21no—
304Dic61—21no—
305Dic61—21no—
306Dic61—21no—
307Dic61—24no—
308Dic61—42no—
309Dic61#52512yes—
310C22×C4×Q8—611no—
311C2×#432—611no—
312#2283—611no—
313#1824—612no—
314#1805—614no—
315#1787—612no—
316#1763—614no—
317C2×C61—22no—
318C2×C61#228011yescharacteristic
319C2×C61C2×#41911yescharacteristic
320C2×C61#289611yescharacteristic
321D61—22no—
322D61#311714yes—
323C23×Q8—611no—
324C2×C4×Q8—611no—
325C2×C4×Q8—612no—
326C2×C4×Q8—612no—
327C2×C4×Q8—612no—
328C2×C4×Q8—612no—
329C2×C4×Q8—611no—
330C2×C4×Q8—611no—
331C2×C4×Q8—1221no—
332C2×C4×Q8—1221no—
333C2×C4×Q8—1221no—
334C2×C4×Q8—1221no—
335C2×C4×Q8—1221no—
336C2×C4×Q8—1221no—
337C2×C4×Q8#692311yescharacteristic, complemented
338C22×C4⋊C4—611no—
339C22×C4⋊C4—1221no—
340C22×C42—611no—
341C22×C42—1221no—
342#432—1221no—
343#432—1221no—
344#432—1221no—
345#432—1221no—
346C2×C4⋊C8—612no—
347C2×#103—618no—
348C2×C22⋊C8—612no—
349C2×#97—612no—
350#383—1221no—
351#382—612no—
352#381—1221no—
353#380—612no—
354C4×C4⋊C4—612no—
355C4×C22⋊C4—1221no—
356#376—1221no—
357#340—618no—
358C61#2074111yescharacteristic, complemented, Sylow
359C22×Q8—612no—
360C22×Q8—612no—
361C22×Q8—611no—
362C22×Q8—1221no—
363C22×Q8—1221no—
364C22×Q8—1221no—
365C22×Q8—1228no—
366C22×Q8C2×#692311yescharacteristic
367C23×C4—611no—
368C23×C4—611no—
369C23×C4—611no—
370C23×C4—1221no—
371C23×C4—1221no—
372C22×C8—614no—
373C4×Q8—21no—
374C4×Q8—21no—
375C4×Q8—612no—
376C4×Q8—612no—
377C4×Q8—612no—
378C4×Q8—612no—
379C4×Q8—612no—
380C4×Q8—612no—
381C4×Q8—1222no—
382C4×Q8—1222no—
383C4×Q8—1222no—
384C4×Q8—1222no—
385C4×Q8—1222no—
386C4×Q8—1222no—
387C4×Q8—1222no—
388C4×Q8—1222no—
389C4×Q8—1221no—
390C4×Q8—1221no—
391C4×Q8—1221no—
392C4×Q8—1221no—
393C4×Q8—1221no—
394C4×Q8—1221no—
395C4×Q8C2×#692312yes—
396C4×Q8C2×#692312yes—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—611no—
399C2×C4⋊C4—612no—
400C2×C4⋊C4—612no—
401C2×C4⋊C4—614no—
402C2×C4⋊C4—1221no—
403C2×C4⋊C4—1221no—
404C2×C4⋊C4—1222no—
405C2×C4⋊C4—1222no—
406C2×C4⋊C4—1222no—
407C2×C4⋊C4—1222no—
408C2×C4⋊C4—1221no—
409C2×C4⋊C4—1221no—
410C2×C4⋊C4—1221no—
411C2×C4⋊C4—1221no—
412C2×C4⋊C4C2×#692311yescharacteristic
413C2×C22⋊C4—1222no—
414C2×C42—21no—
415C2×C42—611no—
416C2×C42—611no—
417C2×C42—611no—
418C2×C42—611no—
419C2×C42—611no—
420C2×C42—611no—
421C2×C42—611no—
422C2×C42—611no—
423C2×C42—611no—
424C2×C42—611no—
425C2×C42—611no—
426C2×C42—1222no—
427C2×C42—1222no—
428C2×C42—1222no—
429C2×C42—1222no—
430C2×C42—1221no—
431C2×C42—1221no—
432C2×C42—1221no—
433C2×C42—1222no—
434C2×C42C2×#692311yescharacteristic
435C4⋊C8—1222no—
436C4⋊C8—1222no—
437#103—12216no—
438C22⋊C8—1222no—
439C22⋊C8—1222no—
440#97—1222no—
441#97—1222no—
442#95—1222no—
443#95—1222no—
444#95—1222no—
445#95—1222no—
446C24—611no—
447C2×Q8—24no—
448C2×Q8—21no—
449C2×Q8—618no—
450C2×Q8—612no—
451C2×Q8—1222no—
452C2×Q8—1222no—
453C2×Q8—1224no—
454C2×Q8—1228no—
455C2×Q8—1224no—
456C2×Q8—1224no—
457C2×Q8—1228no—
458C2×Q8—1228no—
459C2×Q8—1224no—
460C2×Q8—1221no—
461C2×Q8C22×#692312yes—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—611no—
465C22×C4—611no—
466C22×C4—611no—
467C22×C4—611no—
468C22×C4—611no—
469C22×C4—611no—
470C22×C4—611no—
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—1224no—
480C22×C4—1222no—
481C22×C4—1222no—
482C22×C4—1224no—
483C22×C4—1228no—
484C22×C4—1222no—
485C22×C4—1222no—
486C22×C4—1221no—
487C22×C4—1221no—
488C22×C4—1224no—
489C22×C4—2442no—
490C22×C4—2444no—
491C22×C4C22⋊#692311yescharacteristic
492C22×C4C22⋊#692311yescharacteristic
493C22×C4C22×#692311yescharacteristic
494C2×C8—1224no—
495C2×C8—1228no—
496C4⋊C4—22no—
497C4⋊C4—22no—
498C4⋊C4—21no—
499C4⋊C4—612no—
500C4⋊C4—1222no—
501C4⋊C4—1222no—
502C4⋊C4—1222no—
503C4⋊C4—1222no—
504C4⋊C4—1222no—
505C4⋊C4—1222no—
506C4⋊C4—1228no—
507C4⋊C4—1221no—
508C4⋊C4—1222no—
509C4⋊C4—1222no—
510C4⋊C4C22×#692312yes—
511C22⋊C4—2444no—
512C42—22no—
513C42—22no—
514C42—611no—
515C42—611no—
516C42—611no—
517C42—611no—
518C42—611no—
519C42—611no—
520C42—611no—
521C42—611no—
522C42—611no—
523C42—611no—
524C42—611no—
525C42—611no—
526C42—1222no—
527C42—1222no—
528C42—1222no—
529C42—1222no—
530C42—1222no—
531C42—1222no—
532C42—2444no—
533C42C22⋊#692311yescharacteristic
534C42C22⋊#692311yescharacteristic
535C42C22×#692311yescharacteristic
536C42C22×#692311yescharacteristic
537C23—611no—
538C23—614no—
539C23—611no—
540C23—1222no—
541C23—1222no—
542C23C2×C22⋊#692311yescharacteristic
543Q8—24no—
544Q8—22no—
545Q8—614no—
546Q8—1228no—
547Q8—1228no—
548Q8—1224no—
549Q8—1222no—
550Q8#1451985614yes—
551C2×C4—24no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—41no—
557C2×C4—42no—
558C2×C4—611no—
559C2×C4—614no—
560C2×C4—611no—
561C2×C4—611no—
562C2×C4—611no—
563C2×C4—611no—
564C2×C4—611no—
565C2×C4—1222no—
566C2×C4—1222no—
567C2×C4—1222no—
568C2×C4—1222no—
569C2×C4—1222no—
570C2×C4—1222no—
571C2×C4—1222no—
572C2×C4—1222no—
573C2×C4—1228no—
574C2×C4—1228no—
575C2×C4—1222no—
576C2×C4—1224no—
577C2×C4—1222no—
578C2×C4—1222no—
579C2×C4—1222no—
580C2×C4—1222no—
581C2×C4—2441no—
582C2×C4—2441no—
583C2×C4—2444no—
584C2×C4—2444no—
585C2×C4—2441no—
586C2×C4—2444no—
587C2×C4—2444no—
588C2×C4—2444no—
589C2×C4—2442no—
590C2×C4C2×C22⋊#692311yescharacteristic
591C2×C4C2×C22⋊#692311yescharacteristic
592C2×C4C2×C22⋊#692311yescharacteristic
593C2×C4C2×C22⋊#692311yescharacteristic
594C2×C4C2×C22⋊#692311yescharacteristic
595C2×C4C23×#692311yescharacteristic
596C8—2444no—
597C22—21no—
598C22—21no—
599C22—612no—
600C22—612no—
601C22—612no—
602C22—612no—
603C22—1228no—
604C22—1221no—
605C22—1221no—
606C22#1684075512yes—
607C22C22×C22⋊#692311yescharacteristic
608C4—21no—
609C4—21no—
610C4—21no—
611C4—21no—
612C4—24no—
613C4—21no—
614C4—42no—
615C4—612no—
616C4—1221no—
617C4—1221no—
618C4—1221no—
619C4—1221no—
620C4—1221no—
621C4—1224no—
622C4—4884no—
623C4—2442no—
624C4C2×#1451985612yes—
625C2—22no—
626C2—614no—
627C2—1222no—
628C2#2146226311yescharacteristic
629C2C2×#1684075511yescharacteristic
630C2#2146243911yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC2×C4×Q8×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC23×D61C2×D4
cosocleC2×C4×D61C24
hypercenterC2×C4×Q8#6923
hypocenterC61#20741
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
4. #21461690C2semidirect
6. #21461591C2semidirect
25. C2×Q8×Dic61C4semidirect
27. C2×C4×Dic122C4semidirect
29. C2×#14519742C4semidirect
34. C4×Q8×D61C4semidirect
35. C4×Q8×D61C4semidirect
42. C2×C4×Q8×C61C4semidirect
337. C2×C4×Q8#6923semidirect
358. C61#20741semidirect

Maximal subgroups

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

subgroupindex
D61⋊#4322
#214622662
#214617232
#214616902
#214616582
#214615912
C2×C4×Q8×D612
#2074161