Finite Group Databasebeta

← #30615110

Subgroups — #30615110

Order 15616.

1470 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D61⋊#407C211yesmaximal, characteristic
2#21462263C211yesmaximal, characteristic
3#21461726C214yesmaximal, complemented
4#21461725C214yesmaximal, complemented
5#21461498C214yesmaximal, complemented
6C22×#14519735C211yesmaximal, characteristic
7C2×D61⋊M16C2212yes—
8C2×#14519856C2212yes—
9#16840734—21no—
10#16840733C2212yes—
11#16840733C2212yes—
12#16840732—21no—
13D61⋊(C22⋊C8)—21no—
14D61⋊(C22⋊C8)—21no—
15#16840705—21no—
16#16840704—21no—
17#16840704—21no—
18#16840703—21no—
19C4×C22⋊#6923C2212yes—
20C4×C22⋊#6923C2212yes—
21#16840632C22116yescomplemented
22C23×C4×D61C2211yescharacteristic
23C2×#14519735—21no—
24C2×#14519735—21no—
25C2×#14519735—21no—
26C2×#14519735—21no—
27C2×#14519735—21no—
28C2×#14519735—21no—
29C2×#14519735C412yescomplemented
30C2×#14519735C412yescomplemented
31C2×#14519735C412yescomplemented
32C2×#14519735C2212yes—
33C2×#14519735C2212yes—
34C2×#14519735C2212yes—
35C22×C4⋊Dic61C411yescharacteristic, complemented
36C22×#11758198—21no—
37C22×C4×Dic61—21no—
38C22×C4⋊C4×C61C411yescharacteristic, complemented
39C2×#11758213C2314yes—
40D61⋊M16—28no—
41C2×#11758217—22no—
42C2×D61⋊C8—22no—
43#14519856—28no—
44C2×C4⋊#6923—22no—
45C2×C22⋊#6923—22no—
46C2×C22⋊#6923—22no—
47C2×C22⋊#6923—22no—
48C2×C4×#6923C2314yes—
49#14519834—22no—
50#14519834—22no—
51C22⋊#92420—22no—
52C22⋊#92420—22no—
53(C2×#6923)⋊C4—22no—
54(C2×#6923)⋊C4—22no—
55C24×D61D411yescharacteristic
56C23×Dic61—21no—
57C23×Dic61D411yescharacteristic
58C22×C4×D61—28no—
59C22×C4×D61C2×C411yescharacteristic
60C22×C4×D61C2×C411yescharacteristic
61C22×C4×D61C2×C411yescharacteristic
62C22×C4×D61D411yescharacteristic
63C22×C4×D61D411yescharacteristic
64C22×C4×D61D411yescharacteristic
65C22×C4×D61D411yescharacteristic
66C22×C4×D61D411yescharacteristic
67C22×C4×D61D411yescharacteristic
68C22×C4×D61C2311yescharacteristic
69C22×C4×D61C2311yescharacteristic
70C22×C4×D61C2311yescharacteristic
71#14519735—22no—
72#14519735—22no—
73#14519735—22no—
74#14519735—22no—
75#14519735—22no—
76#14519735—22no—
77#14519735—22no—
78#14519735—22no—
79#14519735—22no—
80#14519735—22no—
81#14519735—22no—
82#14519735—22no—
83#14519735C2×C414yes—
84#14519735C2×C414yes—
85#14519735C2×C414yes—
86#14519735C2314yes—
87C2×C4⋊Dic61—21no—
88C2×C4⋊Dic61—21no—
89C2×C4⋊Dic61—21no—
90C2×C4⋊Dic61C2×C412yes—
91C2×C4⋊Dic61C2×C412yes—
92C2×C4⋊Dic61C2×C412yes—
93C2×#11758198—22no—
94C2×#11758198—22no—
95C2×#11758198—22no—
96C2×#11758198—22no—
97C2×#11758198—22no—
98C2×#11758198—22no—
99C2×C4×Dic61—22no—
100C2×C4×Dic61—22no—
101C2×C4×Dic61—22no—
102C2×C4×Dic61—22no—
103C2×C4×Dic61—22no—
104C2×C4×Dic61—22no—
105C23×C4×C61—21no—
106C23×C4×C61C2×C411yescharacteristic
107C2×C4⋊C4×C61—21no—
108C2×C4⋊C4×C61—21no—
109C2×C4⋊C4×C61—21no—
110C2×C4⋊C4×C61C2×C412yes—
111C2×C4⋊C4×C61C2×C412yes—
112C2×C4⋊C4×C61C2×C412yes—
113C24×C61C22⋊C411yescharacteristic
114C23×D61—24no—
115C23×D61—42no—
116C23×D61—42no—
117C23×D61C22⋊C411yescharacteristic
118C23×D61C22⋊C411yescharacteristic
119C23×D61C22⋊C411yescharacteristic
120C23×D61C2×D411yescharacteristic
121C23×D61C2×D411yescharacteristic
122C23×D61C2×D411yescharacteristic
123C22×#6923—24no—
124C22×C4×C61—24no—
125C22×C4×C61—22no—
126C22×C4×C61—22no—
127C22×C4×C61—22no—
128C22×C4×C61—44no—
129C22×C4×C61C22⋊C411yescharacteristic
130C22×C4×C61C22⋊C411yescharacteristic
131C22×C4×C61C22⋊C411yescharacteristic
132C22×C4×C61C22×C411yescharacteristic
133C22×C4×C61C22×C411yescharacteristic
134C22×C4×C61C22×C411yescharacteristic
135C22×Dic61—24no—
136C22×Dic61—22no—
137C22×Dic61—22no—
138C22×Dic61—22no—
139C22×Dic61—44no—
140C22×Dic61C22⋊C411yescharacteristic
141C22×Dic61C22⋊C411yescharacteristic
142C22×Dic61C22⋊C411yescharacteristic
143C22×Dic61C2×D411yescharacteristic
144C22×Dic61C2×D411yescharacteristic
145C22×Dic61C2×D411yescharacteristic
146C2×C4×D61—24no—
147C2×C4×D61—24no—
148C2×C4×D61—24no—
149C2×C4×D61—24no—
150C2×C4×D61—24no—
151C2×C4×D61—24no—
152C2×C4×D61—24no—
153C2×C4×D61—24no—
154C2×C4×D61—24no—
155C2×C4×D61—24no—
156C2×C4×D61—24no—
157C2×C4×D61C22⋊C411yescharacteristic
158C2×C4×D61C22⋊C411yescharacteristic
159C2×C4×D61C22⋊C411yescharacteristic
160C2×C4×D61C22⋊C411yescharacteristic
161C2×C4×D61C22⋊C411yescharacteristic
162C2×C4×D61C22⋊C411yescharacteristic
163C2×C4×D61C22×C411yescharacteristic
164C2×C4×D61C22×C411yescharacteristic
165C2×C4×D61C22×C411yescharacteristic
166C2×C4×D61C2×D411yescharacteristic
167C2×C4×D61C2×D411yescharacteristic
168C2×C4×D61C2×D411yescharacteristic
169C2×C4×D61C2×D411yescharacteristic
170C2×C4×D61C2×D411yescharacteristic
171C2×C4×D61C2×D411yescharacteristic
172C2×C4×D61#4118yes—
173C2×C4×D61C2411yescharacteristic
174C22⋊#6923—44no—
175C22⋊#6923—44no—
176C22⋊#6923—44no—
177#11758217—44no—
178C2×#92420—24no—
179C4⋊#6923—44no—
180C4×#6923—28no—
181#11758213—28no—
182D61⋊C8—44no—
183C4⋊C4×C61—22no—
184C4⋊C4×C61—22no—
185C4⋊C4×C61—22no—
186C4⋊C4×C61C22×C414yes—
187#11758198—24no—
188#11758198—24no—
189#11758198—24no—
190#11758198—24no—
191C4⋊Dic61—22no—
192C4⋊Dic61—22no—
193C4⋊Dic61—22no—
194C4⋊Dic61C22×C414yes—
195C4×Dic61—24no—
196C4×Dic61—24no—
197C4×Dic61—24no—
198C4×Dic61—24no—
199C23×C61—22no—
200C23×C61—22no—
201C23×C61—22no—
202C23×C61C2×C22⋊C411yescharacteristic
203C23×C61C2×C22⋊C411yescharacteristic
204C23×C61C2×C22⋊C411yescharacteristic
205C22×D61—22no—
206C22×D61—22no—
207C22×D61—22no—
208C22×D61—22no—
209C22×D61—22no—
210C22×D61—22no—
211C22×D61—22no—
212C22×D61—22no—
213C22×D61—22no—
214C22×D61—41no—
215C22×D61—41no—
216C22×D61—41no—
217C22×D61—41no—
218C22×D61—41no—
219C22×D61—41no—
220C22×D61—41no—
221C22×D61—41no—
222C22×D61—416no—
223C22×D61C2×C22⋊C411yescharacteristic
224C22×D61C2×C22⋊C411yescharacteristic
225C22×D61C2×C22⋊C411yescharacteristic
226C22×D61#12314yes—
227C22×D61C22×D411yescharacteristic
228C2×#6923—44no—
229C2×#6923—44no—
230C2×#6923—44no—
231C2×C4×C61—22no—
232C2×C4×C61—22no—
233C2×C4×C61—22no—
234C2×C4×C61—22no—
235C2×C4×C61—22no—
236C2×C4×C61—24no—
237C2×C4×C61—44no—
238C2×C4×C61—44no—
239C2×C4×C61—44no—
240C2×C4×C61C2×C22⋊C411yescharacteristic
241C2×C4×C61C2×C22⋊C411yescharacteristic
242C2×C4×C61C2×C22⋊C411yescharacteristic
243C2×C4×C61#11714yes—
244C2×C4×C61C23×C411yescharacteristic
245C2×Dic61—22no—
246C2×Dic61—22no—
247C2×Dic61—22no—
248C2×Dic61—22no—
249C2×Dic61—22no—
250C2×Dic61—24no—
251C2×Dic61—44no—
252C2×Dic61—44no—
253C2×Dic61—44no—
254C2×Dic61C2×C22⋊C411yescharacteristic
255C2×Dic61C2×C22⋊C411yescharacteristic
256C2×Dic61C2×C22⋊C411yescharacteristic
257C2×Dic61#12314yes—
258C2×Dic61C22×D411yescharacteristic
259C4×D61—22no—
260C4×D61—22no—
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—22no—
271C4×D61#11714yes—
272C4×D61#12314yes—
273C4×D61#12314yes—
274C4×D61C2×#4114yes—
275#92420—44no—
276#20705—611nomaximal, Sylow
277C22×C61—28no—
278C22×C61—21no—
279C22×C61—21no—
280C22×C61—21no—
281C22×C61—21no—
282C22×C61—21no—
283C22×C61—21no—
284C22×C61#38112yes—
285C22×C61#42112yes—
286C22×C61#42112yes—
287C22×C61C22×C22⋊C411yescharacteristic
288C2×D61—21no—
289C2×D61—21no—
290C2×D61—21no—
291C2×D61—21no—
292C2×D61—21no—
293C2×D61—21no—
294C2×D61—21no—
295C2×D61—21no—
296C2×D61—21no—
297C2×D61—21no—
298C2×D61—44no—
299C2×D61—44no—
300C2×D61—44no—
301C2×D61—44no—
302C2×D61—44no—
303C2×D61—44no—
304C2×D61#38112yes—
305C2×D61C2×#12312yes—
306#6923—84no—
307C4×C61—21no—
308C4×C61—21no—
309C4×C61—44no—
310C4×C61#38112yes—
311C4×C61C2×#11712yes—
312Dic61—21no—
313Dic61—21no—
314Dic61—44no—
315Dic61#38112yes—
316Dic61C2×#12312yes—
317C22×#117—611no—
318C2×#407—611no—
319#2280—611no—
320#1826—614no—
321#1826—614no—
322#1733—614no—
323C2×C61—22no—
324C2×C61—22no—
325C2×C61—22no—
326C2×C61C2×#38111yescharacteristic
327C2×C61C2×#42111yescharacteristic
328C2×C61C2×#42111yescharacteristic
329D61—22no—
330D61—22no—
331D61—41no—
332D61—41no—
333C24×C4—611no—
334C22×M16—612no—
335C2×#117—612no—
336C2×#117—612no—
337C2×#117—612no—
338C2×#117—612no—
339C2×#117—612no—
340C2×#117—612no—
341C2×#117—612no—
342C2×#117—1221no—
343C2×#117—1221no—
344C2×#117—1221no—
345C2×#117—1221no—
346C2×#117—1221no—
347C2×#117—1221no—
348C22×C4⋊C4—611no—
349C22×C4⋊C4#692311yescharacteristic, complemented
350C22×C22⋊C4—1221no—
351C22×C42—1221no—
352#407—612no—
353#407—612no—
354#407—1221no—
355#407—1221no—
356C2×C22⋊C8—1221no—
357C2×C22⋊C8—1221no—
358#381—1221no—
359#380—1221no—
360#380—1221no—
361#379—1221no—
362C4×C22⋊C4—612no—
363C4×C22⋊C4—612no—
364#339—6116no—
365C61#2070511yescharacteristic, complemented, Sylow
366C25—611no—
367C23×C4—21no—
368C23×C4—611no—
369C23×C4—611no—
370C23×C4—611no—
371C23×C4—611no—
372C23×C4—611no—
373C23×C4—611no—
374C23×C4—611no—
375C23×C4—611no—
376C23×C4—611no—
377C23×C4—611no—
378C23×C4—611no—
379C23×C4—611no—
380C23×C4—611no—
381C23×C4—1228no—
382C23×C4—1221no—
383C23×C4C2×#692311yescharacteristic
384C2×M16—614no—
385C2×M16—1222no—
386C2×M16—1228no—
387C22×C8—1222no—
388#117—614no—
389#117—614no—
390#117—614no—
391#117—614no—
392#117—1222no—
393#117—1222no—
394#117—1222no—
395#117—1222no—
396#117—1222no—
397#117—1222no—
398#117—1222no—
399#117—1222no—
400#117—1222no—
401#117—1222no—
402#117—1222no—
403#117—1222no—
404#117—1228no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—612no—
409C2×C4⋊C4—612no—
410C2×C4⋊C4—612no—
411C2×C4⋊C4—1221no—
412C2×C4⋊C4—1221no—
413C2×C4⋊C4—1221no—
414C2×C4⋊C4—1222no—
415C2×C4⋊C4C2×#692312yes—
416C2×C4⋊C4C2×#692312yes—
417C2×C4⋊C4C2×#692312yes—
418C2×C22⋊C4—1222no—
419C2×C22⋊C4—1222no—
420C2×C22⋊C4—1222no—
421C2×C22⋊C4—1222no—
422C2×C22⋊C4—1222no—
423C2×C22⋊C4—1222no—
424C2×C22⋊C4—1222no—
425C2×C22⋊C4—1222no—
426C2×C22⋊C4—1222no—
427C2×C42—614no—
428C2×C42—1222no—
429C2×C42—1222no—
430C2×C42—1222no—
431C2×C42—1222no—
432C2×C42—1222no—
433C2×C42—1222no—
434C22⋊C8—1222no—
435C22⋊C8—1222no—
436C22⋊C8—1222no—
437C22⋊C8—1222no—
438#95—1222no—
439#95—1222no—
440C24—611no—
441C24—611no—
442C24—611no—
443C24—611no—
444C24—611no—
445C24—611no—
446C24—1224no—
447C24—2442no—
448C24—2442no—
449C24C22⋊#692311yescharacteristic
450C22×C4—24no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—44no—
455C22×C4—611no—
456C22×C4—611no—
457C22×C4—611no—
458C22×C4—618no—
459C22×C4—611no—
460C22×C4—611no—
461C22×C4—611no—
462C22×C4—611no—
463C22×C4—611no—
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—1224no—
479C22×C4—1224no—
480C22×C4—1224no—
481C22×C4—1224no—
482C22×C4—1224no—
483C22×C4—1224no—
484C22×C4—1224no—
485C22×C4—1224no—
486C22×C4—1224no—
487C22×C4—1224no—
488C22×C4—1224no—
489C22×C4—1224no—
490C22×C4—1222no—
491C22×C4—1222no—
492C22×C4—1222no—
493C22×C4—1224no—
494C22×C4—2444no—
495C22×C4C22⋊#692311yescharacteristic
496C22×C4C22⋊#692311yescharacteristic
497C22×C4C22⋊#692311yescharacteristic
498C22×C4C22×#692311yescharacteristic
499C22×C4C22×#692311yescharacteristic
500C22×C4C22×#692311yescharacteristic
501M16—1228no—
502M16—2444no—
503C2×C8—1224no—
504C2×C8—2444no—
505C4⋊C4—22no—
506C4⋊C4—22no—
507C4⋊C4—22no—
508C4⋊C4—614no—
509C4⋊C4—1222no—
510C4⋊C4—1222no—
511C4⋊C4—1222no—
512C4⋊C4—2444no—
513C4⋊C4C22×#692314yes—
514C22⋊C4—1224no—
515C22⋊C4—1224no—
516C22⋊C4—1224no—
517C22⋊C4—1224no—
518C22⋊C4—2444no—
519C22⋊C4—2444no—
520C22⋊C4—2444no—
521C42—1224no—
522C42—1224no—
523C42—1224no—
524C42—1224no—
525C42—1228no—
526C23—22no—
527C23—22no—
528C23—22no—
529C23—611no—
530C23—611no—
531C23—614no—
532C23—611no—
533C23—611no—
534C23—1222no—
535C23—1222no—
536C23—1222no—
537C23—1222no—
538C23—1222no—
539C23—1222no—
540C23—1222no—
541C23—1222no—
542C23—1222no—
543C23—2441no—
544C23—2441no—
545C23—2441no—
546C23—2441no—
547C23—2441no—
548C23—2441no—
549C23—2441no—
550C23—2441no—
551C23—24416no—
552C23C2×C22⋊#692311yescharacteristic
553C23C2×C22⋊#692311yescharacteristic
554C23C2×C22⋊#692311yescharacteristic
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—24no—
561C2×C4—44no—
562C2×C4—44no—
563C2×C4—44no—
564C2×C4—614no—
565C2×C4—611no—
566C2×C4—611no—
567C2×C4—614no—
568C2×C4—614no—
569C2×C4—614no—
570C2×C4—614no—
571C2×C4—611no—
572C2×C4—611no—
573C2×C4—1222no—
574C2×C4—1222no—
575C2×C4—1222no—
576C2×C4—1222no—
577C2×C4—1222no—
578C2×C4—1222no—
579C2×C4—1222no—
580C2×C4—1222no—
581C2×C4—1222no—
582C2×C4—1222no—
583C2×C4—1222no—
584C2×C4—1222no—
585C2×C4—1222no—
586C2×C4—1222no—
587C2×C4—1222no—
588C2×C4—1222no—
589C2×C4—1222no—
590C2×C4—1224no—
591C2×C4—2444no—
592C2×C4—2444no—
593C2×C4—2444no—
594C2×C4—2444no—
595C2×C4—2444no—
596C2×C4—2444no—
597C2×C4C2×C22⋊#692311yescharacteristic
598C2×C4C2×C22⋊#692311yescharacteristic
599C2×C4C2×C22⋊#692311yescharacteristic
600C2×C4#1451985614yes—
601C2×C4C23×#692311yescharacteristic
602C8—2444no—
603C22—28no—
604C22—21no—
605C22—21no—
606C22—21no—
607C22—21no—
608C22—21no—
609C22—21no—
610C22—612no—
611C22—612no—
612C22—1221no—
613C22—1221no—
614C22—1221no—
615C22—1221no—
616C22—1221no—
617C22—1221no—
618C22—1221no—
619C22—1221no—
620C22—1221no—
621C22—1221no—
622C22—2444no—
623C22—2444no—
624C22—2444no—
625C22—2444no—
626C22—2444no—
627C22—2444no—
628C22#1684070512yes—
629C22#1684076012yes—
630C22#1684076112yes—
631C22C22×C22⋊#692311yescharacteristic
632C4—21no—
633C4—21no—
634C4—44no—
635C4—612no—
636C4—612no—
637C4—1221no—
638C4—1221no—
639C4—4884no—
640C4—2444no—
641C4#1684070512yes—
642C4C2×#1451985612yes—
643C2—22no—
644C2—22no—
645C2—22no—
646C2—1222no—
647C2—1222no—
648C2—2441no—
649C2—2441no—
650C2C2×#1684070511yescharacteristic
651C2C2×#1684076011yescharacteristic
652C2C2×#1684076111yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC22×C4⋊C4×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC24×D61D4
cosocleC2×C4×D61C24
hypercenterC22×C4⋊C4#6923
hypocenterC61#20705
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #21461726C2semidirect
4. #21461725C2semidirect
5. #21461498C2semidirect
21. #16840632C22semidirect
29. C2×#14519735C4semidirect
30. C2×#14519735C4semidirect
31. C2×#14519735C4semidirect
35. C22×C4⋊Dic61C4semidirect
38. C22×C4⋊C4×C61C4semidirect
349. C22×C4⋊C4#6923semidirect
365. C61#20705semidirect

Maximal subgroups

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

subgroupindex
D61⋊#4072
#214622632
#214617262
#214617252
#214614982
C22×#145197352
#2070561