Finite Group Databasebeta

← #30611492

Subgroups — #30611492

Order 15616.

1070 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D61⋊#432C211yesmaximal, characteristic, complemented
2C4×D61⋊M16C211yesmaximal, characteristic, complemented
3#21461296C214yesmaximal, complemented
4#21461281C212yesmaximal, complemented
5#21461280C212yesmaximal, complemented
6#21461271C214yesmaximal, complemented
7C2×#16840299C211yesmaximal, characteristic
8C2×D61⋊M16—21no—
9#16840785C2212yescomplemented
10#16840784—21no—
11#16840783C2212yes—
12#16840782—21no—
13D61⋊(C4⋊C8)—21no—
14D61⋊(C22⋊C8)—21no—
15C4×#11758213—21no—
16C4×#11758213C2212yescomplemented
17C4×#11758217—21no—
18C4×#11758217C2212yes—
19#16840721C2212yescomplemented
20#16840721C2212yescomplemented
21C4×D61⋊C8—21no—
22#16840619C2218yescomplemented
23#16840618C2218yescomplemented
24#16840299—21no—
25#16840299—21no—
26#16840299—21no—
27#16840299—21no—
28#16840299C412yes—
29#16840299C412yes—
30#16840299C2212yes—
31#16840299C2212yes—
32C2×#14519772—21no—
33C2×#14519768C2211yescharacteristic
34C2×#14519766C2211yescharacteristic
35C2×#14519762—21no—
36C2×#14519753C411yescharacteristic
37C2×#14519752C411yescharacteristic
38C2×C4×D244—21no—
39C2×C4×D244C411yescharacteristic
40C2×#14519734—21no—
41C2×C42×D61C2211yescharacteristic
42C2×C4×Q8×C61C411yescharacteristic
43C2×#11758213—22no—
44D61⋊M16—28no—
45C2×#11758217—22no—
46C2×D61⋊C8—22no—
47C2×D61⋊C8—22no—
48#14519844—22no—
49C4⋊#92420—22no—
50#14519834—22no—
51C22⋊#92420—22no—
52#14519832—22no—
53#14519832—22no—
54#14519832C2314yes—
55#14519832C2314yes—
56C4×#92420—22no—
57C4×#92420—22no—
58C22×D244—21no—
59C22×D244C2×C411yescharacteristic
60C22×C4×D61—21no—
61C22×C4×D61C2×C411yescharacteristic
62C22×C4×D61D411yescharacteristic
63C22×C4×D61D411yescharacteristic
64#14519772—22no—
65#14519772—22no—
66#14519772—22no—
67#14519772—22no—
68#14519768—21no—
69#14519768—21no—
70#14519768C2×C412yes—
71#14519768C2312yes—
72#14519766—21no—
73#14519766—21no—
74#14519766C2×C412yes—
75#14519766C2312yes—
76#14519762—22no—
77#14519762—22no—
78#14519762—22no—
79#14519762—22no—
80#14519753—21no—
81#14519753—21no—
82#14519753C2×C412yes—
83#14519753C2×C412yes—
84#14519752—21no—
85#14519752—21no—
86#14519752C2×C412yes—
87#14519752C2×C412yes—
88C4×D244—22no—
89C4×D244—22no—
90C4×D244—22no—
91C4×D244—22no—
92C4×D244—21no—
93C4×D244—21no—
94C4×D244C2×C412yes—
95C4×D244C2×C412yes—
96#14519734—22no—
97#14519734—22no—
98#14519734—22no—
99#14519734—22no—
100C2×C4⋊Dic61—21no—
101C2×C4⋊Dic61C2×C411yescharacteristic
102C2×#11758196—21no—
103C2×#11758196—21no—
104C2×#11758198—21no—
105C2×#11758198—21no—
106C2×#11758198—21no—
107C2×#11758198—21no—
108C2×#11758198—21no—
109C2×C4×Dic61D411yescharacteristic
110C2×C4×Dic61D411yescharacteristic
111C2×C4×Dic61C2311yescharacteristic
112C42×D61C2×C411yescharacteristic
113C42×D61C2×C411yescharacteristic
114C42×D61D411yescharacteristic
115C42×D61D411yescharacteristic
116C42×D61D411yescharacteristic
117C42×D61D411yescharacteristic
118C42×D61C2311yescharacteristic
119C42×D61C2311yescharacteristic
120C22×Q8×C61C2×C411yescharacteristic
121C4×Q8×C61—21no—
122C4×Q8×C61—21no—
123C4×Q8×C61C2×C412yes—
124C4×Q8×C61C2×C412yes—
125C2×C4⋊C4×C61—21no—
126C2×C4⋊C4×C61C2×C411yescharacteristic
127C2×C42×C61—21no—
128C2×C42×C61C2×C411yescharacteristic
129C23×D61—21no—
130C23×D61C22⋊C411yescharacteristic
131C2×Q8×C61—21no—
132C2×Q8×C61—42no—
133C2×Q8×C61C22×C412yes—
134C22×C4×C61—21no—
135C22×C4×C61—21no—
136C22×C4×C61C22⋊C411yescharacteristic
137C22×C4×C61C22⋊C411yescharacteristic
138C22×C4×C61C22×C411yescharacteristic
139C22×Dic61—21no—
140C22×Dic61C22⋊C411yescharacteristic
141C22×Dic61C2×D411yescharacteristic
142C22×Dic61C2×D411yescharacteristic
143C2×D244—22no—
144C2×D244—22no—
145C2×D244—21no—
146C2×D244—44no—
147C2×D244—42no—
148C2×D244C22×C412yes—
149C2×C4×D61—24no—
150C2×C4×D61—22no—
151C2×C4×D61—22no—
152C2×C4×D61—42no—
153C2×C4×D61—42no—
154C2×C4×D61—44no—
155C2×C4×D61C22⋊C411yescharacteristic
156C2×C4×D61C22⋊C411yescharacteristic
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×D61C2×D411yescharacteristic
164C2×C4×D61C2×D411yescharacteristic
165C2×C4×D61C2×D411yescharacteristic
166C2×C4×D61C2×D411yescharacteristic
167#11758217—28no—
168C2×#92420—24no—
169C2×#92420—24no—
170#11758213—28no—
171D61⋊C8—28no—
172D61⋊C8—44no—
173C4⋊C4×C61—22no—
174C4⋊C4×C61—22no—
175C4⋊C4×C61—21no—
176C4⋊C4×C61C22×C412yes—
177C42×C61—22no—
178C42×C61—22no—
179C42×C61C22⋊C411yescharacteristic
180C42×C61C22⋊C411yescharacteristic
181C42×C61C22×C411yescharacteristic
182C42×C61C22×C411yescharacteristic
183#11758198—22no—
184#11758198—22no—
185#11758198—22no—
186#11758198—22no—
187#11758198—22no—
188#11758198—22no—
189#11758198—22no—
190#11758198—22no—
191#11758198—22no—
192#11758198—22no—
193C4⋊Dic61—21no—
194C4⋊Dic61—22no—
195C4⋊Dic61—22no—
196C4⋊Dic61C22×C412yes—
197#11758196—22no—
198#11758196—22no—
199#11758196—22no—
200#11758196—22no—
201C4×Dic61C22⋊C411yescharacteristic
202C4×Dic61C22⋊C411yescharacteristic
203C4×Dic61C22⋊C411yescharacteristic
204C4×Dic61C22⋊C411yescharacteristic
205C4×Dic61C22×C411yescharacteristic
206C4×Dic61C2×D411yescharacteristic
207C4×Dic61C2×D411yescharacteristic
208C4×Dic61C2×D411yescharacteristic
209C4×Dic61C2×D411yescharacteristic
210C4×Dic61C2×D411yescharacteristic
211C4×Dic61C2×D411yescharacteristic
212C4×Dic61C2411yescharacteristic
213C23×C61C2×C22⋊C411yescharacteristic
214C22×D61—22no—
215C22×D61—41no—
216C22×D61—41no—
217C22×D61—42no—
218C22×D61—42no—
219C22×D61—42no—
220C22×D61#10414yes—
221C22×D61C2×C22⋊C411yescharacteristic
222C22×D61C2×C22⋊C411yescharacteristic
223Q8×C61—42no—
224Q8×C61—42no—
225C2×C4×C61—22no—
226C2×C4×C61—22no—
227C2×C4×C61—22no—
228C2×C4×C61—22no—
229C2×C4×C61—22no—
230C2×C4×C61—42no—
231C2×C4×C61—42no—
232C2×C4×C61C2×C22⋊C411yescharacteristic
233C2×C4×C61C2×C22⋊C411yescharacteristic
234C2×C4×C61C2×C22⋊C411yescharacteristic
235C2×C4×C61C2×C22⋊C411yescharacteristic
236C2×C4×C61C2×C22⋊C411yescharacteristic
237C2×C4×C61C23×C411yescharacteristic
238C2×Dic61—22no—
239C2×Dic61—22no—
240C2×Dic61—41no—
241C2×Dic61—41no—
242C2×Dic61—42no—
243C2×Dic61C2×C22⋊C411yescharacteristic
244C2×Dic61C2×C22⋊C411yescharacteristic
245C2×Dic61C2×C22⋊C411yescharacteristic
246C2×Dic61C2×C22⋊C411yescharacteristic
247C2×Dic61C22×D411yescharacteristic
248C2×Dic61C22×D411yescharacteristic
249D244—42no—
250D244—44no—
251D244—44no—
252D244—42no—
253C4×D61—22no—
254C4×D61—22no—
255C4×D61—22no—
256C4×D61—22no—
257C4×D61—22no—
258C4×D61—22no—
259C4×D61—22no—
260C4×D61—22no—
261C4×D61—41no—
262C4×D61—41no—
263C4×D61—41no—
264C4×D61—41no—
265C4×D61—44no—
266C4×D61—44no—
267#92420—28no—
268#92420—44no—
269#17650—611nomaximal, Sylow
270C22×C61—21no—
271C22×C61—21no—
272C22×C61C2×#10412yes—
273C22×C61C22×C22⋊C411yescharacteristic
274C2×D61—21no—
275C2×D61—21no—
276C2×D61—21no—
277C2×D61—21no—
278C2×D61—44no—
279C2×D61—42no—
280C2×D61—42no—
281C2×D61—42no—
282C2×D61—84no—
283C2×D61C2×#10412yes—
284C2×D61C2×#10412yes—
285C4×C61—21no—
286C4×C61—21no—
287C4×C61—21no—
288C4×C61—21no—
289C4×C61—42no—
290C4×C61—42no—
291C4×C61#41312yes—
292C4×C61#42112yes—
293Dic61—21no—
294Dic61—21no—
295Dic61—21no—
296Dic61—21no—
297Dic61—21no—
298Dic61—21no—
299Dic61—42no—
300C2×#529—611no—
301C2×#432—611no—
302C2×C4×M16—611no—
303#1532—614no—
304#1528—612no—
305#1527—612no—
306#1524—614no—
307C2×C61—22no—
308C2×C61C2×#41311yescharacteristic
309C2×C61C22×#10411yescharacteristic
310C2×C61C2×#42111yescharacteristic
311D61—22no—
312D61—22no—
313D61—82no—
314C22×M16—1221no—
315#529—612no—
316#529—612no—
317#529—612no—
318#529—612no—
319#529—1221no—
320#529—1221no—
321#529—1221no—
322#529—1221no—
323C2×#126—1221no—
324C2×#125—611no—
325C2×#124—611no—
326C2×#123—1221no—
327C2×C22⋊Q8—611no—
328C2×#121—611no—
329C2×C4×Q8#692311yescharacteristic
330C2×C4×D4—611no—
331C2×C4×D4—1221no—
332C2×#117—1221no—
333C22×C42—611no—
334#432—612no—
335#432—612no—
336#432—1221no—
337#432—1221no—
338C2×C4⋊C8—1221no—
339C2×C22⋊C8—1221no—
340C4×M16—612no—
341C4×M16—612no—
342C4×M16—1221no—
343C4×M16—1221no—
344C2×#97—612no—
345C2×#97—612no—
346C2×C4×C8—1221no—
347#330—618no—
348#329—618no—
349C61#1765011yescharacteristic, complemented, Sylow
350C22×Q8C2×#692311yescharacteristic
351C22×D4—611no—
352C22×D4—1221no—
353C23×C4—611no—
354C23×C4—611no—
355C23×C4—611no—
356C23×C4—1221no—
357C2×M16—1222no—
358C2×M16—1222no—
359C2×M16—1228no—
360C22×C8—1222no—
361C22×C8—1222no—
362#126—1222no—
363#126—1222no—
364#126—1222no—
365#126—1222no—
366#125—612no—
367#125—612no—
368#125—1221no—
369#125—1221no—
370#124—612no—
371#124—612no—
372#124—1221no—
373#124—1221no—
374#123—1222no—
375#123—1222no—
376#123—1222no—
377#123—1222no—
378C22⋊Q8—612no—
379C22⋊Q8—612no—
380C22⋊Q8—1221no—
381C22⋊Q8—1221no—
382#121—612no—
383#121—612no—
384#121—1221no—
385#121—1221no—
386C4×Q8—21no—
387C4×Q8—21no—
388C4×Q8C2×#692312yes—
389C4×Q8C2×#692312yes—
390C4×D4—612no—
391C4×D4—612no—
392C4×D4—1222no—
393C4×D4—1222no—
394C4×D4—1222no—
395C4×D4—1222no—
396C4×D4—1221no—
397C4×D4—1221no—
398#117—1222no—
399#117—1222no—
400#117—1222no—
401#117—1222no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—611no—
404C2×C4⋊C4—1221no—
405C2×C4⋊C4—1221no—
406C2×C4⋊C4—1221no—
407C2×C4⋊C4C2×#692311yescharacteristic
408C2×C22⋊C4—1221no—
409C2×C22⋊C4—1221no—
410C2×C22⋊C4—1221no—
411C2×C22⋊C4—1221no—
412C2×C22⋊C4—1221no—
413C2×C42—21no—
414C2×C42—611no—
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×C42C2×#692311yescharacteristic
426C4⋊C8—1222no—
427C4⋊C8—1222no—
428C22⋊C8—1222no—
429C22⋊C8—1222no—
430#97—614no—
431#97—614no—
432#97—1222no—
433#97—1222no—
434C4×C8—1222no—
435C4×C8—1222no—
436C24—611no—
437C24—1221no—
438C2×Q8—21no—
439C2×Q8—42no—
440C2×Q8C22×#692312yes—
441C2×D4—612no—
442C2×D4—1222no—
443C2×D4—1222no—
444C2×D4—1221no—
445C2×D4—2442no—
446C2×D4—2444no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—611no—
450C22×C4—611no—
451C22×C4—611no—
452C22×C4—611no—
453C22×C4—611no—
454C22×C4—611no—
455C22×C4—611no—
456C22×C4—611no—
457C22×C4—611no—
458C22×C4—611no—
459C22×C4—611no—
460C22×C4—611no—
461C22×C4—611no—
462C22×C4—611no—
463C22×C4—611no—
464C22×C4—1224no—
465C22×C4—1221no—
466C22×C4—1222no—
467C22×C4—1222no—
468C22×C4—2442no—
469C22×C4—2442no—
470C22×C4—2444no—
471C22×C4C22⋊#692311yescharacteristic
472C22×C4C22⋊#692311yescharacteristic
473C22×C4C22×#692311yescharacteristic
474M16—1228no—
475M16—1228no—
476C2×C8—1224no—
477C2×C8—1228no—
478C2×C8—1224no—
479C2×C8—2444no—
480C4⋊C4—22no—
481C4⋊C4—22no—
482C4⋊C4—21no—
483C4⋊C4—612no—
484C4⋊C4—1222no—
485C4⋊C4—1222no—
486C4⋊C4—1222no—
487C4⋊C4—1222no—
488C4⋊C4—1222no—
489C4⋊C4—1222no—
490C4⋊C4—1221no—
491C4⋊C4C22×#692312yes—
492C22⋊C4—1222no—
493C22⋊C4—1222no—
494C22⋊C4—1222no—
495C22⋊C4—1222no—
496C22⋊C4—1222no—
497C22⋊C4—1222no—
498C22⋊C4—1222no—
499C22⋊C4—1222no—
500C22⋊C4—1222no—
501C22⋊C4—1222no—
502C42—22no—
503C42—22no—
504C42—611no—
505C42—611no—
506C42—611no—
507C42—611no—
508C42—611no—
509C42—611no—
510C42—611no—
511C42—611no—
512C42—611no—
513C42—611no—
514C42—611no—
515C42—611no—
516C42C22⋊#692311yescharacteristic
517C42C22⋊#692311yescharacteristic
518C42C22×#692311yescharacteristic
519C42C22×#692311yescharacteristic
520C23—611no—
521C23—611no—
522C23—614no—
523C23—1222no—
524C23—2441no—
525C23—2441no—
526C23—2442no—
527C23—2442no—
528C23—2442no—
529C23C2×C22⋊#692311yescharacteristic
530Q8—42no—
531Q8—42no—
532D4—2442no—
533D4—2444no—
534D4—2444no—
535D4—2442no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—611no—
544C2×C4—611no—
545C2×C4—611no—
546C2×C4—611no—
547C2×C4—611no—
548C2×C4—611no—
549C2×C4—1222no—
550C2×C4—1222no—
551C2×C4—1222no—
552C2×C4—1222no—
553C2×C4—1222no—
554C2×C4—1222no—
555C2×C4—1222no—
556C2×C4—1222no—
557C2×C4—1222no—
558C2×C4—1222no—
559C2×C4—2441no—
560C2×C4—2441no—
561C2×C4—2441no—
562C2×C4—2441no—
563C2×C4—2444no—
564C2×C4—2441no—
565C2×C4—2441no—
566C2×C4—2442no—
567C2×C4—2444no—
568C2×C4C2×C22⋊#692311yescharacteristic
569C2×C4C2×C22⋊#692311yescharacteristic
570C2×C4C2×C22⋊#692311yescharacteristic
571C2×C4C2×C22⋊#692311yescharacteristic
572C2×C4C2×C22⋊#692311yescharacteristic
573C2×C4C23×#692311yescharacteristic
574C8—1228no—
575C8—2444no—
576C22—21no—
577C22—21no—
578C22—612no—
579C22—612no—
580C22—1221no—
581C22—1221no—
582C22—1221no—
583C22—1221no—
584C22—4884no—
585C22—2444no—
586C22—2442no—
587C22—2442no—
588C22—2442no—
589C22D61⋊#10412yes—
590C22C22×C22⋊#692311yescharacteristic
591C4—21no—
592C4—21no—
593C4—21no—
594C4—21no—
595C4—42no—
596C4—42no—
597C4—1221no—
598C4—1221no—
599C4—1221no—
600C4—1221no—
601C4—1221no—
602C4—1221no—
603C4—2442no—
604C4#1684074812yes—
605C4#1684076112yes—
606C2—22no—
607C2—1222no—
608C2—1222no—
609C2—4882no—
610C2C2×#1684074811yescharacteristic
611C2C2×D61⋊#10411yescharacteristic
612C2C2×#1684076111yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC2×C4×Q8×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC2×#14519752C4
cosocleC4×Dic61C24
hypercenterC2×C4×Q8#6923
hypocenterC61#17650
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
1. D61⋊#432C2semidirect
2. C4×D61⋊M16C2semidirect
3. #21461296C2semidirect
4. #21461281C2semidirect
5. #21461280C2semidirect
6. #21461271C2semidirect
9. #16840785C22semidirect
16. C4×#11758213C22semidirect
19. #16840721C22semidirect
20. #16840721C22semidirect
22. #16840619C22semidirect
23. #16840618C22semidirect
349. C61#17650semidirect

Maximal subgroups

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

subgroupindex
D61⋊#4322
C4×D61⋊M162
#214612962
#214612812
#214612802
#214612712
C2×#168402992
#1765061