Finite Group Databasebeta

← D61×#3167 #30549721

Subgroups — D61×#3167 #30549721

Order 15616.

2286 conjugacy classes of subgroups.

The subgroup lattice has 1064 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#533×D61C211yesmaximal, characteristic, complemented
2#532×D61C211yesmaximal, characteristic
3#21456381C211yesmaximal, characteristic, complemented
4#21456380C211yesmaximal, characteristic, complemented
5#21456379C211yesmaximal, characteristic, complemented
6#21456378C211yesmaximal, characteristic, complemented
7#21456377C211yesmaximal, characteristic, complemented
8#21456376C211yesmaximal, characteristic, complemented
9#21456375C214yesmaximal, complemented
10#21456374C211yesmaximal, characteristic, complemented
11#21456373C214yesmaximal, complemented
12#498×D61C211yesmaximal, characteristic, complemented
13#492×D61C211yesmaximal, characteristic, complemented
14#487×D61C211yesmaximal, characteristic, complemented
15#486×D61C211yesmaximal, characteristic, complemented
16#465×D61C214yesmaximal, complemented
17C4×SD16×D61C214yesmaximal, complemented
18C2×C4×C8×D61C211yesmaximal, characteristic, complemented
19C61×#3167C211yesmaximal, characteristic, complemented
20C2×#41×D61—21no—
21C2×SD16×D61C2214yes—
22C22×C8×D61C2212yes—
23#16840319C2211yescharacteristic, complemented
24#16840318—21no—
25#16840317C2211yescharacteristic, complemented
26#16840317C2211yescharacteristic, complemented
27#16840316—21no—
28#16840316C2212yescomplemented
29#16840315—21no—
30#16840314—21no—
31#16840314C2212yescomplemented
32#16840313C2211yescharacteristic
33#16840312C2211yescharacteristic
34#16840311—21no—
35#16840310C2211yescharacteristic
36#16840309—21no—
37#16840309C2212yes—
38#16840308—21no—
39#16840307—21no—
40#16840307C2212yes—
41C4⋊Q8×D61C2211yescharacteristic
42C4⋊Q8×D61C2211yescharacteristic
43C4⋊Q8×D61C2211yescharacteristic
44#127×D61C2211yescharacteristic
45#125×D61—21no—
46#124×D61—21no—
47C22⋊Q8×D61—21no—
48C22⋊Q8×D61C2212yes—
49#121×D61—21no—
50#121×D61C2212yes—
51C4×Q8×D61—21no—
52C4×Q8×D61C2212yes—
53C4×D4×D61—21no—
54C4×D4×D61C2212yes—
55#117×D61—21no—
56C2×C42×D61C2211yescharacteristic
57#16840160C2211yescharacteristic, complemented
58#16840159C2214yescomplemented
59#16840158C2211yescharacteristic, complemented
60#16840158C2211yescharacteristic, complemented
61#16840136C2211yescharacteristic, complemented
62#16840135C2211yescharacteristic, complemented
63#16840134C2211yescharacteristic, complemented
64#16840133C2214yescomplemented
65#16840114C2211yescharacteristic, complemented
66#16840113C2211yescharacteristic, complemented
67#16840112C2211yescharacteristic, complemented
68#16840111C2214yescomplemented
69#16840110C2211yescharacteristic, complemented
70#16840109C2211yescharacteristic, complemented
71#16840108C2211yescharacteristic, complemented
72#16840107C2214yescomplemented
73#16839994C2214yescomplemented
74#16839993C2214yescomplemented
75#16839992C2214yescomplemented
76#16839991C2214yescomplemented
77#16839990C2214yescomplemented
78#16839989C2214yescomplemented
79#16839988C2214yescomplemented
80#16839853C2214yescomplemented
81C4×#11758190C2214yescomplemented
82SD16×Dic61C2214yescomplemented
83C4×#11758201C2214yescomplemented
84#16839849C2214yescomplemented
85C4×#11758200C2214yescomplemented
86#16839847C2214yescomplemented
87#106×D61C2214yes—
88#103×D61C2214yes—
89#102×D61C2214yes—
90C2×C4×#92418C2211yescharacteristic, complemented
91C2×C8×Dic61C2212yescomplemented
92C4×C8×D61C2211yescharacteristic
93C4×C8×D61C2212yes—
94C4×C8×D61C2211yescharacteristic
95C4×C8×D61C2212yescomplemented
96C4×C8×D61C2211yescharacteristic, complemented
97C4×C8×D61C2211yescharacteristic, complemented
98C61×#533C2211yescharacteristic, complemented
99C61×#532C2211yescharacteristic
100C61×#498C2211yescharacteristic, complemented
101C61×#492C2211yescharacteristic, complemented
102C61×#487C2211yescharacteristic, complemented
103C61×#486C2211yescharacteristic, complemented
104C61×#465C2214yescomplemented
105C4×SD16×C61C2214yescomplemented
106C2×C4×C8×C61C2211yescharacteristic, complemented
107C2×#11758226—21no—
108C2×#11758222—21no—
109C2×#11758222—22no—
110C2×#11758224—22no—
111C2×#11758224—21no—
112#41×D61—48no—
113C2×Q8×D61—21no—
114C2×Q8×D61—21no—
115C2×Q8×D61C2312yes—
116C2×D4×D61—22no—
117C2×D4×D61—21no—
118C2×D4×D61—21no—
119C2×D4×D61C2312yes—
120C22×C4×D61—22no—
121C22×C4×D61D411yescharacteristic
122C22×C4×D61D411yescharacteristic
123C22×C4×D61C2311yescharacteristic
124C2×#11758190C2314yes—
125C2×#11758200C2314yes—
126C2×#11758201C2314yes—
127SD16×D61—216no—
128C22×#92418C2312yes—
129C2×C8×D61—28no—
130C2×C8×D61C2312yes—
131C2×C8×D61C2312yes—
132C2×C8×D61C2312yes—
133C2×C8×D61C2312yes—
134#14519777C2311yescharacteristic
135#14519777C2311yescharacteristic
136#14519777C2311yescharacteristic
137#14519776—21no—
138#14519776—21no—
139#14519776—21no—
140#14519776—21no—
141#14519776C2312yes—
142#14519776C2312yes—
143#14519775—21no—
144#14519775—21no—
145#14519775C2312yes—
146#14519774C2311yescharacteristic
147#14519773—21no—
148#14519773—21no—
149#14519773C2312yes—
150#14519769—21no—
151#14519768—21no—
152#14519768—21no—
153#14519767—22no—
154#14519767—22no—
155#14519766—21no—
156#14519765—21no—
157#14519764—21no—
158#14519763—22no—
159#14519763—22no—
160#14519757—21no—
161#14519757C2312yes—
162#14519756—21no—
163#14519756C2312yes—
164#14519755—22no—
165#14519755—22no—
166#14519754—22no—
167#14519754—22no—
168#14519753—21no—
169#14519753C2312yes—
170#14519752—21no—
171#14519752C2312yes—
172#14519751—21no—
173#14519751C2312yes—
174#14519750—22no—
175#14519750—22no—
176#14519749—22no—
177#14519749—22no—
178#14519748—21no—
179#14519748C2312yes—
180Q8×Dic61—21no—
181Q8×Dic61C2312yes—
182C4×Dic122—21no—
183C4×Dic122—22no—
184C4×Dic122—22no—
185C4×Dic122C2312yes—
186#14519742—21no—
187#14519742—22no—
188#14519742—22no—
189#14519742C2312yes—
190C4×D244—21no—
191C4×D244C2312yes—
192D4×Dic61—21no—
193D4×Dic61C2312yes—
194#14519739—21no—
195#14519739C2312yes—
196C4×C22⋊D61—22no—
197C4×C22⋊D61—22no—
198#14519737—22no—
199#14519737—22no—
200#14519736—21no—
201#14519735—21no—
202#14519735—21no—
203#14519734—22no—
204#14519733—22no—
205C4⋊C4×D61—21no—
206C4⋊C4×D61—21no—
207C4⋊C4×D61—21no—
208C4⋊C4×D61—21no—
209C4⋊C4×D61—22no—
210C4⋊C4×D61—22no—
211C4⋊C4×D61C2312yes—
212C4⋊C4×D61C2312yes—
213C22⋊C4×D61—22no—
214C22⋊C4×D61—22no—
215C22⋊C4×D61—22no—
216C2×C4×Dic61D411yescharacteristic
217C2×C4×Dic61D411yescharacteristic
218C2×C4×Dic61C2311yescharacteristic
219C42×D61—22no—
220C42×D61D411yescharacteristic
221C42×D61D411yescharacteristic
222C42×D61D411yescharacteristic
223C42×D61D411yescharacteristic
224C42×D61C2311yescharacteristic
225C42×D61C2311yescharacteristic
226C42×D61C2311yescharacteristic
227C42×D61C2311yescharacteristic
228#14519709C2314yes—
229#14519708C2314yes—
230#14519708C2314yes—
231#14519702C2314yes—
232#14519701C2314yes—
233#14519700C2314yes—
234#14519699C2314yes—
235#14519698C2314yes—
236#14519697C2314yes—
237C4×#92418C2312yes—
238C4×#92418C2311yescharacteristic
239C4×#92418C2311yescharacteristic
240C8×Dic61C2312yes—
241C8×Dic61C2312yes—
242C8×Dic61C2312yes—
243C8×Dic61C2312yes—
244C2×#41×C61—21no—
245C2×SD16×C61C2314yes—
246C22×C8×C61C2312yes—
247C4⋊Q8×C61C2311yescharacteristic
248C4⋊Q8×C61C2311yescharacteristic
249C4⋊Q8×C61C2311yescharacteristic
250#127×C61C2311yescharacteristic
251#125×C61—21no—
252#124×C61—21no—
253C22⋊Q8×C61—21no—
254C22⋊Q8×C61C2312yes—
255#121×C61—21no—
256#121×C61C2312yes—
257C4×Q8×C61—21no—
258C4×Q8×C61C2312yes—
259C4×D4×C61—21no—
260C4×D4×C61C2312yes—
261#117×C61—21no—
262C2×C42×C61C2311yescharacteristic
263#106×C61C2314yes—
264#103×C61C2314yes—
265#102×C61C2314yes—
266C4×C8×C61C2312yes—
267C4×C8×C61C2311yescharacteristic
268C4×C8×C61C2311yescharacteristic
269C23×D61—22no—
270C23×D61C2×D411yescharacteristic
271#41×C61—44no—
272C2×Q8×C61—21no—
273C2×Q8×C61—21no—
274C2×Q8×C61C2412yes—
275C2×D4×C61—22no—
276C2×D4×C61—21no—
277C2×D4×C61—21no—
278C2×D4×C61C2412yes—
279C22×C4×C61—22no—
280C22×C4×C61C2×D411yescharacteristic
281C22×C4×C61C2×D411yescharacteristic
282C22×C4×C61C2411yescharacteristic
283C2×C22⋊D61—22no—
284C2×C22⋊D61—22no—
285C2×C22⋊D61—22no—
286C2×C22⋊D61—22no—
287C2×C22⋊D61—22no—
288C22×Dic61—22no—
289C22×Dic61C2×D411yescharacteristic
290C22×Dic61C2×D411yescharacteristic
291C22×Dic61C2×D411yescharacteristic
292#11758226—44no—
293Q8×D61—28no—
294Q8×D61—44no—
295Q8×D61—44no—
296#11758224—48no—
297#11758224—44no—
298D4×D61—28no—
299D4×D61—48no—
300D4×D61—44no—
301D4×D61—44no—
302#11758222—44no—
303#11758222—48no—
304C2×D244—22no—
305C2×D244—21no—
306C2×D244—21no—
307C2×D244C2412yes—
308C2×C4×D61—24no—
309C2×C4×D61—24no—
310C2×C4×D61—22no—
311C2×C4×D61—22no—
312C2×C4×D61—22no—
313C2×C4×D61—22no—
314C2×C4×D61—22no—
315C2×C4×D61—48no—
316C2×C4×D61SD1618yescomplemented
317C2×C4×D61C2×D411yescharacteristic
318C2×C4×D61C2×D411yescharacteristic
319C2×C4×D61C2×D411yescharacteristic
320C2×C4×D61C2×D411yescharacteristic
321C2×C4×D61C2×D411yescharacteristic
322C2×C4×D61C2×D411yescharacteristic
323C2×C4×D61C2×D411yescharacteristic
324C2×C4×D61C2×D411yescharacteristic
325C2×C4×D61C2×D411yescharacteristic
326C2×C4×D61C2×D411yescharacteristic
327C2×C4×D61C2411yescharacteristic
328C2×C4×D61C2411yescharacteristic
329C2×Dic122—21no—
330C2×Dic122—21no—
331C2×Dic122—22no—
332C2×Dic122—22no—
333C2×Dic122—22no—
334C2×Dic122C2412yes—
335SD16×C61—28no—
336C2×C8×C61—24no—
337C2×C8×C61C2412yes—
338C2×C8×C61C2412yes—
339C4⋊C4×C61—21no—
340C4⋊C4×C61—21no—
341C4⋊C4×C61—21no—
342C4⋊C4×C61—21no—
343C4⋊C4×C61—22no—
344C4⋊C4×C61—22no—
345C4⋊C4×C61C2412yes—
346C4⋊C4×C61C2412yes—
347C22⋊C4×C61—22no—
348C22⋊C4×C61—22no—
349C22⋊C4×C61—22no—
350C42×C61—22no—
351C42×C61C2×D411yescharacteristic
352C42×C61C2×D411yescharacteristic
353C42×C61C2411yescharacteristic
354C42×C61C2411yescharacteristic
355C22⋊Dic61—22no—
356C22⋊Dic61—22no—
357C22⋊Dic61—22no—
358#11758201—28no—
359#11758200—28no—
360#11758198—22no—
361#11758198—22no—
362#11758198—22no—
363#11758198—22no—
364#11758198—22no—
365#11758198—22no—
366C4⋊Dic61—21no—
367C4⋊Dic61—21no—
368C4⋊Dic61—21no—
369C4⋊Dic61—21no—
370C4⋊Dic61—22no—
371C4⋊Dic61—22no—
372C4⋊Dic61C2412yes—
373C4⋊Dic61C2412yes—
374#11758196—22no—
375#11758196—22no—
376#11758196—22no—
377#11758196—22no—
378#11758196—22no—
379#11758196—22no—
380#11758196—22no—
381#11758196—22no—
382#11758196—22no—
383#11758196—22no—
384C4×Dic61—22no—
385C4×Dic61—22no—
386C4×Dic61—22no—
387C4×Dic61C2×D411yescharacteristic
388C4×Dic61C2×D411yescharacteristic
389C4×Dic61C2×D411yescharacteristic
390C4×Dic61C2×D411yescharacteristic
391C4×Dic61C2×D411yescharacteristic
392C4×Dic61C2×D411yescharacteristic
393C4×Dic61C2×D411yescharacteristic
394C4×Dic61C2×D411yescharacteristic
395C4×Dic61C2×D411yescharacteristic
396C4×Dic61C2×D411yescharacteristic
397C4×Dic61C2411yescharacteristic
398C4×Dic61C2411yescharacteristic
399C2×#92418—24no—
400C2×#92418C2412yes—
401C2×#92418C2412yes—
402#11758190—28no—
403C8×D61—24no—
404C8×D61—24no—
405C8×D61—24no—
406C8×D61#4118yescomplemented
407C23×C61—22no—
408C23×C61C22×D411yescharacteristic
409C22×D61—22no—
410C22×D61—22no—
411C22×D61—22no—
412C22×D61—44no—
413C22×D61—44no—
414C22×D61—44no—
415C22×D61C2×SD1614yes—
416C22×D61C22×D411yescharacteristic
417C22×D61C22×D411yescharacteristic
418Q8×C61—24no—
419Q8×C61—42no—
420Q8×C61—42no—
421D4×C61—24no—
422D4×C61—44no—
423D4×C61—42no—
424D4×C61—42no—
425C2×C4×C61—22no—
426C2×C4×C61—22no—
427C2×C4×C61—22no—
428C2×C4×C61—22no—
429C2×C4×C61—22no—
430C2×C4×C61—44no—
431C2×C4×C61C2×SD1614yescomplemented
432C2×C4×C61C22×D411yescharacteristic
433C2×C4×C61C22×D411yescharacteristic
434C2×C4×C61C22×D411yescharacteristic
435C2×C4×C61C22×D411yescharacteristic
436C2×C4×C61C22×D411yescharacteristic
437C2×C4×C61C2511yescharacteristic
438C22⋊D61—44no—
439C22⋊D61—44no—
440C22⋊D61—44no—
441C22⋊D61—44no—
442C22⋊D61—44no—
443C2×Dic61—22no—
444C2×Dic61—22no—
445C2×Dic61—22no—
446C2×Dic61—22no—
447C2×Dic61—22no—
448C2×Dic61—44no—
449C2×Dic61C2×SD1614yescomplemented
450C2×Dic61C22×D411yescharacteristic
451C2×Dic61C22×D411yescharacteristic
452C2×Dic61C22×D411yescharacteristic
453C2×Dic61C22×D411yescharacteristic
454C2×Dic61C22×D411yescharacteristic
455C2×Dic61C22×D411yescharacteristic
456D244—24no—
457D244—44no—
458D244—42no—
459D244—42no—
460C4×D61—22no—
461C4×D61—22no—
462C4×D61—22no—
463C4×D61—22no—
464C4×D61—22no—
465C4×D61—22no—
466C4×D61—44no—
467C4×D61—44no—
468C4×D61—44no—
469C4×D61—44no—
470C4×D61—44no—
471C4×D61C2×SD1614yes—
472C4×D61C2×SD1614yes—
473C4×D61C2×SD1614yescomplemented
474C4×D61C2×SD1614yescomplemented
475C4×D61#13514yes—
476C4×D61C2×#4114yes—
477Dic122—24no—
478Dic122—42no—
479Dic122—42no—
480Dic122—44no—
481Dic122—44no—
482Dic122—44no—
483C8×C61—22no—
484C8×C61C2×#4114yescomplemented
485#92418—22no—
486#92418C2×#4114yescomplemented
487C2×#3167—611nomaximal, Sylow
488C22×C61—21no—
489C22×C61—21no—
490C22×C61—42no—
491C22×C61—42no—
492C22×C61—42no—
493C22×C61C22×SD1612yes—
494C22×C61C23×D411yescharacteristic
495C2×D61—21no—
496C2×D61—21no—
497C2×D61—28no—
498C2×D61—42no—
499C2×D61—42no—
500C2×D61—42no—
501C2×D61—88no—
502C2×D61#53212yes—
503C2×D61C22×SD1612yes—
504C2×D61C22×SD1612yes—
505C2×D61C2×#13512yes—
506C4×C61—21no—
507C4×C61—21no—
508C4×C61—42no—
509C4×C61—42no—
510C4×C61—42no—
511C4×C61C22×SD1612yes—
512C4×C61C22×SD1612yes—
513C4×C61C2×#13512yes—
514C4×C61C22×#4112yes—
515Dic61—21no—
516Dic61—21no—
517Dic61—42no—
518Dic61—42no—
519Dic61—42no—
520Dic61#53212yes—
521Dic61C22×SD1612yes—
522Dic61C22×SD1612yes—
523Dic61C2×#13512yes—
524C2×#533—611no—
525C2×#532—611no—
526#3167—611no—
527#3167—611no—
528#3167—611no—
529#3167—611no—
530#3167—614no—
531#3167—614no—
532#3167—611no—
533#3167—611no—
534#3167—611no—
535#3167D6111yescharacteristic, direct product factor
536C2×#498—611no—
537C2×#492—611no—
538C2×#487—611no—
539C2×#486—611no—
540C2×#465—614no—
541C2×C4×SD16—614no—
542C22×C4×C8—611no—
543C2×C61—22no—
544C2×C61—82no—
545C2×C61C2×#53211yescharacteristic
546C2×C61C23×SD1611yescharacteristic
547C2×C61C22×#13511yescharacteristic
548D61—22no—
549D61—82no—
550D61#316714yesdirect product factor
551C22×#41—1221no—
552C22×SD16—614no—
553C23×C8—612no—
554#533—611no—
555#533—611no—
556#533—612no—
557#533—612no—
558#533—611no—
559#533—1221no—
560#533—1221no—
561#533—1221no—
562#533—1221no—
563#533C2×D6111yescharacteristic, complemented
564#532—611no—
565#532—611no—
566#532—612no—
567#532—612no—
568#532—611no—
569#532—1221no—
570#532—1221no—
571#532—1221no—
572#532—1221no—
573#532C2×D6111yescharacteristic
574C2×C4⋊Q8—611no—
575C2×C4⋊Q8—611no—
576C2×C4⋊Q8—611no—
577C2×#127—611no—
578C2×#125—1221no—
579C2×#124—1221no—
580C2×C22⋊Q8—612no—
581C2×C22⋊Q8—1221no—
582C2×#121—612no—
583C2×#121—1221no—
584C2×C4×Q8—612no—
585C2×C4×Q8—1221no—
586C2×C4×D4—612no—
587C2×C4×D4—1221no—
588C2×#117—1221no—
589C22×C42—611no—
590#498—611no—
591#498—611no—
592#498—614no—
593#498—611no—
594#498C2×D6111yescharacteristic, complemented
595#492—614no—
596#492—611no—
597#492—611no—
598#492—611no—
599#492C2×D6111yescharacteristic, complemented
600#487—611no—
601#487—611no—
602#487—614no—
603#487—611no—
604#487C2×D6111yescharacteristic, complemented
605#486—611no—
606#486—611no—
607#486—614no—
608#486—611no—
609#486C2×D6111yescharacteristic, complemented
610#465—614no—
611#465—614no—
612#465—614no—
613#465—614no—
614#465—614no—
615#465—614no—
616#465—614no—
617#465C2×D6114yescomplemented
618C4×SD16—614no—
619C4×SD16—614no—
620C4×SD16—614no—
621C4×SD16—614no—
622C4×SD16—614no—
623C4×SD16—614no—
624C4×SD16—614no—
625C4×SD16C2×D6114yescomplemented
626C2×#106—614no—
627C2×#103—614no—
628C2×#102—614no—
629C2×C4×C8—612no—
630C2×C4×C8—611no—
631C2×C4×C8—611no—
632C2×C4×C8—611no—
633C2×C4×C8—612no—
634C2×C4×C8—611no—
635C2×C4×C8—611no—
636C2×C4×C8—612no—
637C2×C4×C8C2×D6111yescharacteristic, complemented
638C61C2×#316711yescharacteristic, complemented, Sylow
639C2×#41—21no—
640C2×#41—1222no—
641C2×#41—1222no—
642C2×#41—1221no—
643C2×#41—1221no—
644C2×#41—1221no—
645C2×#41—2448no—
646C22×Q8—612no—
647C22×Q8—1221no—
648C22×Q8—1221no—
649C22×D4—612no—
650C22×D4—1221no—
651C22×D4—1221no—
652C22×D4—1222no—
653C23×C4—611no—
654C23×C4—611no—
655C23×C4—611no—
656C23×C4—1222no—
657C2×SD16—614no—
658C2×SD16—614no—
659C2×SD16—614no—
660C2×SD16—12216no—
661C2×SD16C22×D6114yes—
662C22×C8—612no—
663C22×C8—612no—
664C22×C8—612no—
665C22×C8—612no—
666C22×C8—612no—
667C22×C8—1228no—
668C22×C8C22×D6112yes—
669C4⋊Q8—612no—
670C4⋊Q8—612no—
671C4⋊Q8—612no—
672C4⋊Q8—611no—
673C4⋊Q8—611no—
674C4⋊Q8—611no—
675C4⋊Q8—1221no—
676C4⋊Q8—1221no—
677C4⋊Q8—1221no—
678C4⋊Q8—1221no—
679C4⋊Q8—1221no—
680C4⋊Q8—1221no—
681C4⋊Q8C22×D6111yescharacteristic
682C4⋊Q8C22×D6111yescharacteristic
683C4⋊Q8C22×D6111yescharacteristic
684#127—612no—
685#127—611no—
686#127—1221no—
687#127—1221no—
688#127C22×D6111yescharacteristic
689#125—21no—
690#125—1222no—
691#125—1222no—
692#125—1221no—
693#125—1221no—
694#125—1221no—
695#124—21no—
696#124—1222no—
697#124—1222no—
698#124—1221no—
699#124—1221no—
700#124—1221no—
701C22⋊Q8—21no—
702C22⋊Q8—612no—
703C22⋊Q8—612no—
704C22⋊Q8—612no—
705C22⋊Q8—1222no—
706C22⋊Q8—1222no—
707C22⋊Q8—1222no—
708C22⋊Q8—1222no—
709C22⋊Q8—1221no—
710C22⋊Q8—1221no—
711C22⋊Q8—1221no—
712C22⋊Q8C22×D6112yes—
713#121—21no—
714#121—612no—
715#121—612no—
716#121—612no—
717#121—1222no—
718#121—1222no—
719#121—1221no—
720#121—1222no—
721#121—1221no—
722#121—1222no—
723#121—1221no—
724#121C22×D6112yes—
725C4×Q8—21no—
726C4×Q8—612no—
727C4×Q8—612no—
728C4×Q8—612no—
729C4×Q8—1222no—
730C4×Q8—1222no—
731C4×Q8—1222no—
732C4×Q8—1221no—
733C4×Q8—1222no—
734C4×Q8—1221no—
735C4×Q8—1221no—
736C4×Q8C22×D6112yes—
737C4×D4—21no—
738C4×D4—612no—
739C4×D4—612no—
740C4×D4—612no—
741C4×D4—1222no—
742C4×D4—1222no—
743C4×D4—1221no—
744C4×D4—1222no—
745C4×D4—1222no—
746C4×D4—1221no—
747C4×D4—1221no—
748C4×D4C22×D6112yes—
749#117—21no—
750#117—1222no—
751#117—1222no—
752#117—1221no—
753#117—1221no—
754#117—1221no—
755C2×C4⋊C4—612no—
756C2×C4⋊C4—612no—
757C2×C4⋊C4—1221no—
758C2×C4⋊C4—1221no—
759C2×C4⋊C4—1221no—
760C2×C4⋊C4—1222no—
761C2×C4⋊C4—1222no—
762C2×C4⋊C4—1221no—
763C2×C22⋊C4—1222no—
764C2×C22⋊C4—1222no—
765C2×C22⋊C4—1222no—
766C2×C42—611no—
767C2×C42—611no—
768C2×C42—611no—
769C2×C42—611no—
770C2×C42—611no—
771C2×C42—611no—
772C2×C42—611no—
773C2×C42—611no—
774C2×C42—611no—
775C2×C42—611no—
776C2×C42—611no—
777C2×C42—1222no—
778C2×C42C22×D6111yescharacteristic
779#106—614no—
780#106—614no—
781#106—614no—
782#106C22×D6114yes—
783#103—614no—
784#103—614no—
785#103—614no—
786#103C22×D6114yes—
787#102—614no—
788#102—614no—
789#102—614no—
790#102C22×D6114yes—
791C4×C8—612no—
792C4×C8—612no—
793C4×C8—612no—
794C4×C8—612no—
795C4×C8—612no—
796C4×C8—611no—
797C4×C8—611no—
798C4×C8C22×D6112yes—
799C4×C8C22×D6111yescharacteristic
800C4×C8C22×D6111yescharacteristic
801C24—611no—
802C24—1222no—
803#41—44no—
804#41—2448no—
805#41—2448no—
806#41—2444no—
807#41—2444no—
808#41—2444no—
809C2×Q8—21no—
810C2×Q8—21no—
811C2×Q8—612no—
812C2×Q8—1222no—
813C2×Q8—1222no—
814C2×Q8—1222no—
815C2×Q8—1228no—
816C2×Q8—1221no—
817C2×Q8—1221no—
818C2×Q8—2444no—
819C2×Q8—2444no—
820C2×Q8C23×D6112yes—
821C2×D4—22no—
822C2×D4—21no—
823C2×D4—21no—
824C2×D4—612no—
825C2×D4—1222no—
826C2×D4—1228no—
827C2×D4—1222no—
828C2×D4—1222no—
829C2×D4—1222no—
830C2×D4—1222no—
831C2×D4—1222no—
832C2×D4—1221no—
833C2×D4—1221no—
834C2×D4—2444no—
835C2×D4—2444no—
836C2×D4—2448no—
837C2×D4C23×D6112yes—
838C22×C4—22no—
839C22×C4—611no—
840C22×C4—611no—
841C22×C4—611no—
842C22×C4—611no—
843C22×C4—611no—
844C22×C4—611no—
845C22×C4—611no—
846C22×C4—618no—
847C22×C4—611no—
848C22×C4—611no—
849C22×C4—611no—
850C22×C4—611no—
851C22×C4—611no—
852C22×C4—611no—
853C22×C4—611no—
854C22×C4—611no—
855C22×C4—1224no—
856C22×C4—1224no—
857C22×C4—1222no—
858C22×C4—1222no—
859C22×C4—1222no—
860C22×C4—1222no—
861C22×C4—1222no—
862C22×C4—1222no—
863C22×C4—2448no—
864C22×C4D4×D6111yescharacteristic
865C22×C4D4×D6111yescharacteristic
866C22×C4C23×D6111yescharacteristic
867SD16—28no—
868SD16—1228no—
869SD16—1228no—
870SD16—1228no—
871C2×C8—24no—
872C2×C8—612no—
873C2×C8—618no—
874C2×C8—612no—
875C2×C8—1224no—
876C2×C8—1224no—
877C2×C8—1224no—
878C2×C8—1224no—
879C2×C8C23×D6112yes—
880C2×C8C23×D6112yes—
881C4⋊C4—21no—
882C4⋊C4—21no—
883C4⋊C4—21no—
884C4⋊C4—21no—
885C4⋊C4—22no—
886C4⋊C4—22no—
887C4⋊C4—612no—
888C4⋊C4—612no—
889C4⋊C4—1222no—
890C4⋊C4—1222no—
891C4⋊C4—1222no—
892C4⋊C4—1222no—
893C4⋊C4—1222no—
894C4⋊C4—1222no—
895C4⋊C4—1222no—
896C4⋊C4—1222no—
897C4⋊C4—1222no—
898C4⋊C4—1222no—
899C4⋊C4—1222no—
900C4⋊C4—1222no—
901C4⋊C4—1221no—
902C4⋊C4—1221no—
903C4⋊C4—1221no—
904C4⋊C4—1221no—
905C4⋊C4C23×D6112yes—
906C4⋊C4C23×D6112yes—
907C22⋊C4—22no—
908C22⋊C4—22no—
909C22⋊C4—22no—
910C22⋊C4—1222no—
911C22⋊C4—1222no—
912C22⋊C4—1222no—
913C22⋊C4—1222no—
914C22⋊C4—1222no—
915C22⋊C4—1222no—
916C22⋊C4—1222no—
917C22⋊C4—1222no—
918C22⋊C4—1222no—
919C42—22no—
920C42—611no—
921C42—611no—
922C42—611no—
923C42—611no—
924C42—611no—
925C42—611no—
926C42—611no—
927C42—611no—
928C42—611no—
929C42—611no—
930C42—611no—
931C42—611no—
932C42—1222no—
933C42—1222no—
934C42—1222no—
935C42D4×D6111yescharacteristic
936C42D4×D6111yescharacteristic
937C42C23×D6111yescharacteristic
938C42C23×D6111yescharacteristic
939C23—22no—
940C23—611no—
941C23—614no—
942C23—611no—
943C23—1222no—
944C23—1222no—
945C23—1222no—
946C23—2444no—
947C23—2444no—
948C23—2444no—
949C23C2×D4×D6111yescharacteristic
950Q8—24no—
951Q8—42no—
952Q8—42no—
953Q8—1224no—
954Q8—2444no—
955Q8—2444no—
956Q8—2444no—
957Q8—2442no—
958Q8—2442no—
959D4—24no—
960D4—44no—
961D4—42no—
962D4—42no—
963D4—1224no—
964D4—2444no—
965D4—2444no—
966D4—2444no—
967D4—2444no—
968D4—2444no—
969D4—2444no—
970D4—2442no—
971D4—2442no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—44no—
978C2×C4—614no—
979C2×C4—611no—
980C2×C4—611no—
981C2×C4—611no—
982C2×C4—611no—
983C2×C4—614no—
984C2×C4—614no—
985C2×C4—614no—
986C2×C4—614no—
987C2×C4—614no—
988C2×C4—614no—
989C2×C4—611no—
990C2×C4—611no—
991C2×C4—1222no—
992C2×C4—1222no—
993C2×C4—1222no—
994C2×C4—1222no—
995C2×C4—1222no—
996C2×C4—1222no—
997C2×C4—1222no—
998C2×C4—1222no—
999C2×C4—1222no—
1000C2×C4—1222no—
1001C2×C4—1222no—
1002C2×C4—2444no—
1003C2×C4—2444no—
1004C2×C4—2444no—
1005C2×C4—2444no—
1006C2×C4—2444no—
1007C2×C4—2444no—
1008C2×C4SD16×D6114yescomplemented
1009C2×C4C2×D4×D6111yescharacteristic
1010C2×C4C2×D4×D6111yescharacteristic
1011C2×C4C2×D4×D6111yescharacteristic
1012C2×C4C2×D4×D6111yescharacteristic
1013C2×C4C2×D4×D6111yescharacteristic
1014C2×C4C24×D6111yescharacteristic
1015C8—22no—
1016C8—614no—
1017C8—1222no—
1018C8#41×D6114yescomplemented
1019C22—21no—
1020C22—21no—
1021C22—42no—
1022C22—42no—
1023C22—42no—
1024C22—612no—
1025C22—612no—
1026C22—612no—
1027C22—612no—
1028C22—1228no—
1029C22—1221no—
1030C22—1221no—
1031C22—4888no—
1032C22—2442no—
1033C22—2442no—
1034C22—2442no—
1035C22C2×SD16×D6112yes—
1036C22C22×D4×D6111yescharacteristic
1037C4—21no—
1038C4—21no—
1039C4—42no—
1040C4—42no—
1041C4—42no—
1042C4—612no—
1043C4—612no—
1044C4—612no—
1045C4—612no—
1046C4—1221no—
1047C4—1221no—
1048C4—2442no—
1049C4—2442no—
1050C4—2442no—
1051C4C2×SD16×D6112yes—
1052C4C2×SD16×D6112yes—
1053C4#135×D6112yes—
1054C4C2×#41×D6112yes—
1055C2—22no—
1056C2—82no—
1057C2—614no—
1058C2—1222no—
1059C2—4882no—
1060C2#532×D6111yescharacteristic
1061C2C22×SD16×D6111yescharacteristic
1062C2C2×#135×D6111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#3167C2
socleC22×C61C23×D4
prime radical#532×D61C2
hypercenter#3167D61
hypocenterC61C2×#3167
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3167

Complements

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

NH ≅ G/Ntype
1. #533×D61C2semidirect
3. #21456381C2semidirect
4. #21456380C2semidirect
5. #21456379C2semidirect
6. #21456378C2semidirect
7. #21456377C2semidirect
8. #21456376C2semidirect
9. #21456375C2semidirect
10. #21456374C2semidirect
11. #21456373C2semidirect
12. #498×D61C2semidirect
13. #492×D61C2semidirect
14. #487×D61C2semidirect
15. #486×D61C2semidirect
16. #465×D61C2semidirect
17. C4×SD16×D61C2semidirect
18. C2×C4×C8×D61C2semidirect
19. C61×#3167C2semidirect
23. #16840319C22semidirect
25. #16840317C22semidirect
26. #16840317C22semidirect
28. #16840316C22semidirect
31. #16840314C22semidirect
57. #16840160C22semidirect
58. #16840159C22semidirect
59. #16840158C22semidirect
60. #16840158C22semidirect
61. #16840136C22semidirect
62. #16840135C22semidirect
63. #16840134C22semidirect
64. #16840133C22semidirect
65. #16840114C22semidirect
66. #16840113C22semidirect
67. #16840112C22semidirect
68. #16840111C22semidirect
69. #16840110C22semidirect
70. #16840109C22semidirect
71. #16840108C22semidirect
72. #16840107C22semidirect
73. #16839994C22semidirect
74. #16839993C22semidirect
75. #16839992C22semidirect
76. #16839991C22semidirect
77. #16839990C22semidirect
78. #16839989C22semidirect
79. #16839988C22semidirect
80. #16839853C22semidirect
81. C4×#11758190C22semidirect
82. SD16×Dic61C22semidirect
83. C4×#11758201C22semidirect
84. #16839849C22semidirect
85. C4×#11758200C22semidirect
86. #16839847C22semidirect
90. C2×C4×#92418C22semidirect
91. C2×C8×Dic61C22semidirect
95. C4×C8×D61C22semidirect
96. C4×C8×D61C22semidirect
97. C4×C8×D61C22semidirect
98. C61×#533C22semidirect
100. C61×#498C22semidirect
101. C61×#492C22semidirect
102. C61×#487C22semidirect
103. C61×#486C22semidirect
104. C61×#465C22semidirect
105. C4×SD16×C61C22semidirect
106. C2×C4×C8×C61C22semidirect
316. C2×C4×D61SD16semidirect
406. C8×D61#41semidirect
431. C2×C4×C61C2×SD16semidirect
449. C2×Dic61C2×SD16semidirect
473. C4×D61C2×SD16semidirect
474. C4×D61C2×SD16semidirect
484. C8×C61C2×#41semidirect
486. #92418C2×#41semidirect
535. #3167D61direct (N × H)
550. D61#3167direct (N × H)
563. #533C2×D61semidirect
594. #498C2×D61semidirect
599. #492C2×D61semidirect
604. #487C2×D61semidirect
609. #486C2×D61semidirect
617. #465C2×D61semidirect
625. C4×SD16C2×D61semidirect
637. C2×C4×C8C2×D61semidirect
638. C61C2×#3167semidirect
1008. C2×C4SD16×D61semidirect
1018. C8#41×D61semidirect

Maximal subgroups

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

subgroupindex
#533×D612
#532×D612
#214563812
#214563802
#214563792
#214563782
#214563772
#214563762
#214563752
#214563742
#214563732
#498×D612
#492×D612
#487×D612
#486×D612
#465×D612
C4×SD16×D612
C2×C4×C8×D612
C61×#31672
C2×#316761