Finite Group Databasebeta

← #29647639

Subgroups — #29647639

Order 15616.

930 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459571C211yesmaximal, characteristic
2#21448704C211yesmaximal, characteristic, complemented
3#21444392C211yesmaximal, characteristic, complemented
4#21444384C212yesmaximal, complemented
5#21444363C211yesmaximal, characteristic
6#21444358C212yesmaximal, complemented
7#21444340C211yesmaximal, characteristic, complemented
8#21444332C212yesmaximal, complemented
9#21444311C211yesmaximal, characteristic
10#21444306C212yesmaximal, complemented
11C61×#2924C211yesmaximal, characteristic, complemented
12#16840480—21no—
13#16840467—21no—
14#16840451—21no—
15#16840447—21no—
16#16840445—22no—
17#16840438—22no—
18#16840390C411yescharacteristic, complemented
19#16840383C412yescomplemented
20#16840374C412yescomplemented
21#16840338C411yescharacteristic, complemented
22#16840319C2212yes—
23#16840296C2212yes—
24#16840273C2211yescharacteristic
25C2×#14519756C2211yescharacteristic
26#16840242C411yescharacteristic, complemented
27#16840239C411yescharacteristic, complemented
28#16839661—21no—
29#16839655—22no—
30#16839628C2212yes—
31#16839622C2211yescharacteristic
32C4⋊C4×Dic61—21no—
33C4×C22⋊Dic61C2211yescharacteristic
34#16839608C2212yes—
35#16839500C2212yes—
36#16839500C2212yes—
37#16839500C2212yes—
38#16839500C2211yescharacteristic
39#16839500C2212yes—
40#16839500C2212yes—
41#16839500C2211yescharacteristic
42#16839497C2211yescharacteristic
43#16839497C2212yes—
44#16839497C2211yescharacteristic
45C2×#117×C61C2211yescharacteristic
46C61×#433—22no—
47C61×#432C2212yes—
48C61×#431C2212yes—
49C61×#424—21no—
50C61×#407C2211yescharacteristic
51C2×C22⋊C8×C61C2211yescharacteristic
52C61×#405—21no—
53C2×#11758222C2×C411yescharacteristic
54C22×Dic122C2×C411yescharacteristic
55#14519777C2×C412yes—
56#14519777C2×C412yes—
57#14519776—21no—
58#14519772—22no—
59#14519771—22no—
60#14519770—22no—
61#14519770—22no—
62#14519769—22no—
63#14519769C2×C412yes—
64#14519768—21no—
65#14519767—22no—
66#14519767—22no—
67#14519765C2×C412yes—
68#14519763—22no—
69#14519761—22no—
70#14519760—21no—
71#14519760—22no—
72#14519759—22no—
73#14519757—21no—
74#14519757—21no—
75#14519756—21no—
76#14519756—21no—
77#14519756—22no—
78#14519756C2×C412yes—
79#14519756C2×C411yescharacteristic
80#14519756C2312yes—
81#14519756C2311yescharacteristic
82#14519755—22no—
83#14519754—22no—
84#14519751C2×C411yescharacteristic
85#14519751C2311yescharacteristic
86#14519746—21no—
87C4×Dic122—22no—
88C4×Dic122C2×C412yes—
89C4×Dic122C2×C412yes—
90C4×Dic122C2×C412yes—
91#14519742—21no—
92#14519742—21no—
93C4×D244C2×C412yes—
94C4×C22⋊D61—21no—
95C4×C22⋊D61—21no—
96C4×C22⋊D61—22no—
97#14519737—22no—
98#14519736—22no—
99#14519736C2×C411yescharacteristic
100#14519735—21no—
101#14519734—22no—
102#14519733—22no—
103C2×C4⋊Dic61—21no—
104C2×C4⋊Dic61—22no—
105C2×C4⋊Dic61C2×C411yescharacteristic
106C2×#11758196—21no—
107C4⋊C4×D61—21no—
108C2×C22⋊Dic61—21no—
109C2×C22⋊Dic61—21no—
110C2×C22⋊Dic61—21no—
111C2×C4×Dic61—22no—
112C2×C4×Dic61—21no—
113#14519684—22no—
114#14519684—22no—
115#14519684C2311yescharacteristic
116#14519684C2312yes—
117#14519684C2311yescharacteristic
118C23×C4×C61C2311yescharacteristic
119C2×M16×C61—21no—
120C22×C8×C61—21no—
121#117×C61C2×C411yescharacteristic
122#117×C61C2×C411yescharacteristic
123#117×C61C2×C412yes—
124#117×C61D411yescharacteristic
125#117×C61D411yescharacteristic
126#117×C61D412yes—
127C2×C4⋊C4×C61D411yescharacteristic
128C2×C4⋊C4×C61D411yescharacteristic
129C2×C22⋊C4×C61D412yes—
130C2×C42×C61C2312yes—
131C4⋊C8×C61—22no—
132C4⋊C8×C61—22no—
133C22⋊C8×C61—21no—
134C22⋊C8×C61—21no—
135C22⋊C8×C61C2311yescharacteristic
136C22⋊C8×C61C2311yescharacteristic
137C22⋊C8×C61C2312yes—
138#97×C61—22no—
139C4×C8×C61—22no—
140C24×C61C2×D411yescharacteristic
141C22×C4×C61—42no—
142C22×C4×C61C22×C411yescharacteristic
143C22×C4×C61C22×C411yescharacteristic
144C22×C4×C61C2×D412yes—
145C22×C4×C61C2×D411yescharacteristic
146C22×C4×C61C2×D411yescharacteristic
147C22×C4×C61C2×D412yes—
148C22×C4×C61C2×D411yescharacteristic
149C22×C4×C61C2411yescharacteristic
150C2×C22⋊D61—21no—
151C2×C22⋊D61—21no—
152C2×C22⋊D61—21no—
153C22×Dic61—21no—
154C22×Dic61—21no—
155C22×Dic61—21no—
156C22×Dic61—22no—
157C22×Dic61—21no—
158#11758222—42no—
159C2×D244C22×C411yescharacteristic
160C2×C4×D61—21no—
161C2×C4×D61—22no—
162C2×Dic122—21no—
163C2×Dic122—22no—
164C2×Dic122—42no—
165C2×Dic122C22×C412yes—
166C2×Dic122C22×C411yescharacteristic
167M16×C61—42no—
168C2×C8×C61—21no—
169C2×C8×C61—22no—
170C2×C8×C61—21no—
171C2×C8×C61—42no—
172C4⋊C4×C61C22⋊C411yescharacteristic
173C4⋊C4×C61C22⋊C411yescharacteristic
174C4⋊C4×C61C22⋊C412yes—
175C4⋊C4×C61C22⋊C411yescharacteristic
176C4⋊C4×C61C22⋊C411yescharacteristic
177C4⋊C4×C61C22⋊C412yes—
178C22⋊C4×C61C22⋊C412yes—
179C22⋊C4×C61C22⋊C412yes—
180C22⋊C4×C61C22⋊C412yes—
181C22⋊C4×C61C22⋊C412yes—
182C42×C61C22×C412yes—
183C42×C61C22×C412yes—
184C42×C61C2×D412yes—
185C42×C61C2×D412yes—
186C22⋊Dic61—22no—
187C22⋊Dic61—21no—
188C22⋊Dic61—21no—
189C22⋊Dic61—22no—
190C22⋊Dic61—21no—
191C22⋊Dic61—42no—
192C22⋊Dic61—81no—
193#11758198—22no—
194#11758198—22no—
195#11758198—21no—
196#11758198—22no—
197#11758198—21no—
198C4⋊Dic61—21no—
199C4⋊Dic61—22no—
200C4⋊Dic61—22no—
201C4⋊Dic61—22no—
202C4⋊Dic61—42no—
203C4⋊Dic61—82no—
204C4⋊Dic61C22×C412yes—
205C4⋊Dic61C22×C411yescharacteristic
206C4⋊Dic61C22×C411yescharacteristic
207#11758196—22no—
208#11758196—22no—
209#11758196—22no—
210#11758196—22no—
211#11758196—22no—
212#11758196—22no—
213#11758196—21no—
214#11758196—22no—
215#11758196—21no—
216C4×Dic61—22no—
217C4×Dic61—22no—
218C4×Dic61—22no—
219C4×Dic61—21no—
220C4×Dic61—44no—
221C4×Dic61—42no—
222C23×C61—21no—
223C23×C61—21no—
224C23×C61—41no—
225C23×C61—41no—
226C23×C61C2×C22⋊C411yescharacteristic
227C23×C61C2×C22⋊C411yescharacteristic
228C23×C61C22×D411yescharacteristic
229C22×D61—21no—
230C2×C4×C61—22no—
231C2×C4×C61—22no—
232C2×C4×C61—22no—
233C2×C4×C61—22no—
234C2×C4×C61—22no—
235C2×C4×C61—42no—
236C2×C4×C61—41no—
237C2×C4×C61—41no—
238C2×C4×C61—41no—
239C2×C4×C61C2×C22⋊C412yes—
240C2×C4×C61C2×C22⋊C412yes—
241C2×C4×C61C2×C22⋊C411yescharacteristic
242C2×C4×C61C2×C22⋊C412yes—
243C2×C4×C61C2×C22⋊C412yes—
244C2×C4×C61C2×C22⋊C411yescharacteristic
245C2×C4×C61C23×C411yescharacteristic
246C2×C4×C61C22×D411yescharacteristic
247C22⋊D61—42no—
248C22⋊D61—41no—
249C22⋊D61—41no—
250C22⋊D61—81no—
251C2×Dic61—22no—
252C2×Dic61—21no—
253C2×Dic61—21no—
254C2×Dic61—21no—
255C2×Dic61—22no—
256C2×Dic61—22no—
257C2×Dic61—41no—
258C2×Dic61—42no—
259C2×Dic61—41no—
260C2×Dic61—41no—
261C2×Dic61—42no—
262C2×Dic61—42no—
263C2×Dic61—41no—
264C2×Dic61—41no—
265C2×Dic61—42no—
266C2×Dic61—81no—
267D244—41no—
268C4×D61—42no—
269C4×D61—82no—
270Dic122—42no—
271Dic122—42no—
272Dic122—41no—
273Dic122—82no—
274C8×C61—41no—
275C8×C61—41no—
276C8×C61—42no—
277#17605—611nomaximal, Sylow
278C22×C61—21no—
279C22×C61—21no—
280C22×C61—21no—
281C22×C61—21no—
282C22×C61—21no—
283C22×C61—21no—
284C22×C61—21no—
285C22×C61—21no—
286C22×C61—81no—
287C22×C61—81no—
288C22×C61C22×C22⋊C411yescharacteristic
289C22×C61#57711yescharacteristic
290C22×C61#57811yescharacteristic
291C2×D61—41no—
292C2×D61—41no—
293C2×D61—41no—
294C4×C61—21no—
295C4×C61—21no—
296C4×C61—21no—
297C4×C61—22no—
298C4×C61—22no—
299C4×C61—22no—
300C4×C61—22no—
301C4×C61#41012yes—
302Dic61—42no—
303Dic61—42no—
304Dic61—41no—
305Dic61—41no—
306Dic61—41no—
307Dic61—42no—
308Dic61—82no—
309Dic61—81no—
310#3495—611no—
311#2924D6111yescharacteristic, complemented
312#2346—611no—
313#1520—611no—
314#1518—612no—
315#1513—611no—
316#1512—612no—
317#1508—611no—
318#1506—612no—
319#1501—611no—
320#1500—612no—
321C2×C61—21no—
322C2×C61—21no—
323C2×C61—41no—
324C2×C61—41no—
325C2×C61C2×#41011yescharacteristic
326C2×C61#289811yescharacteristic
327C2×C61#290111yescharacteristic
328D61—81no—
329#556—1221no—
330#554—1221no—
331#552—1221no—
332#552—1222no—
333#552—1221no—
334#551—1222no—
335#544—611no—
336#542—612no—
337#541—612no—
338#536—611no—
339#533—612no—
340#529—612no—
341#525—611no—
342C2×C22⋊Q8—611no—
343#520—611no—
344#519—611no—
345C2×#117C2×D6111yescharacteristic
346#433—22no—
347#432C2×D6112yes—
348#431C2×D6112yes—
349#424—21no—
350#407C2×D6111yescharacteristic
351C2×C22⋊C8C2×D6111yescharacteristic
352#405—21no—
353#389—1221no—
354#388—1222no—
355#382—612no—
356#380—611no—
357C4×C4⋊C4—1221no—
358C4×C22⋊C4—611no—
359#376—612no—
360#328—612no—
361#328—612no—
362#328—611no—
363#328—611no—
364#328—612no—
365#328—612no—
366#328—612no—
367#327—611no—
368#327—612no—
369#327—611no—
370C61#1760511yescharacteristic, complemented, Sylow
371C2×#41—611no—
372C22×Q8—611no—
373C23×C4C22×D6111yescharacteristic
374C2×M16—21no—
375C22×C8—21no—
376C4⋊Q8—612no—
377C4⋊Q8—612no—
378C4⋊Q8—1221no—
379#126—1222no—
380#126—1222no—
381#126—1222no—
382#126—1222no—
383#125—612no—
384#125—1222no—
385#125—1222no—
386#125—1221no—
387#125—1222no—
388#124—612no—
389#124—1222no—
390#123—1222no—
391#123—1221no—
392#123—1222no—
393#123—1222no—
394C22⋊Q8—612no—
395C22⋊Q8—611no—
396C22⋊Q8—612no—
397C22⋊Q8—611no—
398C22⋊Q8—1221no—
399C22⋊Q8—1222no—
400C22⋊Q8—1221no—
401C22⋊Q8—1221no—
402C22⋊Q8—1221no—
403C22⋊Q8—1222no—
404C22⋊Q8—1222no—
405#121—611no—
406#121—611no—
407#120—1221no—
408C4×Q8—612no—
409C4×Q8—612no—
410C4×Q8—612no—
411C4×Q8—1221no—
412C4×Q8—1221no—
413C4×Q8—1222no—
414C4×D4—612no—
415C4×D4—1221no—
416C4×D4—1222no—
417C4×D4—1221no—
418C4×D4—1222no—
419#117—611no—
420#117—1222no—
421#117—1221no—
422#117—1222no—
423#117—1222no—
424#117C4×D6111yescharacteristic
425#117C4×D6111yescharacteristic
426#117C4×D6112yes—
427#117C22⋊D6111yescharacteristic
428#117C22⋊D6112yes—
429#117C22⋊D6111yescharacteristic
430C2×C4⋊C4—611no—
431C2×C4⋊C4—1221no—
432C2×C4⋊C4—1221no—
433C2×C4⋊C4—1222no—
434C2×C4⋊C4—1221no—
435C2×C4⋊C4D24411yescharacteristic
436C2×C4⋊C4D24411yescharacteristic
437C2×C22⋊C4—1221no—
438C2×C22⋊C4—1221no—
439C2×C22⋊C4—1221no—
440C2×C22⋊C4D24412yes—
441C2×C42—1222no—
442C2×C42—1221no—
443C2×C42C22×D6112yes—
444C4⋊C8—22no—
445C4⋊C8—22no—
446C22⋊C8—21no—
447C22⋊C8—21no—
448C22⋊C8C22×D6111yescharacteristic
449C22⋊C8C22×D6111yescharacteristic
450C22⋊C8C22×D6112yes—
451#97—22no—
452C4×C8—22no—
453#95—611no—
454#95—612no—
455#95—611no—
456#95—1222no—
457#95—1222no—
458C24C2×D24411yescharacteristic
459#41—2442no—
460C2×Q8—612no—
461C2×Q8—611no—
462C2×Q8—1222no—
463C2×Q8—1221no—
464C2×Q8—2442no—
465C2×D4—611no—
466C2×D4—1221no—
467C2×D4—1221no—
468C2×D4—1221no—
469C22×C4—42no—
470C22×C4—1221no—
471C22×C4—1221no—
472C22×C4—1221no—
473C22×C4—1222no—
474C22×C4—1221no—
475C22×C4—1221no—
476C22×C4—1222no—
477C22×C4C2×C4×D6111yescharacteristic
478C22×C4C2×C4×D6111yescharacteristic
479C22×C4C2×D24412yes—
480C22×C4C2×D24411yescharacteristic
481C22×C4C2×D24412yes—
482C22×C4C2×C22⋊D6111yescharacteristic
483C22×C4C2×C22⋊D6111yescharacteristic
484C22×C4C23×D6111yescharacteristic
485M16—42no—
486C2×C8—21no—
487C2×C8—22no—
488C2×C8—21no—
489C2×C8—42no—
490C4⋊C4—612no—
491C4⋊C4—611no—
492C4⋊C4—611no—
493C4⋊C4—1222no—
494C4⋊C4—1221no—
495C4⋊C4—1221no—
496C4⋊C4—1222no—
497C4⋊C4—1222no—
498C4⋊C4—1222no—
499C4⋊C4—1222no—
500C4⋊C4—1222no—
501C4⋊C4—1221no—
502C4⋊C4—1222no—
503C4⋊C4—1222no—
504C4⋊C4—1222no—
505C4⋊C4—1222no—
506C4⋊C4—4882no—
507C4⋊C4—2442no—
508C4⋊C4#1175819811yescharacteristic
509C4⋊C4#1175819811yescharacteristic
510C4⋊C4#1175819812yes—
511C4⋊C4#1175819811yescharacteristic
512C4⋊C4#1175819811yescharacteristic
513C4⋊C4#1175819812yes—
514C22⋊C4—1222no—
515C22⋊C4—1221no—
516C22⋊C4—1222no—
517C22⋊C4—1221no—
518C22⋊C4—1221no—
519C22⋊C4—1221no—
520C22⋊C4—1222no—
521C22⋊C4—1222no—
522C22⋊C4—1221no—
523C22⋊C4—1222no—
524C22⋊C4—4881no—
525C22⋊C4—2442no—
526C22⋊C4#1175819812yes—
527C22⋊C4#1175819812yes—
528C22⋊C4#1175819812yes—
529C22⋊C4#1175819812yes—
530C42—1221no—
531C42—1222no—
532C42—1222no—
533C42—1222no—
534C42—2442no—
535C42—2444no—
536C42C2×C4×D6112yes—
537C42C2×C4×D6112yes—
538C42C2×C22⋊D6112yes—
539C42C2×C22⋊D6112yes—
540C23—21no—
541C23—21no—
542C23—41no—
543C23—41no—
544C23—1221no—
545C23C2×#1175819811yescharacteristic
546C23C2×#1175819811yescharacteristic
547C23C22×D24411yescharacteristic
548Q8—4882no—
549Q8—2442no—
550Q8—2441no—
551Q8—2442no—
552D4—4881no—
553D4—2441no—
554D4—2442no—
555D4—2441no—
556D4—2441no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—42no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—1222no—
567C2×C4—1221no—
568C2×C4—1221no—
569C2×C4—1222no—
570C2×C4—1221no—
571C2×C4—1222no—
572C2×C4—4882no—
573C2×C4—4881no—
574C2×C4—2442no—
575C2×C4—2441no—
576C2×C4—2441no—
577C2×C4—2442no—
578C2×C4—2442no—
579C2×C4—2441no—
580C2×C4—2441no—
581C2×C4—2442no—
582C2×C4—2441no—
583C2×C4—2442no—
584C2×C4C2×#1175819812yes—
585C2×C4C2×#1175819812yes—
586C2×C4C2×#1175819812yes—
587C2×C4C2×#1175819812yes—
588C2×C4C2×#1175819811yescharacteristic
589C2×C4C2×#1175819811yescharacteristic
590C2×C4C22×C4×D6111yescharacteristic
591C2×C4C22×C22⋊D6111yescharacteristic
592C8—41no—
593C8—41no—
594C8—42no—
595C22—21no—
596C22—21no—
597C22—21no—
598C22—21no—
599C22—21no—
600C22—21no—
601C22—21no—
602C22—21no—
603C22—81no—
604C22—81no—
605C22—2441no—
606C22—2441no—
607C22—2441no—
608C22C22×#1175819811yescharacteristic
609C22#1684057411yescharacteristic
610C22#1684057911yescharacteristic
611C4—22no—
612C4—22no—
613C4—22no—
614C4—22no—
615C4—21no—
616C4—21no—
617C4—21no—
618C4—4881no—
619C4—4882no—
620C4—2442no—
621C4—2441no—
622C4—2442no—
623C4—2441no—
624C4—2441no—
625C4—2442no—
626C4#1683973512yes—
627C2—21no—
628C2—21no—
629C2—41no—
630C2—41no—
631C2—4881no—
632C2C2×#1683973511yescharacteristic
633C2#2145435311yescharacteristic
634C2#2145436411yescharacteristic
subgroupG/H
centerC22C22×#11758198
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#2924C2
socleC22×C61C22×C22⋊C4
prime radical#16840273C22
cosocleC22×C4×C61C24
hypercenter#2924D61
hypocenterC61#17605
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×#117 ◁ #2924

Complements

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

NH ≅ G/Ntype
2. #21448704C2semidirect
3. #21444392C2semidirect
4. #21444384C2semidirect
6. #21444358C2semidirect
7. #21444340C2semidirect
8. #21444332C2semidirect
10. #21444306C2semidirect
11. C61×#2924C2semidirect
18. #16840390C4semidirect
19. #16840383C4semidirect
20. #16840374C4semidirect
21. #16840338C4semidirect
26. #16840242C4semidirect
27. #16840239C4semidirect
311. #2924D61semidirect
370. C61#17605semidirect

Maximal subgroups

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

subgroupindex
#214595712
#214487042
#214443922
#214443842
#214443632
#214443582
#214443402
#214443322
#214443112
#214443062
C61×#29242
#1760561