Finite Group Databasebeta

← #30610773

Subgroups — #30610773

Order 15616.

1284 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462624C211yesmaximal, characteristic, complemented
2#21462464C211yesmaximal, characteristic, complemented
3#21461165C211yesmaximal, characteristic, complemented
4#21461164C212yesmaximal, complemented
5#21461145C211yesmaximal, characteristic, complemented
6#21461144C212yesmaximal, complemented
7#21461125C211yesmaximal, characteristic, complemented
8#21461124C212yesmaximal, complemented
9D61⋊(D4⋊C8)C211yesmaximal, characteristic, complemented
10C2×D4⋊#92420C212yesmaximal, complemented
11D4×#11758224C211yesmaximal, characteristic
12C2×#14519864—21no—
13#16840811—21no—
14#16840789—22no—
15D4×#92420—21no—
16#16840781C2211yescharacteristic, complemented
17#16840779C2212yescomplemented
18#16840769—21no—
19#16840768—22no—
20#16840766C2211yescharacteristic, complemented
21#16840765C2212yescomplemented
22D61⋊(C4⋊C8)C2211yescharacteristic, complemented
23C2×C4⋊#92420C2212yescomplemented
24C4×D61⋊C8C2211yescharacteristic, complemented
25C2×C4×#92420C2212yescomplemented
26#16840610C2211yescharacteristic, complemented
27#16840610C2211yescharacteristic, complemented
28#16840610C2212yescomplemented
29D4⋊#92420C2211yescharacteristic
30D4⋊#92420C2212yes—
31D4⋊#92420C2211yescharacteristic
32D4⋊#92420C2212yescomplemented
33D4⋊#92420C2212yescomplemented
34D4⋊#92420C2212yescomplemented
35D4⋊#92420C2212yescomplemented
36C22×#11758224—21no—
37#16840432C411yescharacteristic
38D4×Dic122C411yescharacteristic
39#16840418—21no—
40#16840416C411yescharacteristic
41#16840412C412yes—
42#16840406—21no—
43#16840399—22no—
44D4×C22⋊D61C412yes—
45#16840310C2211yescharacteristic
46#16840307C2212yes—
47#16840272—21no—
48#16840268—22no—
49C4×#11758224C2211yescharacteristic
50C2×D4×Dic61C2212yes—
51C4×D4×D61C2211yescharacteristic
52D42×C61C411yescharacteristic
53#14519864—44no—
54C2×#11758213—21no—
55C2×#11758217—22no—
56C2×D61⋊C8—21no—
57C2×D61⋊C8—21no—
58C22×#92420—22no—
59C22×#92420—22no—
60#14519844—21no—
61#14519844—22no—
62#14519844—22no—
63C4⋊#92420—22no—
64C4⋊#92420—21no—
65C4⋊#92420—21no—
66C4⋊#92420C2311yescharacteristic
67C4⋊#92420C2312yes—
68C4⋊#92420C2311yescharacteristic
69#14519834—21no—
70C22⋊#92420—22no—
71C4×#92420—22no—
72C4×#92420—21no—
73C4×#92420C2311yescharacteristic
74C4×#92420C2312yes—
75C4×#92420C2311yescharacteristic
76C2×#11758224—21no—
77C2×#11758224—22no—
78C2×#11758224—22no—
79C2×#11758224—21no—
80C2×#11758224—21no—
81C2×#11758224—44no—
82C2×#11758224—44no—
83C2×#11758224D411yescharacteristic
84C22×Dic122—21no—
85C22×C22⋊D61—22no—
86C2×D4×D61C2×C411yescharacteristic
87C23×Dic61—22no—
88C22×C4×D61—21no—
89#14519777C2×C411yescharacteristic
90#14519776C2×C412yes—
91#14519773C2×C412yes—
92#14519764—21no—
93#14519763—22no—
94#14519761—22no—
95#14519759—22no—
96#14519758—22no—
97#14519757—21no—
98#14519756—21no—
99#14519754—22no—
100#14519754—22no—
101#14519751C2×C412yes—
102#14519749—22no—
103#14519749—22no—
104#14519749—22no—
105#14519748—21no—
106#14519748—21no—
107#14519748C2×C412yes—
108#14519746—22no—
109#14519745—22no—
110C4×Dic122C2×C411yescharacteristic
111#14519742D411yescharacteristic
112C4×D244C2×C411yescharacteristic
113D4×Dic61—22no—
114D4×Dic61—22no—
115D4×Dic61—21no—
116D4×Dic61C2×C412yes—
117D4×Dic61C2×C412yes—
118D4×Dic61D411yescharacteristic
119D4×Dic61C2311yescharacteristic
120D4×Dic61C2312yes—
121#14519739C2311yescharacteristic
122C4×C22⋊D61—21no—
123C4×C22⋊D61C2×C412yes—
124#14519737—21no—
125#14519737—22no—
126#14519737D412yes—
127#14519735D411yescharacteristic
128#14519733D412yes—
129C2×C4⋊Dic61C2×C412yes—
130C4⋊C4×D61C2×C411yescharacteristic
131C2×C22⋊Dic61—22no—
132C22⋊C4×D61—21no—
133C2×C4×Dic61C2312yes—
134C42×D61C2311yescharacteristic
135C22×D4×C61—21no—
136C22×D4×C61C2×C412yes—
137#127×C61C2×C411yescharacteristic
138#121×C61—21no—
139#121×C61C2×C412yes—
140#120×C61—22no—
141C4×D4×C61C2×C411yescharacteristic
142C4×D4×C61C2×C411yescharacteristic
143C24×C61—22no—
144C23×D61—21no—
145C2×D4×C61—24no—
146C2×D4×C61—22no—
147C2×D4×C61—21no—
148C2×D4×C61—22no—
149C2×D4×C61—21no—
150C2×D4×C61—42no—
151C2×D4×C61—44no—
152C2×D4×C61C22⋊C411yescharacteristic
153C2×D4×C61C22×C412yes—
154C2×D4×C61C22×C411yescharacteristic
155C22×C4×C61—21no—
156C22×C4×C61C22×C412yes—
157C2×C22⋊D61—22no—
158C2×C22⋊D61—22no—
159C2×C22⋊D61—21no—
160C2×C22⋊D61—22no—
161C2×C22⋊D61—22no—
162C2×C22⋊D61—48no—
163C2×C22⋊D61C22⋊C412yes—
164C22×Dic61—22no—
165C22×Dic61—22no—
166C22×Dic61—22no—
167C22×Dic61—21no—
168C22×Dic61—22no—
169C22×Dic61—44no—
170C22×Dic61—44no—
171C22×Dic61C2×D412yes—
172C22×Dic61C2×D412yes—
173#11758224—44no—
174#11758224—48no—
175#11758224—44no—
176#11758224—44no—
177#11758224—42no—
178#11758224—42no—
179#11758224—44no—
180#11758224D814yes—
181#11758224SD1614yes—
182D4×D61—22no—
183D4×D61—41no—
184C2×D244C22×C411yescharacteristic
185C2×C4×D61—21no—
186C2×C4×D61—21no—
187C2×C4×D61—21no—
188C2×C4×D61—42no—
189C2×C4×D61—42no—
190C2×C4×D61C22×C411yescharacteristic
191C2×C4×D61C2×D411yescharacteristic
192C2×C4×D61C2×D411yescharacteristic
193C2×Dic122—21no—
194C2×Dic122—22no—
195C2×Dic122—44no—
196C2×Dic122C22⋊C411yescharacteristic
197#11758217—44no—
198C2×#92420—21no—
199C2×#92420—21no—
200C2×#92420—22no—
201C2×#92420—21no—
202C2×#92420—22no—
203C2×#92420—21no—
204C2×#92420—44no—
205C2×#92420—44no—
206#11758213—42no—
207D61⋊C8—42no—
208D61⋊C8—42no—
209C4⋊C4×C61C22⋊C411yescharacteristic
210C4⋊C4×C61C22×C411yescharacteristic
211C22⋊C4×C61—21no—
212C22⋊C4×C61—22no—
213C22⋊C4×C61C22⋊C412yes—
214C42×C61C22×C411yescharacteristic
215C22⋊Dic61—22no—
216C22⋊Dic61—22no—
217C22⋊Dic61—22no—
218C22⋊Dic61—21no—
219C22⋊Dic61—22no—
220C22⋊Dic61C22⋊C412yes—
221#11758198—21no—
222#11758198—22no—
223#11758198—21no—
224#11758198C22⋊C412yes—
225C4⋊Dic61—22no—
226C4⋊Dic61—21no—
227C4⋊Dic61C22⋊C411yescharacteristic
228C4⋊Dic61C22×C411yescharacteristic
229C4⋊Dic61C22×C412yes—
230#11758196—21no—
231#11758196—22no—
232#11758196C22⋊C412yes—
233#11758196C22⋊C412yes—
234C4×Dic61C22×C412yes—
235C4×Dic61C2×D411yescharacteristic
236C4×Dic61C2×D412yes—
237C4×Dic61C2×D411yescharacteristic
238C4×Dic61C2×D412yes—
239C4×Dic61C2411yescharacteristic
240C23×C61—21no—
241C23×C61—22no—
242C23×C61—44no—
243C23×C61—44no—
244C23×C61—82no—
245C23×C61C2×C22⋊C412yes—
246C22×D61—21no—
247C22×D61—42no—
248C22×D61—42no—
249C22×D61—81no—
250C22×D61C2×C22⋊C411yescharacteristic
251D4×C61—22no—
252D4×C61—21no—
253D4×C61—22no—
254D4×C61—44no—
255D4×C61—44no—
256D4×C61—42no—
257D4×C61—81no—
258D4×C61#10214yes—
259D4×C61#13112yescomplemented
260C2×C4×C61—22no—
261C2×C4×C61—22no—
262C2×C4×C61—21no—
263C2×C4×C61—42no—
264C2×C4×C61C2×C22⋊C412yes—
265C2×C4×C61C2×C22⋊C411yescharacteristic
266C2×C4×C61C2×C22⋊C411yescharacteristic
267C2×C4×C61C23×C411yescharacteristic
268C22⋊D61—42no—
269C22⋊D61—44no—
270C22⋊D61—44no—
271C22⋊D61—44no—
272C22⋊D61—82no—
273C22⋊D61#10218yes—
274C2×Dic61—22no—
275C2×Dic61—21no—
276C2×Dic61—42no—
277C2×Dic61—44no—
278C2×Dic61—41no—
279C2×Dic61—42no—
280C2×Dic61—41no—
281C2×Dic61—42no—
282C2×Dic61—44no—
283C2×Dic61—44no—
284C2×Dic61C2×C22⋊C412yes—
285C2×Dic61C2×C22⋊C411yescharacteristic
286C2×Dic61C2×C22⋊C412yes—
287C2×Dic61C2×D814yes—
288C2×Dic61C2×SD1614yes—
289C2×Dic61C22×D411yescharacteristic
290C2×Dic61C22×D411yescharacteristic
291D244—21no—
292D244—21no—
293C4×D61—21no—
294C4×D61—21no—
295C4×D61—41no—
296C4×D61—42no—
297C4×D61—42no—
298C4×D61—41no—
299C4×D61—41no—
300C4×D61C2×D812yes—
301C4×D61C2×SD1612yes—
302Dic122—42no—
303Dic122—44no—
304Dic122#10214yes—
305#92420—22no—
306#92420—41no—
307#92420—42no—
308#92420—41no—
309#92420—41no—
310#92420—42no—
311#17507—611nomaximal, Sylow
312C22×C61—22no—
313C22×C61—22no—
314C22×C61—22no—
315C22×C61—41no—
316C22×C61—41no—
317C22×C61—42no—
318C22×C61—42no—
319C22×C61—42no—
320C22×C61—88no—
321C22×C61C2×#10214yes—
322C22×C61C22×C22⋊C411yescharacteristic
323C2×D61—21no—
324C2×D61—21no—
325C2×D61—41no—
326C2×D61—41no—
327C2×D61—41no—
328C2×D61—84no—
329C2×D61C2×#10212yes—
330C4×C61—22no—
331C4×C61—21no—
332C4×C61—41no—
333C4×C61C2×#10212yes—
334C4×C61C2×#13111yescharacteristic
335C4×C61#56811yescharacteristic
336Dic61—21no—
337Dic61—21no—
338Dic61—22no—
339Dic61—42no—
340Dic61—41no—
341Dic61C2×#10214yes—
342Dic61C22×D811yescharacteristic
343Dic61C22×SD1611yescharacteristic
344D4×#41—611no—
345C8×#41—611no—
346#2906—611no—
347#1492—612no—
348#1492—611no—
349#1486—612no—
350#1486—611no—
351#1480—612no—
352#1480—611no—
353C2×D4⋊C8—612no—
354C2×D4⋊C8—611no—
355C2×C61—24no—
356C2×C61—42no—
357C2×C61—82no—
358C2×C61#288011yescharacteristic
359C2×C61C22×#10211yescharacteristic
360C2×C61#290111yescharacteristic
361D61—22no—
362D61—81no—
363C22×#41—1221no—
364C2×#131—1221no—
365#550—611no—
366D4×Q8—611no—
367#548—1221no—
368#547—612no—
369#547—611no—
370#546—1222no—
371#546—1221no—
372D42—612no—
373D42#692311yescharacteristic
374#532—611no—
375#532—612no—
376#525—1222no—
377#525—1221no—
378C4×#41—611no—
379C2×C4×D4—612no—
380C2×C4×D4—611no—
381C8×Q8—1221no—
382C8×D4—1221no—
383C8×D4—1222no—
384#431—612no—
385#431—611no—
386#424—1222no—
387#424—1221no—
388#423—612no—
389#423—611no—
390C2×C4⋊C8—612no—
391C2×C4⋊C8—611no—
392C2×C4×C8—612no—
393C2×C4×C8—611no—
394D4⋊C8—611no—
395D4⋊C8—612no—
396D4⋊C8—611no—
397D4⋊C8—612no—
398D4⋊C8—612no—
399D4⋊C8—612no—
400D4⋊C8—612no—
401D4⋊C8—611no—
402D4⋊C8—611no—
403D4⋊C8—612no—
404C61#1750711yescharacteristic, complemented, Sylow
405C2×#41—611no—
406C2×#41—1222no—
407C2×#41—1221no—
408C2×#41—1222no—
409C2×#41—1221no—
410C2×#41—1221no—
411C2×#41—2444no—
412C2×#41—2444no—
413C22×Q8—1221no—
414C22×D4—21no—
415C22×D4—611no—
416C22×D4—1222no—
417C22×D4C2×#692312yes—
418C23×C4—1221no—
419C23×C4—1222no—
420#131—2444no—
421C2×M16—1222no—
422C2×M16—1221no—
423C22×C8—1222no—
424C22×C8—1222no—
425C22×C8—1221no—
426C22×C8—1221no—
427C4⋊Q8—612no—
428C4⋊Q8—611no—
429#127—612no—
430#127C2×#692311yescharacteristic
431#124—1222no—
432#124—1221no—
433#123—1222no—
434#123—1222no—
435#123—1222no—
436C22⋊Q8—1222no—
437C22⋊Q8—1222no—
438C22⋊Q8—1221no—
439C22⋊Q8—1221no—
440#121—21no—
441#121—612no—
442#121—612no—
443#121—1222no—
444#121—1221no—
445#121—1222no—
446#121—1221no—
447#121—1222no—
448#121C2×#692312yes—
449#120—22no—
450#120—1222no—
451#120—1222no—
452C4×Q8—611no—
453C4×Q8—611no—
454C4×D4—611no—
455C4×D4—612no—
456C4×D4—612no—
457C4×D4—611no—
458C4×D4—612no—
459C4×D4—612no—
460C4×D4—612no—
461C4×D4—611no—
462C4×D4—611no—
463C4×D4—1221no—
464C4×D4—1222no—
465C4×D4—1221no—
466C4×D4—1222no—
467C4×D4—1222no—
468C4×D4—1221no—
469C4×D4C2×#692311yescharacteristic
470C4×D4C2×#692311yescharacteristic
471#117—611no—
472#117—612no—
473C2×C4⋊C4—612no—
474C2×C4⋊C4—611no—
475C2×C22⋊C4—1221no—
476C2×C22⋊C4—1222no—
477C2×C42—612no—
478C2×C42—611no—
479C4⋊C8—611no—
480C4⋊C8—612no—
481C4⋊C8—611no—
482C4⋊C8—1222no—
483C4⋊C8—1221no—
484C4⋊C8—1221no—
485C4⋊C8—1221no—
486C4⋊C8—1222no—
487C4⋊C8—1222no—
488C22⋊C8—1222no—
489C22⋊C8—1221no—
490C4×C8—611no—
491C4×C8—612no—
492C4×C8—611no—
493C4×C8—1222no—
494C4×C8—1221no—
495C24—22no—
496C24—1221no—
497#41—614no—
498#41—614no—
499#41—2444no—
500#41—2444no—
501#41—2442no—
502#41—2442no—
503#41—2448no—
504#41—2444no—
505#41—2444no—
506C2×Q8—611no—
507C2×Q8—1222no—
508C2×Q8—1221no—
509C2×Q8—2444no—
510C2×D4—24no—
511C2×D4—22no—
512C2×D4—22no—
513C2×D4—21no—
514C2×D4—21no—
515C2×D4—42no—
516C2×D4—44no—
517C2×D4—612no—
518C2×D4—611no—
519C2×D4—1222no—
520C2×D4—1221no—
521C2×D4—1222no—
522C2×D4—1222no—
523C2×D4—1222no—
524C2×D4—1222no—
525C2×D4—2441no—
526C2×D4—2448no—
527C2×D4C22⋊#692311yescharacteristic
528C2×D4C22×#692312yes—
529C2×D4C22×#692311yescharacteristic
530C22×C4—21no—
531C22×C4—612no—
532C22×C4—611no—
533C22×C4—612no—
534C22×C4—611no—
535C22×C4—611no—
536C22×C4—1221no—
537C22×C4—1221no—
538C22×C4—1221no—
539C22×C4—1222no—
540C22×C4—1222no—
541C22×C4—1222no—
542C22×C4—1222no—
543C22×C4—1221no—
544C22×C4—2442no—
545C22×C4—2442no—
546C22×C4—2444no—
547C22×C4—2444no—
548C22×C4C22×#692312yes—
549M16—2442no—
550M16—2444no—
551C2×C8—1221no—
552C2×C8—1221no—
553C2×C8—1222no—
554C2×C8—1221no—
555C2×C8—1222no—
556C2×C8—1221no—
557C2×C8—2442no—
558C2×C8—2444no—
559C2×C8—2442no—
560C2×C8—2444no—
561C4⋊C4—612no—
562C4⋊C4—612no—
563C4⋊C4—611no—
564C4⋊C4—611no—
565C4⋊C4—612no—
566C4⋊C4—1221no—
567C4⋊C4—1222no—
568C4⋊C4—1222no—
569C4⋊C4—1221no—
570C4⋊C4C22⋊#692311yescharacteristic
571C4⋊C4C22×#692311yescharacteristic
572C22⋊C4—21no—
573C22⋊C4—22no—
574C22⋊C4—612no—
575C22⋊C4—612no—
576C22⋊C4—1221no—
577C22⋊C4—1221no—
578C22⋊C4—1222no—
579C22⋊C4—1222no—
580C22⋊C4—1222no—
581C22⋊C4—1222no—
582C22⋊C4—1221no—
583C22⋊C4—1222no—
584C22⋊C4C22⋊#692312yes—
585C42—612no—
586C42—611no—
587C42—612no—
588C42—611no—
589C42—611no—
590C42—612no—
591C42C22×#692311yescharacteristic
592C23—21no—
593C23—22no—
594C23—44no—
595C23—44no—
596C23—82no—
597C23—611no—
598C23—1221no—
599C23—4881no—
600C23—2442no—
601C23—2442no—
602C23C2×C22⋊#692312yes—
603Q8—614no—
604Q8—2444no—
605Q8—2442no—
606D4—22no—
607D4—21no—
608D4—22no—
609D4—44no—
610D4—44no—
611D4—42no—
612D4—81no—
613D4—618no—
614D4—1221no—
615D4—1221no—
616D4—4882no—
617D4—2444no—
618D4—2442no—
619D4—2444no—
620D4—2444no—
621D4#1451983914yes—
622D4#1451986412yescomplemented
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—21no—
626C2×C4—42no—
627C2×C4—614no—
628C2×C4—614no—
629C2×C4—612no—
630C2×C4—611no—
631C2×C4—612no—
632C2×C4—612no—
633C2×C4—611no—
634C2×C4—612no—
635C2×C4—611no—
636C2×C4—1221no—
637C2×C4—1221no—
638C2×C4—1221no—
639C2×C4—1222no—
640C2×C4—2441no—
641C2×C4—2441no—
642C2×C4—2441no—
643C2×C4—2442no—
644C2×C4—2441no—
645C2×C4—2441no—
646C2×C4—2444no—
647C2×C4—2442no—
648C2×C4—2442no—
649C2×C4—2444no—
650C2×C4—2442no—
651C2×C4—2444no—
652C2×C4—2442no—
653C2×C4C2×C22⋊#692312yes—
654C2×C4C2×C22⋊#692311yescharacteristic
655C2×C4C2×C22⋊#692311yescharacteristic
656C2×C4C23×#692311yescharacteristic
657C8—1222no—
658C8—2441no—
659C8—2441no—
660C8—2442no—
661C8—2441no—
662C8—2442no—
663C22—22no—
664C22—22no—
665C22—22no—
666C22—41no—
667C22—41no—
668C22—42no—
669C22—42no—
670C22—42no—
671C22—88no—
672C22—612no—
673C22—1221no—
674C22—1221no—
675C22—4884no—
676C22—2441no—
677C22—2441no—
678C22—2441no—
679C22C2×#1451983914yes—
680C22C22×C22⋊#692311yescharacteristic
681C4—22no—
682C4—21no—
683C4—41no—
684C4—611no—
685C4—611no—
686C4—614no—
687C4—1221no—
688C4—1221no—
689C4—1222no—
690C4—2441no—
691C4—2442no—
692C4C2×#1451983912yes—
693C4C2×#1451986411yescharacteristic
694C4#1684084011yescharacteristic
695C2—24no—
696C2—42no—
697C2—82no—
698C2—1222no—
699C2—4881no—
700C2#2146240711yescharacteristic
701C2C22×#1451983911yescharacteristic
702C2#2146244911yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingD42×C61C4
socleC22×C61C22×C22⋊C4
prime radicalD4×#11758224C2
cosocleC4×Dic61C24
hypercenterD42#6923
hypocenterC61#17507
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ D42

Complements

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

NH ≅ G/Ntype
1. #21462624C2semidirect
2. #21462464C2semidirect
3. #21461165C2semidirect
4. #21461164C2semidirect
5. #21461145C2semidirect
6. #21461144C2semidirect
7. #21461125C2semidirect
8. #21461124C2semidirect
9. D61⋊(D4⋊C8)C2semidirect
10. C2×D4⋊#92420C2semidirect
16. #16840781C22semidirect
17. #16840779C22semidirect
20. #16840766C22semidirect
21. #16840765C22semidirect
22. D61⋊(C4⋊C8)C22semidirect
23. C2×C4⋊#92420C22semidirect
24. C4×D61⋊C8C22semidirect
25. C2×C4×#92420C22semidirect
26. #16840610C22semidirect
27. #16840610C22semidirect
28. #16840610C22semidirect
32. D4⋊#92420C22semidirect
33. D4⋊#92420C22semidirect
34. D4⋊#92420C22semidirect
35. D4⋊#92420C22semidirect
259. D4×C61#131semidirect
404. C61#17507semidirect
622. D4#14519864semidirect

Maximal subgroups

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

subgroupindex
#214626242
#214624642
#214611652
#214611642
#214611452
#214611442
#214611252
#214611242
D61⋊(D4⋊C8)2
C2×D4⋊#924202
D4×#117582242
#1750761