Finite Group Databasebeta

← #29571386

Subgroups — #29571386

Order 15616.

1120 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#11758224C211yesmaximal, characteristic
2#21445796C211yesmaximal, characteristic, complemented
3C4×#14519689C211yesmaximal, characteristic, complemented
4C2×#16839494C211yesmaximal, characteristic, complemented
5C2×#16839492C211yesmaximal, characteristic, complemented
6C2×D4⋊#92418C211yesmaximal, characteristic, complemented
7C2×C61×D4⋊C8C211yesmaximal, characteristic, complemented
8C22×#11758224C411yescharacteristic
9C4×#11758224—22no—
10C4×#11758224—22no—
11C4×#11758224—22no—
12C4×#11758224—22no—
13C2×C4×Dic122C2211yescharacteristic
14C2×#14519742C411yescharacteristic
15C2×D4×Dic61C411yescharacteristic
16C2×C4×C22⋊D61—21no—
17C2×#14519737—21no—
18C2×#14519735C411yescharacteristic
19C2×#14519733—21no—
20C22×C4×Dic61—21no—
21C2×C42×D61C2211yescharacteristic
22C2×C4⋊#92418C2211yescharacteristic
23C2×#14519689—21no—
24C2×#14519689—21no—
25C2×C4×#92418C2211yescharacteristic
26#16839516—21no—
27#16839516—21no—
28#16839494—22no—
29#16839492—22no—
30D4⋊#92418—22no—
31C2×C4×D4×C61C2211yescharacteristic
32C2×C4⋊C8×C61C2211yescharacteristic
33C2×C4×C8×C61C2211yescharacteristic
34C61×D4⋊C8—22no—
35C2×#11758224—22no—
36C2×#11758224—22no—
37C2×#11758224—22no—
38C2×#11758224—22no—
39C2×#11758224—22no—
40C2×#11758224C814yescomplemented
41C22×Dic122C2×C411yescharacteristic
42C22×C22⋊D61—21no—
43C23×Dic61—21no—
44C23×Dic61—21no—
45C22×C4×D61C2×C411yescharacteristic
46C22×C4×D61D411yescharacteristic
47C22×C4×D61D411yescharacteristic
48C22×#92418—21no—
49C22×#92418—21no—
50C4×Dic122—21no—
51C4×Dic122—21no—
52C4×Dic122D412yes—
53C4×Dic122D412yes—
54#14519742—22no—
55#14519742—22no—
56D4×Dic61—22no—
57D4×Dic61—22no—
58C4×C22⋊D61—24no—
59C4×C22⋊D61—24no—
60#14519737—24no—
61#14519737—24no—
62#14519735—22no—
63#14519735—22no—
64#14519733—24no—
65#14519733—24no—
66C2×C4⋊Dic61C2×C411yescharacteristic
67C2×#11758196—21no—
68C2×#11758196—21no—
69C2×C22⋊Dic61—21no—
70C2×#11758198—21no—
71C2×C4×Dic61—24no—
72C2×C4×Dic61—24no—
73C2×C4×Dic61—21no—
74C2×C4×Dic61—21no—
75C2×C4×Dic61—21no—
76C2×C4×Dic61C2×C411yescharacteristic
77C2×C4×Dic61D411yescharacteristic
78C2×C4×Dic61D411yescharacteristic
79C42×D61—21no—
80C42×D61—21no—
81C42×D61—21no—
82C42×D61—21no—
83C4⋊#92418—21no—
84C4⋊#92418—21no—
85#14519689—24no—
86#14519689—42no—
87C4×#92418—21no—
88C4×#92418—21no—
89C22×D4×C61C2×C411yescharacteristic
90C23×C4×C61—21no—
91C22×C8×C61—21no—
92C22×C8×C61—21no—
93C4×D4×C61—21no—
94C4×D4×C61—21no—
95C4×D4×C61D412yes—
96C4×D4×C61D412yes—
97C2×C4⋊C4×C61C2×C411yescharacteristic
98C2×C22⋊C4×C61—21no—
99C2×C42×C61C2311yescharacteristic
100C4⋊C8×C61—21no—
101C4⋊C8×C61—21no—
102C4×C8×C61—21no—
103C4×C8×C61—21no—
104C24×C61—21no—
105C23×D61C22⋊C411yescharacteristic
106C2×D4×C61—21no—
107C2×D4×C61—21no—
108C2×D4×C61—21no—
109C2×D4×C61C22⋊C412yes—
110C2×D4×C61C2×C812yes—
111C2×D4×C61M1612yes—
112C22×C4×C61—21no—
113C22×C4×C61—22no—
114C22×C4×C61—22no—
115C22×C4×C61—41no—
116C22×C4×C61—41no—
117C22×C4×C61—41no—
118C22×C4×C61—41no—
119C22×C4×C61C22×C411yescharacteristic
120C22×C4×C61C2×D411yescharacteristic
121C22×C4×C61C2×D411yescharacteristic
122C2×C22⋊D61—24no—
123C2×C22⋊D61—24no—
124C2×C22⋊D61—24no—
125C22×Dic61—24no—
126C22×Dic61—24no—
127C22×Dic61—21no—
128C22×Dic61—24no—
129C22×Dic61—24no—
130C22×Dic61—21no—
131C22×Dic61—42no—
132C22×Dic61—42no—
133C22×Dic61C22⋊C411yescharacteristic
134C22×Dic61C22⋊C411yescharacteristic
135C22×Dic61C22⋊C411yescharacteristic
136#11758224—28no—
137#11758224—28no—
138#11758224—28no—
139#11758224—28no—
140C2×C4×D61—21no—
141C2×C4×D61—21no—
142C2×C4×D61—21no—
143C2×C4×D61—21no—
144C2×C4×D61—21no—
145C2×C4×D61—21no—
146C2×C4×D61—21no—
147C2×C4×D61—21no—
148C2×C4×D61—21no—
149C2×C4×D61—21no—
150C2×C4×D61—21no—
151C2×C4×D61—21no—
152C2×C4×D61—22no—
153C2×C4×D61—41no—
154C2×C4×D61C2×C812yes—
155C2×C4×D61M1612yes—
156C2×Dic122—21no—
157C2×Dic122—21no—
158C2×Dic122—21no—
159C2×Dic122C22⋊C412yes—
160C2×Dic122C2×C812yes—
161C2×Dic122M1612yes—
162C2×C8×C61—22no—
163C2×C8×C61—41no—
164C2×C8×C61—41no—
165C2×C8×C61—41no—
166C2×C8×C61—41no—
167C2×C8×C61—41no—
168C4⋊C4×C61—21no—
169C4⋊C4×C61C22⋊C412yes—
170C22⋊C4×C61—22no—
171C22⋊C4×C61—22no—
172C42×C61C2×D411yescharacteristic
173C42×C61C2×D411yescharacteristic
174C42×C61C2×D411yescharacteristic
175C42×C61C2×D411yescharacteristic
176C22⋊Dic61—24no—
177#11758198—24no—
178C4⋊Dic61—21no—
179C4⋊Dic61C22⋊C412yes—
180#11758196—24no—
181#11758196—22no—
182#11758196—22no—
183C4×Dic61—24no—
184C4×Dic61—24no—
185C4×Dic61—21no—
186C4×Dic61—21no—
187C4×Dic61—21no—
188C4×Dic61—21no—
189C4×Dic61—21no—
190C4×Dic61—21no—
191C4×Dic61—22no—
192C4×Dic61—22no—
193C2×#92418—22no—
194C2×#92418—41no—
195C2×#92418—41no—
196C2×#92418—41no—
197C2×#92418—41no—
198C2×#92418—41no—
199C23×C61—22no—
200C23×C61—22no—
201C23×C61—22no—
202C23×C61—41no—
203C23×C61—41no—
204C23×C61—41no—
205C23×C61—41no—
206C23×C61C2×C22⋊C411yescharacteristic
207C22×D61—21no—
208C22×D61—21no—
209C22×D61—21no—
210C22×D61—21no—
211C22×D61—21no—
212C22×D61—21no—
213C22×D61C22⋊C812yes—
214D4×C61—22no—
215D4×C61—22no—
216D4×C61—22no—
217D4×C61C22⋊C814yescomplemented
218C2×C4×C61—21no—
219C2×C4×C61—21no—
220C2×C4×C61—22no—
221C2×C4×C61—41no—
222C2×C4×C61—41no—
223C2×C4×C61—42no—
224C2×C4×C61—42no—
225C2×C4×C61—42no—
226C2×C4×C61—42no—
227C2×C4×C61C2×C22⋊C411yescharacteristic
228C2×C4×C61C2×C22⋊C411yescharacteristic
229C2×C4×C61#12011yescharacteristic
230C2×C4×C61#12011yescharacteristic
231C2×C4×C61#12011yescharacteristic
232C2×C4×C61#12011yescharacteristic
233C2×C4×C61C22×C811yescharacteristic
234C2×C4×C61C2×M1611yescharacteristic
235C2×C4×C61C2×M1611yescharacteristic
236C2×C4×C61C2×M1611yescharacteristic
237C2×C4×C61#13511yescharacteristic
238C2×C4×C61#13511yescharacteristic
239C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
240C2×C4×C61#13711yescharacteristic
241C22⋊D61—216no—
242C2×Dic61—216no—
243C2×Dic61—21no—
244C2×Dic61—21no—
245C2×Dic61—22no—
246C2×Dic61—22no—
247C2×Dic61—22no—
248C2×Dic61—21no—
249C2×Dic61—21no—
250C2×Dic61—21no—
251C2×Dic61—22no—
252C2×Dic61—21no—
253C2×Dic61—21no—
254C2×Dic61—48no—
255C2×Dic61—41no—
256C2×Dic61—41no—
257C2×Dic61C22⋊C812yes—
258C2×Dic61#10412yes—
259C4×D61—22no—
260C4×D61—22no—
261C4×D61—22no—
262C4×D61—22no—
263C4×D61—42no—
264C4×D61—42no—
265C4×D61—41no—
266C4×D61—41no—
267C4×D61—41no—
268C4×D61—41no—
269Dic122—22no—
270Dic122—22no—
271Dic122—22no—
272Dic122C22⋊C814yescomplemented
273C8×C61—42no—
274C8×C61—81no—
275#92418—42no—
276#92418—81no—
277#8312—611nomaximal, Sylow
278C22×C61—24no—
279C22×C61—42no—
280C22×C61—42no—
281C22×C61—42no—
282C22×C61—42no—
283C22×C61—42no—
284C22×C61—42no—
285C22×C61#37911yescharacteristic
286C22×C61C2×C22⋊C811yescharacteristic
287C22×C61#40711yescharacteristic
288C22×C61#41611yescharacteristic
289C22×C61#41711yescharacteristic
290C22×C61C2×#10411yescharacteristic
291C22×C61#42111yescharacteristic
292C2×D61—22no—
293C2×D61—22no—
294C2×D61—22no—
295C2×D61—41no—
296C2×D61—41no—
297C2×D61—41no—
298C2×D61—41no—
299C4×C61—21no—
300C4×C61—21no—
301C4×C61—42no—
302C4×C61C2×C22⋊C811yescharacteristic
303C4×C61C2×C22⋊C811yescharacteristic
304C4×C61#40711yescharacteristic
305C4×C61#40711yescharacteristic
306C4×C61#44911yescharacteristic
307C4×C61#44911yescharacteristic
308C4×C61#45211yescharacteristic
309C4×C61#45211yescharacteristic
310Dic61—24no—
311Dic61—22no—
312Dic61—22no—
313Dic61—41no—
314Dic61—42no—
315C2×C4×#41—611no—
316#1797—611no—
317C4×C22⋊C8—611no—
318C2×Q8⋊C8—611no—
319C2×Q8⋊C8—611no—
320C2×D4⋊C8—611no—
321C2×D4⋊C8D6111yescharacteristic, complemented
322C2×C61—44no—
323C2×C61#147611yescharacteristic
324C2×C61#147711yescharacteristic
325C2×C61#148811yescharacteristic
326C2×C61#148911yescharacteristic
327C2×C61#177911yescharacteristic
328C2×C61#178811yescharacteristic
329C2×C61#178911yescharacteristic
330D61—42no—
331C22×#41—611no—
332C4×#41—1222no—
333C4×#41—1222no—
334C4×#41—1222no—
335C4×#41—1222no—
336C2×C4×Q8—611no—
337C2×C4×Q8—611no—
338C2×C4×D4—611no—
339C2×C4×D4—1221no—
340C2×C4×D4—1221no—
341C2×C4×D4C2×D6111yescharacteristic
342C2×#117—611no—
343C2×#117—1221no—
344C22×C42—611no—
345C22×C42—1221no—
346C2×C4⋊C8—611no—
347C2×C4⋊C8C2×D6111yescharacteristic
348C2×C22⋊C8—1221no—
349C2×C22⋊C8—1221no—
350C2×C4×C8—611no—
351C2×C4×C8C2×D6111yescharacteristic
352#336—1221no—
353#336—1221no—
354Q8⋊C8—1222no—
355Q8⋊C8—1222no—
356D4⋊C8—22no—
357D4⋊C8—1222no—
358C61#831211yescharacteristic, complemented, Sylow
359C2×#41—614no—
360C2×#41—1222no—
361C2×#41—1222no—
362C2×#41—1222no—
363C2×#41—1222no—
364C2×#41—1222no—
365C22×Q8—611no—
366C22×D4—1221no—
367C22×D4C4×D6111yescharacteristic
368C23×C4—21no—
369C23×C4—611no—
370C23×C4—611no—
371C23×C4—611no—
372C23×C4—1221no—
373C23×C4—1221no—
374C22×C8—21no—
375C22×C8—21no—
376C22×C8—1221no—
377C22×C8—1221no—
378C4×Q8—612no—
379C4×Q8—612no—
380C4×Q8—1222no—
381C4×Q8—1222no—
382C4×Q8—1221no—
383C4×Q8—1221no—
384C4×D4—21no—
385C4×D4—21no—
386C4×D4—1224no—
387C4×D4—1224no—
388C4×D4—1222no—
389C4×D4—1224no—
390C4×D4—1224no—
391C4×D4—1222no—
392C4×D4D24412yes—
393C4×D4C22⋊D6112yes—
394#117—1224no—
395#117—1224no—
396#117—1222no—
397#117—1222no—
398C2×C4⋊C4—611no—
399C2×C4⋊C4—1221no—
400C2×C4⋊C4—1221no—
401C2×C4⋊C4C4×D6111yescharacteristic
402C2×C22⋊C4—21no—
403C2×C22⋊C4—1221no—
404C2×C22⋊C4—1221no—
405C2×C42—611no—
406C2×C42—611no—
407C2×C42—611no—
408C2×C42—1221no—
409C2×C42—1221no—
410C2×C42—1224no—
411C2×C42—1224no—
412C2×C42—1221no—
413C2×C42—1221no—
414C2×C42—1221no—
415C2×C42—1221no—
416C2×C42—1221no—
417C2×C42C22×D6111yescharacteristic
418C4⋊C8—21no—
419C4⋊C8—21no—
420C4⋊C8—1221no—
421C4⋊C8—1221no—
422C22⋊C8—1224no—
423C22⋊C8—2442no—
424C4×C8—21no—
425C4×C8—21no—
426C4×C8—1221no—
427C4×C8—1221no—
428C24—21no—
429C24—611no—
430#41—1228no—
431#41—1228no—
432#41—1228no—
433#41—1228no—
434C2×Q8—612no—
435C2×Q8—612no—
436C2×Q8—612no—
437C2×Q8—1221no—
438C2×Q8—1221no—
439C2×Q8—1221no—
440C2×D4—21no—
441C2×D4—21no—
442C2×D4—21no—
443C2×D4—1224no—
444C2×D4—1224no—
445C2×D4—1224no—
446C2×D4C8×D6112yes—
447C2×D4#1175818912yes—
448C2×D4#1175819812yes—
449C22×C4—21no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—41no—
453C22×C4—41no—
454C22×C4—41no—
455C22×C4—41no—
456C22×C4—611no—
457C22×C4—611no—
458C22×C4—612no—
459C22×C4—612no—
460C22×C4—611no—
461C22×C4—1222no—
462C22×C4—1224no—
463C22×C4—1224no—
464C22×C4—1224no—
465C22×C4—1221no—
466C22×C4—1221no—
467C22×C4—1221no—
468C22×C4—1221no—
469C22×C4—1221no—
470C22×C4—1224no—
471C22×C4—1221no—
472C22×C4—1221no—
473C22×C4—1221no—
474C22×C4—1221no—
475C22×C4—1221no—
476C22×C4—1221no—
477C22×C4—1221no—
478C22×C4—1221no—
479C22×C4—1221no—
480C22×C4—2441no—
481C22×C4—2442no—
482C22×C4—2442no—
483C22×C4C2×C4×D6111yescharacteristic
484C22×C4D4×D6111yescharacteristic
485C22×C4D4×D6111yescharacteristic
486C2×C8—22no—
487C2×C8—41no—
488C2×C8—41no—
489C2×C8—41no—
490C2×C8—41no—
491C2×C8—41no—
492C2×C8—1222no—
493C2×C8—2441no—
494C2×C8—2441no—
495C2×C8—2441no—
496C2×C8—2441no—
497C2×C8—2441no—
498C4⋊C4—21no—
499C4⋊C4—612no—
500C4⋊C4—1224no—
501C4⋊C4—1221no—
502C4⋊C4—1222no—
503C4⋊C4—1222no—
504C4⋊C4#1175819812yes—
505C22⋊C4—22no—
506C22⋊C4—22no—
507C22⋊C4—1224no—
508C22⋊C4—1224no—
509C42—1224no—
510C42—1224no—
511C42—1221no—
512C42—1221no—
513C42—1221no—
514C42—1221no—
515C42—1222no—
516C42—1221no—
517C42—1221no—
518C42—1222no—
519C42C2×D24411yescharacteristic
520C42D4×D6111yescharacteristic
521C42D4×D6111yescharacteristic
522C42C2×C22⋊D6111yescharacteristic
523C23—22no—
524C23—22no—
525C23—22no—
526C23—41no—
527C23—41no—
528C23—41no—
529C23—41no—
530C23—612no—
531C23—1221no—
532C23—1221no—
533C23—1221no—
534C23—1221no—
535C23—1221no—
536C23—1221no—
537C23C22⋊C4×D6111yescharacteristic
538Q8—614no—
539Q8—1222no—
540Q8—1222no—
541Q8—1222no—
542D4—22no—
543D4—22no—
544D4—22no—
545D4—12216no—
546D4#1451968914yescomplemented
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—22no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—612no—
557C2×C4—612no—
558C2×C4—12216no—
559C2×C4—1222no—
560C2×C4—1221no—
561C2×C4—1222no—
562C2×C4—1221no—
563C2×C4—1221no—
564C2×C4—1221no—
565C2×C4—1222no—
566C2×C4—1222no—
567C2×C4—1222no—
568C2×C4—1222no—
569C2×C4—1222no—
570C2×C4—1221no—
571C2×C4—1221no—
572C2×C4—1222no—
573C2×C4—1221no—
574C2×C4—2442no—
575C2×C4—2442no—
576C2×C4—2448no—
577C2×C4—2441no—
578C2×C4—2441no—
579C2×C4—2441no—
580C2×C4—2441no—
581C2×C4—2441no—
582C2×C4—2441no—
583C2×C4C22⋊C4×D6111yescharacteristic
584C2×C4C2×#1175819811yescharacteristic
585C2×C4#1451974511yescharacteristic
586C2×C4#1451974511yescharacteristic
587C2×C4#1451974711yescharacteristic
588C2×C4#1451974711yescharacteristic
589C2×C4C2×C8×D6111yescharacteristic
590C2×C4M16×D6111yescharacteristic
591C2×C4M16×D6111yescharacteristic
592C2×C4C2×#1175818911yescharacteristic
593C2×C4#1451979611yescharacteristic
594C2×C4#1451979811yescharacteristic
595C2×C4#1451980111yescharacteristic
596C2×C4#1451980611yescharacteristic
597C8—42no—
598C8—81no—
599C8—4881no—
600C8—2442no—
601C22—24no—
602C22—42no—
603C22—42no—
604C22—42no—
605C22—42no—
606C22—42no—
607C22—42no—
608C22—1222no—
609C22—1222no—
610C22—1222no—
611C22—2441no—
612C22—2441no—
613C22—2441no—
614C22—2441no—
615C22#1683961711yescharacteristic
616C22C22⋊C8×D6111yescharacteristic
617C22#1683972411yescharacteristic
618C22#1683975511yescharacteristic
619C22#1683976011yescharacteristic
620C22#104×D6111yescharacteristic
621C22#1683977711yescharacteristic
622C4—21no—
623C4—21no—
624C4—42no—
625C4—1222no—
626C4—1224no—
627C4—1222no—
628C4—2441no—
629C4—2442no—
630C4C22⋊C8×D6111yescharacteristic
631C4C2×#1451968911yescharacteristic
632C4#1683972411yescharacteristic
633C4#1683972511yescharacteristic
634C4#1683990411yescharacteristic
635C4#1683990811yescharacteristic
636C4#1683992111yescharacteristic
637C4#1683992511yescharacteristic
638C2—44no—
639C2—2442no—
640C2#2144419811yescharacteristic
641C2#2144420311yescharacteristic
642C2#2144425011yescharacteristic
643C2#2144425511yescharacteristic
644C2#2144572811yescharacteristic
645C2#2144575611yescharacteristic
646C2#2144576111yescharacteristic
subgroupG/H
centerC22×C4D4×D61
commutatorC2×C4×C61C22×C8
FrattiniC2×C42C22×D61
FittingC2×C61×D4⋊C8C2
socleC23×C61C2×C22⋊C4
prime radicalC22×#11758224C4
cosocleC2×C42×C61C23
hypercenterC2×D4⋊C8D61
hypocenterC61#8312
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #21445796C2semidirect
3. C4×#14519689C2semidirect
4. C2×#16839494C2semidirect
5. C2×#16839492C2semidirect
6. C2×D4⋊#92418C2semidirect
7. C2×C61×D4⋊C8C2semidirect
40. C2×#11758224C8semidirect
217. D4×C61C22⋊C8semidirect
272. Dic122C22⋊C8semidirect
321. C2×D4⋊C8D61semidirect
358. C61#8312semidirect
546. D4#14519689semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#117582242
#214457962
C4×#145196892
C2×#168394942
C2×#168394922
C2×D4⋊#924182
C2×C61×D4⋊C82
#831261