Finite Group Databasebeta

← #29571388

Subgroups — #29571388

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×#11758226C211yesmaximal, characteristic
2#21445796C211yesmaximal, characteristic, complemented
3C4×#14519689C211yesmaximal, characteristic, complemented
4C2×Q8⋊#92418C211yesmaximal, characteristic, complemented
5C2×#16839491C211yesmaximal, characteristic, complemented
6C2×#16839489C211yesmaximal, characteristic, complemented
7C2×C61×Q8⋊C8C211yesmaximal, characteristic, complemented
8C22×#11758226C411yescharacteristic
9C4×#11758226—22no—
10C4×#11758226—22no—
11C4×#11758226—22no—
12C4×#11758226—22no—
13C2×Q8×Dic61C411yescharacteristic
14C2×C4×D244—21no—
15C2×C4×D244C2211yescharacteristic
16C2×#14519739—21no—
17C2×#14519739C411yescharacteristic
18C2×#14519735—21no—
19C2×#14519735C411yescharacteristic
20C2×C42×D61—21no—
21C2×C42×D61C2211yescharacteristic
22C2×C4⋊#92418C2211yescharacteristic
23C2×#14519689—21no—
24C2×#14519689—21no—
25C2×C4×#92418C2211yescharacteristic
26#16839516—21no—
27#16839516—21no—
28Q8⋊#92418—22no—
29#16839491—22no—
30#16839489—22no—
31C2×C4×Q8×C61C2211yescharacteristic
32C2×C4⋊C8×C61C2211yescharacteristic
33C2×C4×C8×C61C2211yescharacteristic
34C61×Q8⋊C8—22no—
35C2×#11758226—22no—
36C2×#11758226—22no—
37C2×#11758226—22no—
38C2×#11758226—22no—
39C2×#11758226—22no—
40C2×#11758226C814yescomplemented
41C22×D244—21no—
42C22×D244C2×C411yescharacteristic
43C22×C4×D61—21no—
44C22×C4×D61—21no—
45C22×C4×D61—21no—
46C22×C4×D61C2×C411yescharacteristic
47C22×C4×D61D411yescharacteristic
48C22×C4×D61D411yescharacteristic
49C22×#92418—21no—
50C22×#92418—21no—
51Q8×Dic61—22no—
52Q8×Dic61—22no—
53C4×D244—24no—
54C4×D244—24no—
55C4×D244—21no—
56C4×D244—21no—
57C4×D244D412yes—
58C4×D244D412yes—
59#14519739—24no—
60#14519739—24no—
61#14519739—22no—
62#14519739—22no—
63#14519735—24no—
64#14519735—24no—
65#14519735—22no—
66#14519735—22no—
67C2×C4⋊Dic61—21no—
68C2×C4⋊Dic61C2×C411yescharacteristic
69C2×#11758198—21no—
70C2×#11758198—21no—
71C2×#11758198—21no—
72C2×C4×Dic61—21no—
73C2×C4×Dic61—21no—
74C2×C4×Dic61C2×C411yescharacteristic
75C2×C4×Dic61D411yescharacteristic
76C2×C4×Dic61D411yescharacteristic
77C42×D61—24no—
78C42×D61—24no—
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×Q8×C61C2×C411yescharacteristic
90C22×C8×C61—21no—
91C22×C8×C61—21no—
92C4×Q8×C61—21no—
93C4×Q8×C61—21no—
94C4×Q8×C61D412yes—
95C4×Q8×C61D412yes—
96C2×C4⋊C4×C61—21no—
97C2×C4⋊C4×C61C2×C411yescharacteristic
98C2×C42×C61—21no—
99C2×C42×C61C2311yescharacteristic
100C4⋊C8×C61—21no—
101C4⋊C8×C61—21no—
102C4×C8×C61—21no—
103C4×C8×C61—21no—
104C23×D61—21no—
105C23×D61C22⋊C411yescharacteristic
106C2×Q8×C61—21no—
107C2×Q8×C61—21no—
108C2×Q8×C61—21no—
109C2×Q8×C61C22⋊C412yes—
110C2×Q8×C61C2×C812yes—
111C2×Q8×C61M1612yes—
112C22×C4×C61—21no—
113C22×C4×C61—21no—
114C22×C4×C61C22×C411yescharacteristic
115C22×C4×C61C2×D411yescharacteristic
116C22×C4×C61C2×D411yescharacteristic
117C22×Dic61—21no—
118C22×Dic61C22⋊C411yescharacteristic
119C22×Dic61C22⋊C411yescharacteristic
120C22×Dic61C22⋊C411yescharacteristic
121#11758226—28no—
122#11758226—28no—
123#11758226—28no—
124#11758226—28no—
125C2×D244—24no—
126C2×D244—24no—
127C2×D244—24no—
128C2×D244—21no—
129C2×D244—21no—
130C2×D244—21no—
131C2×D244C22⋊C412yes—
132C2×D244C2×C812yes—
133C2×D244M1612yes—
134C2×C4×D61—24no—
135C2×C4×D61—24no—
136C2×C4×D61—21no—
137C2×C4×D61—21no—
138C2×C4×D61—21no—
139C2×C4×D61—21no—
140C2×C4×D61—24no—
141C2×C4×D61—24no—
142C2×C4×D61—22no—
143C2×C4×D61—22no—
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×D61—42no—
155C2×C4×D61—41no—
156C2×C4×D61—41no—
157C2×C4×D61—41no—
158C2×C4×D61—41no—
159C2×C4×D61—42no—
160C2×C4×D61C2×C812yes—
161C2×C4×D61M1612yes—
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×C61—22no—
170C4⋊C4×C61—22no—
171C4⋊C4×C61C22⋊C412yes—
172C42×C61—22no—
173C42×C61—22no—
174C42×C61C2×D411yescharacteristic
175C42×C61C2×D411yescharacteristic
176C42×C61C2×D411yescharacteristic
177C42×C61C2×D411yescharacteristic
178#11758198—24no—
179#11758198—24no—
180#11758198—22no—
181#11758198—22no—
182C4⋊Dic61—24no—
183C4⋊Dic61—21no—
184C4⋊Dic61C22⋊C412yes—
185C4×Dic61—24no—
186C4×Dic61—24no—
187C4×Dic61—21no—
188C4×Dic61—21no—
189C4×Dic61—21no—
190C4×Dic61—21no—
191C4×Dic61—21no—
192C4×Dic61—21no—
193C2×#92418—22no—
194C2×#92418—41no—
195C2×#92418—41no—
196C2×#92418—41no—
197C2×#92418—41no—
198C2×#92418—41no—
199C23×C61C2×C22⋊C411yescharacteristic
200C22×D61—21no—
201C22×D61—22no—
202C22×D61—22no—
203C22×D61—21no—
204C22×D61—22no—
205C22×D61—21no—
206C22×D61—21no—
207C22×D61—21no—
208C22×D61—21no—
209C22×D61—41no—
210C22×D61—41no—
211C22×D61—41no—
212C22×D61—41no—
213C22×D61C22⋊C812yes—
214Q8×C61—22no—
215Q8×C61—22no—
216Q8×C61—22no—
217Q8×C61C22⋊C814yescomplemented
218C2×C4×C61—22no—
219C2×C4×C61—22no—
220C2×C4×C61—22no—
221C2×C4×C61—21no—
222C2×C4×C61—21no—
223C2×C4×C61—22no—
224C2×C4×C61—41no—
225C2×C4×C61—41no—
226C2×C4×C61C2×C22⋊C411yescharacteristic
227C2×C4×C61C2×C22⋊C411yescharacteristic
228C2×C4×C61#12011yescharacteristic
229C2×C4×C61#12011yescharacteristic
230C2×C4×C61#12011yescharacteristic
231C2×C4×C61#12011yescharacteristic
232C2×C4×C61C22×C811yescharacteristic
233C2×C4×C61C2×M1611yescharacteristic
234C2×C4×C61C2×M1611yescharacteristic
235C2×C4×C61C2×M1611yescharacteristic
236C2×C4×C61#13511yescharacteristic
237C2×C4×C61#13511yescharacteristic
238C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
239C2×C4×C61#13711yescharacteristic
240C2×Dic61—21no—
241C2×Dic61—21no—
242C2×Dic61—21no—
243C2×Dic61—21no—
244C2×Dic61—21no—
245C2×Dic61—22no—
246C2×Dic61—21no—
247C2×Dic61—21no—
248C2×Dic61—41no—
249C2×Dic61—41no—
250C2×Dic61C22⋊C812yes—
251C2×Dic61#10412yes—
252D244—216no—
253D244—22no—
254D244—22no—
255D244—22no—
256D244C22⋊C814yescomplemented
257C4×D61—216no—
258C4×D61—22no—
259C4×D61—22no—
260C4×D61—22no—
261C4×D61—22no—
262C4×D61—42no—
263C4×D61—42no—
264C4×D61—48no—
265C4×D61—41no—
266C4×D61—41no—
267C4×D61—42no—
268C4×D61—42no—
269C4×D61—41no—
270C4×D61—41no—
271C4×D61—42no—
272C4×D61—42no—
273C8×C61—42no—
274C8×C61—81no—
275#92418—42no—
276#92418—81no—
277#8312—611nomaximal, Sylow
278C22×C61#37911yescharacteristic
279C22×C61C2×C22⋊C811yescharacteristic
280C22×C61#40711yescharacteristic
281C22×C61#41611yescharacteristic
282C22×C61#41711yescharacteristic
283C22×C61C2×#10411yescharacteristic
284C22×C61#42111yescharacteristic
285C2×D61—22no—
286C2×D61—22no—
287C2×D61—22no—
288C2×D61—24no—
289C2×D61—42no—
290C2×D61—42no—
291C2×D61—41no—
292C2×D61—42no—
293C2×D61—41no—
294C2×D61—42no—
295C2×D61—41no—
296C2×D61—42no—
297C2×D61—41no—
298C2×D61—42no—
299C4×C61—24no—
300C4×C61—21no—
301C4×C61—21no—
302C4×C61—42no—
303C4×C61C2×C22⋊C811yescharacteristic
304C4×C61C2×C22⋊C811yescharacteristic
305C4×C61#40711yescharacteristic
306C4×C61#40711yescharacteristic
307C4×C61#44911yescharacteristic
308C4×C61#44911yescharacteristic
309C4×C61#45211yescharacteristic
310C4×C61#45211yescharacteristic
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⋊C8D6111yescharacteristic, complemented
320C2×D4⋊C8—611no—
321C2×D4⋊C8—611no—
322C2×C61#147611yescharacteristic
323C2×C61#147711yescharacteristic
324C2×C61#148811yescharacteristic
325C2×C61#148911yescharacteristic
326C2×C61#177911yescharacteristic
327C2×C61#178811yescharacteristic
328C2×C61#178911yescharacteristic
329D61—42no—
330D61—44no—
331C22×#41—611no—
332C4×#41—1222no—
333C4×#41—1222no—
334C4×#41—1222no—
335C4×#41—1222no—
336C2×C4×Q8—611no—
337C2×C4×Q8C2×D6111yescharacteristic
338C2×C4×D4—611no—
339C2×C4×D4—611no—
340C2×C4×D4—1221no—
341C2×C4×D4—1221no—
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—22no—
355Q8⋊C8—1222no—
356D4⋊C8—1222no—
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×Q8C4×D6111yescharacteristic
366C22×D4—611no—
367C22×D4—1221no—
368C23×C4—611no—
369C23×C4—611no—
370C23×C4—611no—
371C23×C4—1221no—
372C23×C4—1221no—
373C23×C4—1221no—
374C22×C8—21no—
375C22×C8—21no—
376C22×C8—1221no—
377C22×C8—1221no—
378C4×Q8—21no—
379C4×Q8—21no—
380C4×Q8—1222no—
381C4×Q8—1222no—
382C4×Q8D24412yes—
383C4×Q8C22⋊D6112yes—
384C4×D4—612no—
385C4×D4—612no—
386C4×D4—1224no—
387C4×D4—1224no—
388C4×D4—1222no—
389C4×D4—1224no—
390C4×D4—1224no—
391C4×D4—1222no—
392C4×D4—1221no—
393C4×D4—1221no—
394#117—1222no—
395#117—1224no—
396#117—1224no—
397#117—1222no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—611no—
400C2×C4⋊C4—1221no—
401C2×C4⋊C4C4×D6111yescharacteristic
402C2×C22⋊C4—1221no—
403C2×C22⋊C4—1221no—
404C2×C22⋊C4—1221no—
405C2×C42—21no—
406C2×C42—611no—
407C2×C42—611no—
408C2×C42—611no—
409C2×C42—1224no—
410C2×C42—1224no—
411C2×C42—1221no—
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—611no—
429C24—1221no—
430#41—1228no—
431#41—1228no—
432#41—1228no—
433#41—1228no—
434C2×Q8—21no—
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8C8×D6112yes—
438C2×Q8#1175818912yes—
439C2×Q8#1175819812yes—
440C2×D4—612no—
441C2×D4—612no—
442C2×D4—612no—
443C2×D4—1224no—
444C2×D4—1224no—
445C2×D4—1224no—
446C2×D4—1221no—
447C2×D4—1221no—
448C2×D4—1221no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—611no—
452C22×C4—611no—
453C22×C4—612no—
454C22×C4—612no—
455C22×C4—611no—
456C22×C4—1224no—
457C22×C4—1222no—
458C22×C4—1224no—
459C22×C4—1224no—
460C22×C4—1224no—
461C22×C4—1221no—
462C22×C4—1221no—
463C22×C4—1221no—
464C22×C4—1221no—
465C22×C4—1221no—
466C22×C4—1221no—
467C22×C4—1222no—
468C22×C4—1221no—
469C22×C4—1221no—
470C22×C4—1222no—
471C22×C4—1221no—
472C22×C4—1221no—
473C22×C4—1221no—
474C22×C4—1221no—
475C22×C4—1221no—
476C22×C4—2441no—
477C22×C4—2442no—
478C22×C4—2442no—
479C22×C4—2441no—
480C22×C4—2441no—
481C22×C4—2441no—
482C22×C4—2441no—
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—22no—
500C4⋊C4—22no—
501C4⋊C4—612no—
502C4⋊C4—1224no—
503C4⋊C4—1221no—
504C4⋊C4#1175819812yes—
505C22⋊C4—1224no—
506C22⋊C4—1224no—
507C22⋊C4—1222no—
508C22⋊C4—1222no—
509C42—22no—
510C42—22no—
511C42—1224no—
512C42—1224no—
513C42—1221no—
514C42—1221no—
515C42—1221no—
516C42—1221no—
517C42—1221no—
518C42—1221no—
519C42C2×D24411yescharacteristic
520C42D4×D6111yescharacteristic
521C42D4×D6111yescharacteristic
522C42C2×C22⋊D6111yescharacteristic
523C23—612no—
524C23—1222no—
525C23—1222no—
526C23—1221no—
527C23—1221no—
528C23—1221no—
529C23—1221no—
530C23—1221no—
531C23—1222no—
532C23—1221no—
533C23—2441no—
534C23—2441no—
535C23—2441no—
536C23—2441no—
537C23C22⋊C4×D6111yescharacteristic
538Q8—22no—
539Q8—22no—
540Q8—22no—
541Q8#1451968914yescomplemented
542D4—614no—
543D4—12216no—
544D4—1222no—
545D4—1222no—
546D4—1222no—
547C2×C4—22no—
548C2×C4—22no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—612no—
556C2×C4—612no—
557C2×C4—12216no—
558C2×C4—1221no—
559C2×C4—1221no—
560C2×C4—1221no—
561C2×C4—1221no—
562C2×C4—1222no—
563C2×C4—1222no—
564C2×C4—1222no—
565C2×C4—1222no—
566C2×C4—1221no—
567C2×C4—1221no—
568C2×C4—1222no—
569C2×C4—1221no—
570C2×C4—2442no—
571C2×C4—2442no—
572C2×C4—2448no—
573C2×C4—2441no—
574C2×C4—2441no—
575C2×C4—2441no—
576C2×C4—2442no—
577C2×C4—2441no—
578C2×C4—2442no—
579C2×C4—2441no—
580C2×C4—2442no—
581C2×C4—2441no—
582C2×C4—2442no—
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#1451979811yescharacteristic
594C2×C4#1451980011yescharacteristic
595C2×C4#1451980411yescharacteristic
596C2×C4#1451980911yescharacteristic
597C8—42no—
598C8—81no—
599C8—4881no—
600C8—2442no—
601C22—1224no—
602C22—1222no—
603C22—1222no—
604C22—1222no—
605C22—2442no—
606C22—2442no—
607C22—2441no—
608C22—2442no—
609C22—2441no—
610C22—2442no—
611C22—2441no—
612C22—2442no—
613C22—2441no—
614C22—2442no—
615C22#1683961711yescharacteristic
616C22C22⋊C8×D6111yescharacteristic
617C22#1683972411yescharacteristic
618C22#1683975711yescharacteristic
619C22#1683976211yescharacteristic
620C22#104×D6111yescharacteristic
621C22#1683977711yescharacteristic
622C4—24no—
623C4—21no—
624C4—21no—
625C4—42no—
626C4—1222no—
627C4—1222no—
628C4—2441no—
629C4—2442no—
630C4C22⋊C8×D6111yescharacteristic
631C4C2×#1451968911yescharacteristic
632C4#1683972411yescharacteristic
633C4#1683972511yescharacteristic
634C4#1683990611yescharacteristic
635C4#1683991011yescharacteristic
636C4#1683992311yescharacteristic
637C4#1683992711yescharacteristic
638C2—2442no—
639C2—2444no—
640C2#2144420011yescharacteristic
641C2#2144420511yescharacteristic
642C2#2144425211yescharacteristic
643C2#2144425711yescharacteristic
644C2#2144572811yescharacteristic
645C2#2144575811yescharacteristic
646C2#2144576111yescharacteristic
subgroupG/H
centerC22×C4D4×D61
commutatorC2×C4×C61C22×C8
FrattiniC2×C42C22×D61
FittingC2×C61×Q8⋊C8C2
socleC23×C61C2×C22⋊C4
prime radicalC22×#11758226C4
cosocleC2×C42×C61C23
hypercenterC2×Q8⋊C8D61
hypocenterC61#8312
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×Q8⋊C8

Complements

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

NH ≅ G/Ntype
2. #21445796C2semidirect
3. C4×#14519689C2semidirect
4. C2×Q8⋊#92418C2semidirect
5. C2×#16839491C2semidirect
6. C2×#16839489C2semidirect
7. C2×C61×Q8⋊C8C2semidirect
40. C2×#11758226C8semidirect
217. Q8×C61C22⋊C8semidirect
256. D244C22⋊C8semidirect
319. C2×Q8⋊C8D61semidirect
358. C61#8312semidirect
541. Q8#14519689semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#117582262
#214457962
C4×#145196892
C2×Q8⋊#924182
C2×#168394912
C2×#168394892
C2×C61×Q8⋊C82
#831261