Finite Group Databasebeta

← #29571401

Subgroups — #29571401

Order 15616.

868 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840299C211yesmaximal, 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
8#16840299—22no—
9#16840299—22no—
10#16840299—22no—
11#16840299—22no—
12C2×#14519772—21no—
13C2×#14519768C411yescharacteristic
14C2×#14519766C411yescharacteristic
15C2×#14519762—21no—
16C2×#14519753C411yescharacteristic
17C2×#14519752C411yescharacteristic
18C2×C4×D244—21no—
19C2×C4×D244C2211yescharacteristic
20C2×#14519734—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—
35C22×D244—21no—
36C22×D244C2×C411yescharacteristic
37C22×C4×D61—21no—
38C22×C4×D61C2×C411yescharacteristic
39C22×C4×D61D411yescharacteristic
40C22×C4×D61D411yescharacteristic
41C22×#92418—21no—
42C22×#92418—21no—
43#14519772—24no—
44#14519772—24no—
45#14519768—22no—
46#14519768—22no—
47#14519766—22no—
48#14519766—22no—
49#14519762—24no—
50#14519762—24no—
51#14519753—22no—
52#14519753—22no—
53#14519752—22no—
54#14519752—22no—
55C4×D244—24no—
56C4×D244—24no—
57C4×D244—21no—
58C4×D244—21no—
59C4×D244D412yes—
60C4×D244D412yes—
61#14519734—24no—
62#14519734—24no—
63C2×C4⋊Dic61—21no—
64C2×C4⋊Dic61C2×C411yescharacteristic
65C2×#11758196—21no—
66C2×#11758196—21no—
67C2×#11758198—21no—
68C2×#11758198—21no—
69C2×#11758198—21no—
70C2×#11758198—21no—
71C2×#11758198—21no—
72C2×C4×Dic61C2×C411yescharacteristic
73C2×C4×Dic61D411yescharacteristic
74C2×C4×Dic61D411yescharacteristic
75C42×D61—21no—
76C42×D61—21no—
77C42×D61—21no—
78C42×D61—21no—
79C4⋊#92418—21no—
80C4⋊#92418—21no—
81#14519689—24no—
82#14519689—42no—
83C4×#92418—21no—
84C4×#92418—21no—
85C22×Q8×C61C2×C411yescharacteristic
86C22×C8×C61—21no—
87C22×C8×C61—21no—
88C4×Q8×C61—21no—
89C4×Q8×C61—21no—
90C4×Q8×C61D412yes—
91C4×Q8×C61D412yes—
92C2×C4⋊C4×C61—21no—
93C2×C4⋊C4×C61C2×C411yescharacteristic
94C2×C42×C61—21no—
95C2×C42×C61C2311yescharacteristic
96C4⋊C8×C61—21no—
97C4⋊C8×C61—21no—
98C4×C8×C61—21no—
99C4×C8×C61—21no—
100C23×D61—21no—
101C23×D61C22⋊C411yescharacteristic
102C2×Q8×C61—21no—
103C2×Q8×C61—21no—
104C2×Q8×C61—21no—
105C2×Q8×C61—21no—
106C2×Q8×C61—21no—
107C2×Q8×C61C22⋊C412yes—
108C22×C4×C61—21no—
109C22×C4×C61—21no—
110C22×C4×C61C22×C411yescharacteristic
111C22×C4×C61C2×D411yescharacteristic
112C22×C4×C61C2×D411yescharacteristic
113C22×Dic61—21no—
114C22×Dic61C22⋊C411yescharacteristic
115C22×Dic61C22⋊C411yescharacteristic
116C22×Dic61C22⋊C411yescharacteristic
117C2×D244—21no—
118C2×D244—21no—
119C2×D244—21no—
120C2×D244—21no—
121C2×D244—24no—
122C2×D244—21no—
123C2×D244—42no—
124C2×D244—42no—
125C2×D244C22⋊C412yes—
126C2×C4×D61—22no—
127C2×C4×D61—21no—
128C2×C4×D61—21no—
129C2×C4×D61—22no—
130C2×C4×D61—22no—
131C2×C4×D61—21no—
132C2×C4×D61—21no—
133C2×C4×D61—21no—
134C2×C4×D61—21no—
135C2×C4×D61—21no—
136C2×C4×D61—21no—
137C2×C4×D61—21no—
138C2×C4×D61—21no—
139C2×C4×D61—21no—
140C2×C4×D61—21no—
141C2×C4×D61—21no—
142C2×C4×D61—21no—
143C2×C4×D61—41no—
144C2×C4×D61—41no—
145C2×C4×D61—41no—
146C2×C4×D61—41no—
147C2×C4×D61—41no—
148C2×C8×C61—22no—
149C2×C8×C61—41no—
150C2×C8×C61—41no—
151C2×C8×C61—41no—
152C2×C8×C61—41no—
153C2×C8×C61—41no—
154C4⋊C4×C61—21no—
155C4⋊C4×C61—22no—
156C4⋊C4×C61—22no—
157C4⋊C4×C61C22⋊C412yes—
158C42×C61—22no—
159C42×C61—22no—
160C42×C61C2×D411yescharacteristic
161C42×C61C2×D411yescharacteristic
162C42×C61C2×D411yescharacteristic
163C42×C61C2×D411yescharacteristic
164#11758198—24no—
165#11758198—24no—
166#11758198—24no—
167#11758198—24no—
168#11758198—22no—
169#11758198—22no—
170C4⋊Dic61—24no—
171C4⋊Dic61—21no—
172C4⋊Dic61C22⋊C412yes—
173#11758196—24no—
174#11758196—24no—
175C4×Dic61—21no—
176C4×Dic61—21no—
177C4×Dic61—21no—
178C4×Dic61—21no—
179C4×Dic61—21no—
180C4×Dic61—21no—
181C2×#92418—22no—
182C2×#92418—41no—
183C2×#92418—41no—
184C2×#92418—41no—
185C2×#92418—41no—
186C2×#92418—41no—
187C23×C61C2×C22⋊C411yescharacteristic
188C22×D61—21no—
189C22×D61—21no—
190C22×D61—21no—
191C22×D61—21no—
192C22×D61—21no—
193C22×D61—21no—
194C22×D61—22no—
195C22×D61—41no—
196C22×D61—41no—
197C22×D61—41no—
198C22×D61—41no—
199C22×D61—41no—
200C22×D61—41no—
201C22×D61#10412yes—
202Q8×C61—22no—
203Q8×C61—22no—
204Q8×C61—41no—
205Q8×C61—41no—
206C2×C4×C61—21no—
207C2×C4×C61—21no—
208C2×C4×C61—22no—
209C2×C4×C61—22no—
210C2×C4×C61—41no—
211C2×C4×C61—41no—
212C2×C4×C61—41no—
213C2×C4×C61—41no—
214C2×C4×C61C2×C22⋊C411yescharacteristic
215C2×C4×C61C2×C22⋊C411yescharacteristic
216C2×C4×C61#12011yescharacteristic
217C2×C4×C61#12011yescharacteristic
218C2×C4×C61#12011yescharacteristic
219C2×C4×C61#12011yescharacteristic
220C2×C4×C61#13111yescharacteristic
221C2×C4×C61#13111yescharacteristic
222C2×C4×C61#13111yescharacteristic
223C2×C4×C61#13111yescharacteristic
224C2×C4×C61#13511yescharacteristic
225C2×C4×C61#13511yescharacteristic
226C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
227C2×C4×C61#13711yescharacteristic
228C2×Dic61—21no—
229C2×Dic61—21no—
230C2×Dic61—21no—
231C2×Dic61—22no—
232C2×Dic61—21no—
233C2×Dic61—21no—
234C2×Dic61—21no—
235C2×Dic61—21no—
236C2×Dic61—21no—
237C2×Dic61—21no—
238C2×Dic61—41no—
239C2×Dic61—41no—
240D244—22no—
241D244—22no—
242D244—48no—
243D244—41no—
244D244—41no—
245C4×D61—42no—
246C4×D61—42no—
247C4×D61—41no—
248C4×D61—41no—
249C4×D61—41no—
250C4×D61—41no—
251C4×D61—41no—
252C4×D61—41no—
253C4×D61—42no—
254C4×D61—42no—
255C4×D61—41no—
256C4×D61—41no—
257C4×D61—42no—
258C4×D61—42no—
259C8×C61—42no—
260C8×C61—81no—
261#92418—42no—
262#92418—81no—
263#8315—611nomaximal, Sylow
264C22×C61#37911yescharacteristic
265C22×C61#40811yescharacteristic
266C22×C61#40811yescharacteristic
267C22×C61#41611yescharacteristic
268C22×C61#41711yescharacteristic
269C22×C61C2×#10411yescharacteristic
270C22×C61#42111yescharacteristic
271C2×D61—22no—
272C2×D61—22no—
273C2×D61—22no—
274C2×D61—41no—
275C2×D61—41no—
276C2×D61—41no—
277C2×D61—41no—
278C2×D61—42no—
279C2×D61—42no—
280C2×D61—42no—
281C2×D61—81no—
282C2×D61—81no—
283C2×D61—81no—
284C2×D61—81no—
285C4×C61—21no—
286C4×C61—21no—
287C4×C61—42no—
288C4×C61—42no—
289C4×C61#40811yescharacteristic
290C4×C61#40811yescharacteristic
291C4×C61#40811yescharacteristic
292C4×C61#40811yescharacteristic
293C4×C61#44911yescharacteristic
294C4×C61#44911yescharacteristic
295C4×C61#45211yescharacteristic
296C4×C61#45211yescharacteristic
297Dic61—41no—
298Dic61—41no—
299Dic61—42no—
300Dic61—41no—
301C2×#529—611no—
302#1797—611no—
303C4×C22⋊C8—611no—
304C2×Q8⋊C8—611no—
305C2×Q8⋊C8D6111yescharacteristic, complemented
306C2×D4⋊C8—611no—
307C2×D4⋊C8—611no—
308C2×C61#148211yescharacteristic
309C2×C61#148311yescharacteristic
310C2×C61#149411yescharacteristic
311C2×C61#149511yescharacteristic
312C2×C61#178011yescharacteristic
313C2×C61#178811yescharacteristic
314C2×C61#178911yescharacteristic
315D61—42no—
316D61—82no—
317#529—1222no—
318#529—1222no—
319#529—1222no—
320#529—1222no—
321C2×#126—1221no—
322C2×#125—611no—
323C2×#124—611no—
324C2×#123—1221no—
325C2×C22⋊Q8—611no—
326C2×#121—611no—
327C2×C4×Q8C2×D6111yescharacteristic
328C2×C4×D4—611no—
329C2×C4×D4—1221no—
330C2×#117—1221no—
331C22×C42—611no—
332C2×C4⋊C8—611no—
333C2×C4⋊C8C2×D6111yescharacteristic
334C2×C22⋊C8—1221no—
335C2×C22⋊C8—1221no—
336C2×C4×C8—611no—
337C2×C4×C8C2×D6111yescharacteristic
338#336—1221no—
339#336—1221no—
340Q8⋊C8—22no—
341Q8⋊C8—1222no—
342D4⋊C8—1222no—
343D4⋊C8—1222no—
344C61#831511yescharacteristic, complemented, Sylow
345C22×Q8C4×D6111yescharacteristic
346C22×D4—611no—
347C22×D4—1221no—
348C23×C4—611no—
349C23×C4—611no—
350C23×C4—611no—
351C23×C4—1221no—
352C22×C8—21no—
353C22×C8—21no—
354C22×C8—1221no—
355C22×C8—1221no—
356#126—1224no—
357#126—1224no—
358#125—1222no—
359#125—1222no—
360#124—1222no—
361#124—1222no—
362#123—1224no—
363#123—1224no—
364C22⋊Q8—1222no—
365C22⋊Q8—1222no—
366#121—1222no—
367#121—1222no—
368C4×Q8—21no—
369C4×Q8—21no—
370C4×Q8D24412yes—
371C4×Q8C22⋊D6112yes—
372C4×D4—612no—
373C4×D4—612no—
374C4×D4—1224no—
375C4×D4—1224no—
376C4×D4—1221no—
377C4×D4—1221no—
378#117—1224no—
379#117—1224no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—611no—
382C2×C4⋊C4—1221no—
383C2×C4⋊C4—1221no—
384C2×C4⋊C4—1221no—
385C2×C4⋊C4C4×D6111yescharacteristic
386C2×C22⋊C4—1221no—
387C2×C22⋊C4—1221no—
388C2×C22⋊C4—1221no—
389C2×C22⋊C4—1221no—
390C2×C22⋊C4—1221no—
391C2×C42—21no—
392C2×C42—611no—
393C2×C42—611no—
394C2×C42—611no—
395C2×C42—1221no—
396C2×C42—1221no—
397C2×C42—1221no—
398C2×C42—1221no—
399C2×C42C22×D6111yescharacteristic
400C4⋊C8—21no—
401C4⋊C8—21no—
402C4⋊C8—1221no—
403C4⋊C8—1221no—
404C22⋊C8—1224no—
405C22⋊C8—2442no—
406C4×C8—21no—
407C4×C8—21no—
408C4×C8—1221no—
409C4×C8—1221no—
410C24—611no—
411C24—1221no—
412C2×Q8—21no—
413C2×Q8—21no—
414C2×Q8—21no—
415C2×Q8—21no—
416C2×Q8—21no—
417C2×Q8#1175819812yes—
418C2×D4—612no—
419C2×D4—1224no—
420C2×D4—1221no—
421C2×D4—1221no—
422C2×D4—1221no—
423C2×D4—1221no—
424C2×D4—1221no—
425C2×D4—2442no—
426C2×D4—2442no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—611no—
430C22×C4—611no—
431C22×C4—611no—
432C22×C4—1222no—
433C22×C4—1221no—
434C22×C4—1221no—
435C22×C4—1221no—
436C22×C4—1221no—
437C22×C4—1221no—
438C22×C4—1221no—
439C22×C4—1222no—
440C22×C4—1221no—
441C22×C4—1221no—
442C22×C4—1222no—
443C22×C4—1221no—
444C22×C4—1221no—
445C22×C4—1221no—
446C22×C4—1221no—
447C22×C4—1221no—
448C22×C4—1221no—
449C22×C4—1221no—
450C22×C4—2441no—
451C22×C4—2441no—
452C22×C4—2441no—
453C22×C4—2441no—
454C22×C4—2441no—
455C22×C4C2×C4×D6111yescharacteristic
456C22×C4D4×D6111yescharacteristic
457C22×C4D4×D6111yescharacteristic
458C2×C8—22no—
459C2×C8—41no—
460C2×C8—41no—
461C2×C8—41no—
462C2×C8—41no—
463C2×C8—41no—
464C2×C8—1222no—
465C2×C8—2441no—
466C2×C8—2441no—
467C2×C8—2441no—
468C2×C8—2441no—
469C2×C8—2441no—
470C4⋊C4—21no—
471C4⋊C4—22no—
472C4⋊C4—22no—
473C4⋊C4—612no—
474C4⋊C4—1224no—
475C4⋊C4—1224no—
476C4⋊C4—1224no—
477C4⋊C4—1221no—
478C4⋊C4#1175819812yes—
479C22⋊C4—1224no—
480C22⋊C4—1224no—
481C22⋊C4—1224no—
482C22⋊C4—1224no—
483C22⋊C4—1222no—
484C22⋊C4—1222no—
485C42—22no—
486C42—22no—
487C42—1221no—
488C42—1221no—
489C42—1221no—
490C42—1221no—
491C42—1221no—
492C42—1221no—
493C42C2×D24411yescharacteristic
494C42D4×D6111yescharacteristic
495C42D4×D6111yescharacteristic
496C42C2×C22⋊D6111yescharacteristic
497C23—612no—
498C23—1221no—
499C23—1221no—
500C23—1221no—
501C23—1221no—
502C23—1221no—
503C23—1221no—
504C23—1222no—
505C23—2441no—
506C23—2441no—
507C23—2441no—
508C23—2441no—
509C23—2441no—
510C23—2441no—
511C23C22⋊C4×D6111yescharacteristic
512Q8—22no—
513Q8—22no—
514Q8—41no—
515Q8—41no—
516D4—1222no—
517D4—1222no—
518D4—2448no—
519D4—2441no—
520D4—2441no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—1221no—
530C2×C4—1221no—
531C2×C4—1221no—
532C2×C4—1221no—
533C2×C4—1221no—
534C2×C4—1221no—
535C2×C4—1221no—
536C2×C4—1221no—
537C2×C4—1221no—
538C2×C4—1222no—
539C2×C4—2442no—
540C2×C4—2442no—
541C2×C4—2441no—
542C2×C4—2441no—
543C2×C4—2441no—
544C2×C4—2441no—
545C2×C4—2441no—
546C2×C4—2441no—
547C2×C4—2441no—
548C2×C4—2442no—
549C2×C4—2441no—
550C2×C4—2442no—
551C2×C4—2441no—
552C2×C4—2442no—
553C2×C4—2441no—
554C2×C4—2442no—
555C2×C4C22⋊C4×D6111yescharacteristic
556C2×C4C2×#1175819811yescharacteristic
557C2×C4#1451974511yescharacteristic
558C2×C4#1451974511yescharacteristic
559C2×C4#1451974711yescharacteristic
560C2×C4#1451974711yescharacteristic
561C2×C4#1451978311yescharacteristic
562C2×C4#1451978311yescharacteristic
563C2×C4#1451978511yescharacteristic
564C2×C4#1451978511yescharacteristic
565C2×C4#1451979811yescharacteristic
566C2×C4#1451980011yescharacteristic
567C2×C4#1451980411yescharacteristic
568C2×C4#1451980911yescharacteristic
569C8—42no—
570C8—81no—
571C8—4881no—
572C8—2442no—
573C22—1222no—
574C22—1222no—
575C22—1222no—
576C22—4881no—
577C22—4881no—
578C22—4881no—
579C22—4881no—
580C22—2442no—
581C22—2442no—
582C22—2442no—
583C22—2441no—
584C22—2441no—
585C22—2441no—
586C22—2441no—
587C22#1683961711yescharacteristic
588C22#1683972711yescharacteristic
589C22#1683972711yescharacteristic
590C22#1683975711yescharacteristic
591C22#1683976211yescharacteristic
592C22#104×D6111yescharacteristic
593C22#1683977711yescharacteristic
594C4—21no—
595C4—21no—
596C4—42no—
597C4—42no—
598C4—2441no—
599C4—2441no—
600C4—2442no—
601C4—2441no—
602C4#1683972711yescharacteristic
603C4#1683972711yescharacteristic
604C4#1683972811yescharacteristic
605C4#1683973011yescharacteristic
606C4#1683990611yescharacteristic
607C4#1683991011yescharacteristic
608C4#1683992311yescharacteristic
609C4#1683992711yescharacteristic
610C2—4882no—
611C2—2442no—
612C2#2144422611yescharacteristic
613C2#2144423111yescharacteristic
614C2#2144427811yescharacteristic
615C2#2144428311yescharacteristic
616C2#2144573011yescharacteristic
617C2#2144575811yescharacteristic
618C2#2144576111yescharacteristic
subgroupG/H
centerC22×C4D4×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC2×C61×Q8⋊C8C2
socleC23×C61C2×C22⋊C4
prime radicalC2×#14519752C4
cosocleC2×C42×C61C23
hypercenterC2×Q8⋊C8D61
hypocenterC61#8315
LCSG ▷ C22×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
305. C2×Q8⋊C8D61semidirect
344. C61#8315semidirect

Maximal subgroups

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

subgroupindex
C2×#168402992
#214457962
C4×#145196892
C2×Q8⋊#924182
C2×#168394912
C2×#168394892
C2×C61×Q8⋊C82
#831561