Finite Group Databasebeta

← #29650039

Subgroups — #29650039

Order 15616.

624 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455897C211yesmaximal, characteristic
2#21454791C211yesmaximal, characteristic
3C8×Q8×D61C211yesmaximal, characteristic, complemented
4#21444668C211yesmaximal, characteristic, complemented
5#21444666C211yesmaximal, characteristic, complemented
6#21444665C211yesmaximal, characteristic, complemented
7#21444663C211yesmaximal, characteristic, complemented
8#21444639C211yesmaximal, characteristic, complemented
9#21444636C211yesmaximal, characteristic, complemented
10#21444631C211yesmaximal, characteristic, complemented
11#21444603C211yesmaximal, characteristic, complemented
12#21444264C211yesmaximal, characteristic, complemented
13#21444229C211yesmaximal, characteristic
14#21444107C211yesmaximal, characteristic, complemented
15C61×SD16⋊C8C211yesmaximal, characteristic, complemented
16#16840294C2211yescharacteristic
17C4×Q8×D61C2211yescharacteristic
18#16840094C411yescharacteristic
19#16840074C411yescharacteristic
20#16840072C411yescharacteristic
21#16840071C411yescharacteristic
22#16839983C411yescharacteristic
23#16839982C411yescharacteristic
24#16839919C411yescharacteristic
25#16839899C411yescharacteristic
26#16839889C2211yescharacteristic
27Q8×#92418C2211yescharacteristic
28C8×Dic122—21no—
29C8×Dic122C2211yescharacteristic
30C8×Dic122C2211yescharacteristic
31#16839886—21no—
32#16839886C2211yescharacteristic
33C4×Dic244C2211yescharacteristic
34C4×#11758202C2211yescharacteristic
35C4×#11758200C2211yescharacteristic
36#16839840C2211yescharacteristic
37#16839836—21no—
38C8×C22⋊D61—21no—
39#16839820—21no—
40#16839818C2211yescharacteristic
41#16839813C2211yescharacteristic
42C4⋊C8×D61—21no—
43C4⋊C8×D61C2211yescharacteristic
44#16839717—21no—
45C4×#11758189C2211yescharacteristic
46C4×C8×D61—21no—
47C4×C8×D61C2211yescharacteristic
48#16839514C2211yescharacteristic
49#16839513C2211yescharacteristic
50#16839512C2211yescharacteristic
51#16839494C2211yescharacteristic
52#16839494C2211yescharacteristic
53Q8⋊#92418C2211yescharacteristic
54#16839492C2211yescharacteristic
55#16839492C2211yescharacteristic
56D4⋊#92418C2211yescharacteristic
57#16839484C2211yescharacteristic
58#16839484C2211yescharacteristic
59#16839484C2211yescharacteristic
60C8×Q8×C61C2211yescharacteristic
61C4×SD16×C61C2211yescharacteristic
62C8×D4×C61C2211yescharacteristic
63C61×#335C2211yescharacteristic
64C61×Q8⋊C8C2211yescharacteristic
65C61×D4⋊C8C2211yescharacteristic
66C61×#322C2211yescharacteristic
67C2×Q8×D61C2×C411yescharacteristic
68C2×Dic244C2×C411yescharacteristic
69C2×#11758202C2×C411yescharacteristic
70C2×#11758200C2×C411yescharacteristic
71C2×#11758194—21no—
72C2×#11758189—21no—
73C2×C8×D61—21no—
74C2×C8×D61D411yescharacteristic
75C2×C8×D61D411yescharacteristic
76#14519770—21no—
77#14519768C2×C411yescharacteristic
78#14519764C2×C411yescharacteristic
79#14519759—21no—
80#14519757C2×C411yescharacteristic
81#14519748C2×C411yescharacteristic
82Q8×Dic61C2×C411yescharacteristic
83C4×Dic122—21no—
84C4×Dic122C2311yescharacteristic
85C4×Dic122C2311yescharacteristic
86#14519742—21no—
87#14519742C2×C411yescharacteristic
88C4×C22⋊D61—21no—
89#14519736—21no—
90C4⋊C4×D61—21no—
91C4⋊C4×D61C2×C411yescharacteristic
92C42×D61—21no—
93C42×D61C2311yescharacteristic
94#14519711C2×C411yescharacteristic
95#14519710C2×C411yescharacteristic
96#14519708C2×C411yescharacteristic
97C4⋊#92418—21no—
98C4⋊#92418C2311yescharacteristic
99C4⋊#92418C2311yescharacteristic
100#14519706—21no—
101#14519706—21no—
102#14519706—21no—
103#14519706—21no—
104#14519706—21no—
105#14519706C2×C411yescharacteristic
106#14519706C2×C411yescharacteristic
107#14519702C2×C411yescharacteristic
108#14519702C2×C411yescharacteristic
109#14519701C2×C411yescharacteristic
110#14519700C2×C411yescharacteristic
111#14519700C2×C411yescharacteristic
112#14519698C2×C411yescharacteristic
113C22⋊#92418—21no—
114#14519689—21no—
115#14519689C2×C411yescharacteristic
116#14519689C2×C411yescharacteristic
117#14519687—21no—
118#14519687—21no—
119#14519687—21no—
120C4×#92418—21no—
121C4×#92418C2311yescharacteristic
122C4×#92418C2311yescharacteristic
123C4×#92418C2311yescharacteristic
124C8×Dic61—21no—
125C8×Dic61—21no—
126C8×Dic61—21no—
127C8×Dic61D411yescharacteristic
128C8×Dic61D411yescharacteristic
129C2×SD16×C61C2×C411yescharacteristic
130C22×C8×C61—21no—
131C4×Q8×C61C2311yescharacteristic
132C4×D4×C61C2311yescharacteristic
133#106×C61C2×C411yescharacteristic
134C4⋊C8×C61—21no—
135C4⋊C8×C61C2311yescharacteristic
136C4⋊C8×C61C2311yescharacteristic
137#103×C61C2×C411yescharacteristic
138#102×C61C2×C411yescharacteristic
139C22⋊C8×C61—21no—
140C4×C8×C61—21no—
141C4×C8×C61C2311yescharacteristic
142C4×C8×C61C2311yescharacteristic
143C4×C8×C61C2311yescharacteristic
144C2×Q8×C61C22×C411yescharacteristic
145C2×D4×C61C22×C411yescharacteristic
146C22×C4×C61—21no—
147C2×C22⋊D61—21no—
148Q8×D61—22no—
149Q8×D61—22no—
150C2×C4×D61—21no—
151C2×C4×D61—21no—
152C2×C4×D61C22×C411yescharacteristic
153C2×C4×D61C2×D411yescharacteristic
154C2×C4×D61#4111yescharacteristic
155C2×Dic122—21no—
156C2×Dic122C22×C411yescharacteristic
157C2×Dic122C22×C411yescharacteristic
158SD16×C61—22no—
159C2×C8×C61—21no—
160C2×C8×C61—21no—
161C2×C8×C61—21no—
162C2×C8×C61—42no—
163C2×C8×C61C22×C411yescharacteristic
164C2×C8×C61C22×C411yescharacteristic
165C2×C8×C61C2×D411yescharacteristic
166C2×C8×C61C2×D411yescharacteristic
167C4⋊C4×C61—21no—
168C4⋊C4×C61C22×C411yescharacteristic
169C4⋊C4×C61C22×C411yescharacteristic
170C22⋊C4×C61—21no—
171C42×C61—21no—
172C42×C61C2411yescharacteristic
173C22⋊Dic61—21no—
174C22⋊Dic61—21no—
175C22⋊Dic61—21no—
176#11758202—22no—
177#11758200—22no—
178#11758198—21no—
179C4⋊Dic61—21no—
180C4⋊Dic61—21no—
181C4⋊Dic61—21no—
182C4⋊Dic61C22×C411yescharacteristic
183C4⋊Dic61C22×C411yescharacteristic
184#11758196—21no—
185#11758196—21no—
186#11758196—21no—
187#11758196—21no—
188#11758196—21no—
189C4×Dic61—21no—
190C4×Dic61—21no—
191C4×Dic61—21no—
192C4×Dic61—21no—
193C4×Dic61C22×C411yescharacteristic
194C4×Dic61C2×D411yescharacteristic
195C4×Dic61#4111yescharacteristic
196#11758194—42no—
197C2×#92418—21no—
198C2×#92418—21no—
199C2×#92418—21no—
200C2×#92418C22×C411yescharacteristic
201C2×#92418C22×C411yescharacteristic
202C2×#92418C2×D411yescharacteristic
203C2×#92418C2×D411yescharacteristic
204Dic244—22no—
205#11758189—42no—
206C8×D61—22no—
207C8×D61—41no—
208C8×D61—42no—
209C23×C61—21no—
210C22×D61C4×D411yescharacteristic
211Q8×C61—21no—
212Q8×C61#13112yes—
213D4×C61—21no—
214D4×C61—21no—
215C2×C4×C61—21no—
216C2×C4×C61—21no—
217C2×C4×C61—21no—
218C2×C4×C61—41no—
219C2×C4×C61—41no—
220C2×C4×C61C23×C411yescharacteristic
221C2×C4×C61C22×D411yescharacteristic
222C2×C4×C61C2×#4111yescharacteristic
223C22⋊D61—42no—
224C2×Dic61—21no—
225C2×Dic61—21no—
226C2×Dic61—21no—
227C2×Dic61—21no—
228C2×Dic61C4×D411yescharacteristic
229C2×Dic61C4×D411yescharacteristic
230C2×Dic61C4×D411yescharacteristic
231C4×D61—24no—
232C4×D61—22no—
233C4×D61—21no—
234C4×D61—21no—
235C4×D61—21no—
236C4×D61—21no—
237C4×D61—42no—
238Dic122—24no—
239Dic122—21no—
240Dic122—21no—
241Dic122—21no—
242Dic122#13112yes—
243C8×C61—21no—
244C8×C61—21no—
245C8×C61—21no—
246C8×C61—21no—
247C8×C61—41no—
248C8×C61—41no—
249C8×C61—41no—
250#92418—21no—
251#92418—21no—
252#92418—21no—
253#92418—41no—
254#92418—41no—
255#92418—41no—
256#92418#13712yes—
257#17915—611nomaximal, Sylow
258C22×C61—41no—
259C22×C61—41no—
260C22×C61—41no—
261C22×C61C2×C4×D411yescharacteristic
262C2×D61—21no—
263C2×D61—21no—
264C2×D61#44412yes—
265C4×C61—22no—
266C4×C61—21no—
267C4×C61—41no—
268C4×C61—41no—
269C4×C61C2×#13111yescharacteristic
270C4×C61C2×#13111yescharacteristic
271C4×C61C2×#13711yescharacteristic
272C4×C61#57511yescharacteristic
273Dic61—21no—
274Dic61—22no—
275Dic61—21no—
276Dic61—21no—
277Dic61—41no—
278Dic61—41no—
279Dic61—41no—
280#3108—611no—
281#2966—611no—
282C2×C8×Q8—611no—
283#1584—611no—
284#1584—611no—
285#1583—611no—
286#1583—611no—
287#1579—611no—
288#1579—611no—
289SD16⋊C8—611no—
290SD16⋊C8D6111yescharacteristic, complemented
291#1573—611no—
292#1491—611no—
293#1483—611no—
294#1451—611no—
295C2×C61—81no—
296C2×C61#292911yescharacteristic
297C2×C61C4×#13711yescharacteristic
298C2×C61C2×#44411yescharacteristic
299D61—22no—
300#529—611no—
301C2×C4×Q8—611no—
302#483—611no—
303#480—611no—
304#479—611no—
305#479—611no—
306#464—611no—
307#464—611no—
308#451—611no—
309#448—611no—
310#446—611no—
311C8×Q8—611no—
312C8×Q8—611no—
313C8×Q8—611no—
314C8×Q8—611no—
315C8×Q8—1221no—
316C8×Q8—1221no—
317C8×Q8C2×D6111yescharacteristic
318C4×Q16—611no—
319C4×Q16—611no—
320C4×SD16—611no—
321C4×SD16C2×D6111yescharacteristic
322#436—611no—
323#435—1221no—
324C8×D4—1221no—
325C8×D4C2×D6111yescharacteristic
326#433—1221no—
327#432—611no—
328#431—611no—
329C2×C4⋊C8—611no—
330C2×C4⋊C8—1221no—
331#405—1221no—
332C4×M16—611no—
333C2×C4×C8—611no—
334C2×C4×C8—1221no—
335#335—611no—
336#335C2×D6111yescharacteristic
337#334—611no—
338#334—611no—
339Q8⋊C8—611no—
340Q8⋊C8—611no—
341Q8⋊C8—611no—
342Q8⋊C8—611no—
343Q8⋊C8—611no—
344Q8⋊C8C2×D6111yescharacteristic
345D4⋊C8—611no—
346D4⋊C8C2×D6111yescharacteristic
347#322—611no—
348#322—611no—
349#322—611no—
350#322C2×D6111yescharacteristic
351C61#1791511yescharacteristic, complemented, Sylow
352C22×Q8—611no—
353C2×Q16—611no—
354C2×Q16—611no—
355C2×SD16—611no—
356C2×SD16C4×D6111yescharacteristic
357C2×M16—1221no—
358C2×M16—1221no—
359C22×C8—21no—
360C22×C8—611no—
361C22×C8—611no—
362C22×C8—1221no—
363#126—1221no—
364#125—611no—
365#124—611no—
366#123—1221no—
367C22⋊Q8—611no—
368#121—611no—
369C4×Q8—611no—
370C4×Q8—611no—
371C4×Q8—611no—
372C4×Q8—611no—
373C4×Q8—1221no—
374C4×Q8—1221no—
375C4×Q8C22×D6111yescharacteristic
376C4×D4—1221no—
377C4×D4C22×D6111yescharacteristic
378#117—1221no—
379C2×C4⋊C4—611no—
380C2×C4⋊C4—1221no—
381C2×C42—611no—
382C2×C42—1221no—
383#107—611no—
384#107—611no—
385#106—611no—
386#106C4×D6111yescharacteristic
387C4⋊C8—21no—
388C4⋊C8—611no—
389C4⋊C8—611no—
390C4⋊C8—611no—
391C4⋊C8—611no—
392C4⋊C8—1221no—
393C4⋊C8—1221no—
394C4⋊C8—1221no—
395C4⋊C8—1221no—
396C4⋊C8—1221no—
397C4⋊C8—1221no—
398C4⋊C8C22×D6111yescharacteristic
399C4⋊C8C22×D6111yescharacteristic
400#103—611no—
401#103—611no—
402#103—611no—
403#103—611no—
404#103—611no—
405#103C4×D6111yescharacteristic
406#102—611no—
407#102C4×D6111yescharacteristic
408C22⋊C8—21no—
409C22⋊C8—611no—
410C22⋊C8—611no—
411C22⋊C8—1221no—
412C22⋊C8—1221no—
413#97—1221no—
414#97—1221no—
415#97—1221no—
416C4×C8—21no—
417C4×C8—611no—
418C4×C8—611no—
419C4×C8—611no—
420C4×C8—611no—
421C4×C8—611no—
422C4×C8—1221no—
423C4×C8—1221no—
424C4×C8—1221no—
425C4×C8—1221no—
426C4×C8C22×D6111yescharacteristic
427C4×C8C22×D6111yescharacteristic
428C4×C8C22×D6111yescharacteristic
429C2×Q8—611no—
430C2×Q8—611no—
431C2×Q8—1221no—
432C2×Q8—1222no—
433C2×Q8—1222no—
434C2×Q8C2×C4×D6111yescharacteristic
435C2×D4—1221no—
436C2×D4C2×C4×D6111yescharacteristic
437C22×C4—21no—
438C22×C4—611no—
439C22×C4—611no—
440C22×C4—611no—
441C22×C4—1221no—
442C22×C4—1221no—
443Q16—1222no—
444Q16—1222no—
445SD16—22no—
446SD16—1222no—
447M16—2442no—
448M16—2442no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—42no—
453C2×C8—611no—
454C2×C8—611no—
455C2×C8—611no—
456C2×C8—611no—
457C2×C8—1222no—
458C2×C8—1221no—
459C2×C8—1221no—
460C2×C8—1221no—
461C2×C8—2441no—
462C2×C8—2442no—
463C2×C8C2×C4×D6111yescharacteristic
464C2×C8C2×C4×D6111yescharacteristic
465C2×C8D4×D6111yescharacteristic
466C2×C8D4×D6111yescharacteristic
467C4⋊C4—21no—
468C4⋊C4—611no—
469C4⋊C4—611no—
470C4⋊C4—1221no—
471C4⋊C4—1221no—
472C4⋊C4—1221no—
473C4⋊C4—1221no—
474C4⋊C4—1221no—
475C4⋊C4—1221no—
476C4⋊C4—1221no—
477C4⋊C4—1221no—
478C4⋊C4C2×C4×D6111yescharacteristic
479C4⋊C4C2×C4×D6111yescharacteristic
480C22⋊C4—21no—
481C22⋊C4—1221no—
482C22⋊C4—1221no—
483C22⋊C4—1221no—
484C22⋊C4—1221no—
485C42—21no—
486C42—611no—
487C42—611no—
488C42—611no—
489C42—1221no—
490C42—1221no—
491C42—1221no—
492C42—1221no—
493C42C23×D6111yescharacteristic
494C23—21no—
495C23—611no—
496Q8—21no—
497Q8—612no—
498Q8—1224no—
499Q8—1221no—
500Q8—1221no—
501Q8—1221no—
502Q8#1451978312yes—
503D4—21no—
504D4—21no—
505D4—2442no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—611no—
512C2×C4—611no—
513C2×C4—611no—
514C2×C4—1222no—
515C2×C4—1224no—
516C2×C4—1221no—
517C2×C4—1221no—
518C2×C4—1221no—
519C2×C4—1221no—
520C2×C4—1221no—
521C2×C4—1221no—
522C2×C4—1221no—
523C2×C4—1221no—
524C2×C4—2442no—
525C2×C4C22×C4×D6111yescharacteristic
526C2×C4C2×D4×D6111yescharacteristic
527C2×C4#41×D6111yescharacteristic
528C8—21no—
529C8—21no—
530C8—21no—
531C8—21no—
532C8—41no—
533C8—41no—
534C8—41no—
535C8—612no—
536C8—1221no—
537C8—1221no—
538C8—1221no—
539C8—2441no—
540C8—2441no—
541C8—2441no—
542C22—41no—
543C22—41no—
544C22—41no—
545C22—612no—
546C22—1221no—
547C22—1221no—
548C22C4×D4×D6111yescharacteristic
549C4—21no—
550C4—22no—
551C4—41no—
552C4—41no—
553C4—1221no—
554C4—1221no—
555C4—1221no—
556C4—1222no—
557C4—2441no—
558C4—2441no—
559C4—2441no—
560C4#131×D6111yescharacteristic
561C4C2×#1451978311yescharacteristic
562C4#137×D6111yescharacteristic
563C4#1684055811yescharacteristic
564C2—81no—
565C2—1222no—
566C2#2145450811yescharacteristic
567C2#2145464111yescharacteristic
568C2#444×D6111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×SD16⋊C8C2
socleC22×C61C2×C4×D4
prime radical#14519748C2×C4
cosocleC42×C61C24
hypercenterSD16⋊C8D61
hypocenterC61#17915
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ SD16⋊C8

Complements

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

NH ≅ G/Ntype
3. C8×Q8×D61C2semidirect
4. #21444668C2semidirect
5. #21444666C2semidirect
6. #21444665C2semidirect
7. #21444663C2semidirect
8. #21444639C2semidirect
9. #21444636C2semidirect
10. #21444631C2semidirect
11. #21444603C2semidirect
12. #21444264C2semidirect
14. #21444107C2semidirect
15. C61×SD16⋊C8C2semidirect
290. SD16⋊C8D61semidirect
351. C61#17915semidirect

Maximal subgroups

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

subgroupindex
#214558972
#214547912
C8×Q8×D612
#214446682
#214446662
#214446652
#214446632
#214446392
#214446362
#214446312
#214446032
#214442642
#214442292
#214441072
C61×SD16⋊C82
#1791561