Finite Group Databasebeta

← #30597770

Subgroups — #30597770

Order 15616.

640 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22⋊Q8×#6923C211yesmaximal, characteristic
2C22⋊C8×#6923C211yesmaximal, characteristic
3D61⋊#328C211yesmaximal, characteristic
4#21460994C211yesmaximal, characteristic
5#21460694C211yesmaximal, characteristic
6#21460693C211yesmaximal, characteristic
7#328×D61C211yesmaximal, characteristic
8C2×Q8×#6923C411yescharacteristic, complemented
9C22×C4×#6923C2211yescharacteristic
10D61⋊(C22⋊C8)C2211yescharacteristic
11C2×C8×#6923—21no—
12(C2×#6923)⋊Q8C411yescharacteristic, complemented
13#16840713C411yescharacteristic, complemented
14#16840711—21no—
15#16840709—21no—
16#16840704C2211yescharacteristic
17C4⋊C4×#6923—21no—
18C4⋊C4×#6923C411yescharacteristic, complemented
19C22⋊C4×#6923—21no—
20C2×(C2×#6923)⋊C4—21no—
21C2×(C2×#6923)⋊C4—21no—
22C2×(C2×#6923)⋊C4C2211yescharacteristic
23(C2×#6923)⋊C8—21no—
24#16840616C412yescomplemented
25#16840615C412yescomplemented
26C22⋊Q8×D61C2211yescharacteristic
27C22⋊C8×D61C2211yescharacteristic
28#95×D61C2211yescharacteristic
29#16839500C411yescharacteristic, complemented
30#16839499C411yescharacteristic, complemented
31#16839498C411yescharacteristic, complemented
32C61×#328C411yescharacteristic, complemented
33C23×#6923—21no—
34C23×#6923D411yescharacteristic
35C23×#6923D411yescharacteristic
36C2×D61⋊C8—21no—
37Q8×#6923—42no—
38C2×C4⋊#6923—21no—
39C2×C4⋊#6923—21no—
40C2×C4⋊#6923C2×C411yescharacteristic
41C2×C4⋊#6923C2×C411yescharacteristic
42C2×C22⋊#6923—21no—
43C2×C4×#6923—21no—
44C2×C4×#6923—21no—
45C2×C4×#6923—42no—
46C2×C4×#6923C2×C411yescharacteristic
47C2×C4×#6923C2×C411yescharacteristic
48C2×C4×#6923D411yescharacteristic
49C2×C4×#6923D411yescharacteristic
50#14519834C2×C412yes—
51C22⋊#92420—21no—
52C8×#6923—42no—
53(C2×#6923)⋊C4—21no—
54(C2×#6923)⋊C4—21no—
55(C2×#6923)⋊C4—21no—
56(C2×#6923)⋊C4—21no—
57(C2×#6923)⋊C4—21no—
58(C2×#6923)⋊C4—21no—
59(C2×#6923)⋊C4—42no—
60(C2×#6923)⋊C4—42no—
61(C2×#6923)⋊C4C2×C412yes—
62C2×Q8×D61C2×C411yescharacteristic
63C22×C4×D61—21no—
64C22×C4×D61C2311yescharacteristic
65C2×C8×D61—21no—
66#14519757C2×C411yescharacteristic
67#14519756C2×C411yescharacteristic
68#14519755—21no—
69#14519754—21no—
70#14519753C2×C411yescharacteristic
71C4⋊C4×D61—21no—
72C4⋊C4×D61C2×C411yescharacteristic
73C22⋊C4×D61—21no—
74C22⋊#92418C2×C411yescharacteristic
75#14519689—21no—
76#14519684—21no—
77#14519684C2×C411yescharacteristic
78C22⋊Q8×C61C2×C411yescharacteristic
79C22⋊C8×C61C2×C411yescharacteristic
80#95×C61C2×C411yescharacteristic
81C23×D61C2×D411yescharacteristic
82C22×#6923—21no—
83C22×#6923—21no—
84C22×#6923—22no—
85C22×#6923—21no—
86C22×#6923—21no—
87C22×#6923—22no—
88C22×#6923—41no—
89C22×#6923—41no—
90C22×#6923—41no—
91C22×#6923—41no—
92C22×#6923—41no—
93C22×#6923—41no—
94C22×#6923—41no—
95C22×#6923—41no—
96C22×#6923—41no—
97C22×#6923C22⋊C411yescharacteristic
98C22×#6923C22⋊C411yescharacteristic
99C22×#6923C22⋊C411yescharacteristic
100C22×#6923C22⋊C411yescharacteristic
101C22×#6923SD1612yes—
102C22×#6923Q1612yes—
103C2×Q8×C61C4211yescharacteristic
104C22×C4×C61—21no—
105C22×C4×C61C22×C411yescharacteristic
106C22×Dic61—21no—
107C22×Dic61#4111yescharacteristic
108Q8×D61—41no—
109Q8×D61—41no—
110C2×C4×D61—21no—
111C2×C4×D61—21no—
112C2×C4×D61—41no—
113C2×C4×D61—41no—
114C2×C4×D61—41no—
115C2×C4×D61—41no—
116C2×C4×D61—41no—
117C2×C4×D61—41no—
118C2×C4×D61—41no—
119C2×C4×D61—41no—
120C2×C4×D61C22×C411yescharacteristic
121C2×C4×D61C22×C411yescharacteristic
122C2×C4×D61C2×D411yescharacteristic
123C2×C4×D61#4111yescharacteristic
124C2×Dic122—21no—
125C2×Dic122C4211yescharacteristic
126C22⋊#6923—41no—
127C22⋊#6923—41no—
128C2×#92420—22no—
129C4⋊#6923—41no—
130C4⋊#6923—41no—
131C4⋊#6923—42no—
132C4⋊#6923—42no—
133C4×#6923—22no—
134C4×#6923—22no—
135C4×#6923—41no—
136C4×#6923—41no—
137C4×#6923—42no—
138C4×#6923—42no—
139D61⋊C8—41no—
140D61⋊C8—41no—
141C2×C8×C61—21no—
142C4⋊C4×C61—21no—
143C4⋊C4×C61C4211yescharacteristic
144C22⋊C4×C61—21no—
145C22⋊Dic61—21no—
146#11758198—21no—
147#11758198—21no—
148C4⋊Dic61—21no—
149C4⋊Dic61C4211yescharacteristic
150#11758196—21no—
151#11758196—21no—
152#11758196—21no—
153C2×#92418—21no—
154C8×D61—41no—
155C8×D61—41no—
156C23×C61C4×D411yescharacteristic
157C22×D61—21no—
158C22×D61—21no—
159C22×D61—21no—
160C22×D61—21no—
161C22×D61C2×C22⋊C411yescharacteristic
162C22×D61C4×D411yescharacteristic
163C22×D61C2×SD1611yescharacteristic
164C22×D61C2×Q1611yescharacteristic
165C22×D61#13511yescharacteristic
166C22×D61#13511yescharacteristic
167C2×#6923—21no—
168C2×#6923—21no—
169C2×#6923—21no—
170C2×#6923—21no—
171C2×#6923—21no—
172C2×#6923—21no—
173C2×#6923—21no—
174C2×#6923—21no—
175C2×#6923—21no—
176C2×#6923—42no—
177C2×#6923—42no—
178C2×#6923—42no—
179C2×#6923—42no—
180C2×#6923—42no—
181C2×#6923—42no—
182C2×#6923—41no—
183C2×#6923—41no—
184C2×#6923—41no—
185C2×#6923—41no—
186C2×#6923—41no—
187C2×#6923—41no—
188C2×#6923—42no—
189C2×#6923—81no—
190C2×#6923—81no—
191C2×#6923—81no—
192C2×#6923—81no—
193C2×#6923#9912yes—
194C2×#6923#10312yes—
195C2×#6923#10312yes—
196Q8×C61—41no—
197C2×C4×C61—21no—
198C2×C4×C61—21no—
199C2×C4×C61—41no—
200C2×C4×C61—41no—
201C2×C4×C61—41no—
202C2×C4×C61—41no—
203C2×C4×C61C2×C4211yescharacteristic
204C2×C4×C61C4×D411yescharacteristic
205C2×Dic61—21no—
206C2×Dic61—21no—
207C2×Dic61—41no—
208C2×Dic61—41no—
209C2×Dic61—41no—
210C2×Dic61—41no—
211C2×Dic61#11711yescharacteristic
212C2×Dic61C4×D411yescharacteristic
213C4×D61—21no—
214C4×D61—21no—
215C4×D61—21no—
216C4×D61—21no—
217C4×D61—41no—
218C4×D61—41no—
219C4×D61—41no—
220C4×D61—41no—
221C4×D61—41no—
222C4×D61—41no—
223C4×D61—81no—
224C4×D61—81no—
225C4×D61—81no—
226C4×D61—81no—
227Dic122—42no—
228Dic122—41no—
229#92420—42no—
230C8×C61—41no—
231#92418—41no—
232#8221—611nomaximal, Sylow
233C22×C61—21no—
234C22×C61—21no—
235C22×C61C4×C22⋊C411yescharacteristic
236C22×C61C4×SD1611yescharacteristic
237C22×C61C4×Q1611yescharacteristic
238C2×D61—21no—
239C2×D61—21no—
240C2×D61—21no—
241C2×D61—21no—
242C2×D61—21no—
243C2×D61—21no—
244C2×D61—21no—
245C2×D61—21no—
246C2×D61—21no—
247C2×D61—21no—
248C2×D61C2×#9911yescharacteristic
249C2×D61#41011yescharacteristic
250C2×D61C2×#10311yescharacteristic
251C2×D61#41611yescharacteristic
252C2×D61#42111yescharacteristic
253C2×D61#42111yescharacteristic
254C2×D61C4×SD1611yescharacteristic
255C2×D61C4×Q1611yescharacteristic
256#6923—22no—
257#6923—22no—
258#6923—22no—
259#6923—41no—
260#6923—82no—
261#6923—81no—
262#6923—81no—
263C4×C61—21no—
264C4×C61—21no—
265C4×C61—41no—
266C4×C61—41no—
267C4×C61—81no—
268Dic61—21no—
269Dic61—21no—
270Dic61—41no—
271Dic61—41no—
272Dic61—81no—
273C4×C22⋊Q8—611no—
274C4×C22⋊C8—611no—
275C2×#328—611no—
276C2×#328—611no—
277#1434—611no—
278#1294—611no—
279#1294—611no—
280C2×C61—21no—
281C2×C61—21no—
282C2×C61C4×#9911yescharacteristic
283C2×C61#175911yescharacteristic
284C2×C61C4×#10311yescharacteristic
285D61—21no—
286D61—21no—
287D61#151611yescharacteristic
288D61#151811yescharacteristic
289D61#152011yescharacteristic
290D61#152111yescharacteristic
291C2×C22⋊Q8—611no—
292C2×C4×Q8—611no—
293C22×C42—611no—
294C2×C22⋊C8—611no—
295C2×C22⋊C8—611no—
296C2×C4×C8—1221no—
297#391—611no—
298#389—611no—
299#387—1221no—
300#385—1221no—
301#380—611no—
302C4×C4⋊C4—611no—
303C4×C4⋊C4—1221no—
304C4×C22⋊C4—1221no—
305C2×#95—611no—
306C2×#95—611no—
307C2×#95—1221no—
308C2×#95—1221no—
309#336—1221no—
310#328—612no—
311#328—612no—
312#328—611no—
313#328—611no—
314#328—611no—
315#328#692311yescharacteristic, complemented
316C61#822111yescharacteristic, complemented, Sylow
317C22×Q8—611no—
318C23×C4—611no—
319C23×C4—611no—
320C23×C4—611no—
321C23×C4—1221no—
322C23×C4—1221no—
323C22×C8—1221no—
324C22×C8—1221no—
325C22⋊Q8—611no—
326C22⋊Q8—611no—
327C22⋊Q8—611no—
328C22⋊Q8—1221no—
329C22⋊Q8—1221no—
330C22⋊Q8C2×#692311yescharacteristic
331C4×Q8—2442no—
332C2×C4⋊C4—611no—
333C2×C4⋊C4—611no—
334C2×C4⋊C4—611no—
335C2×C4⋊C4—1221no—
336C2×C4⋊C4—1221no—
337C2×C4⋊C4—1221no—
338C2×C22⋊C4—1221no—
339C2×C22⋊C4—1221no—
340C2×C42—611no—
341C2×C42—611no—
342C2×C42—611no—
343C2×C42—611no—
344C2×C42—1221no—
345C2×C42—1221no—
346C2×C42—2442no—
347C22⋊C8—612no—
348C22⋊C8—611no—
349C22⋊C8—1221no—
350C22⋊C8—1221no—
351C22⋊C8C2×#692311yescharacteristic
352C4×C8—2442no—
353#95—612no—
354#95—611no—
355#95—1221no—
356#95—1221no—
357#95—1221no—
358#95—1221no—
359#95—1221no—
360#95—1221no—
361#95—1221no—
362#95—2442no—
363#95—2442no—
364#95C2×#692311yescharacteristic
365C24—611no—
366C2×Q8—611no—
367C2×Q8—1221no—
368C2×Q8—2441no—
369C2×Q8—2441no—
370C2×Q8C4×#692311yescharacteristic
371C22×C4—21no—
372C22×C4—611no—
373C22×C4—611no—
374C22×C4—611no—
375C22×C4—612no—
376C22×C4—612no—
377C22×C4—611no—
378C22×C4—611no—
379C22×C4—611no—
380C22×C4—611no—
381C22×C4—611no—
382C22×C4—611no—
383C22×C4—1221no—
384C22×C4—1221no—
385C22×C4—1222no—
386C22×C4—1221no—
387C22×C4—1221no—
388C22×C4—1222no—
389C22×C4—1221no—
390C22×C4—1221no—
391C22×C4—1221no—
392C22×C4—2441no—
393C22×C4—2441no—
394C22×C4—2441no—
395C22×C4—2441no—
396C22×C4—2441no—
397C22×C4—2441no—
398C22×C4—2441no—
399C22×C4—2441no—
400C22×C4—2441no—
401C22×C4—2441no—
402C22×C4—2441no—
403C22×C4—2441no—
404C22×C4—2441no—
405C22×C4—2441no—
406C22×C4—2441no—
407C22×C4—2441no—
408C22×C4—2441no—
409C22×C4C22×#692311yescharacteristic
410C2×C8—21no—
411C2×C8—1222no—
412C2×C8—1221no—
413C2×C8—2441no—
414C2×C8—2441no—
415C2×C8—2441no—
416C2×C8—2441no—
417C4⋊C4—21no—
418C4⋊C4—611no—
419C4⋊C4—1221no—
420C4⋊C4—1221no—
421C4⋊C4—1221no—
422C4⋊C4—1221no—
423C4⋊C4—2442no—
424C4⋊C4—2441no—
425C4⋊C4—2441no—
426C4⋊C4—2442no—
427C4⋊C4C4×#692311yescharacteristic
428C22⋊C4—21no—
429C22⋊C4—1221no—
430C22⋊C4—1221no—
431C22⋊C4—1221no—
432C22⋊C4—2441no—
433C22⋊C4—2441no—
434C42—1222no—
435C42—1222no—
436C42—2441no—
437C42—2441no—
438C42—2442no—
439C42—2442no—
440C23—611no—
441C23—611no—
442C23—611no—
443C23—611no—
444C23—611no—
445C23—611no—
446C23—1221no—
447C23—1221no—
448C23—1221no—
449C23—1221no—
450C23D4×#692311yescharacteristic
451Q8—41no—
452Q8—2441no—
453Q8—2442no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—41no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—612no—
461C2×C4—612no—
462C2×C4—612no—
463C2×C4—611no—
464C2×C4—611no—
465C2×C4—1221no—
466C2×C4—1221no—
467C2×C4—1221no—
468C2×C4—1221no—
469C2×C4—1221no—
470C2×C4—1221no—
471C2×C4—1221no—
472C2×C4—1221no—
473C2×C4—1221no—
474C2×C4—1221no—
475C2×C4—1221no—
476C2×C4—1221no—
477C2×C4—1221no—
478C2×C4—1221no—
479C2×C4—1221no—
480C2×C4—4881no—
481C2×C4—4881no—
482C2×C4—4881no—
483C2×C4—4881no—
484C2×C4—4881no—
485C2×C4—4881no—
486C2×C4—4881no—
487C2×C4—4881no—
488C2×C4—2441no—
489C2×C4—2441no—
490C2×C4—2441no—
491C2×C4—2441no—
492C2×C4—2441no—
493C2×C4—2441no—
494C2×C4—2441no—
495C2×C4—2442no—
496C2×C4—2442no—
497C2×C4—2442no—
498C2×C4—2442no—
499C2×C4—2441no—
500C2×C4—2441no—
501C2×C4—2441no—
502C2×C4—2441no—
503C2×C4—2441no—
504C2×C4—2441no—
505C2×C4—2441no—
506C2×C4—2441no—
507C2×C4—2442no—
508C2×C4—2442no—
509C2×C4—2442no—
510C2×C4—2441no—
511C2×C4C2×C4×#692311yescharacteristic
512C2×C4D4×#692311yescharacteristic
513C8—41no—
514C8—2441no—
515C8—2442no—
516C22—21no—
517C22—21no—
518C22—611no—
519C22—611no—
520C22—611no—
521C22—611no—
522C22—611no—
523C22—611no—
524C22—611no—
525C22—611no—
526C22—1221no—
527C22—1221no—
528C22—1221no—
529C22—1221no—
530C22—1221no—
531C22—1221no—
532C22—1221no—
533C22—1221no—
534C22—1221no—
535C22—1221no—
536C22C22⋊C4×#692311yescharacteristic
537C22SD16×#692311yescharacteristic
538C22Q16×#692311yescharacteristic
539C4—21no—
540C4—21no—
541C4—41no—
542C4—41no—
543C4—81no—
544C4—1222no—
545C4—1222no—
546C4—1222no—
547C4—1221no—
548C4—1221no—
549C4—4881no—
550C4—4881no—
551C4—4881no—
552C4—4882no—
553C4—2441no—
554C4—2441no—
555C4—2441no—
556C2—21no—
557C2—21no—
558C2—611no—
559C2—611no—
560C2—611no—
561C2—611no—
562C2—1221no—
563C2—1221no—
564C2#99×#692311yescharacteristic
565C2#2146158411yescharacteristic
566C2#103×#692311yescharacteristic
subgroupG/H
centerC22C22⋊C4×#6923
commutatorC2×C4×C61C2×C42
FrattiniC22×C4C22×#6923
FittingC61×#328C4
socleC22×C61C4×C22⋊C4
prime radicalC23×D61C2×D4
cosocleC22×C4×D61C23
hypercenter#328#6923
hypocenterC61#8221
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
8. C2×Q8×#6923C4semidirect
12. (C2×#6923)⋊Q8C4semidirect
13. #16840713C4semidirect
18. C4⋊C4×#6923C4semidirect
24. #16840616C4semidirect
25. #16840615C4semidirect
29. #16839500C4semidirect
30. #16839499C4semidirect
31. #16839498C4semidirect
32. C61×#328C4semidirect
315. #328#6923semidirect
316. C61#8221semidirect

Maximal subgroups

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

subgroupindex
C22⋊Q8×#69232
C22⋊C8×#69232
D61⋊#3282
#214609942
#214606942
#214606932
#328×D612
#822161