Finite Group Databasebeta

← #29650090

Subgroups — #29650090

Order 15616.

596 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454968C211yesmaximal, characteristic
2#21454900C211yesmaximal, characteristic, complemented
3#21444698C211yesmaximal, characteristic, complemented
4#21444691C211yesmaximal, characteristic, complemented
5#21444670C211yesmaximal, characteristic, complemented
6#21444663C211yesmaximal, characteristic, complemented
7#21444638C211yesmaximal, characteristic, complemented
8SD16⋊#92418C211yesmaximal, characteristic, complemented
9Q16×#92418C211yesmaximal, characteristic, complemented
10SD16×#92418C211yesmaximal, characteristic, complemented
11#21444608C211yesmaximal, characteristic, complemented
12#21444248C211yesmaximal, characteristic, complemented
13#21444227C211yesmaximal, characteristic
14#21444119C211yesmaximal, characteristic, complemented
15C61×#3108C211yesmaximal, characteristic
16#16839893C2211yescharacteristic
17Q8×#92418—21no—
18Q8×#92418—21no—
19Q8×#92418C2211yescharacteristic
20Q8×#92418C2211yescharacteristic
21Q8×#92418C2211yescharacteristic
22Q8×#92418C2211yescharacteristic
23Q8×#92418C2211yescharacteristic
24#16839840—21no—
25#16839840C2211yescharacteristic
26#16839834—21no—
27D4×#92418C2211yescharacteristic
28#16839823—21no—
29#16839815—21no—
30#16839815—21no—
31#16839815C2211yescharacteristic
32#16839815C2211yescharacteristic
33#16839815C2211yescharacteristic
34#16839789—21no—
35#16839786C2211yescharacteristic
36#16839515C2211yescharacteristic
37#16839515C2211yescharacteristic
38#16839513C2211yescharacteristic
39#16839513C2211yescharacteristic
40Q8⋊#92418C2211yescharacteristic
41Q8⋊#92418C2211yescharacteristic
42Q8⋊#92418C2211yescharacteristic
43Q8⋊#92418C2211yescharacteristic
44Q8⋊#92418C2211yescharacteristic
45Q8⋊#92418C2211yescharacteristic
46D4⋊#92418C2211yescharacteristic
47D4⋊#92418C2211yescharacteristic
48#16839484C2211yescharacteristic
49#16839484C2211yescharacteristic
50#16839483C2211yescharacteristic
51C8×#92418C2211yescharacteristic
52C61×#529C2211yescharacteristic
53C2×C4×Q8×C61C2211yescharacteristic
54C61×#483C411yescharacteristic
55C61×#480C411yescharacteristic
56C61×#479C411yescharacteristic
57C61×#479C411yescharacteristic
58C61×#464C411yescharacteristic
59C61×#464C411yescharacteristic
60C61×#451C411yescharacteristic
61C61×#448C411yescharacteristic
62C4×Q16×C61C2211yescharacteristic
63C4×Q16×C61C2211yescharacteristic
64C4×SD16×C61C2211yescharacteristic
65C4×SD16×C61C2211yescharacteristic
66C61×#431C2211yescharacteristic
67C2×#11758194—21no—
68C2×#11758194—21no—
69C22×#92418—21no—
70C4⋊#92418—21no—
71C4⋊#92418—21no—
72C4⋊#92418—21no—
73C4⋊#92418—21no—
74C4⋊#92418—21no—
75C4⋊#92418—21no—
76C4⋊#92418—21no—
77C4⋊#92418—21no—
78C4⋊#92418D411yescharacteristic
79C4⋊#92418D411yescharacteristic
80C4⋊#92418C2311yescharacteristic
81C4⋊#92418C2311yescharacteristic
82C4⋊#92418C2311yescharacteristic
83C4⋊#92418C2311yescharacteristic
84C22⋊#92418—21no—
85C22⋊#92418—21no—
86C22⋊#92418—21no—
87C22⋊#92418—21no—
88C22⋊#92418D411yescharacteristic
89C22⋊#92418D411yescharacteristic
90#14519688—21no—
91C4×#92418—21no—
92C4×#92418—21no—
93C4×#92418—21no—
94C4×#92418—21no—
95C4×#92418—21no—
96C4×#92418—21no—
97C4×#92418C2311yescharacteristic
98C4×#92418C2311yescharacteristic
99C4×#92418C2311yescharacteristic
100C4×#92418C2311yescharacteristic
101C22×Q8×C61C2×C411yescharacteristic
102C2×Q16×C61C2×C411yescharacteristic
103C2×Q16×C61C2×C411yescharacteristic
104C2×SD16×C61C2×C411yescharacteristic
105C2×SD16×C61C2×C411yescharacteristic
106#126×C61—21no—
107#125×C61C2×C411yescharacteristic
108#124×C61C2×C411yescharacteristic
109#123×C61—21no—
110C22⋊Q8×C61C2×C411yescharacteristic
111#121×C61C2×C411yescharacteristic
112C4×Q8×C61—21no—
113C4×Q8×C61—21no—
114C4×Q8×C61C2×C411yescharacteristic
115C4×Q8×C61C2×C411yescharacteristic
116C4×Q8×C61C2311yescharacteristic
117C4×Q8×C61C2311yescharacteristic
118C4×Q8×C61C2311yescharacteristic
119C4×D4×C61—21no—
120C4×D4×C61C2311yescharacteristic
121#117×C61—21no—
122C2×C4⋊C4×C61—21no—
123C2×C4⋊C4×C61C2×C411yescharacteristic
124C2×C42×C61—21no—
125C2×C42×C61C2311yescharacteristic
126#107×C61C2×C411yescharacteristic
127#107×C61C2×C411yescharacteristic
128#106×C61C2×C411yescharacteristic
129#106×C61C2×C411yescharacteristic
130C4⋊C8×C61C2×C411yescharacteristic
131C4⋊C8×C61C2×C411yescharacteristic
132#103×C61C2×C411yescharacteristic
133#103×C61C2×C411yescharacteristic
134#103×C61C2×C411yescharacteristic
135#103×C61C2×C411yescharacteristic
136#103×C61C2×C411yescharacteristic
137#103×C61C2×C411yescharacteristic
138#102×C61C2×C411yescharacteristic
139#102×C61C2×C411yescharacteristic
140C22⋊C8×C61C2×C411yescharacteristic
141C22⋊C8×C61C2×C411yescharacteristic
142C4×C8×C61C2311yescharacteristic
143C4×C8×C61C2311yescharacteristic
144C2×Q8×C61—22no—
145C2×Q8×C61—22no—
146C2×Q8×C61—21no—
147C2×Q8×C61C22×C411yescharacteristic
148C2×Q8×C61C22×C411yescharacteristic
149C2×Q8×C61C22×C411yescharacteristic
150C2×D4×C61—21no—
151C2×D4×C61C22×C411yescharacteristic
152C22×C4×C61—21no—
153C22×C4×C61—21no—
154C22×C4×C61—21no—
155C22×C4×C61C22×C411yescharacteristic
156C22×C4×C61C2×D411yescharacteristic
157C22×C4×C61#4111yescharacteristic
158Q16×C61—22no—
159Q16×C61—22no—
160SD16×C61—22no—
161SD16×C61—22no—
162C2×C8×C61C22×C411yescharacteristic
163C2×C8×C61C22×C411yescharacteristic
164C2×C8×C61C22×C411yescharacteristic
165C2×C8×C61C22×C411yescharacteristic
166C4⋊C4×C61—21no—
167C4⋊C4×C61—21no—
168C4⋊C4×C61—21no—
169C4⋊C4×C61—21no—
170C4⋊C4×C61—21no—
171C4⋊C4×C61—21no—
172C4⋊C4×C61—21no—
173C4⋊C4×C61—21no—
174C4⋊C4×C61—21no—
175C4⋊C4×C61C22×C411yescharacteristic
176C4⋊C4×C61C22×C411yescharacteristic
177C4⋊C4×C61C22×C411yescharacteristic
178C4⋊C4×C61C22×C411yescharacteristic
179C22⋊C4×C61—21no—
180C22⋊C4×C61—21no—
181C22⋊C4×C61—21no—
182C22⋊C4×C61—21no—
183C22⋊C4×C61—21no—
184C42×C61—21no—
185C42×C61—21no—
186C42×C61—21no—
187C42×C61—21no—
188C42×C61—21no—
189C42×C61C22×C411yescharacteristic
190C42×C61C2×D411yescharacteristic
191C42×C61#4111yescharacteristic
192C42×C61C2411yescharacteristic
193#11758194—81no—
194#11758194—81no—
195C2×#92418—21no—
196C2×#92418—21no—
197C2×#92418—21no—
198C2×#92418—21no—
199C2×#92418—21no—
200C2×#92418—21no—
201C2×#92418—81no—
202C2×#92418C2×D411yescharacteristic
203C2×#92418C2×D411yescharacteristic
204C2×#92418C2×D411yescharacteristic
205C2×#92418C2×D411yescharacteristic
206C23×C61—21no—
207C23×C61C4×D411yescharacteristic
208Q8×C61—24no—
209Q8×C61—21no—
210Q8×C61—21no—
211Q8×C61—21no—
212Q8×C61—21no—
213Q8×C61#13112yes—
214Q8×C61#13112yes—
215D4×C61—21no—
216D4×C61—21no—
217D4×C61—81no—
218C2×C4×C61—24no—
219C2×C4×C61—21no—
220C2×C4×C61—21no—
221C2×C4×C61—21no—
222C2×C4×C61—21no—
223C2×C4×C61—21no—
224C2×C4×C61—21no—
225C2×C4×C61—21no—
226C2×C4×C61—21no—
227C2×C4×C61—21no—
228C2×C4×C61—21no—
229C2×C4×C61—21no—
230C2×C4×C61—41no—
231C2×C4×C61—41no—
232C2×C4×C61—41no—
233C2×C4×C61—81no—
234C2×C4×C61C4×D411yescharacteristic
235C2×C4×C61C4×D411yescharacteristic
236C2×C4×C61C4×D411yescharacteristic
237C2×C4×C61C23×C411yescharacteristic
238C2×C4×C61C22×D411yescharacteristic
239C2×C4×C61C2×#4111yescharacteristic
240C8×C61—21no—
241C8×C61—21no—
242C8×C61—21no—
243C8×C61—21no—
244#92418—21no—
245#92418—21no—
246#92418—21no—
247#92418—21no—
248#92418—41no—
249#92418—41no—
250#92418—41no—
251#92418—41no—
252#92418—41no—
253#92418—41no—
254#17919—611nomaximal, Sylow
255C22×C61—21no—
256C22×C61—21no—
257C22×C61—21no—
258C22×C61—41no—
259C22×C61—41no—
260C22×C61—41no—
261C22×C61C2×C4×D411yescharacteristic
262C4×C61—22no—
263C4×C61—22no—
264C4×C61—21no—
265C4×C61—21no—
266C4×C61—21no—
267C4×C61—21no—
268C4×C61—41no—
269C4×C61—41no—
270C4×C61—41no—
271C4×C61—41no—
272C4×C61—41no—
273C4×C61C2×#13111yescharacteristic
274C4×C61C2×#13111yescharacteristic
275C4×C61#57711yescharacteristic
276C4×C61#57811yescharacteristic
277#3108D6111yescharacteristic
278#2993—611no—
279#2982—611no—
280#1588—611no—
281#1587—611no—
282#1584—611no—
283#1583—611no—
284#1579—611no—
285SD16⋊C8—611no—
286C8×Q16—611no—
287C8×SD16—611no—
288#1574—611no—
289#1487—611no—
290#1482—611no—
291#1454—611no—
292C2×C61—41no—
293C2×C61—81no—
294C2×C61#292911yescharacteristic
295C2×C61#294711yescharacteristic
296C2×C61#295711yescharacteristic
297#529C2×D6111yescharacteristic
298C2×C4×Q8C2×D6111yescharacteristic
299#483Dic6111yescharacteristic
300#480Dic6111yescharacteristic
301#479Dic6111yescharacteristic
302#479Dic6111yescharacteristic
303#464Dic6111yescharacteristic
304#464Dic6111yescharacteristic
305#451Dic6111yescharacteristic
306#448Dic6111yescharacteristic
307#446—611no—
308C8×Q8—611no—
309C8×Q8—611no—
310C8×Q8—611no—
311C8×Q8—611no—
312C8×Q8—611no—
313C8×Q8—1221no—
314C8×Q8—1221no—
315C4×Q16C2×D6111yescharacteristic
316C4×Q16C2×D6111yescharacteristic
317C4×SD16C2×D6111yescharacteristic
318C4×SD16C2×D6111yescharacteristic
319#436—611no—
320#436—1221no—
321#435—1221no—
322C8×D4—611no—
323#433—1221no—
324#431—611no—
325#431—611no—
326#431—611no—
327#431—1221no—
328#431—1221no—
329#431C2×D6111yescharacteristic
330#424—1221no—
331#423—611no—
332#335—611no—
333#335—611no—
334#334—611no—
335#334—611no—
336Q8⋊C8—611no—
337Q8⋊C8—611no—
338Q8⋊C8—611no—
339Q8⋊C8—611no—
340Q8⋊C8—611no—
341Q8⋊C8—611no—
342D4⋊C8—611no—
343D4⋊C8—611no—
344#322—611no—
345#322—611no—
346#322—611no—
347C82—611no—
348C61#1791911yescharacteristic, complemented, Sylow
349C22×Q8C2×Dic6111yescharacteristic
350C2×Q16C2×Dic6111yescharacteristic
351C2×Q16C2×Dic6111yescharacteristic
352C2×SD16C2×Dic6111yescharacteristic
353C2×SD16C2×Dic6111yescharacteristic
354C2×M16—1221no—
355C2×M16—1221no—
356C22×C8—1221no—
357#126—21no—
358#125C2×Dic6111yescharacteristic
359#124C2×Dic6111yescharacteristic
360#123—21no—
361C22⋊Q8C2×Dic6111yescharacteristic
362#121C2×Dic6111yescharacteristic
363C4×Q8—21no—
364C4×Q8—21no—
365C4×Q8C2×Dic6111yescharacteristic
366C4×Q8C2×Dic6111yescharacteristic
367C4×Q8C22×D6111yescharacteristic
368C4×Q8C22×D6111yescharacteristic
369C4×Q8C22×D6111yescharacteristic
370C4×D4—21no—
371C4×D4C22×D6111yescharacteristic
372#117—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4C2×Dic6111yescharacteristic
375C2×C42—21no—
376C2×C42C22×D6111yescharacteristic
377#107C2×Dic6111yescharacteristic
378#107C2×Dic6111yescharacteristic
379#106C2×Dic6111yescharacteristic
380#106C2×Dic6111yescharacteristic
381C4⋊C8—611no—
382C4⋊C8—611no—
383C4⋊C8—611no—
384C4⋊C8—611no—
385C4⋊C8—611no—
386C4⋊C8—611no—
387C4⋊C8—1221no—
388C4⋊C8—1221no—
389C4⋊C8—1221no—
390C4⋊C8—1221no—
391C4⋊C8—1221no—
392C4⋊C8—1221no—
393C4⋊C8—1221no—
394C4⋊C8—1221no—
395C4⋊C8C2×Dic6111yescharacteristic
396C4⋊C8C2×Dic6111yescharacteristic
397#103C2×Dic6111yescharacteristic
398#103C2×Dic6111yescharacteristic
399#103C2×Dic6111yescharacteristic
400#103C2×Dic6111yescharacteristic
401#103C2×Dic6111yescharacteristic
402#103C2×Dic6111yescharacteristic
403#102C2×Dic6111yescharacteristic
404#102C2×Dic6111yescharacteristic
405C22⋊C8—611no—
406C22⋊C8—611no—
407C22⋊C8—1221no—
408C22⋊C8—1221no—
409C22⋊C8—1221no—
410C22⋊C8—1221no—
411C22⋊C8C2×Dic6111yescharacteristic
412C22⋊C8C2×Dic6111yescharacteristic
413#97—1221no—
414C4×C8—611no—
415C4×C8—611no—
416C4×C8—611no—
417C4×C8—611no—
418C4×C8—1221no—
419C4×C8—1221no—
420C4×C8—1221no—
421C4×C8—1221no—
422C4×C8—1221no—
423C4×C8—1221no—
424C4×C8C22×D6111yescharacteristic
425C4×C8C22×D6111yescharacteristic
426C2×Q8—22no—
427C2×Q8—22no—
428C2×Q8—21no—
429C2×Q8C22×Dic6111yescharacteristic
430C2×Q8C22×Dic6111yescharacteristic
431C2×Q8C22×Dic6111yescharacteristic
432C2×D4—21no—
433C2×D4C22×Dic6111yescharacteristic
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4D4×D6111yescharacteristic
438C22×C4#1175822411yescharacteristic
439C22×C4C22×Dic6111yescharacteristic
440Q16—22no—
441Q16—22no—
442SD16—22no—
443SD16—22no—
444M16—4881no—
445M16—4881no—
446C2×C8—611no—
447C2×C8—611no—
448C2×C8—611no—
449C2×C8—611no—
450C2×C8—1221no—
451C2×C8—1221no—
452C2×C8—1221no—
453C2×C8—1221no—
454C2×C8—1221no—
455C2×C8—1221no—
456C2×C8—4881no—
457C2×C8C22×Dic6111yescharacteristic
458C2×C8C22×Dic6111yescharacteristic
459C2×C8C22×Dic6111yescharacteristic
460C2×C8C22×Dic6111yescharacteristic
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4C22×Dic6111yescharacteristic
471C4⋊C4C22×Dic6111yescharacteristic
472C4⋊C4C22×Dic6111yescharacteristic
473C4⋊C4C22×Dic6111yescharacteristic
474C22⋊C4—21no—
475C22⋊C4—21no—
476C22⋊C4—21no—
477C22⋊C4—21no—
478C22⋊C4—21no—
479C42—21no—
480C42—21no—
481C42—21no—
482C42—21no—
483C42—21no—
484C42D4×D6111yescharacteristic
485C42#1175822411yescharacteristic
486C42C22×Dic6111yescharacteristic
487C42C23×D6111yescharacteristic
488C23—21no—
489C23D4×Dic6111yescharacteristic
490Q8—24no—
491Q8—21no—
492Q8—21no—
493Q8—21no—
494Q8—21no—
495Q8#1451978412yes—
496Q8#1451978412yes—
497D4—21no—
498D4—21no—
499D4—81no—
500C2×C4—24no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—81no—
516C2×C4D4×Dic6111yescharacteristic
517C2×C4D4×Dic6111yescharacteristic
518C2×C4D4×Dic6111yescharacteristic
519C2×C4C23×Dic6111yescharacteristic
520C2×C4C2×D4×D6111yescharacteristic
521C2×C4C2×#1175822411yescharacteristic
522C8—21no—
523C8—21no—
524C8—21no—
525C8—21no—
526C8—1221no—
527C8—1221no—
528C8—1221no—
529C8—1221no—
530C8—2441no—
531C8—2441no—
532C8—2441no—
533C8—2441no—
534C8—2441no—
535C8—2441no—
536C22—21no—
537C22—21no—
538C22—21no—
539C22—41no—
540C22—41no—
541C22—41no—
542C22C2×D4×Dic6111yescharacteristic
543C4—21no—
544C4—21no—
545C4—21no—
546C4—22no—
547C4—22no—
548C4—21no—
549C4—41no—
550C4—41no—
551C4—41no—
552C4—41no—
553C4—41no—
554C4C2×#1451978411yescharacteristic
555C4C2×#1451978411yescharacteristic
556C4#1684057111yescharacteristic
557C4#1684057811yescharacteristic
558C2—41no—
559C2—81no—
560C2#2145451411yescharacteristic
561C2#2145466311yescharacteristic
562C2#2145473611yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#3108C2
socleC22×C61C2×C4×D4
prime radical#121×C61C2×C4
cosocleC42×C61C24
hypercenter#3108D61
hypocenterC61#17919
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3108

Complements

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

NH ≅ G/Ntype
2. #21454900C2semidirect
3. #21444698C2semidirect
4. #21444691C2semidirect
5. #21444670C2semidirect
6. #21444663C2semidirect
7. #21444638C2semidirect
8. SD16⋊#92418C2semidirect
9. Q16×#92418C2semidirect
10. SD16×#92418C2semidirect
11. #21444608C2semidirect
12. #21444248C2semidirect
14. #21444119C2semidirect
348. C61#17919semidirect

Maximal subgroups

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

subgroupindex
#214549682
#214549002
#214446982
#214446912
#214446702
#214446632
#214446382
SD16⋊#924182
Q16×#924182
SD16×#924182
#214446082
#214442482
#214442272
#214441192
C61×#31082
#1791961