Finite Group Databasebeta

← D61×#1692 #29662629

Subgroups — D61×#1692 #29662629

Order 15616.

650 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
1#498×D61C211yesmaximal, characteristic
2#477×D61C211yesmaximal, characteristic
3#462×D61C211yesmaximal, characteristic
4#446×D61C211yesmaximal, characteristic
5#21445328C211yesmaximal, characteristic, complemented
6#21445327C211yesmaximal, characteristic, complemented
7#21445326C211yesmaximal, characteristic, complemented
8#21445325C211yesmaximal, characteristic, complemented
9#21445324C211yesmaximal, characteristic, complemented
10#21445323C211yesmaximal, characteristic, complemented
11#21445322C211yesmaximal, characteristic, complemented
12#335×D61C211yesmaximal, characteristic
13#333×D61C211yesmaximal, characteristic
14#332×D61C211yesmaximal, characteristic
15C61×#1692C211yesmaximal, characteristic, complemented
16C2×Q16×D61—21no—
17C4⋊Q8×D61C2211yescharacteristic
18C4⋊Q8×D61C2211yescharacteristic
19C4×Q8×D61C2211yescharacteristic
20#16840160C2211yescharacteristic
21#16840159—21no—
22#16840159—21no—
23#16840158C2211yescharacteristic
24#16840158C2211yescharacteristic
25#16840058C2211yescharacteristic
26#16840057C2211yescharacteristic
27#16840056—21no—
28#16840055—21no—
29#16840054C2211yescharacteristic
30#16839973C2211yescharacteristic
31#16839972C2211yescharacteristic
32#16839971—21no—
33#16839970—21no—
34#16839969C2211yescharacteristic
35#16839893C2211yescharacteristic
36#16839892C2211yescharacteristic
37#16839891—21no—
38#16839890—21no—
39#16839889C2211yescharacteristic
40#107×D61—21no—
41#106×D61—21no—
42#106×D61—21no—
43C4⋊C8×D61—21no—
44C4⋊C8×D61C2211yescharacteristic
45C4⋊C8×D61C2211yescharacteristic
46C4⋊C8×D61C2211yescharacteristic
47#103×D61—21no—
48#103×D61—21no—
49#97×D61—21no—
50C4×C8×D61C2211yescharacteristic
51#16839515C2211yescharacteristic
52#16839514C2211yescharacteristic
53#16839514C2211yescharacteristic
54#16839511C2211yescharacteristic
55#16839510C2211yescharacteristic
56#16839510C2211yescharacteristic
57#16839509C2211yescharacteristic
58#16839508C2211yescharacteristic
59#16839507C2211yescharacteristic
60C61×#498C2211yescharacteristic
61C61×#477C2211yescharacteristic
62C61×#462C2211yescharacteristic
63C61×#446C2211yescharacteristic
64C61×#335C2211yescharacteristic
65C61×#333C2211yescharacteristic
66C61×#332C2211yescharacteristic
67C2×Q8×D61—21no—
68C2×Q8×D61—21no—
69C2×Q8×D61D411yescharacteristic
70C2×Dic244—21no—
71C2×#11758202—21no—
72C2×#11758202—21no—
73Q16×D61—44no—
74C2×C8×D61—21no—
75C2×C8×D61—21no—
76C2×C8×D61—21no—
77C2×C8×D61D411yescharacteristic
78C2×C8×D61D411yescharacteristic
79#14519777C2311yescharacteristic
80#14519777C2311yescharacteristic
81#14519776—21no—
82#14519776—21no—
83#14519776—21no—
84#14519776—21no—
85#14519775—21no—
86#14519775—21no—
87Q8×Dic61D411yescharacteristic
88C4×Dic122—21no—
89C4×Dic122C2311yescharacteristic
90#14519742—21no—
91#14519742D411yescharacteristic
92C4⋊C4×D61—21no—
93C4⋊C4×D61—21no—
94C4⋊C4×D61—21no—
95C4⋊C4×D61—21no—
96C4⋊C4×D61—21no—
97C4⋊C4×D61D411yescharacteristic
98C42×D61—21no—
99C42×D61C2311yescharacteristic
100#14519711—21no—
101#14519710—21no—
102#14519710—21no—
103#14519709—21no—
104#14519709—21no—
105#14519708—21no—
106#14519708—21no—
107#14519708—21no—
108#14519708—21no—
109C4⋊#92418—21no—
110C4⋊#92418C2311yescharacteristic
111C4⋊#92418C2311yescharacteristic
112C4⋊#92418C2311yescharacteristic
113#14519706—21no—
114#14519706—21no—
115#14519706—21no—
116#14519706—21no—
117#14519706—21no—
118#14519702—21no—
119#14519702—21no—
120#14519701—21no—
121#14519701—21no—
122#14519700—21no—
123#14519700—21no—
124#14519688—21no—
125#14519687—21no—
126#14519687—21no—
127C4×#92418C2311yescharacteristic
128C8×Dic61D411yescharacteristic
129C8×Dic61D411yescharacteristic
130C2×Q16×C61—21no—
131C4⋊Q8×C61C2311yescharacteristic
132C4⋊Q8×C61C2311yescharacteristic
133C4×Q8×C61C2311yescharacteristic
134#107×C61—21no—
135#106×C61—21no—
136#106×C61—21no—
137C4⋊C8×C61—21no—
138C4⋊C8×C61C2311yescharacteristic
139C4⋊C8×C61C2311yescharacteristic
140C4⋊C8×C61C2311yescharacteristic
141#103×C61—21no—
142#103×C61—21no—
143#97×C61—21no—
144C4×C8×C61C2311yescharacteristic
145C2×Q8×C61—21no—
146C2×Q8×C61—21no—
147C2×Q8×C61C2×D411yescharacteristic
148Q8×D61—22no—
149Q8×D61—22no—
150Q8×D61—42no—
151Q8×D61—42no—
152Q8×D61—82no—
153C2×C4×D61—21no—
154C2×C4×D61—21no—
155C2×C4×D61—41no—
156C2×C4×D61—41no—
157C2×C4×D61C2×D411yescharacteristic
158C2×C4×D61C2×D411yescharacteristic
159C2×C4×D61#4111yescharacteristic
160C2×Dic122—21no—
161C2×Dic122—21no—
162C2×Dic122—21no—
163C2×Dic122—41no—
164C2×Dic122—41no—
165C2×Dic122C2×D411yescharacteristic
166Q16×C61—42no—
167C2×C8×C61—21no—
168C2×C8×C61—21no—
169C2×C8×C61—21no—
170C2×C8×C61C2×D411yescharacteristic
171C2×C8×C61C2×D411yescharacteristic
172C4⋊C4×C61—21no—
173C4⋊C4×C61—21no—
174C4⋊C4×C61—21no—
175C4⋊C4×C61—21no—
176C4⋊C4×C61—21no—
177C4⋊C4×C61C2×D411yescharacteristic
178C42×C61—21no—
179C42×C61C2411yescharacteristic
180#11758202—42no—
181#11758202—42no—
182C4⋊Dic61—21no—
183C4⋊Dic61—21no—
184C4⋊Dic61—21no—
185C4⋊Dic61—21no—
186C4⋊Dic61—21no—
187C4⋊Dic61C2×D411yescharacteristic
188#11758196—21no—
189#11758196—21no—
190#11758196—21no—
191#11758196—41no—
192#11758196—41no—
193#11758196—41no—
194#11758196—41no—
195C4×Dic61—21no—
196C4×Dic61—21no—
197C4×Dic61—21no—
198C4×Dic61C2×D411yescharacteristic
199C4×Dic61C2×D411yescharacteristic
200C4×Dic61#4111yescharacteristic
201C2×#92418—21no—
202C2×#92418—21no—
203C2×#92418—21no—
204C2×#92418C2×D411yescharacteristic
205C2×#92418C2×D411yescharacteristic
206Dic244—42no—
207C8×D61—22no—
208C8×D61—42no—
209C8×D61—42no—
210C8×D61—42no—
211C8×D61Q1614yescomplemented
212C22×D61#12111yescharacteristic
213Q8×C61—21no—
214Q8×C61—21no—
215Q8×C61—41no—
216Q8×C61—41no—
217Q8×C61—81no—
218C2×C4×C61—21no—
219C2×C4×C61—21no—
220C2×C4×C61—41no—
221C2×C4×C61—41no—
222C2×C4×C61C22×D411yescharacteristic
223C2×C4×C61C22×D411yescharacteristic
224C2×C4×C61C2×#4111yescharacteristic
225C2×Dic61—21no—
226C2×Dic61—21no—
227C2×Dic61—41no—
228C2×Dic61—41no—
229C2×Dic61#12111yescharacteristic
230C2×Dic61#12111yescharacteristic
231C2×Dic61#12111yescharacteristic
232C4×D61—22no—
233C4×D61—42no—
234C4×D61—42no—
235C4×D61—82no—
236C4×D61—82no—
237C4×D61C2×Q1612yes—
238C4×D61AGL(1,ℤ/8)12yes—
239C4×D61#13712yes—
240C4×D61#13712yes—
241Dic122—21no—
242Dic122—21no—
243Dic122—42no—
244Dic122—41no—
245Dic122—41no—
246Dic122—82no—
247Dic122—82no—
248Dic122—81no—
249C8×C61—21no—
250C8×C61—41no—
251C8×C61—41no—
252C8×C61—41no—
253C8×C61C2×Q1612yescomplemented
254#92418—21no—
255#92418—41no—
256#92418—41no—
257#92418—41no—
258#92418C2×Q1612yescomplemented
259C2×#1692—611nomaximal, Sylow
260C22×C61C2×#12111yescharacteristic
261C2×D61#46212yes—
262C2×D61#46812yes—
263C2×D61#47112yes—
264C4×C61—21no—
265C4×C61—41no—
266C4×C61—41no—
267C4×C61—81no—
268C4×C61—81no—
269C4×C61C22×Q1611yescharacteristic
270C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
271C4×C61C2×#13711yescharacteristic
272C4×C61C2×#13711yescharacteristic
273Dic61—21no—
274Dic61—41no—
275Dic61—41no—
276Dic61—81no—
277Dic61—81no—
278Dic61#46212yes—
279Dic61#46812yes—
280C2×#498—611no—
281C2×#477—611no—
282C2×#462—611no—
283C2×#446—611no—
284#1692—611no—
285#1692—611no—
286#1692—611no—
287#1692—611no—
288#1692—611no—
289#1692—611no—
290#1692—611no—
291#1692D6111yescharacteristic, direct product factor
292C2×#335—611no—
293C2×#333—611no—
294C2×#332—611no—
295C2×C61C2×#46211yescharacteristic
296C2×C61C2×#46811yescharacteristic
297C2×C61C2×#47111yescharacteristic
298D61#169214yesdirect product factor
299C22×Q16—1221no—
300C2×C4⋊Q8—611no—
301C2×C4⋊Q8—611no—
302C2×C4×Q8—611no—
303#498—611no—
304#498—611no—
305#498—611no—
306#498—1221no—
307#498—1221no—
308#498C2×D6111yescharacteristic
309#477—611no—
310#477—611no—
311#477—611no—
312#477—1221no—
313#477—1221no—
314#477C2×D6111yescharacteristic
315#462—611no—
316#462—611no—
317#462—611no—
318#462—1221no—
319#462—1221no—
320#462C2×D6111yescharacteristic
321#446—611no—
322#446—611no—
323#446—611no—
324#446—1221no—
325#446—1221no—
326#446C2×D6111yescharacteristic
327C2×#107—1221no—
328C2×#106—1221no—
329C2×#106—1221no—
330C2×C4⋊C8—611no—
331C2×C4⋊C8—611no—
332C2×C4⋊C8—611no—
333C2×C4⋊C8—1221no—
334C2×#103—1221no—
335C2×#103—1221no—
336C2×#97—1221no—
337C2×C4×C8—611no—
338#335—611no—
339#335—611no—
340#335—611no—
341#335C2×D6111yescharacteristic
342#333—611no—
343#333—611no—
344#333—611no—
345#333C2×D6111yescharacteristic
346#332—611no—
347#332—611no—
348#332—611no—
349#332C2×D6111yescharacteristic
350C61C2×#169211yescharacteristic, complemented, Sylow
351C22×Q8—611no—
352C22×Q8—1221no—
353C22×Q8—1221no—
354C2×Q16—21no—
355C2×Q16—1221no—
356C2×Q16—1221no—
357C2×Q16—1221no—
358C2×Q16—2444no—
359C22×C8—611no—
360C22×C8—611no—
361C22×C8—1221no—
362C22×C8—1221no—
363C22×C8—1221no—
364C4⋊Q8—611no—
365C4⋊Q8—611no—
366C4⋊Q8—1221no—
367C4⋊Q8—1221no—
368C4⋊Q8—1221no—
369C4⋊Q8—1221no—
370C4⋊Q8—1221no—
371C4⋊Q8—1221no—
372C4⋊Q8C22×D6111yescharacteristic
373C4⋊Q8C22×D6111yescharacteristic
374C4×Q8—611no—
375C4×Q8—611no—
376C4×Q8—611no—
377C4×Q8—1221no—
378C4×Q8—1221no—
379C4×Q8C22×D6111yescharacteristic
380C2×C4⋊C4—611no—
381C2×C4⋊C4—1221no—
382C2×C4⋊C4—1221no—
383C2×C4⋊C4—1221no—
384C2×C4⋊C4—1221no—
385C2×C4⋊C4—1221no—
386C2×C42—611no—
387C2×C42—1221no—
388#107—21no—
389#107—1221no—
390#107—1221no—
391#107—1221no—
392#106—21no—
393#106—21no—
394#106—1221no—
395#106—1221no—
396#106—1221no—
397#106—1221no—
398#106—1221no—
399#106—1221no—
400C4⋊C8—21no—
401C4⋊C8—611no—
402C4⋊C8—611no—
403C4⋊C8—611no—
404C4⋊C8—1221no—
405C4⋊C8—1221no—
406C4⋊C8—1221no—
407C4⋊C8—1221no—
408C4⋊C8—1221no—
409C4⋊C8—1221no—
410C4⋊C8C22×D6111yescharacteristic
411C4⋊C8C22×D6111yescharacteristic
412C4⋊C8C22×D6111yescharacteristic
413#103—21no—
414#103—21no—
415#103—1221no—
416#103—1221no—
417#103—1221no—
418#103—1221no—
419#103—1221no—
420#103—1221no—
421#97—21no—
422#97—1221no—
423#97—1221no—
424#97—1221no—
425C4×C8—611no—
426C4×C8—611no—
427C4×C8—611no—
428C4×C8C22×D6111yescharacteristic
429C2×Q8—21no—
430C2×Q8—21no—
431C2×Q8—611no—
432C2×Q8—1221no—
433C2×Q8—1222no—
434C2×Q8—1222no—
435C2×Q8—1221no—
436C2×Q8—1221no—
437C2×Q8—4882no—
438C2×Q8—2441no—
439C2×Q8—2441no—
440C2×Q8—2442no—
441C2×Q8—2442no—
442C2×Q8D4×D6111yescharacteristic
443C22×C4—611no—
444C22×C4—611no—
445C22×C4—611no—
446C22×C4—1221no—
447C22×C4—1221no—
448C22×C4—2441no—
449C22×C4—2441no—
450Q16—42no—
451Q16—2442no—
452Q16—2442no—
453Q16—2442no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—611no—
458C2×C8—614no—
459C2×C8—611no—
460C2×C8—1222no—
461C2×C8—1221no—
462C2×C8—1221no—
463C2×C8—1221no—
464C2×C8—2442no—
465C2×C8—2442no—
466C2×C8—2442no—
467C2×C8D4×D6111yescharacteristic
468C2×C8D4×D6111yescharacteristic
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—611no—
475C4⋊C4—1221no—
476C4⋊C4—1221no—
477C4⋊C4—1221no—
478C4⋊C4—1221no—
479C4⋊C4—1221no—
480C4⋊C4—1221no—
481C4⋊C4—1221no—
482C4⋊C4—1221no—
483C4⋊C4—2441no—
484C4⋊C4—2441no—
485C4⋊C4—2441no—
486C4⋊C4—2441no—
487C4⋊C4D4×D6111yescharacteristic
488C42—21no—
489C42—611no—
490C42—611no—
491C42—611no—
492C42—1221no—
493C42—1221no—
494C42—1221no—
495C42C23×D6111yescharacteristic
496C23—611no—
497Q8—21no—
498Q8—21no—
499Q8—41no—
500Q8—41no—
501Q8—81no—
502Q8—1221no—
503Q8—1221no—
504Q8—4881no—
505Q8—4882no—
506Q8—4882no—
507Q8—2442no—
508Q8—2441no—
509Q8—2441no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—611no—
515C2×C4—611no—
516C2×C4—612no—
517C2×C4—612no—
518C2×C4—612no—
519C2×C4—612no—
520C2×C4—611no—
521C2×C4—1222no—
522C2×C4—1221no—
523C2×C4—1221no—
524C2×C4—4882no—
525C2×C4—4882no—
526C2×C4—2442no—
527C2×C4—2442no—
528C2×C4—2441no—
529C2×C4—2441no—
530C2×C4C2×D4×D6111yescharacteristic
531C2×C4C2×D4×D6111yescharacteristic
532C2×C4#41×D6111yescharacteristic
533C8—21no—
534C8—41no—
535C8—41no—
536C8—41no—
537C8—612no—
538C8—1221no—
539C8—2441no—
540C8—2441no—
541C8—2441no—
542C8Q16×D6112yescomplemented
543C22—612no—
544C22—612no—
545C22—612no—
546C22#121×D6111yescharacteristic
547C4—21no—
548C4—41no—
549C4—41no—
550C4—81no—
551C4—81no—
552C4—612no—
553C4—612no—
554C4—1221no—
555C4—4881no—
556C4—4881no—
557C4—2441no—
558C4—2441no—
559C4C2×Q16×D6111yescharacteristic
560C4AGL(1,ℤ/8)×D6111yescharacteristic
561C4#137×D6111yescharacteristic
562C4#137×D6111yescharacteristic
563C2—614no—
564C2#462×D6111yescharacteristic
565C2#468×D6111yescharacteristic
566C2#471×D6111yescharacteristic
subgroupG/H
centerC22#121×D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#1692C2
socleC22×C61C2×#121
prime radicalC22×D61#121
hypercenter#1692D61
hypocenterC61C2×#1692
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #1692

Complements

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

NH ≅ G/Ntype
5. #21445328C2semidirect
6. #21445327C2semidirect
7. #21445326C2semidirect
8. #21445325C2semidirect
9. #21445324C2semidirect
10. #21445323C2semidirect
11. #21445322C2semidirect
15. C61×#1692C2semidirect
211. C8×D61Q16semidirect
253. C8×C61C2×Q16semidirect
258. #92418C2×Q16semidirect
291. #1692D61direct (N × H)
298. D61#1692direct (N × H)
350. C61C2×#1692semidirect
542. C8Q16×D61semidirect

Maximal subgroups

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

subgroupindex
#498×D612
#477×D612
#462×D612
#446×D612
#214453282
#214453272
#214453262
#214453252
#214453242
#214453232
#214453222
#335×D612
#333×D612
#332×D612
C61×#16922
C2×#169261