Finite Group Databasebeta

← D61×#1718 #29667757

Subgroups — D61×#1718 #29667757

Order 15616.

734 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#500×D61C211yesmaximal, characteristic
2#498×D61C211yesmaximal, characteristic
3#487×D61C211yesmaximal, characteristic
4#487×D61C211yesmaximal, characteristic
5#487×D61C211yesmaximal, characteristic
6#487×D61C211yesmaximal, characteristic
7#21445468C211yesmaximal, characteristic, complemented
8#21445467C211yesmaximal, characteristic, complemented
9#21445466C211yesmaximal, characteristic, complemented
10#21445465C211yesmaximal, characteristic, complemented
11#21445464C211yesmaximal, characteristic, complemented
12#21445463C211yesmaximal, characteristic, complemented
13#21445462C211yesmaximal, characteristic, complemented
14#322×D61C211yesmaximal, characteristic
15C61×#1718C211yesmaximal, characteristic, complemented
16C4⋊Q8×D61C2211yescharacteristic
17C4⋊Q8×D61C2211yescharacteristic
18C4⋊Q8×D61C2211yescharacteristic
19C4⋊Q8×D61C2211yescharacteristic
20#16840167C2211yescharacteristic
21#16840166—22no—
22#16840165C2211yescharacteristic
23#16840165C2211yescharacteristic
24#16840160C2211yescharacteristic
25#16840159—22no—
26#16840158C2211yescharacteristic
27#16840158C2211yescharacteristic
28#16840114C2211yescharacteristic
29#16840114C2211yescharacteristic
30#16840114C2211yescharacteristic
31#16840114C2211yescharacteristic
32#16840113C2211yescharacteristic
33#16840113C2211yescharacteristic
34#16840113C2211yescharacteristic
35#16840113C2211yescharacteristic
36#16840112C2211yescharacteristic
37#16840112C2211yescharacteristic
38#16840112C2211yescharacteristic
39#16840112C2211yescharacteristic
40#16840111—22no—
41#16840111—22no—
42#16840111—22no—
43#16840111—22no—
44#107×D61—22no—
45#106×D61—22no—
46#103×D61—22no—
47#103×D61—22no—
48#103×D61—22no—
49#103×D61—22no—
50C4×C8×D61C2211yescharacteristic
51C4×C8×D61C2211yescharacteristic
52C4×C8×D61C2211yescharacteristic
53#16839484C2211yescharacteristic
54#16839484C2211yescharacteristic
55#16839483C2211yescharacteristic
56C61×#500C2211yescharacteristic
57C61×#498C2211yescharacteristic
58C61×#487C2211yescharacteristic
59C61×#487C2211yescharacteristic
60C61×#487C2211yescharacteristic
61C61×#487C2211yescharacteristic
62C61×#322C2211yescharacteristic
63C2×Q8×D61—21no—
64C2×Q8×D61—21no—
65C2×Q8×D61—21no—
66C2×Q8×D61—21no—
67C2×C8×D61D412yes—
68C2×C8×D61D412yes—
69C2×C8×D61D412yes—
70#14519777C2311yescharacteristic
71#14519777C2311yescharacteristic
72#14519777C2311yescharacteristic
73#14519777C2311yescharacteristic
74#14519776—21no—
75#14519776—21no—
76#14519776—21no—
77#14519776—21no—
78#14519776—21no—
79#14519776—21no—
80#14519776—21no—
81#14519776—21no—
82#14519775—21no—
83#14519775—21no—
84#14519775—21no—
85#14519775—21no—
86C4⋊C4×D61—21no—
87C4⋊C4×D61—21no—
88C4⋊C4×D61—21no—
89C4⋊C4×D61—21no—
90C4⋊C4×D61—21no—
91C4⋊C4×D61—21no—
92C4⋊C4×D61—21no—
93C4⋊C4×D61—21no—
94C42×D61C2311yescharacteristic
95#14519711—22no—
96#14519710—22no—
97#14519710—22no—
98#14519709—22no—
99#14519708—22no—
100#14519708—22no—
101#14519702—22no—
102#14519702—22no—
103#14519702—22no—
104#14519702—22no—
105#14519701—22no—
106#14519701—22no—
107#14519701—22no—
108#14519701—22no—
109#14519700—22no—
110#14519700—22no—
111#14519700—22no—
112#14519700—22no—
113C4×#92418C2311yescharacteristic
114C4×#92418C2311yescharacteristic
115C4×#92418C2311yescharacteristic
116C8×Dic61D412yes—
117C8×Dic61D412yes—
118C8×Dic61D412yes—
119C4⋊Q8×C61C2311yescharacteristic
120C4⋊Q8×C61C2311yescharacteristic
121C4⋊Q8×C61C2311yescharacteristic
122C4⋊Q8×C61C2311yescharacteristic
123#107×C61—22no—
124#106×C61—22no—
125#103×C61—22no—
126#103×C61—22no—
127#103×C61—22no—
128#103×C61—22no—
129C4×C8×C61C2311yescharacteristic
130C4×C8×C61C2311yescharacteristic
131C4×C8×C61C2311yescharacteristic
132C2×Q8×C61—21no—
133C2×Q8×C61—21no—
134C2×Q8×C61—21no—
135C2×Q8×C61—21no—
136Q8×D61—44no—
137Q8×D61—44no—
138Q8×D61—44no—
139Q8×D61—44no—
140C2×C4×D61—41no—
141C2×C4×D61—41no—
142C2×C4×D61—41no—
143C2×C4×D61—41no—
144C2×C4×D61C2×D411yescharacteristic
145C2×C4×D61C2×D411yescharacteristic
146C2×C4×D61C2×D411yescharacteristic
147C2×Dic122—21no—
148C2×Dic122—21no—
149C2×Dic122—21no—
150C2×Dic122—21no—
151C2×Dic122—41no—
152C2×Dic122—41no—
153C2×Dic122—41no—
154C2×Dic122—41no—
155C2×C8×C61C2×D412yes—
156C2×C8×C61C2×D412yes—
157C2×C8×C61C2×D412yes—
158C4⋊C4×C61—21no—
159C4⋊C4×C61—21no—
160C4⋊C4×C61—21no—
161C4⋊C4×C61—21no—
162C4⋊C4×C61—21no—
163C4⋊C4×C61—21no—
164C4⋊C4×C61—21no—
165C4⋊C4×C61—21no—
166C42×C61C2411yescharacteristic
167C4⋊Dic61—21no—
168C4⋊Dic61—21no—
169C4⋊Dic61—21no—
170C4⋊Dic61—21no—
171C4⋊Dic61—21no—
172C4⋊Dic61—21no—
173C4⋊Dic61—21no—
174C4⋊Dic61—21no—
175#11758196—41no—
176#11758196—41no—
177#11758196—41no—
178#11758196—41no—
179#11758196—41no—
180#11758196—41no—
181#11758196—41no—
182#11758196—41no—
183C4×Dic61C2×D411yescharacteristic
184C4×Dic61C2×D411yescharacteristic
185C4×Dic61C2×D411yescharacteristic
186C2×#92418C2×D412yes—
187C2×#92418C2×D412yes—
188C2×#92418C2×D412yes—
189C8×D61—24no—
190C8×D61—24no—
191C8×D61—24no—
192C22×D61#12711yescharacteristic
193Q8×C61—42no—
194Q8×C61—42no—
195Q8×C61—42no—
196Q8×C61—42no—
197C2×C4×C61—41no—
198C2×C4×C61—41no—
199C2×C4×C61—41no—
200C2×C4×C61—41no—
201C2×C4×C61C22×D411yescharacteristic
202C2×C4×C61C22×D411yescharacteristic
203C2×C4×C61C22×D411yescharacteristic
204C2×Dic61—41no—
205C2×Dic61—41no—
206C2×Dic61—41no—
207C2×Dic61—41no—
208C2×Dic61#12711yescharacteristic
209C2×Dic61#12711yescharacteristic
210C2×Dic61#12711yescharacteristic
211C4×D61—82no—
212C4×D61—82no—
213C4×D61—82no—
214C4×D61—82no—
215C4×D61#13514yes—
216C4×D61#13714yes—
217C4×D61#13714yes—
218Dic122—42no—
219Dic122—42no—
220Dic122—42no—
221Dic122—42no—
222Dic122—82no—
223Dic122—82no—
224Dic122—82no—
225Dic122—82no—
226C8×C61—22no—
227C8×C61—22no—
228C8×C61—22no—
229#92418—22no—
230#92418—22no—
231#92418—22no—
232C2×#1718—611nomaximal, Sylow
233C22×C61C2×#12711yescharacteristic
234C2×D61#49512yes—
235C2×D61#49712yes—
236C2×D61#49712yes—
237C4×C61—81no—
238C4×C61—81no—
239C4×C61—81no—
240C4×C61—81no—
241C4×C61C2×#13512yes—
242C4×C61C2×#13712yes—
243C4×C61C2×#13712yes—
244Dic61—81no—
245Dic61—81no—
246Dic61—81no—
247Dic61—81no—
248Dic61#49512yes—
249Dic61#49712yes—
250Dic61#49712yes—
251C2×#500—611no—
252C2×#498—611no—
253C2×#487—611no—
254C2×#487—611no—
255C2×#487—611no—
256C2×#487—611no—
257#1718—611no—
258#1718—611no—
259#1718—611no—
260#1718—611no—
261#1718—611no—
262#1718—611no—
263#1718—611no—
264#1718D6111yescharacteristic, direct product factor
265C2×#322—611no—
266C2×C61C2×#49511yescharacteristic
267C2×C61C2×#49711yescharacteristic
268C2×C61C2×#49711yescharacteristic
269D61#171814yesdirect product factor
270C2×C4⋊Q8—611no—
271C2×C4⋊Q8—611no—
272C2×C4⋊Q8—611no—
273C2×C4⋊Q8—611no—
274#500—611no—
275#500—611no—
276#500—611no—
277#500—1222no—
278#500C2×D6111yescharacteristic
279#498—611no—
280#498—611no—
281#498—611no—
282#498—1222no—
283#498C2×D6111yescharacteristic
284#487—611no—
285#487—611no—
286#487—611no—
287#487—611no—
288#487—611no—
289#487—611no—
290#487—611no—
291#487—611no—
292#487—611no—
293#487—611no—
294#487—611no—
295#487—611no—
296#487—1222no—
297#487—1222no—
298#487—1222no—
299#487—1222no—
300#487C2×D6111yescharacteristic
301#487C2×D6111yescharacteristic
302#487C2×D6111yescharacteristic
303#487C2×D6111yescharacteristic
304C2×#107—1222no—
305C2×#106—1222no—
306C2×#103—1222no—
307C2×#103—1222no—
308C2×#103—1222no—
309C2×#103—1222no—
310C2×C4×C8—611no—
311C2×C4×C8—611no—
312C2×C4×C8—611no—
313#322—611no—
314#322—611no—
315#322—611no—
316#322C2×D6111yescharacteristic
317C61C2×#171811yescharacteristic, complemented, Sylow
318C22×Q8—1221no—
319C22×Q8—1221no—
320C22×Q8—1221no—
321C22×Q8—1221no—
322C22×C8—612no—
323C22×C8—612no—
324C22×C8—612no—
325C4⋊Q8—611no—
326C4⋊Q8—611no—
327C4⋊Q8—611no—
328C4⋊Q8—611no—
329C4⋊Q8—1221no—
330C4⋊Q8—1221no—
331C4⋊Q8—1221no—
332C4⋊Q8—1221no—
333C4⋊Q8—1221no—
334C4⋊Q8—1221no—
335C4⋊Q8—1221no—
336C4⋊Q8—1221no—
337C4⋊Q8—1221no—
338C4⋊Q8—1221no—
339C4⋊Q8—1221no—
340C4⋊Q8—1221no—
341C4⋊Q8C22×D6111yescharacteristic
342C4⋊Q8C22×D6111yescharacteristic
343C4⋊Q8C22×D6111yescharacteristic
344C4⋊Q8C22×D6111yescharacteristic
345C2×C4⋊C4—1221no—
346C2×C4⋊C4—1221no—
347C2×C4⋊C4—1221no—
348C2×C4⋊C4—1221no—
349C2×C4⋊C4—1221no—
350C2×C4⋊C4—1221no—
351C2×C4⋊C4—1221no—
352C2×C4⋊C4—1221no—
353C2×C42—611no—
354#107—22no—
355#107—1222no—
356#107—1222no—
357#107—1222no—
358#106—22no—
359#106—1222no—
360#106—1222no—
361#106—1222no—
362#103—22no—
363#103—22no—
364#103—22no—
365#103—22no—
366#103—1222no—
367#103—1222no—
368#103—1222no—
369#103—1222no—
370#103—1222no—
371#103—1222no—
372#103—1222no—
373#103—1222no—
374#103—1222no—
375#103—1222no—
376#103—1222no—
377#103—1222no—
378C4×C8—612no—
379C4×C8—612no—
380C4×C8—612no—
381C4×C8—611no—
382C4×C8—611no—
383C4×C8—611no—
384C4×C8C22×D6111yescharacteristic
385C4×C8C22×D6111yescharacteristic
386C4×C8C22×D6111yescharacteristic
387C2×Q8—21no—
388C2×Q8—21no—
389C2×Q8—21no—
390C2×Q8—21no—
391C2×Q8—1221no—
392C2×Q8—1221no—
393C2×Q8—1221no—
394C2×Q8—1221no—
395C2×Q8—2441no—
396C2×Q8—2441no—
397C2×Q8—2441no—
398C2×Q8—2441no—
399C2×Q8—2444no—
400C2×Q8—2444no—
401C2×Q8—2444no—
402C2×Q8—2444no—
403C22×C4—611no—
404C22×C4—611no—
405C22×C4—611no—
406C22×C4—2441no—
407C22×C4—2441no—
408C22×C4—2441no—
409C22×C4—2441no—
410C2×C8—612no—
411C2×C8—612no—
412C2×C8—612no—
413C2×C8—1224no—
414C2×C8—1224no—
415C2×C8—1224no—
416C2×C8D4×D6112yes—
417C2×C8D4×D6112yes—
418C2×C8D4×D6112yes—
419C4⋊C4—21no—
420C4⋊C4—21no—
421C4⋊C4—21no—
422C4⋊C4—21no—
423C4⋊C4—21no—
424C4⋊C4—21no—
425C4⋊C4—21no—
426C4⋊C4—21no—
427C4⋊C4—1221no—
428C4⋊C4—1221no—
429C4⋊C4—1221no—
430C4⋊C4—1221no—
431C4⋊C4—1221no—
432C4⋊C4—1221no—
433C4⋊C4—1221no—
434C4⋊C4—1221no—
435C4⋊C4—2441no—
436C4⋊C4—2441no—
437C4⋊C4—2441no—
438C4⋊C4—2441no—
439C4⋊C4—2441no—
440C4⋊C4—2441no—
441C4⋊C4—2441no—
442C4⋊C4—2441no—
443C42—611no—
444C42—611no—
445C42—611no—
446C42C23×D6111yescharacteristic
447C23—611no—
448Q8—42no—
449Q8—42no—
450Q8—42no—
451Q8—42no—
452Q8—4882no—
453Q8—4882no—
454Q8—4882no—
455Q8—4882no—
456Q8—2442no—
457Q8—2442no—
458Q8—2442no—
459Q8—2442no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—41no—
463C2×C4—41no—
464C2×C4—611no—
465C2×C4—611no—
466C2×C4—611no—
467C2×C4—614no—
468C2×C4—614no—
469C2×C4—614no—
470C2×C4—4882no—
471C2×C4—4882no—
472C2×C4—4882no—
473C2×C4—4882no—
474C2×C4—2441no—
475C2×C4—2441no—
476C2×C4—2441no—
477C2×C4—2441no—
478C2×C4C2×D4×D6111yescharacteristic
479C2×C4C2×D4×D6111yescharacteristic
480C2×C4C2×D4×D6111yescharacteristic
481C8—22no—
482C8—22no—
483C8—22no—
484C8—1222no—
485C8—1222no—
486C8—1222no—
487C22—612no—
488C22—612no—
489C22—612no—
490C22#127×D6111yescharacteristic
491C4—81no—
492C4—81no—
493C4—81no—
494C4—81no—
495C4—612no—
496C4—612no—
497C4—612no—
498C4—4881no—
499C4—4881no—
500C4—4881no—
501C4—4881no—
502C4#135×D6112yes—
503C4#137×D6112yes—
504C4#137×D6112yes—
505C2—614no—
506C2#495×D6111yescharacteristic
507C2#497×D6111yescharacteristic
508C2#497×D6111yescharacteristic
subgroupG/H
centerC22#127×D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#1718C2
socleC22×C61C2×#127
prime radicalC22×D61#127
hypercenter#1718D61
hypocenterC61C2×#1718
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #1718

Complements

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

NH ≅ G/Ntype
7. #21445468C2semidirect
8. #21445467C2semidirect
9. #21445466C2semidirect
10. #21445465C2semidirect
11. #21445464C2semidirect
12. #21445463C2semidirect
13. #21445462C2semidirect
15. C61×#1718C2semidirect
264. #1718D61direct (N × H)
269. D61#1718direct (N × H)
317. C61C2×#1718semidirect

Maximal subgroups

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

subgroupindex
#500×D612
#498×D612
#487×D612
#214454682
#214454672
#214454662
#214454652
#214454642
#214454632
#214454622
#322×D612
C61×#17182
C2×#171861