Finite Group Databasebeta

← D61×#1952 #29683555

Subgroups — D61×#1952 #29683555

Order 15616.

918 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#108×D61C211yesmaximal, characteristic
2#428×D61C212yesmaximal
3C2×#107×D61C211yesmaximal, characteristic
4#405×D61C211yesmaximal, characteristic
5#21446605C211yesmaximal, characteristic, complemented
6#21446604C211yesmaximal, characteristic, complemented
7#21446603C212yesmaximal, complemented
8#21446602C211yesmaximal, characteristic, complemented
9#21446601C212yesmaximal, complemented
10#343×D61C212yesmaximal
11C61×#1952C211yesmaximal, characteristic, complemented
12C2×M16×D61C2212yes—
13C2×M16×D61C2211yescharacteristic
14C22×C8×D61C2211yescharacteristic
15#117×D61C2211yescharacteristic
16C2×C4⋊C4×D61C2212yes—
17C2×#14519713C2211yescharacteristic
18C2×#14519712C2212yes—
19#108×D61C418yescomplemented
20#16839805C2212yes—
21#16839804C2212yes—
22#16839803—22no—
23#16839802C2212yes—
24#16839801—22no—
25C2×#14519711C2211yescharacteristic
26C2×#14519710C2212yes—
27#107×D61—21no—
28#107×D61—21no—
29#107×D61—21no—
30#107×D61—21no—
31#107×D61—22no—
32#106×D61—22no—
33#16839720C2211yescharacteristic
34#16839719—21no—
35#16839718C2211yescharacteristic
36#16839717C2211yescharacteristic
37#16839716—21no—
38#97×D61—21no—
39C4×C8×D61—21no—
40#16839531C2212yes—
41#16839530C2212yes—
42#16839530C2212yes—
43C2×#108×C61C2211yescharacteristic
44C61×#428C2212yes—
45C2×#107×C61C2211yescharacteristic
46C61×#405C2211yescharacteristic
47C61×#343C2212yes—
48C22×C4×D61—22no—
49C22×C4×D61C2311yescharacteristic
50C2×#11758194C2312yes—
51C2×#11758194C2311yescharacteristic
52C2×#11758189—21no—
53C2×#11758189—22no—
54M16×D61—24no—
55M16×D61—22no—
56M16×D61C2×C418yes—
57M16×D61Q814yes—
58C22×#92418C2311yescharacteristic
59C2×C8×D61—21no—
60C2×C8×D61—22no—
61C2×C8×D61C2×C414yes—
62C2×C8×D61D411yescharacteristic
63C2×C8×D61D411yescharacteristic
64C2×C8×D61D411yescharacteristic
65C2×C8×D61D411yescharacteristic
66C2×C8×D61Q814yes—
67#14519736C2311yescharacteristic
68#14519735D411yescharacteristic
69#14519735D411yescharacteristic
70#14519734—21no—
71#14519733—21no—
72C2×C4⋊Dic61C2312yes—
73C2×#11758196—22no—
74C4⋊C4×D61—22no—
75C4⋊C4×D61—22no—
76C4⋊C4×D61—22no—
77C4⋊C4×D61—22no—
78C4⋊C4×D61D411yescharacteristic
79C4⋊C4×D61D411yescharacteristic
80C22⋊C4×D61—21no—
81C42×D61—21no—
82#14519713C2×C414yescomplemented
83#14519712C2×C418yescomplemented
84#14519711—21no—
85#14519711—21no—
86#14519711—22no—
87#14519710—22no—
88#14519710—22no—
89#14519710—22no—
90#14519710—22no—
91#14519709—22no—
92#14519708—22no—
93#14519708—22no—
94#14519688—21no—
95#14519687—21no—
96#14519687—21no—
97C4×#92418—21no—
98C8×Dic61—21no—
99C8×Dic61—21no—
100C2×M16×C61C2312yes—
101C2×M16×C61C2311yescharacteristic
102C22×C8×C61C2311yescharacteristic
103#117×C61C2311yescharacteristic
104C2×C4⋊C4×C61C2312yes—
105#108×C61C2×C414yescomplemented
106#107×C61—21no—
107#107×C61—21no—
108#107×C61—22no—
109#106×C61—22no—
110#97×C61—21no—
111C4×C8×C61—21no—
112C23×D61#4111yescharacteristic
113C22×C4×C61—22no—
114C22×C4×C61C2411yescharacteristic
115C22×Dic61—22no—
116C22×Dic61#4111yescharacteristic
117C2×C4×D61—21no—
118C2×C4×D61—21no—
119C2×C4×D61—42no—
120C2×C4×D61—42no—
121C2×C4×D61—84no—
122C2×C4×D61C22×C412yes—
123C2×C4×D61C2×D411yescharacteristic
124C2×C4×D61C2×D411yescharacteristic
125C2×C4×D61C2×D411yescharacteristic
126C2×C4×D61C2×D411yescharacteristic
127C2×C4×D61C2×Q812yes—
128C2×C4×D61C2×Q812yes—
129C2×C4×D61#4112yes—
130M16×C61—22no—
131M16×C61—21no—
132M16×C61C22×C414yes—
133M16×C61C2×Q812yes—
134C2×C8×C61—21no—
135C2×C8×C61—22no—
136C2×C8×C61C22×C412yes—
137C2×C8×C61C2×D411yescharacteristic
138C2×C8×C61C2×D411yescharacteristic
139C2×C8×C61C2×Q812yes—
140C4⋊C4×C61—22no—
141C4⋊C4×C61—22no—
142C4⋊C4×C61C2×D411yescharacteristic
143C4⋊C4×C61C2×D411yescharacteristic
144C22⋊C4×C61—21no—
145C42×C61—21no—
146C22⋊Dic61—21no—
147#11758198—21no—
148#11758198—21no—
149C4⋊Dic61—22no—
150C4⋊Dic61—22no—
151C4⋊Dic61C2×D411yescharacteristic
152C4⋊Dic61C2×D411yescharacteristic
153#11758196—21no—
154#11758196—21no—
155#11758196—42no—
156#11758196—42no—
157C4×Dic61—21no—
158C4×Dic61—21no—
159C4×Dic61—21no—
160#11758194—22no—
161#11758194—21no—
162#11758194C22×C414yes—
163#11758194C2×Q812yes—
164C2×#92418—21no—
165C2×#92418—22no—
166C2×#92418C22×C412yes—
167C2×#92418C2×D411yescharacteristic
168C2×#92418C2×D411yescharacteristic
169C2×#92418C2×Q812yes—
170#11758189—28no—
171#11758189—24no—
172C8×D61—28no—
173C8×D61—24no—
174C8×D61C4⋊C414yes—
175C8×D61C4⋊C414yes—
176C8×D61C4⋊C414yes—
177C8×D61C4⋊C414yes—
178C23×C61C2×#4111yescharacteristic
179C22×D61—22no—
180C22×D61—22no—
181C22×D61C4×Q812yes—
182C22×D61#12111yescharacteristic
183C22×D61#12111yescharacteristic
184C22×D61#12512yes—
185C2×C4×C61—21no—
186C2×C4×C61—21no—
187C2×C4×C61—42no—
188C2×C4×C61—82no—
189C2×C4×C61C23×C411yescharacteristic
190C2×C4×C61C22×D411yescharacteristic
191C2×C4×C61C22×D411yescharacteristic
192C2×C4×C61C22×Q811yescharacteristic
193C2×C4×C61C22×Q811yescharacteristic
194C2×C4×C61C2×#4111yescharacteristic
195C2×Dic61—21no—
196C2×Dic61—21no—
197C2×Dic61—42no—
198C2×Dic61—82no—
199C2×Dic61C4×Q812yes—
200C2×Dic61#12111yescharacteristic
201C2×Dic61#12111yescharacteristic
202C2×Dic61#12512yes—
203C4×D61—42no—
204C4×D61—42no—
205C4×D61—84no—
206C4×D61—84no—
207C4×D61C2×C4⋊C412yes—
208C4×D61C2×C4⋊C412yes—
209C4×D61C4×D412yes—
210C4×D61C4×D412yes—
211C4×D61C22⋊Q812yes—
212C4×D61C22⋊Q812yes—
213C4×D61C4⋊Q812yes—
214C4×D61C4⋊Q812yes—
215C8×C61—24no—
216C8×C61—22no—
217C8×C61C2×C4⋊C412yes—
218C8×C61C2×C4⋊C412yes—
219#92418—24no—
220#92418—22no—
221#92418C2×C4⋊C412yes—
222#92418C2×C4⋊C412yes—
223C2×#1952—611nomaximal, Sylow
224C22×C61—21no—
225C22×C61—21no—
226C22×C61C2×C4×Q811yescharacteristic
227C22×C61C2×#12111yescharacteristic
228C22×C61C2×#12511yescharacteristic
229C2×D61—21no—
230C2×D61—21no—
231C2×D61—24no—
232C2×D61—24no—
233C2×D61#38912yes—
234C2×D61#38912yes—
235C2×D61#47212yes—
236C2×D61#47312yes—
237C4×C61—41no—
238C4×C61—41no—
239C4×C61—82no—
240C4×C61C22×C4⋊C411yescharacteristic
241C4×C61C2×C4×D411yescharacteristic
242C4×C61C2×C22⋊Q811yescharacteristic
243C4×C61C2×C4⋊Q811yescharacteristic
244Dic61—41no—
245Dic61—41no—
246Dic61—82no—
247Dic61#38912yes—
248Dic61#38912yes—
249C22×#108—611no—
250C2×#428—612no—
251C22×#107—611no—
252C2×#405—611no—
253#1952—611no—
254#1952—612no—
255#1952—611no—
256#1952—611no—
257#1952—612no—
258#1952D6111yescharacteristic, direct product factor
259C2×#343—612no—
260C2×C61—21no—
261C2×C61—21no—
262C2×C61C2×#38911yescharacteristic
263C2×C61C2×#47211yescharacteristic
264C2×C61C2×#47311yescharacteristic
265D61—22no—
266D61#195214yesdirect product factor
267C22×M16—611no—
268C22×M16—612no—
269C23×C8—611no—
270C2×#117—611no—
271C22×C4⋊C4—612no—
272C2×#108—612no—
273C2×#108—611no—
274C2×#108—618no—
275C2×#108C2×D6111yescharacteristic
276#428—612no—
277#428—612no—
278#428—612no—
279#428—1222no—
280#428—1222no—
281#428C2×D6112yes—
282C2×#107—611no—
283C2×#107—612no—
284C2×#107—1222no—
285C2×#107—1221no—
286C2×#107—1221no—
287C2×#107—1221no—
288C2×#107—1221no—
289C2×#107C2×D6111yescharacteristic
290C2×#106—1222no—
291#405—611no—
292#405—611no—
293#405—611no—
294#405—1221no—
295#405—1221no—
296#405C2×D6111yescharacteristic
297C2×#97—1221no—
298C2×C4×C8—1221no—
299#343—612no—
300#343—612no—
301#343—612no—
302#343C2×D6112yes—
303C61C2×#195211yescharacteristic, complemented, Sylow
304C23×C4—611no—
305C23×C4—1222no—
306C2×M16—611no—
307C2×M16—612no—
308C2×M16—618no—
309C2×M16—614no—
310C2×M16—1221no—
311C2×M16—1222no—
312C2×M16—1222no—
313C2×M16—1224no—
314C2×M16C22×D6112yes—
315C2×M16C22×D6111yescharacteristic
316C22×C8—611no—
317C22×C8—614no—
318C22×C8—611no—
319C22×C8—611no—
320C22×C8—611no—
321C22×C8—611no—
322C22×C8—614no—
323C22×C8—1221no—
324C22×C8—1222no—
325C22×C8C22×D6111yescharacteristic
326#117—611no—
327#117—611no—
328#117—611no—
329#117—1221no—
330#117—1221no—
331#117C22×D6111yescharacteristic
332C2×C4⋊C4—611no—
333C2×C4⋊C4—611no—
334C2×C4⋊C4—612no—
335C2×C4⋊C4—1222no—
336C2×C4⋊C4—1222no—
337C2×C4⋊C4—1222no—
338C2×C4⋊C4—1222no—
339C2×C4⋊C4—1222no—
340C2×C4⋊C4C22×D6112yes—
341C2×C22⋊C4—1221no—
342C2×C42—1221no—
343#108—618no—
344#108—614no—
345#108C4×D6114yescomplemented
346#107—21no—
347#107—21no—
348#107—22no—
349#107—1222no—
350#107—1222no—
351#107—1222no—
352#107—1222no—
353#107—1221no—
354#107—1221no—
355#107—1222no—
356#106—22no—
357#106—1222no—
358#106—1222no—
359#106—1222no—
360#97—21no—
361#97—1221no—
362#97—1221no—
363#97—1221no—
364C4×C8—21no—
365C4×C8—1221no—
366C4×C8—1221no—
367C4×C8—1221no—
368C24—611no—
369C22×C4—22no—
370C22×C4—611no—
371C22×C4—612no—
372C22×C4—611no—
373C22×C4—611no—
374C22×C4—611no—
375C22×C4—611no—
376C22×C4—612no—
377C22×C4—612no—
378C22×C4—612no—
379C22×C4—1221no—
380C22×C4—1221no—
381C22×C4—1222no—
382C22×C4—4884no—
383C22×C4—2442no—
384C22×C4—2442no—
385C22×C4C23×D6111yescharacteristic
386M16—22no—
387M16—21no—
388M16—614no—
389M16—612no—
390M16—1228no—
391M16—1224no—
392M16—1222no—
393M16—1221no—
394M16C2×C4×D6114yes—
395M16Q8×D6112yes—
396C2×C8—21no—
397C2×C8—22no—
398C2×C8—612no—
399C2×C8—611no—
400C2×C8—611no—
401C2×C8—612no—
402C2×C8—614no—
403C2×C8—614no—
404C2×C8—614no—
405C2×C8—614no—
406C2×C8—1228no—
407C2×C8—1224no—
408C2×C8—1221no—
409C2×C8—1222no—
410C2×C8C2×C4×D6112yes—
411C2×C8D4×D6111yescharacteristic
412C2×C8D4×D6111yescharacteristic
413C2×C8Q8×D6112yes—
414C4⋊C4—22no—
415C4⋊C4—22no—
416C4⋊C4—611no—
417C4⋊C4—611no—
418C4⋊C4—1221no—
419C4⋊C4—1221no—
420C4⋊C4—1222no—
421C4⋊C4—1222no—
422C4⋊C4—2442no—
423C4⋊C4—2442no—
424C4⋊C4D4×D6111yescharacteristic
425C4⋊C4D4×D6111yescharacteristic
426C22⋊C4—21no—
427C22⋊C4—1221no—
428C22⋊C4—1221no—
429C22⋊C4—1221no—
430C42—21no—
431C42—1221no—
432C42—1221no—
433C42—1221no—
434C23—611no—
435C23—612no—
436C23—611no—
437C23—612no—
438C23—1222no—
439C23—1222no—
440C23#41×D6111yescharacteristic
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—42no—
444C2×C4—82no—
445C2×C4—612no—
446C2×C4—611no—
447C2×C4—611no—
448C2×C4—612no—
449C2×C4—612no—
450C2×C4—612no—
451C2×C4—612no—
452C2×C4—612no—
453C2×C4—612no—
454C2×C4—612no—
455C2×C4—612no—
456C2×C4—612no—
457C2×C4—1221no—
458C2×C4—1221no—
459C2×C4—4884no—
460C2×C4—4884no—
461C2×C4—4882no—
462C2×C4—2442no—
463C2×C4—2442no—
464C2×C4—2442no—
465C2×C4C22×C4×D6111yescharacteristic
466C2×C4C2×D4×D6111yescharacteristic
467C2×C4C2×D4×D6111yescharacteristic
468C2×C4C2×Q8×D6111yescharacteristic
469C2×C4C2×Q8×D6111yescharacteristic
470C2×C4#41×D6111yescharacteristic
471C8—24no—
472C8—22no—
473C8—612no—
474C8—612no—
475C8—1224no—
476C8—1222no—
477C8C4⋊C4×D6112yes—
478C8C4⋊C4×D6112yes—
479C22—21no—
480C22—21no—
481C22—612no—
482C22—612no—
483C22—612no—
484C22—612no—
485C22—1224no—
486C22—1224no—
487C22—1221no—
488C22—1221no—
489C22C4×Q8×D6111yescharacteristic
490C22#121×D6111yescharacteristic
491C22#125×D6111yescharacteristic
492C4—41no—
493C4—41no—
494C4—82no—
495C4—612no—
496C4—612no—
497C4—4882no—
498C4—2441no—
499C4—2441no—
500C4C2×C4⋊C4×D6111yescharacteristic
501C4C4×D4×D6111yescharacteristic
502C4C22⋊Q8×D6111yescharacteristic
503C4C4⋊Q8×D6111yescharacteristic
504C2—21no—
505C2—21no—
506C2—614no—
507C2—1222no—
508C2#389×D6111yescharacteristic
509C2#472×D6111yescharacteristic
510C2#473×D6111yescharacteristic
subgroupG/H
centerC22#121×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1952C2
socleC22×C61C2×#121
prime radicalC23×D61#41
cosocleC22×C4×C61C24
hypercenter#1952D61
hypocenterC61C2×#1952
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #1952

Complements

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

NH ≅ G/Ntype
5. #21446605C2semidirect
6. #21446604C2semidirect
7. #21446603C2semidirect
8. #21446602C2semidirect
9. #21446601C2semidirect
11. C61×#1952C2semidirect
19. #108×D61C4semidirect
82. #14519713C2×C4semidirect
83. #14519712C2×C4semidirect
105. #108×C61C2×C4semidirect
258. #1952D61direct (N × H)
266. D61#1952direct (N × H)
303. C61C2×#1952semidirect
345. #108C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#108×D612
#428×D612
C2×#107×D612
#405×D612
#214466052
#214466042
#214466032
#214466022
#214466012
#343×D612
C61×#19522
C2×#195261