Finite Group Databasebeta

← C4×SD32×D61 #29833276

Subgroups — C4×SD32×D61 #29833276

Order 15616.

742 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×SD32×D61C211yesmaximal, characteristic
2C4×Q16×D61C211yesmaximal, characteristic, complemented
3C4×D8×D61C211yesmaximal, characteristic
4#21447674C211yesmaximal, characteristic, complemented
5C4×#14519722C211yesmaximal, characteristic, complemented
6SD32×Dic61C211yesmaximal, characteristic, complemented
7C4×#14519720C211yesmaximal, characteristic, complemented
8#21447670C211yesmaximal, characteristic, complemented
9C4×#14519721C211yesmaximal, characteristic, complemented
10#21447668C211yesmaximal, characteristic, complemented
11#367×D61C211yesmaximal, characteristic, complemented
12#358×D61C211yesmaximal, characteristic, complemented
13#357×D61C211yesmaximal, characteristic
14C4×C16×D61C211yesmaximal, characteristic, complemented
15C4×SD32×C61C211yesmaximal, characteristic, complemented
16C2×Q16×D61C2211yescharacteristic
17C2×D8×D61C2211yescharacteristic
18C4×Q8×D61—21no—
19C4×D4×D61—21no—
20C2×#14519722C2211yescharacteristic
21C2×#14519721C2211yescharacteristic
22C2×#14519720C2211yescharacteristic
23SD32×D61C418yesdirect product factor
24C2×C16×D61C2211yescharacteristic
25C2×C16×D61C2211yescharacteristic
26C4×Dic244C2211yescharacteristic, complemented
27Q16×Dic61C2211yescharacteristic, complemented
28#16839856C2211yescharacteristic, complemented
29C4×#11758202—21no—
30#16839854—21no—
31C4×D488C2211yescharacteristic
32D8×Dic61C2211yescharacteristic
33#16839844C2211yescharacteristic
34C4×#11758199—21no—
35#16839842—21no—
36#107×D61C2211yescharacteristic
37#107×D61C2211yescharacteristic
38#103×D61—21no—
39#102×D61—21no—
40C4×C8×D61C2211yescharacteristic
41#16839590C2211yescharacteristic, complemented
42#16839589C2211yescharacteristic, complemented
43#16839589C2211yescharacteristic, complemented
44#16839567C2211yescharacteristic, complemented
45#16839566C2211yescharacteristic, complemented
46#16839565C2211yescharacteristic, complemented
47#16839564C2211yescharacteristic
48#16839563C2211yescharacteristic
49#16839562C2211yescharacteristic
50C4×#11758185C2211yescharacteristic, complemented
51C16×Dic61C2211yescharacteristic, complemented
52C16×Dic61C2211yescharacteristic, complemented
53C2×SD32×C61C2211yescharacteristic
54C4×Q16×C61C2211yescharacteristic, complemented
55C4×D8×C61C2211yescharacteristic
56C61×#367C2211yescharacteristic, complemented
57C61×#358C2211yescharacteristic, complemented
58C61×#357C2211yescharacteristic
59C4×C16×C61C2211yescharacteristic, complemented
60C2×Q8×D61—21no—
61C2×D4×D61—21no—
62C22×C4×D61—41no—
63C2×Dic244C2311yescharacteristic
64C2×#11758202—21no—
65Q16×D61—22no—
66Q16×D61C2×C414yescomplemented
67C2×D488C2311yescharacteristic
68C2×#11758199—21no—
69D8×D61—22no—
70D8×D61C2×C414yes—
71C2×C8×D61D411yescharacteristic
72C2×C8×D61C2311yescharacteristic
73Q8×Dic61—21no—
74C4×Dic122—21no—
75C4×Dic122—41no—
76#14519742—21no—
77#14519742—41no—
78C4×D244—21no—
79D4×Dic61—21no—
80#14519739—21no—
81C4×C22⋊D61—41no—
82#14519737—41no—
83C4⋊C4×D61—21no—
84C4⋊C4×D61—21no—
85C4⋊C4×D61—41no—
86C22⋊C4×D61—41no—
87C42×D61—41no—
88C42×D61D411yescharacteristic
89#14519722C2×C414yescomplemented
90#14519721C2×C414yescomplemented
91#14519720C2×C414yescomplemented
92C2×#11758185C2311yescharacteristic
93C2×#11758185C2311yescharacteristic
94C16×D61—22no—
95C16×D61C2×C414yescomplemented
96#14519711C2311yescharacteristic
97#14519711C2311yescharacteristic
98#14519710—21no—
99#14519710—21no—
100#14519702—21no—
101#14519701—21no—
102#14519700—21no—
103#14519699—21no—
104#14519698—21no—
105#14519697—21no—
106C4×#92418D411yescharacteristic
107C8×Dic61D411yescharacteristic
108C8×Dic61C2311yescharacteristic
109C2×Q16×C61C2311yescharacteristic
110C2×D8×C61C2311yescharacteristic
111C4×Q8×C61—21no—
112C4×D4×C61—21no—
113SD32×C61C2×C414yescomplemented
114C2×C16×C61C2311yescharacteristic
115C2×C16×C61C2311yescharacteristic
116#107×C61C2311yescharacteristic
117#107×C61C2311yescharacteristic
118#103×C61—21no—
119#102×C61—21no—
120C4×C8×C61C2311yescharacteristic
121C23×D61—41no—
122C2×Q8×C61—21no—
123C2×D4×C61—21no—
124C22×C4×C61—41no—
125C2×C22⋊D61—41no—
126C22×Dic61—41no—
127Q8×D61—24no—
128Q8×D61—42no—
129D4×D61—24no—
130D4×D61—42no—
131C2×D244—21no—
132C2×C4×D61—41no—
133C2×C4×D61—41no—
134C2×C4×D61—41no—
135C2×C4×D61—41no—
136C2×C4×D61—41no—
137C2×C4×D61—84no—
138C2×C4×D61D811yescharacteristic
139C2×C4×D61D811yescharacteristic
140C2×C4×D61C2×D411yescharacteristic
141C2×Dic122—21no—
142C2×Dic122—41no—
143Q16×C61—21no—
144Q16×C61C22×C412yescomplemented
145D8×C61—21no—
146D8×C61C22×C412yes—
147C2×C8×C61C2×D411yescharacteristic
148C2×C8×C61C2411yescharacteristic
149C4⋊C4×C61—21no—
150C4⋊C4×C61—21no—
151C4⋊C4×C61—41no—
152C22⋊C4×C61—41no—
153C42×C61—41no—
154C42×C61C2×D411yescharacteristic
155C22⋊Dic61—41no—
156#11758202—24no—
157#11758199—24no—
158#11758198—41no—
159#11758198—41no—
160C4⋊Dic61—21no—
161C4⋊Dic61—21no—
162C4⋊Dic61—41no—
163#11758196—41no—
164#11758196—41no—
165#11758196—41no—
166#11758196—41no—
167C4×Dic61—41no—
168C4×Dic61—41no—
169C4×Dic61—41no—
170C4×Dic61D811yescharacteristic
171C4×Dic61D811yescharacteristic
172C4×Dic61C2×D411yescharacteristic
173C2×#92418C2×D411yescharacteristic
174C2×#92418C2×D411yescharacteristic
175Dic244—21no—
176Dic244C22×C412yescomplemented
177D488—21no—
178D488C22×C412yes—
179C8×D61—22no—
180C8×D61C22×C412yes—
181C8×D61#4112yes—
182C16×C61—21no—
183C16×C61C22×C412yescomplemented
184#11758185—21no—
185#11758185C22×C412yescomplemented
186C23×C61—41no—
187C22×D61—41no—
188C22×D61—44no—
189C22×D61—82no—
190C22×D61—82no—
191C22×D61C2×D811yescharacteristic
192Q8×C61—22no—
193Q8×C61—41no—
194D4×C61—22no—
195D4×C61—41no—
196C2×C4×C61—41no—
197C2×C4×C61—41no—
198C2×C4×C61—41no—
199C2×C4×C61—82no—
200C2×C4×C61C2×D811yescharacteristic
201C2×C4×C61C2×D811yescharacteristic
202C2×C4×C61C22×D411yescharacteristic
203C22⋊D61—44no—
204C2×Dic61—41no—
205C2×Dic61—41no—
206C2×Dic61—41no—
207C2×Dic61—82no—
208C2×Dic61C2×D811yescharacteristic
209C2×Dic61C2×D811yescharacteristic
210C2×Dic61C2×D811yescharacteristic
211D244—22no—
212D244—41no—
213C4×D61—22no—
214C4×D61—44no—
215C4×D61—82no—
216C4×D61—82no—
217C4×D61—82no—
218C4×D61—82no—
219C4×D61SD3214yesdirect product factor
220C4×D61C4×D412yes—
221C4×D61#13512yes—
222Dic122—22no—
223Dic122—41no—
224Dic122—44no—
225C8×C61—21no—
226C8×C61C23×C411yescharacteristic
227C8×C61C2×#4111yescharacteristic
228#92418—21no—
229#92418C4×D412yes—
230C2×C4×SD32—611nomaximal, Sylow
231C22×C61—42no—
232C22×C61—81no—
233C22×C61—81no—
234C22×C61C22×D811yescharacteristic
235C2×D61—42no—
236C2×D61—81no—
237C2×D61—81no—
238C2×D61—88no—
239C2×D61C4×D812yes—
240C2×D61C2×SD3212yes—
241C2×D61#50812yes—
242C4×C61—21no—
243C4×C61—42no—
244C4×C61—81no—
245C4×C61—81no—
246C4×C61C2×SD3212yescomplemented
247C4×C61C2×C4×D411yescharacteristic
248C4×C61C2×#13511yescharacteristic
249Dic61—21no—
250Dic61—42no—
251Dic61—81no—
252Dic61—81no—
253Dic61C4×D812yes—
254Dic61C2×SD3212yescomplemented
255C22×SD32—611no—
256C2×C4×Q16—611no—
257C2×C4×D8—611no—
258C4×SD32—611no—
259C4×SD32—611no—
260C4×SD32—611no—
261C4×SD32—611no—
262C4×SD32—611no—
263C4×SD32—611no—
264C4×SD32—611no—
265C4×SD32D6111yescharacteristic, direct product factor
266C2×#367—611no—
267C2×#358—611no—
268C2×#357—611no—
269C2×C4×C16—611no—
270C2×C61—82no—
271C2×C61C2×C4×D811yescharacteristic
272C2×C61C22×SD3211yescharacteristic
273C2×C61C2×#50811yescharacteristic
274D61—82no—
275D61C4×SD3214yesdirect product factor
276C22×Q16—611no—
277C22×D8—611no—
278C2×C4×Q8—1221no—
279C2×C4×D4—1221no—
280C2×SD32—611no—
281C2×SD32—611no—
282C2×SD32—618no—
283C2×SD32—611no—
284C2×SD32C2×D6111yescharacteristic
285C22×C16—611no—
286C22×C16—611no—
287C4×Q16—611no—
288C4×Q16—611no—
289C4×Q16—611no—
290C4×Q16—1221no—
291C4×Q16—1221no—
292C4×Q16C2×D6111yescharacteristic, complemented
293C4×D8—611no—
294C4×D8—611no—
295C4×D8—611no—
296C4×D8—1221no—
297C4×D8—1221no—
298C4×D8C2×D6111yescharacteristic
299C2×#107—611no—
300C2×#107—611no—
301C2×#103—1221no—
302C2×#102—1221no—
303C2×C4×C8—611no—
304#367—611no—
305#367—611no—
306#367—611no—
307#367C2×D6111yescharacteristic, complemented
308#358—611no—
309#358—611no—
310#358—611no—
311#358C2×D6111yescharacteristic, complemented
312#357—611no—
313#357—611no—
314#357—611no—
315#357C2×D6111yescharacteristic
316C4×C16—611no—
317C4×C16—611no—
318C4×C16—611no—
319C4×C16C2×D6111yescharacteristic, complemented
320C61C2×C4×SD3211yescharacteristic, complemented, Sylow
321C22×Q8—1221no—
322C22×D4—1221no—
323C23×C4—2441no—
324C2×Q16—614no—
325C2×Q16—611no—
326C2×Q16—1222no—
327C2×Q16—1221no—
328C2×Q16C22×D6111yescharacteristic
329C2×D8—614no—
330C2×D8—611no—
331C2×D8—1222no—
332C2×D8—1221no—
333C2×D8C22×D6111yescharacteristic
334C22×C8—611no—
335C22×C8—611no—
336C4×Q8—21no—
337C4×Q8—1221no—
338C4×Q8—1221no—
339C4×Q8—1221no—
340C4×Q8—2441no—
341C4×Q8—2441no—
342C4×D4—21no—
343C4×D4—1221no—
344C4×D4—1221no—
345C4×D4—1221no—
346C4×D4—2441no—
347C4×D4—2441no—
348C2×C4⋊C4—1221no—
349C2×C4⋊C4—1221no—
350C2×C4⋊C4—2441no—
351C2×C22⋊C4—2441no—
352C2×C42—611no—
353C2×C42—2441no—
354SD32—614no—
355SD32—614no—
356SD32—614no—
357SD32C4×D6114yesdirect product factor
358C2×C16—611no—
359C2×C16—614no—
360C2×C16—611no—
361C2×C16—1222no—
362C2×C16C22×D6111yescharacteristic
363C2×C16C22×D6111yescharacteristic
364#107—611no—
365#107—611no—
366#107—1221no—
367#107—1221no—
368#107C22×D6111yescharacteristic
369#107C22×D6111yescharacteristic
370#103—21no—
371#103—1221no—
372#103—1221no—
373#103—1221no—
374#102—21no—
375#102—1221no—
376#102—1221no—
377#102—1221no—
378C4×C8—611no—
379C4×C8—611no—
380C4×C8—611no—
381C4×C8C22×D6111yescharacteristic
382C24—2441no—
383C2×Q8—21no—
384C2×Q8—1224no—
385C2×Q8—1221no—
386C2×Q8—2441no—
387C2×Q8—2442no—
388C2×D4—21no—
389C2×D4—1224no—
390C2×D4—1221no—
391C2×D4—2442no—
392C2×D4—2441no—
393C22×C4—41no—
394C22×C4—611no—
395C22×C4—611no—
396C22×C4—611no—
397C22×C4—4884no—
398C22×C4—2441no—
399C22×C4—2441no—
400C22×C4—2441no—
401C22×C4—2441no—
402C22×C4—2441no—
403C22×C4—2441no—
404Q16—21no—
405Q16—612no—
406Q16—1224no—
407Q16—1221no—
408Q16C2×C4×D6112yescomplemented
409D8—21no—
410D8—612no—
411D8—1224no—
412D8—1221no—
413D8C2×C4×D6112yes—
414C2×C8—611no—
415C2×C8—612no—
416C2×C8—612no—
417C2×C8—611no—
418C2×C8—1222no—
419C2×C8D4×D6111yescharacteristic
420C2×C8C23×D6111yescharacteristic
421C4⋊C4—21no—
422C4⋊C4—21no—
423C4⋊C4—41no—
424C4⋊C4—1221no—
425C4⋊C4—1221no—
426C4⋊C4—2441no—
427C4⋊C4—2441no—
428C4⋊C4—2441no—
429C4⋊C4—2441no—
430C4⋊C4—2441no—
431C22⋊C4—41no—
432C22⋊C4—2441no—
433C22⋊C4—2441no—
434C22⋊C4—2441no—
435C42—41no—
436C42—611no—
437C42—611no—
438C42—611no—
439C42—2441no—
440C42—2441no—
441C42—2441no—
442C42D4×D6111yescharacteristic
443C16—21no—
444C16—612no—
445C16—1221no—
446C16C2×C4×D6112yescomplemented
447C23—41no—
448C23—611no—
449C23—4882no—
450C23—4882no—
451C23—2444no—
452C23—2441no—
453Q8—22no—
454Q8—41no—
455Q8—1222no—
456Q8—2444no—
457Q8—2441no—
458D4—22no—
459D4—41no—
460D4—1222no—
461D4—2444no—
462D4—2441no—
463C2×C4—41no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—82no—
467C2×C4—611no—
468C2×C4—611no—
469C2×C4—612no—
470C2×C4—612no—
471C2×C4—614no—
472C2×C4—611no—
473C2×C4—1222no—
474C2×C4—4882no—
475C2×C4—4882no—
476C2×C4—4882no—
477C2×C4—4882no—
478C2×C4—4882no—
479C2×C4—2444no—
480C2×C4—2441no—
481C2×C4—2441no—
482C2×C4—2441no—
483C2×C4D8×D6111yescharacteristic
484C2×C4D8×D6111yescharacteristic
485C2×C4C2×D4×D6111yescharacteristic
486C8—21no—
487C8—612no—
488C8—1221no—
489C8C22×C4×D6111yescharacteristic
490C8#41×D6111yescharacteristic
491C22—42no—
492C22—81no—
493C22—81no—
494C22—612no—
495C22—612no—
496C22—612no—
497C22—4888no—
498C22—4881no—
499C22—4881no—
500C22—2442no—
501C22C2×D8×D6111yescharacteristic
502C4—21no—
503C4—42no—
504C4—81no—
505C4—81no—
506C4—612no—
507C4—612no—
508C4—1221no—
509C4—4881no—
510C4—4881no—
511C4—2442no—
512C4SD32×D6112yesdirect product factor
513C4C4×D4×D6111yescharacteristic
514C4#135×D6111yescharacteristic
515C2—82no—
516C2—614no—
517C2—4882no—
518C2C4×D8×D6111yescharacteristic
519C2C2×SD32×D6111yescharacteristic
520C2#508×D6111yescharacteristic
subgroupG/H
centerC2×C4D8×D61
commutatorC8×C61C23×C4
FrattiniC2×C8C23×D61
FittingC4×SD32×C61C2
socleC22×C61C22×D8
prime radicalC2×D8×D61C22
cosocleC2×C8×C61C24
hypercenterC4×SD32D61
hypocenterC61C2×C4×SD32
LCSG ▷ C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×C8 ◁ C4×SD32

Complements

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

NH ≅ G/Ntype
2. C4×Q16×D61C2semidirect
4. #21447674C2semidirect
5. C4×#14519722C2semidirect
6. SD32×Dic61C2semidirect
7. C4×#14519720C2semidirect
8. #21447670C2semidirect
9. C4×#14519721C2semidirect
10. #21447668C2semidirect
11. #367×D61C2semidirect
12. #358×D61C2semidirect
14. C4×C16×D61C2semidirect
15. C4×SD32×C61C2semidirect
23. SD32×D61C4direct (N × H)
26. C4×Dic244C22semidirect
27. Q16×Dic61C22semidirect
28. #16839856C22semidirect
41. #16839590C22semidirect
42. #16839589C22semidirect
43. #16839589C22semidirect
44. #16839567C22semidirect
45. #16839566C22semidirect
46. #16839565C22semidirect
50. C4×#11758185C22semidirect
51. C16×Dic61C22semidirect
52. C16×Dic61C22semidirect
54. C4×Q16×C61C22semidirect
56. C61×#367C22semidirect
57. C61×#358C22semidirect
59. C4×C16×C61C22semidirect
66. Q16×D61C2×C4semidirect
89. #14519722C2×C4semidirect
90. #14519721C2×C4semidirect
91. #14519720C2×C4semidirect
95. C16×D61C2×C4semidirect
113. SD32×C61C2×C4semidirect
144. Q16×C61C22×C4semidirect
176. Dic244C22×C4semidirect
183. C16×C61C22×C4semidirect
185. #11758185C22×C4semidirect
219. C4×D61SD32direct (N × H)
246. C4×C61C2×SD32semidirect
254. Dic61C2×SD32semidirect
265. C4×SD32D61direct (N × H)
275. D61C4×SD32direct (N × H)
292. C4×Q16C2×D61semidirect
307. #367C2×D61semidirect
311. #358C2×D61semidirect
319. C4×C16C2×D61semidirect
320. C61C2×C4×SD32semidirect
357. SD32C4×D61direct (N × H)
408. Q16C2×C4×D61semidirect
446. C16C2×C4×D61semidirect
512. C4SD32×D61direct (N × H)

Maximal subgroups

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

subgroupindex
C2×SD32×D612
C4×Q16×D612
C4×D8×D612
#214476742
C4×#145197222
SD32×Dic612
C4×#145197202
#214476702
C4×#145197212
#214476682
#367×D612
#358×D612
#357×D612
C4×C16×D612
C4×SD32×C612
C2×C4×SD3261