Finite Group Databasebeta

← #30612751

Subgroups — #30612751

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#21462544C211yesmaximal, characteristic, complemented
2D61⋊#436C211yesmaximal, characteristic, complemented
3#21461451C212yesmaximal, complemented
4#21461450C212yesmaximal, complemented
5#21461421C212yesmaximal, complemented
6#21461419C212yesmaximal, complemented
7#21461389C211yesmaximal, characteristic, complemented
8#21461145C211yesmaximal, characteristic, complemented
9#21461126C211yesmaximal, characteristic, complemented
10#21461025C211yesmaximal, characteristic, complemented
11#21455821C211yesmaximal, characteristic
12C2×#14519865—21no—
13C2×D61⋊M16—21no—
14#16840797C2211yescharacteristic
15#16840797C2211yescharacteristic
16#16840796—21no—
17#16840796C2211yescharacteristic
18#16840796C2211yescharacteristic
19#16840796C2212yescomplemented
20#16840795—21no—
21#16840795—21no—
22#16840790—21no—
23#16840790C2212yescomplemented
24#16840781C2211yescharacteristic
25#16840766C2211yescharacteristic
26D61⋊(C4⋊C8)C2211yescharacteristic
27#16840737—21no—
28D61⋊(C22⋊C8)—21no—
29C4×D61⋊C8C2211yescharacteristic
30#16840626C2212yescomplemented
31#16840625C2212yescomplemented
32#16840610C2212yes—
33#16840610C2212yescomplemented
34#16840610C2212yescomplemented
35D4⋊#92420C2212yes—
36#92420⋊C8C2212yescomplemented
37C8×#92420C2212yescomplemented
38#16840313C2211yescharacteristic
39C4×D4×D61C2211yescharacteristic
40#16840077C412yes—
41#16840039C411yescharacteristic
42#16839958C411yescharacteristic
43#16839957C411yescharacteristic
44#16839897C412yes—
45#16839844C2212yes—
46#16839842C2212yes—
47#16839814C2211yescharacteristic
48C61×#474C411yescharacteristic
49#14519865—44no—
50C2×#11758213—21no—
51C2×#11758213—21no—
52C2×#11758213—21no—
53C2×#11758213—22no—
54D61⋊M16—44no—
55C2×#11758217—21no—
56C2×#11758217—21no—
57C2×D61⋊C8—21no—
58C2×D61⋊C8—22no—
59C2×D61⋊C8D411yescharacteristic
60C2×D61⋊C8D411yescharacteristic
61#14519844—21no—
62C4⋊#92420—21no—
63C4⋊#92420—21no—
64C4⋊#92420C2311yescharacteristic
65C4⋊#92420C2311yescharacteristic
66C4⋊#92420C2312yes—
67#14519834—21no—
68#14519834—21no—
69#14519834—21no—
70#14519834—22no—
71#14519834—22no—
72C22⋊#92420—21no—
73C22⋊#92420—21no—
74C4×#92420D411yescharacteristic
75C4×#92420D411yescharacteristic
76C4×#92420C2312yes—
77C4×#92420C2311yescharacteristic
78C4×#92420C2311yescharacteristic
79C2×#11758226—21no—
80C2×D4×D61C2×C411yescharacteristic
81C22×C4×D61—21no—
82C2×D488C2×C412yes—
83C2×#11758199C2×C412yes—
84#14519774C2×C411yescharacteristic
85#14519766—21no—
86#14519752—21no—
87#14519752C2×C412yes—
88C4×D244C2×C411yescharacteristic
89D4×Dic61C2311yescharacteristic
90#14519739—21no—
91#14519739C2311yescharacteristic
92#14519739C2312yes—
93C4×C22⋊D61—21no—
94#14519737—21no—
95C4⋊C4×D61C2×C411yescharacteristic
96C22⋊C4×D61—21no—
97C42×D61C2311yescharacteristic
98#14519710C2×C412yes—
99C4⋊#92418C2×C411yescharacteristic
100#14519699C2×C412yes—
101#14519697C2×C412yes—
102#14519697C2×C412yes—
103#14519689C2×C412yes—
104C8×Dic61C2312yes—
105C4⋊Q8×C61C2×C411yescharacteristic
106C4×D4×C61C2×C411yescharacteristic
107#107×C61C2×C412yes—
108C4⋊C8×C61C2×C411yescharacteristic
109#102×C61C2×C412yes—
110C23×D61—21no—
111C2×Q8×C61—21no—
112C2×D4×C61C22×C411yescharacteristic
113C22×C4×C61—21no—
114C2×C22⋊D61—21no—
115C22×Dic61—21no—
116#11758226—42no—
117#11758226—42no—
118D4×D61—41no—
119D4×D61—41no—
120C2×D244—22no—
121C2×D244—21no—
122C2×D244—21no—
123C2×D244C22×C411yescharacteristic
124C2×D244C22×C412yes—
125C2×C4×D61—21no—
126C2×C4×D61—21no—
127C2×C4×D61—21no—
128C2×C4×D61—22no—
129C2×C4×D61—42no—
130C2×C4×D61—42no—
131C2×C4×D61C22×C411yescharacteristic
132C2×C4×D61C2×D411yescharacteristic
133C2×C4×D61#4111yescharacteristic
134#11758217—42no—
135#11758217—42no—
136C2×#92420—21no—
137C2×#92420—21no—
138C2×#92420—22no—
139C2×#92420—22no—
140C2×#92420C2×D411yescharacteristic
141C2×#92420C2×D411yescharacteristic
142C2×#92420C2×D411yescharacteristic
143C2×#92420C2×D411yescharacteristic
144#11758213—42no—
145#11758213—42no—
146#11758213—42no—
147#11758213—44no—
148D61⋊C8—22no—
149D61⋊C8—42no—
150D61⋊C8—44no—
151D61⋊C8D814yescomplemented
152C2×C8×C61C22×C412yes—
153C4⋊C4×C61—21no—
154C4⋊C4×C61C22×C412yes—
155C4⋊C4×C61C22×C411yescharacteristic
156C22⋊C4×C61—21no—
157C42×C61C22×C411yescharacteristic
158C22⋊Dic61—21no—
159#11758199—42no—
160#11758198—21no—
161#11758198—22no—
162#11758198—21no—
163#11758198—22no—
164C4⋊Dic61C22×C411yescharacteristic
165#11758196—21no—
166C4×Dic61C2×D411yescharacteristic
167C4×Dic61#4111yescharacteristic
168C4×Dic61C2411yescharacteristic
169C2×#92418C22×C412yes—
170D488—42no—
171C23×C61—21no—
172C22×D61—21no—
173C22×D61—22no—
174C22×D61—42no—
175C22×D61—42no—
176C22×D61—42no—
177C22×D61C4×D411yescharacteristic
178Q8×C61—42no—
179D4×C61—21no—
180D4×C61—21no—
181C2×C4×C61—21no—
182C2×C4×C61—22no—
183C2×C4×C61—42no—
184C2×C4×C61C4×D411yescharacteristic
185C2×C4×C61C4×D411yescharacteristic
186C2×C4×C61C23×C411yescharacteristic
187C22⋊D61—42no—
188C2×Dic61—21no—
189C2×Dic61—41no—
190C2×Dic61—41no—
191C2×Dic61C4×D411yescharacteristic
192C2×Dic61C22×D411yescharacteristic
193C2×Dic61C2×#4111yescharacteristic
194D244—21no—
195D244—22no—
196D244—22no—
197D244—21no—
198D244—42no—
199D244—44no—
200D244—42no—
201C4×D61—21no—
202C4×D61—21no—
203C4×D61—41no—
204C4×D61—42no—
205C4×D61—42no—
206C4×D61—42no—
207C4×D61—41no—
208C4×D61—41no—
209C4×D61—42no—
210C4×D61C2×D812yes—
211C4×D61#13512yes—
212#92420—21no—
213#92420—21no—
214#92420—42no—
215#92420—42no—
216#92420—41no—
217#92420—41no—
218#92420C2×D812yes—
219#92420C2×D812yes—
220C8×C61—22no—
221#92418—22no—
222#17928—611nomaximal, Sylow
223C22×C61—41no—
224C22×C61—41no—
225C22×C61—41no—
226C22×C61C2×C4×D411yescharacteristic
227C2×D61—21no—
228C2×D61—21no—
229C2×D61—41no—
230C2×D61—42no—
231C2×D61—41no—
232C2×D61—42no—
233C2×D61—42no—
234C2×D61—41no—
235C2×D61—84no—
236C2×D61C4×D812yes—
237C4×C61—21no—
238C4×C61—41no—
239C4×C61—42no—
240C4×C61C4×D812yes—
241C4×C61#56811yescharacteristic
242C4×C61#56811yescharacteristic
243Dic61—21no—
244Dic61—21no—
245Dic61—41no—
246Dic61C22×D811yescharacteristic
247Dic61C2×#13511yescharacteristic
248#3100—611no—
249#2931—611no—
250C2×#436—611no—
251#1589—612no—
252#1589—612no—
253#1581—612no—
254#1581—612no—
255#1571—611no—
256#1486—611no—
257#1480—611no—
258#1450—611no—
259C2×C61—81no—
260C2×C61#293011yescharacteristic
261C2×C61C2×C4×D811yescharacteristic
262C2×C61#295511yescharacteristic
263D61—22no—
264D61—82no—
265D61—81no—
266C2×#131—1221no—
267C22×M16—1221no—
268#532—611no—
269C2×C4×D4—611no—
270#480—612no—
271#474—611no—
272#474#692311yescharacteristic
273#459—611no—
274#459—611no—
275#447—612no—
276C4×D8—612no—
277C4×D8—612no—
278#436—611no—
279#436—611no—
280#436—611no—
281#436—612no—
282#436—611no—
283#436—1221no—
284#436—1221no—
285#436—1221no—
286C8×D4—612no—
287C8×D4—1221no—
288#431—611no—
289#431—611no—
290#423—611no—
291C2×C4⋊C8—611no—
292#408—1221no—
293C2×C22⋊C8—1221no—
294C2×C4×C8—611no—
295#335—612no—
296#335—612no—
297D4⋊C8—612no—
298D4⋊C8—612no—
299D4⋊C8—612no—
300D4⋊C8—612no—
301#322—612no—
302C82—612no—
303C61#1792811yescharacteristic, complemented, Sylow
304C2×#41—1221no—
305C22×D4—611no—
306C23×C4—1221no—
307C2×D8—612no—
308C2×D8—612no—
309#131—2444no—
310C2×M16—1221no—
311C2×M16—1221no—
312C2×M16—1221no—
313C2×M16—1221no—
314C2×M16—1222no—
315C2×M16—1221no—
316C2×M16—2444no—
317C22×C8—611no—
318C22×C8—611no—
319C22×C8—1222no—
320C22×C8—1221no—
321C4⋊Q8C2×#692311yescharacteristic
322#127—611no—
323#124—1221no—
324#121—612no—
325#121—1221no—
326C4×D4—611no—
327C4×D4—611no—
328C4×D4—612no—
329C4×D4—611no—
330C4×D4—1221no—
331C4×D4—1221no—
332C4×D4—1221no—
333C4×D4C2×#692311yescharacteristic
334C2×C4⋊C4—611no—
335C2×C22⋊C4—1221no—
336C2×C42—611no—
337#107—612no—
338#107C2×#692312yes—
339C4⋊C8—611no—
340C4⋊C8—611no—
341C4⋊C8—612no—
342C4⋊C8—611no—
343C4⋊C8—1221no—
344C4⋊C8—1221no—
345C4⋊C8—1221no—
346C4⋊C8C2×#692311yescharacteristic
347#102—612no—
348#102—612no—
349#102—612no—
350#102C2×#692312yes—
351C22⋊C8—612no—
352C22⋊C8—1221no—
353C22⋊C8—1221no—
354C22⋊C8—1221no—
355C22⋊C8—1221no—
356C22⋊C8—1222no—
357C22⋊C8—1222no—
358C22⋊C8—1221no—
359C4×C8—611no—
360C4×C8—611no—
361C4×C8—611no—
362C4×C8—611no—
363C4×C8—612no—
364C4×C8—612no—
365C24—1221no—
366#41—2442no—
367#41—2442no—
368C2×Q8—21no—
369C2×D4—611no—
370C2×D4—612no—
371C2×D4—1222no—
372C2×D4—1221no—
373C2×D4—1221no—
374C2×D4—1221no—
375C2×D4—2441no—
376C2×D4—2441no—
377C2×D4C22×#692311yescharacteristic
378C22×C4—21no—
379C22×C4—611no—
380C22×C4—611no—
381C22×C4—611no—
382C22×C4—1222no—
383C22×C4—1221no—
384C22×C4—1221no—
385C22×C4—1221no—
386C22×C4—1221no—
387C22×C4—2442no—
388C22×C4—2442no—
389D8—2442no—
390D8—2442no—
391M16—2442no—
392M16—2442no—
393M16—2442no—
394M16—2442no—
395M16—2444no—
396M16—2442no—
397C2×C8—611no—
398C2×C8—611no—
399C2×C8—614no—
400C2×C8—611no—
401C2×C8—611no—
402C2×C8—612no—
403C2×C8—1222no—
404C2×C8—1222no—
405C2×C8—1221no—
406C2×C8—1221no—
407C2×C8—1222no—
408C2×C8—2444no—
409C2×C8—2442no—
410C2×C8C22×#692312yes—
411C4⋊C4—21no—
412C4⋊C4—611no—
413C4⋊C4—1221no—
414C4⋊C4C22×#692311yescharacteristic
415C4⋊C4C22×#692312yes—
416C22⋊C4—21no—
417C22⋊C4—1221no—
418C22⋊C4—1222no—
419C22⋊C4—1222no—
420C22⋊C4—1221no—
421C22⋊C4—1221no—
422C42—611no—
423C42—611no—
424C42—611no—
425C42C22×#692311yescharacteristic
426C23—21no—
427C23—611no—
428C23—1221no—
429C23—1222no—
430C23—2442no—
431C23—2442no—
432C23—2442no—
433Q8—42no—
434D4—21no—
435D4—21no—
436D4—1221no—
437D4—1222no—
438D4—1222no—
439D4—1221no—
440D4—2442no—
441D4—2444no—
442D4—2442no—
443D4—2442no—
444C2×C4—21no—
445C2×C4—22no—
446C2×C4—42no—
447C2×C4—611no—
448C2×C4—612no—
449C2×C4—612no—
450C2×C4—611no—
451C2×C4—611no—
452C2×C4—1221no—
453C2×C4—1221no—
454C2×C4—1221no—
455C2×C4—2441no—
456C2×C4—2442no—
457C2×C4—2441no—
458C2×C4—2441no—
459C2×C4—2442no—
460C2×C4—2442no—
461C2×C4—2441no—
462C2×C4—2441no—
463C2×C4—2442no—
464C2×C4D4×#692311yescharacteristic
465C2×C4D4×#692311yescharacteristic
466C2×C4C23×#692311yescharacteristic
467C8—22no—
468C8—612no—
469C8—612no—
470C8—1221no—
471C8—1221no—
472C8—1222no—
473C8—2442no—
474C8—2441no—
475C8—2441no—
476C8—2442no—
477C22—41no—
478C22—41no—
479C22—41no—
480C22—612no—
481C22—1221no—
482C22—1221no—
483C22—4884no—
484C22—2441no—
485C22—2442no—
486C22—2441no—
487C22—2442no—
488C22—2442no—
489C22—2441no—
490C22C2×D4×#692311yescharacteristic
491C4—21no—
492C4—41no—
493C4—42no—
494C4—611no—
495C4—611no—
496C4—1221no—
497C4—1221no—
498C4—2441no—
499C4D8×#692312yes—
500C4#1684084111yescharacteristic
501C4#1684084211yescharacteristic
502C2—81no—
503C2—1222no—
504C2—4881no—
505C2—4882no—
506C2#2146253911yescharacteristic
507C2C2×D8×#692311yescharacteristic
508C2#2146259211yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#474C4
socleC22×C61C2×C4×D4
prime radical#21455821C2
cosocleC4×Dic61C24
hypercenter#474#6923
hypocenterC61#17928
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
1. #21462544C2semidirect
2. D61⋊#436C2semidirect
3. #21461451C2semidirect
4. #21461450C2semidirect
5. #21461421C2semidirect
6. #21461419C2semidirect
7. #21461389C2semidirect
8. #21461145C2semidirect
9. #21461126C2semidirect
10. #21461025C2semidirect
19. #16840796C22semidirect
23. #16840790C22semidirect
30. #16840626C22semidirect
31. #16840625C22semidirect
33. #16840610C22semidirect
34. #16840610C22semidirect
36. #92420⋊C8C22semidirect
37. C8×#92420C22semidirect
151. D61⋊C8D8semidirect
303. C61#17928semidirect

Maximal subgroups

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

subgroupindex
#214625442
D61⋊#4362
#214614512
#214614502
#214614212
#214614192
#214613892
#214611452
#214611262
#214610252
#214558212
#1792861