Finite Group Databasebeta

← #30603311

Subgroups — #30603311

Order 15616.

874 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462472C211yesmaximal, characteristic, complemented
2#21462439C212yesmaximal
3D61⋊#338C211yesmaximal, characteristic, complemented
4#21461484C212yesmaximal, complemented
5#408×D61C211yesmaximal, characteristic
6C2×D61⋊M16C2212yes—
7C2×#14519856C2212yes—
8#16840773—24no—
9#16840772—22no—
10#16840755—22no—
11#16840754—22no—
12#16840753—24no—
13#16840752—24no—
14#16840631—22no—
15(C2×#6923)⋊C8—24no—
16C2×#41×D61C2211yescharacteristic
17C2×M16×D61C2211yescharacteristic
18C22×C8×D61C2211yescharacteristic
19#16839730C411yescharacteristic, complemented
20#16839729C411yescharacteristic, complemented
21#16839728C411yescharacteristic, complemented
22#16839727—22no—
23C22⋊C8×D61—22no—
24C61×#408C411yescharacteristic, complemented
25C2×#11758213—22no—
26D61⋊M16—22no—
27D61⋊M16—22no—
28D61⋊M16—22no—
29D61⋊M16—22no—
30C2×#11758217—22no—
31C2×D61⋊C8D414yes—
32#14519856—22no—
33#14519856—22no—
34#14519856—22no—
35#14519856—22no—
36C2×C4⋊#6923D414yes—
37C2×C22⋊#6923—22no—
38C2×C4×#6923—22no—
39#14519846—24no—
40#14519845—24no—
41#14519840—28no—
42#14519839—28no—
43C2×#11758226Q811yescharacteristic
44C2×#11758222—21no—
45C2×#11758222C2×C411yescharacteristic
46C2×#11758224—21no—
47C2×#11758224Q811yescharacteristic
48#41×D61—22no—
49#41×D61—22no—
50#41×D61—22no—
51#41×D61—22no—
52C2×Q8×D61D411yescharacteristic
53C2×D4×D61—21no—
54C2×D4×D61D411yescharacteristic
55C22×C4×D61—21no—
56C22×C4×D61C2311yescharacteristic
57C2×#11758194C2×C411yescharacteristic
58C2×#11758189D412yes—
59M16×D61—22no—
60M16×D61—22no—
61C22×#92418C2×C411yescharacteristic
62C2×C8×D61—21no—
63C2×C8×D61—21no—
64C2×C8×D61—22no—
65C2×C8×D61—22no—
66C2×C8×D61D412yes—
67C22⋊#92418—22no—
68#14519689—22no—
69#14519689—22no—
70C2×#41×C61C2×C411yescharacteristic
71C2×M16×C61C2×C411yescharacteristic
72C22×C8×C61C2×C411yescharacteristic
73C22⋊C8×C61—22no—
74C23×D61—21no—
75C23×D61#4111yescharacteristic
76C22×#6923—24no—
77#41×C61—22no—
78#41×C61—22no—
79C2×Q8×C61C4⋊C411yescharacteristic
80C2×D4×C61—21no—
81C2×D4×C61C4⋊C411yescharacteristic
82C22×C4×C61—21no—
83C22×C4×C61C22×C411yescharacteristic
84C2×C22⋊D61—21no—
85C2×C22⋊D61—21no—
86C2×C22⋊D61—21no—
87C22×Dic61—21no—
88C22×Dic61#4111yescharacteristic
89#11758226—22no—
90#11758226—22no—
91Q8×D61—22no—
92Q8×D61—22no—
93#11758224—22no—
94#11758224—22no—
95#11758224—42no—
96#11758224—42no—
97D4×D61—22no—
98D4×D61—22no—
99D4×D61—42no—
100D4×D61—42no—
101#11758222—22no—
102#11758222—22no—
103#11758222—42no—
104#11758222—42no—
105C2×D244—21no—
106C2×D244C4⋊C411yescharacteristic
107C2×C4×D61—21no—
108C2×C4×D61—21no—
109C2×C4×D61—21no—
110C2×C4×D61—41no—
111C2×C4×D61—41no—
112C2×C4×D61—41no—
113C2×C4×D61—41no—
114C2×C4×D61C2×D412yes—
115C2×C4×D61C2×D411yescharacteristic
116C2×C4×D61C2×D412yes—
117C2×C4×D61C2×D411yescharacteristic
118C2×C4×D61C2×D411yescharacteristic
119C2×C4×D61C2×Q811yescharacteristic
120C2×C4×D61#4112yes—
121C2×C4×D61#4112yes—
122C2×Dic122—21no—
123C2×Dic122C4⋊C411yescharacteristic
124C22⋊#6923—42no—
125C22⋊#6923—42no—
126#11758217—42no—
127#11758217—42no—
128C2×#92420—24no—
129C4⋊#6923—24no—
130C4⋊#6923—24no—
131C4×#6923—42no—
132C4×#6923—42no—
133#11758213—42no—
134#11758213—42no—
135D61⋊C8—24no—
136D61⋊C8—24no—
137M16×C61—22no—
138C2×C8×C61—21no—
139C2×C8×C61—22no—
140C2×C8×C61C22⋊C412yes—
141#11758194—22no—
142C2×#92418—21no—
143C2×#92418—22no—
144C2×#92418C22⋊C412yes—
145#11758189—24no—
146C8×D61—22no—
147C8×D61—22no—
148C8×D61—42no—
149C8×D61—41no—
150C8×D61—41no—
151C23×C61—21no—
152C23×C61#11711yescharacteristic
153C22×D61—21no—
154C22×D61—42no—
155C22×D61—44no—
156C22×D61—41no—
157C22×D61—41no—
158C22×D61#12112yes—
159C22×D61#12111yescharacteristic
160C22×D61C22⋊Q811yescharacteristic
161C22×D61#12612yes—
162C2×#6923—48no—
163C2×#6923—44no—
164Q8×C61—22no—
165D4×C61—22no—
166D4×C61—42no—
167C2×C4×C61—21no—
168C2×C4×C61—41no—
169C2×C4×C61—41no—
170C2×C4×C61C2×C22⋊C411yescharacteristic
171C2×C4×C61C2×C4⋊C411yescharacteristic
172C2×C4×C61C4×D412yes—
173C2×C4×C61C4×D412yes—
174C22⋊D61—42no—
175C22⋊D61—42no—
176C22⋊D61—42no—
177C2×Dic61—21no—
178C2×Dic61—41no—
179C2×Dic61—41no—
180C2×Dic61#12111yescharacteristic
181C2×Dic61C22⋊Q811yescharacteristic
182C2×Dic61#12312yes—
183C2×Dic61#12412yes—
184D244—22no—
185D244—42no—
186C4×D61—41no—
187C4×D61—41no—
188C4×D61—41no—
189C4×D61—41no—
190C4×D61—41no—
191C4×D61—41no—
192C4×D61#12011yescharacteristic
193C4×D61#12012yes—
194C4×D61#12112yes—
195C4×D61#12112yes—
196C4×D61C22⋊Q812yes—
197C4×D61C22⋊Q812yes—
198C4×D61#12312yes—
199C4×D61#12311yescharacteristic
200C4×D61#12411yescharacteristic
201C4×D61#12711yescharacteristic
202Dic122—22no—
203Dic122—42no—
204#92420—44no—
205C8×C61—22no—
206C8×C61—41no—
207#92418—22no—
208#92418—41no—
209#11111—611nomaximal, Sylow
210C22×C61—41no—
211C22×C61—42no—
212C22×C61—41no—
213C22×C61#38011yescharacteristic
214C22×C61#38812yes—
215C2×D61—24no—
216C2×D61—22no—
217C2×D61—41no—
218C2×D61—42no—
219C2×D61—42no—
220C2×D61—41no—
221C2×D61—82no—
222C2×D61—82no—
223C2×D61#39211yescharacteristic
224C2×D61#39612yes—
225C2×D61#39711yescharacteristic
226#6923—84no—
227C4×C61—41no—
228C4×C61#38512yes—
229C4×C61#38611yescharacteristic
230C4×C61#39011yescharacteristic
231Dic61—41no—
232Dic61#39311yescharacteristic
233Dic61#39412yes—
234Dic61#39911yescharacteristic
235#2911—611no—
236#2896—612no—
237C2×#408—611no—
238C2×#338—611no—
239#1729—612no—
240C2×C61—21no—
241C2×C61—22no—
242C2×C61—81no—
243C2×C61#143911yescharacteristic
244D61—21no—
245D61—22no—
246D61—81no—
247D61#201712yes—
248C22×#41—611no—
249C22×M16—611no—
250C22×M16—612no—
251C23×C8—611no—
252C2×#117—612no—
253#428—1224no—
254#427—1222no—
255#419—1222no—
256#418—1222no—
257#417—1224no—
258#416—1224no—
259#408—611no—
260#408—611no—
261#408—611no—
262#408—1222no—
263#408#692311yescharacteristic, complemented
264C2×C22⋊C8—1222no—
265#338—1222no—
266#336—1224no—
267C61#1111111yescharacteristic, complemented, Sylow
268C2×#41—611no—
269C2×#41—611no—
270C2×#41—611no—
271C2×#41—1221no—
272C2×#41—1221no—
273C2×#41—1222no—
274C2×#41—1222no—
275C2×#41—1222no—
276C2×#41—1222no—
277C2×#41C2×#692311yescharacteristic
278C22×Q8—611no—
279C22×D4—611no—
280C22×D4—1221no—
281C23×C4—611no—
282C23×C4—1221no—
283C2×M16—611no—
284C2×M16—612no—
285C2×M16—1222no—
286C2×M16—1222no—
287C2×M16—1222no—
288C2×M16—1222no—
289C2×M16—1222no—
290C2×M16—1222no—
291C2×M16—1222no—
292C2×M16—1222no—
293C2×M16C2×#692311yescharacteristic
294C22×C8—612no—
295C22×C8—614no—
296C22×C8—611no—
297C22×C8—1222no—
298C22×C8—1221no—
299C22×C8—1221no—
300C22×C8—1222no—
301C22×C8C2×#692311yescharacteristic
302#117—1222no—
303#117—1222no—
304#117—1222no—
305#117—1222no—
306C2×C4⋊C4—614no—
307C2×C22⋊C4—1222no—
308C2×C42—1222no—
309#107—1224no—
310#106—1224no—
311#103—1228no—
312#102—1228no—
313C22⋊C8—22no—
314C22⋊C8—1222no—
315C22⋊C8—1222no—
316C22⋊C8—1222no—
317C24—611no—
318C24—1221no—
319#41—22no—
320#41—22no—
321#41—1222no—
322#41—1222no—
323#41—1222no—
324#41—1222no—
325#41—1222no—
326#41—1222no—
327#41—2442no—
328#41—2442no—
329#41—2442no—
330#41—2442no—
331C2×Q8—611no—
332C2×Q8—1221no—
333C2×Q8—1222no—
334C2×Q8—1222no—
335C2×Q8C4⋊#692311yescharacteristic
336C2×D4—21no—
337C2×D4—611no—
338C2×D4—1221no—
339C2×D4—1222no—
340C2×D4—1222no—
341C2×D4—1221no—
342C2×D4—1221no—
343C2×D4—1221no—
344C2×D4—2442no—
345C2×D4—2442no—
346C2×D4C4⋊#692311yescharacteristic
347C22×C4—21no—
348C22×C4—611no—
349C22×C4—611no—
350C22×C4—611no—
351C22×C4—611no—
352C22×C4—611no—
353C22×C4—612no—
354C22×C4—612no—
355C22×C4—612no—
356C22×C4—612no—
357C22×C4—1221no—
358C22×C4—1221no—
359C22×C4—1221no—
360C22×C4—1221no—
361C22×C4—1224no—
362C22×C4—2441no—
363C22×C4—2441no—
364C22×C4—2441no—
365C22×C4—2441no—
366C22×C4C22×#692311yescharacteristic
367M16—22no—
368M16—1224no—
369M16—1222no—
370M16—2442no—
371M16—2442no—
372M16—2442no—
373M16—2442no—
374C2×C8—21no—
375C2×C8—22no—
376C2×C8—612no—
377C2×C8—1222no—
378C2×C8—1222no—
379C2×C8—1224no—
380C2×C8—1224no—
381C2×C8—1224no—
382C2×C8—1221no—
383C2×C8—1222no—
384C2×C8—2442no—
385C2×C8—2441no—
386C2×C8—2441no—
387C2×C8C22⋊#692312yes—
388C4⋊C4—1224no—
389C4⋊C4—1224no—
390C22⋊C4—2442no—
391C22⋊C4—2442no—
392C42—2442no—
393C42—2442no—
394C23—21no—
395C23—611no—
396C23—612no—
397C23—611no—
398C23—612no—
399C23—1221no—
400C23—2441no—
401C23—2441no—
402C23—2442no—
403C23—2444no—
404C23#1451985611yescharacteristic
405Q8—22no—
406Q8—1222no—
407Q8—2442no—
408D4—22no—
409D4—42no—
410D4—1222no—
411D4—2442no—
412D4—2442no—
413D4—2442no—
414D4—2442no—
415C2×C4—21no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—611no—
419C2×C4—611no—
420C2×C4—612no—
421C2×C4—612no—
422C2×C4—612no—
423C2×C4—612no—
424C2×C4—612no—
425C2×C4—612no—
426C2×C4—611no—
427C2×C4—612no—
428C2×C4—611no—
429C2×C4—612no—
430C2×C4—611no—
431C2×C4—611no—
432C2×C4—1221no—
433C2×C4—2441no—
434C2×C4—2441no—
435C2×C4—2441no—
436C2×C4—2441no—
437C2×C4—2441no—
438C2×C4—2441no—
439C2×C4—2444no—
440C2×C4—2448no—
441C2×C4—2441no—
442C2×C4—2441no—
443C2×C4C2×C22⋊#692311yescharacteristic
444C2×C4C2×C4⋊#692311yescharacteristic
445C2×C4D4×#692312yes—
446C2×C4D4×#692312yes—
447C8—22no—
448C8—41no—
449C8—1222no—
450C8—2444no—
451C8—2441no—
452C22—41no—
453C22—42no—
454C22—41no—
455C22—611no—
456C22—611no—
457C22—612no—
458C22—1224no—
459C22—1222no—
460C22—4882no—
461C22—4882no—
462C22—2441no—
463C22—2442no—
464C22—2442no—
465C22—2441no—
466C22#1684070411yescharacteristic
467C22#1684071212yes—
468C4—41no—
469C4—611no—
470C4—612no—
471C4—611no—
472C4—4884no—
473C4—2441no—
474C4#1684070912yes—
475C4#1684071011yescharacteristic
476C4#1684071411yescharacteristic
477C2—21no—
478C2—22no—
479C2—81no—
480C2—612no—
481C2—1221no—
482C2—1222no—
483C2—4881no—
484C2#2146100211yescharacteristic
subgroupG/H
centerC4#16840714
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#408C4
socleC2×C61#1439
prime radicalC2×#41×D61C22
cosocleC22×C4×D61C23
hypercenter#408#6923
hypocenterC61#11111
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C22×C4 ◁ #408

Complements

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

NH ≅ G/Ntype
1. #21462472C2semidirect
3. D61⋊#338C2semidirect
4. #21461484C2semidirect
19. #16839730C4semidirect
20. #16839729C4semidirect
21. #16839728C4semidirect
24. C61×#408C4semidirect
263. #408#6923semidirect
267. C61#11111semidirect

Maximal subgroups

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

subgroupindex
#214624722
#214624392
D61⋊#3382
#214614842
#408×D612
#1111161