Finite Group Databasebeta

← #29582338

Subgroups — #29582338

Order 15616.

644 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840048C211yesmaximal, characteristic, complemented
2C2×#16839968C211yesmaximal, characteristic
3#21450742C211yesmaximal, characteristic
4#21446779C211yesmaximal, characteristic, complemented
5C2×#16839492C211yesmaximal, characteristic, complemented
6C2×#16839489C211yesmaximal, characteristic
7C61×#1296C211yesmaximal, characteristic, complemented
8C22×#11758190—21no—
9C2×#14519777C2211yescharacteristic
10C2×#14519757—21no—
11C2×C4×Dic122C2211yescharacteristic
12C2×C4×D244C2211yescharacteristic
13#16840048—22no—
14#16840048—22no—
15#16839968—22no—
16#16839968—22no—
17C2×#14519709—21no—
18C2×#14519702—21no—
19C2×#14519702—21no—
20C2×C4×#92418C2211yescharacteristic
21#16839684—22no—
22#16839663—21no—
23#16839661—21no—
24#16839619—21no—
25#16839524—22no—
26#16839492—22no—
27#16839489—22no—
28C2×C4⋊C8×C61C2211yescharacteristic
29C2×C4⋊C8×C61C2211yescharacteristic
30C61×#384C2211yescharacteristic
31C22×Dic122—21no—
32C22×Dic122D411yescharacteristic
33C22×D244D411yescharacteristic
34C22×C4×D61—21no—
35C2×#11758190—24no—
36C2×#11758190—42no—
37C2×#11758190—42no—
38C22×#92418—21no—
39#14519777—21no—
40#14519777—21no—
41#14519777—21no—
42#14519777D412yes—
43#14519757—42no—
44#14519757—42no—
45C4×Dic122—21no—
46C4×Dic122—21no—
47C4×Dic122—21no—
48C4×Dic122—21no—
49C4×D244—21no—
50C4×D244—21no—
51C4×D244—21no—
52C4×D244—21no—
53C2×C4⋊Dic61—21no—
54C2×C4⋊Dic61—21no—
55C2×C4⋊Dic61—22no—
56C2×C4⋊Dic61D411yescharacteristic
57C2×C4⋊Dic61D411yescharacteristic
58C2×#11758196—21no—
59C2×#11758198—22no—
60C2×#11758198—21no—
61C2×#11758198—22no—
62C2×C4×Dic61—21no—
63#14519709—24no—
64#14519702—24no—
65#14519702—24no—
66C4×#92418—21no—
67C4×#92418—21no—
68#14519684—22no—
69C22×C8×C61—21no—
70C22×C8×C61—21no—
71C2×C4⋊C4×C61—21no—
72C2×C4⋊C4×C61—21no—
73C2×C4⋊C4×C61D412yes—
74C2×C42×C61C2311yescharacteristic
75C4⋊C8×C61—21no—
76C4⋊C8×C61—21no—
77C4⋊C8×C61D412yes—
78C4⋊C8×C61D412yes—
79C23×D61—21no—
80C22×C4×C61—22no—
81C22×C4×C61C2×D411yescharacteristic
82C22×C4×C61C2×D411yescharacteristic
83C22×C4×C61C2×D411yescharacteristic
84C22×Dic61—21no—
85C22×Dic61—21no—
86C22×Dic61—21no—
87C22×Dic61—41no—
88C2×D244—21no—
89C2×D244—21no—
90C2×D244—21no—
91C2×D244—21no—
92C2×D244—21no—
93C2×D244SD1612yes—
94C2×C4×D61—41no—
95C2×C4×D61—41no—
96C2×C4×D61—41no—
97C2×C4×D61—41no—
98C2×C4×D61—41no—
99C2×C4×D61—41no—
100C2×Dic122—21no—
101C2×Dic122—21no—
102C2×Dic122—21no—
103C2×Dic122—21no—
104C2×Dic122—21no—
105C2×Dic122—22no—
106C2×Dic122—41no—
107C2×Dic122—41no—
108C2×Dic122—41no—
109C2×Dic122—41no—
110C2×Dic122—41no—
111C2×Dic122SD1612yescomplemented
112C2×C8×C61—22no—
113C2×C8×C61—22no—
114C2×C8×C61—41no—
115C2×C8×C61—41no—
116C2×C8×C61—41no—
117C2×C8×C61—41no—
118C4⋊C4×C61—42no—
119C4⋊C4×C61—41no—
120C4⋊C4×C61—41no—
121C4⋊C4×C61—41no—
122C4⋊C4×C61—41no—
123C42×C61C2×D411yescharacteristic
124C42×C61C2×D411yescharacteristic
125C42×C61C2×D411yescharacteristic
126C42×C61#4111yescharacteristic
127#11758198—44no—
128#11758198—41no—
129#11758198—41no—
130#11758198—82no—
131C4⋊Dic61—21no—
132C4⋊Dic61—22no—
133C4⋊Dic61—21no—
134C4⋊Dic61—22no—
135C4⋊Dic61—21no—
136C4⋊Dic61—21no—
137C4⋊Dic61—44no—
138C4⋊Dic61—41no—
139C4⋊Dic61—41no—
140#11758196—41no—
141#11758196—41no—
142C4×Dic61—41no—
143C4×Dic61—41no—
144C2×#92418—22no—
145C2×#92418—41no—
146C2×#92418—41no—
147#11758190—48no—
148C23×C61#12011yescharacteristic
149C22×D61—22no—
150C22×D61—41no—
151C22×D61—41no—
152C22×D61—41no—
153C22×D61—41no—
154C22×D61—41no—
155C22×D61—41no—
156C2×C4×C61—21no—
157C2×C4×C61—21no—
158C2×C4×C61—42no—
159C2×C4×C61—42no—
160C2×C4×C61—42no—
161C2×C4×C61#12011yescharacteristic
162C2×C4×C61#12011yescharacteristic
163C2×C4×C61#12111yescharacteristic
164C2×C4×C61#12111yescharacteristic
165C2×C4×C61#12111yescharacteristic
166C2×C4×C61#12711yescharacteristic
167C2×C4×C61C2×SD1611yescharacteristic
168C2×C4×C61C2×SD1611yescharacteristic
169C2×C4×C61#13511yescharacteristic
170C2×C4×C61#13511yescharacteristic
171C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
172C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
173C2×C4×C61#13711yescharacteristic
174C2×C4×C61#13711yescharacteristic
175C2×Dic61—22no—
176C2×Dic61—41no—
177C2×Dic61—41no—
178C2×Dic61—41no—
179C2×Dic61—42no—
180C2×Dic61—41no—
181C2×Dic61—41no—
182C2×Dic61—41no—
183C2×Dic61—41no—
184C2×Dic61—41no—
185C2×Dic61—81no—
186C2×Dic61—81no—
187D244—22no—
188D244—22no—
189D244—41no—
190D244—41no—
191C4×D61—81no—
192C4×D61—81no—
193C4×D61—81no—
194C4×D61—81no—
195Dic122—22no—
196Dic122—22no—
197Dic122—41no—
198Dic122—41no—
199Dic122—42no—
200Dic122—42no—
201Dic122—81no—
202Dic122—81no—
203C8×C61—42no—
204C8×C61—42no—
205#92418—42no—
206#10232—611nomaximal, Sylow
207C22×C61#39211yescharacteristic
208C22×C61#44811yescharacteristic
209C22×C61#44911yescharacteristic
210C22×C61#45011yescharacteristic
211C22×C61#45211yescharacteristic
212C22×C61#45511yescharacteristic
213C22×C61#45611yescharacteristic
214C2×D61—42no—
215C2×D61—42no—
216C2×D61—42no—
217C2×D61—81no—
218C2×D61—81no—
219C2×D61—81no—
220C2×D61—81no—
221C4×C61—21no—
222C4×C61—21no—
223C4×C61—82no—
224C4×C61#44811yescharacteristic
225C4×C61#44911yescharacteristic
226C4×C61#45011yescharacteristic
227C4×C61#45211yescharacteristic
228C4×C61#46511yescharacteristic
229C4×C61#46511yescharacteristic
230C4×C61#46811yescharacteristic
231C4×C61#46811yescharacteristic
232Dic61—42no—
233Dic61—82no—
234Dic61—81no—
235Dic61—81no—
236C2×#475—611no—
237C2×#461—611no—
238#2538—611no—
239#1990—611no—
240C2×Q8⋊C8—611no—
241C2×D4⋊C8—611no—
242#1296D6111yescharacteristic, complemented
243C2×C61#164211yescharacteristic
244C2×C61#164311yescharacteristic
245C2×C61#165011yescharacteristic
246C2×C61#165111yescharacteristic
247C2×C61#200011yescharacteristic
248C2×C61#200011yescharacteristic
249C2×C61#200711yescharacteristic
250D61—82no—
251C22×SD16—1221no—
252C2×C4⋊Q8—611no—
253C2×C22⋊Q8—1221no—
254C2×C4×Q8—611no—
255C2×C4×D4—611no—
256#475—1222no—
257#475—1222no—
258#461—1222no—
259#461—1222no—
260C2×#106—1221no—
261C2×C4⋊C8C2×D6111yescharacteristic
262C2×C4⋊C8C2×D6111yescharacteristic
263C2×#103—1221no—
264C2×#103—1221no—
265C2×C4×C8—611no—
266#396—1222no—
267#390—1221no—
268#389—1221no—
269#384C2×D6111yescharacteristic
270#380—1221no—
271#340—1222no—
272Q8⋊C8—1222no—
273D4⋊C8—1222no—
274C61#1023211yescharacteristic, complemented, Sylow
275C22×Q8—611no—
276C22×Q8—1221no—
277C22×D4—611no—
278C23×C4—1221no—
279C2×SD16—1224no—
280C2×SD16—2442no—
281C2×SD16—2442no—
282C22×C8—21no—
283C22×C8—21no—
284C22×C8—1221no—
285C4⋊Q8—612no—
286C4⋊Q8—1221no—
287C4⋊Q8—1221no—
288C4⋊Q8—1221no—
289C22⋊Q8—2442no—
290C22⋊Q8—2442no—
291C4×Q8—1221no—
292C4×Q8—1221no—
293C4×Q8—1221no—
294C4×Q8—1221no—
295C4×D4—1221no—
296C4×D4—1221no—
297C4×D4—1221no—
298C4×D4—1221no—
299C2×C4⋊C4—21no—
300C2×C4⋊C4—21no—
301C2×C4⋊C4—611no—
302C2×C4⋊C4—611no—
303C2×C4⋊C4—1221no—
304C2×C4⋊C4—1221no—
305C2×C4⋊C4—1222no—
306C2×C4⋊C4—1221no—
307C2×C4⋊C4D24412yes—
308C2×C22⋊C4—1222no—
309C2×C22⋊C4—1222no—
310C2×C22⋊C4—1221no—
311C2×C42—1221no—
312C2×C42C22×D6111yescharacteristic
313#106—1224no—
314C4⋊C8—21no—
315C4⋊C8—21no—
316C4⋊C8D24412yes—
317C4⋊C8D24412yes—
318#103—1224no—
319#103—1224no—
320C4×C8—1221no—
321C4×C8—1221no—
322#95—1222no—
323C24—1221no—
324C2×Q8—612no—
325C2×Q8—1221no—
326C2×Q8—1221no—
327C2×Q8—1221no—
328C2×Q8—1222no—
329C2×Q8—1221no—
330C2×Q8—1221no—
331C2×Q8—2441no—
332C2×Q8—2441no—
333C2×Q8—2441no—
334C2×Q8—2441no—
335C2×Q8—2441no—
336C2×D4—612no—
337C2×D4—1221no—
338C2×D4—1221no—
339C2×D4—1221no—
340C2×D4—1221no—
341C2×D4—1221no—
342C22×C4—22no—
343C22×C4—1221no—
344C22×C4—1221no—
345C22×C4—1221no—
346C22×C4—2441no—
347C22×C4—2441no—
348C22×C4—2441no—
349C22×C4—2441no—
350C22×C4—2441no—
351C22×C4—2441no—
352C22×C4—2441no—
353C22×C4C2×D24411yescharacteristic
354C22×C4D4×D6111yescharacteristic
355C22×C4D4×D6111yescharacteristic
356SD16—2448no—
357C2×C8—22no—
358C2×C8—22no—
359C2×C8—41no—
360C2×C8—41no—
361C2×C8—41no—
362C2×C8—41no—
363C2×C8—1222no—
364C2×C8—2441no—
365C2×C8—2441no—
366C4⋊C4—42no—
367C4⋊C4—41no—
368C4⋊C4—41no—
369C4⋊C4—41no—
370C4⋊C4—41no—
371C4⋊C4—1221no—
372C4⋊C4—1222no—
373C4⋊C4—1221no—
374C4⋊C4—1221no—
375C4⋊C4—1221no—
376C4⋊C4—1222no—
377C4⋊C4—2444no—
378C4⋊C4—2441no—
379C4⋊C4—2441no—
380C4⋊C4—2441no—
381C4⋊C4—2441no—
382C22⋊C4—4882no—
383C22⋊C4—2444no—
384C22⋊C4—2441no—
385C22⋊C4—2441no—
386C42—2441no—
387C42—2441no—
388C42C2×D24411yescharacteristic
389C42C2×D24411yescharacteristic
390C42D4×D6111yescharacteristic
391C42#1175822611yescharacteristic
392C23—1222no—
393C23—2441no—
394C23—2441no—
395C23—2441no—
396C23—2441no—
397C23—2441no—
398C23—2441no—
399C23#1451974711yescharacteristic
400Q8—1222no—
401Q8—1222no—
402Q8—4881no—
403Q8—4881no—
404Q8—2442no—
405Q8—2442no—
406Q8—2441no—
407Q8—2441no—
408D4—1222no—
409D4—1222no—
410D4—2441no—
411D4—2441no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—42no—
415C2×C4—42no—
416C2×C4—42no—
417C2×C4—1222no—
418C2×C4—4881no—
419C2×C4—4881no—
420C2×C4—4881no—
421C2×C4—4881no—
422C2×C4—4881no—
423C2×C4—4881no—
424C2×C4—2441no—
425C2×C4—2441no—
426C2×C4—2441no—
427C2×C4—2441no—
428C2×C4—2441no—
429C2×C4—2441no—
430C2×C4—2442no—
431C2×C4—2441no—
432C2×C4—2441no—
433C2×C4#1451974711yescharacteristic
434C2×C4#1451974711yescharacteristic
435C2×C4#1451975211yescharacteristic
436C2×C4#1451975211yescharacteristic
437C2×C4#1451975211yescharacteristic
438C2×C4#1451977411yescharacteristic
439C2×C4SD16×D6111yescharacteristic
440C2×C4SD16×D6111yescharacteristic
441C2×C4#1451979811yescharacteristic
442C2×C4#1451979811yescharacteristic
443C2×C4#1451980111yescharacteristic
444C2×C4#1451980111yescharacteristic
445C2×C4#1451980911yescharacteristic
446C2×C4#1451980911yescharacteristic
447C8—42no—
448C8—42no—
449C8—2442no—
450C22—4881no—
451C22—4881no—
452C22—4881no—
453C22—4881no—
454C22—2442no—
455C22—2442no—
456C22—2442no—
457C22#1683967211yescharacteristic
458C22#1683990211yescharacteristic
459C22#1683990811yescharacteristic
460C22#1683991411yescharacteristic
461C22#1683992711yescharacteristic
462C22#1683994211yescharacteristic
463C22#1683994711yescharacteristic
464C4—21no—
465C4—21no—
466C4—82no—
467C4—4881no—
468C4—4882no—
469C4—4881no—
470C4—2442no—
471C4#1683990211yescharacteristic
472C4#1683990811yescharacteristic
473C4#1683991411yescharacteristic
474C4#1683992711yescharacteristic
475C4#1683999211yescharacteristic
476C4#1683999211yescharacteristic
477C4#1684000911yescharacteristic
478C4#1684000911yescharacteristic
479C2—4882no—
480C2#2144502011yescharacteristic
481C2#2144502711yescharacteristic
482C2#2144507611yescharacteristic
483C2#2144508311yescharacteristic
484C2#2144682511yescharacteristic
485C2#2144682511yescharacteristic
486C2#2144686811yescharacteristic
subgroupG/H
centerC23#14519747
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1296C2
socleC23×C61#120
prime radicalC22×D244D4
hypercenter#1296D61
hypocenterC61#10232
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1296

Complements

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

NH ≅ G/Ntype
1. C2×#16840048C2semidirect
4. #21446779C2semidirect
5. C2×#16839492C2semidirect
7. C61×#1296C2semidirect
111. C2×Dic122SD16semidirect
242. #1296D61semidirect
274. C61#10232semidirect

Maximal subgroups

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

subgroupindex
C2×#168400482
C2×#168399682
#214507422
#214467792
C2×#168394922
C2×#168394892
C61×#12962
#1023261