Finite Group Databasebeta

← #29663199

Subgroups — #29663199

Order 15616.

660 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21457136C211yesmaximal, characteristic, complemented
2#21457126C211yesmaximal, characteristic
3#21456141C211yesmaximal, characteristic, complemented
4#21454530C211yesmaximal, characteristic, complemented
5#21445365C212yesmaximal, complemented
6#21445351C212yesmaximal, complemented
7#21445269C212yesmaximal, complemented
8#21445255C212yesmaximal, complemented
9C2×#16839514C211yesmaximal, characteristic, complemented
10#21444510C211yesmaximal, characteristic, complemented
11C61×#1547C211yesmaximal, characteristic, complemented
12C2×#14519785—21no—
13#16840319C2211yescharacteristic
14#16840312C2211yescharacteristic
15#16840116—21no—
16#16840116—21no—
17#16840112C2211yescharacteristic
18#16840112C2211yescharacteristic
19#16840108C2211yescharacteristic
20#16840108C2211yescharacteristic
21#16840053C2212yes—
22#16840048—21no—
23#16840042—21no—
24#16840039C2212yes—
25#16839996—22no—
26#16839991—22no—
27#16839968C2212yes—
28#16839963—21no—
29#16839957—21no—
30#16839954C2212yes—
31#16839839—21no—
32#16839839C2212yes—
33#16839827—21no—
34#16839827C2212yes—
35C2×C4⋊#92418C2211yescharacteristic
36#16839758—21no—
37#16839758—21no—
38#16839730—21no—
39C2×C4×#92418C2211yescharacteristic
40#16839514C2212yes—
41#16839514C2212yes—
42#16839510C2212yes—
43#16839507C2212yes—
44C61×#532C2211yescharacteristic
45C61×#423C2211yescharacteristic
46C2×C4⋊C8×C61C2211yescharacteristic
47C61×#332C2212yes—
48C61×#331C2212yes—
49C2×#11758222—21no—
50C2×#11758190—22no—
51C2×#11758199—22no—
52#14519785—44no—
53C2×#11758189—22no—
54C22×#92418—21no—
55C22×#92418D411yescharacteristic
56C22×#92418D411yescharacteristic
57C2×C8×D61—22no—
58#14519777D411yescharacteristic
59#14519777C2311yescharacteristic
60#14519777C2311yescharacteristic
61#14519774D411yescharacteristic
62#14519769—21no—
63#14519765—21no—
64#14519756—21no—
65#14519756—21no—
66#14519751—21no—
67#14519751D412yes—
68C4×Dic122—21no—
69C4×Dic122—21no—
70C4×D244—21no—
71C4×D244C2312yes—
72#14519736—21no—
73#14519710—22no—
74#14519709—22no—
75C4⋊#92418—21no—
76C4⋊#92418C2312yes—
77#14519702—22no—
78#14519701—21no—
79#14519701—21no—
80#14519701—21no—
81#14519701—21no—
82#14519699—22no—
83#14519698—22no—
84#14519698—21no—
85#14519698—21no—
86#14519698—21no—
87#14519698—21no—
88#14519697—22no—
89#14519689—22no—
90#14519689—22no—
91C4×#92418D411yescharacteristic
92C4×#92418D411yescharacteristic
93C4×#92418C2311yescharacteristic
94C4×#92418C2311yescharacteristic
95C2×#41×C61—21no—
96C2×M16×C61—21no—
97C22×C8×C61—21no—
98C4⋊Q8×C61C2311yescharacteristic
99#127×C61C2311yescharacteristic
100#124×C61—21no—
101#121×C61—21no—
102#121×C61—21no—
103C4×D4×C61—21no—
104C4×D4×C61—21no—
105C2×C42×C61C2311yescharacteristic
106C4⋊C8×C61—21no—
107C4⋊C8×C61—21no—
108C4⋊C8×C61C2312yes—
109C4⋊C8×C61C2312yes—
110#41×C61—42no—
111#41×C61—42no—
112C2×Q8×C61—21no—
113C2×D4×C61—21no—
114C2×D4×C61—21no—
115C2×D4×C61—21no—
116C2×D4×C61—41no—
117C22×C4×C61—41no—
118C22×C4×C61C2×D411yescharacteristic
119C22×C4×C61C2×D411yescharacteristic
120C22×C4×C61#4111yescharacteristic
121C2×C22⋊D61—22no—
122#11758222—42no—
123#11758222—42no—
124C2×D244—21no—
125C2×D244—21no—
126C2×D244C2×D412yes—
127C2×C4×D61—22no—
128C2×Dic122—21no—
129C2×Dic122—21no—
130C2×Dic122—21no—
131M16×C61—42no—
132C2×C8×C61—22no—
133C2×C8×C61—22no—
134C2×C8×C61—81no—
135C4⋊C4×C61—21no—
136C4⋊C4×C61—21no—
137C22⋊C4×C61—41no—
138C22⋊C4×C61—41no—
139C42×C61C2×D411yescharacteristic
140C42×C61C2×D411yescharacteristic
141C42×C61#4111yescharacteristic
142C42×C61C2411yescharacteristic
143C22⋊Dic61—41no—
144#11758199—82no—
145#11758198—22no—
146#11758198—22no—
147C4⋊Dic61—21no—
148C4⋊Dic61—21no—
149C4⋊Dic61—21no—
150C4⋊Dic61—21no—
151C4⋊Dic61—21no—
152C4⋊Dic61C2×D412yes—
153#11758196—41no—
154#11758196—41no—
155C4×Dic61—41no—
156C2×#92418—22no—
157C2×#92418—22no—
158C2×#92418—22no—
159C2×#92418—81no—
160C2×#92418C2×D411yescharacteristic
161C2×#92418C2×D411yescharacteristic
162C2×#92418C2×D411yescharacteristic
163C2×#92418C2×D411yescharacteristic
164#11758190—82no—
165#11758189—44no—
166C8×D61—44no—
167C23×C61—41no—
168C23×C61#12111yescharacteristic
169C22×D61—22no—
170Q8×C61—41no—
171Q8×C61—41no—
172D4×C61—41no—
173D4×C61—41no—
174D4×C61—41no—
175D4×C61—41no—
176D4×C61—81no—
177D4×C61—82no—
178C2×C4×C61—21no—
179C2×C4×C61—21no—
180C2×C4×C61—41no—
181C2×C4×C61—41no—
182C2×C4×C61—82no—
183C2×C4×C61#12111yescharacteristic
184C2×C4×C61#12111yescharacteristic
185C2×C4×C61#12111yescharacteristic
186C2×C4×C61#13512yes—
187C2×C4×C61AGL(1,ℤ/8)12yes—
188C2×C4×C61C22×D411yescharacteristic
189C2×C4×C61C22×D411yescharacteristic
190C2×C4×C61C2×#4111yescharacteristic
191C22⋊D61—44no—
192C2×Dic61—22no—
193C2×Dic61—41no—
194C2×Dic61—41no—
195D244—22no—
196D244—22no—
197D244—42no—
198D244—42no—
199C4×D61—42no—
200C4×D61—42no—
201Dic122—42no—
202Dic122—41no—
203Dic122—41no—
204Dic122—81no—
205C8×C61—42no—
206C8×C61—42no—
207#92418—21no—
208#92418—21no—
209#92418—21no—
210#92418—21no—
211#92418—42no—
212#19201—611nomaximal, Sylow
213C22×C61—21no—
214C22×C61—21no—
215C22×C61—81no—
216C22×C61—81no—
217C22×C61—81no—
218C22×C61#46312yes—
219C22×C61C2×#12111yescharacteristic
220C2×D61—42no—
221C2×D61—42no—
222C2×D61—42no—
223C4×C61—21no—
224C4×C61—21no—
225C4×C61—21no—
226C4×C61—81no—
227C4×C61#46312yes—
228C4×C61C2×#13511yescharacteristic
229C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
230C4×C61#57611yescharacteristic
231C4×C61#57811yescharacteristic
232Dic61—42no—
233Dic61—81no—
234Dic61—81no—
235#3246—611no—
236#3245—611no—
237#3131—611no—
238#2931—611no—
239#1699—612no—
240#1697—612no—
241#1683—612no—
242#1681—612no—
243C2×#335—611no—
244#1550—611no—
245#1547D6111yescharacteristic, complemented
246C2×C61—22no—
247C2×C61—161no—
248C2×C61C2×#46311yescharacteristic
249C2×C61#306111yescharacteristic
250C2×C61#306711yescharacteristic
251D61—82no—
252C2×#131—1221no—
253#533—611no—
254#532—611no—
255#532C2×D6111yescharacteristic
256#488—1221no—
257#488—1221no—
258#487—611no—
259#487—611no—
260#486—611no—
261#486—611no—
262#476—612no—
263#475—1221no—
264#474—612no—
265#474—1221no—
266#466—1222no—
267#465—1222no—
268#461—612no—
269#460—1221no—
270#459—612no—
271#459—1221no—
272#436—612no—
273#436—1221no—
274C8×D4—612no—
275C8×D4—1221no—
276#423C2×D6111yescharacteristic
277C2×C4⋊C8—611no—
278C2×C4⋊C8C2×D6111yescharacteristic
279#416—1221no—
280#416—1221no—
281#408—1221no—
282C2×C4×C8—611no—
283#335—612no—
284#335—612no—
285#333—612no—
286#332—612no—
287#332C2×D6112yes—
288#331C2×D6112yes—
289C61#1920111yescharacteristic, complemented, Sylow
290C2×#41—21no—
291C2×#41—1221no—
292C2×SD16—1222no—
293C2×D8—1222no—
294#131—2444no—
295C2×M16—21no—
296C2×M16—1222no—
297C22×C8—21no—
298C22×C8—611no—
299C22×C8—611no—
300C22×C8—1222no—
301C22×C8—1221no—
302C4⋊Q8—611no—
303C4⋊Q8—611no—
304C4⋊Q8—611no—
305C4⋊Q8C22×D6111yescharacteristic
306#127—611no—
307#127C22×D6111yescharacteristic
308#125—1221no—
309#124—21no—
310#124—1221no—
311C22⋊Q8—1221no—
312C22⋊Q8—1221no—
313#121—21no—
314#121—21no—
315#121—612no—
316#121—1221no—
317C4×Q8—1221no—
318C4×Q8—1221no—
319C4×D4—21no—
320C4×D4—21no—
321C4×D4—612no—
322C4×D4—1221no—
323#117—1221no—
324C2×C42C22×D6111yescharacteristic
325#107—1222no—
326#106—1222no—
327C4⋊C8—21no—
328C4⋊C8—21no—
329C4⋊C8—612no—
330C4⋊C8—1221no—
331C4⋊C8C22×D6112yes—
332C4⋊C8C22×D6112yes—
333#103—1222no—
334#103—1221no—
335#103—1221no—
336#103—1221no—
337#103—1221no—
338#102—1222no—
339#102—1222no—
340#102—1222no—
341#102—1221no—
342#102—1221no—
343#102—1221no—
344#102—1221no—
345C22⋊C8—1222no—
346C22⋊C8—1222no—
347C4×C8—611no—
348C4×C8—611no—
349C4×C8—611no—
350C4×C8—611no—
351#41—42no—
352#41—42no—
353#41—2442no—
354#41—2442no—
355C2×Q8—21no—
356C2×Q8—1221no—
357C2×Q8—1221no—
358C2×Q8—1221no—
359C2×D4—21no—
360C2×D4—21no—
361C2×D4—21no—
362C2×D4—41no—
363C2×D4—612no—
364C2×D4—1222no—
365C2×D4—1221no—
366C2×D4—1221no—
367C22×C4—41no—
368C22×C4—1222no—
369C22×C4#1175822211yescharacteristic
370C22×C4D4×D6111yescharacteristic
371C22×C4D4×D6111yescharacteristic
372SD16—4882no—
373D8—4882no—
374M16—42no—
375M16—2444no—
376C2×C8—22no—
377C2×C8—22no—
378C2×C8—81no—
379C2×C8—611no—
380C2×C8—611no—
381C2×C8—611no—
382C2×C8—611no—
383C2×C8—1222no—
384C2×C8—1222no—
385C2×C8—1222no—
386C2×C8—4881no—
387C2×C8—2444no—
388C4⋊C4—21no—
389C4⋊C4—21no—
390C4⋊C4—612no—
391C4⋊C4—1221no—
392C4⋊C4—1221no—
393C4⋊C4—1221no—
394C4⋊C4—1221no—
395C4⋊C4—1221no—
396C4⋊C4—2441no—
397C4⋊C4—2441no—
398C22⋊C4—41no—
399C22⋊C4—41no—
400C22⋊C4—1222no—
401C22⋊C4—1222no—
402C22⋊C4—2441no—
403C42—2441no—
404C42#1175822211yescharacteristic
405C42D4×D6111yescharacteristic
406C42D4×D6111yescharacteristic
407C42C23×D6111yescharacteristic
408C23—41no—
409C23—1222no—
410C23#1451975011yescharacteristic
411Q8—41no—
412Q8—41no—
413Q8—4881no—
414Q8—2441no—
415Q8—2441no—
416Q8—2442no—
417D4—41no—
418D4—41no—
419D4—41no—
420D4—41no—
421D4—81no—
422D4—82no—
423D4—1222no—
424D4—1222no—
425D4—2442no—
426D4—2444no—
427D4—2442no—
428C2×C4—21no—
429C2×C4—21no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—82no—
433C2×C4—1222no—
434C2×C4—2441no—
435C2×C4—2441no—
436C2×C4—2442no—
437C2×C4—2442no—
438C2×C4#1451975011yescharacteristic
439C2×C4#1451975011yescharacteristic
440C2×C4#1451975011yescharacteristic
441C2×C4#1451979812yes—
442C2×C4#1451980112yes—
443C2×C4C2×D4×D6111yescharacteristic
444C2×C4C2×D4×D6111yescharacteristic
445C2×C4C2×#1175822211yescharacteristic
446C8—42no—
447C8—42no—
448C8—1221no—
449C8—1221no—
450C8—1221no—
451C8—1221no—
452C8—2442no—
453C22—21no—
454C22—21no—
455C22—81no—
456C22—81no—
457C22—81no—
458C22—2442no—
459C22—2442no—
460C22—2442no—
461C22#1683997612yes—
462C22C2×#1451975011yescharacteristic
463C4—21no—
464C4—21no—
465C4—21no—
466C4—81no—
467C4—4881no—
468C4—4881no—
469C4—2442no—
470C4#1683997612yes—
471C4C2×#1451979811yescharacteristic
472C4C2×#1451980111yescharacteristic
473C4#1684056611yescharacteristic
474C4#1684057811yescharacteristic
475C2—22no—
476C2—161no—
477C2—4882no—
478C2C2×#1683997611yescharacteristic
479C2#2145548811yescharacteristic
480C2#2145553811yescharacteristic
subgroupG/H
centerC22C2×#14519750
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#1547C2
socleC22×C61C2×#121
prime radical#21457126C2
hypercenter#1547D61
hypocenterC61#19201
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1547

Complements

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

NH ≅ G/Ntype
1. #21457136C2semidirect
3. #21456141C2semidirect
4. #21454530C2semidirect
5. #21445365C2semidirect
6. #21445351C2semidirect
7. #21445269C2semidirect
8. #21445255C2semidirect
9. C2×#16839514C2semidirect
10. #21444510C2semidirect
11. C61×#1547C2semidirect
245. #1547D61semidirect
289. C61#19201semidirect

Maximal subgroups

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

subgroupindex
#214571362
#214571262
#214561412
#214545302
#214453652
#214453512
#214452692
#214452552
C2×#168395142
#214445102
C61×#15472
#1920161