Finite Group Databasebeta

← #29663560

Subgroups — #29663560

Order 15616.

662 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21457126C211yesmaximal, characteristic
2#21456949C211yesmaximal, characteristic, complemented
3#21456212C211yesmaximal, characteristic, complemented
4#21454562C211yesmaximal, characteristic, complemented
5#21445393C212yesmaximal, complemented
6#21445351C212yesmaximal, complemented
7#21445269C212yesmaximal, complemented
8#21445227C212yesmaximal, complemented
9#21444572C211yesmaximal, characteristic, complemented
10C2×#16839510C211yesmaximal, characteristic, complemented
11C61×#1540C211yesmaximal, characteristic, complemented
12C2×#14519783—21no—
13#16840312C2211yescharacteristic
14C2×#14519777C2211yescharacteristic
15#16840160—21no—
16#16840121—22no—
17#16840112C2212yes—
18#16840109—21no—
19#16840108C2212yes—
20#16840081—22no—
21#16840053C2212yes—
22#16840053C2212yes—
23#16840042—21no—
24#16840039C2212yes—
25#16839996—22no—
26#16839957—21no—
27#16839954C2212yes—
28#16839839C2212yes—
29#16839832—22no—
30#16839827C2212yes—
31C2×C4⋊#92418C2211yescharacteristic
32#16839763—21no—
33#16839763—21no—
34#16839728—21no—
35C4×#11758194C2211yescharacteristic
36#16839514C2212yes—
37#16839512C2212yes—
38#16839510C2212yes—
39#16839510C2212yes—
40C61×#532C2211yescharacteristic
41C61×#431C2211yescharacteristic
42C2×C4⋊C8×C61C2211yescharacteristic
43C61×#332C2211yescharacteristic
44C61×#332C2211yescharacteristic
45C61×#331C2211yescharacteristic
46C61×#331C2211yescharacteristic
47C2×#11758222—21no—
48C22×Dic122—21no—
49C2×#11758199—22no—
50#14519783—44no—
51C2×#11758194D411yescharacteristic
52C2×#11758194D411yescharacteristic
53C2×#11758189—22no—
54C22×#92418—21no—
55C2×C8×D61—22no—
56#14519777—21no—
57#14519777—21no—
58#14519777—21no—
59#14519777D411yescharacteristic
60#14519777C2312yes—
61#14519774D411yescharacteristic
62#14519765—21no—
63#14519751—21no—
64#14519751D412yes—
65C4×D244—21no—
66C4×D244C2312yes—
67C2×C4⋊Dic61—21no—
68C2×C4⋊Dic61—21no—
69#14519710—22no—
70#14519709—22no—
71#14519709—22no—
72C4⋊#92418—21no—
73C4⋊#92418C2312yes—
74#14519701—22no—
75#14519701—22no—
76#14519699—22no—
77#14519699—22no—
78#14519698—22no—
79#14519698—22no—
80#14519698—22no—
81#14519697—22no—
82#14519689—22no—
83#14519689—22no—
84#14519688D412yes—
85C4×#92418C2312yes—
86C2×#41×C61—21no—
87C22×C8×C61—21no—
88C4⋊Q8×C61C2311yescharacteristic
89#127×C61C2311yescharacteristic
90#124×C61—21no—
91#121×C61—21no—
92#121×C61—21no—
93C4×D4×C61—21no—
94C4×D4×C61—21no—
95C2×C42×C61C2311yescharacteristic
96C4⋊C8×C61—21no—
97C4⋊C8×C61C2311yescharacteristic
98C4⋊C8×C61C2311yescharacteristic
99C4⋊C8×C61C2311yescharacteristic
100C4⋊C8×C61C2311yescharacteristic
101C22⋊C8×C61—21no—
102C4×C8×C61—21no—
103#41×C61—42no—
104#41×C61—42no—
105C2×Q8×C61—21no—
106C2×D4×C61—21no—
107C2×D4×C61—21no—
108C2×D4×C61—21no—
109C2×D4×C61—41no—
110C22×C4×C61—41no—
111C22×C4×C61C2×D411yescharacteristic
112C22×C4×C61C2×D411yescharacteristic
113C22×C4×C61#4111yescharacteristic
114C2×C22⋊D61—22no—
115C22×Dic61—41no—
116#11758222—42no—
117#11758222—42no—
118C2×D244—21no—
119C2×D244—21no—
120C2×D244C2×D412yes—
121C2×C4×D61—22no—
122C2×Dic122—21no—
123C2×Dic122—22no—
124C2×Dic122—41no—
125C2×Dic122—82no—
126C2×C8×C61—21no—
127C2×C8×C61—21no—
128C2×C8×C61—21no—
129C2×C8×C61—21no—
130C2×C8×C61—42no—
131C4⋊C4×C61—21no—
132C4⋊C4×C61—21no—
133C22⋊C4×C61—41no—
134C22⋊C4×C61—41no—
135C42×C61C2×D411yescharacteristic
136C42×C61C2×D411yescharacteristic
137C42×C61#4111yescharacteristic
138C42×C61C2411yescharacteristic
139#11758199—82no—
140#11758198—22no—
141#11758198—22no—
142C4⋊Dic61—21no—
143C4⋊Dic61—22no—
144C4⋊Dic61—22no—
145C4⋊Dic61—41no—
146C4⋊Dic61—41no—
147C4⋊Dic61C2×D412yes—
148#11758194—22no—
149#11758194—22no—
150C2×#92418—22no—
151C2×#92418—81no—
152C2×#92418C2×D412yes—
153C2×#92418C2×D412yes—
154#11758189—44no—
155C8×D61—44no—
156C23×C61—41no—
157C23×C61#12111yescharacteristic
158C22×D61—22no—
159Q8×C61—41no—
160Q8×C61—41no—
161D4×C61—41no—
162D4×C61—41no—
163D4×C61—41no—
164D4×C61—41no—
165D4×C61—81no—
166D4×C61—82no—
167C2×C4×C61—21no—
168C2×C4×C61—21no—
169C2×C4×C61—41no—
170C2×C4×C61—41no—
171C2×C4×C61—82no—
172C2×C4×C61#12111yescharacteristic
173C2×C4×C61#12111yescharacteristic
174C2×C4×C61#12111yescharacteristic
175C2×C4×C61#13512yes—
176C2×C4×C61AGL(1,ℤ/8)12yes—
177C2×C4×C61C22×D411yescharacteristic
178C2×C4×C61C22×D411yescharacteristic
179C2×C4×C61C2×#4111yescharacteristic
180C22⋊D61—44no—
181C2×Dic61—22no—
182C2×Dic61—42no—
183C2×Dic61—82no—
184D244—22no—
185D244—22no—
186D244—42no—
187D244—81no—
188C4×D61—42no—
189C4×D61—42no—
190Dic122—42no—
191Dic122—82no—
192Dic122—82no—
193C8×C61—41no—
194C8×C61—41no—
195C8×C61—41no—
196C8×C61—41no—
197#92418—22no—
198#92418—22no—
199#92418—42no—
200#19236—611nomaximal, Sylow
201C22×C61—21no—
202C22×C61—21no—
203C22×C61—81no—
204C22×C61—81no—
205C22×C61—81no—
206C22×C61#46312yes—
207C22×C61C2×#12111yescharacteristic
208C2×D61—42no—
209C2×D61—42no—
210C2×D61—42no—
211C4×C61—21no—
212C4×C61—21no—
213C4×C61—21no—
214C4×C61—81no—
215C4×C61#46312yes—
216C4×C61C2×#13511yescharacteristic
217C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
218C4×C61#57711yescharacteristic
219C4×C61#57811yescharacteristic
220Dic61—42no—
221Dic61—82no—
222#3245—611no—
223#3227—611no—
224#3141—611no—
225#2935—611no—
226#1703—612no—
227#1697—612no—
228#1683—612no—
229#1677—612no—
230#1565—611no—
231C2×#333—611no—
232#1540D6111yescharacteristic, complemented
233C2×C61—22no—
234C2×C61—161no—
235C2×C61C2×#46311yescharacteristic
236C2×C61#306311yescharacteristic
237C2×C61#306811yescharacteristic
238D61—82no—
239C2×#131—1221no—
240#532—611no—
241#532C2×D6111yescharacteristic
242C2×C4⋊Q8—611no—
243#498—1221no—
244#489—1222no—
245#487—612no—
246#486—612no—
247#486—1221no—
248#481—1222no—
249#476—612no—
250#476—612no—
251#474—612no—
252#474—1221no—
253#466—1222no—
254#459—612no—
255#459—1221no—
256#436—612no—
257#435—1222no—
258C8×D4—612no—
259#431C2×D6111yescharacteristic
260C2×C4⋊C8—611no—
261C2×C4⋊C8C2×D6111yescharacteristic
262#417—1221no—
263#417—1221no—
264#408—1221no—
265C4×M16—611no—
266#335—612no—
267#334—612no—
268#333—612no—
269#333—612no—
270#332C2×D6111yescharacteristic
271#332C2×D6111yescharacteristic
272#331C2×D6111yescharacteristic
273#331C2×D6111yescharacteristic
274C61#1923611yescharacteristic, complemented, Sylow
275C2×#41—21no—
276C2×#41—1221no—
277C22×Q8—1221no—
278C2×D8—1222no—
279#131—2444no—
280C2×M16—611no—
281C2×M16—611no—
282C2×M16—1222no—
283C22×C8—21no—
284C22×C8—1222no—
285C22×C8—1221no—
286C4⋊Q8—611no—
287C4⋊Q8—612no—
288C4⋊Q8—1221no—
289C4⋊Q8—1221no—
290C4⋊Q8—1221no—
291C4⋊Q8C22×D6111yescharacteristic
292#127—611no—
293#127C22×D6111yescharacteristic
294#124—21no—
295#124—1221no—
296#121—21no—
297#121—21no—
298#121—612no—
299#121—1221no—
300C4×D4—21no—
301C4×D4—21no—
302C4×D4—612no—
303C4×D4—1221no—
304C2×C4⋊C4—1221no—
305C2×C4⋊C4—1221no—
306C2×C42C22×D6111yescharacteristic
307#107—1222no—
308#106—1222no—
309#106—1222no—
310C4⋊C8—21no—
311C4⋊C8—612no—
312C4⋊C8—1221no—
313C4⋊C8C22×D6111yescharacteristic
314C4⋊C8C22×D6111yescharacteristic
315C4⋊C8C22×D6111yescharacteristic
316C4⋊C8C22×D6111yescharacteristic
317#103—1222no—
318#103—1222no—
319#102—1222no—
320#102—1222no—
321#102—1222no—
322#102—1222no—
323#102—1222no—
324#102—1222no—
325C22⋊C8—21no—
326C22⋊C8—1222no—
327C22⋊C8—1222no—
328#97—612no—
329C4×C8—21no—
330C4×C8—612no—
331#41—42no—
332#41—42no—
333#41—2442no—
334#41—2442no—
335C2×Q8—21no—
336C2×Q8—1221no—
337C2×Q8—1222no—
338C2×Q8—4882no—
339C2×Q8—2441no—
340C2×D4—21no—
341C2×D4—21no—
342C2×D4—21no—
343C2×D4—41no—
344C2×D4—612no—
345C2×D4—1222no—
346C2×D4—1221no—
347C2×D4—1221no—
348C22×C4—41no—
349C22×C4—1222no—
350C22×C4—2441no—
351C22×C4#1175822211yescharacteristic
352C22×C4D4×D6111yescharacteristic
353C22×C4D4×D6111yescharacteristic
354D8—4882no—
355M16—1222no—
356M16—1222no—
357M16—2444no—
358C2×C8—21no—
359C2×C8—21no—
360C2×C8—21no—
361C2×C8—21no—
362C2×C8—42no—
363C2×C8—612no—
364C2×C8—612no—
365C2×C8—1222no—
366C2×C8—4881no—
367C2×C8—2444no—
368C4⋊C4—21no—
369C4⋊C4—21no—
370C4⋊C4—612no—
371C4⋊C4—1221no—
372C4⋊C4—1222no—
373C4⋊C4—1222no—
374C4⋊C4—2441no—
375C4⋊C4—2441no—
376C22⋊C4—41no—
377C22⋊C4—41no—
378C22⋊C4—1222no—
379C22⋊C4—1222no—
380C42#1175822211yescharacteristic
381C42D4×D6111yescharacteristic
382C42D4×D6111yescharacteristic
383C42C23×D6111yescharacteristic
384C23—41no—
385C23—1222no—
386C23#1451975011yescharacteristic
387Q8—41no—
388Q8—41no—
389Q8—4882no—
390Q8—4882no—
391Q8—2442no—
392D4—41no—
393D4—41no—
394D4—41no—
395D4—41no—
396D4—81no—
397D4—82no—
398D4—1222no—
399D4—1222no—
400D4—4881no—
401D4—2444no—
402D4—2442no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—82no—
408C2×C4—1222no—
409C2×C4—4882no—
410C2×C4—2442no—
411C2×C4—2442no—
412C2×C4—2442no—
413C2×C4#1451975011yescharacteristic
414C2×C4#1451975011yescharacteristic
415C2×C4#1451975011yescharacteristic
416C2×C4#1451979812yes—
417C2×C4#1451980112yes—
418C2×C4C2×D4×D6111yescharacteristic
419C2×C4C2×D4×D6111yescharacteristic
420C2×C4C2×#1175822211yescharacteristic
421C8—41no—
422C8—41no—
423C8—41no—
424C8—41no—
425C8—1222no—
426C8—1222no—
427C8—2442no—
428C22—21no—
429C22—21no—
430C22—81no—
431C22—81no—
432C22—81no—
433C22—2442no—
434C22—2442no—
435C22—2442no—
436C22#1683997612yes—
437C22C2×#1451975011yescharacteristic
438C4—21no—
439C4—21no—
440C4—21no—
441C4—81no—
442C4—4882no—
443C4—2442no—
444C4#1683997612yes—
445C4C2×#1451979811yescharacteristic
446C4C2×#1451980111yescharacteristic
447C4#1684056911yescharacteristic
448C4#1684057611yescharacteristic
449C2—22no—
450C2—161no—
451C2—4882no—
452C2C2×#1683997611yescharacteristic
453C2#2145551311yescharacteristic
454C2#2145555011yescharacteristic
subgroupG/H
centerC22C2×#14519750
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#1540C2
socleC22×C61C2×#121
prime radical#21457126C2
hypercenter#1540D61
hypocenterC61#19236
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1540

Complements

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

NH ≅ G/Ntype
2. #21456949C2semidirect
3. #21456212C2semidirect
4. #21454562C2semidirect
5. #21445393C2semidirect
6. #21445351C2semidirect
7. #21445269C2semidirect
8. #21445227C2semidirect
9. #21444572C2semidirect
10. C2×#16839510C2semidirect
11. C61×#1540C2semidirect
232. #1540D61semidirect
274. C61#19236semidirect

Maximal subgroups

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

subgroupindex
#214571262
#214569492
#214562122
#214545622
#214453932
#214453512
#214452692
#214452272
#214445722
C2×#168395102
C61×#15402
#1923661