Finite Group Databasebeta

← #29576311

Subgroups — #29576311

Order 15616.

512 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455850C211yesmaximal, characteristic
2#21448297C211yesmaximal, characteristic, complemented
3#21446646C211yesmaximal, characteristic
4#21444315C211yesmaximal, characteristic
5#21443720C211yesmaximal, characteristic, complemented
6#21443651C211yesmaximal, characteristic, complemented
7C61×#1487C211yesmaximal, characteristic, complemented
8#16840312C2211yescharacteristic
9#16840080—21no—
10#16840047C412yescomplemented
11#16839962C412yescomplemented
12#16839901—21no—
13C4×#11758201—22no—
14#16839815C2211yescharacteristic
15C2×#14519703—21no—
16C2×#14519703—21no—
17#16839669—21no—
18#16839661—21no—
19#16839648—22no—
20C4×C4⋊Dic61—21no—
21C4×C4⋊Dic61C2211yescharacteristic
22#16839608—21no—
23C42×Dic61C2211yescharacteristic
24#16839497—22no—
25C2×C4×Q8×C61C2211yescharacteristic
26C61×#431C2211yescharacteristic
27C61×#423C2211yescharacteristic
28C61×Q8⋊C8—22no—
29C2×#11758222—21no—
30C2×#11758201—22no—
31#14519777C2×C411yescharacteristic
32#14519774C2×C411yescharacteristic
33#14519765—21no—
34#14519751—21no—
35#14519751—21no—
36C4×D244—21no—
37C4×D244—21no—
38C2×C4⋊Dic61—22no—
39C2×C4⋊Dic61—21no—
40C2×C4×Dic61—21no—
41C2×C4×Dic61—21no—
42C2×C4×Dic61—21no—
43C2×C4×Dic61D411yescharacteristic
44C2×C4×Dic61D411yescharacteristic
45#14519708—22no—
46C4⋊#92418C2×C412yes—
47#14519703—42no—
48#14519703—42no—
49#14519701—22no—
50#14519697—22no—
51C22⋊#92418—21no—
52C4×#92418—21no—
53#14519684—22no—
54#14519684—22no—
55#14519684—22no—
56#14519684D412yes—
57C22×Q8×C61D411yescharacteristic
58C2×M16×C61—21no—
59C4×Q8×C61—21no—
60C4×Q8×C61—21no—
61C4×Q8×C61C2×C412yes—
62C4×Q8×C61D412yes—
63C2×C4⋊C4×C61—21no—
64C2×C4⋊C4×C61D411yescharacteristic
65C2×C42×C61—21no—
66C2×C42×C61C2311yescharacteristic
67C4⋊C8×C61—21no—
68C4⋊C8×C61—21no—
69C4⋊C8×C61—21no—
70C22⋊C8×C61—21no—
71C4×C8×C61—21no—
72C2×Q8×C61—21no—
73C2×Q8×C61—42no—
74C2×Q8×C61C22⋊C412yes—
75C22×C4×C61—21no—
76C22×C4×C61—21no—
77C22×C4×C61C2×D411yescharacteristic
78C22×C4×C61C2×D411yescharacteristic
79C22×C4×C61C2×D411yescharacteristic
80C2×C22⋊D61—41no—
81C22×Dic61—21no—
82C22×Dic61—21no—
83C22×Dic61—22no—
84#11758222—41no—
85#11758222—41no—
86#11758222—41no—
87#11758222—41no—
88C2×D244—21no—
89C2×D244—21no—
90C2×D244—21no—
91C2×C4×D61—41no—
92C2×Dic122—21no—
93M16×C61—41no—
94M16×C61—41no—
95C2×C8×C61—41no—
96C2×C8×C61—41no—
97C4⋊C4×C61—22no—
98C4⋊C4×C61—22no—
99C4⋊C4×C61—21no—
100C4⋊C4×C61C22⋊C412yes—
101C42×C61—22no—
102C42×C61—22no—
103C42×C61C22×C411yescharacteristic
104C42×C61C2×D411yescharacteristic
105C42×C61#4111yescharacteristic
106C42×C61#4111yescharacteristic
107#11758201—44no—
108#11758198—41no—
109#11758198—41no—
110C4⋊Dic61—21no—
111C4⋊Dic61—21no—
112C4⋊Dic61—44no—
113C4⋊Dic61—42no—
114C4×Dic61—21no—
115C4×Dic61—21no—
116C4×Dic61—21no—
117C4×Dic61—42no—
118C4×Dic61—42no—
119C4×Dic61—41no—
120C4×Dic61—41no—
121C4×Dic61SD1612yescomplemented
122C2×#92418—22no—
123C23×C61#12011yescharacteristic
124C22×D61—41no—
125Q8×C61—22no—
126Q8×C61—22no—
127Q8×C61—42no—
128C2×C4×C61—22no—
129C2×C4×C61—22no—
130C2×C4×C61—22no—
131C2×C4×C61—41no—
132C2×C4×C61—42no—
133C2×C4×C61—42no—
134C2×C4×C61C2×C22⋊C411yescharacteristic
135C2×C4×C61C4×D411yescharacteristic
136C2×C4×C61C4×D411yescharacteristic
137C2×C4×C61#12111yescharacteristic
138C2×C4×C61#12111yescharacteristic
139C2×C4×C61#12311yescharacteristic
140C2×C4×C61C2×SD1611yescharacteristic
141C2×C4×C61#13511yescharacteristic
142C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
143C2×C4×C61#13711yescharacteristic
144C22⋊D61—81no—
145C22⋊D61—81no—
146C2×Dic61—22no—
147C2×Dic61—22no—
148C2×Dic61—41no—
149C2×Dic61—41no—
150C2×Dic61—41no—
151C2×Dic61—41no—
152C2×Dic61—42no—
153C2×Dic61—42no—
154C2×Dic61—41no—
155C2×Dic61—42no—
156D244—42no—
157D244—41no—
158D244—41no—
159D244—81no—
160C4×D61—81no—
161C4×D61—81no—
162Dic122—41no—
163Dic122—41no—
164C8×C61—81no—
165C8×C61—81no—
166#92418—42no—
167#9238—611nomaximal, Sylow
168C22×C61—21no—
169C22×C61—21no—
170C22×C61#38611yescharacteristic
171C22×C61#44811yescharacteristic
172C22×C61#44911yescharacteristic
173C2×D61—81no—
174C2×D61—81no—
175C2×D61—81no—
176C4×C61—21no—
177C4×C61—21no—
178C4×C61—21no—
179C4×C61—42no—
180C4×C61—42no—
181C4×C61#42112yes—
182C4×C61C4×SD1611yescharacteristic
183C4×C61#44011yescharacteristic
184C4×C61#46011yescharacteristic
185C4×C61#46411yescharacteristic
186Dic61—42no—
187Dic61—42no—
188Dic61—82no—
189Dic61—81no—
190#3103—611no—
191#2295—611no—
192#1962—611no—
193#1502—611no—
194#1487D6111yescharacteristic, complemented
195#1303—611no—
196#1276—611no—
197C2×C61—21no—
198C2×C61—21no—
199C2×C61#188011yescharacteristic
200C2×C61#189711yescharacteristic
201C2×C61#190611yescharacteristic
202D61—161no—
203#532—611no—
204C2×C4×Q8C2×D6111yescharacteristic
205#481—1221no—
206#475—612no—
207#460—612no—
208#448—1221no—
209C4×SD16—1222no—
210#431—611no—
211#431C2×D6111yescharacteristic
212#423C2×D6111yescharacteristic
213C2×#104—1221no—
214C2×#104—1221no—
215#391—1221no—
216#389—1221no—
217#387—1222no—
218C4×C4⋊C4—611no—
219C4×C4⋊C4—1221no—
220#376—1221no—
221C43—611no—
222#327—1222no—
223Q8⋊C8—22no—
224C61#923811yescharacteristic, complemented, Sylow
225C2×#41—1221no—
226C22×Q8D24411yescharacteristic
227C2×SD16—1222no—
228C2×M16—21no—
229C4⋊Q8—611no—
230#127—611no—
231#124—1221no—
232#121—1221no—
233#121—1221no—
234C4×Q8—21no—
235C4×Q8—21no—
236C4×Q8C4×D6112yes—
237C4×Q8C22⋊D6112yes—
238C4×D4—1221no—
239C4×D4—1221no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—1222no—
242C2×C4⋊C4—1221no—
243C2×C4⋊C4D24411yescharacteristic
244C2×C42—21no—
245C2×C42—611no—
246C2×C42—611no—
247C2×C42—1221no—
248C2×C42—1221no—
249C2×C42—1221no—
250C2×C42C22×D6111yescharacteristic
251#106—1222no—
252C4⋊C8—21no—
253C4⋊C8—21no—
254C4⋊C8—21no—
255C4⋊C8—612no—
256#104—2442no—
257#104—2442no—
258#103—1222no—
259#102—1222no—
260C22⋊C8—21no—
261C22⋊C8—1221no—
262C4×C8—21no—
263C4×C8—1221no—
264#95—612no—
265#95—1222no—
266#95—1222no—
267#95—1222no—
268#41—2441no—
269#41—2441no—
270#41—2441no—
271#41—2441no—
272C2×Q8—21no—
273C2×Q8—42no—
274C2×Q8—1221no—
275C2×Q8#1175819812yes—
276C2×D4—1221no—
277C2×D4—1221no—
278C2×D4—1221no—
279C2×D4—2441no—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—1221no—
283C22×C4—1221no—
284C22×C4—1222no—
285C22×C4—2441no—
286C22×C4C2×D24411yescharacteristic
287C22×C4D4×D6111yescharacteristic
288C22×C4D4×D6111yescharacteristic
289SD16—2444no—
290M16—41no—
291M16—41no—
292C2×C8—41no—
293C2×C8—41no—
294C2×C8—1222no—
295C4⋊C4—22no—
296C4⋊C4—22no—
297C4⋊C4—21no—
298C4⋊C4—1221no—
299C4⋊C4—1221no—
300C4⋊C4—2442no—
301C4⋊C4—2444no—
302C4⋊C4#1175819812yes—
303C22⋊C4—2441no—
304C22⋊C4—2441no—
305C42—22no—
306C42—22no—
307C42—612no—
308C42—1221no—
309C42—1221no—
310C42—1221no—
311C42—2442no—
312C42—2442no—
313C42—2441no—
314C42—2441no—
315C42C2×C4×D6111yescharacteristic
316C42#1175822411yescharacteristic
317C42#1175822411yescharacteristic
318C42C2×C22⋊D6111yescharacteristic
319C23—2441no—
320C23#1451974711yescharacteristic
321Q8—22no—
322Q8—22no—
323Q8—42no—
324Q8—2441no—
325Q8—2441no—
326D4—4881no—
327D4—4881no—
328D4—4881no—
329D4—2442no—
330D4—2441no—
331D4—2441no—
332C2×C4—22no—
333C2×C4—22no—
334C2×C4—22no—
335C2×C4—41no—
336C2×C4—42no—
337C2×C4—42no—
338C2×C4—1222no—
339C2×C4—1222no—
340C2×C4—4881no—
341C2×C4—4881no—
342C2×C4—2442no—
343C2×C4—2442no—
344C2×C4—2441no—
345C2×C4—2442no—
346C2×C4—2441no—
347C2×C4—2441no—
348C2×C4—2441no—
349C2×C4—2441no—
350C2×C4C2×#1175819811yescharacteristic
351C2×C4#1451973711yescharacteristic
352C2×C4#1451973711yescharacteristic
353C2×C4#1451974911yescharacteristic
354C2×C4#1451974911yescharacteristic
355C2×C4#1451976111yescharacteristic
356C2×C4SD16×D6111yescharacteristic
357C2×C4#1451980011yescharacteristic
358C2×C4#1451980411yescharacteristic
359C2×C4#1451980911yescharacteristic
360C8—81no—
361C8—81no—
362C8—2442no—
363C22—21no—
364C22—21no—
365C22—4881no—
366C22—4881no—
367C22—4881no—
368C22#1683963911yescharacteristic
369C22#1683990211yescharacteristic
370C22#1683991011yescharacteristic
371C4—21no—
372C4—21no—
373C4—21no—
374C4—42no—
375C4—42no—
376C4—4882no—
377C4—4881no—
378C4—2442no—
379C4—2442no—
380C4#1683977812yes—
381C4#1683984711yescharacteristic
382C4#1683986511yescharacteristic
383C4#1683996011yescharacteristic
384C4#1683998611yescharacteristic
385C2—21no—
386C2—21no—
387C2—9761no—
388C2#2144617211yescharacteristic
389C2#2144626511yescharacteristic
390C2#2144631811yescharacteristic
subgroupG/H
centerC2×C4#14519749
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1487C2
socleC22×C61#386
prime radical#16840312C22
cosocleC2×C42×C61C23
hypercenter#1487D61
hypocenterC61#9238
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1487

Complements

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

NH ≅ G/Ntype
2. #21448297C2semidirect
5. #21443720C2semidirect
6. #21443651C2semidirect
7. C61×#1487C2semidirect
10. #16840047C4semidirect
11. #16839962C4semidirect
121. C4×Dic61SD16semidirect
194. #1487D61semidirect
224. C61#9238semidirect

Maximal subgroups

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

subgroupindex
#214558502
#214482972
#214466462
#214443152
#214437202
#214436512
C61×#14872
#923861