Finite Group Databasebeta

← #29576286

Subgroups — #29576286

Order 15616.

604 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 604 conjugacy classes of subgroups — too many to draw. Only its 115 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455851C211yesmaximal, characteristic
2C4×#14519742C211yesmaximal, characteristic, complemented
3#21446646C211yesmaximal, characteristic
4#21444313C211yesmaximal, characteristic
5#21444247C211yesmaximal, characteristic, complemented
6#21443651C211yesmaximal, characteristic, complemented
7C61×#1303C211yesmaximal, characteristic, complemented
8#16840312C2211yescharacteristic
9C2×C4×Dic122C2211yescharacteristic
10C2×#14519742—21no—
11#16840081—21no—
12#16840048C412yescomplemented
13#16839963C412yescomplemented
14#16839903—21no—
15C4×#11758190—22no—
16#16839815C2211yescharacteristic
17C2×#14519703—21no—
18C2×#14519703—21no—
19C4⋊C4×Dic61—21no—
20C4×#11758196—21no—
21#16839613—22no—
22C42×Dic61—21no—
23C42×Dic61C2211yescharacteristic
24#16839495—22no—
25#16839492—22no—
26C61×#431C2211yescharacteristic
27C61×#423C2211yescharacteristic
28C4×C4⋊C4×C61C2211yescharacteristic
29C2×#11758222—21no—
30C22×Dic122D411yescharacteristic
31C2×#11758190—22no—
32#14519777C2×C411yescharacteristic
33#14519774C2×C411yescharacteristic
34#14519765—21no—
35#14519751—21no—
36#14519751—21no—
37C4×Dic122—21no—
38C4×Dic122—21no—
39C4×Dic122C2×C412yes—
40C4×Dic122D412yes—
41#14519742—28no—
42C4×D244—21no—
43C4×D244—21no—
44C2×C4⋊Dic61D411yescharacteristic
45C2×#11758196—22no—
46C2×#11758196—21no—
47C2×C4×Dic61—22no—
48C2×C4×Dic61—21no—
49C2×C4×Dic61—21no—
50C2×C4×Dic61—22no—
51C2×C4×Dic61—21no—
52C2×C4×Dic61D411yescharacteristic
53C2×C4×Dic61D411yescharacteristic
54#14519709—22no—
55C4⋊#92418—21no—
56#14519703—42no—
57#14519703—42no—
58#14519702—22no—
59#14519699—22no—
60C22⋊#92418—21no—
61C4×#92418—21no—
62#14519684—22no—
63C2×M16×C61—21no—
64C2×C4⋊C4×C61—21no—
65C2×C42×C61—21no—
66C2×C42×C61C2311yescharacteristic
67C4⋊C8×C61—21no—
68C4⋊C8×C61—21no—
69C4⋊C8×C61C2×C412yes—
70C22⋊C8×C61—21no—
71C4×C8×C61—21no—
72#95×C61D412yes—
73C22×C4×C61—22no—
74C22×C4×C61C2×D411yescharacteristic
75C22×C4×C61C2×D411yescharacteristic
76C22×C4×C61C2×D411yescharacteristic
77C2×C22⋊D61—41no—
78C22×Dic61—21no—
79C22×Dic61—21no—
80C22×Dic61—21no—
81C22×Dic61—21no—
82#11758222—41no—
83#11758222—41no—
84#11758222—41no—
85#11758222—41no—
86C2×D244—21no—
87C2×D244—21no—
88C2×D244—21no—
89C2×C4×D61—41no—
90C2×Dic122—21no—
91C2×Dic122—24no—
92C2×Dic122—21no—
93C2×Dic122C22⋊C412yes—
94M16×C61—41no—
95M16×C61—41no—
96C2×C8×C61—22no—
97C2×C8×C61—41no—
98C4⋊C4×C61—24no—
99C42×C61—41no—
100C42×C61—41no—
101C42×C61C22×C411yescharacteristic
102C42×C61C2×D411yescharacteristic
103C42×C61#4111yescharacteristic
104C42×C61#4111yescharacteristic
105#11758198—41no—
106#11758198—41no—
107C4⋊Dic61—21no—
108C4⋊Dic61—21no—
109C4⋊Dic61—21no—
110C4⋊Dic61C22⋊C412yes—
111#11758196—28no—
112#11758196—22no—
113#11758196—22no—
114C4×Dic61—28no—
115C4×Dic61—24no—
116C4×Dic61—22no—
117C4×Dic61—22no—
118C4×Dic61—21no—
119C4×Dic61—21no—
120C4×Dic61—21no—
121C4×Dic61—42no—
122C4×Dic61—44no—
123C4×Dic61SD1612yescomplemented
124C2×#92418—41no—
125#11758190—44no—
126C23×C61#12011yescharacteristic
127C22×D61—41no—
128C2×C4×C61—22no—
129C2×C4×C61—24no—
130C2×C4×C61—41no—
131C2×C4×C61—42no—
132C2×C4×C61—42no—
133C2×C4×C61C2×C22⋊C411yescharacteristic
134C2×C4×C61C4×D411yescharacteristic
135C2×C4×C61C4×D411yescharacteristic
136C2×C4×C61#12111yescharacteristic
137C2×C4×C61#12111yescharacteristic
138C2×C4×C61#12311yescharacteristic
139C2×C4×C61C2×SD1611yescharacteristic
140C2×C4×C61#13511yescharacteristic
141C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
142C2×C4×C61#13711yescharacteristic
143C22⋊D61—81no—
144C22⋊D61—81no—
145C2×Dic61—22no—
146C2×Dic61—24no—
147C2×Dic61—22no—
148C2×Dic61—22no—
149C2×Dic61—22no—
150C2×Dic61—22no—
151C2×Dic61—22no—
152C2×Dic61—41no—
153C2×Dic61—42no—
154C2×Dic61—41no—
155C2×Dic61—41no—
156D244—42no—
157D244—41no—
158D244—41no—
159D244—81no—
160C4×D61—81no—
161C4×D61—81no—
162Dic122—24no—
163Dic122—22no—
164Dic122—41no—
165Dic122—41no—
166Dic122#10414yescomplemented
167C8×C61—42no—
168C8×C61—81no—
169#92418—81no—
170#9234—611nomaximal, Sylow
171C22×C61—21no—
172C22×C61—21no—
173C22×C61#38611yescharacteristic
174C22×C61#44811yescharacteristic
175C22×C61#44911yescharacteristic
176C2×D61—81no—
177C2×D61—81no—
178C2×D61—81no—
179C4×C61—21no—
180C4×C61—21no—
181C4×C61—21no—
182C4×C61—44no—
183C4×C61C2×#10412yes—
184C4×C61C4×SD1611yescharacteristic
185C4×C61#44011yescharacteristic
186C4×C61#46011yescharacteristic
187C4×C61#46411yescharacteristic
188Dic61—24no—
189Dic61—24no—
190Dic61—42no—
191Dic61—42no—
192Dic61—81no—
193#3103—611no—
194C42×Q8—611no—
195#1962—611no—
196#1502—611no—
197#1487—611no—
198#1303D6111yescharacteristic, complemented
199#1276—611no—
200C2×C61—21no—
201C2×C61—21no—
202C2×C61#188011yescharacteristic
203C2×C61#189611yescharacteristic
204C2×C61#190611yescharacteristic
205D61—161no—
206#532—611no—
207C2×C4×Q8—611no—
208C2×C4×Q8—1221no—
209#481—1221no—
210#475—612no—
211#460—612no—
212#448—1221no—
213C4×SD16—1222no—
214#431—611no—
215#431C2×D6111yescharacteristic
216#423C2×D6111yescharacteristic
217C2×#104—1221no—
218C2×#104—1221no—
219C4×C4⋊C4—1221no—
220C4×C4⋊C4—1221no—
221C4×C4⋊C4—1222no—
222C4×C4⋊C4C2×D6111yescharacteristic
223C43—611no—
224C43—1221no—
225#327—1222no—
226Q8⋊C8—1222no—
227C61#923411yescharacteristic, complemented, Sylow
228C2×#41—1221no—
229C22×Q8—611no—
230C2×SD16—1222no—
231C2×M16—21no—
232C4⋊Q8—611no—
233#127—611no—
234#124—1221no—
235#121—1221no—
236#121—1221no—
237C4×Q8—612no—
238C4×Q8—612no—
239C4×Q8—1228no—
240C4×Q8—1221no—
241C4×Q8—1221no—
242C4×D4—1221no—
243C4×D4—1221no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—611no—
246C2×C4⋊C4—1222no—
247C2×C4⋊C4—1221no—
248C2×C42—21no—
249C2×C42—611no—
250C2×C42—611no—
251C2×C42—1222no—
252C2×C42—1221no—
253C2×C42—1221no—
254C2×C42—1222no—
255C2×C42—1221no—
256C2×C42C22×D6111yescharacteristic
257#106—1222no—
258C4⋊C8—21no—
259C4⋊C8—21no—
260C4⋊C8—1221no—
261C4⋊C8C4×D6112yes—
262#104—2442no—
263#104—2442no—
264#103—1222no—
265#102—1222no—
266C22⋊C8—21no—
267C22⋊C8—1221no—
268C4×C8—21no—
269C4×C8—1221no—
270#95—1222no—
271#95D24412yes—
272#41—2441no—
273#41—2441no—
274#41—2441no—
275#41—2441no—
276C2×Q8—612no—
277C2×Q8—1224no—
278C2×Q8—1221no—
279C2×Q8—1221no—
280C2×D4—1221no—
281C2×D4—1221no—
282C2×D4—1221no—
283C2×D4—2441no—
284C22×C4—22no—
285C22×C4—1221no—
286C22×C4—1221no—
287C22×C4—1221no—
288C22×C4—1221no—
289C22×C4—2441no—
290C22×C4C2×D24411yescharacteristic
291C22×C4D4×D6111yescharacteristic
292C22×C4D4×D6111yescharacteristic
293SD16—2444no—
294M16—41no—
295M16—41no—
296C2×C8—22no—
297C2×C8—41no—
298C2×C8—2441no—
299C4⋊C4—24no—
300C4⋊C4—612no—
301C4⋊C4—1228no—
302C4⋊C4—1222no—
303C4⋊C4—1222no—
304C4⋊C4—1221no—
305C4⋊C4—1221no—
306C4⋊C4—1221no—
307C22⋊C4—2441no—
308C22⋊C4—2441no—
309C42—41no—
310C42—41no—
311C42—612no—
312C42—1224no—
313C42—1228no—
314C42—1221no—
315C42—1222no—
316C42—1222no—
317C42—1221no—
318C42—1221no—
319C42—2442no—
320C42—2444no—
321C42C2×C4×D6111yescharacteristic
322C42#1175822211yescharacteristic
323C42D4×D6111yescharacteristic
324C42#1175822611yescharacteristic
325C23—2441no—
326C23#1451974711yescharacteristic
327Q8—614no—
328Q8—1224no—
329Q8—1222no—
330Q8—2441no—
331Q8—2441no—
332D4—4881no—
333D4—4881no—
334D4—4881no—
335D4—2442no—
336D4—2441no—
337D4—2441no—
338C2×C4—22no—
339C2×C4—24no—
340C2×C4—41no—
341C2×C4—42no—
342C2×C4—42no—
343C2×C4—1222no—
344C2×C4—1224no—
345C2×C4—1222no—
346C2×C4—1222no—
347C2×C4—1222no—
348C2×C4—1222no—
349C2×C4—1222no—
350C2×C4—4881no—
351C2×C4—4881no—
352C2×C4—2441no—
353C2×C4—2441no—
354C2×C4—2442no—
355C2×C4—2441no—
356C2×C4C22⋊C4×D6111yescharacteristic
357C2×C4#1451973911yescharacteristic
358C2×C4C4×D24411yescharacteristic
359C2×C4#1451975011yescharacteristic
360C2×C4#1451975211yescharacteristic
361C2×C4#1451976211yescharacteristic
362C2×C4SD16×D6111yescharacteristic
363C2×C4#1451979811yescharacteristic
364C2×C4#1451980111yescharacteristic
365C2×C4#1451980911yescharacteristic
366C8—42no—
367C8—81no—
368C8—4881no—
369C22—21no—
370C22—21no—
371C22—4881no—
372C22—4881no—
373C22—4881no—
374C22#1683964011yescharacteristic
375C22#1683990211yescharacteristic
376C22#1683990811yescharacteristic
377C4—21no—
378C4—21no—
379C4—21no—
380C4—44no—
381C4—1224no—
382C4—1224no—
383C4—4881no—
384C4—2442no—
385C4—2442no—
386C4#104×D6112yes—
387C4#1683984911yescharacteristic
388C4#1683986111yescharacteristic
389C4#1683996111yescharacteristic
390C4#1683998711yescharacteristic
391C2—21no—
392C2—21no—
393C2—9761no—
394C2#2144617511yescharacteristic
395C2#2144626111yescharacteristic
396C2#2144632111yescharacteristic
subgroupG/H
centerC2×C4#14519750
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1303C2
socleC22×C61#386
prime radical#16840312C22
cosocleC2×C42×C61C23
hypercenter#1303D61
hypocenterC61#9234
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1303

Complements

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

NH ≅ G/Ntype
2. C4×#14519742C2semidirect
5. #21444247C2semidirect
6. #21443651C2semidirect
7. C61×#1303C2semidirect
12. #16840048C4semidirect
13. #16839963C4semidirect
123. C4×Dic61SD16semidirect
166. Dic122#104semidirect
198. #1303D61semidirect
227. C61#9234semidirect

Maximal subgroups

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

subgroupindex
#214558512
C4×#145197422
#214466462
#214443132
#214442472
#214436512
C61×#13032
#923461