Finite Group Databasebeta

← #29580979

Subgroups — #29580979

Order 15616.

636 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 636 conjugacy classes of subgroups — too many to draw. Only its 103 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#21456265C211yesmaximal, characteristic, complemented
2#21455819C212yesmaximal, complemented
3#21444217C212yesmaximal, complemented
4#21443650C211yesmaximal, characteristic, complemented
5C61×#1955C211yesmaximal, characteristic, complemented
6C2×#14519799—22no—
7#16840312C2212yes—
8#16840156—22no—
9#16840151—22no—
10#16840075—22no—
11#16840042—22no—
12#16839957—22no—
13#16839896—22no—
14C4×#11758199—24no—
15#16839815C2212yes—
16#16839489—24no—
17C2×C4×D4×C61C2211yescharacteristic
18C2×C4⋊C8×C61C2211yescharacteristic
19C2×C22⋊C8×C61—22no—
20C2×#97×C61C2211yescharacteristic
21C2×#11758222—22no—
22#14519799—44no—
23#14519799—44no—
24C2×Dic244—22no—
25C2×#11758190—24no—
26C2×D488—22no—
27C2×#11758199—24no—
28#14519777D412yes—
29#14519774D412yes—
30#14519765—22no—
31#14519751—22no—
32#14519751—22no—
33C4×D244—22no—
34C4×D244—22no—
35#14519710—24no—
36C4⋊#92418—22no—
37#14519698—24no—
38#14519697—24no—
39C22⋊#92418—22no—
40C4×#92418D414yes—
41C22×D4×C61D411yescharacteristic
42C23×C4×C61—21no—
43C22×C8×C61—21no—
44C22×C8×C61D412yes—
45C4×D4×C61—22no—
46C4×D4×C61—22no—
47C2×C4⋊C4×C61D411yescharacteristic
48C2×C22⋊C4×C61—21no—
49C2×C42×C61C2311yescharacteristic
50C4⋊C8×C61—22no—
51C22⋊C8×C61—44no—
52#97×C61—22no—
53C24×C61—21no—
54C2×D4×C61—22no—
55C2×D4×C61—42no—
56C22×C4×C61—21no—
57C22×C4×C61—41no—
58C22×C4×C61—41no—
59C22×C4×C61—42no—
60C22×C4×C61—42no—
61C22×C4×C61C2×D411yescharacteristic
62C22×C4×C61C2×D411yescharacteristic
63C22×C4×C61#4111yescharacteristic
64C2×C22⋊D61—42no—
65#11758222—44no—
66#11758222—44no—
67C2×D244—22no—
68C2×D244—22no—
69C2×D244—22no—
70C2×C4×D61—42no—
71C2×Dic122—22no—
72C2×C8×C61—22no—
73C2×C8×C61—22no—
74C2×C8×C61—41no—
75C2×C8×C61—42no—
76C2×C8×C61D814yescomplemented
77C4⋊C4×C61—22no—
78C22⋊C4×C61—42no—
79C42×C61C2×D412yes—
80C42×C61C2×D412yes—
81#11758199—48no—
82#11758198—42no—
83#11758198—42no—
84C4⋊Dic61—22no—
85C4⋊Dic61—22no—
86C2×#92418—24no—
87Dic244—44no—
88D488—44no—
89#11758190—48no—
90C23×C61—22no—
91C23×C61—41no—
92C23×C61—42no—
93C23×C61—41no—
94C23×C61—42no—
95C23×C61#12111yescharacteristic
96C22×D61—42no—
97D4×C61—24no—
98D4×C61—42no—
99C2×C4×C61—41no—
100C2×C4×C61—41no—
101C2×C4×C61—41no—
102C2×C4×C61—42no—
103C2×C4×C61—82no—
104C2×C4×C61—81no—
105C2×C4×C61—81no—
106C2×C4×C61#12012yes—
107C2×C4×C61#12011yescharacteristic
108C2×C4×C61#12112yes—
109C2×C4×C61#12711yescharacteristic
110C2×C4×C61C2×D812yes—
111C2×C4×C61AGL(1,ℤ/8)12yes—
112C22⋊D61—84no—
113C2×Dic61—42no—
114D244—44no—
115D244—44no—
116D244—44no—
117C4×D61—82no—
118C4×D61—82no—
119Dic122—44no—
120C8×C61—24no—
121C8×C61—81no—
122#92418—44no—
123#10032—611nomaximal, Sylow
124C22×C61—21no—
125C22×C61—21no—
126C22×C61—44no—
127C22×C61—42no—
128C22×C61—82no—
129C22×C61—81no—
130C22×C61—81no—
131C22×C61#39211yescharacteristic
132C22×C61#45912yes—
133C2×D61—82no—
134C2×D61—82no—
135C2×D61—82no—
136C4×C61—22no—
137C4×C61—22no—
138C4×C61—81no—
139C4×C61#44712yes—
140C4×C61#49311yescharacteristic
141C4×C61#49611yescharacteristic
142Dic61—82no—
143#3150—611no—
144#3100—612no—
145#1955D6111yescharacteristic, complemented
146#1480—612no—
147#1275—611no—
148C2×C61—22no—
149C2×C61—82no—
150C2×C61#201011yescharacteristic
151C2×C61#201111yescharacteristic
152C2×C61#201711yescharacteristic
153D61—162no—
154C2×#135—1222no—
155#532—612no—
156C2×C4×D4C2×D6111yescharacteristic
157#497—1222no—
158#496—1222no—
159#480—1222no—
160#474—1222no—
161#459—1222no—
162#447—1222no—
163C4×D8—1224no—
164#431—612no—
165C2×C4⋊C8C2×D6111yescharacteristic
166C2×C22⋊C8—22no—
167C2×#97C2×D6111yescharacteristic
168D4⋊C8—1224no—
169C61#1003211yescharacteristic, complemented, Sylow
170C2×#41—1222no—
171C22×D4D24411yescharacteristic
172C23×C4—21no—
173#135—2444no—
174#135—2444no—
175C2×Q16—1222no—
176C2×SD16—1224no—
177C2×D8—1222no—
178C2×D8—1224no—
179C22×C8—21no—
180C22×C8C22⋊D6112yes—
181C4⋊Q8—612no—
182#127—612no—
183#124—1222no—
184#121—1222no—
185#121—1222no—
186C4×D4—22no—
187C4×D4—22no—
188C4×D4—1222no—
189C4×D4—1222no—
190C2×C4⋊C4D24411yescharacteristic
191C2×C22⋊C4—21no—
192C2×C42C22×D6111yescharacteristic
193#107—1224no—
194C4⋊C8—22no—
195C4⋊C8—1222no—
196#102—1224no—
197#102—1224no—
198C22⋊C8—44no—
199C22⋊C8—1222no—
200#97—22no—
201C4×C8—614no—
202C24—21no—
203#41—2444no—
204#41—2444no—
205C2×Q8—1222no—
206C2×D4—22no—
207C2×D4—42no—
208C2×D4—1222no—
209C2×D4—1222no—
210C2×D4—1222no—
211C2×D4—2442no—
212C22×C4—21no—
213C22×C4—41no—
214C22×C4—41no—
215C22×C4—42no—
216C22×C4—42no—
217C22×C4—2442no—
218C22×C4C2×D24411yescharacteristic
219C22×C4#1175822211yescharacteristic
220C22×C4C2×C22⋊D6111yescharacteristic
221Q16—2444no—
222SD16—2448no—
223D8—2444no—
224D8—2448no—
225C2×C8—22no—
226C2×C8—22no—
227C2×C8—41no—
228C2×C8—42no—
229C2×C8—1224no—
230C2×C8#1175819914yescomplemented
231C4⋊C4—22no—
232C4⋊C4—1222no—
233C4⋊C4—1222no—
234C22⋊C4—42no—
235C22⋊C4—2442no—
236C22⋊C4—2442no—
237C42D4×D6112yes—
238C42D4×D6112yes—
239C23—22no—
240C23—41no—
241C23—42no—
242C23—42no—
243C23—41no—
244C23—2442no—
245C23#1451975111yescharacteristic
246Q8—2444no—
247D4—24no—
248D4—42no—
249D4—4884no—
250D4—2444no—
251D4—2444no—
252D4—2444no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—42no—
256C2×C4—41no—
257C2×C4—81no—
258C2×C4—82no—
259C2×C4—81no—
260C2×C4—4882no—
261C2×C4—4882no—
262C2×C4—2442no—
263C2×C4#1451974511yescharacteristic
264C2×C4#1451974712yes—
265C2×C4#1451975012yes—
266C2×C4#1451977311yescharacteristic
267C2×C4C2×#1175819912yes—
268C2×C4#1451980212yes—
269C8—24no—
270C8—81no—
271C8—2444no—
272C22—21no—
273C22—21no—
274C22—44no—
275C22—42no—
276C22—82no—
277C22—81no—
278C22—81no—
279C22—4882no—
280C22—4882no—
281C22—4882no—
282C22#1683967111yescharacteristic
283C22#1683995712yes—
284C4—22no—
285C4—22no—
286C4—81no—
287C4—4882no—
288C4#1683989512yes—
289C4#1684013811yescharacteristic
290C4#1684015211yescharacteristic
291C2—22no—
292C2—82no—
293C2—9762no—
294C2#2144688611yescharacteristic
295C2#2144688911yescharacteristic
296C2#2144692311yescharacteristic
subgroupG/H
centerC2×C4#14519773
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1955C2
socleC22×C61#392
hypercenter#1955D61
hypocenterC61#10032
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1955

Complements

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

NH ≅ G/Ntype
1. #21456265C2semidirect
2. #21455819C2semidirect
3. #21444217C2semidirect
4. #21443650C2semidirect
5. C61×#1955C2semidirect
76. C2×C8×C61D8semidirect
145. #1955D61semidirect
169. C61#10032semidirect
230. C2×C8#11758199semidirect

Maximal subgroups

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

subgroupindex
#214562652
#214558192
#214442172
#214436502
C61×#19552
#1003261