Finite Group Databasebeta

← #29593805

Subgroups — #29593805

Order 15616.

350 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 73 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
1D4×Dic244C211yesmaximal, characteristic
2#21448048C211yesmaximal, characteristic, complemented
3#21447958C211yesmaximal, characteristic, complemented
4#21443867C211yesmaximal, characteristic, complemented
5#21443782C211yesmaximal, characteristic, complemented
6D4⋊#11758185C211yesmaximal, characteristic
7C61×#1673C211yesmaximal, characteristic
8C22×Dic244—21no—
9D4×Dic122—21no—
10#16840142C2211yescharacteristic
11#16840003—21no—
12#16839973—21no—
13#16839920—22no—
14C4×Dic244C2211yescharacteristic
15#16839589—21no—
16C4⋊#11758185C2211yescharacteristic
17#16839565—21no—
18#16839565—22no—
19C4×#11758185C2211yescharacteristic
20C61×#500C2211yescharacteristic
21C61×#461—21no—
22C8×D4×C61C2211yescharacteristic
23C61×#335C2211yescharacteristic
24C61×#332—21no—
25C22×Dic122—22no—
26C2×Dic244—22no—
27C2×Dic244—21no—
28C2×Dic244—42no—
29C2×Dic244—42no—
30C2×Dic244D411yescharacteristic
31C2×Dic244D412yes—
32#14519777—21no—
33#14519776—41no—
34#14519756—22no—
35#14519754—42no—
36C4×Dic122—21no—
37D4×Dic61—41no—
38C2×#11758185—21no—
39C2×#11758185—21no—
40#14519711D411yescharacteristic
41#14519702—22no—
42#14519702—21no—
43C2×SD16×C61—41no—
44C22×C8×C61—21no—
45C4⋊Q8×C61—21no—
46C4×D4×C61D411yescharacteristic
47#107×C61—21no—
48#107×C61—21no—
49C4⋊C8×C61—21no—
50C4⋊C8×C61D411yescharacteristic
51#103×C61—41no—
52C22⋊C8×C61—21no—
53C4×C8×C61C2311yescharacteristic
54C2×Q8×C61—41no—
55C2×D4×C61D811yescharacteristic
56C22×C4×C61—21no—
57C22×Dic61—42no—
58C2×Dic122—21no—
59C2×Dic122—22no—
60C2×Dic122—44no—
61C2×Dic122—42no—
62C2×Dic122—82no—
63SD16×C61—82no—
64C2×C8×C61—21no—
65C2×C8×C61—41no—
66C2×C8×C61—41no—
67C2×C8×C61—41no—
68C2×C8×C61C2×D411yescharacteristic
69C2×C8×C61C2×D411yescharacteristic
70C4⋊C4×C61—41no—
71C4⋊C4×C61—41no—
72C4⋊C4×C61D811yescharacteristic
73C22⋊C4×C61—21no—
74C42×C61C2×D411yescharacteristic
75C22⋊Dic61—42no—
76C4⋊Dic61—21no—
77C4⋊Dic61—41no—
78C4⋊Dic61—41no—
79#11758196—42no—
80#11758196—41no—
81C4×Dic61—41no—
82Dic244—21no—
83Dic244—42no—
84Dic244—44no—
85Dic244—41no—
86Dic244—41no—
87Dic244SD1612yescomplemented
88#11758185—41no—
89#11758185—41no—
90C23×C61—21no—
91Q8×C61—81no—
92Q8×C61—81no—
93D4×C61—21no—
94D4×C61SD3212yes—
95C2×C4×C61—21no—
96C2×C4×C61—41no—
97C2×C4×C61—41no—
98C2×C4×C61—81no—
99C2×C4×C61#12011yescharacteristic
100C2×C4×C61C2×D811yescharacteristic
101C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
102C2×Dic61—41no—
103C2×Dic61—41no—
104C2×Dic61—42no—
105C2×Dic61—84no—
106Dic122—22no—
107Dic122—41no—
108Dic122—42no—
109Dic122—42no—
110Dic122—84no—
111C8×C61—21no—
112C8×C61—41no—
113C8×C61—81no—
114C8×C61C2×SD1611yescharacteristic
115C8×C61AGL(1,ℤ/8)11yescharacteristic
116#12370—611nomaximal, Sylow
117C22×C61—22no—
118C22×C61—41no—
119C22×C61—41no—
120C22×C61#44711yescharacteristic
121C4×C61—21no—
122C4×C61—41no—
123C4×C61—161no—
124C4×C61#45011yescharacteristic
125C4×C61#45511yescharacteristic
126C4×C61C2×SD3211yescharacteristic
127C4×C61#51011yescharacteristic
128Dic61—42no—
129Dic61—82no—
130Dic61—81no—
131D4×Q16—611no—
132#2241—611no—
133#2225—611no—
134#1673D6111yescharacteristic
135#1362—611no—
136#1332—611no—
137D4⋊C16—611no—
138C2×C61—42no—
139C2×C61#163911yescharacteristic
140C2×C61#218511yescharacteristic
141C2×C61#219511yescharacteristic
142C22×Q16—1221no—
143D4×Q8—1221no—
144#500C2×D6111yescharacteristic
145#494—611no—
146#467—1221no—
147#462—1221no—
148#461—21no—
149#451—1222no—
150C4×Q16—611no—
151C8×D4C2×D6111yescharacteristic
152#367—1221no—
153C4⋊C16—611no—
154#358—1221no—
155#358—1222no—
156C4×C16—611no—
157#335C2×D6111yescharacteristic
158#332—21no—
159C61#1237011yescharacteristic, complemented, Sylow
160C22×Q8—1222no—
161C2×Q16—611no—
162C2×Q16—612no—
163C2×Q16—1222no—
164C2×Q16—1221no—
165C2×Q16—2442no—
166C2×Q16—2442no—
167C2×SD16—41no—
168C22×C8—21no—
169C4⋊Q8—21no—
170C4⋊Q8—1221no—
171C4⋊Q8—2441no—
172C22⋊Q8—1222no—
173C22⋊Q8—2442no—
174C4×Q8—1221no—
175C4×D4—2441no—
176C4×D4C22⋊D6111yescharacteristic
177C2×C16—1221no—
178C2×C16—1221no—
179#107—21no—
180#107—21no—
181#107—611no—
182C4⋊C8—21no—
183C4⋊C8C22⋊D6111yescharacteristic
184#103—41no—
185#103—1222no—
186#103—1221no—
187C22⋊C8—21no—
188C4×C8C22×D6111yescharacteristic
189C2×Q8—41no—
190C2×Q8—1221no—
191C2×Q8—1222no—
192C2×Q8—4882no—
193C2×Q8—2442no—
194C2×Q8—2444no—
195C2×D4#1175819911yescharacteristic
196C22×C4—21no—
197C22×C4—2442no—
198Q16—612no—
199Q16—1221no—
200Q16—2442no—
201Q16—2444no—
202Q16—2441no—
203Q16—2441no—
204SD16—82no—
205C2×C8—21no—
206C2×C8—41no—
207C2×C8—41no—
208C2×C8—41no—
209C2×C8D4×D6111yescharacteristic
210C2×C8D4×D6111yescharacteristic
211C4⋊C4—41no—
212C4⋊C4—41no—
213C4⋊C4—1221no—
214C4⋊C4—2442no—
215C4⋊C4—2441no—
216C4⋊C4—2441no—
217C4⋊C4—2441no—
218C4⋊C4#1175819911yescharacteristic
219C22⋊C4—21no—
220C22⋊C4—2442no—
221C42—2441no—
222C42C2×C22⋊D6111yescharacteristic
223C16—2441no—
224C16—2441no—
225C23—21no—
226Q8—81no—
227Q8—81no—
228Q8—1222no—
229Q8—4884no—
230Q8—2442no—
231Q8—2442no—
232Q8—2441no—
233D4—21no—
234D4#1451972112yes—
235C2×C4—21no—
236C2×C4—41no—
237C2×C4—41no—
238C2×C4—81no—
239C2×C4—4884no—
240C2×C4—2441no—
241C2×C4—2442no—
242C2×C4—2441no—
243C2×C4#1451974511yescharacteristic
244C2×C4C2×#1175819911yescharacteristic
245C2×C4#1451980211yescharacteristic
246C8—21no—
247C8—41no—
248C8—81no—
249C8SD16×D6111yescharacteristic
250C8#1451980411yescharacteristic
251C22—22no—
252C22—41no—
253C22—41no—
254C22#1683989511yescharacteristic
255C4—21no—
256C4—41no—
257C4—161no—
258C4—4881no—
259C4—4882no—
260C4—2442no—
261C4#1683991111yescharacteristic
262C4#1683993811yescharacteristic
263C4C2×#1451972111yescharacteristic
264C4#1684020211yescharacteristic
265C2—42no—
266C2#2144499611yescharacteristic
267C2#2144773511yescharacteristic
268C2#2144779511yescharacteristic
subgroupG/H
centerC22#16839895
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#1673C2
socleC22×C61#447
prime radicalC2×D4×C61D8
hypercenter#1673D61
hypocenterC61#12370
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C8×D4 ◁ #1673

Complements

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

NH ≅ G/Ntype
2. #21448048C2semidirect
3. #21447958C2semidirect
4. #21443867C2semidirect
5. #21443782C2semidirect
87. Dic244SD16semidirect
159. C61#12370semidirect

Maximal subgroups

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

subgroupindex
D4×Dic2442
#214480482
#214479582
#214438672
#214437822
D4⋊#117581852
C61×#16732
#1237061