Finite Group Databasebeta

← #29593833

Subgroups — #29593833

Order 15616.

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

normal subgroups only

This group has 344 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#21447968C211yesmaximal, characteristic, complemented
4#21443867C211yesmaximal, characteristic, complemented
5#21443782C211yesmaximal, characteristic, complemented
6D4⋊#11758185C211yesmaximal, characteristic
7C61×#1675C211yesmaximal, characteristic
8C22×Dic244—21no—
9D4×Dic122—21no—
10#16840142C2211yescharacteristic
11#16840003—21no—
12#16839973—21no—
13#16839920—22no—
14C4×Dic244C2211yescharacteristic
15#16839587—21no—
16C4⋊#11758185C2211yescharacteristic
17#16839565—21no—
18#16839565—22no—
19C4×#11758185C2211yescharacteristic
20C61×#500C2211yescharacteristic
21C61×#476—21no—
22C8×D4×C61C2211yescharacteristic
23C61×#335C2211yescharacteristic
24C61×#333—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—
43C22×C8×C61—21no—
44C4⋊Q8×C61—21no—
45C4×D4×C61D411yescharacteristic
46#107×C61—21no—
47#107×C61—21no—
48#106×C61—41no—
49C4⋊C8×C61—21no—
50C4⋊C8×C61D411yescharacteristic
51#102×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—
63C2×C8×C61—21no—
64C2×C8×C61—41no—
65C2×C8×C61—41no—
66C2×C8×C61—41no—
67C2×C8×C61C2×D411yescharacteristic
68C2×C8×C61C2×D411yescharacteristic
69C4⋊C4×C61—41no—
70C4⋊C4×C61—41no—
71C4⋊C4×C61D811yescharacteristic
72C22⋊C4×C61—21no—
73C42×C61C2×D411yescharacteristic
74C22⋊Dic61—42no—
75C4⋊Dic61—21no—
76C4⋊Dic61—41no—
77C4⋊Dic61—41no—
78#11758196—42no—
79#11758196—41no—
80C4×Dic61—41no—
81Dic244—21no—
82Dic244—42no—
83Dic244—44no—
84Dic244—41no—
85Dic244—41no—
86Dic244SD1612yes—
87#11758185—41no—
88#11758185—41no—
89C23×C61—21no—
90Q8×C61—161no—
91D4×C61—21no—
92D4×C61Q3212yes—
93C2×C4×C61—21no—
94C2×C4×C61—41no—
95C2×C4×C61—41no—
96C2×C4×C61—81no—
97C2×C4×C61#12011yescharacteristic
98C2×C4×C61C2×D811yescharacteristic
99C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
100C2×Dic61—41no—
101C2×Dic61—41no—
102C2×Dic61—42no—
103C2×Dic61—84no—
104Dic122—22no—
105Dic122—41no—
106Dic122—42no—
107Dic122—42no—
108Dic122—84no—
109C8×C61—21no—
110C8×C61—41no—
111C8×C61—81no—
112C8×C61C2×SD1611yescharacteristic
113C8×C61AGL(1,ℤ/8)11yescharacteristic
114#12374—611nomaximal, Sylow
115C22×C61—22no—
116C22×C61—41no—
117C22×C61—41no—
118C22×C61#44711yescharacteristic
119C4×C61—21no—
120C4×C61—41no—
121C4×C61—161no—
122C4×C61#45011yescharacteristic
123C4×C61#45511yescharacteristic
124C4×C61C2×Q3211yescharacteristic
125C4×C61#51011yescharacteristic
126Dic61—42no—
127Dic61—82no—
128Dic61—81no—
129D4×Q16—611no—
130#2241—611no—
131#2227—611no—
132#1675D6111yescharacteristic
133#1362—611no—
134#1332—611no—
135D4⋊C16—611no—
136C2×C61—42no—
137C2×C61#163911yescharacteristic
138C2×C61#218811yescharacteristic
139C2×C61#219311yescharacteristic
140C22×Q16—1221no—
141D4×Q8—1221no—
142#500C2×D6111yescharacteristic
143#494—611no—
144#476—21no—
145#467—1221no—
146#462—1221no—
147#451—1222no—
148C4×Q16—611no—
149C8×D4C2×D6111yescharacteristic
150#366—1221no—
151C4⋊C16—611no—
152#358—1221no—
153#358—1222no—
154C4×C16—611no—
155#335C2×D6111yescharacteristic
156#333—21no—
157C61#1237411yescharacteristic, complemented, Sylow
158C22×Q8—1222no—
159C2×Q16—611no—
160C2×Q16—612no—
161C2×Q16—1222no—
162C2×Q16—1221no—
163C2×Q16—2442no—
164C2×Q16—2442no—
165C22×C8—21no—
166C4⋊Q8—21no—
167C4⋊Q8—1221no—
168C4⋊Q8—2441no—
169C22⋊Q8—1222no—
170C22⋊Q8—2442no—
171C4×Q8—1221no—
172C4×D4—2441no—
173C4×D4C22⋊D6111yescharacteristic
174C2×C16—1221no—
175C2×C16—1221no—
176#107—21no—
177#107—21no—
178#107—611no—
179#106—41no—
180C4⋊C8—21no—
181C4⋊C8C22⋊D6111yescharacteristic
182#103—1222no—
183#103—1221no—
184#102—41no—
185C22⋊C8—21no—
186C4×C8C22×D6111yescharacteristic
187C2×Q8—41no—
188C2×Q8—1221no—
189C2×Q8—1222no—
190C2×Q8—4882no—
191C2×Q8—2442no—
192C2×Q8—2444no—
193C2×D4#1175819911yescharacteristic
194C22×C4—21no—
195C22×C4—2442no—
196Q16—612no—
197Q16—1221no—
198Q16—2442no—
199Q16—2444no—
200Q16—2441no—
201Q16—2441no—
202C2×C8—21no—
203C2×C8—41no—
204C2×C8—41no—
205C2×C8—41no—
206C2×C8D4×D6111yescharacteristic
207C2×C8D4×D6111yescharacteristic
208C4⋊C4—41no—
209C4⋊C4—41no—
210C4⋊C4—1221no—
211C4⋊C4—2442no—
212C4⋊C4—2441no—
213C4⋊C4—2441no—
214C4⋊C4—2441no—
215C4⋊C4#1175819911yescharacteristic
216C22⋊C4—21no—
217C22⋊C4—2442no—
218C42—2441no—
219C42C2×C22⋊D6111yescharacteristic
220C16—2441no—
221C16—2441no—
222C23—21no—
223Q8—161no—
224Q8—1222no—
225Q8—4884no—
226Q8—2442no—
227Q8—2442no—
228Q8—2441no—
229D4—21no—
230D4#1451972312yes—
231C2×C4—21no—
232C2×C4—41no—
233C2×C4—41no—
234C2×C4—81no—
235C2×C4—4884no—
236C2×C4—2441no—
237C2×C4—2442no—
238C2×C4—2441no—
239C2×C4#1451974511yescharacteristic
240C2×C4C2×#1175819911yescharacteristic
241C2×C4#1451980211yescharacteristic
242C8—21no—
243C8—41no—
244C8—81no—
245C8SD16×D6111yescharacteristic
246C8#1451980411yescharacteristic
247C22—22no—
248C22—41no—
249C22—41no—
250C22#1683989511yescharacteristic
251C4—21no—
252C4—41no—
253C4—161no—
254C4—4881no—
255C4—4882no—
256C4—2442no—
257C4#1683991111yescharacteristic
258C4#1683993811yescharacteristic
259C4C2×#1451972311yescharacteristic
260C4#1684020211yescharacteristic
261C2—42no—
262C2#2144499611yescharacteristic
263C2#2144775211yescharacteristic
264C2#2144778111yescharacteristic
subgroupG/H
centerC22#16839895
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#1675C2
socleC22×C61#447
prime radicalC2×D4×C61D8
hypercenter#1675D61
hypocenterC61#12374
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C8×D4 ◁ #1675

Complements

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

NH ≅ G/Ntype
2. #21448048C2semidirect
3. #21447968C2semidirect
4. #21443867C2semidirect
5. #21443782C2semidirect
157. C61#12374semidirect

Maximal subgroups

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

subgroupindex
D4×Dic2442
#214480482
#214479682
#214438672
#214437822
D4⋊#117581852
C61×#16752
#1237461