Finite Group Databasebeta

← #21456816

Subgroups — #21456816

Order 7808.

434 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 434 conjugacy classes of subgroups — too many to draw. Only its 121 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#16840312C211yesmaximal, characteristic, complemented
2#16840312C211yesmaximal, characteristic, complemented
3#16840151C212yesmaximal, complemented
4#16840122C212yesmaximal, complemented
5#16839968C212yesmaximal, complemented
6#16839958C212yesmaximal, complemented
7#16839909C214yesmaximal, complemented
8C61×#432C211yesmaximal, characteristic, complemented
9C2×#11758222—21no—
10C2×#11758222C2212yes—
11C2×#11758190C2214yes—
12C2×D488C2214yes—
13#14519777C2211yescharacteristic
14#14519777C2211yescharacteristic
15#14519774C2211yescharacteristic
16#14519774C2211yescharacteristic
17#14519765—21no—
18#14519765C2212yes—
19#14519751—21no—
20#14519751—21no—
21#14519751—21no—
22#14519751C2212yes—
23C4×D244—21no—
24C4×D244—21no—
25C4×D244—21no—
26C4×D244C2212yes—
27#14519702C2214yes—
28#14519699C2214yes—
29C2×C42×C61C2211yescharacteristic
30C4⋊C8×C61C2212yes—
31C22⋊C8×C61C2212yes—
32#97×C61C2212yes—
33C22×C4×C61D411yescharacteristic
34C22×C4×C61D411yescharacteristic
35C22×C4×C61C2311yescharacteristic
36C2×C22⋊D61—22no—
37C2×C22⋊D61—22no—
38#11758222—44no—
39#11758222—44no—
40C2×D244—21no—
41C2×D244—21no—
42C2×D244—21no—
43C2×D244—21no—
44C2×D244C2312yes—
45C2×D244C2312yes—
46C2×C4×D61—22no—
47C2×C4×D61—22no—
48C2×Dic122—21no—
49C2×Dic122C2312yes—
50C2×C8×C61C2314yes—
51C42×C61D411yescharacteristic
52C42×C61D411yescharacteristic
53C42×C61C2311yescharacteristic
54C42×C61C2311yescharacteristic
55#11758198—22no—
56#11758198—22no—
57#11758198—22no—
58#11758198—22no—
59C4⋊Dic61—21no—
60C4⋊Dic61—21no—
61C4⋊Dic61—21no—
62C4⋊Dic61C2312yes—
63D488—44no—
64#11758190—44no—
65C23×C61C2×D411yescharacteristic
66C22×D61—22no—
67C22×D61—22no—
68C2×C4×C61—22no—
69C2×C4×C61—22no—
70C2×C4×C61—41no—
71C2×C4×C61C2×D411yescharacteristic
72C2×C4×C61C2×D411yescharacteristic
73C2×C4×C61C2×D411yescharacteristic
74C2×C4×C61C2×D411yescharacteristic
75C2×C4×C61C2×D411yescharacteristic
76C2×C4×C61C2411yescharacteristic
77C22⋊D61—44no—
78C22⋊D61—44no—
79C2×Dic61—22no—
80C2×Dic61—22no—
81D244—22no—
82D244—22no—
83D244—24no—
84D244—42no—
85D244—42no—
86D244—42no—
87D244—42no—
88C4×D61—44no—
89C4×D61—44no—
90Dic122—24no—
91Dic122—42no—
92C8×C61—24no—
93C22×C61—21no—
94C22×C61—21no—
95C22×C61—21no—
96C22×C61C22×D411yescharacteristic
97C2×D61—42no—
98C2×D61—42no—
99C2×D61—42no—
100C2×D61—42no—
101C2×D61—42no—
102C2×D61—42no—
103C4×C61—21no—
104C4×C61—21no—
105C4×C61—21no—
106C4×C61—21no—
107C4×C61AGL(1,ℤ/8)12yes—
108C4×C61H(5,𝔽2)12yes—
109Dic61—42no—
110Dic61—42no—
111#3214—611nomaximal, Sylow
112C2×C61—41no—
113C2×C61#53511yescharacteristic
114C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
115C2×C61#57511yescharacteristic
116D61—82no—
117D61—82no—
118#532—611no—
119#532—611no—
120#496—612no—
121#489—612no—
122#461—612no—
123#459—612no—
124#449—614no—
125#432D6111yescharacteristic, complemented
126C61#321411yescharacteristic, complemented, Sylow
127C2×#41—612no—
128C2×#41—1221no—
129C2×SD16—614no—
130C2×D8—614no—
131C4⋊Q8—611no—
132C4⋊Q8—611no—
133#127—611no—
134#127—611no—
135#124—612no—
136#124—1221no—
137#121—612no—
138#121—1221no—
139#121—1221no—
140#121—1221no—
141C4×D4—612no—
142C4×D4—1221no—
143C4×D4—1221no—
144C4×D4—1221no—
145C2×C42C2×D6111yescharacteristic
146C4⋊C8C2×D6112yes—
147#103—614no—
148#102—614no—
149C22⋊C8C2×D6112yes—
150#97C2×D6112yes—
151#41—2444no—
152#41—2444no—
153C2×Q8—612no—
154C2×Q8—1221no—
155C2×D4—612no—
156C2×D4—612no—
157C2×D4—1222no—
158C2×D4—1222no—
159C2×D4—1221no—
160C2×D4—1221no—
161C2×D4—1221no—
162C2×D4—1221no—
163C22×C4—1222no—
164C22×C4—1222no—
165C22×C4D24411yescharacteristic
166C22×C4D24411yescharacteristic
167C22×C4C22×D6111yescharacteristic
168SD16—2444no—
169D8—2444no—
170C2×C8C22×D6114yes—
171C4⋊C4—612no—
172C4⋊C4—1221no—
173C4⋊C4—1221no—
174C4⋊C4—1221no—
175C22⋊C4—1222no—
176C22⋊C4—1222no—
177C22⋊C4—1222no—
178C22⋊C4—1222no—
179C42D24411yescharacteristic
180C42D24411yescharacteristic
181C42C22×D6111yescharacteristic
182C42C22×D6111yescharacteristic
183C23—1222no—
184C23—1222no—
185C23C2×D24411yescharacteristic
186Q8—1224no—
187Q8—2442no—
188D4—1222no—
189D4—1224no—
190D4—1222no—
191D4—2442no—
192D4—2442no—
193D4—2442no—
194D4—2444no—
195D4—2444no—
196D4—2442no—
197C2×C4—22no—
198C2×C4—22no—
199C2×C4—41no—
200C2×C4—1222no—
201C2×C4—1222no—
202C2×C4—2444no—
203C2×C4—2444no—
204C2×C4C2×D24411yescharacteristic
205C2×C4C2×D24411yescharacteristic
206C2×C4C2×D24411yescharacteristic
207C2×C4C2×D24411yescharacteristic
208C2×C4C2×D24411yescharacteristic
209C2×C4C23×D6111yescharacteristic
210C8—24no—
211C22—21no—
212C22—21no—
213C22—21no—
214C22—2442no—
215C22—2442no—
216C22—2442no—
217C22—2442no—
218C22—2442no—
219C22—2442no—
220C22C22×D24411yescharacteristic
221C4—21no—
222C4—21no—
223C4—21no—
224C4—21no—
225C4—2442no—
226C4—2442no—
227C4#1451980512yes—
228C4#1451982312yes—
229C2—41no—
230C2—4882no—
231C2—4882no—
232C2#1684033111yescharacteristic
233C2C2×#1451980511yescharacteristic
234C2#1684056211yescharacteristic
subgroupG/H
centerC22C22×D244
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#432C2
socleC22×C61C22×D4
hypercenter#432D61
hypocenterC61#3214
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
1. #16840312C2semidirect
2. #16840312C2semidirect
3. #16840151C2semidirect
4. #16840122C2semidirect
5. #16839968C2semidirect
6. #16839958C2semidirect
7. #16839909C2semidirect
8. C61×#432C2semidirect
125. #432D61semidirect
126. C61#3214semidirect