Finite Group Databasebeta

← #21444234

Subgroups — #21444234

Order 7808.

262 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 67 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#16840309C211yesmaximal, characteristic
2#16839814C211yesmaximal, characteristic, complemented
3C4×#11758189C211yesmaximal, characteristic, complemented
4#16839491C211yesmaximal, characteristic, complemented
5D4⋊#92418C211yesmaximal, characteristic, complemented
6#16839489C211yesmaximal, characteristic, complemented
7C61×D4⋊C8C211yesmaximal, characteristic, complemented
8C2×#11758222—21no—
9C2×#11758189—21no—
10#14519776C411yescharacteristic
11#14519773C411yescharacteristic
12#14519763—21no—
13#14519752C411yescharacteristic
14#14519750—21no—
15#14519748C411yescharacteristic
16C4×D244C2211yescharacteristic
17C4×C22⋊D61—21no—
18C42×D61C2211yescharacteristic
19C4⋊#92418C2211yescharacteristic
20#14519689—21no—
21#14519687—21no—
22C4×#92418C2211yescharacteristic
23C8×Dic61—21no—
24C4×D4×C61C2211yescharacteristic
25C4⋊C8×C61C2211yescharacteristic
26C4×C8×C61C2211yescharacteristic
27C2×D4×C61C2×C411yescharacteristic
28C22×C4×C61—21no—
29C2×C22⋊D61—21no—
30C2×C22⋊D61—21no—
31C2×C22⋊D61—21no—
32#11758222—42no—
33#11758222—42no—
34C2×D244—21no—
35C2×D244C2×C411yescharacteristic
36C2×C4×D61—21no—
37C2×C4×D61C2×C411yescharacteristic
38C2×C4×D61D411yescharacteristic
39C2×C4×D61D411yescharacteristic
40C2×Dic122—21no—
41C2×C8×C61—21no—
42C2×C8×C61—21no—
43C4⋊C4×C61C2×C411yescharacteristic
44C22⋊C4×C61—21no—
45C42×C61C2311yescharacteristic
46C22⋊Dic61—21no—
47#11758198—21no—
48#11758198—21no—
49C4⋊Dic61C2×C411yescharacteristic
50#11758196—21no—
51C4×Dic61C2×C411yescharacteristic
52C4×Dic61D411yescharacteristic
53C4×Dic61D411yescharacteristic
54C2×#92418—21no—
55C2×#92418—21no—
56#11758189—24no—
57C23×C61—21no—
58C22×D61—21no—
59C22×D61C22⋊C411yescharacteristic
60D4×C61—21no—
61D4×C61—21no—
62C2×C4×C61—21no—
63C2×C4×C61—41no—
64C2×C4×C61—41no—
65C2×C4×C61C22×C411yescharacteristic
66C2×C4×C61C2×D411yescharacteristic
67C2×C4×C61C2×D411yescharacteristic
68C22⋊D61—42no—
69C22⋊D61—42no—
70C22⋊D61—42no—
71C2×Dic61—21no—
72C2×Dic61C22⋊C411yescharacteristic
73C2×Dic61C22⋊C411yescharacteristic
74C2×Dic61C22⋊C411yescharacteristic
75D244—21no—
76D244—21no—
77D244—42no—
78C4×D61—21no—
79C4×D61—21no—
80C4×D61—21no—
81C4×D61—21no—
82C4×D61—22no—
83C4×D61—41no—
84C4×D61—41no—
85Dic122—42no—
86C8×C61—22no—
87C8×C61—41no—
88#92418—22no—
89#92418—41no—
90C22×C61—41no—
91C22×C61—41no—
92C22×C61—41no—
93C22×C61C2×C22⋊C411yescharacteristic
94C2×D61—21no—
95C2×D61—21no—
96C2×D61—21no—
97C2×D61—41no—
98C2×D61—41no—
99C2×D61—41no—
100C4×C61—21no—
101C4×C61—41no—
102C4×C61#13111yescharacteristic
103C4×C61#13111yescharacteristic
104C4×C61AGL(1,ℤ/8)11yescharacteristic
105C4×C61AGL(1,ℤ/8)11yescharacteristic
106Dic61—21no—
107Dic61—21no—
108Dic61—41no—
109Dic61#10412yes—
110#1484—611nomaximal, Sylow
111C2×C61—81no—
112C2×C61#40811yescharacteristic
113C2×C61#41811yescharacteristic
114C2×C61C2×#10411yescharacteristic
115D61—41no—
116D61—81no—
117#532—611no—
118#431—611no—
119C4×M16—611no—
120D4⋊C8—611no—
121D4⋊C8—611no—
122D4⋊C8—611no—
123D4⋊C8D6111yescharacteristic, complemented
124C61#148411yescharacteristic, complemented, Sylow
125C2×#41—1221no—
126C2×M16—1221no—
127C4⋊Q8—611no—
128#127—611no—
129#124—1221no—
130#121—611no—
131#121—611no—
132#121—1221no—
133C4×D4—611no—
134C4×D4—1221no—
135C4×D4C2×D6111yescharacteristic
136C2×C42—611no—
137C4⋊C8—611no—
138C4⋊C8C2×D6111yescharacteristic
139C22⋊C8—1221no—
140#97—1221no—
141C4×C8—611no—
142C4×C8—1221no—
143C4×C8C2×D6111yescharacteristic
144#41—2442no—
145#41—2442no—
146C2×Q8—1221no—
147C2×D4—611no—
148C2×D4—1221no—
149C2×D4—1221no—
150C2×D4—1221no—
151C2×D4—1221no—
152C2×D4C4×D6111yescharacteristic
153C22×C4—21no—
154C22×C4—611no—
155C22×C4—611no—
156C22×C4—611no—
157C22×C4—1221no—
158M16—1224no—
159C2×C8—21no—
160C2×C8—21no—
161C2×C8—1221no—
162C2×C8—1221no—
163C4⋊C4—611no—
164C4⋊C4—1221no—
165C4⋊C4C4×D6111yescharacteristic
166C22⋊C4—21no—
167C22⋊C4—1221no—
168C22⋊C4—1221no—
169C22⋊C4—1221no—
170C42—611no—
171C42—611no—
172C42—611no—
173C42C22×D6111yescharacteristic
174C23—21no—
175C23—611no—
176C23—1221no—
177Q8—2442no—
178D4—21no—
179D4—21no—
180D4—1221no—
181D4—1221no—
182D4—2442no—
183D4—2442no—
184D4—2442no—
185D4—2442no—
186C2×C4—21no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—611no—
190C2×C4—611no—
191C2×C4—611no—
192C2×C4—1222no—
193C2×C4—1221no—
194C2×C4—1221no—
195C2×C4—1221no—
196C2×C4—1221no—
197C2×C4—1221no—
198C2×C4—2441no—
199C2×C4—2441no—
200C2×C4C2×C4×D6111yescharacteristic
201C2×C4D4×D6111yescharacteristic
202C2×C4D4×D6111yescharacteristic
203C8—22no—
204C8—41no—
205C8—1222no—
206C8—2441no—
207C22—41no—
208C22—41no—
209C22—41no—
210C22—1221no—
211C22—1221no—
212C22—1221no—
213C22—2441no—
214C22—2441no—
215C22—2441no—
216C22C22⋊C4×D6111yescharacteristic
217C4—21no—
218C4—41no—
219C4—612no—
220C4—1221no—
221C4—1221no—
222C4—2441no—
223C4#1451978311yescharacteristic
224C4#1451978511yescharacteristic
225C4#1451980111yescharacteristic
226C4#1451980411yescharacteristic
227C2—81no—
228C2—4881no—
229C2—2441no—
230C2#1683972711yescharacteristic
231C2#1683976511yescharacteristic
232C2#104×D6111yescharacteristic
subgroupG/H
centerC2×C4D4×D61
commutatorC2×C4×C61C22×C4
FrattiniC42C22×D61
FittingC61×D4⋊C8C2
socleC22×C61C2×C22⋊C4
hypercenterD4⋊C8D61
hypocenterC61#1484
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #16839814C2semidirect
3. C4×#11758189C2semidirect
4. #16839491C2semidirect
5. D4⋊#92418C2semidirect
6. #16839489C2semidirect
7. C61×D4⋊C8C2semidirect
123. D4⋊C8D61semidirect
124. C61#1484semidirect