Finite Group Databasebeta

← #21444364

Subgroups — #21444364

Order 7808.

252 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 61 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#16840307C211yesmaximal, characteristic
2#16839816C211yesmaximal, characteristic, complemented
3#16839629C211yesmaximal, characteristic, complemented
4#16839497C211yesmaximal, characteristic, complemented
5#16839496C211yesmaximal, characteristic, complemented
6#16839495C211yesmaximal, characteristic, complemented
7C61×#327C211yesmaximal, characteristic, complemented
8C2×#11758224—21no—
9#14519776C411yescharacteristic, complemented
10#14519773C411yescharacteristic, complemented
11#14519763—21no—
12#14519751C2211yescharacteristic
13#14519749—21no—
14D4×Dic61C411yescharacteristic, complemented
15#14519739C411yescharacteristic, complemented
16#14519737—21no—
17C2×C4×Dic61C2211yescharacteristic
18#14519706—21no—
19C22⋊#92418C2211yescharacteristic
20#14519687—21no—
21#14519684—21no—
22#14519684—21no—
23#14519684C2211yescharacteristic
24#121×C61C2211yescharacteristic
25C22⋊C8×C61C2211yescharacteristic
26#95×C61C2211yescharacteristic
27C2×D4×C61—21no—
28C2×D4×C61C2×C411yescharacteristic
29C22×C4×C61—21no—
30C22×C4×C61C2311yescharacteristic
31C2×C22⋊D61—21no—
32C2×C22⋊D61—21no—
33C2×C22⋊D61—21no—
34C22×Dic61—21no—
35C22×Dic61—21no—
36C22×Dic61D411yescharacteristic
37C22×Dic61D411yescharacteristic
38#11758224—42no—
39#11758224—42no—
40C2×D244C2×C411yescharacteristic
41C2×C4×D61—21no—
42C2×Dic122—21no—
43C2×C8×C61—21no—
44C4⋊C4×C61C2×C411yescharacteristic
45C22⋊C4×C61—21no—
46C22⋊Dic61—21no—
47#11758198—21no—
48#11758198—21no—
49C4⋊Dic61C2×C411yescharacteristic
50#11758196—21no—
51C4×Dic61C2×C411yescharacteristic
52C4×Dic61C2×C411yescharacteristic
53C4×Dic61D411yescharacteristic
54C4×Dic61D411yescharacteristic
55C2×#92418—21no—
56C23×C61—21no—
57C23×C61C2×D411yescharacteristic
58C22×D61—21no—
59D4×C61—41no—
60D4×C61—41no—
61D4×C61—41no—
62C2×C4×C61—21no—
63C2×C4×C61—41no—
64C2×C4×C61—41no—
65C2×C4×C61—41no—
66C2×C4×C61—41no—
67C2×C4×C61C22×C411yescharacteristic
68C2×C4×C61C2×D411yescharacteristic
69C22⋊D61—42no—
70C22⋊D61—42no—
71C22⋊D61—41no—
72C22⋊D61—41no—
73C2×Dic61—21no—
74C2×Dic61—21no—
75C2×Dic61—21no—
76C2×Dic61—41no—
77C2×Dic61—42no—
78C2×Dic61—41no—
79C2×Dic61—41no—
80C2×Dic61—41no—
81C2×Dic61C22⋊C411yescharacteristic
82C2×Dic61C22⋊C411yescharacteristic
83C2×Dic61C22⋊C411yescharacteristic
84C2×Dic61C22⋊C411yescharacteristic
85D244—41no—
86C4×D61—42no—
87Dic122—42no—
88C8×C61—41no—
89#92418—41no—
90C22×C61—21no—
91C22×C61—21no—
92C22×C61—41no—
93C22×C61—41no—
94C22×C61—41no—
95C22×C61C2×C22⋊C411yescharacteristic
96C22×C61AGL(1,ℤ/8)11yescharacteristic
97C22×C61AGL(1,ℤ/8)11yescharacteristic
98C2×D61—41no—
99C2×D61—41no—
100C2×D61—41no—
101C4×C61—21no—
102C4×C61—21no—
103C4×C61—41no—
104C4×C61—81no—
105Dic61—21no—
106Dic61—21no—
107Dic61—21no—
108Dic61—21no—
109Dic61—41no—
110Dic61—81no—
111#1514—611nomaximal, Sylow
112C2×C61—21no—
113C2×C61—21no—
114C2×C61—81no—
115C2×C61#41011yescharacteristic
116C2×C61#41811yescharacteristic
117C2×C61#42111yescharacteristic
118D61—81no—
119#532—611no—
120#432—611no—
121#383—611no—
122#327—611no—
123#327—611no—
124#327—611no—
125#327D6111yescharacteristic, complemented
126C61#151411yescharacteristic, complemented, Sylow
127C2×#41—1221no—
128C4⋊Q8—611no—
129#127—611no—
130#124—1221no—
131#121—611no—
132#121—1221no—
133#121C2×D6111yescharacteristic
134C4×D4—611no—
135C4×D4—611no—
136C4×D4—1221no—
137C2×C42—611no—
138C4⋊C8—1221no—
139C22⋊C8—611no—
140C22⋊C8C2×D6111yescharacteristic
141#97—1221no—
142#95—611no—
143#95—1221no—
144#95—1221no—
145#95C2×D6111yescharacteristic
146#41—2442no—
147#41—2442no—
148C2×Q8—1221no—
149C2×D4—21no—
150C2×D4—611no—
151C2×D4—1221no—
152C2×D4—1221no—
153C2×D4—1221no—
154C2×D4C4×D6111yescharacteristic
155C22×C4—21no—
156C22×C4—611no—
157C22×C4—611no—
158C22×C4—1221no—
159C22×C4—1221no—
160C22×C4—1221no—
161C22×C4C22×D6111yescharacteristic
162C2×C8—21no—
163C2×C8—1221no—
164C4⋊C4—611no—
165C4⋊C4—1221no—
166C4⋊C4C4×D6111yescharacteristic
167C22⋊C4—21no—
168C22⋊C4—1221no—
169C22⋊C4—1221no—
170C22⋊C4—1221no—
171C42—611no—
172C42—611no—
173C42—611no—
174C42—611no—
175C23—21no—
176C23—1221no—
177C23D4×D6111yescharacteristic
178Q8—2442no—
179D4—41no—
180D4—41no—
181D4—41no—
182D4—2441no—
183D4—2442no—
184D4—2442no—
185D4—2441no—
186D4—2441no—
187C2×C4—21no—
188C2×C4—41no—
189C2×C4—41no—
190C2×C4—41no—
191C2×C4—41no—
192C2×C4—611no—
193C2×C4—611no—
194C2×C4—611no—
195C2×C4—611no—
196C2×C4—1221no—
197C2×C4—1221no—
198C2×C4—1221no—
199C2×C4—2442no—
200C2×C4—2441no—
201C2×C4—2442no—
202C2×C4—2441no—
203C2×C4—2441no—
204C2×C4—2441no—
205C2×C4C2×C4×D6111yescharacteristic
206C2×C4D4×D6111yescharacteristic
207C8—41no—
208C8—2441no—
209C22—21no—
210C22—21no—
211C22—41no—
212C22—41no—
213C22—41no—
214C22—2441no—
215C22—2441no—
216C22—2441no—
217C22C22⋊C4×D6111yescharacteristic
218C22#1451980111yescharacteristic
219C22#1451980411yescharacteristic
220C4—21no—
221C4—21no—
222C4—41no—
223C4—81no—
224C4—1221no—
225C4—1221no—
226C4—1221no—
227C4—1221no—
228C4—4881no—
229C4—2441no—
230C2—21no—
231C2—21no—
232C2—81no—
233C2—4881no—
234C2#1683973411yescharacteristic
235C2#1683976511yescharacteristic
236C2#1683977711yescharacteristic
subgroupG/H
centerC22C22⋊C4×D61
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC61×#327C2
socleC22×C61C2×C22⋊C4
hypercenter#327D61
hypocenterC61#1514
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

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

NH ≅ G/Ntype
2. #16839816C2semidirect
3. #16839629C2semidirect
4. #16839497C2semidirect
5. #16839496C2semidirect
6. #16839495C2semidirect
7. C61×#327C2semidirect
9. #14519776C4semidirect
10. #14519773C4semidirect
14. D4×Dic61C4semidirect
15. #14519739C4semidirect
125. #327D61semidirect
126. C61#1514semidirect