Finite Group Databasebeta

← #21445772

Subgroups — #21445772

Order 7808.

620 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 620 conjugacy classes of subgroups — too many to draw. Only its 101 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
1C2×#14519822C211yesmaximal, characteristic
2C2×#14519705C212yesmaximal, complemented
3#16839761C212yesmaximal, complemented
4C2×#14519694C211yesmaximal, characteristic, complemented
5C61×#390C211yesmaximal, characteristic, complemented
6#14519822—22no—
7#14519822—24no—
8#14519822C414yescomplemented
9C2×#11758222C2212yes—
10C2×#11758224—22no—
11C22×C22⋊D61—22no—
12C2×D4×D61—22no—
13C2×#11758194C2212yescomplemented
14#14519705—24no—
15#14519700—22no—
16#14519697—22no—
17#14519694—22no—
18C22×D4×C61C2211yescharacteristic
19C2×C4⋊C4×C61C2211yescharacteristic, complemented
20C2×C22⋊C4×C61—22no—
21C2×C42×C61C2211yescharacteristic, complemented
22C24×C61D412yes—
23C23×D61—22no—
24C2×D4×C61—22no—
25C2×D4×C61—22no—
26C2×D4×C61C2×C412yes—
27C2×D4×C61D412yes—
28C22×C4×C61—21no—
29C22×C4×C61—21no—
30C22×C4×C61C2311yescharacteristic
31C2×C22⋊D61—24no—
32C2×C22⋊D61—28no—
33C2×C22⋊D61—28no—
34C2×C22⋊D61—22no—
35C22×Dic61—22no—
36#11758224—28no—
37#11758224—28no—
38D4×D61—28no—
39D4×D61—28no—
40#11758222—22no—
41#11758222—22no—
42#11758222C2×C414yes—
43#11758222D414yes—
44C2×D244D412yes—
45C2×C4×D61—22no—
46C2×Dic122D412yes—
47C4⋊C4×C61—22no—
48C22⋊C4×C61—44no—
49C42×C61—22no—
50#11758194—22no—
51#11758194—22no—
52C2×#92418—22no—
53C23×C61—22no—
54C23×C61—22no—
55C23×C61—42no—
56C23×C61—42no—
57C23×C61C22⋊C414yes—
58C23×C61C2×D411yescharacteristic
59C22×D61—22no—
60C22×D61—28no—
61C22×D61—82no—
62C22×D61—82no—
63D4×C61—24no—
64D4×C61—24no—
65C2×C4×C61—22no—
66C2×C4×C61—41no—
67C2×C4×C61—41no—
68C2×C4×C61—42no—
69C2×C4×C61—41no—
70C2×C4×C61C22×C411yescharacteristic
71C2×C4×C61C2×D412yes—
72C2×C4×C61C2×D412yes—
73C2×C4×C61C2×D411yescharacteristic
74C22⋊D61—216no—
75C22⋊D61—24no—
76C22⋊D61—24no—
77C2×Dic61—28no—
78C2×Dic61—22no—
79D244—22no—
80D244C22⋊C414yescomplemented
81C4×D61—24no—
82C4×D61—24no—
83Dic122—22no—
84Dic122C22⋊C414yescomplemented
85#92418—42no—
86C22×C61—21no—
87C22×C61—21no—
88C22×C61—24no—
89C22×C61—44no—
90C22×C61—42no—
91C22×C61—42no—
92C22×C61—82no—
93C22×C61C2×C22⋊C411yescharacteristic
94C22×C61#12011yescharacteristic
95C22×C61#12011yescharacteristic
96C2×D61—24no—
97C2×D61—42no—
98C2×D61—42no—
99C2×D61—88no—
100C4×C61—42no—
101C4×C61—81no—
102C4×C61C2×C22⋊C412yes—
103C4×C61#12012yes—
104Dic61—24no—
105#1792—611nomaximal, Sylow
106C2×C61—21no—
107C2×C61—21no—
108C2×C61—44no—
109C2×C61#37911yescharacteristic
110C2×C61#45311yescharacteristic
111C2×C61#45511yescharacteristic
112D61—44no—
113C2×H(5,𝔽2)—611no—
114C2×#104—612no—
115#417—612no—
116C2×#100—611no—
117#390D6111yescharacteristic, complemented
118C61#179211yescharacteristic, complemented, Sylow
119H(5,𝔽2)—614no—
120H(5,𝔽2)—1224no—
121H(5,𝔽2)—1222no—
122C2×#41—612no—
123C2×#41—1222no—
124C22×D4—1222no—
125C22×D4—1222no—
126C22×D4C2×D6111yescharacteristic
127C2×M16—612no—
128C2×C4⋊C4C2×D6111yescharacteristic, complemented
129C2×C22⋊C4—22no—
130C2×C42C2×D6111yescharacteristic, complemented
131#104—1224no—
132#103—1222no—
133#102—1222no—
134#100—1222no—
135C24—1222no—
136C24C22⋊D6112yes—
137#41—614no—
138#41—614no—
139#41—1228no—
140#41—1228no—
141#41—1222no—
142#41—1222no—
143C2×Q8—612no—
144C2×D4—22no—
145C2×D4—22no—
146C2×D4—612no—
147C2×D4—1228no—
148C2×D4—1228no—
149C2×D4—1224no—
150C2×D4—1228no—
151C2×D4—1228no—
152C2×D4—1222no—
153C2×D4C4×D6112yes—
154C2×D4D24412yes—
155C22×C4—21no—
156C22×C4—21no—
157C22×C4—1222no—
158C22×C4—1222no—
159C22×C4C22×D6111yescharacteristic
160M16—1222no—
161M16—1222no—
162C2×C8—1222no—
163C4⋊C4—22no—
164C22⋊C4—44no—
165C42—22no—
166C23—22no—
167C23—22no—
168C23—42no—
169C23—42no—
170C23—1228no—
171C23—1222no—
172C23—4882no—
173C23—4882no—
174C23#1175819814yes—
175C23C2×C22⋊D6111yescharacteristic
176Q8—614no—
177Q8—1222no—
178D4—24no—
179D4—24no—
180D4—614no—
181D4—12216no—
182D4—1224no—
183D4—1224no—
184D4—1222no—
185C2×C4—22no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—42no—
189C2×C4—41no—
190C2×C4—1228no—
191C2×C4—1222no—
192C2×C4—1224no—
193C2×C4—1224no—
194C2×C4C2×C4×D6111yescharacteristic
195C2×C4C2×D24411yescharacteristic
196C2×C4D4×D6112yes—
197C2×C4D4×D6112yes—
198C8—2442no—
199C22—21no—
200C22—21no—
201C22—24no—
202C22—44no—
203C22—42no—
204C22—42no—
205C22—82no—
206C22—1224no—
207C22—4888no—
208C22—2442no—
209C22—2442no—
210C22C2×#1175819811yescharacteristic
211C22#1451974511yescharacteristic
212C22#1451974511yescharacteristic
213C4—42no—
214C4—81no—
215C4—1224no—
216C4C22⋊C4×D6112yes—
217C4#1451974712yes—
218C2—21no—
219C2—21no—
220C2—44no—
221C2—2444no—
222C2#1683961711yescharacteristic
223C2#1683992911yescharacteristic
224C2#1683993911yescharacteristic
subgroupG/H
centerC22#14519745
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC61×#390C2
socleC22×C61#120
hypercenter#390D61
hypocenterC61#1792
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #390

Complements

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

NH ≅ G/Ntype
2. C2×#14519705C2semidirect
3. #16839761C2semidirect
4. C2×#14519694C2semidirect
5. C61×#390C2semidirect
8. #14519822C4semidirect
13. C2×#11758194C22semidirect
19. C2×C4⋊C4×C61C22semidirect
21. C2×C42×C61C22semidirect
80. D244C22⋊C4semidirect
84. Dic122C22⋊C4semidirect
117. #390D61semidirect
118. C61#1792semidirect
128. C2×C4⋊C4C2×D61semidirect
130. C2×C42C2×D61semidirect