Finite Group Databasebeta

← #21447082

Subgroups — #21447082

Order 7808.

276 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 276 conjugacy classes of subgroups — too many to draw. Only its 69 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
1C22×#11758190C211yesmaximal, characteristic
2#16839770C211yesmaximal, characteristic, complemented
3#16839766C211yesmaximal, characteristic
4C2×#14519695C211yesmaximal, characteristic, complemented
5C2×#14519693C211yesmaximal, characteristic
6#16839527C211yesmaximal, characteristic, complemented
7C61×#424C211yesmaximal, characteristic, complemented
8C22×Dic122C2211yescharacteristic
9C22×D244C2211yescharacteristic
10C2×#11758190—22no—
11C2×#11758190—22no—
12C2×#11758190—22no—
13C2×#11758194C2211yescharacteristic
14C2×#11758194C2211yescharacteristic
15#14519700—22no—
16#14519697—22no—
17#14519695—22no—
18#14519693—22no—
19C2×M16×C61C2211yescharacteristic
20C22×C8×C61C2211yescharacteristic
21#117×C61C2211yescharacteristic
22C4⋊C8×C61—22no—
23C23×D61—21no—
24C22×C4×C61C2311yescharacteristic
25C22×Dic61—21no—
26C2×D244—21no—
27C2×D244—21no—
28C2×D244—21no—
29C2×D244—21no—
30C2×D244—21no—
31C2×D244D412yes—
32C2×Dic122—21no—
33C2×Dic122—21no—
34C2×Dic122—21no—
35C2×Dic122—21no—
36C2×Dic122—21no—
37C2×Dic122D412yes—
38M16×C61—21no—
39M16×C61—21no—
40C2×C8×C61—21no—
41C2×C8×C61—21no—
42C2×C8×C61—21no—
43C2×C8×C61D412yes—
44C4⋊C4×C61D412yes—
45C22⋊C4×C61—21no—
46C42×C61—21no—
47#11758194—21no—
48#11758194—21no—
49#11758194—21no—
50#11758194—21no—
51C2×#92418—21no—
52C2×#92418—21no—
53#11758190—28no—
54C23×C61#4111yescharacteristic
55C22×D61—22no—
56C22×D61—41no—
57C22×D61—41no—
58C22×D61—82no—
59C2×C4×C61—22no—
60C2×C4×C61C2×D411yescharacteristic
61C2×C4×C61C2×D411yescharacteristic
62C2×C4×C61C2×D411yescharacteristic
63C2×C4×C61C2×D411yescharacteristic
64C2×C4×C61#4111yescharacteristic
65C2×C4×C61#4111yescharacteristic
66C2×Dic61—22no—
67C2×Dic61—41no—
68C2×Dic61—41no—
69D244—22no—
70D244—22no—
71D244—41no—
72D244—41no—
73Dic122—22no—
74Dic122—22no—
75Dic122—41no—
76Dic122—41no—
77C8×C61—22no—
78C8×C61—41no—
79#92418—41no—
80#92418—41no—
81C22×C61—22no—
82C22×C61#12111yescharacteristic
83C22×C61#12311yescharacteristic
84C22×C61#12311yescharacteristic
85C2×D61—42no—
86C2×D61—82no—
87C2×D61—82no—
88C2×D61—82no—
89C4×C61—42no—
90C4×C61#12011yescharacteristic
91C4×C61#12111yescharacteristic
92C4×C61#12111yescharacteristic
93C4×C61#12411yescharacteristic
94Dic61—42no—
95#2046—611nomaximal, Sylow
96C2×C61—21no—
97C2×C61—21no—
98C2×C61#39411yescharacteristic
99C2×C61#47112yes—
100D61—82no—
101C22×SD16—611no—
102#424D6111yescharacteristic, complemented
103#419—611no—
104#418—611no—
105C2×#101—611no—
106C2×#100—611no—
107#341—611no—
108C61#204611yescharacteristic, complemented, Sylow
109C22×Q8—611no—
110C22×D4—611no—
111C2×SD16—1222no—
112C2×SD16—1222no—
113C2×SD16—1222no—
114C2×M16—611no—
115C2×M16—611no—
116C2×M16C2×D6111yescharacteristic
117C22×C8C2×D6111yescharacteristic
118#117C2×D6111yescharacteristic
119C4⋊C8—22no—
120#103—1222no—
121#102—1222no—
122#101—1222no—
123#100—1222no—
124C24—1221no—
125C2×Q8—612no—
126C2×Q8—1221no—
127C2×Q8—1221no—
128C2×Q8—1221no—
129C2×Q8—1221no—
130C2×Q8—1221no—
131C2×D4—612no—
132C2×D4—1221no—
133C2×D4—1221no—
134C2×D4—1221no—
135C2×D4—1221no—
136C2×D4—1221no—
137C22×C4—1221no—
138C22×C4C22×D6111yescharacteristic
139SD16—1228no—
140M16—21no—
141M16—21no—
142M16—1221no—
143M16—1221no—
144M16—1221no—
145M16—1221no—
146C2×C8—21no—
147C2×C8—21no—
148C2×C8—21no—
149C2×C8—1221no—
150C2×C8—1221no—
151C2×C8C22⋊D6112yes—
152C4⋊C4D24412yes—
153C22⋊C4—21no—
154C42—21no—
155C23—1222no—
156C23—4882no—
157C23—2441no—
158C23—2441no—
159C23#1175822211yescharacteristic
160Q8—1222no—
161Q8—1222no—
162Q8—2441no—
163Q8—2441no—
164D4—1222no—
165D4—1222no—
166D4—2441no—
167D4—2441no—
168C2×C4—22no—
169C2×C4—1222no—
170C2×C4—2441no—
171C2×C4—2441no—
172C2×C4C2×D24411yescharacteristic
173C2×C4D4×D6111yescharacteristic
174C2×C4D4×D6111yescharacteristic
175C2×C4#1175822611yescharacteristic
176C2×C4#1175822611yescharacteristic
177C2×C4C2×C22⋊D6111yescharacteristic
178C8—22no—
179C8—41no—
180C8—2441no—
181C8—2441no—
182C22—22no—
183C22—4882no—
184C22—4882no—
185C22—4882no—
186C22—2442no—
187C22#1451975111yescharacteristic
188C22#1451976211yescharacteristic
189C22#1451976211yescharacteristic
190C4—42no—
191C4—2442no—
192C4#1451974511yescharacteristic
193C4#1451975211yescharacteristic
194C4#1451975211yescharacteristic
195C4#1451976611yescharacteristic
196C2—21no—
197C2—21no—
198C2—4882no—
199C2#1683967911yescharacteristic
200C2#1684002512yes—
subgroupG/H
centerC22#14519751
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC61×#424C2
socleC22×C61#121
hypercenter#424D61
hypocenterC61#2046
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #424

Complements

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

NH ≅ G/Ntype
2. #16839770C2semidirect
4. C2×#14519695C2semidirect
6. #16839527C2semidirect
7. C61×#424C2semidirect
102. #424D61semidirect
108. C61#2046semidirect