Finite Group Databasebeta

← #21457290

Subgroups — #21457290

Order 7808.

346 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 117 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#16840383C212yesmaximal, complemented
2#16840053C212yesmaximal, complemented
3#16840048C212yesmaximal, complemented
4#16840020C211yesmaximal, characteristic, complemented
5#16840015C211yesmaximal, characteristic
6#16839991C212yesmaximal, complemented
7#16839985C212yesmaximal, complemented
8#16839978C212yesmaximal, complemented
9C61×#424C211yesmaximal, characteristic, complemented
10C2×Dic244C2211yescharacteristic
11C2×#11758190C2212yes—
12C2×D488C2211yescharacteristic
13#14519777C2212yes—
14#14519772—22no—
15#14519765C2212yes—
16#14519763—22no—
17#14519759—22no—
18#14519756C2212yes—
19#14519755—22no—
20#14519751C2212yes—
21C4×Dic122C2212yes—
22C4×D244C2212yes—
23#14519709C2212yes—
24#14519709C2211yescharacteristic
25#14519709C2211yescharacteristic
26#14519702C2212yes—
27#14519702C2212yes—
28#14519699C2212yes—
29#14519699C2212yes—
30C2×M16×C61C2211yescharacteristic
31C22×C8×C61C2211yescharacteristic
32#117×C61C2211yescharacteristic
33C4⋊C8×C61C2212yes—
34C4⋊C8×C61C2212yes—
35C22×C4×C61C2311yescharacteristic
36C2×C22⋊D61—22no—
37C2×D244C2312yes—
38C2×C4×D61—22no—
39C2×Dic122—22no—
40C2×Dic122C2312yes—
41M16×C61—41no—
42C2×C8×C61—41no—
43C2×C8×C61C2312yes—
44C2×C8×C61C2311yescharacteristic
45C2×C8×C61C2311yescharacteristic
46C4⋊C4×C61D412yes—
47C22⋊C4×C61D411yescharacteristic
48C22⋊C4×C61D411yescharacteristic
49C42×C61C2312yes—
50C22⋊Dic61—22no—
51#11758198—22no—
52#11758198—22no—
53#11758198—22no—
54#11758198—22no—
55C4⋊Dic61—22no—
56C4⋊Dic61C2312yes—
57C4⋊Dic61C2312yes—
58#11758196—22no—
59#11758196—22no—
60C4×Dic61—22no—
61Dic244—41no—
62D488—41no—
63#11758190—42no—
64C23×C61C2×D411yescharacteristic
65C22×D61—22no—
66C2×C4×C61—21no—
67C2×C4×C61—21no—
68C2×C4×C61C2×D412yes—
69C2×C4×C61C2×D411yescharacteristic
70C2×C4×C61C2×D412yes—
71C2×C4×C61C2411yescharacteristic
72C22⋊D61—82no—
73C2×Dic61—22no—
74C2×Dic61—22no—
75C2×Dic61—22no—
76D244—22no—
77D244—22no—
78C4×D61—82no—
79Dic122—22no—
80Dic122—22no—
81Dic122—82no—
82C8×C61—22no—
83C8×C61—21no—
84C8×C61—21no—
85C22×C61—21no—
86C22×C61—22no—
87C22×C61C22×D411yescharacteristic
88C2×D61—42no—
89C2×D61—42no—
90C2×D61—42no—
91C4×C61—21no—
92C4×C61—22no—
93C4×C61—22no—
94C4×C61H(5,𝔽2)11yescharacteristic
95C4×C612−1+411yescharacteristic
96Dic61—42no—
97Dic61—42no—
98Dic61—42no—
99#3263—611nomaximal, Sylow
100C2×C61—41no—
101C2×C61#53711yescharacteristic
102C2×C61#57712yes—
103D61—82no—
104#542—612no—
105#476—612no—
106#475—612no—
107#470—611no—
108#469—611no—
109#465—612no—
110#464—612no—
111#463—612no—
112#424D6111yescharacteristic, complemented
113C61#326311yescharacteristic, complemented, Sylow
114C2×Q16—611no—
115C2×SD16—612no—
116C2×D8—611no—
117C2×M16C2×D6111yescharacteristic
118C22×C8C2×D6111yescharacteristic
119C4⋊Q8—612no—
120#126—1222no—
121#124—612no—
122#124—1222no—
123#123—1222no—
124C22⋊Q8—612no—
125C22⋊Q8—1222no—
126#121—612no—
127C4×Q8—612no—
128C4×D4—612no—
129#117C2×D6111yescharacteristic
130#106—612no—
131#106—611no—
132#106—611no—
133C4⋊C8C2×D6112yes—
134C4⋊C8C2×D6112yes—
135#103—612no—
136#103—612no—
137#102—612no—
138#102—612no—
139C2×Q8—612no—
140C2×Q8—1222no—
141C2×D4—612no—
142C2×D4—1222no—
143C22×C4—1222no—
144C22×C4C22×D6111yescharacteristic
145Q16—2441no—
146SD16—2442no—
147D8—2441no—
148M16—41no—
149C2×C8—41no—
150C2×C8C22×D6111yescharacteristic
151C2×C8C22×D6112yes—
152C2×C8C22×D6111yescharacteristic
153C4⋊C4—612no—
154C4⋊C4—612no—
155C4⋊C4—1222no—
156C4⋊C4—1222no—
157C4⋊C4—1222no—
158C4⋊C4D24412yes—
159C22⋊C4—1222no—
160C22⋊C4—1222no—
161C22⋊C4—1222no—
162C22⋊C4—1222no—
163C22⋊C4—1222no—
164C22⋊C4D24411yescharacteristic
165C22⋊C4D24411yescharacteristic
166C42—1222no—
167C42C22×D6112yes—
168C23—1222no—
169C23C2×D24411yescharacteristic
170Q8—1222no—
171Q8—1222no—
172Q8—4882no—
173D4—1222no—
174D4—1222no—
175D4—4882no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—1222no—
179C2×C4—1222no—
180C2×C4—1222no—
181C2×C4—4882no—
182C2×C4C2×D24412yes—
183C2×C4C2×D24412yes—
184C2×C4C2×D24411yescharacteristic
185C2×C4C23×D6111yescharacteristic
186C8—22no—
187C8—21no—
188C8—21no—
189C22—22no—
190C22—21no—
191C22—2442no—
192C22—2442no—
193C22—2442no—
194C22C22×D24411yescharacteristic
195C4—22no—
196C4—22no—
197C4—21no—
198C4—2442no—
199C4—2442no—
200C4—2442no—
201C4#1451982211yescharacteristic
202C4#1451982511yescharacteristic
203C2—41no—
204C2—4882no—
205C2#1684034311yescharacteristic
206C2#1684057412yes—
subgroupG/H
centerC22C22×D244
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#424C2
socleC22×C61C22×D4
hypercenter#424D61
hypocenterC61#3263
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ #117 ◁ #424

Complements

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

NH ≅ G/Ntype
1. #16840383C2semidirect
2. #16840053C2semidirect
3. #16840048C2semidirect
4. #16840020C2semidirect
6. #16839991C2semidirect
7. #16839985C2semidirect
8. #16839978C2semidirect
9. C61×#424C2semidirect
112. #424D61semidirect
113. C61#3263semidirect