Finite Group Databasebeta

← #21456314

Subgroups — #21456314

Order 7808.

532 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 532 conjugacy classes of subgroups — too many to draw. Only its 149 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×#14519807C212yesmaximal, complemented
2C22×Dic244C211yesmaximal, characteristic, complemented
3#16840333C212yesmaximal, complemented
4#16840153C214yesmaximal, complemented
5#16840145C212yesmaximal, complemented
6#16840140C212yesmaximal, complemented
7#16839717C211yesmaximal, characteristic, complemented
8C2×#135×C61C211yesmaximal, characteristic
9C22×Dic122C2212yes—
10#14519807—28no—
11C2×Dic244—24no—
12C2×Dic244C2212yes—
13C2×Dic244C2212yes—
14C2×#11758202C2214yes—
15C2×#11758200C2214yes—
16C2×#11758194C2211yescharacteristic
17#14519775C2214yes—
18#14519764C2214yes—
19#14519758—24no—
20#14519756—24no—
21#14519736C2211yescharacteristic
22#14519687C2212yes—
23C8×Dic61C2212yes—
24C2×#41×C61C2212yes—
25#135×C61—24no—
26C2×Q16×C61C2211yescharacteristic
27C2×SD16×C61C2212yes—
28C2×D8×C61C2211yescharacteristic
29C22×C8×C61C2211yescharacteristic
30#41×C61—24no—
31#41×C61—24no—
32C2×Q8×C61C2312yes—
33C2×D4×C61—22no—
34C2×D4×C61C2312yes—
35C22×C4×C61—22no—
36C22×C4×C61C2311yescharacteristic
37C22×Dic61—22no—
38C2×Dic122—24no—
39C2×Dic122—24no—
40C2×Dic122—22no—
41C2×Dic122C2314yes—
42Q16×C61—22no—
43SD16×C61—24no—
44D8×C61—22no—
45C2×C8×C61D414yes—
46C2×C8×C61C2311yescharacteristic
47C2×C8×C61C2311yescharacteristic
48C22⋊Dic61—28no—
49C22⋊Dic61D412yes—
50#11758202—28no—
51#11758200—28no—
52C4⋊Dic61D412yes—
53#11758196—28no—
54C4×Dic61C2312yes—
55#11758194D414yes—
56C2×#92418C2312yes—
57Dic244—24no—
58Dic244—24no—
59C23×C61—22no—
60C23×C61C2×D411yescharacteristic
61Q8×C61—22no—
62Q8×C61—22no—
63D4×C61—22no—
64D4×C61—22no—
65D4×C61—44no—
66C2×C4×C61—22no—
67C2×C4×C61—44no—
68C2×C4×C61C2×D411yescharacteristic
69C2×C4×C61C2×D412yes—
70C2×C4×C61C2×D412yes—
71C2×C4×C61C2411yescharacteristic
72C2×Dic61—24no—
73C2×Dic61—44no—
74C2×Dic61C2×D414yes—
75Dic122—24no—
76Dic122—24no—
77Dic122—44no—
78C8×C61C2×D412yes—
79C8×C61C2×D412yes—
80#92418C2×D414yes—
81C22×C61—22no—
82C22×C61—42no—
83C22×C61—44no—
84C22×C61#12712yes—
85C22×C61C22×D411yescharacteristic
86C4×C61—42no—
87C4×C61#12712yes—
88C4×C61C22×D411yescharacteristic
89C4×C61C22×D411yescharacteristic
90Dic61—24no—
91Dic61—44no—
92#3156—611nomaximal, Sylow
93C2×C61—22no—
94C2×C61—82no—
95C2×C61C2×#12711yescharacteristic
96C2×C61#57812yes—
97C2×#137—612no—
98C2×#135D6111yescharacteristic
99C22×Q16—611no—
100#536—612no—
101#497—614no—
102#495—612no—
103#494—612no—
104#405—611no—
105C61#315611yescharacteristic, complemented, Sylow
106C2×#41C2×D6112yes—
107C22×Q8—612no—
108#137—1228no—
109#135—24no—
110C2×Q16—614no—
111C2×Q16—612no—
112C2×Q16—612no—
113C2×Q16—1224no—
114C2×Q16C2×D6111yescharacteristic
115C2×SD16—614no—
116C2×SD16C2×D6112yes—
117C2×D8C2×D6111yescharacteristic
118C2×M16—611no—
119C22×C8C2×D6111yescharacteristic
120C4⋊Q8—614no—
121#124—614no—
122#123—1224no—
123C22⋊Q8—1224no—
124#117—611no—
125#97—612no—
126C4×C8—612no—
127#41—24no—
128#41—24no—
129C2×Q8—614no—
130C2×Q8—1222no—
131C2×Q8—1224no—
132C2×Q8—1224no—
133C2×Q8C22×D6112yes—
134C2×D4—22no—
135C2×D4C22×D6112yes—
136C22×C4—22no—
137C22×C4—1222no—
138C22×C4C22×D6111yescharacteristic
139Q16—22no—
140Q16—1228no—
141Q16—1224no—
142Q16—1224no—
143SD16—24no—
144SD16—1228no—
145D8—22no—
146M16—614no—
147C2×C8—612no—
148C2×C8C22⋊D6114yes—
149C2×C8C22×D6111yescharacteristic
150C2×C8C22×D6111yescharacteristic
151C4⋊C4—612no—
152C4⋊C4—1228no—
153C22⋊C4—612no—
154C22⋊C4—1228no—
155C42—612no—
156C23—22no—
157C23D4×D6111yescharacteristic
158Q8—22no—
159Q8—22no—
160Q8—1224no—
161Q8—1224no—
162Q8—2444no—
163D4—22no—
164D4—22no—
165D4—44no—
166C2×C4—22no—
167C2×C4—44no—
168C2×C4—614no—
169C2×C4—1224no—
170C2×C4—2444no—
171C2×C4D4×D6112yes—
172C2×C4D4×D6111yescharacteristic
173C2×C4C2×C22⋊D6112yes—
174C2×C4C23×D6111yescharacteristic
175C8—614no—
176C8C2×C22⋊D6112yes—
177C8C2×C22⋊D6112yes—
178C22—22no—
179C22—42no—
180C22—44no—
181C22#1451977312yes—
182C22C2×D4×D6111yescharacteristic
183C4—42no—
184C4—1224no—
185C4—2444no—
186C4#1451977312yes—
187C4C2×D4×D6111yescharacteristic
188C4C22×C22⋊D6111yescharacteristic
189C2—22no—
190C2—82no—
191C2C2×#1451977311yescharacteristic
192C2#1684057612yes—
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC2×#135×C61C2
socleC22×C61C22×D4
hypercenterC2×#135D61
hypocenterC61#3156
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#135

Complements

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

NH ≅ G/Ntype
1. C2×#14519807C2semidirect
2. C22×Dic244C2semidirect
3. #16840333C2semidirect
4. #16840153C2semidirect
5. #16840145C2semidirect
6. #16840140C2semidirect
7. #16839717C2semidirect
105. C61#3156semidirect