Finite Group Databasebeta

← #21455306

Subgroups — #21455306

Order 7808.

480 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 157 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
2C2×#14519777C211yesmaximal, characteristic, complemented
3#16839972C214yesmaximal, complemented
4#16839967C214yesmaximal, complemented
5#16839786C211yesmaximal, characteristic, complemented
6#16839770C212yesmaximal, complemented
7C4×#41×C61C211yesmaximal, characteristic
8C22×Dic122C2212yes—
9#14519807—28no—
10C2×#11758202C2214yes—
11C2×#11758200C2214yes—
12C2×#11758194C2212yes—
13#14519777—21no—
14#14519777—21no—
15#14519777C2214yes—
16C2×C4⋊Dic61—22no—
17C4⋊#92418C2214yes—
18#14519700C2218yes—
19C2×#41×C61C2211yescharacteristic
20C4×Q8×C61C2212yes—
21C4×D4×C61—22no—
22C4×D4×C61C2212yes—
23#117×C61—21no—
24#117×C61C2211yescharacteristic
25C2×C42×C61—21no—
26C2×C42×C61C2211yescharacteristic
27#41×C61—22no—
28#41×C61D414yes—
29C2×Q8×C61C2311yescharacteristic
30C2×D4×C61—21no—
31C2×D4×C61C2311yescharacteristic
32C22×C4×C61—21no—
33C22×C4×C61—22no—
34C22×C4×C61D412yes—
35C22×C4×C61C2311yescharacteristic
36C22×Dic61—22no—
37C2×Dic122—24no—
38C2×Dic122—24no—
39C2×Dic122—22no—
40C2×Dic122C2314yes—
41C4⋊C4×C61—22no—
42C4⋊C4×C61C2312yes—
43C22⋊C4×C61—21no—
44C22⋊C4×C61—22no—
45C42×C61—21no—
46C42×C61—22no—
47C42×C61D411yescharacteristic
48C42×C61D411yescharacteristic
49C42×C61C2312yes—
50#11758202—28no—
51#11758200—28no—
52C4⋊Dic61—24no—
53C4⋊Dic61—24no—
54#11758194—24no—
55C2×#92418C2314yes—
56C23×C61—21no—
57C23×C61C2×D411yescharacteristic
58Q8×C61—21no—
59Q8×C61C2×D412yes—
60D4×C61—24no—
61D4×C61—21no—
62D4×C61C2×D412yes—
63C2×C4×C61—21no—
64C2×C4×C61—24no—
65C2×C4×C61—24no—
66C2×C4×C61—22no—
67C2×C4×C61—44no—
68C2×C4×C61C2×D412yes—
69C2×C4×C61C2×D411yescharacteristic
70C2×C4×C61C2×D412yes—
71C2×C4×C61C2×D412yes—
72C2×C4×C61#4112yes—
73C2×C4×C61C2411yescharacteristic
74C2×Dic61—24no—
75C2×Dic61—44no—
76Dic122—24no—
77Dic122—24no—
78Dic122—44no—
79#92418—24no—
80C22×C61—22no—
81C22×C61—22no—
82C22×C61—42no—
83C22×C61#12112yes—
84C22×C61C22×D411yescharacteristic
85C4×C61—22no—
86C4×C61—22no—
87C4×C61—42no—
88C4×C61#12112yes—
89C4×C61#13714yescomplemented
90C4×C61C22×D411yescharacteristic
91C4×C61C2×#4111yescharacteristic
92Dic61—44no—
93#3039—611nomaximal, Sylow
94C2×C61—22no—
95C2×C61—42no—
96C2×C61C2×#12111yescharacteristic
97C2×C61C2×#13712yes—
98C2×#137—612no—
99C2×C4⋊Q8—611no—
100C4×#41D6111yescharacteristic
101#462—614no—
102#461—614no—
103#423—611no—
104#419—612no—
105C61#303911yescharacteristic, complemented, Sylow
106C2×#41C2×D6111yescharacteristic
107C22×Q8—612no—
108#137—1228no—
109C2×Q16—614no—
110C2×SD16—614no—
111C2×M16—612no—
112C4⋊Q8—614no—
113C4⋊Q8—1221no—
114C4⋊Q8—1221no—
115C4×Q8C2×D6112yes—
116C4×D4—22no—
117C4×D4C2×D6112yes—
118#117—21no—
119#117C2×D6111yescharacteristic
120C2×C4⋊C4—1222no—
121C2×C42—21no—
122C2×C42C2×D6111yescharacteristic
123C4⋊C8—614no—
124#103—618no—
125#41—22no—
126#41D24414yes—
127C2×Q8—614no—
128C2×Q8—1222no—
129C2×Q8—1224no—
130C2×Q8—1224no—
131C2×Q8C22×D6111yescharacteristic
132C2×D4—21no—
133C2×D4C22×D6111yescharacteristic
134C22×C4—21no—
135C22×C4—22no—
136C22×C4—1222no—
137C22×C4C22⋊D6112yes—
138C22×C4C22×D6111yescharacteristic
139Q16—1228no—
140SD16—1228no—
141M16—1224no—
142C2×C8—614no—
143C4⋊C4—22no—
144C4⋊C4—1224no—
145C4⋊C4—1224no—
146C4⋊C4C22×D6112yes—
147C22⋊C4—21no—
148C22⋊C4—22no—
149C42—21no—
150C42—22no—
151C42C22⋊D6111yescharacteristic
152C42C22⋊D6111yescharacteristic
153C42C22×D6112yes—
154C23—21no—
155C23C2×C22⋊D6111yescharacteristic
156Q8—21no—
157Q8—1224no—
158Q8—1224no—
159Q8—2444no—
160Q8C2×D24412yes—
161D4—24no—
162D4—21no—
163D4C2×D24412yes—
164C2×C4—21no—
165C2×C4—24no—
166C2×C4—24no—
167C2×C4—22no—
168C2×C4—44no—
169C2×C4—1224no—
170C2×C4—2444no—
171C2×C4C2×D24412yes—
172C2×C4#1175822212yes—
173C2×C4C2×C22⋊D6112yes—
174C2×C4C2×C22⋊D6111yescharacteristic
175C2×C4C2×C22⋊D6112yes—
176C2×C4C23×D6111yescharacteristic
177C8—1224no—
178C22—22no—
179C22—22no—
180C22—42no—
181C22#1451975112yes—
182C22C22×C22⋊D6111yescharacteristic
183C4—22no—
184C4—22no—
185C4—42no—
186C4—2444no—
187C4#1451975112yes—
188C4#1451980714yescomplemented
189C4C22×D24411yescharacteristic
190C4C2×#1175822211yescharacteristic
191C2—22no—
192C2—42no—
193C2C2×#1451975111yescharacteristic
194C2C2×#1451980712yes—
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC4×#41×C61C2
socleC22×C61C22×D4
hypercenterC4×#41D61
hypocenterC61#3039
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×#41

Complements

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

NH ≅ G/Ntype
2. C2×#14519777C2semidirect
3. #16839972C2semidirect
4. #16839967C2semidirect
5. #16839786C2semidirect
6. #16839770C2semidirect
89. C4×C61#137semidirect
105. C61#3039semidirect
188. C4#14519807semidirect