Finite Group Databasebeta

← #23774540

Subgroups — #23774540

Order 10112.

360 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 125 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#19099118C211yesmaximal, characteristic
2C4⋊Q8×D79C211yesmaximal, characteristic
3#19098961C211yesmaximal, characteristic, complemented
4#19098959C211yesmaximal, characteristic, complemented
5#19098913C211yesmaximal, characteristic, complemented
6#19098892C214yesmaximal
7#19098846C214yesmaximal, complemented
8#19098614C211yesmaximal, characteristic
9#487×C79C211yesmaximal, characteristic, complemented
10C2×Q8×D79—21no—
11#14579161C2211yescharacteristic
12#14579161C2211yescharacteristic
13#14579160—21no—
14#14579160C2212yes—
15#14579159—21no—
16#14579152—21no—
17#14579141—21no—
18#14579137C2212yes—
19Q8×Dic79C2212yes—
20#14579126—21no—
21#14579119—21no—
22C4⋊C4×D79—21no—
23C4⋊C4×D79C2212yes—
24C42×D79C2211yescharacteristic
25#14579093C2214yes—
26#14579092C2214yes—
27Dic79⋊C8C2212yes—
28#14579085C2214yes—
29(C2×D79)⋊C8C2212yes—
30C4×C79⋊C8C2211yescharacteristic
31C4⋊Q8×C79C2211yescharacteristic
32C4⋊Q8×C79C2211yescharacteristic
33#103×C79C2214yes—
34C4×C8×C79C2211yescharacteristic
35C2×Dic158—22no—
36C2×Dic158—21no—
37C2×Dic158—21no—
38Q8×D79—44no—
39C2×C4×D79—22no—
40C2×C4×D79D411yescharacteristic
41C2×C4×D79D411yescharacteristic
42C2×C4×D79C2311yescharacteristic
43C2×C79⋊C8C2312yes—
44C4⋊Dic79—22no—
45C4⋊Dic79—21no—
46C4⋊Dic79—21no—
47C4⋊Dic79C2312yes—
48C4⋊Dic79C2312yes—
49Dic79⋊C4—22no—
50Dic79⋊C4—22no—
51Dic79⋊C4—22no—
52(C2×D79)⋊C4—22no—
53C4×Dic79—22no—
54C4×Dic79D411yescharacteristic
55C4×Dic79D411yescharacteristic
56C4×Dic79C2311yescharacteristic
57C2×Q8×C79—21no—
58C2×Q8×C79C2312yes—
59C2×C8×C79C2312yes—
60C4⋊C4×C79—21no—
61C4⋊C4×C79—21no—
62C4⋊C4×C79—21no—
63C4⋊C4×C79C2312yes—
64C42×C79C2311yescharacteristic
65C22×D79C2×D411yescharacteristic
66Q8×C79—24no—
67Q8×C79—42no—
68C2×C4×C79—22no—
69C2×C4×C79—22no—
70C2×C4×C79C2×D411yescharacteristic
71C2×C4×C79C2×D411yescharacteristic
72C2×C4×C79C2411yescharacteristic
73C2×Dic79—22no—
74C2×Dic79—22no—
75C2×Dic79C2×D411yescharacteristic
76C2×Dic79C2×D411yescharacteristic
77C2×Dic79C2×D411yescharacteristic
78C4×D79—22no—
79C4×D79—22no—
80C4×D79—44no—
81C4×D79SD1614yes—
82Dic158—42no—
83Dic158—42no—
84Dic158—44no—
85C8×C79—22no—
86C79⋊C8—22no—
87C22×C79C22×D411yescharacteristic
88C2×D79—21no—
89C2×D79—21no—
90C2×D79C2×SD1612yes—
91C4×C79—42no—
92C4×C79—42no—
93C4×C79C2×SD1612yes—
94C4×C79#13712yes—
95C4×C792−1+412yes—
96Dic79—21no—
97Dic79—21no—
98Dic79—42no—
99Dic79—42no—
100Dic79C2×SD1612yes—
101C2×C79#53611yescharacteristic
102C2×C79C22×SD1611yescharacteristic
103C2×C79C2×#13711yescharacteristic
104D79—22no—
105#3229—791nomaximal, Sylow
106C79#322911yescharacteristic, complemented, Sylow
107#533—791no—
108C2×C4⋊Q8—791no—
109#498—791no—
110#498—791no—
111#487—791no—
112#487D7911yescharacteristic, complemented
113#483—794no—
114#475—794no—
115#431—791no—
116C22×Q8—1581no—
117C4⋊Q8—792no—
118C4⋊Q8—791no—
119C4⋊Q8—791no—
120C4⋊Q8—1581no—
121C4⋊Q8—1581no—
122C4⋊Q8C2×D7911yescharacteristic
123C4⋊Q8C2×D7911yescharacteristic
124#125—1581no—
125C22⋊Q8—792no—
126C22⋊Q8—1581no—
127C4×Q8—792no—
128C4×Q8—1581no—
129#117—1581no—
130C2×C4⋊C4—792no—
131C2×C4⋊C4—1581no—
132C2×C42—791no—
133#106—794no—
134#106—794no—
135C4⋊C8—792no—
136#103—794no—
137#103C2×D7914yes—
138C22⋊C8—792no—
139C4×C8—791no—
140C4×C8C2×D7911yescharacteristic
141C2×Q8—21no—
142C2×Q8—3164no—
143C2×Q8—1582no—
144C2×Q8—1581no—
145C2×Q8—1581no—
146C2×Q8C22×D7912yes—
147C22×C4—791no—
148C22×C4—791no—
149C22×C4—791no—
150C22×C4—1582no—
151C2×C8—792no—
152C2×C8C22×D7912yes—
153C4⋊C4—21no—
154C4⋊C4—21no—
155C4⋊C4—21no—
156C4⋊C4—792no—
157C4⋊C4—792no—
158C4⋊C4—1582no—
159C4⋊C4—1582no—
160C4⋊C4—1582no—
161C4⋊C4—1582no—
162C4⋊C4—1581no—
163C4⋊C4—1581no—
164C4⋊C4C22×D7912yes—
165C22⋊C4—1582no—
166C42—791no—
167C42—791no—
168C42—791no—
169C42—1582no—
170C42C22×D7911yescharacteristic
171C23—791no—
172Q8—24no—
173Q8—42no—
174Q8—3164no—
175Q8—3162no—
176Q8—3162no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—3164no—
180C2×C4—791no—
181C2×C4—794no—
182C2×C4—791no—
183C2×C4—791no—
184C2×C4—1582no—
185C2×C4—1582no—
186C2×C4—1582no—
187C2×C4—1582no—
188C2×C4D4×D7911yescharacteristic
189C2×C4D4×D7911yescharacteristic
190C2×C4C23×D7911yescharacteristic
191C8—22no—
192C8—1582no—
193C22—792no—
194C22—1581no—
195C22—1581no—
196C22C2×D4×D7911yescharacteristic
197C4—42no—
198C4—42no—
199C4—3162no—
200C4—3162no—
201C4—792no—
202C4—1581no—
203C4—1581no—
204C4SD16×D7912yes—
205C4#1457919312yes—
206C4#1457920812yes—
207C2—1582no—
208C2#1909913311yescharacteristic
209C2C2×SD16×D7911yescharacteristic
210C2C2×#1457919311yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#487×C79C2
socleC22×C79C22×D4
prime radicalC22×D79C2×D4
hypercenter#487D79
hypocenterC79#3229
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
3. #19098961C2semidirect
4. #19098959C2semidirect
5. #19098913C2semidirect
7. #19098846C2semidirect
9. #487×C79C2semidirect
106. C79#3229semidirect
112. #487D79semidirect