Finite Group Databasebeta

← #23774326

Subgroups — #23774326

Order 10112.

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

normal subgroups only

This group has 428 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#19099114C211yesmaximal, characteristic
2C4⋊Q8×D79C211yesmaximal, characteristic, complemented
3#19098937C211yesmaximal, characteristic, complemented
4#19098936C211yesmaximal, characteristic, complemented
5#19098915C211yesmaximal, characteristic, complemented
6#19098767C214yesmaximal, complemented
7#19098703C214yesmaximal, complemented
8#19098614C211yesmaximal, characteristic, complemented
9#487×C79C211yesmaximal, characteristic, complemented
10C2×#11929625—21no—
11C2×Q8×D79C2212yes—
12C2×#11929613C2214yes—
13C2×#11929611C2214yes—
14#14579161C2211yescharacteristic
15#14579160—21no—
16#14579160—21no—
17#14579159C2212yes—
18#14579158C2211yescharacteristic
19#14579150—21no—
20#14579136—21no—
21#14579136C2212yes—
22#14579123—21no—
23#14579123C2212yes—
24C4⋊C4×D79—21no—
25C4⋊C4×D79—21no—
26C42×D79C2211yescharacteristic
27Dic79⋊C8C2212yes—
28#14579084C2214yes—
29(C2×D79)⋊C8C2212yes—
30C4×C79⋊C8C2211yescharacteristic
31C4⋊Q8×C79C2211yescharacteristic
32C4⋊Q8×C79C2211yescharacteristic
33#103×C79C2214yes—
34C4×C8×C79C2211yescharacteristic
35#11929625—44no—
36C2×Dic158—22no—
37C2×Dic158C2312yes—
38Q8×D79—44no—
39C2×D316—22no—
40C2×D316—21no—
41C2×D316—21no—
42C2×D316C2312yes—
43C2×C4×D79—22no—
44C2×C4×D79—22no—
45C2×C4×D79D411yescharacteristic
46C2×C4×D79D411yescharacteristic
47C2×C4×D79C2311yescharacteristic
48#11929613—44no—
49#11929611—44no—
50C2×C79⋊C8C2312yes—
51C4⋊Dic79—21no—
52C4⋊Dic79—21no—
53Dic79⋊C4—22no—
54Dic79⋊C4—22no—
55(C2×D79)⋊C4—22no—
56(C2×D79)⋊C4—22no—
57C4×Dic79D411yescharacteristic
58C4×Dic79D411yescharacteristic
59C4×Dic79C2311yescharacteristic
60C2×Q8×C79—21no—
61C2×Q8×C79C2312yes—
62C2×C8×C79C2312yes—
63C4⋊C4×C79—21no—
64C4⋊C4×C79—21no—
65C4⋊C4×C79—21no—
66C4⋊C4×C79C2312yes—
67C42×C79C2311yescharacteristic
68C22×D79—22no—
69C22×D79C2×D411yescharacteristic
70Q8×C79—24no—
71Q8×C79—42no—
72C2×C4×C79—22no—
73C2×C4×C79—22no—
74C2×C4×C79C2×D411yescharacteristic
75C2×C4×C79C2×D411yescharacteristic
76C2×C4×C79C2411yescharacteristic
77C2×Dic79—22no—
78C2×Dic79C2×D411yescharacteristic
79C2×Dic79C2×D411yescharacteristic
80C2×Dic79C2×D411yescharacteristic
81D316—24no—
82D316—44no—
83D316—42no—
84D316—42no—
85C4×D79—22no—
86C4×D79—22no—
87C4×D79—44no—
88C4×D79—44no—
89C4×D79SD1614yescomplemented
90Dic158—24no—
91Dic158—44no—
92C8×C79—22no—
93C79⋊C8—22no—
94C22×C79C22×D411yescharacteristic
95C2×D79—21no—
96C2×D79—21no—
97C2×D79—42no—
98C2×D79—42no—
99C2×D79—42no—
100C2×D79C2×SD1612yes—
101C4×C79—42no—
102C4×C79—42no—
103C4×C79C2×SD1612yes—
104C4×C79#13712yes—
105C4×C79H(5,𝔽2)12yes—
106Dic79—21no—
107Dic79—21no—
108Dic79—42no—
109Dic79C2×SD1612yes—
110C2×C79#53511yescharacteristic
111C2×C79C22×SD1611yescharacteristic
112C2×C79C2×#13711yescharacteristic
113D79—22no—
114D79—82no—
115#3206—791nomaximal, Sylow
116C79#320611yescharacteristic, complemented, Sylow
117#532—791no—
118C2×C4⋊Q8—791no—
119#492—791no—
120#492—791no—
121#487—791no—
122#487D7911yescharacteristic, complemented
123#461—794no—
124#448—794no—
125#431—791no—
126C2×#41—1581no—
127C22×Q8—792no—
128C2×SD16—794no—
129C2×SD16—794no—
130C4⋊Q8—792no—
131C4⋊Q8—791no—
132C4⋊Q8—1581no—
133C4⋊Q8—1581no—
134C4⋊Q8C2×D7911yescharacteristic
135C4⋊Q8C2×D7911yescharacteristic
136#127—791no—
137#124—1581no—
138#121—792no—
139#121—1581no—
140C4×D4—792no—
141C4×D4—1581no—
142C2×C4⋊C4—1581no—
143C2×C4⋊C4—1581no—
144C2×C42—791no—
145C4⋊C8—792no—
146#103—794no—
147#103C2×D7914yes—
148C22⋊C8—792no—
149C4×C8—791no—
150C4×C8C2×D7911yescharacteristic
151#41—3164no—
152C2×Q8—21no—
153C2×Q8—3164no—
154C2×Q8—792no—
155C2×Q8—1582no—
156C2×Q8C22×D7912yes—
157C2×D4—792no—
158C2×D4—1582no—
159C2×D4—1581no—
160C2×D4—1581no—
161C22×C4—791no—
162C22×C4—791no—
163C22×C4—791no—
164C22×C4—1582no—
165C22×C4—1582no—
166SD16—3164no—
167SD16—3164no—
168C2×C8—792no—
169C2×C8C22×D7912yes—
170C4⋊C4—21no—
171C4⋊C4—21no—
172C4⋊C4—21no—
173C4⋊C4—1582no—
174C4⋊C4—1582no—
175C4⋊C4—1581no—
176C4⋊C4—1581no—
177C4⋊C4C22×D7912yes—
178C22⋊C4—1582no—
179C22⋊C4—1582no—
180C42—791no—
181C42—791no—
182C42—791no—
183C42C22×D7911yescharacteristic
184C23—791no—
185C23—1582no—
186Q8—24no—
187Q8—42no—
188Q8—3164no—
189Q8—1584no—
190D4—3164no—
191D4—3162no—
192D4—3162no—
193D4—1584no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—3164no—
197C2×C4—3164no—
198C2×C4—791no—
199C2×C4—794no—
200C2×C4—791no—
201C2×C4—791no—
202C2×C4—1582no—
203C2×C4—1582no—
204C2×C4—1582no—
205C2×C4D4×D7911yescharacteristic
206C2×C4D4×D7911yescharacteristic
207C2×C4C23×D7911yescharacteristic
208C8—22no—
209C8—1582no—
210C22—3162no—
211C22—3162no—
212C22—3162no—
213C22—792no—
214C22—1581no—
215C22—1581no—
216C22C2×D4×D7911yescharacteristic
217C4—42no—
218C4—42no—
219C4—3162no—
220C4—792no—
221C4—1581no—
222C4—1581no—
223C4SD16×D7912yes—
224C4#1457919312yes—
225C4#1457920712yes—
226C2—6322no—
227C2—1582no—
228C2#1909913111yescharacteristic
229C2C2×SD16×D7911yescharacteristic
230C2C2×#1457919311yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#487×C79C2
socleC22×C79C22×D4
prime radical#19099114C2
hypercenter#487D79
hypocenterC79#3206
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
2. C4⋊Q8×D79C2semidirect
3. #19098937C2semidirect
4. #19098936C2semidirect
5. #19098915C2semidirect
6. #19098767C2semidirect
7. #19098703C2semidirect
8. #19098614C2semidirect
9. #487×C79C2semidirect
89. C4×D79SD16semidirect
116. C79#3206semidirect
122. #487D79semidirect