Finite Group Databasebeta

← #23776208

Subgroups — #23776208

Order 10112.

326 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 115 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#19099288C211yesmaximal, characteristic
2#19099288C211yesmaximal, characteristic
3#19098930C212yesmaximal
4#19098872C212yesmaximal
5#19098845C211yesmaximal, characteristic
6#19098772C212yesmaximal
7#19098770C211yesmaximal, characteristic
8#19098693C211yesmaximal, characteristic
9#19098667C212yesmaximal
10C4×Dic316C211yesmaximal, characteristic
11#487×C79C211yesmaximal, characteristic
12C2×Dic316C2211yescharacteristic
13C2×#11929614C2212yes—
14#14579159—21no—
15#14579159C2212yes—
16#14579152—21no—
17#14579152C2212yes—
18#14579151—22no—
19#14579151—22no—
20Q8×Dic79—21no—
21Q8×Dic79C2212yes—
22C4×Dic158C2211yescharacteristic
23C4×Dic158C2211yescharacteristic
24C4×Dic158C2211yescharacteristic
25#14579126—21no—
26#14579126C2212yes—
27#14579095C2211yescharacteristic
28#14579092C2212yes—
29C4⋊(C79⋊C8)C2211yescharacteristic
30Dic79⋊C8C2212yes—
31#14579086C2211yescharacteristic
32#14579086C2211yescharacteristic
33#14579085C2212yes—
34#14579084C2212yes—
35#14579071C2212yes—
36C4⋊Q8×C79C2211yescharacteristic
37C4⋊Q8×C79C2211yescharacteristic
38#103×C79C2212yes—
39#103×C79C2212yes—
40C4×C8×C79C2211yescharacteristic
41C2×Dic158D411yescharacteristic
42C2×Dic158C2311yescharacteristic
43C2×Dic158C2311yescharacteristic
44Dic316—22no—
45#11929614—24no—
46C2×C79⋊C8C2312yes—
47C4⋊Dic79—22no—
48C4⋊Dic79—22no—
49C4⋊Dic79D411yescharacteristic
50C4⋊Dic79C2311yescharacteristic
51C4⋊Dic79C2311yescharacteristic
52Dic79⋊C4—22no—
53Dic79⋊C4—22no—
54Dic79⋊C4—22no—
55Dic79⋊C4—22no—
56Dic79⋊C4—21no—
57Dic79⋊C4—21no—
58Dic79⋊C4D412yes—
59C4×Dic79—22no—
60C4×Dic79—22no—
61C4×Dic79—21no—
62C4×Dic79—21no—
63C4×Dic79C2312yes—
64C2×Q8×C79—21no—
65C2×Q8×C79C2312yes—
66C2×C8×C79C2311yescharacteristic
67C2×C8×C79C2311yescharacteristic
68C4⋊C4×C79—21no—
69C4⋊C4×C79—21no—
70C4⋊C4×C79—21no—
71C4⋊C4×C79C2312yes—
72C42×C79C2311yescharacteristic
73Q8×C79—22no—
74Q8×C79—22no—
75Q8×C79—42no—
76C2×C4×C79—22no—
77C2×C4×C79—22no—
78C2×C4×C79C2×D411yescharacteristic
79C2×C4×C79C2×D411yescharacteristic
80C2×C4×C79C2411yescharacteristic
81C2×Dic79—21no—
82C2×Dic79—21no—
83C2×Dic79—21no—
84C2×Dic79—21no—
85C2×Dic79C2×D412yes—
86C2×Dic79C2×D412yes—
87Dic158—22no—
88Dic158—21no—
89Dic158—21no—
90Dic158—21no—
91Dic158#4112yes—
92C8×C79—21no—
93C8×C79—21no—
94C79⋊C8—22no—
95C22×C79C22×D411yescharacteristic
96C4×C79—21no—
97C4×C79—42no—
98C4×C79—42no—
99C4×C79#13712yes—
100C4×C79C2×#4111yescharacteristic
101C4×C792−1+411yescharacteristic
102Dic79—22no—
103Dic79—22no—
104Dic79—22no—
105Dic79—41no—
106Dic79—41no—
107Dic79—41no—
108C2×C79#54811yescharacteristic
109C2×C79C2×#13711yescharacteristic
110C2×C79#57811yescharacteristic
111#3374—791nomaximal, Sylow
112C79#337411yescharacteristic, complemented, Sylow
113#557—791no—
114#557—791no—
115#491—792no—
116#487D7911yescharacteristic
117#479—792no—
118#475—791no—
119#462—791no—
120#462—792no—
121#446—791no—
122#441—792no—
123C4×Q16—791no—
124C2×Q16—792no—
125C2×Q16—791no—
126C4⋊Q8—792no—
127C4⋊Q8—1581no—
128C4⋊Q8C2×D7911yescharacteristic
129C4⋊Q8C2×D7911yescharacteristic
130#125—792no—
131#125—1582no—
132#125—1582no—
133#125—1581no—
134C4×Q8—791no—
135C4×Q8—792no—
136C4×Q8—792no—
137C4×Q8—791no—
138C4×Q8—791no—
139C4×Q8—1581no—
140C4×Q8—1581no—
141#107—791no—
142#106—792no—
143C4⋊C8—792no—
144C4⋊C8—791no—
145#103—792no—
146#103—791no—
147#103—791no—
148#103—792no—
149#103C2×D7912yes—
150#103C2×D7912yes—
151#97—792no—
152C4×C8C2×D7911yescharacteristic
153C2×Q8—21no—
154C2×Q8—791no—
155C2×Q8—791no—
156C2×Q8—791no—
157C2×Q8C22×D7912yes—
158Q16—1582no—
159Q16—1584no—
160C2×C8—792no—
161C2×C8C22×D7911yescharacteristic
162C2×C8C22×D7911yescharacteristic
163C4⋊C4—21no—
164C4⋊C4—21no—
165C4⋊C4—21no—
166C4⋊C4—792no—
167C4⋊C4—791no—
168C4⋊C4—791no—
169C4⋊C4—791no—
170C4⋊C4—1582no—
171C4⋊C4—1582no—
172C4⋊C4—1582no—
173C4⋊C4—1582no—
174C4⋊C4—1582no—
175C4⋊C4—1582no—
176C4⋊C4—1581no—
177C4⋊C4—1581no—
178C4⋊C4C22×D7912yes—
179C42—792no—
180C42—1582no—
181C42—1582no—
182C42—1581no—
183C42—1581no—
184C42C22×D7911yescharacteristic
185Q8—22no—
186Q8—22no—
187Q8—42no—
188Q8—792no—
189Q8—1581no—
190Q8—1581no—
191Q8—1581no—
192Q8—1582no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—792no—
196C2×C4—792no—
197C2×C4—1581no—
198C2×C4—1581no—
199C2×C4—1581no—
200C2×C4—1581no—
201C2×C4D4×D7911yescharacteristic
202C2×C4D4×D7911yescharacteristic
203C2×C4C23×D7911yescharacteristic
204C8—21no—
205C8—21no—
206C8—1582no—
207C22C2×D4×D7911yescharacteristic
208C4—21no—
209C4—42no—
210C4—42no—
211C4—3161no—
212C4—3161no—
213C4—3161no—
214C4—1582no—
215C4—1582no—
216C4—1582no—
217C4#1457919012yes—
218C4#41×D7911yescharacteristic
219C4#1457920811yescharacteristic
220C2#1909922111yescharacteristic
221C2C2×#1457919011yescharacteristic
222C2#1909937611yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#487×C79C2
socle, prime radicalC22×C79C22×D4
hypercenter#487D79
hypocenterC79#3374
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
112. C79#3374semidirect