Finite Group Databasebeta

← #23764391

Subgroups — #23764391

Order 10112.

228 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 83 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×#14579152C211yesmaximal, characteristic
2#19098586C211yesmaximal, characteristic
3M16×Dic79C211yesmaximal, characteristic
4#19098332C211yesmaximal, characteristic
5#19098331C211yesmaximal, characteristic
6#19098331C211yesmaximal, characteristic
7#343×C79C211yesmaximal, characteristic
8C2×#11929608C2211yescharacteristic
9C2×#11929608C2211yescharacteristic
10#14579152—21no—
11#14579152—21no—
12#14579152—21no—
13#14579152—21no—
14C2×C4⋊Dic79C412yes—
15C2×C4⋊Dic79C2211yescharacteristic
16C2×Dic79⋊C4C412yes—
17C2×C4×Dic79C2211yescharacteristic
18Dic79⋊C8—21no—
19Dic79⋊C8—21no—
20#14579071—21no—
21C8×Dic79—21no—
22C2×M16×C79C2211yescharacteristic
23C2×M16×C79C2211yescharacteristic
24C2×C4⋊C4×C79C2211yescharacteristic
25C22×Dic79C2×C412yes—
26C22×Dic79C2×C411yescharacteristic
27C22×Dic79C2×C411yescharacteristic
28#11929608—21no—
29#11929608—21no—
30#11929608—21no—
31#11929608Q812yes—
32C2×C79⋊C8—21no—
33C2×C79⋊C8—21no—
34C4⋊Dic79—22no—
35C4⋊Dic79—22no—
36C4⋊Dic79—21no—
37C4⋊Dic79—21no—
38Dic79⋊C4—22no—
39Dic79⋊C4—22no—
40C4×Dic79D411yescharacteristic
41C4×Dic79D411yescharacteristic
42C4×Dic79D411yescharacteristic
43C4×Dic79D411yescharacteristic
44C22×C4×C79C2×C412yes—
45C22×C4×C79C2311yescharacteristic
46M16×C79—21no—
47M16×C79—21no—
48M16×C79—21no—
49M16×C79Q812yes—
50C2×C8×C79—21no—
51C2×C8×C79—21no—
52C4⋊C4×C79—21no—
53C4⋊C4×C79—21no—
54C23×C79C22×C411yescharacteristic
55C2×C4×C79—22no—
56C2×C4×C79—42no—
57C2×C4×C79C2×D411yescharacteristic
58C2×C4×C79C2×D411yescharacteristic
59C2×C4×C79C2×Q811yescharacteristic
60C2×C4×C79C2×Q811yescharacteristic
61C2×C4×C79#4111yescharacteristic
62C2×C4×C79#4111yescharacteristic
63C2×Dic79—22no—
64C2×Dic79—41no—
65C2×Dic79—41no—
66C2×Dic79—42no—
67C2×Dic79C22⋊C411yescharacteristic
68C2×Dic79C22⋊C411yescharacteristic
69C2×Dic79C22⋊C411yescharacteristic
70C2×Dic79C22⋊C411yescharacteristic
71C8×C79—22no—
72C8×C79—41no—
73C79⋊C8—22no—
74C79⋊C8—41no—
75C22×C79—21no—
76C22×C79—21no—
77C22×C79C2×C22⋊C411yescharacteristic
78C22×C79C4×Q811yescharacteristic
79C22×C79C4×Q811yescharacteristic
80C4×C79—42no—
81C4×C79C22⋊Q811yescharacteristic
82C4×C79C22⋊Q811yescharacteristic
83C4×C79#12411yescharacteristic
84C4×C79C4⋊Q811yescharacteristic
85Dic79—21no—
86Dic79—21no—
87Dic79—21no—
88Dic79—21no—
89Dic79—42no—
90C2×C79—21no—
91C2×C79—21no—
92C2×C79#39111yescharacteristic
93C2×C79#41311yescharacteristic
94C2×C79#41311yescharacteristic
95#1998—791nomaximal, Sylow
96C79#199811yescharacteristic, complemented, Sylow
97C2×#125—791no—
98#423—791no—
99C4×M16—791no—
100#343—791no—
101#343—791no—
102#343—791no—
103#343D7911yescharacteristic
104C2×M16—791no—
105C2×M16—791no—
106C2×M16C2×D7911yescharacteristic
107C2×M16C2×D7911yescharacteristic
108#125—1581no—
109#125—1581no—
110#125—1581no—
111#125—1581no—
112C2×C4⋊C4—791no—
113C2×C4⋊C4—792no—
114C2×C4⋊C4—792no—
115C2×C4⋊C4C2×D7911yescharacteristic
116C2×C42—791no—
117C4⋊C8—1581no—
118C4⋊C8—1581no—
119#97—1581no—
120C4×C8—1581no—
121C22×C4—791no—
122C22×C4—791no—
123C22×C4—792no—
124C22×C4C4×D7912yes—
125C22×C4C22×D7911yescharacteristic
126M16—21no—
127M16—21no—
128M16—21no—
129M16—792no—
130M16—1581no—
131M16—1581no—
132M16—1581no—
133M16Dic15812yes—
134C2×C8—21no—
135C2×C8—21no—
136C2×C8—1581no—
137C2×C8—1581no—
138C4⋊C4—21no—
139C4⋊C4—21no—
140C4⋊C4—1582no—
141C4⋊C4—1582no—
142C4⋊C4—1582no—
143C4⋊C4—1582no—
144C4⋊C4—1581no—
145C4⋊C4—1581no—
146C42—791no—
147C42—791no—
148C42—791no—
149C42—791no—
150C23C2×C4×D7911yescharacteristic
151C2×C4—22no—
152C2×C4—42no—
153C2×C4—3162no—
154C2×C4—3161no—
155C2×C4—3161no—
156C2×C4—791no—
157C2×C4—791no—
158C2×C4—791no—
159C2×C4—791no—
160C2×C4—1582no—
161C2×C4D4×D7911yescharacteristic
162C2×C4D4×D7911yescharacteristic
163C2×C4Q8×D7911yescharacteristic
164C2×C4C2×Dic15811yescharacteristic
165C2×C4#1192962311yescharacteristic
166C2×C4#1192962411yescharacteristic
167C8—22no—
168C8—41no—
169C8—3161no—
170C8—1582no—
171C22—21no—
172C22—21no—
173C22C22⋊C4×D7911yescharacteristic
174C22#1457912611yescharacteristic
175C22C4×Dic15811yescharacteristic
176C4—42no—
177C4—3162no—
178C4—1581no—
179C4—1581no—
180C4—1581no—
181C4—1581no—
182C4#1457913811yescharacteristic
183C4#1457913911yescharacteristic
184C4#1457914711yescharacteristic
185C4#1457916011yescharacteristic
186C2—21no—
187C2—21no—
188C2#1909846711yescharacteristic
189C2#1909854411yescharacteristic
190C2#1909854611yescharacteristic
subgroupG/H
centerC22C22⋊C4×D79
commutator, prime radicalC23×C79C22×C4
FrattiniC22×C4C22×D79
Fitting#343×C79C2
socleC22×C79C2×C22⋊C4
cosocleC22×C4×C79C23
hypercenter#343D79
hypocenterC79#1998
LCSG ▷ C23×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ #343

Complements

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

NH ≅ G/Ntype
96. C79#1998semidirect