Finite Group Databasebeta

← #23764898

Subgroups — #23764898

Order 10112.

224 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 89 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×#14579093C211yesmaximal, characteristic
2#19098461C211yesmaximal, characteristic
3#19098461C211yesmaximal, characteristic
4#19098326C211yesmaximal, characteristic
5#19098326C211yesmaximal, characteristic
6#19098326C211yesmaximal, characteristic
7C2×C4⋊C8×C79C211yesmaximal, characteristic
8C2×C4⋊Dic79C2211yescharacteristic
9C2×C4⋊Dic79C2211yescharacteristic
10C2×C4⋊Dic79C2211yescharacteristic
11C2×C4⋊Dic79C2211yescharacteristic
12C2×Dic79⋊C4—21no—
13C2×Dic79⋊C4—21no—
14#14579093—22no—
15C79⋊#95—21no—
16C79⋊#95—21no—
17C22×C8×C79C2211yescharacteristic
18C22×C8×C79C2211yescharacteristic
19C2×C42×C79C2211yescharacteristic
20C4⋊C8×C79—22no—
21C22×Dic79—21no—
22C22×Dic79—21no—
23C22×Dic79—21no—
24C22×Dic79—21no—
25C4⋊Dic79—21no—
26C4⋊Dic79—21no—
27C4⋊Dic79—21no—
28C4⋊Dic79—21no—
29C4⋊Dic79—21no—
30C4⋊Dic79—21no—
31C4⋊Dic79Q812yes—
32C4⋊Dic79Q812yes—
33Dic79⋊C4—42no—
34Dic79⋊C4—42no—
35C22×C4×C79D411yescharacteristic
36C22×C4×C79D411yescharacteristic
37C22×C4×C79C2311yescharacteristic
38C2×C8×C79—21no—
39C2×C8×C79—21no—
40C2×C8×C79—21no—
41C2×C8×C79—21no—
42C2×C8×C79—21no—
43C2×C8×C79D412yes—
44C42×C79—21no—
45C42×C79—21no—
46C23×C79C2×D411yescharacteristic
47C2×C4×C79—21no—
48C2×C4×C79—21no—
49C2×C4×C79—21no—
50C2×C4×C79—21no—
51C2×C4×C79—21no—
52C2×C4×C79SD1612yes—
53C2×C4×C79C2×D411yescharacteristic
54C2×C4×C79C2×Q811yescharacteristic
55C2×C4×C79C2×Q811yescharacteristic
56C2×C4×C79#4111yescharacteristic
57C2×C4×C79#4111yescharacteristic
58C2×C4×C79#4111yescharacteristic
59C2×Dic79—22no—
60C2×Dic79—22no—
61C2×Dic79—41no—
62C2×Dic79—41no—
63C2×Dic79—41no—
64C2×Dic79—41no—
65C2×Dic79—41no—
66C2×Dic79—41no—
67C2×Dic79—41no—
68C2×Dic79—41no—
69C2×Dic79—41no—
70C2×Dic79—41no—
71C8×C79—22no—
72C8×C79—41no—
73C22×C79#12111yescharacteristic
74C22×C79C22⋊Q811yescharacteristic
75C22×C79C22⋊Q811yescharacteristic
76C22×C79C2×SD1611yescharacteristic
77C22×C79#13511yescharacteristic
78C22×C79AGL(1,ℤ/8)11yescharacteristic
79C22×C79#13711yescharacteristic
80C4×C79—22no—
81C4×C79—41no—
82C4×C79#12311yescharacteristic
83C4×C79#12511yescharacteristic
84C4×C79#12511yescharacteristic
85C4×C79C4⋊Q811yescharacteristic
86Dic79—42no—
87Dic79—42no—
88Dic79—81no—
89Dic79—81no—
90C2×C79#39811yescharacteristic
91C2×C79#46511yescharacteristic
92C2×C79#46811yescharacteristic
93C2×C79#47511yescharacteristic
94C2×C79#47611yescharacteristic
95C2×C79#47811yescharacteristic
96C2×C79#47911yescharacteristic
97#2088—791nomaximal, Sylow
98C79#208811yescharacteristic, complemented, Sylow
99C2×#106—791no—
100C2×C4⋊C8D7911yescharacteristic
101#389—791no—
102#389—791no—
103#340—791no—
104#340—791no—
105#340—791no—
106C22×C8C2×D7911yescharacteristic
107C22×C8C2×D7911yescharacteristic
108C2×C4⋊C4—791no—
109C2×C4⋊C4—791no—
110C2×C4⋊C4—791no—
111C2×C4⋊C4—791no—
112C2×C4⋊C4—1581no—
113C2×C4⋊C4—1581no—
114C2×C42C2×D7911yescharacteristic
115#106—1582no—
116C4⋊C8—22no—
117#95—1581no—
118#95—1581no—
119C22×C4—1581no—
120C22×C4—1581no—
121C22×C4—1581no—
122C22×C4—1581no—
123C22×C4D31611yescharacteristic
124C22×C4D31611yescharacteristic
125C22×C4C22×D7911yescharacteristic
126C2×C8—21no—
127C2×C8—21no—
128C2×C8—21no—
129C2×C8—21no—
130C2×C8—21no—
131C2×C8C22⋊D7912yes—
132C4⋊C4—3162no—
133C4⋊C4—3162no—
134C4⋊C4—792no—
135C4⋊C4—792no—
136C4⋊C4—1581no—
137C4⋊C4—1581no—
138C4⋊C4—1581no—
139C4⋊C4—1581no—
140C4⋊C4—1581no—
141C4⋊C4—1581no—
142C42—21no—
143C42—21no—
144C23C2×D31611yescharacteristic
145C2×C4—21no—
146C2×C4—21no—
147C2×C4—21no—
148C2×C4—21no—
149C2×C4—21no—
150C2×C4—3161no—
151C2×C4—3161no—
152C2×C4—3161no—
153C2×C4—3161no—
154C2×C4—3161no—
155C2×C4—3161no—
156C2×C4—3161no—
157C2×C4—3161no—
158C2×C4—3161no—
159C2×C4—3161no—
160C2×C4—1582no—
161C2×C4—1582no—
162C2×C4#1192961312yes—
163C2×C4C2×C22⋊D7911yescharacteristic
164C2×C4Q8×D7911yescharacteristic
165C2×C4Q8×D7911yescharacteristic
166C2×C4#1192962311yescharacteristic
167C2×C4#1192962311yescharacteristic
168C2×C4#1192962411yescharacteristic
169C8—22no—
170C8—41no—
171C22#1457913511yescharacteristic
172C22#1457914111yescharacteristic
173C22#1457914111yescharacteristic
174C22C2×#1192961311yescharacteristic
175C22#1457918311yescharacteristic
176C22#1457918911yescharacteristic
177C22#1457919411yescharacteristic
178C4—22no—
179C4—41no—
180C4—3162no—
181C4—3162no—
182C4—6321no—
183C4—6321no—
184C4#1457914211yescharacteristic
185C4#1457915111yescharacteristic
186C4#1457915111yescharacteristic
187C4#1457915911yescharacteristic
188C2#1909849311yescharacteristic
189C2#1909879211yescharacteristic
190C2#1909880911yescharacteristic
191C2#1909884911yescharacteristic
192C2#1909885411yescharacteristic
193C2#1909886411yescharacteristic
194C2#1909887111yescharacteristic
subgroupG/H
centerC23C2×D316
commutator, cosocleC22×C4×C79C23
FrattiniC22×C4C22×D79
FittingC2×C4⋊C8×C79C2
socle, prime radicalC23×C79C2×D4
hypercenterC2×C4⋊C8D79
hypocenterC79#2088
LCSG ▷ C22×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4⋊C8

Complements

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

NH ≅ G/Ntype
98. C79#2088semidirect