Finite Group Databasebeta

← #23764780

Subgroups — #23764780

Order 10112.

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

normal subgroups only

This group has 248 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
2C2×#14579086C211yesmaximal, characteristic
3C2×#14579086C211yesmaximal, characteristic
4#19098469C211yesmaximal, characteristic
5#19098461C211yesmaximal, characteristic
6#19098326C211yesmaximal, characteristic
7C2×C4⋊C8×C79C211yesmaximal, characteristic
8C22×Dic158C2211yescharacteristic
9C2×C4⋊Dic79C2211yescharacteristic
10C2×C4⋊Dic79C2211yescharacteristic
11C2×C4⋊Dic79C2211yescharacteristic
12C2×Dic79⋊C4—21no—
13#14579093—22no—
14#14579086—22no—
15#14579086—22no—
16C79⋊#95—21no—
17C79⋊#95—21no—
18C79⋊#95—21no—
19C22×C8×C79C2211yescharacteristic
20C22×C8×C79C2211yescharacteristic
21C2×C42×C79C2211yescharacteristic
22C4⋊C8×C79—22no—
23C2×Dic158—21no—
24C2×Dic158—21no—
25C2×Dic158—21no—
26C2×Dic158—21no—
27C2×Dic158—21no—
28C2×Dic158Q812yes—
29C22×Dic79—21no—
30C22×Dic79—21no—
31C22×Dic79—21no—
32C22×Dic79—21no—
33C4⋊Dic79—21no—
34C4⋊Dic79—21no—
35C4⋊Dic79—21no—
36C4⋊Dic79—21no—
37C4⋊Dic79—21no—
38C4⋊Dic79D412yes—
39Dic79⋊C4—42no—
40C22×C4×C79D411yescharacteristic
41C22×C4×C79D411yescharacteristic
42C22×C4×C79C2311yescharacteristic
43C2×C8×C79—21no—
44C2×C8×C79—21no—
45C2×C8×C79—21no—
46C2×C8×C79—21no—
47C2×C8×C79—21no—
48C2×C8×C79D412yes—
49C42×C79—21no—
50C42×C79—21no—
51C23×C79C2×D411yescharacteristic
52C2×C4×C79—21no—
53C2×C4×C79—21no—
54C2×C4×C79—21no—
55C2×C4×C79—21no—
56C2×C4×C79—21no—
57C2×C4×C79SD1612yes—
58C2×C4×C79C2×D411yescharacteristic
59C2×C4×C79C2×D411yescharacteristic
60C2×C4×C79C2×Q811yescharacteristic
61C2×C4×C79#4111yescharacteristic
62C2×C4×C79#4111yescharacteristic
63C2×C4×C79#4111yescharacteristic
64C2×Dic79—22no—
65C2×Dic79—22no—
66C2×Dic79—41no—
67C2×Dic79—41no—
68C2×Dic79—41no—
69C2×Dic79—41no—
70C2×Dic79—41no—
71C2×Dic79—41no—
72C2×Dic79—41no—
73C2×Dic79—41no—
74C2×Dic79—41no—
75C2×Dic79—41no—
76Dic158—22no—
77Dic158—22no—
78Dic158—41no—
79Dic158—41no—
80C8×C79—22no—
81C8×C79—41no—
82C22×C79#12111yescharacteristic
83C22×C79#12111yescharacteristic
84C22×C79C22⋊Q811yescharacteristic
85C22×C79C2×SD1611yescharacteristic
86C22×C79#13511yescharacteristic
87C22×C79#13711yescharacteristic
88C22×C79#13711yescharacteristic
89C4×C79—22no—
90C4×C79—41no—
91C4×C79#12111yescharacteristic
92C4×C79C22⋊Q811yescharacteristic
93C4×C79C22⋊Q811yescharacteristic
94C4×C79#12611yescharacteristic
95Dic79—42no—
96Dic79—42no—
97Dic79—81no—
98Dic79—81no—
99C2×C79#39611yescharacteristic
100C2×C79#46111yescharacteristic
101C2×C79#46411yescharacteristic
102C2×C79#46511yescharacteristic
103C2×C79#47011yescharacteristic
104C2×C79#47511yescharacteristic
105C2×C79#47911yescharacteristic
106#2066—791nomaximal, Sylow
107C79#206611yescharacteristic, complemented, Sylow
108C2×#106—791no—
109C2×C4⋊C8D7911yescharacteristic
110C2×#103—791no—
111C2×#103—791no—
112#391—791no—
113#389—791no—
114#340—791no—
115C22×Q8—791no—
116C22×C8C2×D7911yescharacteristic
117C22×C8C2×D7911yescharacteristic
118C2×C4⋊C4—791no—
119C2×C4⋊C4—791no—
120C2×C4⋊C4—791no—
121C2×C4⋊C4—1581no—
122C2×C42C2×D7911yescharacteristic
123#106—1582no—
124C4⋊C8—22no—
125#103—1582no—
126#103—1582no—
127#95—1581no—
128#95—1581no—
129#95—1581no—
130C2×Q8—792no—
131C2×Q8—1581no—
132C2×Q8—1581no—
133C2×Q8—1581no—
134C2×Q8—1581no—
135C2×Q8—1581no—
136C22×C4—1581no—
137C22×C4—1581no—
138C22×C4—1581no—
139C22×C4—1581no—
140C22×C4D31611yescharacteristic
141C22×C4D31611yescharacteristic
142C22×C4C22×D7911yescharacteristic
143C2×C8—21no—
144C2×C8—21no—
145C2×C8—21no—
146C2×C8—21no—
147C2×C8—21no—
148C2×C8C22⋊D7912yes—
149C4⋊C4—3162no—
150C4⋊C4—792no—
151C4⋊C4—1581no—
152C4⋊C4—1581no—
153C4⋊C4—1581no—
154C4⋊C4—1581no—
155C4⋊C4—1581no—
156C42—21no—
157C42—21no—
158C23C2×D31611yescharacteristic
159Q8—3161no—
160Q8—3161no—
161Q8—1582no—
162Q8—1582no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—3161no—
169C2×C4—3161no—
170C2×C4—3161no—
171C2×C4—3161no—
172C2×C4—3161no—
173C2×C4—3161no—
174C2×C4—3161no—
175C2×C4—3161no—
176C2×C4—3161no—
177C2×C4—3161no—
178C2×C4—1582no—
179C2×C4—1582no—
180C2×C4#1192961312yes—
181C2×C4D4×D7911yescharacteristic
182C2×C4C2×C22⋊D7911yescharacteristic
183C2×C4Q8×D7911yescharacteristic
184C2×C4#1192962311yescharacteristic
185C2×C4#1192962411yescharacteristic
186C2×C4#1192962511yescharacteristic
187C8—22no—
188C8—41no—
189C22#1457913511yescharacteristic
190C22#1457913611yescharacteristic
191C22#1457914111yescharacteristic
192C22C2×#1192961311yescharacteristic
193C22#1457918311yescharacteristic
194C22#1457919411yescharacteristic
195C22#1457919411yescharacteristic
196C4—22no—
197C4—41no—
198C4—3162no—
199C4—3162no—
200C4—6321no—
201C4—6321no—
202C4#1457913311yescharacteristic
203C4#1457913711yescharacteristic
204C4#1457913911yescharacteristic
205C4#1457915611yescharacteristic
206C2#1909848511yescharacteristic
207C2#1909876911yescharacteristic
208C2#1909878611yescharacteristic
209C2#1909879211yescharacteristic
210C2#1909882111yescharacteristic
211C2#1909884911yescharacteristic
212C2#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#2066
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
107. C79#2066semidirect