Finite Group Databasebeta

← #23764786

Subgroups — #23764786

Order 10112.

284 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 87 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×#14579095C211yesmaximal, characteristic, complemented
2C2×Dic79⋊C8C211yesmaximal, characteristic, complemented
3C2×#14579082C211yesmaximal, characteristic
4#19098466C211yesmaximal, characteristic
5#19098459C211yesmaximal, characteristic, complemented
6#19098325C211yesmaximal, characteristic, complemented
7C2×#102×C79C211yesmaximal, characteristic
8C22×C79⋊C8C2211yescharacteristic
9C2×C4⋊Dic79C2211yescharacteristic
10C2×C4⋊Dic79C2211yescharacteristic
11C2×Dic79⋊C4—21no—
12C2×C22⋊Dic79—21no—
13C2×C22⋊Dic79—21no—
14C2×C4×Dic79C2211yescharacteristic
15#14579095—22no—
16Dic79⋊C8—22no—
17#14579082—22no—
18C79⋊#95—21no—
19C22×D4×C79C2211yescharacteristic
20C22×C8×C79C2211yescharacteristic
21C2×C4⋊C4×C79C2211yescharacteristic
22#102×C79—22no—
23C22×Dic79—21no—
24C22×Dic79—21no—
25C22×Dic79D411yescharacteristic
26C22×Dic79D411yescharacteristic
27C2×C79⋊C8—21no—
28C2×C79⋊C8—21no—
29C2×C79⋊C8—21no—
30C4⋊Dic79—21no—
31C4⋊Dic79—21no—
32C4⋊Dic79—21no—
33C4⋊Dic79D412yes—
34Dic79⋊C4—42no—
35C22⋊Dic79—42no—
36C22⋊Dic79—42no—
37C4×Dic79—21no—
38C4×Dic79—21no—
39C24×C79—21no—
40C2×D4×C79—21no—
41C2×D4×C79—21no—
42C2×D4×C79—21no—
43C2×D4×C79—21no—
44C2×D4×C79—21no—
45C2×D4×C79Q812yes—
46C22×C4×C79—21no—
47C22×C4×C79C2311yescharacteristic
48C2×C8×C79—21no—
49C2×C8×C79—21no—
50C2×C8×C79D412yes—
51C4⋊C4×C79—21no—
52C4⋊C4×C79—21no—
53C23×C79—22no—
54C23×C79—41no—
55C23×C79—41no—
56C23×C79—41no—
57C23×C79—41no—
58C23×C79—41no—
59C23×C79—41no—
60C23×C79C2×D411yescharacteristic
61D4×C79—22no—
62D4×C79—22no—
63D4×C79—41no—
64D4×C79—41no—
65C2×C4×C79—41no—
66C2×C4×C79—41no—
67C2×C4×C79—41no—
68C2×C4×C79C2×D411yescharacteristic
69C2×C4×C79C2×D411yescharacteristic
70C2×C4×C79C2×Q811yescharacteristic
71C2×C4×C79#4111yescharacteristic
72C2×C4×C79#4111yescharacteristic
73C2×C4×C79#4111yescharacteristic
74C2×Dic79—21no—
75C2×Dic79—21no—
76C2×Dic79—21no—
77C2×Dic79—22no—
78C2×Dic79—21no—
79C2×Dic79—21no—
80C2×Dic79—41no—
81C2×Dic79—41no—
82C2×Dic79—41no—
83C2×Dic79—41no—
84C2×Dic79—41no—
85C2×Dic79D812yes—
86C8×C79—22no—
87C79⋊C8—41no—
88C22×C79—42no—
89C22×C79—42no—
90C22×C79—42no—
91C22×C79—81no—
92C22×C79—81no—
93C22×C79—81no—
94C22×C79—81no—
95C22×C79#12111yescharacteristic
96C22×C79#12111yescharacteristic
97C22×C79C22⋊Q811yescharacteristic
98C22×C79C2×D811yescharacteristic
99C22×C79#13511yescharacteristic
100C22×C79AGL(1,ℤ/8)11yescharacteristic
101C22×C79#13711yescharacteristic
102C4×C79—81no—
103C4×C79#12111yescharacteristic
104C4×C79C22⋊Q811yescharacteristic
105C4×C79C22⋊Q811yescharacteristic
106C4×C79#12611yescharacteristic
107Dic79—22no—
108Dic79—42no—
109Dic79—41no—
110Dic79—81no—
111C2×C79—82no—
112C2×C79#39611yescharacteristic
113C2×C79#45911yescharacteristic
114C2×C79#46411yescharacteristic
115C2×C79#46611yescharacteristic
116C2×C79#46811yescharacteristic
117C2×C79#47411yescharacteristic
118C2×C79#47811yescharacteristic
119#2067—791nomaximal, Sylow
120C79#206711yescharacteristic, complemented, Sylow
121C2×#107—791no—
122C2×C4⋊C8—791no—
123C2×#102—791no—
124C2×#102D7911yescharacteristic
125#390—791no—
126#389—791no—
127#340—791no—
128C22×D4C2×D7911yescharacteristic
129C22×C8—791no—
130C22×C8C2×D7911yescharacteristic
131C2×C4⋊C4—791no—
132C2×C4⋊C4—791no—
133C2×C4⋊C4—1581no—
134C2×C4⋊C4C2×D7911yescharacteristic
135C2×C22⋊C4—1581no—
136C2×C22⋊C4—1581no—
137C2×C42—791no—
138#107—1582no—
139C4⋊C8—1582no—
140#102—22no—
141#102—1582no—
142#95—1581no—
143C24—21no—
144C2×D4—21no—
145C2×D4—21no—
146C2×D4—21no—
147C2×D4—21no—
148C2×D4—21no—
149C2×D4Dic15812yes—
150C22×C4—21no—
151C22×C4—791no—
152C22×C4—791no—
153C22×C4—1581no—
154C22×C4—1581no—
155C22×C4C22×D7911yescharacteristic
156C2×C8—21no—
157C2×C8—21no—
158C2×C8—1581no—
159C2×C8—1581no—
160C2×C8—1581no—
161C2×C8C22⋊D7912yes—
162C4⋊C4—21no—
163C4⋊C4—21no—
164C4⋊C4—3162no—
165C4⋊C4—792no—
166C4⋊C4—1581no—
167C4⋊C4—1581no—
168C4⋊C4—1581no—
169C22⋊C4—3162no—
170C22⋊C4—3162no—
171C42—1581no—
172C42—1581no—
173C23—22no—
174C23—41no—
175C23—41no—
176C23—41no—
177C23—41no—
178C23—41no—
179C23—41no—
180C23D4×D7911yescharacteristic
181D4—22no—
182D4—22no—
183D4—41no—
184D4—41no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—3161no—
189C2×C4—3161no—
190C2×C4—3161no—
191C2×C4—3161no—
192C2×C4—3161no—
193C2×C4—792no—
194C2×C4—1581no—
195C2×C4—1582no—
196C2×C4—1581no—
197C2×C4—1581no—
198C2×C4—1581no—
199C2×C4—1581no—
200C2×C4D4×D7911yescharacteristic
201C2×C4C2×C22⋊D7911yescharacteristic
202C2×C4C2×Dic15811yescharacteristic
203C2×C4#1192962311yescharacteristic
204C2×C4#1192962311yescharacteristic
205C2×C4#1192962411yescharacteristic
206C8—22no—
207C8—3161no—
208C22—42no—
209C22—42no—
210C22—42no—
211C22—81no—
212C22—81no—
213C22—81no—
214C22—81no—
215C22#1457913211yescharacteristic
216C22#1457913411yescharacteristic
217C22#1457913811yescharacteristic
218C22D8×D7911yescharacteristic
219C22#1457918011yescharacteristic
220C22#1457918811yescharacteristic
221C22#1457919011yescharacteristic
222C4—81no—
223C4—3162no—
224C4—3161no—
225C4—6321no—
226C4—1582no—
227C4#1457913311yescharacteristic
228C4#1457913811yescharacteristic
229C4#1457914011yescharacteristic
230C4#1457915411yescharacteristic
231C2—82no—
232C2#1909848611yescharacteristic
233C2#1909875711yescharacteristic
234C2#1909878411yescharacteristic
235C2#1909879611yescharacteristic
236C2#1909880611yescharacteristic
237C2#1909884111yescharacteristic
238C2#1909886111yescharacteristic
subgroupG/H
centerC23D4×D79
commutator, cosocleC22×C4×C79C23
FrattiniC22×C4C22×D79
FittingC2×#102×C79C2
socleC23×C79C2×D4
prime radicalC22×D4×C79C22
hypercenterC2×#102D79
hypocenterC79#2067
LCSG ▷ C22×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
1. C2×#14579095C2semidirect
2. C2×Dic79⋊C8C2semidirect
5. #19098459C2semidirect
6. #19098325C2semidirect
120. C79#2067semidirect