Finite Group Databasebeta

← #23764036

Subgroups — #23764036

Order 10112.

254 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 254 conjugacy classes of subgroups — too many to draw. Only its 99 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×#14579085C211yesmaximal, characteristic
3#19098470C211yesmaximal, characteristic
4C4⋊C4×Dic79C211yesmaximal, characteristic
5#19098325C211yesmaximal, characteristic
6#19098317C211yesmaximal, characteristic
7C2×#103×C79C211yesmaximal, characteristic
8C22×C79⋊C8C2211yescharacteristic
9C2×C4⋊Dic79C2211yescharacteristic
10C2×C4⋊Dic79C2211yescharacteristic
11C2×C4×Dic79—21no—
12C2×C4×Dic79C2211yescharacteristic
13#14579093—22no—
14#14579085—22no—
15C79⋊#95—21no—
16C79⋊#95—21no—
17C79⋊#95—21no—
18C22×Q8×C79C2211yescharacteristic
19C22×C8×C79C2211yescharacteristic
20C2×C4⋊C4×C79C2211yescharacteristic
21#103×C79C414yescomplemented
22C22×Dic79—21no—
23C22×Dic79—21no—
24C22×Dic79D411yescharacteristic
25C22×Dic79D411yescharacteristic
26C2×C79⋊C8—21no—
27C2×C79⋊C8—21no—
28C2×C79⋊C8—21no—
29C4⋊Dic79—21no—
30C4⋊Dic79—21no—
31C4⋊Dic79—21no—
32C4⋊Dic79D412yes—
33C4×Dic79—21no—
34C4×Dic79—21no—
35C4×Dic79—42no—
36C2×Q8×C79—21no—
37C2×Q8×C79—21no—
38C2×Q8×C79—21no—
39C2×Q8×C79—21no—
40C2×Q8×C79—21no—
41C2×Q8×C79C2×C412yes—
42C22×C4×C79—21no—
43C22×C4×C79—21no—
44C22×C4×C79C2311yescharacteristic
45C2×C8×C79—21no—
46C2×C8×C79—21no—
47C2×C8×C79C2×C412yes—
48C4⋊C4×C79—21no—
49C4⋊C4×C79C2×C412yes—
50C23×C79C2×D411yescharacteristic
51Q8×C79—22no—
52Q8×C79—22no—
53Q8×C79—41no—
54Q8×C79—41no—
55C2×C4×C79—22no—
56C2×C4×C79—22no—
57C2×C4×C79—41no—
58C2×C4×C79—41no—
59C2×C4×C79—41no—
60C2×C4×C79—41no—
61C2×C4×C79C22×C411yescharacteristic
62C2×C4×C79C2×D411yescharacteristic
63C2×C4×C79#4111yescharacteristic
64C2×C4×C79#4111yescharacteristic
65C2×C4×C79#4111yescharacteristic
66C2×C4×C79#4111yescharacteristic
67C2×Dic79—21no—
68C2×Dic79—21no—
69C2×Dic79—22no—
70C2×Dic79—21no—
71C2×Dic79—21no—
72C2×Dic79—21no—
73C2×Dic79—41no—
74C2×Dic79—41no—
75C2×Dic79—41no—
76C2×Dic79—41no—
77C2×Dic79—41no—
78C2×Dic79SD1612yes—
79C8×C79—22no—
80C79⋊C8—41no—
81C22×C79C4×D411yescharacteristic
82C22×C79#12111yescharacteristic
83C22×C79#12311yescharacteristic
84C22×C79C2×SD1611yescharacteristic
85C22×C79#13511yescharacteristic
86C22×C79#13711yescharacteristic
87C22×C79#13711yescharacteristic
88C4×C79—42no—
89C4×C79—42no—
90C4×C79#11711yescharacteristic
91C4×C79C4×D411yescharacteristic
92C4×C79#12411yescharacteristic
93C4×C79#12611yescharacteristic
94Dic79—22no—
95Dic79—42no—
96Dic79—41no—
97Dic79—81no—
98C2×C79#38811yescharacteristic
99C2×C79C4×SD1611yescharacteristic
100C2×C79#44111yescharacteristic
101C2×C79#46111yescharacteristic
102C2×C79#46411yescharacteristic
103C2×C79#48311yescharacteristic
104C2×C79#48511yescharacteristic
105#1927—791nomaximal, Sylow
106C79#192711yescharacteristic, complemented, Sylow
107C2×#106—791no—
108C2×#103—791no—
109C2×#103D7911yescharacteristic
110#391—791no—
111C4×C4⋊C4—791no—
112#340—791no—
113#336—791no—
114C22×Q8C2×D7911yescharacteristic
115C22×C8—791no—
116C22×C8C2×D7911yescharacteristic
117C2×C4⋊C4—791no—
118C2×C4⋊C4—791no—
119C2×C4⋊C4C2×D7911yescharacteristic
120C2×C42—791no—
121C2×C42—1581no—
122#106—1582no—
123#103—1582no—
124#103Dic7914yescomplemented
125#95—1581no—
126#95—1581no—
127#95—1581no—
128C2×Q8—21no—
129C2×Q8—21no—
130C2×Q8—21no—
131C2×Q8—21no—
132C2×Q8—21no—
133C2×Q8C2×Dic7912yes—
134C22×C4—21no—
135C22×C4—21no—
136C22×C4—791no—
137C22×C4—791no—
138C22×C4—1581no—
139C22×C4—1581no—
140C22×C4C22×D7911yescharacteristic
141C2×C8—21no—
142C2×C8—21no—
143C2×C8—1581no—
144C2×C8—1581no—
145C2×C8—1581no—
146C2×C8C2×Dic7912yes—
147C4⋊C4—21no—
148C4⋊C4—792no—
149C4⋊C4—1581no—
150C4⋊C4—1581no—
151C4⋊C4—1581no—
152C4⋊C4C2×Dic7912yes—
153C42—3162no—
154C42—1581no—
155C42—1581no—
156C23D4×D7911yescharacteristic
157Q8—22no—
158Q8—22no—
159Q8—41no—
160Q8—41no—
161C2×C4—22no—
162C2×C4—22no—
163C2×C4—41no—
164C2×C4—41no—
165C2×C4—41no—
166C2×C4—41no—
167C2×C4—3161no—
168C2×C4—3161no—
169C2×C4—3161no—
170C2×C4—3161no—
171C2×C4—3161no—
172C2×C4—792no—
173C2×C4—1582no—
174C2×C4—1581no—
175C2×C4—1581no—
176C2×C4—1581no—
177C2×C4—1581no—
178C2×C4—1581no—
179C2×C4C22×Dic7911yescharacteristic
180C2×C4D4×D7911yescharacteristic
181C2×C4#1192962311yescharacteristic
182C2×C4#1192962311yescharacteristic
183C2×C4#1192962411yescharacteristic
184C2×C4#1192962411yescharacteristic
185C8—22no—
186C8—3161no—
187C22D4×Dic7911yescharacteristic
188C22#1457913411yescharacteristic
189C22#1457914311yescharacteristic
190C22SD16×D7911yescharacteristic
191C22#1457918211yescharacteristic
192C22#1457919311yescharacteristic
193C22#1457919311yescharacteristic
194C4—42no—
195C4—42no—
196C4—3161no—
197C4—3162no—
198C4—6321no—
199C4—1582no—
200C4#1457912011yescharacteristic
201C4D4×Dic7911yescharacteristic
202C4#1457914711yescharacteristic
203C4#1457915411yescharacteristic
204C2#1909845611yescharacteristic
205C2SD16×Dic7911yescharacteristic
206C2#1909867011yescharacteristic
207C2#1909876711yescharacteristic
208C2#1909878811yescharacteristic
209C2#1909889211yescharacteristic
210C2#1909890211yescharacteristic
subgroupG/H
centerC23D4×D79
commutatorC2×C4×C79C22×C4
FrattiniC22×C4C22×D79
FittingC2×#103×C79C2
socle, prime radicalC23×C79C2×D4
cosocleC22×C4×C79C23
hypercenterC2×#103D79
hypocenterC79#1927
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
21. #103×C79C4semidirect
106. C79#1927semidirect
124. #103Dic79semidirect