Finite Group Databasebeta

← #23764115

Subgroups — #23764115

Order 10112.

260 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 117 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×Dic79⋊C8C211yesmaximal, characteristic
2C2×Dic79⋊C8C211yesmaximal, characteristic
3C2×C8×Dic79C211yesmaximal, characteristic
4C4×Dic79⋊C4C211yesmaximal, characteristic
5#19098318C211yesmaximal, characteristic
6#19098317C211yesmaximal, characteristic
7C2×C4⋊C8×C79C211yesmaximal, characteristic
8C22×C79⋊C8C2211yescharacteristic
9C22×C79⋊C8C2211yescharacteristic
10C2×Dic79⋊C4C411yescharacteristic
11C2×Dic79⋊C4C411yescharacteristic
12C2×C4×Dic79C2211yescharacteristic
13C2×C4×Dic79C2211yescharacteristic
14Dic79⋊C8—22no—
15Dic79⋊C8—22no—
16C8×Dic79—22no—
17C79⋊#95C411yescharacteristic
18C79⋊#95C411yescharacteristic
19C22×C8×C79C2211yescharacteristic
20C22×C8×C79C2211yescharacteristic
21C2×C42×C79C2211yescharacteristic
22C4⋊C8×C79—22no—
23C22×Dic79C2×C411yescharacteristic
24C22×Dic79C2×C411yescharacteristic
25C22×Dic79C2×C411yescharacteristic
26C22×Dic79C2×C411yescharacteristic
27C2×C79⋊C8—21no—
28C2×C79⋊C8—21no—
29C2×C79⋊C8—21no—
30C2×C79⋊C8—21no—
31C2×C79⋊C8—21no—
32C2×C79⋊C8Q812yes—
33Dic79⋊C4—22no—
34Dic79⋊C4C814yescomplemented
35C4×Dic79—21no—
36C4×Dic79—21no—
37C4×Dic79D412yes—
38C4×Dic79Q812yes—
39C22×C4×C79C2×C411yescharacteristic
40C22×C4×C79C2×C411yescharacteristic
41C22×C4×C79C2311yescharacteristic
42C2×C8×C79—21no—
43C2×C8×C79—21no—
44C2×C8×C79—21no—
45C2×C8×C79—21no—
46C2×C8×C79—21no—
47C2×C8×C79D412yes—
48C42×C79—21no—
49C42×C79—21no—
50C23×C79C22×C411yescharacteristic
51C2×C4×C79—21no—
52C2×C4×C79—21no—
53C2×C4×C79—21no—
54C2×C4×C79—21no—
55C2×C4×C79—21no—
56C2×C4×C79C2×C812yes—
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—21no—
64C2×Dic79—21no—
65C2×Dic79—21no—
66C2×Dic79—21no—
67C2×Dic79—21no—
68C2×Dic79—21no—
69C2×Dic79—21no—
70C2×Dic79C4⋊C412yes—
71C2×Dic79C4⋊C412yes—
72C2×Dic79C2×C812yes—
73C2×Dic79C2×C812yes—
74C2×Dic79M1612yes—
75C8×C79—22no—
76C8×C79—41no—
77C79⋊C8—22no—
78C79⋊C8—41no—
79C22×C79C2×C4⋊C411yescharacteristic
80C22×C79C4×D411yescharacteristic
81C22×C79C4×Q811yescharacteristic
82C22×C79C22×C811yescharacteristic
83C22×C79C2×M1611yescharacteristic
84C22×C79#13111yescharacteristic
85C22×C79#13111yescharacteristic
86C4×C79—22no—
87C4×C79—41no—
88C4×C79#12111yescharacteristic
89C4×C79C22⋊Q811yescharacteristic
90C4×C79#12511yescharacteristic
91C4×C79C4⋊Q811yescharacteristic
92Dic79—22no—
93Dic79—22no—
94Dic79—41no—
95Dic79C4⋊C814yescomplemented
96C2×C79#38911yescharacteristic
97C2×C79C2×C4⋊C811yescharacteristic
98C2×C79#42411yescharacteristic
99C2×C79C8×D411yescharacteristic
100C2×C79#43611yescharacteristic
101C2×C79C8×Q811yescharacteristic
102C2×C79#44611yescharacteristic
103#1939—791nomaximal, Sylow
104C79#193911yescharacteristic, complemented, Sylow
105C2×C4⋊C8—791no—
106C2×C4⋊C8—791no—
107C2×C4⋊C8D7911yescharacteristic
108C2×C4×C8—791no—
109C4×C4⋊C4—791no—
110#336—791no—
111#336—791no—
112C22×C8—791no—
113C22×C8—791no—
114C22×C8C2×D7911yescharacteristic
115C22×C8C2×D7911yescharacteristic
116C2×C4⋊C4—791no—
117C2×C4⋊C4—791no—
118C2×C42—791no—
119C2×C42—791no—
120C2×C42C2×D7911yescharacteristic
121C4⋊C8—22no—
122C4⋊C8—1582no—
123C4⋊C8—1582no—
124C4×C8—1582no—
125#95—791no—
126#95—791no—
127C22×C4—791no—
128C22×C4—791no—
129C22×C4—791no—
130C22×C4—791no—
131C22×C4C4×D7911yescharacteristic
132C22×C4C4×D7911yescharacteristic
133C22×C4C22×D7911yescharacteristic
134C2×C8—21no—
135C2×C8—21no—
136C2×C8—21no—
137C2×C8—21no—
138C2×C8—21no—
139C2×C8—792no—
140C2×C8—1581no—
141C2×C8—1581no—
142C2×C8—1581no—
143C2×C8—1581no—
144C2×C8—1581no—
145C2×C8C22⋊D7912yes—
146C4⋊C4—794no—
147C4⋊C4—1582no—
148C42—21no—
149C42—21no—
150C42—792no—
151C42—792no—
152C42—1581no—
153C42—1581no—
154C23C2×C4×D7911yescharacteristic
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—21no—
159C2×C4—21no—
160C2×C4—792no—
161C2×C4—792no—
162C2×C4—792no—
163C2×C4—792no—
164C2×C4—792no—
165C2×C4—1581no—
166C2×C4—1581no—
167C2×C4—1581no—
168C2×C4—1581no—
169C2×C4—1581no—
170C2×C4—1581no—
171C2×C4—1581no—
172C2×C4C8×D7912yes—
173C2×C4D4×D7911yescharacteristic
174C2×C4C2×C22⋊D7911yescharacteristic
175C2×C4Q8×D7911yescharacteristic
176C2×C4Q8×D7911yescharacteristic
177C2×C4#1192962311yescharacteristic
178C2×C4#1192962411yescharacteristic
179C8—22no—
180C8—41no—
181C8—3161no—
182C8—1582no—
183C22C4⋊C4×D7911yescharacteristic
184C22C4×C22⋊D7911yescharacteristic
185C22#1457912611yescharacteristic
186C22C2×C8×D7911yescharacteristic
187C22M16×D7911yescharacteristic
188C22#1457916711yescharacteristic
189C22#1457916911yescharacteristic
190C4—22no—
191C4—41no—
192C4—3161no—
193C4—794no—
194C4—1582no—
195C4—1582no—
196C4#1457913311yescharacteristic
197C4#1457913911yescharacteristic
198C4#1457915111yescharacteristic
199C4#1457915911yescharacteristic
200C2#1909845811yescharacteristic
201C2C4⋊C8×D7911yescharacteristic
202C2#1909858811yescharacteristic
203C2C8×C22⋊D7911yescharacteristic
204C2#1909863911yescharacteristic
205C2#1909868711yescharacteristic
206C2#1909869211yescharacteristic
subgroupG/H
center, FrattiniC22×C4C22×D79
commutatorC22×C79C22×C8
FittingC2×C4⋊C8×C79C2
socle, prime radicalC23×C79C22×C4
cosocleC22×C4×C79C23
hypercenterC2×C4⋊C8D79
hypocenterC79#1939
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22×C4 ◁ C2×C4⋊C8

Complements

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

NH ≅ G/Ntype
34. Dic79⋊C4C8semidirect
95. Dic79C4⋊C8semidirect
104. C79#1939semidirect