Finite Group Databasebeta

← #23763958

Subgroups — #23763958

Order 10112.

240 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 105 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×C8×Dic79C211yesmaximal, characteristic
3C4×C4⋊Dic79C211yesmaximal, characteristic
4#19098318C211yesmaximal, characteristic
5#19098317C211yesmaximal, characteristic
6#19098317C211yesmaximal, characteristic
7#336×C79C211yesmaximal, characteristic
8C22×C79⋊C8C2211yescharacteristic
9C22×C79⋊C8C2211yescharacteristic
10C2×C4⋊Dic79C411yescharacteristic
11C2×C4⋊Dic79C411yescharacteristic
12C2×C4×Dic79C2211yescharacteristic
13C2×C4×Dic79C2211yescharacteristic
14Dic79⋊C8—22no—
15C8×Dic79—22no—
16C79⋊#95C411yescharacteristic
17C79⋊#95C411yescharacteristic
18C22×C8×C79C2211yescharacteristic
19C22×C8×C79C2211yescharacteristic
20C2×C42×C79C2211yescharacteristic
21C22×Dic79C2×C411yescharacteristic
22C22×Dic79C2×C411yescharacteristic
23C22×Dic79C2×C411yescharacteristic
24C22×Dic79C2×C411yescharacteristic
25C2×C79⋊C8—21no—
26C2×C79⋊C8—21no—
27C2×C79⋊C8—21no—
28C2×C79⋊C8—21no—
29C2×C79⋊C8—21no—
30C2×C79⋊C8Q812yes—
31C4⋊Dic79—22no—
32C4⋊Dic79C814yescomplemented
33C4×Dic79—21no—
34C4×Dic79—21no—
35C4×Dic79—21no—
36C4×Dic79—21no—
37C22×C4×C79C2×C411yescharacteristic
38C22×C4×C79C2×C411yescharacteristic
39C22×C4×C79C2311yescharacteristic
40C2×C8×C79—21no—
41C2×C8×C79—21no—
42C2×C8×C79—21no—
43C2×C8×C79—21no—
44C2×C8×C79—21no—
45C2×C8×C79D412yes—
46C42×C79—21no—
47C42×C79—21no—
48C23×C79C22×C411yescharacteristic
49C2×C4×C79—21no—
50C2×C4×C79—21no—
51C2×C4×C79—21no—
52C2×C4×C79—21no—
53C2×C4×C79—21no—
54C2×C4×C79C2×C812yes—
55C2×C4×C79C2×D411yescharacteristic
56C2×C4×C79C2×Q811yescharacteristic
57C2×C4×C79#4111yescharacteristic
58C2×C4×C79#4111yescharacteristic
59C2×C4×C79#4111yescharacteristic
60C2×C4×C79#4111yescharacteristic
61C2×Dic79—21no—
62C2×Dic79—21no—
63C2×Dic79—21no—
64C2×Dic79—21no—
65C2×Dic79—21no—
66C2×Dic79—21no—
67C2×Dic79—21no—
68C2×Dic79—21no—
69C2×Dic79—21no—
70C2×Dic79C2×C812yes—
71C2×Dic79C2×C812yes—
72C2×Dic79M1612yes—
73C8×C79—22no—
74C8×C79—41no—
75C79⋊C8—22no—
76C79⋊C8—41no—
77C22×C79#11711yescharacteristic
78C22×C79C4×D411yescharacteristic
79C22×C79C4×Q811yescharacteristic
80C22×C79C22×C811yescharacteristic
81C22×C79C2×M1611yescharacteristic
82C22×C79#13111yescharacteristic
83C22×C79#13111yescharacteristic
84C4×C79—22no—
85C4×C79—41no—
86C4×C79C22⋊Q811yescharacteristic
87C4×C79#12311yescharacteristic
88C4×C79#12511yescharacteristic
89C4×C79#12611yescharacteristic
90Dic79—22no—
91Dic79—22no—
92Dic79—22no—
93Dic79—41no—
94C2×C79#38711yescharacteristic
95C2×C79#43111yescharacteristic
96C2×C79#43311yescharacteristic
97C2×C79C8×D411yescharacteristic
98C2×C79#43511yescharacteristic
99C2×C79C8×Q811yescharacteristic
100C2×C79#44611yescharacteristic
101#1916—791nomaximal, Sylow
102C79#191611yescharacteristic, complemented, Sylow
103C2×C4⋊C8—791no—
104C2×C4×C8—791no—
105C4×C4⋊C4—791no—
106#336—791no—
107#336—791no—
108#336—791no—
109#336D7911yescharacteristic
110C22×C8—791no—
111C22×C8—791no—
112C22×C8C2×D7911yescharacteristic
113C22×C8C2×D7911yescharacteristic
114C2×C4⋊C4—791no—
115C2×C4⋊C4—791no—
116C2×C42—791no—
117C2×C42—791no—
118C2×C42C2×D7911yescharacteristic
119C4⋊C8—1582no—
120C4×C8—1582no—
121#95—791no—
122#95—791no—
123C22×C4—791no—
124C22×C4—791no—
125C22×C4—791no—
126C22×C4—791no—
127C22×C4C4×D7911yescharacteristic
128C22×C4C4×D7911yescharacteristic
129C22×C4C22×D7911yescharacteristic
130C2×C8—21no—
131C2×C8—21no—
132C2×C8—21no—
133C2×C8—21no—
134C2×C8—21no—
135C2×C8—792no—
136C2×C8—1581no—
137C2×C8—1581no—
138C2×C8—1581no—
139C2×C8—1581no—
140C2×C8—1581no—
141C2×C8D31612yes—
142C4⋊C4—794no—
143C4⋊C4—1582no—
144C42—21no—
145C42—21no—
146C42—1581no—
147C42—1581no—
148C42—1581no—
149C42—1581no—
150C23C2×C4×D7911yescharacteristic
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—21no—
156C2×C4—792no—
157C2×C4—792no—
158C2×C4—792no—
159C2×C4—1581no—
160C2×C4—1581no—
161C2×C4—1581no—
162C2×C4—1581no—
163C2×C4—1581no—
164C2×C4—1581no—
165C2×C4—1581no—
166C2×C4—1581no—
167C2×C4—1581no—
168C2×C4C8×D7912yes—
169C2×C4C2×D31611yescharacteristic
170C2×C4Q8×D7911yescharacteristic
171C2×C4#1192962311yescharacteristic
172C2×C4#1192962311yescharacteristic
173C2×C4#1192962311yescharacteristic
174C2×C4#1192962411yescharacteristic
175C8—22no—
176C8—41no—
177C8—3161no—
178C8—1582no—
179C22#1457911711yescharacteristic
180C22C4×D31611yescharacteristic
181C22#1457912611yescharacteristic
182C22C2×C8×D7911yescharacteristic
183C22M16×D7911yescharacteristic
184C22#1457916711yescharacteristic
185C22#1457916911yescharacteristic
186C4—22no—
187C4—41no—
188C4—3161no—
189C4—1582no—
190C4—1582no—
191C4—1582no—
192C4#1457914111yescharacteristic
193C4#1457914511yescharacteristic
194C4#1457915111yescharacteristic
195C4#1457915411yescharacteristic
196C2#1909844811yescharacteristic
197C2#1909861311yescharacteristic
198C2#1909862111yescharacteristic
199C2C8×D31611yescharacteristic
200C2#1909863611yescharacteristic
201C2#1909868711yescharacteristic
202C2#1909869211yescharacteristic
subgroupG/H
center, FrattiniC22×C4C22×D79
commutatorC22×C79C22×C8
Fitting#336×C79C2
socle, prime radicalC23×C79C22×C4
cosocleC22×C4×C79C23
hypercenter#336D79
hypocenterC79#1916
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22×C4 ◁ #336

Complements

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

NH ≅ G/Ntype
32. C4⋊Dic79C8semidirect
102. C79#1916semidirect