Finite Group Databasebeta

← #23763532

Subgroups — #23763532

Order 10112.

224 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 93 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×#14579071C211yesmaximal, characteristic
2#19098432C211yesmaximal, characteristic
3#19098428C211yesmaximal, characteristic
4#19098326C211yesmaximal, characteristic
5#19098325C211yesmaximal, characteristic
6#19098325C211yesmaximal, characteristic
7#340×C79C211yesmaximal, characteristic
8C22×C79⋊C8C2211yescharacteristic
9C2×C4⋊Dic79C2211yescharacteristic
10C2×C4⋊Dic79C2211yescharacteristic
11C2×Dic79⋊C4—21no—
12C2×Dic79⋊C4—21no—
13C2×C4×Dic79C2211yescharacteristic
14#14579071C414yescomplemented
15C79⋊#95—21no—
16C79⋊#95—21no—
17C22×C8×C79C2211yescharacteristic
18C2×C4⋊C4×C79C2211yescharacteristic
19C2×C4⋊C4×C79C2211yescharacteristic
20C22×Dic79—21no—
21C22×Dic79—21no—
22C22×Dic79D411yescharacteristic
23C22×Dic79D411yescharacteristic
24C2×C79⋊C8—21no—
25C2×C79⋊C8—21no—
26C2×C79⋊C8C2×C412yes—
27C4⋊Dic79—21no—
28C4⋊Dic79—21no—
29C4⋊Dic79—21no—
30C4⋊Dic79—21no—
31Dic79⋊C4—42no—
32Dic79⋊C4—42no—
33C4×Dic79C2×C412yes—
34C4×Dic79Q812yes—
35C22×C4×C79—21no—
36C22×C4×C79—21no—
37C22×C4×C79C2311yescharacteristic
38C2×C8×C79—21no—
39C2×C8×C79—21no—
40C2×C8×C79C2×C412yes—
41C4⋊C4×C79—21no—
42C4⋊C4×C79—21no—
43C4⋊C4×C79—21no—
44C4⋊C4×C79—21no—
45C23×C79C2×D411yescharacteristic
46C2×C4×C79—41no—
47C2×C4×C79—41no—
48C2×C4×C79—41no—
49C2×C4×C79—41no—
50C2×C4×C79—41no—
51C2×C4×C79—41no—
52C2×C4×C79C22×C411yescharacteristic
53C2×C4×C79C2×Q811yescharacteristic
54C2×C4×C79#4111yescharacteristic
55C2×C4×C79#4111yescharacteristic
56C2×C4×C79#4111yescharacteristic
57C2×C4×C79#4111yescharacteristic
58C2×Dic79—21no—
59C2×Dic79—21no—
60C2×Dic79—21no—
61C2×Dic79—21no—
62C2×Dic79—41no—
63C2×Dic79—41no—
64C2×Dic79—41no—
65C2×Dic79—41no—
66C2×Dic79—41no—
67C2×Dic79—41no—
68C2×Dic79C4⋊C412yes—
69C2×Dic79C4⋊C412yes—
70C8×C79—22no—
71C79⋊C8—22no—
72C22×C79C2×C4⋊C411yescharacteristic
73C22×C79#12411yescharacteristic
74C22×C79#12411yescharacteristic
75C22×C79AGL(1,ℤ/8)11yescharacteristic
76C22×C79AGL(1,ℤ/8)11yescharacteristic
77C22×C79#13711yescharacteristic
78C22×C79#13711yescharacteristic
79C4×C79—81no—
80C4×C79—81no—
81C4×C79#11711yescharacteristic
82C4×C79#11711yescharacteristic
83C4×C79#12511yescharacteristic
84C4×C79#12511yescharacteristic
85Dic79—22no—
86Dic79—22no—
87Dic79—81no—
88Dic79—81no—
89C2×C79#38211yescharacteristic
90C2×C79#42811yescharacteristic
91C2×C79#42811yescharacteristic
92C2×C79#48911yescharacteristic
93C2×C79#48911yescharacteristic
94C2×C79#49011yescharacteristic
95C2×C79#49111yescharacteristic
96#1836—791nomaximal, Sylow
97C79#183611yescharacteristic, complemented, Sylow
98C2×#97—791no—
99#384—791no—
100#382—791no—
101#340—791no—
102#340—791no—
103#340—791no—
104#340D7911yescharacteristic
105C22×C8—791no—
106C22×C8C2×D7911yescharacteristic
107C2×C4⋊C4—791no—
108C2×C4⋊C4—791no—
109C2×C4⋊C4—1581no—
110C2×C4⋊C4—1581no—
111C2×C4⋊C4C2×D7911yescharacteristic
112C2×C4⋊C4C2×D7911yescharacteristic
113C2×C42—791no—
114#97—794no—
115#95—1581no—
116#95—1581no—
117C22×C4—21no—
118C22×C4—21no—
119C22×C4—791no—
120C22×C4—791no—
121C22×C4—1581no—
122C22×C4—1581no—
123C22×C4C22×D7911yescharacteristic
124C2×C8—21no—
125C2×C8—21no—
126C2×C8—792no—
127C2×C8—1581no—
128C2×C8—1581no—
129C2×C8C4×D7912yes—
130C4⋊C4—21no—
131C4⋊C4—21no—
132C4⋊C4—21no—
133C4⋊C4—21no—
134C4⋊C4—3162no—
135C4⋊C4—3162no—
136C4⋊C4—1581no—
137C4⋊C4—1581no—
138C4⋊C4—1581no—
139C4⋊C4—1581no—
140C42—792no—
141C42—792no—
142C23D4×D7911yescharacteristic
143C2×C4—41no—
144C2×C4—41no—
145C2×C4—41no—
146C2×C4—41no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—3161no—
150C2×C4—3161no—
151C2×C4—3161no—
152C2×C4—3161no—
153C2×C4—3161no—
154C2×C4—3161no—
155C2×C4—792no—
156C2×C4—792no—
157C2×C4—1581no—
158C2×C4—1581no—
159C2×C4—1581no—
160C2×C4—1581no—
161C2×C4C2×C4×D7911yescharacteristic
162C2×C4Q8×D7911yescharacteristic
163C2×C4#1192962311yescharacteristic
164C2×C4#1192962311yescharacteristic
165C2×C4#1192962411yescharacteristic
166C2×C4#1192962411yescharacteristic
167C8—22no—
168C8—1582no—
169C22C4⋊C4×D7911yescharacteristic
170C22#1457914711yescharacteristic
171C22#1457914711yescharacteristic
172C22#1457918511yescharacteristic
173C22#1457918811yescharacteristic
174C22#1457919011yescharacteristic
175C22#1457919311yescharacteristic
176C4—81no—
177C4—81no—
178C4—6321no—
179C4—6321no—
180C4—1582no—
181C4—1582no—
182C4#1457911711yescharacteristic
183C4#1457911811yescharacteristic
184C4#1457915111yescharacteristic
185C4#1457915111yescharacteristic
186C2#1909842711yescharacteristic
187C2#1909860211yescharacteristic
188C2#1909860411yescharacteristic
189C2#1909892111yescharacteristic
190C2#1909892411yescharacteristic
191C2#1909892611yescharacteristic
192C2#1909893011yescharacteristic
subgroupG/H
centerC23D4×D79
commutatorC2×C4×C79C22×C4
FrattiniC22×C4C22×D79
Fitting#340×C79C2
socle, prime radicalC23×C79C2×D4
cosocleC22×C4×C79C23
hypercenter#340D79
hypocenterC79#1836
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
14. #14579071C4semidirect
97. C79#1836semidirect