Finite Group Databasebeta

← #23764296

Subgroups — #23764296

Order 10112.

284 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 85 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×#14579183C211yesmaximal, characteristic
2#19098581C212yesmaximal, complemented
3#19098536C212yesmaximal, complemented
4#19098518C211yesmaximal, characteristic, complemented
5#427×C79C211yesmaximal, characteristic, complemented
6C2×#11929624C2212yes—
7#14579183—21no—
8#14579183—21no—
9#14579183—21no—
10#14579183—21no—
11C2×Dic316C411yescharacteristic, complemented
12C2×#11929613C412yescomplemented
13C2×D632C411yescharacteristic, complemented
14C2×#11929608C2211yescharacteristic
15#14579120C2211yescharacteristic
16#14579089—24no—
17#14579075—24no—
18#14579071—21no—
19C8×Dic79—21no—
20C22×C8×C79C2211yescharacteristic
21#117×C79C2212yes—
22#107×C79—21no—
23#106×C79—21no—
24#11929624—22no—
25#11929624—22no—
26#11929624—22no—
27#11929624—22no—
28C2×Dic158C2×C412yes—
29C2×D316C2×C412yes—
30C2×C22⋊D79—22no—
31C2×C4×D79—22no—
32Dic316—21no—
33Dic316—21no—
34#11929613—22no—
35#11929613—22no—
36D632—21no—
37D632—21no—
38#11929608—21no—
39#11929608D412yes—
40C2×C79⋊C8—21no—
41C4⋊Dic79—21no—
42C22⋊Dic79D412yes—
43C4×Dic79—21no—
44C22×C4×C79C2311yescharacteristic
45C2×C8×C79C2×C411yescharacteristic
46C2×C8×C79C2×C411yescharacteristic
47C2×C8×C79D411yescharacteristic
48C2×C8×C79D411yescharacteristic
49C2×C8×C79D411yescharacteristic
50C2×C8×C79D411yescharacteristic
51C4⋊C4×C79—22no—
52C22⋊C4×C79—22no—
53C42×C79—22no—
54C23×C79C2×D411yescharacteristic
55C22×D79—22no—
56C2×C4×C79—42no—
57C2×C4×C79C22×C411yescharacteristic
58C2×C4×C79C2×D411yescharacteristic
59C2×C4×C79C2×D411yescharacteristic
60C2×C4×C79C2×D411yescharacteristic
61C2×C4×C79#4111yescharacteristic
62C2×C4×C79#4111yescharacteristic
63C22⋊D79—42no—
64C22⋊D79—42no—
65C2×Dic79—22no—
66C2×Dic79—22no—
67D316—22no—
68D316—22no—
69C4×D79—42no—
70C4×D79—42no—
71Dic158—22no—
72Dic158—22no—
73C8×C79C22⋊C411yescharacteristic
74C8×C79C22⋊C411yescharacteristic
75C8×C79C22⋊C411yescharacteristic
76C8×C79C22⋊C411yescharacteristic
77C79⋊C8—22no—
78C22×C79—41no—
79C22×C79C4×D411yescharacteristic
80C22×C79#12111yescharacteristic
81C22×C79#12711yescharacteristic
82C2×D79—42no—
83C2×D79—82no—
84C4×C79—82no—
85C4×C79C2×C22⋊C411yescharacteristic
86C4×C79C4×D411yescharacteristic
87C4×C79#12111yescharacteristic
88C4×C79#12411yescharacteristic
89Dic79—42no—
90Dic79—42no—
91C2×C79—21no—
92C2×C79—21no—
93C2×C79—21no—
94C2×C79#39011yescharacteristic
95D79—82no—
96#1976—791nomaximal, Sylow
97C79#197611yescharacteristic, complemented, Sylow
98C2×#135—791no—
99#427D7911yescharacteristic, complemented
100#421—792no—
101#410—792no—
102#405—791no—
103C2×#41—792no—
104#135—1581no—
105#135—1581no—
106#135—1581no—
107#135—1581no—
108C2×Q16—791no—
109C2×SD16—792no—
110C2×D8—791no—
111C2×M16—791no—
112C22×C8C2×D7911yescharacteristic
113#117—791no—
114#117C2×D7912yes—
115#107—21no—
116#106—21no—
117#104—1584no—
118#99—1584no—
119#97—1581no—
120C4×C8—1581no—
121#41—1582no—
122#41—1582no—
123#41—1582no—
124#41—1582no—
125C2×Q8—792no—
126C2×D4—792no—
127C2×D4—1582no—
128C22×C4—1582no—
129C22×C4C22×D7911yescharacteristic
130Q16—1581no—
131Q16—1581no—
132SD16—1582no—
133SD16—1582no—
134D8—1581no—
135D8—1581no—
136M16—792no—
137M16—1581no—
138C2×C8—1581no—
139C2×C8C4×D7911yescharacteristic
140C2×C8C4×D7911yescharacteristic
141C2×C8D31611yescharacteristic
142C2×C8D31611yescharacteristic
143C2×C8C22⋊D7911yescharacteristic
144C2×C8C22⋊D7911yescharacteristic
145C4⋊C4—22no—
146C4⋊C4—1581no—
147C22⋊C4—22no—
148C22⋊C4—792no—
149C42—22no—
150C42—1581no—
151C23—1582no—
152C23D4×D7911yescharacteristic
153Q8—1582no—
154Q8—1582no—
155D4—3162no—
156D4—3162no—
157D4—1582no—
158D4—1582no—
159C2×C4—42no—
160C2×C4—3162no—
161C2×C4—3162no—
162C2×C4—1582no—
163C2×C4—1582no—
164C2×C4C2×C4×D7911yescharacteristic
165C2×C4D4×D7911yescharacteristic
166C2×C4C2×C22⋊D7911yescharacteristic
167C2×C4C2×D31611yescharacteristic
168C2×C4#1192962511yescharacteristic
169C2×C4#1192962511yescharacteristic
170C8—1582no—
171C8(C2×D79)⋊C411yescharacteristic
172C8(C2×D79)⋊C411yescharacteristic
173C8(C2×D79)⋊C411yescharacteristic
174C8(C2×D79)⋊C411yescharacteristic
175C22—41no—
176C22—3162no—
177C22—6322no—
178C22#1457912311yescharacteristic
179C22#1457913611yescharacteristic
180C22#1457915711yescharacteristic
181C4—82no—
182C4—3162no—
183C4—3162no—
184C4C2×(C2×D79)⋊C411yescharacteristic
185C4#1457912311yescharacteristic
186C4#1457913611yescharacteristic
187C4#1457915011yescharacteristic
188C2—21no—
189C2—21no—
190C2—21no—
191C2—6322no—
192C2#1909846411yescharacteristic
subgroupG/H
centerC4#14579136
commutatorC2×C4×C79C22×C4
FrattiniC22×C4C22×D79
Fitting#427×C79C2
socleC2×C79#390
prime radicalC2×#14579183C2
cosocleC22×C4×C79C23
hypercenter#427D79
hypocenterC79#1976
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C4 ◁ C22×C4 ◁ #427

Complements

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

NH ≅ G/Ntype
2. #19098581C2semidirect
3. #19098536C2semidirect
4. #19098518C2semidirect
5. #427×C79C2semidirect
11. C2×Dic316C4semidirect
12. C2×#11929613C4semidirect
13. C2×D632C4semidirect
97. C79#1976semidirect
99. #427D79semidirect