Finite Group Databasebeta

← #23774485

Subgroups — #23774485

Order 10112.

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

normal subgroups only

This group has 364 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
1#19099175C211yesmaximal, characteristic, complemented
2#19099139C211yesmaximal, characteristic
3#19098957C211yesmaximal, characteristic, complemented
4#19098943C211yesmaximal, characteristic, complemented
5#19098932C211yesmaximal, characteristic, complemented
6#19098918C211yesmaximal, characteristic, complemented
7#19098786C212yesmaximal, complemented
8#19098774C212yesmaximal, complemented
9#19098727C212yesmaximal
10#19098721C212yesmaximal, complemented
11#433×C79C211yesmaximal, characteristic, complemented
12C2×#11929624C2211yescharacteristic
13C22×Dic158C2211yescharacteristic
14C2×Dic316C2212yes—
15C2×Dic316C2212yes—
16C2×Dic316C2212yes—
17C2×#11929613C2212yes—
18#14579161C2211yescharacteristic
19#14579161C2211yescharacteristic
20#14579161C2211yescharacteristic
21#14579154—22no—
22#14579153C2211yescharacteristic
23#14579151—22no—
24#14579149C2211yescharacteristic
25#14579149C2211yescharacteristic
26#14579145—22no—
27#14579141—22no—
28#14579140C2212yes—
29C4×Dic158C2212yes—
30#14579086C2212yes—
31#14579086C2212yes—
32#14579086C2212yes—
33#14579083C2212yes—
34#117×C79C2211yescharacteristic
35C4⋊C8×C79C2212yes—
36C22⋊C8×C79C2212yes—
37#97×C79C2211yescharacteristic
38C4×C8×C79C2211yescharacteristic
39#11929624—42no—
40C2×Dic158—21no—
41C2×Dic158—42no—
42C2×Dic158C2311yescharacteristic
43C2×Dic158C2311yescharacteristic
44C2×Dic158C2311yescharacteristic
45C2×Dic158C2312yes—
46C2×D316C2311yescharacteristic
47C2×C22⋊D79—21no—
48C22×Dic79—21no—
49C2×C4×D79—21no—
50Dic316—42no—
51Dic316—42no—
52Dic316—42no—
53#11929613—42no—
54C4⋊Dic79—22no—
55C4⋊Dic79—22no—
56C4⋊Dic79—22no—
57C4⋊Dic79C2312yes—
58Dic79⋊C4—22no—
59Dic79⋊C4—22no—
60Dic79⋊C4—22no—
61C22⋊Dic79—22no—
62(C2×D79)⋊C4—22no—
63(C2×D79)⋊C4—22no—
64C4×Dic79—22no—
65C22×C4×C79C2311yescharacteristic
66C2×C8×C79C2312yes—
67C2×C8×C79C2312yes—
68C4⋊C4×C79D412yes—
69C22⋊C4×C79D412yes—
70C42×C79C2311yescharacteristic
71C42×C79C2311yescharacteristic
72C23×C79C2×D411yescharacteristic
73C22×D79—21no—
74C2×C4×C79—22no—
75C2×C4×C79C2×D412yes—
76C2×C4×C79C2×D412yes—
77C2×C4×C79C2×D411yescharacteristic
78C2×C4×C79C2411yescharacteristic
79C22⋊D79—42no—
80C2×Dic79—22no—
81C2×Dic79—22no—
82C2×Dic79—21no—
83C2×Dic79—21no—
84C2×Dic79—21no—
85C2×Dic79—42no—
86D316—22no—
87C4×D79—42no—
88Dic158—22no—
89Dic158—22no—
90Dic158—22no—
91Dic158—22no—
92Dic158—22no—
93Dic158—42no—
94C8×C79—22no—
95C8×C79—22no—
96C22×C79—21no—
97C22×C79—22no—
98C22×C79C22×D411yescharacteristic
99C2×D79—41no—
100C2×D79—42no—
101C4×C79—21no—
102C4×C79—22no—
103C4×C79—22no—
104C4×C79H(5,𝔽2)12yes—
105Dic79—41no—
106Dic79—41no—
107Dic79—41no—
108Dic79—42no—
109Dic79—42no—
110C2×C79—41no—
111C2×C79#53511yescharacteristic
112C2×C79#57812yes—
113D79—81no—
114#3223—791nomaximal, Sylow
115C79#322311yescharacteristic, complemented, Sylow
116#541—791no—
117#536—791no—
118#497—791no—
119#494—791no—
120#491—791no—
121#488—791no—
122#464—792no—
123#462—792no—
124#452—792no—
125#451—792no—
126#433D7911yescharacteristic, complemented
127C2×#41—791no—
128C22×Q8—791no—
129C2×Q16—792no—
130C2×Q16—792no—
131C2×Q16—792no—
132C2×SD16—792no—
133C4⋊Q8—791no—
134C4⋊Q8—791no—
135C4⋊Q8—791no—
136#126—1582no—
137#125—791no—
138#125—1582no—
139#124—791no—
140#124—791no—
141#123—1582no—
142C22⋊Q8—792no—
143C22⋊Q8—1582no—
144C4×Q8—792no—
145#117C2×D7911yescharacteristic
146C4⋊C8C2×D7912yes—
147#103—792no—
148#103—792no—
149#103—792no—
150#102—792no—
151C22⋊C8C2×D7912yes—
152#97C2×D7911yescharacteristic
153C4×C8C2×D7911yescharacteristic
154#41—3162no—
155C2×Q8—3162no—
156C2×Q8—791no—
157C2×Q8—791no—
158C2×Q8—791no—
159C2×Q8—792no—
160C2×Q8—1581no—
161C2×D4—791no—
162C2×D4—1581no—
163C22×C4—1581no—
164C22×C4—1581no—
165C22×C4C22×D7911yescharacteristic
166Q16—3162no—
167Q16—3162no—
168Q16—3162no—
169SD16—3162no—
170C2×C8C22×D7912yes—
171C2×C8C22×D7912yes—
172C4⋊C4—792no—
173C4⋊C4—1582no—
174C4⋊C4—1582no—
175C4⋊C4—1582no—
176C4⋊C4—1582no—
177C4⋊C4—1582no—
178C4⋊C4—1582no—
179C4⋊C4D31612yes—
180C22⋊C4—1582no—
181C22⋊C4—1582no—
182C22⋊C4—1582no—
183C22⋊C4D31612yes—
184C42—1582no—
185C42C22×D7911yescharacteristic
186C42C22×D7911yescharacteristic
187C23—1581no—
188C23C2×D31611yescharacteristic
189Q8—3162no—
190Q8—1582no—
191Q8—1582no—
192Q8—1582no—
193Q8—1582no—
194Q8—1582no—
195D4—3162no—
196D4—1582no—
197C2×C4—22no—
198C2×C4—3162no—
199C2×C4—3162no—
200C2×C4—1582no—
201C2×C4—1582no—
202C2×C4—1581no—
203C2×C4—1581no—
204C2×C4—1581no—
205C2×C4C2×D31612yes—
206C2×C4C2×D31612yes—
207C2×C4C2×D31611yescharacteristic
208C2×C4C23×D7911yescharacteristic
209C8—22no—
210C8—22no—
211C22—22no—
212C22—21no—
213C22—3162no—
214C22—3161no—
215C22C22×D31611yescharacteristic
216C4—22no—
217C4—22no—
218C4—21no—
219C4—3162no—
220C4—3161no—
221C4—3161no—
222C4—3161no—
223C4—3162no—
224C4#1457920712yes—
225C2—41no—
226C2—6321no—
227C2#1909913211yescharacteristic
228C2#1909938012yes—
subgroupG/H
centerC22C22×D316
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#433×C79C2
socleC22×C79C22×D4
prime radicalC2×#11929624C22
hypercenter#433D79
hypocenterC79#3223
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #19099175C2semidirect
3. #19098957C2semidirect
4. #19098943C2semidirect
5. #19098932C2semidirect
6. #19098918C2semidirect
7. #19098786C2semidirect
8. #19098774C2semidirect
10. #19098721C2semidirect
11. #433×C79C2semidirect
115. C79#3223semidirect
126. #433D79semidirect