Finite Group Databasebeta

← #23774476

Subgroups — #23774476

Order 10112.

364 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 109 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#19099174C211yesmaximal, characteristic, complemented
2#19099138C211yesmaximal, characteristic
3#19098955C211yesmaximal, characteristic, complemented
4#19098931C211yesmaximal, characteristic, complemented
5#19098918C211yesmaximal, characteristic, complemented
6#19098787C212yesmaximal, complemented
7#19098771C212yesmaximal, complemented
8#19098724C212yesmaximal
9#19098717C212yesmaximal, complemented
10#19098622C211yesmaximal, characteristic, complemented
11#494×C79C211yesmaximal, characteristic, complemented
12C2×#11929625C2211yescharacteristic
13C2×Q8×D79C2211yescharacteristic
14C2×#11929614C2212yes—
15C2×#11929611C2212yes—
16#14579159C2211yescharacteristic
17#14579156—22no—
18#14579153C2211yescharacteristic
19#14579151—22no—
20#14579150C2211yescharacteristic
21#14579149C2211yescharacteristic
22#14579146—22no—
23#14579139—22no—
24#14579137C2212yes—
25Q8×Dic79C2212yes—
26#14579118C2211yescharacteristic
27Dic79⋊C8C2212yes—
28#14579086C2212yes—
29#14579085C2212yes—
30#14579085C2212yes—
31#14579083C2212yes—
32(C2×D79)⋊C8C2212yes—
33#14579072C2211yescharacteristic
34C2×Q16×C79C2212yes—
35C2×Q16×C79C2212yes—
36C4⋊Q8×C79C2211yescharacteristic
37C4⋊Q8×C79C2211yescharacteristic
38C4×C8×C79C2211yescharacteristic
39#11929625—42no—
40C2×Dic158—21no—
41C2×Dic158C2311yescharacteristic
42Q8×D79—42no—
43C2×D316—21no—
44C2×D316C2311yescharacteristic
45C2×C4×D79—21no—
46C2×C4×D79—21no—
47C2×C4×D79C2311yescharacteristic
48#11929614—42no—
49#11929611—42no—
50C2×C79⋊C8C2312yes—
51C4⋊Dic79—22no—
52C4⋊Dic79C2312yes—
53Dic79⋊C4—22no—
54Dic79⋊C4—22no—
55Dic79⋊C4—22no—
56Dic79⋊C4D412yes—
57(C2×D79)⋊C4—22no—
58(C2×D79)⋊C4—22no—
59(C2×D79)⋊C4—22no—
60(C2×D79)⋊C4D412yes—
61C4×Dic79—22no—
62C4×Dic79C2311yescharacteristic
63C2×Q8×C79C2311yescharacteristic
64C2×Q8×C79C2311yescharacteristic
65C2×Q8×C79C2312yes—
66Q16×C79—42no—
67Q16×C79—42no—
68C2×C8×C79C2312yes—
69C4⋊C4×C79—22no—
70C4⋊C4×C79—22no—
71C42×C79C2311yescharacteristic
72C22×D79—21no—
73C22×D79C2×D411yescharacteristic
74Q8×C79—22no—
75Q8×C79—22no—
76Q8×C79—22no—
77Q8×C79—22no—
78C2×C4×C79—22no—
79C2×C4×C79—21no—
80C2×C4×C79—21no—
81C2×C4×C79C2×D412yes—
82C2×C4×C79C2411yescharacteristic
83C2×Dic79—22no—
84C2×Dic79—21no—
85C2×Dic79C2×D412yes—
86C2×Dic79C2×D411yescharacteristic
87D316—22no—
88D316—42no—
89C4×D79—22no—
90C4×D79—42no—
91C4×D79—42no—
92Dic158—22no—
93Dic158—42no—
94C8×C79—22no—
95C79⋊C8—22no—
96C22×C79C22×D411yescharacteristic
97C2×D79—21no—
98C2×D79—22no—
99C2×D79—41no—
100C2×D79—42no—
101C4×C79—22no—
102C4×C79—42no—
103C4×C79—41no—
104C4×C79—41no—
105C4×C79H(5,𝔽2)12yes—
106Dic79—21no—
107Dic79—22no—
108Dic79—41no—
109Dic79—42no—
110C2×C79#53511yescharacteristic
111C2×C79#57812yes—
112D79—41no—
113D79—81no—
114#3223—791nomaximal, Sylow
115C79#322311yescharacteristic, complemented, Sylow
116#541—791no—
117#536—791no—
118#497—791no—
119#494D7911yescharacteristic, complemented
120#491—791no—
121#488—791no—
122#464—792no—
123#462—792no—
124#452—792no—
125#451—792no—
126#433—791no—
127C2×#41—791no—
128C22×Q8—791no—
129C2×Q16—792no—
130C2×Q16C2×D7912yes—
131C2×Q16C2×D7912yes—
132C2×SD16—792no—
133C4⋊Q8—791no—
134C4⋊Q8C2×D7911yescharacteristic
135C4⋊Q8C2×D7911yescharacteristic
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#117—791no—
146C4⋊C8—792no—
147#103—792no—
148#103—792no—
149#103—792no—
150#102—792no—
151C22⋊C8—792no—
152#97—791no—
153C4×C8C2×D7911yescharacteristic
154#41—3162no—
155C2×Q8—3162no—
156C2×Q8—791no—
157C2×Q8—1581no—
158C2×Q8C22×D7911yescharacteristic
159C2×Q8C22×D7911yescharacteristic
160C2×Q8C22×D7912yes—
161C2×D4—791no—
162C2×D4—1581no—
163C22×C4—791no—
164C22×C4—1581no—
165C22×C4—1581no—
166Q16—42no—
167Q16—42no—
168Q16—3162no—
169SD16—3162no—
170C2×C8—792no—
171C2×C8C22×D7912yes—
172C4⋊C4—22no—
173C4⋊C4—22no—
174C4⋊C4—792no—
175C4⋊C4—792no—
176C4⋊C4—1582no—
177C4⋊C4—1582no—
178C4⋊C4—1582no—
179C4⋊C4—1582no—
180C22⋊C4—792no—
181C22⋊C4—1582no—
182C22⋊C4—1582no—
183C22⋊C4—1582no—
184C42—791no—
185C42—1582no—
186C42C22×D7911yescharacteristic
187C23—791no—
188C23—1581no—
189Q8—22no—
190Q8—22no—
191Q8—22no—
192Q8—22no—
193Q8—3162no—
194Q8—1582no—
195D4—3162no—
196D4—1582no—
197C2×C4—22no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—3162no—
201C2×C4—3162no—
202C2×C4—792no—
203C2×C4—791no—
204C2×C4—1582no—
205C2×C4—1581no—
206C2×C4—1582no—
207C2×C4D4×D7912yes—
208C2×C4C23×D7911yescharacteristic
209C8—22no—
210C8—1582no—
211C22—3162no—
212C22—3161no—
213C22—1582no—
214C22—1581no—
215C22C2×D4×D7911yescharacteristic
216C4—22no—
217C4—41no—
218C4—41no—
219C4—42no—
220C4—3162no—
221C4—3161no—
222C4—1582no—
223C4—1581no—
224C4#1457920612yes—
225C2—3161no—
226C2—6321no—
227C2#1909912611yescharacteristic
228C2#1909937612yes—
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#494×C79C2
socleC22×C79C22×D4
prime radicalC2×#11929625C22
hypercenter#494D79
hypocenterC79#3223
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C42 ◁ #494

Complements

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

NH ≅ G/Ntype
1. #19099174C2semidirect
3. #19098955C2semidirect
4. #19098931C2semidirect
5. #19098918C2semidirect
6. #19098787C2semidirect
7. #19098771C2semidirect
9. #19098717C2semidirect
10. #19098622C2semidirect
11. #494×C79C2semidirect
115. C79#3223semidirect
119. #494D79semidirect