Finite Group Databasebeta

← #23764714

Subgroups — #23764714

Order 10112.

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

normal subgroups only

This group has 324 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
1C22×#11929611C211yesmaximal, characteristic
2C2×Dic79⋊C8C211yesmaximal, characteristic, complemented
3C2×#14579083C211yesmaximal, characteristic
4#19098470C211yesmaximal, characteristic, complemented
5#19098464C211yesmaximal, characteristic
6#19098325C211yesmaximal, characteristic, complemented
7C2×#103×C79C211yesmaximal, characteristic, complemented
8C22×D316C2211yescharacteristic
9C2×#11929611—22no—
10C2×#11929611—22no—
11C2×#11929611—22no—
12C22×C79⋊C8C2211yescharacteristic
13C2×C4⋊Dic79C2211yescharacteristic
14C2×(C2×D79)⋊C4—21no—
15C2×(C2×D79)⋊C4—21no—
16C2×C4×Dic79C2211yescharacteristic
17Dic79⋊C8—22no—
18#14579083—22no—
19C79⋊#95—21no—
20C79⋊#95—21no—
21C22×Q8×C79C2211yescharacteristic
22C22×C8×C79C2211yescharacteristic
23C2×C4⋊C4×C79C2211yescharacteristic
24#103×C79—22no—
25C23×D79—21no—
26C2×D316—21no—
27C2×D316—21no—
28C2×D316—21no—
29C2×D316—21no—
30C2×D316—21no—
31C2×D316D412yes—
32C22×Dic79—21no—
33C22×Dic79D411yescharacteristic
34C22×Dic79D411yescharacteristic
35#11929611—28no—
36C2×C79⋊C8—21no—
37C2×C79⋊C8—21no—
38C2×C79⋊C8D412yes—
39C4⋊Dic79—21no—
40C4⋊Dic79—21no—
41(C2×D79)⋊C4—42no—
42(C2×D79)⋊C4—42no—
43C4×Dic79—21no—
44C4×Dic79—21no—
45C2×Q8×C79—21no—
46C2×Q8×C79—21no—
47C2×Q8×C79—21no—
48C2×Q8×C79—21no—
49C2×Q8×C79—21no—
50C2×Q8×C79D412yes—
51C22×C4×C79—21no—
52C22×C4×C79—21no—
53C22×C4×C79C2311yescharacteristic
54C2×C8×C79—21no—
55C2×C8×C79—21no—
56C2×C8×C79—21no—
57C4⋊C4×C79—21no—
58C4⋊C4×C79—21no—
59C23×C79C2×D411yescharacteristic
60C22×D79—22no—
61C22×D79—41no—
62C22×D79—41no—
63C22×D79—41no—
64C22×D79—41no—
65C22×D79—41no—
66C22×D79—41no—
67Q8×C79—22no—
68Q8×C79—22no—
69Q8×C79—41no—
70Q8×C79—41no—
71C2×C4×C79—22no—
72C2×C4×C79—41no—
73C2×C4×C79—41no—
74C2×C4×C79—41no—
75C2×C4×C79—41no—
76C2×C4×C79—41no—
77C2×C4×C79C2×D411yescharacteristic
78C2×C4×C79C2×D411yescharacteristic
79C2×C4×C79C2×D411yescharacteristic
80C2×C4×C79#4111yescharacteristic
81C2×C4×C79#4111yescharacteristic
82C2×C4×C79#4111yescharacteristic
83C2×Dic79—21no—
84C2×Dic79—21no—
85C2×Dic79—21no—
86C2×Dic79—21no—
87C2×Dic79—21no—
88C2×Dic79—41no—
89C2×Dic79—41no—
90C2×Dic79—41no—
91C2×Dic79SD1612yescomplemented
92D316—22no—
93D316—22no—
94D316—41no—
95D316—41no—
96C8×C79—41no—
97C79⋊C8—22no—
98C22×C79#12111yescharacteristic
99C22×C79#12111yescharacteristic
100C22×C79#12111yescharacteristic
101C22×C79C2×SD1611yescharacteristic
102C22×C79#13511yescharacteristic
103C22×C79AGL(1,ℤ/8)11yescharacteristic
104C22×C79#13711yescharacteristic
105C2×D79—42no—
106C2×D79—42no—
107C2×D79—42no—
108C2×D79—81no—
109C2×D79—81no—
110C2×D79—81no—
111C2×D79—81no—
112C4×C79—42no—
113C4×C79—81no—
114C4×C79#12011yescharacteristic
115C4×C79#12311yescharacteristic
116C4×C79#12311yescharacteristic
117C4×C79#12411yescharacteristic
118Dic79—22no—
119Dic79—41no—
120Dic79—81no—
121C2×C79#39411yescharacteristic
122C2×C79#46011yescharacteristic
123C2×C79#46111yescharacteristic
124C2×C79#46311yescharacteristic
125C2×C79#46411yescharacteristic
126C2×C79#46511yescharacteristic
127C2×C79#46811yescharacteristic
128D79—82no—
129#2055—791nomaximal, Sylow
130C79#205511yescharacteristic, complemented, Sylow
131C22×SD16—791no—
132C2×C4⋊C8—791no—
133C2×#103D7911yescharacteristic, complemented
134C2×#102—791no—
135#391—791no—
136#390—791no—
137#340—791no—
138C22×Q8C2×D7911yescharacteristic
139C22×D4—791no—
140C2×SD16—1582no—
141C2×SD16—1582no—
142C2×SD16—1582no—
143C22×C8—791no—
144C22×C8C2×D7911yescharacteristic
145C2×C4⋊C4—791no—
146C2×C4⋊C4C2×D7911yescharacteristic
147C2×C22⋊C4—1581no—
148C2×C22⋊C4—1581no—
149C2×C42—791no—
150C4⋊C8—1582no—
151#103—22no—
152#102—1582no—
153#95—1581no—
154#95—1581no—
155C24—1581no—
156C2×Q8—21no—
157C2×Q8—21no—
158C2×Q8—21no—
159C2×Q8—21no—
160C2×Q8—21no—
161C2×Q8C22⋊D7912yes—
162C2×D4—792no—
163C2×D4—1581no—
164C2×D4—1581no—
165C2×D4—1581no—
166C2×D4—1581no—
167C2×D4—1581no—
168C22×C4—21no—
169C22×C4—21no—
170C22×C4—791no—
171C22×C4—791no—
172C22×C4—1581no—
173C22×C4C22×D7911yescharacteristic
174SD16—1588no—
175C2×C8—21no—
176C2×C8—21no—
177C2×C8—21no—
178C2×C8—792no—
179C2×C8—1581no—
180C2×C8—1581no—
181C4⋊C4—21no—
182C4⋊C4—21no—
183C4⋊C4—1581no—
184C4⋊C4—1581no—
185C22⋊C4—3162no—
186C22⋊C4—3162no—
187C42—1581no—
188C42—1581no—
189C23—3161no—
190C23—3161no—
191C23—3161no—
192C23—3161no—
193C23—3161no—
194C23—3161no—
195C23—1582no—
196C23D4×D7911yescharacteristic
197Q8—22no—
198Q8—22no—
199Q8—41no—
200Q8—41no—
201D4—3161no—
202D4—3161no—
203D4—1582no—
204D4—1582no—
205C2×C4—22no—
206C2×C4—41no—
207C2×C4—41no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—3161no—
212C2×C4—3161no—
213C2×C4—3161no—
214C2×C4—792no—
215C2×C4—1581no—
216C2×C4—1581no—
217C2×C4—1581no—
218C2×C4—1581no—
219C2×C4—1581no—
220C2×C4D4×D7911yescharacteristic
221C2×C4D4×D7911yescharacteristic
222C2×C4C2×C22⋊D7911yescharacteristic
223C2×C4#1192962311yescharacteristic
224C2×C4#1192962411yescharacteristic
225C2×C4#1192962411yescharacteristic
226C8—41no—
227C8—1582no—
228C22—3162no—
229C22—3162no—
230C22—3162no—
231C22—6321no—
232C22—6321no—
233C22—6321no—
234C22—6321no—
235C22#1457913311yescharacteristic
236C22#1457913411yescharacteristic
237C22#1457913411yescharacteristic
238C22SD16×D7911yescharacteristic
239C22#1457918411yescharacteristic
240C22#1457918811yescharacteristic
241C22#1457919311yescharacteristic
242C4—42no—
243C4—81no—
244C4—3161no—
245C4—6321no—
246C4—1582no—
247C4#1457912911yescharacteristic
248C4#1457914311yescharacteristic
249C4#1457914411yescharacteristic
250C4#1457914711yescharacteristic
251C2—6322no—
252C2#1909847811yescharacteristic
253C2#1909876111yescharacteristic
254C2#1909876711yescharacteristic
255C2#1909878111yescharacteristic
256C2#1909878711yescharacteristic
257C2#1909879511yescharacteristic
258C2#1909881211yescharacteristic
subgroupG/H
centerC23D4×D79
commutator, cosocleC22×C4×C79C23
FrattiniC22×C4C22×D79
FittingC2×#103×C79C2
socleC23×C79C2×D4
prime radicalC22×D316C22
hypercenterC2×#103D79
hypocenterC79#2055
LCSG ▷ C22×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
2. C2×Dic79⋊C8C2semidirect
4. #19098470C2semidirect
6. #19098325C2semidirect
7. C2×#103×C79C2semidirect
91. C2×Dic79SD16semidirect
130. C79#2055semidirect
133. C2×#103D79semidirect