Finite Group Databasebeta

← #23773202

Subgroups — #23773202

Order 10112.

376 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 143 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#19099116C211yesmaximal, characteristic
2C2×Q8×Dic79C211yesmaximal, characteristic
3#19098872C212yesmaximal, complemented
4#19098868C212yesmaximal, complemented
5#19098856C212yesmaximal, complemented
6#19098846C212yesmaximal, complemented
7#19098606C211yesmaximal, characteristic
8#19098605C211yesmaximal, characteristic
9#19098586C211yesmaximal, characteristic
10#19098572C211yesmaximal, characteristic
11#419×C79C211yesmaximal, characteristic
12C2×#11929608C2211yescharacteristic
13#14579160C2211yescharacteristic
14#14579160C2211yescharacteristic
15#14579152C2211yescharacteristic
16#14579152C2211yescharacteristic
17#14579138—21no—
18#14579138—21no—
19Q8×Dic79—21no—
20Q8×Dic79—21no—
21Q8×Dic79C2212yes—
22Q8×Dic79C2212yes—
23C4×Dic158—21no—
24C4×Dic158—21no—
25#14579120C2211yescharacteristic
26C2×C4⋊Dic79—21no—
27C2×C4⋊Dic79C2211yescharacteristic
28C2×C4×Dic79—21no—
29C2×C4×Dic79C2211yescharacteristic
30#14579095C2212yes—
31#14579094C2212yes—
32#14579093C2212yes—
33#14579092C2212yes—
34Dic79⋊C8C2212yes—
35Dic79⋊C8C2212yes—
36#14579085C2212yes—
37#14579085C2212yes—
38C22×Q8×C79C2211yescharacteristic
39C2×M16×C79C2211yescharacteristic
40#117×C79C2211yescharacteristic
41#103×C79C2212yes—
42#103×C79C2212yes—
43C2×Dic158—21no—
44C2×Dic158—21no—
45C22×Dic79—21no—
46C22×Dic79D411yescharacteristic
47C22×Dic79D411yescharacteristic
48#11929608—22no—
49C2×C79⋊C8C2312yes—
50C4⋊Dic79—22no—
51C4⋊Dic79—22no—
52C4⋊Dic79—21no—
53C4⋊Dic79—21no—
54C4⋊Dic79—21no—
55C4⋊Dic79C2311yescharacteristic
56C4⋊Dic79C2311yescharacteristic
57C4⋊Dic79C2312yes—
58Dic79⋊C4—21no—
59Dic79⋊C4—21no—
60Dic79⋊C4—21no—
61Dic79⋊C4—21no—
62C22⋊Dic79—21no—
63C4×Dic79—22no—
64C4×Dic79—22no—
65C4×Dic79—21no—
66C4×Dic79D411yescharacteristic
67C4×Dic79D411yescharacteristic
68C4×Dic79C2311yescharacteristic
69C4×Dic79C2311yescharacteristic
70C2×Q8×C79—21no—
71C2×Q8×C79—22no—
72C2×Q8×C79Q814yescomplemented
73C2×Q8×C79C2312yes—
74C22×C4×C79—21no—
75C22×C4×C79C2311yescharacteristic
76M16×C79—22no—
77C2×C8×C79C2312yes—
78C4⋊C4×C79C2311yescharacteristic
79C4⋊C4×C79C2311yescharacteristic
80C22⋊C4×C79—21no—
81C42×C79—21no—
82C23×C79C2×D411yescharacteristic
83Q8×C79—24no—
84Q8×C79—22no—
85Q8×C79C2×Q814yes—
86C2×C4×C79—24no—
87C2×C4×C79—22no—
88C2×C4×C79—21no—
89C2×C4×C79—21no—
90C2×C4×C79C2×D411yescharacteristic
91C2×C4×C79C2×Q812yes—
92C2×C4×C79#4112yes—
93C2×C4×C79C2411yescharacteristic
94C2×Dic79—22no—
95C2×Dic79—22no—
96C2×Dic79—21no—
97C2×Dic79—21no—
98C2×Dic79—41no—
99C2×Dic79—42no—
100C2×Dic79C2×D411yescharacteristic
101C2×Dic79C2×D411yescharacteristic
102C2×Dic79C2×D411yescharacteristic
103C2×Dic79C2×D411yescharacteristic
104Dic158—42no—
105Dic158—42no—
106C8×C79—22no—
107C79⋊C8—22no—
108C22×C79—21no—
109C22×C79—21no—
110C22×C79C22⋊Q812yes—
111C22×C79C22×D411yescharacteristic
112C4×C79—24no—
113C4×C79—41no—
114C4×C79—41no—
115C4×C79C22⋊Q812yes—
116C4×C79C22×Q811yescharacteristic
117C4×C79C2×#4111yescharacteristic
118Dic79—21no—
119Dic79—21no—
120Dic79—21no—
121Dic79—41no—
122Dic79—41no—
123Dic79—42no—
124Dic79#13712yes—
125C2×C79—22no—
126C2×C79C2×C22⋊Q811yescharacteristic
127C2×C79C2×#13711yescharacteristic
128C2×C79#57511yescharacteristic
129#3078—791nomaximal, Sylow
130C79#307811yescharacteristic, complemented, Sylow
131#533—791no—
132C2×C4×Q8—791no—
133#479—792no—
134#479—792no—
135#477—792no—
136#475—792no—
137#428—791no—
138#428—791no—
139#423—791no—
140#419—791no—
141#419D7911yescharacteristic
142C22×Q8C2×D7911yescharacteristic
143C2×M16—791no—
144C2×M16C2×D7911yescharacteristic
145C4⋊Q8—791no—
146C4⋊Q8—791no—
147#125—791no—
148#125—791no—
149C22⋊Q8—1581no—
150C22⋊Q8—1581no—
151C4×Q8—792no—
152C4×Q8—792no—
153C4×Q8—1581no—
154C4×Q8—1581no—
155C4×Q8—1581no—
156C4×Q8—1581no—
157#117—791no—
158#117C2×D7911yescharacteristic
159C2×C4⋊C4—791no—
160C2×C4⋊C4—1581no—
161C2×C42—791no—
162C2×C42—1581no—
163#107—792no—
164#107—792no—
165#106—792no—
166#106—792no—
167C4⋊C8—792no—
168C4⋊C8—792no—
169#103—792no—
170#103—792no—
171#103C2×D7912yes—
172#103C2×D7912yes—
173C2×Q8—21no—
174C2×Q8—22no—
175C2×Q8—1581no—
176C2×Q8—1581no—
177C2×Q8Dic15814yescomplemented
178C2×Q8C22×D7912yes—
179C22×C4—21no—
180C22×C4—791no—
181C22×C4—791no—
182C22×C4—1581no—
183C22×C4C22×D7911yescharacteristic
184M16—22no—
185M16—1582no—
186C2×C8—792no—
187C2×C8C22×D7912yes—
188C4⋊C4—791no—
189C4⋊C4—791no—
190C4⋊C4—792no—
191C4⋊C4—1581no—
192C4⋊C4—1581no—
193C4⋊C4—1581no—
194C4⋊C4—1581no—
195C4⋊C4—1582no—
196C4⋊C4—1582no—
197C4⋊C4—1581no—
198C4⋊C4—1581no—
199C4⋊C4—1581no—
200C4⋊C4C22×D7911yescharacteristic
201C4⋊C4C22×D7911yescharacteristic
202C22⋊C4—21no—
203C22⋊C4—1581no—
204C42—21no—
205C42—791no—
206C42—791no—
207C42—791no—
208C42—791no—
209C42—1582no—
210C42—1582no—
211C42—1581no—
212C23D4×D7911yescharacteristic
213Q8—22no—
214Q8—24no—
215Q8—3162no—
216Q8—3162no—
217Q8C2×Dic15814yes—
218C2×C4—24no—
219C2×C4—22no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—3162no—
223C2×C4—3161no—
224C2×C4—791no—
225C2×C4—791no—
226C2×C4—791no—
227C2×C4—791no—
228C2×C4—1582no—
229C2×C4—1581no—
230C2×C4—1581no—
231C2×C4—1582no—
232C2×C4D4×D7911yescharacteristic
233C2×C4C2×Dic15812yes—
234C2×C4#1192962312yes—
235C2×C4C23×D7911yescharacteristic
236C8—22no—
237C8—1582no—
238C22—21no—
239C22—21no—
240C22#1457913812yes—
241C22C2×D4×D7911yescharacteristic
242C4—24no—
243C4—41no—
244C4—41no—
245C4—3161no—
246C4—3162no—
247C4—3161no—
248C4—792no—
249C4—1581no—
250C4—1581no—
251C4—1581no—
252C4#1457913812yes—
253C4C22×Dic15811yescharacteristic
254C4C2×#1192962311yescharacteristic
255C2—22no—
256C2C2×#1457913811yescharacteristic
257C2#137×D7911yescharacteristic
258C2#1909936211yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#419×C79C2
socleC22×C79C22×D4
prime radicalC23×C79C2×D4
hypercenter#419D79
hypocenterC79#3078
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
3. #19098872C2semidirect
4. #19098868C2semidirect
5. #19098856C2semidirect
6. #19098846C2semidirect
72. C2×Q8×C79Q8semidirect
130. C79#3078semidirect
177. C2×Q8Dic158semidirect