Finite Group Databasebeta

← #23773204

Subgroups — #23773204

Order 10112.

376 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 135 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×#14579126C211yesmaximal, characteristic
3#19098873C212yesmaximal, complemented
4#19098869C212yesmaximal, complemented
5#19098857C212yesmaximal, complemented
6#19098847C212yesmaximal, complemented
7#19098603C211yesmaximal, characteristic
8#19098586C211yesmaximal, characteristic
9#19098573C211yesmaximal, characteristic
10#19098571C211yesmaximal, characteristic
11#428×C79C211yesmaximal, characteristic
12C22×Dic158C2211yescharacteristic
13C2×#11929608C2211yescharacteristic
14#14579160C2211yescharacteristic
15#14579160C2211yescharacteristic
16#14579152C2211yescharacteristic
17#14579152C2211yescharacteristic
18#14579138—21no—
19#14579138—21no—
20C4×Dic158—21no—
21C4×Dic158—21no—
22#14579126—21no—
23#14579126—21no—
24#14579126C2212yes—
25#14579126C2212yes—
26#14579120C2211yescharacteristic
27C2×Dic79⋊C4—21no—
28C2×C4×Dic79—21no—
29C2×C4×Dic79C2211yescharacteristic
30#14579094C2212yes—
31#14579092C2212yes—
32Dic79⋊C8C2212yes—
33Dic79⋊C8C2212yes—
34#14579086C2212yes—
35#14579086C2212yes—
36#14579084C2212yes—
37#14579084C2212yes—
38C2×M16×C79C2211yescharacteristic
39#117×C79C2211yescharacteristic
40C2×C4⋊C4×C79C2211yescharacteristic
41#107×C79C2212yes—
42#106×C79C2212yes—
43C2×Dic158—21no—
44C2×Dic158—21no—
45C2×Dic158—21no—
46C2×Dic158—22no—
47C2×Dic158Q814yescomplemented
48C2×Dic158C2312yes—
49C22×Dic79—21no—
50C22×Dic79D411yescharacteristic
51C22×Dic79D411yescharacteristic
52#11929608—22no—
53C2×C79⋊C8C2312yes—
54C4⋊Dic79—21no—
55C4⋊Dic79—21no—
56C4⋊Dic79C2311yescharacteristic
57C4⋊Dic79C2311yescharacteristic
58Dic79⋊C4—22no—
59Dic79⋊C4—22no—
60Dic79⋊C4—21no—
61Dic79⋊C4—21no—
62Dic79⋊C4—21no—
63Dic79⋊C4—21no—
64C22⋊Dic79—21no—
65C4×Dic79—22no—
66C4×Dic79—22no—
67C4×Dic79—21no—
68C4×Dic79D411yescharacteristic
69C4×Dic79D411yescharacteristic
70C4×Dic79C2311yescharacteristic
71C4×Dic79C2311yescharacteristic
72C22×C4×C79—21no—
73C22×C4×C79C2311yescharacteristic
74M16×C79—22no—
75C2×C8×C79C2312yes—
76C4⋊C4×C79—21no—
77C4⋊C4×C79C2311yescharacteristic
78C4⋊C4×C79C2312yes—
79C4⋊C4×C79C2311yescharacteristic
80C22⋊C4×C79—21no—
81C42×C79—21no—
82C23×C79C2×D411yescharacteristic
83C2×C4×C79—22no—
84C2×C4×C79—21no—
85C2×C4×C79—21no—
86C2×C4×C79—42no—
87C2×C4×C79C2×D411yescharacteristic
88C2×C4×C79C2×Q812yes—
89C2×C4×C79#4112yes—
90C2×C4×C79C2411yescharacteristic
91C2×Dic79—24no—
92C2×Dic79—22no—
93C2×Dic79—22no—
94C2×Dic79—21no—
95C2×Dic79—21no—
96C2×Dic79—41no—
97C2×Dic79C2×D411yescharacteristic
98C2×Dic79C2×D411yescharacteristic
99C2×Dic79C2×D411yescharacteristic
100C2×Dic79C2×D411yescharacteristic
101Dic158—24no—
102Dic158—22no—
103Dic158—42no—
104Dic158—42no—
105Dic158C2×Q814yes—
106C8×C79—22no—
107C79⋊C8—22no—
108C22×C79—21no—
109C22×C79—21no—
110C22×C79C22⋊Q812yes—
111C22×C79C22×D411yescharacteristic
112C4×C79—41no—
113C4×C79—42no—
114C4×C79—41no—
115C4×C79C22⋊Q812yes—
116C4×C79C22×Q811yescharacteristic
117C4×C79C2×#4111yescharacteristic
118Dic79—24no—
119Dic79—21no—
120Dic79—21no—
121Dic79—21no—
122Dic79—41no—
123Dic79—41no—
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#428D7911yescharacteristic
139#423—791no—
140#419—791no—
141#419—791no—
142C22×Q8—791no—
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—1581no—
160C2×C4⋊C4C2×D7911yescharacteristic
161C2×C42—791no—
162C2×C42—1581no—
163#107—792no—
164#107C2×D7912yes—
165#106—792no—
166#106C2×D7912yes—
167C4⋊C8—792no—
168C4⋊C8—792no—
169#103—792no—
170#103—792no—
171#103—792no—
172#103—792no—
173C2×Q8—794no—
174C2×Q8—792no—
175C2×Q8—1581no—
176C2×Q8—1581no—
177C2×Q8—1581no—
178C2×Q8—1582no—
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—21no—
189C4⋊C4—791no—
190C4⋊C4—791no—
191C4⋊C4—1582no—
192C4⋊C4—1582no—
193C4⋊C4—1581no—
194C4⋊C4—1581no—
195C4⋊C4—1581no—
196C4⋊C4—1581no—
197C4⋊C4—1581no—
198C4⋊C4—1581no—
199C4⋊C4C22×D7911yescharacteristic
200C4⋊C4C22×D7911yescharacteristic
201C4⋊C4C22×D7912yes—
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—3162no—
214Q8—3162no—
215Q8—794no—
216Q8—1582no—
217Q8—1584no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—22no—
221C2×C4—42no—
222C2×C4—3161no—
223C2×C4—791no—
224C2×C4—791no—
225C2×C4—791no—
226C2×C4—791no—
227C2×C4—1581no—
228C2×C4—1581no—
229C2×C4—1582no—
230C2×C4—1584no—
231C2×C4—1582no—
232C2×C4D4×D7911yescharacteristic
233C2×C4Q8×D7912yes—
234C2×C4#1192962412yes—
235C2×C4C23×D7911yescharacteristic
236C8—22no—
237C8—1582no—
238C22—21no—
239C22—21no—
240C22#1457913912yes—
241C22C2×D4×D7911yescharacteristic
242C4—41no—
243C4—42no—
244C4—41no—
245C4—3161no—
246C4—3161no—
247C4—792no—
248C4—1584no—
249C4—1581no—
250C4—1581no—
251C4—1581no—
252C4#1457913912yes—
253C4C2×Q8×D7911yescharacteristic
254C4C2×#1192962411yescharacteristic
255C2—22no—
256C2C2×#1457913911yescharacteristic
257C2#137×D7911yescharacteristic
258C2#1909935911yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#428×C79C2
socleC22×C79C22×D4
prime radicalC23×C79C2×D4
hypercenter#428D79
hypocenterC79#3078
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
3. #19098873C2semidirect
4. #19098869C2semidirect
5. #19098857C2semidirect
6. #19098847C2semidirect
47. C2×Dic158Q8semidirect
130. C79#3078semidirect