Finite Group Databasebeta

← #23774108

Subgroups — #23774108

Order 10112.

366 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 366 conjugacy classes of subgroups — too many to draw. Only its 115 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#19099118C211yesmaximal, characteristic, complemented
2#19099098C211yesmaximal, characteristic
3#19098973C211yesmaximal, characteristic, complemented
4#19098955C211yesmaximal, characteristic, complemented
5#19098923C211yesmaximal, characteristic, complemented
6#19098803C212yesmaximal, complemented
7#19098795C212yesmaximal
8#19098667C212yesmaximal, complemented
9#19098666C212yesmaximal, complemented
10#97×D79C211yesmaximal, characteristic, complemented
11#491×C79C211yesmaximal, characteristic, complemented
12C2×#11929614C2212yes—
13C2×#11929611C2212yes—
14C2×C8×D79C2212yes—
15#14579161C2211yescharacteristic
16#14579156—21no—
17#14579152—21no—
18#14579149C2211yescharacteristic
19#14579146—21no—
20#14579141—21no—
21#14579141C2211yescharacteristic
22#14579137C2212yes—
23#14579136C2211yescharacteristic
24Q8×Dic79C2212yes—
25#14579126—21no—
26#14579126C2211yescharacteristic
27#14579123—21no—
28#14579123C2211yescharacteristic
29#14579119—21no—
30#14579119—21no—
31C42×D79C2211yescharacteristic
32#14579094C2212yes—
33#14579092C2212yes—
34#14579086C2212yes—
35#14579083C2212yes—
36#14579072C2211yescharacteristic
37#14579071C2212yes—
38C4⋊Q8×C79C2211yescharacteristic
39#125×C79C2211yescharacteristic
40#103×C79C2212yes—
41#103×C79C2212yes—
42#97×C79C2211yescharacteristic
43C2×Dic158—21no—
44C2×Dic158C2311yescharacteristic
45C2×D316—21no—
46C2×D316C2311yescharacteristic
47C2×C4×D79—21no—
48C2×C4×D79D411yescharacteristic
49C2×C4×D79D411yescharacteristic
50C2×C4×D79C2311yescharacteristic
51#11929614—24no—
52#11929611—24no—
53C2×C79⋊C8C2312yes—
54C8×D79—24no—
55C4⋊Dic79—21no—
56C4⋊Dic79—22no—
57C4⋊Dic79—21no—
58C4⋊Dic79C2312yes—
59Dic79⋊C4—22no—
60Dic79⋊C4—21no—
61(C2×D79)⋊C4—21no—
62(C2×D79)⋊C4—21no—
63(C2×D79)⋊C4—22no—
64(C2×D79)⋊C4—21no—
65(C2×D79)⋊C4—21no—
66(C2×D79)⋊C4—21no—
67C4×Dic79—21no—
68C4×Dic79—22no—
69C4×Dic79D411yescharacteristic
70C4×Dic79D411yescharacteristic
71C4×Dic79C2311yescharacteristic
72C2×Q8×C79C2312yes—
73C2×C8×C79C2312yes—
74C4⋊C4×C79—21no—
75C4⋊C4×C79—21no—
76C4⋊C4×C79—21no—
77C4⋊C4×C79—21no—
78C4⋊C4×C79C2311yescharacteristic
79C4⋊C4×C79C2311yescharacteristic
80C42×C79C2311yescharacteristic
81C22×D79—21no—
82C22×D79C2×D411yescharacteristic
83Q8×C79—22no—
84Q8×C79—22no—
85C2×C4×C79—22no—
86C2×C4×C79—21no—
87C2×C4×C79—21no—
88C2×C4×C79C2×D411yescharacteristic
89C2×C4×C79C2×D411yescharacteristic
90C2×C4×C79C2411yescharacteristic
91C2×Dic79—21no—
92C2×Dic79—22no—
93C2×Dic79C2×D411yescharacteristic
94C2×Dic79C2×D411yescharacteristic
95C2×Dic79C2×D411yescharacteristic
96D316—22no—
97D316—42no—
98C4×D79—22no—
99C4×D79—22no—
100C4×D79—41no—
101C4×D79—42no—
102Dic158—22no—
103Dic158—42no—
104C8×C79—22no—
105C79⋊C8#4114yes—
106C22×C79C22×D411yescharacteristic
107C2×D79—21no—
108C2×D79—21no—
109C2×D79—41no—
110C2×D79—41no—
111C2×D79—41no—
112C2×D79#13712yes—
113C4×C79—21no—
114C4×C79—21no—
115C4×C79—42no—
116C4×C79—41no—
117C4×C79—41no—
118C4×C79C2×#4112yes—
119Dic79—21no—
120Dic79—21no—
121Dic79—21no—
122Dic79—41no—
123Dic79—42no—
124C2×C79#53211yescharacteristic
125C2×C79C2×#13711yescharacteristic
126C2×C79#57511yescharacteristic
127D79—22no—
128D79—81no—
129#3181—791nomaximal, Sylow
130C79#318111yescharacteristic, complemented, Sylow
131#533—791no—
132#529—791no—
133#501—791no—
134#497—791no—
135#491D7911yescharacteristic, complemented
136#489—791no—
137#467—792no—
138#465—792no—
139#441—792no—
140#440—792no—
141C2×#97—791no—
142C2×Q16—792no—
143C2×SD16—792no—
144C22×C8—792no—
145C4⋊Q8—791no—
146C4⋊Q8C2×D7911yescharacteristic
147#126—1581no—
148#125—1581no—
149#125C2×D7911yescharacteristic
150#124—791no—
151#123—1581no—
152C22⋊Q8—792no—
153C22⋊Q8—791no—
154C22⋊Q8—1581no—
155#121—791no—
156C4×Q8—792no—
157C4×Q8—791no—
158C4×Q8—1581no—
159C4×D4—791no—
160C4×D4—1581no—
161#117—1581no—
162#117—1581no—
163C2×C42—791no—
164#107—792no—
165#106—792no—
166#103—792no—
167#103C2×D7912yes—
168#103C2×D7912yes—
169#102—792no—
170#97—792no—
171#97—791no—
172#97C2×D7911yescharacteristic
173C2×Q8—791no—
174C2×Q8—1581no—
175C2×Q8C22×D7912yes—
176C2×D4—791no—
177C2×D4—1581no—
178C22×C4—791no—
179C22×C4—791no—
180C22×C4—791no—
181C22×C4—1581no—
182Q16—1584no—
183SD16—1584no—
184C2×C8—792no—
185C2×C8—1584no—
186C2×C8C22×D7912yes—
187C4⋊C4—21no—
188C4⋊C4—21no—
189C4⋊C4—21no—
190C4⋊C4—21no—
191C4⋊C4—792no—
192C4⋊C4—1581no—
193C4⋊C4—1582no—
194C4⋊C4—1581no—
195C4⋊C4—1582no—
196C4⋊C4—1581no—
197C4⋊C4C22×D7911yescharacteristic
198C4⋊C4C22×D7911yescharacteristic
199C22⋊C4—1581no—
200C22⋊C4—1581no—
201C22⋊C4—1582no—
202C22⋊C4—1581no—
203C22⋊C4—1581no—
204C22⋊C4—1581no—
205C42—791no—
206C42—791no—
207C42—791no—
208C42—1581no—
209C42—1582no—
210C42C22×D7911yescharacteristic
211C23—791no—
212C23—1581no—
213Q8—22no—
214Q8—22no—
215Q8—3162no—
216Q8—1582no—
217D4—3162no—
218D4—1582no—
219C2×C4—22no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—3161no—
223C2×C4—3162no—
224C2×C4—791no—
225C2×C4—791no—
226C2×C4—791no—
227C2×C4—1582no—
228C2×C4—1581no—
229C2×C4—1582no—
230C2×C4—1582no—
231C2×C4D4×D7911yescharacteristic
232C2×C4D4×D7911yescharacteristic
233C2×C4C23×D7911yescharacteristic
234C8—22no—
235C8—794no—
236C22—3161no—
237C22—3161no—
238C22—3161no—
239C22—792no—
240C22—1581no—
241C22—1581no—
242C22C2×D4×D7911yescharacteristic
243C4—21no—
244C4—21no—
245C4—41no—
246C4—41no—
247C4—42no—
248C4—3162no—
249C4—3161no—
250C4—1581no—
251C4—1581no—
252C4—1581no—
253C4#41×D7912yes—
254C2—6321no—
255C2—1582no—
256C2#1909911211yescharacteristic
257C2#137×D7911yescharacteristic
258C2#1909936211yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#491×C79C2
socleC22×C79C22×D4
prime radical#14579136C22
hypercenter#491D79
hypocenterC79#3181
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C42 ◁ #491

Complements

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

NH ≅ G/Ntype
1. #19099118C2semidirect
3. #19098973C2semidirect
4. #19098955C2semidirect
5. #19098923C2semidirect
6. #19098803C2semidirect
8. #19098667C2semidirect
9. #19098666C2semidirect
10. #97×D79C2semidirect
11. #491×C79C2semidirect
130. C79#3181semidirect
135. #491D79semidirect