Finite Group Databasebeta

← #23767884

Subgroups — #23767884

Order 10112.

512 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 149 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
1C2×#14579137C211yesmaximal, characteristic
2C2×C4⋊C4×D79C211yesmaximal, characteristic
3#19098504C214yesmaximal, complemented
4#19098470C211yesmaximal, characteristic, complemented
5#19098429C211yesmaximal, characteristic, complemented
6#19098428C211yesmaximal, characteristic, complemented
7#19098425C214yesmaximal
8C4×(C2×D79)⋊C4C211yesmaximal, characteristic
9#391×C79C211yesmaximal, characteristic, complemented
10C22×C4×D79C2212yes—
11C22×C4×D79C2211yescharacteristic
12#14579137—24no—
13C2×C4⋊Dic79C2211yescharacteristic
14C2×C4⋊Dic79C2211yescharacteristic
15C2×Dic79⋊C4C2212yes—
16C2×Dic79⋊C4C2212yes—
17C4⋊C4×D79—24no—
18C2×(C2×D79)⋊C4C2212yes—
19C2×(C2×D79)⋊C4C2212yes—
20C2×C4×Dic79C2211yescharacteristic
21C79⋊#95C2212yes—
22C79⋊#95C2214yes—
23C79⋊#95C2214yes—
24C79⋊#95C2214yes—
25C22×Q8×C79C2211yescharacteristic
26C2×C4⋊C4×C79C2211yescharacteristic
27C2×C42×C79C2211yescharacteristic
28#95×C79C2214yes—
29C23×D79C2311yescharacteristic
30C22×Dic79C2312yes—
31C22×Dic79C2312yes—
32C22×Dic79C2312yes—
33C22×Dic79C2311yescharacteristic
34C2×C4×D79—24no—
35C2×C4×D79—28no—
36C2×C4×D79—22no—
37C2×C4×D79—22no—
38C2×C4×D79D414yes—
39C4⋊Dic79—22no—
40C4⋊Dic79—22no—
41Dic79⋊C4—24no—
42Dic79⋊C4—24no—
43(C2×D79)⋊C4—24no—
44(C2×D79)⋊C4—24no—
45C4×Dic79—22no—
46C2×Q8×C79—22no—
47C2×Q8×C79—22no—
48C2×Q8×C79—22no—
49C22×C4×C79C2312yes—
50C22×C4×C79C2312yes—
51C22×C4×C79C2312yes—
52C22×C4×C79C2311yescharacteristic
53C4⋊C4×C79—22no—
54C42×C79—22no—
55C23×C79C2411yescharacteristic
56C22×D79—21no—
57C22×D79—21no—
58C22×D79—22no—
59C22×D79C2×D412yes—
60C22×D79#4114yes—
61Q8×C79—44no—
62C2×C4×C79—22no—
63C2×C4×C79—22no—
64C2×C4×C79—22no—
65C2×C4×C79—24no—
66C2×C4×C79—22no—
67C2×C4×C79—22no—
68C2×C4×C79—22no—
69C2×C4×C79—22no—
70C2×C4×C79C2×D412yes—
71C2×C4×C79#4112yes—
72C2×C4×C79#4112yes—
73C2×Dic79—21no—
74C2×Dic79—21no—
75C2×Dic79—22no—
76C2×Dic79—22no—
77C2×Dic79—22no—
78C2×Dic79—22no—
79C2×Dic79—24no—
80C2×Dic79—24no—
81C2×Dic79—22no—
82C2×Dic79C2×D412yes—
83C4×D79—28no—
84C4×D79—48no—
85C22×C79C22×D411yescharacteristic
86C22×C79C2×#4112yes—
87C22×C79C2×#4111yescharacteristic
88C22×C79C2×#4111yescharacteristic
89C22×C792−1+412yes—
90C2×D79—22no—
91C2×D79—22no—
92C2×D79—24no—
93C2×D79—24no—
94C2×D79#12414yes—
95C4×C79—42no—
96C4×C79—42no—
97C4×C79—42no—
98C4×C79#12314yes—
99Dic79—22no—
100Dic79—42no—
101Dic79—42no—
102Dic79—42no—
103C2×C79C2×#12311yescharacteristic
104C2×C79C2×#12411yescharacteristic
105C2×C79#53611yescharacteristic
106C2×C79#55212yes—
107C2×C79#55212yes—
108D79—24no—
109#2503—791nomaximal, Sylow
110C79#250311yescharacteristic, complemented, Sylow
111C2×C22⋊Q8—791no—
112C22×C4⋊C4—791no—
113#400—794no—
114#391—791no—
115#391D7911yescharacteristic, complemented
116#382—791no—
117#382—791no—
118#381—794no—
119C4×C22⋊C4—791no—
120C22×Q8C2×D7911yescharacteristic
121C23×C4—791no—
122C23×C4—792no—
123C22⋊Q8—1584no—
124C2×C4⋊C4—791no—
125C2×C4⋊C4—792no—
126C2×C4⋊C4—791no—
127C2×C4⋊C4—792no—
128C2×C4⋊C4—1584no—
129C2×C4⋊C4C2×D7911yescharacteristic
130C2×C22⋊C4—792no—
131C2×C22⋊C4—792no—
132C2×C42—791no—
133C2×C42C2×D7911yescharacteristic
134#95—792no—
135#95—794no—
136#95—794no—
137#95—794no—
138#95C2×D7914yes—
139C24—791no—
140C2×Q8—22no—
141C2×Q8—22no—
142C2×Q8—22no—
143C22×C4—791no—
144C22×C4—794no—
145C22×C4—792no—
146C22×C4—792no—
147C22×C4—792no—
148C22×C4—1584no—
149C22×C4—1588no—
150C22×C4—1582no—
151C22×C4—1582no—
152C22×C4C22×D7912yes—
153C22×C4C22×D7912yes—
154C22×C4C22×D7912yes—
155C22×C4C22×D7911yescharacteristic
156C4⋊C4—22no—
157C4⋊C4—1584no—
158C4⋊C4—1584no—
159C4⋊C4—1582no—
160C4⋊C4—1582no—
161C22⋊C4—1584no—
162C22⋊C4—1584no—
163C42—22no—
164C42—1582no—
165C23—794no—
166C23—792no—
167C23—1581no—
168C23—1581no—
169C23—1582no—
170C23C23×D7911yescharacteristic
171Q8—44no—
172C2×C4—22no—
173C2×C4—24no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—3168no—
181C2×C4—792no—
182C2×C4—1582no—
183C2×C4—1584no—
184C2×C4—1582no—
185C2×C4—1584no—
186C2×C4—1582no—
187C2×C4—1582no—
188C2×C4—1582no—
189C2×C4—1581no—
190C2×C4—1581no—
191C2×C4—1588no—
192C2×C4D4×D7912yes—
193C2×C4#1192962312yes—
194C2×C4#1192962412yes—
195C22—794no—
196C22—1582no—
197C22—1584no—
198C22—1584no—
199C22—1582no—
200C22C2×D4×D7911yescharacteristic
201C22#41×D7912yes—
202C22C2×#1192962311yescharacteristic
203C22C2×#1192962411yescharacteristic
204C22#1457920912yes—
205C4—42no—
206C4—42no—
207C4—42no—
208C4—3162no—
209C4—3162no—
210C4—3162no—
211C4—1582no—
212C4#1457914314yes—
213C2—1584no—
214C2C2×#1457914311yescharacteristic
215C2#124×D7911yescharacteristic
216C2#1909913811yescharacteristic
217C2#1909924712yes—
218C2#1909925412yes—
subgroupG/H
center, FrattiniC23C23×D79
commutator, socle, cosocleC23×C79C24
Fitting#391×C79C2
prime radicalC23×D79C23
hypercenter#391D79
hypocenterC79#2503
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
3. #19098504C2semidirect
4. #19098470C2semidirect
5. #19098429C2semidirect
6. #19098428C2semidirect
9. #391×C79C2semidirect
110. C79#2503semidirect
115. #391D79semidirect