Finite Group Databasebeta

← #23767877

Subgroups — #23767877

Order 10112.

544 conjugacy classes of subgroups; only the 169 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 169 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#19098497C214yesmaximal, complemented
4#19098470C211yesmaximal, characteristic, complemented
5#19098437C214yesmaximal
6#19098433C211yesmaximal, characteristic, complemented
7#19098432C211yesmaximal, characteristic, complemented
8C4×(C2×D79)⋊C4C211yesmaximal, characteristic
9#391×C79C211yesmaximal, characteristic, complemented
10C22×C4×D79C2211yescharacteristic
11C22×C4×D79C2212yes—
12#14579137—24no—
13C2×C4⋊Dic79C2211yescharacteristic
14C2×C4⋊Dic79C2211yescharacteristic
15C2×C4⋊Dic79C2214yes—
16C2×Dic79⋊C4C2212yes—
17C2×Dic79⋊C4C2212yes—
18C2×Dic79⋊C4C2214yes—
19C4⋊C4×D79—24no—
20C2×(C2×D79)⋊C4C2212yes—
21C2×(C2×D79)⋊C4C2212yes—
22C2×C4×Dic79C2211yescharacteristic
23C79⋊#95C2212yes—
24C79⋊#95C2214yes—
25C22×Q8×C79C2211yescharacteristic
26C2×C4⋊C4×C79C2211yescharacteristic
27C2×C42×C79C2211yescharacteristic
28#95×C79C2214yes—
29C23×D79C2311yescharacteristic
30C22×Dic79C2312yes—
31C22×Dic79C2312yes—
32C22×Dic79C2311yescharacteristic
33C22×Dic79C2312yes—
34C2×C4×D79—24no—
35C2×C4×D79—22no—
36C2×C4×D79—22no—
37C2×C4×D79—44no—
38C2×C4×D79D414yes—
39C4⋊Dic79—22no—
40C4⋊Dic79—22no—
41C4⋊Dic79—44no—
42Dic79⋊C4—24no—
43Dic79⋊C4—24no—
44Dic79⋊C4—44no—
45(C2×D79)⋊C4—24no—
46(C2×D79)⋊C4Q818yescomplemented
47C4×Dic79—22no—
48C2×Q8×C79—22no—
49C2×Q8×C79—22no—
50C2×Q8×C79—22no—
51C22×C4×C79C2312yes—
52C22×C4×C79C2312yes—
53C22×C4×C79C2312yes—
54C22×C4×C79C2311yescharacteristic
55C4⋊C4×C79—22no—
56C42×C79—22no—
57C23×C79C2411yescharacteristic
58C22×D79—21no—
59C22×D79—21no—
60C22×D79—22no—
61C22×D79C2×D412yes—
62C22×D79C2×Q814yes—
63Q8×C79—44no—
64C2×C4×C79—22no—
65C2×C4×C79—22no—
66C2×C4×C79—22no—
67C2×C4×C79—22no—
68C2×C4×C79—22no—
69C2×C4×C79—22no—
70C2×C4×C79—24no—
71C2×C4×C79C2×D412yes—
72C2×C4×C79C2×Q814yes—
73C2×C4×C79#4112yes—
74C2×C4×C79#4112yes—
75C2×Dic79—22no—
76C2×Dic79—21no—
77C2×Dic79—21no—
78C2×Dic79—22no—
79C2×Dic79—22no—
80C2×Dic79—22no—
81C2×Dic79—24no—
82C2×Dic79—24no—
83C2×Dic79C2×D412yes—
84C2×Dic79C2×Q814yes—
85C4×D79—28no—
86C4×D79—48no—
87C22×C79C22×D411yescharacteristic
88C22×C79C22×Q812yes—
89C22×C79C2×#4111yescharacteristic
90C22×C79C2×#4111yescharacteristic
91C22×C79H(5,𝔽2)12yes—
92C2×D79—22no—
93C2×D79—22no—
94C2×D79—24no—
95C2×D79—24no—
96C2×D79C4⋊Q814yes—
97C4×C79—24no—
98C4×C79—42no—
99C4×C79—42no—
100C4×C79#12314yes—
101Dic79—22no—
102Dic79—24no—
103Dic79—42no—
104Dic79—42no—
105C2×C79C2×#12311yescharacteristic
106C2×C79C2×C4⋊Q811yescharacteristic
107C2×C79#53511yescharacteristic
108C2×C79#55412yes—
109C2×C79#55412yes—
110D79—24no—
111#2502—791nomaximal, Sylow
112C79#250211yescharacteristic, complemented, Sylow
113C2×C22⋊Q8—791no—
114C22×C4⋊C4—791no—
115#398—794no—
116#391—791no—
117#391D7911yescharacteristic, complemented
118#385—794no—
119#384—791no—
120#384—791no—
121C4×C22⋊C4—791no—
122C22×Q8C2×D7911yescharacteristic
123C23×C4—792no—
124C23×C4—791no—
125C22⋊Q8—1584no—
126C2×C4⋊C4—794no—
127C2×C4⋊C4—794no—
128C2×C4⋊C4—791no—
129C2×C4⋊C4—792no—
130C2×C4⋊C4—791no—
131C2×C4⋊C4—792no—
132C2×C4⋊C4—1584no—
133C2×C4⋊C4C2×D7911yescharacteristic
134C2×C22⋊C4—792no—
135C2×C22⋊C4—792no—
136C2×C42—791no—
137C2×C42C2×D7911yescharacteristic
138#95—792no—
139#95—794no—
140#95C2×D7914yes—
141C24—791no—
142C2×Q8—22no—
143C2×Q8—22no—
144C2×Q8—22no—
145C22×C4—3164no—
146C22×C4—792no—
147C22×C4—791no—
148C22×C4—794no—
149C22×C4—792no—
150C22×C4—792no—
151C22×C4—1584no—
152C22×C4—1582no—
153C22×C4—1582no—
154C22×C4C22×D7912yes—
155C22×C4C22×D7912yes—
156C22×C4C22×D7912yes—
157C22×C4C22×D7911yescharacteristic
158C4⋊C4—22no—
159C4⋊C4—3164no—
160C4⋊C4—3164no—
161C4⋊C4—1584no—
162C4⋊C4—1584no—
163C4⋊C4—1582no—
164C4⋊C4—1582no—
165C22⋊C4—798no—
166C22⋊C4—1584no—
167C42—22no—
168C42—1582no—
169C23—794no—
170C23—792no—
171C23—1581no—
172C23—1581no—
173C23—1582no—
174C23C23×D7911yescharacteristic
175Q8—44no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—24no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—3168no—
184C2×C4—794no—
185C2×C4—792no—
186C2×C4—1584no—
187C2×C4—1584no—
188C2×C4—1582no—
189C2×C4—1582no—
190C2×C4—1581no—
191C2×C4—1582no—
192C2×C4—1581no—
193C2×C4—1582no—
194C2×C4—1588no—
195C2×C4D4×D7912yes—
196C2×C4Q8×D7914yes—
197C2×C4#1192962312yes—
198C2×C4#1192962412yes—
199C22—794no—
200C22—1584no—
201C22—1584no—
202C22—1582no—
203C22—1582no—
204C22C2×D4×D7911yescharacteristic
205C22C2×Q8×D7912yes—
206C22C2×#1192962311yescharacteristic
207C22C2×#1192962411yescharacteristic
208C22#1457920712yes—
209C4—24no—
210C4—42no—
211C4—42no—
212C4—3162no—
213C4—3162no—
214C4—1584no—
215C4—1582no—
216C4#1457914314yes—
217C2—1584no—
218C2C2×#1457914311yescharacteristic
219C2C4⋊Q8×D7911yescharacteristic
220C2#1909913111yescharacteristic
221C2#1909927112yes—
222C2#1909927312yes—
subgroupG/H
center, FrattiniC23C23×D79
commutator, socle, cosocleC23×C79C24
Fitting#391×C79C2
prime radicalC23×D79C23
hypercenter#391D79
hypocenterC79#2502
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
3. #19098497C2semidirect
4. #19098470C2semidirect
6. #19098433C2semidirect
7. #19098432C2semidirect
9. #391×C79C2semidirect
46. (C2×D79)⋊C4Q8semidirect
112. C79#2502semidirect
117. #391D79semidirect