Finite Group Databasebeta

← #23773207

Subgroups — #23773207

Order 10112.

376 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 145 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#19099120C211yesmaximal, characteristic
2C2×C4×Dic158C211yesmaximal, characteristic
3#19098871C214yesmaximal, complemented
4#19098859C212yesmaximal, complemented
5#19098849C212yesmaximal, complemented
6#19098605C212yesmaximal
7#19098573C212yesmaximal
8#423×C79C211yesmaximal, characteristic
9C22×Dic158C2211yescharacteristic
10#14579161C2211yescharacteristic
11#14579161C2211yescharacteristic
12#14579153C2212yes—
13#14579140—21no—
14#14579140—21no—
15C4×Dic158—21no—
16C4×Dic158—21no—
17C4×Dic158—21no—
18C4×Dic158—21no—
19C4×Dic158C2212yes—
20C4×Dic158C2212yes—
21#14579120C2212yes—
22C2×C4⋊Dic79C2211yescharacteristic
23C2×Dic79⋊C4—21no—
24C2×C4×Dic79—21no—
25#14579095C2214yes—
26#14579093C2214yes—
27#14579086C2214yes—
28#14579086C2214yes—
29C2×M16×C79C2212yes—
30C2×C42×C79C2211yescharacteristic
31C4⋊C8×C79C2212yes—
32C4⋊C8×C79C2212yes—
33C2×Dic158—21no—
34C2×Dic158—21no—
35C2×Dic158—21no—
36C2×Dic158—22no—
37C2×Dic158Q814yescomplemented
38C2×Dic158C2312yes—
39C22×Dic79—21no—
40C22×Dic79—21no—
41C4⋊Dic79—21no—
42C4⋊Dic79—21no—
43C4⋊Dic79—21no—
44C4⋊Dic79C2312yes—
45C4⋊Dic79C2312yes—
46C4⋊Dic79C2312yes—
47Dic79⋊C4—22no—
48Dic79⋊C4—22no—
49Dic79⋊C4—22no—
50Dic79⋊C4—22no—
51C22⋊Dic79—22no—
52C4×Dic79—22no—
53C4×Dic79—22no—
54C4×Dic79—22no—
55C22×C4×C79D411yescharacteristic
56C22×C4×C79D411yescharacteristic
57C22×C4×C79C2311yescharacteristic
58M16×C79—24no—
59C2×C8×C79C2314yes—
60C42×C79D411yescharacteristic
61C42×C79D411yescharacteristic
62C42×C79C2311yescharacteristic
63C42×C79C2311yescharacteristic
64C23×C79C2×D411yescharacteristic
65C2×C4×C79—22no—
66C2×C4×C79—41no—
67C2×C4×C79C2×D411yescharacteristic
68C2×C4×C79C2×D411yescharacteristic
69C2×C4×C79C2×D411yescharacteristic
70C2×C4×C79C2×D411yescharacteristic
71C2×C4×C79C2×D411yescharacteristic
72C2×C4×C79C2×Q812yes—
73C2×C4×C79#4112yes—
74C2×C4×C79C2411yescharacteristic
75C2×Dic79—24no—
76C2×Dic79—22no—
77C2×Dic79—22no—
78C2×Dic79—22no—
79C2×Dic79—22no—
80C2×Dic79—42no—
81Dic158—24no—
82Dic158—22no—
83Dic158—42no—
84Dic158—42no—
85Dic158C2×Q814yes—
86C8×C79—24no—
87C22×C79—21no—
88C22×C79—21no—
89C22×C79C22⋊Q812yes—
90C22×C79C22×D411yescharacteristic
91C4×C79—21no—
92C4×C79—21no—
93C4×C79—21no—
94C4×C79C22⋊Q812yes—
95C4×C79#13712yes—
96C4×C79C22×Q811yescharacteristic
97C4×C79C2×#4111yescharacteristic
98Dic79—24no—
99Dic79—42no—
100Dic79—42no—
101Dic79—42no—
102C2×C79—22no—
103C2×C79C2×C22⋊Q811yescharacteristic
104C2×C79C2×#13711yescharacteristic
105C2×C79#57511yescharacteristic
106#3078—791nomaximal, Sylow
107C79#307811yescharacteristic, complemented, Sylow
108#533—791no—
109C2×C4×Q8—791no—
110#479—794no—
111#477—792no—
112#475—792no—
113#428—792no—
114#423D7911yescharacteristic
115#419—792no—
116C22×Q8—791no—
117C2×M16C2×D7912yes—
118C4⋊Q8—791no—
119C4⋊Q8—791no—
120#125—792no—
121C22⋊Q8—1581no—
122C22⋊Q8—1581no—
123C4×Q8—792no—
124C4×Q8—792no—
125C4×Q8—1581no—
126C4×Q8—1581no—
127C4×Q8—1581no—
128C4×Q8—1581no—
129#117—792no—
130C2×C4⋊C4—791no—
131C2×C4⋊C4—1581no—
132C2×C42—1581no—
133C2×C42C2×D7911yescharacteristic
134#107—794no—
135#106—794no—
136C4⋊C8C2×D7912yes—
137C4⋊C8C2×D7912yes—
138#103—794no—
139#103—794no—
140C2×Q8—794no—
141C2×Q8—792no—
142C2×Q8—1581no—
143C2×Q8—1581no—
144C2×Q8—1581no—
145C2×Q8—1582no—
146C22×C4—1581no—
147C22×C4—1581no—
148C22×C4D31611yescharacteristic
149C22×C4D31611yescharacteristic
150C22×C4C22×D7911yescharacteristic
151M16—24no—
152C2×C8C22×D7914yes—
153C4⋊C4—792no—
154C4⋊C4—792no—
155C4⋊C4—792no—
156C4⋊C4—1582no—
157C4⋊C4—1582no—
158C4⋊C4—1582no—
159C4⋊C4—1582no—
160C4⋊C4—1581no—
161C4⋊C4—1581no—
162C4⋊C4—1581no—
163C22⋊C4—1582no—
164C42—1582no—
165C42—1582no—
166C42—1582no—
167C42D31611yescharacteristic
168C42D31611yescharacteristic
169C42C22×D7911yescharacteristic
170C42C22×D7911yescharacteristic
171C23C2×D31611yescharacteristic
172Q8—3162no—
173Q8—3162no—
174Q8—794no—
175Q8—1582no—
176Q8—1584no—
177C2×C4—22no—
178C2×C4—41no—
179C2×C4—3162no—
180C2×C4—1582no—
181C2×C4—1582no—
182C2×C4—1582no—
183C2×C4—1584no—
184C2×C4—1582no—
185C2×C4C2×D31611yescharacteristic
186C2×C4C2×D31611yescharacteristic
187C2×C4C2×D31611yescharacteristic
188C2×C4C2×D31611yescharacteristic
189C2×C4C2×D31611yescharacteristic
190C2×C4Q8×D7912yes—
191C2×C4#1192962312yes—
192C2×C4C23×D7911yescharacteristic
193C8—24no—
194C22—21no—
195C22—21no—
196C22#1457914112yes—
197C22C22×D31611yescharacteristic
198C4—21no—
199C4—21no—
200C4—21no—
201C4—3162no—
202C4—3162no—
203C4—3162no—
204C4—1584no—
205C4#1457914112yes—
206C4#1457919412yes—
207C4C2×Q8×D7911yescharacteristic
208C4C2×#1192962311yescharacteristic
209C2—22no—
210C2C2×#1457914111yescharacteristic
211C2C2×#1457919411yescharacteristic
212C2#1909936311yescharacteristic
subgroupG/H
centerC22C22×D316
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#423×C79C2
socleC22×C79C22×D4
prime radicalC23×C79C2×D4
hypercenter#423D79
hypocenterC79#3078
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C2×C42 ◁ #423

Complements

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

NH ≅ G/Ntype
3. #19098871C2semidirect
4. #19098859C2semidirect
5. #19098849C2semidirect
37. C2×Dic158Q8semidirect
107. C79#3078semidirect