Finite Group Databasebeta

← #23773201

Subgroups — #23773201

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
1C2×C4×Dic158C211yesmaximal, characteristic
2#19098867C214yesmaximal, complemented
3#19098855C212yesmaximal, complemented
4#19098845C212yesmaximal, complemented
5#19098606C212yesmaximal
6#19098587C211yesmaximal, characteristic
7#19098571C212yesmaximal
8#533×C79C211yesmaximal, characteristic
9C22×Dic158C2211yescharacteristic
10C2×#11929608C2212yes—
11C4×Dic158—21no—
12C4×Dic158—21no—
13C4×Dic158C2212yes—
14C4×Dic158C2212yes—
15C2×C4⋊Dic79C2211yescharacteristic
16C2×Dic79⋊C4—21no—
17C2×C4×Dic79—21no—
18#14579094C2214yes—
19#14579092C2214yes—
20C4⋊(C79⋊C8)C2212yes—
21C4⋊(C79⋊C8)C2212yes—
22#14579084C2214yes—
23#14579084C2214yes—
24C4⋊Q8×C79C2211yescharacteristic
25C4⋊Q8×C79C2211yescharacteristic
26#125×C79C2212yes—
27C22⋊Q8×C79—21no—
28C22⋊Q8×C79—21no—
29C4×Q8×C79—21no—
30C4×Q8×C79—21no—
31#117×C79C2212yes—
32C2×C42×C79C2211yescharacteristic
33C2×Dic158—21no—
34C2×Dic158—22no—
35C2×Dic158Q814yescomplemented
36C2×Dic158C2312yes—
37C22×Dic79—21no—
38C22×Dic79—21no—
39#11929608—24no—
40C2×C79⋊C8C2314yes—
41C4⋊Dic79—21no—
42C4⋊Dic79C2312yes—
43Dic79⋊C4—22no—
44Dic79⋊C4—22no—
45C4×Dic79—22no—
46C4×Dic79—22no—
47C2×Q8×C79—21no—
48C2×Q8×C79—21no—
49C22×C4×C79D411yescharacteristic
50C22×C4×C79D411yescharacteristic
51C22×C4×C79C2311yescharacteristic
52C4⋊C4×C79—22no—
53C4⋊C4×C79—22no—
54C4⋊C4×C79—21no—
55C4⋊C4×C79—21no—
56C4⋊C4×C79C2312yes—
57C4⋊C4×C79C2312yes—
58C22⋊C4×C79—22no—
59C42×C79—22no—
60C42×C79D411yescharacteristic
61C42×C79D411yescharacteristic
62C42×C79C2311yescharacteristic
63C42×C79C2311yescharacteristic
64C23×C79C2×D411yescharacteristic
65Q8×C79—42no—
66Q8×C79—42no—
67C2×C4×C79—22no—
68C2×C4×C79—22no—
69C2×C4×C79—22no—
70C2×C4×C79—41no—
71C2×C4×C79C2×D411yescharacteristic
72C2×C4×C79C2×D411yescharacteristic
73C2×C4×C79C2×D411yescharacteristic
74C2×C4×C79C2×D411yescharacteristic
75C2×C4×C79C2×D411yescharacteristic
76C2×C4×C79C2×Q812yes—
77C2×C4×C79#4112yes—
78C2×C4×C79C2411yescharacteristic
79C2×Dic79—24no—
80C2×Dic79—22no—
81C2×Dic79—22no—
82C2×Dic79—42no—
83Dic158—24no—
84Dic158—22no—
85Dic158C2×Q814yes—
86C79⋊C8—24no—
87C22×C79—21no—
88C22×C79—21no—
89C22×C79C22⋊Q812yes—
90C22×C79C22×D411yescharacteristic
91C4×C79—21no—
92C4×C79—21no—
93C4×C79—21no—
94C4×C79—42no—
95C4×C79—42no—
96C4×C79C22⋊Q812yes—
97C4×C79#13712yes—
98C4×C79C22×Q811yescharacteristic
99C4×C79C2×#4111yescharacteristic
100Dic79—24no—
101Dic79—42no—
102C2×C79—22no—
103C2×C79C2×C22⋊Q811yescharacteristic
104C2×C79C2×#13711yescharacteristic
105C2×C79#57511yescharacteristic
106#3078—791nomaximal, Sylow
107C79#307811yescharacteristic, complemented, Sylow
108#533D7911yescharacteristic
109C2×C4×Q8—791no—
110#479—794no—
111#477—792no—
112#475—792no—
113#428—792no—
114#423—791no—
115#419—792no—
116C22×Q8—791no—
117C2×M16—792no—
118C4⋊Q8C2×D7911yescharacteristic
119C4⋊Q8C2×D7911yescharacteristic
120#125C2×D7912yes—
121C22⋊Q8—21no—
122C22⋊Q8—21no—
123C4×Q8—21no—
124C4×Q8—21no—
125C4×Q8—792no—
126C4×Q8—792no—
127C4×Q8—1581no—
128C4×Q8—1581no—
129#117C2×D7912yes—
130C2×C4⋊C4—791no—
131C2×C4⋊C4—1581no—
132C2×C42—1581no—
133C2×C42C2×D7911yescharacteristic
134#107—794no—
135#106—794no—
136C4⋊C8—792no—
137C4⋊C8—792no—
138#103—794no—
139#103—794no—
140C2×Q8—21no—
141C2×Q8—21no—
142C2×Q8—794no—
143C2×Q8—792no—
144C2×Q8—1581no—
145C2×Q8—1582no—
146C22×C4—1581no—
147C22×C4—1581no—
148C22×C4C22⋊D7911yescharacteristic
149C22×C4C22⋊D7911yescharacteristic
150C22×C4C22×D7911yescharacteristic
151M16—1584no—
152C2×C8—794no—
153C4⋊C4—22no—
154C4⋊C4—22no—
155C4⋊C4—21no—
156C4⋊C4—21no—
157C4⋊C4—792no—
158C4⋊C4—1582no—
159C4⋊C4—1582no—
160C4⋊C4—1581no—
161C4⋊C4C22×D7912yes—
162C4⋊C4C22×D7912yes—
163C22⋊C4—22no—
164C42—22no—
165C42—1582no—
166C42—1582no—
167C42C22⋊D7911yescharacteristic
168C42C22⋊D7911yescharacteristic
169C42C22×D7911yescharacteristic
170C42C22×D7911yescharacteristic
171C23C2×C22⋊D7911yescharacteristic
172Q8—42no—
173Q8—42no—
174Q8—794no—
175Q8—1582no—
176Q8—1584no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—41no—
181C2×C4—3162no—
182C2×C4—1582no—
183C2×C4—1584no—
184C2×C4—1582no—
185C2×C4C2×C22⋊D7911yescharacteristic
186C2×C4C2×C22⋊D7911yescharacteristic
187C2×C4C2×C22⋊D7911yescharacteristic
188C2×C4C2×C22⋊D7911yescharacteristic
189C2×C4C2×C22⋊D7911yescharacteristic
190C2×C4Q8×D7912yes—
191C2×C4#1192962512yes—
192C2×C4C23×D7911yescharacteristic
193C8—1584no—
194C22—21no—
195C22—21no—
196C22#1457913712yes—
197C22C22×C22⋊D7911yescharacteristic
198C4—21no—
199C4—21no—
200C4—21no—
201C4—42no—
202C4—42no—
203C4—3162no—
204C4—1584no—
205C4#1457913712yes—
206C4#1457919112yes—
207C4C2×Q8×D7911yescharacteristic
208C4C2×#1192962511yescharacteristic
209C2—22no—
210C2C2×#1457913711yescharacteristic
211C2C2×#1457919111yescharacteristic
212C2#1909936111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#533×C79C2
socleC22×C79C22×D4
prime radicalC23×C79C2×D4
hypercenter#533D79
hypocenterC79#3078
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C2×C42 ◁ #533

Complements

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

NH ≅ G/Ntype
2. #19098867C2semidirect
3. #19098855C2semidirect
4. #19098845C2semidirect
35. C2×Dic158Q8semidirect
107. C79#3078semidirect