Finite Group Databasebeta

← #23773778

Subgroups — #23773778

Order 10112.

380 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 129 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#19099116C211yesmaximal, characteristic
2C2×#14579159C211yesmaximal, characteristic
3#19098930C214yesmaximal, complemented
4#19098912C214yesmaximal, complemented
5#19098573C211yesmaximal, characteristic
6#19098572C211yesmaximal, characteristic
7#19098571C211yesmaximal, characteristic
8M16×Dic79C211yesmaximal, characteristic
9#419×C79C211yesmaximal, characteristic
10C22×Dic158C2211yescharacteristic
11C2×#11929608C2211yescharacteristic
12#14579160C2212yes—
13#14579159—22no—
14#14579159C2212yes—
15#14579159C2212yes—
16#14579152C2212yes—
17#14579138—22no—
18C4×Dic158—22no—
19#14579120C2211yescharacteristic
20C2×Dic79⋊C4—22no—
21C2×C4×Dic79C2211yescharacteristic
22#14579086C2214yes—
23#14579085C2214yes—
24#14579084C2214yes—
25#14579071C2212yes—
26C8×Dic79C2212yes—
27C22×Q8×C79C2211yescharacteristic
28C2×M16×C79C2211yescharacteristic
29#117×C79C2211yescharacteristic
30#103×C79C2214yes—
31C2×Dic158—22no—
32C2×Dic158—21no—
33C2×Dic158—22no—
34C2×Dic158—22no—
35C2×Dic158C2312yes—
36C22×Dic79—21no—
37C22×Dic79D412yes—
38#11929608—22no—
39C2×C79⋊C8C2312yes—
40C4⋊Dic79—22no—
41C4⋊Dic79C2312yes—
42Dic79⋊C4—24no—
43Dic79⋊C4—24no—
44Dic79⋊C4—22no—
45Dic79⋊C4—22no—
46C22⋊Dic79—21no—
47C4×Dic79—21no—
48C4×Dic79D412yes—
49C4×Dic79C2311yescharacteristic
50C4×Dic79C2311yescharacteristic
51C2×Q8×C79—21no—
52C2×Q8×C79—22no—
53C2×Q8×C79—22no—
54C2×Q8×C79C2312yes—
55C22×C4×C79—21no—
56C22×C4×C79C2311yescharacteristic
57M16×C79—22no—
58C2×C8×C79C2312yes—
59C4⋊C4×C79C2312yes—
60C22⋊C4×C79—21no—
61C42×C79—21no—
62C23×C79C2×D411yescharacteristic
63Q8×C79—22no—
64Q8×C79—22no—
65Q8×C79—42no—
66C2×C4×C79—22no—
67C2×C4×C79—22no—
68C2×C4×C79—42no—
69C2×C4×C79C2×D411yescharacteristic
70C2×C4×C79#4112yes—
71C2×C4×C79#4112yes—
72C2×C4×C79C2411yescharacteristic
73C2×Dic79—24no—
74C2×Dic79—22no—
75C2×Dic79—22no—
76C2×Dic79—42no—
77C2×Dic79C2×D412yes—
78C2×Dic79C2×D412yes—
79Dic158—22no—
80Dic158—22no—
81Dic158—42no—
82Dic158—44no—
83C8×C79—22no—
84C79⋊C8—22no—
85C22×C79—22no—
86C22×C79#12412yes—
87C22×C79C22×D411yescharacteristic
88C4×C79—42no—
89C4×C79—42no—
90C4×C79#12412yes—
91C4×C79C2×#4111yescharacteristic
92C4×C79C2×#4111yescharacteristic
93Dic79—22no—
94Dic79—42no—
95Dic79—42no—
96Dic79#13714yes—
97C2×C79—22no—
98C2×C79C2×#12411yescharacteristic
99C2×C79C2×#13712yes—
100#3139—791nomaximal, Sylow
101C79#313911yescharacteristic, complemented, Sylow
102#533—791no—
103C2×C4⋊Q8—791no—
104#491—794no—
105#487—794no—
106#419—791no—
107#419—791no—
108#419—791no—
109#419D7911yescharacteristic
110C4×M16—791no—
111C22×Q8—791no—
112C22×Q8C2×D7911yescharacteristic
113C2×M16—791no—
114C2×M16C2×D7911yescharacteristic
115C4⋊Q8—792no—
116C4⋊Q8—792no—
117C4⋊Q8—792no—
118C4⋊Q8—1582no—
119#125—792no—
120C22⋊Q8—1582no—
121C4×Q8—1582no—
122#117—791no—
123#117C2×D7911yescharacteristic
124C2×C4⋊C4—1582no—
125C2×C42—791no—
126#103—794no—
127#103—794no—
128#103—794no—
129#103C2×D7914yes—
130#97—792no—
131C4×C8—792no—
132C2×Q8—21no—
133C2×Q8—22no—
134C2×Q8—22no—
135C2×Q8—792no—
136C2×Q8—1582no—
137C2×Q8—1582no—
138C2×Q8—1582no—
139C2×Q8—1581no—
140C2×Q8C22×D7912yes—
141C22×C4—21no—
142C22×C4—792no—
143C22×C4—1581no—
144C22×C4C22×D7911yescharacteristic
145M16—22no—
146M16—1582no—
147C2×C8—792no—
148C2×C8C22×D7912yes—
149C4⋊C4—792no—
150C4⋊C4—1584no—
151C4⋊C4—1584no—
152C4⋊C4—1582no—
153C4⋊C4—1582no—
154C4⋊C4—1582no—
155C4⋊C4C22×D7912yes—
156C22⋊C4—21no—
157C22⋊C4—1581no—
158C42—21no—
159C42—792no—
160C42—791no—
161C42—791no—
162C42—1581no—
163C23D4×D7911yescharacteristic
164Q8—22no—
165Q8—22no—
166Q8—42no—
167Q8—3164no—
168Q8—3162no—
169Q8—1582no—
170Q8—1582no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—42no—
174C2×C4—3162no—
175C2×C4—792no—
176C2×C4—792no—
177C2×C4—1582no—
178C2×C4—1582no—
179C2×C4—1584no—
180C2×C4D4×D7911yescharacteristic
181C2×C4#1192962312yes—
182C2×C4#1192962412yes—
183C2×C4C23×D7911yescharacteristic
184C8—22no—
185C8—1582no—
186C22—22no—
187C22#1457914712yes—
188C22C2×D4×D7911yescharacteristic
189C4—42no—
190C4—42no—
191C4—3162no—
192C4—3162no—
193C4—794no—
194C4—1582no—
195C4#1457914712yes—
196C4C2×#1192962311yescharacteristic
197C4C2×#1192962411yescharacteristic
198C2—22no—
199C2C2×#1457914711yescharacteristic
200C2#137×D7912yes—
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#419×C79C2
socleC22×C79C22×D4
prime radicalC23×C79C2×D4
hypercenter#419D79
hypocenterC79#3139
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
3. #19098930C2semidirect
4. #19098912C2semidirect
101. C79#3139semidirect