Finite Group Databasebeta

← #23776199

Subgroups — #23776199

Order 10112.

326 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 123 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#19099291C211yesmaximal, characteristic
2#19098931C212yesmaximal
3#19098913C211yesmaximal, characteristic
4#19098870C212yesmaximal
5#19098848C211yesmaximal, characteristic
6#19098770C211yesmaximal, characteristic
7#19098770C212yesmaximal
8#19098694C211yesmaximal, characteristic
9#19098668C212yesmaximal
10C4×#11929614C211yesmaximal, characteristic
11#557×C79C211yesmaximal, characteristic
12C2×#11929614C2211yescharacteristic
13C2×#11929614C2212yes—
14#14579161C2211yescharacteristic
15#14579159—21no—
16#14579153C2212yes—
17#14579151—22no—
18C4×Dic158C2211yescharacteristic
19C4×Dic158C2212yes—
20#14579126—21no—
21#14579094C2211yescharacteristic
22#14579092C2212yes—
23C4⋊(C79⋊C8)C2211yescharacteristic
24C4⋊(C79⋊C8)C2212yes—
25#14579085C2211yescharacteristic
26#14579085C2212yes—
27#14579085C2212yes—
28#14579085C2212yes—
29#14579085C2212yes—
30#14579084C2211yescharacteristic
31#14579072C2212yes—
32C4×C79⋊C8C2211yescharacteristic
33C4⋊Q8×C79C2211yescharacteristic
34C4⋊Q8×C79C2212yes—
35#125×C79—21no—
36#125×C79—22no—
37C4×Q8×C79—21no—
38C4×Q8×C79C2211yescharacteristic
39C4×Q8×C79C2212yes—
40C4×Q8×C79C2211yescharacteristic
41C2×Dic158—21no—
42C2×Dic158C2311yescharacteristic
43#11929614—22no—
44#11929614—24no—
45C2×C79⋊C8C2311yescharacteristic
46C2×C79⋊C8C2311yescharacteristic
47C2×C79⋊C8C2312yes—
48C4⋊Dic79—21no—
49C4⋊Dic79C2312yes—
50C4⋊Dic79C2311yescharacteristic
51Dic79⋊C4—22no—
52Dic79⋊C4—21no—
53Dic79⋊C4—22no—
54Dic79⋊C4—22no—
55C4×Dic79—22no—
56C4×Dic79—21no—
57C2×Q8×C79D411yescharacteristic
58C2×Q8×C79C2311yescharacteristic
59C2×Q8×C79C2312yes—
60C4⋊C4×C79—22no—
61C4⋊C4×C79—21no—
62C4⋊C4×C79—22no—
63C4⋊C4×C79—21no—
64C4⋊C4×C79—22no—
65C4⋊C4×C79—21no—
66C4⋊C4×C79D411yescharacteristic
67C4⋊C4×C79D412yes—
68C4⋊C4×C79C2311yescharacteristic
69C42×C79—22no—
70C42×C79—21no—
71C42×C79C2311yescharacteristic
72C42×C79C2312yes—
73Q8×C79—22no—
74Q8×C79—21no—
75Q8×C79—22no—
76Q8×C79—21no—
77Q8×C79—22no—
78C2×C4×C79—21no—
79C2×C4×C79—22no—
80C2×C4×C79—21no—
81C2×C4×C79C2×D412yes—
82C2×C4×C79C2×D412yes—
83C2×C4×C79C2×D411yescharacteristic
84C2×C4×C79C2×D411yescharacteristic
85C2×C4×C79C2411yescharacteristic
86C2×Dic79—21no—
87C2×Dic79—21no—
88C2×Dic79—22no—
89Dic158—21no—
90Dic158—42no—
91Dic158#4112yes—
92C79⋊C8—21no—
93C79⋊C8—22no—
94C79⋊C8—21no—
95C22×C79C22×D411yescharacteristic
96C4×C79—22no—
97C4×C79—22no—
98C4×C79—21no—
99C4×C79—42no—
100C4×C79—41no—
101C4×C79—41no—
102C4×C79#13712yes—
103C4×C79C2×#4111yescharacteristic
104C4×C792−1+411yescharacteristic
105Dic79—22no—
106Dic79—42no—
107Dic79—41no—
108C2×C79#54811yescharacteristic
109C2×C79C2×#13711yescharacteristic
110C2×C79#57811yescharacteristic
111#3374—791nomaximal, Sylow
112C79#337411yescharacteristic, complemented, Sylow
113#557—791no—
114#557D7911yescharacteristic
115#491—792no—
116#487—791no—
117#479—792no—
118#475—791no—
119#462—792no—
120#462—791no—
121#446—791no—
122#441—792no—
123C4×Q16—791no—
124C2×Q16—791no—
125C2×Q16—792no—
126C4⋊Q8—791no—
127C4⋊Q8—1581no—
128C4⋊Q8C2×D7911yescharacteristic
129C4⋊Q8C2×D7912yes—
130#125—21no—
131#125—22no—
132#125—792no—
133#125—1582no—
134C4×Q8—21no—
135C4×Q8—791no—
136C4×Q8—792no—
137C4×Q8—1581no—
138C4×Q8C2×D7911yescharacteristic
139C4×Q8C2×D7912yes—
140C4×Q8C2×D7911yescharacteristic
141#107—791no—
142#106—792no—
143C4⋊C8—791no—
144C4⋊C8—792no—
145#103—791no—
146#103—792no—
147#103—792no—
148#103—792no—
149#103—792no—
150#103—791no—
151#97—792no—
152C4×C8—791no—
153C2×Q8—791no—
154C2×Q8—1581no—
155C2×Q8C22⋊D7911yescharacteristic
156C2×Q8C22×D7911yescharacteristic
157C2×Q8C22×D7912yes—
158Q16—1582no—
159Q16—1584no—
160C2×C8—791no—
161C2×C8—791no—
162C2×C8—792no—
163C4⋊C4—22no—
164C4⋊C4—21no—
165C4⋊C4—22no—
166C4⋊C4—21no—
167C4⋊C4—22no—
168C4⋊C4—21no—
169C4⋊C4—792no—
170C4⋊C4—791no—
171C4⋊C4—1581no—
172C4⋊C4—1582no—
173C4⋊C4—1582no—
174C4⋊C4—1582no—
175C4⋊C4—1581no—
176C4⋊C4C22⋊D7911yescharacteristic
177C4⋊C4C22⋊D7912yes—
178C4⋊C4C22×D7911yescharacteristic
179C42—22no—
180C42—21no—
181C42—1582no—
182C42—1581no—
183C42C22×D7911yescharacteristic
184C42C22×D7912yes—
185Q8—22no—
186Q8—21no—
187Q8—22no—
188Q8—21no—
189Q8—22no—
190Q8—3162no—
191Q8—792no—
192Q8—1581no—
193C2×C4—21no—
194C2×C4—22no—
195C2×C4—21no—
196C2×C4—1581no—
197C2×C4—1582no—
198C2×C4—1581no—
199C2×C4C2×C22⋊D7912yes—
200C2×C4C2×C22⋊D7912yes—
201C2×C4C2×C22⋊D7911yescharacteristic
202C2×C4C2×C22⋊D7911yescharacteristic
203C2×C4C23×D7911yescharacteristic
204C8—1581no—
205C8—1582no—
206C8—1581no—
207C22C22×C22⋊D7911yescharacteristic
208C4—22no—
209C4—22no—
210C4—21no—
211C4—42no—
212C4—41no—
213C4—41no—
214C4—3162no—
215C4—3161no—
216C4—1582no—
217C4#1457919212yes—
218C4#41×D7911yescharacteristic
219C4#1457920811yescharacteristic
220C2#1909922011yescharacteristic
221C2C2×#1457919211yescharacteristic
222C2#1909937811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#557×C79C2
socle, prime radicalC22×C79C22×D4
hypercenter#557D79
hypocenterC79#3374
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #557

Complements

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

NH ≅ G/Ntype
112. C79#3374semidirect