Finite Group Databasebeta

← #23776202

Subgroups — #23776202

Order 10112.

326 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 115 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#19099288C211yesmaximal, characteristic
3#19098930C212yesmaximal
4#19098915C211yesmaximal, characteristic
5#19098873C212yesmaximal
6#19098774C211yesmaximal, characteristic
7#19098772C212yesmaximal
8#19098690C211yesmaximal, characteristic
9#19098669C212yesmaximal
10C4×#11929614C211yesmaximal, characteristic
11#475×C79C211yesmaximal, characteristic
12C2×Dic316C2212yes—
13C2×#11929614C2211yescharacteristic
14#14579161C2211yescharacteristic
15#14579159—21no—
16#14579159C2212yes—
17#14579153—21no—
18#14579152C2212yes—
19#14579151—22no—
20#14579151—22no—
21Q8×Dic79—21no—
22C4×Dic158—21no—
23C4×Dic158C2211yescharacteristic
24C4×Dic158C2211yescharacteristic
25#14579126C2212yes—
26#14579126C2212yes—
27#14579094C2211yescharacteristic
28Dic79⋊C8C2212yes—
29#14579086C2212yes—
30#14579085C2211yescharacteristic
31#14579084C2211yescharacteristic
32#14579084C2212yes—
33#14579084C2212yes—
34#14579071C2212yes—
35C4×C79⋊C8C2211yescharacteristic
36C4⋊Q8×C79C2211yescharacteristic
37C4×Q8×C79C2211yescharacteristic
38#106×C79C2212yes—
39C4⋊C8×C79C2211yescharacteristic
40#103×C79C2212yes—
41C2×Dic158D411yescharacteristic
42C2×Dic158C2312yes—
43C2×Dic158C2311yescharacteristic
44Dic316—24no—
45#11929614—22no—
46C2×C79⋊C8C2311yescharacteristic
47C2×C79⋊C8C2311yescharacteristic
48C4⋊Dic79—22no—
49C4⋊Dic79—21no—
50C4⋊Dic79—21no—
51C4⋊Dic79D411yescharacteristic
52C4⋊Dic79C2311yescharacteristic
53Dic79⋊C4—22no—
54Dic79⋊C4—22no—
55Dic79⋊C4—22no—
56Dic79⋊C4—22no—
57Dic79⋊C4—22no—
58Dic79⋊C4—21no—
59Dic79⋊C4D412yes—
60C4×Dic79—22no—
61C4×Dic79—22no—
62C4×Dic79—21no—
63C4×Dic79C2312yes—
64C2×Q8×C79—21no—
65C2×Q8×C79C2311yescharacteristic
66C2×C8×C79C2312yes—
67C4⋊C4×C79—21no—
68C4⋊C4×C79—21no—
69C4⋊C4×C79C2312yes—
70C4⋊C4×C79C2311yescharacteristic
71C42×C79—21no—
72C42×C79C2311yescharacteristic
73Q8×C79—21no—
74Q8×C79—21no—
75Q8×C79—42no—
76C2×C4×C79—21no—
77C2×C4×C79—22no—
78C2×C4×C79—21no—
79C2×C4×C79C2×D411yescharacteristic
80C2×C4×C79C2×D411yescharacteristic
81C2×C4×C79C2411yescharacteristic
82C2×Dic79—21no—
83C2×Dic79—21no—
84C2×Dic79—22no—
85C2×Dic79C2×D412yes—
86C2×Dic79C2×D412yes—
87Dic158—22no—
88Dic158—21no—
89Dic158—22no—
90Dic158—22no—
91Dic158#4112yes—
92C8×C79—22no—
93C79⋊C8—21no—
94C79⋊C8—21no—
95C22×C79C22×D411yescharacteristic
96C4×C79—21no—
97C4×C79—41no—
98C4×C79—42no—
99C4×C79—41no—
100C4×C79#13712yes—
101C4×C79C2×#4111yescharacteristic
102C4×C792−1+411yescharacteristic
103Dic79—22no—
104Dic79—22no—
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#557—791no—
115#491—792no—
116#487—791no—
117#479—792no—
118#475D7911yescharacteristic
119#462—791no—
120#462—792no—
121#446—791no—
122#441—792no—
123C4×Q16—791no—
124C2×Q16—791no—
125C2×Q16—792no—
126C4⋊Q8—792no—
127C4⋊Q8—791no—
128C4⋊Q8—1581no—
129C4⋊Q8C2×D7911yescharacteristic
130#125—792no—
131#125—1581no—
132#125—1582no—
133#125—1582no—
134C4×Q8—791no—
135C4×Q8—792no—
136C4×Q8—792no—
137C4×Q8—791no—
138C4×Q8—1581no—
139C4×Q8—1581no—
140C4×Q8C2×D7911yescharacteristic
141#107—791no—
142#106C2×D7912yes—
143C4⋊C8—792no—
144C4⋊C8C2×D7911yescharacteristic
145#103—791no—
146#103—792no—
147#103—791no—
148#103—792no—
149#103—792no—
150#103C2×D7912yes—
151#97—792no—
152C4×C8—791no—
153C2×Q8—21no—
154C2×Q8—791no—
155C2×Q8—791no—
156C2×Q8—792no—
157C2×Q8C22×D7911yescharacteristic
158Q16—1584no—
159Q16—1582no—
160C2×C8—791no—
161C2×C8—791no—
162C2×C8C22×D7912yes—
163C4⋊C4—21no—
164C4⋊C4—21no—
165C4⋊C4—792no—
166C4⋊C4—791no—
167C4⋊C4—791no—
168C4⋊C4—1582no—
169C4⋊C4—1582no—
170C4⋊C4—1582no—
171C4⋊C4—1582no—
172C4⋊C4—1582no—
173C4⋊C4—1582no—
174C4⋊C4—1581no—
175C4⋊C4—1581no—
176C4⋊C4—1581no—
177C4⋊C4C22×D7912yes—
178C4⋊C4C22×D7911yescharacteristic
179C42—21no—
180C42—792no—
181C42—1582no—
182C42—1582no—
183C42—1581no—
184C42C22×D7911yescharacteristic
185Q8—21no—
186Q8—21no—
187Q8—42no—
188Q8—792no—
189Q8—1582no—
190Q8—1582no—
191Q8—1581no—
192Q8—1582no—
193C2×C4—21no—
194C2×C4—21no—
195C2×C4—22no—
196C2×C4—792no—
197C2×C4—792no—
198C2×C4—1581no—
199C2×C4—1582no—
200C2×C4—1581no—
201C2×C4D4×D7911yescharacteristic
202C2×C4D4×D7911yescharacteristic
203C2×C4C23×D7911yescharacteristic
204C8—22no—
205C8—1581no—
206C8—1581no—
207C22C2×D4×D7911yescharacteristic
208C4—21no—
209C4—41no—
210C4—42no—
211C4—41no—
212C4—3162no—
213C4—3161no—
214C4—1582no—
215C4—1582no—
216C4—1582no—
217C4#1457919012yes—
218C4#41×D7911yescharacteristic
219C4#1457920911yescharacteristic
220C2#1909922311yescharacteristic
221C2C2×#1457919011yescharacteristic
222C2#1909937911yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#475×C79C2
socle, prime radicalC22×C79C22×D4
hypercenter#475D79
hypocenterC79#3374
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C42 ◁ #475

Complements

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

NH ≅ G/Ntype
112. C79#3374semidirect