Finite Group Databasebeta

← #23764321

Subgroups — #23764321

Order 10112.

324 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 107 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×#14579159C211yesmaximal, characteristic
2C2×Dic79⋊C8C211yesmaximal, characteristic
3C2×#14579086C211yesmaximal, characteristic
4C2×#14579085C211yesmaximal, characteristic
5C2×#14579084C211yesmaximal, characteristic
6C4⋊C4×Dic79C211yesmaximal, characteristic
7C2×#103×C79C211yesmaximal, characteristic
8C22×Dic158C2211yescharacteristic
9C22×C79⋊C8C2211yescharacteristic
10#14579159—22no—
11#14579159C414yescomplemented
12C2×C4⋊Dic79C2211yescharacteristic
13C2×Dic79⋊C4—21no—
14C2×Dic79⋊C4—21no—
15C2×C4×Dic79—21no—
16C2×C4×Dic79C2211yescharacteristic
17Dic79⋊C8—22no—
18#14579086—22no—
19#14579085—22no—
20#14579084—22no—
21C79⋊#95—21no—
22C22×Q8×C79C2211yescharacteristic
23C22×C8×C79C2211yescharacteristic
24C2×C4⋊C4×C79C2211yescharacteristic
25#103×C79—22no—
26C2×Dic158—21no—
27C2×Dic158—21no—
28C2×Dic158—21no—
29C2×Dic158—21no—
30C2×Dic158—21no—
31C2×Dic158C2×C412yes—
32C22×Dic79—21no—
33C22×Dic79—21no—
34C22×Dic79D411yescharacteristic
35C22×Dic79D411yescharacteristic
36C2×C79⋊C8—21no—
37C2×C79⋊C8—21no—
38C2×C79⋊C8—21no—
39C4⋊Dic79—21no—
40C4⋊Dic79D412yes—
41Dic79⋊C4—24no—
42Dic79⋊C4—24no—
43C4×Dic79—42no—
44C4×Dic79C2×C412yes—
45C4×Dic79D412yes—
46C2×Q8×C79—21no—
47C2×Q8×C79—21no—
48C2×Q8×C79—21no—
49C2×Q8×C79—21no—
50C2×Q8×C79—21no—
51C2×Q8×C79C2×C412yes—
52C22×C4×C79—21no—
53C22×C4×C79—21no—
54C22×C4×C79C2311yescharacteristic
55C2×C8×C79—21no—
56C2×C8×C79—21no—
57C2×C8×C79—21no—
58C4⋊C4×C79—21no—
59C4⋊C4×C79D412yes—
60C23×C79C2×D411yescharacteristic
61Q8×C79—22no—
62Q8×C79—22no—
63Q8×C79—41no—
64Q8×C79—41no—
65C2×C4×C79—22no—
66C2×C4×C79—22no—
67C2×C4×C79—41no—
68C2×C4×C79—41no—
69C2×C4×C79—41no—
70C2×C4×C79—41no—
71C2×C4×C79C22×C411yescharacteristic
72C2×C4×C79C2×D411yescharacteristic
73C2×C4×C79C2×D411yescharacteristic
74C2×C4×C79C2×D411yescharacteristic
75C2×C4×C79#4111yescharacteristic
76C2×C4×C79#4111yescharacteristic
77C2×Dic79—21no—
78C2×Dic79—21no—
79C2×Dic79—22no—
80C2×Dic79—22no—
81C2×Dic79—41no—
82C2×Dic79—41no—
83C2×Dic79—41no—
84C2×Dic79—41no—
85C2×Dic79C22⋊C412yes—
86C2×Dic79C22⋊C412yes—
87C2×Dic79SD1612yes—
88C2×Dic79Q1612yes—
89Dic158—22no—
90Dic158—22no—
91Dic158—41no—
92Dic158—41no—
93C8×C79—41no—
94C79⋊C8—41no—
95C22×C79C2×C22⋊C411yescharacteristic
96C22×C79#12111yescharacteristic
97C22×C79#12111yescharacteristic
98C22×C79C2×SD1611yescharacteristic
99C22×C79C2×Q1611yescharacteristic
100C22×C79#13711yescharacteristic
101C22×C79#13711yescharacteristic
102C4×C79—42no—
103C4×C79—42no—
104C4×C79C4×D411yescharacteristic
105C4×C79C4×D411yescharacteristic
106C4×C79#12411yescharacteristic
107C4×C79#12711yescharacteristic
108Dic79—22no—
109Dic79—42no—
110Dic79—42no—
111Dic79#10314yescomplemented
112C2×C79#39011yescharacteristic
113C2×C79C2×#10311yescharacteristic
114C2×C79#41911yescharacteristic
115C2×C79#46111yescharacteristic
116C2×C79#46111yescharacteristic
117C2×C79#46211yescharacteristic
118C2×C79#46211yescharacteristic
119#1981—791nomaximal, Sylow
120C79#198111yescharacteristic, complemented, Sylow
121C2×C4⋊Q8—791no—
122C2×C4⋊C8—791no—
123C2×#103—791no—
124C2×#103—791no—
125C2×#103—791no—
126C2×#103D7911yescharacteristic
127C4×C4⋊C4—791no—
128C22×Q8—791no—
129C22×Q8C2×D7911yescharacteristic
130C22×C8—791no—
131C22×C8C2×D7911yescharacteristic
132C4⋊Q8—794no—
133C4⋊Q8—1582no—
134C2×C4⋊C4—791no—
135C2×C4⋊C4—1581no—
136C2×C4⋊C4—1581no—
137C2×C4⋊C4C2×D7911yescharacteristic
138C2×C42—791no—
139C2×C42—1581no—
140C4⋊C8—1582no—
141#103—22no—
142#103—1582no—
143#103—1582no—
144#103—1582no—
145#95—1581no—
146C2×Q8—21no—
147C2×Q8—21no—
148C2×Q8—21no—
149C2×Q8—21no—
150C2×Q8—21no—
151C2×Q8—792no—
152C2×Q8—1581no—
153C2×Q8—1581no—
154C2×Q8—1581no—
155C2×Q8—1581no—
156C2×Q8—1581no—
157C2×Q8C4×D7912yes—
158C22×C4—21no—
159C22×C4—21no—
160C22×C4—791no—
161C22×C4—791no—
162C22×C4—1581no—
163C22×C4—1581no—
164C22×C4C22×D7911yescharacteristic
165C2×C8—21no—
166C2×C8—21no—
167C2×C8—21no—
168C2×C8—1581no—
169C2×C8—1581no—
170C2×C8—1581no—
171C4⋊C4—21no—
172C4⋊C4—792no—
173C4⋊C4—1584no—
174C4⋊C4—1584no—
175C4⋊C4—1581no—
176C4⋊C4C22⋊D7912yes—
177C42—3162no—
178C42—792no—
179C42—792no—
180C23D4×D7911yescharacteristic
181Q8—22no—
182Q8—22no—
183Q8—41no—
184Q8—41no—
185Q8—3161no—
186Q8—3161no—
187Q8—1582no—
188Q8—1582no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—41no—
195C2×C4—3161no—
196C2×C4—3161no—
197C2×C4—3161no—
198C2×C4—3161no—
199C2×C4—792no—
200C2×C4—792no—
201C2×C4—792no—
202C2×C4—792no—
203C2×C4—1582no—
204C2×C4—1582no—
205C2×C4—1581no—
206C2×C4—1581no—
207C2×C4C2×C4×D7911yescharacteristic
208C2×C4D4×D7911yescharacteristic
209C2×C4D4×D7911yescharacteristic
210C2×C4C2×C22⋊D7911yescharacteristic
211C2×C4#1192962311yescharacteristic
212C2×C4#1192962411yescharacteristic
213C8—41no—
214C8—3161no—
215C22C22⋊C4×D7911yescharacteristic
216C22#1457913311yescharacteristic
217C22#1457913411yescharacteristic
218C22SD16×D7911yescharacteristic
219C22Q16×D7911yescharacteristic
220C22#1457919011yescharacteristic
221C22#1457919311yescharacteristic
222C4—42no—
223C4—42no—
224C4—3162no—
225C4—3162no—
226C4—794no—
227C4—1582no—
228C4(C22⋊D79)⋊C411yescharacteristic
229C4C4×C22⋊D7911yescharacteristic
230C4#1457914711yescharacteristic
231C4#1457915711yescharacteristic
232C2#1909846311yescharacteristic
233C2#103×D7911yescharacteristic
234C2#1909857011yescharacteristic
235C2#1909876611yescharacteristic
236C2#1909876711yescharacteristic
237C2#1909877111yescharacteristic
238C2#1909877211yescharacteristic
subgroupG/H
centerC23D4×D79
commutatorC2×C4×C79C22×C4
FrattiniC22×C4C22×D79
FittingC2×#103×C79C2
socle, prime radicalC23×C79C2×D4
cosocleC22×C4×C79C23
hypercenterC2×#103D79
hypocenterC79#1981
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
11. #14579159C4semidirect
111. Dic79#103semidirect
120. C79#1981semidirect