Finite Group Databasebeta

← #23764331

Subgroups — #23764331

Order 10112.

344 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 99 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×#14579148C211yesmaximal, characteristic
2C2×Dic79⋊C8C211yesmaximal, characteristic, complemented
3C2×#14579086C211yesmaximal, characteristic, complemented
4C2×#14579084C211yesmaximal, characteristic, complemented
5C2×#14579082C211yesmaximal, characteristic
6C4⋊C4×Dic79C211yesmaximal, characteristic, complemented
7C2×#102×C79C211yesmaximal, characteristic
8C22×Dic158C2211yescharacteristic
9C22×C79⋊C8C2211yescharacteristic
10#14579148—22no—
11#14579148C414yescomplemented
12C2×C4⋊Dic79C2211yescharacteristic
13C2×C22⋊Dic79—21no—
14C2×C22⋊Dic79—21no—
15C2×C4×Dic79—21no—
16C2×C4×Dic79C2211yescharacteristic
17Dic79⋊C8—22no—
18#14579086—22no—
19#14579084—22no—
20#14579082—22no—
21C79⋊#95—21no—
22C22×D4×C79C2211yescharacteristic
23C22×C8×C79C2211yescharacteristic
24C2×C4⋊C4×C79C2211yescharacteristic
25#102×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—
41C22⋊Dic79—24no—
42C22⋊Dic79—24no—
43C4×Dic79—42no—
44C4×Dic79C2×C412yes—
45C4×Dic79D412yes—
46C24×C79—21no—
47C2×D4×C79—21no—
48C2×D4×C79—21no—
49C2×D4×C79—21no—
50C2×D4×C79—21no—
51C2×D4×C79—21no—
52C2×D4×C79C2×C412yes—
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×C79—22no—
61C23×C79—41no—
62C23×C79—41no—
63C23×C79—41no—
64C23×C79—41no—
65C23×C79—41no—
66C23×C79—41no—
67C23×C79C2×D411yescharacteristic
68D4×C79—22no—
69D4×C79—22no—
70D4×C79—41no—
71D4×C79—41no—
72C2×C4×C79—22no—
73C2×C4×C79—41no—
74C2×C4×C79—41no—
75C2×C4×C79C22×C411yescharacteristic
76C2×C4×C79C2×D411yescharacteristic
77C2×C4×C79C2×D411yescharacteristic
78C2×C4×C79C2×D411yescharacteristic
79C2×C4×C79#4111yescharacteristic
80C2×C4×C79#4111yescharacteristic
81C2×Dic79—21no—
82C2×Dic79—21no—
83C2×Dic79—21no—
84C2×Dic79—21no—
85C2×Dic79—22no—
86C2×Dic79—22no—
87C2×Dic79—41no—
88C2×Dic79—41no—
89C2×Dic79—41no—
90C2×Dic79—41no—
91C2×Dic79C22⋊C412yes—
92C2×Dic79C22⋊C412yes—
93Dic158—22no—
94Dic158—22no—
95Dic158—41no—
96Dic158—41no—
97C8×C79—41no—
98C79⋊C8—41no—
99C22×C79—42no—
100C22×C79—42no—
101C22×C79—42no—
102C22×C79—81no—
103C22×C79—81no—
104C22×C79—81no—
105C22×C79—81no—
106C22×C79C2×C22⋊C411yescharacteristic
107C22×C79#12111yescharacteristic
108C22×C79#12111yescharacteristic
109C22×C79#13511yescharacteristic
110C22×C79#13511yescharacteristic
111C22×C79AGL(1,ℤ/8)11yescharacteristic
112C22×C79#13711yescharacteristic
113C4×C79—42no—
114C4×C79C4×D411yescharacteristic
115C4×C79C4×D411yescharacteristic
116C4×C79#12411yescharacteristic
117C4×C79#12711yescharacteristic
118Dic79—22no—
119Dic79—22no—
120Dic79—42no—
121Dic79—42no—
122C2×C79—82no—
123C2×C79#39011yescharacteristic
124C2×C79#41611yescharacteristic
125C2×C79#41711yescharacteristic
126C2×C79#46311yescharacteristic
127C2×C79#46311yescharacteristic
128C2×C79#46411yescharacteristic
129C2×C79#46411yescharacteristic
130#1983—791nomaximal, Sylow
131C79#198311yescharacteristic, complemented, Sylow
132C2×#124—791no—
133C2×C4⋊C8—791no—
134C2×#103—791no—
135C2×#103—791no—
136C2×#102—791no—
137C2×#102D7911yescharacteristic
138C4×C4⋊C4—791no—
139C22×Q8—791no—
140C22×D4C2×D7911yescharacteristic
141C22×C8—791no—
142C22×C8C2×D7911yescharacteristic
143#124—794no—
144#124—1582no—
145C2×C4⋊C4—791no—
146C2×C4⋊C4C2×D7911yescharacteristic
147C2×C22⋊C4—1581no—
148C2×C22⋊C4—1581no—
149C2×C42—791no—
150C2×C42—1581no—
151C4⋊C8—1582no—
152#103—1582no—
153#103—1582no—
154#102—22no—
155#102—1582no—
156#95—1581no—
157C24—21no—
158C2×Q8—792no—
159C2×Q8—1581no—
160C2×Q8—1581no—
161C2×Q8—1581no—
162C2×Q8—1581no—
163C2×Q8—1581no—
164C2×D4—21no—
165C2×D4—21no—
166C2×D4—21no—
167C2×D4—21no—
168C2×D4—21no—
169C2×D4C4×D7912yes—
170C22×C4—21no—
171C22×C4—791no—
172C22×C4—791no—
173C22×C4—1581no—
174C22×C4—1581no—
175C22×C4C22×D7911yescharacteristic
176C2×C8—21no—
177C2×C8—21no—
178C2×C8—21no—
179C2×C8—1581no—
180C2×C8—1581no—
181C2×C8—1581no—
182C4⋊C4—21no—
183C4⋊C4—792no—
184C4⋊C4—1581no—
185C4⋊C4C22⋊D7912yes—
186C22⋊C4—1584no—
187C22⋊C4—1584no—
188C42—3162no—
189C42—792no—
190C42—792no—
191C23—22no—
192C23—41no—
193C23—41no—
194C23—41no—
195C23—41no—
196C23—41no—
197C23—41no—
198C23D4×D7911yescharacteristic
199Q8—3161no—
200Q8—3161no—
201Q8—1582no—
202Q8—1582no—
203D4—22no—
204D4—22no—
205D4—41no—
206D4—41no—
207C2×C4—22no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—3161no—
211C2×C4—3161no—
212C2×C4—3161no—
213C2×C4—3161no—
214C2×C4—792no—
215C2×C4—792no—
216C2×C4—1582no—
217C2×C4—1582no—
218C2×C4—1581no—
219C2×C4—1581no—
220C2×C4—1581no—
221C2×C4—1581no—
222C2×C4C2×C4×D7911yescharacteristic
223C2×C4D4×D7911yescharacteristic
224C2×C4D4×D7911yescharacteristic
225C2×C4C2×C22⋊D7911yescharacteristic
226C2×C4#1192962311yescharacteristic
227C2×C4#1192962411yescharacteristic
228C8—41no—
229C8—3161no—
230C22—42no—
231C22—42no—
232C22—42no—
233C22—81no—
234C22—81no—
235C22—81no—
236C22—81no—
237C22C22⋊C4×D7911yescharacteristic
238C22#1457913311yescharacteristic
239C22#1457913411yescharacteristic
240C22#1457918011yescharacteristic
241C22#1457918211yescharacteristic
242C22#1457918511yescharacteristic
243C22#1457919011yescharacteristic
244C4—42no—
245C4—3162no—
246C4—3162no—
247C4—1582no—
248C4—1582no—
249C4(C22⋊D79)⋊C411yescharacteristic
250C4C4×C22⋊D7911yescharacteristic
251C4#1457914711yescharacteristic
252C4#1457915711yescharacteristic
253C2—82no—
254C2#1909846311yescharacteristic
255C2#1909855611yescharacteristic
256C2#1909856111yescharacteristic
257C2#1909877611yescharacteristic
258C2#1909877711yescharacteristic
259C2#1909878311yescharacteristic
260C2#1909878411yescharacteristic
subgroupG/H
centerC23D4×D79
commutatorC2×C4×C79C22×C4
FrattiniC22×C4C22×D79
FittingC2×#102×C79C2
socleC23×C79C2×D4
prime radicalC22×D4×C79C22
cosocleC22×C4×C79C23
hypercenterC2×#102D79
hypocenterC79#1983
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
2. C2×Dic79⋊C8C2semidirect
3. C2×#14579086C2semidirect
4. C2×#14579084C2semidirect
6. C4⋊C4×Dic79C2semidirect
11. #14579148C4semidirect
131. C79#1983semidirect