Finite Group Databasebeta

← #23771454

Subgroups — #23771454

Order 10112.

464 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 464 conjugacy classes of subgroups — too many to draw. Only its 125 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×#14579152C211yesmaximal, characteristic, complemented
2C2×#14579147C211yesmaximal, characteristic
3#19098498C211yesmaximal, characteristic, complemented
4#19098490C211yesmaximal, characteristic, complemented
5#19098488C211yesmaximal, characteristic, complemented
6#19098486C212yesmaximal, complemented
7#19098485C212yesmaximal, complemented
8#19098483C212yesmaximal, complemented
9#19098478C212yesmaximal
10#19098427C211yesmaximal, characteristic, complemented
11#399×C79C211yesmaximal, characteristic, complemented
12C22×Dic158C2211yescharacteristic
13C22×C22⋊D79C2211yescharacteristic
14#14579152—24no—
15#14579147—24no—
16C2×C4⋊Dic79C2212yes—
17C2×C4⋊Dic79C2211yescharacteristic
18C2×Dic79⋊C4C2212yes—
19C2×Dic79⋊C4C2212yes—
20C2×Dic79⋊C4C2212yes—
21C2×C22⋊Dic79C2211yescharacteristic
22C2×C22⋊Dic79C2212yes—
23C2×(C2×D79)⋊C4C2211yescharacteristic
24C2×(C2×D79)⋊C4C2211yescharacteristic
25C2×(C2×D79)⋊C4C2212yes—
26C2×(C2×D79)⋊C4C2212yes—
27C2×C4×Dic79C2211yescharacteristic
28C79⋊#95C2212yes—
29C79⋊#95C2211yescharacteristic
30C79⋊#95C2212yes—
31C79⋊#95C2212yes—
32C2×C4⋊C4×C79C2211yescharacteristic
33C2×C4⋊C4×C79C2212yes—
34C2×C22⋊C4×C79C2211yescharacteristic
35C2×C22⋊C4×C79C2212yes—
36#95×C79C2211yescharacteristic
37C23×D79C2311yescharacteristic
38C2×Dic158—22no—
39C2×Dic158—42no—
40C2×C22⋊D79—22no—
41C2×C22⋊D79—42no—
42C22×Dic79C2311yescharacteristic
43C22×Dic79C2312yes—
44C22×Dic79C2312yes—
45C22×Dic79C2311yescharacteristic
46C22×Dic79C2311yescharacteristic
47C4⋊Dic79—24no—
48C4⋊Dic79—22no—
49Dic79⋊C4—24no—
50Dic79⋊C4—42no—
51Dic79⋊C4—42no—
52C22⋊Dic79—22no—
53C22⋊Dic79—42no—
54(C2×D79)⋊C4—22no—
55(C2×D79)⋊C4—22no—
56(C2×D79)⋊C4—42no—
57(C2×D79)⋊C4—42no—
58C4×Dic79D414yes—
59C24×C79C2311yescharacteristic
60C22×C4×C79C2311yescharacteristic
61C22×C4×C79C2312yes—
62C22×C4×C79C2312yes—
63C22×C4×C79C2311yescharacteristic
64C4⋊C4×C79—22no—
65C4⋊C4×C79—42no—
66C22⋊C4×C79—22no—
67C22⋊C4×C79—42no—
68C23×C79—21no—
69C23×C79—21no—
70C23×C79—22no—
71C23×C79—22no—
72C23×C79—21no—
73C23×C79C2411yescharacteristic
74C22×D79—21no—
75C22×D79—21no—
76C22×D79—22no—
77C22×D79—22no—
78C22×D79—21no—
79C2×C4×C79—22no—
80C2×C4×C79—21no—
81C2×C4×C79—22no—
82C2×C4×C79—22no—
83C2×C4×C79—22no—
84C2×C4×C79—22no—
85C2×C4×C79—22no—
86C2×C4×C79—22no—
87C2×C4×C79—22no—
88C2×C4×C79C2×D412yes—
89C22⋊D79—44no—
90C2×Dic79—21no—
91C2×Dic79—22no—
92C2×Dic79—21no—
93C2×Dic79—21no—
94C2×Dic79—22no—
95C2×Dic79—22no—
96C2×Dic79—22no—
97C2×Dic79—22no—
98C2×Dic79—22no—
99C2×Dic79—22no—
100C2×Dic79—22no—
101C2×Dic79C2×D412yes—
102C2×Dic79C2×D412yes—
103Dic158—44no—
104C22×C79—41no—
105C22×C79—41no—
106C22×C79—41no—
107C22×C79—42no—
108C22×C79—42no—
109C22×C79C22×D411yescharacteristic
110C22×C79H(5,𝔽2)12yes—
111C22×C79H(5,𝔽2)11yescharacteristic
112C22×C792−1+412yes—
113C22×C792−1+411yescharacteristic
114C2×D79—41no—
115C2×D79—41no—
116C2×D79—41no—
117C2×D79—42no—
118C2×D79—42no—
119C4×C79—22no—
120C4×C79—42no—
121C4×C79—41no—
122C4×C79—42no—
123Dic79—22no—
124Dic79—22no—
125Dic79—41no—
126Dic79—42no—
127Dic79—42no—
128C2×C79—81no—
129C2×C79#53511yescharacteristic
130C2×C79#53611yescharacteristic
131C2×C79#53711yescharacteristic
132C2×C79#56212yes—
133C2×C79#56312yes—
134D79—81no—
135#2820—791nomaximal, Sylow
136C79#282011yescharacteristic, complemented, Sylow
137C2×#125—791no—
138C2×#124—791no—
139#399—791no—
140#399D7911yescharacteristic, complemented
141#397—791no—
142#397—791no—
143#396—792no—
144#396—792no—
145#395—792no—
146#394—792no—
147#382—791no—
148C22×Q8—791no—
149C22×D4—791no—
150#125—1584no—
151#124—1584no—
152C2×C4⋊C4—792no—
153C2×C4⋊C4—792no—
154C2×C4⋊C4—792no—
155C2×C4⋊C4—792no—
156C2×C4⋊C4—791no—
157C2×C4⋊C4C2×D7911yescharacteristic
158C2×C4⋊C4C2×D7912yes—
159C2×C22⋊C4—792no—
160C2×C22⋊C4—792no—
161C2×C22⋊C4—792no—
162C2×C22⋊C4—791no—
163C2×C22⋊C4—791no—
164C2×C22⋊C4—791no—
165C2×C22⋊C4C2×D7911yescharacteristic
166C2×C22⋊C4C2×D7912yes—
167C2×C42—791no—
168#95—792no—
169#95—791no—
170#95—792no—
171#95—792no—
172#95C2×D7911yescharacteristic
173C24—791no—
174C24C22×D7911yescharacteristic
175C2×Q8—3162no—
176C2×Q8—1582no—
177C2×D4—3162no—
178C2×D4—1582no—
179C22×C4—791no—
180C22×C4—791no—
181C22×C4—792no—
182C22×C4—792no—
183C22×C4—791no—
184C22×C4C22×D7912yes—
185C22×C4C22×D7911yescharacteristic
186C22×C4C22×D7912yes—
187C22×C4C22×D7911yescharacteristic
188C4⋊C4—22no—
189C4⋊C4—42no—
190C4⋊C4—3162no—
191C4⋊C4—3162no—
192C4⋊C4—1584no—
193C4⋊C4—1584no—
194C4⋊C4—1582no—
195C22⋊C4—22no—
196C22⋊C4—42no—
197C22⋊C4—3162no—
198C22⋊C4—3162no—
199C22⋊C4—3162no—
200C22⋊C4—1582no—
201C22⋊C4—1582no—
202C22⋊C4—1582no—
203C42—794no—
204C23—22no—
205C23—21no—
206C23—22no—
207C23—21no—
208C23—21no—
209C23—1582no—
210C23—1581no—
211C23—1582no—
212C23—1581no—
213C23—1581no—
214C23C23×D7911yescharacteristic
215Q8—3164no—
216D4—3164no—
217C2×C4—22no—
218C2×C4—22no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—21no—
225C2×C4—22no—
226C2×C4—792no—
227C2×C4—792no—
228C2×C4—1582no—
229C2×C4—1582no—
230C2×C4—1582no—
231C2×C4—1582no—
232C2×C4—1582no—
233C2×C4—1582no—
234C2×C4—1581no—
235C2×C4—1582no—
236C2×C4—1582no—
237C2×C4—1581no—
238C2×C4—1581no—
239C2×C4D4×D7912yes—
240C22—41no—
241C22—42no—
242C22—42no—
243C22—41no—
244C22—41no—
245C22—3161no—
246C22—3162no—
247C22—3162no—
248C22—3161no—
249C22—3161no—
250C22C2×D4×D7911yescharacteristic
251C22#1457920612yes—
252C22#1457920711yescharacteristic
253C22#1457920812yes—
254C22#1457920911yescharacteristic
255C4—22no—
256C4—42no—
257C4—41no—
258C4—42no—
259C4—3162no—
260C4—3162no—
261C4—3161no—
262C4—1582no—
263C4—1582no—
264C2—81no—
265C2—6321no—
266C2#1909912611yescharacteristic
267C2#1909913511yescharacteristic
268C2#1909914311yescharacteristic
269C2#1909931012yes—
270C2#1909931412yes—
subgroupG/H
center, FrattiniC23C23×D79
commutator, socle, cosocleC23×C79C24
Fitting#399×C79C2
prime radicalC22×C22⋊D79C22
hypercenter#399D79
hypocenterC79#2820
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C23 ◁ #399

Complements

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

NH ≅ G/Ntype
1. C2×#14579152C2semidirect
3. #19098498C2semidirect
4. #19098490C2semidirect
5. #19098488C2semidirect
6. #19098486C2semidirect
7. #19098485C2semidirect
8. #19098483C2semidirect
10. #19098427C2semidirect
11. #399×C79C2semidirect
136. C79#2820semidirect
140. #399D79semidirect