Finite Group Databasebeta

← #23769274

Subgroups — #23769274

Order 10112.

512 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 131 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×(C22⋊D79)⋊C4C211yesmaximal, characteristic
3#19098498C211yesmaximal, characteristic, complemented
4#19098496C212yesmaximal, complemented
5#19098490C211yesmaximal, characteristic, complemented
6#19098488C211yesmaximal, characteristic, complemented
7#19098479C212yesmaximal
8#19098435C212yesmaximal, complemented
9#19098434C212yesmaximal, complemented
10#19098430C211yesmaximal, characteristic, complemented
11#399×C79C211yesmaximal, characteristic, complemented
12C22×C22⋊D79C2211yescharacteristic
13C23×Dic79C2211yescharacteristic
14C22×C4×D79C2211yescharacteristic
15#14579152—24no—
16(C22⋊D79)⋊C4—24no—
17C2×C4⋊Dic79C2212yes—
18C2×C4⋊Dic79C2211yescharacteristic
19C2×Dic79⋊C4C2212yes—
20C2×Dic79⋊C4C2211yescharacteristic
21C2×Dic79⋊C4C2212yes—
22C2×C22⋊Dic79C2212yes—
23C2×(C2×D79)⋊C4C2212yes—
24C2×(C2×D79)⋊C4C2211yescharacteristic
25C2×(C2×D79)⋊C4C2212yes—
26C2×C4×Dic79C2211yescharacteristic
27C79⋊#95C2212yes—
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×C22⋊D79—22no—
39C2×C22⋊D79—22no—
40C2×C22⋊D79—22no—
41C22×Dic79—22no—
42C22×Dic79—42no—
43C22×Dic79C2312yes—
44C22×Dic79C2312yes—
45C22×Dic79C2311yescharacteristic
46C22×Dic79C2311yescharacteristic
47C22×Dic79C2311yescharacteristic
48C2×C4×D79—22no—
49C2×C4×D79—42no—
50C4⋊Dic79—24no—
51C4⋊Dic79—22no—
52Dic79⋊C4—22no—
53Dic79⋊C4—24no—
54Dic79⋊C4—42no—
55C22⋊Dic79—24no—
56(C2×D79)⋊C4—24no—
57(C2×D79)⋊C4—22no—
58(C2×D79)⋊C4—42no—
59C4×Dic79D414yes—
60C24×C79C2311yescharacteristic
61C22×C4×C79C2312yes—
62C22×C4×C79C2311yescharacteristic
63C22×C4×C79C2312yes—
64C22×C4×C79C2311yescharacteristic
65C4⋊C4×C79—22no—
66C4⋊C4×C79—42no—
67C22⋊C4×C79—22no—
68C22⋊C4×C79—42no—
69C23×C79—21no—
70C23×C79—21no—
71C23×C79—22no—
72C23×C79—22no—
73C23×C79#4112yes—
74C23×C79C2411yescharacteristic
75C22×D79—21no—
76C22×D79—21no—
77C22×D79—22no—
78C22×D79—22no—
79C22×D79#4112yes—
80C2×C4×C79—22no—
81C2×C4×C79—22no—
82C2×C4×C79—21no—
83C2×C4×C79—22no—
84C2×C4×C79—22no—
85C2×C4×C79—22no—
86C2×C4×C79—22no—
87C2×C4×C79—22no—
88C2×C4×C79—22no—
89C2×C4×C79C2×D412yes—
90C22⋊D79—28no—
91C2×Dic79—21no—
92C2×Dic79—21no—
93C2×Dic79—22no—
94C2×Dic79—21no—
95C2×Dic79—22no—
96C2×Dic79—22no—
97C2×Dic79—22no—
98C2×Dic79—22no—
99C2×Dic79—22no—
100C2×Dic79—22no—
101C2×Dic79—22no—
102C2×Dic79—44no—
103C2×Dic79C2×D412yes—
104C2×Dic79C2×D412yes—
105C4×D79—44no—
106C22×C79—22no—
107C22×C79—24no—
108C22×C79—41no—
109C22×C79—41no—
110C22×C79—42no—
111C22×C79C22×D411yescharacteristic
112C22×C79C2×#4111yescharacteristic
113C22×C79C2×#4111yescharacteristic
114C22×C79H(5,𝔽2)12yes—
115C22×C792−1+412yes—
116C2×D79—22no—
117C2×D79—24no—
118C2×D79—41no—
119C2×D79—41no—
120C2×D79—42no—
121C4×C79—22no—
122C4×C79—42no—
123C4×C79—41no—
124C4×C79—42no—
125Dic79—22no—
126Dic79—22no—
127Dic79—42no—
128Dic79—41no—
129Dic79—42no—
130C2×C79—42no—
131C2×C79#52511yescharacteristic
132C2×C79#53511yescharacteristic
133C2×C79#53611yescharacteristic
134C2×C79#53912yes—
135C2×C79#53912yes—
136D79—42no—
137#2633—791nomaximal, Sylow
138C79#263311yescharacteristic, complemented, Sylow
139C2×#125—791no—
140C2×C4×D4—791no—
141#399—791no—
142#399D7911yescharacteristic, complemented
143#398—792no—
144#397—791no—
145#397—791no—
146#394—792no—
147#385—792no—
148#385—792no—
149#383—791no—
150C22×D4—791no—
151C23×C4—791no—
152C23×C4—791no—
153#125—1584no—
154C4×D4—1584no—
155C2×C4⋊C4—792no—
156C2×C4⋊C4—791no—
157C2×C4⋊C4—792no—
158C2×C4⋊C4—792no—
159C2×C4⋊C4—791no—
160C2×C4⋊C4C2×D7911yescharacteristic
161C2×C4⋊C4C2×D7912yes—
162C2×C22⋊C4—792no—
163C2×C22⋊C4—792no—
164C2×C22⋊C4—791no—
165C2×C22⋊C4—792no—
166C2×C22⋊C4C2×D7911yescharacteristic
167C2×C22⋊C4C2×D7912yes—
168C2×C42—791no—
169#95—792no—
170#95—792no—
171#95—791no—
172#95—792no—
173#95—792no—
174#95C2×D7911yescharacteristic
175C24—791no—
176C24C22×D7911yescharacteristic
177C2×D4—1582no—
178C2×D4—1582no—
179C2×D4—1582no—
180C22×C4—3162no—
181C22×C4—3162no—
182C22×C4—791no—
183C22×C4—791no—
184C22×C4—792no—
185C22×C4—792no—
186C22×C4—791no—
187C22×C4—1582no—
188C22×C4—1582no—
189C22×C4C22×D7912yes—
190C22×C4C22×D7911yescharacteristic
191C22×C4C22×D7912yes—
192C22×C4C22×D7911yescharacteristic
193C4⋊C4—22no—
194C4⋊C4—42no—
195C4⋊C4—3162no—
196C4⋊C4—1582no—
197C4⋊C4—1584no—
198C4⋊C4—1584no—
199C4⋊C4—1582no—
200C22⋊C4—22no—
201C22⋊C4—42no—
202C22⋊C4—3162no—
203C22⋊C4—1584no—
204C22⋊C4—1584no—
205C22⋊C4—1582no—
206C42—794no—
207C23—21no—
208C23—22no—
209C23—22no—
210C23—21no—
211C23—792no—
212C23—1581no—
213C23—1582no—
214C23—1582no—
215C23—1581no—
216C23#1192962512yes—
217C23C23×D7911yescharacteristic
218D4—1588no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—21no—
227C2×C4—22no—
228C2×C4—3164no—
229C2×C4—3164no—
230C2×C4—792no—
231C2×C4—792no—
232C2×C4—1582no—
233C2×C4—1582no—
234C2×C4—1582no—
235C2×C4—1582no—
236C2×C4—1582no—
237C2×C4—1582no—
238C2×C4—1581no—
239C2×C4—1582no—
240C2×C4—1581no—
241C2×C4—1581no—
242C2×C4—1582no—
243C2×C4D4×D7912yes—
244C22—24no—
245C22—22no—
246C22—42no—
247C22—41no—
248C22—41no—
249C22—3162no—
250C22—3161no—
251C22—3161no—
252C22—1584no—
253C22—1582no—
254C22C2×D4×D7911yescharacteristic
255C22#41×D7911yescharacteristic
256C22C2×#1192962511yescharacteristic
257C22#1457920612yes—
258C22#1457920812yes—
259C4—22no—
260C4—42no—
261C4—41no—
262C4—42no—
263C4—3162no—
264C4—3162no—
265C4—3161no—
266C4—1582no—
267C4—1582no—
268C2—42no—
269C2—3162no—
270C2#1909907611yescharacteristic
271C2#1909912611yescharacteristic
272C2#1909913511yescharacteristic
273C2#1909915612yes—
274C2#1909916212yes—
subgroupG/H
center, FrattiniC23C23×D79
commutator, socle, cosocleC23×C79C24
Fitting#399×C79C2
prime radicalC22×C22⋊D79C22
hypercenter#399D79
hypocenterC79#2633
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. #19098496C2semidirect
5. #19098490C2semidirect
6. #19098488C2semidirect
8. #19098435C2semidirect
9. #19098434C2semidirect
10. #19098430C2semidirect
11. #399×C79C2semidirect
138. C79#2633semidirect
142. #399D79semidirect