Finite Group Databasebeta

← #23769181

Subgroups — #23769181

Order 10112.

526 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 133 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×#14579146C211yesmaximal, characteristic
2C2×C4⋊C4×D79C211yesmaximal, characteristic, complemented
3#19098504C212yesmaximal, complemented
4#19098498C212yesmaximal, complemented
5#19098493C211yesmaximal, characteristic, complemented
6#19098490C211yesmaximal, characteristic, complemented
7#19098489C211yesmaximal, characteristic, complemented
8#19098441C212yesmaximal
9#19098434C212yesmaximal, complemented
10#19098425C211yesmaximal, characteristic, complemented
11#398×C79C211yesmaximal, characteristic, complemented
12C22×D316C2211yescharacteristic
13C22×C4×D79C2211yescharacteristic
14C22×C4×D79C2212yes—
15#14579146—24no—
16C2×C4⋊Dic79C2211yescharacteristic
17C2×Dic79⋊C4C2212yes—
18C2×Dic79⋊C4C2211yescharacteristic
19C2×Dic79⋊C4C2212yes—
20C4⋊C4×D79—24no—
21C2×(C2×D79)⋊C4C2212yes—
22C2×(C2×D79)⋊C4C2211yescharacteristic
23C2×(C2×D79)⋊C4C2211yescharacteristic
24C2×(C2×D79)⋊C4C2211yescharacteristic
25C2×(C2×D79)⋊C4C2212yes—
26C2×(C2×D79)⋊C4C2212yes—
27C79⋊#95C2211yescharacteristic
28C79⋊#95C2212yes—
29C79⋊#95C2212yes—
30C79⋊#95C2212yes—
31C79⋊#95C2212yes—
32C2×C4⋊C4×C79C2211yescharacteristic
33C2×C4⋊C4×C79C2211yescharacteristic
34C2×C4⋊C4×C79C2212yes—
35#95×C79C2211yescharacteristic
36#95×C79C2212yes—
37C23×D79C2311yescharacteristic
38C23×D79C2311yescharacteristic
39C2×D316—22no—
40C2×D316—24no—
41C22×Dic79C2311yescharacteristic
42C22×Dic79C2312yes—
43C22×Dic79C2312yes—
44C22×Dic79C2311yescharacteristic
45C2×C4×D79—24no—
46C2×C4×D79—24no—
47C2×C4×D79—42no—
48C2×C4×D79—42no—
49C2×C4×D79D414yes—
50C4⋊Dic79—22no—
51Dic79⋊C4—24no—
52Dic79⋊C4—22no—
53Dic79⋊C4—42no—
54(C2×D79)⋊C4—22no—
55(C2×D79)⋊C4—22no—
56(C2×D79)⋊C4—24no—
57(C2×D79)⋊C4—22no—
58(C2×D79)⋊C4—42no—
59(C2×D79)⋊C4—42no—
60C22×C4×C79C2312yes—
61C22×C4×C79C2311yescharacteristic
62C22×C4×C79C2312yes—
63C22×C4×C79C2311yescharacteristic
64C22×C4×C79C2311yescharacteristic
65C4⋊C4×C79—22no—
66C4⋊C4×C79—22no—
67C4⋊C4×C79—42no—
68C23×C79C2411yescharacteristic
69C22×D79—21no—
70C22×D79—21no—
71C22×D79—22no—
72C22×D79—21no—
73C22×D79—22no—
74C22×D79—21no—
75C22×D79—21no—
76C22×D79—22no—
77C22×D79C2×D412yes—
78C22×D79#4114yes—
79C2×C4×C79—22no—
80C2×C4×C79—21no—
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—21no—
88C2×C4×C79—22no—
89C2×C4×C79—21no—
90C2×C4×C79—22no—
91C2×C4×C79C2×D412yes—
92C2×Dic79—22no—
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—
102D316—44no—
103C4×D79—28no—
104C4×D79—48no—
105C22×C79C22×D411yescharacteristic
106C22×C79C2×#4112yes—
107C22×C79H(5,𝔽2)11yescharacteristic
108C22×C79H(5,𝔽2)11yescharacteristic
109C22×C792−1+412yes—
110C2×D79—22no—
111C2×D79—22no—
112C2×D79—24no—
113C2×D79—24no—
114C2×D79—41no—
115C2×D79—41no—
116C2×D79—41no—
117C2×D79—42no—
118C2×D79—42no—
119C2×D79#12314yes—
120C4×C79—22no—
121C4×C79—41no—
122C4×C79—41no—
123C4×C79—42no—
124C4×C79—42no—
125Dic79—22no—
126Dic79—42no—
127Dic79—41no—
128Dic79—42no—
129C2×C79C2×#12311yescharacteristic
130C2×C79#53511yescharacteristic
131C2×C79#53611yescharacteristic
132C2×C79#53912yes—
133C2×C79#53912yes—
134D79—24no—
135D79—81no—
136#2623—791nomaximal, Sylow
137C79#262311yescharacteristic, complemented, Sylow
138C2×#123—791no—
139C22×C4⋊C4—791no—
140#400—792no—
141#399—792no—
142#398—791no—
143#398D7911yescharacteristic, complemented
144#397—791no—
145#397—791no—
146#386—792no—
147#385—792no—
148#381—791no—
149C22×D4—791no—
150C23×C4—792no—
151C23×C4—791no—
152#123—1584no—
153C2×C4⋊C4—792no—
154C2×C4⋊C4—791no—
155C2×C4⋊C4—792no—
156C2×C4⋊C4—791no—
157C2×C4⋊C4—1584no—
158C2×C4⋊C4C2×D7911yescharacteristic
159C2×C4⋊C4C2×D7911yescharacteristic
160C2×C4⋊C4C2×D7912yes—
161C2×C22⋊C4—792no—
162C2×C22⋊C4—792no—
163C2×C22⋊C4—791no—
164C2×C22⋊C4—791no—
165C2×C22⋊C4—791no—
166C2×C22⋊C4—792no—
167#95—791no—
168#95—792no—
169#95—792no—
170#95—792no—
171#95—792no—
172#95C2×D7911yescharacteristic
173#95C2×D7912yes—
174C24—791no—
175C24—791no—
176C2×D4—1582no—
177C2×D4—1584no—
178C22×C4—3162no—
179C22×C4—3162no—
180C22×C4—791no—
181C22×C4—794no—
182C22×C4—792no—
183C22×C4—791no—
184C22×C4—792no—
185C22×C4—1584no—
186C22×C4—1584no—
187C22×C4C22×D7912yes—
188C22×C4C22×D7911yescharacteristic
189C22×C4C22×D7912yes—
190C22×C4C22×D7911yescharacteristic
191C22×C4C22×D7911yescharacteristic
192C4⋊C4—22no—
193C4⋊C4—22no—
194C4⋊C4—42no—
195C4⋊C4—3162no—
196C4⋊C4—1584no—
197C4⋊C4—1582no—
198C4⋊C4—1582no—
199C22⋊C4—3162no—
200C22⋊C4—3162no—
201C22⋊C4—1582no—
202C22⋊C4—1584no—
203C22⋊C4—1582no—
204C22⋊C4—1582no—
205C23—794no—
206C23—792no—
207C23—1582no—
208C23—1581no—
209C23—1581no—
210C23—1582no—
211C23—1581no—
212C23—1581no—
213C23—1581no—
214C23—1582no—
215C23C23×D7911yescharacteristic
216D4—3164no—
217C2×C4—22no—
218C2×C4—22no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—21no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—21no—
225C2×C4—22no—
226C2×C4—21no—
227C2×C4—22no—
228C2×C4—21no—
229C2×C4—3168no—
230C2×C4—792no—
231C2×C4—1588no—
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—1582no—
241C2×C4D4×D7912yes—
242C22—3161no—
243C22—3162no—
244C22—3162no—
245C22—3161no—
246C22—3161no—
247C22—794no—
248C22—1582no—
249C22—1584no—
250C22—1584no—
251C22—1582no—
252C22C2×D4×D7911yescharacteristic
253C22#41×D7912yes—
254C22#1457920611yescharacteristic
255C22#1457920711yescharacteristic
256C22#1457920912yes—
257C4—22no—
258C4—42no—
259C4—41no—
260C4—42no—
261C4—41no—
262C4—3161no—
263C4—3162no—
264C4—3162no—
265C4—1582no—
266C2—6321no—
267C2—1584no—
268C2#123×D7911yescharacteristic
269C2#1909912911yescharacteristic
270C2#1909913811yescharacteristic
271C2#1909915912yes—
272C2#1909916112yes—
subgroupG/H
center, FrattiniC23C23×D79
commutator, socle, cosocleC23×C79C24
Fitting#398×C79C2
prime radicalC22×D316C22
hypercenter#398D79
hypocenterC79#2623
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C4×D79C2semidirect
3. #19098504C2semidirect
4. #19098498C2semidirect
5. #19098493C2semidirect
6. #19098490C2semidirect
7. #19098489C2semidirect
9. #19098434C2semidirect
10. #19098425C2semidirect
11. #398×C79C2semidirect
137. C79#2623semidirect
143. #398D79semidirect