Finite Group Databasebeta

← #23769539

Subgroups — #23769539

Order 10112.

534 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 534 conjugacy classes of subgroups — too many to draw. Only its 137 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×#14579155C211yesmaximal, characteristic, complemented
2#19098486C212yesmaximal, complemented
3#19098482C211yesmaximal, characteristic, complemented
4#19098479C212yesmaximal, complemented
5#19098477C211yesmaximal, characteristic, complemented
6#19098474C211yesmaximal, characteristic, complemented
7#19098471C211yesmaximal, characteristic
8#19098463C212yesmaximal, complemented
9#19098457C212yesmaximal, complemented
10C4×C4⋊Dic79C211yesmaximal, characteristic, complemented
11C2×#124×C79C211yesmaximal, characteristic, complemented
12C22×C22⋊D79C2212yes—
13#14579155—24no—
14C2×C4⋊Dic79C2212yes—
15C2×Dic79⋊C4C2211yescharacteristic
16C2×Dic79⋊C4C2211yescharacteristic
17C2×Dic79⋊C4C2211yescharacteristic
18C2×Dic79⋊C4C2212yes—
19C2×C22⋊Dic79C2212yes—
20C2×C22⋊Dic79C2212yes—
21C2×C22⋊Dic79C2212yes—
22C2×(C2×D79)⋊C4C2211yescharacteristic
23C2×(C2×D79)⋊C4C2211yescharacteristic
24C2×(C2×D79)⋊C4C2211yescharacteristic
25C2×(C2×D79)⋊C4C2212yes—
26C2×C4×Dic79C2212yes—
27C79⋊#95C2211yescharacteristic
28C79⋊#95C2211yescharacteristic
29C79⋊#95C2212yes—
30C79⋊#95C2212yes—
31C22×Q8×C79C2211yescharacteristic
32C22×D4×C79C2211yescharacteristic
33#124×C79—24no—
34C2×C22⋊C4×C79C2212yes—
35C2×C22⋊C4×C79C2212yes—
36C2×C42×C79C2211yescharacteristic
37C23×D79C2311yescharacteristic
38C2×C22⋊D79—24no—
39C2×C22⋊D79—42no—
40C2×C22⋊D79—42no—
41C22×Dic79C2312yes—
42C22×Dic79C2311yescharacteristic
43C22×Dic79C2311yescharacteristic
44C22×Dic79C2311yescharacteristic
45C22×Dic79C2312yes—
46C4⋊Dic79—24no—
47Dic79⋊C4—22no—
48Dic79⋊C4—22no—
49Dic79⋊C4—22no—
50Dic79⋊C4—42no—
51C22⋊Dic79—24no—
52C22⋊Dic79—42no—
53C22⋊Dic79—42no—
54(C2×D79)⋊C4—22no—
55(C2×D79)⋊C4—22no—
56(C2×D79)⋊C4—22no—
57(C2×D79)⋊C4—42no—
58C4×Dic79—42no—
59C24×C79C2312yes—
60C2×Q8×C79—22no—
61C2×Q8×C79—42no—
62C2×D4×C79—22no—
63C2×D4×C79—42no—
64C22×C4×C79C2312yes—
65C22×C4×C79C2311yescharacteristic
66C22×C4×C79C2311yescharacteristic
67C22×C4×C79C2311yescharacteristic
68C22⋊C4×C79—24no—
69C22⋊C4×C79—24no—
70C42×C79D414yescomplemented
71C23×C79—22no—
72C23×C79—22no—
73C23×C79—22no—
74C23×C79—22no—
75C23×C79—22no—
76C23×C79—22no—
77C23×C79—22no—
78C23×C79C2411yescharacteristic
79C22×D79—21no—
80C22×D79—22no—
81C22×D79—22no—
82C22×D79—21no—
83C22×D79—21no—
84Q8×C79—44no—
85D4×C79—44no—
86C2×C4×C79—22no—
87C2×C4×C79—21no—
88C2×C4×C79—22no—
89C2×C4×C79—21no—
90C2×C4×C79—22no—
91C2×C4×C79—22no—
92C2×C4×C79—22no—
93C2×C4×C79C2×D412yes—
94C2×C4×C79C2×D412yes—
95C2×C4×C79C2×D412yes—
96C22⋊D79—48no—
97C2×Dic79—22no—
98C2×Dic79—22no—
99C2×Dic79—21no—
100C2×Dic79—21no—
101C2×Dic79—21no—
102C2×Dic79—22no—
103C2×Dic79—22no—
104C2×Dic79—22no—
105C2×Dic79—22no—
106C2×Dic79—21no—
107C2×Dic79—22no—
108C2×Dic79—21no—
109C2×Dic79#4114yes—
110C22×C79—42no—
111C22×C79—42no—
112C22×C79—42no—
113C22×C79—42no—
114C22×C79—42no—
115C22×C79—42no—
116C22×C79—42no—
117C22×C79C22×D411yescharacteristic
118C22×C79C2×#4112yes—
119C22×C79H(5,𝔽2)12yes—
120C22×C79H(5,𝔽2)11yescharacteristic
121C22×C792−1+411yescharacteristic
122C2×D79—41no—
123C2×D79—41no—
124C2×D79—41no—
125C2×D79—42no—
126C2×D79—42no—
127C4×C79—22no—
128C4×C79—22no—
129C4×C79—22no—
130C4×C79—42no—
131Dic79—24no—
132Dic79—41no—
133Dic79—41no—
134Dic79—41no—
135Dic79—42no—
136C2×C79—82no—
137C2×C79#53211yescharacteristic
138C2×C79#53511yescharacteristic
139C2×C79#53711yescharacteristic
140C2×C79#53812yes—
141C2×C79#54212yes—
142D79—81no—
143#2662—791nomaximal, Sylow
144C79#266211yescharacteristic, complemented, Sylow
145C2×#126—791no—
146C2×#124D7911yescharacteristic, complemented
147#396—792no—
148#395—791no—
149#394—791no—
150#394—792no—
151#393—791no—
152#392—791no—
153#390—792no—
154#388—792no—
155C4×C4⋊C4—791no—
156C22×Q8C2×D7911yescharacteristic
157C22×D4—792no—
158C22×D4C2×D7911yescharacteristic
159#126—1584no—
160#124—24no—
161C2×C4⋊C4—792no—
162C2×C4⋊C4—791no—
163C2×C4⋊C4—791no—
164C2×C4⋊C4—791no—
165C2×C4⋊C4—792no—
166C2×C22⋊C4—792no—
167C2×C22⋊C4—792no—
168C2×C22⋊C4—792no—
169C2×C22⋊C4—792no—
170C2×C22⋊C4—791no—
171C2×C22⋊C4—791no—
172C2×C22⋊C4—791no—
173C2×C22⋊C4C2×D7912yes—
174C2×C22⋊C4C2×D7912yes—
175C2×C42—792no—
176C2×C42C2×D7911yescharacteristic
177#95—791no—
178#95—791no—
179#95—792no—
180#95—792no—
181C24—791no—
182C24C22×D7912yes—
183C2×Q8—22no—
184C2×Q8—42no—
185C2×D4—22no—
186C2×D4—42no—
187C2×D4—3162no—
188C2×D4—3162no—
189C2×D4—1584no—
190C22×C4—792no—
191C22×C4—792no—
192C22×C4—791no—
193C22×C4—791no—
194C22×C4—791no—
195C22×C4C22×D7912yes—
196C22×C4C22×D7911yescharacteristic
197C22×C4C22×D7911yescharacteristic
198C22×C4C22×D7911yescharacteristic
199C4⋊C4—3162no—
200C4⋊C4—1584no—
201C4⋊C4—1582no—
202C4⋊C4—1582no—
203C4⋊C4—1582no—
204C22⋊C4—24no—
205C22⋊C4—24no—
206C22⋊C4—3162no—
207C22⋊C4—3162no—
208C22⋊C4—3162no—
209C22⋊C4—1584no—
210C22⋊C4—1582no—
211C22⋊C4—1582no—
212C22⋊C4—1582no—
213C42—3162no—
214C42C22⋊D7914yescomplemented
215C23—22no—
216C23—22no—
217C23—22no—
218C23—22no—
219C23—22no—
220C23—22no—
221C23—22no—
222C23—1582no—
223C23—1582no—
224C23—1581no—
225C23—1581no—
226C23—1581no—
227C23C23×D7911yescharacteristic
228Q8—44no—
229D4—44no—
230D4—3168no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—22no—
238C2×C4—794no—
239C2×C4—1582no—
240C2×C4—1582no—
241C2×C4—1582no—
242C2×C4—1582no—
243C2×C4—1582no—
244C2×C4—1581no—
245C2×C4—1581no—
246C2×C4—1581no—
247C2×C4—1581no—
248C2×C4—1581no—
249C2×C4—1582no—
250C2×C4—1582no—
251C2×C4C2×C22⋊D7912yes—
252C2×C4C2×C22⋊D7912yes—
253C2×C4C2×C22⋊D7912yes—
254C22—42no—
255C22—42no—
256C22—42no—
257C22—42no—
258C22—42no—
259C22—42no—
260C22—42no—
261C22—3161no—
262C22—3162no—
263C22—3162no—
264C22—3161no—
265C22—3161no—
266C22C22×C22⋊D7911yescharacteristic
267C22#41×D7912yes—
268C22#1457920612yes—
269C22#1457920711yescharacteristic
270C22#1457920811yescharacteristic
271C4—22no—
272C4—22no—
273C4—22no—
274C4—42no—
275C4—3161no—
276C4—3162no—
277C4—3161no—
278C4—3161no—
279C4—1584no—
280C2—82no—
281C2—6321no—
282C2#1909910911yescharacteristic
283C2#1909913011yescharacteristic
284C2#1909914111yescharacteristic
285C2#1909914712yes—
286C2#1909917712yes—
subgroupG/H
center, FrattiniC23C23×D79
commutator, socle, cosocleC23×C79C24
FittingC2×#124×C79C2
prime radical#19098471C2
hypercenterC2×#124D79
hypocenterC79#2662
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
1. C2×#14579155C2semidirect
2. #19098486C2semidirect
3. #19098482C2semidirect
4. #19098479C2semidirect
5. #19098477C2semidirect
6. #19098474C2semidirect
8. #19098463C2semidirect
9. #19098457C2semidirect
10. C4×C4⋊Dic79C2semidirect
11. C2×#124×C79C2semidirect
70. C42×C79D4semidirect
144. C79#2662semidirect
146. C2×#124D79semidirect
214. C42C22⋊D79semidirect