Finite Group Databasebeta

← #23774174

Subgroups — #23774174

Order 10112.

416 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 121 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×#14579141C211yesmaximal, characteristic
2C22⋊Q8×D79C211yesmaximal, characteristic
3#19098900C212yesmaximal, complemented
4#19098898C211yesmaximal, characteristic, complemented
5#19098805C212yesmaximal, complemented
6#19098803C212yesmaximal, complemented
7#19098721C211yesmaximal, characteristic, complemented
8#19098720C212yesmaximal, complemented
9#19098718C211yesmaximal, characteristic, complemented
10C22⋊C8×D79C211yesmaximal, characteristic
11#484×C79C211yesmaximal, characteristic, complemented
12C22×Dic158C2211yescharacteristic
13C2×Q8×D79C2211yescharacteristic
14C22×C4×D79C2211yescharacteristic
15C2×Dic316C2212yescomplemented
16C2×#11929614C2212yescomplemented
17C2×C8×D79C2212yes—
18#14579141—21no—
19#14579141—21no—
20#14579141C2212yes—
21#14579141C2211yescharacteristic
22#14579141C2212yes—
23#14579140C2211yescharacteristic
24#14579139—21no—
25#14579138—21no—
26#14579137C2211yescharacteristic
27C2×C4⋊Dic79—21no—
28C4⋊C4×D79—21no—
29C4⋊C4×D79C2211yescharacteristic
30C2×(C2×D79)⋊C4—21no—
31C22⋊C4×D79—21no—
32#14579094C2212yescomplemented
33#14579086C2212yescomplemented
34#14579084C2212yescomplemented
35#14579084C2212yescomplemented
36C22⋊(C79⋊C8)C2211yescharacteristic
37(C2×D79)⋊C8C2212yes—
38C22⋊Q8×C79C2211yescharacteristic
39C2×C4⋊C4×C79C2211yescharacteristic
40#107×C79C2212yescomplemented
41#103×C79C2212yescomplemented
42C22⋊C8×C79C2211yescharacteristic
43C23×D79D411yescharacteristic
44C2×Dic158—21no—
45C2×Dic158—21no—
46C2×Dic158—42no—
47C2×Dic158C2311yescharacteristic
48C2×Dic158C2312yes—
49Q8×D79—42no—
50C22×Dic79—21no—
51C22×Dic79D411yescharacteristic
52C2×C4×D79—21no—
53C2×C4×D79—21no—
54C2×C4×D79—42no—
55C2×C4×D79D411yescharacteristic
56C2×C4×D79D411yescharacteristic
57C2×C4×D79C2311yescharacteristic
58C2×C4×D79C2311yescharacteristic
59Dic316—42no—
60#11929614—42no—
61C2×C79⋊C8C2312yes—
62C8×D79—42no—
63C4⋊Dic79—21no—
64C4⋊Dic79—22no—
65C4⋊Dic79—22no—
66C4⋊Dic79C2311yescharacteristic
67Dic79⋊C4—21no—
68Dic79⋊C4—21no—
69Dic79⋊C4—21no—
70C22⋊Dic79—21no—
71(C2×D79)⋊C4—21no—
72(C2×D79)⋊C4—21no—
73(C2×D79)⋊C4—22no—
74(C2×D79)⋊C4—22no—
75C2×Q8×C79C2311yescharacteristic
76C22×C4×C79—21no—
77C22×C4×C79C2311yescharacteristic
78C2×C8×C79C2312yes—
79C4⋊C4×C79—21no—
80C4⋊C4×C79—21no—
81C4⋊C4×C79C2312yes—
82C4⋊C4×C79C2311yescharacteristic
83C22⋊C4×C79—21no—
84C23×C79C2×D411yescharacteristic
85C22×D79—41no—
86C22×D79—41no—
87C22×D79Q1614yescomplemented
88C22×D79C2×D411yescharacteristic
89C22×D79C2×D411yescharacteristic
90Q8×C79—22no—
91C2×C4×C79—22no—
92C2×C4×C79—22no—
93C2×C4×C79—21no—
94C2×C4×C79—21no—
95C2×C4×C79—42no—
96C2×C4×C79C2×D411yescharacteristic
97C2×C4×C79C2411yescharacteristic
98C2×Dic79—22no—
99C2×Dic79—21no—
100C2×Dic79—21no—
101C2×Dic79—41no—
102C2×Dic79—42no—
103C2×Dic79C2×D411yescharacteristic
104C2×Dic79C2×D411yescharacteristic
105C4×D79—22no—
106C4×D79—22no—
107C4×D79—41no—
108C4×D79—41no—
109C4×D79—42no—
110C4×D79—42no—
111Dic158—22no—
112Dic158—22no—
113Dic158—22no—
114Dic158—42no—
115Dic158—42no—
116C8×C79—22no—
117C79⋊C8—22no—
118C22×C79—21no—
119C22×C79—21no—
120C22×C79C2×Q1612yes—
121C22×C79C22×D411yescharacteristic
122C2×D79—21no—
123C2×D79—21no—
124C2×D79—21no—
125C2×D79—21no—
126C2×D79—44no—
127C2×D79C2×Q1612yes—
128C2×D79C2×Q1612yes—
129C4×C79—21no—
130C4×C79—41no—
131C4×C79—42no—
132C4×C79—41no—
133C4×C79H(5,𝔽2)12yes—
134Dic79—21no—
135Dic79—21no—
136Dic79—41no—
137Dic79—42no—
138Dic79—41no—
139C2×C79—22no—
140C2×C79#53411yescharacteristic
141C2×C79C22×Q1611yescharacteristic
142C2×C79#57511yescharacteristic
143D79—22no—
144D79—22no—
145#3189—791nomaximal, Sylow
146C79#318911yescharacteristic, complemented, Sylow
147C2×C22⋊Q8—791no—
148C2×C22⋊Q8—791no—
149#484—791no—
150#484—792no—
151#484D7911yescharacteristic, complemented
152#467—792no—
153#467—792no—
154#451—791no—
155#451—792no—
156#451—791no—
157C2×C22⋊C8—791no—
158C22×Q8—791no—
159C22×Q8—791no—
160C23×C4—791no—
161C2×Q16—792no—
162C2×Q16—792no—
163C22×C8—792no—
164C22⋊Q8—791no—
165C22⋊Q8—791no—
166C22⋊Q8—792no—
167C22⋊Q8—791no—
168C22⋊Q8—792no—
169C22⋊Q8—1581no—
170C22⋊Q8—1581no—
171C22⋊Q8—1581no—
172C22⋊Q8—1581no—
173C22⋊Q8C2×D7911yescharacteristic
174C2×C4⋊C4—791no—
175C2×C4⋊C4—1581no—
176C2×C4⋊C4—1581no—
177C2×C4⋊C4C2×D7911yescharacteristic
178C2×C22⋊C4—1581no—
179C2×C22⋊C4—1581no—
180#107—792no—
181#107C2×D7912yescomplemented
182#103—792no—
183#103—792no—
184#103—792no—
185#103C2×D7912yescomplemented
186C22⋊C8—791no—
187C22⋊C8—792no—
188C22⋊C8C2×D7911yescharacteristic
189C24—791no—
190C2×Q8—3162no—
191C2×Q8—3162no—
192C2×Q8—791no—
193C2×Q8—792no—
194C2×Q8—1581no—
195C2×Q8—1581no—
196C2×Q8C22×D7911yescharacteristic
197C22×C4—21no—
198C22×C4—3162no—
199C22×C4—791no—
200C22×C4—791no—
201C22×C4—791no—
202C22×C4—791no—
203C22×C4—791no—
204C22×C4—1581no—
205C22×C4—1581no—
206C22×C4—1581no—
207C22×C4C22×D7911yescharacteristic
208Q16—3162no—
209Q16—3162no—
210C2×C8—3162no—
211C2×C8—792no—
212C2×C8C22×D7912yes—
213C4⋊C4—21no—
214C4⋊C4—21no—
215C4⋊C4—791no—
216C4⋊C4—1581no—
217C4⋊C4—1581no—
218C4⋊C4—1581no—
219C4⋊C4—1582no—
220C4⋊C4—1582no—
221C4⋊C4—1581no—
222C4⋊C4C22×D7911yescharacteristic
223C4⋊C4C22×D7912yes—
224C22⋊C4—21no—
225C22⋊C4—1581no—
226C22⋊C4—1581no—
227C22⋊C4—1582no—
228C22⋊C4—1582no—
229C22⋊C4—1581no—
230C23—3161no—
231C23—3161no—
232C23—794no—
233C23—791no—
234C23—791no—
235C23D4×D7911yescharacteristic
236Q8—22no—
237Q8—3162no—
238Q8—3162no—
239Q8—1582no—
240Q8—1582no—
241Q8—1582no—
242C2×C4—22no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—22no—
246C2×C4—42no—
247C2×C4—3161no—
248C2×C4—3161no—
249C2×C4—3162no—
250C2×C4—3162no—
251C2×C4—3162no—
252C2×C4—3161no—
253C2×C4—791no—
254C2×C4—791no—
255C2×C4—1581no—
256C2×C4—1582no—
257C2×C4—1581no—
258C2×C4—1582no—
259C2×C4—1582no—
260C2×C4D4×D7911yescharacteristic
261C2×C4C23×D7911yescharacteristic
262C8—22no—
263C8—1582no—
264C22—21no—
265C22—21no—
266C22—3164no—
267C22—792no—
268C22—792no—
269C22—1581no—
270C22—1581no—
271C22—1581no—
272C22—1581no—
273C22Q16×D7912yes—
274C22C2×D4×D7911yescharacteristic
275C4—21no—
276C4—42no—
277C4—41no—
278C4—41no—
279C4—3161no—
280C4—3161no—
281C4—3162no—
282C4—1581no—
283C4—1581no—
284C4#1457920712yes—
285C2—22no—
286C2—1582no—
287C2—1582no—
288C2#1909912411yescharacteristic
289C2C2×Q16×D7911yescharacteristic
290C2#1909935911yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#484×C79C2
socleC22×C79C22×D4
prime radicalC23×D79D4
hypercenter#484D79
hypocenterC79#3189
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
3. #19098900C2semidirect
4. #19098898C2semidirect
5. #19098805C2semidirect
6. #19098803C2semidirect
7. #19098721C2semidirect
8. #19098720C2semidirect
9. #19098718C2semidirect
11. #484×C79C2semidirect
15. C2×Dic316C22semidirect
16. C2×#11929614C22semidirect
32. #14579094C22semidirect
33. #14579086C22semidirect
34. #14579084C22semidirect
35. #14579084C22semidirect
40. #107×C79C22semidirect
41. #103×C79C22semidirect
87. C22×D79Q16semidirect
146. C79#3189semidirect
151. #484D79semidirect
181. #107C2×D79semidirect
185. #103C2×D79semidirect