Finite Group Databasebeta

← #23766639

Subgroups — #23766639

Order 10112.

696 conjugacy classes of subgroups; only the 155 normal subgroups are shown.

normal subgroups only

This group has 696 conjugacy classes of subgroups — too many to draw. Only its 155 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×D4×Dic79C211yesmaximal, characteristic, complemented
2C2×(C22⋊D79)⋊C4C212yesmaximal, complemented
3C2×#14579119C211yesmaximal, characteristic, complemented
4#19098493C211yesmaximal, characteristic, complemented
5#19098490C211yesmaximal, characteristic, complemented
6#19098486C212yesmaximal, complemented
7#19098478C212yesmaximal, complemented
8#19098471C211yesmaximal, characteristic
9#19098414C211yesmaximal, characteristic, complemented
10C22⋊C4×Dic79C212yesmaximal, complemented
11#394×C79C211yesmaximal, characteristic, complemented
12C22×C22⋊D79C2212yes—
13C23×Dic79C2212yes—
14C22×C4×D79C2211yescharacteristic
15D4×Dic79—24no—
16(C22⋊D79)⋊C4—28no—
17#14579119—24no—
18C2×C4⋊Dic79C2211yescharacteristic
19C2×C4⋊Dic79C2211yescharacteristic
20C2×Dic79⋊C4C2212yes—
21C2×Dic79⋊C4C2212yes—
22C2×C22⋊Dic79C2212yes—
23C2×C22⋊Dic79C2212yes—
24C2×(C2×D79)⋊C4C2211yescharacteristic
25C2×(C2×D79)⋊C4C2211yescharacteristic
26C2×(C2×D79)⋊C4C2212yes—
27C2×C4×Dic79C2211yescharacteristic
28C2×C4×Dic79C2212yes—
29C2×C4×Dic79C2211yescharacteristic
30C79⋊#95C2212yes—
31C79⋊#95C2212yes—
32C79⋊#95C2211yescharacteristic
33C22×D4×C79C2211yescharacteristic
34C2×C4⋊C4×C79C2211yescharacteristic
35C2×C22⋊C4×C79C2212yes—
36C2×C22⋊C4×C79C2212yes—
37#95×C79C2211yescharacteristic
38C23×D79C2311yescharacteristic
39C2×C22⋊D79—24no—
40C2×C22⋊D79—24no—
41C2×C22⋊D79—24no—
42C22×Dic79—24no—
43C22×Dic79—24no—
44C22×Dic79—24no—
45C22×Dic79C2311yescharacteristic
46C22×Dic79C2312yes—
47C22×Dic79C2311yescharacteristic
48C22×Dic79C2312yes—
49C22×Dic79C2311yescharacteristic
50C2×C4×D79—22no—
51C2×C4×D79—22no—
52C2×C4×D79D414yescomplemented
53C4⋊Dic79—22no—
54C4⋊Dic79—22no—
55Dic79⋊C4—24no—
56Dic79⋊C4—24no—
57C22⋊Dic79—24no—
58C22⋊Dic79—24no—
59(C2×D79)⋊C4—22no—
60(C2×D79)⋊C4—24no—
61(C2×D79)⋊C4—22no—
62C4×Dic79—22no—
63C4×Dic79—24no—
64C4×Dic79D414yescomplemented
65C24×C79C2312yes—
66C2×D4×C79—24no—
67C2×D4×C79—22no—
68C22×C4×C79C2312yes—
69C22×C4×C79C2311yescharacteristic
70C22×C4×C79C2311yescharacteristic
71C22×C4×C79C2311yescharacteristic
72C4⋊C4×C79—22no—
73C22⋊C4×C79—24no—
74C22⋊C4×C79—24no—
75C23×C79—22no—
76C23×C79—22no—
77C23×C79—22no—
78C23×C79—22no—
79C23×C79—22no—
80C23×C79—22no—
81C23×C79#4114yes—
82C23×C79C2411yescharacteristic
83C22×D79—21no—
84C22×D79—21no—
85C22×D79—22no—
86C22×D79—22no—
87C22×D79C2×D412yes—
88D4×C79—28no—
89C2×C4×C79—21no—
90C2×C4×C79—21no—
91C2×C4×C79—22no—
92C2×C4×C79—22no—
93C2×C4×C79—21no—
94C2×C4×C79—22no—
95C2×C4×C79—22no—
96C2×C4×C79—22no—
97C2×C4×C79C2×D412yes—
98C2×C4×C79C2×D412yes—
99C22⋊D79—216no—
100C2×Dic79—22no—
101C2×Dic79—22no—
102C2×Dic79—22no—
103C2×Dic79—21no—
104C2×Dic79—22no—
105C2×Dic79—22no—
106C2×Dic79—22no—
107C2×Dic79—22no—
108C2×Dic79—48no—
109C2×Dic79C2×D412yes—
110C2×Dic79C2×D412yes—
111C2×Dic79C2×D412yes—
112C2×Dic79#4114yes—
113C2×Dic79#4112yes—
114C4×D79—28no—
115C22×C79—24no—
116C22×C79—24no—
117C22×C79—24no—
118C22×C79—42no—
119C22×C79—42no—
120C22×C79—42no—
121C22×C79—42no—
122C22×C79C22×D411yescharacteristic
123C22×C79C22×D411yescharacteristic
124C22×C79C2×#4111yescharacteristic
125C22×C79C2×#4112yes—
126C22×C79C2×#4112yes—
127C2×D79—22no—
128C2×D79—24no—
129C2×D79—41no—
130C2×D79—42no—
131C2×D79—41no—
132C4×C79—22no—
133C4×C79—22no—
134C4×C79—41no—
135C4×C79—42no—
136Dic79—24no—
137Dic79—22no—
138Dic79—42no—
139Dic79—41no—
140Dic79#12114yes—
141C2×C79—44no—
142C2×C79C2×#12111yescharacteristic
143C2×C79#52511yescharacteristic
144C2×C79#52512yes—
145C2×C79#52912yes—
146C2×C79#53211yescharacteristic
147D79—42no—
148#2392—791nomaximal, Sylow
149C79#239211yescharacteristic, complemented, Sylow
150C2×C4×D4—791no—
151C2×C4×D4—792no—
152C2×#117—791no—
153#398—791no—
154#397—791no—
155#396—792no—
156#394—792no—
157#394D7911yescharacteristic, complemented
158#392—791no—
159C4×C4⋊C4—791no—
160C4×C22⋊C4—792no—
161C22×D4—792no—
162C22×D4C2×D7911yescharacteristic
163C23×C4—791no—
164C23×C4—792no—
165C4×D4—1584no—
166C4×D4—1588no—
167#117—1584no—
168C2×C4⋊C4—791no—
169C2×C4⋊C4—792no—
170C2×C4⋊C4—791no—
171C2×C4⋊C4—792no—
172C2×C4⋊C4C2×D7911yescharacteristic
173C2×C22⋊C4—792no—
174C2×C22⋊C4—792no—
175C2×C22⋊C4—791no—
176C2×C22⋊C4—791no—
177C2×C22⋊C4—792no—
178C2×C22⋊C4C2×D7912yes—
179C2×C22⋊C4C2×D7912yes—
180C2×C42—791no—
181C2×C42—791no—
182C2×C42—792no—
183#95—792no—
184#95—792no—
185#95—791no—
186#95C2×D7911yescharacteristic
187C24—791no—
188C24C22×D7912yes—
189C2×D4—24no—
190C2×D4—22no—
191C2×D4—1584no—
192C2×D4—1584no—
193C2×D4—1584no—
194C22×C4—791no—
195C22×C4—792no—
196C22×C4—791no—
197C22×C4—794no—
198C22×C4—791no—
199C22×C4—792no—
200C22×C4—1582no—
201C22×C4—1582no—
202C22×C4—1584no—
203C22×C4—1584no—
204C22×C4—1584no—
205C22×C4C22×D7911yescharacteristic
206C22×C4C22×D7912yes—
207C22×C4C22×D7911yescharacteristic
208C22×C4C22×D7911yescharacteristic
209C4⋊C4—22no—
210C4⋊C4—1584no—
211C4⋊C4—1582no—
212C4⋊C4—1584no—
213C4⋊C4—1582no—
214C22⋊C4—24no—
215C22⋊C4—24no—
216C22⋊C4—1582no—
217C22⋊C4—1584no—
218C22⋊C4—1584no—
219C22⋊C4—1584no—
220C22⋊C4—1582no—
221C42—794no—
222C42—1582no—
223C42—1584no—
224C23—22no—
225C23—22no—
226C23—22no—
227C23—22no—
228C23—22no—
229C23—22no—
230C23—792no—
231C23—1581no—
232C23—1582no—
233C23—1582no—
234C23—1581no—
235C23#1192962314yes—
236C23C23×D7911yescharacteristic
237D4—28no—
238D4—15816no—
239C2×C4—21no—
240C2×C4—22no—
241C2×C4—21no—
242C2×C4—22no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—21no—
247C2×C4—3168no—
248C2×C4—792no—
249C2×C4—792no—
250C2×C4—792no—
251C2×C4—794no—
252C2×C4—792no—
253C2×C4—1588no—
254C2×C4—1582no—
255C2×C4—1582no—
256C2×C4—1581no—
257C2×C4—1582no—
258C2×C4—1582no—
259C2×C4—1582no—
260C2×C4—1582no—
261C2×C4—1582no—
262C2×C4D4×D7912yes—
263C2×C4D4×D7912yes—
264C22—24no—
265C22—24no—
266C22—24no—
267C22—42no—
268C22—42no—
269C22—42no—
270C22—42no—
271C22—3161no—
272C22—3162no—
273C22—3161no—
274C22—1582no—
275C22—1584no—
276C22C2×D4×D7911yescharacteristic
277C22C2×D4×D7911yescharacteristic
278C22#41×D7911yescharacteristic
279C22#41×D7912yes—
280C22C2×#1192962312yes—
281C4—22no—
282C4—22no—
283C4—41no—
284C4—42no—
285C4—3162no—
286C4—3161no—
287C4—794no—
288C4—1584no—
289C4—1582no—
290C2—44no—
291C2—3162no—
292C2#121×D7911yescharacteristic
293C2#1909906911yescharacteristic
294C2#1909907312yes—
295C2#1909909012yes—
296C2#1909911211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D79
commutator, socle, cosocleC23×C79C24
Fitting#394×C79C2
prime radical#19098471C2
hypercenter#394D79
hypocenterC79#2392
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
1. C2×D4×Dic79C2semidirect
2. C2×(C22⋊D79)⋊C4C2semidirect
3. C2×#14579119C2semidirect
4. #19098493C2semidirect
5. #19098490C2semidirect
6. #19098486C2semidirect
7. #19098478C2semidirect
9. #19098414C2semidirect
10. C22⋊C4×Dic79C2semidirect
11. #394×C79C2semidirect
52. C2×C4×D79D4semidirect
64. C4×Dic79D4semidirect
149. C79#2392semidirect
157. #394D79semidirect