Finite Group Databasebeta

← #23768752

Subgroups — #23768752

Order 10112.

584 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 584 conjugacy classes of subgroups — too many to draw. Only its 153 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×(C22⋊D79)⋊C4C211yesmaximal, characteristic
2C22×Dic79⋊C4C211yesmaximal, characteristic, complemented
3#19098494C212yesmaximal, complemented
4#19098487C212yesmaximal, complemented
5#19098445C212yesmaximal, complemented
6#19098442C211yesmaximal, characteristic
7#19098440C211yesmaximal, characteristic
8#19098435C211yesmaximal, characteristic, complemented
9#19098434C212yesmaximal, complemented
10#19098421C211yesmaximal, characteristic, complemented
11#385×C79C211yesmaximal, characteristic, complemented
12C22×C22⋊D79C2211yescharacteristic
13C23×Dic79C2211yescharacteristic
14C23×Dic79C2211yescharacteristic
15C22×C4×D79C2211yescharacteristic
16(C22⋊D79)⋊C4—24no—
17C2×Dic79⋊C4—24no—
18C2×Dic79⋊C4C2212yes—
19C2×Dic79⋊C4C2212yes—
20C2×Dic79⋊C4C2212yes—
21C2×Dic79⋊C4C2211yescharacteristic
22C2×Dic79⋊C4C2212yes—
23C2×C22⋊Dic79C2211yescharacteristic
24C2×(C2×D79)⋊C4C2212yes—
25C2×(C2×D79)⋊C4C2211yescharacteristic
26C2×(C2×D79)⋊C4C2212yes—
27C2×C4×Dic79C2211yescharacteristic
28C79⋊#95C2212yes—
29C79⋊#95C2212yes—
30C79⋊#95C2212yes—
31C79⋊#95C2212yes—
32C23×C4×C79C2211yescharacteristic
33C2×C4⋊C4×C79C2212yes—
34C2×C22⋊C4×C79C2211yescharacteristic
35C2×C22⋊C4×C79C2211yescharacteristic
36#95×C79C2212yes—
37C23×D79C2311yescharacteristic
38C2×C22⋊D79—22no—
39C2×C22⋊D79—22no—
40C2×C22⋊D79Q814yes—
41C22×Dic79—24no—
42C22×Dic79—22no—
43C22×Dic79—42no—
44C22×Dic79D414yes—
45C22×Dic79C2312yes—
46C22×Dic79C2311yescharacteristic
47C22×Dic79C2311yescharacteristic
48C22×Dic79C2311yescharacteristic
49C22×Dic79C2312yes—
50C2×C4×D79—22no—
51C2×C4×D79—42no—
52Dic79⋊C4—24no—
53Dic79⋊C4—24no—
54Dic79⋊C4—22no—
55Dic79⋊C4—24no—
56Dic79⋊C4—42no—
57C22⋊Dic79—22no—
58(C2×D79)⋊C4—22no—
59(C2×D79)⋊C4—24no—
60(C2×D79)⋊C4—42no—
61C4×Dic79—22no—
62C24×C79C2311yescharacteristic
63C22×C4×C79—22no—
64C22×C4×C79—42no—
65C22×C4×C79C2311yescharacteristic
66C22×C4×C79C2312yes—
67C22×C4×C79C2312yes—
68C22×C4×C79C2311yescharacteristic
69C4⋊C4×C79—42no—
70C22⋊C4×C79—22no—
71C22⋊C4×C79—22no—
72C23×C79—22no—
73C23×C79—22no—
74C23×C79C2×D412yes—
75C23×C79C2×Q812yes—
76C23×C79#4112yes—
77C23×C79C2411yescharacteristic
78C22×D79—21no—
79C22×D79—22no—
80C22×D79—21no—
81C22×D79—22no—
82C22×D79C2×Q812yes—
83C2×C4×C79—21no—
84C2×C4×C79—22no—
85C2×C4×C79—21no—
86C2×C4×C79—22no—
87C2×C4×C79—22no—
88C2×C4×C79—22no—
89C2×C4×C79—22no—
90C2×C4×C79—22no—
91C2×C4×C79—22no—
92C2×C4×C79—22no—
93C2×C4×C79—44no—
94C22⋊D79—28no—
95C2×Dic79—28no—
96C2×Dic79—21no—
97C2×Dic79—22no—
98C2×Dic79—22no—
99C2×Dic79—21no—
100C2×Dic79—22no—
101C2×Dic79—22no—
102C2×Dic79—22no—
103C2×Dic79—22no—
104C2×Dic79—22no—
105C2×Dic79—44no—
106C2×Dic79C2×D412yes—
107C2×Dic79C2×D412yes—
108C2×Dic79C2×Q812yes—
109C2×Dic79#4114yes—
110C4×D79—44no—
111C22×C79—22no—
112C22×C79—22no—
113C22×C79—24no—
114C22×C79—24no—
115C22×C79C22⋊Q814yes—
116C22×C79C22×D411yescharacteristic
117C22×C79C22×Q811yescharacteristic
118C22×C79C2×#4112yes—
119C22×C79C2×#4111yescharacteristic
120C22×C79H(5,𝔽2)12yes—
121C2×D79—22no—
122C2×D79—24no—
123C2×D79—41no—
124C2×D79—41no—
125C2×D79—42no—
126C4×C79—41no—
127C4×C79—42no—
128C4×C79—41no—
129C4×C79—42no—
130Dic79—22no—
131Dic79—24no—
132Dic79—22no—
133Dic79—22no—
134Dic79—42no—
135C2×C79—24no—
136C2×C79C2×C22⋊Q811yescharacteristic
137C2×C79#52511yescharacteristic
138C2×C79#53411yescharacteristic
139C2×C79#55312yes—
140C2×C79#55412yes—
141D79—42no—
142#2579—791nomaximal, Sylow
143C79#257911yescharacteristic, complemented, Sylow
144C2×C4×D4—791no—
145C22×C4⋊C4—791no—
146#398—792no—
147#396—792no—
148#387—792no—
149#386—791no—
150#386—791no—
151#385—792no—
152#385—791no—
153#385D7911yescharacteristic, complemented
154#380—791no—
155C22×D4—791no—
156C23×C4—791no—
157C23×C4—791no—
158C23×C4—791no—
159C23×C4C2×D7911yescharacteristic
160C4×D4—1584no—
161C2×C4⋊C4—792no—
162C2×C4⋊C4—792no—
163C2×C4⋊C4—792no—
164C2×C4⋊C4—791no—
165C2×C4⋊C4—792no—
166C2×C4⋊C4—1584no—
167C2×C4⋊C4C2×D7912yes—
168C2×C22⋊C4—792no—
169C2×C22⋊C4—791no—
170C2×C22⋊C4—791no—
171C2×C22⋊C4—792no—
172C2×C22⋊C4C2×D7911yescharacteristic
173C2×C22⋊C4C2×D7911yescharacteristic
174C2×C42—791no—
175#95—792no—
176#95—792no—
177#95—792no—
178#95—792no—
179#95C2×D7912yes—
180C24—791no—
181C24C22×D7911yescharacteristic
182C2×D4—794no—
183C2×D4—1582no—
184C2×D4—1582no—
185C22×C4—22no—
186C22×C4—42no—
187C22×C4—3162no—
188C22×C4—3162no—
189C22×C4—794no—
190C22×C4—791no—
191C22×C4—791no—
192C22×C4—792no—
193C22×C4—791no—
194C22×C4—792no—
195C22×C4—1582no—
196C22×C4—1584no—
197C22×C4—1582no—
198C22×C4C22×D7912yes—
199C22×C4C22×D7911yescharacteristic
200C22×C4C22×D7912yes—
201C22×C4C22×D7911yescharacteristic
202C4⋊C4—42no—
203C4⋊C4—3162no—
204C4⋊C4—1584no—
205C4⋊C4—1584no—
206C4⋊C4—1584no—
207C4⋊C4—1582no—
208C22⋊C4—22no—
209C22⋊C4—22no—
210C22⋊C4—3162no—
211C22⋊C4—1584no—
212C22⋊C4—1582no—
213C22⋊C4—1582no—
214C42—1582no—
215C23—22no—
216C23—22no—
217C23—792no—
218C23—1582no—
219C23—1581no—
220C23—1582no—
221C23—1581no—
222C23D4×D7912yes—
223C23Q8×D7912yes—
224C23#1192962412yes—
225C23C23×D7911yescharacteristic
226D4—1588no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—22no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—22no—
237C2×C4—44no—
238C2×C4—3164no—
239C2×C4—3164no—
240C2×C4—792no—
241C2×C4—794no—
242C2×C4—792no—
243C2×C4—792no—
244C2×C4—1582no—
245C2×C4—1582no—
246C2×C4—1582no—
247C2×C4—1588no—
248C2×C4—1582no—
249C2×C4—1581no—
250C2×C4—1582no—
251C2×C4—1582no—
252C2×C4—1581no—
253C2×C4—1582no—
254C22—24no—
255C22—24no—
256C22—22no—
257C22—22no—
258C22—3162no—
259C22—3161no—
260C22—3161no—
261C22—1584no—
262C22—1582no—
263C22#1457913914yes—
264C22C2×D4×D7911yescharacteristic
265C22C2×Q8×D7911yescharacteristic
266C22#41×D7912yes—
267C22C2×#1192962411yescharacteristic
268C22#1457920612yes—
269C4—42no—
270C4—41no—
271C4—42no—
272C4—41no—
273C4—3162no—
274C4—1582no—
275C4—1584no—
276C4—1582no—
277C4—1582no—
278C2—24no—
279C2—3162no—
280C2C2×#1457913911yescharacteristic
281C2#1909907111yescharacteristic
282C2#1909912311yescharacteristic
283C2#1909926212yes—
284C2#1909926712yes—
subgroupG/H
center, FrattiniC23C23×D79
commutator, socle, cosocleC23×C79C24
Fitting#385×C79C2
prime radicalC22×C22⋊D79C22
hypercenter#385D79
hypocenterC79#2579
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
2. C22×Dic79⋊C4C2semidirect
3. #19098494C2semidirect
4. #19098487C2semidirect
5. #19098445C2semidirect
8. #19098435C2semidirect
9. #19098434C2semidirect
10. #19098421C2semidirect
11. #385×C79C2semidirect
143. C79#2579semidirect
153. #385D79semidirect