Finite Group Databasebeta

← #23768774

Subgroups — #23768774

Order 10112.

544 conjugacy classes of subgroups; only the 159 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 159 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
2C2×C4⋊C4×D79C211yesmaximal, characteristic
3#19098494C211yesmaximal, characteristic, complemented
4#19098484C211yesmaximal, characteristic, complemented
5#19098483C211yesmaximal, characteristic, complemented
6#19098462C212yesmaximal, complemented
7#19098460C212yesmaximal, complemented
8#19098437C212yesmaximal
9#19098434C212yesmaximal
10#19098410C211yesmaximal, characteristic
11#398×C79C211yesmaximal, characteristic, complemented
12C22×Dic158C2211yescharacteristic
13C22×C4×D79C2211yescharacteristic
14C22×C4×D79C2211yescharacteristic
15C22×C4×D79C2211yescharacteristic
16#14579141—24no—
17C2×C4⋊Dic79C2212yes—
18C2×C4⋊Dic79C2211yescharacteristic
19C2×C4⋊Dic79C2212yes—
20C2×Dic79⋊C4C2212yes—
21C2×Dic79⋊C4C2211yescharacteristic
22C2×Dic79⋊C4C2211yescharacteristic
23C2×Dic79⋊C4C2212yes—
24C4⋊C4×D79—24no—
25C2×(C2×D79)⋊C4C2212yes—
26C2×(C2×D79)⋊C4C2212yes—
27C2×C4×Dic79C2212yes—
28C79⋊#95C2211yescharacteristic
29C79⋊#95C2212yes—
30C79⋊#95C2212yes—
31C79⋊#95C2212yes—
32C2×C4⋊C4×C79C2212yes—
33C2×C4⋊C4×C79C2211yescharacteristic
34C2×C4⋊C4×C79C2211yescharacteristic
35#95×C79C2211yescharacteristic
36#95×C79C2212yes—
37C23×D79C2311yescharacteristic
38C2×Dic158—22no—
39C2×Dic158—42no—
40C22×Dic79C2312yes—
41C22×Dic79C2311yescharacteristic
42C22×Dic79C2311yescharacteristic
43C22×Dic79C2312yes—
44C22×Dic79C2311yescharacteristic
45C2×C4×D79—22no—
46C2×C4×D79—22no—
47C2×C4×D79—22no—
48C2×C4×D79—22no—
49C2×C4×D79—42no—
50C2×C4×D79—42no—
51C2×C4×D79D414yes—
52C4⋊Dic79—22no—
53C4⋊Dic79—24no—
54C4⋊Dic79—42no—
55Dic79⋊C4—22no—
56Dic79⋊C4—24no—
57Dic79⋊C4—22no—
58Dic79⋊C4—42no—
59(C2×D79)⋊C4—24no—
60(C2×D79)⋊C4Q818yescomplemented
61C4×Dic79—42no—
62C22×C4×C79C2311yescharacteristic
63C22×C4×C79C2312yes—
64C22×C4×C79C2311yescharacteristic
65C22×C4×C79C2312yes—
66C22×C4×C79C2311yescharacteristic
67C4⋊C4×C79—22no—
68C4⋊C4×C79—22no—
69C4⋊C4×C79—24no—
70C23×C79C2411yescharacteristic
71C22×D79—21no—
72C22×D79—21no—
73C22×D79—22no—
74C22×D79C2×D412yes—
75C22×D79C2×Q814yes—
76C2×C4×C79—21no—
77C2×C4×C79—21no—
78C2×C4×C79—22no—
79C2×C4×C79—22no—
80C2×C4×C79—22no—
81C2×C4×C79—22no—
82C2×C4×C79—21no—
83C2×C4×C79—22no—
84C2×C4×C79—22no—
85C2×C4×C79—22no—
86C2×C4×C79C2×D412yes—
87C2×C4×C79C2×Q814yes—
88C2×C4×C79#4112yes—
89C2×Dic79—21no—
90C2×Dic79—22no—
91C2×Dic79—21no—
92C2×Dic79—22no—
93C2×Dic79—22no—
94C2×Dic79—22no—
95C2×Dic79—21no—
96C2×Dic79—22no—
97C2×Dic79—22no—
98C2×Dic79—22no—
99C2×Dic79C2×D412yes—
100C2×Dic79C2×Q814yes—
101C2×Dic79#4112yes—
102C4×D79—28no—
103C4×D79—44no—
104C4×D79—44no—
105Dic158—44no—
106C22×C79C22×D411yescharacteristic
107C22×C79C22×Q812yes—
108C22×C79C2×#4111yescharacteristic
109C22×C79C2×#4111yescharacteristic
110C22×C79H(5,𝔽2)12yes—
111C2×D79—22no—
112C2×D79—22no—
113C2×D79—24no—
114C2×D79—24no—
115C2×D79C4⋊Q814yes—
116C4×C79—22no—
117C4×C79—22no—
118C4×C79—24no—
119C4×C79—42no—
120C4×C79—41no—
121Dic79—22no—
122Dic79—22no—
123Dic79—24no—
124Dic79—42no—
125Dic79—41no—
126C2×C79#52511yescharacteristic
127C2×C79C2×C4⋊Q811yescharacteristic
128C2×C79#53411yescharacteristic
129C2×C79#55412yes—
130C2×C79#55412yes—
131D79—24no—
132#2583—791nomaximal, Sylow
133C79#258311yescharacteristic, complemented, Sylow
134C2×C22⋊Q8—791no—
135C22×C4⋊C4—791no—
136#398—791no—
137#398D7911yescharacteristic, complemented
138#395—791no—
139#395—791no—
140#389—792no—
141#389—792no—
142#385—792no—
143#385—792no—
144C4×C22⋊C4—791no—
145C22×Q8—791no—
146C23×C4—791no—
147C23×C4—791no—
148C23×C4—791no—
149C22⋊Q8—1584no—
150C2×C4⋊C4—792no—
151C2×C4⋊C4—792no—
152C2×C4⋊C4—791no—
153C2×C4⋊C4—791no—
154C2×C4⋊C4—791no—
155C2×C4⋊C4—792no—
156C2×C4⋊C4—792no—
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×C42—792no—
164#95—791no—
165#95—792no—
166#95—792no—
167#95—792no—
168#95C2×D7911yescharacteristic
169#95C2×D7912yes—
170C24—791no—
171C2×Q8—3162no—
172C2×Q8—1582no—
173C22×C4—3162no—
174C22×C4—3162no—
175C22×C4—794no—
176C22×C4—792no—
177C22×C4—791no—
178C22×C4—791no—
179C22×C4—792no—
180C22×C4—791no—
181C22×C4—1582no—
182C22×C4—1582no—
183C22×C4—1582no—
184C22×C4—1582no—
185C22×C4C22×D7912yes—
186C22×C4C22×D7911yescharacteristic
187C22×C4C22×D7911yescharacteristic
188C22×C4C22×D7912yes—
189C22×C4C22×D7911yescharacteristic
190C4⋊C4—22no—
191C4⋊C4—22no—
192C4⋊C4—24no—
193C4⋊C4—3162no—
194C4⋊C4—3162no—
195C4⋊C4—1584no—
196C4⋊C4—1582no—
197C4⋊C4—1582no—
198C4⋊C4—1584no—
199C4⋊C4—1582no—
200C22⋊C4—798no—
201C22⋊C4—1584no—
202C42—3162no—
203C23—794no—
204C23—792no—
205C23—1581no—
206C23—1581no—
207C23—1582no—
208C23C23×D7911yescharacteristic
209Q8—3164no—
210C2×C4—21no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—21no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—22no—
219C2×C4—21no—
220C2×C4—3164no—
221C2×C4—3164no—
222C2×C4—794no—
223C2×C4—792no—
224C2×C4—792no—
225C2×C4—1588no—
226C2×C4—1582no—
227C2×C4—1582no—
228C2×C4—1582no—
229C2×C4—1582no—
230C2×C4—1581no—
231C2×C4—1582no—
232C2×C4—1581no—
233C2×C4—1582no—
234C2×C4—1582no—
235C2×C4—1581no—
236C2×C4D4×D7912yes—
237C2×C4Q8×D7914yes—
238C2×C4#1192962312yes—
239C22—794no—
240C22—1584no—
241C22—1584no—
242C22—1582no—
243C22—1582no—
244C22C2×D4×D7911yescharacteristic
245C22C2×Q8×D7912yes—
246C22#41×D7911yescharacteristic
247C22C2×#1192962311yescharacteristic
248C22#1457920712yes—
249C4—24no—
250C4—22no—
251C4—22no—
252C4—42no—
253C4—41no—
254C4—3161no—
255C4—3162no—
256C4—1584no—
257C4—1582no—
258C4—1582no—
259C2—1584no—
260C2#1909907311yescharacteristic
261C2C4⋊Q8×D7911yescharacteristic
262C2#1909912411yescharacteristic
263C2#1909926912yes—
264C2#1909927112yes—
subgroupG/H
center, FrattiniC23C23×D79
commutator, socle, cosocleC23×C79C24
Fitting#398×C79C2
prime radicalC23×D79C23
hypercenter#398D79
hypocenterC79#2583
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
3. #19098494C2semidirect
4. #19098484C2semidirect
5. #19098483C2semidirect
6. #19098462C2semidirect
7. #19098460C2semidirect
11. #398×C79C2semidirect
60. (C2×D79)⋊C4Q8semidirect
133. C79#2583semidirect
137. #398D79semidirect