Finite Group Databasebeta

← #23769265

Subgroups — #23769265

Order 10112.

500 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 131 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×#14579148C211yesmaximal, characteristic
2C2×#14579126C211yesmaximal, characteristic, complemented
3#19098499C212yesmaximal, complemented
4#19098484C211yesmaximal, characteristic, complemented
5#19098483C211yesmaximal, characteristic, complemented
6#19098477C211yesmaximal, characteristic
7#19098475C212yesmaximal, complemented
8#19098457C212yesmaximal, complemented
9#19098456C212yesmaximal, complemented
10#19098430C211yesmaximal, characteristic, complemented
11#394×C79C211yesmaximal, characteristic
12C22×Dic158C2211yescharacteristic
13C22×Dic158C2211yescharacteristic
14#14579148—24no—
15#14579126—24no—
16C2×C4⋊Dic79C2212yes—
17C2×Dic79⋊C4C2211yescharacteristic
18C2×Dic79⋊C4C2211yescharacteristic
19C2×Dic79⋊C4C2212yes—
20C2×C22⋊Dic79C2212yes—
21C2×C22⋊Dic79C2212yes—
22C2×C22⋊Dic79C2212yes—
23C2×C22⋊Dic79C2212yes—
24C2×C4×Dic79C2211yescharacteristic
25C2×C4×Dic79C2211yescharacteristic
26C2×C4×Dic79C2211yescharacteristic
27C79⋊#95C2212yes—
28C79⋊#95C2212yes—
29C79⋊#95C2211yescharacteristic
30C79⋊#95C2212yes—
31C79⋊#95C2212yes—
32C22×D4×C79C2211yescharacteristic
33C2×C4⋊C4×C79C2211yescharacteristic
34C2×C22⋊C4×C79C2212yes—
35C2×C22⋊C4×C79C2212yes—
36#95×C79C2211yescharacteristic
37C2×Dic158—22no—
38C2×Dic158—22no—
39C2×Dic158—22no—
40C2×Dic158—22no—
41C2×Dic158—42no—
42C22×Dic79C2312yes—
43C22×Dic79C2312yes—
44C22×Dic79C2311yescharacteristic
45C22×Dic79C2311yescharacteristic
46C22×Dic79C2311yescharacteristic
47C22×Dic79C2311yescharacteristic
48C4⋊Dic79—42no—
49Dic79⋊C4—22no—
50Dic79⋊C4—22no—
51Dic79⋊C4—42no—
52C22⋊Dic79—24no—
53C22⋊Dic79—24no—
54C22⋊Dic79—24no—
55C22⋊Dic79—42no—
56C4×Dic79—22no—
57C4×Dic79—22no—
58C4×Dic79D414yes—
59C24×C79C2312yes—
60C2×D4×C79—22no—
61C2×D4×C79—42no—
62C22×C4×C79C2312yes—
63C22×C4×C79C2311yescharacteristic
64C22×C4×C79C2311yescharacteristic
65C22×C4×C79C2311yescharacteristic
66C4⋊C4×C79—22no—
67C22⋊C4×C79—24no—
68C22⋊C4×C79—42no—
69C23×C79—22no—
70C23×C79—22no—
71C23×C79—22no—
72C23×C79—22no—
73C23×C79—22no—
74C23×C79—22no—
75C23×C79—22no—
76C23×C79C2411yescharacteristic
77D4×C79—44no—
78C2×C4×C79—21no—
79C2×C4×C79—21no—
80C2×C4×C79—22no—
81C2×C4×C79—21no—
82C2×C4×C79—22no—
83C2×C4×C79—22no—
84C2×C4×C79—22no—
85C2×C4×C79—22no—
86C2×C4×C79C2×D412yes—
87C2×C4×C79#4112yes—
88C2×Dic79—21no—
89C2×Dic79—21no—
90C2×Dic79—21no—
91C2×Dic79—21no—
92C2×Dic79—22no—
93C2×Dic79—21no—
94C2×Dic79—22no—
95C2×Dic79—22no—
96C2×Dic79—22no—
97C2×Dic79—22no—
98C2×Dic79—22no—
99C2×Dic79—22no—
100C2×Dic79—22no—
101C2×Dic79C2×D412yes—
102C2×Dic79C2×D412yes—
103C2×Dic79#4112yes—
104Dic158—28no—
105Dic158—44no—
106C22×C79—42no—
107C22×C79—42no—
108C22×C79—42no—
109C22×C79—42no—
110C22×C79—42no—
111C22×C79—42no—
112C22×C79—42no—
113C22×C79C22×D411yescharacteristic
114C22×C79C2×#4111yescharacteristic
115C22×C79C2×#4111yescharacteristic
116C22×C79H(5,𝔽2)12yes—
117C22×C792−1+412yes—
118C4×C79—22no—
119C4×C79—22no—
120C4×C79—41no—
121C4×C79—42no—
122Dic79—22no—
123Dic79—22no—
124Dic79—22no—
125Dic79—42no—
126Dic79—41no—
127Dic79—42no—
128C2×C79—82no—
129C2×C79#52511yescharacteristic
130C2×C79#53511yescharacteristic
131C2×C79#53611yescharacteristic
132C2×C79#54212yes—
133C2×C79#54212yes—
134#2632—791nomaximal, Sylow
135C79#263211yescharacteristic, complemented, Sylow
136C2×#124—791no—
137C2×C4×Q8—791no—
138#399—792no—
139#395—791no—
140#395—791no—
141#394—791no—
142#394D7911yescharacteristic
143#393—792no—
144#388—792no—
145#388—792no—
146#383—791no—
147C22×Q8—791no—
148C22×Q8—791no—
149C22×D4C2×D7911yescharacteristic
150#124—1584no—
151C4×Q8—1584no—
152C2×C4⋊C4—792no—
153C2×C4⋊C4—792no—
154C2×C4⋊C4—791no—
155C2×C4⋊C4—791no—
156C2×C4⋊C4C2×D7911yescharacteristic
157C2×C22⋊C4—792no—
158C2×C22⋊C4—792no—
159C2×C22⋊C4—792no—
160C2×C22⋊C4—792no—
161C2×C22⋊C4C2×D7912yes—
162C2×C22⋊C4C2×D7912yes—
163C2×C42—791no—
164C2×C42—791no—
165C2×C42—791no—
166#95—792no—
167#95—792no—
168#95—791no—
169#95—792no—
170#95—792no—
171#95C2×D7911yescharacteristic
172C24C22×D7912yes—
173C2×Q8—3162no—
174C2×Q8—1582no—
175C2×Q8—1582no—
176C2×Q8—1582no—
177C2×Q8—1582no—
178C2×D4—22no—
179C2×D4—42no—
180C22×C4—791no—
181C22×C4—791no—
182C22×C4—791no—
183C22×C4—792no—
184C22×C4—792no—
185C22×C4—791no—
186C22×C4C22×D7912yes—
187C22×C4C22×D7911yescharacteristic
188C22×C4C22×D7911yescharacteristic
189C22×C4C22×D7911yescharacteristic
190C4⋊C4—22no—
191C4⋊C4—3162no—
192C4⋊C4—3162no—
193C4⋊C4—1582no—
194C4⋊C4—1582no—
195C22⋊C4—24no—
196C22⋊C4—42no—
197C22⋊C4—3162no—
198C22⋊C4—1584no—
199C22⋊C4—1584no—
200C22⋊C4—1584no—
201C42—794no—
202C42—1582no—
203C42—1582no—
204C23—22no—
205C23—22no—
206C23—22no—
207C23—22no—
208C23—22no—
209C23—22no—
210C23—22no—
211C23C23×D7911yescharacteristic
212Q8—3164no—
213Q8—1588no—
214D4—44no—
215C2×C4—21no—
216C2×C4—22no—
217C2×C4—21no—
218C2×C4—22no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—21no—
223C2×C4—792no—
224C2×C4—792no—
225C2×C4—792no—
226C2×C4—1582no—
227C2×C4—1582no—
228C2×C4—1582no—
229C2×C4—1582no—
230C2×C4—1582no—
231C2×C4—1582no—
232C2×C4—1581no—
233C2×C4—1582no—
234C2×C4—1581no—
235C2×C4—1581no—
236C2×C4—1581no—
237C2×C4—1582no—
238C2×C4—1581no—
239C2×C4D4×D7912yes—
240C2×C4#1192962312yes—
241C22—42no—
242C22—42no—
243C22—42no—
244C22—42no—
245C22—42no—
246C22—42no—
247C22—42no—
248C22C2×D4×D7911yescharacteristic
249C22#41×D7911yescharacteristic
250C22C2×#1192962311yescharacteristic
251C22#1457920612yes—
252C22#1457920812yes—
253C4—22no—
254C4—22no—
255C4—42no—
256C4—41no—
257C4—3162no—
258C4—3162no—
259C4—3161no—
260C4—1582no—
261C4—1582no—
262C4—1582no—
263C2—82no—
264C2#1909907311yescharacteristic
265C2#1909912811yescharacteristic
266C2#1909913311yescharacteristic
267C2#1909918012yes—
268C2#1909918112yes—
subgroupG/H
center, FrattiniC23C23×D79
commutator, socle, cosocleC23×C79C24
Fitting#394×C79C2
prime radicalC22×D4×C79C22
hypercenter#394D79
hypocenterC79#2632
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
2. C2×#14579126C2semidirect
3. #19098499C2semidirect
4. #19098484C2semidirect
5. #19098483C2semidirect
7. #19098475C2semidirect
8. #19098457C2semidirect
9. #19098456C2semidirect
10. #19098430C2semidirect
135. C79#2632semidirect