Finite Group Databasebeta

← #23769038

Subgroups — #23769038

Order 10112.

470 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 470 conjugacy classes of subgroups — too many to draw. Only its 145 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×#14579155C211yesmaximal, characteristic
2C2×C4×Dic158C211yesmaximal, characteristic, complemented
3#19098503C211yesmaximal, characteristic, complemented
4#19098500C211yesmaximal, characteristic
5#19098484C211yesmaximal, characteristic, complemented
6#19098476C211yesmaximal, characteristic
7#19098461C212yesmaximal, complemented
8#19098455C212yesmaximal
9#19098454C212yesmaximal
10#19098448C212yesmaximal, complemented
11#376×C79C211yesmaximal, characteristic, complemented
12C22×Dic158C2211yescharacteristic
13#14579155—24no—
14C4×Dic158—24no—
15C2×C4⋊Dic79C2212yes—
16C2×C4⋊Dic79C2212yes—
17C2×C4⋊Dic79C2211yescharacteristic
18C2×Dic79⋊C4C2211yescharacteristic
19C2×Dic79⋊C4C2212yes—
20C2×Dic79⋊C4C2211yescharacteristic
21C2×Dic79⋊C4C2211yescharacteristic
22C2×(C2×D79)⋊C4C2211yescharacteristic
23C2×(C2×D79)⋊C4C2212yes—
24C2×(C2×D79)⋊C4C2212yes—
25C2×(C2×D79)⋊C4C2211yescharacteristic
26C2×(C2×D79)⋊C4C2211yescharacteristic
27C2×C4×Dic79C2212yes—
28C79⋊#95C2212yes—
29C79⋊#95C2212yes—
30C79⋊#95C2212yes—
31C79⋊#95C2212yes—
32C2×C42×C79C2212yes—
33C2×C42×C79C2211yescharacteristic
34#95×C79C2212yes—
35#95×C79C2211yescharacteristic
36#95×C79C2211yescharacteristic
37C23×D79C2311yescharacteristic
38C2×Dic158—24no—
39C2×Dic158—22no—
40C22×Dic79C2311yescharacteristic
41C22×Dic79C2312yes—
42C22×Dic79C2311yescharacteristic
43C22×Dic79C2311yescharacteristic
44C22×Dic79C2312yes—
45C4⋊Dic79—24no—
46C4⋊Dic79—22no—
47C4⋊Dic79—24no—
48Dic79⋊C4—24no—
49Dic79⋊C4—22no—
50Dic79⋊C4—22no—
51Dic79⋊C4—22no—
52(C2×D79)⋊C4—24no—
53(C2×D79)⋊C4—22no—
54(C2×D79)⋊C4—22no—
55(C2×D79)⋊C4—22no—
56(C2×D79)⋊C4—24no—
57C4×Dic79—24no—
58C22×C4×C79C2312yes—
59C22×C4×C79C2311yescharacteristic
60C22×C4×C79C2311yescharacteristic
61C22×C4×C79C2311yescharacteristic
62C22×C4×C79C2312yes—
63C42×C79—24no—
64C42×C79D414yes—
65C23×C79C2411yescharacteristic
66C22×D79—21no—
67C22×D79—22no—
68C22×D79—22no—
69C22×D79—21no—
70C22×D79—21no—
71C2×C4×C79—22no—
72C2×C4×C79—22no—
73C2×C4×C79—22no—
74C2×C4×C79—21no—
75C2×C4×C79—21no—
76C2×C4×C79—22no—
77C2×C4×C79—22no—
78C2×C4×C79—22no—
79C2×C4×C79—22no—
80C2×C4×C79C2×D412yes—
81C2×C4×C79C2×D412yes—
82C2×C4×C79C2×D412yes—
83C2×C4×C79#4114yes—
84C2×Dic79—22no—
85C2×Dic79—22no—
86C2×Dic79—22no—
87C2×Dic79—21no—
88C2×Dic79—21no—
89C2×Dic79—21no—
90C2×Dic79—22no—
91C2×Dic79—22no—
92C2×Dic79—22no—
93C2×Dic79—22no—
94C2×Dic79—21no—
95C2×Dic79—21no—
96C2×Dic79#4114yes—
97Dic158—28no—
98C22×C79C22×D411yescharacteristic
99C22×C79C2×#4112yes—
100C22×C79C2×#4112yes—
101C22×C792−1+411yescharacteristic
102C22×C792−1+411yescharacteristic
103C2×D79—41no—
104C2×D79—41no—
105C2×D79—41no—
106C2×D79—42no—
107C2×D79—42no—
108C4×C79—22no—
109C4×C79—22no—
110C4×C79—22no—
111C4×C79—24no—
112C4×C79—42no—
113Dic79—24no—
114Dic79—41no—
115Dic79—42no—
116Dic79—41no—
117Dic79—41no—
118C2×C79#52511yescharacteristic
119C2×C79#53211yescharacteristic
120C2×C79#53611yescharacteristic
121C2×C79#55212yes—
122C2×C79#55612yes—
123D79—81no—
124#2604—791nomaximal, Sylow
125C79#260411yescharacteristic, complemented, Sylow
126C2×#126—791no—
127C2×C4×Q8—791no—
128#400—791no—
129#399—791no—
130#395—791no—
131#393—791no—
132#389—792no—
133#388—792no—
134#388—792no—
135#387—792no—
136#376D7911yescharacteristic, complemented
137C22×Q8—791no—
138#126—1584no—
139C4×Q8—1584no—
140C2×C4⋊C4—792no—
141C2×C4⋊C4—791no—
142C2×C4⋊C4—791no—
143C2×C4⋊C4—791no—
144C2×C4⋊C4—791no—
145C2×C4⋊C4—792no—
146C2×C4⋊C4—792no—
147C2×C22⋊C4—791no—
148C2×C22⋊C4—791no—
149C2×C22⋊C4—791no—
150C2×C22⋊C4—792no—
151C2×C22⋊C4—792no—
152C2×C42—792no—
153C2×C42C2×D7912yes—
154C2×C42C2×D7911yescharacteristic
155#95—792no—
156#95—792no—
157#95—792no—
158#95—792no—
159#95C2×D7912yes—
160#95C2×D7911yescharacteristic
161#95C2×D7911yescharacteristic
162C24—791no—
163C2×Q8—1584no—
164C2×Q8—1582no—
165C22×C4—792no—
166C22×C4—791no—
167C22×C4—792no—
168C22×C4—791no—
169C22×C4—791no—
170C22×C4C22×D7912yes—
171C22×C4C22×D7911yescharacteristic
172C22×C4C22×D7911yescharacteristic
173C22×C4C22×D7911yescharacteristic
174C22×C4C22×D7912yes—
175C4⋊C4—1584no—
176C4⋊C4—1584no—
177C4⋊C4—1582no—
178C4⋊C4—1582no—
179C4⋊C4—1582no—
180C4⋊C4—1582no—
181C4⋊C4—1584no—
182C22⋊C4—1584no—
183C22⋊C4—1582no—
184C22⋊C4—1582no—
185C22⋊C4—1582no—
186C22⋊C4—1584no—
187C42—24no—
188C42—1584no—
189C42D31614yes—
190C23—1582no—
191C23—1582no—
192C23—1581no—
193C23—1581no—
194C23—1581no—
195C23C23×D7911yescharacteristic
196Q8—1588no—
197C2×C4—22no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—794no—
207C2×C4—1582no—
208C2×C4—1582no—
209C2×C4—1582no—
210C2×C4—1582no—
211C2×C4—1581no—
212C2×C4—1581no—
213C2×C4—1582no—
214C2×C4—1581no—
215C2×C4—1581no—
216C2×C4—1581no—
217C2×C4—1582no—
218C2×C4—1582no—
219C2×C4C2×D31612yes—
220C2×C4C2×D31612yes—
221C2×C4C2×D31612yes—
222C2×C4#1192962414yes—
223C22—3161no—
224C22—3162no—
225C22—3162no—
226C22—3161no—
227C22—3161no—
228C22C22×D31611yescharacteristic
229C22#41×D7912yes—
230C22C2×#1192962412yes—
231C22#1457920811yescharacteristic
232C22#1457920811yescharacteristic
233C4—22no—
234C4—24no—
235C4—22no—
236C4—22no—
237C4—42no—
238C4—3161no—
239C4—3161no—
240C4—3162no—
241C4—3161no—
242C4—1584no—
243C2—6321no—
244C2#1909907511yescharacteristic
245C2#1909911311yescharacteristic
246C2#1909913911yescharacteristic
247C2#1909924612yes—
248C2#1909928112yes—
subgroupG/H
center, FrattiniC23C23×D79
commutator, socle, cosocleC23×C79C24
Fitting#376×C79C2
prime radicalC23×D79C23
hypercenter#376D79
hypocenterC79#2604
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C23 ◁ #376

Complements

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

NH ≅ G/Ntype
2. C2×C4×Dic158C2semidirect
3. #19098503C2semidirect
5. #19098484C2semidirect
7. #19098461C2semidirect
10. #19098448C2semidirect
11. #376×C79C2semidirect
125. C79#2604semidirect
136. #376D79semidirect