Finite Group Databasebeta

← #23764484

Subgroups — #23764484

Order 10112.

406 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 93 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
1C22×#11929613C211yesmaximal, characteristic
2C22×#11929611C211yesmaximal, characteristic
3C2×#14579159C211yesmaximal, characteristic, complemented
4C2×#14579084C211yesmaximal, characteristic, complemented
5#19098464C211yesmaximal, characteristic
6#19098317C211yesmaximal, characteristic, complemented
7C2×#103×C79C211yesmaximal, characteristic, complemented
8C22×Dic158C2211yescharacteristic
9C22×D316C2211yescharacteristic
10C2×#11929613—22no—
11C2×#11929613—22no—
12C2×#11929613—22no—
13C2×#11929611—22no—
14C2×#11929611—22no—
15C2×#11929611—22no—
16C22×C79⋊C8C2211yescharacteristic
17#14579159—22no—
18#14579159—22no—
19C2×Dic79⋊C4—22no—
20C2×(C2×D79)⋊C4—22no—
21C2×C4×Dic79C2211yescharacteristic
22#14579084—22no—
23C22×Q8×C79C2211yescharacteristic
24C22×C8×C79C2211yescharacteristic
25C2×C4⋊C4×C79C2211yescharacteristic
26#103×C79—22no—
27C23×D79—21no—
28C2×Dic158—21no—
29C2×Dic158—21no—
30C2×Dic158—21no—
31C2×Dic158—21no—
32C2×Dic158—21no—
33C2×Dic158D412yes—
34C2×D316—21no—
35C2×D316—21no—
36C2×D316—21no—
37C2×D316—21no—
38C2×D316—21no—
39C2×D316D412yes—
40C22×Dic79—21no—
41C22×Dic79D412yes—
42#11929613—28no—
43#11929611—28no—
44C2×C79⋊C8—21no—
45C2×C79⋊C8—21no—
46C2×C79⋊C8D412yes—
47Dic79⋊C4—28no—
48(C2×D79)⋊C4—44no—
49C4×Dic79—21no—
50C4×Dic79—21no—
51C2×Q8×C79—21no—
52C2×Q8×C79—21no—
53C2×Q8×C79—21no—
54C2×Q8×C79—21no—
55C2×Q8×C79—21no—
56C2×Q8×C79D412yes—
57C22×C4×C79—21no—
58C22×C4×C79—21no—
59C22×C4×C79C2311yescharacteristic
60C2×C8×C79—21no—
61C2×C8×C79—21no—
62C2×C8×C79D412yes—
63C4⋊C4×C79—21no—
64C4⋊C4×C79—21no—
65C23×C79C2×D411yescharacteristic
66C22×D79—22no—
67C22×D79—41no—
68C22×D79—41no—
69C22×D79—42no—
70C22×D79—42no—
71Q8×C79—22no—
72Q8×C79—22no—
73Q8×C79—41no—
74Q8×C79—41no—
75C2×C4×C79—22no—
76C2×C4×C79—41no—
77C2×C4×C79—41no—
78C2×C4×C79—41no—
79C2×C4×C79—42no—
80C2×C4×C79C2×D411yescharacteristic
81C2×C4×C79C2×D411yescharacteristic
82C2×C4×C79C2×D411yescharacteristic
83C2×C4×C79C2×D411yescharacteristic
84C2×C4×C79C2×D411yescharacteristic
85C2×C4×C79#4111yescharacteristic
86C2×Dic79—22no—
87C2×Dic79—22no—
88C2×Dic79—22no—
89C2×Dic79—41no—
90C2×Dic79—41no—
91C2×Dic79SD1614yescomplemented
92D316—22no—
93D316—22no—
94D316—41no—
95D316—41no—
96Dic158—22no—
97Dic158—22no—
98Dic158—41no—
99Dic158—41no—
100C8×C79—22no—
101C79⋊C8—22no—
102C22×C79#12011yescharacteristic
103C22×C79#12111yescharacteristic
104C22×C79#12711yescharacteristic
105C22×C79C2×SD1612yes—
106C22×C79#13712yes—
107C2×D79—42no—
108C2×D79—44no—
109C2×D79—82no—
110C2×D79—81no—
111C2×D79—81no—
112C4×C79—42no—
113C4×C79—81no—
114C4×C79#12011yescharacteristic
115C4×C79#12011yescharacteristic
116C4×C79#12111yescharacteristic
117C4×C79#12111yescharacteristic
118Dic79—24no—
119Dic79—42no—
120C2×C79#39211yescharacteristic
121C2×C79#44812yes—
122C2×C79#46112yes—
123C2×C79#49211yescharacteristic
124C2×C79#49711yescharacteristic
125D79—82no—
126#2013—791nomaximal, Sylow
127C79#201311yescharacteristic, complemented, Sylow
128C22×SD16—791no—
129C22×SD16—791no—
130C2×C4⋊Q8—791no—
131C2×#103—791no—
132C2×#103D7911yescharacteristic, complemented
133#390—791no—
134#336—791no—
135C22×Q8—791no—
136C22×Q8C2×D7911yescharacteristic
137C22×D4—791no—
138C2×SD16—1582no—
139C2×SD16—1582no—
140C2×SD16—1582no—
141C2×SD16—1582no—
142C2×SD16—1582no—
143C2×SD16—1582no—
144C22×C8—791no—
145C22×C8C2×D7911yescharacteristic
146C4⋊Q8—1582no—
147C4⋊Q8—1582no—
148C2×C4⋊C4—1582no—
149C2×C4⋊C4C2×D7911yescharacteristic
150C2×C22⋊C4—1582no—
151C2×C42—791no—
152#103—22no—
153#103—1582no—
154C24—1581no—
155C2×Q8—21no—
156C2×Q8—21no—
157C2×Q8—21no—
158C2×Q8—21no—
159C2×Q8—21no—
160C2×Q8—792no—
161C2×Q8—1581no—
162C2×Q8—1581no—
163C2×Q8—1581no—
164C2×Q8—1581no—
165C2×Q8—1581no—
166C2×Q8D31612yes—
167C2×D4—792no—
168C2×D4—1581no—
169C2×D4—1581no—
170C2×D4—1581no—
171C2×D4—1581no—
172C2×D4—1581no—
173C22×C4—21no—
174C22×C4—21no—
175C22×C4—792no—
176C22×C4—1581no—
177C22×C4C22×D7911yescharacteristic
178SD16—1588no—
179SD16—1588no—
180C2×C8—21no—
181C2×C8—21no—
182C2×C8—792no—
183C2×C8—1581no—
184C2×C8—1581no—
185C2×C8C22⋊D7912yes—
186C4⋊C4—21no—
187C4⋊C4—21no—
188C4⋊C4—1588no—
189C22⋊C4—3164no—
190C42—1581no—
191C42—1581no—
192C23—3161no—
193C23—3161no—
194C23—3162no—
195C23—3162no—
196C23—1582no—
197C23D4×D7911yescharacteristic
198Q8—22no—
199Q8—22no—
200Q8—41no—
201Q8—41no—
202Q8—3161no—
203Q8—3161no—
204Q8—1582no—
205Q8—1582no—
206D4—3161no—
207D4—3161no—
208D4—1582no—
209D4—1582no—
210C2×C4—22no—
211C2×C4—41no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—42no—
215C2×C4—3161no—
216C2×C4—3161no—
217C2×C4—794no—
218C2×C4—1582no—
219C2×C4—1582no—
220C2×C4—1582no—
221C2×C4D4×D7911yescharacteristic
222C2×C4D4×D7911yescharacteristic
223C2×C4D4×D7911yescharacteristic
224C2×C4C2×C22⋊D7911yescharacteristic
225C2×C4C2×D31611yescharacteristic
226C2×C4#1192962411yescharacteristic
227C8—22no—
228C8—1582no—
229C22—3162no—
230C22—3164no—
231C22—6321no—
232C22—6321no—
233C22—6322no—
234C22#1457913111yescharacteristic
235C22#1457913411yescharacteristic
236C22#1457915711yescharacteristic
237C22SD16×D7912yes—
238C22#1457919312yes—
239C4—42no—
240C4—81no—
241C4—3162no—
242C4—1584no—
243C4#1457912911yescharacteristic
244C4#1457913111yescharacteristic
245C4#1457913411yescharacteristic
246C4#1457913511yescharacteristic
247C2—6322no—
248C2#1909847211yescharacteristic
249C2#1909870312yes—
250C2#1909876712yes—
251C2#1909893411yescharacteristic
252C2#1909895611yescharacteristic
subgroupG/H
centerC23D4×D79
commutator, cosocleC22×C4×C79C23
FrattiniC22×C4C22×D79
FittingC2×#103×C79C2
socleC23×C79C2×D4
prime radicalC22×D316C22
hypercenterC2×#103D79
hypocenterC79#2013
LCSG ▷ C22×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
3. C2×#14579159C2semidirect
4. C2×#14579084C2semidirect
6. #19098317C2semidirect
7. C2×#103×C79C2semidirect
91. C2×Dic79SD16semidirect
127. C79#2013semidirect
132. C2×#103D79semidirect