Finite Group Databasebeta

← #23773243

Subgroups — #23773243

Order 10112.

362 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 141 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
1#19099191C211yesmaximal, characteristic
2#19099040C211yesmaximal, characteristic
3#19098871C212yesmaximal, complemented
4#19098871C212yesmaximal, complemented
5#19098859C212yesmaximal, complemented
6#19098849C212yesmaximal, complemented
7#19098605C211yesmaximal, characteristic
8#19098601C211yesmaximal, characteristic
9#19098573C211yesmaximal, characteristic
10C2×#14579086C211yesmaximal, characteristic
11#424×C79C211yesmaximal, characteristic
12C22×Dic158C2211yescharacteristic
13#14579161C2212yes—
14#14579160—21no—
15#14579153C2212yes—
16#14579152—21no—
17#14579138—22no—
18C4×Dic158C2212yes—
19C4×Dic158C2212yes—
20#14579126—21no—
21#14579126—21no—
22#14579120C2211yescharacteristic
23#14579120C2211yescharacteristic
24#14579117—22no—
25C2×C4⋊Dic79C2211yescharacteristic
26#14579095C2211yescharacteristic
27#14579095C2211yescharacteristic
28#14579095C2212yes—
29#14579093C2211yescharacteristic
30#14579093C2212yes—
31#14579093C2211yescharacteristic
32#14579086C2212yes—
33#14579086C2212yes—
34#14579086C2212yes—
35#14579086C2212yes—
36C2×M16×C79C2211yescharacteristic
37C22×C8×C79C2211yescharacteristic
38#117×C79C2211yescharacteristic
39C4⋊C8×C79C2212yes—
40C4⋊C8×C79C2212yes—
41C2×Dic158—21no—
42C2×Dic158—22no—
43C2×Dic158—22no—
44C2×Dic158Q814yescomplemented
45C2×Dic158C2312yes—
46C22×Dic79—21no—
47C22×Dic79—21no—
48C4⋊Dic79—21no—
49C4⋊Dic79—22no—
50C4⋊Dic79C2312yes—
51C4⋊Dic79C2311yescharacteristic
52C4⋊Dic79C2311yescharacteristic
53C4⋊Dic79C2311yescharacteristic
54C4⋊Dic79C2311yescharacteristic
55Dic79⋊C4—22no—
56Dic79⋊C4—22no—
57Dic79⋊C4—22no—
58Dic79⋊C4—22no—
59C22⋊Dic79—21no—
60C22⋊Dic79—21no—
61C4×Dic79—22no—
62C4×Dic79—22no—
63C4×Dic79—21no—
64C4×Dic79—21no—
65C22×C4×C79C2311yescharacteristic
66M16×C79—22no—
67C2×C8×C79—22no—
68C2×C8×C79C2311yescharacteristic
69C2×C8×C79C2311yescharacteristic
70C2×C8×C79C2312yes—
71C4⋊C4×C79D411yescharacteristic
72C4⋊C4×C79D411yescharacteristic
73C22⋊C4×C79D412yes—
74C42×C79C2312yes—
75C23×C79C2×D411yescharacteristic
76C2×C4×C79C2×D412yes—
77C2×C4×C79C2×D412yes—
78C2×C4×C79C2×D411yescharacteristic
79C2×C4×C79C2×Q812yes—
80C2×C4×C79#4112yes—
81C2×C4×C79C2411yescharacteristic
82C2×Dic79—24no—
83C2×Dic79—22no—
84C2×Dic79—21no—
85C2×Dic79—21no—
86C2×Dic79—21no—
87C2×Dic79—21no—
88C2×Dic79—22no—
89C2×Dic79—81no—
90Dic158—24no—
91Dic158—22no—
92Dic158—82no—
93Dic158C2×Q814yes—
94C8×C79—21no—
95C8×C79—21no—
96C8×C79—22no—
97C22×C79—21no—
98C22×C79—21no—
99C22×C79C22⋊Q812yes—
100C22×C79C22×D411yescharacteristic
101C4×C79—22no—
102C4×C79—22no—
103C4×C79C22⋊Q812yes—
104C4×C79C22×Q811yescharacteristic
105C4×C79C2×#4111yescharacteristic
106Dic79—24no—
107Dic79—41no—
108Dic79—42no—
109Dic79—41no—
110Dic79—41no—
111Dic79—41no—
112C2×C79—22no—
113C2×C79C2×C22⋊Q811yescharacteristic
114C2×C79#57711yescharacteristic
115C2×C79#57811yescharacteristic
116#3082—791nomaximal, Sylow
117C79#308211yescharacteristic, complemented, Sylow
118#544—791no—
119#519—791no—
120#479—792no—
121#479—792no—
122#477—792no—
123#475—792no—
124#428—791no—
125#427—791no—
126#424D7911yescharacteristic
127#419—791no—
128C2×#103—791no—
129C22×Q8—791no—
130C2×M16C2×D7911yescharacteristic
131C22×C8C2×D7911yescharacteristic
132C4⋊Q8—792no—
133C4⋊Q8—1581no—
134#125—792no—
135#125—1581no—
136C22⋊Q8—1582no—
137C4×Q8—792no—
138C4×Q8—792no—
139C4×Q8—1581no—
140C4×Q8—1581no—
141#117—791no—
142#117—791no—
143#117—1582no—
144#117C2×D7911yescharacteristic
145C2×C4⋊C4—791no—
146#107—791no—
147#107—791no—
148#107—792no—
149#106—791no—
150#106—791no—
151#106—792no—
152C4⋊C8C2×D7912yes—
153C4⋊C8C2×D7912yes—
154#103—792no—
155#103—792no—
156#103—792no—
157#103—792no—
158C2×Q8—794no—
159C2×Q8—792no—
160C2×Q8—1582no—
161C2×Q8—1581no—
162C2×Q8—1582no—
163C22×C4—1581no—
164C22×C4—1581no—
165C22×C4C22×D7911yescharacteristic
166M16—22no—
167C2×C8—22no—
168C2×C8C22×D7911yescharacteristic
169C2×C8C22×D7912yes—
170C2×C8C22×D7911yescharacteristic
171C4⋊C4—792no—
172C4⋊C4—791no—
173C4⋊C4—791no—
174C4⋊C4—791no—
175C4⋊C4—791no—
176C4⋊C4—1582no—
177C4⋊C4—1582no—
178C4⋊C4—1582no—
179C4⋊C4—1582no—
180C4⋊C4—1581no—
181C4⋊C4—1582no—
182C4⋊C4D31611yescharacteristic
183C4⋊C4D31611yescharacteristic
184C22⋊C4—1581no—
185C22⋊C4—1581no—
186C22⋊C4D31612yes—
187C42—1581no—
188C42—1581no—
189C42—1582no—
190C42—1582no—
191C42C22×D7912yes—
192C23C2×D31611yescharacteristic
193Q8—794no—
194Q8—6322no—
195Q8—1582no—
196Q8—1584no—
197C2×C4—6321no—
198C2×C4—1581no—
199C2×C4—1581no—
200C2×C4—1581no—
201C2×C4—1581no—
202C2×C4—1582no—
203C2×C4—1584no—
204C2×C4—1582no—
205C2×C4C2×D31612yes—
206C2×C4C2×D31612yes—
207C2×C4C2×D31611yescharacteristic
208C2×C4Q8×D7912yes—
209C2×C4#1192962312yes—
210C2×C4C23×D7911yescharacteristic
211C8—21no—
212C8—21no—
213C8—22no—
214C22—21no—
215C22—21no—
216C22#1457914112yes—
217C22C22×D31611yescharacteristic
218C4—22no—
219C4—22no—
220C4—3162no—
221C4—3161no—
222C4—3161no—
223C4—3161no—
224C4—3161no—
225C4—1584no—
226C4#1457914112yes—
227C4C2×Q8×D7911yescharacteristic
228C4C2×#1192962311yescharacteristic
229C2—22no—
230C2C2×#1457914111yescharacteristic
231C2#1909937511yescharacteristic
232C2#1909938011yescharacteristic
subgroupG/H
centerC22C22×D316
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#424×C79C2
socleC22×C79C22×D4
prime radicalC23×C79C2×D4
hypercenter#424D79
hypocenterC79#3082
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ #117 ◁ #424

Complements

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

NH ≅ G/Ntype
3. #19098871C2semidirect
4. #19098871C2semidirect
5. #19098859C2semidirect
6. #19098849C2semidirect
44. C2×Dic158Q8semidirect
117. C79#3082semidirect