Finite Group Databasebeta

← #23763408

Subgroups — #23763408

Order 10112.

356 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 356 conjugacy classes of subgroups — too many to draw. Only its 109 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×D4×Dic79C211yesmaximal, characteristic
2C2×Dic79⋊C8C211yesmaximal, characteristic, complemented
3C2×#14579082C211yesmaximal, characteristic
4#19098428C211yesmaximal, characteristic, complemented
5#19098326C211yesmaximal, characteristic, complemented
6#19098325C211yesmaximal, characteristic, complemented
7C2×#102×C79C211yesmaximal, characteristic
8C23×Dic79—21no—
9C22×C79⋊C8C2211yescharacteristic
10D4×Dic79—22no—
11D4×Dic79C414yescomplemented
12C2×C4⋊Dic79C2211yescharacteristic
13C2×C4⋊Dic79C2211yescharacteristic
14C2×C22⋊Dic79—21no—
15C2×C4×Dic79C2211yescharacteristic
16Dic79⋊C8—22no—
17#14579082—22no—
18C79⋊#95—21no—
19C79⋊#95—21no—
20C22×D4×C79C2211yescharacteristic
21C22×C8×C79C2211yescharacteristic
22C2×C4⋊C4×C79C2211yescharacteristic
23#102×C79—22no—
24C22×Dic79—24no—
25C22×Dic79—21no—
26C22×Dic79—21no—
27C22×Dic79—42no—
28C22×Dic79—42no—
29C22×Dic79D411yescharacteristic
30C22×Dic79D411yescharacteristic
31C2×C79⋊C8—21no—
32C2×C79⋊C8—21no—
33C2×C79⋊C8—21no—
34C4⋊Dic79—21no—
35C4⋊Dic79—21no—
36C4⋊Dic79—21no—
37C4⋊Dic79C2×C412yes—
38C22⋊Dic79—24no—
39C4×Dic79C2×C412yes—
40C4×Dic79D412yes—
41C24×C79—21no—
42C2×D4×C79—21no—
43C2×D4×C79—21no—
44C2×D4×C79—21no—
45C2×D4×C79C2×C412yes—
46C2×D4×C79D412yes—
47C2×D4×C79Q812yes—
48C22×C4×C79—21no—
49C22×C4×C79C2311yescharacteristic
50C2×C8×C79—21no—
51C2×C8×C79—21no—
52C2×C8×C79—21no—
53C4⋊C4×C79—21no—
54C4⋊C4×C79—21no—
55C23×C79—22no—
56C23×C79—22no—
57C23×C79—22no—
58C23×C79—41no—
59C23×C79—41no—
60C23×C79—41no—
61C23×C79—41no—
62C23×C79C2×D411yescharacteristic
63D4×C79—22no—
64D4×C79—22no—
65D4×C79—22no—
66D4×C79C4⋊C414yes—
67C2×C4×C79—41no—
68C2×C4×C79—41no—
69C2×C4×C79—41no—
70C2×C4×C79C22×C411yescharacteristic
71C2×C4×C79C2×D411yescharacteristic
72C2×C4×C79C2×D411yescharacteristic
73C2×C4×C79C2×Q811yescharacteristic
74C2×C4×C79#4111yescharacteristic
75C2×C4×C79#4111yescharacteristic
76C2×Dic79—21no—
77C2×Dic79—21no—
78C2×Dic79—21no—
79C2×Dic79—21no—
80C2×Dic79—22no—
81C2×Dic79—48no—
82C2×Dic79—41no—
83C2×Dic79—41no—
84C2×Dic79—41no—
85C2×Dic79—41no—
86C2×Dic79—41no—
87C2×Dic79C22⋊C412yes—
88C2×Dic79C22⋊C412yes—
89C8×C79—41no—
90C79⋊C8—41no—
91C22×C79—24no—
92C22×C79—42no—
93C22×C79—42no—
94C22×C79—42no—
95C22×C79—42no—
96C22×C79—42no—
97C22×C79—42no—
98C22×C79C2×C22⋊C411yescharacteristic
99C22×C79#12111yescharacteristic
100C22×C79C22⋊Q811yescharacteristic
101C22×C79#13511yescharacteristic
102C22×C79#13511yescharacteristic
103C22×C79AGL(1,ℤ/8)11yescharacteristic
104C22×C79AGL(1,ℤ/8)11yescharacteristic
105C4×C79—81no—
106C4×C79C2×C4⋊C411yescharacteristic
107C4×C79#11711yescharacteristic
108C4×C79#12111yescharacteristic
109C4×C79C22⋊Q811yescharacteristic
110Dic79—22no—
111Dic79—22no—
112Dic79—42no—
113Dic79—81no—
114C2×C79—44no—
115C2×C79#38011yescharacteristic
116C2×C79#41611yescharacteristic
117C2×C79#41811yescharacteristic
118C2×C79#46311yescharacteristic
119C2×C79#46311yescharacteristic
120C2×C79#47811yescharacteristic
121C2×C79#47811yescharacteristic
122#1804—791nomaximal, Sylow
123C79#180411yescharacteristic, complemented, Sylow
124C2×C4×D4—791no—
125C2×C4⋊C8—791no—
126C2×#102—791no—
127C2×#102D7911yescharacteristic
128#382—791no—
129#340—791no—
130#340—791no—
131C22×D4C2×D7911yescharacteristic
132C23×C4—1581no—
133C22×C8—791no—
134C22×C8C2×D7911yescharacteristic
135C4×D4—794no—
136C4×D4—1582no—
137C2×C4⋊C4—791no—
138C2×C4⋊C4—791no—
139C2×C4⋊C4C2×D7911yescharacteristic
140C2×C22⋊C4—1581no—
141C2×C42—791no—
142C4⋊C8—1582no—
143#102—22no—
144#102—1582no—
145#95—1581no—
146#95—1581no—
147C24—21no—
148C2×D4—21no—
149C2×D4—21no—
150C2×D4—21no—
151C2×D4Dic15812yes—
152C2×D4C4×D7912yes—
153C2×D4C22⋊D7912yes—
154C22×C4—21no—
155C22×C4—3162no—
156C22×C4—3162no—
157C22×C4—791no—
158C22×C4—791no—
159C22×C4—1581no—
160C22×C4—1584no—
161C22×C4—1581no—
162C22×C4C22×D7911yescharacteristic
163C2×C8—21no—
164C2×C8—21no—
165C2×C8—21no—
166C2×C8—1581no—
167C2×C8—1581no—
168C2×C8—1581no—
169C4⋊C4—21no—
170C4⋊C4—21no—
171C4⋊C4—792no—
172C4⋊C4—1581no—
173C4⋊C4—1581no—
174C4⋊C4—1581no—
175C22⋊C4—1584no—
176C42—792no—
177C42—792no—
178C23—22no—
179C23—22no—
180C23—22no—
181C23—41no—
182C23—41no—
183C23—41no—
184C23—41no—
185C23D4×D7911yescharacteristic
186D4—22no—
187D4—22no—
188D4—22no—
189D4Dic79⋊C414yes—
190C2×C4—41no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—3161no—
194C2×C4—3161no—
195C2×C4—3168no—
196C2×C4—3161no—
197C2×C4—3161no—
198C2×C4—3161no—
199C2×C4—792no—
200C2×C4—792no—
201C2×C4—1582no—
202C2×C4—1581no—
203C2×C4—1581no—
204C2×C4—1581no—
205C2×C4—1581no—
206C2×C4C2×C4×D7911yescharacteristic
207C2×C4D4×D7911yescharacteristic
208C2×C4C2×C22⋊D7911yescharacteristic
209C2×C4C2×Dic15811yescharacteristic
210C2×C4#1192962311yescharacteristic
211C2×C4#1192962311yescharacteristic
212C8—41no—
213C8—3161no—
214C22—24no—
215C22—42no—
216C22—42no—
217C22—42no—
218C22—42no—
219C22—42no—
220C22—42no—
221C22C22⋊C4×D7911yescharacteristic
222C22#1457913311yescharacteristic
223C22#1457913811yescharacteristic
224C22#1457918011yescharacteristic
225C22#1457918211yescharacteristic
226C22#1457918511yescharacteristic
227C22#1457918811yescharacteristic
228C4—81no—
229C4—3162no—
230C4—6321no—
231C4—1582no—
232C4—1582no—
233C4C2×Dic79⋊C411yescharacteristic
234C4#1457911711yescharacteristic
235C4#1457913311yescharacteristic
236C4#1457913811yescharacteristic
237C2—44no—
238C2#1909842111yescharacteristic
239C2#1909855611yescharacteristic
240C2#1909856611yescharacteristic
241C2#1909877611yescharacteristic
242C2#1909878011yescharacteristic
243C2#1909886111yescharacteristic
244C2#1909886511yescharacteristic
subgroupG/H
centerC23D4×D79
commutatorC2×C4×C79C22×C4
FrattiniC22×C4C22×D79
FittingC2×#102×C79C2
socleC23×C79C2×D4
prime radicalC22×D4×C79C22
cosocleC22×C4×C79C23
hypercenterC2×#102D79
hypocenterC79#1804
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
2. C2×Dic79⋊C8C2semidirect
4. #19098428C2semidirect
5. #19098326C2semidirect
6. #19098325C2semidirect
11. D4×Dic79C4semidirect
123. C79#1804semidirect