Finite Group Databasebeta

← #23764018

Subgroups — #23764018

Order 10112.

290 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 91 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×#14579094C211yesmaximal, characteristic, complemented
2C2×#14579083C211yesmaximal, characteristic
3C2×#14579081C211yesmaximal, characteristic
4#19098464C211yesmaximal, characteristic
5C4⋊C4×Dic79C211yesmaximal, characteristic, complemented
6#19098317C211yesmaximal, characteristic, complemented
7#340×C79C211yesmaximal, characteristic, complemented
8C22×D316C2211yescharacteristic
9C22×C79⋊C8C2211yescharacteristic
10C2×C4⋊Dic79C2211yescharacteristic
11C2×(C2×D79)⋊C4—21no—
12C2×(C2×D79)⋊C4—21no—
13C2×C4×Dic79—21no—
14C2×C4×Dic79C2211yescharacteristic
15#14579094—22no—
16#14579083—22no—
17#14579081C414yescomplemented
18C79⋊#95—21no—
19C22×C8×C79C2211yescharacteristic
20C2×C4⋊C4×C79C2211yescharacteristic
21C2×C4⋊C4×C79C2211yescharacteristic
22C23×D79—21no—
23C2×D316—21no—
24C2×D316—21no—
25C2×D316—21no—
26C2×D316—21no—
27C2×D316—21no—
28C2×D316C2×C412yes—
29C22×Dic79—21no—
30C22×Dic79D411yescharacteristic
31C22×Dic79D411yescharacteristic
32C2×C79⋊C8—21no—
33C2×C79⋊C8—21no—
34C2×C79⋊C8C2×C412yes—
35C4⋊Dic79—21no—
36C4⋊Dic79D412yes—
37(C2×D79)⋊C4—42no—
38(C2×D79)⋊C4—42no—
39C4×Dic79—21no—
40C4×Dic79—21no—
41C4×Dic79—42no—
42C22×C4×C79—21no—
43C22×C4×C79—21no—
44C22×C4×C79C2311yescharacteristic
45C2×C8×C79—21no—
46C2×C8×C79—21no—
47C2×C8×C79—21no—
48C4⋊C4×C79—21no—
49C4⋊C4×C79—21no—
50C4⋊C4×C79—21no—
51C4⋊C4×C79C2×C412yes—
52C23×C79C2×D411yescharacteristic
53C22×D79—22no—
54C22×D79—41no—
55C22×D79—41no—
56C22×D79—41no—
57C22×D79—41no—
58C22×D79—41no—
59C22×D79—41no—
60C2×C4×C79—22no—
61C2×C4×C79—41no—
62C2×C4×C79—41no—
63C2×C4×C79—41no—
64C2×C4×C79—41no—
65C2×C4×C79—41no—
66C2×C4×C79C22×C411yescharacteristic
67C2×C4×C79C2×D411yescharacteristic
68C2×C4×C79#4111yescharacteristic
69C2×C4×C79#4111yescharacteristic
70C2×C4×C79#4111yescharacteristic
71C2×C4×C79#4111yescharacteristic
72C2×Dic79—21no—
73C2×Dic79—21no—
74C2×Dic79—22no—
75C2×Dic79—21no—
76C2×Dic79—21no—
77C2×Dic79—21no—
78C2×Dic79—41no—
79C2×Dic79—41no—
80C2×Dic79D812yes—
81D316—22no—
82D316—22no—
83D316—41no—
84D316—41no—
85C8×C79—41no—
86C79⋊C8—22no—
87C22×C79C4×D411yescharacteristic
88C22×C79#12111yescharacteristic
89C22×C79#12311yescharacteristic
90C22×C79C2×D811yescharacteristic
91C22×C79#13511yescharacteristic
92C22×C79AGL(1,ℤ/8)11yescharacteristic
93C22×C79#13711yescharacteristic
94C2×D79—42no—
95C2×D79—42no—
96C2×D79—42no—
97C2×D79—81no—
98C2×D79—81no—
99C2×D79—81no—
100C2×D79—81no—
101C4×C79—42no—
102C4×C79—81no—
103C4×C79#11711yescharacteristic
104C4×C79C4×D411yescharacteristic
105C4×C79#12411yescharacteristic
106C4×C79#12611yescharacteristic
107Dic79—22no—
108Dic79—42no—
109Dic79—41no—
110C2×C79#38811yescharacteristic
111C2×C79C4×D811yescharacteristic
112C2×C79#44011yescharacteristic
113C2×C79#45911yescharacteristic
114C2×C79#46411yescharacteristic
115C2×C79#48011yescharacteristic
116C2×C79#48211yescharacteristic
117D79—82no—
118#1925—791nomaximal, Sylow
119C79#192511yescharacteristic, complemented, Sylow
120C2×#107—791no—
121C2×#102—791no—
122C2×#102—791no—
123#390—791no—
124C4×C4⋊C4—791no—
125#340D7911yescharacteristic, complemented
126#336—791no—
127C22×D4—791no—
128C22×C8—791no—
129C22×C8C2×D7911yescharacteristic
130C2×C4⋊C4—791no—
131C2×C4⋊C4C2×D7911yescharacteristic
132C2×C4⋊C4C2×D7911yescharacteristic
133C2×C22⋊C4—1581no—
134C2×C22⋊C4—1581no—
135C2×C42—791no—
136C2×C42—1581no—
137#107—1582no—
138#102—794no—
139#102—1582no—
140#95—1581no—
141C24—1581no—
142C2×D4—792no—
143C2×D4—1581no—
144C2×D4—1581no—
145C2×D4—1581no—
146C2×D4—1581no—
147C2×D4—1581no—
148C22×C4—21no—
149C22×C4—21no—
150C22×C4—791no—
151C22×C4—791no—
152C22×C4—1581no—
153C22×C4C22×D7911yescharacteristic
154C2×C8—21no—
155C2×C8—21no—
156C2×C8—21no—
157C2×C8—792no—
158C2×C8—1581no—
159C2×C8—1581no—
160C4⋊C4—21no—
161C4⋊C4—21no—
162C4⋊C4—21no—
163C4⋊C4—792no—
164C4⋊C4—1581no—
165C4⋊C4C4×D7912yes—
166C22⋊C4—3162no—
167C22⋊C4—3162no—
168C42—3162no—
169C42—1581no—
170C42—1581no—
171C23—3161no—
172C23—3161no—
173C23—3161no—
174C23—3161no—
175C23—3161no—
176C23—3161no—
177C23—1582no—
178C23D4×D7911yescharacteristic
179D4—3161no—
180D4—3161no—
181D4—1582no—
182D4—1582no—
183C2×C4—22no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—3161no—
190C2×C4—3161no—
191C2×C4—792no—
192C2×C4—1582no—
193C2×C4—1581no—
194C2×C4—1581no—
195C2×C4—1581no—
196C2×C4—1581no—
197C2×C4—1581no—
198C2×C4C2×C4×D7911yescharacteristic
199C2×C4D4×D7911yescharacteristic
200C2×C4#1192962311yescharacteristic
201C2×C4#1192962411yescharacteristic
202C2×C4#1192962411yescharacteristic
203C2×C4#1192962511yescharacteristic
204C8—41no—
205C8—1582no—
206C22—3162no—
207C22—3162no—
208C22—3162no—
209C22—6321no—
210C22—6321no—
211C22—6321no—
212C22—6321no—
213C22(C22⋊D79)⋊C411yescharacteristic
214C22#1457913411yescharacteristic
215C22#1457914611yescharacteristic
216C22D8×D7911yescharacteristic
217C22#1457918211yescharacteristic
218C22#1457918811yescharacteristic
219C22#1457919311yescharacteristic
220C4—42no—
221C4—81no—
222C4—3161no—
223C4—3162no—
224C4—1582no—
225C4#1457911811yescharacteristic
226C4#1457912311yescharacteristic
227C4#1457914711yescharacteristic
228C4#1457915611yescharacteristic
229C2—6322no—
230C2#1909845211yescharacteristic
231C2#1909864311yescharacteristic
232C2#1909866611yescharacteristic
233C2#1909875711yescharacteristic
234C2#1909878811yescharacteristic
235C2#1909887811yescharacteristic
236C2#1909888911yescharacteristic
subgroupG/H
centerC23D4×D79
commutatorC2×C4×C79C22×C4
FrattiniC22×C4C22×D79
Fitting#340×C79C2
socleC23×C79C2×D4
prime radicalC22×D316C22
cosocleC22×C4×C79C23
hypercenter#340D79
hypocenterC79#1925
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
1. C2×#14579094C2semidirect
5. C4⋊C4×Dic79C2semidirect
6. #19098317C2semidirect
7. #340×C79C2semidirect
17. #14579081C4semidirect
119. C79#1925semidirect
125. #340D79semidirect