Finite Group Databasebeta

← #23764017

Subgroups — #23764017

Order 10112.

290 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 95 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×#14579082C211yesmaximal, characteristic
3C2×#14579082C211yesmaximal, characteristic
4C4×C4⋊Dic79C211yesmaximal, characteristic, complemented
5#19098325C211yesmaximal, characteristic, complemented
6#19098318C211yesmaximal, characteristic, complemented
7#390×C79C211yesmaximal, characteristic
8C22×C79⋊C8C2211yescharacteristic
9C22×C79⋊C8C2211yescharacteristic
10C2×C4⋊Dic79C2211yescharacteristic
11C2×C4⋊Dic79C2211yescharacteristic
12C2×C4×Dic79—21no—
13#14579094—22no—
14#14579082—22no—
15#14579082C414yescomplemented
16C79⋊#95—21no—
17C22×D4×C79C2211yescharacteristic
18C2×C4⋊C4×C79C2211yescharacteristic
19C2×C22⋊C4×C79—21no—
20C2×C22⋊C4×C79—21no—
21C2×C42×C79C2211yescharacteristic
22C22×Dic79—21no—
23C22×Dic79—21no—
24C2×C79⋊C8—21no—
25C2×C79⋊C8—21no—
26C2×C79⋊C8—21no—
27C2×C79⋊C8—21no—
28C2×C79⋊C8—21no—
29C2×C79⋊C8C2×C412yes—
30C4⋊Dic79—21no—
31C4⋊Dic79—21no—
32C4⋊Dic79C2×C412yes—
33C4⋊Dic79D412yes—
34C4×Dic79—42no—
35C24×C79—21no—
36C2×D4×C79—21no—
37C2×D4×C79—21no—
38C2×D4×C79—21no—
39C2×D4×C79—21no—
40C2×D4×C79—21no—
41C2×D4×C79C2×C412yes—
42C22×C4×C79—21no—
43C22×C4×C79D411yescharacteristic
44C22×C4×C79D411yescharacteristic
45C22×C4×C79C2311yescharacteristic
46C4⋊C4×C79—21no—
47C4⋊C4×C79—21no—
48C22⋊C4×C79—42no—
49C22⋊C4×C79—42no—
50C42×C79—21no—
51C42×C79—21no—
52C23×C79—22no—
53C23×C79—41no—
54C23×C79—41no—
55C23×C79—41no—
56C23×C79—41no—
57C23×C79—41no—
58C23×C79—41no—
59C23×C79C2×D411yescharacteristic
60D4×C79—22no—
61D4×C79—22no—
62D4×C79—41no—
63D4×C79—41no—
64C2×C4×C79—21no—
65C2×C4×C79—21no—
66C2×C4×C79—21no—
67C2×C4×C79—21no—
68C2×C4×C79—21no—
69C2×C4×C79—41no—
70C2×C4×C79—41no—
71C2×C4×C79—41no—
72C2×C4×C79D812yes—
73C2×C4×C79C22×C411yescharacteristic
74C2×C4×C79C2×D411yescharacteristic
75C2×C4×C79#4111yescharacteristic
76C2×C4×C79#4111yescharacteristic
77C2×C4×C79#4111yescharacteristic
78C2×C4×C79#4111yescharacteristic
79C2×Dic79—22no—
80C2×Dic79—22no—
81C2×Dic79—41no—
82C2×Dic79—41no—
83C2×Dic79—41no—
84C2×Dic79—41no—
85C79⋊C8—22no—
86C79⋊C8—41no—
87C22×C79—42no—
88C22×C79—42no—
89C22×C79—42no—
90C22×C79—81no—
91C22×C79—81no—
92C22×C79—81no—
93C22×C79—81no—
94C22×C79C4×D411yescharacteristic
95C22×C79#12111yescharacteristic
96C22×C79#12311yescharacteristic
97C22×C79C2×D811yescharacteristic
98C22×C79#13511yescharacteristic
99C22×C79AGL(1,ℤ/8)11yescharacteristic
100C22×C79#13711yescharacteristic
101C4×C79—22no—
102C4×C79—41no—
103C4×C79—81no—
104C4×C79#11711yescharacteristic
105C4×C79C4×D411yescharacteristic
106C4×C79#12411yescharacteristic
107C4×C79#12611yescharacteristic
108Dic79—42no—
109Dic79—42no—
110C2×C79—82no—
111C2×C79#38811yescharacteristic
112C2×C79C4×D811yescharacteristic
113C2×C79#44011yescharacteristic
114C2×C79#45911yescharacteristic
115C2×C79#46411yescharacteristic
116C2×C79#48011yescharacteristic
117C2×C79#48211yescharacteristic
118#1925—791nomaximal, Sylow
119C79#192511yescharacteristic, complemented, Sylow
120C2×#107—791no—
121C2×#102—791no—
122C2×#102—791no—
123#390D7911yescharacteristic
124C4×C4⋊C4—791no—
125#340—791no—
126#336—791no—
127C22×D4C2×D7911yescharacteristic
128C22×C8—791no—
129C22×C8—791no—
130C2×C4⋊C4—791no—
131C2×C4⋊C4—791no—
132C2×C4⋊C4C2×D7911yescharacteristic
133C2×C22⋊C4—21no—
134C2×C22⋊C4—21no—
135C2×C42—1581no—
136C2×C42C2×D7911yescharacteristic
137#107—1582no—
138#102—794no—
139#102—1582no—
140#95—1581no—
141C24—21no—
142C2×D4—21no—
143C2×D4—21no—
144C2×D4—21no—
145C2×D4—21no—
146C2×D4—21no—
147C2×D4C4×D7912yes—
148C22×C4—21no—
149C22×C4—1581no—
150C22×C4—1581no—
151C22×C4C22⋊D7911yescharacteristic
152C22×C4C22⋊D7911yescharacteristic
153C22×C4C22×D7911yescharacteristic
154C2×C8—792no—
155C2×C8—1581no—
156C2×C8—1581no—
157C2×C8—1581no—
158C2×C8—1581no—
159C2×C8—1581no—
160C4⋊C4—21no—
161C4⋊C4—21no—
162C4⋊C4—792no—
163C4⋊C4—792no—
164C4⋊C4—1581no—
165C4⋊C4—1581no—
166C22⋊C4—42no—
167C22⋊C4—42no—
168C42—21no—
169C42—21no—
170C42—3162no—
171C23—22no—
172C23—41no—
173C23—41no—
174C23—41no—
175C23—41no—
176C23—41no—
177C23—41no—
178C23C2×C22⋊D7911yescharacteristic
179D4—22no—
180D4—22no—
181D4—41no—
182D4—41no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—21no—
188C2×C4—41no—
189C2×C4—41no—
190C2×C4—41no—
191C2×C4—3161no—
192C2×C4—3161no—
193C2×C4—3161no—
194C2×C4—3161no—
195C2×C4—1582no—
196C2×C4—1582no—
197C2×C4#1192960912yes—
198C2×C4C2×C4×D7911yescharacteristic
199C2×C4D4×D7911yescharacteristic
200C2×C4#1192962311yescharacteristic
201C2×C4#1192962311yescharacteristic
202C2×C4#1192962311yescharacteristic
203C2×C4#1192962411yescharacteristic
204C8—3161no—
205C8—1582no—
206C22—42no—
207C22—42no—
208C22—42no—
209C22—81no—
210C22—81no—
211C22—81no—
212C22—81no—
213C22C4×C22⋊D7911yescharacteristic
214C22#1457913211yescharacteristic
215C22#1457914211yescharacteristic
216C22C2×#1192960911yescharacteristic
217C22#1457918111yescharacteristic
218C22#1457918711yescharacteristic
219C22#1457919111yescharacteristic
220C4—22no—
221C4—41no—
222C4—81no—
223C4—3162no—
224C4—3162no—
225C4#1457911711yescharacteristic
226C4(C22⋊D79)⋊C411yescharacteristic
227C4#1457914711yescharacteristic
228C4#1457915411yescharacteristic
229C2—82no—
230C2#1909845111yescharacteristic
231C2C4×#1192960911yescharacteristic
232C2#1909866311yescharacteristic
233C2#1909875511yescharacteristic
234C2#1909878211yescharacteristic
235C2#1909887411yescharacteristic
236C2#1909888411yescharacteristic
subgroupG/H
centerC23C2×C22⋊D79
commutatorC2×C4×C79C22×C4
FrattiniC22×C4C22×D79
Fitting#390×C79C2
socleC23×C79C2×D4
prime radicalC22×D4×C79C22
cosocleC22×C4×C79C23
hypercenter#390D79
hypocenterC79#1925
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×C42 ◁ #390

Complements

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

NH ≅ G/Ntype
1. C2×#14579094C2semidirect
4. C4×C4⋊Dic79C2semidirect
5. #19098325C2semidirect
6. #19098318C2semidirect
15. #14579082C4semidirect
119. C79#1925semidirect