Finite Group Databasebeta

← #23764792

Subgroups — #23764792

Order 10112.

248 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 89 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
2C2×C4⋊(C79⋊C8)C211yesmaximal, characteristic
3C2×#14579084C211yesmaximal, characteristic
4C2×#14579084C211yesmaximal, characteristic
5#19098469C211yesmaximal, characteristic
6#19098325C211yesmaximal, characteristic
7#389×C79C211yesmaximal, characteristic
8C22×Dic158C2211yescharacteristic
9C22×C79⋊C8C2211yescharacteristic
10C22×C79⋊C8C2211yescharacteristic
11C2×C4⋊Dic79C2211yescharacteristic
12#14579094—22no—
13C4⋊(C79⋊C8)—22no—
14#14579084—22no—
15#14579084—22no—
16C79⋊#95—21no—
17C79⋊#95—21no—
18C2×C4⋊C4×C79—21no—
19C2×C4⋊C4×C79C2211yescharacteristic
20C2×C4⋊C4×C79C2211yescharacteristic
21C2×C42×C79C2211yescharacteristic
22#95×C79—21no—
23C2×Dic158—21no—
24C2×Dic158—21no—
25C2×Dic158—21no—
26C2×Dic158—21no—
27C2×Dic158—21no—
28C2×Dic158Q812yes—
29C22×Dic79—21no—
30C22×Dic79—21no—
31C2×C79⋊C8—21no—
32C2×C79⋊C8—21no—
33C2×C79⋊C8—21no—
34C2×C79⋊C8—21no—
35C2×C79⋊C8—21no—
36C2×C79⋊C8D412yes—
37C4⋊Dic79—21no—
38C4⋊Dic79—21no—
39C22×C4×C79—21no—
40C22×C4×C79—21no—
41C22×C4×C79D411yescharacteristic
42C22×C4×C79D411yescharacteristic
43C22×C4×C79C2311yescharacteristic
44C4⋊C4×C79—21no—
45C4⋊C4×C79—21no—
46C4⋊C4×C79—21no—
47C4⋊C4×C79—42no—
48C4⋊C4×C79D412yes—
49C42×C79—21no—
50C42×C79—21no—
51C23×C79C2×D411yescharacteristic
52C2×C4×C79—21no—
53C2×C4×C79—21no—
54C2×C4×C79—21no—
55C2×C4×C79—22no—
56C2×C4×C79—21no—
57C2×C4×C79—21no—
58C2×C4×C79—41no—
59C2×C4×C79—41no—
60C2×C4×C79—41no—
61C2×C4×C79—41no—
62C2×C4×C79—41no—
63C2×C4×C79Q1612yes—
64C2×C4×C79C2×D411yescharacteristic
65C2×C4×C79C2×D411yescharacteristic
66C2×C4×C79C2×Q811yescharacteristic
67C2×C4×C79#4111yescharacteristic
68C2×C4×C79#4111yescharacteristic
69C2×C4×C79#4111yescharacteristic
70C2×Dic79—22no—
71C2×Dic79—41no—
72C2×Dic79—41no—
73C2×Dic79—41no—
74C2×Dic79—41no—
75C2×Dic79—41no—
76Dic158—22no—
77Dic158—22no—
78Dic158—41no—
79Dic158—41no—
80C79⋊C8—22no—
81C79⋊C8—41no—
82C22×C79#12111yescharacteristic
83C22×C79#12111yescharacteristic
84C22×C79C22⋊Q811yescharacteristic
85C22×C79C2×Q1611yescharacteristic
86C22×C79#13511yescharacteristic
87C22×C79AGL(1,ℤ/8)11yescharacteristic
88C22×C79#13711yescharacteristic
89C4×C79—22no—
90C4×C79—42no—
91C4×C79—41no—
92C4×C79—81no—
93C4×C79#12111yescharacteristic
94C4×C79C22⋊Q811yescharacteristic
95C4×C79C22⋊Q811yescharacteristic
96C4×C79#12611yescharacteristic
97Dic79—42no—
98Dic79—81no—
99C2×C79#39611yescharacteristic
100C2×C79#46211yescharacteristic
101C2×C79#46311yescharacteristic
102C2×C79#46711yescharacteristic
103C2×C79#46811yescharacteristic
104C2×C79#47711yescharacteristic
105C2×C79#47911yescharacteristic
106#2068—791nomaximal, Sylow
107C79#206811yescharacteristic, complemented, Sylow
108C2×#107—791no—
109C2×C4⋊C8—791no—
110C2×#103—791no—
111C2×#103—791no—
112#391—791no—
113#389D7911yescharacteristic
114#340—791no—
115C22×Q8—791no—
116C22×C8—791no—
117C22×C8—791no—
118C2×C4⋊C4—21no—
119C2×C4⋊C4—791no—
120C2×C4⋊C4C2×D7911yescharacteristic
121C2×C4⋊C4C2×D7911yescharacteristic
122C2×C42C2×D7911yescharacteristic
123#107—1582no—
124C4⋊C8—1582no—
125#103—1582no—
126#103—1582no—
127#95—21no—
128#95—1581no—
129#95—1581no—
130C2×Q8—792no—
131C2×Q8—1581no—
132C2×Q8—1581no—
133C2×Q8—1581no—
134C2×Q8—1581no—
135C2×Q8—1581no—
136C22×C4—21no—
137C22×C4—21no—
138C22×C4—1581no—
139C22×C4—1581no—
140C22×C4C22⋊D7911yescharacteristic
141C22×C4C22⋊D7911yescharacteristic
142C22×C4C22×D7911yescharacteristic
143C2×C8—792no—
144C2×C8—1581no—
145C2×C8—1581no—
146C2×C8—1581no—
147C2×C8—1581no—
148C2×C8—1581no—
149C4⋊C4—21no—
150C4⋊C4—21no—
151C4⋊C4—21no—
152C4⋊C4—42no—
153C4⋊C4—1581no—
154C4⋊C4—1581no—
155C4⋊C4D31612yes—
156C42—21no—
157C42—21no—
158C23C2×C22⋊D7911yescharacteristic
159Q8—3161no—
160Q8—3161no—
161Q8—1582no—
162Q8—1582no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—22no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—3161no—
175C2×C4—3161no—
176C2×C4—3161no—
177C2×C4—3161no—
178C2×C4—3161no—
179C2×C4—1582no—
180C2×C4#1192961412yes—
181C2×C4D4×D7911yescharacteristic
182C2×C4C2×D31611yescharacteristic
183C2×C4Q8×D7911yescharacteristic
184C2×C4#1192962311yescharacteristic
185C2×C4#1192962411yescharacteristic
186C2×C4#1192962511yescharacteristic
187C8—3161no—
188C8—1582no—
189C22#1457913311yescharacteristic
190C22#1457913511yescharacteristic
191C22#1457913711yescharacteristic
192C22C2×#1192961411yescharacteristic
193C22#1457918111yescharacteristic
194C22#1457918711yescharacteristic
195C22#1457919111yescharacteristic
196C4—22no—
197C4—42no—
198C4—41no—
199C4—81no—
200C4—3162no—
201C4—6321no—
202C4#1457913611yescharacteristic
203C4#1457913911yescharacteristic
204C4#1457914111yescharacteristic
205C4#1457915611yescharacteristic
206C2#1909848511yescharacteristic
207C2#1909877311yescharacteristic
208C2#1909877811yescharacteristic
209C2#1909880211yescharacteristic
210C2#1909880711yescharacteristic
211C2#1909885511yescharacteristic
212C2#1909886711yescharacteristic
subgroupG/H
centerC23C2×C22⋊D79
commutator, cosocleC22×C4×C79C23
FrattiniC22×C4C22×D79
Fitting#389×C79C2
socle, prime radicalC23×C79C2×D4
hypercenter#389D79
hypocenterC79#2068
LCSG ▷ C22×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×C42 ◁ #389

Complements

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

NH ≅ G/Ntype
107. C79#2068semidirect