Finite Group Databasebeta

← #23764822

Subgroups — #23764822

Order 10112.

222 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 222 conjugacy classes of subgroups — too many to draw. Only its 77 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×#14579086C211yesmaximal, characteristic
2C2×#14579084C211yesmaximal, characteristic
3#19098468C211yesmaximal, characteristic
4#19098428C211yesmaximal, characteristic
5#19098325C211yesmaximal, characteristic
6#19098317C211yesmaximal, characteristic
7#340×C79C211yesmaximal, characteristic
8C22×Dic158C2211yescharacteristic
9C22×C79⋊C8C2211yescharacteristic
10C2×C4⋊Dic79C2211yescharacteristic
11C2×C4×Dic79C2211yescharacteristic
12#14579086—22no—
13#14579084—22no—
14C79⋊#95—21no—
15C79⋊#95—21no—
16C79⋊#95—21no—
17C79⋊#95—21no—
18C22×C8×C79C2211yescharacteristic
19C2×C4⋊C4×C79C2211yescharacteristic
20C2×C4⋊C4×C79C2211yescharacteristic
21C2×Dic158—21no—
22C2×Dic158—21no—
23C2×Dic158—21no—
24C2×Dic158—21no—
25C2×Dic158—21no—
26C2×Dic158D412yes—
27C22×Dic79—21no—
28C22×Dic79—21no—
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×Dic79—21no—
38C22×C4×C79—21no—
39C22×C4×C79—21no—
40C22×C4×C79C2311yescharacteristic
41C2×C8×C79—21no—
42C2×C8×C79—21no—
43C2×C8×C79—21no—
44C4⋊C4×C79—21no—
45C4⋊C4×C79—21no—
46C4⋊C4×C79—21no—
47C4⋊C4×C79—21no—
48C23×C79C2×D411yescharacteristic
49C2×C4×C79—41no—
50C2×C4×C79—41no—
51C2×C4×C79—41no—
52C2×C4×C79—41no—
53C2×C4×C79—41no—
54C2×C4×C79—41no—
55C2×C4×C79C2×D411yescharacteristic
56C2×C4×C79#4111yescharacteristic
57C2×C4×C79#4111yescharacteristic
58C2×C4×C79#4111yescharacteristic
59C2×C4×C79#4111yescharacteristic
60C2×C4×C79#4111yescharacteristic
61C2×Dic79—22no—
62C2×Dic79—21no—
63C2×Dic79—21no—
64C2×Dic79—21no—
65C2×Dic79—21no—
66C2×Dic79—21no—
67C2×Dic79—21no—
68C2×Dic79—41no—
69C2×Dic79—41no—
70C2×Dic79—41no—
71C2×Dic79—41no—
72C2×Dic79—41no—
73Dic158—22no—
74Dic158—22no—
75Dic158—41no—
76Dic158—41no—
77C8×C79—41no—
78C79⋊C8—41no—
79C22×C79#12111yescharacteristic
80C22×C79#12311yescharacteristic
81C22×C79#12411yescharacteristic
82C22×C79#13511yescharacteristic
83C22×C79#13511yescharacteristic
84C22×C79#13711yescharacteristic
85C22×C79#13711yescharacteristic
86C4×C79—81no—
87C4×C79—81no—
88C4×C79#12311yescharacteristic
89C4×C79#12311yescharacteristic
90C4×C79#12611yescharacteristic
91C4×C79#12611yescharacteristic
92Dic79—42no—
93Dic79—41no—
94Dic79—41no—
95Dic79—81no—
96C2×C79#39711yescharacteristic
97C2×C79#46411yescharacteristic
98C2×C79#46411yescharacteristic
99C2×C79#48511yescharacteristic
100C2×C79#48511yescharacteristic
101C2×C79#48811yescharacteristic
102C2×C79#49111yescharacteristic
103#2074—791nomaximal, Sylow
104C79#207411yescharacteristic, complemented, Sylow
105C2×#103—791no—
106C2×#103—791no—
107#391—791no—
108#382—791no—
109#340—791no—
110#340D7911yescharacteristic
111#336—791no—
112C22×Q8—791no—
113C22×C8—791no—
114C22×C8C2×D7911yescharacteristic
115C2×C4⋊C4—791no—
116C2×C4⋊C4C2×D7911yescharacteristic
117C2×C4⋊C4C2×D7911yescharacteristic
118C2×C42—791no—
119#103—1582no—
120#103—1582no—
121#95—1581no—
122#95—1581no—
123#95—1581no—
124#95—1581no—
125C2×Q8—792no—
126C2×Q8—1581no—
127C2×Q8—1581no—
128C2×Q8—1581no—
129C2×Q8—1581no—
130C2×Q8—1581no—
131C22×C4—21no—
132C22×C4—21no—
133C22×C4—791no—
134C22×C4—791no—
135C22×C4—1581no—
136C22×C4—1581no—
137C22×C4C22×D7911yescharacteristic
138C2×C8—21no—
139C2×C8—21no—
140C2×C8—21no—
141C2×C8—1581no—
142C2×C8—1581no—
143C2×C8—1581no—
144C4⋊C4—21no—
145C4⋊C4—21no—
146C4⋊C4—21no—
147C4⋊C4—21no—
148C4⋊C4—1581no—
149C4⋊C4—1581no—
150C42—1581no—
151C42—1581no—
152C23D4×D7911yescharacteristic
153Q8—3161no—
154Q8—3161no—
155Q8—1582no—
156Q8—1582no—
157C2×C4—41no—
158C2×C4—41no—
159C2×C4—41no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—41no—
163C2×C4—3161no—
164C2×C4—3161no—
165C2×C4—3161no—
166C2×C4—3161no—
167C2×C4—3161no—
168C2×C4—1582no—
169C2×C4—1581no—
170C2×C4—1581no—
171C2×C4—1581no—
172C2×C4—1581no—
173C2×C4—1581no—
174C2×C4—1581no—
175C2×C4D4×D7911yescharacteristic
176C2×C4#1192962311yescharacteristic
177C2×C4#1192962411yescharacteristic
178C2×C4#1192962411yescharacteristic
179C2×C4#1192962411yescharacteristic
180C2×C4#1192962511yescharacteristic
181C8—41no—
182C8—3161no—
183C22#1457913411yescharacteristic
184C22#1457914611yescharacteristic
185C22#1457914711yescharacteristic
186C22#1457918011yescharacteristic
187C22#1457918211yescharacteristic
188C22#1457919011yescharacteristic
189C22#1457919311yescharacteristic
190C4—81no—
191C4—81no—
192C4—3161no—
193C4—3161no—
194C4—3162no—
195C4—6321no—
196C4#1457914311yescharacteristic
197C4#1457914611yescharacteristic
198C4#1457915511yescharacteristic
199C4#1457915611yescharacteristic
200C2#1909849211yescharacteristic
201C2#1909878411yescharacteristic
202C2#1909878811yescharacteristic
203C2#1909890611yescharacteristic
204C2#1909890711yescharacteristic
205C2#1909891611yescharacteristic
206C2#1909893011yescharacteristic
subgroupG/H
centerC23D4×D79
commutator, cosocleC22×C4×C79C23
FrattiniC22×C4C22×D79
Fitting#340×C79C2
socle, prime radicalC23×C79C2×D4
hypercenter#340D79
hypocenterC79#2074
LCSG ▷ C22×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
104. C79#2074semidirect