Finite Group Databasebeta

← #23762462

Subgroups — #23762462

Order 10112.

278 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 278 conjugacy classes of subgroups — too many to draw. Only its 55 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
1#19099233C211yesmaximal, characteristic, complemented
2#19098760C211yesmaximal, characteristic, complemented
3#19098755C211yesmaximal, characteristic, complemented
4#19098307C211yesmaximal, characteristic, complemented
5#19098295C211yesmaximal, characteristic, complemented
6#19098292C211yesmaximal, characteristic, complemented
7#493×C79C211yesmaximal, characteristic, complemented
8C2×#11929623—21no—
9C2×#11929612—21no—
10C2×#11929609—21no—
11#14579157—21no—
12#14579133—22no—
13#14579132—21no—
14C4×Dic158C2211yescharacteristic
15C4×D316C2211yescharacteristic
16D4×Dic79—21no—
17C4⋊(C79⋊C8)C2211yescharacteristic
18C4⋊(C79⋊C8)C2211yescharacteristic
19#14579082—21no—
20#14579082—21no—
21C2×D8×C79—22no—
22#127×C79C2211yescharacteristic
23#127×C79C2211yescharacteristic
24C4×C8×C79C2211yescharacteristic
25#11929623—42no—
26#11929623—42no—
27C2×Dic158D411yescharacteristic
28C2×D316D411yescharacteristic
29C2×C22⋊D79—22no—
30C2×C22⋊D79—22no—
31C22×Dic79—22no—
32C2×C4×D79—21no—
33#11929612—42no—
34#11929609—42no—
35C2×C79⋊C8—21no—
36C2×C79⋊C8—21no—
37C4⋊Dic79D411yescharacteristic
38C4⋊Dic79D411yescharacteristic
39Dic79⋊C4—21no—
40C22⋊Dic79—22no—
41(C2×D79)⋊C4—21no—
42C4×Dic79—21no—
43C2×D4×C79—21no—
44C2×D4×C79—21no—
45C2×D4×C79—21no—
46C2×D4×C79—21no—
47C2×D4×C79—21no—
48C2×D4×C79D412yes—
49D8×C79—44no—
50C2×C8×C79—21no—
51C42×C79C2311yescharacteristic
52C23×C79—22no—
53C23×C79—41no—
54C22×D79—21no—
55D4×C79—42no—
56D4×C79—42no—
57D4×C79—41no—
58D4×C79—41no—
59D4×C79—41no—
60D4×C79—41no—
61D4×C79—41no—
62D4×C79—41no—
63D4×C79—41no—
64D4×C79—41no—
65C2×C4×C79C2×D411yescharacteristic
66C2×C4×C79C2×D411yescharacteristic
67C2×C4×C79C2×D411yescharacteristic
68C22⋊D79—44no—
69C22⋊D79—82no—
70C2×Dic79—21no—
71C2×Dic79—21no—
72C2×Dic79—21no—
73C2×Dic79—44no—
74D316—21no—
75D316—21no—
76C4×D79—41no—
77C4×D79—41no—
78Dic158—21no—
79Dic158D812yescomplemented
80C8×C79—22no—
81C79⋊C8—41no—
82C79⋊C8—41no—
83C22×C79—42no—
84C22×C79—42no—
85C22×C79—42no—
86C22×C79—81no—
87C22×C79—81no—
88C22×C79—81no—
89C22×C79#12011yescharacteristic
90C2×D79—41no—
91C2×D79—41no—
92C2×D79—41no—
93C4×C79—21no—
94C4×C79C2×D811yescharacteristic
95C4×C79#13511yescharacteristic
96C4×C79AGL(1,ℤ/8)11yescharacteristic
97C4×C79AGL(1,ℤ/8)11yescharacteristic
98Dic79—22no—
99Dic79—41no—
100Dic79—41no—
101C2×C79—82no—
102C2×C79—161no—
103C2×C79#44711yescharacteristic
104C2×C79#44911yescharacteristic
105C2×C79#45311yescharacteristic
106D79—81no—
107#1621—791nomaximal, Sylow
108C79#162111yescharacteristic, complemented, Sylow
109#550—791no—
110#493D7911yescharacteristic, complemented
111#460—791no—
112#459—791no—
113#331—791no—
114Q8⋊C8—791no—
115D4⋊C8—791no—
116C2×#41—1581no—
117C2×SD16—1581no—
118C2×D8—22no—
119C2×D8—1581no—
120#127—1581no—
121#127C2×D7911yescharacteristic
122#127C2×D7911yescharacteristic
123#121—1581no—
124#121—1582no—
125C4×Q8—791no—
126C4×D4—791no—
127C4×D4—1581no—
128C4⋊C8—791no—
129C4⋊C8—791no—
130#102—1581no—
131#102—1581no—
132C4×C8C2×D7911yescharacteristic
133#41—3162no—
134#41—3162no—
135C2×Q8—791no—
136C2×D4—21no—
137C2×D4—21no—
138C2×D4—21no—
139C2×D4—21no—
140C2×D4—21no—
141C2×D4—791no—
142C2×D4—1582no—
143C2×D4—1582no—
144C2×D4C22⋊D7912yes—
145C22×C4—1582no—
146C22×C4—1581no—
147SD16—3162no—
148D8—44no—
149D8—3162no—
150C2×C8—21no—
151C2×C8—1581no—
152C2×C8—1581no—
153C4⋊C4—791no—
154C4⋊C4—791no—
155C4⋊C4—1581no—
156C22⋊C4—1582no—
157C22⋊C4—1581no—
158C42—1581no—
159C42C22×D7911yescharacteristic
160C23—22no—
161C23—41no—
162C23—1581no—
163Q8—792no—
164Q8—1581no—
165D4—42no—
166D4—42no—
167D4—41no—
168D4—41no—
169D4—41no—
170D4—41no—
171D4—41no—
172D4—41no—
173D4—41no—
174D4—41no—
175D4—3164no—
176D4—6322no—
177D4—1581no—
178D4—1581no—
179C2×C4—3164no—
180C2×C4—3161no—
181C2×C4—3161no—
182C2×C4—1581no—
183C2×C4—1581no—
184C2×C4—1581no—
185C2×C4D4×D7911yescharacteristic
186C2×C4D4×D7911yescharacteristic
187C2×C4C2×C22⋊D7911yescharacteristic
188C8—22no—
189C8—3161no—
190C8—3161no—
191C22—42no—
192C22—42no—
193C22—42no—
194C22—81no—
195C22—81no—
196C22—81no—
197C22—3161no—
198C22—3161no—
199C22—3161no—
200C22#1457912911yescharacteristic
201C4—21no—
202C4—3161no—
203C4—3161no—
204C4—1582no—
205C4D8×D7911yescharacteristic
206C4#1457918011yescharacteristic
207C4#1457918511yescharacteristic
208C4#1457918511yescharacteristic
209C2—82no—
210C2—161no—
211C2—6321no—
212C2#1909869511yescharacteristic
213C2#1909870511yescharacteristic
214C2#1909873011yescharacteristic
subgroupG/H
centerC22#14579129
commutator, cosocleC42×C79C23
FrattiniC42C22×D79
Fitting#493×C79C2
socleC22×C79#120
hypercenter#493D79
hypocenterC79#1621
LCSG ▷ C42×C79 ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ C42 ◁ #493

Complements

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

NH ≅ G/Ntype
1. #19099233C2semidirect
2. #19098760C2semidirect
3. #19098755C2semidirect
4. #19098307C2semidirect
5. #19098295C2semidirect
6. #19098292C2semidirect
7. #493×C79C2semidirect
79. Dic158D8semidirect
108. C79#1621semidirect
110. #493D79semidirect