Finite Group Databasebeta

← #23763613

Subgroups — #23763613

Order 10112.

272 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 83 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#19099040C211yesmaximal, characteristic
2#19098603C211yesmaximal, characteristic
3C2×#14579079C211yesmaximal, characteristic
4#19098468C211yesmaximal, characteristic
5#19098324C211yesmaximal, characteristic
6#19098322C211yesmaximal, characteristic
7#428×C79C211yesmaximal, characteristic
8C22×Dic158C2211yescharacteristic
9C2×#11929608C2211yescharacteristic
10C4×Dic158—21no—
11C4×Dic158—21no—
12#14579126—21no—
13#14579126—21no—
14#14579120C2211yescharacteristic
15#14579117—22no—
16C2×C4×Dic79C2211yescharacteristic
17#14579094—21no—
18#14579092—21no—
19#14579079C414yescomplemented
20C79⋊#95—22no—
21C2×M16×C79C2211yescharacteristic
22#117×C79C2211yescharacteristic
23C2×C4⋊C4×C79C2211yescharacteristic
24#107×C79—21no—
25#106×C79—21no—
26C2×Dic158—21no—
27C2×Dic158—21no—
28C2×Dic158—21no—
29C2×Dic158—21no—
30C2×Dic158C2×C412yes—
31C2×Dic158Q812yes—
32C22×Dic79—21no—
33C22×Dic79D412yes—
34#11929608—21no—
35#11929608C2×C412yes—
36C2×C79⋊C8—21no—
37C4⋊Dic79D411yescharacteristic
38C4⋊Dic79D411yescharacteristic
39Dic79⋊C4—22no—
40Dic79⋊C4—22no—
41C22⋊Dic79—21no—
42C4×Dic79—22no—
43C4×Dic79—22no—
44C4×Dic79—21no—
45C4×Dic79—21no—
46C4×Dic79—21no—
47C22×C4×C79—21no—
48C22×C4×C79C2311yescharacteristic
49M16×C79—21no—
50M16×C79C2×C412yes—
51C2×C8×C79—21no—
52C4⋊C4×C79—21no—
53C4⋊C4×C79—21no—
54C4⋊C4×C79D411yescharacteristic
55C4⋊C4×C79D411yescharacteristic
56C22⋊C4×C79—21no—
57C42×C79—21no—
58C23×C79C2×D411yescharacteristic
59C2×C4×C79—21no—
60C2×C4×C79—21no—
61C2×C4×C79—42no—
62C2×C4×C79—41no—
63C2×C4×C79C22×C411yescharacteristic
64C2×C4×C79C2×D411yescharacteristic
65C2×C4×C79C2×D411yescharacteristic
66C2×C4×C79C2×Q811yescharacteristic
67C2×C4×C79#4111yescharacteristic
68C2×C4×C79#4111yescharacteristic
69C2×Dic79—22no—
70C2×Dic79—22no—
71C2×Dic79—22no—
72C2×Dic79—21no—
73C2×Dic79—21no—
74C2×Dic79—41no—
75C2×Dic79—41no—
76C2×Dic79C4⋊C414yes—
77Dic158—22no—
78Dic158—22no—
79Dic158—22no—
80Dic158—22no—
81C8×C79—22no—
82C79⋊C8—22no—
83C22×C79—21no—
84C22×C79—21no—
85C22×C79C2×C4⋊C411yescharacteristic
86C22×C79#12011yescharacteristic
87C22×C79#12311yescharacteristic
88C4×C79—41no—
89C4×C79—41no—
90C4×C79—81no—
91C4×C79C4×D411yescharacteristic
92C4×C79C4×D411yescharacteristic
93C4×C79C22⋊Q811yescharacteristic
94C4×C79C22⋊Q811yescharacteristic
95Dic79—24no—
96Dic79—42no—
97Dic79—41no—
98Dic79—41no—
99C2×C79—21no—
100C2×C79—21no—
101C2×C79#38511yescharacteristic
102C2×C79#45411yescharacteristic
103C2×C79#45611yescharacteristic
104#1857—791nomaximal, Sylow
105C79#185711yescharacteristic, complemented, Sylow
106#519—791no—
107#428—791no—
108#428D7911yescharacteristic
109C2×#101—791no—
110#391—791no—
111#339—791no—
112#339—791no—
113C22×Q8—791no—
114C2×M16—791no—
115C2×M16C2×D7911yescharacteristic
116C4×Q8—1581no—
117C4×Q8—1581no—
118C4×Q8—1581no—
119C4×Q8—1581no—
120#117—791no—
121#117—1582no—
122#117C2×D7911yescharacteristic
123C2×C4⋊C4C2×D7911yescharacteristic
124C2×C42—791no—
125#107—21no—
126#107—1581no—
127#106—21no—
128#106—1581no—
129#101—794no—
130#95—1582no—
131C2×Q8—792no—
132C2×Q8—792no—
133C2×Q8—1581no—
134C2×Q8—1581no—
135C2×Q8—1581no—
136C2×Q8—1581no—
137C22×C4—21no—
138C22×C4—792no—
139C22×C4—1581no—
140C22×C4C22×D7911yescharacteristic
141M16—21no—
142M16—792no—
143M16—1581no—
144M16C4×D7912yes—
145C2×C8—21no—
146C2×C8—1581no—
147C4⋊C4—21no—
148C4⋊C4—21no—
149C4⋊C4—791no—
150C4⋊C4—791no—
151C4⋊C4—1582no—
152C4⋊C4—1582no—
153C4⋊C4C22⋊D7911yescharacteristic
154C4⋊C4C22⋊D7911yescharacteristic
155C22⋊C4—21no—
156C22⋊C4—1581no—
157C42—21no—
158C42—1582no—
159C42—1582no—
160C42—1581no—
161C42—1581no—
162C42—1581no—
163C23D4×D7911yescharacteristic
164Q8—1582no—
165Q8—1582no—
166Q8—1582no—
167Q8—1582no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—42no—
171C2×C4—41no—
172C2×C4—3161no—
173C2×C4—3161no—
174C2×C4—794no—
175C2×C4—1582no—
176C2×C4—1581no—
177C2×C4—1581no—
178C2×C4—1582no—
179C2×C4—1582no—
180C2×C4C2×C4×D7911yescharacteristic
181C2×C4D4×D7911yescharacteristic
182C2×C4C2×C22⋊D7911yescharacteristic
183C2×C4Q8×D7911yescharacteristic
184C2×C4#1192962411yescharacteristic
185C2×C4#1192962511yescharacteristic
186C8—22no—
187C8—1582no—
188C22—21no—
189C22—21no—
190C22C4⋊C4×D7911yescharacteristic
191C22#1457912911yescharacteristic
192C22#1457914611yescharacteristic
193C4—41no—
194C4—41no—
195C4—81no—
196C4—3162no—
197C4—3161no—
198C4—3161no—
199C4—1584no—
200C4C4×C22⋊D7911yescharacteristic
201C4#1457912311yescharacteristic
202C4#1457913711yescharacteristic
203C4#1457913911yescharacteristic
204C2—21no—
205C2—21no—
206C2#1909843411yescharacteristic
207C2#1909873411yescharacteristic
208C2#1909874411yescharacteristic
subgroupG/H
centerC22#14579129
commutatorC2×C4×C79C22×C4
FrattiniC22×C4C22×D79
Fitting#428×C79C2
socleC22×C79#120
prime radicalC23×C79C2×D4
cosocleC22×C4×C79C23
hypercenter#428D79
hypocenterC79#1857
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
19. #14579079C4semidirect
105. C79#1857semidirect