Finite Group Databasebeta

← #23764052

Subgroups — #23764052

Order 10112.

212 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 75 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#19098603C211yesmaximal, characteristic
2#19098572C211yesmaximal, characteristic
3C2×#14579080C211yesmaximal, characteristic
4#19098518C211yesmaximal, characteristic
5#19098332C211yesmaximal, characteristic
6#19098328C211yesmaximal, characteristic
7C2×#103×C79C211yesmaximal, characteristic
8C2×#11929608C2211yescharacteristic
9C2×#11929608C2211yescharacteristic
10C2×#11929608C2211yescharacteristic
11#14579120C2211yescharacteristic
12#14579094—21no—
13#14579092—21no—
14#14579085—21no—
15#14579085—21no—
16#14579080C414yescomplemented
17#14579071—21no—
18C8×Dic79—21no—
19C22×Q8×C79C2211yescharacteristic
20C22×C8×C79C2211yescharacteristic
21C2×C4⋊C4×C79C2211yescharacteristic
22#103×C79—21no—
23#103×C79—21no—
24#11929608—21no—
25#11929608—21no—
26#11929608—21no—
27#11929608—21no—
28#11929608C2×C412yes—
29#11929608C2×C412yes—
30C2×C79⋊C8—21no—
31C2×C79⋊C8—21no—
32C2×C79⋊C8—21no—
33C4⋊Dic79D411yescharacteristic
34C4⋊Dic79D411yescharacteristic
35C22⋊Dic79—21no—
36C4×Dic79—21no—
37C2×Q8×C79—21no—
38C2×Q8×C79—21no—
39C2×Q8×C79—21no—
40C2×Q8×C79—21no—
41C2×Q8×C79—21no—
42C2×Q8×C79C2×C412yes—
43C22×C4×C79—21no—
44C22×C4×C79—21no—
45C22×C4×C79C2311yescharacteristic
46C2×C8×C79—21no—
47C2×C8×C79—21no—
48C2×C8×C79D411yescharacteristic
49C2×C8×C79D411yescharacteristic
50C4⋊C4×C79—21no—
51C4⋊C4×C79—21no—
52C23×C79#4111yescharacteristic
53Q8×C79—22no—
54Q8×C79—22no—
55Q8×C79—41no—
56Q8×C79—41no—
57C2×C4×C79—22no—
58C2×C4×C79—41no—
59C2×C4×C79—41no—
60C2×C4×C79—41no—
61C2×C4×C79—81no—
62C2×C4×C79C22×C411yescharacteristic
63C2×C4×C79C2×D411yescharacteristic
64C2×C4×C79C2×D411yescharacteristic
65C2×C4×C79#4111yescharacteristic
66C2×C4×C79#4111yescharacteristic
67C2×C4×C79#4111yescharacteristic
68C2×Dic79—21no—
69C2×Dic79—21no—
70C8×C79—21no—
71C8×C79—21no—
72C79⋊C8—22no—
73C79⋊C8—22no—
74C79⋊C8—41no—
75C22×C79—21no—
76C22×C79—21no—
77C22×C79#11711yescharacteristic
78C22×C79#12111yescharacteristic
79C22×C79#12611yescharacteristic
80C4×C79—42no—
81C4×C79—81no—
82C4×C79C4×D411yescharacteristic
83C4×C79C4×D411yescharacteristic
84C4×C79#12311yescharacteristic
85C4×C79#12411yescharacteristic
86Dic79—41no—
87Dic79—41no—
88C2×C79—21no—
89C2×C79—21no—
90C2×C79#38811yescharacteristic
91C2×C79#47111yescharacteristic
92C2×C79#47311yescharacteristic
93#1930—791nomaximal, Sylow
94C79#193011yescharacteristic, complemented, Sylow
95#428—791no—
96#419—791no—
97C2×#103D7911yescharacteristic
98C2×#101—791no—
99#405—791no—
100#343—791no—
101#341—791no—
102C22×Q8C2×D7911yescharacteristic
103C2×M16—791no—
104C2×M16—791no—
105C2×M16—791no—
106C22×C8C2×D7911yescharacteristic
107#117—791no—
108C2×C4⋊C4C2×D7911yescharacteristic
109#107—1581no—
110#106—1581no—
111#103—21no—
112#103—21no—
113#103—1581no—
114#103—1581no—
115#101—794no—
116#97—1581no—
117C4×C8—1581no—
118C2×Q8—21no—
119C2×Q8—21no—
120C2×Q8—21no—
121C2×Q8—21no—
122C2×Q8—21no—
123C2×Q8C4×D7912yes—
124C22×C4—21no—
125C22×C4—21no—
126C22×C4C22×D7911yescharacteristic
127M16—792no—
128M16—792no—
129M16—1581no—
130M16—1581no—
131M16—1581no—
132M16—1581no—
133C2×C8—21no—
134C2×C8—21no—
135C2×C8—1581no—
136C2×C8—1581no—
137C2×C8—1581no—
138C2×C8C22⋊D7911yescharacteristic
139C2×C8C22⋊D7911yescharacteristic
140C4⋊C4—21no—
141C4⋊C4—21no—
142C4⋊C4—791no—
143C4⋊C4—791no—
144C22⋊C4—1581no—
145C42—1581no—
146C23#1192962311yescharacteristic
147Q8—22no—
148Q8—22no—
149Q8—41no—
150Q8—41no—
151C2×C4—22no—
152C2×C4—41no—
153C2×C4—41no—
154C2×C4—41no—
155C2×C4—81no—
156C2×C4—1581no—
157C2×C4—1581no—
158C2×C4C2×C4×D7911yescharacteristic
159C2×C4D4×D7911yescharacteristic
160C2×C4C2×C22⋊D7911yescharacteristic
161C2×C4#1192962311yescharacteristic
162C2×C4#1192962311yescharacteristic
163C2×C4#1192962411yescharacteristic
164C8—21no—
165C8—21no—
166C8—3161no—
167C8—1582no—
168C8—1582no—
169C22—21no—
170C22—21no—
171C22#1457911711yescharacteristic
172C22#1457913211yescharacteristic
173C22#1457915411yescharacteristic
174C4—42no—
175C4—81no—
176C4—3161no—
177C4—3161no—
178C4(C22⋊D79)⋊C411yescharacteristic
179C4C4×C22⋊D7911yescharacteristic
180C4#1457914211yescharacteristic
181C4#1457914711yescharacteristic
182C2—21no—
183C2—21no—
184C2#1909845111yescharacteristic
185C2#1909882311yescharacteristic
186C2#1909883511yescharacteristic
subgroupG/H
centerC22#14579132
commutatorC2×C4×C79C22×C4
FrattiniC22×C4C22×D79
FittingC2×#103×C79C2
socleC22×C79#121
prime radicalC23×C79#41
cosocleC22×C4×C79C23
hypercenterC2×#103D79
hypocenterC79#1930
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
16. #14579080C4semidirect
94. C79#1930semidirect