Finite Group Databasebeta

← #23764055

Subgroups — #23764055

Order 10112.

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

normal subgroups only

This group has 212 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
1#19098606C211yesmaximal, characteristic
2#19098571C211yesmaximal, characteristic
3C2×#14579086C211yesmaximal, characteristic
4C2×#14579079C211yesmaximal, characteristic
5#19098331C211yesmaximal, characteristic
6#19098328C211yesmaximal, characteristic
7#405×C79C211yesmaximal, characteristic
8C22×Dic158C2211yescharacteristic
9C2×#11929608C2211yescharacteristic
10C2×#11929608C2211yescharacteristic
11C2×C4⋊Dic79C2211yescharacteristic
12#14579094—21no—
13#14579092—21no—
14#14579086—21no—
15#14579086—21no—
16#14579084—21no—
17#14579084—21no—
18#14579079C414yescomplemented
19C2×M16×C79C2211yescharacteristic
20C22×C8×C79C2211yescharacteristic
21#117×C79C2211yescharacteristic
22#97×C79—21no—
23C4×C8×C79—21no—
24C2×Dic158—21no—
25C2×Dic158—21no—
26C2×Dic158—21no—
27C2×Dic158—21no—
28C2×Dic158—21no—
29C2×Dic158C2×C412yes—
30C22×Dic79—21no—
31C22×Dic79—21no—
32#11929608—21no—
33#11929608—21no—
34#11929608—21no—
35#11929608C2×C412yes—
36C2×C79⋊C8—21no—
37C2×C79⋊C8—21no—
38C4⋊Dic79—21no—
39C4⋊Dic79—21no—
40C22×C4×C79C2311yescharacteristic
41M16×C79—21no—
42M16×C79C2×C412yes—
43C2×C8×C79—21no—
44C2×C8×C79—21no—
45C2×C8×C79—21no—
46C2×C8×C79D411yescharacteristic
47C2×C8×C79D411yescharacteristic
48C4⋊C4×C79D411yescharacteristic
49C4⋊C4×C79D411yescharacteristic
50C22⋊C4×C79—21no—
51C42×C79—21no—
52C23×C79#4111yescharacteristic
53C2×C4×C79—21no—
54C2×C4×C79—21no—
55C2×C4×C79C22×C411yescharacteristic
56C2×C4×C79C2×D411yescharacteristic
57C2×C4×C79C2×D411yescharacteristic
58C2×C4×C79#4111yescharacteristic
59C2×C4×C79#4111yescharacteristic
60C2×C4×C79#4111yescharacteristic
61C2×Dic79—22no—
62C2×Dic79—41no—
63C2×Dic79—41no—
64C2×Dic79—41no—
65C2×Dic79—81no—
66Dic158—22no—
67Dic158—22no—
68Dic158—41no—
69Dic158—41no—
70C8×C79—22no—
71C8×C79—21no—
72C8×C79—21no—
73C79⋊C8—22no—
74C79⋊C8—41no—
75C22×C79—21no—
76C22×C79—21no—
77C22×C79#11711yescharacteristic
78C22×C79#12111yescharacteristic
79C22×C79#12611yescharacteristic
80C4×C79—41no—
81C4×C79—41no—
82C4×C79C4×D411yescharacteristic
83C4×C79C4×D411yescharacteristic
84C4×C79#12311yescharacteristic
85C4×C79#12411yescharacteristic
86Dic79—42no—
87Dic79—81no—
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×#103—791no—
98C2×#101—791no—
99#405D7911yescharacteristic
100#343—791no—
101#341—791no—
102C22×Q8—791no—
103C2×M16—791no—
104C2×M16—791no—
105C2×M16C2×D7911yescharacteristic
106C22×C8C2×D7911yescharacteristic
107#117C2×D7911yescharacteristic
108C2×C4⋊C4—791no—
109#107—1581no—
110#106—1581no—
111#103—1581no—
112#103—1581no—
113#103—1581no—
114#103—1581no—
115#101—794no—
116#97—21no—
117C4×C8—21no—
118C2×Q8—792no—
119C2×Q8—1581no—
120C2×Q8—1581no—
121C2×Q8—1581no—
122C2×Q8—1581no—
123C2×Q8—1581no—
124C22×C4—1581no—
125C22×C4—1581no—
126C22×C4C22×D7911yescharacteristic
127M16—21no—
128M16—792no—
129M16—1581no—
130M16—1581no—
131M16—1581no—
132M16C4×D7912yes—
133C2×C8—21no—
134C2×C8—21no—
135C2×C8—21no—
136C2×C8—1581no—
137C2×C8—1581no—
138C2×C8C22⋊D7911yescharacteristic
139C2×C8C22⋊D7911yescharacteristic
140C4⋊C4—1581no—
141C4⋊C4—1581no—
142C4⋊C4D31611yescharacteristic
143C4⋊C4D31611yescharacteristic
144C22⋊C4—21no—
145C42—21no—
146C23#1192962411yescharacteristic
147Q8—3161no—
148Q8—3161no—
149Q8—1582no—
150Q8—1582no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—3161no—
154C2×C4—3161no—
155C2×C4—3161no—
156C2×C4—6321no—
157C2×C4—1582no—
158C2×C4C2×C4×D7911yescharacteristic
159C2×C4C2×C22⋊D7911yescharacteristic
160C2×C4C2×D31611yescharacteristic
161C2×C4#1192962411yescharacteristic
162C2×C4#1192962411yescharacteristic
163C2×C4#1192962411yescharacteristic
164C8—22no—
165C8—21no—
166C8—21no—
167C8—3161no—
168C8—1582no—
169C22—21no—
170C22—21no—
171C22#1457911811yescharacteristic
172C22#1457913511yescharacteristic
173C22#1457915511yescharacteristic
174C4—41no—
175C4—41no—
176C4—3162no—
177C4—6321no—
178C4C4×C22⋊D7911yescharacteristic
179C4C4×D31611yescharacteristic
180C4#1457914411yescharacteristic
181C4#1457914911yescharacteristic
182C2—21no—
183C2—21no—
184C2#1909845411yescharacteristic
185C2#1909882611yescharacteristic
186C2#1909883811yescharacteristic
subgroupG/H
centerC22#14579135
commutatorC2×C4×C79C22×C4
FrattiniC22×C4C22×D79
Fitting#405×C79C2
socleC22×C79#121
prime radicalC23×C79#41
cosocleC22×C4×C79C23
hypercenter#405D79
hypocenterC79#1930
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ #405

Complements

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

NH ≅ G/Ntype
18. #14579079C4semidirect
94. C79#1930semidirect