Finite Group Databasebeta

← #28406483

Subgroups — #28406483

Order 14464.

262 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 62 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#20299584C211yesmaximal, characteristic
2#20299577C211yesmaximal, characteristic
3#20299469C212yesmaximal, complemented
4#20299465C212yesmaximal, complemented
5C4×#14268647C211yesmaximal, characteristic
6D113⋊M16C2212yes—
7#16813701C2212yes—
8#16813683—21no—
9#16813682—21no—
10#16813681—21no—
11#16813680—21no—
12C2×#14268647C2211yescharacteristic
13C4×Dic226—21no—
14C4×D452—21no—
15C4×C22⋊D113—21no—
16C4×C22⋊D113—21no—
17#16813581C411yescharacteristic, complemented
18#16813579C411yescharacteristic, complemented
19#16813579C2211yescharacteristic
20C42×D113C411yescharacteristic, complemented
21C42×D113C2211yescharacteristic
22C2×C42×C113C411yescharacteristic, complemented
23#14268657—22no—
24#14268656—22no—
25#14268655—22no—
26C4⋊#90673—22no—
27C22⋊#90673—22no—
28C4×#90673—22no—
29#14268647—22no—
30#14268647—22no—
31C2×Dic226D411yescharacteristic
32C2×D452D411yescharacteristic
33C2×C22⋊D113D411yescharacteristic
34C2×C22⋊D113D411yescharacteristic
35C2×C4×D113—21no—
36C2×C4×D113—21no—
37C2×C4×D113C2×C411yescharacteristic
38C2×C4×D113C2311yescharacteristic
39C4⋊Dic113—21no—
40#14268626—21no—
41#14268626—21no—
42C22⋊Dic113—21no—
43#14268624—21no—
44#14268624—21no—
45C4×Dic113—21no—
46C4×Dic113—21no—
47C4×Dic113C2×C411yescharacteristic
48C4×Dic113C2×C411yescharacteristic
49C22×C4×C113—21no—
50C22×C4×C113C2×C411yescharacteristic
51C42×C113—21no—
52C42×C113C2×C411yescharacteristic
53C42×C113C2×C411yescharacteristic
54C23×C113C22⋊C411yescharacteristic
55C22×D113C22⋊C411yescharacteristic
56C22×D113C2×D411yescharacteristic
57C2×#90673—42no—
58C2×C4×C113—21no—
59C2×C4×C113—21no—
60C2×C4×C113—21no—
61C2×C4×C113—21no—
62C2×C4×C113—42no—
63C2×C4×C113C22⋊C411yescharacteristic
64C2×C4×C113C22×C411yescharacteristic
65C22⋊D113—22no—
66C22⋊D113—22no—
67C2×Dic113—21no—
68C2×Dic113—21no—
69C2×Dic113C22⋊C411yescharacteristic
70C2×Dic113C2×D411yescharacteristic
71D452—22no—
72C4×D113—21no—
73C4×D113—21no—
74C4×D113—42no—
75C4×D113—42no—
76C4×D113#4112yes—
77C4×D113#4112yes—
78Dic226—22no—
79#11744753—42no—
80C22×C113—21no—
81C22×C113—41no—
82C22×C113C2×C22⋊C411yescharacteristic
83C2×D113—21no—
84C2×D113—41no—
85C2×D113—41no—
86C2×D113#12312yes—
87#90673—82no—
88C4×C113—22no—
89C4×C113—21no—
90C4×C113—41no—
91C4×C113#11711yescharacteristic
92C4×C113#11711yescharacteristic
93Dic113—21no—
94Dic113—41no—
95Dic113—41no—
96Dic113#12312yes—
97C2×C113—21no—
98C2×C113—41no—
99C2×C113#38111yescharacteristic
100D113—22no—
101D113—41no—
102#1827—1131nomaximal, Sylow
103C113#182711yescharacteristic, complemented, Sylow
104C4×#41—1131no—
105#413—1131no—
106#410—1131no—
107#339—1132no—
108H(3,ℤ/4)—1132no—
109C2×#41—1131no—
110C2×M16—1132no—
111C4×Q8—2261no—
112C4×D4—2261no—
113C4×D4—2261no—
114C4×D4—2261no—
115#117—1131no—
116#117—1131no—
117#117—1131no—
118#117—1132no—
119C2×C42—1131no—
120C2×C42—1131no—
121C2×C42#9067311yescharacteristic, complemented
122#101—2261no—
123#100—2261no—
124#99—2261no—
125#99—2261no—
126#41—2262no—
127#41—2262no—
128C2×Q8—1131no—
129C2×D4—1131no—
130C2×D4—1131no—
131C2×D4—1131no—
132C22×C4—21no—
133C22×C4—1131no—
134C22×C4—1131no—
135C22×C4—2261no—
136C22×C4—2261no—
137C22×C4C2×#9067311yescharacteristic
138M16—2262no—
139M16—2262no—
140C2×C8—2262no—
141C4⋊C4—2261no—
142C4⋊C4—2261no—
143C4⋊C4—2262no—
144C4⋊C4—2261no—
145C22⋊C4—2261no—
146C22⋊C4—2261no—
147C22⋊C4—2262no—
148C22⋊C4—2261no—
149C42—21no—
150C42—1131no—
151C42—1131no—
152C42—2261no—
153C42—2261no—
154C42—2262no—
155C42C2×#9067311yescharacteristic
156C42C2×#9067311yescharacteristic
157C23—1131no—
158C23—1131no—
159C23C22⋊#9067311yescharacteristic
160Q8—2262no—
161D4—2262no—
162D4—2262no—
163D4—2262no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—42no—
169C2×C4—1131no—
170C2×C4—1132no—
171C2×C4—1132no—
172C2×C4—1131no—
173C2×C4—4522no—
174C2×C4—4522no—
175C2×C4—4522no—
176C2×C4—2261no—
177C2×C4—2261no—
178C2×C4—2261no—
179C2×C4—2261no—
180C2×C4C22⋊#9067311yescharacteristic
181C2×C4C22×#9067311yescharacteristic
182C8—4522no—
183C22—21no—
184C22—41no—
185C22—1132no—
186C22—4521no—
187C22—4521no—
188C22—2261no—
189C22C2×C22⋊#9067311yescharacteristic
190C4—22no—
191C4—21no—
192C4—41no—
193C4—1132no—
194C4—9042no—
195C4—4521no—
196C4—4521no—
197C4—2261no—
198C4#1681370111yescharacteristic
199C4#1681370111yescharacteristic
200C2—21no—
201C2—41no—
202C2—4521no—
203C2—2262no—
204C2#2029954111yescharacteristic
subgroupG/H
centerC4#16813701
commutatorC2×C4×C113C22×C4
FrattiniC2×C4C22×#90673
FittingC2×C42×C113C4
socleC2×C113#381
prime radicalC2×#14268647C22
cosocleC2×C4×D113C23
hypercenterC2×C42#90673
hypocenterC113#1827
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C4 ◁ C42 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
3. #20299469C2semidirect
4. #20299465C2semidirect
17. #16813581C4semidirect
18. #16813579C4semidirect
20. C42×D113C4semidirect
22. C2×C42×C113C4semidirect
103. C113#1827semidirect
121. C2×C42#90673semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#202995842
#202995772
#202994692
#202994652
C4×#142686472
#1827113