Finite Group Databasebeta

← #27195626

Subgroups — #27195626

Order 13184.

324 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 93 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#20268558C211yesmaximal, characteristic, complemented
2#20267808C211yesmaximal, characteristic, complemented
3#20267796C211yesmaximal, characteristic, complemented
4C2×#15692938C211yesmaximal, characteristic, complemented
5#20267562C211yesmaximal, characteristic, complemented
6C103⋊#338C211yesmaximal, characteristic, complemented
7C2×AGL(1,ℤ/8)×C103C211yesmaximal, characteristic
8#15693028—22no—
9#15693028—22no—
10C2×#13110089—22no—
11C2×#13110089C2211yescharacteristic
12C2×#13110089C2211yescharacteristic
13C2×#13110089C2211yescharacteristic
14#15692980C2211yescharacteristic
15#15692948—22no—
16#15692942—22no—
17#15692938—22no—
18C2×#41×C103C2211yescharacteristic
19C22×D4×C103C2211yescharacteristic
20AGL(1,ℤ/8)×C103—22no—
21AGL(1,ℤ/8)×C103—22no—
22C2×SD16×C103C412yescomplemented
23C2×D8×C103C412yescomplemented
24C2×M16×C103C2211yescharacteristic
25#13110089—24no—
26#13110089—21no—
27#13110089—21no—
28#13110089—21no—
29#13110089—21no—
30#13110089—21no—
31#13110089D412yes—
32C2×C103⋊C8—24no—
33C2×C103⋊C8—21no—
34C2×C103⋊C8—21no—
35C2×C103⋊C8D412yes—
36C4⋊Dic103—21no—
37C22⋊Dic103—21no—
38C4×Dic103—21no—
39C24×C103—21no—
40#41×C103—21no—
41#41×C103—21no—
42#41×C103D412yes—
43#41×C103D412yes—
44C2×Q8×C103C2×C411yescharacteristic
45C2×D4×C103—21no—
46C2×D4×C103—21no—
47C2×D4×C103—21no—
48C2×D4×C103—21no—
49C2×D4×C103—21no—
50C2×D4×C103—21no—
51C2×D4×C103C2×C412yes—
52C2×D4×C103C2×C411yescharacteristic
53C22×C4×C103—21no—
54C22×C4×C103C2311yescharacteristic
55SD16×C103—24no—
56D8×C103—24no—
57M16×C103—21no—
58M16×C103—21no—
59C2×C8×C103C2×C412yes—
60C23×C103—21no—
61C23×C103—22no—
62C23×C103—41no—
63C23×C103—41no—
64C23×C103—82no—
65C23×C103#4111yescharacteristic
66Q8×C103—21no—
67Q8×C103C22⋊C412yes—
68D4×C103—22no—
69D4×C103—22no—
70D4×C103—22no—
71D4×C103—21no—
72D4×C103—22no—
73D4×C103—41no—
74D4×C103—41no—
75D4×C103C22⋊C412yes—
76C2×C4×C103—21no—
77C2×C4×C103—22no—
78C2×C4×C103—22no—
79C2×C4×C103C22×C411yescharacteristic
80C2×C4×C103C2×D411yescharacteristic
81C2×C4×C103C2×D411yescharacteristic
82C2×C4×C103C2×D411yescharacteristic
83C2×C4×C103C2×D411yescharacteristic
84C2×C4×C103#4111yescharacteristic
85C2×Dic103—41no—
86C8×C103—22no—
87C103⋊C8—22no—
88C103⋊C8—22no—
89C103⋊C8—41no—
90C22×C103—22no—
91C22×C103—41no—
92C22×C103—42no—
93C22×C103—81no—
94C22×C103—82no—
95C22×C103—82no—
96C22×C103—82no—
97C22×C103C4×D411yescharacteristic
98C22×C103#12111yescharacteristic
99C22×C103#12311yescharacteristic
100C4×C103—22no—
101C4×C103C2×C22⋊C411yescharacteristic
102C4×C103C4×D411yescharacteristic
103C4×C103#12011yescharacteristic
104C4×C103#12111yescharacteristic
105Dic103—81no—
106C2×C103—21no—
107C2×C103—21no—
108C2×C103—21no—
109C2×C103—42no—
110C2×C103—82no—
111C2×C103#38611yescharacteristic
112#1903—1031nomaximal, Sylow
113C103#190311yescharacteristic, complemented, Sylow
114C2×AGL(1,ℤ/8)D10311yescharacteristic
115#568—1031no—
116#421—1031no—
117#418—1031no—
118C2×#100—1031no—
119#344—1031no—
120#338—1031no—
121C2×#41C2×D10311yescharacteristic
122C22×D4C2×D10311yescharacteristic
123AGL(1,ℤ/8)—22no—
124AGL(1,ℤ/8)—22no—
125C2×SD16Dic10312yescomplemented
126C2×D8Dic10312yescomplemented
127#131—2062no—
128#131—2062no—
129C2×M16—1031no—
130C2×M16—1031no—
131C2×M16—1031no—
132C2×M16—2062no—
133C2×M16C2×D10311yescharacteristic
134#117—1031no—
135#104—2062no—
136#102—2062no—
137#100—2062no—
138C24—21no—
139#41—21no—
140#41—21no—
141#41C22⋊D10312yes—
142#41C22⋊D10312yes—
143C2×Q8C2×Dic10311yescharacteristic
144C2×D4—21no—
145C2×D4—21no—
146C2×D4—21no—
147C2×D4—21no—
148C2×D4—21no—
149C2×D4—21no—
150C2×D4C2×Dic10312yes—
151C2×D4C2×Dic10311yescharacteristic
152C22×C4—21no—
153C22×C4C22×D10311yescharacteristic
154SD16—24no—
155D8—24no—
156M16—21no—
157M16—21no—
158M16—1032no—
159M16—2061no—
160M16—2061no—
161M16—2064no—
162M16—2061no—
163M16—2061no—
164M16—2061no—
165C2×C8—1032no—
166C2×C8—2061no—
167C2×C8—2064no—
168C2×C8—2061no—
169C2×C8C2×Dic10312yes—
170C4⋊C4—2061no—
171C22⋊C4—2061no—
172C42—2061no—
173C23—21no—
174C23—22no—
175C23—41no—
176C23—41no—
177C23—82no—
178C23#1311010411yescharacteristic
179Q8—21no—
180Q8C22⋊Dic10312yes—
181D4—22no—
182D4—22no—
183D4—22no—
184D4—21no—
185D4—22no—
186D4—41no—
187D4—41no—
188D4C22⋊Dic10312yes—
189C2×C4—21no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—4121no—
193C2×C4C22×Dic10311yescharacteristic
194C2×C4D4×D10311yescharacteristic
195C2×C4D4×D10311yescharacteristic
196C2×C4C2×C22⋊D10311yescharacteristic
197C2×C4C2×C22⋊D10311yescharacteristic
198C2×C4#1311010411yescharacteristic
199C8—22no—
200C8—4121no—
201C8—2062no—
202C8—2062no—
203C22—22no—
204C22—41no—
205C22—42no—
206C22—81no—
207C22—82no—
208C22—82no—
209C22—82no—
210C22D4×Dic10311yescharacteristic
211C22#1569299311yescharacteristic
212C22#1569300211yescharacteristic
213C4—22no—
214C4—8241no—
215C4C2×C22⋊Dic10311yescharacteristic
216C4D4×Dic10311yescharacteristic
217C4#1569298911yescharacteristic
218C4#1569299311yescharacteristic
219C2—21no—
220C2—21no—
221C2—21no—
222C2—42no—
223C2—82no—
224C2#2026767111yescharacteristic
subgroupG/H
centerC2#20267671
commutatorC2×C4×C103C22×C4
FrattiniC22×C4C22×D103
Fitting, prime radicalC2×AGL(1,ℤ/8)×C103C2
socleC2×C103#386
cosocleC22×C4×C103C23
hypercenterC2×AGL(1,ℤ/8)D103
hypocenterC103#1903
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. #20268558C2semidirect
2. #20267808C2semidirect
3. #20267796C2semidirect
4. C2×#15692938C2semidirect
5. #20267562C2semidirect
6. C103⋊#338C2semidirect
22. C2×SD16×C103C4semidirect
23. C2×D8×C103C4semidirect
113. C103#1903semidirect
125. C2×SD16Dic103semidirect
126. C2×D8Dic103semidirect

Maximal subgroups

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

subgroupindex
#202685582
#202678082
#202677962
C2×#156929382
#202675622
C103⋊#3382
C2×AGL(1,ℤ/8)×C1032
#1903103