Finite Group Databasebeta

← #27196827

Subgroups — #27196827

Order 13184.

250 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 65 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#20268337C211yesmaximal, characteristic
2#20267775C211yesmaximal, characteristic, complemented
3#20267589C212yesmaximal, complemented
4#20267587C212yesmaximal, complemented
5#413×C103C211yesmaximal, characteristic, complemented
6C2×#13110105C411yescharacteristic
7C2×#13110089—21no—
8#15693019C2211yescharacteristic
9#15693017C411yescharacteristic
10#15693010C2211yescharacteristic
11#15693008C411yescharacteristic
12#15692993—21no—
13#15692993—21no—
14C4×C22⋊D103—21no—
15C4×C22⋊D103—21no—
16C2×C4×Dic103C411yescharacteristic
17#15692940C2212yes—
18#15692938—21no—
19C2×#41×C103C2211yescharacteristic
20C2×M16×C103—21no—
21#101×C103C2212yes—
22#100×C103—21no—
23#13110105—41no—
24#13110105—41no—
25C2×Dic206C2×C411yescharacteristic
26C2×D412C2×C411yescharacteristic
27C2×C22⋊D103—21no—
28C2×C22⋊D103—21no—
29C2×C22⋊D103—21no—
30C22×Dic103—21no—
31C2×C4×D103—21no—
32#13110089—22no—
33#13110089—41no—
34C2×C103⋊C8—41no—
35Dic103⋊C4—21no—
36Dic103⋊C4—21no—
37C22⋊Dic103—21no—
38C22⋊Dic103—21no—
39(C2×D103)⋊C4—21no—
40(C2×D103)⋊C4—21no—
41C4×Dic103—21no—
42C4×Dic103C2×C411yescharacteristic
43C4×Dic103C2×C411yescharacteristic
44#41×C103—41no—
45#41×C103—41no—
46C2×Q8×C103C2311yescharacteristic
47C2×D4×C103C2×C411yescharacteristic
48C2×D4×C103D411yescharacteristic
49C2×D4×C103D411yescharacteristic
50C22×C4×C103C2×C411yescharacteristic
51C22×C4×C103D411yescharacteristic
52C22×C4×C103D411yescharacteristic
53M16×C103—22no—
54M16×C103—41no—
55C2×C8×C103—41no—
56C23×C103C22⋊C411yescharacteristic
57C23×C103C22⋊C411yescharacteristic
58C23×C103C22⋊C411yescharacteristic
59C22×D103—21no—
60Q8×C103—41no—
61D4×C103—41no—
62D4×C103—41no—
63D4×C103—41no—
64C2×C4×C103—21no—
65C2×C4×C103—21no—
66C2×C4×C103—21no—
67C2×C4×C103—21no—
68C2×C4×C103—21no—
69C2×C4×C103—21no—
70C2×C4×C103C22⋊C411yescharacteristic
71C2×C4×C103C22×C411yescharacteristic
72C2×C4×C103C2×D411yescharacteristic
73C2×C4×C103C2×D411yescharacteristic
74C22⋊D103—42no—
75C22⋊D103—42no—
76C22⋊D103—42no—
77C2×Dic103—21no—
78C2×Dic103—21no—
79C2×Dic103—21no—
80C2×Dic103—42no—
81D412—41no—
82C4×D103—41no—
83C4×D103—41no—
84Dic206—41no—
85C8×C103—42no—
86C103⋊C8—42no—
87C22×C103—21no—
88C22×C103—21no—
89C22×C103—21no—
90C22×C103—41no—
91C22×C103—41no—
92C22×C103—41no—
93C22×C103C2×C22⋊C411yescharacteristic
94C2×D103—41no—
95C2×D103—41no—
96C2×D103—41no—
97C4×C103—21no—
98C4×C103—21no—
99C4×C103—21no—
100C4×C103#9911yescharacteristic
101C4×C103#9911yescharacteristic
102Dic103—22no—
103Dic103—41no—
104Dic103—41no—
105C2×C103—21no—
106C2×C103—41no—
107C2×C103—41no—
108C2×C103—41no—
109C2×C103C2×#9911yescharacteristic
110D103—81no—
111#2132—1031nomaximal, Sylow
112C103#213211yescharacteristic, complemented, Sylow
113#532—1031no—
114#413—1031no—
115#413D10311yescharacteristic, complemented
116#356—1032no—
117#355—1032no—
118C2×#41—1031no—
119C2×#41C2×D10311yescharacteristic
120C2×M16—21no—
121C2×M16—2061no—
122C4⋊Q8—1031no—
123#127—1031no—
124#124—1031no—
125#124—1031no—
126#121—2061no—
127#121—2061no—
128C4×D4—2061no—
129C4×D4—2061no—
130C2×C42—1031no—
131#101—1032no—
132#101C2×D10312yes—
133#100—21no—
134#100—2061no—
135#41—41no—
136#41—41no—
137#41—4121no—
138#41—4121no—
139C2×Q8—1031no—
140C2×Q8C22×D10311yescharacteristic
141C2×D4—1031no—
142C2×D4—2061no—
143C2×D4—2061no—
144C2×D4—2061no—
145C2×D4C4×D10311yescharacteristic
146C2×D4D41211yescharacteristic
147C2×D4C22⋊D10311yescharacteristic
148C22×C4—2061no—
149C22×C4—2061no—
150C22×C4C4×D10311yescharacteristic
151C22×C4D41211yescharacteristic
152C22×C4C22⋊D10311yescharacteristic
153M16—22no—
154M16—41no—
155M16—4121no—
156M16—2062no—
157C2×C8—41no—
158C2×C8—4121no—
159C4⋊C4—2061no—
160C4⋊C4—2061no—
161C22⋊C4—2061no—
162C22⋊C4—2061no—
163C22⋊C4—2061no—
164C22⋊C4—2061no—
165C42—1031no—
166C42—1031no—
167C42—2061no—
168C23—2061no—
169C23(C2×D103)⋊C411yescharacteristic
170C23(C2×D103)⋊C411yescharacteristic
171C23(C2×D103)⋊C411yescharacteristic
172Q8—41no—
173Q8—4121no—
174D4—41no—
175D4—41no—
176D4—41no—
177D4—4121no—
178D4—4122no—
179D4—4122no—
180D4—4122no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—4122no—
188C2×C4—4121no—
189C2×C4—4121no—
190C2×C4—2061no—
191C2×C4—2061no—
192C2×C4—2061no—
193C2×C4(C2×D103)⋊C411yescharacteristic
194C2×C4C2×C4×D10311yescharacteristic
195C2×C4C2×C22⋊D10311yescharacteristic
196C2×C4C2×D41211yescharacteristic
197C8—42no—
198C8—4122no—
199C22—21no—
200C22—21no—
201C22—21no—
202C22—41no—
203C22—41no—
204C22—41no—
205C22—4121no—
206C22—4121no—
207C22—4121no—
208C22C2×(C2×D103)⋊C411yescharacteristic
209C4—21no—
210C4—21no—
211C4—21no—
212C4—4121no—
213C4—4121no—
214C4—2062no—
215C4#1569293511yescharacteristic
216C4#1569293511yescharacteristic
217C2—21no—
218C2—41no—
219C2—41no—
220C2—41no—
221C2—8241no—
222C2C2×#1569293511yescharacteristic
subgroupG/H
centerC4#15692935
commutatorC2×C4×C103C22×C4
FrattiniC2×Q8C22×D103
Fitting#413×C103C2
socleC2×C103C2×#99
prime radical#20268337C2
cosocleC2×Q8×C103C23
hypercenter#413D103
hypocenterC103#2132
LCSG ▷ C2×C4×C103 ▷ C22×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×#41 ◁ #413

Complements

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

NH ≅ G/Ntype
2. #20267775C2semidirect
3. #20267589C2semidirect
4. #20267587C2semidirect
5. #413×C103C2semidirect
112. C103#2132semidirect
115. #413D103semidirect

Maximal subgroups

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

subgroupindex
#202683372
#202677752
#202675892
#202675872
#413×C1032
#2132103