Finite Group Databasebeta

← #27195663

Subgroups — #27195663

Order 13184.

312 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 79 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#20268557C211yesmaximal, characteristic
2#20268365C211yesmaximal, characteristic
3#20267800C211yesmaximal, characteristic, complemented
4#20267764C211yesmaximal, characteristic
5#20267548C211yesmaximal, characteristic, complemented
6#20267547C211yesmaximal, characteristic, complemented
7#419×C103C211yesmaximal, characteristic, complemented
8C2×#13110105C2211yescharacteristic
9#15693029—22no—
10#15693027—22no—
11C2×#13110089C2211yescharacteristic
12M16×D103—22no—
13#15693019C412yescomplemented
14#15693010C412yescomplemented
15#15693004—22no—
16#15692997—22no—
17#15692980C2211yescharacteristic
18#15692980C2211yescharacteristic
19#15692945—22no—
20#15692935—22no—
21C22×Q8×C103C2211yescharacteristic
22C2×M16×C103C2211yescharacteristic
23#117×C103C2211yescharacteristic
24#103×C103—22no—
25#13110105—21no—
26#13110105—21no—
27#13110105—21no—
28#13110105—21no—
29C2×Dic206C2×C411yescharacteristic
30C2×D412C2×C411yescharacteristic
31C2×C22⋊D103D412yes—
32C2×C4×D103D412yes—
33#13110089—21no—
34#13110089—21no—
35#13110088—24no—
36C2×C103⋊C8D412yes—
37C8×D103—24no—
38C4⋊Dic103—21no—
39C4⋊Dic103—21no—
40Dic103⋊C4—24no—
41C22⋊Dic103—21no—
42C22⋊Dic103—21no—
43(C2×D103)⋊C4—24no—
44C4×Dic103—21no—
45C4×Dic103C2×C412yes—
46C2×Q8×C103—21no—
47C2×Q8×C103—21no—
48C2×Q8×C103—21no—
49C2×Q8×C103—21no—
50C2×Q8×C103—21no—
51C2×Q8×C103C2×C412yes—
52C22×C4×C103—21no—
53C22×C4×C103C2311yescharacteristic
54M16×C103—21no—
55M16×C103—21no—
56C2×C8×C103D412yes—
57C4⋊C4×C103—21no—
58C22⋊C4×C103—21no—
59C42×C103—21no—
60C23×C103C2×D411yescharacteristic
61C22×D103C22⋊C412yes—
62Q8×C103—22no—
63Q8×C103—22no—
64Q8×C103—41no—
65Q8×C103—41no—
66C2×C4×C103—22no—
67C2×C4×C103—41no—
68C2×C4×C103—41no—
69C2×C4×C103—41no—
70C2×C4×C103C22×C411yescharacteristic
71C2×C4×C103C2×D411yescharacteristic
72C2×C4×C103C2×D411yescharacteristic
73C2×C4×C103C2×D411yescharacteristic
74C2×C4×C103#4111yescharacteristic
75C2×C4×C103#4111yescharacteristic
76C22⋊D103—22no—
77C22⋊D103—22no—
78C2×Dic103—22no—
79C2×Dic103—41no—
80C2×Dic103C22⋊C412yes—
81D412—21no—
82D412—21no—
83C4×D103—22no—
84C4×D103—22no—
85Dic206—21no—
86Dic206—21no—
87C8×C103—22no—
88C103⋊C8—22no—
89C22×C103—41no—
90C22×C103C2×C22⋊C411yescharacteristic
91C22×C103#12111yescharacteristic
92C22×C103#12111yescharacteristic
93C2×D103—22no—
94C2×D103—42no—
95C4×C103—42no—
96C4×C103—81no—
97C4×C103C4×D411yescharacteristic
98C4×C103C4×D411yescharacteristic
99C4×C103#12011yescharacteristic
100C4×C103#12311yescharacteristic
101Dic103—22no—
102Dic103—42no—
103Dic103—81no—
104C2×C103—21no—
105C2×C103—21no—
106C2×C103—21no—
107C2×C103#38611yescharacteristic
108D103—42no—
109#1909—1031nomaximal, Sylow
110C103#190911yescharacteristic, complemented, Sylow
111#568—1031no—
112#536—1031no—
113#419—1031no—
114#419D10311yescharacteristic, complemented
115#410—1031no—
116H(3,ℤ/4)—1031no—
117H(3,ℤ/4)—1031no—
118C2×#41—1031no—
119C22×Q8C2×D10311yescharacteristic
120#131—2062no—
121#131—2062no—
122C2×M16—1031no—
123C2×M16—2062no—
124C2×M16C2×D10311yescharacteristic
125C4⋊Q8—1032no—
126#124—1032no—
127#123—2062no—
128C22⋊Q8—2062no—
129#117—1031no—
130#117—1031no—
131#117C2×D10311yescharacteristic
132#103—22no—
133#103—2062no—
134#99—2062no—
135#41—2061no—
136#41—2061no—
137#41—2061no—
138#41—2061no—
139C2×Q8—21no—
140C2×Q8—21no—
141C2×Q8—21no—
142C2×Q8—21no—
143C2×Q8—21no—
144C2×Q8—1031no—
145C2×Q8C4×D10312yes—
146C2×D4—1032no—
147C2×D4—1031no—
148C22×C4—21no—
149C22×C4—1032no—
150C22×C4C22×D10311yescharacteristic
151M16—21no—
152M16—21no—
153M16—2064no—
154M16—2061no—
155M16—2061no—
156C2×C8—1032no—
157C2×C8—2064no—
158C2×C8C22⋊D10312yes—
159C4⋊C4—21no—
160C4⋊C4—2064no—
161C4⋊C4—2061no—
162C4⋊C4—2061no—
163C22⋊C4—21no—
164C22⋊C4—2064no—
165C22⋊C4—2061no—
166C22⋊C4—2061no—
167C42—21no—
168C42—1032no—
169C42—2061no—
170C23—1032no—
171C23D4×D10311yescharacteristic
172Q8—22no—
173Q8—22no—
174Q8—41no—
175Q8—41no—
176Q8—2061no—
177Q8—2061no—
178D4—2062no—
179D4—2062no—
180D4—2061no—
181D4—2061no—
182C2×C4—22no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—1032no—
187C2×C4—4121no—
188C2×C4—2062no—
189C2×C4—2062no—
190C2×C4—2062no—
191C2×C4C2×C4×D10311yescharacteristic
192C2×C4D4×D10311yescharacteristic
193C2×C4D4×D10311yescharacteristic
194C2×C4C2×C22⋊D10311yescharacteristic
195C2×C4#1311010411yescharacteristic
196C2×C4#1311010511yescharacteristic
197C8—22no—
198C8—2062no—
199C22—41no—
200C22—4122no—
201C22—2062no—
202C22C22⋊C4×D10311yescharacteristic
203C22#1569299211yescharacteristic
204C22#1569299411yescharacteristic
205C4—42no—
206C4—81no—
207C4—8241no—
208C4—4122no—
209C4—2062no—
210C4(C22⋊D103)⋊C411yescharacteristic
211C4C4×C22⋊D10311yescharacteristic
212C4#1569298911yescharacteristic
213C4#1569300311yescharacteristic
214C2—21no—
215C2—21no—
216C2—21no—
217C2—4122no—
218C2#2026766711yescharacteristic
subgroupG/H
centerC2#20267667
commutatorC2×C4×C103C22×C4
FrattiniC22×C4C22×D103
Fitting#419×C103C2
socleC2×C103#386
prime radicalC2×#13110105C22
cosocleC22×C4×C103C23
hypercenter#419D103
hypocenterC103#1909
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C2 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
3. #20267800C2semidirect
5. #20267548C2semidirect
6. #20267547C2semidirect
7. #419×C103C2semidirect
13. #15693019C4semidirect
14. #15693010C4semidirect
110. C103#1909semidirect
114. #419D103semidirect

Maximal subgroups

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

subgroupindex
#202685572
#202683652
#202678002
#202677642
#202675482
#202675472
#419×C1032
#1909103