Finite Group Databasebeta

← #28363134

Subgroups — #28363134

Order 13952.

262 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 73 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#20295494C211yesmaximal, characteristic
2#20295008C211yesmaximal, characteristic
3#20294999C211yesmaximal, characteristic
4#20294787C211yesmaximal, characteristic, complemented
5#20294785C211yesmaximal, characteristic, complemented
6#20294782C211yesmaximal, characteristic, complemented
7H(3,ℤ/4)×C109C211yesmaximal, characteristic, complemented
8C2×#13182029C2211yescharacteristic
9C2×#13182013C2211yescharacteristic
10#16812664—21no—
11#16812661—21no—
12#16812659—22no—
13#16812658C2211yescharacteristic
14#16812656C412yescomplemented
15C2×C4×Dic109C2211yescharacteristic
16C42×D109C412yescomplemented
17#16812617—21no—
18#16812615—21no—
19#16812613—22no—
20C2×M16×C109C2211yescharacteristic
21#117×C109C2211yescharacteristic
22#117×C109C2211yescharacteristic
23#13182029—21no—
24#13182029—21no—
25#13182029—21no—
26#13182029—21no—
27C2×Dic218D411yescharacteristic
28C2×D436D411yescharacteristic
29C2×C22⋊D109D412yes—
30C22×Dic109—21no—
31C2×C4×D109—22no—
32C2×C4×D109C2×C412yes—
33#13182013—21no—
34#13182013—21no—
35C2×#11724784—21no—
36C4⋊Dic109—21no—
37#13182008—22no—
38C22⋊Dic109—21no—
39#13182006—22no—
40C4×Dic109—21no—
41C4×Dic109—22no—
42C4×Dic109—21no—
43C4×Dic109C2×C411yescharacteristic
44C4×Dic109C2×C411yescharacteristic
45C22×C4×C109C2311yescharacteristic
46M16×C109—21no—
47M16×C109—21no—
48C2×C8×C109—21no—
49C4⋊C4×C109—21no—
50C4⋊C4×C109—21no—
51C22⋊C4×C109—21no—
52C22⋊C4×C109—21no—
53C42×C109—21no—
54C42×C109C2×C412yes—
55C23×C109C2×D411yescharacteristic
56C22×D109C22⋊C412yes—
57C2×C4×C109—22no—
58C2×C4×C109—41no—
59C2×C4×C109C22×C411yescharacteristic
60C2×C4×C109C2×D411yescharacteristic
61C2×C4×C109#4111yescharacteristic
62C2×C4×C109#4111yescharacteristic
63C2×C4×C109#4111yescharacteristic
64C2×C4×C109#4111yescharacteristic
65C22⋊D109—22no—
66C22⋊D109—22no—
67C2×Dic109—21no—
68C2×Dic109—21no—
69C2×Dic109—42no—
70C2×Dic109—41no—
71C2×Dic109C22⋊C412yes—
72D436—21no—
73D436—21no—
74C4×D109—22no—
75C4×D109—22no—
76C4×D109—44no—
77Dic218—21no—
78Dic218—21no—
79C8×C109—41no—
80#11724784—41no—
81C22×C109—41no—
82C22×C109C2×C22⋊C411yescharacteristic
83C22×C109#12311yescharacteristic
84C22×C109#12311yescharacteristic
85C2×D109—22no—
86C2×D109—42no—
87C4×C109—42no—
88C4×C109—81no—
89C4×C109#11711yescharacteristic
90C4×C109#11711yescharacteristic
91C4×C109#12311yescharacteristic
92C4×C109#12311yescharacteristic
93Dic109—22no—
94Dic109—22no—
95Dic109—41no—
96Dic109—81no—
97C2×C109—21no—
98C2×C109—21no—
99C2×C109—21no—
100C2×C109#38111yescharacteristic
101D109—42no—
102#1827—1091nomaximal, Sylow
103C109#182711yescharacteristic, complemented, Sylow
104C4×#41—1091no—
105#413—1091no—
106#410—1091no—
107#339—1091no—
108#339—1091no—
109H(3,ℤ/4)—1091no—
110H(3,ℤ/4)D10911yescharacteristic, complemented
111C2×#41—1091no—
112C2×M16—1091no—
113C2×M16C2×D10911yescharacteristic
114C4×Q8—2181no—
115C4×D4—2182no—
116C4×D4—2181no—
117#117—1092no—
118#117—1091no—
119#117C2×D10911yescharacteristic
120#117C2×D10911yescharacteristic
121C2×C42—1091no—
122C2×C42—1092no—
123#101—2181no—
124#100—2181no—
125#99—2182no—
126#41—2181no—
127#41—2181no—
128#41—2181no—
129#41—2181no—
130C2×Q8—1091no—
131C2×D4—1092no—
132C2×D4—1091no—
133C22×C4—1092no—
134C22×C4—2182no—
135C22×C4—2181no—
136C22×C4C22×D10911yescharacteristic
137M16—21no—
138M16—21no—
139M16—2181no—
140M16—2181no—
141C2×C8—21no—
142C2×C8—2181no—
143C4⋊C4—21no—
144C4⋊C4—21no—
145C4⋊C4—2182no—
146C4⋊C4—2181no—
147C22⋊C4—21no—
148C22⋊C4—21no—
149C22⋊C4—2182no—
150C22⋊C4—2181no—
151C42—21no—
152C42—1091no—
153C42—1091no—
154C42—2182no—
155C42—2181no—
156C42—2181no—
157C42C4×D10912yes—
158C23—1092no—
159C23D4×D10911yescharacteristic
160Q8—2181no—
161Q8—2181no—
162D4—2182no—
163D4—2182no—
164D4—2181no—
165D4—2181no—
166C2×C4—22no—
167C2×C4—41no—
168C2×C4—1092no—
169C2×C4—4364no—
170C2×C4—4361no—
171C2×C4—4362no—
172C2×C4—2181no—
173C2×C4—2181no—
174C2×C4—2182no—
175C2×C4—2182no—
176C2×C4C2×C4×D10911yescharacteristic
177C2×C4D4×D10911yescharacteristic
178C2×C4#1318202811yescharacteristic
179C2×C4#1318202911yescharacteristic
180C2×C4#1318202911yescharacteristic
181C2×C4#1318203011yescharacteristic
182C8—41no—
183C8—4361no—
184C22—41no—
185C22—4362no—
186C22—2182no—
187C22C22⋊C4×D10911yescharacteristic
188C22#1681268111yescharacteristic
189C22#1681268411yescharacteristic
190C4—42no—
191C4—81no—
192C4—8721no—
193C4—4361no—
194C4—2182no—
195C4—2182no—
196C4#1681265611yescharacteristic
197C4#1681265711yescharacteristic
198C4#1681268111yescharacteristic
199C4#1681268411yescharacteristic
200C2—21no—
201C2—21no—
202C2—21no—
203C2—4362no—
204C2#2029488811yescharacteristic
subgroupG/H
centerC4#16812656
commutatorC2×C4×C109C22×C4
FrattiniC22×C4C22×D109
FittingH(3,ℤ/4)×C109C2
socleC2×C109#381
prime radicalC2×#13182029C22
cosocleC22×C4×C109C23
hypercenterH(3,ℤ/4)D109
hypocenterC109#1827
LCSG ▷ C2×C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C4 ◁ #117 ◁ H(3,ℤ/4)

Complements

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

NH ≅ G/Ntype
4. #20294787C2semidirect
5. #20294785C2semidirect
6. #20294782C2semidirect
7. H(3,ℤ/4)×C109C2semidirect
14. #16812656C4semidirect
16. C42×D109C4semidirect
103. C109#1827semidirect
110. H(3,ℤ/4)D109semidirect

Maximal subgroups

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

subgroupindex
#202954942
#202950082
#202949992
#202947872
#202947852
#202947822
H(3,ℤ/4)×C1092
#1827109