Finite Group Databasebeta

← #28373131

Subgroups — #28373131

Order 13952.

444 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 133 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#20295583C211yesmaximal, characteristic, complemented
2#20295361C212yesmaximal, complemented
3#20295306C212yesmaximal, complemented
4#20295231C212yesmaximal, complemented
5#20295177C212yesmaximal
6#20295126C214yesmaximal, complemented
7#20295083C211yesmaximal, characteristic, complemented
8C2×C4×D4×C109C211yesmaximal, characteristic
9C2×#13182017C2214yes—
10#16812699C2211yescharacteristic, complemented
11#16812699C2211yescharacteristic, complemented
12#16812691—21no—
13#16812678—21no—
14#16812678C2212yes—
15C4×Dic218—21no—
16C4×Dic218C2212yescomplemented
17#16812658—21no—
18#16812632C2214yescomplemented
19C4⋊#11724784C2212yescomplemented
20#16812622C2214yescomplemented
21#16812620C2214yes—
22C22⋊#11724784C2212yes—
23#16812610C2212yescomplemented
24C22×D4×C109C2211yescharacteristic
25C23×C4×C109—21no—
26C4×D4×C109—21no—
27C4×D4×C109—21no—
28C4×D4×C109C2212yes—
29C4×D4×C109C2212yes—
30C2×C4⋊C4×C109C2211yescharacteristic
31C2×C22⋊C4×C109—21no—
32C2×C42×C109C2211yescharacteristic
33C2×Dic218—21no—
34C2×Dic218C2312yes—
35#13182017—28no—
36C2×#11724784C2314yes—
37C4⋊Dic109—21no—
38C4⋊Dic109—21no—
39C4⋊Dic109—21no—
40C4⋊Dic109C2312yes—
41#13182008—22no—
42#13182008—22no—
43C22⋊Dic109—22no—
44C4×Dic109—22no—
45C24×C109—21no—
46C2×D4×C109—24no—
47C2×D4×C109—21no—
48C2×D4×C109C2312yes—
49C22×C4×C109—21no—
50C22×C4×C109—22no—
51C22×C4×C109—22no—
52C22×C4×C109—44no—
53C22×C4×C109D411yescharacteristic
54C22×C4×C109D411yescharacteristic
55C22×C4×C109C2311yescharacteristic
56C4⋊C4×C109—21no—
57C4⋊C4×C109C2312yes—
58C22⋊C4×C109—22no—
59C22⋊C4×C109—22no—
60C42×C109D411yescharacteristic
61C42×C109D411yescharacteristic
62C42×C109C2311yescharacteristic
63C42×C109C2311yescharacteristic
64C23×C109—24no—
65C23×C109—22no—
66C23×C109—42no—
67C23×C109—42no—
68C23×C109C2×D411yescharacteristic
69D4×C109—24no—
70D4×C109—22no—
71D4×C109#4114yes—
72C2×C4×C109—22no—
73C2×C4×C109—22no—
74C2×C4×C109—22no—
75C2×C4×C109—22no—
76C2×C4×C109—44no—
77C2×C4×C109—42no—
78C2×C4×C109—44no—
79C2×C4×C109C2×D411yescharacteristic
80C2×C4×C109C2×D411yescharacteristic
81C2×C4×C109C2×D411yescharacteristic
82C2×C4×C109C2×D411yescharacteristic
83C2×C4×C109C2×D411yescharacteristic
84C2×C4×C109C2411yescharacteristic
85C2×Dic109—22no—
86C2×Dic109—22no—
87Dic218—24no—
88Dic218—42no—
89#11724784—24no—
90C22×C109—21no—
91C22×C109—21no—
92C22×C109—24no—
93C22×C109—48no—
94C22×C109—42no—
95C22×C109—42no—
96C22×C109#13712yes—
97C22×C109C22×D411yescharacteristic
98C4×C109—21no—
99C4×C109—21no—
100C4×C109—21no—
101C4×C109—21no—
102C4×C109—42no—
103C4×C109AGL(1,ℤ/8)12yes—
104C4×C109C2×#4112yes—
105Dic109—42no—
106Dic109—42no—
107C2×C109—22no—
108C2×C109—44no—
109C2×C109#52511yescharacteristic
110C2×C109C2×AGL(1,ℤ/8)11yescharacteristic
111C2×C109C2×#13711yescharacteristic
112#3110—1091nomaximal, Sylow
113C109#311011yescharacteristic, complemented, Sylow
114#533—1091no—
115C2×C4×D4D10911yescharacteristic
116#484—1092no—
117#474—1092no—
118#461—1092no—
119#450—1092no—
120#440—1094no—
121#432—1091no—
122C22×D4C2×D10911yescharacteristic
123C23×C4—21no—
124C2×SD16—1094no—
125C4⋊Q8—1091no—
126C4⋊Q8—1091no—
127#125—2181no—
128C22⋊Q8—1092no—
129C22⋊Q8—2181no—
130C4×Q8—1092no—
131C4×Q8—2181no—
132C4×D4—21no—
133C4×D4—21no—
134C4×D4C2×D10912yes—
135C4×D4C2×D10912yes—
136#117—2181no—
137C2×C4⋊C4C2×D10911yescharacteristic
138C2×C22⋊C4—21no—
139C2×C42C2×D10911yescharacteristic
140#107—1094no—
141C4⋊C8—1092no—
142#103—1094no—
143#102—1094no—
144C22⋊C8—1092no—
145#97—1092no—
146C24—21no—
147C2×Q8—1092no—
148C2×Q8—2181no—
149C2×D4—24no—
150C2×D4—21no—
151C2×D4C22×D10912yes—
152C22×C4—21no—
153C22×C4—22no—
154C22×C4—22no—
155C22×C4—44no—
156C22×C4C22⋊D10911yescharacteristic
157C22×C4C22⋊D10911yescharacteristic
158C22×C4C22×D10911yescharacteristic
159SD16—2188no—
160C2×C8—1094no—
161C4⋊C4—21no—
162C4⋊C4—1092no—
163C4⋊C4—2182no—
164C4⋊C4—2182no—
165C4⋊C4—2181no—
166C4⋊C4—2181no—
167C4⋊C4—2181no—
168C4⋊C4C22×D10912yes—
169C22⋊C4—22no—
170C22⋊C4—22no—
171C22⋊C4—2182no—
172C42—2182no—
173C42C22⋊D10911yescharacteristic
174C42C22⋊D10911yescharacteristic
175C42C22×D10911yescharacteristic
176C42C22×D10911yescharacteristic
177C23—24no—
178C23—22no—
179C23—42no—
180C23—42no—
181C23C2×C22⋊D10911yescharacteristic
182Q8—4362no—
183Q8—2184no—
184D4—24no—
185D4—22no—
186D4#1318202914yes—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—44no—
192C2×C4—42no—
193C2×C4—44no—
194C2×C4—2182no—
195C2×C4—2182no—
196C2×C4C2×C22⋊D10911yescharacteristic
197C2×C4C2×C22⋊D10911yescharacteristic
198C2×C4C2×C22⋊D10911yescharacteristic
199C2×C4C2×C22⋊D10911yescharacteristic
200C2×C4C2×C22⋊D10911yescharacteristic
201C2×C4C23×D10911yescharacteristic
202C8—2184no—
203C22—21no—
204C22—21no—
205C22—24no—
206C22—48no—
207C22—42no—
208C22—42no—
209C22#1681272912yes—
210C22C22×C22⋊D10911yescharacteristic
211C4—21no—
212C4—21no—
213C4—21no—
214C4—21no—
215C4—42no—
216C4—4362no—
217C4—4362no—
218C4#1681272512yes—
219C4C2×#1318202912yes—
220C2—22no—
221C2—44no—
222C2#2029553711yescharacteristic
223C2C2×#1681272511yescharacteristic
224C2C2×#1681272911yescharacteristic
subgroupG/H
centerC22C22×C22⋊D109
commutator, cosocleC2×C4×C109C24
FrattiniC2×C4C23×D109
FittingC2×C4×D4×C109C2
socleC22×C109C22×D4
prime radicalC22×D4×C109C22
hypercenterC2×C4×D4D109
hypocenterC109#3110
LCSG ▷ C2×C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. #20295583C2semidirect
2. #20295361C2semidirect
3. #20295306C2semidirect
4. #20295231C2semidirect
6. #20295126C2semidirect
7. #20295083C2semidirect
10. #16812699C22semidirect
11. #16812699C22semidirect
16. C4×Dic218C22semidirect
18. #16812632C22semidirect
19. C4⋊#11724784C22semidirect
20. #16812622C22semidirect
23. #16812610C22semidirect
113. C109#3110semidirect

Maximal subgroups

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

subgroupindex
#202955832
#202953612
#202953062
#202952312
#202951772
#202951262
#202950832
C2×C4×D4×C1092
#3110109