Finite Group Databasebeta

← #28373162

Subgroups — #28373162

Order 13952.

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

normal subgroups only

This group has 380 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
2#20295356C212yesmaximal
3#20295311C212yesmaximal, complemented
4#20295236C212yesmaximal, complemented
5#20295182C212yesmaximal
6#20295131C214yesmaximal, complemented
7#20295083C211yesmaximal, characteristic
8C2×C4×Q8×C109C211yesmaximal, characteristic
9C2×#13182019C2214yes—
10#16812699C2211yescharacteristic
11#16812699C2211yescharacteristic
12#16812691—21no—
13#16812678—21no—
14#16812678C2212yes—
15C4×Dic218—21no—
16C4×Dic218C2212yes—
17#16812658—21no—
18#16812630C2214yes—
19C4⋊#11724784C2212yes—
20#16812623C2214yes—
21#16812622C2214yes—
22C22⋊#11724784C2212yes—
23#16812610C2212yes—
24C22×Q8×C109C2211yescharacteristic
25C4×Q8×C109—21no—
26C4×Q8×C109—21no—
27C4×Q8×C109C2212yes—
28C4×Q8×C109C2212yes—
29C2×C4⋊C4×C109—21no—
30C2×C4⋊C4×C109C2211yescharacteristic
31C2×C42×C109—21no—
32C2×C42×C109C2211yescharacteristic
33C2×Dic218—21no—
34C2×Dic218C2312yes—
35#13182019—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—
45C2×Q8×C109—24no—
46C2×Q8×C109—21no—
47C2×Q8×C109C2312yes—
48C22×C4×C109—21no—
49C22×C4×C109—21no—
50C22×C4×C109D411yescharacteristic
51C22×C4×C109D411yescharacteristic
52C22×C4×C109C2311yescharacteristic
53C4⋊C4×C109—22no—
54C4⋊C4×C109—22no—
55C4⋊C4×C109—21no—
56C4⋊C4×C109C2312yes—
57C42×C109—22no—
58C42×C109—22no—
59C42×C109D411yescharacteristic
60C42×C109D411yescharacteristic
61C42×C109C2311yescharacteristic
62C42×C109C2311yescharacteristic
63C23×C109C2×D411yescharacteristic
64Q8×C109—24no—
65Q8×C109—22no—
66Q8×C109#4114yes—
67C2×C4×C109—24no—
68C2×C4×C109—22no—
69C2×C4×C109—22no—
70C2×C4×C109—22no—
71C2×C4×C109—22no—
72C2×C4×C109—22no—
73C2×C4×C109—42no—
74C2×C4×C109C2×D411yescharacteristic
75C2×C4×C109C2×D411yescharacteristic
76C2×C4×C109C2×D411yescharacteristic
77C2×C4×C109C2×D411yescharacteristic
78C2×C4×C109C2×D411yescharacteristic
79C2×C4×C109C2411yescharacteristic
80C2×Dic109—22no—
81C2×Dic109—22no—
82Dic218—24no—
83Dic218—42no—
84#11724784—24no—
85C22×C109—21no—
86C22×C109—21no—
87C22×C109#13712yes—
88C22×C109C22×D411yescharacteristic
89C4×C109—24no—
90C4×C109—21no—
91C4×C109—21no—
92C4×C109—21no—
93C4×C109—21no—
94C4×C109—42no—
95C4×C109#13712yes—
96C4×C109C2×#4112yes—
97Dic109—42no—
98Dic109—42no—
99C2×C109—22no—
100C2×C109#52511yescharacteristic
101C2×C109C2×#13711yescharacteristic
102C2×C109C2×#13711yescharacteristic
103#3113—1091nomaximal, Sylow
104C109#311311yescharacteristic, complemented, Sylow
105#533—1091no—
106C2×C4×Q8D10911yescharacteristic
107#483—1092no—
108#475—1092no—
109#462—1092no—
110#451—1092no—
111#441—1094no—
112#432—1091no—
113C22×Q8C2×D10911yescharacteristic
114C2×Q16—1094no—
115C4⋊Q8—1091no—
116C4⋊Q8—1091no—
117#125—2181no—
118C22⋊Q8—1092no—
119C22⋊Q8—2181no—
120C4×Q8—21no—
121C4×Q8—21no—
122C4×Q8—1092no—
123C4×Q8—2181no—
124C4×Q8C2×D10912yes—
125C4×Q8C2×D10912yes—
126#117—2181no—
127C2×C4⋊C4—21no—
128C2×C4⋊C4C2×D10911yescharacteristic
129C2×C42—21no—
130C2×C42C2×D10911yescharacteristic
131#106—1094no—
132C4⋊C8—1092no—
133#103—1094no—
134#103—1094no—
135C22⋊C8—1092no—
136#97—1092no—
137C2×Q8—24no—
138C2×Q8—21no—
139C2×Q8—1092no—
140C2×Q8—2181no—
141C2×Q8C22×D10912yes—
142C22×C4—21no—
143C22×C4—21no—
144C22×C4C22⋊D10911yescharacteristic
145C22×C4C22⋊D10911yescharacteristic
146C22×C4C22×D10911yescharacteristic
147Q16—2188no—
148C2×C8—1094no—
149C4⋊C4—22no—
150C4⋊C4—22no—
151C4⋊C4—21no—
152C4⋊C4—1092no—
153C4⋊C4—2182no—
154C4⋊C4—2182no—
155C4⋊C4—2181no—
156C4⋊C4—2181no—
157C4⋊C4—2181no—
158C4⋊C4C22×D10912yes—
159C22⋊C4—2182no—
160C42—22no—
161C42—22no—
162C42—2182no—
163C42C22⋊D10911yescharacteristic
164C42C22⋊D10911yescharacteristic
165C42C22×D10911yescharacteristic
166C42C22×D10911yescharacteristic
167C23C2×C22⋊D10911yescharacteristic
168Q8—24no—
169Q8—22no—
170Q8—4362no—
171Q8—2184no—
172Q8#1318202914yes—
173C2×C4—24no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—42no—
180C2×C4—2182no—
181C2×C4—2182no—
182C2×C4C2×C22⋊D10911yescharacteristic
183C2×C4C2×C22⋊D10911yescharacteristic
184C2×C4C2×C22⋊D10911yescharacteristic
185C2×C4C2×C22⋊D10911yescharacteristic
186C2×C4C2×C22⋊D10911yescharacteristic
187C2×C4C23×D10911yescharacteristic
188C8—2184no—
189C22—21no—
190C22—21no—
191C22#1681272912yes—
192C22C22×C22⋊D10911yescharacteristic
193C4—24no—
194C4—21no—
195C4—21no—
196C4—21no—
197C4—21no—
198C4—42no—
199C4—4362no—
200C4—4362no—
201C4#1681273012yes—
202C4C2×#1318202912yes—
203C2—22no—
204C2#2029553711yescharacteristic
205C2C2×#1681272911yescharacteristic
206C2C2×#1681273011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D109
commutator, cosocleC2×C4×C109C24
FrattiniC2×C4C23×D109
FittingC2×C4×Q8×C109C2
socleC22×C109C22×D4
prime radicalC23×C109C2×D4
hypercenterC2×C4×Q8D109
hypocenterC109#3113
LCSG ▷ C2×C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
3. #20295311C2semidirect
4. #20295236C2semidirect
6. #20295131C2semidirect
104. C109#3113semidirect

Maximal subgroups

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

subgroupindex
#202955832
#202953562
#202953112
#202952362
#202951822
#202951312
#202950832
C2×C4×Q8×C1092
#3113109