Finite Group Databasebeta

← #28378987

Subgroups — #28378987

Order 13952.

324 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 68 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#20296093C211yesmaximal, characteristic
2#20296037C212yesmaximal, complemented
3#20295978C211yesmaximal, characteristic
4#20295898C212yesmaximal, complemented
5#100×D109C211yesmaximal, characteristic
6D4×#89137—22no—
7D4×#89137—22no—
8#16812778C2212yes—
9C2×C4⋊#89137C2211yescharacteristic
10C2×C22⋊#89137—22no—
11C2×C22⋊#89137—22no—
12C2×C4×#89137C2211yescharacteristic
13#16812768—22no—
14#16812767—22no—
15C2×D4×D109C2211yescharacteristic
16M16×D109C2212yes—
17#16812616C411yescharacteristic, complemented
18#16812615C412yescomplemented
19#100×C109C411yescharacteristic, complemented
20C22×#89137—21no—
21C22×#89137—22no—
22C22×#89137—22no—
23C22×#89137—21no—
24C4⋊#89137—22no—
25C4⋊#89137D412yes—
26C4⋊#89137D412yes—
27C22⋊#89137—24no—
28C22⋊#89137—22no—
29C22⋊#89137—44no—
30C4×#89137—22no—
31C4×#89137—22no—
32C23×D109D412yes—
33C2×D436C2×C411yescharacteristic
34C2×C22⋊D109Q812yes—
35D4×D109—22no—
36D4×D109—22no—
37C2×C4×D109C2311yescharacteristic
38#13182013C2×C412yescomplemented
39#13182012—22no—
40C8×D109—22no—
41C2×D4×C109C2×C411yescharacteristic
42M16×C109C2×C412yescomplemented
43C23×C109C4⋊C412yes—
44C22×D109—22no—
45C22×D109—22no—
46C22×D109—42no—
47C22×D109—42no—
48C22×D109C4⋊C412yes—
49C22×D109C2×D411yescharacteristic
50C2×#89137—22no—
51C2×#89137—22no—
52C2×#89137—22no—
53C2×#89137—41no—
54C2×#89137—41no—
55C2×#89137—42no—
56C2×#89137—41no—
57C2×#89137—82no—
58C2×#89137—82no—
59D4×C109—22no—
60C2×C4×C109C22×C411yescharacteristic
61C22⋊D109—24no—
62C2×Dic109C2×Q811yescharacteristic
63D436—22no—
64C4×D109C2×D412yes—
65C4×D109#4112yes—
66C8×C109—22no—
67#11724784—22no—
68C22×C109—22no—
69C22×C109—42no—
70C22×C109C2×C4⋊C411yescharacteristic
71C2×D109—21no—
72C2×D109—21no—
73C2×D109—22no—
74C2×D109—42no—
75C2×D109—42no—
76C2×D109—42no—
77C2×D109—82no—
78C2×D109#12011yescharacteristic
79C2×D109#12311yescharacteristic
80#89137—42no—
81#89137—42no—
82#89137—42no—
83#89137—81no—
84C4×C109C4×D412yes—
85Dic109C22⋊Q812yes—
86C2×C109—21no—
87C2×C109—42no—
88C2×C109#38511yescharacteristic
89D109—21no—
90D109—42no—
91D109#45311yescharacteristic
92D109#45511yescharacteristic
93#1856—1091nomaximal, Sylow
94C109#185611yescharacteristic, complemented, Sylow
95#518—1091no—
96#428—1092no—
97C2×#100—1091no—
98#390—1091no—
99#339—1092no—
100C22×D4—1091no—
101C2×M16—1092no—
102C4×D4—2182no—
103C4×D4—2182no—
104#117—1092no—
105C2×C4⋊C4—1091no—
106C2×C22⋊C4—2182no—
107C2×C22⋊C4—2182no—
108C2×C42—1091no—
109#107—2182no—
110#106—2182no—
111#100—1091no—
112#100—1092no—
113#100#8913711yescharacteristic, complemented
114C24—1092no—
115C2×D4—1092no—
116C2×D4—1091no—
117C2×D4—2182no—
118C2×D4—2182no—
119C2×D4C2×#8913711yescharacteristic
120C22×C4—1091no—
121C22×C4—2182no—
122C22×C4—2182no—
123C22×C4—2181no—
124C22×C4—2181no—
125M16—1092no—
126M16—2182no—
127M16C2×#8913712yescomplemented
128C2×C8—2182no—
129C4⋊C4—1092no—
130C4⋊C4—1092no—
131C4⋊C4—2182no—
132C22⋊C4—4364no—
133C22⋊C4—2182no—
134C22⋊C4—2184no—
135C42—2182no—
136C42—2182no—
137C23—1091no—
138C23—1092no—
139C23—4362no—
140C23—4362no—
141C23—2182no—
142C23—2182no—
143C23C4⋊#8913712yes—
144D4—22no—
145D4—2184no—
146D4—2182no—
147C2×C4—8722no—
148C2×C4—8722no—
149C2×C4—1091no—
150C2×C4—1092no—
151C2×C4—1092no—
152C2×C4—4361no—
153C2×C4—4362no—
154C2×C4—4361no—
155C2×C4—4361no—
156C2×C4—2182no—
157C2×C4—2182no—
158C2×C4—2182no—
159C2×C4C22×#8913711yescharacteristic
160C8—22no—
161C8—2182no—
162C22—22no—
163C22—42no—
164C22—8722no—
165C22—1091no—
166C22—1091no—
167C22—4362no—
168C22—4362no—
169C22—4362no—
170C22—2181no—
171C22—2181no—
172C22—2182no—
173C22C2×C4⋊#8913711yescharacteristic
174C4—8721no—
175C4—1092no—
176C4—4362no—
177C4—4362no—
178C4—4362no—
179C4D4×#8913712yes—
180C2—21no—
181C2—42no—
182C2—1091no—
183C2—1091no—
184C2—4362no—
185C2—2181no—
186C2#2029597311yescharacteristic
subgroupG/H
centerC2#20295973
commutatorC2×C4×C109C22×C4
FrattiniC2×C4C22×#89137
Fitting#100×C109C4
socleC2×C109#385
prime radicalC2×D4×D109C22
cosocleC2×C4×D109C23
hypercenter#100#89137
hypocenterC109#1856
LCSG ▷ C2×C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C2 ◁ C2×C4 ◁ #100

Complements

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

NH ≅ G/Ntype
2. #20296037C2semidirect
4. #20295898C2semidirect
17. #16812616C4semidirect
18. #16812615C4semidirect
19. #100×C109C4semidirect
38. #13182013C2×C4semidirect
42. M16×C109C2×C4semidirect
94. C109#1856semidirect
113. #100#89137semidirect
127. M16C2×#89137semidirect

Maximal subgroups

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

subgroupindex
#202960932
#202960372
#202959782
#202958982
#100×D1092
#1856109