Finite Group Databasebeta

← #28378348

Subgroups — #28378348

Order 13952.

234 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 62 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
1D109⋊(C4⋊C8)C211yesmaximal, characteristic, complemented
2C4×#13182039C211yesmaximal, characteristic, complemented
3Q8⋊#11724786C212yesmaximal, complemented
4D4⋊#11724786C212yesmaximal, complemented
5#20295555C211yesmaximal, characteristic
6C2×#13182039—21no—
7C2×D109⋊C8—21no—
8#16812766—21no—
9C4⋊#11724786C2212yes—
10#16812754—21no—
11C4×#11724786C2212yes—
12#16812692—21no—
13#16812691C411yescharacteristic
14#16812681—21no—
15#16812675C411yescharacteristic
16#16812670C411yescharacteristic
17Q8×Dic109C2211yescharacteristic
18D4×Dic109C2211yescharacteristic
19#16812659—21no—
20#16812655—21no—
21C42×D109C2211yescharacteristic
22#124×C109C411yescharacteristic
23#13182039—24no—
24D109⋊C8—42no—
25C2×#11724786—22no—
26C2×#11724786—22no—
27C2×C22⋊D109—21no—
28C22×Dic109—21no—
29C2×C4×D109C2×C411yescharacteristic
30C2×C4×D109D411yescharacteristic
31C2×C4×D109D411yescharacteristic
32C4⋊Dic109—21no—
33C4⋊Dic109C2×C411yescharacteristic
34C4⋊Dic109C2×C411yescharacteristic
35#13182008—21no—
36#13182008—21no—
37#13182008—21no—
38C22⋊Dic109—21no—
39C22⋊Dic109—21no—
40#13182006—21no—
41C4×Dic109—21no—
42C4×Dic109D411yescharacteristic
43C4×Dic109D411yescharacteristic
44C4×Dic109C2311yescharacteristic
45C2×Q8×C109C2×C411yescharacteristic
46C2×D4×C109C2×C411yescharacteristic
47C22⋊C4×C109—21no—
48C22⋊C4×C109—21no—
49C42×C109C2×C411yescharacteristic
50C23×C109—21no—
51C22×D109C22⋊C411yescharacteristic
52Q8×C109—22no—
53D4×C109—22no—
54C2×C4×C109—21no—
55C2×C4×C109C22⋊C411yescharacteristic
56C2×C4×C109C22⋊C411yescharacteristic
57C2×C4×C109C22×C411yescharacteristic
58C22⋊D109—42no—
59C2×Dic109—21no—
60C2×Dic109—21no—
61C2×Dic109—41no—
62C2×Dic109—41no—
63C2×Dic109C22⋊C411yescharacteristic
64C2×Dic109C2×D411yescharacteristic
65C2×Dic109C2×D411yescharacteristic
66C4×D109—22no—
67C4×D109—22no—
68C4×D109—21no—
69C4×D109—21no—
70#11724786—24no—
71#11724786—42no—
72C22×C109—41no—
73C22×C109—41no—
74C22×C109—41no—
75C22×C109C2×C22⋊C411yescharacteristic
76C2×D109—21no—
77C2×D109—21no—
78C2×D109#10412yes—
79C4×C109—21no—
80C4×C109—21no—
81C4×C109—41no—
82C4×C109#13112yes—
83Dic109—21no—
84Dic109—21no—
85Dic109—41no—
86Dic109—41no—
87Dic109AGL(1,ℤ/8)11yescharacteristic
88Dic109#13711yescharacteristic
89C2×C109—81no—
90C2×C109#40811yescharacteristic
91C2×C109#41711yescharacteristic
92C2×C109C2×#10411yescharacteristic
93D109—22no—
94#1483—1091nomaximal, Sylow
95C109#148311yescharacteristic, complemented, Sylow
96#529—1091no—
97C2×C4⋊C8—1091no—
98C4×M16—1091no—
99Q8⋊C8—1092no—
100D4⋊C8—1092no—
101C2×M16—2181no—
102C22×C8—2181no—
103#126—2181no—
104#125—1091no—
105#124#8913711yescharacteristic
106#123—2181no—
107C22⋊Q8—1091no—
108#121—1091no—
109C4×Q8—1091no—
110C4×D4—1091no—
111C4×D4—2181no—
112#117—2181no—
113C2×C42—1091no—
114C4⋊C8—1092no—
115C4⋊C8—2181no—
116#97—2181no—
117C4×C8—1092no—
118C2×Q8C2×#8913711yescharacteristic
119C2×D4—2181no—
120C2×D4C2×#8913711yescharacteristic
121C22×C4—1091no—
122C22×C4—1091no—
123C22×C4—1091no—
124C22×C4—2181no—
125M16—2184no—
126C2×C8—4362no—
127C2×C8—2182no—
128C2×C8—2182no—
129C4⋊C4—1091no—
130C4⋊C4—1091no—
131C4⋊C4—2181no—
132C4⋊C4—2181no—
133C4⋊C4—2181no—
134C4⋊C4—2181no—
135C22⋊C4—21no—
136C22⋊C4—21no—
137C22⋊C4—2181no—
138C22⋊C4—2181no—
139C22⋊C4—2181no—
140C42—1091no—
141C42—1091no—
142C42—1091no—
143C42—2181no—
144C42C2×#8913711yescharacteristic
145C23—21no—
146C23—1091no—
147Q8—22no—
148D4—22no—
149D4—4362no—
150C2×C4—21no—
151C2×C4—1091no—
152C2×C4—1091no—
153C2×C4—1091no—
154C2×C4—4361no—
155C2×C4—4361no—
156C2×C4—2181no—
157C2×C4—2181no—
158C2×C4—2182no—
159C2×C4—2181no—
160C2×C4—2181no—
161C2×C4—2182no—
162C2×C4C22⋊#8913711yescharacteristic
163C2×C4C22⋊#8913711yescharacteristic
164C2×C4C22×#8913711yescharacteristic
165C8—4362no—
166C8—2184no—
167C22—41no—
168C22—41no—
169C22—41no—
170C22—1092no—
171C22—2181no—
172C22—2181no—
173C22C2×C22⋊#8913711yescharacteristic
174C4—21no—
175C4—21no—
176C4—41no—
177C4—1091no—
178C4—1091no—
179C4—4361no—
180C4—4361no—
181C4—2181no—
182C4—2181no—
183C4#1681278612yes—
184C2—81no—
185C2—2182no—
186C2#2029600011yescharacteristic
187C2#2029601711yescharacteristic
188C2D109⋊#10411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#89137
commutatorC2×C4×C109C22×C4
FrattiniC2×C4C22×#89137
Fitting#124×C109C4
socleC22×C109C2×C22⋊C4
prime radical#16812670C4
cosocleC4×Dic109C23
hypercenter#124#89137
hypocenterC109#1483
LCSG ▷ C2×C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
1. D109⋊(C4⋊C8)C2semidirect
2. C4×#13182039C2semidirect
3. Q8⋊#11724786C2semidirect
4. D4⋊#11724786C2semidirect
95. C109#1483semidirect

Maximal subgroups

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

subgroupindex
D109⋊(C4⋊C8)2
C4×#131820392
Q8⋊#117247862
D4⋊#117247862
#202955552
#1483109