Finite Group Databasebeta

← #28373416

Subgroups — #28373416

Order 13952.

400 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 125 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#20295579C211yesmaximal, characteristic, complemented
2C2×#16812686C211yesmaximal, characteristic
3#20295384C214yesmaximal, complemented
4#20295379C214yesmaximal, complemented
5#20295036C211yesmaximal, characteristic, complemented
6#20295034C211yesmaximal, characteristic, complemented
7#20295031C211yesmaximal, characteristic
8M16×Dic109C211yesmaximal, characteristic, complemented
9#418×C109C211yesmaximal, characteristic
10C22×Dic218C2211yescharacteristic
11C2×#13182013C2211yescharacteristic
12#16812698C2212yescomplemented
13#16812690C2212yescomplemented
14#16812686—22no—
15#16812686C2212yes—
16#16812686C2212yes—
17#16812676—22no—
18C4×Dic218—22no—
19#16812658C2211yescharacteristic
20C2×C22⋊Dic109—22no—
21C2×C4×Dic109C2211yescharacteristic
22#16812624C2214yescomplemented
23#16812622C2214yescomplemented
24#16812620C2214yes—
25#16812609C2212yescomplemented
26C8×Dic109C2212yescomplemented
27C22×D4×C109C2211yescharacteristic
28C2×M16×C109C2211yescharacteristic
29#117×C109C2211yescharacteristic
30#102×C109C2214yes—
31C2×Dic218—22no—
32C2×Dic218—22no—
33C2×Dic218—21no—
34C2×Dic218—22no—
35C2×Dic218C2312yes—
36C22×Dic109—21no—
37C22×Dic109D412yes—
38#13182013—22no—
39C2×#11724784C2312yes—
40C4⋊Dic109—22no—
41C4⋊Dic109C2312yes—
42#13182008—22no—
43#13182008—22no—
44C22⋊Dic109—21no—
45C22⋊Dic109—24no—
46C22⋊Dic109—24no—
47C4×Dic109—21no—
48C4×Dic109D412yes—
49C4×Dic109C2311yescharacteristic
50C4×Dic109C2311yescharacteristic
51C24×C109—21no—
52C2×D4×C109—21no—
53C2×D4×C109—22no—
54C2×D4×C109—22no—
55C2×D4×C109C2312yes—
56C22×C4×C109C2311yescharacteristic
57M16×C109—22no—
58C2×C8×C109C2312yes—
59C4⋊C4×C109C2312yes—
60C22⋊C4×C109—21no—
61C42×C109—21no—
62C23×C109—22no—
63C23×C109—44no—
64C23×C109—42no—
65C23×C109C2×D411yescharacteristic
66D4×C109—22no—
67D4×C109—22no—
68D4×C109—42no—
69C2×C4×C109—22no—
70C2×C4×C109C2×D411yescharacteristic
71C2×C4×C109#4112yes—
72C2×C4×C109#4112yes—
73C2×C4×C109C2411yescharacteristic
74C2×Dic109—22no—
75C2×Dic109—22no—
76C2×Dic109—42no—
77C2×Dic109—42no—
78C2×Dic109C2×D412yes—
79C2×Dic109C2×D412yes—
80Dic218—22no—
81Dic218—22no—
82Dic218—44no—
83Dic218—42no—
84C8×C109—22no—
85#11724784—22no—
86C22×C109—22no—
87C22×C109—42no—
88C22×C109—44no—
89C22×C109—84no—
90C22×C109#12412yes—
91C22×C109C22×D411yescharacteristic
92C4×C109—42no—
93C4×C109#12412yes—
94C4×C109C2×#4111yescharacteristic
95C4×C109C2×#4111yescharacteristic
96Dic109—22no—
97Dic109—22no—
98Dic109—42no—
99Dic109—42no—
100C2×C109—22no—
101C2×C109—82no—
102C2×C109C2×#12411yescharacteristic
103C2×C109#57512yes—
104#3140—1091nomaximal, Sylow
105C109#314011yescharacteristic, complemented, Sylow
106#533—1091no—
107C2×#124—1091no—
108#489—1094no—
109#488—1094no—
110#419—1091no—
111#419—1091no—
112#418—1091no—
113#418D10911yescharacteristic
114C4×M16—1091no—
115C22×Q8—1091no—
116C22×D4C2×D10911yescharacteristic
117C2×M16—1091no—
118C2×M16C2×D10911yescharacteristic
119C4⋊Q8—1092no—
120#125—1092no—
121#124—1092no—
122#124—1092no—
123#124—2182no—
124C22⋊Q8—2182no—
125C4×Q8—2182no—
126#117—1091no—
127#117C2×D10911yescharacteristic
128C2×C22⋊C4—2182no—
129C2×C42—1091no—
130#103—1094no—
131#103—1094no—
132#102—1094no—
133#102C2×D10914yes—
134#97—1092no—
135C4×C8—1092no—
136C24—21no—
137C2×Q8—1092no—
138C2×Q8—2182no—
139C2×Q8—2182no—
140C2×Q8—2182no—
141C2×Q8—2181no—
142C2×D4—21no—
143C2×D4—22no—
144C2×D4—22no—
145C2×D4C22×D10912yes—
146C22×C4—1092no—
147C22×C4—2181no—
148C22×C4C22×D10911yescharacteristic
149M16—22no—
150M16—2182no—
151C2×C8—1092no—
152C2×C8C22×D10912yes—
153C4⋊C4—1092no—
154C4⋊C4—2182no—
155C4⋊C4—2182no—
156C4⋊C4—2182no—
157C4⋊C4C22×D10912yes—
158C22⋊C4—21no—
159C22⋊C4—2184no—
160C22⋊C4—2184no—
161C22⋊C4—2181no—
162C42—21no—
163C42—1092no—
164C42—1091no—
165C42—1091no—
166C42—2181no—
167C23—22no—
168C23—44no—
169C23—42no—
170C23D4×D10911yescharacteristic
171Q8—4364no—
172Q8—4362no—
173Q8—2182no—
174Q8—2182no—
175D4—22no—
176D4—22no—
177D4—42no—
178C2×C4—22no—
179C2×C4—1092no—
180C2×C4—1092no—
181C2×C4—4362no—
182C2×C4—4362no—
183C2×C4—2182no—
184C2×C4—2182no—
185C2×C4D4×D10911yescharacteristic
186C2×C4#1318202812yes—
187C2×C4#1318202912yes—
188C2×C4C23×D10911yescharacteristic
189C8—22no—
190C8—2182no—
191C22—22no—
192C22—42no—
193C22—44no—
194C22—84no—
195C22#1681268512yes—
196C22C2×D4×D10911yescharacteristic
197C4—42no—
198C4—4362no—
199C4—4362no—
200C4—2182no—
201C4—2182no—
202C4#1681268512yes—
203C4C2×#1318202811yescharacteristic
204C4C2×#1318202911yescharacteristic
205C2—22no—
206C2—82no—
207C2C2×#1681268511yescharacteristic
208C2#2029582212yes—
subgroupG/H
centerC22C2×D4×D109
commutator, cosocleC2×C4×C109C24
FrattiniC2×C4C23×D109
Fitting#418×C109C2
socleC22×C109C22×D4
prime radicalC22×D4×C109C22
hypercenter#418D109
hypocenterC109#3140
LCSG ▷ C2×C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
1. #20295579C2semidirect
3. #20295384C2semidirect
4. #20295379C2semidirect
5. #20295036C2semidirect
6. #20295034C2semidirect
8. M16×Dic109C2semidirect
12. #16812698C22semidirect
13. #16812690C22semidirect
22. #16812624C22semidirect
23. #16812622C22semidirect
25. #16812609C22semidirect
26. C8×Dic109C22semidirect
105. C109#3140semidirect

Maximal subgroups

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

subgroupindex
#202955792
C2×#168126862
#202953842
#202953792
#202950362
#202950342
#202950312
M16×Dic1092
#418×C1092
#3140109