Finite Group Databasebeta

← #28374503

Subgroups — #28374503

Order 13952.

346 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 117 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#20295647C212yesmaximal, complemented
2#20295317C212yesmaximal, complemented
3#20295312C212yesmaximal, complemented
4#20295284C211yesmaximal, characteristic, complemented
5#20295279C211yesmaximal, characteristic
6#20295255C212yesmaximal, complemented
7#20295249C212yesmaximal, complemented
8#20295242C212yesmaximal, complemented
9#424×C109C211yesmaximal, characteristic, complemented
10C2×Dic436C2211yescharacteristic
11C2×#13182018C2212yes—
12C2×D872C2211yescharacteristic
13#16812699C2212yes—
14#16812694—22no—
15#16812687C2212yes—
16#16812685—22no—
17#16812681—22no—
18#16812678C2212yes—
19#16812677—22no—
20#16812673C2212yes—
21C4×Dic218C2212yes—
22C4×D436C2212yes—
23#16812631C2212yes—
24#16812631C2211yescharacteristic
25#16812631C2211yescharacteristic
26#16812624C2212yes—
27#16812624C2212yes—
28#16812621C2212yes—
29#16812621C2212yes—
30C2×M16×C109C2211yescharacteristic
31C22×C8×C109C2211yescharacteristic
32#117×C109C2211yescharacteristic
33C4⋊C8×C109C2212yes—
34C4⋊C8×C109C2212yes—
35C2×Dic218—22no—
36C2×Dic218C2312yes—
37C2×D436C2312yes—
38C2×C22⋊D109—22no—
39C2×C4×D109—22no—
40Dic436—41no—
41#13182018—42no—
42D872—41no—
43C4⋊Dic109—22no—
44C4⋊Dic109C2312yes—
45C4⋊Dic109C2312yes—
46#13182008—22no—
47#13182008—22no—
48C22⋊Dic109—22no—
49#13182006—22no—
50#13182006—22no—
51#13182006—22no—
52#13182006—22no—
53C4×Dic109—22no—
54C22×C4×C109C2311yescharacteristic
55M16×C109—41no—
56C2×C8×C109—41no—
57C2×C8×C109C2312yes—
58C2×C8×C109C2311yescharacteristic
59C2×C8×C109C2311yescharacteristic
60C4⋊C4×C109D412yes—
61C22⋊C4×C109D411yescharacteristic
62C22⋊C4×C109D411yescharacteristic
63C42×C109C2312yes—
64C23×C109C2×D411yescharacteristic
65C22×D109—22no—
66C2×C4×C109—21no—
67C2×C4×C109—21no—
68C2×C4×C109C2×D412yes—
69C2×C4×C109C2×D412yes—
70C2×C4×C109C2×D411yescharacteristic
71C2×C4×C109C2411yescharacteristic
72C22⋊D109—82no—
73C2×Dic109—22no—
74C2×Dic109—22no—
75C2×Dic109—22no—
76D436—22no—
77D436—22no—
78C4×D109—82no—
79Dic218—22no—
80Dic218—22no—
81Dic218—82no—
82C8×C109—22no—
83C8×C109—21no—
84C8×C109—21no—
85C22×C109—21no—
86C22×C109—22no—
87C22×C109C22×D411yescharacteristic
88C2×D109—42no—
89C2×D109—42no—
90C2×D109—42no—
91C4×C109—21no—
92C4×C109—22no—
93C4×C109—22no—
94C4×C109H(5,𝔽2)11yescharacteristic
95C4×C1092−1+411yescharacteristic
96Dic109—42no—
97Dic109—42no—
98Dic109—42no—
99C2×C109—41no—
100C2×C109#53711yescharacteristic
101C2×C109#57712yes—
102D109—82no—
103#3263—1091nomaximal, Sylow
104C109#326311yescharacteristic, complemented, Sylow
105#542—1092no—
106#476—1092no—
107#475—1092no—
108#470—1091no—
109#469—1091no—
110#465—1092no—
111#464—1092no—
112#463—1092no—
113#424D10911yescharacteristic, complemented
114C2×Q16—1091no—
115C2×SD16—1092no—
116C2×D8—1091no—
117C2×M16C2×D10911yescharacteristic
118C22×C8C2×D10911yescharacteristic
119C4⋊Q8—1092no—
120#126—2182no—
121#124—1092no—
122#124—2182no—
123#123—2182no—
124C22⋊Q8—1092no—
125C22⋊Q8—2182no—
126#121—1092no—
127C4×Q8—1092no—
128C4×D4—1092no—
129#117C2×D10911yescharacteristic
130#106—1092no—
131#106—1091no—
132#106—1091no—
133C4⋊C8C2×D10912yes—
134C4⋊C8C2×D10912yes—
135#103—1092no—
136#103—1092no—
137#102—1092no—
138#102—1092no—
139C2×Q8—1092no—
140C2×Q8—2182no—
141C2×D4—1092no—
142C2×D4—2182no—
143C22×C4—2182no—
144C22×C4C22×D10911yescharacteristic
145Q16—4361no—
146SD16—4362no—
147D8—4361no—
148M16—41no—
149C2×C8—41no—
150C2×C8C22×D10911yescharacteristic
151C2×C8C22×D10912yes—
152C2×C8C22×D10911yescharacteristic
153C4⋊C4—1092no—
154C4⋊C4—1092no—
155C4⋊C4—2182no—
156C4⋊C4—2182no—
157C4⋊C4—2182no—
158C4⋊C4D43612yes—
159C22⋊C4—2182no—
160C22⋊C4—2182no—
161C22⋊C4—2182no—
162C22⋊C4—2182no—
163C22⋊C4—2182no—
164C22⋊C4D43611yescharacteristic
165C22⋊C4D43611yescharacteristic
166C42—2182no—
167C42C22×D10912yes—
168C23—2182no—
169C23C2×D43611yescharacteristic
170Q8—8722no—
171Q8—2182no—
172Q8—2182no—
173D4—8722no—
174D4—2182no—
175D4—2182no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—8722no—
179C2×C4—2182no—
180C2×C4—2182no—
181C2×C4—2182no—
182C2×C4C2×D43612yes—
183C2×C4C2×D43612yes—
184C2×C4C2×D43611yescharacteristic
185C2×C4C23×D10911yescharacteristic
186C8—22no—
187C8—21no—
188C8—21no—
189C22—22no—
190C22—21no—
191C22—4362no—
192C22—4362no—
193C22—4362no—
194C22C22×D43611yescharacteristic
195C4—22no—
196C4—22no—
197C4—21no—
198C4—4362no—
199C4—4362no—
200C4—4362no—
201C4#1681274411yescharacteristic
202C4#1681274711yescharacteristic
203C2—41no—
204C2—8722no—
205C2#2029560711yescharacteristic
206C2#2029583812yes—
subgroupG/H
centerC22C22×D436
commutator, cosocleC2×C4×C109C24
FrattiniC2×C4C23×D109
Fitting#424×C109C2
socleC22×C109C22×D4
prime radical#20295279C2
hypercenter#424D109
hypocenterC109#3263
LCSG ▷ C2×C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ #117 ◁ #424

Complements

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

NH ≅ G/Ntype
1. #20295647C2semidirect
2. #20295317C2semidirect
3. #20295312C2semidirect
4. #20295284C2semidirect
6. #20295255C2semidirect
7. #20295249C2semidirect
8. #20295242C2semidirect
9. #424×C109C2semidirect
104. C109#3263semidirect
113. #424D109semidirect

Maximal subgroups

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

subgroupindex
#202956472
#202953172
#202953122
#202952842
#202952792
#202952552
#202952492
#202952422
#424×C1092
#3263109