Finite Group Databasebeta

← #28374498

Subgroups — #28374498

Order 13952.

346 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 109 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#20295649C212yesmaximal, complemented
2#20295315C212yesmaximal, complemented
3#20295309C212yesmaximal, complemented
4#20295279C211yesmaximal, characteristic
5#20295257C212yesmaximal, complemented
6#20295250C212yesmaximal, complemented
7#20295244C212yesmaximal, complemented
8#20295054C211yesmaximal, characteristic, complemented
9#470×C109C211yesmaximal, characteristic, complemented
10C2×#13182016C2212yes—
11C2×D872C2211yescharacteristic
12C22×#11724784C2211yescharacteristic
13#16812698C2212yes—
14#16812694—22no—
15#16812688C2212yes—
16#16812685—22no—
17#16812681—22no—
18#16812679—22no—
19#16812673C2212yes—
20Q8×Dic109C2212yes—
21#16812661C2212yes—
22#16812658C2211yescharacteristic
23#16812631C2211yescharacteristic
24#16812630C2212yes—
25#16812628C2212yes—
26#16812628C2212yes—
27#16812623C2212yes—
28#16812621C2212yes—
29#16812619C2212yes—
30C2×Q16×C109C2211yescharacteristic
31C2×M16×C109C2211yescharacteristic
32C22⋊Q8×C109C2212yes—
33#106×C109C2211yescharacteristic
34#103×C109C2212yes—
35C2×Dic218—22no—
36C2×D436C2312yes—
37C2×C22⋊D109—22no—
38C2×C4×D109—22no—
39#13182016—42no—
40D872—41no—
41C2×#11724784—41no—
42C2×#11724784C2312yes—
43C4⋊Dic109—22no—
44C4⋊Dic109D412yes—
45C4⋊Dic109C2312yes—
46#13182008—22no—
47C22⋊Dic109D411yescharacteristic
48C22⋊Dic109D411yescharacteristic
49#13182006—22no—
50#13182006—22no—
51#13182006—22no—
52#13182006—22no—
53C4×Dic109—22no—
54C4×Dic109C2312yes—
55C2×Q8×C109C2312yes—
56C22×C4×C109C2311yescharacteristic
57Q16×C109—41no—
58M16×C109—41no—
59C2×C8×C109C2311yescharacteristic
60C2×C8×C109C2311yescharacteristic
61C4⋊C4×C109—22no—
62C4⋊C4×C109C2312yes—
63C22⋊C4×C109—22no—
64C23×C109C2×D411yescharacteristic
65C22×D109—22no—
66Q8×C109—22no—
67Q8×C109—22no—
68C2×C4×C109—21no—
69C2×C4×C109—21no—
70C2×C4×C109—22no—
71C2×C4×C109—22no—
72C2×C4×C109C2×D411yescharacteristic
73C2×C4×C109C2411yescharacteristic
74C22⋊D109—82no—
75C2×Dic109—22no—
76C2×Dic109C2×D412yes—
77C2×Dic109C2×D412yes—
78D436—22no—
79D436—22no—
80C4×D109—82no—
81Dic218—82no—
82C8×C109—21no—
83C8×C109—21no—
84#11724784—22no—
85C22×C109—21no—
86C22×C109—22no—
87C22×C109C22×D411yescharacteristic
88C2×D109—42no—
89C2×D109—42no—
90C2×D109—42no—
91C4×C109—21no—
92C4×C109—42no—
93C4×C109—42no—
94C4×C109H(5,𝔽2)11yescharacteristic
95C4×C1092−1+411yescharacteristic
96Dic109—22no—
97Dic109—22no—
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#470D10911yescharacteristic, complemented
109#469—1091no—
110#465—1092no—
111#464—1092no—
112#463—1092no—
113#424—1091no—
114C2×Q16C2×D10911yescharacteristic
115C2×SD16—1092no—
116C2×D8—1091no—
117C2×M16C2×D10911yescharacteristic
118C22×C8—1091no—
119C4⋊Q8—1092no—
120#126—2182no—
121#124—1092no—
122#124—2182no—
123#123—2182no—
124C22⋊Q8—2182no—
125C22⋊Q8C2×D10912yes—
126#121—1092no—
127C4×Q8—1092no—
128C4×D4—1092no—
129#117—1091no—
130#106—1091no—
131#106—1092no—
132#106C2×D10911yescharacteristic
133C4⋊C8—1092no—
134C4⋊C8—1092no—
135#103—1092no—
136#103C2×D10912yes—
137#102—1092no—
138#102—1092no—
139C2×Q8—2182no—
140C2×Q8C22×D10912yes—
141C2×D4—1092no—
142C2×D4—2182no—
143C22×C4—2182no—
144C22×C4C22×D10911yescharacteristic
145Q16—41no—
146SD16—4362no—
147D8—4361no—
148M16—41no—
149C2×C8—1092no—
150C2×C8—4361no—
151C2×C8C22×D10911yescharacteristic
152C2×C8C22×D10911yescharacteristic
153C4⋊C4—22no—
154C4⋊C4—1092no—
155C4⋊C4—1092no—
156C4⋊C4—2182no—
157C4⋊C4—2182no—
158C4⋊C4C22×D10912yes—
159C22⋊C4—22no—
160C22⋊C4—1091no—
161C22⋊C4—1091no—
162C22⋊C4—2182no—
163C22⋊C4—2182no—
164C22⋊C4—2182no—
165C22⋊C4—2182no—
166C42—1092no—
167C42—2182no—
168C23—2182no—
169C23D4×D10911yescharacteristic
170Q8—22no—
171Q8—22no—
172Q8—8722no—
173D4—8722no—
174D4—2182no—
175D4—2182no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—8722no—
181C2×C4—1092no—
182C2×C4—1092no—
183C2×C4—2182no—
184C2×C4D4×D10911yescharacteristic
185C2×C4C23×D10911yescharacteristic
186C8—21no—
187C8—21no—
188C8—2182no—
189C22—22no—
190C22—21no—
191C22—4362no—
192C22—4362no—
193C22—4362no—
194C22C2×D4×D10911yescharacteristic
195C4—21no—
196C4—42no—
197C4—42no—
198C4—4362no—
199C4—2182no—
200C4—2182no—
201C4#1681274411yescharacteristic
202C4#1681274611yescharacteristic
203C2—41no—
204C2—8722no—
205C2#2029560311yescharacteristic
206C2#2029583512yes—
subgroupG/H
centerC22C2×D4×D109
commutator, cosocleC2×C4×C109C24
FrattiniC2×C4C23×D109
Fitting#470×C109C2
socleC22×C109C22×D4
prime radical#20295279C2
hypercenter#470D109
hypocenterC109#3263
LCSG ▷ C2×C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ C22×C4 ◁ #470

Complements

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

NH ≅ G/Ntype
1. #20295649C2semidirect
2. #20295315C2semidirect
3. #20295309C2semidirect
5. #20295257C2semidirect
6. #20295250C2semidirect
7. #20295244C2semidirect
8. #20295054C2semidirect
9. #470×C109C2semidirect
104. C109#3263semidirect
108. #470D109semidirect

Maximal subgroups

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

subgroupindex
#202956492
#202953152
#202953092
#202952792
#202952572
#202952502
#202952442
#202950542
#470×C1092
#3263109