Finite Group Databasebeta

← #28374427

Subgroups — #28374427

Order 13952.

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

normal subgroups only

This group has 354 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#20295557C212yesmaximal, complemented
2#20295336C212yesmaximal, complemented
3#20295328C212yesmaximal, complemented
4#20295284C211yesmaximal, characteristic, complemented
5#20295270C212yesmaximal, complemented
6#20295247C212yesmaximal, complemented
7#20295239C212yesmaximal, complemented
8#20295049C211yesmaximal, characteristic, complemented
9#469×C109C211yesmaximal, characteristic
10C2×Dic436C2211yescharacteristic
11C2×#13182017C2212yes—
12C2×#13182013C2211yescharacteristic
13#16812692—22no—
14#16812690C2212yes—
15#16812686C2212yes—
16#16812680—22no—
17#16812678C2212yes—
18#16812664C2212yes—
19D4×Dic109—22no—
20D4×Dic109C2212yes—
21#16812655—22no—
22C2×C4×Dic109C2211yescharacteristic
23#16812632C2212yes—
24#16812631C2211yescharacteristic
25#16812628C2212yes—
26#16812628C2212yes—
27#16812624C2212yes—
28#16812622C2212yes—
29#16812620C2212yes—
30C2×D8×C109C2211yescharacteristic
31C2×M16×C109C2211yescharacteristic
32#121×C109C2212yes—
33#106×C109C2211yescharacteristic
34#102×C109C2212yes—
35C2×Dic218C2312yes—
36C22×Dic109—22no—
37C22×Dic109D412yes—
38Dic436—41no—
39#13182017—42no—
40#13182013—41no—
41C2×#11724784C2312yes—
42C4⋊Dic109—22no—
43C4⋊Dic109C2312yes—
44#13182008—22no—
45#13182008—22no—
46#13182008—22no—
47C22⋊Dic109—22no—
48C22⋊Dic109—22no—
49C22⋊Dic109—22no—
50C22⋊Dic109—22no—
51C4×Dic109—22no—
52C4×Dic109D411yescharacteristic
53C4×Dic109D411yescharacteristic
54C4×Dic109C2312yes—
55C2×D4×C109—22no—
56C2×D4×C109C2312yes—
57C22×C4×C109C2311yescharacteristic
58D8×C109—41no—
59M16×C109—41no—
60C2×C8×C109C2311yescharacteristic
61C2×C8×C109C2311yescharacteristic
62C4⋊C4×C109C2312yes—
63C22⋊C4×C109—22no—
64C23×C109—22no—
65C23×C109C2×D411yescharacteristic
66D4×C109—22no—
67D4×C109—22no—
68D4×C109—44no—
69C2×C4×C109—21no—
70C2×C4×C109—21no—
71C2×C4×C109—22no—
72C2×C4×C109C2×D411yescharacteristic
73C2×C4×C109C2411yescharacteristic
74C2×Dic109—22no—
75C2×Dic109—22no—
76C2×Dic109—42no—
77C2×Dic109—44no—
78C2×Dic109C2×D412yes—
79C2×Dic109C2×D412yes—
80Dic218—22no—
81Dic218—22no—
82C8×C109—21no—
83C8×C109—21no—
84#11724784—22no—
85C22×C109—21no—
86C22×C109—22no—
87C22×C109—42no—
88C22×C109—42no—
89C22×C109—42no—
90C22×C109C22×D411yescharacteristic
91C4×C109—21no—
92C4×C109—42no—
93C4×C109H(5,𝔽2)11yescharacteristic
94C4×C1092−1+411yescharacteristic
95Dic109—22no—
96Dic109—22no—
97Dic109—42no—
98Dic109—42no—
99C2×C109—41no—
100C2×C109—82no—
101C2×C109#53711yescharacteristic
102C2×C109#57512yes—
103#3256—1091nomaximal, Sylow
104C109#325611yescharacteristic, complemented, Sylow
105#529—1092no—
106#479—1092no—
107#478—1092no—
108#470—1091no—
109#469D10911yescharacteristic
110#468—1092no—
111#464—1092no—
112#463—1092no—
113#423—1091no—
114C2×Q16—1091no—
115C2×SD16—1092no—
116C2×D8C2×D10911yescharacteristic
117C2×M16—1091no—
118C2×M16C2×D10911yescharacteristic
119#126—2182no—
120#125—1092no—
121#124—1092no—
122#123—2182no—
123C22⋊Q8—1092no—
124#121C2×D10912yes—
125C4×Q8—1092no—
126C4×D4—1092no—
127C4×D4—2182no—
128#117—2182no—
129C2×C42—1091no—
130#107—1092no—
131#106—1091no—
132#106C2×D10911yescharacteristic
133C4⋊C8—1092no—
134C4⋊C8—1092no—
135#103—1092no—
136#103—1092no—
137#102—1092no—
138#102C2×D10912yes—
139C2×Q8—1092no—
140C2×D4—22no—
141C2×D4C22×D10912yes—
142C22×C4—1092no—
143C22×C4—2182no—
144C22×C4C22×D10911yescharacteristic
145Q16—4361no—
146SD16—4362no—
147D8—41no—
148M16—41no—
149M16—4361no—
150C2×C8—1092no—
151C2×C8C22×D10911yescharacteristic
152C2×C8C22×D10911yescharacteristic
153C4⋊C4—1092no—
154C4⋊C4—2182no—
155C4⋊C4—2182no—
156C4⋊C4—2182no—
157C4⋊C4—2182no—
158C4⋊C4C22×D10912yes—
159C22⋊C4—22no—
160C22⋊C4—2182no—
161C22⋊C4—2182no—
162C22⋊C4—2182no—
163C22⋊C4—2182no—
164C42—1091no—
165C42—1091no—
166C42—1092no—
167C42—2182no—
168C23—22no—
169C23D4×D10911yescharacteristic
170Q8—2182no—
171Q8—2182no—
172D4—22no—
173D4—22no—
174D4—44no—
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—22no—
178C2×C4—1092no—
179C2×C4—1092no—
180C2×C4—4364no—
181C2×C4—4362no—
182C2×C4—2182no—
183C2×C4—2182no—
184C2×C4D4×D10911yescharacteristic
185C2×C4C23×D10911yescharacteristic
186C8—21no—
187C8—21no—
188C8—2182no—
189C22—22no—
190C22—21no—
191C22—42no—
192C22—42no—
193C22—42no—
194C22C2×D4×D10911yescharacteristic
195C4—21no—
196C4—42no—
197C4—4362no—
198C4—4362no—
199C4—2182no—
200C4—2182no—
201C4#1681274411yescharacteristic
202C4#1681274611yescharacteristic
203C2—41no—
204C2—82no—
205C2#2029560311yescharacteristic
206C2#2029582212yes—
subgroupG/H
centerC22C2×D4×D109
commutator, cosocleC2×C4×C109C24
FrattiniC2×C4C23×D109
Fitting, prime radical#469×C109C2
socleC22×C109C22×D4
hypercenter#469D109
hypocenterC109#3256
LCSG ▷ C2×C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ C22×C4 ◁ #469

Complements

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

NH ≅ G/Ntype
1. #20295557C2semidirect
2. #20295336C2semidirect
3. #20295328C2semidirect
4. #20295284C2semidirect
5. #20295270C2semidirect
6. #20295247C2semidirect
7. #20295239C2semidirect
8. #20295049C2semidirect
104. C109#3256semidirect

Maximal subgroups

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

subgroupindex
#202955572
#202953362
#202953282
#202952842
#202952702
#202952472
#202952392
#202950492
#469×C1092
#3256109