Finite Group Databasebeta

← #28373324

Subgroups — #28373324

Order 13952.

382 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 121 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#20295631C211yesmaximal, characteristic
2#20295503C211yesmaximal, characteristic, complemented
3#20295351C212yesmaximal, complemented
4#20295334C212yesmaximal, complemented
5#20295227C212yesmaximal, complemented
6#20295167C212yesmaximal, complemented
7#20295128C212yesmaximal, complemented
8C4×#13182018C212yesmaximal, complemented
9#433×C109C211yesmaximal, characteristic, complemented
10C22×Dic218C2211yescharacteristic
11C2×#13182018C2212yes—
12C2×#13182018C2212yes—
13#16812696C2211yescharacteristic
14#16812691C2211yescharacteristic
15#16812684—22no—
16#16812673C2212yes—
17#16812672—22no—
18C4×Dic218C2212yes—
19C4×Dic218C2212yes—
20#16812664—22no—
21C4×D436C2212yes—
22#16812658C2211yescharacteristic
23#16812655—22no—
24#16812633C2212yes—
25#16812631C2212yes—
26#16812624C2212yes—
27#16812624C2212yes—
28#16812621C2212yes—
29#16812621C2212yes—
30#117×C109C2211yescharacteristic
31C4⋊C8×C109C2212yes—
32C22⋊C8×C109C2212yes—
33#97×C109C2211yescharacteristic
34C4×C8×C109C2211yescharacteristic
35C2×Dic218—21no—
36C2×Dic218—24no—
37C2×Dic218C2312yes—
38C2×D436—22no—
39C2×D436C2312yes—
40C2×C22⋊D109—22no—
41C22×Dic109—21no—
42C2×C4×D109—22no—
43#13182018—24no—
44#13182018—24no—
45C4⋊Dic109C2312yes—
46C4⋊Dic109C2312yes—
47#13182008—22no—
48#13182008—22no—
49#13182008—22no—
50C22⋊Dic109—21no—
51#13182006—22no—
52#13182006—22no—
53C4×Dic109—22no—
54C4×Dic109—22no—
55C4×Dic109—21no—
56C22×C4×C109C2311yescharacteristic
57C2×C8×C109C2312yes—
58C2×C8×C109C2312yes—
59C4⋊C4×C109D412yes—
60C22⋊C4×C109D412yes—
61C42×C109C2311yescharacteristic
62C42×C109C2311yescharacteristic
63C23×C109C2×D411yescharacteristic
64C22×D109—22no—
65C2×C4×C109—22no—
66C2×C4×C109C2×D412yes—
67C2×C4×C109C2×D412yes—
68C2×C4×C109C2×D411yescharacteristic
69C2×C4×C109C2411yescharacteristic
70C22⋊D109—82no—
71C2×Dic109—24no—
72C2×Dic109—22no—
73C2×Dic109—22no—
74C2×Dic109—22no—
75D436—22no—
76D436—22no—
77D436—82no—
78C4×D109—82no—
79Dic218—24no—
80Dic218—22no—
81Dic218#4114yes—
82C8×C109—22no—
83C8×C109—22no—
84C22×C109—21no—
85C22×C109—22no—
86C22×C109C22×D411yescharacteristic
87C2×D109—42no—
88C2×D109—42no—
89C2×D109—42no—
90C4×C109—21no—
91C4×C109—22no—
92C4×C109—22no—
93C4×C109C2×#4112yes—
94Dic109—24no—
95Dic109—42no—
96Dic109—42no—
97C2×C109—41no—
98C2×C109#52511yescharacteristic
99C2×C109#57712yes—
100D109—82no—
101#3126—1091nomaximal, Sylow
102C109#312611yescharacteristic, complemented, Sylow
103#540—1091no—
104#519—1091no—
105#482—1092no—
106#479—1092no—
107#460—1092no—
108#448—1092no—
109#440—1092no—
110C4×SD16—1092no—
111#433D10911yescharacteristic, complemented
112C22×Q8—1091no—
113C2×SD16—1092no—
114C2×SD16—1092no—
115#127—1091no—
116#125—1091no—
117#123—2182no—
118#121—1092no—
119#121—2182no—
120C4×Q8—1092no—
121C4×Q8—1092no—
122C4×Q8—2182no—
123C4×D4—1092no—
124#117—1091no—
125#117—2182no—
126#117C2×D10911yescharacteristic
127#107—1092no—
128#106—1092no—
129C4⋊C8C2×D10912yes—
130#103—1092no—
131#103—1092no—
132#102—1092no—
133#102—1092no—
134C22⋊C8C2×D10912yes—
135#97C2×D10911yescharacteristic
136C4×C8C2×D10911yescharacteristic
137C2×Q8—1092no—
138C2×Q8—2184no—
139C2×Q8—2181no—
140C2×D4—1092no—
141C2×D4—2182no—
142C2×D4—2182no—
143C22×C4—2182no—
144C22×C4—2181no—
145C22×C4C22×D10911yescharacteristic
146SD16—2184no—
147SD16—2184no—
148C2×C8C22×D10912yes—
149C2×C8C22×D10912yes—
150C4⋊C4—1092no—
151C4⋊C4—1092no—
152C4⋊C4—2182no—
153C4⋊C4—2182no—
154C4⋊C4—2182no—
155C4⋊C4D43612yes—
156C22⋊C4—2181no—
157C22⋊C4—2182no—
158C22⋊C4—2182no—
159C22⋊C4D43612yes—
160C42—2181no—
161C42—2182no—
162C42—2182no—
163C42C22×D10911yescharacteristic
164C42C22×D10911yescharacteristic
165C23—2182no—
166C23C2×D43611yescharacteristic
167Q8—1094no—
168Q8—2184no—
169Q8—2182no—
170D4—8722no—
171D4—8722no—
172D4—2182no—
173D4—2182no—
174C2×C4—22no—
175C2×C4—8722no—
176C2×C4—2182no—
177C2×C4—2182no—
178C2×C4—2184no—
179C2×C4—2182no—
180C2×C4C2×D43612yes—
181C2×C4C2×D43612yes—
182C2×C4C2×D43611yescharacteristic
183C2×C4C23×D10911yescharacteristic
184C8—22no—
185C8—22no—
186C22—21no—
187C22—22no—
188C22—4362no—
189C22—4362no—
190C22—4362no—
191C22C22×D43611yescharacteristic
192C4—21no—
193C4—22no—
194C4—22no—
195C4—4362no—
196C4—4362no—
197C4—2184no—
198C4#41×D10912yes—
199C2—41no—
200C2—8722no—
201C2#2029553811yescharacteristic
202C2#2029583812yes—
subgroupG/H
centerC22C22×D436
commutator, cosocleC2×C4×C109C24
FrattiniC2×C4C23×D109
Fitting#433×C109C2
socleC22×C109C22×D4
prime radical#20295631C2
hypercenter#433D109
hypocenterC109#3126
LCSG ▷ C2×C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
2. #20295503C2semidirect
3. #20295351C2semidirect
4. #20295334C2semidirect
5. #20295227C2semidirect
6. #20295167C2semidirect
7. #20295128C2semidirect
8. C4×#13182018C2semidirect
9. #433×C109C2semidirect
102. C109#3126semidirect
111. #433D109semidirect

Maximal subgroups

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

subgroupindex
#202956312
#202955032
#202953512
#202953342
#202952272
#202951672
#202951282
C4×#131820182
#433×C1092
#3126109