Finite Group Databasebeta

← #28364283

Subgroups — #28364283

Order 13952.

382 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 69 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#20295588C211yesmaximal, characteristic
2C2×#16812613C212yesmaximal, complemented
3#20294905C212yesmaximal, complemented
4#20294793C211yesmaximal, characteristic, complemented
5#385×C109C211yesmaximal, characteristic, complemented
6C22×C22⋊D109C2212yes—
7#16812683—22no—
8#16812673—21no—
9#16812673—21no—
10#16812669—22no—
11C2×C22⋊Dic109C2212yes—
12C2×#13182006—22no—
13#16812613—24no—
14#16812606—22no—
15C23×C4×C109C2211yescharacteristic
16C2×C4⋊C4×C109—21no—
17C2×C22⋊C4×C109C2211yescharacteristic
18C2×C22⋊C4×C109C2211yescharacteristic
19#95×C109—21no—
20C23×D109D412yes—
21C2×D436—21no—
22C2×D436—21no—
23C2×C22⋊D109—22no—
24C2×C22⋊D109—22no—
25C2×C22⋊D109—22no—
26C2×C22⋊D109—22no—
27C2×C22⋊D109—22no—
28C2×C22⋊D109—22no—
29C22×Dic109—22no—
30C22×Dic109D412yes—
31C4⋊Dic109—21no—
32C4⋊Dic109—21no—
33C22⋊Dic109—22no—
34C22⋊Dic109—22no—
35#13182006—22no—
36#13182006—22no—
37#13182006—44no—
38C24×C109C2311yescharacteristic
39C22×C4×C109—21no—
40C22×C4×C109—21no—
41C22×C4×C109—22no—
42C22×C4×C109—42no—
43C22×C4×C109D411yescharacteristic
44C22×C4×C109D411yescharacteristic
45C4⋊C4×C109—42no—
46C22⋊C4×C109—22no—
47C22⋊C4×C109—21no—
48C22⋊C4×C109D412yescomplemented
49C23×C109—41no—
50C23×C109—41no—
51C23×C109C2×D412yes—
52C23×C109C2×D411yescharacteristic
53C23×C109C2×D411yescharacteristic
54C23×C109#4111yescharacteristic
55C23×C109#4112yes—
56C22×D109—22no—
57C22×D109—22no—
58C22×D109—22no—
59C22×D109—42no—
60C22×D109—42no—
61C2×C4×C109—22no—
62C2×C4×C109—24no—
63C2×C4×C109—21no—
64C2×C4×C109—21no—
65C2×C4×C109—22no—
66C2×C4×C109—41no—
67C2×C4×C109—41no—
68C2×C4×C109—42no—
69C2×C4×C109—41no—
70C2×C4×C109—41no—
71C2×C4×C109—41no—
72C2×C4×C109—41no—
73C22⋊D109—42no—
74C22⋊D109—42no—
75C22⋊D109—42no—
76C22⋊D109—42no—
77C2×Dic109—22no—
78C2×Dic109—22no—
79C2×Dic109—22no—
80C2×Dic109—42no—
81C2×Dic109—42no—
82C2×Dic109—42no—
83D436—81no—
84D436—81no—
85C22×C109—22no—
86C22×C109—21no—
87C22×C109—22no—
88C22×C109—21no—
89C22×C109—41no—
90C22×C109—41no—
91C22×C109—42no—
92C22×C109#12011yescharacteristic
93C22×C109#12111yescharacteristic
94C22×C109#12112yes—
95C22×C109#12312yes—
96C22×C109#12411yescharacteristic
97C2×D109—44no—
98C2×D109—42no—
99C2×D109—42no—
100C2×D109—42no—
101C2×D109—82no—
102C4×C109—42no—
103C4×C109—41no—
104C4×C109—42no—
105C4×C109—41no—
106Dic109—42no—
107Dic109—82no—
108C2×C109—22no—
109C2×C109—21no—
110C2×C109—22no—
111C2×C109—21no—
112C2×C109#39411yescharacteristic
113C2×C109B(4,𝔽2)11yescharacteristic
114C2×C109#45811yescharacteristic
115D109—82no—
116#2044—1091nomaximal, Sylow
117C109#204411yescharacteristic, complemented, Sylow
118#534—1091no—
119C2×#99—1092no—
120#386—1092no—
121#385D10911yescharacteristic, complemented
122#342—1091no—
123C22×D4—1092no—
124C23×C4C2×D10911yescharacteristic
125#123—2182no—
126#121—2181no—
127#121—2181no—
128#120—2182no—
129C2×C4⋊C4—21no—
130C2×C22⋊C4—1092no—
131C2×C22⋊C4—2182no—
132C2×C22⋊C4C2×D10911yescharacteristic
133C2×C22⋊C4C2×D10911yescharacteristic
134#99—2184no—
135#95—21no—
136#95—2182no—
137C24—1092no—
138C24C22×D10911yescharacteristic
139C2×D4—2181no—
140C2×D4—2181no—
141C2×D4—2182no—
142C2×D4—2182no—
143C2×D4—2182no—
144C2×D4—2182no—
145C2×D4—2182no—
146C2×D4—2182no—
147C22×C4—22no—
148C22×C4—21no—
149C22×C4—21no—
150C22×C4—42no—
151C22×C4—1092no—
152C22×C4—2182no—
153C22×C4C22⋊D10911yescharacteristic
154C22×C4C22⋊D10911yescharacteristic
155C4⋊C4—42no—
156C4⋊C4—2181no—
157C4⋊C4—2181no—
158C22⋊C4—22no—
159C22⋊C4—21no—
160C22⋊C4—4364no—
161C22⋊C4—2182no—
162C22⋊C4—2182no—
163C22⋊C4—2182no—
164C22⋊C4—2182no—
165C22⋊C4D43612yescomplemented
166C23—41no—
167C23—41no—
168C23—4362no—
169C23—4362no—
170C23—2182no—
171C23—2182no—
172C23—2182no—
173C23D4×D10912yes—
174C23C2×C22⋊D10911yescharacteristic
175C23C2×D43611yescharacteristic
176C23#1318202911yescharacteristic
177C23#1318203012yes—
178D4—8721no—
179D4—8721no—
180D4—4362no—
181D4—4362no—
182D4—4362no—
183D4—4362no—
184C2×C4—24no—
185C2×C4—22no—
186C2×C4—21no—
187C2×C4—21no—
188C2×C4—22no—
189C2×C4—41no—
190C2×C4—41no—
191C2×C4—42no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—41no—
195C2×C4—41no—
196C2×C4—4362no—
197C2×C4—4362no—
198C2×C4—4362no—
199C2×C4—2182no—
200C2×C4—2182no—
201C2×C4—2182no—
202C22—21no—
203C22—22no—
204C22—21no—
205C22—22no—
206C22—41no—
207C22—41no—
208C22—42no—
209C22—8722no—
210C22—4364no—
211C22—4362no—
212C22—4362no—
213C22—4362no—
214C22#1681266711yescharacteristic
215C22#1681267311yescharacteristic
216C22#1681267412yes—
217C22#1681268412yes—
218C22#1681268811yescharacteristic
219C4—42no—
220C4—42no—
221C4—41no—
222C4—41no—
223C4—8722no—
224C4—4362no—
225C2—21no—
226C2—22no—
227C2—22no—
228C2—21no—
229C2—8722no—
230C2#2029494311yescharacteristic
231C2#2029521211yescharacteristic
232C2#2029521511yescharacteristic
subgroupG/H
centerC22#16812667
commutator, cosocleC24×C109C23
FrattiniC24C22×D109
Fitting#385×C109C2
socleC22×C109#120
prime radical#20295588C2
hypercenter#385D109
hypocenterC109#2044
LCSG ▷ C24×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ C24 ◁ #385

Complements

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

NH ≅ G/Ntype
2. C2×#16812613C2semidirect
3. #20294905C2semidirect
4. #20294793C2semidirect
5. #385×C109C2semidirect
48. C22⋊C4×C109D4semidirect
117. C109#2044semidirect
121. #385D109semidirect
165. C22⋊C4D436semidirect

Maximal subgroups

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

subgroupindex
#202955882
C2×#168126132
#202949052
#202947932
#385×C1092
#2044109