Finite Group Databasebeta

← #28365039

Subgroups — #28365039

Order 13952.

260 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 45 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#20295215C211yesmaximal, characteristic, complemented
2#20295212C211yesmaximal, characteristic, complemented
3#20295193C211yesmaximal, characteristic, complemented
4#20294819C211yesmaximal, characteristic, complemented
5#20294816C211yesmaximal, characteristic, complemented
6#20294813C211yesmaximal, characteristic, complemented
7#560×C109C211yesmaximal, characteristic, complemented
8#16812744C2211yescharacteristic
9#16812725—21no—
10#16812682—21no—
11#16812668—21no—
12#16812627—21no—
13#16812616C2211yescharacteristic
14#16812614C2211yescharacteristic
15#16812614C2211yescharacteristic
16#16812613—21no—
17#16812613—21no—
18#127×C109C2211yescharacteristic
19#126×C109—21no—
20#123×C109—21no—
21#123×C109C2211yescharacteristic
22#121×C109—21no—
23#121×C109—21no—
24#121×C109—21no—
25#120×C109—21no—
26#120×C109C2211yescharacteristic
27#13182029—21no—
28#13182028—41no—
29C2×C22⋊D109—21no—
30C2×C22⋊D109—21no—
31C2×C22⋊D109—41no—
32D4×D109—41no—
33#13182017—41no—
34#13182014—41no—
35#13182013—21no—
36#13182008—41no—
37C22⋊Dic109—21no—
38C22⋊Dic109—21no—
39C22⋊Dic109—41no—
40#13182006—41no—
41C24×C109D411yescharacteristic
42C2×D4×C109—21no—
43C2×D4×C109—21no—
44C2×D4×C109—21no—
45C2×D4×C109—21no—
46C2×D4×C109—21no—
47C2×D4×C109D411yescharacteristic, complemented
48C2×D4×C109C2311yescharacteristic
49C22×C4×C109—21no—
50C22×C4×C109D411yescharacteristic, complemented
51C4⋊C4×C109—21no—
52C4⋊C4×C109—21no—
53C4⋊C4×C109—21no—
54C22⋊C4×C109—21no—
55C22⋊C4×C109—21no—
56C22⋊C4×C109—21no—
57C22⋊C4×C109—21no—
58C22⋊C4×C109—21no—
59C22⋊C4×C109D411yescharacteristic
60C22⋊C4×C109D411yescharacteristic, complemented
61C42×C109D411yescharacteristic, complemented
62C23×C109—21no—
63C23×C109—21no—
64C23×C109—41no—
65C23×C109—81no—
66C23×C109C2×D411yescharacteristic
67C23×C109C2×D411yescharacteristic
68C22×D109—21no—
69C22×D109—21no—
70D4×C109—41no—
71D4×C109—41no—
72D4×C109—81no—
73D4×C109—81no—
74D4×C109—81no—
75D4×C109—81no—
76D4×C109—81no—
77C2×C4×C109—21no—
78C2×C4×C109—21no—
79C2×C4×C109—21no—
80C2×C4×C109—21no—
81C2×C4×C109—41no—
82C2×C4×C109—81no—
83C2×C4×C109C2×D411yescharacteristic
84C22⋊D109—41no—
85C22⋊D109—41no—
86C22⋊D109—41no—
87C22⋊D109—82no—
88C2×Dic109—21no—
89C2×Dic109—21no—
90C2×Dic109—41no—
91C2×Dic109—41no—
92D436—21no—
93C4×D109—41no—
94Dic218—21no—
95#11724784—41no—
96C22×C109—21no—
97C22×C109—21no—
98C22×C109—41no—
99C22×C109—41no—
100C22×C109—41no—
101C22×C109—41no—
102C22×C109—41no—
103C22×C109—41no—
104C22×C109—42no—
105C22×C109—41no—
106C22×C109—41no—
107C22×C109—81no—
108C22×C109#12011yescharacteristic
109C2×D109—41no—
110C2×D109—81no—
111C2×D109—81no—
112C4×C109—21no—
113C4×C109—41no—
114C4×C109—41no—
115C4×C109—41no—
116C4×C109—41no—
117Dic109—41no—
118Dic109—81no—
119Dic109—81no—
120C2×C109—21no—
121C2×C109—41no—
122C2×C109—41no—
123C2×C109—81no—
124C2×C109—81no—
125C2×C109B(4,𝔽2)11yescharacteristic
126D109—81no—
127#2200—1091nomaximal, Sylow
128C109#220011yescharacteristic, complemented, Sylow
129#560D10911yescharacteristic, complemented
130#458—1091no—
131B(4,𝔽2)—1091no—
132#453—1091no—
133#353—1091no—
134#352—1091no—
135AΣL(1,𝔽16)—1091no—
136H(5,𝔽2)—1091no—
137AGL(1,ℤ/8)—2181no—
138#127C2×D10911yescharacteristic
139#126—21no—
140#123—21no—
141#123—2181no—
142#123C2×D10911yescharacteristic
143#121—21no—
144#121—21no—
145#121—21no—
146#120—21no—
147#120—2181no—
148#120C2×D10911yescharacteristic
149#104—2181no—
150#100—1091no—
151#99—1091no—
152#99—1091no—
153#99—2181no—
154#99—2181no—
155C24C22⋊D10911yescharacteristic
156#41—4361no—
157#41—2181no—
158C2×D4—21no—
159C2×D4—21no—
160C2×D4—21no—
161C2×D4—21no—
162C2×D4—21no—
163C2×D4—4361no—
164C2×D4—4361no—
165C2×D4—2181no—
166C2×D4—2181no—
167C2×D4C22⋊D10911yescharacteristic, complemented
168C2×D4C22×D10911yescharacteristic
169C22×C4—21no—
170C22×C4C22⋊D10911yescharacteristic, complemented
171SD16—4361no—
172D8—4361no—
173M16—2181no—
174C4⋊C4—21no—
175C4⋊C4—21no—
176C4⋊C4—21no—
177C4⋊C4—4361no—
178C22⋊C4—21no—
179C22⋊C4—21no—
180C22⋊C4—21no—
181C22⋊C4—21no—
182C22⋊C4—21no—
183C22⋊C4—4361no—
184C22⋊C4—4361no—
185C22⋊C4—2181no—
186C22⋊C4—2181no—
187C22⋊C4C22⋊D10911yescharacteristic
188C22⋊C4C22⋊D10911yescharacteristic, complemented
189C42C22⋊D10911yescharacteristic, complemented
190C23—21no—
191C23—21no—
192C23—41no—
193C23—81no—
194C23—2181no—
195C23—2181no—
196C23C2×C22⋊D10911yescharacteristic
197C23C2×C22⋊D10911yescharacteristic
198Q8—2181no—
199D4—41no—
200D4—41no—
201D4—81no—
202D4—81no—
203D4—81no—
204D4—81no—
205D4—81no—
206D4—8722no—
207D4—4361no—
208D4—4361no—
209D4—4361no—
210D4—2181no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—41no—
216C2×C4—81no—
217C2×C4—4361no—
218C2×C4—4361no—
219C2×C4—4361no—
220C2×C4—2181no—
221C2×C4—2181no—
222C2×C4C2×C22⋊D10911yescharacteristic
223C8—4361no—
224C22—21no—
225C22—21no—
226C22—41no—
227C22—41no—
228C22—41no—
229C22—41no—
230C22—41no—
231C22—41no—
232C22—42no—
233C22—41no—
234C22—41no—
235C22—81no—
236C22—8721no—
237C22—8721no—
238C22—4361no—
239C22#1681266811yescharacteristic
240C4—21no—
241C4—41no—
242C4—41no—
243C4—41no—
244C4—41no—
245C4—8721no—
246C4—8721no—
247C4—4361no—
248C2—21no—
249C2—41no—
250C2—41no—
251C2—81no—
252C2—81no—
253C2—8721no—
254C2#2029521311yescharacteristic
subgroupG/H
centerC2#20295213
commutator, cosocleC2×D4×C109C23
FrattiniC2×D4C22×D109
Fitting#560×C109C2
socleC2×C109B(4,𝔽2)
hypercenter#560D109
hypocenterC109#2200
LCSG ▷ C2×D4×C109 ▷ C22×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #560

Complements

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

NH ≅ G/Ntype
1. #20295215C2semidirect
2. #20295212C2semidirect
3. #20295193C2semidirect
4. #20294819C2semidirect
5. #20294816C2semidirect
6. #20294813C2semidirect
7. #560×C109C2semidirect
47. C2×D4×C109D4semidirect
50. C22×C4×C109D4semidirect
60. C22⋊C4×C109D4semidirect
61. C42×C109D4semidirect
128. C109#2200semidirect
129. #560D109semidirect
167. C2×D4C22⋊D109semidirect
170. C22×C4C22⋊D109semidirect
188. C22⋊C4C22⋊D109semidirect
189. C42C22⋊D109semidirect

Maximal subgroups

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

subgroupindex
#202952152
#202952122
#202951932
#202948192
#202948162
#202948132
#560×C1092
#2200109