Finite Group Databasebeta

← #28366289

Subgroups — #28366289

Order 13952.

560 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 560 conjugacy classes of subgroups — too many to draw. Only its 157 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
1C2×C4×C22⋊D109C211yesmaximal, characteristic
2#20294964C211yesmaximal, characteristic, complemented
3#20294961C211yesmaximal, characteristic, complemented
4#20294957C211yesmaximal, characteristic, complemented
5#20294954C212yesmaximal, complemented
6#20294952C211yesmaximal, characteristic, complemented
7#20294941C212yesmaximal
8C4×#13182008C212yesmaximal, complemented
9C4×#13182006C212yesmaximal, complemented
10C4×C22⋊Dic109C211yesmaximal, characteristic, complemented
11C2×#117×C109C211yesmaximal, characteristic, complemented
12C22×C22⋊D109C2211yescharacteristic
13C22×C4×D109C2211yescharacteristic
14C4×C22⋊D109—24no—
15C2×#13182008C2212yes—
16C2×#13182008C2212yes—
17C2×#13182008C2211yescharacteristic
18C2×C22⋊Dic109C2212yes—
19C2×C22⋊Dic109C2211yescharacteristic
20C2×#13182006C2212yes—
21C2×#13182006C2212yes—
22C2×#13182006C2211yescharacteristic
23C2×C4×Dic109C2211yescharacteristic
24C2×C4×Dic109C2212yes—
25#16812606C2212yes—
26#16812606C2212yes—
27#16812606C2211yescharacteristic
28#16812606C2212yes—
29#16812606C2212yes—
30#16812606C2211yescharacteristic
31C23×C4×C109C2211yescharacteristic
32#117×C109—24no—
33C2×C4⋊C4×C109C2211yescharacteristic
34C2×C4⋊C4×C109C2211yescharacteristic
35C2×C22⋊C4×C109C2212yes—
36C2×C42×C109C2212yes—
37C23×D109C2311yescharacteristic
38C2×C22⋊D109—22no—
39C2×C22⋊D109—22no—
40C2×C22⋊D109—22no—
41C22×Dic109C2312yes—
42C22×Dic109C2311yescharacteristic
43C22×Dic109C2311yescharacteristic
44C22×Dic109C2312yes—
45C22×Dic109C2311yescharacteristic
46C2×C4×D109—22no—
47C2×C4×D109—24no—
48#13182008—22no—
49#13182008—24no—
50#13182008—24no—
51C22⋊Dic109—22no—
52C22⋊Dic109—24no—
53#13182006—24no—
54#13182006—22no—
55#13182006—24no—
56C4×Dic109—22no—
57C4×Dic109—24no—
58C24×C109C2311yescharacteristic
59C22×C4×C109—24no—
60C22×C4×C109D414yes—
61C22×C4×C109C2312yes—
62C22×C4×C109C2312yes—
63C22×C4×C109C2311yescharacteristic
64C22×C4×C109C2311yescharacteristic
65C4⋊C4×C109—22no—
66C4⋊C4×C109—22no—
67C22⋊C4×C109—24no—
68C42×C109—24no—
69C23×C109—22no—
70C23×C109—22no—
71C23×C109—21no—
72C23×C109—21no—
73C23×C109C2×D412yes—
74C23×C109C2411yescharacteristic
75C22×D109—21no—
76C22×D109—22no—
77C22×D109—22no—
78C22×D109—21no—
79C22×D109#4112yes—
80C2×C4×C109—22no—
81C2×C4×C109—28no—
82C2×C4×C109—22no—
83C2×C4×C109—22no—
84C2×C4×C109—22no—
85C2×C4×C109—22no—
86C2×C4×C109—22no—
87C2×C4×C109—22no—
88C2×C4×C109C2×D412yes—
89C2×C4×C109C2×D412yes—
90C2×C4×C109#4114yes—
91C22⋊D109—28no—
92C2×Dic109—21no—
93C2×Dic109—22no—
94C2×Dic109—22no—
95C2×Dic109—21no—
96C2×Dic109—21no—
97C2×Dic109—21no—
98C2×Dic109—22no—
99C2×Dic109—22no—
100C2×Dic109—22no—
101C2×Dic109—22no—
102C2×Dic109—22no—
103C2×Dic109#4114yes—
104C2×Dic109#4112yes—
105C4×D109—44no—
106C22×C109—22no—
107C22×C109—22no—
108C22×C109—22no—
109C22×C109—42no—
110C22×C109—42no—
111C22×C109C22×D411yescharacteristic
112C22×C109C2×#4111yescharacteristic
113C22×C109C2×#4111yescharacteristic
114C22×C109C2×#4112yes—
115C22×C109C2×#4112yes—
116C2×D109—22no—
117C2×D109—24no—
118C2×D109—41no—
119C2×D109—42no—
120C2×D109—41no—
121C4×C109—22no—
122C4×C109—42no—
123C4×C109—42no—
124C4×C109#12314yes—
125Dic109—22no—
126Dic109—24no—
127Dic109—41no—
128Dic109—42no—
129Dic109—41no—
130C2×C109—42no—
131C2×C109C2×#12311yescharacteristic
132C2×C109#52511yescharacteristic
133C2×C109#52912yes—
134C2×C109#52912yes—
135C2×C109#53211yescharacteristic
136D109—42no—
137#2395—1091nomaximal, Sylow
138C109#239511yescharacteristic, complemented, Sylow
139C2×C4×D4—1091no—
140C2×#117D10911yescharacteristic, complemented
141#400—1091no—
142#399—1091no—
143#398—1091no—
144#397—1091no—
145#397—1092no—
146#394—1092no—
147C4×C4⋊C4—1092no—
148C4×C22⋊C4—1091no—
149C4×C22⋊C4—1092no—
150C22×D4—1091no—
151C23×C4—1091no—
152C23×C4C2×D10911yescharacteristic
153C4×D4—2184no—
154#117—24no—
155C2×C4⋊C4—1091no—
156C2×C4⋊C4—1092no—
157C2×C4⋊C4—1092no—
158C2×C4⋊C4C2×D10911yescharacteristic
159C2×C4⋊C4C2×D10911yescharacteristic
160C2×C22⋊C4—1091no—
161C2×C22⋊C4—1092no—
162C2×C22⋊C4—1091no—
163C2×C22⋊C4—1092no—
164C2×C22⋊C4—1092no—
165C2×C22⋊C4C2×D10912yes—
166C2×C42—1091no—
167C2×C42—1092no—
168C2×C42C2×D10912yes—
169#95—1092no—
170#95—1091no—
171#95—1092no—
172#95—1091no—
173#95—1092no—
174#95—1092no—
175C24—1091no—
176C24C22×D10911yescharacteristic
177C2×D4—2182no—
178C2×D4—2182no—
179C2×D4—2182no—
180C22×C4—24no—
181C22×C4—1092no—
182C22×C4—1091no—
183C22×C4—1092no—
184C22×C4—1091no—
185C22×C4—1091no—
186C22×C4—2182no—
187C22×C4—2184no—
188C22×C4C22⋊D10914yes—
189C22×C4C22×D10912yes—
190C22×C4C22×D10912yes—
191C22×C4C22×D10911yescharacteristic
192C22×C4C22×D10911yescharacteristic
193C4⋊C4—22no—
194C4⋊C4—22no—
195C4⋊C4—2184no—
196C4⋊C4—2184no—
197C4⋊C4—2182no—
198C22⋊C4—24no—
199C22⋊C4—2184no—
200C22⋊C4—2184no—
201C22⋊C4—2184no—
202C22⋊C4—2182no—
203C22⋊C4—2182no—
204C42—24no—
205C42—2182no—
206C42—2184no—
207C23—22no—
208C23—21no—
209C23—21no—
210C23—22no—
211C23—1092no—
212C23—2181no—
213C23—2182no—
214C23—2181no—
215C23—2182no—
216C23C2×C22⋊D10912yes—
217C23C23×D10911yescharacteristic
218D4—2188no—
219C2×C4—22no—
220C2×C4—28no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—22no—
227C2×C4—1094no—
228C2×C4—1092no—
229C2×C4—4364no—
230C2×C4—2181no—
231C2×C4—2181no—
232C2×C4—2182no—
233C2×C4—2182no—
234C2×C4—2182no—
235C2×C4—2182no—
236C2×C4—2182no—
237C2×C4—2181no—
238C2×C4—2182no—
239C2×C4—2181no—
240C2×C4—2182no—
241C2×C4C2×C22⋊D10912yes—
242C2×C4C2×C22⋊D10912yes—
243C2×C4#1318202914yes—
244C22—22no—
245C22—22no—
246C22—22no—
247C22—42no—
248C22—42no—
249C22—4361no—
250C22—4362no—
251C22—4361no—
252C22—2182no—
253C22—2184no—
254C22C22×C22⋊D10911yescharacteristic
255C22#41×D10911yescharacteristic
256C22#41×D10911yescharacteristic
257C22#41×D10912yes—
258C22C2×#1318202912yes—
259C4—22no—
260C4—42no—
261C4—42no—
262C4—4361no—
263C4—4362no—
264C4—4361no—
265C4—2182no—
266C4—2184no—
267C4#1681268214yes—
268C2—42no—
269C2—4362no—
270C2C2×#1681268211yescharacteristic
271C2#2029553311yescharacteristic
272C2#2029555412yes—
273C2#2029555412yes—
274C2#2029557211yescharacteristic
subgroupG/H
centerC22×C4C22×D109
commutator, socle, cosocleC23×C109C24
FrattiniC23C23×D109
FittingC2×#117×C109C2
prime radicalC22×C22⋊D109C22
hypercenterC2×#117D109
hypocenterC109#2395
LCSG ▷ C23×C109 ▷ C109
UCSC1 ◁ C22×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
2. #20294964C2semidirect
3. #20294961C2semidirect
4. #20294957C2semidirect
5. #20294954C2semidirect
6. #20294952C2semidirect
8. C4×#13182008C2semidirect
9. C4×#13182006C2semidirect
10. C4×C22⋊Dic109C2semidirect
11. C2×#117×C109C2semidirect
138. C109#2395semidirect
140. C2×#117D109semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C22⋊D1092
#202949642
#202949612
#202949572
#202949542
#202949522
#202949412
C4×#131820082
C4×#131820062
C4×C22⋊Dic1092
C2×#117×C1092
#2395109