Finite Group Databasebeta

← #28371325

Subgroups — #28371325

Order 13952.

1102 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 1102 conjugacy classes of subgroups — too many to draw. Only its 181 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
1C23×C4×D109C211yesmaximal, characteristic, complemented
2C2×#16812683C211yesmaximal, characteristic, complemented
3C2×#16812682C211yesmaximal, characteristic, complemented
4C2×#16812669C211yesmaximal, characteristic
5#20294904C214yesmaximal, complemented
6#20294900C214yesmaximal, complemented
7#20294887C211yesmaximal, characteristic, complemented
8#20294881C211yesmaximal, characteristic, complemented
9#381×C109C211yesmaximal, characteristic, complemented
10C24×D109C2211yescharacteristic
11C22×D436C2212yes—
12C22×C22⋊D109C2211yescharacteristic
13C23×Dic109C2211yescharacteristic
14C22×C4×D109—24no—
15C22×C4×D109—24no—
16C22×C4×D109—24no—
17C22×C4×D109C2214yes—
18#16812683—24no—
19#16812682—24no—
20#16812669—24no—
21C2×C4⋊Dic109C2212yescomplemented
22C2×#13182008C2212yescomplemented
23C2×C22⋊Dic109C2211yescharacteristic
24C2×#13182006C2212yes—
25C2×#13182006C2214yes—
26C2×#13182006C2212yescomplemented
27C2×#13182006C2212yescomplemented
28#16812606C2214yescomplemented
29C23×C4×C109C2211yescharacteristic
30C2×C22⋊C4×C109C2211yescharacteristic
31C2×C22⋊C4×C109C2211yescharacteristic
32#95×C109C2214yescomplemented
33C23×D109—22no—
34C23×D109—22no—
35C23×D109—28no—
36C23×D109D414yes—
37C23×D109C2311yescharacteristic
38C23×D109C2312yes—
39C2×D436—24no—
40C2×D436—28no—
41C2×C22⋊D109—22no—
42C2×C22⋊D109—22no—
43C2×C22⋊D109—22no—
44C22×Dic109—22no—
45C22×Dic109—22no—
46C22×Dic109D414yescomplemented
47C22×Dic109C2312yes—
48C22×Dic109C2311yescharacteristic
49C22×Dic109C2312yes—
50C2×C4×D109—232no—
51C2×C4×D109—28no—
52C2×C4×D109—28no—
53C2×C4×D109—28no—
54C4⋊Dic109—24no—
55#13182008—24no—
56C22⋊Dic109—22no—
57#13182006—24no—
58#13182006—28no—
59#13182006—24no—
60#13182006—24no—
61C24×C109C2311yescharacteristic
62C22×C4×C109—22no—
63C22×C4×C109—22no—
64C22×C4×C109D414yescomplemented
65C22×C4×C109C2312yes—
66C22×C4×C109C2312yes—
67C22×C4×C109C2312yes—
68C22⋊C4×C109—22no—
69C22⋊C4×C109—22no—
70C23×C109—24no—
71C23×C109C2×D412yes—
72C23×C109C2×D412yes—
73C23×C109C2×D412yes—
74C23×C109C2411yescharacteristic
75C22×D109—216no—
76C22×D109—216no—
77C22×D109—28no—
78C22×D109—22no—
79C22×D109—22no—
80C22×D109—24no—
81C22×D109—216no—
82C22×D109—21no—
83C22×D109—21no—
84C22×D109—21no—
85C22×D109—24no—
86C22×D109C2×D414yes—
87C22×D109#4118yes—
88C2×C4×C109—28no—
89C2×C4×C109—22no—
90C2×C4×C109—22no—
91C2×C4×C109—22no—
92C2×C4×C109—22no—
93C2×C4×C109—24no—
94C2×C4×C109—24no—
95C2×C4×C109C2×D414yes—
96C22⋊D109—44no—
97C2×Dic109—28no—
98C2×Dic109—22no—
99C2×Dic109—22no—
100C2×Dic109—21no—
101C2×Dic109—22no—
102C2×Dic109—21no—
103C2×Dic109—21no—
104C2×Dic109—24no—
105C2×Dic109C2×D414yes—
106D436—48no—
107C4×D109—232no—
108C22×C109—24no—
109C22×C109—24no—
110C22×C109—24no—
111C22×C109#12014yes—
112C22×C109C22×D411yescharacteristic
113C22×C109C22×D411yescharacteristic
114C22×C109C22×D411yescharacteristic
115C22×C109C2×#4114yes—
116C2×D109—232no—
117C2×D109—24no—
118C2×D109—24no—
119C2×D109—28no—
120C2×D109—28no—
121C2×D109—41no—
122C2×D109—42no—
123C2×D109—42no—
124C2×D109—42no—
125C2×D109#12318yescomplemented
126C4×C109—24no—
127C4×C109—42no—
128C4×C109—42no—
129Dic109—24no—
130Dic109—41no—
131Dic109—42no—
132C2×C109—24no—
133C2×C109C2×#12011yescharacteristic
134C2×C109C2×#12312yes—
135C2×C109#52512yes—
136C2×C109#52512yes—
137D109—28no—
138D109—81no—
139#2849—1091nomaximal, Sylow
140C109#284911yescharacteristic, complemented, Sylow
141C24×C4—1091no—
142C2×#123—1091no—
143C2×#123—1091no—
144C2×#120—1091no—
145#386—1094no—
146#385—1094no—
147#381—1091no—
148#381D10911yescharacteristic, complemented
149#379—1091no—
150C25—1091no—
151C22×D4—1091no—
152C22×D4—1092no—
153C23×C4—1091no—
154C23×C4—1094no—
155C23×C4—2184no—
156C23×C4—2184no—
157C23×C4—2184no—
158C23×C4C2×D10911yescharacteristic
159#123—2184no—
160#123—2184no—
161#120—2184no—
162C2×C4⋊C4—1092no—
163C2×C4⋊C4—1092no—
164C2×C22⋊C4—1091no—
165C2×C22⋊C4—1092no—
166C2×C22⋊C4—1092no—
167C2×C22⋊C4—1092no—
168C2×C22⋊C4—1094no—
169C2×C22⋊C4C2×D10911yescharacteristic
170C2×C22⋊C4C2×D10911yescharacteristic
171#95—1094no—
172#95C2×D10914yescomplemented
173C24—1092no—
174C24—1094no—
175C24—1091no—
176C24—2188no—
177C24—2182no—
178C24—2182no—
179C24C22×D10911yescharacteristic
180C2×D4—2184no—
181C2×D4—2188no—
182C2×D4—2182no—
183C2×D4—2182no—
184C2×D4—2182no—
185C22×C4—22no—
186C22×C4—22no—
187C22×C4—1094no—
188C22×C4—1092no—
189C22×C4—1092no—
190C22×C4—1091no—
191C22×C4—2188no—
192C22×C4—2188no—
193C22×C4—21832no—
194C22×C4—2182no—
195C22×C4—2182no—
196C22×C4—2188no—
197C22×C4D43614yescomplemented
198C22×C4C22×D10912yes—
199C22×C4C22×D10912yes—
200C22×C4C22×D10912yes—
201C4⋊C4—2184no—
202C4⋊C4—2184no—
203C22⋊C4—22no—
204C22⋊C4—22no—
205C22⋊C4—2184no—
206C22⋊C4—2188no—
207C22⋊C4—2184no—
208C22⋊C4—2182no—
209C22⋊C4—2184no—
210C23—24no—
211C23—1094no—
212C23—1098no—
213C23—21816no—
214C23—21816no—
215C23—21816no—
216C23—2181no—
217C23—2181no—
218C23—2181no—
219C23—2184no—
220C23—2188no—
221C23—2182no—
222C23—2182no—
223C23—2184no—
224C23D4×D10912yes—
225C23D4×D10912yes—
226C23C2×D43612yes—
227C23C23×D10911yescharacteristic
228D4—4368no—
229D4—4364no—
230C2×C4—28no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—22no—
235C2×C4—24no—
236C2×C4—24no—
237C2×C4—1094no—
238C2×C4—21832no—
239C2×C4—2181no—
240C2×C4—2181no—
241C2×C4—2182no—
242C2×C4—2181no—
243C2×C4—2184no—
244C2×C4—2188no—
245C2×C4—2182no—
246C2×C4—2182no—
247C2×C4C2×D43614yes—
248C22—24no—
249C22—24no—
250C22—24no—
251C22—1098no—
252C22—4361no—
253C22—4362no—
254C22—4362no—
255C22—4362no—
256C22—21832no—
257C22—2184no—
258C22—2184no—
259C22—2188no—
260C22—2188no—
261C22#1681266914yes—
262C22C2×D4×D10911yescharacteristic
263C22C2×D4×D10911yescharacteristic
264C22C22×D43611yescharacteristic
265C22#41×D10914yes—
266C4—24no—
267C4—42no—
268C4—42no—
269C4—4361no—
270C4—4362no—
271C4—2184no—
272C2—24no—
273C2—8721no—
274C2—2188no—
275C2C2×#1681266911yescharacteristic
276C2#123×D10912yes—
277C2#2029553412yes—
278C2#2029553812yes—
subgroupG/H
center, FrattiniC23C23×D109
commutator, socle, cosocleC23×C109C24
Fitting#381×C109C2
prime radicalC2×#16812669C2
hypercenter#381D109
hypocenterC109#2849
LCSG ▷ C23×C109 ▷ C109
UCSC1 ◁ C23 ◁ #381

Complements

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

NH ≅ G/Ntype
1. C23×C4×D109C2semidirect
2. C2×#16812683C2semidirect
3. C2×#16812682C2semidirect
5. #20294904C2semidirect
6. #20294900C2semidirect
7. #20294887C2semidirect
8. #20294881C2semidirect
9. #381×C109C2semidirect
21. C2×C4⋊Dic109C22semidirect
22. C2×#13182008C22semidirect
26. C2×#13182006C22semidirect
27. C2×#13182006C22semidirect
28. #16812606C22semidirect
32. #95×C109C22semidirect
46. C22×Dic109D4semidirect
64. C22×C4×C109D4semidirect
125. C2×D109#123semidirect
140. C109#2849semidirect
148. #381D109semidirect
172. #95C2×D109semidirect
197. C22×C4D436semidirect

Maximal subgroups

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

subgroupindex
C23×C4×D1092
C2×#168126832
C2×#168126822
C2×#168126692
#202949042
#202949002
#202948872
#202948812
#381×C1092
#2849109