Finite Group Databasebeta

← #28373172

Subgroups — #28373172

Order 13952.

450 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 450 conjugacy classes of subgroups — too many to draw. Only its 125 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#20295560C211yesmaximal, characteristic, complemented
2C2×C4×D436C211yesmaximal, characteristic, complemented
3#20295357C211yesmaximal, characteristic, complemented
4#20295340C211yesmaximal, characteristic, complemented
5#20295327C212yesmaximal, complemented
6#20295242C212yesmaximal, complemented
7#20295179C211yesmaximal, characteristic, complemented
8#20295162C211yesmaximal, characteristic
9#20295139C212yesmaximal, complemented
10#20295128C212yesmaximal, complemented
11#432×C109C211yesmaximal, characteristic, complemented
12C22×D436C2211yescharacteristic
13C22×C4×D109—21no—
14C2×#13182018C2212yes—
15C2×D872C2212yes—
16#16812693—21no—
17#16812691C2211yescharacteristic, complemented
18#16812687C2211yescharacteristic, complemented
19#16812682—21no—
20#16812678C2211yescharacteristic
21#16812673C2211yescharacteristic
22C4×Dic218C2211yescharacteristic, complemented
23C4×D436—21no—
24C4×D436—21no—
25C4×D436C2212yes—
26C4×D436C2212yes—
27C4×D436C2211yescharacteristic, complemented
28C4×C22⋊D109—21no—
29#16812656—21no—
30C2×C4⋊Dic109C2211yescharacteristic
31C2×#13182006—21no—
32#16812633C2212yescomplemented
33#16812631C2212yescomplemented
34#16812624C2212yescomplemented
35#16812621C2212yes—
36#16812621C2212yes—
37#16812621C2212yescomplemented
38C2×C42×C109C2211yescharacteristic
39C4⋊C8×C109C2212yescomplemented
40C22⋊C8×C109C2211yescharacteristic
41C22⋊C8×C109C2211yescharacteristic
42#97×C109C2212yescomplemented
43C23×D109—21no—
44C2×Dic218C2311yescharacteristic
45C2×D436—21no—
46C2×D436—24no—
47C2×D436C2311yescharacteristic
48C2×D436C2312yes—
49C2×C22⋊D109—21no—
50C22×Dic109—21no—
51C2×C4×D109—21no—
52C2×C4×D109—22no—
53C2×C4×D109—22no—
54C2×C4×D109—44no—
55#13182018—24no—
56D872—24no—
57C4⋊Dic109—21no—
58C4⋊Dic109C2311yescharacteristic
59C4⋊Dic109C2311yescharacteristic
60C4⋊Dic109C2312yes—
61#13182008—21no—
62#13182008—21no—
63#13182008—21no—
64#13182008—21no—
65C22⋊Dic109—21no—
66#13182006—22no—
67#13182006—22no—
68#13182006—21no—
69#13182006—21no—
70#13182006—21no—
71#13182006—21no—
72C4×Dic109—21no—
73C22×C4×C109D411yescharacteristic
74C22×C4×C109D411yescharacteristic
75C22×C4×C109C2311yescharacteristic
76C2×C8×C109C2312yes—
77C2×C8×C109C2312yes—
78C42×C109D411yescharacteristic
79C42×C109D411yescharacteristic
80C42×C109C2311yescharacteristic
81C42×C109C2311yescharacteristic
82C23×C109C2×D411yescharacteristic
83C22×D109—24no—
84C22×D109—22no—
85C22×D109—21no—
86C22×D109—42no—
87C22×D109—42no—
88C2×C4×C109—22no—
89C2×C4×C109—22no—
90C2×C4×C109—41no—
91C2×C4×C109C2×D411yescharacteristic
92C2×C4×C109C2×D411yescharacteristic
93C2×C4×C109C2×D411yescharacteristic
94C2×C4×C109C2×D411yescharacteristic
95C2×C4×C109C2×D411yescharacteristic
96C2×C4×C109C2411yescharacteristic
97C22⋊D109—42no—
98C2×Dic109—21no—
99C2×Dic109—21no—
100C2×Dic109—22no—
101C2×Dic109—21no—
102C2×Dic109—42no—
103D436—24no—
104D436—22no—
105D436—22no—
106D436#4114yes—
107C4×D109—42no—
108C4×D109—44no—
109C4×D109—44no—
110Dic218—22no—
111C8×C109—22no—
112C8×C109—22no—
113C22×C109—21no—
114C22×C109—21no—
115C22×C109AGL(1,ℤ/8)12yes—
116C22×C109C22×D411yescharacteristic
117C2×D109—24no—
118C2×D109—48no—
119C2×D109—42no—
120C2×D109—42no—
121C2×D109—41no—
122C2×D109—41no—
123C2×D109—41no—
124C4×C109—21no—
125C4×C109—21no—
126C4×C109—21no—
127C4×C109—21no—
128C4×C109—21no—
129C4×C109C2×#4112yes—
130Dic109—41no—
131Dic109—42no—
132Dic109—41no—
133Dic109—41no—
134C2×C109—22no—
135C2×C109#52511yescharacteristic
136C2×C109C2×AGL(1,ℤ/8)11yescharacteristic
137C2×C109#57511yescharacteristic
138D109—44no—
139D109—81no—
140#3114—1091nomaximal, Sylow
141C109#311411yescharacteristic, complemented, Sylow
142#529—1091no—
143C2×C4×D4—1091no—
144#483—1091no—
145#480—1091no—
146#478—1092no—
147#463—1092no—
148#450—1091no—
149#447—1091no—
150#442—1092no—
151#440—1092no—
152#432D10911yescharacteristic, complemented
153C22×D4—1091no—
154C23×C4—2181no—
155C2×SD16—1092no—
156C2×D8—1092no—
157#126—2181no—
158#125—1091no—
159#124—1091no—
160#123—2181no—
161C22⋊Q8—1091no—
162#121—1091no—
163C4×Q8—1091no—
164C4×D4—1092no—
165C4×D4—1092no—
166C4×D4—1091no—
167C4×D4—2181no—
168C4×D4—2181no—
169C4×D4—2181no—
170#117—2181no—
171C2×C4⋊C4—1091no—
172C2×C22⋊C4—2181no—
173C2×C42C2×D10911yescharacteristic
174#107—1092no—
175#106—1092no—
176C4⋊C8C2×D10912yescomplemented
177#103—1092no—
178#102—1092no—
179#102—1092no—
180#102—1092no—
181C22⋊C8C2×D10911yescharacteristic
182C22⋊C8C2×D10911yescharacteristic
183#97C2×D10912yescomplemented
184C24—2181no—
185C2×Q8—1091no—
186C2×D4—1092no—
187C2×D4—1091no—
188C2×D4—2184no—
189C2×D4—2181no—
190C2×D4—2181no—
191C22×C4—4364no—
192C22×C4—2181no—
193C22×C4—2181no—
194C22×C4—2182no—
195C22×C4—2182no—
196C22×C4D43611yescharacteristic
197C22×C4D43611yescharacteristic
198C22×C4C22×D10911yescharacteristic
199SD16—2184no—
200D8—2184no—
201C2×C8C22×D10912yes—
202C2×C8C22×D10912yes—
203C4⋊C4—1091no—
204C4⋊C4—1091no—
205C4⋊C4—1092no—
206C4⋊C4—2181no—
207C4⋊C4—2181no—
208C4⋊C4—2181no—
209C4⋊C4—2181no—
210C4⋊C4—2181no—
211C22⋊C4—2181no—
212C22⋊C4—2182no—
213C22⋊C4—2182no—
214C22⋊C4—2181no—
215C22⋊C4—2181no—
216C22⋊C4—2181no—
217C22⋊C4—2181no—
218C42—2181no—
219C42D43611yescharacteristic
220C42D43611yescharacteristic
221C42C22×D10911yescharacteristic
222C42C22×D10911yescharacteristic
223C23—4362no—
224C23—4362no—
225C23—2184no—
226C23—2181no—
227C23—2182no—
228C23C2×D43611yescharacteristic
229Q8—2182no—
230D4—1094no—
231D4—4362no—
232D4—2184no—
233D4—2182no—
234D4—2182no—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—41no—
238C2×C4—4364no—
239C2×C4—4364no—
240C2×C4—4362no—
241C2×C4—4362no—
242C2×C4—2181no—
243C2×C4—2181no—
244C2×C4—2181no—
245C2×C4—2182no—
246C2×C4C2×D43611yescharacteristic
247C2×C4C2×D43611yescharacteristic
248C2×C4C2×D43611yescharacteristic
249C2×C4C2×D43611yescharacteristic
250C2×C4C2×D43611yescharacteristic
251C2×C4C23×D10911yescharacteristic
252C8—22no—
253C8—22no—
254C22—21no—
255C22—21no—
256C22—4368no—
257C22—4361no—
258C22—4361no—
259C22—4361no—
260C22—4362no—
261C22—4362no—
262C22—2184no—
263C22#1681272712yes—
264C22C22×D43611yescharacteristic
265C4—21no—
266C4—21no—
267C4—21no—
268C4—21no—
269C4—21no—
270C4—4361no—
271C4—4362no—
272C4—4361no—
273C4—4361no—
274C4#41×D10912yes—
275C2—22no—
276C2—8721no—
277C2—4364no—
278C2#2029553811yescharacteristic
279C2C2×#1681272711yescharacteristic
280C2#2029582611yescharacteristic
subgroupG/H
centerC22C22×D436
commutator, cosocleC2×C4×C109C24
FrattiniC2×C4C23×D109
Fitting#432×C109C2
socleC22×C109C22×D4
prime radical#20295162C2
hypercenter#432D109
hypocenterC109#3114
LCSG ▷ C2×C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
1. #20295560C2semidirect
2. C2×C4×D436C2semidirect
3. #20295357C2semidirect
4. #20295340C2semidirect
5. #20295327C2semidirect
6. #20295242C2semidirect
7. #20295179C2semidirect
9. #20295139C2semidirect
10. #20295128C2semidirect
11. #432×C109C2semidirect
17. #16812691C22semidirect
18. #16812687C22semidirect
22. C4×Dic218C22semidirect
27. C4×D436C22semidirect
32. #16812633C22semidirect
33. #16812631C22semidirect
34. #16812624C22semidirect
37. #16812621C22semidirect
39. C4⋊C8×C109C22semidirect
42. #97×C109C22semidirect
141. C109#3114semidirect
152. #432D109semidirect
176. C4⋊C8C2×D109semidirect
183. #97C2×D109semidirect

Maximal subgroups

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

subgroupindex
#202955602
C2×C4×D4362
#202953572
#202953402
#202953272
#202952422
#202951792
#202951622
#202951392
#202951282
#432×C1092
#3114109