Finite Group Databasebeta

← #28374820

Subgroups — #28374820

Order 13952.

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

normal subgroups only

This group has 454 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#20295840C211yesmaximal, characteristic, complemented
2#20295838C212yesmaximal, complemented
3#20295828C211yesmaximal, characteristic, complemented
4#20295410C211yesmaximal, characteristic, complemented
5#20295302C211yesmaximal, characteristic, complemented
6#20295297C211yesmaximal, characteristic, complemented
7#20295289C212yesmaximal, complemented
8#20295205C212yesmaximal, complemented
9#20295200C212yesmaximal, complemented
10#20295144C211yesmaximal, characteristic, complemented
11#443×C109C211yesmaximal, characteristic, complemented
12#16812746C2212yescomplemented
13#16812745C2212yes—
14#16812732—22no—
15#16812732C2212yes—
16#16812729C2212yescomplemented
17#16812728—22no—
18#16812727—22no—
19#16812727C2212yescomplemented
20#16812726—22no—
21#16812724C2212yes—
22#16812722—21no—
23#16812721—22no—
24#16812721C2211yescharacteristic
25#16812718—21no—
26C2×Dic436C2211yescharacteristic, complemented
27Q16×D109—21no—
28C2×#13182018—22no—
29C2×#13182018C2212yescomplemented
30C2×D872C2211yescharacteristic
31D8×D109—21no—
32#16812705C2211yescharacteristic
33#16812705C2211yescharacteristic, complemented
34#16812687C2212yescomplemented
35#16812635C2211yescharacteristic, complemented
36#16812627C2211yescharacteristic
37#16812627C2211yescharacteristic, complemented
38#16812617C2212yescomplemented
39#16812615C2212yescomplemented
40#135×C109C2211yescharacteristic
41#131×C109C2212yescomplemented
42#108×C109C2211yescharacteristic, complemented
43#104×C109C2212yescomplemented
44C4×C8×C109C2211yescharacteristic, complemented
45#13182030—22no—
46#13182029—22no—
47#13182029—22no—
48#13182029C2311yescharacteristic
49#13182029C2311yescharacteristic
50#13182028—22no—
51#13182028—42no—
52C2×Dic218—22no—
53C2×Dic218C2312yes—
54Q8×D109—22no—
55C2×D436—22no—
56C2×D436C2312yes—
57D4×D109—22no—
58D4×D109—42no—
59Dic436—22no—
60Dic436—21no—
61Dic436—21no—
62Dic436D411yescharacteristic
63#13182019—22no—
64#13182018—22no—
65#13182018—22no—
66#13182018—22no—
67#13182018—22no—
68#13182018D411yescharacteristic
69#13182018D411yescharacteristic
70#13182017—22no—
71#13182016—22no—
72D872—22no—
73D872—21no—
74D872—21no—
75D872D411yescharacteristic
76#13182014—22no—
77#13182013C2311yescharacteristic
78#13182013C2311yescharacteristic
79#13182012—21no—
80#13182012—21no—
81C8×D109—21no—
82C8×D109—21no—
83#13182006—42no—
84#41×C109C2312yes—
85Q16×C109D411yescharacteristic
86SD16×C109D412yes—
87D8×C109D411yescharacteristic
88M16×C109—22no—
89M16×C109C2312yes—
90C2×C8×C109—22no—
91C2×C8×C109C2311yescharacteristic
92C2×C8×C109C2311yescharacteristic
93C42×C109C2311yescharacteristic
94C22×D109—22no—
95C22×D109—42no—
96Q8×C109C2×D412yes—
97D4×C109—22no—
98D4×C109C2×D412yes—
99C2×C4×C109—22no—
100C2×C4×C109—21no—
101C2×C4×C109C2411yescharacteristic
102C22⋊D109—21no—
103C22⋊D109—21no—
104C22⋊D109—42no—
105C22⋊D109—42no—
106C2×Dic109—22no—
107C2×Dic109—42no—
108D436—22no—
109D436—22no—
110D436—42no—
111D436C2×D411yescharacteristic
112D436C2×D411yescharacteristic
113C4×D109—21no—
114C4×D109—21no—
115C4×D109—42no—
116C4×D109—42no—
117Dic218—22no—
118Dic218—22no—
119Dic218—42no—
120Dic218C2×D411yescharacteristic
121Dic218C2×D411yescharacteristic
122C8×C109—22no—
123C8×C109C2×D411yescharacteristic
124C8×C109C2×D411yescharacteristic
125C8×C109C2×D411yescharacteristic
126C8×C109C2×D411yescharacteristic
127#11724784—21no—
128#11724784—21no—
129C22×C109—22no—
130C22×C109H(5,𝔽2)11yescharacteristic
131C2×D109—21no—
132C2×D109—21no—
133C2×D109—42no—
134C2×D109—82no—
135C2×D109—162no—
136C4×C109—22no—
137C4×C109—41no—
138C4×C109C22×D411yescharacteristic
139C4×C109C22×D411yescharacteristic
140Dic109—21no—
141Dic109—21no—
142Dic109—42no—
143C2×C109—21no—
144C2×C109—42no—
145C2×C109D4211yescharacteristic
146D109—41no—
147D109—41no—
148D109—82no—
149#3290—1091nomaximal, Sylow
150C109#329011yescharacteristic, complemented, Sylow
151#578—1091no—
152#577—1092no—
153#576—1091no—
154#495—1091no—
155#473—1091no—
156#472—1091no—
157#471—1092no—
158#455—1092no—
159#454—1092no—
160#443—1091no—
161#443D10911yescharacteristic, complemented
1622−1+4—1092no—
163H(5,𝔽2)—1092no—
164#137—1092no—
165#137—1092no—
166#137—2182no—
167#137—2182no—
168AGL(1,ℤ/8)—1092no—
169AGL(1,ℤ/8)—1092no—
170AGL(1,ℤ/8)—2182no—
171AGL(1,ℤ/8)—2182no—
172#135—1091no—
173#135—2182no—
174#135—2181no—
175#135—2181no—
176#135C2×D10911yescharacteristic
177C2×Q16—1091no—
178C2×Q16—2181no—
179C2×SD16—1092no—
180C2×SD16—2182no—
181C2×D8—1091no—
182C2×D8—2181no—
183#131—1091no—
184#131—1091no—
185#131C2×D10912yescomplemented
186#124—1092no—
187#108—1091no—
188#108C2×D10911yescharacteristic, complemented
189#104—1091no—
190#104—1091no—
191#104C2×D10912yescomplemented
192#101—1092no—
193#100—1092no—
194C4×C8C2×D10911yescharacteristic, complemented
195#41—1091no—
196#41—1091no—
197#41—4362no—
198#41—2182no—
199#41—2182no—
200#41—2182no—
201#41—2182no—
202#41C22×D10912yes—
203C2×Q8—1092no—
204C2×Q8—2182no—
205C2×Q8—2182no—
206C2×D4—1092no—
207C2×D4—4362no—
208C2×D4—2182no—
209C2×D4—2182no—
210Q16—1091no—
211Q16—2182no—
212Q16—2182no—
213Q16—2181no—
214Q16—2181no—
215Q16D43611yescharacteristic
216SD16—1091no—
217SD16—1091no—
218SD16—2182no—
219SD16—2182no—
220SD16—2182no—
221SD16—2182no—
222SD16—2182no—
223SD16—2182no—
224SD16D43612yes—
225D8—1091no—
226D8—2182no—
227D8—2182no—
228D8—2181no—
229D8—2181no—
230D8D43611yescharacteristic
231M16—22no—
232M16—1091no—
233M16—1091no—
234M16—2181no—
235M16—2181no—
236M16C22×D10912yes—
237C2×C8—22no—
238C2×C8—2181no—
239C2×C8—2181no—
240C2×C8C22×D10911yescharacteristic
241C2×C8C22×D10911yescharacteristic
242C22⋊C4—4362no—
243C42C22×D10911yescharacteristic
244C23—4362no—
245C23—2182no—
246Q8—1091no—
247Q8—1091no—
248Q8—4362no—
249Q8—2182no—
250Q8—2182no—
251Q8C2×D43612yes—
252D4—22no—
253D4—1091no—
254D4—1091no—
255D4—4362no—
256D4—4362no—
257D4—4362no—
258D4—2181no—
259D4—2181no—
260D4—2182no—
261D4—2182no—
262D4C2×D43612yes—
263C2×C4—22no—
264C2×C4—21no—
265C2×C4—4362no—
266C2×C4—4362no—
267C2×C4—4362no—
268C2×C4—2182no—
269C2×C4—2181no—
270C2×C4—2181no—
271C2×C4C23×D10911yescharacteristic
272C8—22no—
273C8—2181no—
274C8—2181no—
275C8D4×D10911yescharacteristic
276C8D4×D10911yescharacteristic
277C8C2×D43611yescharacteristic
278C8C2×D43611yescharacteristic
279C22—22no—
280C22—8722no—
281C22—4362no—
282C22—17442no—
283C22—2181no—
284C22—2181no—
285C22#1681274511yescharacteristic
286C4—22no—
287C4—41no—
288C4—4362no—
289C4—2181no—
290C4—2181no—
291C4C2×D4×D10911yescharacteristic
292C4C22×D43611yescharacteristic
293C2—21no—
294C2—42no—
295C2—8722no—
296C2—4361no—
297C2—4361no—
298C2D4×D43611yescharacteristic
subgroupG/H
centerC2D4×D436
commutator, cosocleC2×C4×C109C24
FrattiniC2×C4C23×D109
Fitting#443×C109C2
socleC2×C109D42
hypercenter#443D109
hypocenterC109#3290
LCSG ▷ C2×C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C2 ◁ C2×C4 ◁ #443

Complements

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

NH ≅ G/Ntype
1. #20295840C2semidirect
2. #20295838C2semidirect
3. #20295828C2semidirect
4. #20295410C2semidirect
5. #20295302C2semidirect
6. #20295297C2semidirect
7. #20295289C2semidirect
8. #20295205C2semidirect
9. #20295200C2semidirect
10. #20295144C2semidirect
11. #443×C109C2semidirect
12. #16812746C22semidirect
16. #16812729C22semidirect
19. #16812727C22semidirect
26. C2×Dic436C22semidirect
29. C2×#13182018C22semidirect
33. #16812705C22semidirect
34. #16812687C22semidirect
35. #16812635C22semidirect
37. #16812627C22semidirect
38. #16812617C22semidirect
39. #16812615C22semidirect
41. #131×C109C22semidirect
42. #108×C109C22semidirect
43. #104×C109C22semidirect
44. C4×C8×C109C22semidirect
150. C109#3290semidirect
161. #443D109semidirect
185. #131C2×D109semidirect
188. #108C2×D109semidirect
191. #104C2×D109semidirect
194. C4×C8C2×D109semidirect

Maximal subgroups

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

subgroupindex
#202958402
#202958382
#202958282
#202954102
#202953022
#202952972
#202952892
#202952052
#202952002
#202951442
#443×C1092
#3290109