Finite Group Databasebeta

← SD16×D596 #34056388

Subgroups — SD16×D596 #34056388

Order 19072.

546 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 546 conjugacy classes of subgroups — too many to draw. Only its 141 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×SD16×D149C212yesmaximal, complemented
2Q8×D596C211yesmaximal, characteristic, complemented
3D4×D596C211yesmaximal, characteristic
4#23749998C211yesmaximal, characteristic, complemented
5#23749855C212yesmaximal, complemented
6#23749830C211yesmaximal, characteristic, complemented
7#23749825C211yesmaximal, characteristic, complemented
8#23749777C212yesmaximal, complemented
9#23749765C212yesmaximal, complemented
10C8×D596C211yesmaximal, characteristic, complemented
11C4×SD16×C149C211yesmaximal, characteristic, complemented
12C2×Q8×D149C2212yescomplemented
13C22×D596—21no—
14C2×D4×D149C2212yes—
15C2×#14558725C2212yescomplemented
16C2×#14558725C2212yescomplemented
17C2×#14558724C2212yes—
18C2×#14558723C2212yescomplemented
19SD16×D149—28no—
20C2×C8×D149C2212yescomplemented
21#18011911—21no—
22#18011911C2211yescharacteristic, complemented
23#18011908C2211yescharacteristic
24#18011891—22no—
25#18011891C2212yescomplemented
26#18011886C2212yes—
27#18011885—21no—
28#18011881—22no—
29C4×D596—21no—
30C4×D596C2211yescharacteristic
31C4⋊#11924746C2211yescharacteristic, complemented
32#18011834C2212yescomplemented
33#18011831C2212yescomplemented
34#18011823C2212yescomplemented
35C2×SD16×C149C2211yescharacteristic
36C4×Q8×C149C2211yescharacteristic, complemented
37C4×D4×C149C2211yescharacteristic
38#106×C149C2211yescharacteristic, complemented
39#103×C149C2211yescharacteristic, complemented
40#102×C149C2211yescharacteristic
41C4×C8×C149C2211yescharacteristic, complemented
42C23×D149—22no—
43C2×Dic298—22no—
44C2×Dic298C2312yes—
45Q8×D149—24no—
46Q8×D149—42no—
47C2×D596—22no—
48C2×D596—21no—
49C2×D596—21no—
50C2×D596—44no—
51C2×D596D411yescharacteristic
52C2×D596C2312yes—
53C2×C22⋊D149—22no—
54D4×D149—24no—
55D4×D149—42no—
56C2×C4×D149—22no—
57C2×C4×D149C2312yes—
58#14558725—24no—
59#14558725—42no—
60#14558724—24no—
61#14558723—24no—
62C2×#11924746C2312yes—
63C8×D149—24no—
64C4⋊Dic149—22no—
65C4⋊Dic149—21no—
66C4⋊Dic149—21no—
67C4⋊Dic149D411yescharacteristic
68#14558713—22no—
69#14558713—22no—
70#14558713D412yes—
71C2×Q8×C149C2311yescharacteristic
72C2×D4×C149C2311yescharacteristic
73C22×C4×C149—21no—
74SD16×C149D414yescomplemented
75C2×C8×C149C2311yescharacteristic
76C2×C8×C149C2311yescharacteristic
77C4⋊C4×C149—21no—
78C4⋊C4×C149C2311yescharacteristic
79C4⋊C4×C149C2311yescharacteristic
80C22⋊C4×C149—21no—
81C42×C149—21no—
82C42×C149C2311yescharacteristic
83C22×D149—22no—
84C22×D149—44no—
85C22×D149—44no—
86C22×D149—82no—
87C22×D149C2×D412yes—
88Dic298—22no—
89Dic298—22no—
90Dic298—44no—
91D596—22no—
92D596—22no—
93D596—44no—
94D596—42no—
95D596—81no—
96D596SD1614yesdirect product factor
97C22⋊D149—44no—
98C2×Dic149—22no—
99C2×Dic149C2×D412yes—
100C4×D149—22no—
101C4×D149—22no—
102C4×D149—44no—
103#11924746—22no—
104C23×C149—21no—
105Q8×C149—21no—
106Q8×C149C2×D412yescomplemented
107D4×C149—21no—
108D4×C149C2×D412yes—
109C2×C4×C149—21no—
110C2×C4×C149—21no—
111C2×C4×C149—21no—
112C2×C4×C149—42no—
113C2×C4×C149C2×D411yescharacteristic
114C2×C4×C149C2×D411yescharacteristic
115C2×C4×C149C2411yescharacteristic
116C8×C149—21no—
117C8×C149C2×D412yescomplemented
118C22×C149—22no—
119C22×C149—41no—
120C22×C149—41no—
121C22×C149C22×D411yescharacteristic
122C2×D149—22no—
123C2×D149—22no—
124C2×D149—42no—
125C2×D149—42no—
126C2×D149—42no—
127C2×D149—88no—
128C2×D149C2×SD1614yescomplemented
129C4×C149—22no—
130C4×C149—21no—
131C4×C149—41no—
132C4×C149—41no—
133C4×C149C2×SD1612yescomplemented
134C4×C149C22×D411yescharacteristic
135C4×C149H(5,𝔽2)11yescharacteristic
136Dic149—22no—
137Dic149—42no—
138C2×C149—42no—
139C2×C149D4211yescharacteristic
140C2×C149C22×SD1611yescharacteristic
141C2×C149#57711yescharacteristic
142D149—24no—
143D149—82no—
144C149D4×SD1611yescharacteristic, complemented, Sylow
145D4×SD16—1491nomaximal, Sylow
146C22×SD16—1492no—
147D4×Q8—1491no—
148D42—1491no—
149#492—1491no—
150#465—1492no—
151#461—1491no—
152#460—1491no—
153#450—1492no—
154#448—1492no—
155C4×SD16D14911yescharacteristic, complemented
156C8×D4—1491no—
157C22×Q8—1492no—
158C22×D4—2981no—
159C22×D4—1492no—
160C2×SD16—2988no—
161C2×SD16—1492no—
162C2×SD16—1492no—
163C2×SD16—1492no—
164C2×SD16—1492no—
165C2×SD16C2×D14911yescharacteristic
166C22×C8—1492no—
167C4⋊Q8—2981no—
168C4⋊Q8—1491no—
169#127—1491no—
170C22⋊Q8—2982no—
171C22⋊Q8—1492no—
172#121—2981no—
173#121—1492no—
174#120—2982no—
175C4×Q8C2×D14911yescharacteristic, complemented
176C4×D4—2981no—
177C4×D4—1491no—
178C4×D4C2×D14911yescharacteristic
179#106C2×D14911yescharacteristic, complemented
180C4⋊C8—1491no—
181#103—1492no—
182#103C2×D14911yescharacteristic, complemented
183#102—1492no—
184#102C2×D14911yescharacteristic
185C22⋊C8—1492no—
186C4×C8C2×D14911yescharacteristic, complemented
187C24—2982no—
188C2×Q8—2982no—
189C2×Q8—2984no—
190C2×Q8—5962no—
191C2×Q8—1492no—
192C2×Q8C22×D14911yescharacteristic
193C2×D4—2982no—
194C2×D4—2984no—
195C2×D4—2982no—
196C2×D4—2981no—
197C2×D4—2981no—
198C2×D4—5964no—
199C2×D4—5962no—
200C2×D4—1491no—
201C2×D4—1492no—
202C2×D4C22×D14911yescharacteristic
203C22×C4—21no—
204C22×C4—2982no—
205C22×C4—1492no—
206SD16—2984no—
207SD16—2984no—
208SD16—2984no—
209SD16—5962no—
210SD16D59614yesdirect product factor
211C2×C8—2984no—
212C2×C8—1492no—
213C2×C8C22×D14911yescharacteristic
214C2×C8C22×D14911yescharacteristic
215C4⋊C4—21no—
216C4⋊C4—2982no—
217C4⋊C4—2981no—
218C4⋊C4—2981no—
219C4⋊C4—1491no—
220C4⋊C4C22×D14911yescharacteristic
221C4⋊C4C22×D14911yescharacteristic
222C22⋊C4—21no—
223C22⋊C4—2982no—
224C22⋊C4—2982no—
225C22⋊C4—1492no—
226C42—21no—
227C42C22×D14911yescharacteristic
228C23—21no—
229C23—2982no—
230C23—5964no—
231C23—5964no—
232C23—1492no—
233C23—11922no—
234Q8—21no—
235Q8—2982no—
236Q8—2982no—
237Q8—5964no—
238Q8C2×D59612yescomplemented
239D4—21no—
240D4—2982no—
241D4—2982no—
242D4—5964no—
243D4—5964no—
244D4—5962no—
245D4—1494no—
246D4—11921no—
247D4C2×D59612yes—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—42no—
252C2×C4—2982no—
253C2×C4—2982no—
254C2×C4—2982no—
255C2×C4—5964no—
256C2×C4—1492no—
257C2×C4D4×D14911yescharacteristic
258C2×C4D4×D14911yescharacteristic
259C2×C4C23×D14911yescharacteristic
260C8—21no—
261C8—2982no—
262C8C2×D59612yescomplemented
263C22—22no—
264C22—41no—
265C22—41no—
266C22—2982no—
267C22—2982no—
268C22—5962no—
269C22—5962no—
270C22—5962no—
271C22—1494no—
272C22—11928no—
273C22C2×D4×D14911yescharacteristic
274C4—21no—
275C4—22no—
276C4—41no—
277C4—41no—
278C4—2982no—
279C4—5962no—
280C4SD16×D14912yescomplemented
281C4C22×D59611yescharacteristic
282C4#1801195711yescharacteristic
283C2—42no—
284C2—2984no—
285C2—11922no—
286C2D4×D59611yescharacteristic
287C2C2×SD16×D14911yescharacteristic
288C2#2375043211yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
FittingC4×SD16×C149C2
socleC22×C149C22×D4
prime radicalD4×D596C2
hypercenterC4×SD16D149
hypocenterC149D4×SD16
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
1. C2×SD16×D149C2semidirect
2. Q8×D596C2semidirect
4. #23749998C2semidirect
5. #23749855C2semidirect
6. #23749830C2semidirect
7. #23749825C2semidirect
8. #23749777C2semidirect
9. #23749765C2semidirect
10. C8×D596C2semidirect
11. C4×SD16×C149C2semidirect
12. C2×Q8×D149C22semidirect
15. C2×#14558725C22semidirect
16. C2×#14558725C22semidirect
18. C2×#14558723C22semidirect
20. C2×C8×D149C22semidirect
22. #18011911C22semidirect
25. #18011891C22semidirect
31. C4⋊#11924746C22semidirect
32. #18011834C22semidirect
33. #18011831C22semidirect
34. #18011823C22semidirect
36. C4×Q8×C149C22semidirect
38. #106×C149C22semidirect
39. #103×C149C22semidirect
41. C4×C8×C149C22semidirect
74. SD16×C149D4semidirect
96. D596SD16direct (N × H)
106. Q8×C149C2×D4semidirect
117. C8×C149C2×D4semidirect
128. C2×D149C2×SD16semidirect
133. C4×C149C2×SD16semidirect
144. C149D4×SD16semidirect
155. C4×SD16D149semidirect
175. C4×Q8C2×D149semidirect
179. #106C2×D149semidirect
182. #103C2×D149semidirect
186. C4×C8C2×D149semidirect
210. SD16D596direct (N × H)
238. Q8C2×D596semidirect
262. C8C2×D596semidirect
280. C4SD16×D149semidirect

Maximal subgroups

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

subgroupindex
C2×SD16×D1492
Q8×D5962
D4×D5962
#237499982
#237498552
#237498302
#237498252
#237497772
#237497652
C8×D5962
C4×SD16×C1492
D4×SD16149