Finite Group Databasebeta

← #34056382

Subgroups — #34056382

Order 19072.

546 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 546 conjugacy classes of subgroups — too many to draw. Only its 133 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
3#23750260C211yesmaximal, characteristic
4#23749997C211yesmaximal, characteristic, complemented
5#23749853C212yesmaximal, complemented
6#23749831C211yesmaximal, characteristic, complemented
7#23749777C212yesmaximal, complemented
8#23749762C212yesmaximal, complemented
9C4×#14558723C211yesmaximal, characteristic, complemented
10#23749690C211yesmaximal, characteristic, complemented
11#460×C149C211yesmaximal, characteristic, complemented
12C2×Q8×D149C2212yescomplemented
13C2×D4×D149—21no—
14C2×D4×D149C2212yes—
15C2×#14558725C2212yes—
16C2×#14558724C2212yescomplemented
17C2×#14558724C2212yescomplemented
18C2×#14558723C2211yescharacteristic
19SD16×D149—28no—
20C2×C8×D149C2212yescomplemented
21#18011911—21no—
22#18011911C2211yescharacteristic, complemented
23#18011891—22no—
24#18011891C2212yescomplemented
25#18011882—21no—
26#18011882C2212yes—
27#18011879—22no—
28C4×D596—21no—
29C4×D596C2211yescharacteristic
30C4×D596C2211yescharacteristic
31#18011842C2211yescharacteristic, complemented
32#18011836C2212yescomplemented
33#18011835C2211yescharacteristic, complemented
34#18011831C2211yescharacteristic
35#18011823C2212yescomplemented
36C4×#11924746C2211yescharacteristic, complemented
37C2×SD16×C149C2212yescomplemented
38#127×C149C2211yescharacteristic
39C4×Q8×C149C2211yescharacteristic, complemented
40C4⋊C8×C149C2211yescharacteristic, complemented
41#102×C149C2212yescomplemented
42C23×D149—22no—
43C2×Dic298—22no—
44C2×Dic298C2312yes—
45Q8×D149—24no—
46Q8×D149—42no—
47C2×D596D411yescharacteristic
48C2×D596C2311yescharacteristic
49C2×C22⋊D149—22no—
50C2×C22⋊D149—22no—
51D4×D149—24no—
52D4×D149—42no—
53D4×D149—44no—
54C2×C4×D149—22no—
55C2×C4×D149—21no—
56C2×C4×D149C2312yes—
57#14558725—24no—
58#14558724—24no—
59#14558724—42no—
60#14558723D414yescomplemented
61C2×#11924746C2311yescharacteristic
62C2×#11924746C2311yescharacteristic
63C8×D149—24no—
64C4⋊Dic149—22no—
65C4⋊Dic149—21no—
66C4⋊Dic149—21no—
67C4⋊Dic149D411yescharacteristic
68C4⋊Dic149C2311yescharacteristic
69C22⋊Dic149—22no—
70#14558713—22no—
71#14558713—21no—
72#14558713D412yes—
73C2×Q8×C149C2311yescharacteristic
74C2×D4×C149—21no—
75C2×D4×C149—21no—
76C2×D4×C149C2312yes—
77SD16×C149—24no—
78C2×C8×C149C2312yes—
79C4⋊C4×C149—21no—
80C4⋊C4×C149C2311yescharacteristic
81C42×C149—21no—
82C42×C149C2311yescharacteristic
83C22×D149—21no—
84C22×D149—44no—
85C22×D149—44no—
86C22×D149—82no—
87C22×D149C2×D412yes—
88Dic298—22no—
89Dic298—22no—
90Dic298—44no—
91D596—21no—
92D596SD1614yescomplemented
93D596C2×D412yes—
94C22⋊D149—44no—
95C22⋊D149—44no—
96C2×Dic149—21no—
97C2×Dic149—22no—
98C2×Dic149C2×D412yes—
99C4×D149—22no—
100C4×D149—22no—
101C4×D149—44no—
102C4×D149—42no—
103#11924746—21no—
104#11924746C2×D412yescomplemented
105C23×C149—22no—
106Q8×C149—21no—
107Q8×C149C2×D412yescomplemented
108D4×C149—22no—
109D4×C149—22no—
110D4×C149—42no—
111D4×C149—81no—
112C2×C4×C149—21no—
113C2×C4×C149—21no—
114C2×C4×C149C2×D411yescharacteristic
115C2×C4×C149C2×D411yescharacteristic
116C2×C4×C149C2411yescharacteristic
117C8×C149—22no—
118C22×C149—42no—
119C22×C149—42no—
120C22×C149—42no—
121C22×C149C22×D411yescharacteristic
122C2×D149—22no—
123C2×D149—22no—
124C2×D149—22no—
125C2×D149—41no—
126C2×D149—41no—
127C2×D149—88no—
128C2×D149C2×SD1614yescomplemented
129C4×C149—22no—
130C4×C149—21no—
131C4×C149—41no—
132C4×C149C2×SD1612yescomplemented
133C4×C149C22×D411yescharacteristic
134C4×C149H(5,𝔽2)11yescharacteristic
135Dic149—22no—
136Dic149—42no—
137Dic149—41no—
138C2×C149—82no—
139C2×C149D4211yescharacteristic
140C2×C149C22×SD1611yescharacteristic
141C2×C149#57711yescharacteristic
142D149—24no—
143D149—42no—
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#460D14911yescharacteristic, complemented
153#450—1492no—
154#448—1492no—
155C4×SD16—1491no—
156C8×D4—1491no—
157C22×Q8—1492no—
158C22×D4—2981no—
159C22×D4—1492no—
160C2×SD16—2988no—
161C2×SD16—1492no—
162C2×SD16—1492no—
163C2×SD16—1491no—
164C2×SD16—1492no—
165C2×SD16C2×D14912yescomplemented
166C22×C8—1492no—
167C4⋊Q8—2981no—
168C4⋊Q8—1491no—
169#127C2×D14911yescharacteristic
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×D4—1491no—
179#106—1491no—
180C4⋊C8C2×D14911yescharacteristic, complemented
181#103—1491no—
182#103—1492no—
183#102—1491no—
184#102C2×D14912yescomplemented
185C22⋊C8—1492no—
186C4×C8—1491no—
187C24—2982no—
188C2×Q8—2982no—
189C2×Q8—2984no—
190C2×Q8—5962no—
191C2×Q8—1492no—
192C2×Q8C22×D14911yescharacteristic
193C2×D4—21no—
194C2×D4—21no—
195C2×D4—2984no—
196C2×D4—2982no—
197C2×D4—2982no—
198C2×D4—5962no—
199C2×D4—5964no—
200C2×D4—1491no—
201C2×D4—1491no—
202C2×D4C22×D14912yes—
203C22×C4—2982no—
204C22×C4—2981no—
205C22×C4—1492no—
206SD16—24no—
207SD16—2984no—
208SD16—2984no—
209SD16—5962no—
210SD16—1494no—
211C2×C8—2984no—
212C2×C8—1491no—
213C2×C8—1491no—
214C2×C8C22×D14912yes—
215C4⋊C4—21no—
216C4⋊C4—2982no—
217C4⋊C4—2981no—
218C4⋊C4—2981no—
219C4⋊C4—1491no—
220C4⋊C4—1491no—
221C4⋊C4C22×D14911yescharacteristic
222C22⋊C4—2982no—
223C22⋊C4—2982no—
224C22⋊C4—2981no—
225C22⋊C4—1492no—
226C42—21no—
227C42C22×D14911yescharacteristic
228C23—22no—
229C23—2981no—
230C23—5964no—
231C23—5964no—
232C23—1492no—
233C23—11922no—
234Q8—21no—
235Q8—2982no—
236Q8—2982no—
237Q8—5964no—
238Q8D4×D14912yescomplemented
239D4—22no—
240D4—22no—
241D4—42no—
242D4—81no—
243D4—2981no—
244D4—5964no—
245D4—5964no—
246D4—1494no—
247D4—1492no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—2982no—
251C2×C4—2982no—
252C2×C4—2981no—
253C2×C4—2982no—
254C2×C4—5964no—
255C2×C4—5962no—
256C2×C4—1492no—
257C2×C4D4×D14911yescharacteristic
258C2×C4D4×D14911yescharacteristic
259C2×C4C23×D14911yescharacteristic
260C8—22no—
261C8—2981no—
262C8—1492no—
263C22—42no—
264C22—42no—
265C22—42no—
266C22—2982no—
267C22—2982no—
268C22—2982no—
269C22—5961no—
270C22—5961no—
271C22—1494no—
272C22—11928no—
273C22C2×D4×D14911yescharacteristic
274C4—21no—
275C4—22no—
276C4—41no—
277C4—2982no—
278C4—5962no—
279C4—5961no—
280C4SD16×D14912yescomplemented
281C4C2×D4×D14911yescharacteristic
282C4#1801195711yescharacteristic
283C2—82no—
284C2—2984no—
285C2—5962no—
286C2#2375025911yescharacteristic
287C2C2×SD16×D14911yescharacteristic
288C2#2375043511yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#460×C149C2
socleC22×C149C22×D4
prime radical#23750260C2
hypercenter#460D149
hypocenterC149D4×SD16
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #460

Complements

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

NH ≅ G/Ntype
1. C2×SD16×D149C2semidirect
2. Q8×D596C2semidirect
4. #23749997C2semidirect
5. #23749853C2semidirect
6. #23749831C2semidirect
7. #23749777C2semidirect
8. #23749762C2semidirect
9. C4×#14558723C2semidirect
10. #23749690C2semidirect
11. #460×C149C2semidirect
12. C2×Q8×D149C22semidirect
16. C2×#14558724C22semidirect
17. C2×#14558724C22semidirect
20. C2×C8×D149C22semidirect
22. #18011911C22semidirect
24. #18011891C22semidirect
31. #18011842C22semidirect
32. #18011836C22semidirect
33. #18011835C22semidirect
35. #18011823C22semidirect
36. C4×#11924746C22semidirect
37. C2×SD16×C149C22semidirect
39. C4×Q8×C149C22semidirect
40. C4⋊C8×C149C22semidirect
41. #102×C149C22semidirect
60. #14558723D4semidirect
92. D596SD16semidirect
104. #11924746C2×D4semidirect
107. Q8×C149C2×D4semidirect
128. C2×D149C2×SD16semidirect
132. C4×C149C2×SD16semidirect
144. C149D4×SD16semidirect
152. #460D149semidirect
165. C2×SD16C2×D149semidirect
175. C4×Q8C2×D149semidirect
180. C4⋊C8C2×D149semidirect
184. #102C2×D149semidirect
238. Q8D4×D149semidirect
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
#237502602
#237499972
#237498532
#237498312
#237497772
#237497622
C4×#145587232
#237496902
#460×C1492
D4×SD16149