Finite Group Databasebeta

← #34056477

Subgroups — #34056477

Order 19072.

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#23750433C212yesmaximal, complemented
2#23750427C211yesmaximal, characteristic, complemented
3#23750010C211yesmaximal, characteristic, complemented
4#23749897C211yesmaximal, characteristic, complemented
5#23749895C211yesmaximal, characteristic, complemented
6#23749890C212yesmaximal, complemented
7#23749801C212yesmaximal, complemented
8#23749798C212yesmaximal, complemented
9#23749742C211yesmaximal, characteristic, complemented
10#23749740C211yesmaximal, characteristic, complemented
11#578×C149C211yesmaximal, characteristic, complemented
12#18011957C2212yes—
13#18011942—22no—
14#18011942C2212yes—
15#18011938—22no—
16#18011936—22no—
17#18011936C2212yes—
18#18011936C2212yescomplemented
19#18011934—21no—
20#18011931—22no—
21#18011931C2211yescharacteristic
22C2×#14558723—22no—
23C2×#14558723C2212yescomplemented
24C2×D1192C2211yescharacteristic
25D8×D149—21no—
26#18011918C2212yescomplemented
27#18011917C2211yescharacteristic
28#18011900C2212yescomplemented
29#18011847C2211yescharacteristic, complemented
30#18011846C2211yescharacteristic, complemented
31#18011838C2211yescharacteristic, complemented
32#18011838C2212yescomplemented
33#18011837C2211yescharacteristic
34#18011830C2212yescomplemented
35#18011827C2212yescomplemented
36C8×Dic149C2211yescharacteristic, complemented
372−1+4×C149C2212yescomplemented
38#137×C149—22no—
39#137×C149C2212yescomplemented
40#135×C149—21no—
41#135×C149C2211yescharacteristic
42C2×Q16×C149—21no—
43C2×Q16×C149C2211yescharacteristic, complemented
44#131×C149C2211yescharacteristic, complemented
45#14558737—22no—
46#14558736—22no—
47#14558736C2311yescharacteristic
48C2×D596—22no—
49C2×D596C2312yes—
50D4×D149—22no—
51D4×D149—42no—
52#14558726—22no—
53#14558726D411yescharacteristic
54#14558724D411yescharacteristic
55#14558723—22no—
56#14558723—22no—
57#14558723—22no—
58#14558723—22no—
59#14558723—22no—
60#14558723D411yescharacteristic
61D1192—21no—
62D1192—21no—
63#14558721—22no—
64#14558721—22no—
65#14558721D411yescharacteristic
66#14558720—22no—
67#14558720C2311yescharacteristic
68#14558720C2312yes—
69#14558719—21no—
70C2×#11924746—22no—
71C2×#11924746C2311yescharacteristic
72C8×D149—21no—
73#14558713—42no—
74C4×Dic149C2311yescharacteristic
75#41×C149—22no—
76#41×C149—22no—
77#41×C149—42no—
78#41×C149C2312yes—
79#41×C149C2311yescharacteristic
80C2×Q8×C149—22no—
81C2×Q8×C149—22no—
82C2×Q8×C149C2312yes—
83Q16×C149—22no—
84Q16×C149—21no—
85Q16×C149—21no—
86Q16×C149D411yescharacteristic
87SD16×C149—22no—
88SD16×C149D412yes—
89D8×C149D411yescharacteristic
90M16×C149—21no—
91M16×C149C2311yescharacteristic
92C2×C8×C149—21no—
93C2×C8×C149C2311yescharacteristic
94C22×D149—22no—
95C22×D149—42no—
96Dic298C2×D411yescharacteristic
97D596—22no—
98D596—22no—
99D596—42no—
100D596C2×D411yescharacteristic
101C22⋊D149—21no—
102C22⋊D149—42no—
103C2×Dic149—21no—
104C4×D149—21no—
105C4×D149—42no—
106#11924746—22no—
107#11924746—21no—
108#11924746C2×D411yescharacteristic
109#11924746C2×D411yescharacteristic
110Q8×C149—22no—
111Q8×C149—22no—
112Q8×C149—42no—
113Q8×C149C2×D411yescharacteristic
114Q8×C149C2×D412yes—
115D4×C149—22no—
116D4×C149—21no—
117D4×C149—42no—
118D4×C149C2×D411yescharacteristic
119D4×C149C2×D412yes—
120C2×C4×C149—22no—
121C2×C4×C149—21no—
122C2×C4×C149—22no—
123C2×C4×C149—42no—
124C2×C4×C149—42no—
125C2×C4×C149C2411yescharacteristic
126C8×C149—21no—
127C8×C149C2×D411yescharacteristic
128C8×C149C2×D411yescharacteristic
129C22×C149—21no—
130C22×C149—22no—
131C22×C149H(5,𝔽2)11yescharacteristic
132C2×D149—21no—
133C2×D149—42no—
134C2×D149—82no—
135C2×D149—162no—
136C4×C149—21no—
137C4×C149—22no—
138C4×C149—42no—
139C4×C149C22×D411yescharacteristic
140C4×C149C22×D411yescharacteristic
141Dic149—21no—
142Dic149—41no—
143C2×C149—21no—
144C2×C149—42no—
145C2×C149—41no—
146C2×C149D4211yescharacteristic
147D149—41no—
148D149—82no—
149C149#329011yescharacteristic, complemented, Sylow
150#3290—1491nomaximal, Sylow
151#578D14911yescharacteristic, complemented
152#577—1492no—
153#576—1491no—
154#495—1491no—
155#473—1491no—
156#472—1491no—
157#471—1492no—
158#455—1492no—
159#454—1492no—
160#443—1491no—
161#443—1491no—
1622−1+4C2×D14912yescomplemented
163H(5,𝔽2)—1492no—
164#137—22no—
165#137—2982no—
166#137—1492no—
167#137C2×D14912yescomplemented
168AGL(1,ℤ/8)—2982no—
169AGL(1,ℤ/8)—2982no—
170AGL(1,ℤ/8)—1492no—
171AGL(1,ℤ/8)—1492no—
172#135—21no—
173#135—2981no—
174#135—2982no—
175#135—1491no—
176#135C2×D14911yescharacteristic
177C2×Q16—21no—
178C2×Q16C2×D14911yescharacteristic, complemented
179C2×SD16—2982no—
180C2×SD16—1492no—
181C2×D8—2981no—
182C2×D8—1491no—
183#131—1492no—
184#131—1491no—
185#131C2×D14911yescharacteristic, complemented
186#124—1492no—
187#108—1491no—
188#108—1491no—
189#104—1491no—
190#104—1492no—
191#104—1491no—
192#101—1492no—
193#100—1492no—
194C4×C8—1491no—
195#41—22no—
196#41—22no—
197#41—42no—
198#41—2982no—
199#41—2982no—
200#41—1491no—
201#41C22×D14911yescharacteristic
202#41C22×D14912yes—
203C2×Q8—22no—
204C2×Q8—22no—
205C2×Q8C22×D14912yes—
206C2×D4—2982no—
207C2×D4—2982no—
208C2×D4—5962no—
209C2×D4—1492no—
210Q16—22no—
211Q16—21no—
212Q16—21no—
213Q16—2982no—
214Q16—1491no—
215Q16C22⋊D14911yescharacteristic
216SD16—22no—
217SD16—2982no—
218SD16—2982no—
219SD16—2982no—
220SD16—2982no—
221SD16—2982no—
222SD16—1491no—
223SD16—1491no—
224SD16C22⋊D14912yes—
225D8—2982no—
226D8—2982no—
227D8—2981no—
228D8—2981no—
229D8—1491no—
230D8C22⋊D14911yescharacteristic
231M16—21no—
232M16—2982no—
233M16—2981no—
234M16—1492no—
235M16—1491no—
236M16C22×D14911yescharacteristic
237C2×C8—21no—
238C2×C8—2982no—
239C2×C8—2981no—
240C2×C8—1491no—
241C2×C8C22×D14911yescharacteristic
242C22⋊C4—5962no—
243C42—1491no—
244C23—2982no—
245C23—5962no—
246Q8—22no—
247Q8—22no—
248Q8—42no—
249Q8—1491no—
250Q8D4×D14911yescharacteristic
251Q8C2×C22⋊D14912yes—
252D4—22no—
253D4—21no—
254D4—42no—
255D4—2981no—
256D4—2982no—
257D4—2982no—
258D4—5962no—
259D4—5962no—
260D4—1491no—
261D4D4×D14911yescharacteristic
262D4C2×C22⋊D14912yes—
263C2×C4—22no—
264C2×C4—21no—
265C2×C4—22no—
266C2×C4—42no—
267C2×C4—42no—
268C2×C4—2981no—
269C2×C4—2981no—
270C2×C4—5962no—
271C2×C4C23×D14911yescharacteristic
272C8—21no—
273C8—2982no—
274C8—2981no—
275C8—1491no—
276C8—1491no—
277C8C2×C22⋊D14911yescharacteristic
278C8C2×C22⋊D14911yescharacteristic
279C22—21no—
280C22—22no—
281C22—2981no—
282C22—23842no—
283C22—5962no—
284C22—11922no—
285C22#1801195611yescharacteristic
286C4—21no—
287C4—22no—
288C4—42no—
289C4—2981no—
290C4—5961no—
291C4C2×D4×D14911yescharacteristic
292C4C22×C22⋊D14911yescharacteristic
293C2—21no—
294C2—42no—
295C2—41no—
296C2—5961no—
297C2—11922no—
298C2D4×C22⋊D14911yescharacteristic
subgroupG/H
centerC2D4×C22⋊D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#578×C149C2
socleC2×C149D42
hypercenter#578D149
hypocenterC149#3290
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C2 ◁ C2×C4 ◁ #578

Complements

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

NH ≅ G/Ntype
1. #23750433C2semidirect
2. #23750427C2semidirect
3. #23750010C2semidirect
4. #23749897C2semidirect
5. #23749895C2semidirect
6. #23749890C2semidirect
7. #23749801C2semidirect
8. #23749798C2semidirect
9. #23749742C2semidirect
10. #23749740C2semidirect
11. #578×C149C2semidirect
18. #18011936C22semidirect
23. C2×#14558723C22semidirect
26. #18011918C22semidirect
28. #18011900C22semidirect
29. #18011847C22semidirect
30. #18011846C22semidirect
31. #18011838C22semidirect
32. #18011838C22semidirect
34. #18011830C22semidirect
35. #18011827C22semidirect
36. C8×Dic149C22semidirect
37. 2−1+4×C149C22semidirect
39. #137×C149C22semidirect
43. C2×Q16×C149C22semidirect
44. #131×C149C22semidirect
149. C149#3290semidirect
151. #578D149semidirect
162. 2−1+4C2×D149semidirect
167. #137C2×D149semidirect
178. C2×Q16C2×D149semidirect
185. #131C2×D149semidirect

Maximal subgroups

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

subgroupindex
#237504332
#237504272
#237500102
#237498972
#237498952
#237498902
#237498012
#237497982
#237497422
#237497402
#578×C1492
#3290149