Finite Group Databasebeta

← #34055168

Subgroups — #34055168

Order 19072.

564 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 564 conjugacy classes of subgroups — too many to draw. Only its 149 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×#18011941C211yesmaximal, characteristic, complemented
2C2×#18011936C211yesmaximal, characteristic, complemented
3C22×#14558725C211yesmaximal, characteristic, complemented
4#23750196C211yesmaximal, characteristic, complemented
5#23750189C211yesmaximal, characteristic, complemented
6#23750018C212yesmaximal, complemented
7#23750013C212yesmaximal, complemented
8#23750006C212yesmaximal, complemented
9#23749996C212yesmaximal, complemented
10#23749580C211yesmaximal, characteristic, complemented
11C2×#135×C149C211yesmaximal, characteristic, complemented
12C22×Dic298C2211yescharacteristic
13C22×D596C2211yescharacteristic
14#18011941—24no—
15#18011936—24no—
16C2×#14558726C2212yescomplemented
17C2×#14558725—24no—
18C2×#14558725C2212yes—
19C2×#14558725C2212yes—
20C2×#14558724C2212yescomplemented
21C2×#14558723C2212yes—
22C2×#14558721C2212yes—
23C2×#14558720C2211yescharacteristic
24#18011909C2212yescomplemented
25#18011907C2212yes—
26#18011900C2212yes—
27#18011898C2212yescomplemented
28#18011892—22no—
29#18011890—22no—
30#18011885—22no—
31#18011879—22no—
32#18011870C2211yescharacteristic
33#18011821C2212yescomplemented
34C8×Dic149C2212yescomplemented
35C2×#41×C149C2211yescharacteristic
36C2×#41×C149C2211yescharacteristic
37#135×C149—24no—
38C2×Q16×C149C2211yescharacteristic, complemented
39C2×SD16×C149C2211yescharacteristic, complemented
40C2×SD16×C149C2211yescharacteristic, complemented
41C2×D8×C149C2211yescharacteristic, complemented
42C22×C8×C149C2211yescharacteristic
43C23×D149—21no—
44C2×Dic298—21no—
45C2×Dic298—22no—
46C2×Dic298—22no—
47C2×Dic298C2312yes—
48C2×D596—22no—
49C2×D596—22no—
50C2×D596—21no—
51C2×D596C2312yes—
52C2×C22⋊D149—24no—
53C22×Dic149—21no—
54#14558726—24no—
55#14558725—24no—
56#14558725—24no—
57#14558724—24no—
58#14558723—24no—
59#14558721—24no—
60#14558720D414yescomplemented
61C2×#11924746C2312yes—
62C4⋊Dic149D412yes—
63#14558715—24no—
64C22⋊Dic149—24no—
65C22⋊Dic149D412yes—
66#14558713—24no—
67C4×Dic149C2312yes—
68#41×C149—22no—
69#41×C149—22no—
70#41×C149—22no—
71#41×C149—22no—
72C2×Q8×C149C2311yescharacteristic
73C2×Q8×C149C2311yescharacteristic
74C2×D4×C149—21no—
75C2×D4×C149—21no—
76C2×D4×C149C2311yescharacteristic
77C2×D4×C149C2311yescharacteristic
78C22×C4×C149—21no—
79C22×C4×C149—21no—
80C22×C4×C149C2311yescharacteristic
81Q16×C149—22no—
82SD16×C149—22no—
83SD16×C149—22no—
84D8×C149—22no—
85C2×C8×C149D414yescomplemented
86C2×C8×C149C2311yescharacteristic
87C2×C8×C149C2311yescharacteristic
88C22×D149—22no—
89C22×D149—42no—
90C22×D149—82no—
91Dic298—22no—
92Dic298—22no—
93Dic298—42no—
94D596—22no—
95D596—22no—
96D596—42no—
97C22⋊D149—84no—
98C2×Dic149—22no—
99C2×Dic149—42no—
100C2×Dic149C2×D414yes—
101#11924746C2×D414yes—
102C23×C149—21no—
103C23×C149—21no—
104C23×C149C2×D411yescharacteristic
105Q8×C149—21no—
106Q8×C149—21no—
107Q8×C149—21no—
108Q8×C149—21no—
109D4×C149—21no—
110D4×C149—21no—
111D4×C149—21no—
112D4×C149—21no—
113D4×C149—42no—
114D4×C149—42no—
115C2×C4×C149—21no—
116C2×C4×C149—21no—
117C2×C4×C149—42no—
118C2×C4×C149—42no—
119C2×C4×C149C2×D411yescharacteristic
120C2×C4×C149C2×D412yes—
121C2×C4×C149C2×D412yes—
122C2×C4×C149C2411yescharacteristic
123C8×C149C2×D412yes—
124C8×C149C2×D412yes—
125C22×C149—22no—
126C22×C149—41no—
127C22×C149—41no—
128C22×C149—42no—
129C22×C149—42no—
130C22×C149#12712yes—
131C22×C149C22×D411yescharacteristic
132C2×D149—42no—
133C2×D149—44no—
134C2×D149—84no—
135C4×C149—41no—
136C4×C149—41no—
137C4×C149#12712yes—
138C4×C149C22×D411yescharacteristic
139C4×C149C22×D411yescharacteristic
140Dic149—24no—
141Dic149—42no—
142C2×C149—22no—
143C2×C149—81no—
144C2×C149—81no—
145C2×C149C2×#12711yescharacteristic
146C2×C149#57712yes—
147D149—82no—
148C149#315411yescharacteristic, complemented, Sylow
149#3154—1491nomaximal, Sylow
150C2×#137—1491no—
151C2×AGL(1,ℤ/8)—1491no—
152C2×#135D14911yescharacteristic, complemented
153C22×SD16—1491no—
154#536—1491no—
155#535—1491no—
156#497—1492no—
157#496—1492no—
158#495—1492no—
159#492—1492no—
160#405—1491no—
161C2×#41C2×D14911yescharacteristic
162C2×#41C2×D14911yescharacteristic
163C22×Q8—1491no—
164C22×D4—1491no—
165#137—2984no—
166AGL(1,ℤ/8)—2984no—
167#135—24no—
168C2×Q16—1492no—
169C2×Q16C2×D14911yescharacteristic, complemented
170C2×SD16—2984no—
171C2×SD16—1492no—
172C2×SD16—1492no—
173C2×SD16—1492no—
174C2×SD16—1492no—
175C2×SD16C2×D14911yescharacteristic, complemented
176C2×SD16C2×D14911yescharacteristic, complemented
177C2×D8—1492no—
178C2×D8C2×D14911yescharacteristic, complemented
179C2×M16—1491no—
180C22×C8C2×D14911yescharacteristic
181C4⋊Q8—1492no—
182#127—1492no—
183#124—1492no—
184#124—1492no—
185#123—2982no—
186C22⋊Q8—2982no—
187#121—2982no—
188#120—2982no—
189#117—1491no—
190#97—1492no—
191C4×C8—1492no—
192C24—2981no—
193#41—22no—
194#41—22no—
195#41—22no—
196#41—22no—
197C2×Q8—2981no—
198C2×Q8—2982no—
199C2×Q8—2982no—
200C2×Q8—1492no—
201C2×Q8C22×D14911yescharacteristic
202C2×Q8C22×D14911yescharacteristic
203C2×D4—21no—
204C2×D4—21no—
205C2×D4—2984no—
206C2×D4—2982no—
207C2×D4—2981no—
208C2×D4—2982no—
209C2×D4—1492no—
210C2×D4C22×D14911yescharacteristic
211C2×D4C22×D14911yescharacteristic
212C22×C4—21no—
213C22×C4—21no—
214C22×C4—2981no—
215C22×C4C22×D14911yescharacteristic
216Q16—22no—
217Q16—2984no—
218SD16—22no—
219SD16—22no—
220SD16—2984no—
221SD16—2984no—
222SD16—2984no—
223SD16—2984no—
224D8—22no—
225D8—2984no—
226M16—1494no—
227C2×C8—1492no—
228C2×C8C22⋊D14914yescomplemented
229C2×C8C22×D14911yescharacteristic
230C2×C8C22×D14911yescharacteristic
231C4⋊C4—2984no—
232C4⋊C4—1492no—
233C22⋊C4—2984no—
234C22⋊C4—2984no—
235C22⋊C4—1492no—
236C42—1492no—
237C23—21no—
238C23—21no—
239C23—2982no—
240C23—5962no—
241C23—11922no—
242C23D4×D14911yescharacteristic
243Q8—21no—
244Q8—21no—
245Q8—21no—
246Q8—21no—
247Q8—2982no—
248Q8—2982no—
249Q8—5962no—
250D4—21no—
251D4—21no—
252D4—21no—
253D4—21no—
254D4—42no—
255D4—42no—
256D4—2982no—
257D4—2982no—
258D4—5962no—
259D4—11924no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—42no—
263C2×C4—42no—
264C2×C4—2982no—
265C2×C4—5962no—
266C2×C4—1494no—
267C2×C4D4×D14911yescharacteristic
268C2×C4D4×D14912yes—
269C2×C4C2×C22⋊D14912yes—
270C2×C4C23×D14911yescharacteristic
271C8—1494no—
272C8C2×C22⋊D14912yes—
273C8C2×C22⋊D14912yes—
274C22—22no—
275C22—41no—
276C22—41no—
277C22—42no—
278C22—42no—
279C22—5962no—
280C22—5964no—
281C22—11924no—
282C22#1801190712yes—
283C22C2×D4×D14911yescharacteristic
284C4—41no—
285C4—41no—
286C4—2984no—
287C4—5962no—
288C4#1801190712yes—
289C4C2×D4×D14911yescharacteristic
290C4C22×C22⋊D14911yescharacteristic
291C2—22no—
292C2—81no—
293C2—81no—
294C2—11922no—
295C2C2×#1801190711yescharacteristic
296C2#2375043212yes—
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
FittingC2×#135×C149C2
socleC22×C149C22×D4
hypercenterC2×#135D149
hypocenterC149#3154
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#135

Complements

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

NH ≅ G/Ntype
1. C2×#18011941C2semidirect
2. C2×#18011936C2semidirect
3. C22×#14558725C2semidirect
4. #23750196C2semidirect
5. #23750189C2semidirect
6. #23750018C2semidirect
7. #23750013C2semidirect
8. #23750006C2semidirect
9. #23749996C2semidirect
10. #23749580C2semidirect
11. C2×#135×C149C2semidirect
16. C2×#14558726C22semidirect
20. C2×#14558724C22semidirect
24. #18011909C22semidirect
27. #18011898C22semidirect
33. #18011821C22semidirect
34. C8×Dic149C22semidirect
38. C2×Q16×C149C22semidirect
39. C2×SD16×C149C22semidirect
40. C2×SD16×C149C22semidirect
41. C2×D8×C149C22semidirect
60. #14558720D4semidirect
85. C2×C8×C149D4semidirect
148. C149#3154semidirect
152. C2×#135D149semidirect
169. C2×Q16C2×D149semidirect
175. C2×SD16C2×D149semidirect
176. C2×SD16C2×D149semidirect
178. C2×D8C2×D149semidirect
228. C2×C8C22⋊D149semidirect

Maximal subgroups

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

subgroupindex
C2×#180119412
C2×#180119362
C22×#145587252
#237501962
#237501892
#237500182
#237500132
#237500062
#237499962
#237495802
C2×#135×C1492
#3154149