Finite Group Databasebeta

← #34054229

Subgroups — #34054229

Order 19072.

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

normal subgroups only

This group has 504 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×#18011939C211yesmaximal, characteristic, complemented
2C2×#18011931C211yesmaximal, characteristic, complemented
3#23750189C211yesmaximal, characteristic, complemented
4#23750106C211yesmaximal, characteristic, complemented
5#23749850C212yesmaximal, complemented
6#23749843C212yesmaximal, complemented
7#23749824C212yesmaximal, complemented
8#23749819C212yesmaximal, complemented
9#23749653C211yesmaximal, characteristic, complemented
10C2×#18011831C211yesmaximal, characteristic, complemented
11#417×C149C211yesmaximal, characteristic, complemented
12C2×#14558736C2211yescharacteristic
13C22×D596C2211yescharacteristic
14#18011939—24no—
15#18011931—24no—
16C2×#14558726C2211yescharacteristic, complemented
17C2×#14558725C2212yes—
18C2×#14558724C2211yescharacteristic, complemented
19C2×#14558723C2211yescharacteristic, complemented
20C2×D1192C2212yes—
21C2×#14558721C2211yescharacteristic, complemented
22C22×#11924746C2211yescharacteristic
23#18011907C2212yes—
24#18011900C2212yes—
25#18011885—21no—
26#18011885—21no—
27#18011879—22no—
28#18011876C2212yescomplemented
29#18011873C2212yescomplemented
30C4×C22⋊D149—22no—
31#18011870C2211yescharacteristic
32#18011869—21no—
33C4⋊C4×D149—21no—
34#18011840C2212yescomplemented
35#18011840C2212yescomplemented
36#18011831C2212yes—
37#18011831C2212yes—
38C2×#41×C149C2211yescharacteristic
39C2×M16×C149C2211yescharacteristic
40C2×C4⋊C4×C149C2211yescharacteristic
41#103×C149C2212yescomplemented
42#102×C149C2212yescomplemented
43C23×D149—21no—
44#14558736—22no—
45#14558736D414yescomplemented
46C2×Dic298C2311yescharacteristic
47C2×D596—22no—
48C2×D596—21no—
49C2×D596—22no—
50C2×D596C2312yes—
51C2×D596C2311yescharacteristic
52C2×C22⋊D149—22no—
53C2×C22⋊D149—22no—
54C2×C22⋊D149—21no—
55C2×C4×D149—22no—
56C2×C4×D149—21no—
57#14558726—22no—
58#14558725—24no—
59#14558724—22no—
60#14558723—22no—
61D1192—24no—
62#14558721—22no—
63C2×#11924746—22no—
64C2×#11924746C2311yescharacteristic
65C2×#11924746C2311yescharacteristic
66C4⋊Dic149D411yescharacteristic
67C4⋊Dic149D411yescharacteristic
68#14558715—22no—
69C22⋊Dic149D412yes—
70#14558713—22no—
71#14558713—22no—
72#14558713—22no—
73C4×Dic149—22no—
74C4×Dic149C2312yes—
75#41×C149—22no—
76#41×C149—22no—
77C2×Q8×C149C2311yescharacteristic
78C2×D4×C149—21no—
79C2×D4×C149C2311yescharacteristic
80C22×C4×C149—21no—
81C22×C4×C149—21no—
82C22×C4×C149C2311yescharacteristic
83M16×C149—22no—
84C2×C8×C149C2312yes—
85C4⋊C4×C149—21no—
86C4⋊C4×C149C2312yes—
87C22×D149—21no—
88C22×D149—22no—
89C22×D149—42no—
90C22×D149—81no—
91C22×D149—81no—
92Dic298—21no—
93Dic298C2×D412yes—
94D596—22no—
95D596—21no—
96D596—22no—
97D596—42no—
98D596C2×D412yes—
99C22⋊D149—24no—
100C22⋊D149—82no—
101C22⋊D149—82no—
102C2×Dic149—21no—
103C2×Dic149C2×D412yes—
104C2×Dic149C2×D412yes—
105C4×D149—24no—
106C4×D149—82no—
107#11924746—21no—
108#11924746—21no—
109C23×C149—21no—
110C23×C149C2×D411yescharacteristic
111Q8×C149—21no—
112Q8×C149—21no—
113D4×C149—21no—
114D4×C149—21no—
115D4×C149—42no—
116C2×C4×C149—22no—
117C2×C4×C149—21no—
118C2×C4×C149—42no—
119C2×C4×C149—81no—
120C2×C4×C149C2×D411yescharacteristic
121C2×C4×C149C2×D412yes—
122C2×C4×C149#4112yes—
123C2×C4×C149C2411yescharacteristic
124C8×C149—22no—
125C22×C149—21no—
126C22×C149—21no—
127C22×C149—41no—
128C22×C149—41no—
129C22×C149—41no—
130C22×C149#12112yes—
131C22×C149C22×D411yescharacteristic
132C2×D149—22no—
133C2×D149—41no—
134C2×D149—41no—
135C2×D149—42no—
136C2×D149—42no—
137C2×D149—42no—
138C2×D149—84no—
139C4×C149—41no—
140C4×C149—42no—
141C4×C149#12112yes—
142C4×C149C22×D411yescharacteristic
143C4×C149C2×#4111yescharacteristic
144Dic149—22no—
145Dic149—22no—
146Dic149—22no—
147C2×C149—22no—
148C2×C149—81no—
149C2×C149C2×#12111yescharacteristic
150C2×C149#57611yescharacteristic
151C2×C149#57711yescharacteristic
152D149—42no—
153D149—82no—
154C149#304511yescharacteristic, complemented, Sylow
155#3045—1491nomaximal, Sylow
156C2×AGL(1,ℤ/8)—1491no—
157C2×#135—1491no—
158#535—1491no—
159#520—1491no—
160#464—1492no—
161#463—1492no—
162#460—1492no—
163#459—1492no—
164#424—1491no—
165#417D14911yescharacteristic, complemented
166C2×#102—1491no—
167C2×#41—1491no—
168C2×#41C2×D14911yescharacteristic
169C22×D4—1491no—
170AGL(1,ℤ/8)—2984no—
171#135—2984no—
172C2×Q16—1491no—
173C2×SD16—1491no—
174C2×SD16—1491no—
175C2×SD16—1492no—
176C2×D8—1491no—
177C2×D8—1492no—
178C2×M16C2×D14911yescharacteristic
179C22×C8—1491no—
180#127—1492no—
181#124—1492no—
182#121—2981no—
183#121—2981no—
184#120—2982no—
185C4×Q8—1492no—
186C4×D4—2982no—
187C4×D4—1492no—
188#117—2981no—
189#117—1491no—
190C2×C4⋊C4—2981no—
191C2×C4⋊C4C2×D14911yescharacteristic
192C4⋊C8—1492no—
193C4⋊C8—1492no—
194#103C2×D14912yescomplemented
195#102—1492no—
196#102—1492no—
197#102C2×D14912yescomplemented
198C24—2981no—
199#41—22no—
200#41—22no—
201#41—2982no—
202#41—1494no—
203C2×Q8—1491no—
204C2×Q8C22×D14911yescharacteristic
205C2×D4—21no—
206C2×D4—2981no—
207C2×D4—2982no—
208C2×D4—2982no—
209C2×D4—2982no—
210C2×D4—2981no—
211C2×D4—2982no—
212C2×D4—1492no—
213C2×D4—1491no—
214C2×D4C22×D14911yescharacteristic
215C22×C4—21no—
216C22×C4—21no—
217C22×C4—2982no—
218C22×C4—2981no—
219C22×C4C22×D14911yescharacteristic
220Q16—2982no—
221SD16—2984no—
222SD16—2982no—
223SD16—2982no—
224D8—2984no—
225D8—2982no—
226M16—22no—
227C2×C8—2982no—
228C2×C8—1491no—
229C2×C8—1491no—
230C2×C8C22×D14912yes—
231C4⋊C4—21no—
232C4⋊C4—2982no—
233C4⋊C4—1491no—
234C4⋊C4—1491no—
235C4⋊C4C22×D14912yes—
236C22⋊C4—2982no—
237C22⋊C4—2982no—
238C22⋊C4—2982no—
239C22⋊C4—1492no—
240C42—2982no—
241C42—1492no—
242C23—21no—
243C23—2981no—
244C23—2982no—
245C23—5962no—
246C23—11921no—
247C23—11921no—
248C23D4×D14911yescharacteristic
249Q8—21no—
250Q8—21no—
251Q8—2981no—
252Q8—1492no—
253D4—21no—
254D4—21no—
255D4—42no—
256D4—2984no—
257D4—2982no—
258D4—2981no—
259D4—2982no—
260D4—5962no—
261D4—1492no—
262D4—11922no—
263D4—11922no—
264C2×C4—22no—
265C2×C4—21no—
266C2×C4—42no—
267C2×C4—81no—
268C2×C4—2981no—
269C2×C4—2984no—
270C2×C4—1492no—
271C2×C4—1492no—
272C2×C4—11922no—
273C2×C4D4×D14912yes—
274C2×C4D4×D14911yescharacteristic
275C2×C4#1455873612yes—
276C2×C4C23×D14911yescharacteristic
277C8—22no—
278C8—2981no—
279C8—2981no—
280C22—21no—
281C22—21no—
282C22—41no—
283C22—41no—
284C22—41no—
285C22—2982no—
286C22—5961no—
287C22—5961no—
288C22—5962no—
289C22—5962no—
290C22—5962no—
291C22—11924no—
292C22#1801188412yes—
293C22C2×D4×D14911yescharacteristic
294C4—42no—
295C4—41no—
296C4—2982no—
297C4—2982no—
298C4—2982no—
299C4#1801188412yes—
300C4C2×D4×D14911yescharacteristic
301C4C2×#1455873611yescharacteristic
302C2—22no—
303C2—81no—
304C2—5962no—
305C2—11922no—
306C2C2×#1801188411yescharacteristic
307C2#2375042911yescharacteristic
308C2#2375043411yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#417×C149C2
socleC22×C149C22×D4
hypercenter#417D149
hypocenterC149#3045
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

Complements

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

NH ≅ G/Ntype
1. C2×#18011939C2semidirect
2. C2×#18011931C2semidirect
3. #23750189C2semidirect
4. #23750106C2semidirect
5. #23749850C2semidirect
6. #23749843C2semidirect
7. #23749824C2semidirect
8. #23749819C2semidirect
9. #23749653C2semidirect
10. C2×#18011831C2semidirect
11. #417×C149C2semidirect
16. C2×#14558726C22semidirect
18. C2×#14558724C22semidirect
19. C2×#14558723C22semidirect
21. C2×#14558721C22semidirect
28. #18011876C22semidirect
29. #18011873C22semidirect
34. #18011840C22semidirect
35. #18011840C22semidirect
41. #103×C149C22semidirect
42. #102×C149C22semidirect
45. #14558736D4semidirect
154. C149#3045semidirect
165. #417D149semidirect
194. #103C2×D149semidirect
197. #102C2×D149semidirect

Maximal subgroups

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

subgroupindex
C2×#180119392
C2×#180119312
#237501892
#237501062
#237498502
#237498432
#237498242
#237498192
#237496532
C2×#180118312
#417×C1492
#3045149