Finite Group Databasebeta

← #34054235

Subgroups — #34054235

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×#18011937C211yesmaximal, characteristic, complemented
2C2×#18011933C211yesmaximal, characteristic, complemented
3#23750192C211yesmaximal, characteristic, complemented
4#23750106C211yesmaximal, characteristic, complemented
5#23749846C212yesmaximal, complemented
6#23749839C212yesmaximal, complemented
7#23749824C212yesmaximal, complemented
8#23749819C212yesmaximal, complemented
9#23749651C211yesmaximal, characteristic, complemented
10#23749624C211yesmaximal, characteristic, complemented
11C2×#102×C149C211yesmaximal, characteristic, complemented
12C2×#14558736C2211yescharacteristic
13C2×#14558736C2211yescharacteristic
14#18011937—24no—
15#18011933—24no—
16C2×Dic596C2211yescharacteristic, complemented
17C2×#14558725C2211yescharacteristic, complemented
18C2×#14558725C2211yescharacteristic, complemented
19C2×#14558724C2212yes—
20C2×D1192C2211yescharacteristic, complemented
21C2×#14558721C2212yes—
22C2×#14558720C2211yescharacteristic
23#18011907C2212yes—
24#18011898C2212yes—
25#18011882—21no—
26#18011882—21no—
27#18011880—22no—
28#18011876C2212yescomplemented
29#18011873C2212yescomplemented
30C4×C22⋊D149—22no—
31#18011870C2211yescharacteristic
32#18011869—21no—
33C4⋊C4×D149—21no—
34#18011840C2212yescomplemented
35#18011840C2212yescomplemented
36#18011834C2212yescomplemented
37#18011831C2212yescomplemented
38C22×D4×C149C2211yescharacteristic
39C22×C8×C149C2211yescharacteristic
40C2×C4⋊C4×C149C2211yescharacteristic
41#102×C149C2212yes—
42#102×C149C2212yes—
43#14558736—22no—
44#14558736—22no—
45#14558736—22no—
46#14558736D414yescomplemented
47C2×Dic298C2311yescharacteristic
48C2×Dic298C2311yescharacteristic
49C2×D596C2311yescharacteristic
50C2×D596C2311yescharacteristic
51C2×C22⋊D149—22no—
52C2×C22⋊D149—22no—
53C2×C22⋊D149—21no—
54C2×C22⋊D149—21no—
55C2×C4×D149—22no—
56C2×C4×D149—21no—
57C2×C4×D149—21no—
58Dic596—22no—
59#14558725—22no—
60#14558725—22no—
61#14558724—24no—
62D1192—22no—
63#14558721—24no—
64#14558720—22no—
65C2×#11924746C2312yes—
66C4⋊Dic149D411yescharacteristic
67C4⋊Dic149D411yescharacteristic
68#14558715—22no—
69C22⋊Dic149—22no—
70C22⋊Dic149—22no—
71C22⋊Dic149D412yes—
72#14558713—22no—
73C4×Dic149—22no—
74C4×Dic149C2312yes—
75C24×C149—21no—
76C2×D4×C149—22no—
77C2×D4×C149—21no—
78C2×D4×C149—22no—
79C2×D4×C149C2312yes—
80C22×C4×C149—21no—
81C22×C4×C149C2311yescharacteristic
82C2×C8×C149—22no—
83C2×C8×C149C2311yescharacteristic
84C2×C8×C149C2311yescharacteristic
85C4⋊C4×C149—21no—
86C4⋊C4×C149C2312yes—
87C22×D149—21no—
88C22×D149—21no—
89Dic298—21no—
90Dic298—21no—
91Dic298—21no—
92Dic298C2×D412yes—
93D596—21no—
94D596—21no—
95D596—21no—
96D596C2×D412yes—
97C22⋊D149—24no—
98C22⋊D149—42no—
99C22⋊D149—82no—
100C22⋊D149—82no—
101C2×Dic149—21no—
102C2×Dic149—21no—
103C2×Dic149C2×D412yes—
104C2×Dic149C2×D412yes—
105C4×D149—24no—
106C4×D149—42no—
107C4×D149—82no—
108#11924746—22no—
109C23×C149—22no—
110C23×C149—42no—
111C23×C149—81no—
112C23×C149—81no—
113C23×C149C2×D411yescharacteristic
114D4×C149—22no—
115D4×C149—22no—
116D4×C149—42no—
117C2×C4×C149—22no—
118C2×C4×C149—81no—
119C2×C4×C149C2×D411yescharacteristic
120C2×C4×C149C2×D412yes—
121C2×C4×C149#4112yes—
122C2×C4×C149C2411yescharacteristic
123C8×C149—21no—
124C8×C149—21no—
125C22×C149—21no—
126C22×C149—21no—
127C22×C149—42no—
128C22×C149—42no—
129C22×C149—42no—
130C22×C149—84no—
131C22×C149#12112yes—
132C22×C149C22×D411yescharacteristic
133C2×D149—22no—
134C2×D149—41no—
135C2×D149—41no—
136C2×D149—41no—
137C2×D149—41no—
138C2×D149—41no—
139C4×C149—42no—
140C4×C149#12112yes—
141C4×C149C22×D411yescharacteristic
142C4×C149C2×#4111yescharacteristic
143Dic149—22no—
144Dic149—22no—
145Dic149—22no—
146Dic149—41no—
147C2×C149—22no—
148C2×C149—82no—
149C2×C149C2×#12111yescharacteristic
150C2×C149#57611yescharacteristic
151C2×C149#57711yescharacteristic
152D149—42no—
153D149—81no—
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#417—1491no—
166C2×#102D14911yescharacteristic, complemented
167C2×#41—1491no—
168C2×#41—1491no—
169C22×D4C2×D14911yescharacteristic
170AGL(1,ℤ/8)—2984no—
171#135—2984no—
172C2×Q16—1491no—
173C2×SD16—1492no—
174C2×SD16—1491no—
175C2×SD16—1491no—
176C2×D8—1492no—
177C2×D8—1491no—
178C2×M16—1491no—
179C22×C8C2×D14911yescharacteristic
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#103—1492no—
195#102—1492no—
196#102C2×D14912yes—
197#102C2×D14912yes—
198C24—21no—
199#41—2982no—
200#41—2982no—
201#41—2982no—
202#41—1494no—
203C2×Q8—1491no—
204C2×Q8—1491no—
205C2×D4—22no—
206C2×D4—21no—
207C2×D4—22no—
208C2×D4—2981no—
209C2×D4—2981no—
210C2×D4—2982no—
211C2×D4—2982no—
212C2×D4—1491no—
213C2×D4—1491no—
214C2×D4C22×D14912yes—
215C22×C4—21no—
216C22×C4—2982no—
217C22×C4—2981no—
218C22×C4—2981no—
219C22×C4C22×D14911yescharacteristic
220Q16—2982no—
221SD16—2982no—
222SD16—2982no—
223SD16—2984no—
224D8—2982no—
225D8—2984no—
226M16—2982no—
227C2×C8—22no—
228C2×C8—1492no—
229C2×C8C22×D14911yescharacteristic
230C2×C8C22×D14911yescharacteristic
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—22no—
243C23—42no—
244C23—81no—
245C23—81no—
246C23—2981no—
247C23—2981no—
248C23D4×D14911yescharacteristic
249Q8—2981no—
250Q8—2981no—
251Q8—2981no—
252Q8—1492no—
253D4—22no—
254D4—22no—
255D4—42no—
256D4—2984no—
257D4—2981no—
258D4—2981no—
259D4—2981no—
260D4—5962no—
261D4—1492no—
262D4—11922no—
263D4—11922no—
264C2×C4—22no—
265C2×C4—81no—
266C2×C4—2981no—
267C2×C4—2984no—
268C2×C4—2981no—
269C2×C4—5962no—
270C2×C4—1492no—
271C2×C4—1492no—
272C2×C4—11922no—
273C2×C4D4×D14912yes—
274C2×C4D4×D14911yescharacteristic
275C2×C4#1455873612yes—
276C2×C4C23×D14911yescharacteristic
277C8—21no—
278C8—21no—
279C8—2982no—
280C22—21no—
281C22—21no—
282C22—42no—
283C22—42no—
284C22—42no—
285C22—84no—
286C22—2982no—
287C22—5961no—
288C22—5961no—
289C22—5961no—
290C22—5961no—
291C22—5961no—
292C22#1801188412yes—
293C22C2×D4×D14911yescharacteristic
294C4—42no—
295C4—2982no—
296C4—2982no—
297C4—2982no—
298C4—5961no—
299C4#1801188412yes—
300C4C2×D4×D14911yescharacteristic
301C4C2×#1455873611yescharacteristic
302C2—22no—
303C2—82no—
304C2—5962no—
305C2—11921no—
306C2C2×#1801188411yescharacteristic
307C2#2375042611yescharacteristic
308C2#2375043111yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
FittingC2×#102×C149C2
socleC22×C149C22×D4
hypercenterC2×#102D149
hypocenterC149#3045
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
1. C2×#18011937C2semidirect
2. C2×#18011933C2semidirect
3. #23750192C2semidirect
4. #23750106C2semidirect
5. #23749846C2semidirect
6. #23749839C2semidirect
7. #23749824C2semidirect
8. #23749819C2semidirect
9. #23749651C2semidirect
10. #23749624C2semidirect
11. C2×#102×C149C2semidirect
16. C2×Dic596C22semidirect
17. C2×#14558725C22semidirect
18. C2×#14558725C22semidirect
20. C2×D1192C22semidirect
28. #18011876C22semidirect
29. #18011873C22semidirect
34. #18011840C22semidirect
35. #18011840C22semidirect
36. #18011834C22semidirect
37. #18011831C22semidirect
46. #14558736D4semidirect
154. C149#3045semidirect
166. C2×#102D149semidirect

Maximal subgroups

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

subgroupindex
C2×#180119372
C2×#180119332
#237501922
#237501062
#237498462
#237498392
#237498242
#237498192
#237496512
#237496242
C2×#102×C1492
#3045149