Finite Group Databasebeta

← #34054226

Subgroups — #34054226

Order 19072.

504 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 141 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×#18011931C211yesmaximal, characteristic, complemented
3#23750105C211yesmaximal, characteristic, complemented
4#23749844C212yesmaximal, complemented
5#23749837C212yesmaximal, complemented
6#23749822C212yesmaximal, complemented
7#23749817C212yesmaximal, complemented
8#23749652C211yesmaximal, characteristic, complemented
9#23749626C211yesmaximal, characteristic, complemented
10C2×#18011832C211yesmaximal, characteristic, complemented
11#535×C149C211yesmaximal, characteristic, complemented
12C2×#14558736C2211yescharacteristic
13#18011937—24no—
14#18011931—24no—
15C2×#14558726C2211yescharacteristic, complemented
16C2×#14558724C2212yes—
17C2×#14558724C2211yescharacteristic, complemented
18C2×#14558723C2211yescharacteristic, complemented
19C2×#14558721C2212yes—
20C2×#14558721C2211yescharacteristic, complemented
21C2×#14558720C2211yescharacteristic
22C22×#11924746C2211yescharacteristic
23C4×Dic298C2212yescomplemented
24C4×D596C2212yescomplemented
25#18011871—22no—
26#18011869—21no—
27C2×C4⋊Dic149C2211yescharacteristic
28C4⋊C4×D149—21no—
29C4⋊#11924746C2212yescomplemented
30C4⋊#11924746C2212yescomplemented
31#18011835C2212yescomplemented
32#18011832C2212yes—
33#18011832C2212yes—
34#18011832C2212yescomplemented
35C2×#41×C149C2211yescharacteristic
36C22×D4×C149C2211yescharacteristic
37#127×C149C2212yes—
38#124×C149C2212yes—
39#121×C149—21no—
40#121×C149—21no—
41#120×C149—22no—
42#117×C149C2211yescharacteristic
43#14558736—22no—
44#14558736D414yescomplemented
45C2×Dic298C2311yescharacteristic
46C2×D596C2311yescharacteristic
47C2×C22⋊D149—21no—
48C22×Dic149—21no—
49C2×C4×D149—21no—
50C2×C4×D149—22no—
51#14558726—22no—
52#14558724—24no—
53#14558724—22no—
54#14558723—22no—
55#14558721—24no—
56#14558721—22no—
57#14558720—22no—
58C2×#11924746—22no—
59C2×#11924746C2311yescharacteristic
60C2×#11924746C2311yescharacteristic
61C2×#11924746C2312yes—
62C4⋊Dic149—21no—
63C4⋊Dic149C2312yes—
64#14558715—22no—
65#14558713—22no—
66C4×Dic149—22no—
67C24×C149—21no—
68#41×C149—22no—
69#41×C149—22no—
70C2×Q8×C149C2311yescharacteristic
71C2×D4×C149—21no—
72C2×D4×C149—22no—
73C2×D4×C149—21no—
74C2×D4×C149—22no—
75C2×D4×C149—22no—
76C2×D4×C149—22no—
77C2×D4×C149C2312yes—
78C2×D4×C149C2311yescharacteristic
79C22×C4×C149—21no—
80C22×C4×C149C2311yescharacteristic
81C4⋊C4×C149D411yescharacteristic
82C4⋊C4×C149D411yescharacteristic
83C22⋊C4×C149—22no—
84C22⋊C4×C149—22no—
85C22⋊C4×C149D412yes—
86C42×C149C2312yes—
87C22×D149—21no—
88Dic298—21no—
89Dic298C2×D412yes—
90D596—21no—
91D596C2×D412yes—
92C22⋊D149—24no—
93C2×Dic149—21no—
94C2×Dic149—22no—
95C2×Dic149—81no—
96C4×D149—24no—
97C4×D149—82no—
98#11924746—22no—
99#11924746—21no—
100#11924746—21no—
101C23×C149—22no—
102C23×C149—21no—
103C23×C149—42no—
104C23×C149—81no—
105C23×C149—81no—
106C23×C149C2×D411yescharacteristic
107Q8×C149—21no—
108Q8×C149—21no—
109D4×C149—22no—
110D4×C149—21no—
111D4×C149—22no—
112D4×C149—21no—
113D4×C149—42no—
114D4×C149—42no—
115D4×C149—82no—
116D4×C149—82no—
117C2×C4×C149—21no—
118C2×C4×C149—42no—
119C2×C4×C149C2×D412yes—
120C2×C4×C149C2×D412yes—
121C2×C4×C149C2×D412yes—
122C2×C4×C149C2×D411yescharacteristic
123C2×C4×C149#4112yes—
124C2×C4×C149C2411yescharacteristic
125C22×C149—21no—
126C22×C149—21no—
127C22×C149—41no—
128C22×C149—42no—
129C22×C149—41no—
130C22×C149—42no—
131C22×C149—41no—
132C22×C149—42no—
133C22×C149—84no—
134C22×C149#12112yes—
135C22×C149C22×D411yescharacteristic
136C2×D149—22no—
137C2×D149—41no—
138C2×D149—41no—
139C4×C149—22no—
140C4×C149—22no—
141C4×C149—41no—
142C4×C149#12112yes—
143C4×C149C22×D411yescharacteristic
144C4×C149C2×#4111yescharacteristic
145Dic149—22no—
146Dic149—42no—
147C2×C149—22no—
148C2×C149—81no—
149C2×C149—82no—
150C2×C149C2×#12111yescharacteristic
151C2×C149#57611yescharacteristic
152C2×C149#57711yescharacteristic
153D149—42no—
154C149#304511yescharacteristic, complemented, Sylow
155#3045—1491nomaximal, Sylow
156C2×AGL(1,ℤ/8)—1491no—
157C2×#135—1491no—
158#535D14911yescharacteristic, complemented
159#520—1491no—
160#464—1492no—
161#463—1492no—
162#460—1492no—
163#459—1492no—
164#424—1491no—
165#417—1491no—
166C2×#102—1491no—
167C2×#41—1491no—
168C2×#41C2×D14911yescharacteristic
169C22×D4C2×D14911yescharacteristic
170AGL(1,ℤ/8)—2984no—
171#135—2984no—
172C2×Q16—1491no—
173C2×SD16—1491no—
174C2×SD16—1492no—
175C2×SD16—1491no—
176C2×D8—1492no—
177C2×D8—1491no—
178C2×M16—1491no—
179C22×C8—1491no—
180#127C2×D14912yes—
181#124C2×D14912yes—
182#121—21no—
183#121—21no—
184#120—22no—
185C4×Q8—1492no—
186C4×D4—2982no—
187C4×D4—1492no—
188#117—2981no—
189#117C2×D14911yescharacteristic
190C2×C4⋊C4—2981no—
191C2×C4⋊C4—1491no—
192C4⋊C8—1492no—
193C4⋊C8—1492no—
194#103—1492no—
195#102—1492no—
196#102—1492no—
197#102—1492no—
198C24—21no—
199#41—22no—
200#41—22no—
201#41—2982no—
202#41—1494no—
203C2×Q8—1491no—
204C2×Q8C22×D14911yescharacteristic
205C2×D4—21no—
206C2×D4—22no—
207C2×D4—21no—
208C2×D4—22no—
209C2×D4—22no—
210C2×D4—22no—
211C2×D4—2981no—
212C2×D4—1491no—
213C2×D4C22×D14912yes—
214C2×D4C22×D14911yescharacteristic
215C22×C4—21no—
216C22×C4—2981no—
217C22×C4—2981no—
218C22×C4—2982no—
219C22×C4C22×D14911yescharacteristic
220Q16—2982no—
221SD16—2982no—
222SD16—2984no—
223SD16—2982no—
224D8—2982no—
225D8—2984no—
226M16—2982no—
227C2×C8—2982no—
228C2×C8—1491no—
229C2×C8—1491no—
230C2×C8—1492no—
231C4⋊C4—2981no—
232C4⋊C4—2982no—
233C4⋊C4—1492no—
234C4⋊C4C22⋊D14911yescharacteristic
235C4⋊C4C22⋊D14911yescharacteristic
236C22⋊C4—22no—
237C22⋊C4—22no—
238C22⋊C4—2982no—
239C22⋊C4C22⋊D14912yes—
240C42—2982no—
241C42C22×D14912yes—
242C23—22no—
243C23—21no—
244C23—42no—
245C23—81no—
246C23—81no—
247C23—2981no—
248C23C2×C22⋊D14911yescharacteristic
249Q8—21no—
250Q8—21no—
251Q8—2981no—
252Q8—1492no—
253D4—22no—
254D4—21no—
255D4—22no—
256D4—21no—
257D4—42no—
258D4—42no—
259D4—82no—
260D4—82no—
261D4—2984no—
262D4—2981no—
263D4—1492no—
264C2×C4—21no—
265C2×C4—42no—
266C2×C4—2981no—
267C2×C4—2984no—
268C2×C4—2982no—
269C2×C4—11922no—
270C2×C4—11921no—
271C2×C4D4×D14912yes—
272C2×C4C2×C22⋊D14912yes—
273C2×C4C2×C22⋊D14912yes—
274C2×C4C2×C22⋊D14911yescharacteristic
275C2×C4#1455873512yes—
276C2×C4C23×D14911yescharacteristic
277C8—2981no—
278C8—2981no—
279C8—2982no—
280C22—21no—
281C22—21no—
282C22—41no—
283C22—42no—
284C22—41no—
285C22—42no—
286C22—41no—
287C22—42no—
288C22—84no—
289C22—2982no—
290C22—5961no—
291C22—5961no—
292C22#1801188212yes—
293C22C22×C22⋊D14911yescharacteristic
294C4—22no—
295C4—22no—
296C4—41no—
297C4—2982no—
298C4—5962no—
299C4#1801188212yes—
300C4C2×D4×D14911yescharacteristic
301C4C2×#1455873511yescharacteristic
302C2—22no—
303C2—82no—
304C2—81no—
305C2—5962no—
306C2C2×#1801188211yescharacteristic
307C2#2375042811yescharacteristic
308C2#2375043611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#535×C149C2
socleC22×C149C22×D4
hypercenter#535D149
hypocenterC149#3045
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ #117 ◁ #535

Complements

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

NH ≅ G/Ntype
1. C2×#18011937C2semidirect
2. C2×#18011931C2semidirect
3. #23750105C2semidirect
4. #23749844C2semidirect
5. #23749837C2semidirect
6. #23749822C2semidirect
7. #23749817C2semidirect
8. #23749652C2semidirect
9. #23749626C2semidirect
10. C2×#18011832C2semidirect
11. #535×C149C2semidirect
15. C2×#14558726C22semidirect
17. C2×#14558724C22semidirect
18. C2×#14558723C22semidirect
20. C2×#14558721C22semidirect
23. C4×Dic298C22semidirect
24. C4×D596C22semidirect
29. C4⋊#11924746C22semidirect
30. C4⋊#11924746C22semidirect
31. #18011835C22semidirect
34. #18011832C22semidirect
44. #14558736D4semidirect
154. C149#3045semidirect
158. #535D149semidirect

Maximal subgroups

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

subgroupindex
C2×#180119372
C2×#180119312
#237501052
#237498442
#237498372
#237498222
#237498172
#237496522
#237496262
C2×#180118322
#535×C1492
#3045149