Finite Group Databasebeta

← #34055076

Subgroups — #34055076

Order 19072.

400 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 117 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#23750180C211yesmaximal, characteristic, complemented
2#124×D149C211yesmaximal, characteristic
3#23749987C211yesmaximal, characteristic, complemented
4#23749985C211yesmaximal, characteristic, complemented
5#23749984C211yesmaximal, characteristic, complemented
6#23749981C212yesmaximal, complemented
7#23749978C212yesmaximal, complemented
8#23749632C212yesmaximal, complemented
9#23749628C212yesmaximal
10#23749577C211yesmaximal, characteristic, complemented
11#489×C149C211yesmaximal, characteristic, complemented
12C2×Q8×D149C2211yescharacteristic
13C2×D4×D149C2211yescharacteristic
14C2×#14558719C2212yes—
15#18011911C2211yescharacteristic, complemented
16#18011902C2212yescomplemented
17#18011900C2211yescharacteristic
18#18011899C2211yescharacteristic
19#18011898C2211yescharacteristic
20#18011897—21no—
21#18011897—21no—
22#18011891—21no—
23#18011887—21no—
24Q8×Dic149—21no—
25#18011876—21no—
26#18011869C2212yes—
27C22⋊C4×D149—21no—
28C22⋊C4×D149—21no—
29C42×D149C2211yescharacteristic
30#18011836C2212yescomplemented
31#18011835C2212yescomplemented
32#18011834C2212yescomplemented
33#18011833C2212yes—
34#18011832C2212yes—
35#18011831C2212yes—
36#18011822C2211yescharacteristic, complemented
37C8×Dic149C2212yescomplemented
38C4⋊Q8×C149C2211yescharacteristic, complemented
39#124×C149C2211yescharacteristic
40#103×C149C2212yescomplemented
41#102×C149C2212yes—
42#97×C149C2211yescharacteristic, complemented
43C23×D149—21no—
44C2×Dic298—21no—
45C2×Dic298—21no—
46C2×Dic298C2311yescharacteristic
47Q8×D149—24no—
48C2×D596C2311yescharacteristic
49C2×C22⋊D149—21no—
50D4×D149—24no—
51C2×C4×D149—21no—
52C2×C4×D149D411yescharacteristic
53C2×C4×D149D411yescharacteristic
54C2×C4×D149C2311yescharacteristic
55#14558719—24no—
56C2×#11924746C2312yes—
57C4⋊Dic149—22no—
58C4⋊Dic149—21no—
59C4⋊Dic149C2312yes—
60#14558715—22no—
61C22⋊Dic149—21no—
62C22⋊Dic149—21no—
63#14558713—22no—
64#14558713—21no—
65#14558713—21no—
66#14558713—21no—
67#14558713—21no—
68C4×Dic149—22no—
69C4×Dic149D411yescharacteristic
70C4×Dic149D411yescharacteristic
71C4×Dic149C2311yescharacteristic
72C2×Q8×C149—21no—
73C2×Q8×C149C2311yescharacteristic
74C2×D4×C149C2311yescharacteristic
75C2×C8×C149C2312yes—
76C4⋊C4×C149—21no—
77C4⋊C4×C149C2312yes—
78C22⋊C4×C149—21no—
79C22⋊C4×C149—21no—
80C42×C149C2311yescharacteristic
81C22×D149—21no—
82C22×D149—42no—
83C22×D149—42no—
84C22×D149—42no—
85C22×D149C2×D411yescharacteristic
86Dic298—22no—
87Dic298—42no—
88Dic298—42no—
89D596—22no—
90C22⋊D149—42no—
91C2×Dic149—21no—
92C2×Dic149—22no—
93C2×Dic149C2×D411yescharacteristic
94C2×Dic149C2×D411yescharacteristic
95C2×Dic149C2×D411yescharacteristic
96C4×D149—41no—
97C4×D149—41no—
98C4×D149—42no—
99C4×D149#4114yes—
100#11924746—22no—
101C23×C149—21no—
102Q8×C149—22no—
103Q8×C149—42no—
104D4×C149—22no—
105C2×C4×C149—21no—
106C2×C4×C149—22no—
107C2×C4×C149C2×D411yescharacteristic
108C2×C4×C149C2×D411yescharacteristic
109C2×C4×C149C2411yescharacteristic
110C8×C149—22no—
111C22×C149—41no—
112C22×C149—41no—
113C22×C149—41no—
114C22×C149C22×D411yescharacteristic
115C2×D149—21no—
116C2×D149—21no—
117C2×D149—41no—
118C2×D149—41no—
119C2×D149—41no—
120C2×D149—84no—
121C2×D149#12412yes—
122C4×C149—21no—
123C4×C149—21no—
124C4×C149—41no—
125C4×C149—42no—
126C4×C149C2×#4112yes—
127Dic149—21no—
128Dic149—21no—
129Dic149—41no—
130Dic149—42no—
131Dic149#12412yes—
132C2×C149—81no—
133C2×C149C2×#12411yescharacteristic
134C2×C149#57511yescharacteristic
135C2×C149#57511yescharacteristic
136D149—22no—
137D149—81no—
138C149#314011yescharacteristic, complemented, Sylow
139#3140—1491nomaximal, Sylow
140#533—1491no—
141C2×#124—1491no—
142#489—1491no—
143#489—1491no—
144#489—1491no—
145#489D14911yescharacteristic, complemented
146#488—1492no—
147#488—1492no—
148#419—1492no—
149#418—1492no—
150C4×M16—1491no—
151C22×Q8—1491no—
152C22×D4—1491no—
153C2×M16—1492no—
154C4⋊Q8—1491no—
155C4⋊Q8C2×D14911yescharacteristic, complemented
156#125—1492no—
157#124—2981no—
158#124—2981no—
159#124—1491no—
160#124—1491no—
161#124—1491no—
162#124C2×D14911yescharacteristic
163C22⋊Q8—2981no—
164C22⋊Q8—2981no—
165C4×Q8—2981no—
166C4×Q8—2981no—
167#117—1492no—
168C2×C22⋊C4—2981no—
169C2×C22⋊C4—2981no—
170C2×C42—1491no—
171#103—1492no—
172#103—1492no—
173#103—1492no—
174#103C2×D14912yescomplemented
175#102—1492no—
176#102—1492no—
177#102—1492no—
178#102C2×D14912yes—
179#97—1491no—
180#97C2×D14911yescharacteristic, complemented
181C4×C8—1492no—
182C24—2981no—
183C2×Q8—21no—
184C2×Q8—2981no—
185C2×Q8—2981no—
186C2×Q8—2984no—
187C2×Q8—1491no—
188C2×Q8C22×D14911yescharacteristic
189C2×D4—2984no—
190C2×D4—2981no—
191C2×D4—1491no—
192C2×D4C22×D14911yescharacteristic
193C22×C4—2981no—
194C22×C4—1491no—
195C22×C4—1491no—
196C22×C4—1491no—
197M16—2984no—
198C2×C8—1492no—
199C2×C8C22×D14912yes—
200C4⋊C4—21no—
201C4⋊C4—2982no—
202C4⋊C4—2982no—
203C4⋊C4—2981no—
204C4⋊C4—1492no—
205C4⋊C4C22×D14912yes—
206C22⋊C4—21no—
207C22⋊C4—21no—
208C22⋊C4—2982no—
209C22⋊C4—2981no—
210C22⋊C4—2981no—
211C22⋊C4—2981no—
212C22⋊C4—2981no—
213C22⋊C4—2981no—
214C22⋊C4—2981no—
215C42—2982no—
216C42—1491no—
217C42—1491no—
218C42—1491no—
219C42C22×D14911yescharacteristic
220C23—21no—
221C23—2981no—
222C23—5962no—
223C23—5962no—
224C23—5962no—
225C23—1491no—
226Q8—22no—
227Q8—42no—
228Q8—2982no—
229Q8—5962no—
230Q8—5962no—
231D4—22no—
232D4—2982no—
233D4—5962no—
234C2×C4—22no—
235C2×C4—21no—
236C2×C4—2982no—
237C2×C4—2981no—
238C2×C4—5961no—
239C2×C4—5961no—
240C2×C4—5962no—
241C2×C4—1491no—
242C2×C4—1491no—
243C2×C4—1491no—
244C2×C4—1494no—
245C2×C4D4×D14911yescharacteristic
246C2×C4D4×D14911yescharacteristic
247C2×C4C23×D14911yescharacteristic
248C8—22no—
249C8—2982no—
250C22—41no—
251C22—41no—
252C22—41no—
253C22—2981no—
254C22—2981no—
255C22—5961no—
256C22—5961no—
257C22—5961no—
258C22—1492no—
259C22—11924no—
260C22C2×D4×D14911yescharacteristic
261C4—21no—
262C4—21no—
263C4—42no—
264C4—41no—
265C4—2981no—
266C4—2981no—
267C4—5962no—
268C4—5961no—
269C4—1492no—
270C4#41×D14912yes—
271C2—81no—
272C2—2982no—
273C2—11921no—
274C2#124×D14911yescharacteristic
275C2#2375042111yescharacteristic
276C2#2375042411yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#489×C149C2
socleC22×C149C22×D4
prime radicalC2×D4×D149C22
hypercenter#489D149
hypocenterC149#3140
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
1. #23750180C2semidirect
3. #23749987C2semidirect
4. #23749985C2semidirect
5. #23749984C2semidirect
6. #23749981C2semidirect
7. #23749978C2semidirect
8. #23749632C2semidirect
10. #23749577C2semidirect
11. #489×C149C2semidirect
15. #18011911C22semidirect
16. #18011902C22semidirect
30. #18011836C22semidirect
31. #18011835C22semidirect
32. #18011834C22semidirect
36. #18011822C22semidirect
37. C8×Dic149C22semidirect
38. C4⋊Q8×C149C22semidirect
40. #103×C149C22semidirect
42. #97×C149C22semidirect
138. C149#3140semidirect
145. #489D149semidirect
155. C4⋊Q8C2×D149semidirect
174. #103C2×D149semidirect
180. #97C2×D149semidirect

Maximal subgroups

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

subgroupindex
#237501802
#124×D1492
#237499872
#237499852
#237499842
#237499812
#237499782
#237496322
#237496282
#237495772
#489×C1492
#3140149