Finite Group Databasebeta

← #34056509

Subgroups — #34056509

Order 19072.

462 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 139 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
1D4×D596C211yesmaximal, characteristic
2#23749973C211yesmaximal, characteristic, complemented
3#23749943C212yesmaximal, complemented
4#23749912C211yesmaximal, characteristic, complemented
5#23749856C212yesmaximal, complemented
6#23749825C211yesmaximal, characteristic, complemented
7#23749775C212yesmaximal, complemented
8C4×#14558723C211yesmaximal, characteristic, complemented
9D4×#11924746C211yesmaximal, characteristic, complemented
10C2×#18011831C212yesmaximal, complemented
11#554×C149C211yesmaximal, characteristic, complemented
12C22×D596C2212yes—
13C2×D4×D149—21no—
14C2×#14558723C2211yescharacteristic
15C2×#14558723C2212yescomplemented
16C22×#11924746C2212yescomplemented
17#18011908C2211yescharacteristic
18#18011886—21no—
19#18011885C2212yes—
20#18011881—22no—
21C4×D596C2211yescharacteristic
22#18011842C2212yescomplemented
23#18011842C2211yescharacteristic, complemented
24C4⋊#11924746C2211yescharacteristic, complemented
25#18011835C2211yescharacteristic, complemented
26#18011831C2212yes—
27#18011831C2211yescharacteristic
28#18011831C2212yescomplemented
29#18011831C2212yescomplemented
30#18011831C2212yescomplemented
31C22⋊#11924746C2212yescomplemented
32C4×#11924746C2211yescharacteristic, complemented
33C4⋊Q8×C149C2211yescharacteristic, complemented
34#125×C149—21no—
35C22⋊Q8×C149—22no—
36C22⋊Q8×C149C2212yescomplemented
37C4×Q8×C149C2211yescharacteristic, complemented
38C4×D4×C149—21no—
39C4×D4×C149C2211yescharacteristic
40C2×C4⋊C4×C149C2212yescomplemented
41C23×D149—22no—
42C2×D596—24no—
43C2×D596—21no—
44C2×D596—22no—
45C2×D596—21no—
46C2×D596—42no—
47C2×D596C2312yes—
48C2×D596C2311yescharacteristic
49C2×C22⋊D149—22no—
50D4×D149—44no—
51C2×C4×D149—21no—
52#14558723—22no—
53#14558723—42no—
54C2×#11924746—42no—
55C2×#11924746C2311yescharacteristic
56C2×#11924746C2312yes—
57C2×#11924746C2311yescharacteristic
58C4⋊Dic149C2311yescharacteristic
59#14558713—21no—
60#14558713—22no—
61C2×Q8×C149—21no—
62C2×Q8×C149C2311yescharacteristic
63C2×D4×C149D411yescharacteristic
64C22×C4×C149—22no—
65C22×C4×C149C2312yes—
66C4⋊C4×C149—22no—
67C4⋊C4×C149—21no—
68C4⋊C4×C149—21no—
69C4⋊C4×C149—22no—
70C4⋊C4×C149D411yescharacteristic
71C4⋊C4×C149C2311yescharacteristic
72C4⋊C4×C149C2312yes—
73C22⋊C4×C149—22no—
74C22⋊C4×C149D412yes—
75C42×C149—21no—
76C42×C149C2311yescharacteristic
77C22×D149—21no—
78C22×D149—22no—
79C22×D149—44no—
80C22×D149—44no—
81C22×D149—82no—
82D596—22no—
83D596—21no—
84D596—22no—
85D596—44no—
86D596—42no—
87D596—81no—
88D596#4112yes—
89C22⋊D149—44no—
90C2×Dic149—21no—
91C4×D149—42no—
92#11924746—21no—
93#11924746—22no—
94#11924746—21no—
95C23×C149C2×D412yes—
96Q8×C149—21no—
97Q8×C149—21no—
98Q8×C149—81no—
99D4×C149SD1614yescomplemented
100C2×C4×C149—22no—
101C2×C4×C149—22no—
102C2×C4×C149—21no—
103C2×C4×C149—21no—
104C2×C4×C149—22no—
105C2×C4×C149—82no—
106C2×C4×C149C2×D411yescharacteristic
107C2×C4×C149C2×D412yes—
108C2×C4×C149C2×D411yescharacteristic
109C2×C4×C149C2411yescharacteristic
110C22×C149—22no—
111C22×C149—22no—
112C22×C149C2×SD1614yes—
113C22×C149C22×D411yescharacteristic
114C2×D149—22no—
115C2×D149—41no—
116C2×D149—41no—
117C2×D149—42no—
118C2×D149—42no—
119C2×D149—42no—
120C2×D149—88no—
121C4×C149—22no—
122C4×C149—21no—
123C4×C149—41no—
124C4×C149—41no—
125C4×C149—42no—
126C4×C149C2×SD1612yes—
127C4×C149C2×#4111yescharacteristic
128C4×C149H(5,𝔽2)11yescharacteristic
129Dic149—41no—
130C2×C149—24no—
131C2×C149#54611yescharacteristic
132C2×C149C22×SD1611yescharacteristic
133C2×C149#57611yescharacteristic
134D149—42no—
135D149—82no—
136C149#329511yescharacteristic, complemented, Sylow
137#3295—1491nomaximal, Sylow
138#554D14911yescharacteristic, complemented
139D42—1491no—
140#486—1491no—
141#481—1492no—
142#476—1491no—
143#465—1492no—
144#460—1491no—
145#450—1492no—
146C4×SD16—1491no—
147C8×D4—1491no—
148C2×#102—1492no—
149C22×D4—2981no—
150C22×D4—1492no—
151C2×SD16—1491no—
152C2×SD16—1492no—
153C22×C8—1492no—
154C4⋊Q8C2×D14911yescharacteristic, complemented
155#127—1491no—
156#125—21no—
157C22⋊Q8—22no—
158C22⋊Q8C2×D14912yescomplemented
159#121—2981no—
160#121—1492no—
161#120—2982no—
162C4×Q8C2×D14911yescharacteristic, complemented
163C4×D4—21no—
164C4×D4—1491no—
165C4×D4C2×D14911yescharacteristic
166C2×C4⋊C4C2×D14912yescomplemented
167#106—1491no—
168#106—1492no—
169C4⋊C8—1491no—
170#103—1491no—
171#102—1491no—
172#102—1492no—
173#102—1492no—
174#102—1492no—
175#102—1492no—
176C22⋊C8—1492no—
177C4×C8—1491no—
178C24—2982no—
179C2×Q8—21no—
180C2×Q8C22×D14911yescharacteristic
181C2×D4—2984no—
182C2×D4—2982no—
183C2×D4—2982no—
184C2×D4—2981no—
185C2×D4—2981no—
186C2×D4—5962no—
187C2×D4—5964no—
188C2×D4—1492no—
189C2×D4—1491no—
190C2×D4C22⋊D14911yescharacteristic
191C22×C4—22no—
192C22×C4—2981no—
193C22×C4C22×D14912yes—
194SD16—2982no—
195SD16—5962no—
196C2×C8—5962no—
197C2×C8—1491no—
198C2×C8—1491no—
199C2×C8—1492no—
200C4⋊C4—22no—
201C4⋊C4—21no—
202C4⋊C4—21no—
203C4⋊C4—22no—
204C4⋊C4—1491no—
205C4⋊C4C22⋊D14911yescharacteristic
206C4⋊C4C22×D14911yescharacteristic
207C4⋊C4C22×D14912yes—
208C22⋊C4—22no—
209C22⋊C4—2981no—
210C22⋊C4—2982no—
211C22⋊C4C22⋊D14912yes—
212C42—21no—
213C42C22×D14911yescharacteristic
214C23—2981no—
215C23—2982no—
216C23—5964no—
217C23—5964no—
218C23—11922no—
219C23C2×C22⋊D14912yes—
220Q8—21no—
221Q8—21no—
222Q8—81no—
223D4—2982no—
224D4—2981no—
225D4—2982no—
226D4—5964no—
227D4—5964no—
228D4—5962no—
229D4—1492no—
230D4—11921no—
231D4#1455872314yescomplemented
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—22no—
237C2×C4—82no—
238C2×C4—2981no—
239C2×C4—5962no—
240C2×C4C2×C22⋊D14911yescharacteristic
241C2×C4C2×C22⋊D14912yes—
242C2×C4C2×C22⋊D14911yescharacteristic
243C2×C4C23×D14911yescharacteristic
244C8—2981no—
245C8—2981no—
246C8—2982no—
247C22—22no—
248C22—22no—
249C22—2982no—
250C22—5961no—
251C22—5961no—
252C22—5962no—
253C22—5962no—
254C22—5962no—
255C22—11928no—
256C22C2×#1455872314yes—
257C22C22×C22⋊D14911yescharacteristic
258C4—21no—
259C4—22no—
260C4—41no—
261C4—42no—
262C4—41no—
263C4—5961no—
264C4C2×#1455872312yes—
265C4#41×D14911yescharacteristic
266C4#1801195711yescharacteristic
267C2—24no—
268C2—5962no—
269C2—11922no—
270C2#2375026311yescharacteristic
271C2C22×#1455872311yescharacteristic
272C2#2375042811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#554×C149C2
socleC22×C149C22×D4
prime radicalD4×D596C2
hypercenter#554D149
hypocenterC149#3295
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C4×D4 ◁ #554

Complements

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

NH ≅ G/Ntype
2. #23749973C2semidirect
3. #23749943C2semidirect
4. #23749912C2semidirect
5. #23749856C2semidirect
6. #23749825C2semidirect
7. #23749775C2semidirect
8. C4×#14558723C2semidirect
9. D4×#11924746C2semidirect
10. C2×#18011831C2semidirect
11. #554×C149C2semidirect
15. C2×#14558723C22semidirect
16. C22×#11924746C22semidirect
22. #18011842C22semidirect
23. #18011842C22semidirect
24. C4⋊#11924746C22semidirect
25. #18011835C22semidirect
28. #18011831C22semidirect
29. #18011831C22semidirect
30. #18011831C22semidirect
31. C22⋊#11924746C22semidirect
32. C4×#11924746C22semidirect
33. C4⋊Q8×C149C22semidirect
36. C22⋊Q8×C149C22semidirect
37. C4×Q8×C149C22semidirect
40. C2×C4⋊C4×C149C22semidirect
99. D4×C149SD16semidirect
136. C149#3295semidirect
138. #554D149semidirect
154. C4⋊Q8C2×D149semidirect
158. C22⋊Q8C2×D149semidirect
162. C4×Q8C2×D149semidirect
166. C2×C4⋊C4C2×D149semidirect
231. D4#14558723semidirect

Maximal subgroups

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

subgroupindex
D4×D5962
#237499732
#237499432
#237499122
#237498562
#237498252
#237497752
C4×#145587232
D4×#119247462
C2×#180118312
#554×C1492
#3295149