Finite Group Databasebeta

← #34054214

Subgroups — #34054214

Order 19072.

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

normal subgroups only

This group has 490 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
1C22×#14558723C211yesmaximal, characteristic, complemented
2#23750189C211yesmaximal, characteristic
3#23750103C211yesmaximal, characteristic, complemented
4#23749849C214yesmaximal, complemented
5#23749823C214yesmaximal, complemented
6#23749653C211yesmaximal, characteristic, complemented
7#23749631C211yesmaximal, characteristic, complemented
8#23749621C211yesmaximal, characteristic, complemented
9C2×#137×C149C211yesmaximal, characteristic, complemented
10C22×D596C2211yescharacteristic
11C2×#14558723—24no—
12C2×#14558723C2214yes—
13C22×#11924746C2211yescharacteristic
14#18011907C2212yes—
15#18011900C2212yes—
16#18011885—22no—
17#18011879—22no—
18Q8×Dic149—22no—
19Q8×Dic149C2214yescomplemented
20#18011870—22no—
21#18011870C2211yescharacteristic
22#18011870C2211yescharacteristic
23#18011840C2214yescomplemented
24#18011835C2212yescomplemented
25#18011833C2214yes—
26#18011832C2212yescomplemented
27C2×#41×C149C2211yescharacteristic
28C22×Q8×C149C2211yescharacteristic
29#137×C149—24no—
30C2×Q16×C149C2212yescomplemented
31C2×SD16×C149C2212yescomplemented
32C2×M16×C149C2211yescharacteristic
33C23×D149—21no—
34C2×D596—22no—
35C2×D596—21no—
36C2×D596—22no—
37C2×D596C2312yes—
38C2×C22⋊D149—24no—
39#14558723—28no—
40C2×#11924746—22no—
41C2×#11924746C2312yes—
42C4⋊Dic149—24no—
43C4⋊Dic149D412yes—
44C4⋊Dic149C2312yes—
45C22⋊Dic149—21no—
46C22⋊Dic149D412yes—
47#14558713—24no—
48C4×Dic149—24no—
49C4×Dic149—21no—
50C4×Dic149C2312yes—
51#41×C149—22no—
52#41×C149—22no—
53C2×Q8×C149—21no—
54C2×Q8×C149—22no—
55C2×Q8×C149D414yescomplemented
56C2×Q8×C149C2311yescharacteristic
57C2×Q8×C149C2312yes—
58C2×D4×C149—21no—
59C2×D4×C149C2311yescharacteristic
60C22×C4×C149—21no—
61C22×C4×C149—21no—
62C22×C4×C149C2311yescharacteristic
63Q16×C149—24no—
64SD16×C149—24no—
65M16×C149—22no—
66C2×C8×C149C2312yes—
67C22×D149—22no—
68C22×D149—42no—
69C22×D149—82no—
70D596—22no—
71D596—22no—
72D596—42no—
73C22⋊D149—84no—
74C2×Dic149—22no—
75C2×Dic149C2×D414yes—
76#11924746—22no—
77C23×C149—21no—
78C23×C149C2×D411yescharacteristic
79Q8×C149—24no—
80Q8×C149—22no—
81Q8×C149—21no—
82Q8×C149—21no—
83Q8×C149C2×D414yes—
84D4×C149—21no—
85D4×C149—21no—
86D4×C149—42no—
87C2×C4×C149—24no—
88C2×C4×C149—22no—
89C2×C4×C149—21no—
90C2×C4×C149—42no—
91C2×C4×C149C2×D411yescharacteristic
92C2×C4×C149C2×D412yes—
93C2×C4×C149#4112yes—
94C2×C4×C149C2411yescharacteristic
95C8×C149—22no—
96C22×C149—22no—
97C22×C149—41no—
98C22×C149—42no—
99C22×C149#12112yes—
100C22×C149C22×D411yescharacteristic
101C2×D149—42no—
102C2×D149—44no—
103C2×D149—84no—
104C4×C149—24no—
105C4×C149—41no—
106C4×C149#12112yes—
107C4×C149C22×D411yescharacteristic
108C4×C149C2×#4111yescharacteristic
109Dic149—24no—
110Dic149—42no—
111C2×C149—22no—
112C2×C149—81no—
113C2×C149C2×#12111yescharacteristic
114C2×C149#57712yes—
115D149—82no—
116C149#304311yescharacteristic, complemented, Sylow
117#3043—1491nomaximal, Sylow
118C2×#137D14911yescharacteristic, complemented
119C22×SD16—1491no—
120#535—1491no—
121#519—1491no—
122#464—1494no—
123#460—1494no—
124#424—1491no—
125#418—1491no—
126#416—1491no—
127C2×#41C2×D14911yescharacteristic
128C22×Q8C2×D14911yescharacteristic
129C22×D4—1491no—
130#137—24no—
131C2×Q16C2×D14912yescomplemented
132C2×SD16—2984no—
133C2×SD16—1494no—
134C2×SD16C2×D14912yescomplemented
135C2×M16C2×D14911yescharacteristic
136C22×C8—1491no—
137#127—1492no—
138#124—1492no—
139#121—2982no—
140#120—2982no—
141C4×Q8—2982no—
142C4×Q8—1494no—
143#117—2982no—
144#117—1491no—
145#117—1491no—
146C4⋊C8—1494no—
147#103—1492no—
148#102—1492no—
149#102—1494no—
150C24—2981no—
151#41—22no—
152#41—22no—
153C2×Q8—21no—
154C2×Q8—22no—
155C2×Q8C22⋊D14914yescomplemented
156C2×Q8C22×D14911yescharacteristic
157C2×Q8C22×D14912yes—
158C2×D4—21no—
159C2×D4—2984no—
160C2×D4—2981no—
161C2×D4—2982no—
162C2×D4—2982no—
163C2×D4—1492no—
164C2×D4C22×D14911yescharacteristic
165C22×C4—21no—
166C22×C4—21no—
167C22×C4C22×D14911yescharacteristic
168Q16—24no—
169SD16—24no—
170SD16—2988no—
171M16—22no—
172C2×C8—2982no—
173C2×C8—1492no—
174C2×C8C22×D14912yes—
175C4⋊C4—2984no—
176C4⋊C4—1492no—
177C4⋊C4—1492no—
178C22⋊C4—2984no—
179C22⋊C4—2981no—
180C22⋊C4—1492no—
181C42—2984no—
182C42—2981no—
183C42—1492no—
184C23—21no—
185C23—2982no—
186C23—5962no—
187C23—11922no—
188C23D4×D14911yescharacteristic
189Q8—22no—
190Q8—24no—
191Q8—21no—
192Q8—21no—
193Q8C2×C22⋊D14914yes—
194D4—21no—
195D4—21no—
196D4—42no—
197D4—2982no—
198D4—2982no—
199D4—5962no—
200D4—11924no—
201C2×C4—22no—
202C2×C4—24no—
203C2×C4—21no—
204C2×C4—42no—
205C2×C4—2982no—
206C2×C4—1494no—
207C2×C4D4×D14911yescharacteristic
208C2×C4C2×C22⋊D14912yes—
209C2×C4#1455873512yes—
210C2×C4C23×D14911yescharacteristic
211C8—22no—
212C8—2982no—
213C22—22no—
214C22—42no—
215C22—41no—
216C22—5964no—
217C22—5962no—
218C22—11924no—
219C22#1801188312yes—
220C22C2×D4×D14911yescharacteristic
221C4—24no—
222C4—41no—
223C4—2984no—
224C4—5962no—
225C4#1801188312yes—
226C4C22×C22⋊D14911yescharacteristic
227C4C2×#1455873511yescharacteristic
228C2—22no—
229C2—81no—
230C2—11922no—
231C2C2×#1801188311yescharacteristic
232C2#2375043412yes—
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
FittingC2×#137×C149C2
socleC22×C149C22×D4
prime radical#23750189C2
hypercenterC2×#137D149
hypocenterC149#3043
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
1. C22×#14558723C2semidirect
3. #23750103C2semidirect
4. #23749849C2semidirect
5. #23749823C2semidirect
6. #23749653C2semidirect
7. #23749631C2semidirect
8. #23749621C2semidirect
9. C2×#137×C149C2semidirect
19. Q8×Dic149C22semidirect
23. #18011840C22semidirect
24. #18011835C22semidirect
26. #18011832C22semidirect
30. C2×Q16×C149C22semidirect
31. C2×SD16×C149C22semidirect
55. C2×Q8×C149D4semidirect
116. C149#3043semidirect
118. C2×#137D149semidirect
131. C2×Q16C2×D149semidirect
134. C2×SD16C2×D149semidirect
155. C2×Q8C22⋊D149semidirect

Maximal subgroups

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

subgroupindex
C22×#145587232
#237501892
#237501032
#237498492
#237498232
#237496532
#237496312
#237496212
C2×#137×C1492
#3043149