Finite Group Databasebeta

← #34055815

Subgroups — #34055815

Order 19072.

404 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 404 conjugacy classes of subgroups — too many to draw. Only its 125 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#23750173C211yesmaximal, characteristic
2C4⋊Q8×D149C211yesmaximal, characteristic, complemented
3#23750023C211yesmaximal, characteristic, complemented
4#23750021C211yesmaximal, characteristic, complemented
5#23749971C211yesmaximal, characteristic, complemented
6#23749942C214yesmaximal, complemented
7#23749913C214yesmaximal, complemented
8#23749676C211yesmaximal, characteristic, complemented
9#486×C149C211yesmaximal, characteristic, complemented
10C2×#14558735—21no—
11C2×Q8×D149—21no—
12#18011911C2211yescharacteristic
13#18011911C2211yescharacteristic
14#18011910—21no—
15#18011910C2212yes—
16#18011909—21no—
17#18011898—21no—
18#18011882—21no—
19#18011882C2212yes—
20D4×Dic149—21no—
21D4×Dic149C2212yes—
22C4⋊C4×D149—21no—
23C4⋊C4×D149C2212yes—
24C42×D149C2211yescharacteristic
25#18011843C2214yes—
26#18011842C2214yes—
27#18011840C2212yes—
28#18011832C2214yes—
29#18011823C2212yes—
30C4×#11924746C2211yescharacteristic
31C4⋊Q8×C149C2211yescharacteristic
32#127×C149C2211yescharacteristic
33#102×C149C2214yes—
34C4×C8×C149C2211yescharacteristic
35#14558735—44no—
36C2×Dic298—22no—
37C2×Dic298—21no—
38C2×Dic298—21no—
39Q8×D149—44no—
40C2×C22⋊D149—22no—
41C22×Dic149—22no—
42C2×C4×D149—22no—
43C2×C4×D149D411yescharacteristic
44C2×C4×D149D411yescharacteristic
45C2×C4×D149C2311yescharacteristic
46C2×#11924746C2312yes—
47C4⋊Dic149—21no—
48C4⋊Dic149—21no—
49C4⋊Dic149C2312yes—
50C4⋊Dic149C2312yes—
51#14558715—22no—
52#14558715—22no—
53C22⋊Dic149—22no—
54C22⋊Dic149—22no—
55C4×Dic149D411yescharacteristic
56C4×Dic149D411yescharacteristic
57C4×Dic149C2311yescharacteristic
58C2×Q8×C149—21no—
59C2×D4×C149—21no—
60C2×D4×C149—21no—
61C2×D4×C149C2312yes—
62C2×C8×C149C2312yes—
63C4⋊C4×C149—21no—
64C4⋊C4×C149C2312yes—
65C42×C149C2311yescharacteristic
66C22×D149C2×D411yescharacteristic
67Dic298—44no—
68Dic298—42no—
69Dic298—42no—
70C22⋊D149—44no—
71C2×Dic149—22no—
72C2×Dic149—22no—
73C2×Dic149—44no—
74C2×Dic149C2×D411yescharacteristic
75C2×Dic149C2×D411yescharacteristic
76C2×Dic149C2×D411yescharacteristic
77C4×D149—22no—
78C4×D149—22no—
79C4×D149—44no—
80C4×D149SD1614yes—
81#11924746—22no—
82C23×C149—22no—
83Q8×C149—42no—
84D4×C149—24no—
85D4×C149—42no—
86D4×C149—42no—
87C2×C4×C149—22no—
88C2×C4×C149C2×D411yescharacteristic
89C2×C4×C149C2×D411yescharacteristic
90C2×C4×C149C2411yescharacteristic
91C8×C149—22no—
92C22×C149—42no—
93C22×C149—42no—
94C22×C149—42no—
95C22×C149C22×D411yescharacteristic
96C2×D149—21no—
97C2×D149—21no—
98C2×D149C2×SD1612yes—
99C4×C149—42no—
100C4×C149C2×SD1612yes—
101C4×C149AGL(1,ℤ/8)12yes—
102C4×C1492−1+412yes—
103Dic149—21no—
104Dic149—21no—
105Dic149—42no—
106Dic149—42no—
107Dic149C2×SD1612yes—
108C2×C149—82no—
109C2×C149#53611yescharacteristic
110C2×C149C22×SD1611yescharacteristic
111C2×C149C2×AGL(1,ℤ/8)11yescharacteristic
112D149—22no—
113C149#322711yescharacteristic, complemented, Sylow
114#3227—1491nomaximal, Sylow
115#532—1491no—
116C2×C4⋊Q8—1491no—
117#498—1491no—
118#498—1491no—
119#486—1491no—
120#486D14911yescharacteristic, complemented
121#481—1494no—
122#476—1494no—
123#431—1491no—
124C2×#41—2981no—
125C22×Q8—2981no—
126C4⋊Q8—2981no—
127C4⋊Q8—2981no—
128C4⋊Q8—1492no—
129C4⋊Q8—1491no—
130C4⋊Q8—1491no—
131C4⋊Q8C2×D14911yescharacteristic
132#127C2×D14911yescharacteristic
133#124—2981no—
134#121—2981no—
135#121—1492no—
136C4×D4—2981no—
137C4×D4—1492no—
138C2×C4⋊C4—2981no—
139C2×C4⋊C4—1492no—
140C2×C42—1491no—
141#106—1494no—
142#106—1494no—
143C4⋊C8—1492no—
144#102—1494no—
145#102C2×D14914yes—
146C22⋊C8—1492no—
147C4×C8—1491no—
148C4×C8C2×D14911yescharacteristic
149#41—5964no—
150C2×Q8—21no—
151C2×Q8—2982no—
152C2×Q8—2981no—
153C2×Q8—2981no—
154C2×Q8—5964no—
155C2×D4—21no—
156C2×D4—21no—
157C2×D4—2982no—
158C2×D4C22×D14912yes—
159C22×C4—2982no—
160C22×C4—2982no—
161C22×C4—1491no—
162C22×C4—1491no—
163C22×C4—1491no—
164C2×C8—1492no—
165C2×C8C22×D14912yes—
166C4⋊C4—21no—
167C4⋊C4—2982no—
168C4⋊C4—2982no—
169C4⋊C4—2981no—
170C4⋊C4—2981no—
171C4⋊C4—1492no—
172C4⋊C4—1492no—
173C4⋊C4C22×D14912yes—
174C22⋊C4—2982no—
175C22⋊C4—2982no—
176C42—1491no—
177C42—1491no—
178C42—1491no—
179C42C22×D14911yescharacteristic
180C23—22no—
181C23—1491no—
182Q8—42no—
183Q8—5964no—
184Q8—5962no—
185Q8—5962no—
186D4—24no—
187D4—42no—
188D4—42no—
189D4—5964no—
190C2×C4—22no—
191C2×C4—2982no—
192C2×C4—2982no—
193C2×C4—2982no—
194C2×C4—2982no—
195C2×C4—5964no—
196C2×C4—5964no—
197C2×C4—1491no—
198C2×C4—1491no—
199C2×C4—1491no—
200C2×C4—1494no—
201C2×C4D4×D14911yescharacteristic
202C2×C4D4×D14911yescharacteristic
203C2×C4C23×D14911yescharacteristic
204C8—22no—
205C8—2982no—
206C22—42no—
207C22—42no—
208C22—42no—
209C22—2981no—
210C22—2981no—
211C22—1492no—
212C22C2×D4×D14911yescharacteristic
213C4—42no—
214C4—2981no—
215C4—2981no—
216C4—5962no—
217C4—5962no—
218C4—1492no—
219C4SD16×D14912yes—
220C4#1801193512yes—
221C4#1801195812yes—
222C2—82no—
223C2—2982no—
224C2#2375019511yescharacteristic
225C2C2×SD16×D14911yescharacteristic
226C2C2×#1801193511yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#486×C149C2
socleC22×C149C22×D4
prime radical#23750173C2
hypercenter#486D149
hypocenterC149#3227
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
2. C4⋊Q8×D149C2semidirect
3. #23750023C2semidirect
4. #23750021C2semidirect
5. #23749971C2semidirect
6. #23749942C2semidirect
7. #23749913C2semidirect
8. #23749676C2semidirect
9. #486×C149C2semidirect
113. C149#3227semidirect
120. #486D149semidirect

Maximal subgroups

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

subgroupindex
#237501732
C4⋊Q8×D1492
#237500232
#237500212
#237499712
#237499422
#237499132
#237496762
#486×C1492
#3227149