Finite Group Databasebeta

← #34055081

Subgroups — #34055081

Order 19072.

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

normal subgroups only

This group has 424 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#23749983C214yesmaximal, complemented
4#23749977C211yesmaximal, characteristic, complemented
5#23749976C211yesmaximal, characteristic, complemented
6#23749971C211yesmaximal, characteristic, complemented
7#23749623C214yesmaximal, complemented
8C4×#14558719C211yesmaximal, characteristic, complemented
9#486×C149C211yesmaximal, characteristic, complemented
10C2×#14558735C2212yes—
11C2×Q8×D149—21no—
12C2×#14558719C2212yes—
13#18011911C2211yescharacteristic
14#18011911C2211yescharacteristic
15#18011910—21no—
16#18011910C2212yes—
17#18011909—21no—
18#18011898C2212yes—
19#18011882—21no—
20#18011882—21no—
21D4×Dic149—21no—
22D4×Dic149—21no—
23C4⋊C4×D149—21no—
24C4⋊C4×D149C2212yes—
25C42×D149C2211yescharacteristic
26#18011836C2214yes—
27#18011834C2214yes—
28#18011832C2214yes—
29#18011821C2212yes—
30C4×#11924746C2211yescharacteristic
31C4⋊Q8×C149C2211yescharacteristic
32#127×C149C2211yescharacteristic
33#102×C149C2214yes—
34C4×C8×C149C2211yescharacteristic
35#14558735—28no—
36C2×Dic298—22no—
37C2×Dic298—21no—
38C2×Dic298C2312yes—
39Q8×D149—44no—
40C2×C22⋊D149—22no—
41C22×Dic149—22no—
42C2×C4×D149—22no—
43C2×C4×D149D411yescharacteristic
44C2×C4×D149D411yescharacteristic
45C2×C4×D149C2311yescharacteristic
46#14558719—24no—
47C2×#11924746C2312yes—
48C4⋊Dic149—21no—
49C4⋊Dic149—21no—
50C4⋊Dic149—21no—
51C4⋊Dic149C2312yes—
52#14558715—22no—
53#14558715—22no—
54C22⋊Dic149—22no—
55C22⋊Dic149—22no—
56C4×Dic149D411yescharacteristic
57C4×Dic149D411yescharacteristic
58C4×Dic149C2311yescharacteristic
59C2×Q8×C149—21no—
60C2×D4×C149—21no—
61C2×D4×C149—21no—
62C2×D4×C149C2312yes—
63C2×C8×C149C2312yes—
64C4⋊C4×C149—21no—
65C4⋊C4×C149C2312yes—
66C42×C149C2311yescharacteristic
67C22×D149C2×D411yescharacteristic
68Dic298—24no—
69Dic298—44no—
70Dic298—42no—
71C22⋊D149—44no—
72C2×Dic149—22no—
73C2×Dic149—22no—
74C2×Dic149—44no—
75C2×Dic149C2×D411yescharacteristic
76C2×Dic149C2×D411yescharacteristic
77C2×Dic149C2×D411yescharacteristic
78C4×D149—22no—
79C4×D149—22no—
80C4×D149—44no—
81C4×D149#4114yes—
82#11924746—22no—
83C23×C149—22no—
84Q8×C149—42no—
85D4×C149—24no—
86D4×C149—42no—
87D4×C149—42no—
88C2×C4×C149—22no—
89C2×C4×C149C2×D411yescharacteristic
90C2×C4×C149C2×D411yescharacteristic
91C2×C4×C149C2411yescharacteristic
92C8×C149—22no—
93C22×C149—42no—
94C22×C149—42no—
95C22×C149—42no—
96C22×C149C22×D411yescharacteristic
97C2×D149—21no—
98C2×D149—21no—
99C2×D149#12412yes—
100C4×C149—42no—
101C4×C149AGL(1,ℤ/8)12yes—
102C4×C149#13712yes—
103C4×C149C2×#4112yes—
104Dic149—21no—
105Dic149—21no—
106Dic149—42no—
107Dic149—42no—
108Dic149#12412yes—
109C2×C149—82no—
110C2×C149C2×#12411yescharacteristic
111C2×C149C2×AGL(1,ℤ/8)11yescharacteristic
112C2×C149C2×#13711yescharacteristic
113D149—22no—
114C149#314111yescharacteristic, complemented, Sylow
115#3141—1491nomaximal, Sylow
116#532—1491no—
117C2×C4⋊Q8—1491no—
118#489—1494no—
119#487—1491no—
120#487—1491no—
121#486—1491no—
122#486D14911yescharacteristic, complemented
123#417—1494no—
124C4×M16—1491no—
125C2×#41—1492no—
126C22×Q8—2981no—
127C2×M16—1492no—
128C4⋊Q8—2981no—
129C4⋊Q8—2981no—
130C4⋊Q8—1492no—
131C4⋊Q8—1491no—
132C4⋊Q8—1491no—
133C4⋊Q8C2×D14911yescharacteristic
134#127C2×D14911yescharacteristic
135#124—1492no—
136#121—2981no—
137#121—2981no—
138C4×D4—2981no—
139C4×D4—2981no—
140C2×C4⋊C4—2981no—
141C2×C4⋊C4—1492no—
142C2×C42—1491no—
143#103—1494no—
144#103—1494no—
145#102—1494no—
146#102C2×D14914yes—
147#97—1492no—
148C4×C8—1491no—
149C4×C8C2×D14911yescharacteristic
150#41—2988no—
151C2×Q8—21no—
152C2×Q8—2982no—
153C2×Q8—2981no—
154C2×Q8—5964no—
155C2×Q8—1492no—
156C2×D4—21no—
157C2×D4—21no—
158C2×D4—2982no—
159C2×D4C22×D14912yes—
160C22×C4—2982no—
161C22×C4—2982no—
162C22×C4—1491no—
163C22×C4—1491no—
164C22×C4—1491no—
165M16—2984no—
166C2×C8—1492no—
167C2×C8C22×D14912yes—
168C4⋊C4—21no—
169C4⋊C4—2982no—
170C4⋊C4—2982no—
171C4⋊C4—2981no—
172C4⋊C4—2981no—
173C4⋊C4—2981no—
174C4⋊C4—1492no—
175C4⋊C4C22×D14912yes—
176C22⋊C4—2982no—
177C22⋊C4—2982no—
178C42—1491no—
179C42—1491no—
180C42—1491no—
181C42C22×D14911yescharacteristic
182C23—22no—
183C23—1491no—
184Q8—42no—
185Q8—2984no—
186Q8—5964no—
187Q8—5962no—
188D4—24no—
189D4—42no—
190D4—42no—
191D4—5964no—
192C2×C4—22no—
193C2×C4—2982no—
194C2×C4—2982no—
195C2×C4—2982no—
196C2×C4—2982no—
197C2×C4—5964no—
198C2×C4—5964no—
199C2×C4—1491no—
200C2×C4—1491no—
201C2×C4—1491no—
202C2×C4—1494no—
203C2×C4D4×D14911yescharacteristic
204C2×C4D4×D14911yescharacteristic
205C2×C4C23×D14911yescharacteristic
206C8—22no—
207C8—2982no—
208C22—42no—
209C22—42no—
210C22—42no—
211C22—2981no—
212C22—2981no—
213C22—1492no—
214C22C2×D4×D14911yescharacteristic
215C4—42no—
216C4—2981no—
217C4—2981no—
218C4—5962no—
219C4—5962no—
220C4—1492no—
221C4#1801193512yes—
222C4#1801194012yes—
223C4#41×D14912yes—
224C2—82no—
225C2—2982no—
226C2#124×D14911yescharacteristic
227C2C2×#1801193511yescharacteristic
228C2C2×#1801194011yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#486×C149C2
socleC22×C149C22×D4
prime radical#23750173C2
hypercenter#486D149
hypocenterC149#3141
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. #23749983C2semidirect
4. #23749977C2semidirect
5. #23749976C2semidirect
6. #23749971C2semidirect
7. #23749623C2semidirect
8. C4×#14558719C2semidirect
9. #486×C149C2semidirect
114. C149#3141semidirect
122. #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
#237499832
#237499772
#237499762
#237499712
#237496232
C4×#145587192
#486×C1492
#3141149