Finite Group Databasebeta

← #34055838

Subgroups — #34055838

Order 19072.

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

normal subgroups only

This group has 360 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#23750180C211yesmaximal, characteristic
2C4⋊Q8×D149C211yesmaximal, characteristic
3#23750030C211yesmaximal, characteristic, complemented
4#23750028C211yesmaximal, characteristic, complemented
5#23749975C211yesmaximal, characteristic, complemented
6#23749959C214yesmaximal
7#23749918C214yesmaximal, complemented
8#23749676C211yesmaximal, characteristic
9#487×C149C211yesmaximal, characteristic, complemented
10C2×Q8×D149—21no—
11#18011911C2211yescharacteristic
12#18011911C2211yescharacteristic
13#18011910—21no—
14#18011910C2212yes—
15#18011909—21no—
16#18011902—21no—
17#18011891—21no—
18#18011887C2212yes—
19Q8×Dic149C2212yes—
20#18011876—21no—
21#18011869—21no—
22C4⋊C4×D149—21no—
23C4⋊C4×D149C2212yes—
24C42×D149C2211yescharacteristic
25#18011845C2214yes—
26#18011844C2214yes—
27#18011840C2212yes—
28#18011835C2214yes—
29#18011823C2212yes—
30C4×#11924746C2211yescharacteristic
31C4⋊Q8×C149C2211yescharacteristic
32C4⋊Q8×C149C2211yescharacteristic
33#103×C149C2214yes—
34C4×C8×C149C2211yescharacteristic
35C2×Dic298—22no—
36C2×Dic298—21no—
37C2×Dic298—21no—
38Q8×D149—44no—
39C2×C4×D149—22no—
40C2×C4×D149D411yescharacteristic
41C2×C4×D149D411yescharacteristic
42C2×C4×D149C2311yescharacteristic
43C2×#11924746C2312yes—
44C4⋊Dic149—22no—
45C4⋊Dic149—21no—
46C4⋊Dic149—21no—
47C4⋊Dic149C2312yes—
48C4⋊Dic149C2312yes—
49#14558715—22no—
50#14558715—22no—
51#14558715—22no—
52#14558713—22no—
53C4×Dic149—22no—
54C4×Dic149D411yescharacteristic
55C4×Dic149D411yescharacteristic
56C4×Dic149C2311yescharacteristic
57C2×Q8×C149—21no—
58C2×Q8×C149C2312yes—
59C2×C8×C149C2312yes—
60C4⋊C4×C149—21no—
61C4⋊C4×C149—21no—
62C4⋊C4×C149—21no—
63C4⋊C4×C149C2312yes—
64C42×C149C2311yescharacteristic
65C22×D149C2×D411yescharacteristic
66Dic298—44no—
67Dic298—42no—
68Dic298—42no—
69C2×Dic149—22no—
70C2×Dic149—22no—
71C2×Dic149C2×D411yescharacteristic
72C2×Dic149C2×D411yescharacteristic
73C2×Dic149C2×D411yescharacteristic
74C4×D149—22no—
75C4×D149—22no—
76C4×D149—44no—
77C4×D149Q1614yes—
78#11924746—22no—
79Q8×C149—24no—
80Q8×C149—42no—
81C2×C4×C149—22no—
82C2×C4×C149—22no—
83C2×C4×C149C2×D411yescharacteristic
84C2×C4×C149C2×D411yescharacteristic
85C2×C4×C149C2411yescharacteristic
86C8×C149—22no—
87C22×C149C22×D411yescharacteristic
88C2×D149—21no—
89C2×D149—21no—
90C2×D149C2×Q1612yes—
91C4×C149—42no—
92C4×C149—42no—
93C4×C149C2×Q1612yes—
94C4×C149AGL(1,ℤ/8)12yes—
95C4×C1492−1+412yes—
96Dic149—21no—
97Dic149—21no—
98Dic149—42no—
99Dic149—42no—
100Dic149C2×Q1612yes—
101C2×C149#53611yescharacteristic
102C2×C149C22×Q1611yescharacteristic
103C2×C149C2×AGL(1,ℤ/8)11yescharacteristic
104D149—22no—
105C149#323011yescharacteristic, complemented, Sylow
106#3230—1491nomaximal, Sylow
107#533—1491no—
108C2×C4⋊Q8—1491no—
109#500—1491no—
110#500—1491no—
111#487—1491no—
112#487D14911yescharacteristic, complemented
113#484—1494no—
114#477—1494no—
115#431—1491no—
116C22×Q8—2981no—
117C4⋊Q8—2981no—
118C4⋊Q8—2981no—
119C4⋊Q8—1492no—
120C4⋊Q8—1491no—
121C4⋊Q8—1491no—
122C4⋊Q8C2×D14911yescharacteristic
123C4⋊Q8C2×D14911yescharacteristic
124#125—2981no—
125C22⋊Q8—2981no—
126C22⋊Q8—1492no—
127C4×Q8—2981no—
128C4×Q8—1492no—
129#117—2981no—
130C2×C4⋊C4—2981no—
131C2×C4⋊C4—1492no—
132C2×C42—1491no—
133#107—1494no—
134#107—1494no—
135C4⋊C8—1492no—
136#103—1494no—
137#103C2×D14914yes—
138C22⋊C8—1492no—
139C4×C8—1491no—
140C4×C8C2×D14911yescharacteristic
141C2×Q8—21no—
142C2×Q8—2982no—
143C2×Q8—2981no—
144C2×Q8—2981no—
145C2×Q8—5964no—
146C2×Q8C22×D14912yes—
147C22×C4—2982no—
148C22×C4—1491no—
149C22×C4—1491no—
150C22×C4—1491no—
151C2×C8—1492no—
152C2×C8C22×D14912yes—
153C4⋊C4—21no—
154C4⋊C4—21no—
155C4⋊C4—21no—
156C4⋊C4—2982no—
157C4⋊C4—2982no—
158C4⋊C4—2982no—
159C4⋊C4—2982no—
160C4⋊C4—2981no—
161C4⋊C4—2981no—
162C4⋊C4—1492no—
163C4⋊C4—1492no—
164C4⋊C4C22×D14912yes—
165C22⋊C4—2982no—
166C42—2982no—
167C42—1491no—
168C42—1491no—
169C42—1491no—
170C42C22×D14911yescharacteristic
171C23—1491no—
172Q8—24no—
173Q8—42no—
174Q8—5964no—
175Q8—5962no—
176Q8—5962no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—2982no—
180C2×C4—2982no—
181C2×C4—2982no—
182C2×C4—2982no—
183C2×C4—5964no—
184C2×C4—1491no—
185C2×C4—1491no—
186C2×C4—1491no—
187C2×C4—1494no—
188C2×C4D4×D14911yescharacteristic
189C2×C4D4×D14911yescharacteristic
190C2×C4C23×D14911yescharacteristic
191C8—22no—
192C8—2982no—
193C22—2981no—
194C22—2981no—
195C22—1492no—
196C22C2×D4×D14911yescharacteristic
197C4—42no—
198C4—42no—
199C4—2981no—
200C4—2981no—
201C4—5962no—
202C4—5962no—
203C4—1492no—
204C4Q16×D14912yes—
205C4#1801193812yes—
206C4#1801195812yes—
207C2—2982no—
208C2#2375019511yescharacteristic
209C2C2×Q16×D14911yescharacteristic
210C2C2×#1801193811yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#487×C149C2
socleC22×C149C22×D4
prime radicalC22×D149C2×D4
hypercenter#487D149
hypocenterC149#3230
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
3. #23750030C2semidirect
4. #23750028C2semidirect
5. #23749975C2semidirect
7. #23749918C2semidirect
9. #487×C149C2semidirect
105. C149#3230semidirect
112. #487D149semidirect

Maximal subgroups

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

subgroupindex
#237501802
C4⋊Q8×D1492
#237500302
#237500282
#237499752
#237499592
#237499182
#237496762
#487×C1492
#3230149