Finite Group Databasebeta

← #34054809

Subgroups — #34054809

Order 19072.

424 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 129 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
1C2×C4×Dic298C211yesmaximal, characteristic, complemented
2#23749936C212yesmaximal, complemented
3#23749917C212yesmaximal, complemented
4#23749822C212yesmaximal, complemented
5#23749763C212yesmaximal, complemented
6#23749725C214yesmaximal, complemented
7#23749682C211yesmaximal, characteristic, complemented
8#532×C149C211yesmaximal, characteristic
9C22×Dic298C2211yescharacteristic
10C2×#14558724C2214yes—
11C4×Dic298—21no—
12C4×Dic298—21no—
13C4×Dic298C2212yes—
14C4×Dic298C2212yes—
15C2×C4⋊Dic149C2211yescharacteristic
16C2×#14558715—21no—
17C2×C4×Dic149—21no—
18#18011844C2214yes—
19C4⋊#11924746C2212yes—
20#18011834C2214yes—
21#18011832C2214yes—
22C22⋊#11924746C2212yes—
23#18011822C2212yes—
24C2×#41×C149—21no—
25C4⋊Q8×C149C2211yescharacteristic
26#127×C149C2211yescharacteristic
27#124×C149—21no—
28#121×C149—21no—
29#121×C149C2212yes—
30C4×D4×C149—21no—
31C4×D4×C149C2212yes—
32C2×C42×C149C2211yescharacteristic
33C2×Dic298—24no—
34C2×Dic298—21no—
35C2×Dic298C2312yes—
36C22×Dic149—21no—
37C22×Dic149—21no—
38#14558724—28no—
39C2×#11924746C2314yes—
40C4⋊Dic149—21no—
41C4⋊Dic149C2312yes—
42#14558715—22no—
43#14558715—22no—
44C4×Dic149—22no—
45C4×Dic149—22no—
46#41×C149—44no—
47C2×Q8×C149—21no—
48C2×D4×C149—22no—
49C2×D4×C149—21no—
50C2×D4×C149—21no—
51C2×D4×C149C2312yes—
52C22×C4×C149—22no—
53C22×C4×C149D411yescharacteristic
54C22×C4×C149D411yescharacteristic
55C22×C4×C149C2311yescharacteristic
56C4⋊C4×C149—21no—
57C4⋊C4×C149C2312yes—
58C22⋊C4×C149—22no—
59C22⋊C4×C149—22no—
60C42×C149D411yescharacteristic
61C42×C149D411yescharacteristic
62C42×C149C2311yescharacteristic
63C42×C149C2311yescharacteristic
64Dic298—24no—
65Dic298—22no—
66Dic298#4114yescomplemented
67C2×Dic149—24no—
68C2×Dic149—22no—
69C2×Dic149—22no—
70C2×Dic149—42no—
71#11924746—24no—
72C23×C149—22no—
73C23×C149C2×D411yescharacteristic
74Q8×C149—42no—
75D4×C149—24no—
76D4×C149—42no—
77D4×C149—44no—
78D4×C149—42no—
79C2×C4×C149—22no—
80C2×C4×C149—22no—
81C2×C4×C149—22no—
82C2×C4×C149—22no—
83C2×C4×C149—44no—
84C2×C4×C149C2×D411yescharacteristic
85C2×C4×C149C2×D411yescharacteristic
86C2×C4×C149C2×D411yescharacteristic
87C2×C4×C149C2×D411yescharacteristic
88C2×C4×C149C2×D411yescharacteristic
89C2×C4×C149C2411yescharacteristic
90C22×C149—21no—
91C22×C149—21no—
92C22×C149—42no—
93C22×C149—42no—
94C22×C149—42no—
95C22×C149AGL(1,ℤ/8)12yes—
96C22×C149C22×D411yescharacteristic
97C4×C149—21no—
98C4×C149—21no—
99C4×C149—21no—
100C4×C149—21no—
101C4×C149—42no—
102C4×C149#13712yes—
103C4×C149C2×#4112yes—
104Dic149—24no—
105Dic149—42no—
106C2×C149—22no—
107C2×C149—82no—
108C2×C149#52511yescharacteristic
109C2×C149C2×AGL(1,ℤ/8)11yescharacteristic
110C2×C149C2×#13711yescharacteristic
111C149#311211yescharacteristic, complemented, Sylow
112#3112—1491nomaximal, Sylow
113#532D14911yescharacteristic
114C2×C4×Q8—1491no—
115#480—1492no—
116#477—1492no—
117#460—1492no—
118#448—1492no—
119#440—1494no—
120#432—1491no—
121C2×#41—21no—
122C22×Q8—1491no—
123C2×SD16—1494no—
124C4⋊Q8C2×D14911yescharacteristic
125#127C2×D14911yescharacteristic
126#124—21no—
127#121—21no—
128#121C2×D14912yes—
129C4×Q8—2981no—
130C4×Q8—2981no—
131C4×Q8—1492no—
132C4×Q8—1492no—
133C4×D4—21no—
134C4×D4C2×D14912yes—
135C2×C4⋊C4—2981no—
136C2×C4⋊C4—1491no—
137C2×C42—2981no—
138C2×C42C2×D14911yescharacteristic
139#107—1494no—
140C4⋊C8—1492no—
141#103—1494no—
142#102—1494no—
143C22⋊C8—1492no—
144#97—1492no—
145#41—44no—
146C2×Q8—21no—
147C2×Q8—2984no—
148C2×Q8—2981no—
149C2×Q8—1492no—
150C2×D4—22no—
151C2×D4—21no—
152C2×D4—21no—
153C2×D4C22×D14912yes—
154C22×C4—22no—
155C22×C4—2981no—
156C22×C4—2981no—
157C22×C4C22⋊D14911yescharacteristic
158C22×C4C22⋊D14911yescharacteristic
159C22×C4C22×D14911yescharacteristic
160SD16—2988no—
161C2×C8—1494no—
162C4⋊C4—21no—
163C4⋊C4—2982no—
164C4⋊C4—2982no—
165C4⋊C4—2981no—
166C4⋊C4—1492no—
167C4⋊C4C22×D14912yes—
168C22⋊C4—22no—
169C22⋊C4—22no—
170C42—2982no—
171C42—2982no—
172C42C22⋊D14911yescharacteristic
173C42C22⋊D14911yescharacteristic
174C42C22×D14911yescharacteristic
175C42C22×D14911yescharacteristic
176C23—22no—
177C23C2×C22⋊D14911yescharacteristic
178Q8—42no—
179Q8—2984no—
180Q8—2982no—
181Q8—1494no—
182D4—24no—
183D4—42no—
184D4—44no—
185D4—42no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—44no—
191C2×C4—2984no—
192C2×C4—2982no—
193C2×C4—2982no—
194C2×C4—5962no—
195C2×C4C2×C22⋊D14911yescharacteristic
196C2×C4C2×C22⋊D14911yescharacteristic
197C2×C4C2×C22⋊D14911yescharacteristic
198C2×C4C2×C22⋊D14911yescharacteristic
199C2×C4C2×C22⋊D14911yescharacteristic
200C2×C4C23×D14911yescharacteristic
201C8—2984no—
202C22—21no—
203C22—21no—
204C22—42no—
205C22—42no—
206C22—42no—
207C22#1801193712yes—
208C22C22×C22⋊D14911yescharacteristic
209C4—21no—
210C4—21no—
211C4—21no—
212C4—21no—
213C4—42no—
214C4—2984no—
215C4—5962no—
216C4#1801194112yes—
217C4#41×D14912yes—
218C2—22no—
219C2—82no—
220C2#2375013211yescharacteristic
221C2C2×#1801193711yescharacteristic
222C2C2×#1801194111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting, prime radical#532×C149C2
socleC22×C149C22×D4
hypercenter#532D149
hypocenterC149#3112
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C2×C42 ◁ #532

Complements

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

NH ≅ G/Ntype
1. C2×C4×Dic298C2semidirect
2. #23749936C2semidirect
3. #23749917C2semidirect
4. #23749822C2semidirect
5. #23749763C2semidirect
6. #23749725C2semidirect
7. #23749682C2semidirect
66. Dic298#41semidirect
111. C149#3112semidirect

Maximal subgroups

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

subgroupindex
C2×C4×Dic2982
#237499362
#237499172
#237498222
#237497632
#237497252
#237496822
#532×C1492
#3112149