Finite Group Databasebeta

← #34054814

Subgroups — #34054814

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
1#23750175C211yesmaximal, characteristic
2C2×C4×Dic298C211yesmaximal, characteristic, complemented
3#23749939C212yesmaximal, complemented
4#23749921C212yesmaximal, complemented
5#23749826C212yesmaximal, complemented
6#23749766C212yesmaximal, complemented
7#23749727C214yesmaximal, complemented
8#432×C149C211yesmaximal, characteristic, complemented
9C2×#14558736—21no—
10C22×Dic298C2211yescharacteristic
11C2×#14558725C2214yes—
12#18011911C2211yescharacteristic
13#18011908C2211yescharacteristic
14#18011899—21no—
15#18011885—21no—
16#18011885C2212yes—
17C4×Dic298—21no—
18C4×Dic298—21no—
19C4×Dic298C2212yes—
20C4×Dic298C2212yes—
21C4×D596—21no—
22C4×D596C2212yes—
23C2×C4⋊Dic149C2211yescharacteristic
24C2×#14558715—21no—
25C2×C4×Dic149—21no—
26#18011845C2214yes—
27#18011836C2214yes—
28#18011833C2214yes—
29C2×C42×C149C2211yescharacteristic
30C4⋊C8×C149C2212yes—
31C22⋊C8×C149C2212yes—
32#97×C149C2212yes—
33#14558736—44no—
34C2×Dic298—24no—
35C2×Dic298—21no—
36C2×Dic298—21no—
37C2×Dic298C2312yes—
38C2×D596—21no—
39C2×D596—21no—
40C2×D596C2312yes—
41C2×C22⋊D149—22no—
42C22×Dic149—21no—
43C22×Dic149—21no—
44C2×C4×D149—22no—
45#14558725—28no—
46C4⋊Dic149—21no—
47C4⋊Dic149—21no—
48C4⋊Dic149C2312yes—
49C4⋊Dic149C2312yes—
50#14558715—22no—
51#14558715—22no—
52#14558713—22no—
53#14558713—22no—
54C4×Dic149—22no—
55C4×Dic149—22no—
56C22×C4×C149D411yescharacteristic
57C22×C4×C149D411yescharacteristic
58C22×C4×C149C2311yescharacteristic
59C2×C8×C149C2314yes—
60C42×C149D411yescharacteristic
61C42×C149D411yescharacteristic
62C42×C149C2311yescharacteristic
63C42×C149C2311yescharacteristic
64C22×D149—22no—
65Dic298—24no—
66Dic298—22no—
67Dic298—42no—
68Dic298#4114yescomplemented
69D596—24no—
70D596—42no—
71D596—42no—
72C22⋊D149—44no—
73C2×Dic149—24no—
74C2×Dic149—22no—
75C2×Dic149—22no—
76C2×Dic149—22no—
77C2×Dic149—42no—
78C4×D149—44no—
79C23×C149C2×D411yescharacteristic
80C2×C4×C149—22no—
81C2×C4×C149—22no—
82C2×C4×C149—22no—
83C2×C4×C149C2×D411yescharacteristic
84C2×C4×C149C2×D411yescharacteristic
85C2×C4×C149C2×D411yescharacteristic
86C2×C4×C149C2×D411yescharacteristic
87C2×C4×C149C2×D411yescharacteristic
88C2×C4×C149C2411yescharacteristic
89C8×C149—24no—
90C22×C149—21no—
91C22×C149—21no—
92C22×C149AGL(1,ℤ/8)12yes—
93C22×C149C22×D411yescharacteristic
94C2×D149—42no—
95C2×D149—42no—
96C2×D149—42no—
97C4×C149—21no—
98C4×C149—21no—
99C4×C149—21no—
100C4×C149—21no—
101C4×C149#13712yes—
102C4×C149C2×#4112yes—
103Dic149—24no—
104Dic149—42no—
105Dic149—42no—
106C2×C149—22no—
107C2×C149#52511yescharacteristic
108C2×C149C2×AGL(1,ℤ/8)11yescharacteristic
109C2×C149C2×#13711yescharacteristic
110D149—82no—
111C149#311211yescharacteristic, complemented, Sylow
112#3112—1491nomaximal, Sylow
113#532—1491no—
114C2×C4×Q8—1491no—
115#480—1492no—
116#477—1492no—
117#460—1492no—
118#448—1492no—
119#440—1494no—
120#432D14911yescharacteristic, complemented
121C2×#41—2981no—
122C22×Q8—1491no—
123C2×SD16—1494no—
124C4⋊Q8—1491no—
125#127—1491no—
126#124—2981no—
127#121—2981no—
128#121—1492no—
129C4×Q8—2981no—
130C4×Q8—2981no—
131C4×Q8—1492no—
132C4×Q8—1492no—
133C4×D4—2981no—
134C4×D4—1492no—
135C2×C4⋊C4—2981no—
136C2×C4⋊C4—1491no—
137C2×C42—2981no—
138C2×C42C2×D14911yescharacteristic
139#107—1494no—
140C4⋊C8C2×D14912yes—
141#103—1494no—
142#102—1494no—
143C22⋊C8C2×D14912yes—
144#97C2×D14912yes—
145#41—5964no—
146C2×Q8—2984no—
147C2×Q8—2981no—
148C2×Q8—2981no—
149C2×Q8—1492no—
150C2×D4—2982no—
151C2×D4—2981no—
152C2×D4—2981no—
153C2×D4—1492no—
154C22×C4—2981no—
155C22×C4—2981no—
156C22×C4—2982no—
157C22×C4D59611yescharacteristic
158C22×C4D59611yescharacteristic
159C22×C4C22×D14911yescharacteristic
160SD16—2988no—
161C2×C8C22×D14914yes—
162C4⋊C4—2982no—
163C4⋊C4—2982no—
164C4⋊C4—2981no—
165C4⋊C4—2981no—
166C4⋊C4—1492no—
167C4⋊C4—1492no—
168C22⋊C4—2982no—
169C22⋊C4—2982no—
170C42—2982no—
171C42—2982no—
172C42D59611yescharacteristic
173C42D59611yescharacteristic
174C42C22×D14911yescharacteristic
175C42C22×D14911yescharacteristic
176C23—2982no—
177C23C2×D59611yescharacteristic
178Q8—2984no—
179Q8—2982no—
180Q8—5962no—
181Q8—1494no—
182D4—2984no—
183D4—5962no—
184D4—5964no—
185D4—5962no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—2984no—
190C2×C4—2982no—
191C2×C4—2982no—
192C2×C4—2982no—
193C2×C4—5964no—
194C2×C4—5962no—
195C2×C4C2×D59611yescharacteristic
196C2×C4C2×D59611yescharacteristic
197C2×C4C2×D59611yescharacteristic
198C2×C4C2×D59611yescharacteristic
199C2×C4C2×D59611yescharacteristic
200C2×C4C23×D14911yescharacteristic
201C8—24no—
202C22—21no—
203C22—21no—
204C22—5962no—
205C22—5962no—
206C22—5962no—
207C22#1801193912yes—
208C22C22×D59611yescharacteristic
209C4—21no—
210C4—21no—
211C4—21no—
212C4—21no—
213C4—2984no—
214C4—5962no—
215C4—5962no—
216C4#1801194412yes—
217C4#41×D14912yes—
218C2—22no—
219C2—11922no—
220C2#2375013711yescharacteristic
221C2C2×#1801193911yescharacteristic
222C2C2×#1801194411yescharacteristic
subgroupG/H
centerC22C22×D596
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#432×C149C2
socleC22×C149C22×D4
prime radical#23750175C2
hypercenter#432D149
hypocenterC149#3112
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
2. C2×C4×Dic298C2semidirect
3. #23749939C2semidirect
4. #23749921C2semidirect
5. #23749826C2semidirect
6. #23749766C2semidirect
7. #23749727C2semidirect
8. #432×C149C2semidirect
68. Dic298#41semidirect
111. C149#3112semidirect
120. #432D149semidirect

Maximal subgroups

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

subgroupindex
#237501752
C2×C4×Dic2982
#237499392
#237499212
#237498262
#237497662
#237497272
#432×C1492
#3112149