Finite Group Databasebeta

← #34045549

Subgroups — #34045549

Order 19072.

312 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 103 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
1C22×#14558726C211yesmaximal, characteristic
2C2×#18011844C211yesmaximal, characteristic
3C2×#18011836C211yesmaximal, characteristic
4C2×C8×Dic149C211yesmaximal, characteristic
5#23749532C211yesmaximal, characteristic
6#23749530C211yesmaximal, characteristic
7C2×#103×C149C211yesmaximal, characteristic
8C22×Dic298C2211yescharacteristic
9C2×#14558726—22no—
10C2×#14558726—22no—
11C2×#14558726C414yescomplemented
12C22×#11924746C2211yescharacteristic
13C2×C4⋊Dic149C2211yescharacteristic
14C2×C4×Dic149C2211yescharacteristic
15#18011844—22no—
16#18011836—22no—
17C8×Dic149—22no—
18#18011818—22no—
19#18011818—22no—
20C22×Q8×C149C2211yescharacteristic
21C22×C8×C149C2211yescharacteristic
22C2×C4⋊C4×C149C2211yescharacteristic
23#103×C149—22no—
24C2×Dic298—21no—
25C2×Dic298—21no—
26C2×Dic298—21no—
27C2×Dic298—21no—
28C2×Dic298—21no—
29C2×Dic298C2×C412yes—
30C22×Dic149—21no—
31C22×Dic149—21no—
32C22×Dic149D412yes—
33#14558726—28no—
34C2×#11924746C2×C412yes—
35C2×#11924746D412yes—
36C2×#11924746D412yes—
37C4⋊Dic149—21no—
38C4⋊Dic149—21no—
39C4×Dic149—21no—
40C4×Dic149—21no—
41C2×Q8×C149—21no—
42C2×Q8×C149—21no—
43C2×Q8×C149—21no—
44C2×Q8×C149—21no—
45C2×Q8×C149—21no—
46C2×Q8×C149C2×C412yes—
47C22×C4×C149—21no—
48C22×C4×C149—21no—
49C22×C4×C149C2311yescharacteristic
50C2×C8×C149—21no—
51C2×C8×C149—21no—
52C2×C8×C149D412yes—
53C4⋊C4×C149—21no—
54C4⋊C4×C149—21no—
55Dic298—22no—
56Dic298—22no—
57Dic298—41no—
58Dic298—41no—
59C2×Dic149—22no—
60C2×Dic149—22no—
61C2×Dic149—22no—
62C2×Dic149—41no—
63C2×Dic149—41no—
64C2×Dic149—41no—
65C2×Dic149—42no—
66C2×Dic149Q1614yescomplemented
67#11924746C22⋊C414yes—
68C23×C149C2×D411yescharacteristic
69Q8×C149—22no—
70Q8×C149—22no—
71Q8×C149—41no—
72Q8×C149—41no—
73C2×C4×C149—22no—
74C2×C4×C149—41no—
75C2×C4×C149—41no—
76C2×C4×C149—41no—
77C2×C4×C149—42no—
78C2×C4×C149C22×C411yescharacteristic
79C2×C4×C149C2×D411yescharacteristic
80C2×C4×C149C2×D411yescharacteristic
81C2×C4×C149C2×D411yescharacteristic
82C2×C4×C149#4111yescharacteristic
83C2×C4×C149#4111yescharacteristic
84C8×C149—22no—
85C22×C149C4×D411yescharacteristic
86C22×C149#12111yescharacteristic
87C22×C149#12711yescharacteristic
88C22×C149C2×Q1612yes—
89C22×C149#13512yes—
90C4×C149—42no—
91C4×C149—81no—
92C4×C149C2×C22⋊C411yescharacteristic
93C4×C149C4×D411yescharacteristic
94C4×C149#12111yescharacteristic
95C4×C149#12411yescharacteristic
96Dic149—24no—
97Dic149—42no—
98Dic149—81no—
99C2×C149#39011yescharacteristic
100C2×C149C4×Q1612yes—
101C2×C149#46712yes—
102C2×C149#49411yescharacteristic
103C2×C149#49511yescharacteristic
104C149#196911yescharacteristic, complemented, Sylow
105#1969—1491nomaximal, Sylow
106C22×Q16—1491no—
107C2×#107—1491no—
108C2×#103—1491no—
109C2×#103D14911yescharacteristic
110C2×C4×C8—1491no—
111#391—1491no—
112#391—1491no—
113C22×Q8—1491no—
114C22×Q8C2×D14911yescharacteristic
115C2×Q16—2982no—
116C2×Q16—2982no—
117C2×Q16—1494no—
118C22×C8—1491no—
119C22×C8C2×D14911yescharacteristic
120C2×C4⋊C4—1491no—
121C2×C4⋊C4C2×D14911yescharacteristic
122C2×C42—1491no—
123#107—2982no—
124#103—22no—
125#103—2982no—
126C4×C8—2982no—
127#95—2982no—
128#95—2982no—
129C2×Q8—21no—
130C2×Q8—21no—
131C2×Q8—21no—
132C2×Q8—21no—
133C2×Q8—21no—
134C2×Q8—2981no—
135C2×Q8—2981no—
136C2×Q8—2981no—
137C2×Q8—2981no—
138C2×Q8—2981no—
139C2×Q8—1492no—
140C2×Q8C4×D14912yes—
141C22×C4—21no—
142C22×C4—21no—
143C22×C4—2981no—
144C22×C4—2981no—
145C22×C4—1492no—
146C22×C4C22×D14911yescharacteristic
147Q16—2988no—
148C2×C8—21no—
149C2×C8—21no—
150C2×C8—1492no—
151C2×C8—1492no—
152C2×C8—1492no—
153C2×C8C22⋊D14912yes—
154C4⋊C4—21no—
155C4⋊C4—21no—
156C4⋊C4—2981no—
157C4⋊C4—2981no—
158C42—2981no—
159C42—2981no—
160C23D4×D14911yescharacteristic
161Q8—22no—
162Q8—22no—
163Q8—41no—
164Q8—41no—
165Q8—2982no—
166Q8—2982no—
167Q8—5961no—
168Q8—5961no—
169C2×C4—22no—
170C2×C4—41no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—42no—
174C2×C4—2982no—
175C2×C4—2982no—
176C2×C4—2982no—
177C2×C4—5961no—
178C2×C4—5961no—
179C2×C4—5961no—
180C2×C4—5962no—
181C2×C4—1494no—
182C2×C4C2×C4×D14911yescharacteristic
183C2×C4D4×D14911yescharacteristic
184C2×C4D4×D14911yescharacteristic
185C2×C4C2×C22⋊D14911yescharacteristic
186C2×C4#1455873511yescharacteristic
187C2×C4#1455873611yescharacteristic
188C8—22no—
189C8—1494no—
190C22#1801187111yescharacteristic
191C22#1801188411yescharacteristic
192C22#1801190711yescharacteristic
193C22Q16×D14912yes—
194C22#1801193212yes—
195C4—42no—
196C4—81no—
197C4—2984no—
198C4—5962no—
199C4—11921no—
200C4C22⋊C4×D14911yescharacteristic
201C4C4×C22⋊D14911yescharacteristic
202C4#1801188311yescharacteristic
203C4#1801189711yescharacteristic
204C2#2374952511yescharacteristic
205C2#2374971712yes—
206C2#2374986512yes—
207C2#2375000311yescharacteristic
208C2#2375000611yescharacteristic
subgroupG/H
centerC23D4×D149
commutatorC2×C4×C149C22×C4
FrattiniC22×C4C22×D149
FittingC2×#103×C149C2
socle, prime radicalC23×C149C2×D4
cosocleC22×C4×C149C23
hypercenterC2×#103D149
hypocenterC149#1969
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
11. C2×#14558726C4semidirect
66. C2×Dic149Q16semidirect
104. C149#1969semidirect

Maximal subgroups

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

subgroupindex
C22×#145587262
C2×#180118442
C2×#180118362
C2×C8×Dic1492
#237495322
#237495302
C2×#103×C1492
#1969149