Finite Group Databasebeta

← #34045603

Subgroups — #34045603

Order 19072.

276 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 276 conjugacy classes of subgroups — too many to draw. Only its 83 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×#18011846C211yesmaximal, characteristic
3#23749635C211yesmaximal, characteristic
4#23749634C211yesmaximal, characteristic
5C2×#18011829C211yesmaximal, characteristic
6#23749583C211yesmaximal, characteristic
7C2×#101×C149C211yesmaximal, characteristic
8C22×Dic298C2211yescharacteristic
9C2×#14558726—21no—
10C2×#14558726—21no—
11C2×#14558726—22no—
12C2×#14558726C414yescomplemented
13C2×#14558720C2211yescharacteristic
14C22×#11924746C2211yescharacteristic
15#18011870C2211yescharacteristic
16#18011846—22no—
17#18011836—22no—
18#18011835—22no—
19#18011829—22no—
20#18011821—21no—
21C8×Dic149—21no—
22C22×Q8×C149C2211yescharacteristic
23C2×M16×C149C2211yescharacteristic
24C2×M16×C149C2211yescharacteristic
25#101×C149—22no—
26C2×Dic298—21no—
27C2×Dic298—21no—
28C2×Dic298—21no—
29C2×Dic298—21no—
30C2×Dic298—21no—
31C2×Dic298C2×C412yes—
32C22×Dic149—21no—
33#14558726—24no—
34#14558726—24no—
35#14558720—21no—
36#14558720—21no—
37C2×#11924746—21no—
38C2×#11924746C2×C412yes—
39C2×#11924746D411yescharacteristic
40C2×#11924746D411yescharacteristic
41C2×#11924746D412yes—
42C4⋊Dic149D412yes—
43C22⋊Dic149—21no—
44C4×Dic149—21no—
45C2×Q8×C149—21no—
46C2×Q8×C149—21no—
47C2×Q8×C149—21no—
48C2×Q8×C149—21no—
49C2×Q8×C149—21no—
50C2×Q8×C149C2×C412yes—
51C22×C4×C149—21no—
52C22×C4×C149C2311yescharacteristic
53M16×C149—21no—
54M16×C149—21no—
55M16×C149—21no—
56M16×C149D412yes—
57C2×C8×C149—21no—
58C2×C8×C149—21no—
59Dic298—22no—
60Dic298—22no—
61Dic298—41no—
62Dic298—41no—
63C2×Dic149—22no—
64C2×Dic149—22no—
65C2×Dic149—41no—
66C2×Dic149—41no—
67#11924746—41no—
68#11924746C22⋊C412yes—
69#11924746C22⋊C412yes—
70C23×C149#4111yescharacteristic
71Q8×C149—22no—
72Q8×C149—22no—
73Q8×C149—41no—
74Q8×C149—41no—
75C2×C4×C149—22no—
76C2×C4×C149—41no—
77C2×C4×C149—41no—
78C2×C4×C149C22×C411yescharacteristic
79C2×C4×C149C2×D411yescharacteristic
80C2×C4×C149C2×D411yescharacteristic
81C2×C4×C149C2×D411yescharacteristic
82C2×C4×C149C2×D411yescharacteristic
83C2×C4×C149#4111yescharacteristic
84C8×C149—22no—
85C8×C149—41no—
86C22×C149—22no—
87C22×C149C4×D411yescharacteristic
88C22×C149#12111yescharacteristic
89C22×C149#12411yescharacteristic
90C4×C149—42no—
91C4×C149C2×C22⋊C411yescharacteristic
92C4×C149C4×D411yescharacteristic
93C4×C149#12111yescharacteristic
94C4×C149#12711yescharacteristic
95Dic149—42no—
96Dic149—42no—
97C2×C149—21no—
98C2×C149—21no—
99C2×C149#39011yescharacteristic
100C2×C149#47312yes—
101C149#197911yescharacteristic, complemented, Sylow
102#1979—1491nomaximal, Sylow
103C22×Q16—1491no—
104C2×#108—1491no—
105#419—1491no—
106#419—1491no—
107C2×#101—1491no—
108C2×#101D14911yescharacteristic
109#405—1491no—
110C22×Q8—1491no—
111C22×Q8C2×D14911yescharacteristic
112C2×Q16—2981no—
113C2×Q16—2981no—
114C2×Q16—2982no—
115C2×Q16—1494no—
116C2×M16—1491no—
117C2×M16C2×D14911yescharacteristic
118C2×M16C2×D14911yescharacteristic
119C22×C8—1491no—
120#117—1491no—
121#108—2982no—
122#103—2982no—
123#103—2982no—
124#101—22no—
125#101—2982no—
126#97—2981no—
127C4×C8—2981no—
128C2×Q8—21no—
129C2×Q8—21no—
130C2×Q8—21no—
131C2×Q8—21no—
132C2×Q8—21no—
133C2×Q8—2981no—
134C2×Q8—2981no—
135C2×Q8—2981no—
136C2×Q8—2981no—
137C2×Q8—2981no—
138C2×Q8—1492no—
139C2×Q8C4×D14912yes—
140C22×C4—21no—
141C22×C4—2981no—
142C22×C4C22×D14911yescharacteristic
143Q16—2984no—
144Q16—2984no—
145M16—21no—
146M16—21no—
147M16—21no—
148M16—2981no—
149M16—2981no—
150M16C22⋊D14912yes—
151C2×C8—21no—
152C2×C8—21no—
153C2×C8—2981no—
154C2×C8—1492no—
155C2×C8—1491no—
156C2×C8—1491no—
157C2×C8—1492no—
158C4⋊C4—1492no—
159C22⋊C4—2981no—
160C42—2981no—
161C23#1455873611yescharacteristic
162Q8—22no—
163Q8—22no—
164Q8—41no—
165Q8—41no—
166Q8—2982no—
167Q8—2982no—
168Q8—5961no—
169Q8—5961no—
170C2×C4—22no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—2982no—
174C2×C4—2982no—
175C2×C4—5961no—
176C2×C4—5961no—
177C2×C4C2×C4×D14911yescharacteristic
178C2×C4D4×D14911yescharacteristic
179C2×C4D4×D14911yescharacteristic
180C2×C4D4×D14911yescharacteristic
181C2×C4C2×C22⋊D14911yescharacteristic
182C2×C4#1455873511yescharacteristic
183C8—22no—
184C8—41no—
185C8—5961no—
186C8—1492no—
187C8—1492no—
188C22—22no—
189C22C4×C22⋊D14911yescharacteristic
190C22#1801188411yescharacteristic
191C22#1801189711yescharacteristic
192C4—42no—
193C4—5962no—
194C4—5962no—
195C4C22⋊C4×D14911yescharacteristic
196C4#1801187111yescharacteristic
197C4#1801188311yescharacteristic
198C4#1801190711yescharacteristic
199C2—21no—
200C2—21no—
201C2#2374952511yescharacteristic
202C2#2374989912yes—
subgroupG/H
centerC22#18011884
commutatorC2×C4×C149C22×C4
FrattiniC22×C4C22×D149
FittingC2×#101×C149C2
socleC22×C149#121
prime radicalC23×C149#41
cosocleC22×C4×C149C23
hypercenterC2×#101D149
hypocenterC149#1979
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
12. C2×#14558726C4semidirect
101. C149#1979semidirect

Maximal subgroups

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

subgroupindex
C22×#145587262
C2×#180118462
#237496352
#237496342
C2×#180118292
#237495832
C2×#101×C1492
#1979149